The graph of a function f is shown below.
Use the graph of the function to find its average rate of change from x=
-3 to x=1. simplify your answer as much as possible.

Answer:

S₁₆ = 344

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = - 1 and d = a₂ - a₁ = 2 - (- 1) = 2 + 1 = 3 , then

S₁₆ = \(\frac{16}{2}\) [ (2 × - 1) + (15 × 3) ]

     = 8 (- 2 + 45)

     = 8 × 43

     = 344

Draw the graph of x-axis which is lesser than 5 .

What is  Graph inequality ?

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The standard error tells us how much we can expect the sample proportion to vary from the true proportion in repeated samples of the same size. Option (d) correctly states that "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion." This means that if we were to take many samples of 100 students from the same school and calculate the proportion of students who bring a reusable water bottle from home in each sample, about 95% of the sample proportions would fall within +/-0.048 of the true proportion.

The correct option is (d) "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion."

The standard error of the sample proportion can be calculated using the formula:

SE = √[p*(1-p) / n]

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 37/100 = 0.37 and the sample size is 100. Plugging in these values, we get:

SE = sqrt[0.37*(1-0.37) / 100] = 0.048

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Answer:

1.2 miles

Step-by-step explanation:

5.3 - 4.1 = 1.2 miles

Answer:

Step-by-step explanation:

5.3 - 4.1 = 1.2

1.2 miles difference.

This is because from Washington to Lanberry it is 4.1 miles. From Washington to Newberry it is 5.3., SO, if you subtract it you will get 1.2 miles difference.

Hope this helped,

kavitha

Answer:

slope=1/4

y-intercept=3

y=.25x+3

Step-by-step explanation:

slope=rise over run so

slope=1/4

y-intercept is the value of y where the line crosses the y axis..

y-intercept=3

In y=mx+b form m is slope and b is y-intercept so...

y=.25x+3

Answer:

0 liters

Step-by-step explanation:

The first step in solving this problem is to find the volume of water that was originally in the tank when it was filled up to of its height. Since the tank is rectangular, we can use the formula for the volume of a rectangular prism:

Volume of tank = length x width x height = 100 cm x 80 cm x 30 cm = 240,000 cm³

Since the tank was filled up to of its height, the volume of water in the tank at this point is:

Volume of water in tank = 100 cm x 80 cm x 30 cm x 0.5 = 1,200,000 cm³

To find the amount of water that was poured into the tank to fill it up to 3 of its height, we need to subtract the volume of water that was originally in the tank from the total volume of water when it is 3 filled, which is 384 liters or 384,000 cm³ (since 1 liter = 1000 cm³):

Volume of water poured into tank = Volume of water when 3 filled - Volume of water in tank at of its height

= 384,000 cm³ - 1,200,000 cm³

= -816,000 cm³

Wait a minute, this result is negative, which means there was no water poured into the tank to reach the 3 filled level. In fact, it suggests that there was an excess of water that had to be removed from the tank to reach the desired level. This could be because the dimensions of the tank were not exact or because the tank was not level when filled to the first level.

Therefore, the answer to the problem is 0 liters or 0 cm³.

Note: It is important to always check the result of a calculation to ensure it makes sense in the context of the problem. In this case, the negative volume of water poured into the tank indicates that there may be an error in the problem statement or in the measurements provided.

The images best represents the result is image W.

We have, the image is rotated about the x-axis.

Now, rotating around x axis can give the other half of the image.

Also, rotating about x axis gives the mirror image of the figure.

So, the rotation leads to a circle.

and, In three dimensional we can say that Sphere.

Thus, the required image is W.

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Answer:

-2x² - 10xy + 2y²

Step-by-step explanation:

4x² - 9xy - 4y² - 6x² - xy + 6y² =

= 4x² - 6x² - 9xy - xy - 4y² + 6y²

= -2x² - 10xy + 2y²

we have

f(x)=8x+6

we know that

The rule for a vertical compresion of f(x) is equal to

(x,y) -------> (x, ay)

where a is the factor

so

(x,f(x)) -------> (x,1/4f(x))

thet means

g(x)=1/4{8x+6}

g(x)=2x+1.5

Hope it helps :)

\(x + 4y = 9 \\

-x - 2y = 3 \\ eliminate \: one \: variable \: by \\ adding \: the \: equations \\ 2y = 12 \\ divide \: both \: sides \\ y = 6 \\ substitute \: the \: value \: of \: y \\ \: into \: equation \: ...2 \\ - x - 2(6) = 3 \\ solve \: the \: equation \\ - x - 12 = 3 \\ - x = 3 + 12 \\ - x = 15 \\ x = - 15 \\ SOLUTION \\ x = - 15 \\ y = 6 \\ Hope \: it \: helps :)\)

Answer: There were 51 students

Step-by-step explanation: Divide 362 by 7 which equals 51 with 5 students remaining! Hope this helps!

The probability that in a given race, her finishing time will be between 75 and 78 seconds, using the normal distribution, is of:

0.4772 = 47.72%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for the finishing times are given as follows:

\(\mu = 75, \sigma = 1.5\)

The probability that in a given race, her finishing time will be between 75 and 78 seconds, is the p-value of Z when X = 78 subtracted by the p-value of Z when X = 75, hence:

X = 78:

Z = (78 - 75)/1.5

Z = 2

Z = 2 has a p-value of 0.9772.

X = 75:

Z = (75 - 75)/1.5

Z = 0

Z = 0 has a p-value of 0.5.

0.9772 - 0.5 = 0.4772 = 47.72%.

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Answer:

 \(\dfrac{x^2+8x+8}{2x+4}\\\\\)

Step-by-step explanation:

Simplify:

        \(\dfrac{3x + 4}{x +2}+\dfrac{x^2+2x}{2x+ 4}\)

Multiply the denominator and the numerator of the first term by 2,

                        \(=\dfrac{2*(3x +4)}{2*(x+ 2)}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{2*3x+2*8}{2*x +2*2}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{6x+8}{2x+4}+\dfrac{x^2+2x}{2x+4}\)

                       \(\sf = \dfrac{6x+8+x^2+2x}{2x+4}\\\\\text{\bf Combine like terms,}\\\\=\dfrac{x^2+8x+8}{2x+4}\\\\\)

(A) The range and IQR for boxplot 1 is 10 and 6 respectively.

(B) The range and IQR for boxplot 2 is 12 and 7 respectively.

The interquartile range defines the difference between the third and the first quartile.

The formula for the interquartile range is given below.

Interquartile range = Upper Quartile – Lower Quartile = Q­3 – Q­1

The range is the difference between the lowest and highest values.

The formula for the interquartile range is given below.

Range = Maximum – Minimum

(A) For boxplot 1, we need to find the range and IQR from the given data set.

So, let 34 be the maximum and 24 be the minimum.

\(\text{Range}=\sf 34-24\)

\(\text{Range}=\sf10\)

Therefore, the range is 10.

Now time to find the IQR.

So, let 33 be Q3 and 27 be Q1.

\(\text{IQR}=\sf 33-27\)

\(\text{IQR}=\sf 6\)

Therefore, the IQR is 6.

(B) Now for boxplot 2, we will do the same thing as from part A.

Let's find the range.

So, let 24 be the maximum and 12 be the minimum.

\(\text{Range}=\sf 24-12\)

\(\text{Range}=\sf12\)

Hence, the range is 12.

Now for the IQR.

So, let 22 be Q3 and 15 be Q1.

\(\text{IQR}=\sf 22-15\)

\(\text{IQR}=\sf 7\)

Hence, the IQR is 7.

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Answer:

Step-by-step explanation:

for 5 it is the blues

Answer:

D is the answer

Step-by-step explanation:

Answer:

1/13

Step-by-step explanation:

Step-by-step explanation:

So, drawing a given unit has a probability of 4/52=1/13. Once a card of a certain unit is drawn, there are just 3 cards of the same unit left, so the probability of drawing the second of the same unit is 3/51=1/17.

In a hypothetical situation, an incorrect dosage calculation due to an error in metric system to Imperial System conversion could lead to potential harm to the patient. To avoid such errors, it is crucial to ensure accurate and precise conversions between the metric and Imperial systems. As a nurse, I will double-check my calculations, use reliable conversion charts or tools, and consult with colleagues or supervisors when in doubt. Additionally, ongoing education and training on dosage calculations and metric system conversions will be important to maintain proficiency and prevent errors in the future.

~~~Harsha~~~

Answer:

The value of a₅ is 1875.

Step-by-step explanation:

Given:

a₁ = 3

aₙ = 5aₙ₋₁

To find the value of a₅, we can apply the recursive formula to compute each term successively:

Step 1: Compute a₂

a₂ = 5a₁ = 5(3) = 15

Step 2: Compute a₃

a₃ = 5a₂ = 5(15) = 75

Step 3: Compute a₄

a₄ = 5a₃ = 5(75) = 375

Step 4: Compute a₅

a₅ = 5a₄ = 5(375) = 1875

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

The probability is 406/625

Step-by-step explanation:

If they are of different materials, we have the following combinations of selection;

(gold and silver) or ( silver and titanium) or (gold and titanium )

The number of earrings present is 13 + 10 + 12 = 25

Probability of selecting a gold earring is 13/25

Probability of a silver is 10/25

Probability of a titanium is 12/25

Substituting these into the probabilities, we have;

(13/25 * 10/25) + (10/25 * 12/25) + (13/25 * 12/25)

= 130/625 + 120/625 + 156/625 = 406/625

Answer:

2.3 hours

Step-by-step explanation:

From 3:12 pm to 4:12 pm, one hour passes.

From 4:12 pm to 5:12 pm, another hour passes.

From 5:12 pm to 5:30 pm, there are 18 minutes that pass.

Therefore, the total time elapsed is 2 hours and 18 minutes out of 60 minutes in an hour.

To convert this to a fraction, we can write:

2 hours + 18 minutes = 2 + 18/60 hours = 2.3 hours

So, 2.3/1 hour passes from 3:12 pm to 5:30 pm.

Answer:

it is the first one because you times the 9 because it says twice and divide it by 3 because you donate to 3 parks

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

First, subtract 3 from both sides.

2x + 3 = 7

     - 3    -3

2x       = 4

Then, divide both sides by 2.

2x / 2 = 4 / 2

x = 2

Answer:

the solution for x is x = 2

Step-by-step explanation:

To solve for x, we need to get x by itself on one side of the equation. First, we can subtract 3 from both sides to get:

2x + 3 - 3 = 7 - 3

Simplifying the left side gives us:

2x = 4

Then, we can divide both sides by 2 to get:

2x / 2 = 4 / 2

Simplifying the left side gives us:

x = 2

Answer:

31

Step-by-step explanation:

Given :-

And we need to find the value of AB .

Pythagoras Theorem :-

Using that ,

\(:\implies\) h² = p² + b²

\(:\implies\) h² = 36² + 15²

\(:\implies\) h² = 1296 + 225

\(:\implies\) h² = 1521

\(:\implies\) h = 31

Hence the value of Hypotenuse is 31 .

Answer:

w=18

Step-by-step explanation:

-1-2 = =3

w/-6 = -3

-6x-3 = 18

w=18

Answer:

w = 18

Step-by-step explanation:

\(\frac{w}{-6}+2=-1\\\frac{w}{-6}=-3\\w=18\)