A school changed their playground from a square shape into a rectangle to accommodate the remodel of the gymnasium. They added 50 feet to one side of the playground and decreased the other side by 20 feet. (A) Write an expression that could be used to express the area of the new playground. (B) Evaluate the expression assuming the original playground has the given side lengths: 50 ft, 100 ft, and 150ft. (C) Do you think there will ever be a time when the new playground will not have a larger area than the old playground? Explain your reasoning.

Answer:

7. 35% of 160 = 56

160 + 56 = 216

There are 216 PTA members this year

8. $4,860

Step by Step: to find out what she pays in total, you have to find out what number is 4% of 4500, so you multiply .04 by 4500 to get 180. multiply that by two to get the total amount of interest he has to pay. then add it to the loan to get 4,860.

9. $2560

if 10%=256

then 10 times the amount 100% is 2560

10. 20/100 = 0.2

0.2 x 20 = 4

4 of the shops are ice cream shops.

Step-by-step explanation:

Answer:

Step-by-step explanation:

gradient = 5 = [k-(-1)]/[6-2]

[k+1]/4 = 5

k+1=20

k=19

The value of k in the line that passes through the points A(2, -1) and (6, k) with a gradient of 5 is found to be 19 by using the formula for gradient and solving the resulting equation for k.

To find the value of k in the line that passes through the points A(2, -1) and (6, k) with a gradient of 5, we'll use the formula for gradient, which is (y2 - y1) / (x2 - x1).

The given points can be substituted into the formula as follows: The gradient (m) is 5. The point A(2, -1) will be x1 and y1, and point B(6, k) will be x2 and y2. Now, we set up the formula as follows: 5 = (k - (-1)) / (6 - 2).

By simplifying, the equation becomes 5 = (k + 1) / 4. To find the value of k, we just need to solve this equation for k, which is done by multiplying both sides of the equation by 4 (to get rid of the denominator on the right side) and then subtracting 1 from both sides to isolate k. So, the equation becomes: k = 5 * 4 - 1. After carrying out the multiplication and subtraction, we find that k = 20 - 1 = 19.

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Answer:

y= - 11

Step-by-step explanation:

A line with a slope of 0 is a horizontal line, parallel to the x- axis with equation

y = c ( c is the value of the y- coordinates the line passes through )

the line passes through (- 13, - 11 ) with y- coordinate - 11, then

y = - 11 ← equation of line

Answer:

y = -11

Step-by-step explanation:

A line with slope as 0, is a horizontal line ( In other words parallel to x-axis).

There is no rise, only run.

Equation of the line is y = c.

   y = -11

Answer:

4

Step-by-step explanation:

Answer:

The three points are

(-2,1)

(-3,2)

(-4,3)

Step-by-step explanation:

These points solve the problem, you could have other points as well such as (-5,4), (-6,7) and so on

Answer:

3.14 square inches or π square inches

Step-by-step explanation:

The radius of a circle is 1 inch. What is the area?

r=1 in

The formula for the area of a circle is given as:

πr²

The radius (r) = 1 inch

Hence,

Area of the circle = π × 1²

= 3.1415926536 square inches

Approximately = 3.14 square inches or we can say that the Area of the circle = π square inches

The Matlab & Simulink model consists of a Clock block to generate a time signal, a Gain block to multiply the time signal by 2, and a Differential Equation block to solve the given differential equation. The Scope block is used to visualize the behavior of the variable x over time.

To construct a Matlab & Simulink model for the given mathematical model, we can use Simulink's Differential Equation block and a Clock and Gain block. Here's a step-by-step guide:

1. Open Simulink in Matlab.

2. Drag and drop a Clock block from the Simulink Library Browser into the model.

3. Drag and drop a Gain block from the Simulink Library Browser into the model.

4. Double-click on the Gain block and set the Gain value to 2.

5. Drag and drop a Differential Equation block from the Simulink Library Browser into the model.

6. Double-click on the Differential Equation block and enter the equation `d²x + 3 + 4*x + 6 = 5*cos(2*t)`.

7. Connect the output of the Clock block to the input of the Gain block, and the output of the Gain block to the input of the Differential Equation block.

8. Connect the output of the Differential Equation block to a Scope block from the Simulink Library Browser.

9. Run the simulation.

The Scope block will show the behavior of the value of x over time according to the given mathematical model.

In conclusion, The Clock block provides the independent variable t, and the Differential Equation block evaluates the given equation to compute the value of x. The simulation shows the dynamic response of x as influenced by the equation and the time signal.

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Answer:

x = - 4

Step-by-step explanation:

given a quadratic function in standard form

y = ax² + bx + c ( a ≠ 0 ) then the axis of symmetry is

x = - \(\frac{b}{2a}\)

h(x) = 5x² + 40x + 64 ← is in standard form

with a = 5 , b = 40 , then axis of symmetry is

x = - \(\frac{40}{10}\) = - 4

Answer:

2.3333333333333333333333333333333 sec

Answer:

110

Step-by-step explanation:

the sum of straight angle is 180

the sum of angle of triangle=180

angle E=180-120=60

triangle BDE: <B=180-60-90=30

<B in triangle ACB=180-(130+30)=20)

in traingle ACB: <A = 180-(90+20)=70

angle x=180-70=110 degrees

The function that is increasing and has a domain of (1, infinity) is A. F(x) = log(x - 1) + 2.


To determine the increasing function with the specified domain, let's analyze each option:

A. F(x) = log(x - 1) + 2
This function is increasing because the logarithm of a positive number is always increasing. The domain is (1, infinity), which matches the requirement.

B. F(x) = -log(x - 2) + 1
This function is decreasing because the negative sign in front of the logarithm inverts the increase. The domain is (2, infinity), which does not match the requirement.

C. F(x) = -log(x - 1) + 2
This function is also decreasing because of the negative sign in front of the logarithm. The domain is (1, infinity), which matches the requirement, but the function is not increasing.

D. F(x) = log(x - 2) + 1
This function is increasing because the logarithm of a positive number is always increasing. However, the domain is (2, infinity), which does not match the requirement.

The function that is increasing and has a domain of (1, infinity) is A. F(x) = log(x - 1) + 2.

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Answer:

17C5+11C5

Step-by-step explanation:

Well there are 17 and chooses 5 that's 17C5

there are 11 men abd chooses 5 that's 11C5

so add them up

17C5+11C5

The combination helps us to know the number of ways an object can be selected without a particular manner. The number of ways in which 5 men and 5 women can be selected is 2,858,856.

Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.

The combination helps us to know the number of ways an object can be selected without a particular manner. A combination is denoted by 'C'.

\(^nC_r = \dfrac{n!}{(n-r)!r!}\ , \ \ ^nP_r = \dfrac{n!}{(n-r)!}\)

where,

n is the number of choices available,

r is the choices to be made.

Given that from a group of 17 women and 11 men, a researcher wants to randomly select 5 women and 5 men for a study.

Now, the number of ways for selection can be written as,

Number of ways in which men can be selected = ¹¹C₅ = 462

Number of ways in which women can be selected = ¹⁷C₅ = 6188

Further, the number of ways for selection can be written as,

Number of ways = Number of ways in which men can be selected × Number of ways in which women can be selected

Number of ways = 462 × 6188

Number of ways = 2,858,856

Hence, the number of ways in which 5 men and 5 women can be selected is 2,858,856.

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Answer:

0.9115

Step-by-step explanation:

Using a binomial probability function :

P(x =x) = nCx * p^x * (1 - p)^(n - r)

Probability of success, p = 0.55

1 - p = 1 - 0.55 = 0.45

n = 8

x = 2

P(x > 2 ) = p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6) + p(x = 7) + p(x =8)

To save computation time, we could use the binomial probability calculator :

P(x > 2 ) = 0.9115

Answer: he washed 18 windows

Step-by-step explanation: count by 10

Answer:

A

Step-by-step explanation:

Simon will mostly make more than ten points, so do A

Answer:

a

Step-by-step explanation:

Answer: 27 students

Step-by-step explanation:

First take 45 + 90 = 135 students total

20% = 0.2

Then take 135 times 0.2 = 27 students

For part a, the confidence interval for the population proportion of college students who work to pay for tuition and living expenses is 0.42 to 0.52, with a certain level of confidence (usually 95% or 99%).
For part b, the confidence interval is slightly wider and ranges from 0.41 to 0.53. This could be due to a larger sample size or a lower level of confidence.
For part c, as the confidence level increases from 95% to 99%, the margin of error becomes larger.

a. To calculate the confidence interval for the population proportion of college students who work to pay for tuition and living expenses, we use the given range of 0.42 to 0.52. This interval indicates that we can be confident that the true population proportion falls between 42% and 52% of college students. This means that we are 95% confident that the true population proportion falls within this interval based on the sample data.

b. Similarly, for the second provided confidence interval, we use the given range of 0.41 to 0.53. This interval indicates that we can be confident that the true population proportion falls between 41% and 53% of college students.

c. When the confidence level is increased, the margin of error becomes larger. This is because a higher confidence level requires a wider interval to ensure that the true population proportion falls within the specified range with greater certainty. This is because a higher level of confidence requires a wider interval to capture the true population proportion. As a result, the precision of the estimate decreases as the margin of error increases.

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Neil is growing sugar crystals for his science fair experiment. He wants to find out if the amount of sugar affects the size of the crystal. Neil adds 18 tablespoons of sugar to his first bowl of water. He plans to add less sugar to the second bowl.

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The given statement is True. A discrete probability distribution can be expressed in a graph, table, or formula, as long as it gives the probability associated with each value of the discrete random variable.

A Discrete probability distribution is a statistical term used to describe the probability distribution of a random variable that can take on a finite or countably infinite number of distinct outcomes. In other words, a discrete random variable is one that can only take on a specific set of values, while a continuous random variable can take on any value within a specified range.Examples of discrete random variables include the number of children in a family, the number of accidents that occur in a given day, and the number of red cars that pass through an intersection in an hour. A discrete probability distribution is a way of describing the probabilities associated with each of these possible outcomes.In summary, a discrete probability distribution can be expressed in a graph, table, or formula, as long as it gives the probability associated with each value of the discrete random variable. This is because a discrete random variable can only take on a specific set of values, making it easy to calculate the probabilities associated with each outcome.

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Answer:

342

Step-by-step explanation:

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Answer:

25/100 or 1/4

Step-by2-step explanation:

40+20+25+15=100

so then if there id 100 you got 25/100 but then you got to simplify and you get  1/4.

Answer:

I don't understand the answer list, but the answer should be a 1/4 chance, or 25%.

Step-by-step explanation:

Black is 40, while yellow is 20, orange is 25 and purple is 15. If we add those all together, we get 100. We need the probability that one is orange, so we divide.

\(\frac{25}{100}\) is equal to \(\frac{1}{4}\) or 25%.

She has a 25% chance of the band being orange.

Answer:

  3

Step-by-step explanation:

You want the middle term of the geometric sequence 6, __, 3/2.

The first term of this sequence is a1. With common ratio r, the first three terms are ...

If we multiply the first and third terms, we get ...

  (a1)(a1·r²) = (a1)²·r² = (a1·r)² . . . . . the square of the middle term

Then the middle term is ...

  a1·r = √(6·3/2) = √(18/2) = √9 = 3

The middle term of the sequence is 3.

__

Additional comment

That lets us see that the common ratio is r = 3/6 = 1/2.

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The inequalities for the given situation are obtained as 5x - 4y ≥ 20 and  6x + 4y ≥ 24.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Let x be the number of shoes sold, y be the number of belts sold, a be the number of t-shirts sold, and b be the number of sweaters sold.

For the sale of shoes and belts, we can write the inequality -

5x - 4y ≥ 20

This inequality states that the total profit from selling shoes and belts (5x - 4y) must be at least $20.

To graph this inequality, we can first solve for y -

-4y ≥ -5x + 20

y ≤ (5/4)x - 5

This is the equation of a line with a slope of 5/4 and a y-intercept of -5.

We can graph this line as a straight line and shade the region below it to represent the valid solutions.

For the sale of t-shirts and sweaters, we can write the inequality -

6x + 4y ≥ 24

This inequality states that the total profit from selling t-shirts and sweaters (6x + 4y) must be at least $24.

To graph this inequality, we can first solve for y -

4y ≥ -6x + 24

y ≥ (-3/2)x + 6

This is the equation of a line with a slope of -3/2 and a y-intercept of 6.

We can graph this line as a straight line and shade the region above it to represent the valid solutions.

To choose a solution, we need to find a point that satisfies both inequalities.

One such point is (4, 0), which means that 4 shoes and 0 belts are sold, and 4 t-shirts and 0 sweaters are sold.

This gives a total profit of -

= 5(4) - 4(0) + 6(4) + 4(0)

= 20 + 24

= $44

Therefore, selling 4 shoes, 0 belts, 4 t-shirts, and 0 sweaters would achieve the desired profits.

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Macys sells shoes and belts. The store makes $5 profit on the sale of shoes (x) but loses $4 on the sale of each belt (y). The store wants to make a profit of at least $20 from the sale of shoes and belts.

They also sell t-shirts and sweaters. They make $6 profit on the sale of t-shirts(x) and $4 on the sale of sweaters (y). The store wants to make a profit of at least $24 from the sale of t-shirts and sweaters. Write and graph the inequalities that describe both situations and choose a solution.

If a mill worker measures the width of a plank and the width of the plank is 15.8 dm, then the width of the plank in meters is 1.58

The width of the plank in decimeter = 15.8 dm

Conversion is the process of the converting the given measurement like length, mass etc, from one unit to another unit

We have to find the width of the plank in meter

We know that,

1 decimeter = 0.1 meter

Convert the given decimeter to meter  

15.8 decimeter = 15.8 × 0.1

Multiply the numbers

= 1.58 meters

Therefore, the width of the plank in meter is 1.58

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The given question in incomplete, the complete question is :

A millworker measures the width of a plank. The width is 15.8 dm . what is the width in meters?

The probability of having 3 or fewer Hispanics on the 15-member union executive committee, chosen at random from all the workers, can be calculated using the binomial probability formula.

The situation can be modeled as a binomial distribution, where we have n = 15 trials (the number of members on the executive committee) and a probability of success (selecting a Hispanic worker) p = 0.30 (the proportion of Hispanic workers among all the workers). We are interested in finding the probability of having 3 or fewer successes (Hispanic members) in these 15 trials.

To calculate this probability, we can use the binomial probability formula:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Where P(X = k) represents the probability of exactly k successes in the 15 trials.

Using this formula, we can substitute the values into the formula and calculate the probability.

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Answer:

163.3

Step-by-step explanation:

3.14*r^2*h

h=13

4/2 = 2

r=2

2^2 = 4

3.14*4 = 12.56

12.56*13 = 163.28

Rounded = 163.3

I believe the answer is 163.3

Answer: Bladder

Step-by-step explanation:

The walls of the bladder contain very few blood vessels and are lined with guanine crystals, which make them impermeable to gases. By adjusting the gas pressurising organ using the gas gland or oval window the fish can obtain neutral buoyancy and ascend and descend to a large range of depths.