The first question:
"A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?"
Since the spinner has an equal chance of landing on each of its eight regions, the probability of landing on region three is 1/8, and the probability of landing on region six is also 1/8.
To find the probability of both events occurring (landing on region three and region six), you multiply the probabilities together:
P(landing on region three and region six) = P(landing on region three) * P(landing on region six) = (1/8) * (1/8) = 1/64.
Therefore, the probability of landing on both region three and region six is 1/64.
The events are mutually exclusive because it is not possible for the spinner to land on both region three and region six simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The second question:
"A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?"
To find the probability of either event occurring (purple or number greater than 5), we need to calculate the probabilities separately and then add them.
The probability of picking a purple jersey is 4/10 since there are four purple jerseys out of a total of ten jerseys.
The probability of picking a jersey with a number greater than 5 is 2/10 since there are two jerseys numbered 6 and above out of a total of ten jerseys.
To find the probability of either event occurring, we add the probabilities together:
P(purple or number greater than 5) = P(purple) + P(number greater than 5) = (4/10) + (2/10) = 6/10 = 3/5.
Therefore, the probability of picking a purple jersey or a jersey with a number greater than 5 is 3/5.
The events are overlapping since it is possible for the jersey to be both purple and have a number greater than 5.
--------------------------------------------------------------------------------------------------------------------------
The third question:
"A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?"
To find the probability of either event occurring (milk chocolate or no peanuts inside), we need to calculate the probabilities separately and then add them.
The probability of selecting a milk chocolate is 6/10 since there are six milk chocolates out of a total of ten chocolates.
The probability of selecting a chocolate with no peanuts inside is 7/10 since there are seven chocolates without peanuts out of a total of ten chocolates.
To find the probability of either event occurring, we add the probabilities together:
P(milk chocolate or no peanuts inside) = P(milk chocolate) + P(no peanuts inside) = (6/10) + (7/10) = 13/10.
Therefore, the probability of selecting a milk chocolate or a chocolate with no peanuts inside is 13/10.
The events are mutually exclusive since a chocolate cannot be both a milk chocolate and have no peanuts inside simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The fourth question:
"You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?"
The probability of the coin landing heads up is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely.
The probability of rolling an even number on the die is 3
/6 or 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.
To find the probability of both events occurring (coin lands heads up and die shows an even number), we multiply the probabilities together:
P(coin lands heads up and die shows an even number) = P(coin lands heads up) * P(die shows an even number) = (1/2) * (1/2) = 1/4.
Therefore, the probability of the coin landing heads up and the die showing an even number is 1/4.
The events are independent since the outcome of flipping the coin does not affect the outcome of rolling the die.
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
what is the midpoint of 70 and 90
Answer:
80
Step-by-step explanation:
Just average the two numbers to get (70+90)/2 = 160/2 = 80
Answer:
Step-by-step explanation:
To find the midpoint between two numbers, you add them together and divide the sum by 2.
In this case, the midpoint between 70 and 90 would be:
(70 + 90) / 2 = 160 / 2 = 80.
Therefore, the midpoint between 70 and 90 is 80.
Michael has $15 and wants to buy a combination of cupcakes and fudge to feed at least three siblings. A cupcake costs $2, and a piece of fudge costs $3
This system of inequalities models the scenario:
2x + 3y <15
x+y≥ 3
Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)
Part B: Is the point (5, 1) included in the solution area for the system? Justify your answer mathematically. (3 points)
Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points).
***PLEASE MAKE IT EASY FOR ME SO ITS EASY TO TYPE*** 15 POINTS
Step-by-step explanation:
Part A: The graph of the system of inequalities consists of two lines and a shaded region.
The line 2x + 3y = 15 is a solid line (because of the "less than" symbol in the inequality) and is graphed using a straight line connecting two points. For example, when x = 0, y = 5, and when x = 7.5, y = 0.
The line x + y = 3 is a solid line (because of the "greater than or equal to" symbol in the inequality) and is graphed using a straight line connecting two points. For example, when x = 0, y = 3, and when x = 3, y = 0.
The shaded region represents the solution set. It is the area below the line 2x + 3y = 15 and above or on the line x + y = 3. This shaded region satisfies both inequalities simultaneously.
Part B: To determine if the point (5, 1) is included in the solution area, we substitute x = 5 and y = 1 into both inequalities:
2x + 3y < 15:
2(5) + 3(1) < 15
10 + 3 < 15
13 < 15
Since 13 is less than 15, the point (5, 1) satisfies the first inequality.
x + y ≥ 3:
5 + 1 ≥ 3
6 ≥ 3
Since 6 is greater than or equal to 3, the point (5, 1) satisfies the second inequality.
Since the point (5, 1) satisfies both inequalities, it is included in the solution area for the system.
Part C: Let's choose the point (2, 2) as another example from the solution set.
Interpretation in real-world context:
When we have x = 2 and y = 2, it means Michael decides to buy 2 cupcakes and 2 pieces of fudge. This combination of sweets satisfies the conditions set in the inequalities, ensuring that he can feed at least three siblings.
The point (2, 2) represents a valid solution in which Michael spends a total of $10 (2 cupcakes * $2/cupcake + 2 fudges * $3/fudge = $4 + $6 = $10). With this choice, he can afford to buy enough treats to feed his three siblings while staying within his budget of $15.
Which expression is equivalent to (f + g) (4)?
• ¡(4) + g(4)
• f(x) + g(4)
• ¡(4 + g(4))
• 4(f(x) + g(x))
The correct expression that is equivalent to (f + g) (4) is: f(4) + g(4).
The expression (f + g) (4) represents the sum of two functions, f(x) and g(x), evaluated at x = 4. To find the equivalent expression, we need to simplify it.
In (f + g) (4), the parentheses indicate that the addition operation is performed first, adding the functions f(x) and g(x) together. Then, the resulting sum is evaluated at x = 4. So, the expression simplifies to f(4) + g(4), where we substitute x with 4 in both functions.
The other options provided:
• ¡(4) + g(4): This option is not correct because the negation operator (!) applied to a value does not make sense in this context.
• f(x) + g(4): This option is not correct because it does not evaluate the sum of the functions at x = 4; it keeps the variable x in the expression.
• ¡(4 + g(4)): This option is not correct because it applies the negation operator to the sum of 4 and g(4), which is not equivalent to (f + g) (4).
• 4(f(x) + g(x)): This option is not correct because it introduces a constant factor of 4 to the sum of the functions, which is not equivalent to (f + g) (4).
The correct expression equivalent to (f + g) (4) is f(4) + g(4).
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This option is not equivalent to (f + g)(4).
The expression (f + g)(4) specifically represents the sum of functions f and g evaluated at x = 4.
To determine which expression is equivalent to (f + g)(4), let's break it down step by step.
The expression (f + g)(4) represents the value obtained by evaluating the sum of functions f and g at x = 4.
We substitute x = 4 into both functions and then add the results.
Let's evaluate each option to see which one matches this process:
¡(4) + g(4):
This option involves evaluating the function f at x = 4 and adding it to the value obtained by evaluating function g at x = 4.
It does not represent the sum of the functions f and g evaluated at x = 4.
This option is not equivalent to (f + g)(4).
f(x) + g(4):
This option involves adding the value of function f at an arbitrary point x to the value obtained by evaluating function g at x = 4.
It does not specifically represent the sum of functions f and g evaluated at x = 4.
This option is not equivalent to (f + g)(4).
¡(4 + g(4)):
This option involves evaluating the function g at x = 4 and adding it to the value obtained by adding 4 to the result.
It does not represent the sum of functions f and g evaluated at x = 4.
This option is not equivalent to (f + g)(4).
4(f(x) + g(x)):
This option involves evaluating the functions f and g at an arbitrary point x, summing the results and then multiplying the sum by 4.
It does not specifically represent the sum of functions f and g evaluated at x = 4.
None of the given options is equivalent to (f + g)(4).
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please help quickly
Which two values of x are roots of the polynomial below?
Answer:
A, C
Step-by-step explanation:
x² + 3x - 5 = 0
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{3^2 - 4(1)(-5)}}{2(1)} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{29}}{2} [/tex]
If the mass of a proton is 1.67 × 10-24 gram, what is the mass of 2,000 protons?
Answer:
3.34 * 10^-21 g
Step-by-step explanation:
1.67*10^-24 * 2000 = 1.67 * 10^-24 * 2 *10^3 = 3.34 * 10^-21 g
PLS HELP ACTUAL ANSWERS
A random survey was conducted to gather information about age and employment status. The table shows the data collected.
0-17 years old 18+ years old Total
607
Has a Job
Does Not Have a Job
Total
A
B
C
240
679
What is the probability that a randomly selected student does NOT have a job, given that they are 18+ years old?
97
337
97
679
240
240
265
97
679
337
P
look at photo for reference
Answer: 337
Step-by-step explanation: it is 337 because if you subtract it all you get that
Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink. What fraction of the bouquet is pink roses? There are 12 roses in a dozen.
StartFraction 5 Over 12 EndFraction
StartFraction 7 Over 12 EndFraction
StartFraction 5 Over 7 EndFraction
Give me Author/year in mathemathics,?
Answer:
Isaac Newton (late 17th century) - Newton made significant contributions to calculus and mathematical physics. His book "Philosophiæ Naturalis Principia Mathematica" laid the groundwork for classical mechanics.
How can identify which form of verb is appropriate to use in paragraph among present simple, past simple, present perfect and past perfect tense.
To determine the appropriate verb form, consider the time of the action, its relation to the present or past events, and whether it is a general fact, completed action, ongoing situation, or action preceding another. Choose the verb tense that accurately conveys the intended meaning in the paragraph.
To determine which form of verb is appropriate to use in a paragraph, you need to consider the context and the intended meaning of the sentence or paragraph. Here are some general guidelines for using different tenses:
Present Simple Tense:
Use the present simple tense to talk about general facts, habits, routines, and permanent situations.
Example: "The sun rises in the east."
Past Simple Tense:
Use the past simple tense to talk about completed actions or events in the past.
Example: "She studied abroad last year."
Present Perfect Tense:
Use the present perfect tense to talk about past actions or events that have a connection to the present or when the exact time of the action is not specified.
Example: "I have visited Paris several times."
Past Perfect Tense:
Use the past perfect tense to talk about an action or event that happened before another past action or event.
Example: "She had already eaten dinner when I arrived."
To determine which tense to use, consider the timeline of events and the relationship between them. If you are referring to a specific time in the past, the past simple tense might be appropriate. If you want to emphasize the connection to the present, the present perfect tense might be suitable. If you need to establish a sequence of events in the past, the past perfect tense could be used.
However, it's important to note that these guidelines are not absolute, and there can be variations based on specific contexts and writing styles. It's always best to consult grammar rules and consider the meaning and context of your sentences to choose the most appropriate verb tense for your paragraph.
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Whats the answer for this questions?
Answer:
7(20) + (1/2)(20)(9) = 140 + 90 = 230 cm²
a/(2x - 3) + b/(3x + 4) = (x + 7)/(6x ^ 2 - x - 12)
There are no valid values of 'a' and 'b' that satisfy the given equation.
To solve the equation:a/(2x - 3) + b/(3x + 4) = (x + 7)/(6x^2 - x - 12)
We need to find the values of 'a' and 'b' that satisfy the equation.
First, let's find the common denominator of the fractions on the left-hand side of the equation, which is (2x - 3)(3x + 4):
[(a)(3x + 4) + (b)(2x - 3)] / [(2x - 3)(3x + 4)] = (x + 7)/(6x^2 - x - 12)
Expanding the numerator on the left-hand side, we get:
(3ax + 4a + 2bx - 3b) / [(2x - 3)(3x + 4)] = (x + 7)/(6x^2 - x - 12)
Combining like terms in the numerator:
(5ax + 2bx + 4a - 3b) / [(2x - 3)(3x + 4)] = (x + 7)/(6x^2 - x - 12)
Now, we can equate the numerators on both sides of the equation:
5ax + 2bx + 4a - 3b = x + 7
To solve for 'a' and 'b', we need to match the coefficients of 'x' and the constant terms on both sides of the equation.
Matching the coefficients of 'x':
5a = 1 (coefficient of 'x' on the right-hand side is 1)
2b = 1 (coefficient of 'x' on the left-hand side is 1)
Matching the constant terms:
4a - 3b = 7
We have a system of equations:
5a = 1
2b = 1
4a - 3b = 7
Solving the first equation for 'a':
a = 1/5
Solving the second equation for 'b':
b = 1/2
Substituting the values of 'a' and 'b' into the third equation:
4(1/5) - 3(1/2) = 7
4/5 - 3/2 = 7
(8 - 15)/10 = 7
-7/10 = 7
The equation is inconsistent, and there is no solution that satisfies all the conditions.
As a result, the preceding equation cannot be satisfied by any real values for 'a' and 'b'.
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Can some please help me I don’t understand this?
Please due tmr morning thanks!
The numbers to complete the pythagorean triple in the equation (n² - 1)² + k² = (n² + 1)² are B. 35 and 37
What is the pythagorean triple?A pythagorean triple is a set of 3 numbers that obey the pythagorean theorem.
Given the equation
(n² - 1)² + k² = (n² + 1)², we need to find the remaining numbers generated by the equation when k = 12. So, we proceed as follows/
Since we have the equation
(n² - 1)² + k² = (n² + 1)²
Subtracting (n² + 1)², from both sides, we have that
(n² - 1)² - (n² + 1)² + k² = (n² + 1)² - (n² + 1)²
(n² - 1)² - (n² + 1)² + k² = 0
Now, subtracting k from both sides, we have that
(n² - 1)² - (n² + 1)² + k² = 0
(n² - 1)² - (n² + 1)² + k² - k² = 0 - k²
(n² - 1)² - (n² + 1)² + 0 = - k²
(n² - 1)² - (n² + 1)² = - k²
Using the difference of two squares a² - b² = (a + b)(a - b)
(n² - 1)² - (n² + 1)² = - k²
(n² - 1 + n² + 1)[n² - 1 - (n² + 1)] = - k²
(n² + n² - 1 + 1)[n² - n² - 1 - 1)] = - k²
(2n² + 0)[0 - 2)] = - k²
(2n²)(- 2) = - k²
-4n² = - k²
4n² = k²
n² = k²/4
Taking square root of both sides, we have that
n = √(k²/4)
n = k/2
Since k = 12, we have that
n = 12/2
n = 6
So, the first number is (n² - 1) = (6² - 1)
= 36 - 1
= 35
The second number is (n² + 1) = (6² + 1)
= 36 + 1
= 37
So, the numbers are B. 35 and 37
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How much fencing is required to enclose a circular garden whose radius is 21 m
Answer:182.12 meters of fencing required.
Step-by-step explanation:
How to make 1001 from nine 9. Use can use 9 in any way
Using the given operations and nine 9s, you can make 1001.
How to make 1001 from nine 9. Use can use 9 in any wayTo make 1001 using nine 9s, you can use the following mathematical operations:
1. (9 + 9 + 9) * 9 * 9 - 9 - 9 - 9 = 1001
- Adding three 9s together: (9 + 9 + 9) = 27
- Multiplying the sum by two 9s: (27 * 9 * 9) = 2187
- Subtracting three 9s: (2187 - 9 - 9 - 9) = 2160
- Adding one 9: (2160 + 9) = 2169
- Adding 832 (which is (9 * 9 * 9 + 9 * 9 + 9)) to 2169: (2169 + 832) = 3001
- Subtracting two 9s: (3001 - 9 - 9) = 2983
- Adding nine 9s: (2983 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9) = 1001
Therefore, using the given operations and nine 9s, you can make 1001.
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a/(2x - 3) + b/(3x + 4) = (x + 7)/(6x ^ 2 - x - 12)
Answer:
[tex] \frac{a}{2x - 3} + \frac{b}{3x +4} = \frac{x + 7}{ 6{x}^{2} - x - 12} [/tex]
[tex](3x + 4)a + (2x - 3)b = x + 7[/tex]
3a + 2b = 1---->9a + 6b = 3
4a - 3b = 7---->8a - 6b = 14
--------------- ----------------
17a = 17
a = 1, b = -1
Find the area of the shape shown below.
Answer:
The answer is 32
Step-by-step explanation:
The formula for finding the area of a trapezoid is:
((base 1 + base 2)/ 2 )* h
Now all you have to do is substitute the numbers in.
Note: bases will always be the ones like 12 and 4 in this case. We have just named then 1 and 2.
Answer:
32 square units
Step-by-step explanation:
[tex]\displaystyle A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+4)(4)=\frac{1}{2}(16)(4)=\frac{1}{2}(64)=32[/tex]
Note that [tex]b_1[/tex] and [tex]b_2[/tex] are the lengths of each base of the trapezoid, so it doesn't matter which is which.
Find the value of the combination. 13C5
Answer:
[tex]_{13}C_5=1287[/tex]
Step-by-step explanation:
[tex]\displaystyle _nC_r=\frac{n!}{r!(n-r)!}\\\\_{13}C_5=\frac{13!}{5!(13-5)!}\\\\_{13}C_5=\frac{13!}{5!\cdot8!}\\\\_{13}C_5=\frac{13*12*11*10*9}{5*4*3*2*1}\\\\_{13}C_5=\frac{154440}{120}\\\\_{13}C_5=1287[/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13!}{5!(13 - 5)!} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13!}{5!(8)!} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13!}{5! \times 8!} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13 \times 12 \times 11 \times 10 \times 9 \times 8!}{5! \times 8!} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13 \times 12 \times 11 \times 10 \times 9 \times \cancel{8!}}{5! \times \cancel{8!}} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{13 \times 12 \times 11 \times 10 \times 9 }{5 \times 4 \times 3 \times 2 \times 1} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{156 \times 110 \times 9 }{20 \times 6 \times 1} \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{156 \times 990 }{20 \times 6 } \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = \frac{154440 }{120 } \\ [/tex]
[tex] \sf \hookrightarrow \: \: {}^{13}{ C}_{5} \: = 1287 \\ [/tex]
Naomi wants to save $100,000, so she makes quarterly payments of $1,500 into an account that earns 4.4%/a compounded quarterly. (If you are using TVM Solver, please ensure you provide screenshots of your work or breakdown how you entered everything into the solver).
How long will it take her to reach her goal?
Would doubling her payment amount save her half the time needed to save? Support your statement.
Naomi will take approximately 93 quarters (around 23 years and 3 months) to save $100,000 by making quarterly payments of $1,500 with a 4.4% interest rate.
Doubling her payment amount would save her time, but the exact time saved would require recalculating with the new payment amount.
To calculate the time it will take for Naomi to reach her goal of $100,000, we can use the future value formula for a series of periodic payments:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value (goal amount) = $100,000
P = Payment amount per period = $1,500
r = Interest rate per period = 4.4% per year / 4 (quarterly compounding) = 1.1% per quarter
n = Number of periods (quarters) to reach the goal (what we need to find)
Plugging in the values, we have:
$100,000 = $1,500 * [(1 + 0.011)^n - 1] / 0.011
Simplifying the equation, we have:
[(1 + 0.011)^n - 1] = $100,000 * 0.011 / $1,500
[(1.011)^n - 1] = 0.073333...
Now, we can solve this equation for n using logarithms:
n = log(0.073333...) / log(1.011)
Using a financial calculator or an online calculator, we find that n ≈ 92.33 quarters.
Since Naomi is making quarterly payments, we round up to the next whole number, giving us a total of 93 quarters.
Therefore, it will take Naomi approximately 93 quarters (or around 23 years and 3 months) to reach her goal of $100,000.
Doubling her payment amount to $3,000 per quarter would indeed save her time in reaching her goal. The higher payment amount means she would accumulate the desired amount faster. However, to determine the exact time saved, we would need to recalculate using the same formula as above with P = $3,000. The time saved will depend on the specific calculation result.
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Suppose you have entered a 48-mile biathlon that consists of a run and a bicycle race. During your run, your average
velocity is 5 miles per hour, and during your bicycle race, your average velocity is 23 miles per hour. You finish the race
in 6 hours. What is the distance of the run? What is the distance of the bicycle race?
The distance of the run is miles.
The distance of the bicycle race is approximately 24.61 miles.
Let's assume the distance of the run is 'x' miles and the distance of the bicycle race is 'y' miles.
We know that average velocity is equal to the total distance divided by the total time taken.
We can use this information to form two equations based on the given average velocities and total time.
For the run:
Average velocity = Distance of the run / Time taken for the run
5 mph = x miles / T hours ---(Equation 1)
For the bicycle race:
Average velocity = Distance of the bicycle race / Time taken for the bicycle race
23 mph = y miles / (6 - T) hours ---(Equation 2)
Since the total time for the race is 6 hours, we can substitute (6 - T) for the time taken during the bicycle race.
Now, we can solve these equations simultaneously to find the values of 'x' and 'y'.
From Equation 1, we have:
5T = x
From Equation 2, we have:
23(6 - T) = y
Now, we substitute the value of 'x' in terms of 'T' from Equation 1 into Equation 2:
23(6 - T) = 5T
138 - 23T = 5T
138 = 28T
T = 138 / 28
T ≈ 4.93 hours
Substituting this value back into Equation 1, we can find 'x':
5(4.93) = x
x ≈ 24.65 miles
Therefore, the distance of the run is approximately 24.65 miles.
To find the distance of the bicycle race, we substitute the value of 'T' back into Equation 2:
23(6 - 4.93) = y
23(1.07) = y
y ≈ 24.61 miles
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Find the center and radius of the circle represented by the equation below.
Answer:
centre = (5, - 6 ) , radius = 7
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² - 10x + 12y + 12 = 0 ( subtract 12 from both sides )
x² + y² - 10x + 12y = - 12 ( collect terms in x/ y )
x² - 10x + y² + 12y = - 12
using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 5)x + 25 + y² + 2(6)y + 36 = - 12 + 25 + 36
(x - 5)² + (y + 6)² = 49 = 7² ← in standard form
with centre (5, - 6 ) and radius = 7
Answer:
Center = (5, -6)
Radius = 7
Step-by-step explanation:
To find the center and the radius of the circle represented by the given equation, rewrite the equation in standard form by completing the square.
To complete the square, begin by moving the constant to the right side of the equation and collecting like terms on the left side of the equation:
[tex]x^2-10x+y^2+12y=-12[/tex]
Add the square of half the coefficient of the term in x and the term in y to both sides of the equation:
[tex]x^2-10x+\left(\dfrac{-10}{2}\right)^2+y^2+12y+\left(\dfrac{12}{2}\right)^2=-12+\left(\dfrac{-10}{2}\right)^2+\left(\dfrac{12}{2}\right)^2[/tex]
Simplify:
[tex]x^2-10x+(-5)^2+y^2+12y+(6)^2=-12+(-5)^2+(6)^2[/tex]
[tex]x^2-10x+25+y^2+12y+36=-12+25+36[/tex]
[tex]x^2-10x+25+y^2+12y+36=49[/tex]
Factor the perfect square trinomials on the left side:
[tex](x-5)^2+(y+6)^2=49[/tex]
The standard equation of a circle is:
[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]
where:
(h, k) is the center.r is the radius.Comparing this with the rewritten given equation, we get
[tex]h = 5[/tex][tex]k = -6[/tex][tex]r^2 = 49 \implies r=7[/tex]Therefore, the center of the circle is (5, -6) and its radius is r = 7.
A grocery store owner polled ten customers to determine how many times they went to the grocery store in April. The results of his poll are shown below.
12,9,4,8,25,6,8,5,18,13
Determine the appropriate shape of the distribution.
A. The data does not show a latter
B. Left skewed
C. Symmetrical
D. Right skewed
Answer:
D. Right skewed
Step-by-step explanation:
To determine the shape of the distribution, we can examine the given data:
12, 9, 4, 8, 25, 6, 8, 5, 18, 13
One way to determine the shape of the distribution is by visualizing it using a histogram or a box plot. However, without the exact frequency of each value, we cannot create an accurate visual representation.
Alternatively, we can examine the skewness of the distribution. Skewness is a measure of the asymmetry of a distribution. If the data is skewed to the left, it is left-skewed or negatively skewed. If it is skewed to the right, it is right-skewed or positively skewed. If the data is symmetric and evenly distributed, it is considered a symmetrical distribution.
Let's calculate the skewness of the given data to determine the shape:
Skewness = (3 * (mean - median)) / standard deviation
First, let's calculate the mean, median, and standard deviation of the data:
Mean = (12 + 9 + 4 + 8 + 25 + 6 + 8 + 5 + 18 + 13) / 10 = 10.8
Median = the middle value when the data is arranged in ascending order:
4, 5, 6, 8, 8, 9, 12, 13, 18, 25
Median = (8 + 9) / 2 = 8.5
Next, let's calculate the standard deviation:
Step 1: Calculate the squared differences from the mean for each value:
(12 - 10.8)^2, (9 - 10.8)^2, (4 - 10.8)^2, (8 - 10.8)^2, (25 - 10.8)^2, (6 - 10.8)^2, (8 - 10.8)^2, (5 - 10.8)^2, (18 - 10.8)^2, (13 - 10.8)^2
Step 2: Calculate the sum of squared differences:
(1.44 + 2.88 + 45.76 + 8.64 + 228.01 + 22.09 + 8.64 + 32.49 + 47.04 + 4.84) = 411.73
Step 3: Calculate the variance:
Variance = sum of squared differences / (n - 1) = 411.73 / (10 - 1) = 45.75
Step 4: Calculate the standard deviation:
Standard deviation = square root of variance = √45.75 = 6.76 (approximately)
Now we can calculate the skewness:
Skewness = (3 * (mean - median)) / standard deviation
Skewness = (3 * (10.8 - 8.5)) / 6.76
Skewness = 6.4 / 6.76
Skewness ≈ 0.95
Since the skewness is positive (0.95), the data is right-skewed or positively skewed. Therefore, the appropriate shape of the distribution is:
D. Right skewed
A wooden board in the shape of a rectangle prism measures 0.3 m by 2.1 m by 0.1 m and has a mass of 0.17 kilogram. What is the density of the board?
Enter your answer as a decimal in the box. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
To find the density of the wooden board, we need to divide the mass of the board by its volume. The volume of a rectangular prism is calculated by multiplying its length, width, and height.
Given:
Length (l) = 0.3 m
Width (w) = 2.1 m
Height (h) = 0.1 m
Mass (m) = 0.17 kg
Volume (V) = l × w × h
V = 0.3 m × 2.1 m × 0.1 m
V = 0.063 m³
Density (ρ) = mass / volume
ρ = 0.17 kg / 0.063 m³
ρ ≈ 2.7 kg/m³
The density of the wooden board is approximately 2.7 kg/m³.
help please its due in 2 hrs
Answer:
Step-by-step explanation:
La semana pasada, una tienda de velas recibió $355,60 por vender 20 velas. Las velas pequeñas se vendieron a $10,98 y las velas grandes a $27,98. ¿Cuántas velas grandes vendió la tienda?
Answer:
Para resolver este problema, podemos plantear un sistema de ecuaciones. Si definimos "p" como el número de velas pequeñas y "g" como el número de velas grandes, podemos expresar la información del problema de la siguiente manera:
p + g = 20 (la tienda vendió un total de 20 velas) 10.98p + 27.98g = 355.60 (el ingreso total por la venta de velas fue de $355.60)
Podemos resolver este sistema de ecuaciones utilizando el método de sustitución. Despejando "p" de la primera ecuación, obtenemos:
p = 20 - g
Luego, sustituimos esta expresión de "p" en la segunda ecuación:
10.98(20 - g) + 27.98g = 355.60
220.20 - 10.98g + 27.98g = 355.60
17.00g = 135.40
g = 8
Por lo tanto, la tienda vendió 8 velas grandes.
Step-by-step explanation:
This example using cluster sampling, how do we know whether these estimates are considered valid?
The estimates are not correct because we are to find the proportion and sample error of the given values. The proportion expresses the number of opposing votes to the total number of voters. Also, the sampling error follows the formula of [tex]SE = Z\sqrt{P(1 - P/n)}[/tex]
The right estimate to use
The exact formula used in the expression is quite different from the standard formula for calculating the standard error. We are supposed to find the root of the standard deviation but that is not the case as can be seen in the formula above.
So, the main issue with this formula is that the square root is not considered in the proportion formula used by the council, so it is not a valid estimate.
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A container holds 2 pounds of peanuts. How many ounces of peanuts are in the container? (1 pound = 16 ounces)
16 ounces
32 ounces
36 ounces
40 ounces '
PLEASEEE HELPPP
Find the center of the ellipse defined by the equation shown below. If necessary, round to the nearest tenth. 100pts
The center of the ellipse defined by the equation 9x^2 + 4y^2 + 18z - 23 = 0 is (0, 0, 0).
9x^2 + 4y^2 + 18z - 23 = 0 must be rearranged to its standard form in order to determine the location of the ellipse's centre. The ellipse equation has the following standard form:
(x - h)^2/a^2 + (y - k)^2/b^2 + (z - l)^2/c^2 = 1,
where (h, k, l) represents the center of the ellipse, and a, b, and c are the semi-major, semi-minor, and semi-vertical axes, respectively.
Let's rearrange the given equation to match the standard form:
9x^2 + 4y^2 + 18z - 23 = 0
Dividing by 23 to simplify the equation:
(9x^2)/23 + (4y^2)/23 + 18z/23 - 1 = 0
Now, we can rewrite the equation as:
(9x^2)/23 + (4y^2)/23 + 18z/23 = 1
Comparing this with the standard form, we can identify the values of a, b, and c:
a^2 = 23/9
b^2 = 23/4
c^2 = 23/18
Taking the square roots of these values:
a ≈ √(23/9) ≈ 1.53
b ≈ √(23/4) ≈ 1.92
c ≈ √(23/18) ≈ 1.23
Therefore, the semi-major axis (a) is approximately 1.53, the semi-minor axis (b) is approximately 1.92, and the semi-vertical axis (c) is approximately 1.23.
The center of the ellipse is represented by the values (h, k, l). Since the equation does not involve any shifts or translations, the center is located at the origin (0, 0, 0).
As a result, (0, 0, 0) is the centre of the ellipse formed by the equation (9x2 + 4y2 + 18z - 23 = 0).
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Answer:
Center: (-3, 1)
Step-by-step explanation:
The center of an ellipse is always the point that is equidistant from the two foci and the two vertices.
In order to find the center of the ellipse, we can complete the square in both the x and y terms.
First, we move the constant term to the right side of the equation:
[tex]9x^2+18x + 4y^2-8y = 23[/tex]
In order to complete the square in x, we take half of the coefficient of x and square it, then add it to both sides of the equation.The coefficient of x is 18, so half of it is 9, and squaring that gives us 81. Adding 81 to both sides of the equation gives us:
[tex]9x^2+18x + 81 = 23 + 81[/tex]
which combines the terms in x into a squared term:
[tex](9x+9)^2 = 104[/tex]
Similarly:
In order to complete the square in y, we take half of the coefficient of y and square it, then add it to both sides of the equation. The coefficient of y is -4, so half of it is -2, and squaring that gives us 4. Adding 4 to both sides of the equation gives us:[tex]4y^2-8y + 4 = 23 + 4[/tex]
which combines the terms in y into a squared term:
[tex](2y-2)^2 = 27[/tex]
Now that we have completed the square in both x and y, we can write the equation in standard form for an ellipse:
[tex]\frac{(x+3)^2}{11^2} + \frac{(y-1)^2}{3^2} = 1[/tex]
The standard form for an ellipse is:
[tex]\boxed{\bold{\frac{(x-h)^2}{a^2} +\frac{ (y-k)^2}{b^2} =1 }}[/tex]
where (h, k) is the center of the ellipse, a is the radius in the x-direction, and b is the radius in the y-direction.
In the equation for our ellipse, (h, k) = (-3, 1).
So the center of the ellipse is at the point (-3, 1).
In the nearest tenth, this is (-3.0, 1.0).
faste او انوار کو کسی Q2. 3 balls are drawns from the box containing six white balls five red balls and four blue balls find the probabi- lity. that they are draw from the other blue red and white if each ball is (i) Replaced (ii) Not replace.
The probability of drawing blue, red, and white balls consecutively is 120/3375 with replacement and 120/2730 without replacement.
To calculate the probability of drawing three balls from a box containing six white balls, five red balls, and four blue balls, we need to consider two scenarios: with replacement and without replacement.
(i) With replacement:
When each ball is replaced after it is drawn, the total number of balls remains the same for each draw. Therefore, the probability of drawing a specific color on each draw remains constant.
The probability of drawing a blue ball on each draw is 4/15, the probability of drawing a red ball is 5/15, and the probability of drawing a white ball is 6/15 (assuming all colors are equally likely to be drawn).
To find the probability of drawing a blue, red, and white ball consecutively, we multiply the probabilities together since the events are independent:
P(Blue, Red, White) = (4/15) * (5/15) * (6/15) = 120/3375
(ii) Without replacement:
When the balls are not replaced after being drawn, the total number of balls decreases for each subsequent draw. This affects the probability of each color being drawn on subsequent draws.
For the first draw, the probability of drawing a blue ball is 4/15, a red ball is 5/15, and a white ball is 6/15.
For the second draw, the probability of drawing a blue ball is 3/14, a red ball is 5/14 (as one blue ball is already drawn), and a white ball is 6/14.
For the third draw, the probability of drawing a blue ball is 2/13, a red ball is 4/13 (as two blue balls and one red ball are already drawn), and a white ball is 6/13.
To find the probability of drawing a blue, red, and white ball consecutively without replacement, we multiply the probabilities together:
P(Blue, Red, White) = (4/15) * (5/14) * (6/13) = 120/2730
Therefore, the probability of drawing blue, red, and white balls consecutively is 120/3375 with replacement and 120/2730 without replacement.
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i need help!!!! does anyone know this..!!???
The period of the frequency factor b that is given in the diagram above would be = 0.2 sec.
How to determine the period of the frequency factor b given above?The frequency of a water wave is defined as the number of times the wave completes a cycle within a given period of time. While the period is the time it takes for the completion of a cycle.
The dot the represents the frequency factor b is the green dot on the wave table. Therefore the period as traced from the graph= 0.2 sec.
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See Picture:
Given :
Prove :
Answer:
statmen there for this should me solved and abcd are proof
reason bcz this is not equal square