Please help me. I really need help with this proof.
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Check the picture below.

[tex]\bf \textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=&area~of\\ &its~base\\ h=&height\\ \cline{1-2} B=&\stackrel{4\times 4}{16}\\ h=&4 \end{cases}\implies V=\cfrac{1}{3}(16)(4)\implies V=\cfrac{64}{3}\implies V=21.\overline{3}[/tex]

Answer:

21.03^3  this is the answer.

Answer:

B. f -1(x) = x + 2 / 5

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

Step-by-step explanation:

To find the inverse of a function we need to interchange x and y an solve for y.

Since [tex]f(x)=y[/tex], then

[tex]f(x)=5x-2[/tex]

[tex]y=5x-2[/tex]

[tex]x=5y-2[/tex]

Add 2 to both sides

[tex]x+2=5y-2+2[/tex]

[tex]x+2=5y[/tex]

Divide both sides by 5

[tex]\frac{x+2}{5}=\frac{5y}{5}[/tex]

[tex]\frac{x+2}{5}=y[/tex]

[tex]y=\frac{x+2}{5}[/tex]

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

We can conclude that the correct answer is B. f -1(x) = x + 2 / 5

Answer:

- 0.0625

Step-by-step explanation:

Again, I don't know of another way besides Calculus other than letting x = something very tiny.

When you use calculus, the answer approaches - 1/16 = - 0.0625 (I think). So we'll let x = 0.01 and see how that goes.

numerator: 1/(0.01 + 4) - 1/4

(0.24938 - 0.25) / 0.01

- 0.000623 / 0.01 = - 0.0623 which is  pretty close considering what I used for x. You could try it with 0.0001 which will get much closer.

X^(3•2) =X^ 6

Think of an example such as :

(2^3)^2=8^2=64 is the same with

2^(3•2) = 2^6 = 64

Answer= x^6

When two exponents are multiplied together the two exponents multiply.

Answer: 12800m^2

This shape is made up of a rectangle and a triangle.

Rectangle

= 120 x 60

= 7200

Triangle

= (200 - 60) x (120 - 40) x 0.5

= 140 x 80 x 0.5

= 5600

Total Shape

= 7200 + 5600

= 12800m^2

A = 0.5 x 10.4 x 16.9

A = 87.88

The area of the triangle is 87.88 ft²

Answer:

The difference in investment between the smallest investor an largest investor is $40,000

Step-by-step explanation:

Let

x ---> the contribution of the smallest investor

y ---> the contribution of the middle investor

z ---> the contribution of the largest investor

we know that

x+y+z=140,000 -----> equation A

x/y=3/4 -----> y=(4/3)x ----> equation B

x/z=3/7 ----> z=(7/3)x ----> equation C

substitute equation B and equation C in equation A and solve for x

x+(4/3)x+(7/3)x=140,000

(14/3)x=140,000

x=140,000*3/14

x=$30,000

Find the value of y

y=(4/3)x ----> y=(4/3)(30,000)=$40,000

Find the value of z

z=(7/3)x ----> z=(7/3)(30,000)=$70,000

Find the difference in investment between the smallest investor an largest investor

z-x=$70,000-$30,000=$40,000

The number of runners run at most 2 miles per day is 13.

2 miles = 6

3 miles = 4

4 miles = 2

5 miles = 1

Now if we add this,

So,

= 6 + 4 + 2 + 1

= 13

Learn more: brainly.com/question/17429689

Answer:

13

Step-by-step explanation:

Its easy, but its a trick question into getting you to click 6

Answer:

Final answer is [tex]-112\cdot\sqrt{2}a^5[/tex].

Step-by-step explanation:

Given expression is [tex](a-\sqrt{2})^8[/tex].

Now we need to find the fourth term of the given expression  [tex](a-\sqrt{2})^8[/tex]. So apply the nth term formula using binomial expansion.

exponent n=8

4th term means we use r=4-1=3

x=2, [tex]y=-\sqrt{2}[/tex]

rth term in expansion of [tex](x+y)^n[/tex] is given by formula:

[tex]\frac{n!}{\left(n-r\right)!\cdot r!}x^{\left(n-r\right)}\cdot y^r[/tex]

[tex]=\frac{8!}{\left(8-3\right)!\cdot3!}\cdot a^{\left(8-3\right)}\cdot\left(-\sqrt{2}\right)^3[/tex]

[tex]=\frac{8!}{5!\cdot3!}\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]

[tex]=\frac{40320}{120\cdot6}\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]

[tex]=56\cdot a^5\cdot\left(-2\sqrt{2}\right)[/tex]

[tex]=-112a^5\cdot\sqrt{2}[/tex]

[tex]=-112\cdot\sqrt{2}a^5[/tex]

Hence final answer is [tex]-112\cdot\sqrt{2}a^5[/tex].

Answer:

The T-shirts cost $10 and the jeans cost $20.

Step-by-step explanation:

I guess you want to find the cost of the T-shirts and jeans at his first buy,

Let the cost be  $t and $j for T-shirts and jeans respectively.

Then we have the system:

2t + j = 40...................(1)

and a month later:

0.5*2t  + 0.5*5j = 60

t + 2.5j = 60................(2)

Multiply by - 2:

-2t - 5j = -120.............(3)

Adding equations (1) and (3):

-4j = -80

j = -80 /  -4

j =  $20.

Substituting j = 20 into equation (2):

t + 2.5(20) = 60

t = 60 - 50

t = $10.

t = $55

Add all the times together:

27.81 + 26.89 + 26.55 + 25.48 = 106.73 seconds.

1 minute = 60 seconds.

106 - 60 = 46

Total time: 1 minute and 46.73 seconds.

Answer:

106.73

Step-by-step explanation:

27.81 + 26.89 + 26.55 + 25.48 = 106.78

So in conclusion, the answer is 106.78

Answer:

  3, -8, 11

Step-by-step explanation:

The first factor is zero when x=3.

The second factor is zero when x=-8.

The third factor is zero when x=11.

Whenever any factor is zero, the polynomial is zero.

The zeros are 3, -8, 11.

19/50 of the baseball caps in the store are blue and on sale.

Let's say there are a total of 100 baseball caps in the store. Then, 2/3 of them are blue, which is:

2/3 x 100 = 66.67 (approximately 67)

So, there are approximately 67 blue baseball caps in the store. Out of these, 4/7 are on sale, which is:

4/7 x 67 = 38 (rounded to the nearest whole number)

Therefore, there are approximately 38 blue baseball caps that are on sale in the store.

The fraction of baseball caps in the store that are blue and on sale is:

38/100 = 19/50

So, 19/50 of the baseball caps in the store are blue and on sale.

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To find the fraction of baseball caps in the store that are blue and on sale, multiply the fractions representing the proportion of blue caps and the proportion of blue caps that are on sale.

To find the fraction of baseball caps in the store that are blue and on sale, we need to multiply the fractions representing the proportion of blue caps and the proportion of blue caps that are on sale.

Given that 2/3 of the caps are blue and 4/7 of the blue caps are on sale, we can calculate the fraction of blue caps that are on sale by multiplying 2/3 and 4/7:

2/3 * 4/7 = 8/21

Therefore, 8/21 of the baseball caps in the store are blue and on sale.

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Answer: B Scientific Method

Answer:

A. $4397.9

Explanation:

We are given that Kendra sold 200 shares and that the price per share was $22.1

This means that:

Total value = 200 * 22.1 = $4420

Now, we know that the broker charged 0.5% commission on the total value

This means that:

Broker's charge = 0.5% * 4420 = 0.005 * 4420 = $22.1

Therefore,

Kendra's return = Total value - broker's charge

Kendra's return = 4420 - 22.1 = $4397.9

Hope this helps :)

Answer:

$4,397.90

Step-by-step explanation:

Answer:

The Phase Shift is how far the function is shifted horizontally from the usual position.

Step-by-step explanation:

Answer:

12-5.5=h

12-5.5=6.5

Kyle needs to volunteer 6.5 more hours.

Step-by-step explanation:

Answer:

5.5 + h = 12

Step-by-step explanation:

Here, h represents the number of hours, Kyle still needs to volunteer this week,

Given,

He volunteered 5.5 hours at the library this week.

Since, the total number of hours he needs to volunteer = 5.5 + h

According to the question,

5.5 + h = 12

Which is the required equation.

Answer:

The answer would be the large album has 54 more stamps than the small album.

Step-by-step explanation:

... 92 - 38 = 54

Do you need a drawing done though?

Answer:

  $388.16

Step-by-step explanation:

Her monthly interest rate is 3.8%/12, so the amount of interest due on the first payment is ...

  $260,000 × 0.038/12 ≈ $823.33

Then the amount applied to the principal is ...

  $1211.49 -823.33 = $388.16

Answer:

12

Step-by-step explanation:

96 / 8

Answer:

12 Cups are needed!

Step-by-step explanation:

You find the answer by dividing 96 milkshakes by 8 Milkshakes and find that 12 cups are needed.

:)

Answer:

Step-by-step explanation:

So the table means that there are 20 1's, 120 2's, 40 3's, and 20 4's.

The total number is 20+120+40+20 = 200.

So the probability of each is:

1: 20/200 = 0.10

2: 120/200 = 0.60

3: 40/200 = 0.20

4: 20/200 = 0.10

A bar graph that represents the probability distribution of each card is shown in the image below.

In Mathematics and Statistics, a frequency table can be used for the graphical representation of the frequencies or relative frequencies that are associated with a categorical variable or data set.

Based on the frequency, the total number of deck of cards can be calculated as follows;

Total number of deck of cards = 20 + 120 + 40 + 20

Total number of deck of cards = 200 cards.

Next, we would determine the probability distribution of each card as follows:

P(X = 1) = 20/200 = 0.10.

P(X = 2) = 120/200 = 0.60.

P(X = 3) = 40/200 = 0.20.

P(X = 4) = 20/200 = 0.10.

Answer:

B

Step-by-step explanation:

The exponential function [tex]y=a^x[/tex] shows the exponential growth if [tex]a>1.[/tex]

Consider choice B.

If x=1, then [tex]y=2=2^1;[/tex]

if x=2, then [tex]y=4=2^2;[/tex]

if x=3, then [tex]y=8=2^3;[/tex]

if x=4, then [tex]y=16=2^4.[/tex]

This means that the function [tex]y=2^x[/tex] represents the table B.

ANSWER

See attachment

EXPLANATION

The table that represent a geometric sequence is the one shown in the attachment with y-values

[tex]2,4,8,16,...[/tex]

We can see that, the subsequent term is obtained by multiplying the previous term by 2.

In other words, there is a bit ratio of 2.

Here the table represents a geometric sequence.

Answer:

Step-by-step explanation:

I(x)=P(13x) = 2(13x)²+3(13x) +4

I(x)=P(13x).= 338x²+39x+4

[tex]f(x)=2\sqrt x[/tex] is continuous on [0, 4] and differentiable on (0, 4), so the MVT holds. We have

[tex]f'(x)=\dfrac1{\sqrt x}[/tex]

so that by the MVT, there is some [tex]c\in(0,4)[/tex] such that

[tex]f'(c)=\dfrac{f(4)-f(0)}{4-0}\implies\dfrac1{\sqrt c}=\dfrac{2\sqrt4}4=1[/tex]

[tex]\implies1=\sqrt c\implies \boxed{c=1}[/tex]

Answer:

x= 16/9

Step-by-step explanation:

[tex]f(x) = 2\sqrt{x}[/tex] is differentiable on [0,4] so the Mean Value Theorem For Integrals applies.

Average Value of the Integral:

[tex]\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx = \frac{1}{4-0} \int\limits^4_0 {2\sqrt{x} } \, dx[/tex]

After evaluating you will get  [tex]\frac{8}{3}[/tex]

Now, this is the average value so you still need to find the x-value using the original equation:

[tex]\frac{8}{3} =2\sqrt{x}\\\\\frac{4}{3} = \sqrt{x}\\\\\frac{16}{9} =x[/tex]

Answer:

1

Step-by-step explanation:

y = mx + b

y = 1/2 x - 1

y = 1/2 (4) - 1

y = 2 - 1

y = 1

When x = 4, the function y = (1/2)x - 1 evaluates to y = 1. This linear equation has a slope of 1/2 and a y-intercept of -1.

To find the value of the function y = (1/2)x - 1 when x = 4, you simply need to substitute x = 4 into the equation and solve for y:

y = (1/2)(4) - 1

y = 2 - 1

y = 1

So, when x = 4, the value of the function y is 1.

In a more general sense, this equation represents a linear function with a slope of 1/2 and a y-intercept of -1. The slope (1/2) represents the rate of change, meaning that for every unit increase in x, y increases by 1/2. The y-intercept (-1) is the value of y when x is 0.

When x = 4, as calculated above, y is 1. This means that if you were to plot this function on a coordinate plane, the point (4, 1) would lie on the graph.

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Answer: The required function would be [tex]x^2+3x-40[/tex]

Step-by-step explanation:

Since we have given that

There are two real zeroes :

x = -8 and x = 5

So, we need to find the function satisfying the above two zeroes:

Let α = -8 and β = 5

So, it means it is a quadratic equation :

[tex]x^2-(\alpha +\beta)x+\alpha \beta \\\\=x^2-(-8+5)x+-8\times 5\\\\=x^2+3x-40[/tex]

Hence, the required function would be [tex]x^2+3x-40[/tex]

Answer:

The answer is A

Step-by-step explanation:

Answer:  B) -6x³ + 4x²

Step-by-step explanation:

         f(x): -3x⁴ - 2x³ + 3x²

     + g(x): 3x⁴ - 4x³ +   x²

f(x) + g(x):        - 6x³ + 4x²

Answer:

D

Step-by-step explanation:

C is also possible but it is not purely random and it is not mentioned the mall is in her district.

Answer:  D) Mail a questionnaire to random households.

Step-by-step explanation:

A) You are limited to only listeners of the radio show

B) You are limited to only those that are wiling and able to attend the meeting.

C) You are limited to only shoppers at that particular mall.

D) Randomly selecting households is the least biased method of responses from the district.

Answer:

Option B) $122,140

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=5\ years\\ P=\$100,000\\ r=0.04[/tex]  

substitute in the formula above  

[tex]A=\$100,000(e)^{0.04*5}=\$122,140.28[/tex]  

Round to the nearest dollar

[tex]\$122,140.28=\$122,140[/tex]  

Answer:

1 is my answer but I could be wrong