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The measure of the missing angle is 21°.

1. Measure the length of each side of the triangle.

2. Using the triangle inequality theorem, determine the angles of the triangle.

3. Use the formula to calculate the measure of each interior and exterior angle.

Solution:

To measure a missing angle of triangle,

∠ABC + ∠ACB + ∠CAB = 180°

x + 132° + 27° = 180°

x + 159°  = 180°

x = 180° - 159°

x = 21°

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YES, This is an observational study.

The variables in this study are:

Media usage: categorical (explanatory variable)

Tiredness: quantitative (response variable)

This is an observational study. The researchers are observing and measuring the relationship between media usage and tiredness, but they are not manipulating or controlling any variables. They are collecting data by randomly selecting homes to visit and interviewing the adult member of the household whose birthday was nearest.

An observational study draws conclusions from a sample of a population in disciplines like epidemiology, social sciences, psychology, and statistics when the independent variable is not under the researcher's control due to ethical considerations or practical limitations. One typical observational study examines how a therapy may affect its participants, but the researcher has no control over which group the subjects are assigned to—the treated group or the control group. Unlike experiments like randomized controlled trials, when each subject is arbitrarily assigned to either a treated group or a control group, this does not happen. Observational studies naturally create challenges for inferential analysis because they lack an assignment mechanism.

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The expected profit in the long run can be determined by calculating the expected value of the total revenue from selling the lobsters. The expected total revenue is the sum of the expected revenue from selling the lobsters to the restaurant and the from selling the lobsters to the grocery store.

The expected value of the revenue from selling the lobsters to the restaurant can be calculated by multiplying the expected price per pound from the restaurant by the expected amount of lobsters caught in a day. The expected price per pound from the restaurant follows a triangular distribution with minimum value $1.50, maximum value $5.50, and likeliest value $3.50. The expected amount of lobsters caught in a day follows a normal distribution with mean 1,500 pounds and standard deviation sqrt(12,500) pounds.

The expected value of the revenue from selling the lobsters to the grocery store can be calculated by multiplying the expected price per pound from the grocery store by the expected amount of lobsters caught in a day. The expected price per pound from the grocery store is decreasing with more lobsters: $3.85 - 50.0005 * y, where y is the total lobster amount sold in pounds. The expected amount of lobsters caught in a day follows a normal distribution with mean 1,500 pounds and standard deviation sqrt(12,500) pounds.

Given the expected values of the total revenue from selling the lobsters to the restaurant and the grocery store, Amir can use simulation to determine the optimal percentage of lobsters to sell to the restaurant in order to maximize his expected profit in the long run. He can run several simulations with different percentages of lobsters to be sold to the restaurant and compare the expected profits for each simulation. The percentage that produces the highest expected profit is the optimal percentage for Amir to maximize his expected profit in the long run.

Amir can use simulation to determine the optimal percentage of lobsters to sell to the restaurant in order to maximize his expected profit in the long run. He can calculate the expected value of the total revenue from selling the lobsters to the restaurant and the grocery store, and then run several simulations with different percentages of lobsters to be sold to the restaurant to compare the expected profits for each simulation. The percentage that produces the highest expected profit is the optimal percentage for Amir to maximize his expected profit in the long run.

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The system of equations is y = 35 - 2.2x and y = 1.7x.

The solution of the system of equations is (8.97,15.25).

At about 8.97 seconds, both elevators will be about 15.25 feet above the ground.

What is an elevator?

An elevator, often known as a lift, is a car that moves vertically in a shaft to transport passengers or freight between the levels of a multistory building. Most modern elevators are propelled by electric motors via a system of wires and sheave with the assistance of a counterweight (pulleys).

Given that there are two elevators in an office. The 4th floor of the office at 35 feet above the ground and is descending at a rate of 2.2 feet per second.

The equation represents the height of the elevator above the ground after x seconds is y = 35 + (-2.2)x. Since the elevator is descending at a rate of 2.2 feet per second.

The other elevator starts out at ground level and rises at a rate of 1.7 feet per second.

The equation represents the height of the elevator above the ground after x seconds is y = 1.7x. Since the elevator is rising at a rate of 1.7 feet per second.

The system of equations is

y = 35 + (-2.2)x .....(i)

y = 1.7x   ........(ii)

Solve the equations substitution method.

Putting y = 1.7x in equation (i)

1.7x = 35 + (-2.2)x

1.7x = 35 - 2.2x

Add 2.2x on both sides:

1.7x + 2.2x = 35

3.9x = 35

Divide both sides by 3.9:

x = 35/3.9

x = 8.97

Putting x = 8.97 in equation (ii)

y = 1.7 × 8.97

y = 15.25

After 8.97 seconds, the elevators will be 15.25 feet above the ground.

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Answer: No, x^2 is not a quadratic equation. It is a monomial equation. A quadratic equation has the form ax^2 + bx + c = 0, where a, b, and c are constants.

Step-by-step explanation:

Answer:

6.000277798 x 10^20

Answer:

UMMMM Wait IM sorry What grade are you in? I'm in fifth.

Step-by-step explanation:

The equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice is  

y = 0.25*85.

What is percentage?

A number or ratio expressed as a fraction of 100 is known as a percentage in mathematics. Though the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. An amount that is a percentage is dimensionless and has no assigned measurement.

Given:

The current box holds 85 ounces, 25% less rice.

We have to find the equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice.

Let, y be the original amount of ounces of rice in a box.

The current box holds 85 ounces.

The 25% less than 85 ounces are 85*0.25.

So, the equation becomes y = 0.25*85.

Hence, the equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice is  

y = 0.25*85.

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To solve the equation (3.4)(6.7) using the standard algorithm, first multiply 3.4 and 6.7. Then, the result is 22.78.

The standard algorithm for multiplication is a step-by-step process that involves breaking down the numbers being multiplied into simpler parts, and then multiplying those parts together.

First, you would need to multiply the ones place of the first number (4) by the ones place of the second number (7), which would give you 28.

Next, you would need to multiply the ones place of the first number (4) by the tens place of the second number (6), which would give you 24.

Then, you would add the two products from steps 1 and 2 to get the result: 28 + 24 = 52.

Alternatively, you can use the distributive property of multiplication to simplify the problem.

(3.4)(6.7) = 3.46 + 3.40.7 = 22.8

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The meaning of Dilation is changing the size of an object without changing its shape. The size of the object may be decreased or increased based on the scale factor.

One example of dilation math is a square of side 5 units can be dilated to a square of side 25 units, but the shape of the square remains the same.

Dilation is the method of resizing or transforming an object. It is a transformation that makes the objects larger or smaller with the help of the given scale factor.

The new figure get after dilation is called the image and the real image is called the pre-image. Dilation can be of two types:

1. Expansion - It happens when the size of an object is increased.

2. Contraction - it happens when the size of an object is decreased.

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Answer:

y = 120.8

Step-by-step explanation:

y − 58.8 = 62

Add 58.8 to both sides

y = 120.8

Let's check

120.8 - 58.8 = 62

62 = 62

So, y = 120.8 is the correct answer.

Answer:y= 120.8 I hope this helps

Step-by-step explanation:

y-58.8=62

Move the constant to the right-hand side and change its sign

Like this

Y=62+58.8

Then Add the numbers 62 and 58.8

Which will give you

Plus bring down your y

Your answer is y=120.8

18-12=6, peter now has 6 dimes left after buying a drink. Since the number he has left is ONE HALF of the number of pennies he has. 6x2=12.

peter has 12 pennies. hoped that helped

The box has 18 glazed donut hole that Chad bought.

The percentage of glazed donut holes = 60%

The percentage of powdered sugar donut hole = (100 - 60) % = 40%

Let us consider the total number of donut hole in the box bought by Chad to be 'x'

Number of powdered sugar donut hole = 12

Hence, we can say that the number of powdered sugar donut hole in the box Chad bought is:

(40% of x) = 12

Therefore, x = (12 x 100) / 40 = 30

Since the total number of donut hole in the box = 30

The number of glazed donut hole = 30 - 12 = 18

Thus, the box that Chad bought had 18 glazed donut hole.

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Answer:

Step-by-step explanation:

Sara will win a medal if she keeps practicing gymnastics.

Answer:

24wx + x

Step-by-step explanation:

3( wx8) + x

3(8wx) +x

3 × 8wx + x

\ /

24wx + x

Answer: There are 520 pounds of dog and cat food

Step-by-step explanation:

1. 14+12= 26

2. 26x20=520

Answer:6

Step-by-step explanation: 6,12,18

9,18

Andrew would need to invest $61,300 for the account to reach $93,000.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

The equation to find final amount in compound interest is,

A = P (1 + r/n)^(n t)

Here A is the final amount, P is the initial amount, r is the rate of interest, n is the number of times compounding is done in a year, t is the time in years.

Given, A = $93,000

t = 19 years

r = 2.2% = 0.022

n = 4 (since compounding is quarterly)

93,000 = P [1 + (0.022/4)]^(4×19)

93,000 = P [1.0055]^(76)

93,000 = P (1.517)

P = 61,297.8516

To the nearest hundred dollars, P = $61,300

Hence the principal amount Andrew need to invest is $61,300.

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As per the given equation, the first plant is produce 2x+21 more items than second plant.

The term equation is known as a mathematical statement that shows that two mathematical expressions are equal.

Here we have given that the first plant produces 5x+14 items daily

And the second plant produces 3x-7 items daily

In order to find the number of items produced on first plant, then we have to calculate the differences between number of items by the two plants daily, then it can be written as by using the equations,

=> (5x+14) - (3x-7)

Now, we have to expand the equations, then we get

=> 5x+14 - 3x+7

=> 2x+21

Therefore, first plant produces 2x+21 more items daily than the second plant.

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Answer:

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6} \vphantom{\dfrac12} x&-4&1&2&3&6 \\\cline{1-6} \vphantom{\dfrac12} f(x)&-20&5&10&15&30 \\\cline{1-6}\end{array}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=5x[/tex]

To complete the function table, substitute each given value of x into the given function:

[tex]x=-4 \implies f(-4)=5(-4)=-20[/tex]

[tex]x=1 \implies f(1)=5(1)=5[/tex]

[tex]x=2 \implies f(2)=5(2)=10[/tex]

[tex]x=3 \implies f(3)=5(3)=15[/tex]

[tex]x=6 \implies f(6)=5(6)=30[/tex]

Completed table:

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6} \vphantom{\dfrac12} x&-4&1&2&3&6 \\\cline{1-6} \vphantom{\dfrac12} f(x)&-20&5&10&15&30 \\\cline{1-6}\end{array}[/tex]

Answer:

so basically all you have to do is round.

Step-by-step explanation:

Angle EBF is 45 degrees because angle ABC is 90 degrees and line D divides each side into two equal parts.

Given that lines AB and BC are parallel. Angles ABD and CBD are bisected by the dashed rays. Angle EBF is measured at 45 degrees because angle ABC is 90 degrees, line D divides each side into two equal parts, and half of 90 degrees is 45 degrees.

As a result, the angle EBF is 45 degrees because angle ABC is 90 degrees and line D divides each side into two equal parts, and half of 90 degrees is 45 degrees.

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The slope is 2 using the slope-intercept form. As the slope of the line in slope-intercept form is the coefficient of x, the slope of the line is -2.

The slope of a line governs its steepness. Using mathematics, the gradient is expressed as "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical (rise) to the horizontal (run) change in distance between any two sites. Every time the equation for a straight line is written as y = mx + b, the slope-intercept representation of the equation is utilized. At the location of the y-intercept, the line has a slope of m, b, and c. (0, b). As an example, the y-intercept of the equation y = 3x - 7 has a value of 3. (0, 7).

given

The slope is 2 using the slope-intercept form.

As the slope of the line in slope-intercept form is the coefficient of x, the slope of the line is -2.

Divide the difference in elevation between two points by the distance between them, multiply the result by 100, and that is the percent slope. The term "rise" refers to the elevational difference between two places. The run is the distance separating the points. The formula for percent slope is (rise / run) x 100.

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-1016 is a rational number and integer

Integers are basically the whole numbers that can be positive, negative, or zero. In integers, fractional numbers are not included. For instance, -2, -3,0,1,5, and so on are integers.

A rational number, in Mathematics, can be defined as any number which can be represented in the form of p/q where q ≠ 0.

Example of rational numbers are 1/2 , 2/1 , 3/5 e.t.c.

All positive and negative integers are also rational numbers.

Therefore the number -1016 is a both a rational number and an integer.

This is because all positive and negative numbers are integers.

And -1016 can be written as -1061/1 which makes it a rational number.

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Therefore , the solution of the given problem of factorization comes out to be x=0 and x=1/3.

The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.

Here,

Given:

thus . We do factorization of given expression and

we come on a result

=>  3x - 9x²

=> 3x (1 -3x)

x=0 and x=1/3

Therefore , the solution of the given problem of factorization comes out to be x=0 and x=1/3.

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Answer: To find out how many seconds it will take to print 300 copies of the Sport Report, we can use the formula:

time = (number of copies) / (rate of printing)

We know that the rate of printing for The Informer is 450 copies in 15 seconds. To find the rate of printing per second, we can divide the number of copies by the time in seconds:

rate of printing = 450 / 15 = 30 copies per second

So to find out how long it will take to print 300 copies of the Sport Report, we can use this rate of printing and plug it into the time formula:

time = (number of copies) / (rate of printing)

time = 300 / 30

time = 10 seconds

Therefore, it will take 10 seconds to print 300 copies of the Sport Report at the same rate as The Informer.

Step-by-step explanation:

An equation of the line that passes through the point (6, 0) and had a slope of -5/6 is y = -5x/6 + 5.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Given the following parameters:

Substituting the given parameters into the point-slope formula, the equation of the line is given by;

y - y₁ = m(x - x₁)

y - 0 = -5/6(x - 6)

y = -5x/6 + 5

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