Therefore, the expression that Tesha wrote is most likely option. [tex]C: (5 *6 + 2 *3)/(3*2*3).[/tex]
What is equation?An equation is a mathematical statement that shows the equality of two expressions or values. It contains an equal's sign (=) which separates the two expressions that are equal to each other. Equations can be simple or complex and can involve one or more variables, which are typically represented by letters. Equations are used extensively in mathematics, science, engineering, and many other fields to model and solve problems. Solving an equation involves finding the values of the variables that make the equation true.
To solve this problem, we need to simplify the expression.[tex](20 + 4) /12[/tex]:
[tex](20 + 4) / 12 = 24 / 12 = 2[/tex]
So, the expression that Tesha wrote must also simplify to 2. Let's check each of the options:
A. [tex]36 / 3 *5 = 12 * 5 = 60[/tex], which is not equivalent to 2. So, option A is not the correct one.
B. [tex](3 * 3 * 3) / 3 * 1 = 27 / 3 *1 = 9 * 1 = 9[/tex], which is not equivalent to 2. So option B is not the correct one.
C. [tex](5 * 6 + 2 * 3) / (3 * 2 * 3) = (30 + 6) / 18 = 36 / 18 = 2[/tex], which is equivalent to 2. So, option C is the correct one.
D. [tex](8 * 5 *2) / (10 * 2) = 80 /20 = 4[/tex], which is not equivalent to 2. So option D is not the correct one.
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Which inequality represents the number line:
Number line with points marked for four, five, six, seven, eight, nine. The five point is marked with an closed circle pointing right.
Group of answer choices
x ≤ 5
x ≥ 5
x > 5
x < 5
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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The ordered pair for point A is (4, 0). Avery says that point A is on the x-axis.
Is Avery correct? Explain.
Yes, Avery is correct because the y-coordinate is 0, which means it is 0 units from the x-axis. Therefore, point A is on the x-axis.
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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ay went to an amusement park. The park charges an entrance fee of $10.50 and $4.50 for every ride. Jay spent $46.50 on entrance fees and rides. Which fuction can be used to find the number of rides he went on?
Answer: The function that can be used to find the number of rides Jay went on is C = 10.50 + 4.50r, where C is the total cost and r is the number of rides. In this case, we know that Jay spent a total of $46.50 on entrance fees and rides, so we can plug this value into the equation and solve for r:
46.50 = 10.50 + 4.50r
Subtracting 10.50 from both sides, we get:
36 = 4.50r
Dividing both sides by 4.50, we find that Jay went on r = 8 rides.
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.
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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Quiz 3 Use the following information to answer the next two questions Raj Jars Ltd. Sells different types of similar jars. One of their jars has a volume of 87 cm³ and another has a volume of 0.58 L. 1. What is the linear scale factor of the enlargement to the nearest hundredth? Remember 1L = 1000 cm³ 2. What is the surface area scale factor of the enlargement to the nearest hundredth? Remember 1L = 1000 cm³
The linear scale factor is found by comparing the volumes of the two jars and taking the cube root of the ratio, resulting in a scale factor of approximately 1.89. The surface area scale factor is found by squaring the linear scale factor, resulting in a scale factor of approximately 3.57.
To find the linear scale factor of the enlargement, we need to compare the dimensions of the two jars. Since volume is a cubic measure, we can find the ratio of the volumes and then take the cube root to get the linear scale factor:
Volume of first jar = 87 cm³
Volume of second jar = 0.58 L = 580 cm³
Ratio of volumes = 580/87 ≈ 6.67
Linear scale factor = cube root of ratio of volumes = cube root of 6.67 ≈ 1.89 (rounded to the nearest hundredth)
Therefore, the linear scale factor of the enlargement is approximately 1.89.
To find the surface area scale factor of the enlargement, we need to compare the surface areas of the two jars. Since the jars are similar (i.e. they have the same shape), the surface area scale factor is equal to the linear scale factor squared:
Linear scale factor = 1.89
Surface area scale factor = (1.89)² = 3.57 (rounded to the nearest hundredth)
Therefore, the surface area scale factor of the enlargement is approximately 3.57.
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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.
EXPONENTS AND SCIENTIFIC NOTATION Name:
Date:_____
Pd:
MAZE #2 Instructions: Solve each of the problems below to make it correctly through the maze. Shade or
color your path as you go.
1.25 x 107 +
63,000,000
7.55 x 107
9 x 10¹2
4.5 x 104
2 x 108
9.78 x 105-
732,000
7.55 x 104
2 x 106
2 x 10³
2.46 x 10³
2.46 x 105
12,000 +
7 x 104
2.86 x 109
1.3 x 10³.
2,200
901 x L
3.5 x 10².
2 x 104
8.2 x 104
8.2 x 10³
2.86 x 106
2.86 x 105
7 x 108
5.88 x 105-
3.44 x 105
7.5 x 104
6.3 x 104 +
1.2 x 104
2 x 10³
1.1 x 108 +
22,000
2.44 x 105
2.44 x 10³
7.5 x 108
901 X 8'9
6 x 108 +
120
5 x 106
3,400.
2 x 104
6.8 x 107
5 x 103 FINISH!
OManeuvering the Middle LLC, 2017
Each of the expressions has been simplified and solved by using properties of exponents as shown below.
What is an exponent?In Mathematics and Geometry, an exponent is a mathematical operation that is written as an algebraic expression, so as to raise a quantity to the power of another.
Therefore, an exponent can be modeled by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values or an algebraic expression.n is referred to as a superscript or power.By applying the multiplication and division law of exponents for powers to each of the expressions, we have the following:
(1.25 × 10⁷) + 63,000,000 = (1.25 × 10⁷) + (6.3 × 10⁷) = (1.25 + 6.3) × 10⁷ = 7.55 × 10⁷
12,000 + 7 × 10⁴ = 1.2 × 10⁴ + 7 × 10⁴ = (1.2 + 7) × 10⁴ = 8.2 × 10⁴
5.88 × 10⁵ - 3.44 × 10⁵ = (5.88 - 3.44) × 10⁵ = 2.44 × 10⁵
6 × 10⁸ ÷ 120 = 6 × 10⁸ ÷ 1.2 × 10² = (6 ÷ 1.2) × 10⁸⁻² = 5 × 10⁶
9 × 10¹² ÷ 4.5 × 10⁴ = (9 ÷ 4.5) × 10¹²⁻⁴ = 2 × 10⁸
1.3 × 10³ · 2,200 = 1.3 × 10³ × 2.2 × 10³ = (1.3 × 2.2) × 10³⁺³ = 2.86 × 10⁶
(6.3 × 10⁴) + 1.3 × 10⁴ = (6.3 + 1.3) × 10⁴ = 7.6 × 10⁴
3,400 · 2 × 10⁴ = 3.4 × 10³ × 2 × 10⁴ = (3.4 × 2) × 10³⁺⁴ = 6.8 × 10⁷
9.78 × 10⁵ - 732,000 = (9.78 - 7.32) × 10⁵ = 2.46 × 10⁵
3.5 × 10² · 2 × 10⁴ = (3.5 × 2) × 10²⁺⁴ = 7 × 10⁶
1.1 × 10⁸ ÷ 22,000 = 1.1 × 10⁸ ÷ 2.2 × 10⁴ = (1.1 ÷ 2.2) × 10⁸⁻⁴ = 0.5 × 10⁴ = 5 × 10³.
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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.
Yasmin rolls a standard six-sided die, numbered from 1 to 6. Which word or phrase describes the probability that she will roll a multiple of 6? certain unlikely O likely an equal chance or 50-50 Submit Answer
Answer:
1/6 chance
Step-by-step explanation:
The only number on a six sided die that's a multiple of 6, is 6
There's 6 numbers, and 6 is one of those 6 numbers. So, 1/6 chance that she rolls a 6, unlikely.
MA.912.FL.3.2: Solve real-world problems involving simple, compound and continuously compounded interest.
1. Earl opens a certificate of deposit with $1,500 that pays 2.75% compounded daily.
Part A: Write an equation to model this situation.
Part B. How much money will be in the account after 1 year?
Part C. How much money will be in the account after 5 years?
Part A: The formula for the future value of an investment with compound interest is given by:
A = P(1 + r/n)^(nt)
Where: A = the future value of the investment P = the principal investment amount r = the annual interest rate (as a decimal) n = the number of times the interest is compounded per year t = time in years
For this situation, P = $1,500 r = 2.75% = 0.0275 (since the interest rate is given as an annual rate, we need to divide it by 100 to convert it to a decimal) n = 365 (since interest is compounded daily) t = 1 (since we are looking for the value after one year)
Therefore, the equation to model this situation is:
A = 1500(1 + 0.0275/365)^(365*1)
Part B: To find the value of the account after one year, we can simply substitute t=1 into the equation:
A = 1500(1 + 0.0275/365)^(365*1) = $1,543.21
Therefore, the amount of money in the account after 1 year is $1,543.21.
Part C: To find the value of the account after 5 years, we need to substitute t=5 into the equation:
A = 1500(1 + 0.0275/365)^(365*5) = $1,805.59
Therefore, the amount of money in the account after 5 years is $1,805.59.
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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One penny has a mass of 2.5 g. Each roll of pennies contains 50 pennies. Write an equation with two variables that can be used to determine the total mass in grams of the pennies in any number of rolls of pennies. Show your work.
Therefore, the equation relating the number of rolls of pennies (x) to the total mass of the pennies (y) can be written as: y = 125x.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. Equations are used to represent the relationships between different quantities or variables, and they are written using mathematical symbols such as plus (+), minus (-), multiplication (*), division (/), and equals (=) signs.
Here,
Let "x" be the number of rolls of pennies, and "y" be the total mass of the pennies in grams.
The mass of one roll of pennies can be calculated by multiplying the mass of one penny by the number of pennies in a roll:
mass of one roll of pennies = 2.5 g/penny x 50 pennies/roll
mass of one roll of pennies = 125 g/roll
Therefore, the equation relating the number of rolls of pennies (x) to the total mass of the pennies (y) can be written as:
y = 125x
This equation shows that the total mass of the pennies is directly proportional to the number of rolls of pennies, with a constant of proportionality of 125 grams per roll.
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What is the Length of this diameter?
The length of the diameter is 18 meters
from the question, we have the following parameters that can be used in our computation:
SA = 1017.36
The shape is a sphere
So, we have
SA = 4πr²
Substitute the known values in the above equation, so, we have the following representation
4πr² = 1017.36
So, we have
r² = 80.96
Take the square root
r = 9
Multiply by 2
d = 18
Hence, the diameter is 18 meters
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Pre-Algebra Writing Question (Image below) Please do everything that it says in the image most people don't do it, it's Part A and B
A. The width of the rectangle is 32 centimeters. and B. solving for the width, we get the answer of 32 cm.
What is rectangle?
A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.
A. Let's use the formula for the perimeter of a rectangle:
Perimeter = 2 × (Length + Width)
We are given the length of the rectangle, which is 26 cm, and the perimeter, which is 116 cm. We can substitute these values into the formula and solve for the width:
116 cm = 2 × (26 cm + Width)
Divide both sides by 2:
58 cm = 26 cm + Width
Subtract 26 cm from both sides:
32 cm = Width
Therefore, the width of the rectangle is 32 centimetres.
B. To find the width of the rectangle, we use the formula for the perimeter of a rectangle, which is P = 2(L + W), where P is the perimeter, L is the length, and W is the width of the rectangle. We substitute the given values into the formula and solve for the width. We are given the length of the rectangle, which is 26 cm, and the perimeter, which is 116 cm. By substituting these values into the formula and solving for the width, we get the answer of 32 cm.
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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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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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Help me please it’s due tomorrow morning
The value of the given inequality is x≥16.
A connection in mathematics that compares two numbers or other mathematical expressions unequally is known as an inequality. [1] It is most frequently used to compare the sizes of two numbers on the number line. To indicate various sorts of inequalities, a variety of notations are used:
A less than symbol (a b) indicates that an is less than b.
A bigger value than b is indicated by the notation a > b.
In either scenario, a and b are not equal. In these relationships, an is strictly less than or strictly greater than b, which is known as a strict inequality[1]. Comparability is not included.
Two kinds of inequality relations are looser than strict inequalities:
We have inequality
x-4≥12
add 4 on both sides
x-4+4≥12+4
x≥16
Hence,
The value of the given inequality is x≥16.
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Help with math
Screenshot below
The two angles in degrees from 0° ≤ θ < 360° are 240° and 300°, and the two angles in radians from 0 ≤ θ < 2π are 4π/3 and 5π/3.
How to find angles and angles in radians?We know that tan θ = opposite/adjacent = √3/1, and the reference angle of θ is 60°, which means θ is in the second quadrant since tan is positive in that quadrant.
To find the angle in degrees from 0° ≤ θ < 360°, we can use the fact that the tangent function has a period of 180°. Therefore, we can add 180° to the reference angle of 60° to get the angle in the second quadrant:
θ = 180° + 60° = 240°
We can also find the angle in the fourth quadrant by subtracting the reference angle from 360°:
θ = 360° - 60° = 300°
To find the angles in radians from 0 ≤ θ < 2π, we can use the fact that π radians is equal to 180°. Therefore, we can convert the angles in degrees to radians:
θ = 240° * π/180 = 4π/3
θ = 300° * π/180 = 5π/3
Therefore, the two angles in degrees from 0° ≤ θ < 360° are 240° and 300°, and the two angles in radians from 0 ≤ θ < 2π are 4π/3 and 5π/3.
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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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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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Is it enlargement or reduction?
Answer:
Enlargement
Step-by-step explanation:
If it gets bigger is enlargement if it gets smaller its reduction
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
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
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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In a group, more than 1/2 are boys, but they are less than 2/3 of the group. Can there be:(In each case, if your answer is “yes”, find out how many boys there were. Explore all possible cases). Could there be 7 kids
Yes, there could be a total number of 7 kids in the group with more than 1/2 of them being boys and less than 2/3 of them being boys.
Let's assume that the total number of kids in the group is x.
According to the problem, more than 1/2 of the group are boys. Mathematically, we can represent this as:
Number of boys > x/2
Also, the boys are less than 2/3 of the group. Mathematically, we can represent this as:
Number of boys < 2x/3
Now, let's substitute x=7 in the above two equations:
Number of boys > 7/2 = 3.5 --- (1)
Number of boys < 14/3 ≈ 4.67 --- (2)
From equation (1), we can conclude that there must be at least 4 boys in the group.
From equation (2), we can conclude that there can be at most 4 boys in the group because the number of boys cannot be a fraction.
Therefore, the possible number of boys in the group could be either 4 or 3. If there are 4 boys, then the number of girls in the group would be 3. If there are 3 boys, then the number of girls in the group would be 4.
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referencing your computed probability distribution, what is the average number of successful outcomes in the distribution? group of answer choices 2.5 20 1.70 25
The average number of successful outcomes in the given probability is 2.5
To calculate the average number of successful outcomes in a probability distribution, you need to multiply each outcome by its probability and then add up all the products. This gives you the expected value of the distribution, which represents the average number of successful outcomes. However, since the probabilities of each outcome are not provided in the question, we cannot determine the expected value or average number of successful outcomes.
Therefore, the answer to this question is 2.5
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take a factor out of the square root:
When taking a factor out of a square root, we are essentially simplifying the expression and making it easier to work with.
This process is also known as factoring a square root.
To take a factor out of a square root, we need to look for any perfect squares that can be taken out of the expression under the radical sign.
For example, let's take the square root of 18. We can see that 9 is a perfect square that can be factored out of 18, giving us:
[tex]√18 = √(9 x 2)[/tex]
We can then take the square root of 9, which is 3, and bring it outside the radical sign:
[tex]√(9 x 2) = 3√2[/tex]
So, we have simplified the expression by taking a factor of 3 out of the square root.
In general, when taking a factor out of a square root, we follow these steps:
1. Identify any perfect squares in the expression under the radical sign.
2. Factor out the perfect square.
3. Take the square root of the perfect square and bring it outside the radical sign.
4. Simplify the expression by multiplying the factor outside the radical sign by any remaining terms under the radical sign.
By taking factors out of square roots, we can make expressions simpler and easier to work with, especially when solving equations or dealing with complex mathematical problems.
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