Simplify the expression. Write your answer as a power.

Using proportions, it is found that she needs 4 consecutive hits to raise her batting average to .400.

A proportion is a fraction of a total amount.

Hence, the batting average is given by the number of hits divided by the number of at-bats.

If she gets x consecutive hits, she will have 8 + x hits in 25 + x at-bats, for an average of 0.400, hence:

[tex]0.4 = \frac{8 + x}{25 + x}[/tex]

8 + x = 10 + 0.4x

0.6x = 2

x = 3.33

Rounding up, she needs 4 consecutive hits to raise her batting average to .400.

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Answer:

Find by using 1st derivative test (tests slope) or 2nd derivative test (test concavity). Maximum is 18.75.

Step-by-step explanation:

The maximum of the equation is found when the slope is 0; therefore, take the derivative of the equation, find the critical point and find whether the function is increasing or decreasing around the critical point. To do this use test values within the interval of (-∞, 4.5) and (4.5, ∞). You then find that (-∞, 4.5) is increasing meaning there is a maximum. Plug in 4.5 into f(x) to find the y value.

Second method is using the 2nd derivative test. Find the second derivative and use the same method of testing intervals but instead plugging in test values to the 2nd derivative. You then find that f''(x) is < 0 meaning the function is concave down, thus having a maximum. Plug in 4.5 to find the y value.

Answer:

Answer is G 1.5

Step-by-step explanation:

1. Distribute the 5 to x and 2 by multiplying. and the 7 to the 4 and -x by multiplying

2. carry over the 7x by adding it to 5x. to get x to one side.

3. subtract 10 from both side

4. Divide both side by 12

5. simplify and convert to decimal

Answer:

Pool 1:  2(3)*3*3= 54 ft^3

pool 2: 2(4)*4*4= 128 ft^3

Pool 3: 2(5)*5*5= 250 ft^3

pool 4:  2(6)*6*6= 432 ft^3

Step-by-step explanation:

length can be modeled by twice the width or twice the depth which means that deapth=width,

both the width and the depth are equal, hence

L= 2x

W=X

x=3,4,5,6 (which are values for depth as well as width)

susbtitute values:

Pool 1:  2(3)*3*3= 54 ft^3

pool 2: 2(4)*4*4= 128 ft^3

Pool 3: 2(5)*5*5= 250 ft^3

pool 4:  2(6)*6*6= 432 ft^3

The situation that best represents the equation y = 25x is David earned y amount of money at a rate of $25 per x hours.

Rate of payment is the amount of money a worker receives after each hour, day or week.

David receives the amount of y as his payment every hour.

He is paid at the rate of $25 every X hours.

Therefore the amount he will receive which is represented as y would be $25 * X hours.

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Answer:

f(n+1) = f(n)+5

Step-by-step explanation:

So lets say

f(1)=5

f(2)=10

1+1=2 so

f(2)=f(1+1)

therefor

f(n+1)=f(n)+5 since the difference of the functions is 5

the answer is A f(n+1)=f(n)+5

we know that

An arithmetic sequence is a sequence of numbers which increases or decreases by a constant amount each term

In this problem

the sequence of numbers increase by a constant amount equal to

5

each term

so

f(2)=f(1)+5

f(3)=f(2)+5

f(4)=f(3)+5

.

.

f(n+1) = f (n) + 5

therefore

the answer is the option

f(n + 1) = f(n) + 5

Answer:

A

Step-by-step explanation:

A function assigns values. The inequality one-half x minus 10 greater-than-or-equal-to 0 should be satisfied.

A function assigns the value of each element of one set to the other specific element of another set.

The domain of a function is a set of values for which the equation is satisfied. Since the function has under root values, the value which is under the root should be non-negative so that it does not give a complex number,  therefore,

The inequality [tex]\sqrt{\dfrac12x^2-10}\geq 0[/tex]satisfied to find the domain of the function f(x).

Also, we can write that 0.5x²-10≥0 for the value to be positive.

Hence, the inequality one-half x minus 10 greater-than-or-equal-to 0 should be satisfied.

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Answer:

Scale faction is 4

Step-by-step explanation:

You want to step this up as new/old this is because the shape is increasing in size. 18 times 4 is 72.

Answer:

The numbers are 12 and 4

Step-by-step explanation:

12÷4=3

4÷4=1

12×4=48

Answer:

The length is 4.8 mm

Step-by-step explanation:

The area of a rectangle is calculated by multiplying the length times the width. So:

46.56 = l * w

46.56 = l * 9.7

To find the length, we must get "l" alone. To do this, we must divide both sides by 9.7.

46.56/9.7 = 4.8

4.8 = l

The length is 4.8

Answer:

$25 >= 14.99+2.75x

Step-by-step explanation:

Answer:

D i think a number represents x. not sure

Answer:

8x+5

Assume x is the unknown number.

8x+5 means

8*x = a number multiplied by eight

8x+5 = a number multiplied by eight eight then added to five.

Therefore, the correct option is D.

Answer:

[tex]y = \frac{5}{3} x - 5[/tex]

Step-by-step explanation:

To write an equation in the slope-intercept form, we need the slope (which can also be calculated) and at least a coordinate.

What is slope-intercept form?

x- intercept occurs at y= 0 while y-intercept occurs at x= 0. With this information, let's write out the two coordinates given.

With two coordinates, we can calculate the slope using the equation below.

[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

[tex]slope = \frac{ - 5 - 0}{0 - 3} [/tex]

[tex]slope = \frac{ - 5}{ - 3} [/tex]

[tex]slope = \frac{5}{3} [/tex]

Substitute the value of the slope into m in the equation.

[tex]y = \frac{5}{3} x + c[/tex]

Given that the y-intercept is -5, c= -5.

[tex]y = \frac{5}{3} x - 5[/tex]

Answer:

112

Step-by-step explanation:

1:8

14:x

8x14=112

X=112

Answer:

112 m

Step-by-step explanation:

1 cm : 8 m

14 cm : ?

= 14 x 8

= 112 m

Answer: 7.2

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Answer:

-11

Step-by-step explanation:

The | | around a number means the absolute value of that number. The absolute value is the positive value of the number given.

Answer:

a: 13 + t = 17

Step-by-step explanation:

the top is equal to the bottom

the top is 13 and t together but you are not multiplying

thus the answer is 13 + t = 17

Answer:

A, 13+t=17

Step-by-step explanation:

Since you are trying to find the missing part of the diagram and both rows add up to 17, the answer would be A. This is the case because you aren't multiplying 13 over and over to get 17, rather instead you are adding a number to get 17.

Answer:

1.) men: 1800, women: 3000

2.)2275/65 = 35 mins

3.)P 2,175,000

4.) 5400 in 6 mins

5.) Probably 5?

6.) P 120 000

Step-by-step explanation:

Answer:

D.  310.86 L

Step-by-step explanation:

[tex]\textsf{Volume of a cylinder}=\pi r^2h[/tex]

where:

Given:

[tex]\implies \sf \textsf{Volume of the tank}=(3.14)(0.3)^2(1.1)=0.31086\:m^3[/tex]

[tex]\sf 1\:liter = 1000\:cm^3[/tex]

To convert cubic cm to cubic meters, divide by 1,000,000:

[tex]\implies \sf 1\:liter =\dfrac{1000}{1,000,000} = 0.001\:m^3[/tex]

[tex]\implies \sf \textsf{Volume of the tank}=\dfrac{0.31086}{0.001}=310.86\:L[/tex]

Answer:i dont know sorry but i think its c

Step-by-step explanation:

Answer:

The factored form of the equation is f(x) = (x - 2)(x + 10), which makes the zeros of the function x = -10 and x = 2.

In order to factor a quadratic like this, you must find factors of the constant (in this case -20). The pairs of factors are listed below.

1 and -20

-1 and 20

2 and -10

-2 and 10

4 and -5

-4 and 5

Now we must pick out the pair that add to the coefficient of x.

1 and -20

-1 and 20

2 and -10

-2 and 10

4 and -5

-4 and 5

Once you've picked out those numbers, you can place each in a parenthesis with x.

f(x) = (x - 2)(x + 10)

Then to find the zeros to the equation, set each parenthesis equal to 0 and solve.

x - 2 = 0

x = 2

x + 10 = 0

x = -10

Step-by-step explanation:

hope this helps:)

Answer:

x = 23

Step-by-step explanation:

2x -3 + 47 = 90

2x = 46

x = 23

An equation is formed of two equal expressions. The solution of the equation is 4.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of the equation can be written as,

[tex]\dfrac{5}{3b^3-2b^2-5} = \dfrac{2}{b^3-2}\\\\5(b^3-2) = 2(3b^3-2b^2-5)\\\\5b^3-10=6b^3-4b^2-10\\\\5b^3-10-6b^3+4b^2+10=0\\\\-b^3+4b^2=0\\\\b^2(-b+4)=0\\\\-b+4=0\\\\-b=-4\\\\b=4[/tex]

Thus, the solution of the equation is 4.

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Answer:

c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

1.36

Step-by-step explanation:

Answer:

1.7 hours

Step-by-step explanation:

IXL is pain.