Give three observations that can be made from the graph (average time a student spends playing a sport in the fall)

Answer: $28.80 per year

Answer: The building is 54 feet tall.

Step-by-step explanation:

Answer:

0,1

2,2

4,3

6,4

Step-by-step explanation:

Some Examples

4 = 1/2 (6) + 1

4 = 3 + 1

4=4

----------

2 = 1/2 (2) + 1

2 = 1 + 1

2 = 2

h

0

2

4

6

...................

Answer:

f(x) = 3x – 1

Step-by-step explanation:

f(x) = 3x – 7 also known as y = 3x – 7

Translated 6 units up:

y (+ 6) = 3x – 7

y + 6 = 3x – 7

y = 3x – 13

2 units right:

y = 3(x + 2) – 7

y = 3x + 6 – 7

y = 3x – 1

Answer:

Step-by-step explanation:

the function f(x)=3x-7 is:

vertically compressed by a factor of three

down 7 units

now we translate it 6 units up

so... f(x)=3x-7⇒f(x)=3x-7+6⇒f(x)=3x-1

to translate a linear function horizontally, you have to consider:

f(x-h)=mx+b, where h is the horizontal shift,

thus, to translate f(x)=3x-1     2 units right, we do it :

f(x-2)=3x-1  

f(x)+f(-2)=3x-1  

f(-2)=3*(-2)-1

f(-2)=-6-1

f(-2)=-7

f(x)+(-7)=3x-1  

f(x)-7=3x-1  

f(x)=3x+6

Answer:

x = 3

TU = 35

UV = 35

TV = 70

Step-by-step explanation:

As U is the midpoint of TV:

⇒ TU = UV

⇒ 8x + 11 = 12x - 1

⇒ 8x + 11 - 11 = 12x - 1 - 11

⇒ 8x = 12x - 12

⇒ 8x - 12x = 12x - 12 - 12x

⇒ -4x = -12

⇒ -4x ÷ -4 = -12 ÷ -4

⇒ x = 3

Substitute the found value of x into the expression for TU:

⇒ TU = 8x + 11

⇒ TU = 8(3) + 11

⇒ TU = 24 + 11

⇒ TU = 35

Using the transitive property of equality:

As UV = TU and TU = 15 then UV = 35

Using the segment addition postulate:

⇒ TV = TU + UV

⇒ TV = 35 + 35

⇒ TV = 70

Hence

9514 1404 393

Answer:

  2/3

Step-by-step explanation:

Let x represent the fraction of Cheryl's income she spent in September. Then 1-x is the fraction she saved.

In October, her spending increased by 0.2x, and her savings decreased by 0.4(1 -x). Since Cheryl spends or saves all of her income, these two change amounts must be equal:

  0.2x = 0.4(1 -x)

  x = 2(1 -x) . . . . . . multiply by 5 to clear fractions

  x = 2 -2x . . . . . . eliminate parentheses

  3x = 2 . . . . . . . . add 2x

  x = 2/3 . . . . . . divide by 3

Cheryl spent 2/3 of her income in September.

The expression is x = (PA - PB) / (2 * (24 + 12)).Alfonso's marginal cost is $9 and Bernice's marginal cost is $12.Alfonso's best-response function can be determined by maximizing profit function with respect to PA.

The expression for the location of the indifferent consumer can be derived using the Hotelling model, where the consumer is equidistant between the two parks. Let x represent the distance from Alfonso's Wonderland. The expression is x = (PA - PB) / (2 * (24 + 12)).

The profit function for Bernice's Wild Rides can be found by subtracting the marginal cost of $12 from the revenue function, which is equal to the price PB multiplied by the number of customers.

Bernice's best-response function can be determined by maximizing their profit function with respect to PB.

The profit function for Alfonso's Wonderland, with a marginal cost of $6, can be found similarly by subtracting the marginal cost from the revenue function, which is equal to the price PA multiplied by the number of customers.

Alfonso's best-response function can be determined by maximizing their profit function with respect to PA.

The equilibrium prices and profits can be found by solving the simultaneous equations formed by the best-response functions of both parks.

Repeat steps 4 and 5 for the case where Alfonso's marginal cost is $9.

Repeat step 6 for the case where Alfonso's marginal cost is $9 and Bernice's marginal cost is $12.

By following these steps, we can determine the maximum price Alfonso's Wonderland should pay, the likely price they will have to pay, and the consequences of Bernice's Wild Rides acquiring the exclusive rights.

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The smallest sample size that will result in a margin of error of no more than 5% for a 95% confidence interval is given as follows:

385.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The margin of error is modeled as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

We have no estimate, hence we consider that:

\(\pi = 0.5\)

The minimum sample size is obtained as n when M = 0.05, hence:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.05 = 1.96\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.05\sqrt{n} = 1.96 \times 0.5\)

\(\sqrt{n} = 1.96 \times 10\) (0.5/0.05 = 10).

\((\sqrt{n})^2 = (1.96 \times 10)^2\)

n = 384.16

Hence rounded to 385, as a sample size of 384 would have a margin of error slightly above 0.05.

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Answer:

60$ and 10$ dollar maybe

Answer:

19t+4

Step-by-step explanation:

Perimeter just means add up all the sides

(t+5)+(8t-10)+(t+5)+(9t+4)

= t+8t+t+9t+5-10+5+4

=19t+4

We can be 95% confident that the true population mean TV viewing time is between 3.812 and 4.388 hours.

To calculate the 95% confidence interval, we use the formula:

CI = x' ± Zα/2 * (σ/√n)

Where:

x' = sample mean

Zα/2 = the Z-score associated with the desired confidence level (in this case, 95%, so Zα/2 = 1.96)

σ = population standard deviation

n = sample size

Substituting the given values, we get:

CI = 4.1 ± 1.96 * (1.3/√78)

Calculating the standard error (SE) first:

SE = σ/√n

SE = 1.3/√78

SE ≈ 0.147

Then we substitute the SE value in the CI formula:

CI = 4.1 ± 1.96 * 0.147

CI = 4.1 ± 0.288

CI = (3.812, 4.388)

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Answer:

Step-by-step explanation:second part complete

Answer:

13.48

Step-by-step explanation:

Answer:

9.6 ounces butter

8 ounces sugar

12 ounces flour

4 eggs

Step-by-step explanation:

I'm going to write them down so it's easier for me to look at.

12 ounces butter

10 ounces sugar

15 ounces flour

5 eggs

Now make a ratio: 12 : 15 = 4 : 5

Apply this to all of the ingredients.

12 * 0.8 = 9.6

10 * 0.8 = 8

15 * 0.8 = 12

5 * 0.8 = 4

Answer:

Below in bold.

Step-by-step explanation:

12 is  12/15 = 4/5 of 15 so you multiply the amounts of each ingredient by 4/5 or 0.8.

Butter: 12 * 0.8 = 9.6 oz.

Sugar:  10 * 0.8 = 8 oz.

Flour:  15 * 0.8 = 12 oz.

Eggs: 5 * 0.8 = 4 eggs.

Answer:

yes, it is

Step-by-step explanation:

The table shows a constant rate of change

y-5 7 9 11

5, 5+2, 7+2 ,9+2

Answer:

its equivalet to 9-8x

Step-by-step explanation:

The p and t represent Principal and time and interest is 517.7

We are given the formula to find the interest. So, the formula is -

I = (PRT) ÷ 100

In this formula, I refers to interest, P refers to Principal, R refers to rate of interest and T refers to time. Time will be in years and division by 100 is done for rate of interest.

Keep the values in formula to calculate the interest -

As per the known fact, 12 months = 1 year

So, 20 months = (1 ÷ 12) × 20

20 months = 1.67 years

Interest = (2500 × 12.4 × 1.67) ÷ 100

Performing multiplication in numerator

Interest = 51,770 ÷ 100

Performing division to find the interest

Interest = 517.7

Hence, p refers to principal and t refers to time. The interest that Gordon will receive will be 517.7.

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In hypothesis testing, the null hypothesis (H0) represents the default assumption or the status quo, while the alternative hypothesis (H1) represents the opposing or alternative claim. The appropriate null and alternative hypotheses for this situation can be stated as follows:

Null hypothesis (H0): The mean number of pounds of fruit with the new fertilizer is equal to the mean number of pounds of fruit with the old fertilizer (mu = 388).

Alternative hypothesis (H1): The mean number of pounds of fruit with the new fertilizer is greater than the mean number of pounds of fruit with the old fertilizer

\(\(\mu > 388\)\)

This notation indicates that the mean value, represented by the Greek letter μ, is greater than 388.

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The work done in this case is  4/3 lb-ft

To determine the work done in stretching the spring from its natural length, we need to use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement from its natural length.

Hooke's Law can be expressed as:

F = kx

Where:

In this case, we are given that a force of 16 lb is required to stretch the spring 2 inches beyond its natural length. Therefore, we can set up the equation as:

16 lb = k *2 in

To find the spring constant, we need to convert the units of force and displacement to a consistent system. Let's convert inches to feet since the pound (lb) is commonly used with the foot (ft):

1 ft = 12 in

Converting the displacement:

2 in = 2/12 ft = 1/6 ft

Now, our equation becomes:

16 lb = k * (1/6 ft)

To find the value of k, we can solve for it:

k = (16 lb) / (1/6 ft)

k = 16 lb * (6 ft)

k = 96 lb/ft

Now that we have the spring constant, we can determine the work done in stretching the spring from its natural length.

The work done on an object is given by the formula:

W = (1/2)kx²

Where:

In this case, the displacement is the additional 2 inches beyond the natural length, which is equal to 1/6 ft. Plugging the values into the formula:

W = (1/2) * (96 lb/ft) * (1/6 ft)²

W = (1/2) * 96 lb/ft * (1/36) ft²

W = 48 lb/ft * (1/36) ft

W = 48/36 lb-ft

W = 4/3 lb-ft

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The null hypothesis to test for instruments' relevance is option D) H0:π2=0 or π3=0 or π4=0.In order to test the relevance of the instrument, the first stage equation's null hypothesis should be stated as: H0: π2 = 0 or π3 = 0 or π4 = 0.The relevance requirement will be fulfilled if we can refute the null hypothesis.

The null hypothesis will not be rejected if the F-statistic is less than 10.0. However, if the F-statistic is greater than 10.0, the null hypothesis will be rejected, indicating that the variables are relevant and that the instrument satisfies the relevance requirement.In summary, to test for instruments' relevance in TSLS, the null hypothesis of the first stage equation is stated as H0: π2 = 0 or π3 = 0 or π4 = 0.

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Based on the information, the two integers are 30 and 31.

Let the first integer be x. The second consecutive integer will be (x + 1).

So, the smaller integer = 2x

The larger integer = 3(x + 1)

Their sum = 153

Forming the equation now -

2x + 3(x + 1) = 153

Performing multiplication on Left Hand Side of the equation

2x + 3x + 3 = 153

Performing addition on Left Hand Side of the equation

5x = 153 - 3

Performing subtraction on Right Hand Side of the equation

5x = 150

x = 150/5

Performing division on Right and Side of the equation

x = 30

Smaller integer = 30

Large integer = 30 + 1

Large integer = 31

Thus, the two integers are 30 and 31.

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The expression (3/4) + (6/4) simplifies to 9/4 or 2.25.

In this expression, we follow the order of operations, which states that we should perform operations inside parentheses first. Here, we have two fractions inside parentheses: (3/4) and (6/4). We can add these fractions by finding a common denominator, which is 4 in this case.

For (3/4), the numerator stays the same, and we multiply the denominator by 1 to get 4 as the common denominator. So, (3/4) becomes (3/4) * (4/4) = 12/16.

Similarly, for (6/4), the numerator stays the same, and we multiply the denominator by 1 to get 4 as the common denominator. So, (6/4) becomes (6/4) * (4/4) = 24/16.

Now, we can add these fractions: (12/16) + (24/16) = 36/16.

Finally, we simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4. Thus, 36/16 simplifies to 9/4 or 2.25.

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The one which uses Sir Ronald Fisher's F-distribution for the test statistic is to compare several population means simultaneously.

The F-distribution was developed by Sir Ronald Fisher to study the behavior of two variances from random samples taken from two independent normal populations. The F-distribution allows us to use a F statistic to compare two populations.

The F-distribution is also known as a right-skewed distribution used commonly in another statistical test called an Analysis of Variance (ANOVA). For ANOVA tests we can use the F-distribution to check whether the variance among the means of two populations significantly differ. The F-distribution can also be used in regression analysis to compare the fit of different models.

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Answer:

261

Step-by-step explanation:

first find the area of the triangle

A=9x10/2

A=90/2

A=45

then add it 4 times

then find the area of the square

A=9x9

A=81

and add them all

45+45+45+45+81=261

Answer: x = 35

Step-by-step explanation:

Answer:

D. -0.25 0.25

Step-by-step explanation:

Based on the numbers marked on the horizontal number line, the statement that is true is:

D. -0.25 0.25

The numbers marked on the number line indicate that the interval between -0.25 and 0.25 is represented.

The values are;

⇒ F ∩ H = Ф

⇒ F ∪ H = (- ∞, 7]

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

F and H are defined as;

F = {v | v < 4 }

H = {v | v ≥ 7 }

Now,

Since, F and H are defined as;

F = {v | v < 4 }

H = {v | v ≥ 7 }

Hence, The values are;

F ∩ H = {v | v < 4 } ∩  {v | v ≥ 7 }

         = Ф

And, F ∪ H = {v | v < 4 } ∪  {v | v ≥ 7 }

                 = (- ∞, 7]

Thus, The values are;

⇒ F ∩ H = Ф

⇒ F ∪ H = (- ∞, 7]

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The equation of the plane passing through the point (1, 4, -4) with normal vector 〈3, 5, -2〉 can be written as:

3(x - 1) + 5(y - 4) - 2(z + 4) = 0

Expanding and rearranging terms, we get:

3x + 5y - 2z - 23 = 0

To parameterize this plane, we can let:

x = s

y = t

z = (3s + 5t - 23) / 2

Therefore, the parameterization of the plane is:

r (s,t) = <s, t, (3s + 5t - 23) / 2>

By definition, "to parameterize" means "to express in terms of parameters". A mathematical technique known as parameterization involves representing the state of a system, process, or model as a function of a set of independent variables known as parameters.

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Based on the relationship between the number of orders served by Mary, Joe, and Deandre, the number of orders they each served was:

Assuming that the number of orders served by Mary was x, the formula for the total orders served would be:

Deandre's orders + Mary's orders + Joe's orders = 95
3x + x + (x - 10) = 95

Solving for Mary's orders gives:

3x + x + x - 10 = 95

5x - 10 = 95

5x = 95 + 10

x = 105 / 5

x = 21

Number of orders by Deandre:

= 21 x 3

= 63 orders

Orders by Joe:

= 21 - 10

= 11 orders

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