what’s the area of a circle with the diameter of 3/4 (0.75)

Answer:

Option D. 108 g

Step-by-step explanation:

we know that

The density is equal to the mass divided by the volume

D=m/V

Solve for the mass m

m=D*V

we have

D=2.7 g/cm³

V=40 cm³

substitute

m=(2.7)(40)=108 g

Answer:

#5: 180 paperclips in total.

#6: 126 stamps in total.

#7: Elena should give Lucy 15 colored pencils.

Step-by-step explanation:

This explanation solves each question by setting a single unknown, [tex]x[/tex].

Let [tex]x[/tex] the initial number of paperclips of Antonio. That should also be the number of Abby's paperclips.

Initially:

Antonio gives [tex]30[/tex] paperclips to Abby. After that,

Abby now possess twice as many paperclips as Antonio does. In other words,

[tex]2(x - 30) = x + 30[/tex].

By the distributive property:

[tex]2x - 60 = x + 30[/tex].

Substract [tex]x - 60[/tex] from both sides

[tex]x = 30 - (-60) = 90[/tex].

Both Antonio and Abby initially possess 90 paperclips. That's 180 in total.

Similarly, let [tex]x[/tex] be the number of Emily's stamps. That should be the same as the number of Jasmine's stamps.

Initially:

After Emily gives [tex]42[/tex] stamps to Jasmine:

Jasmine now possesses twice as many stamps as Emily does. In other words,

[tex]2(x-42) = x+42[/tex].

[tex]x = 42 + 2\times 42 = 126[/tex].

Jasmine used to possess 126 stamps. Now she possesses [tex]126 + 42 = 168[/tex] stamps after receiving [tex]42[/tex] stamps from Emily.

Let the number of pencils that Elena needs to give to Lucy be [tex]x[/tex].

Initially:

After Elena gives [tex]x[/tex] pencils to Lucy:

Elena should now possess four more pencils than Lucy does. In other words,

[tex]\underbrace{60 - x}_{\text{Elena's}} = \underbrace{(26 + x)}_{\text{Lucy's}} +4[/tex].

[tex]2x = 30[/tex].

[tex]x = 15[/tex].

Answer:

Sprite: 5/8

Step-by-step explanation:

Let's assume the amount poured out was equal of both liquids:

Convert them into eighths:

Fruit juice: 4/8

Sprite: 4/8

Now to remove 1/4 total we need to remove 1 of each:

Fruit juice: 3/8

Sprite: 3/8

Now add those two we took off to the Sprite:

Fruit juice: 3/8

Sprite: 5/8

[tex]\frac{7}{8}[/tex] of the punch is now Sprite

For given question,

Abby pours out  [tex]\frac{1}{4}[/tex]  of the liquid, and then fills the bowl up again with Sprite.

This means, the fraction of Sprite in the bowl is,

[tex]1-\frac{1}{4} = \frac{3}{4}[/tex]             ................(i)

We know that the liquid has  [tex]\frac{1}{2}[/tex] fruit juice and [tex]\frac{1}{2}[/tex] Sprite.

This means, out of [tex]\frac{1}{4}[/tex] of poured liquid [tex]\frac{1}{2}[/tex] is Sprite.

So, the amount of Sprite in the liquid would be,

[tex]\frac{1}{4}\times \frac{1}{2}=\frac{1}{8}[/tex]                           ..................(ii)

Now we find the total fraction of Sprite in the punch.

From (i) and (ii),

[tex]\frac{3}{4}+\frac{1}{8}\\\\ =\frac{3\times 2}{4\times 2}+\frac{1}{8}\\\\ =\frac{6}{8}+\frac{1}{8}\\\\ =\frac{7}{8}[/tex]

Therefore, [tex]\frac{7}{8}[/tex] of the punch is now Sprite

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Answer: Option A.

Step-by-step explanation:

The surface area of a right rectangular prism can be calculated with this formula:

[tex]SA = 2(wl + lh + hw)[/tex]

Where "w" is the width. "l" is the lenght and "h" is the height.

We know that:

[tex]w=6in\\l=9in\\h=18in[/tex]

Knowing this values, we can substitute them into the formula.

Therefore we get that the surface area of a right rectangular prism is this:

[tex]SA = 2[(6in)(9in) + (9in)(18in) +(18in)(6in)][/tex]

[tex]SA=648in^2[/tex]

This matches with the option A.

Answer:

D

Step-by-step explanation:

Given

- 4(x - 6) + 3(a - 7)

distribute the first parenthesis by - 4 and the second by 3

= - 4x + 24 + 3a - 21

= - 4x + 3a + 3 → D

Answer:

Step-by-step explanation:

Twelve

You are correct, but I have a small comment.

As far as I can see, you have both 12 and 13 correct. The short way to do 12 is just to divide 72 into 360

360 / 72 = 5

The more general formula  is 360 / central angle = # of sides.

What the question means is that if your start with a polygon (it is a regular polygon by the way), and rotate it around its center, how many sides does it have in order that when you go through 72 degrees, the figure looks like it did when you started.

If the polygon is completely unmarked, then the idea is that it will look like you haven't done anything to the polygon even though you have rotated it 72 degrees.

The way you did 13 is exactly how it should be done.

Answer:

x<1.5

Step-by-step explanation:

The equation is

[tex]f(x)=-x^2+3x+8[/tex]

Use a graphing tool to find the vertex of the parabola.When you get the vertex from the graph, you can now write the increase as ; all x-values less than the x-value of the vertex value in the graph

From the graph, the vertex is at (1.5,10.25), the parabola opens down with maximum value y=10.25

The interval of increase is x<1.5

Answer:

[tex]x \geq \frac{3}{2}[/tex]

Step-by-step explanation:

First, the first derivative of the function is computed to distinguish which interval is increasing.

[tex]f'(x) = -2\cdot x + 3[/tex]

An interval is increasing only if slope is increasing as long as x increases. Then, it is quite evident that curve is increasing for:

[tex]x \geq \frac{3}{2}[/tex]

Answer:

<2 = 97

Step-by-step explanation:

Definition: Supplementary angles are 2 or more angles with the same vertex that add up to 180o

Solution

<1 = 83

<2 = ?

Total = 180o

<1 + <2 = 180                   Substitute for angle 1

83 + <2 = 180                  Subtract 83 from both sides.

83 - 83 + <2 = 180 - 83   Do the subtraction

<2 = 97 degrees

The supplement of an 83-degree angle is the angle that adds up to 180 degrees with it. By subtracting 83 from 180, we find that the supplement of the angle is 97 degrees.

The question is asking for the supplement of an angle that measures 83 degrees. In geometry, the supplement of an angle is the angle that, when added to the original angle, equals 180 degrees. To find the supplement of an 83-degree angle, you subtract 83 from 180.

Step-by-step solution:

Answer:

0.76

Step-by-step explanation:

The mean of the data including the outlier is:

Mean = (40.55 + 41.51 + 42.01 + 38.76 + 36.32 + 34.28 + 35.38 + 37.48 + 40.87 + 48.32 + 41.59 + 42.71)/12 = 39.98 seconds.

In this case, the outlier comes to be the data: 48.32. If we don't consider that data point, the mean equals:

Mean = (40.55 + 41.51 + 42.01 + 38.76 + 36.32 + 34.28 + 35.38 + 37.48 + 40.87  + 41.59 + 42.71)/11 = 39.22

The difference is:  39.98 - 39.22 = 0.76

Answer:

C . 0.76

Step-by-step explanation:

We are given that on the first of each month , Shelly runs a 5 k race. She keeps track of her times to track her progress. Her time in minutes is recorded in the table:

Jan  40.55 Feb 41.51

March 42.01 Apr 38.76

May 36.32  June 34.28

July 35.38  Aug 37.48

Sept 40.87 Oct 48.32

Nov 41.59 Dec 42.71

We have to find the difference between the mean of the data , including the outlier and excluding the outlier

Outlier: That observation which is different from other observations.

The outlier in the given observations is 48.32 because is different from other observations.

Mean of the data including the outlier

Mean =[tex]\frac{Sum \;of\;observations}{Total\;number\;of\;observations}[/tex]

Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+48.32+41.59+42.71}{12}[/tex]

Mean=[tex]\frac{479.78}{12}[/tex]

Mean=39.982

Mean of the data excluding the outlier

Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+41.59+42.71}{11}

Mean=[tex]\frac{431.46}{11}[/tex]

Mean=39.224

Difference between mean of the data including the outlier and excluding the outlier=39.982-39.224=0.758

Difference between mean of the data including the outlier and excluding the outlier=0.76

Answer Answer:

Step-by-step explanation:

We are given that on the first of each month , Shelly runs a 5 k race. She keeps track of her times to track her progress. Her time in minutes is recorded in the table:

Jan  40.55 Feb 41.51

March 42.01 Apr 38.76

May 36.32  June 34.28

July 35.38  Aug 37.48

Sept 40.87 Oct 48.32

Nov 41.59 Dec 42.71

We have to find the difference between the mean of the data , including the outlier and excluding the outlier

Outlier: That observation which is different from other observations.

The outlier in the given observations is 48.32 because is different from other observations.

Mean of the data including the outlier

Mean =[tex]\frac{Sum \;of\;observations}{Total\;number\;of\;observations}[/tex]

Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+48.32+41.59+42.71}{12}[/tex]

Mean=[tex]\frac{479.78}{12}[/tex]

Mean=39.982

Mean of the data excluding the outlier

Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+41.59+42.71}{11}

Mean=[tex]\frac{431.46}{11}[/tex]

Mean=39.224

Difference between mean of the data including the outlier and excluding the outlier=39.982-39.224=0.758

Difference between mean of the data including the outlier and excluding the outlier=0.76

Answer :C . 0.76

Answer: 15 represents where Jerry is after the elevation dropped 25 meters and then rose 40 meters.

Answer:

15 represents that Jerry hiked up 15 meters from his starting position.

Step-by-step explanation:

It is given that Jerry hiked downhill to a valley where the elevation dropped 25 meters below his starting position. Then, he hiked up to a hill that was 40 meters higher than the valley.

Hiked downhill = 25 meters

Hiked up = 40 meters

The given equation is

[tex]-25+40=15[/tex]

Here, hiked downhill represented by negative sign and hiked up represents by positive sign.

So, positive 15 represents that Jerry hiked up 15 meters from his starting position.

Answer:

Part 1) The vertex is the point (0.50,2.50)

part 2) [tex]y=-58[/tex]

Step-by-step explanation:

we have

[tex]y=-2x^{2} +2x+2[/tex]

Part 1) Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]y-2=-2x^{2} +2x[/tex]

Factor the leading coefficient

[tex]y-2=-2(x^{2} -x)[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]y-2-0.50=-2(x^{2} -x+0.25)[/tex]

[tex]y-2.50=-2(x^{2} -x+0.25)[/tex]

[tex]y-2.50=-2(x-0.50)^{2}[/tex]

[tex]y=-2(x-0.50)^{2}+2.50[/tex] -----> equation in vertex form

The vertex is the point (0.50,2.50)

Part 2) Find the value of y for x=6

substitute the value of x in the equation

[tex]y=-2(6)^{2} +2(6)+2[/tex]

[tex]y=-72 +12+2[/tex]

[tex]y=-58[/tex]

Answer:

(1, −3) (3, −5)

Slope = Y2 -Y1 / X2 - X1

Slope = -5 --3 / 3 -1

Slope = -2 / 2

Slope = -1

Step-by-step explanation:

Answer:

Vertical Distance = [tex]y_{2}-y_{1}[/tex]

Step-by-step explanation:

Here we are asked about the formula for vertical distance between two coordinates.

Suppose there are two coordinates

[tex](x_{1},y_{1})  ; (x_{2},y_{2})[/tex]

Vertical distance between two coordinates is the distance between the y coordinates of the two coordinates.

This can be find out with the formula

[tex]D_{y}=y_{2}-y_{1}[/tex]

For example:

Let two coordinates are (2,4) and (5,2)

Here the vertical distance can be find by using above formula as

[tex]D_{y}[/tex]=4-2

[tex]D_{y}[/tex]=2 units.

Answer:

The solution is -2/7 not –14.

Answer:

its D

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Since we are given self defining variables, h is obviously referring to the plant's height and y is referring to the plant's years or age.

Then, since a plant's height is 1.4 times its age, age multiplied by 1.4 should be the plants height.

The equation would come out to [tex]h=1.4y[/tex]

[tex]\bf \stackrel{\textit{difference of squares}}{(6+3i)(6-3i)}\implies (6)^2-(3i)^2\implies \stackrel{\textit{recall }i^2=-1}{36-(3^2 i^2)}\implies 36-(9\cdot -1) \\\\\\ 36+9\implies 45[/tex]

Step-by-step explanation:

6*6 - 6*3i + 6*3i -3i*3i

36-18i+18i-9i^2

36-9(-1)= 36+9= 45

Answer: The value of the y-intercept is [tex]-\frac{3}{5}[/tex]

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

In this case we know that the line passes through point [tex](0.4,-\frac{1}{2})[/tex] and has a slope of [tex]\frac{1}{4}[/tex]. Then we can substitute the following values into  [tex]y=mx+b[/tex]:

[tex]x=0.4\\\\y=-\frac{1}{2}\\\\m=\frac{1}{4}[/tex]

Then:

[tex]-\frac{1}{2}=\frac{1}{4}(0.4)+b[/tex]

And finally, we must solve for "b":

[tex]-\frac{1}{2}=\frac{1}{4}(0.4)+b\\\\-\frac{1}{2}-\frac{1}{10}=b\\\\b=-\frac{3}{5}[/tex]

For this case we have that by definition, the slope-intersection equation of a line is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

y: It is the cut point with the "y" axis

They tell us as data that:

[tex]m = \frac {1} {4}[/tex]

So, the equation is:

[tex]y = \frac {1} {4} x + b[/tex]

We substitute the given point to find "b":

[tex]- \frac {1} {2} = \frac {1} {4} (0.4) + b\\- \frac {1} {2} = \frac {0.4} {4} + b\\b = - \frac {1} {2} - \frac {0.4} {4}\\b = -0.5-0.1\\b = -0.6[/tex]

Thus, the cut point with the y axis is -0.6

Answer:

[tex]b = -0.6[/tex]

Answer:

the answer is 78

Step-by-step explanation:

subtracting 141 from both sides

[tex]y+141-141=219-141\\simplify\\y=78[/tex]

Answer:

The answer is 78.

Step-by-step explanation:

To find y or the answer, you must do the inverse operation when you want to the value of the unknown. So in this case, we must use subtraction. Also, in this process you must replace y with 219. After doing this, the equation will read [tex]219 - 141 = y.[/tex] Now isolate the equation.

Ex.

[tex]219 - 141 = 78.[/tex]

Therefore, the answer is 78.

P.S. That is the way how I can explain it to you. If you have any other requirements, please contact me (with my brainly account).

Answer: The answer is below, so the picture shows  you can find the measure of any of the three sides, simply by knowing the measure of at least one side in the triangle. The hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle.

* Which means this triangle is a 30° - 60° - 90°.

* Hopefully this helps:) Mark me the brainliest:)!!!!

This is a right triangle

ANSWER

[tex]- \frac{2}{3} [/tex]

EXPLANATION

The given given equation is

[tex]2y - 3x = 8[/tex]

We need to rewrite this equation in the slope-intercept form:

[tex]y = mx + b[/tex]

We add 3x to both sides.

[tex]2y - 3x + 3x=8 + 3x[/tex]

[tex] \implies \: 2y = 3x + 8[/tex]

We divide through by 2 to get,

[tex]y = \frac{3}{2}x + 4[/tex]

The slope of this line is

[tex]m = \frac{3}{2} [/tex]

Let the slope of the line perpendicular to this line be 'n' .

Then the product of the slopes of two perpendicular lines is always negative 1.

[tex]m \times n = - 1[/tex]

[tex] \implies \: \frac{3}{2} n = - 1[/tex]

[tex]\implies \: \frac{2}{3} \times \frac{3}{2}n = - 1 \times \frac{2}{3} [/tex]

[tex]n = - \frac{2}{3} [/tex]

Therefore the slope of the new line is

[tex] - \frac{2}{3} [/tex]

Answer:

C) -2/3

Step-by-step explanation:

2y-3x=8

2y=3x-8

Divide 2 from each number to get:

y=3/2-4

The opposite reciprocal of 3/2 is -2/3

Answer:

Her mistake was that she should have used –1 for moving below the lobby.

Step-by-step explanation:

Lets denote the lobby as Floor zero (0)

- if you go up, you add a positive value to this quantity.

- if you go down, you add a negative value to this quantity.

Lets assume that moving through each floor is equivalent to advancing one unit

* She first took an elevator one floor down

(-1)

Then she took the elevator back up 5 floors to her office

(+5)

Her movement is described by the expression

(-1) + (5)

Her mistake was that she should have used –1 for moving below the lobby.

Answer:

A

Step-by-step explanation:

Answer:

x < 48.8 ≈ 49

Step-by-step explanation:

11.22x − 200 < 347.96

add 200 to both sides

11.22x − 200 + 200 < 347.96 + 200

11.22x < 547.96

divide via by 11.22

x < 547.96/11.22

x < 48.8 ≈ 49

Answer: The value of x < 48.83.

Step-by-step explanation:

Since we have given that

[tex]11.22x-200<347.96[/tex]

We need to find the value of x:

First we add 200 on the both sides:

[tex]11.22x-200+200<347.96+200\\\\11.22x<547.96[/tex]

Now, we divide it by 11.22 on both the sides:

[tex]\dfrac{11.22x}{11.22}<\dfrac{547.96}{11.22}\\\\x<48.83[/tex]

Hence, the value of x < 48.83.

Answer:

[tex]x^{24}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex]

Hence

[tex](x^{3}) ^{8}[/tex] = [tex]x^{3(8)}[/tex] = [tex]x^{24}[/tex]

I cannot say that I am entirely sure of the answer so let me know if it doesn't make sense, but I will try to explain as best as I can nonetheless.

1. The graph of f''(x) represents the graph of the second derivative of f(x). Now, we know that the graph is continuous and decreasing. I think that the most important thing here is to mentally visualise the graph - if it is decreasing and has an x-intercept at x = -3, then we can say the following:

a) for all values of x before -3, f''(x) is positive

b) at x = -3, f''(x) is 0

c) for all values of x after x = -3, f''(x) is negative

2. What this means in terms of the graph f'(x) is the following:

a) for values of x less than -3, the gradient of the graph of f'(x) is positive and becoming less positive as x reaches 0

b) at x = -3, the gradient of the graph of f'(x) is 0

c) for values of x more than -3, the gradient of the graph of f'(x) is negative and becoming more negative as x reaches ∞

With this in mind, maybe try drawing a quick sketch to guide you (I would include one here but I have trouble adding attachments so I hope you'll forgive my lack of one) - it could perhaps look something similar to -(x + 3)^2 (but wouldn't be restricted to this - remember, it is just a visual aid).

3. Now, we need to work from the graph of f'(x) to the graph of f(x).

What we need to notice is that the graph of f'(x) takes the form of a concave down graph - this means that the gradient of the graph of f(x) immediately to either side of x = -3 changes from being either:

a) + >> ++ >> +++ >> ++ >> +

(Here, the number of + symbols signifies the strength of the positive gradient. >> represents an arrow.

So, the gradient starts off less positive, becomes more positives, reaches its peak, and then becomes gradually less positive again - imagine this being represented by f'(x) = -(x + 3)^2 + 5 (again, remember this is just a visual aid) )

b) --- >> -- >> - >> -- >> ---

(Likewise, the number of - symbols signifies the strength of the negative gradient.

So, the gradient starts off very negative, becomes less negative, reaches its peak, and then gradually becomes more negative again - you can see that this is effectively the same pattern as above: there is an increasing trend and then a decreasing trend. You can imagine this as being represented by the graph f'(x) = -(x + 3)^2 - 5)

c) -- >> - >> 0 >> - >> --

(Here, the gradient is negative, becomes less negative, reaches 0, then gradually becomes more negative - again, there is the same increasing trend followed by a decreasing trend. You can imagine this as being represented by the graph f'(x) = -(x + 3)^2)

It is this increasing trend in the gradient up to x = -3 followed by a decreasing trend that is crucial to take note of - this signifies that there is a point of inflection at x = -3. What we must remember here is that a point of inflection is characterised by a change in the curvature of the graph - either from concave up to concave down or from concave down to concave up. In our case, this would be a transition from concave up to concave down as the gradient gradually becomes more positive until it reaches its highest value at x = -3 and then gradually becomes less positive. Thus, we can say that answer B (the graph of f has an inflection point at x = -3) is correct.

Looking at the other answers:

A - The graph of f cannot be always concave down since there is a clear change in the gradient from less positive to more positive to less positive again (if it were always concave down the gradient would just gradually become more negative)

C - A relative minimum is characterised by the fact that the gradient to the left of the minimum is negative, the gradient at the minimum is 0, and the gradient to the right of the minimum is positive. Since this isn't the case for our graph, this is not the correct answer.

D - This is only a viable answer if none of the others are correct; since we have identified B as correct, this is incorrect.

I hope this helped but if you have any questions or problems with my working, please don't hesitate to comment below.

The correct statement about the function is,

⇒ The graph of f is always concave down.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Since, We have to given that;

The graph of f’’(x) is continuous and decreasing with an x-intercept at

x = - 3 .

We know that;

⇒ f(x) is a function then the solutions to the equation f′(x) = 0 gives the maximum and minimum values to f(x)

Hence, The value of  x  gives maximum if f′′(x) is negative and minimum if  f′′(x) is positive.

- Inflection points of the function  f(x) are found the solutions of the equation f′′(x) = 0

- The graph of f'(x) is continuous means that the graph is unbroken line

- The graph of f'(x) decreasing with an x-intercept at x = 2 means f'(2) = 0

- The differentiation of a function equal to zero at the critical point  (minimum or maximum) of the function

Since, f'(x) = 0 at x = 2

Hence, The x-coordinate of the critical point of f(x) is 2

Now,  If the differentiation of the function is decreasing, then the critical point of the function is maximum point.

Since,  f'(x) is decreasing

Hence, The critical point of the f(x) is maximum point

That means the slope of curve is negative

Hence,  The graph of f is concave down at x = 2

Thus, The correct answer is the graph of f is always concave down.

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Answer:

The answer is 4√7 - 8

Step-by-step explanation:

12/√7+2

Rationalize the denominator

=12/7+2 * √7-2/√7-2

=12√7-24/7-4

=12√7-24/3

By taking common from numerator we get

=12(√7-2)/3

=4√7-8

Answer:

The answer is 4√7 - 8

Step-by-step explanation:

Konichiwa~! (Hello~!) My name is Zalgo and I am here to help you today! In order to turn this into a ration, you need to look at the equation itself and think about how you could do it, which is quite simple. You could do 2:46 or 46:2.

I hope that this helps! :T

"Stay Brainly and stay proud!" - Zalgo

Check the picture below.  So the sector looks more  or less like that one.

we know a full circle has an arc of 2π, so how much is 7/8 of 2π?  well, is simply its product.

[tex]\bf ~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\pi \cdot \cfrac{7}{\underset{4}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{7\pi }{4}[/tex]

Certainly! Let's find the measure of the sector's arc given the ratio of the sector's area to the total area of the circle.
First, let's denote the area of the circle as A and the area of the sector as S.
We are given that the ratio S/A = 7/8. The total area of a circle is given by the formula A = πr^2 (where r is the radius of the circle), but since we are dealing with ratios, we don't need the specific values for π or r, as they will cancel out.
Now, the area of a sector of a circle is a fraction of the total area of the circle. This fraction is equal to the angle θ (in degrees) of the sector divided by the total angle in the circle (which is 360 degrees). So, the area of the sector S can be calculated by the formula:
\[ S = \frac{θ}{360} \times A \]
Now let's use the given ratio:
\[ \frac{S}{A} = \frac{7}{8} \]
\[ \frac{\frac{θ}{360} \times A}{A} = \frac{7}{8} \]
\[ \frac{θ}{360} = \frac{7}{8} \]
Next, we cross-multiply to solve for θ:
\[ 8θ = 7 \times 360 \]
\[ θ = \frac{7 \times 360}{8} \]
\[ θ = 7 \times 45 \]
\[ θ = 315 \]
So, the measure of the sector's arc is 315 degrees.