This table shows values that represent an exponential function.
What is the average rate of change for this function for the interval from x = 1
to x = 3?

Answer:

2√2−3

Step-by-step explanation:

Simplify each term.

Since there are no imaginary terms, the complex conjugate is the same as the simplified expression.

Hope this can help

Answer:

answer is B

Step-by-step explanation:

4x+21+3x-5=121

7x+16=121

x=15

angle ABD =4(15)+21=81

Answer:

0

Step-by-step explanation:

3^2 is 9, and (-3)^2 is 9.

so, 9-9=0

Answer:

Step-by-step explanation:

Given,

Radius ( r ) = 10

Height ( h ) = 6

pi ( π ) = 3.14

now, let's find the volume of given cone:

[tex]\pi {r}^{2} \frac{h}{3} [/tex]

Plug the values

[tex] = 3.14 \times {10}^{2} \times \frac{6}{3} [/tex]

Evaluate the power

[tex] = 3.14 \times 100 \times \frac{6}{3} [/tex]

Calculate

[tex] = 628 \: {units}^{3} [/tex]

Hope this helps..

Best regards!!

Answer:

The answer is 200π units³ .

Step-by-step explanation:

Given that the formula of volume of cone is V = 1/3×π×r²×h where r represents radius and h is height. Then, you have to substitute the value of radius and height into the formula :

[tex]v = \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]

[tex]let \: r = 10 \: , \: h = 6[/tex]

[tex]v = \frac{1}{3} \times \pi \times {10}^{2} \times 6[/tex]

[tex]v = \frac{1}{3} \times \pi \times 600[/tex]

[tex]v = 200\pi \: {units}^{3} [/tex]

Answer:

  $2192.60

Step-by-step explanation:

March 4 is day 63 of the year. So, the amount of tax that Kelly needs to refund to Mason is the tax for the remaining 365 -63 = 302 days of the year.

Kelly will owe Mason ...

  (302/365)($2650) = $2192.6027 ≈ $2192.60

Answer:

The probability that the person is between 65 and 69 inches is 0.5403

Step-by-step explanation:

Mean height = [tex]\mu = 66[/tex]

Standard deviation = [tex]\sigma = 2.5[/tex]

We are supposed to find What is the probability that the person is between 65 and 69 inches i.e.P(65<x<69)

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

At x = 65

[tex]Z=\frac{65-66}{2.5}[/tex]

Z=-0.4

Refer the z table for p value

P(x<65)=0.3446

At x = 69

[tex]Z=\frac{69-66}{2.5}[/tex]

Z=1.2

P(x<69)=0.8849

So,P(65<x<69)=P(x<69)-P(x<65)=0.8849-0.3446=0.5403

Hence the probability that the person is between 65 and 69 inches is 0.5403

Answer:

11 / 12 or 0.9167

Step-by-step explanation:

Given:

3/4 + 1/6

Find:

Value with expression

Computation:

"3/4 added to number 1/6"

3/4 + 1/6

By taking LCM

[9 + 2] / 12

11 / 12 or 0.9167

Answer:

15 pt

Step-by-step explanation:

to convert qt to pt you multiply by 2 so 7 and 1/2 times 2 is 15

Answer:

Step-by-step explanation:

A basketball is basically a sphere, so it suffices to calculate the surface are of the ball to determine the amount of required material. Given a sphere of radius r we have that the surface area is [tex]4\pi r^2[/tex]

In this case, r = 11.14 cm. So the area is aproximately 1159.48 squared cm. (1159.48 = [tex]4\pi (11.14)^2[/tex])

Hey there! I'm happy to help!

We want to find the probability that the player makes at least seven out of eight free throws. First, we find the probability of them making seven free throws.

[tex]\frac{1}{2}^7=\frac{1}{128}[/tex]

Then, we find the probability of them making eight, which is another possibility that fits this.

[tex]\frac{1}{2}^8=\frac{1}{256}[/tex]

Now, we add the probability of these two events happening.

[tex]\frac{1}{128}+\frac{1}{256}=\frac{3}{256}[/tex]

Therefore, the probability that the player makes at least seven of eight free throws is 3/256 or about 1.17%

Have a wonderful day! :D

Answer:

35 degree angle a cute angle

Answer:

Step-by-step explanation:

A and B are supplementary angles since the lines are parallel

A + B = 180

6x-18 + 14x+38 = 180

Combine like terms

20x +20 = 180

Subtract 20 from each side

20x+20 -20 =180-20

20x = 160

Divide by 20

20x/20 =160/20

x = 8

Answer:

b. the approx time it takes an investment to double in value

Answer:

S = [0.2069,0.7931]

Step-by-step explanation:

Transition Matrix:

[tex]P=\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

Stationary matrix S for the transition matrix P is obtained by computing powers of the transition matrix P ( k powers ) until all the two rows of transition matrix p are equal or identical.

Transition matrix P raised to the power 2 (at k = 2)

[tex]P^{2} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

[tex]P^{2} =\left[\begin{array}{ccc}0.2203&0.7797\\0.2034&0.7966\end{array}\right][/tex]

Transition matrix P raised to the power 3 (at k = 3)

[tex]P^{3} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

[tex]P^{3} =\left[\begin{array}{ccc}0.2203&0.7797\\0.2034&0.7966\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

  [tex]P^{3} =\left[\begin{array}{ccc}0.2086&0.7914\\0.2064&0.7936\end{array}\right][/tex]

Transition matrix P raised to the power 4 (at k = 4)

[tex]P^{4} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

[tex]P^{4} =\left[\begin{array}{ccc}0.2086&0.7914\\0.2064&0.7936\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

[tex]P^{4} =\left[\begin{array}{ccc}0.2071&0.7929\\0.2068&0.7932\end{array}\right][/tex]

Transition matrix P raised to the power 5 (at k = 5)

[tex]P^{5} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

[tex]P^{5} =\left[\begin{array}{ccc}0.2071&0.7929\\0.2068&0.7932\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right][/tex]

[tex]P^{5} =\left[\begin{array}{ccc}0.2069&0.7931\\0.2069&0.7931\end{array}\right][/tex]

P⁵ at k = 5 both the rows identical. Hence the stationary matrix S is:

S = [ 0.2069 , 0.7931 ]

Answer:

x = 1/2

Step-by-step explanation:

2(4x+2) = 4x - 12(x-1)

Distribute

8x +4 = 4x - 12x +12

Combine like terms

8x + 4 = -8x +12

Add 8x to each side

8x+4+8x = -8x+12 +8x

16x+4 = 12

Subtract 4 from each side

16x +4-4 = 12-4

16x = 8

Divide by 16

16x/16 =8/16

x = 1/2

Answer:

x = 1/2

Step-by-step explanation:

2(4x+2) = 4x - 12(x-1)

Expand brackets.

8x + 4 = 4x - 12x + 12

Subtract 4 on both sides.

8x = 4x - 12x + 12 - 4

Subtract 4x and add 12x on both sides.

8x - 4x + 12x = 12 - 4

Combine like terms.

16x = 8

Divide both sides by 16.

x = 8/16 = 1/2

Answer:

y > 2x + 1

Step-by-step explanation:

(1 is the y intercept) 2/1 is the gradient so 2 up and 1 across

Answer:

D. ⅔

Step-by-step explanation:

I hope it helps :)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\ m = \frac{3 - 1}{5 - 2} = \frac{2}{3} \\ m = \frac{2}{3} [/tex]

Answer:

3

Step-by-step explanation:

Use this equation

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] substitute

-6-3/0-3 subtract

-9/-3 simplify

-3/-1 two negitives cansle out

3/1=3

Hope this helpes, if it did, please consider giving me brainliest, it will help me a lot. If you have any questions, feel free to ask.

Have a good day! :)

Answer:

3

Step-by-step explanation:

To find the slope, we use the slope formula

m= ( y2-y1)/(x2-x1)

   = ( -6 -3)/(0 -3)

    = -9/-3

    = 3

Answer:

The answer for dy/dx is 3/4t .

Step-by-step explanation:

First, you have to differentiate x and y expressions in term of t :

[tex]x = a {t}^{4} [/tex]

[tex] \frac{dx}{dt} = 4a {t}^{3} [/tex]

[tex]y = a {t}^{3} [/tex]

[tex] \frac{dy}{dt} = 3a {t}^{2} [/tex]

Next, we can assume that dy/dt ÷ dx/dt = dy/dx. So we have to substitute the expressions :

[tex] \frac{dy}{dt} \div \frac{dx}{dt} = \frac{dy}{dt} \times \frac{dt}{dx} = \frac{dy}{dx} [/tex]

[tex] \frac{dy}{dx} = 3a {t}^{2} \div 4a {t}^{3} [/tex]

[tex] \frac{dy}{dx} = 3a {t}^{2} \times \frac{1}{4a {t}^{3} } [/tex]

[tex] \frac{dy}{dx} = \frac{3}{4t} [/tex]

Answer:

60 cm

Step-by-step explanation:

You need to use ratios to solve.  If the scale is 1:30 then the wheel is 2:(?).  Cross-multiply the fractions and solve for x.

1/30 = 2/x

1x = 30*2

x = 60

The wheel is 60 cm in diameter.

Answer:

60 centimeters

Step-by-step explanation:

The scale is 1:30. The wheel diameter is 2 while the actual size of the wheel is unknown. Therefore, the scale for the wheel is 2:x

Let’s set up a proportion.

1/30=2/x

First, cross multiply. Multiply the numerator of the first fraction by the denominator of the second. Then, multiply the numerator of the second by the denominator of the first.

1*x= 2*30

1x=20*30

x=20*30

x=60

Add appropriate units, in this case centimeters (cm).

x= 60 cm

The actual diameter of the wheel is 60 centimeters.

If it has a single zero that means it has to be just touching the x-axis with its tip.

We know that if it has only one zero, the discriminant equals 0.

So,

[tex]D=b^2-4ac=0\implies (-k)^2-4(1)(9)=0[/tex]

Solving for k,

[tex]k=\pm\sqrt{36}=\boxed{\pm{6}}[/tex].

Hope this helps.

Concepts:

Answer:

First option and fifth option

-2x-1=3^(-x) and 2^(-x)+2= -5^x + 3 don't intersect.

Therefore, the graphs have no solution.

Answer:

We accept H₀

p-value = 0,1618

Step-by-step explanation:

We are going to solve a one tail proportion-test ( right tail)

We assume Normal distribution

Sample population 1000

Political strategist to test  wants to test:

Null hypothesis                             H₀           p = p₀       or   p = 26 %

Alternate hypothesis                    Hₐ           p > p₀        or  p > 26%

We assume CI  90 % then

α = 10 %     α = 0,1    and  z score for α = 0,1  is critical value

z = 2,32          ( note  2,32 is z score for α = 0,1017 "good approximation")

To compute z(s)

z(s)  =  ( p -p₀ ) / √ p₀q₀/n

z(s)  =  ( 0,29 - 0,26 ) /√ 0,26*0,74/1000

z(s)  = 0,03 / 0,014

z(s) = 2,14

We compare z(s) and z(c)

z(s) < z(c)

2,14 < 2,32

z(s) is in the acceptance region we accept H₀

The p-value for z(s) is from z-table

p-value = 0,1618

A - No

B - No

C - Yes

D - Yes

.

C and D are alternate exterior angles

Answer:

15%

Step-by-step explanation:

To calculate the margin of error, we can adopt this formula

Margin of error = critical value* (standard deviation/sqrt of sample size)

Where critical value is 2.33, sd is 0.78 and sample size is150.

Thus, we have:

Margin of error = 2.33*(0.78/√150)

Margin of error = 2.33*(0.78/12.2474)

Margin of error =2.33*0.06369

Margin of error = 0.1484 which is a 15% margin of error

Answer:

See below.

Step-by-step explanation:

So, we have the zeros -4 with a multiplicity of 1, zeros 2 with a multiplicity of 3, and f(0)=64.

Recall that if something is a zero, then the equation must contain (x - n), where n is that something. In other words, for a polynomial with a zero of -4 with a multiplicity of 1, then (x+4)^1 must be a factor.

Therefore, (x-2)^3 (multiplicity of 3) must also be a factor.

Lastly, f(0)=64 tells that when x=0, f(x)=64. Don't simply add 64 (like what I did, horribly wrong). Instead, to keep the zeros constant, we need to multiply like this:

In other words, we will have:

[tex]f(x)=(x+4)(x-2)^3\cdot n[/tex], where n is some value.

Let's determine n first. We know that f(0)=64, thus:

[tex]f(0)=64=4(-2)^3\cdot n[/tex]

[tex]64=-32n, n=-2[/tex]

Now, let's expand:

Expand:

[tex]f(x)=(x+4)(x^2-4x+4)(x-2)(-2)[/tex]

[tex]f(x)=(x^2+2x-8)(x^2-4x+4)(-2)[/tex]

[tex]f(x)=(x^4-4x^3+4x^2+2x^3-8x^2+8x-8x^2+32x-32)(-2)[/tex]

[tex]f(x)=-2x^4+4x^3+24x^2-80x+64[/tex]

This is the simplest it can get.

Answer:

a. $849.45

Step-by-step explanation:

In the above question, we are given the following information

Coupon rate = 10%

Face value = 1000

Maturity = n = 20 years

t = number of periods = compounded semi annually = 2

Percent yield = 12% = 0.12

Bond Value formula =

C/t × ([1 -( 1/ 1 + r/t)-^nt ÷] r/t) +( F/ (1 + r/t)^nt)

C = coupon rate × face value = 10% × 1000 = 100

Bond value:

= 100/2 × ( [1 - (1 /1 + 0.12/2)^-20×2]÷ 0.12/2)+ (1000/( 1 + 0.12/2)^20×2

= 50 × ( [1 - (1 /1 + 0.06) ^40] ÷ 0.06) + ( 1000/ (1 + 0.06) ^40

= 50 × ( [1 - (1/ (1.06) ^40] ÷ 0.06 ) + (1000/(1.06)^40)

= 50 × 15.046296872 + 97.222187709

= $849.45

Bond value = $849.45

Answer: The concentration will be 8 milligrams per liter at 2 hours and 4 hours.

Step-by-step explanation:

GIven: The concentration of a certain painkiller supplied by serum varies in its effectiveness over time according to the following function, [tex]C (t) = - t^2 + 6t[/tex] where C is the concentration of the painkiller in the serum measured in milligrams per liter so that it takes effect during t hours.

Put C(t)=8, then we get

[tex]8=-t^2+6t\\\\\Rightarrow\ t^2-6t+8=0\\\\\Rightarrow\ t^2-2t-4t+8=0\\\\\Rightarrow\ t(t-2)-4(t-2)=0\\\\\Rightarrow\ (t-2)(t-4)=0\\\\\Rightarrow\ t=2,4[/tex]

At t=2, [tex]C(t)=-(2)^2+6(2)=-4+12=8[/tex]

At t=4, [tex]C(t)=-(4)^2+6(4)=-16+24=8[/tex]

Hence, the concentration will be 8 milligrams per liter at 2 hours and  4 hours.

Answer:

[tex]\boxed{\frac{1}{8} }[/tex]

Step-by-step explanation:

[tex]\frac{5}{4} / 10[/tex]

Changing "division" into multiplication and inverting the term after it:

[tex]\frac{5}{4} * \frac{1}{10}[/tex]

=> [tex]\frac{1*1}{4*2}[/tex]

=> 1/8

Answer:

1/8

Step-by-step explanation:

Well to do 5/4 ÷ 10 let's set up the following.

[tex]\frac{5}{4} / \frac{10}{1}[/tex]

Then we use the keep, change, and flip rule.

So keep 5/4 change the / to a * and flip the 10/1 ro a 1/10.

[tex]\frac{5}{4} * \frac{1}{10}[/tex]

Now we multiply them to get,

5/40

simplified

1/8

Thus,

the answer is 1/8.

Hope this helps :)

Answer:

C and E

Step-by-step explanation:

He got it on ap.ex

The area of the pyramid can be found using the formula SA = BA + LA and SA= BA + 1/2ps option (C) and (E) are correct.

In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the center of the square.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a pyramid with a square base:

The perimeter of the base is p

The slant height is s.

The base area is BA

The lateral area is LA.

We can find the area of the pyramid as follows:

SA = BA + LA

SA= BA + 1/2ps

Thus, the area of the pyramid can be found using the formula SA = BA + LA and SA= BA + 1/2ps option (C) and (E) are correct.

Learn more about the pyramid here:

brainly.com/question/13057463

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