Which mathematicians first used the symbol pi Why?

Answer:

  No, the clay will not pour out easily. I know this because the angle of the truck bed is less than 50°, which is the minimum angle for easy pouring.

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Sin = Opposite/Hypotenuse

If α represents the angle of the truck bed, this means ...

  sin(α) = 9/15

We can find α using the inverse sine function:

  α = arcsin(9/15) ≈ 36.87°

We note this angle is less than 50° so we expect the clay will not pour out easily.

Using the tangent function of trigonometry, we find that the angle of the raised dump truck is approximately 30.96°. Since this is less than the necessary 50°, the clay will not pour out easily when the dump truck is raised to 9 feet.

In order to solve this problem, we need to use trigonometry, specifically the tangent function. We form a right triangle, using the truck's bed length (15 feet) as the hypotenuse, the height it's been lifted (9 feet) as the opposite, and we want to find the angle this makes with the ground.

We use the relationship in trigonometry: Tan(angle) = Opposite/Hypotenuse. Converting the values to this equation, Tan(angle) = 9/15. Solving this gives us the angle as the inverse tan of 9/15.

Using a calculator to find the Inverse tan (also known as arctan or tan^-1) of 9/15 gives us an angle, which is approximately 30.96°.

No, The clay will not pour out easily when the body of the dump truck is raised to 9 feet. I know this because the body angle of the dump truck (approximately 30.96°) is less than the necessary 50° for the clay to pour out easily.

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Answer:

  C)  65,535

Step-by-step explanation:

You can add up the 8 terms ...

  3, 12, 48, 192, 768, 3072, 12288, 49152

to find their sum is 65535.

_____

Estimating

Knowing the last term (49152) allows you to make the correct choice, since the sum will be more than that and less than double that.

_____

Using the formula

You know the formula for the sum of a geometric sequence is ...

  S = a1(r^n -1)/(r -1)

where a1 is the first term (3), r is the common ratio (4), and n is the number of terms (8).

Filling in the values, you find the sum is ...

  S = 3(4^8 -1)/(4-1) = 4^8 -1 = 65535

The sum of the geometric sequence 3, 12, 48, ... with 8 terms is 65,535. We use the geometric sum formula and identify a common ratio of 4 to compute the answer, which is option C.

To find the sum of a geometric sequence, we use the formula S = a * (1 - r^n) / (1 - r), where S is the sum of the sequence, a is the first term, r is the common ratio, and n is the number of terms. In this sequence, the first term a is 3, and we can find the common ratio r by dividing the second term by the first term: r = 12 / 3 = 4. With 8 terms in the sequence, we can calculate the sum.

S = 3 * (1 - 4^8) / (1 - 4) = 3 * (1 - 65536) / (1 - 4) = 3 * (-65535) / (-3) = 65535.

Therefore, the sum of the sequence is 65,535, which corresponds to option C.

The equation used to solve for x in the given diagram is 7x + 11x = 90, representing the total sum as 90 degrees.

In the diagram, you have an angle formed by two given lines. To find the value of x, you can use the fact that the total sum is 90 degrees.

1. The first angle of the diagram is labeled as 7x.

2. The second angle of the diagram is labeled as 11x.

So, the equation for the sum of these angles should equal 90 degrees:

7x + 11x = 90

Now, you can simplify the equation:

18x = 90

To isolate x, divide both sides by 18:

18x / 18 = 90/ 18

x = 5

So, the equation used to solve for x is indeed 7x + 11x = 90, which simplifies to 18x = 90 when considering the angles around the point.

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The given question pertains to different aspects of probability in Mathematics, such as combinations, proportions and matched pairs. Each concept is used to determine the likelihood of an event occurring and they all play integral roles in statistical analysis.

The details indicate that this question pertains to probability in Mathematics especially applied to situations like combinatorics, proportions and matched pairs. So let's explore each of those concepts with the details given:

In probability, the concept of combinations is important because it helps to determine the likelihood of a particular event occurring. For instance, P(choosing all five numbers correctly) relates to the probability of choosing numbers correctly in a given set. It's determined by P(choosing 1st number correctly) * P(choosing 2nd number correctly) * P(choosing 5th number correctly).

The term 'two proportions' perhaps refers to odds ratio or probability comparison between two events.

This is a statistical technique often used in studies where each individual or item has a unique match - for example, a study comparing the math scores of twins. Here, it seems like an insight into statistical analysis where outcomes are compared within matched pairs. Therefore, these different concepts are all part of probability and statistics.

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Check the picture below.

make sure your calculator is in Degree mode.

Answer:

x=56.7

Step-by-step explanation:

From the given triangle, the opposite side of angle x is 66 mm

79 mm is opposite to the right angle, so hypotenuse = 79 mm

we know the opposite side and the hypotenuse

To find the angle we use sin

[tex]sin(x)= \frac{opposite side}{hypotenuse}[/tex]

opposite side = 66

hypotenuse = 79

[tex]sin(x)= \frac{66}{79}[/tex]

[tex]x=sin^{-1}(\frac{66}{79})[/tex]

x=56.66199855

Round the answer to nearest tenth

x=56.7

Answer:

  (g◦f)(-6) = -9

Step-by-step explanation:

(g◦f)(-6) means g(f(-6))

Put the number where the variable is and evaluate.

  f(-6) = 3/2(-6) +5 = -9 +5 = -4

  g(f(-6)) = g(-4) = 7 -(-4)² = 7 -16 = -9

Then ...

  (g◦f)(-6) = -9

Let's say x is J because it's Lemon Juice.

It's said that the pH of J is less than 4 so: pH(J) < 4 and pH(J) is greater than 1.5 so: pH(J) > 1.5

Now we can construct:

[tex]1.5 < pH(J) \wedge pH(J) < 4[/tex]

Or simply:

[tex]1.5 < pH(J) < 4[/tex]

We can also write this with an interval:

[tex]pH(J)\in(1.5, 4)[/tex]

Hope this helps.

r3t40

Inequalities are used  to relate unequal expressions.

The compound inequality that represents the normal range of pH values of lemon juice: (b) 1.5 < x < 4

Let the pH of lemon juice be represented with x.

x less than 4 means: x < 4

x greater than 1.5 means x > 1.5

So, we have:

x < 4 and x > 1.5

Rewrite as:

x > 1.5 and x < 4

Express x > 1.5 as 1.5 < x

1.5 < x and x < 4

Combine the inequalities

1.5 < x < 4

Hence, the required compound inequality is: (b) 1.5 < x < 4

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Answer:

The coordinates of H′ are (-2,0).

Step-by-step explanation:

It is given that square EFGH stretches vertically by a factor of 2.5 with respect to the x-axis to create rectangle E′F′G′H′.

If a figure stretches vertically by a factor of 2.5 with respect to the x-axis, then the x-coordinates remains same and the points which lie on the axis are also remains the same after stretch.

It is given that the coordinates of H are (-2,0). This point lie on the x-axis, therefore it will remains the same after stretch.

Therefore the coordinates of H′ are (-2,0).

Answer:

  x = 3, x = -1/6 are the zeros

Step-by-step explanation:

I find graphing the equation using a graphing calculator to be about the fastest way to find the zeros.

__

For this equation, you can look for factors of 6·(-3) = -18 that have a sum of -17. Those are -18 and +1, so the factorization of the equation is ...

  y = (1/6)(6x -18)(6x +1) = (x -3)(6x +1)

The roots are the values of x that make the factors be zero, so x=3 and x=-1/6.

__

You can also use the quadratic formula to find the zeros. That tells you the solution to ...

  ax² +bx +c = 0

is

  x = (-b ±√(b²-4ac))/(2a)

Comparing your equation to the standard form, you can identify the coefficients as ...

  a = 6, b = -17, c = -3

so the zeros are ...

  x = (-(-17) ±√((-17)² -4(6)(-3)))/(2(6))

  x = (17 ±√369)/12 = (17 ±19)/12 = {-2, 36}/12 = {-1/6, 3}

The zeros are x = -1/6 and x = 3.

To find zeros of a quadratic equation, you use the quadratic formula. Applying this formula to the equation y = 6x^2 - 17x - 3 yields two solutions, representing the two points where the function intersects the x-axis.

The subject of this question concerns finding the zeros of a given quadratic equation, y = 6x^2 - 17x - 3. Zeros are the x-values that make the equation equal to zero or to point where the function intersects the x-axis.

To find the zeros, we'll use the quadratic formula, which is derived from an equation of the form ax² + bx + c = 0: x = [ -b ± sqrt(b^2 - 4ac) ] / (2a).

Applying the quadratic formula to your equation, with a = 6, b = -17, and c = -3, we get the two solutions, which are the zeros of the equation: x = [ 17 ± sqrt((-17)^2 - 4*6*-3) ] / (2*6). Computing this, we get two solutions, or two zeros, which are the points where your function y = 6x^2 - 17x -3 crosses the x-axis.

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Answer: [tex](gof)(-7) =495[/tex]

Step-by-step explanation:

Given the functions f(x) and g(x), to find [tex](gof)(x)[/tex] you need to substitute [tex]x=f(x)=x^2 + 6[/tex] into the function g(x):

[tex](gof)(x) = ( x^2 + 6)+ 8( x^2 + 6)\\\\(gof)(x)=x^2 + 6+ 8x^2 + 48\\\\(gof)(x)=9x^2 + 54[/tex]

Now, to find  [tex](gof)(-7)[/tex] you must substitute [tex]x=-7[/tex] into [tex](gof)(x)[/tex], then you get:

[tex](gof)(-7) = 9(-7)^2 + 54\\\\(gof)(-7) =9(49)+54\\\\(gof)(-7) =441+54\\\\(gof)(-7) =495[/tex]

Answer:

240 i think

Step-by-step explanation:

Answer:

[tex]m\widehat {DBC}=240^{\circ}[/tex]

Step-by-step explanation:

We have been given image of a circle. We are asked to find measure of arc DBC.

[tex]m\widehat {DBC}=\widehat {DB}+\widehat {BA}+\widehat {AC}[/tex]

We know that central angle is equal to measure of corresponding arc, so measure of arc DB will be equal to measure of angle DPB.

Since angle APC and angle DPB are vertical angles, so measure of angle DPB will be equal to measure of angle APC that is 60 degrees.

[tex]m\widehat {DBC}=60^{\circ}+120^{\circ}+60^{\circ}[/tex]

[tex]m\widehat {DBC}=120^{\circ}+120^{\circ}[/tex]

[tex]m\widehat {DBC}=240^{\circ}[/tex]

Therefore, the measure of arc DBC is 240 degrees.

Answer:

googles explanation is below

Step-by-step explanation:

Rule 3: Subtracting a negative number from a negative number – a minus sign followed by a negative sign, turns the two signs into a plus sign. So, instead of subtracting a negative, you are adding a positive. Basically, - (-4) becomes +4, and then you add the numbers. For example, say we have the problem -2 - –4.

Step-by-step explanation & answer:

Let

x = "one number", then

4x+2 = "the other number"

If the sum is decreased by two, that gives

sum decreased by two = (x+4x+2) - 2 = 5x

The sum decreased by two = 25 (given)

therefore

5x = 25

x = 5

So

"one number" = 5

"another number" = 4x+2 = 4*5+2 = 22

X=33/17

Here is how it works

By the way what you are working with is called improper factions, which is when the big number is placed over the smaller number.

Now 33/17 is also 1 16/17

35/17 is also 2 1/17

Now we can the proper fractions which are 1 16/17 and 2 1/17

1+2=3 and 16/17 + 1/17 equals 1

3+1=4

I enjoyed solving your problem. please vote my answer brainliest..thanks

Answer:

b. 2002

Step-by-step explanation:

divide the geometry kids by total kids to take calculus.

The experimental probability of a freshman studying geometry taking a calculus class before graduation was greatest in 2002.Option B is correct.

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts.

The The experimental probability of a freshman studying geometry taking a calculus class before graduation is obtained by dividing the  number of students taking calculus to the number of students of student taking statics.

Referred to the excel table in the attachment for the probability.

The experimental probability of a freshman studying geometry taking a calculus class before graduation in 2002 is found at;

[tex]\rm P_{2002}(\%) = \frac{512}{822} \times 100 \\\\ P_{2002}(\%) =62.29[/tex]

The experimental probability of a freshman studying geometry taking a calculus class before graduation was greatest in 2002.Option B is correct.

Hence,Option B is correct.

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Answer:

13/27

Step-by-step explanation:

1/3 ÷ 9/13

Copy dot flip

1/3 * 13/9

13/27

The geometric series out of the considered option having the common ratio as 2 is given by: Option C. 14, 28, 56, 112, ...

There are three parameters which differentiate between which geometric sequence we're talking about.

The first parameter is the initial value of the sequence.

The second parameter is the quantity by which we multiply previous term to get the next term.

The third parameter is the length of the sequence. It can be finite or infinite.

Suppose the initial term of a geometric sequence is 'a'

and the term by which we multiply the previous term to get the next term is 'r' (also called the common ratio)

Then the sequence would look like

[tex]a, \: ar, \: ar^2, \: ar^3, \: \cdots[/tex]

(till the terms to which it is defined)

If the initial term is 'a', then the geometric sequence with common ratio = 2 would look like:

[tex]a, \: a(2), \: a(2)^2, \: a(2)^3, \: \cdots\\\\a, \: a(2), \: a(4), \: a(8), \: \cdots[/tex]

Checking all the options to see which one has got common ratio 2:

Initial term a = 14,

The geometric sequence with a = 14, and r = 2 would be:

[tex]14, 14(2), 14(4), 56(8), \cdots\\\\14, 28, 56, 112, \cdots\\[/tex]

The sequence  14, 16, 18, 20, ... doesn't match with it, so its not correct option.

Initial term a = 64,

The geometric sequence with a = 14, and r = 2 would be:

[tex]64, 64(2), 64(4), 64(8), \cdots\\\\64, 128, 256, 512, \cdots\\[/tex]

The sequence 64, 32, 16, 8, ... doesn't match with it, so its not correct option.

Initial term a = 64,

The geometric sequence with a = 14, and r = 2 would be:

[tex]14, 14(2), 14(4), 56(8), \cdots\\\\14, 28, 56, 112, \cdots\\[/tex]

The sequence  14, 28, 56, 112, ... matches with it, so its correct option.

Initial term a = 87,

The geometric sequence with a = 87, and r = 2 would be:

[tex]87, 87(2), 87(4), 87(8), \cdots\\\\87, 174, 348, 696, \cdots\\[/tex]

The sequence 87, 85, 83, 81, ... doesn't match with it, so its not correct option.

Thus, the geometric series out of the considered option having the common ratio as 2 is given by: Option C. 14, 28, 56, 112, ...

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Answer:

A. 3(t+2)

Step-by-step explanation:

We can easily solve your question by using any computational tool or calculator

Please see attached images for a full analysis of your problem

The result is

A. 3(t+2)

[tex]\bf \cfrac{~~\frac{4t^2-16}{8}~~}{\frac{t-2}{6}}\implies \cfrac{4(t^2-4)}{8}\cdot\cfrac{6}{t-2}\implies \cfrac{4\stackrel{\stackrel{difference}{of~squares}}{(t^2-2^2)}}{\underset{4}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot\cfrac{\stackrel{3}{\begin{matrix} 6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}~~}{t-2}[/tex]

[tex]\bf \cfrac{\begin{matrix} 4 (t-2) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(t+2)}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{3}{~~\begin{matrix} t-2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 3(t+2)[/tex]

Answer:

  $37 3/8

Step-by-step explanation:

Add the rise to the opening price to find the closing price.

  33 1/8 + 4 1/4 = (33 +4) + (1/8 +2/8) = 37 3/8 . . . . . . dollars per share

Final answer:

The closing price of Nagasaki Corporation's stock, after adding the increase of [tex]\$4 \frac{1}{4}[/tex]to the opening price of [tex]\$33\frac{1}{8}[/tex], was  [tex]\$37\frac{3}{8}[/tex] per share.

Explanation:

The student asked: On the morning of June 4, the stock of Nagasaki Corporation opened at a price of  [tex]$33\frac{1}{8}[/tex]per share. At the end of the day, the price had risen [tex]$4 \frac{1}{4}[/tex] per share. What was the price at the end of the day?

To find the closing price of the stock, we need to add the increase to the opening price:

Convert the mixed numbers to improper fractions: [tex]\$33\frac{1}{8} = \frac{265}{8} \ and\ \$4\frac{1}{4} = \frac{17}{4}[/tex]

Find a common denominator to add the fractions: Since 8 and 4 are both multiples of 4, we will convert [tex]\frac{17}{4} to \frac{34}{8}.[/tex]

Add the fractions [tex]: \frac{265}{8} + \frac{34}{8} = \frac{299}{8}[/tex]

Convert the improper fraction back to a mixed number: [tex]\frac{299}{8} = $37\frac{3}{8}[/tex]

Therefore, the closing price of the stock was  [tex]$37\frac{3}{8}[/tex]per share.

Answer: n = g/5

Step-by-step explanation:

Answer:

Both 3:1

Step-by-step explanation:

30:10 Divide by 10

3:1

45:15 Divided by 15

3 : 1

Answer:

the same

Step-by-step explanation:

A

The first equation has slope 6 and y intercept -4.  I'd plot y intercept (0,-4) and (1,2), and connect the dots and extend for the first line.

The second equation has slope 5 and y intercept -3.  I'd plot y intercept (0,-3) and (1,2), and connect the dots and extend for the second line.

We stumbled on the solution, both lines contain (1,2)

B

I don't like the graphing.  This is algebra, not connect the dots.

We have two equations for y, we equate them to find the x where they meet.

6x - 4 = 5x - 3

6x - 5x = -3 + 4

x = 1

y = 6(1) - 4 = 2

Check:  y = 5(1) - 3 = 2, good

Answer: (1, 2)

The given geometric sequence is 4, 16, 64, 256.

Given: Geometric Sequences

Among the given sequences, geometric sequence will be identified if the ration between two adjacent numbers is constant for the given sequence.

Option (A): 5, 12, 17, 29, 46

Common ratio (r) is:

r = 12/5 = 2.4

r = 17/12 = 1.4

r = 29/17 = 1.7

r = 46/29 = 1.6

Here, common ratio is not constant.

Hence, option (A) is incorrect.

Option (B): 3, 7, 11, 15, 19

Common ratio (r) is:

r = 7/3 = 2.3

r = 11/7 = 1.5

r = 15/11 = 1.3

r = 19/15 = 1.3

Here, common ratio is not constant.

Hence, option (B) is incorrect.

Option (C): 4, 6, 10, 16, 26

Common ratio (r) is:

r = 6/4 = 1.5

r = 10/6 = 1.66

r = 16/10 = 1.6

r = 26/16 = 1.62

Here, common ratio is not constant.

Hence, option (C) is incorrect.

Option (D): 4, 16, 64, 256

Common ratio (r) is:

r = 16/4 = 4

r = 64/16 = 4

r = 256/64 = 4

Here, common ratio is constant.

Hence, option (D) is correct.

Therefore, the geometric sequence is 4, 16, 64, 256.

Correct option is (D).

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Every letter is either red or blue. So the probability is 0.

[tex]|\Omega|=7\\|A|=0\\\\P(A)=\dfrac{0}{7}=0[/tex]

Answer:

10"

Step-by-step explanation:

The volume for a cube is V = l × w × h

But since this is a cube, all the sides aree the same length, so we could rewrite this in terms of x as:

V = [tex]x^3[/tex]

If we know the volume to be 1000, we sub it in for V:

[tex]1000=x^3[/tex]

We "undo" a cube by taking the cubed root of both sides.  The cubd root of x cubed is just x, and the cubed root of 1000 is 10.  Therefore, x = 10

Answer:

The correct answer option is B. [tex] S _ n = a _ 1 [ \frac { 1 - r ^ n } { 1 - r } ] [/tex].

Step-by-step explanation:

The following is the formula that is used to find the sum of a geometric progession:

[tex] S _ n = a _ 1 [ \frac { 1 - r ^ n } { 1 - r } ] [/tex]

where [tex]S_n[/tex] is the sum, [tex]a_1[/tex] is the first term, [tex]r[/tex] is the common ratio while [tex]n[/tex] is the number of terms.

The formula which can be used to find the sum of the first n terms of a geometric sequence is:

          [tex]S_n=a_1(\dfrac{1-r^n}{1-r})[/tex]

Geometric sequence--

A sequence is said to be a geometric sequence if each of the term of a sequence is a constant multiple of the preceding term of the sequence.

This constant multiple is known as a common ratio and is denoted by r.

Also, if the first term of the sequence is: [tex]a_1[/tex]

Then the sequence is given by:

[tex]a_1,\ a_2=a_1r,\ a_3=a_1r^2,\ a_4=a_1r^3,\ .............a_n=a_1r^{n-1},\ .....[/tex]

The sum of the first n terms of the sequence is given by:

[tex]S_n=a_1(\dfrac{1-r^n}{1-r})[/tex]

Answer:

sin(x°) = 11/s

Step-by-step explanation:

The tangent is the ratio of sine to cosine, so ...

tan(x°) = sin(x°)/cos(x°)

Multiplying by cos(x°) gives ...

sin(x°) = cos(x°)·tan(x°) = (r/s)·(11/r)

sin(x°) = 11/s

Answer:

sin x° = 11 divided by s

Step-by-step explanation:

Given,

tan x° = 11 divided by r

[tex]\implies tan x^{\circ}=\frac{11}{r}[/tex]

Also, cos x° = r divided by s

[tex]\implies cos x^{\circ}=\frac{r}{s}[/tex]

We know that,

[tex]\frac{sinx^{\circ}}{cos x^{\circ}}=tan x^{\circ}[/tex]

[tex]\implies sinx^{\circ}= tan x^{\circ}\times cos x^{\circ}[/tex]  ( by cross multiplication )

By substituting the values,

[tex]sin x^{\circ}=\frac{11}{r}\times \frac{r}{s}=\frac{11r}{rs}=\frac{11}{s}[/tex]

⇒ sin x° = 11 divided by s

Answer:

C. [tex]52\sqrt{3}\ ft^2[/tex]

Step-by-step explanation:

Use formula for the area of trapezoid

[tex]A=\dfrac{a+b}{2}\cdot h,[/tex]

where a is the smaller base, b is the larger base and h is the height.

From the diagram,

[tex]a=11\ ft\\ \\b=15\ ft\\ \\h=4\sqrt{3}\ ft[/tex]

So, the area of trapezoid is

[tex]A=\dfrac{11+15}{2}\cdot 4\sqrt{3}=13\cdot 4\sqrt{3}=52\sqrt{3}\ ft^2[/tex]

Answer:

  A. 17 1/2 . . . cubic feet

Step-by-step explanation:

The volume is the product of the length, width, and height. If your calculator doesn't deal with mixed numbers, it can be convenient to use one that does.

  (4 ft)(2 1/2 ft)(1 3/4 ft) = 17 1/2 ft³

The volume of the box is 17 1/2 cubic feet.

____

You can also convert the numbers to decimal to use on your calculator:

  4 × 2.5 × 1.75 = 17.500

Or convert them to improper fractions:

  4 × 5/2 × 7/4 = 35/2 = 17 1/2

Final answer:

The volume of the box is 17 1/2 cubic feet, making the correct answer A. 17 1/2.

Explanation:

To find the volume of the box, we need to multiply its length, width, and height together.

The formula for volume is Volume = length × width × height.

Given that the box has a length of 4 feet, a width of 2 1/2 feet, and a height of 1 3/4 feet, we first need to convert these measurements into improper fractions or decimals to make the multiplication easier.

Width: 2 1/2 feet = 5/2 feet
Height: 1 3/4 feet = 7/4 feet

Volume = 4 feet × (5/2 feet) × (7/4 feet) = 20/2 × 7/4 = 10 × 7/4 = 70/4 = 17 1/2 cubic feet.

Therefore, the correct answer is A. 17 1/2 cubic feet.

[tex]AB=\sqrt{(10-1)^2+(3-7)^2}=\sqrt{81+16}=\sqrt{97}\approx9.85[/tex]