The AP Calculus exam scores were released in July. The Secondary Math Specialist prepared the box plot shown to present the scores to the superintendent. What's the range of scores that represents the middle 50 percent of the students who took the test?

A. 65%–94%
B. 65%–89%
C. 81%–89%
D. 65%–81%

Equation step-by-step:

4n - 18 = 52 → we take -18 to the right side of the equation

4n = 52 + 18 → we solve for 52 + 18

4n = 70 → we take 4 to the right side of the equation

n = 70 / 4 → we solve for 70 / 4

n = 17,5 → final answer

Hope it helped,

BioTeacher101

There are eight fish in each tank. Because 72 divided by 9 is 8.

Hello,

Please, see the attached files.

Thanks.

There are 80.5 kilometres in 50 miles.

1 mile= 1.61 km

50 miles= x

1x= 50*1.61

x=80.1

80.1 kilometers

The answer is 8.

You divide 88 by 11 to find out how much Bianca haves.

Given options : Two intersecting circles are drawn with a radius in each marked. the image will be linked.

Given options : An equilateral triangle inscribed in a circle

A square inscribed in a circle

A regular pentagon inscribed in a circle

A regular hexagon inscribed in a circle.

Note. When we join an intersection point of two circles and centers of the circles it would form an equilateral triangle that would be inscribe inside a common portion of both circles..

Therefore, an equilateral triangle inscribed in a circle would be correct option.

She is completing an equilateral triangle inscribed in a circle.

The correct equation which describes a line with an x-intercept of 3 is C. x = 3. This implies a vertical line where the x-value is always 3, regardless of the y-value.

In response to your query about which of the following equations describes a line with an x-intercept of 3, the direct answer is C. x = 3. An x-intercept is the point where a line crosses the x-axis. For an equation to have an x-intercept of 3, it means that when y is 0, x equals 3. By plotting this on a graph, y can be any real number, but x will always stay 3. Therefore, the equation x = 3, which option C represents, is the correct description for a line with an x-intercept of 3.

It's important to note that, in terms of linear equations (generally represented as y = mx + b, where m represents the slope and b represents the y-intercept), x = 3 can be perceived as a vertical line that intersects the x-axis at point 3.

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Answer:

Option C.

Option B.

Step-by-step explanation:

By definition, the square of a number is that number times itself.

The square root of a perfect square is a whole number.

Since the square root of another number (not perfect square) is not a whole number, you can estimate it finding two perfect square roots that number is between.

1) Observe that 4 and 9 are perfect squares:

[tex]4=2^2\\9=3^2[/tex]

And 8 is between those numbers.

Therefore, the square roots [tex]\sqrt{4}[/tex] and [tex]\sqrt{9}[/tex] are used to estimage [tex]\sqrt{8}[/tex]

2) Notice 36 and 49 are perfect squares:

[tex]36=6^2\\49=7^2[/tex]

And 42 is between those numbers.

Therefore, the square roots [tex]\sqrt{36}[/tex] and [tex]\sqrt{49}[/tex] are used to estimage [tex]\sqrt{42}[/tex]

The square roots used to estimate √8 are √4 and √9 while the square roots to estimate √42 are √36 and √49.

The two square roots that are used to estimate √8 are √4 and √9 since the value of √8 falls between the value of these two square roots (2 and 3). The reason why these are chosen is due to √8 being greater than √4 and less than √9. Similarly, the two square roots to estimate √42 are √36 and √49. The square root of 42 is more than the square root of 36 (which is 6) and less than the square root of 49 (which is 7). Therefore, to estimate the square roots, we find two perfect squares that the number falls between.

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Answer = 0 ≤ x ≤ 25

Explanation:  

Break the word equation into two for better understanding  

-20 less than or equal to 2x -20 >>>> -20 ≤ 2x -20

2x -20 less than or equal to 30 >>>> 2x -20 ≤ 30

Keeping in view the question we deduce the equation  

-20 ≤ 2x -20 ≤ 30

Solve and simplify the above equation accordingly, by breaking down the equation

-20 ≤ 2x -20      and   2x -20 ≤ 30

-20+20 ≤ 2x      and   2x ≤ 30 +20

    0 ≤ x (0/2)    and     x ≤ 25 (50/2)

So,    0 ≤ x ≤ 25

Answer:

17

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

Answer:

best ans is { f(x)| –∞ < f(x) ≤ 4}

Step-by-step explanation:

usually to find the range of a fn, u need to see what the value can be. the graph show only a small range of x values. but u can see f(x) is definitely <  4. so the ans is { f(x)| –∞ < f(x) ≤ 4}

The range of the graph will be (–∞, 4]. Then the correct option is B.

The domain means all the possible values of x and the range means all the possible values of y.

From the graph, we can conclude that the curve gets saturated at y = 4 and as the value of x approached to infinity, the value of y approach to negative infinity.

The range of the graph will be (–∞, 4].

Then the correct option is B.

More about the domain and range link is given below.

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Answer:Each installment will be of 60 and 16th will be the last payment.

Step-by-step explanation:

To find the monthly repayment by Oscar we first find the sequence.

For that first we put [tex] n=1 [/tex] in

[tex] F(n)=900-60(n-1)[/tex]

[tex] F(1)= 900-60(1-1) = 900 [/tex]

Now for [tex]n=2 [/tex]

[tex] F(2)=900-60(2-1)=840[/tex]

For [tex]n=3[/tex]

[tex] F(3)=900-60(3-1)=900-120=780[/tex]

So the sequenxe is 900,840,780......

As the amount is decreasing by 900-840=840-780=60

Therefore each installment will be equal to 60

For last payment amount will become 0

i.e.[tex]F(n) =0[/tex]

[tex] 900-60(n-1)=0[/tex]

[tex] 900-60n+60=0 [/tex]

[tex] 960=60n [/tex]

[tex]n = 960\div60[/tex]

[tex]n = 16 [/tex]

Last month will be 16th

The amount Oscar pays monthly is $900, and he will make his last payment in month 16.

To find the amount Oscar pays monthly, we can subtract the amount he repays in each month from the previous month's balance. The formula F(n) = 900 - 60(n-1) represents the remaining amount Oscar needs to repay at the beginning of month n. By plugging in n = 1, we can find the initial balance and the amount he paid that month. To find the month in which he makes his last payment, we can set F(n) to zero and solve for n.

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Answer:(x+5i) (x-5i) is the right answer

The expression x^2 + 25 can be factored over the complex numbers as (x + 5i) and (x - 5i). This is achieved using the sum of squares formula a^2 + b^2 = (a + bi)(a - bi).

The expression you are tasked with factoring is x2 + 25.

This is a sum of squares expression and can be factored using the formula a2 + b2 = (a + bi)(a - bi), where 'i' represents the complex numbers.

So, x2 + 25 can be factored as (x + 5i)(x - 5i).

This is because the square root of 25 is 5, and 'i' represents the imaginary number.

So the factors of the expression x2 + 25 over the complex numbers are (x + 5i) and (x - 5i).

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D. (X-3)(4x)+(x-3)(2)

Answer:

[tex](x-3)(4x)+)x-3)(2)[/tex]

Step-by-step explanation:

Multiply [tex](x-3)(4x+2)[/tex] using the distributive property.

Distributive property is a(b+c) is a times b + a times c

Distribute a inside the parenthesis

When we are given with two parenthesis , we distribute first parenthesis inside the second parenthesis

In the given expression, distribute (x-3) inside the second parenthesis

[tex](x-3)(4x+2)[/tex]

[tex](x-3)(4x)+)x-3)(2)[/tex]

The other constrain would be the number of hours it takes to make each one.

4 hours for a mountain bike would be 4x

5 hours for a road bike would be 5y

The hours need to be less than or equal to a total of 300 hours.

The missing constraint would be 4x + 5y ≤ 300.

Answer:

4x + 5y ≤ 300

Step-by-step explanation:

x: no of mt bike n y: no. of road bike

4 labor hrs for 1 mt bike n 5 labor hrs for 1 road bike

company has at most 300 labor hrs per day

so the contraint is 4x + 5y ≤ 300

Hello there

Since  there is 1 foot water in the tank the total volume = 3*2 * 1

= 6 cubic feet.  

volume of 6 cu. feet corresponds to 1 foot of water in height, this will help you find your answer

The Perez family's rectangular fish tank can hold 18 cubic feet of water by multiplying the length, width, and height (3ft x 2ft x 3ft).

To calculate the amount of water the Perez family's rectangular fish tank can hold, we use the formula for the volume of a rectangle, which is length * width * height.

Given:

The volume (V) is calculated as:

V = l * w * h

V = 3 feet * 2 feet * 3 feet

V = 18 cubic feet

Therefore, the rectangular fish tank can hold 18 cubic feet of water.

Here we are given first that Nuclear power provided 78% of the energy used in france in 2005.

Now this was written in decimal as 0.78.

Then we have to write it in fraction form.

So first we have here two digits after the decimal, so in denominator we will have 100,

[tex]\frac{78}{100}[/tex]

Now we have to convert this into simplest form.

For that we have to find HCF of 78 and 100.

The HCF of 78 and 100 is 2, so we will divide both numerator and denominator by 2,

[tex]\frac{78/2}{100/2}[/tex]

This gives us:

[tex]\frac{39}{50}[/tex]

Answer: The simplest form of 0.78 as as fraction is 39/50.

Answer:

The initial number of books he had=50

The number of books he has after adding new books=56

Step-by-step explanation:

Step 1: Derive formula for percentage increase

The formula for calculating the percentage increase is;

p={(f-i)/i}×100

where;

p=the percentage increase

f=the final number of books he had

i=the initial number of he had

In our case;

p=12%

(f-i)=defines the increase in the number of books=6

i=unknown

Substitute and solve for i;

12%=6/i

(12/100)=6/i

(12/100)×i=6

i=6×100/12

i=50

The initial number of books he had=50

The number of books he has after adding new books=50+6=56

For this case we have:

The area of the piece of fabric is given by [tex]A = a * b[/tex]

Where

[tex]a = \frac{1}{3}yards[/tex]

[tex]b = 3 \frac{5}{8}yards[/tex]

Substituting in the formula of the area we have:

[tex]A = \frac{1}{3}* 3 \frac{5}{8}\\[/tex]

[tex]A = \frac{1}{3}* (3 + \frac{5}{8})\\[/tex]

[tex]A = 1 + \frac{5}{24}[/tex]

[tex]A = 1\frac{5}{24}yards ^ 2\\[/tex]

Thus, the area of the piece of fabric is given by: [tex]A = 1\frac{5}{24}yards ^ 2\\[/tex]

Answer:

[tex]A = 1\frac{5}{24}yards ^ 2\\[/tex]

1/3 x 3 5/8 = (1/3 x 3) + (1/3 x 5/8)

= 3/3 + 5/24

= 29/24

The time period which has the greatest rate of change is from 0 to 5 minutes, because the steeper the line is, the greater the slope is. Hope this helps!

[tex]0-5\ min\\\\\dfrac{3\ km}{5\ min}=0.6\ \dfrac{km}{min}\\\\5-20\ min\\\\\dfrac{(4-3)\ km}{(20-5)\ min}=\dfrac{1\ km}{15\ min}\approx0.067\ \dfrac{km}{h}\\\\20-35\\\\\dfrac{(6-4)\ min}{(35-20)\ min}=\dfrac{2\ km}{15\ min}\approx0.133\ \dfrac{km}{min}\\\\0.067 < 0.133 < 0.6\\\\Therefore\ your\ answer\ is: A)\ 0\ to\ 5\ minutes[/tex]

Answer:

$3.08

Step-by-step explanation:

First you have to find how much each stamp costs. So u take 2.20 ÷ 5 = 0.44.

Next you take 0.44 x 7 and you should get $3.08

Answer: R' = [tex](3\frac{1}{3} ,1\frac{2}{3})[/tex], S' = [tex](3\frac{1}{3} ,-3\frac{1}{3})[/tex], T' = [tex](-1\frac{2}{3} ,-3\frac{1}{3})[/tex]

Step-by-step explanation:

R = (2, 1)  ⇒  R' = [tex](\frac{5}{3})2 , (\frac{5}{3})1 = (\frac{10}{3} , \frac{5}{3})[/tex]

S = (2, -2)  ⇒  S' = [tex](\frac{5}{3})2 , (\frac{5}{3})(-2) = (\frac{10}{3} , \frac{-10}{3})[/tex]

T = (-1, -2)  ⇒  T' = [tex](\frac{5}{3})(-1) , (\frac{5}{3})(-2) = (\frac{-5}{3} , \frac{-10}{3})[/tex]

Plot the coordinates.

Mrs. Dimas should have $10 left over, you will also be able to buy 8 basketballs.