Give the prime factorization of 300 in exponential form

Question:

Solution:

Consider the following functions:

and

the composition g(g(x)) would be:

then

On the other hand, the composition h(h(x)) would be:

then:

So that, we can conclude that the correct answer is:

and

The limit of the function as x approaches -2 is 20.To find the limit of the function (if it exists), we can substitute the given value into the function and simplify. Given function: f(x) = 4x² + 5x - 6x + 2

To find the limit as x approaches -2, we substitute -2 into the function:

f(-2) = 4(-2)² + 5(-2) - 6(-2) + 2
      = 4(4) - 10 + 12 + 2
      = 16 - 10 + 12 + 2
      = 20

Therefore, the limit of the function as x approaches -2 is 20.

To write a simpler function that agrees with the given function at all but one point, we can use a graphing utility. By plotting the given function and observing its behavior, we can create a simpler function that matches the original function except at one point.

However, without further information about the specific behavior of the given function, it is not possible to provide a more detailed explanation or a graph of the simpler function.

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Solution:

The only term that has a x-variable is "-95x".

The coefficient of x is -95.

\(\qquad \qquad\huge \underline{\boxed{\sf Answer}}\)

let's evaluate ~

\(\qquad \sf  \dashrightarrow \: ( {x}^{2} + x - 12)( {x}^{2} + 10x + 25)\)

\(\qquad \sf  \dashrightarrow \: {x}^{4} + 10 {x}^{3} + 25 {x}^{2} + {x}^{3} + 10 {x}^{2} + 25x - 12 {x}^{2} - 120x - 300\)

\(\qquad \sf  \dashrightarrow \: {x}^{4} + 11 {x}^{3} + 23 {x}^{2} - 95x - 300\)

In the given expression we can clearly observe that the Coefficient of x is " -95 "

The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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Answer:

I'm stuck too like is so aggravating

Answer:

x = 50°

Step-by-step explanation:

Step 1.

180° - 80° (because there are 180 degrees in a triangle) = 100°

Step 2.

100° ÷ 2 = 50° (because the two angles on the bottom are identical, as this is an isosceles triangle - which we know because the two sides on the left and right are both the same length, 7 units)

Step 3.

Answer: x = 50°

Answer:

6x + 3 depending if i read it right

Step-by-step explanation:

if you mean

g(f(x)) then:

2(3x + 2) - 1

6x + 4 - 1

6x + 3

The equivalent expressions to \(24^{-7}\) are given as follows:

C. \(\left(\frac{1}{24^{-7}}\right)^{-1}\)

F. \((24^3 \times 24^4)^{-1}\)

Equivalent expressions are expressions that have the same value for all possible values of the variables. In other words, equivalent expressions are different ways of writing the same mathematical idea.

The exponent in the denominator can be moved to the numerator with the changed signal, hence:

\(\left(\frac{1}{24^{-7}}\right)^{-1} = (24^7)^{-1}\)

Applying the power of power rule, we multiply the powers, hence:

\((24^7)^{-1} = 24^{-7}\)

When two terms with the same base and different exponents are multiplied, we add the bases and keep the exponents, hence:

\((24^3 \times 24^4)^{-1} = (24^7)^{-1} = 24^{-7}\)

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Answer:

(Hope this helps can I pls have brainlist (crown)☺️)

Step-by-step explanation:

To find the x-intercept, substitute in  0  for  y yand solve for  x . To find the y-intercept, substitute in  0  for  x and solve for  y .

x-intercept(s):  ( 6 , 0 )

y-intercept(s):  ( 0 , − 2 )

Use the slope-intercept form  y = m x + b to find the slope  m and y-intercept  b .

Slope: \(\frac{1}{3}\)

graph in pic

(Credit: M a t h w a y)

Answer:

Step-by-step explanation:

6) We would like to find out the area of the following arcs with ,

As we know that the area of sector is given by ,

\(\longrightarrow Area =\dfrac{\theta}{360^o}\times \pi r^2 \)

Here on substituting the respective values , we have ,

\(\longrightarrow Area =\dfrac{75}{360}\times \dfrac{22}{7}\times 16m \times 16m \\\)

Simplify,

\(\longrightarrow \underline{\underline{Area =167.61 \ m^2}}\)

8) Again we would like to find out the area with ,

Firstly we know that ,

\(\longrightarrow \pi \ rad = 180^o\)

So ,

\(\longrightarrow 2\pi rad = 360^o \)

Therefore , the formula becomes ,

\(\longrightarrow Area =\dfrac{\theta}{2\pi}\times πr^2 \)

Substitute ,

\(\longrightarrow Area =\dfrac{19\pi}{12\times 2\pi}\times \pi r^2\\ \)

So that,

\(\longrightarrow Area =\dfrac{19}{24}\times \dfrac{22}{7}\times 14ft \times 14ft \\ \)

Simplify,

\(\longrightarrow \underline{\underline{ Area = 487.66 ft^2 }}\)

And we are done !

#1

Area

#2

Area

The least amount of paint that is needed to paint the walls of a room with a rectangular prism shape is 1. 8 gallons.

There would be two walls with 10 x 16 dimensions so the area is :

= 2 x 10 x 16

= 320 square feet

Two walls with 20 x 10 dimensions :

= 2 x 20 x 10

= 400 square feet

The total area is :

= 400 + 320

= 720 square feet

One gallon of paint can cover 400 square feet so the number of gallons needed is:

= 720 / 400

= 1. 8 gallons

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Full question is:

One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 20 feet, a width of 16 feet, and a height of 10 feet? Write your answer as a decimal.

Answer:

y-axis

negative

positive

Step-by-step explanation:

in that order.

Answer:

\(\frac{3}{17}, \\0.176, \\18\%\)

Step-by-step explanation:

The area a total of 4+3+6+5=18 balls, consisting of:

After a green ball is selected (implied that it is not replaced or put back), there will be 17 balls total, consisting of:

Therefore, the probability of drawing another green one is:

\(\boxed{\frac{3}{17}=0.176=18\%}\)

Step-by-step explanation:

cross multiply both sides

2(6x+1)=3(5x–2)

12x+2=15x–6

collect like terms

+2+6=15x–12x

8=3x

divide both sides by 3

8\3=3x\3

therefore, the final answer is

8\3

thank you

please mark as the brainliest

Answer:

The mean of y

Step-by-step explanation:

In statistics, correlation is the degree of the linear relationship between two variables. The correlation coefficient is the numerical measure of the linear relationship of two variables, It is measured in the range -1 to 1. When the coefficient is negative, the variables are said to have a negative correlation, while it is a positive correlation or have a strong linear relationship if the correlation coefficient is positive.

When the correlation coefficient is zero, both variables have no linear relationship and the best predictions of each variable would be the mean.

This is:

Solve:

Answer: 80%

Answer:

Step-by-step explanation:

20 percent

0.12

Step-by-step explanation:

21x²-2x +1/2 = 0

x² - 2x ×21 + 1/2× 21 = 0

Answer:

The z-score for the statistics test grade is of 1.11.

The z-score for the calculus test grade is 7.3.

Due to the higher z-score, the student performed better on the calculus test relative to the other students in each class

Step-by-step explanation:

Z-score:

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

The grade with the higher z-score is better relative to the other students in each class.

Statistics:

Mean of 79 and standard deviation of 4.5, so \(\mu = 79, \sigma = 4.5\)

Student got 84, so \(X = 84\)

The z-score is:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{84 - 79}{4.5}\)

\(Z = 1.11\)

The z-score for the statistics test grade is of 1.11.

Calculus:

Mean of 69, standard deviation of 3.7, so \(\mu = 69, \sigma = 3.7\)

Student got 96, so \(X = 96\)

The z-score is:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{96 - 69}{3.7}\)

\(Z = 7.3\)

The z-score for the calculus test grade is 7.3.

On which test did the student perform better relative to the other students in each class?

Due to the higher z-score, the student performed better on the calculus test relative to the other students in each class

Answer:

It's option 'B'

Please mark as brainliest

Answer:

sometimes you think that but it's not real and your fruit snacks are just being eaten by furry fat mice sugar WILL attract ants

Step-by-step explanation:

have a good day

The probability of advancing five spaces is 0.2307.

Given that, the odds in favor of advancing five spaces are 3/10.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

The probability of advancing five spaces can be obtained as:

P =Odds/1+Odds

= \(\frac{\frac{3}{10} }{1+\frac{3}{10} }\)

= \(\frac{\frac{3}{10} }{\frac{13}{10} }\)

= 3/13

= 0.2307

Therefore, the probability of advancing five spaces is 0.2307.

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Solve for ML by setting up a ratio:

Height/ length = unknown length/ height

6/8 = ML/6

Cross multiply:

8ML =36

Divide both sides by 8

ML = 4.5

JL = JM + ML = 8 + 4.5 = 12.5

JL = 12.5

Answer:

$640

Step-by-step explanation:

Step-by-step explanation:

f(x) = ax + b

f(5) = 62 => 5a+b = 62

f(14) =98 => 14a+b= 98

________-

-9a = -36

a = -36/-9 = 4

5a + b = 62

5(4) +b=62

20+b = 62

b = 62-20

b = 42

1) f(x) = 4x + 42

2) the money was in the register at the beginning of the day = $42.00 (option d)

Answer:

d

Step-by-step explanation:

Answer:

a. As given in the question, some towns are located high in the Rockies above the sea level and some are located in the south-central valley of the California below the sea level as well. The meaningful zero does not exists here and the variable of interest is continuous(quantitative). Hence, the elevations can be best described as an interval data.

b. The unemployment rate can not be negative. Therefore, the meaningful zero exist here. Hence, the unemployment rate can be best described as ratio data.

The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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Answer:

(m-(1/3))(m^2+(1/3)m+(1/9)

Step-by-step explanation:

Just use the difference of cubes