The table of values represents an exponential function ​f(x). What is the average rate of change over the interval −2≤x≤2? Enter your answer, as a decimal rounded to the nearest hundredth, in the box.
−3 64
−2 16
−1 4
0 1
1 1/4
2 1/16
3 1/64
(Worth 60pts)

Answer: 124

Step-by-step explanation:

As we know, the total number of positive divisors of n is the product of one more than each exponent in the prime factorization of n.

We know this product is equal to 11.

Since 11 is prime, so there can be only one number in this product, so the prime factorization of n must be [tex]$n=p^{10}$[/tex], where p is a prime number.

We take a cube of the prime factorization of n to give us a prime factorization for [tex]n^3[/tex]

[tex]$$n^{3}=\left(p^{10}\right)^{3}=p^{30} .$$[/tex]

We see that [tex]n^{3}\text{ has }$30+1=31$[/tex] positive divisors.

Now, [tex]8n^3=2^3\times p^{30}[/tex]

Totald divisiors = [tex](3+1)(30+1)=4\times31=124[/tex]

Hence, the number of positive divisors of [tex]8n^3=124[/tex]

Answer: 105

Step-by-step explanation:

Given

The ratio of men to women working for a company is 4:7

There are total of 165 employees

Suppose, there is  4x men and 7x women such that the ratio remains constant

[tex]\therefore 4x+7x=165\\\Rightarrow 11x=165\\\Rightarrow x=15[/tex]

[tex]\text{Men= }4\times 15=60\\\text{Women= }7\times 15=105[/tex]

Answer:

Step-by-step explanation:

Tangents from the point outside the circle are equal

NL = JL  

NM + ML =JK + KL

2x - 7 + 9 = 8 + 10  

     2x + 2 = 18      {Subtract 2 from both sides}

           2x = 18 - 2

          2x  = 16   {Divide both sides by 2}

             x = 16/2

x = 8

MN = 2*8 - 7 = 16 - 7 = 9

MN = 9

Answer:

cosθ = sinθ/tanθ

Step-by-step explanation:

tanθ = sinθ/cosθ (Given)

cosθ(tanθ) = sinθ (Mulitplied cosθ on both sides)

cosθ = sinθ/tanθ (Divided tanθ on both sides)

Given:

The table of value and y is inversely proportional to square of x.

To find:

The value of c and d.

Solution:

It is given that y is inversely proportional to square of x. So,

[tex]y\propto \dfrac{1}{x^2}[/tex]

[tex]y=k\dfrac{1}{x^2}[/tex]               ...(i)

Where, k is the contant of proportionality.

From the given table it is clear that [tex]y=4[/tex] and [tex]x=3[/tex]. Putting these values in (i), we get

[tex]4=k\dfrac{1}{3^2}[/tex]

[tex]4=\dfrac{k}{9}[/tex]

[tex]4\times 9=k[/tex]

[tex]36=k[/tex]

Putting [tex]k=36[/tex] in (i), we get

[tex]y=36\dfrac{1}{x^2}[/tex]

[tex]y=\dfrac{36}{x^2}[/tex]             ...(ii)

Putting [tex]x=5,y=c[/tex] in (ii), we get

[tex]c=\dfrac{36}{(5)^2}[/tex]

[tex]c=\dfrac{36}{25}[/tex]

Putting [tex]x=d,y=2[/tex] in (ii), we get

[tex]2=\dfrac{36}{d^2}[/tex]

[tex]d^2=\dfrac{36}{2}[/tex]

[tex]d^2=18[/tex]

Taking square root on both sides, we get

[tex]d=\pm \sqrt{18}[/tex]

[tex]d=\pm 3\sqrt{2}[/tex]

Therefore, the required values are [tex]c=\dfrac{36}{25}[/tex] and [tex]d=\pm 3\sqrt{2}[/tex].

Answer:

8.238

Step-by-step explanation:

it might not be right, but it was not fast either XDDD

dang, i took to long to tell u

:)

Answer:

56 cups of water

Step-by-step explanation:

Katrina drinks 0.5 gallons of water per day

We have 7 days in a week, hence, the number of gallons of water she drinks per week is calculated as:

1 day = 0.5 gallons

7 days = x

Cross Multiply

1 day × x = 7 days × 0.5 gallons

x = 7 days × 0.5 gallons/1 day

x = 3.5 gallons

Note that 16 cups = 1 gallon

The number of cups of water she drinks per week is

1 gallon = 16 cups

3.5 gallons = x

Cross Multiply

1 gallons × x = 3.5 gallons × 16 cups

x = 3.5 gallons × 16 cups/1 gallons

x = 56 cups

Therefore, Katrina drinks 56 cups of water in a week

Answer:

E Ticket sales are not affected by the number of cloudy days per month.

Step-by-step explanation:

From the scatter plot Given, using visual observation, we can infer that the relationship between theme park ticket sales and the number of cloudy sales is randomly scattered with no defined linear pattern. That is, the plot does not ascertain of the number of ticket sales increases with increasing number of cloudy days, or vice versa. Hence, the relationship will best the described as concluding that ticket sales are not affected by the number of cloudy days per month.

Answer:

Step-by-step explanation:

B is correct answer

Answer:

35,691

Step-by-step explanation:

First step, look at the diagram and you see that you have a sphere and a cone.

The total surface area of a sphere is

[tex]A = 4\pi r^{2} \\A = 4\pi 39^{2} \\A = 19,113[/tex]

Since you only have half of a sphere, the surface area is 9,556.5

The surface area of the cone is

[tex]A = pi r(r+\sqrt{h^{2}+r^{2} }) A = \pi39(39+\sqrt{42^{2} +39^{2} } \\A=11,800[/tex]

You don't need the bottom of the cone however as it is connected to the half sphere.

So substract the area of a circle with a radius of 39 from the product of 19,113 + 11,800

The area of the circle is 4,778

Answer:

your answer is y=-8 for sure

Answer:

tn=t¹+d(n-1)

Step-by-step explanation:

d=common difference

t¹=1st term

n= the nth term

Answer:

Step-by-step explanation:

Sequence, so easiest way is difference between any 2 consecutive numbers

Neg 3 to 2, difference is 5

2 to 7, difference is 5

7 to 12 , difference is 5

So sequence result for n

= starting point + (n-1)(5)

Eg 2nd, N= 2

Starting point is neg 3

Sequence = -3 + 2-1 (5) = -3 + 5 = 2

9th, n = 9

-3 + 8(5)

-3 + 40

37

Answer:

Escribí esto, así que espero que quede claro.

Step-by-step explanation:

Maybe 256x square 8

Jenny rolled 1/18

Answer:

D. 1/18

Answer:

x = 105

Step-by-step explanation:

The angles are corresponding angles and corresponding angles are equal if the lines are parallel

x = 105

Answer:

105°

Step-by-step explanation:

The angles are corresponding therefore they are equal

Answer:

[tex]x=\pm \sqrt{11} \\y=-4.[/tex]

Step-by-step explanation:

[tex]\left \{ {{3x^2+4y=17} \atop {2x^2+5y=2}} \right. \\\\Then\\\\\left \{ {{2 \times (3x^2+4y)=2 \times 17} \atop {3\times(2x^2+5y)=3\times2}} \right. \\\\\left \{ {{6x^2+8y=34 \quad (1)} \atop {6x^2+15y=6\quad (2)}} \right.\\\\(1)-(2) \Rightarrow -7y=28 \Rightarrow y =-4.\\Since \: \: 2x^2+5y=2 \Rightarrow 2x^2=2-5y\\\Rightarrow 2x^2=2+20=22\\\Rightarrow x^2=22:2=11\\\Rightarrow x=\pm \sqrt{11}.[/tex]

Answer:

9°

Step-by-step explanation:

m / sin L M = o / sin L O

41/sin L M = 98/sin 22°

=> sin L M = 41×sin 22°/98

= 41×0,3746 / 98

= 0,1567

so, L M = sin~¹ 0,1567 = 9°

Answer:

Step-by-step explanation:

Answer:

$72.00

Step-by-step explanation:

Amount of discounted money

= 10/100 x $80.00

= $8

Amount he will pay

= $80.00 - $8.00

= $72.00

Answer:

A. y = -(x + 5)^2 + 4

Step-by-step explanation:

After a small online search, I've found that the options are:

A. y = -(x + 5)^2 + 4

B. y = -(x - 5)^2 + 4

C. y = -(x + 5)^2 - 4

D. y = -(x - 5)^2 - 4

For a quadratic equation with a vertex at the point (h, k) is written as:

y = a*(x - h)^2 + k

Where a is the leading coefficient.

So, if here we have the vertex at (-5, 4)

y = a*(x - (-5))^2 + 4

y = a(x + 5)^2 + 4

Then the correct option is the first one, where a = -1, then the correct option is A.

Answer:

Angle F

Step-by-step explanation:

=====================================================

Explanation:

We see that angle A = angle E as shown by the arc marking. The tickmark says that side AB is the same length as side EF.

In the letter sequences "AB" and "EF", erase the first letters A and E to be left with B and F. This is one way to show how angle B pairs with angle F, and that is enough to show the two angles are congruent.

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete; However, one can deduce from the options that the question refers to percentage change.

I will give two illustrations that shows how to calculate percentage change.

Illustration 1

Consider goods x with the following price change.

[tex]Old = \$45[/tex]

[tex]New = \$55[/tex]

The percentage change is:

[tex]\%Change = \frac{New - Old}{Old} * 100\%[/tex]

[tex]\%Change = \frac{55-45}{45} * 100\%[/tex]

[tex]\%Change = \frac{10}{45} * 100\%[/tex]

[tex]\%Change = \frac{1000}{45} \%[/tex]

[tex]\%Change = 22.22\%[/tex]

This means there is a 22.22% increase

Illustration 2

Consider goods x with the following price change.

[tex]Old = \$45[/tex]

[tex]New = \$35[/tex]

The percentage change is:

[tex]\%Change = \frac{New - Old}{Old} * 100\%[/tex]

[tex]\%Change = \frac{35-45}{45} * 100\%[/tex]

[tex]\%Change = \frac{-10}{45} * 100\%[/tex]

[tex]\%Change = -\frac{1000}{45} \%[/tex]

[tex]\%Change = -22.22\%[/tex]

The negative sign indicates percentage decrease

So, this means there is a 22.22% decrease

Answer:

132m

Step-by-step explanation:

Height of tower B = Height of tower A + difference in height between tower B and A

The difference in height can be determined using tan

tan 23 = opposite / adjacent

tan 23 = opposite / 151

0.4245 x 151 = opposite

opposite = 64m

Height of tower B =  64m + 68m = 132m

Answer:

23

Step-by-step explanation:

I DID 7*3+2 & GOT 23

Answer:

2.03% Rate of Population Growth.

Step-by-step explanation:

According to the Question,

Given, In 2006 the population was 1148 and in 2014 the population was 1348.

2006⇒2014  (8 Years)

So, [tex]1148 * (1+\frac{x}{100} )^{8} = 1348[/tex]

[tex](1+\frac{x}{100} ) = \sqrt[8]{1.1742}[/tex]

(1 + x/100) = 1.0202

x/100 = 0.020276

x = 2.03% Rate of Population Growth

Answer:

A -  y = cos(x-1)

Step-by-step explanation:

This is what it looks like when you graph y = cos(x-1). It matches the graph on your question exactly, this graph is just using trig concepts.

Please give me brainliest if my answer was right. :)

Answer:

48 in³

Step-by-step explanation:

the volume = ½×3×4 × 8 = 48 in³