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Ninety students auditioned for the school play. One-third of those who auditioned were cast, 6 in major roles. What fraction of those who were cast got major roles? Write your answer as a decimal.(1 point)

The measure of the smaller angle is 23⁰ and the measure of the larger angle is 67⁰.

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

So we can say that two angles are complementary if they sum up to 90 degrees.

From the given statement;

y = 3x - 2  -------(1)

y + x = 90  --------(2) (since they are complementary)

substitute for y in equation (2)

3x - 2 + x = 90

4x = 92

x = 92/4

x = 23 ⁰

y = 3(23) - 2

y = 67⁰

Thus, the measure of the smaller angle is 23⁰ and the measure of the larger angle is 67⁰.

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Answer: 53/30

Step-by-step explanation:

4/6 + 2/4 + 3/5 =

2/3 + 1/2 + 3/5 =      ==> Simplify Denominators

30/30 * (2/3 + 1/2 + 3/5)=  ==> Have matching denominators by multiplying by the LCM (Least common multiple) of the denominators

(2*30/3 + 1*30/2 + 3*30/5)/30=

(60/3 + 30/2 + 90/5)/30=

(20 + 15 + 18)/30=

(35 + 18)/30=53/30

Answer:

A) (4,1)

B) (2,-1)

To solve the equation, add 18 to both sides, then divide by 6. The solution is t = 8.

A linear equation is an equation of which the highest degree of its variables is 1.

Steps to solve linear equations:

Recall that if  we subtract or add the same number to both sides of an equation, it does not change the equality.

The given problem:

Solve 6t-18 = 30

The variable is t. Isolate the variable by adding 18 to both sides:

6t -18 +18 = 30 +18

6t = 48

Divide both sides by 6

6t : 6 = 48 : 6

t = 8 (solved)

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Answer:

C (8 to the x/3 power)

Based on the given parameters, there are 1119360 feet in 212 miles

The given parameters are

12 inches = 1 foot

5,280 feet = 1 mile.

Multiply both sides of 5,280 feet = 1 mile by 212

So, we have

212 * 5,280 feet = 1 mile * 212

Evaluate the product

1119360 feet = 212 miles

The above means that there are 1119360 feet is 212 miles

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Answer:

324, 900, 9

Step-by-step explanation:

When a shape has its size increased by a scale factor, the size of its lengths are multiplied by this scale factor, yet its area is actually multiplied by the scale factor squared. This is due to two lengths being multiplied to contribute to the area, not just one. If it was a volume, you would multiply by the scale factor cubed!

Onto the answer, just follow the advice above:

36 * 3^2 = 36 * 9 = 324 square inches,

36 * 5^2 = 36 * 25 = 900 square inches,

36 * 0.5^2 = 36 * 0.25 = 9 square inches.

Hope this helps :)

Using simple interest, Alice need to invest 25000 now in order to get 12 000 saved in 4 years' time at 12% simple interest.

The daily interest rate, the principle, and the number of days between payments are multiplied to determine simple interest. Consumers who pay their loans off on time or ahead of schedule each month benefit from simple interest. Simple interest loans are frequently used for auto loans and short-term personal loans.

Given,

simple interest = 12000

rate of interest = 12%

time  = 4 years

Simple interest = P × R × T / 100

12000 = P × 12 × 4 / 100

P = 25000

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The area of triangle par on the grid is the vertex p is on ordered pair 7 and 6.

Soccer on CBS Sports is various TV programs that have broadcasted soccer matches in the US on CBS, CBS Sports Organization, and Paramount+. These matches are from Global, European, and American contests. Affiliation football, all the more usually known as just football or soccer, is a group activity played between two groups of 11 players who essentially utilize their feet to impel the ball around a rectangular field called a pitch. Soccer, or football as it's known beyond North America, is the most famous game on the planet. Thus, how could it be played, who plays it, and a lot more inquiries are responded to here.

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The term that best represents the intersection of two pages of an open book is point.

A third item made up of everything that is simultaneously contained in all of the other things is called an intersection of two or more objects in mathematics. In Euclidean geometry, for instance, the intersection of two lines in a plane that are not parallel is where they come together. More broadly, the set of elements that are a part of all of the sets is what is meant by the intersection of sets in set theory. The items being considered do not need to be in a shared space, unlike the Euclidean concept.

A point is the most frequent shape for an intersection in plane geometry, while there are other shapes that can be used as well. An intersection is an item of lesser dimension that is incident to each in incidence geometry, which is typically applied to flats.

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Answer:

spam question

Step-by-step explanation:

Answer:

If you have a table of values like those above and you can find the value for f(n) . you go about finding the value of f (n-1)

Step-by-step explanation:

The amount that Rebecca will be paid for overtime work is $12.75.

From the information, Rebecca's boss pays her time and a half for overtime work at the comic book store. Her regular wage is $8.50.

The amount for overtime will be:

= (1.5 × $8.50)

= $12.75

Therefore, the amount that Rebecca will be paid for overtime work is $12.75.

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The inequality that is equivalent to the given inequality is -10x + 10 < 13  

From the question, we are to determine the inequality that is equivalent to the given inequality

The given inequality is -10(x - 1) < 13

To determine the inequality that is equivalent to this inequality, we will solve the given inequality

Solving the inequality

-10(x - 1) < 13

Apply the distributive property

-10x + 10 < 13

Subtract 10 from both sides of the inequality

-10x + 10 - 10 < 13 - 10

-10x < 3

Divide both sides by -10 and reverse the sign

x > -3/10

From the steps of solving the inequality, the inequality that is equivalent to the given inequality is -10x + 10 < 13  

Hence, the inequality that is equivalent to the given inequality is -10x + 10 < 13  

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Answer:

C. -10x + 10 < 13

If 115.2 million million households have at least one TV and  82% have basic cable TV, then the number of households have basic cable TV is

94464000.

Given,

The total number of household have at least one TV = 115.2 millions

The percentage of household have basic cable TV = 82%

Then, the number of household have basic cable TV

=115200000×[tex]\frac{82}{100}[/tex]

=94464000

Hence, if 115.2 million million households have at least one TV and  82% have basic cable TV, then the number of households have basic cable TV is 94464000.

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Based on the 1.5 × IQR rule for outliers, there is no evidence to support the student's claim because there is only one outlier at 58 minutes.

An outlier is also referred to as anomalous data and it can be defined as a numerical value that is either unusually too small or large (big) in comparison with the overall pattern of the numerical values contained in a data set.

IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.

Mathematically, interquartile range (IQR) is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):

IQR = Q₃ - Q₁

Based on the given data set, the following interquartile ranges was calculated by using Excel:

Q₃ = 31.5

Q₁ = 20.5

Now, the interquartile range (IQR) is given by:

IQR = Q₃ - Q₁

IQR = 31.5 - 20.5

IQR = 11

Based on the 1.5 × IQR rule for outliers, we have:

1.5 × IQR = 1.5 × 11 = 16.5

Therefore, our fences will be 16.5 points below Q₁ and 16.5 points above Q₃:

Lower fence = 20.5 - 16.5 = 4.5

Upper fence = 4.5 + 31.5 = 36.

In conclusion, we can reasonably infer and logically deduce that there is no evidence to support the student's claim because there is only one outlier at 58 minutes.

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Complete Question:

The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list.

9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58

One of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1.5 × IQR rule for outliers, is there evidence to support the student's claim?

Answer: x=9

Step-by-step explanation:

x+1= 10

x-1+1=10-1

x=10-1

x=9

Answer:

10

Step-by-step explanation:

hope it helps

Answer:

10

Step-by-step explanation:

ya its right

The fraction of the total pies remained is option (A) 23/20 is the correct answer.

In this question,

A host served two pies, one apple and one cherry.

Dinner guests ate twenty-five percent of the apple pie and sixty percent of the cherry pie.

Apple pie = 25%

∴ Remaining = 100% - 25%

⇒ 75%  

⇒ Fraction of apple pie remained is 3/4

Cherry pie = 60%

∴ Remaining = 100% - 60%

⇒ 40%

⇒ Fraction of cherry pie remained is 2/5

Thus fraction of the total pies remained is

⇒ 3/4 + 2/5

⇒ (15+8) / 20

⇒ 23/20

Hence we can conclude that the fraction of the total pies remained is option (A) 23/20 is the correct answer.

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The numbers given in scientific notation will be arranged from least to greatest as: 7.6×10⁻²⁰, 5.5×10⁻¹¹, 2.4×10², 8.9×10², 9.2×10⁴, 7.6×10²⁰.

Scientific notation of numbers may be defined as the way of representation of bigger numbers into powers of 10. This helps in reducing space as well as it helps in conveniently solving the problem. For example, scientific notation of 92000 may be written as 9.2×10⁴.

Here in the number 7.6×10⁻²⁰ the power of 10 is maximum but with a negative value so it is the least number. Then comes the number 5.5×10⁻¹¹ as its power are also negative but greater than the previous number. Similarly using the above logic, the other numbers will be placed, and the greatest number would be 7.6×10²⁰ as it has the maximum power of 10 that too with a positive sign.

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The numbers in the equations are -4 and -26

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

Let the numbers be x and y

A system of linear equations is a collection of at least two linear equations. So, we have the following linear equations

y = 5x - 6

x - y = 22

Substitute y = 5x - 6 in x - y = 22

x -5x + 6 = 22

Evaluate the like terms

-4x = 16

Divide both sides by -4

x = -4

Substitute x = -4 in y = 5x - 6

y = 5 * -4 - 6

Evaluate

y = -26

Hence, the numbers are -4 and -26

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The inverse of the given function,f(t) = 100 . 2^(t/4) is 4 * log2(x/100).

What is the inverse of a function?

An inverse of a function f(x), is defined as another function that undoes the operations performed on the function. It is denoted by f^(-1).

Calculation of the inverse of a function

We are given a function,

f(t) = 100 . 2^(t/4)

Let us assume that f^(-1) represents the inverse of a function

Replacing f(t) with y, we get,

y = 100 . 2^(t/4)

Now, replace further t with y and y with x

x = 100 . 2^(y/4)

Rearranging, we have,

2^(y/4) = x / 100

Taking log both sides, we get,

(y/4) log 2 = log (x/100)

y/4 = log2(x/100)

y = 4 * log2(x/100)

Further, replace x with t and y with f^(-1), i.e.

f^(-1) = 4 * log2(t/100)

Hence, the inverse of the given function, f(t) = 100 . 2^(t/4) is 4 * log2(x/100).

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Answer:

(-6 ÷ 5) × (-6 ÷ 8) = 9/10 or 0.9

Step-by-step explanation:

Hi!

Use the Slope Formula:

[tex]\begin{gathered}\\\bullet\implies\boldsymbol{\displaystyle\frac{y_2-y_1}{x_2-x_1}} \\\\\boldsymbol{Setting\:the\:Values}\\\bullet \boldsymbol{y_2=3}\\\bullet\boldsymbol{x_2=8}\\\bullet\boldsymbol{y_1=3}\\\bullet\boldsymbol{x_1=-2}\\\\\boldsymbol{Solving\:for\:the\:slope}\\\boldsymbol{\displaystyle\frac{3-3}{8-(-2)}}\\\boldsymbol{\dfrac{0}{8+2}}\\\boldsymbol{Slope\longrightarrow0}\end{gathered}[/tex]

I hope I helped! ^^

The final step to be performed in the mathematical expression, (Σx)2 is square the sum of the scores

Sum of squares is a statistical method for calculating the dispersion of data points in regression analysis. By deviating the least from the data, the sum of squares can be used to identify the function that fits the data the best. The purpose of a regression analysis is to assess how well a data series can be fitted to a function that could provide insight into the process by which the data series was created. In the world of finance, the sum of squares can be used to calculate the variation in asset values.

A statistical measure of departure from the mean is the sum of squares. Variation is another name for it. The squared differences of each data point are added together to calculate it. The sum of squares is calculated by squaring the separation between each data point and the line of best fit, then adding the results. The line of greatest fit will reduce this value to the minimum.

We first find the sum, and then square the sum.

ΣX = 1 + 0 + 2 + 4 = 7

So,  ΣX + 1 = 8

Mean = ( 4+6+14 )/3 = 8

Mean =  ΣX*f /  Σf = (5*2 + 4*1 + 3*3 + 2*2 + 1*2) / (2+1+3+2+2) = 29/10

Subtract 3 points from the score X=3

Changing the lowest score to a lower one will increase the range.

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The final step to be performed in the mathematical expression, (Σx)2 is square the sum of the scores

Sum of squares is a statistical method for calculating the dispersion of data points in regression analysis. By deviating the least from the data, the sum of squares can be used to identify the function that fits the data the best. The purpose of a regression analysis is to assess how well a data series can be fitted to a function that could provide insight into the process by which the data series was created. In the world of finance, the sum of squares can be used to calculate the variation in asset values.

A statistical measure of departure from the mean is the sum of squares. Variation is another name for it. The squared differences of each data point are added together to calculate it. The sum of squares is calculated by squaring the separation between each data point and the line of best fit, then adding the results. The line of greatest fit will reduce this value to the minimum.

We first find the sum, and then square the sum.

ΣX = 1 + 0 + 2 + 4 = 7

So,  ΣX + 1 = 8

Mean = ( 4+6+14 )/3 = 8

Mean =  ΣX*f /  Σf = (5*2 + 4*1 + 3*3 + 2*2 + 1*2) / (2+1+3+2+2) = 29/10

Subtract 3 points from the score X=3

Changing the lowest score to a lower one will increase the range.

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Answer:

Answers will be. ............ 36+38

Step-by-step explanation:

Try it on calculator

Answer:

6

Step-by-step explanation:

You count with your fingers. 1,2,3,4,5,6! Congrats you got your answer.

Answer:

16

Step-by-step explanation:

A____(6)_____B____(10)_____C

6+10=16

Hope this helps!

Answer: 36 years old

Step-by-step explanation:

T=Tanya. M=Marcus

T=M+28

T+6=3(M+6)

T+6-6=3(M+6)-6

T=3(M+6)-6

M+28=3(M+6)-6

M+34=3M+18

34=2M+18

2M=16

M=8

T=M+28

T=8+28

T=36 years old

The current age of Tanya is equivalent to 45 years old.

Given is that Tanya is 28 years older than Marcus. In 6 years, Tanya will be three times as old as Marcus

Assume the initial age of Tanya is {x} years and that of Marcus is {y} years old. So, we can write -

x = y + 28         ....... Eq[1]

x + 6 = 3y         ........ Eq[2]

Using Eq[1] in Eq[2], we get -

y + 28 + 6 = 3y

y + 34 = 3y

2y = 34

y = 17

Than, we can write [x] as -

x = 17 + 28

x = 45

Therefore, the current age of Tanya is equivalent to 45 years old.

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