What is the average rate of change of f(x), represented by the table of values, over the interval [-2, 3]?
x f(x)
-6 2.5
-
22.5
02
20
A. 5
B. 25
c. 1
D.
0.5

let's firstly convert the mixed fraction to improper fraction.

[tex]\bf \stackrel{mixed}{10\frac{2}{3}}\implies \cfrac{10\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{32}{3}} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{-\frac{32}{3}})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-\left( -\frac{32}{3} \right)}{-3-4}\implies \cfrac{1+\frac{32}{3}}{-7}\implies \cfrac{\frac{3+32}{3}}{-7}[/tex]

[tex]\bf \cfrac{~~\frac{35}{3}~~}{\frac{-7}{1}} \implies \cfrac{\stackrel{5}{~~\begin{matrix} 35 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}~~}{3}\cdot \cfrac{1}{~~\begin{matrix} -7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies -\cfrac{5}{3}[/tex]

Answer: No

Step-by-step explanation: 5/3 is greater than 1 because 1 is the same as 3/3 and 5/3 is greater than 3/3 making 5/3 greater than 1.

Step-by-step explanation:

1.4+8.59= 9.99

12 X 9.99 = 119.88

Answer:396

Step-by-step explanation:Arc length = radius * angle in radians

you know radius = Diameter/2 = D/2

80 deg = (80pi/180) rad

then,

88 pi = (D/2) * (80 pi /180)

sloving for D

D = 396

The diameter of the circle which measures is 80° and length arc is 88π is 396

length of arc = ∅ / 360 × 2πr

where

r = radius

∅ = centre angle = 80°

length of arc = 80 / 360 ×2πr

length of arc = 88π

Therefore,

88π = 16 / 36 πr

cross multiply

88π × 36 = 16πr

3168π = 16πr

divide both sides by 16π

198 = r

Recall

diameter = 2(radius)

Therefore,

diameter of the circle = 2 × 198

diameter of the circle = 396

learn more on length of arc here: https://brainly.com/question/15373642

Answer:

There are 12 bills of 10$ and 11 bills of 20$

Step-by-step explanation:

Let

x ------> number of 10$ bills

y -----> number of 20$ bills

we know that

x+y=23 -----> x=23-y -----> equation A

10x+20y=340 ----> equation B

substitute equation A in equation B and solve for y

10(23-y)+20y=340

230-10y+20y=340

10y=340-230

y=110/10=11

Find the value of x

x=23-y ----> x=23-11=12

therefore

There are 12 bills of 10$ and 11 bills of 20$

Answer:

The expressions in ascending order would be:

[tex]\frac{3x^2+1}{2(x-1)} < \frac{x^2-1}{1-2x} < \frac{x^2}{1-2x} < \frac{2x^2+x}{2}[/tex]

At x = -2

Explanation:

First, we will evaluate the given expressions at x = -2

1- The first expression:

[tex]\frac{x^2}{1-2x}=\frac{(-2)^2}{1-2(-2)}=\frac{4}{5}[/tex]

2- The second expression:

[tex]\frac{x^2-1}{1-2x}=\frac{(-2)^2-1}{1-2(-2)}=\frac{3}{5}[/tex]

3- The third expression:

[tex]\frac{2x^2+x}{2}=\frac{2(-2)^2+(-2)}{2}=3[/tex]

4- The fourth expression:

[tex]\frac{3x^2+1}{2(x-1)}=\frac{3(-2)^2+1}{2(-2-1)}=-\frac{13}{6}[/tex]

Then, we will arrange the values in an ascending order:

[tex]-\frac{13}{6} < \frac{3}{5} < \frac{4}{5} < 3[/tex]

Finally, we arrange the expressions based on the value arrangement:

[tex]\frac{3x^2+1}{2(x-1)} < \frac{x^2-1}{1-2x} < \frac{x^2}{1-2x} < \frac{2x^2+x}{2}[/tex]

Hope this helps :)

Answer:

x<3

Step-by-step explanation:

The circle is open and the arrow is going left so its going to be less then. The circle is on 3 so the answer is c. x<3.

Answer:

I would say the length is 8 and the width is 2

Step-by-step explanation:

Note that : ( Length = L ,  Width = W  ,  Area = A)

A = L x W - the area is 16 as given in the question, therefore:  

16 = L x W <- this is your 1st equation  

L = 4W - Length is 4 times the width, this is your second equation  

Take your second equation and substitute it into the first one:  

16 = 4W x W -> simplify this:  

16 = 4W^2  

Divide both sides of the equation by 4 to isolate the W^2  

16 ÷ 4 = (4w^2) ÷ 4 -> this will equal to:  

4 = w^2  

Now you want to get rid of '^2', you want to isolate w. To do this you need to find the square root of both sides of the equation  

√ 4 = √ w^2 -> this will equal to:  

2 = w  

Now that you have the value of w just sub it into the first equation  

16 = L x W  

16 = L x 2  

16 ÷ 2 = L  

8 = L  

therefore the length is 8 and the width is 2  

Answer:

20.49 feet to the nearest hundredth.

Step-by-step explanation:

Using the Pythagoras Theorem:

38^2 = h^2 + 32^2

h^2 = 38^2 - 32^2

h^2 = 420

h = √420

h = 20.494 m.

Your question asks to find the height of the building.

To find the answer to your question, we would need to use the Pythagorean theorem.

Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]

What we would do is plug in the numbers that we already know into the equation, and then we simply solve.

We would plug 32 to a and plug 38 into c

Your equation should look like this:

[tex]32^2+b^2=38^2[/tex]

Now, we solve:

[tex]32^2+b^2=38^2\\\\1024+b^2=38^2\\\\1024+b^2=1444\\\\b^2=420\\\\\sqrt{b} =\sqrt{420} \\\\b=20.493[/tex]

We would jkust round to the nearest hundredths place, therefore giving you the answer of 20.49.

This means that the height of the building would be 20.49 meters

20.49 meters would be your FINAL answer.

Answer:

D no mode

Step-by-step explanation:

You need to have a number seen at least twice to have a mode.

Answer:

There is no mode

Step-by-step explanation:

Mode is when numbers are repeated, and there are no numbers repeated

Answer:

9/50

Step-by-step explanation:

18/100

Divide the top and bottom by 2

9/50

This is in simplest form

Answer:

The correct answer option is D. 60.

Step-by-step explanation:

We are given the diagram of two prisms with known side lengths other than x. Given that these prisms are similar, we are to find the value of x.

Considering the similarity of these prisms, we will use the ratio method to find x.

[tex] \frac { 3 } { 2 0 } = \frac { 9 } { x } [/tex]

[tex] x = \frac { 6 \times 2 0 } { 3 } [/tex]

x = 60

Answer: OPTION D

Step-by-step explanation:

Given the similar prisms shown in the image, the first step is to set up the following proportion, where "x"  is the missing lenght:

[tex]\frac{9}{3}=\frac{x}{20}[/tex]

And finally you need to solve for the lenght "x" to find its value.

To solve for "x" you can multiply both sides of the equation by 20.

Then, the result is:

[tex](20)(\frac{9}{3})=(\frac{x}{20})(20)\\\\\frac{9*20}{3}=x\\\\\frac{180}{3}=x\\\\x=60[/tex]

Answer: c. x=-1 and x=7

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

-4 + -3 = -7

-7 + 6 = -1

-7 + 6 = -1 because when you are adding a positive and negative number you subtract and then add the sign of the bigger number.

4-9=5

-2--8=6

y=mx+b

slope/mx=6/1

base/y intercept=5

Answer: The equation for the line in  point-slope form :[tex] (y+2)=\dfrac{-6}{5}(x-4)[/tex]

The equation in slope-intercept form : [tex]y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]

Step-by-step explanation:

The equation of a line in point slope form passing through points (a,b) and (c,d) is given by :-

[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]

Now, the point slope form passing through points (4, -2) and (9, -8) is given by :-

[tex](y-(-2))=\dfrac{-8-(-2)}{9-4}(x-4)\\\\\Rightarrow (y+2)=\dfrac{-6}{5}(x-4)[/tex]

The equation for the line in  point-slope form :[tex] (y+2)=\dfrac{-6}{5}(x-4)[/tex]

Further if we simplify the equation , we get

[tex] y+2=\dfrac{-6}{5}x+\dfrac{24}{5}\\\\\Rightarrow\ y=\dfrac{-6}{5}x+\dfrac{24}{5}-2\\\\\Rightarrow\ y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]

The equation in slope-intercept form : [tex]y=\dfrac{-6}{5}x+\dfrac{14}{5}[/tex]

Answer:

D) About one-fourth of the cable-television customers are not satisfied.

Step-by-step explanation:

First you find out how many cable-television customers are not satisfied, which is 285. The you find out the total number of cable-television users in the sample, which is 1,109. Then you divide the number of unsatisfied by the total, 285/1109, to get .2569 or 25%

Answer:D) About one-fourth of the cable-television customers are not satisfied.

Step-by-step explanation:

Answer:

A. rolling a two and landing on tails

Answer:60%

Step-by-step explanation:

Final answer:

Lucinda will mark up the price of her flower arrangements by 60% to make a $6.00 profit on each one, which costs her $10.00 to prepare. The correct answer is option a.

Explanation:

Lucinda wishes to make a profit of $6.00 on each flower arrangement she sells, on top of the $10.00 it costs her to prepare one. To calculate the percentage markup, we use the formula: Markup Percentage = (Profit / Cost) × 100%. In Lucinda's case, the profit is $6.00 and the cost is $10.00.

So, the calculation will look like this:

Markup Percentage = ($6.00 / $10.00) × 100% = 0.6 × 100% = 60%.

Therefore, Lucinda will mark up the price by 60% to achieve her desired profit. The correct answer to the question is option a.

Answer:

C) 35 Degrees

Step-by-step explanation:

To find the degree of an exterior angle, subtract the larger arc, DE, degree by the smaller arc, BC, and then divide by 2! Which is 35. 118-48/ 2 = 35.

Answer:

18 square units.

Step-by-step explanation:

graph the square or find the difference then multiply the base by the hight.

The solution to the inequality is [tex]\( \{ x \,|\, x < \frac{15}{2} \} \),[/tex] indicating all real numbers less than [tex]\( \frac{15}{2} \).[/tex]

To solve the inequality [tex]\(2x - 8 < 7\)[/tex], we'll isolate  x by adding 8 to both sides and then dividing both sides by 2.

Here's the step-by-step calculation:

Starting inequality:

[tex]\[ 2x - 8 < 7 \][/tex]

Add 8 to both sides:

[tex]\[ 2x - 8 + 8 < 7 + 8 \][/tex]

[tex]\[ 2x < 15 \][/tex]

Divide both sides by 2:

[tex]\[ \frac{2x}{2} < \frac{15}{2} \][/tex]

[tex]\[ x < \frac{15}{2} \][/tex]

So, the solution to the inequality is [tex]\(x < \frac{15}{2}\).[/tex]

Now, let's express the solution set in set-builder notation. The solution set for x consists of all real numbers less than [tex]\( \frac{15}{2} \)[/tex]. This can be written as:

[tex]\[ \{ x \,|\, x < \frac{15}{2} \} \][/tex]

So, the correct option is:

[tex]\[ \boxed{\{ x \,|\, x < \frac{15}{2} \}} \][/tex]

Answer:

C) B= -1 C= -2

Step-by-step explanation:

Answer:  2460 calories

Step-by-step explanation:

2129 + 2348 + 1863 = 6340

2200 x 4 = 8800

8800 - 6340 = 2460

Final answer:

Samuel must consume 2460 calories on Thursday to achieve his target average daily calorie intake of 2200 over the four days.

Explanation:

To find out how many calories Samuel must consume on Thursday to have an average daily intake of 2200 calories, we first calculate the total number of calories he should have consumed over four days. This is done by multiplying the desired daily average (2200 calories) by the number of days (4), which equals 8800 calories.

Next, we add the calories Samuel consumed from Monday to Wednesday, which amounts to 2129 (Monday) + 2348 (Tuesday) + 1863 (Wednesday) = 6340 calories.

To find the calories for Thursday, we subtract the total consumed so far (6340 calories) from the desired four-day total (8800 calories). This gives us 8800 - 6340 = 2460 calories.

Therefore, Samuel must consume 2460 calories on Thursday to achieve an average of 2200 calories per day over the four days.

Answer:

Df=[-7,∞)

Step-by-step explanation:

Answer:

x∈R {x ≥ -7}

Step-by-step explanation:

The domain of the function can only include real numbers. This means whatever happens under the square root sign (i.e. the radicand) cannot be less than 0 (since you can't take the square root of a negative number).

To find the domain, set the radicand ≥ 0:

7 + x ≥ 0

x ≥ -7

Answer:

-30.

Step-by-step explanation:

Slope = rise / run

= (57-27) / (1 - 2)

= -30.

The slope of the line passing through points (1,57) and (2,27) is; 30.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

It can be calculated as;

Slope = rise/run

Given that the line passes through points (1,57) and (2,27), we need to find the slope of the line.

Slope = rise/run

Slope = (57-27) / (1 - 2)

Slope = -30.

Therefore, the slope of the line passing through points (1,57) and (2,27) is; 30.

Learn more about slope here:

https://brainly.com/question/2503591

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You must remember that a polynomial is written like so...

ax^2 + bx + c

In this case...

a = 1

b = -18

c = 81

To factor you must find two numbers who both add up to b (-18) AND multiply to c (81)

-9 + -9 = -18

-9 * -9 = 81

so...

D. (x - 9)(x - 9)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:B (x+9)(x+9)

Step-by-step explanation: just did it and (x-9)(x-9) is the WRONg answer. the correct answer is B (x+9)(x+9)

1. This question refers to conditional probability and is asking us to find the probability of Q occurring, given that R occurs. What this means is that we must divide the probability of Q and R occurring by the probability of R occurring (this is because we have the condition that R occurs). This may be written as such:

Pr(Q|R) = Pr(Q ∩ R) / Pr(R)

2. Now, the first step is to find Pr(Q ∩ R). This is given by the value in the centre of the Venn Diagram (ie. in the cross-over between the two circles) divided by the total of all the values:

Pr(Q ∩ R) = 3/(8 + 3 + 4 + 22)

= 3/37

3. The next step is to find Pr(R). This is given by the value in the circle denoted R (including the cross-over with Q) divided by the total of all the values.

Pr(R) = (4 + 3)/(8 + 3 + 4 + 22)

= 7/37

4. Thus, we can now subtitute the probabilities we defined in 2. and 3. into the formula for conditional probability we defined in 1.:

Pr(Q|R) = (3/37) / (7/37)

= 3/7

Thus, the answer is B.

Note that technically there is no need to write out the full probabilities before coming to this answer. The same exact answer could be found by using Pr(Q ∩ R) = 3 and Pr(R) = 7. This works because they are part of the same universal set - in other words, since the total of all the values in the Venn Diagram remains constant, the denominators of the two probabilities would be the same (given that no cancelling is done) and these denominators would be cancelled out when dividing Pr(Q ∩ R) by Pr(R). This can be particularly useful for a multiple choice question such as this one.