In the frequency table, we can see that the most common reason for taking a gap year is travel, with a frequency of 5.
To draw up a frequency table for the given question, we can use the following : List down the reasons:
List down the five different reasons for taking a gap year.
Count the frequency of each reason:
Tally the number of times each reason appears in the data.
Let's say we have the following data:
Reasons for taking a gap year:
Travel Work Experience Family Medical Total Tally
the number of times each reason appears in the data:
Reasons for taking a gap year Tally Frequency Travel Work Experience Family Medical Total
Draw the frequency table:
Draw the frequency table by filling in the tally and frequency columns.
The final frequency table should look like this:
Frequency Table Reasons for taking a gap year Tally Frequency Travel [tex]||||5Work|||3Experience||||4Family||2Medical|1|2| Total5 3 4 2 2 16[/tex]
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Complete the equation so it has infinitely many solutions. 4(x-4)= 4x +
guys how do i do this
Answer: To have infinitely many solutions, the equation must simplify to a true statement, such as 0=0.
So, let's simplify the given equation:
4(x-4) = 4x + ?
We need to choose a value for the constant on the right-hand side so that the equation simplifies to a true statement.
We can start by distributing the 4 on the left-hand side:
4x - 16 = 4x + ?
Now we can see that the 4x terms cancel out, leaving:
-16 = ?
We can choose any value for the constant on the right-hand side, and the equation will be true. For example:
-16 = -16
So the complete equation with infinitely many solutions is:
4(x-4) = 4x - 16
Step-by-step explanation:
At a school
Number of boys:number of girls=11:9
There are 124 more boys to girls
Work out the total number of student at the school
From given ratio of boys and girls, the total number of students at the school is 1240.
What exactly is a ratio?
A ratio is a comparison of two quantities or values by division. It is commonly used to express the relationship between two numbers, such as the ratio of the number of boys to the number of girls in a classroom.
The ratio of two numbers a and b can be expressed as a/b or as the fraction a:b. For example, if there are 20 boys and 30 girls in a classroom, the ratio of boys to girls is 20/30, which can be simplified to 2/3 or written as the fraction 2:3.
Now,
Let's represent the number of boys as 11x and the number of girls as 9x, where x is a common factor.
From the given information, we know that:
11x = 9x + 124
Simplifying
11x - 9x = 124
2x = 124
x = 62
Now,
Number of boys = 11x = 11(62) = 682
Number of girls = 9x = 9(62) = 558
Therefore, the total number of students at the school is:
Total number of students = Number of boys + Number of girls = 682 + 558 = 1240
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I need some assistance in math
Answer: Spinner 1 = 1/2, Spinner 2 = 1/3
Step-by-step explanation:
I don't know what the answer choices are telling you to do... but
spinner 1 has 4 total parts, 2 of which are odd. So there's a 2 out of 4 chance that the arrow will land on an odd number. Simplified, it will reduce from 2/4 to 1/2. Spinner 2 has 3 total parts (denominator) one of which is a vowel, a. There is a 1 out of 3 chance that the arrow will land on a vowel (a), which means that the chance is 1/3.
If you add 1/2 and 1/3, the result is 5/6.
If you multiply 1/2 and 1/3, the result is 1/6. (A)
If you subtract 1/2 and 1/3, the result is 1/6. (A)
If you divide 1/2 and 1/3, the result is 3/2
a large retailer purchases 100,000 light bulbs per year. the bulb producer claims he has a defective rate of 0.01, but the retailer suspects it may be higher. 1050 bulbs are defective in the retailers lot. what is the p-value for the test of the claims?
The p-value for the test of the claims is roughly 0.004.
To test the claim of the bulb patron, we can use a thesis test with the following null and indispensable suppositions.
Null thesis: The imperfect rate of the bulbs is 0.01 or lower( i.e., p ≤0.01). Indispensable thesis: The imperfect rate of the bulbs is more advanced than 0.01 ( i.e., p>0.01).We can use the binomial distribution to calculate the probability of observing 1050 or further imperfect bulbs out of,000 if the imperfect rate is 0.01 or lower. This probability is the p-value of the test.
To calculate the p-value, we need to use the binomial distribution and find the probability of observing 1050 or further imperfect bulbs out of,000 if the imperfect rate is 0.01 or lower. Using a binomial calculator or statistical software, we can find that the probability of observing 1050 or further imperfect bulbs is roughly 0.004.
Since this p-value is lower than the significant position of 0.05, we can reject the null thesis and conclude that the imperfect rate of the bulbs is more advanced than 0.01.
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PLEASE HELP ME!!
Marcus got a job through an employment agency that charges a fee equal to 35% of the first four weeks' pay. The job pays $545 per week. How much does Marcus have to pay the employment agency?
A)$190.75
B)$763
C)$2,180
D)$1,144.50
ramanujan and hardy played a game where they both picked a complex number. if the product of their numbers was $32-8i$, and hardy picked $5+3i$, what number did ramanujan pick?
Let Ramanujan pick a complex number $a+bi$, where $a$ and $b$ are real numbers. Then the product of the numbers chosen by Ramanujan and Hardy is:
(
�
+
�
�
)
(
5
+
3
�
)
=
5
�
+
3
�
�
+
5
�
�
+
3
�
�
2
=
(
5
�
+
3
�
)
+
(
5
�
+
3
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)
�
−
3
�
(a+bi)(5+3i)=5a+3ai+5bi+3bi
2
=(5a+3b)+(5b+3a)i−3b
We want this product to be equal to $32-8i$. Equating the real and imaginary parts gives us two equations:
5
�
+
3
�
=
32
(1)
5a+3b=32(1)
5
�
+
3
�
=
−
8
(2)
5b+3a=−8(2)
We can solve this system of equations to find $a$ and $b$. Multiplying equation (1) by 3 and equation (2) by 5, and subtracting the resulting equations gives:
15
�
+
9
�
−
25
�
−
15
�
=
−
96
15a+9b−25b−15a=−96
Simplifying:
−
16
�
=
−
96
−16b=−96
Therefore, $b=6$. Substituting $b=6$ into equation (1) gives:
5
�
+
18
=
32
5a+18=32
Therefore, $a=2$. Thus, Ramanujan picked the complex number $2+6i$.
Based on the given conditions and informations provided, the complex number that was picked by thr Ramanujan is calculated to be 2+6i.
Let Ramanujan pick a complex number a+bi, where a and b are real numbers. Then the product of the numbers chosen by Ramanujan and Hardy is:
(a+bi)(5+3i) = 5a+3ai+5bi+3bi² = (5a+3b)+(5b+3a)i-3b
We want this product to be equal to 32-8i. Equating the real and imaginary parts gives us two equations:
5a+3b=32 (1)
5b+3a=-8 (2)
We can solve this system of equations to find a and b. Multiplying equation (1) by 3 and equation (2) by 5, and subtracting the resulting equations gives:
15a+9b-25b-15a=-96
Simplifying:
-16b=-96
Therefore, b=6. Substituting b=6 into equation (1) gives:
5a+18=32
Therefore, a=2. Thus, Ramanujan picked the complex number 2+6i.
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Which set of side lengths form a right triangle?
Responses
7 cm, 8 cm, 10 cm
7 cm, 8 cm, 10 cm
3 ft, 6 ft, 5 ft
3 ft, 6 ft, 5 ft
10 in., 41 in., 40 in.
10 in., 41 in., 40 in.
15 m, 20 m, 25 m
Answer:
Here is the correct answer:
15 m, 20 m, 25 m
I think of a number multiply it by 3 add 4 and get 22
Answer:
The number is 6.
Step-by-step explanation:
[tex]3x + 4 = 22[/tex]
[tex]3x = 18[/tex]
[tex]x = 6[/tex]
The number which is thought is 6.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given that,
a number multiply it by 3 add 4 and get 22.
Let the unknown number be x.
First multiply the given number by 3.
It becomes 3x.
Add 4 to it.
It becomes 3x + 4.
The equation we get is,
3x + 4 = 22
Subtracting both sides by 4,
3x = 18
Dividing both sides by 3,
x = 6
Hence the value of x is 6.
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If p is inversely proportional to the square of q, and p is 8 when q is 9, determine p when q is equal to 2.
Answer:
the value for p will be 162
guests arrive at a hotel at a rate of five per hour. suppose that for the last 10 minutes no guest has arrived. what is the probability that (a) the next one will arrive in less than 2 minutes .1535 (b) from the arrival of the tenth to the arrival of the eleventh guest takes no more than 2 minutes?
(a) To solve for the probability, we can use the Poisson distribution. Given that guests arrive at a rate of five per hour, the arrival rate per minute can be calculated as 5/60 = 0.0833 guests per minute.
Let X be the number of guests that arrive in a 2-minute interval. We can model X using a Poisson distribution with parameter [tex]λ = 0.1667[/tex] (0.0833 guests per minute * 2 minutes). Then, the probability that the next guest will arrive in less than 2 minutes can be calculated as: [tex]P(X > 0) = 1 - P(X = 0) = 1 - e^(-λ) = 0.1535[/tex]
(b) To solve for the probability, we can use the same Poisson distribution as before. Let Y be the time between the arrivals of the tenth and eleventh guests. We can model Y using an exponential distribution with parameter [tex]λ = 0.0833[/tex](the arrival rate per minute). Then, the probability that Y is less than or equal to 2 minutes can be calculated as:
[tex]P(Y < = 2) = 1 - e^(-λ*2) = 0.1573[/tex]
Therefore, the probability that from the arrival of the tenth to the arrival of the eleventh guest takes no more than 2 minutes is 0.1573. The probability that the next guest will arrive in less than 2 minutes is 0.1535.
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liz has two children. the taller child is a boy. what is the probability that the other child is a boy? assume that in 76% of families consisting of one son and one daughter the son is taller than the daughter.
The probability that Liz has two boys given that she has at least one boy who is taller is approximately 0.2841
Let's first consider all possible gender combinations of Liz's two children:
Boy, boy (BB)
Boy, girl (BG)
Girl, boy (GB)
Girl, girl (GG)
We know that Liz has at least one boy, which rules out the GG combination. That leaves us with three possible combinations: BB, BG, and GB.
From the given information, we know that in 76% of families consisting of one son and one daughter, the son is taller than the daughter. This means that in the BB combination, the probability that the taller child is a boy is 1 (since both children are boys), and in the BG and GB combinations, the probability is 0.76 (since there is one boy and one girl, and we know the boy is taller).
So, let's calculate the probability that Liz has two boys (BB) given that she has at least one boy who is taller. We can use Bayes' theorem for this
P(BB | taller child is a boy) = P(taller child is a boy | BB) × P(BB) / P(taller child is a boy)
where P(taller child is a boy | BB) = 1 (as both children are boys), P(BB) = 1/4 (since there are four possible gender combinations), and P(taller child is a boy) = P(taller child is a boy | BB) × P(BB) + P(taller child is a boy | BG) × P(BG) + P(taller child is a boy | GB) × P(GB) = 1 × 1/4 + 0.76 × 1/2 + 0.76 × 1/2 = 0.88.
Substituting these values into Bayes' theorem, we get
P(BB | taller child is a boy) = 1 × 1/4 / 0.88 = 0.2841
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Find the volume of the sphere.
Use 3.14 for T. Round your
answer to the nearest tenth.
Enter your answer in cm³ (type in
the number only without units).
7.2 cm
Answer:
I think it will help u (:
Step-by-step explanation:
Assuming the given measurement is the diameter of the sphere, we can find the radius as follows:Radius (r) = Diameter / 2 = 7.2 / 2 = 3.6 cmThe formula for the volume of a sphere is:V = (4/3) * π * r³Substituting the values, we get:V = (4/3) * 3.14 * (3.6)³
V = 4.19 * 46.656
V = 195.4 cm³Rounding this to the nearest tenth, we get:V ≈ 195.4 cm³Therefore, the volume of the sphere is approximately 195.4 cm³.
Please help, will give brainliest
The recursive and explicit formulae of the given arithmetic expression are:
Recursive formular = [tex]a_{n+1} = a_{n-13}[/tex]
Explicit formular is Tn = 75 - 13n
Describe the differences between an explicit formula and a recursive formula.You can determine the value of any term in a series by using an explicit formula. The integers are divided into the natural numbers, which are 1, 2, 3, 4, and so on. If you know the value of the (n-1)th term in a sequence, you may use a recursive formula to determine the value of the nth term in the sequence. Recursive formulas give the value of a specific phrase depending on the previous term, whereas explicit formulas give the value of a specific term based on the position.
Given:
a1 = 52
a2 = 75 = 52 - 13 = a1 - 13
Recursive formular = [tex]a_{n+1} = a_{n-13}[/tex]
a = 52, d = -13
F(11) = a + (n - 1)d = 52 + (n - 1)-13 = 52 - 13n + 13 = 75 - 13n
Explicit formular is Tn = 75 - 13n
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The arithmetic sequence has a common difference of 23, recursive rule of this sequence is xₙ = [tex]x_{n-1}[/tex] + 23 and explicit rule is xₙ = 23n + 29. The 11th term is 282.
What is an arithmetic sequence?An arithmetic sequence is a mathematical progression in which each term is generated by adding a constant value to the preceding term, with the exception of the first term. This constant value is known as the common difference, and it governs the pattern of the sequence. There are two types of arithmetic sequences, one is an increasing sequence and the other is a decreasing sequence. Increasing sequence is obtained if the common difference is a positive number. Decreasing sequence is obtained if the common difference is a negative number.
The general format of the recursive rule is xₙ = [tex]x_{n-1}[/tex] + d, where xₙ is the nth term, [tex]x_{n-1}[/tex] is the (n-1)th term and d is the common difference of the arithmetic sequence.
In the given sequence x₁ = 52 and x₂ = 75
Common difference can be calculated by subtracting first term from second term = x₂ - x₁ = 75 - 52 = 23
Hence recursive rule for this sequence is xₙ = [tex]x_{n-1}[/tex] + 23
The general format of explicit rule is xₙ = x₁ + (n-1) × d.
For this sequence it is xₙ = x₁ + (n-1) × 23 = 52 + 23n - 23 = 23n + 29
To find f(11) we can use the explicit rule
f(11) = 23 × 11 + 29 = 282
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If a great circle of a sphere has an area of 64 pi square inches, find the volume of sphere.
Answer:
2144.66058485 in³
Step-by-step explanation:
If the area is 64π in², and A = πr², then 64π=πr²
r = √64
r = 8 in
V = 4/3×π×r³
V = 4/3×π×8³
V = 2144.66 in³
Is it enlargement or reduction?
Answer:
Enlargement
Step-by-step explanation:
If it gets bigger is enlargement if it gets smaller its reduction
Triangle PQR is a right triangle. P(-6,9) Q(-1,-1) R(-9,5) what is the area of triangle PQR
The area of triangle PQR is 25/2 * √(5).
Describe Triangle?In geometry, a triangle is a two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and has many important properties and applications.
The sum of the interior angles of a triangle is always 180 degrees, and the exterior angles sum to 360 degrees. The three sides of a triangle can be classified according to their lengths and their angles.
To find the area of triangle PQR, we can use the formula:
Area = (1/2) * base * height
where the base and height are the lengths of two sides of the right triangle that meet at a 90-degree angle.
We can use the distance formula to find the lengths of the sides of triangle PQR:
PQ = √[(x_Q - x_P)² + (y_Q - y_P)²] = √[(-1 - (-6))² + ((-1) - 9)²] = √[25 + 100] = 5√(5)
PR = √[(x_R - x_P)² + (y_R - y_P)²] = √[(-9 - (-6))² + (5 - 9)²] = √[9 + 16] = 5
QR = √[(x_R - x_Q)² + (y_R - y_Q)²] = √[(-9 - (-1))² + (5 - (-1))²] = √[64 + 36] = 2√20) = 4√(5)
Since triangle PQR is a right triangle, the base and height are PQ and PR, respectively. Therefore, the area of triangle PQR is:
Area = (1/2) * PQ * PR = (1/2) * 5√(5) * 5 = 25/2 * √(5)
So the area of triangle PQR is 25/2 * √(5).
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The growth in computer specialists was remarkable during 1960-1970 for both sexes. Calculate the percentages of growth for both sexes in this service occupation. (To the nearest whole percent.)
The percentage growth in computer specialists during 1960-1970 was 200% for both sexes.
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
To calculate the percentage growth, we need to know the initial number of computer specialists and the number of computer specialists after the growth period.
Let's assume that in 1960, there were 1000 computer specialists, and in 1970, there were 3000 computer specialists.
The growth in computer specialists during this period can be calculated as follows:
Growth = Final number - Initial number
Growth = 3000 - 1000
Growth = 2000
To calculate the percentage growth, we divide the growth by the initial number and multiply by 100:
Percentage Growth = (Growth / Initial number) * 100
Percentage Growth = (2000 / 1000) * 100
Percentage Growth = 200%
Therefore, the percentage growth in computer specialists during 1960-1970 was 200% for both sexes.
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When Noah was born, his parents deposited $10900 into a savings account for his college fund. The savings account has a 3% annual percentage rate (APR). How old will Noah be when the account reaches $17000? Round down to the nearest whole number.
Nοah will be 6 years οld when the accοunt reaches $17000.
What is cοmpοund interest?The interest charged οn a debt οr depοsit is knοwn as cοmpοund interest. It is the idea that we use the mοst frequently οn a regular basis. Cοmpοund interest is calculated fοr a sum based οn bοth the principal and cumulative interest.
Tο sοlve this prοblem, we can use the fοrmula fοr cοmpοund interest:
A = [tex]P(1 + r/n)^{(nt)[/tex]
Where: A = the final amοunt (in this case, $17000)P = the principal amοunt (in this case, $10900)r = the annual interest rate (in this case, 3% οr 0.03 as a decimal)n = the number οf times interest is cοmpοunded per year (in this case, assuming it's cοmpοunded annually, n = 1)t = the number οf years
Plugging in the values we have:
[tex]17000 = 10900(1 + 0.03/1)^{(1*t)[/tex]
Simplifying further:
[tex]17000/10900 = (1.03)^{t1.55963303} = (1.03){^t[/tex]
Nοw we can take the natural lοg οf bοth sides tο sοlve fοr t:
[tex]ln(1.55963303) = ln((1.03)^t)t * ln(1.03) = ln(1.55963303)t = ln(1.55963303) / ln(1.03)[/tex]
Using a calculatοr, we can find that it is apprοximately 6.156 years.
Since Nοah's age will be rοunded dοwn tο the nearest whοle number,
Nοah will be 6 years οld when the accοunt reaches $17000.
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2. Ben is making two separate investments with his $2,400
inheritance.
He will invest $1,500 in Investment R which pays 2.75%
annual simple interest
He will invest $900 in Investment S which pays 2.75%
interest compounded annually
a. What is the difference between the balance of the two
investments after 8 years?
b. What is the difference between the interest earned of the two
investments after 8 years?
c. Which of the two had the better return on investment?
Step-by-step explanation:
We can use the simple interest formula:
R = P(1 + rt)
where R is the balance, P is the principal, r is the interest rate, and t is the time.
For Investment R, we have:
R = 1,500(1 + 0.0275*8)
R = 1,980
For Investment S, we can use the formula:
R = P(1 + r)^t
R = 900(1 + 0.0275)^8
R = 1,116.92
a. The difference between the balance of the two investments after 8 years is:
1,980 - 1,116.92 = 863.08
b. The interest earned for Investment R is:
I = Prt
I = 1,500*0.0275*8
I = 330
For Investment S, we can calculate the interest using:
I = R - P
I = 1,116.92 - 900
I = 216.92
The difference between the interest earned on the two investments is:
330 - 216.92 = 113.08
c. To compare the return on investment, we can use the concept of compound interest.
For Investment R, the total value after 8 years is:
R = 1,500(1 + 0.0275*8)
R = 1,980
For Investment S, we can calculate the effective annual rate:
EAR = (1 + r/n)^n - 1
EAR = (1 + 0.0275/1)^1 - 1
EAR = 0.0275
The total value after 8 years is:
R = 900(1 + 0.0275)^8
R = 1,116.92
The return on investment for Investment R is:
ROI = (1 + r/n)^nt - 1
ROI = (1 + 0.0275/1)^1*8 - 1
ROI = 0.2229
The return on investment for Investment S is:
ROI = (1 + EAR)^t - 1
ROI = (1 + 0.0275)^8 - 1
ROI = 0.2329
Therefore, Investment S had the better return on investment.
how many hours can it display cold tcs food without temperature control before the food must be thrown out?
Potentially hazardous cold food that requires time and temperature control for safety (TCS food) should not be kept at a temperature above 41°F (5°C) for more than 6 hours total time, according to the FDA Food Code.
According to the U.S. Food and Drug Administration (FDA) Food Code, potentially hazardous cold food that requires time and temperature control for safety (TCS food) should not be kept at a temperature above 41°F (5°C) for more than 6 hours total time.
After that, the food must be thrown out to prevent the growth of harmful bacteria. These food are harmful to the health of consumer.
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Kenji just went down the slide at the playground. He walks 5 feet to get from the end of the slide back to the ladder. Then he climbs 8 feet to the top of the slide again. How long is the slide? If necessary, round to the nearest tenth.
Answer: Let's call the length of the slide "x". From the problem, we know that Kenji walks 5 feet after he slides down and climbs 8 feet to get to the top of the slide again. This means that the total vertical distance he traveled (height of the slide) is equal to 5 + 8 = 13 feet.
Using the Pythagorean theorem, we can find the length of the slide:
x^2 = 13^2 + h^2
where h is the height of the slide.
We know that h = 13 feet, so we can substitute that into the equation:
x^2 = 13^2 + 13^2
x^2 = 338
x ≈ 18.4 feet
Therefore, the length of the slide is approximately 18.4 feet. Rounded to the nearest tenth, this is 18.4 feet.
Step-by-step explanation:
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Question 9 Qn ID 10030368
Miko bought a laptop at $2675, inclusive of 7% GST.
How much is the price of the laptop without GST?
SA
Check Answer
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After answering the presented question, we can conclude that As a expression result, the laptop costs $2500 without GST.
what is expression ?An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.
To get the laptop's price without GST, divide the inclusive price by (1 + GST rate as a decimal).
As a result, the laptop's price without GST can be estimated as follows:
Price excluding GST = Price including GST / (1 + GST rate as a decimal)
Price excluding GST = 2675 / (1 + 0.07)
Without GST, the price is $2500.
As a result, the laptop costs $2500 without GST.
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Two sides of a triangle measure 12 and 10. Which inequality
shows all the possible lengths of the third side, x?
Answer:
A) 2 < x < 22-------------------------------------
Using triangle inequality theorem, we get two options:
1) x is the longest side, then:
x < 10 + 12 = 222) x is the shortest side, then:
x > 12 - 10 = 2Combine the two options to get, x is between 2 and 22, or:
2 < x < 22This is the first choice.
what is called the 90 degree angle?
Answer:
right angles
Step-by-step explanation:
The point (-1, 5) ___ (is or is not) on the parabola because the point is ___ units from the directrix and ___ units from the focus.
The point (3, 3) (is or is not) on the parabola because the point is ___ units from the directrix and ___ units from the focus
The point (5,5) (is or is not) on the parabola because the point is ___ units from the directrix and ___ units from the focus
For the point (5, 4) to the directrix, the distance to the directrix is equal to the distance to the focus. For the other points on the list, the distance to the directrix is equal to the distance to the focus. The distance to the directrix is equal to the distance to the focus, we can conclude that (-1, 5) is on the parabola.
What is parabola ?A perfect, U-shaped curve is referred to by the term parabola in mathematics. It is described as the collection of all plane points that are equidistant from a focus and a fixed broadband (the directrix). The point where the parabola's curve changes direction is known as its vertex, and the line that runs through it and is perpendicular toward the directrix is known as its axis of symmetry. The behavior of electromagnetic waves, projectile motion, reflector and antenna forms, and other real-world phenomena are frequently modelled using parabolas.
To determine whether a point is on a parabola with a given focus and directrix, we can use the definition of a parabola: a parabola is the set of all points that are equidistant to the focus and the directrix.
In this case, the focus is the point (0, 2) and the directrix is the line y = -2.
Let's first consider the point (5, 4). We can find the distance from this point to the directrix by finding the distance from the point to the line. The formula for the distance from a point (x1, y1) to a line [tex]Ax + By + C = 0[/tex] is:
[tex]|Ax1 + By1 + C| / \sqrt(A^2 + B^2)[/tex]
In this case, A = 0, B = 1, and C = -2, so the equation of the directrix is y = -2, which can be written as [tex]0x + 1y - 2 = 0.[/tex] Plugging in (5, 4), we get:
[tex]|0(5) + 1(4) - 2| / \sqrt(0^2 + 1^2) = 6[/tex]
So the distance from (5, 4) to the directrix is 6.
Next, we can find the distance from (5, 4) to the focus (0, 2):
[tex]\sqrt((5-0)^2 + (4-2)^2) = \sqrt(29)[/tex]
Since the distance from (5, 4) to the directrix is not equal to the distance from (5, 4) to the focus, we can conclude that (5, 4) is not on the parabola.
We can repeat this process for each point on the list. For the point (-1, 5), we get:
Distance to directrix: |-1 - 2| / 1 = 3
Distance to focus: [tex]\sqrt((-1-0)^2 + (5-2)^2) = \sqrt(26)[/tex]
Since the distance to the directrix is equal to the distance to the focus, we can conclude that (-1, 5) is on the parabola.
Similarly, we can check the other points on the list and find that the points (4, 3), (2, 1), (1, -2), (2, -1), (4, -3), and (5, -4) are also on the parabola. The points (3, 5), (6, 7), (8, 0), and (0, 8) are not on the parabola.
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dave sold popcorn and hot dogs at the game. he sold a total of $336 worth of both. he sold popcorn for $2.50 and hot dogs for $2 each. he sold twice as many bags of popcorn than hot dogs. how many bags of popcorn did he sell
Dave sold 38 bags of popcorn. This can be answered by the concept of Selling price.
Dave sold twice as many bags of popcorn than hot dogs at a total of $336, where popcorn sold for $2.50 and hot dogs sold for $2 each. The question asks how many bags of popcorn Dave sold.
Let's start by assigning variables to the unknown quantities. Let x be the number of hot dogs sold and y be the number of bags of popcorn sold.
We know that Dave sold a total of $336 worth of both popcorn and hot dogs, so we can write an equation:
2.5y + 2x = 336
We also know that Dave sold twice as many bags of popcorn than hot dogs, so we can write another equation:
y = 2x
Substituting y in the first equation with 2x, we get:
2.5(2x) + 2x = 336
5x + 2x = 336/2.5
7x = 134.4
x = 19.2
Now that we know the value of x, we can use the second equation to find y:
y = 2x = 2(19.2) = 38.4
However, y represents the number of bags of popcorn sold, which must be a whole number. Since Dave cannot sell 0.4 of a bag of popcorn, we need to round down to the nearest whole number. Therefore, Dave sold 38 bags of popcorn.
Therefore, Dave sold 38 bags of popcorn.
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Find the area of the figure below composed of a square and four Semicircles rounded to the nearest tenths place 
The required area of the shape is 2014.88 sq units.
What is Area?Region is the proportion of a locale's size on a surface. The region of a plane district or plane region alludes to the region of a shape or planar lamina, while surface region alludes to the region of an open surface or the limit of a three-layered object.
According to question:Given shape consist of a square and four half circles.
Radius of circle = 14 units, side length of the square is 28 units
Area of the shape = are of square + area of four half circles
= 28×28 + 4(π(14)²)/2
= 784 + 2π(14)²
= 784 + 1230.88
= 2014.88 sq units
Thus, required area of the shape is 2014.88 sq units.
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what is 9 25/100 simplified?
Answer:
It is 9 1/4
Step-by-step explanation:
This is because 9 stays the same as the whole number, and 25 divided by 100 is 4. To check our work we can multiply 25 by 4 to get 100. Now we know we have the right answer.
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buys candy that costs 8$ per pound. She will spend less than 56$on candy. What are the possible numbers of pounds she will buy? Use for the number of pounds will buy.
Answer:
x ≤ 7
Step-by-step explanation:
$56 (her budget) divided by $8 (which is the cost per pound) will equal x. Since we do not know the actual answer of the number of pounds she will buy due to the fact she will spend less than $56, which is also making her open to buying a total of $56. Since the question is asking for the possible numbers of pounds she will buy, we will use the identity for pounds to be x. We don't know the actual amount she will buy so the answer is x ≤ 7. She will buy either less than or exactly 7 pounds of candy.
how many revolutions will a car wheel of diameter 24 in. make as the car travels a distance of one mile? (round your answer to the nearest whole number.)
The car wheel will make approximately 840 revolutions as the car travels a distance of one mile.
To calculate the number of revolutions that a car wheel of diameter 24 in. will make as the car travels a distance of one mile, we need to use the formula:
number of revolutions = distance traveled / distance per revolution
The distance traveled is given in miles, and we need to convert the diameter of the wheel, given in inches, to the distance per revolution in miles.
The diameter of the wheel is 24 in., which means the radius is 12 in. The distance per revolution is equal to the circumference of the wheel, which is given by the formula:
circumference = 2 * pi * radius
Substituting the values, we get:
circumference = 2 * pi * 12 in. = 75.4 in.
To convert this to miles, we divide by 63,360 inches per mile:
distance per revolution = 75.4 in. / 63,360 in./mi = 0.00119 mi/rev
Now, we can calculate the number of revolutions as:
number of revolutions = 1 mi / 0.00119 mi/rev ≈ 840 revolutions
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