What is the correct prime factorization of 24? 2 ∙ 2 ∙ 6 2 ∙ 3 ∙ 3 2 ∙ 2 ∙ 3 ∙ 3 2 ∙ 2 ∙ 2 ∙ 3

The image after a dilation with scale factor k=3, then the vertices of triangle X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, the triangle with vertices X(−3, 2), Y(2, 3), and Z(1,−1) and scale factor k=3.

Now, X(-3, 2)→3(-3, 2)→X'(-9, 6)

Y(2, 3)→3(2, 3)→Y'(6, 9)

Z(1,-1)→3(1, -1)→Z'(3, -3)

Vertices of X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).

Therefore, the image after a dilation with scale factor k=3, then the vertices of triangle X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).

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The probability that at least one of ten random numbers drawn from a standard normal distribution will exceed 2.66 is 0.045.

This can be calculated using the complementary probability formula, which is 1 - P(x ≤ 2.66), where P(x ≤ 2.66) is the probability that all ten numbers are less than or equal to 2.66.

The probability that all ten numbers are less than or equal to 2.66 can be calculated using the normal distribution function, which gives the probability that a random variable x follows a normal distribution with mean μ and standard deviation σ. For a standard normal distribution, the mean is 0 and the standard deviation is 1, so the probability that all ten numbers are less than or equal to 2.66 can be calculated as:

where Φ(x) is the normal distribution function.

Substituting this value into the complementary probability formula, we get:

Thus, the probability that at least one of ten random numbers drawn from a standard normal distribution will exceed 2.66 is 0.045.

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Answer: Yes, Montoya's square root will equal the number of blocks in one side of the graph-paper square.

Step-by-step explanation: The square root of a number is the number that, when multiplied by itself, produces the original number. For example, the square root of 16 is 4, because 4 * 4 = 16.

If Montoya has cut out a perfectly square section of graph paper, the number of blocks in the square will be the same as the number of blocks in one side of the square multiplied by the number of blocks in the other side of the square. In other words, the number of blocks in the square will be the square of the number of blocks in one side of the square.

Therefore, when Montoya takes the square root of the number of blocks in the square, she will get the number of blocks in one side of the square.

For example, if Montoya's square has 4 blocks on each side, the number of blocks in the square will be 4 * 4 = 16, and the square root of 16 will be 4, which is the number of blocks in one side of the square.

Answer: 9.7

Step-by-step explanation: 97 divided by 10 is 9.7

Answer:

Answer = 8 books every month

Step-by-step explanation:

Answer:

Step-by-step explanation:

(2, 0), (4, -6)

(-6 -0)/(4 - 2)= -6/2= -3

y - 0 = -3(x - 2)

y = -3x + 6

or

f(x) = -3x + 6

Answer:

Step-by-step explanation:y= -3x + 6

The random variable Y does not have a binomial distribution, therefore this is not a binomial experiment

Here, a computer is used to randomly dial a telephone number

Then the  operator asks the answering person whether she has time to answer some questions.

Y is the number of calls made until the first person replies that she is willing to answer the questions

There is no independent variable the affect the value of the Y. here the number of trial are not fixed, so there wont be any binomial distribution

Therefore, this is not a binomial experiment, because y does not have a binomial distribution

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a) The percentage of the survey respondents liked hamburgers but do not like burritos is of: 46.34%.

b) The marginal relative frequency of all customers who like hamburgers is of: 0.6537.

c) The lowest joint frequency is not liking neither of hamburgers or burritos.

The relative frequency is obtained as the division of the number of desired outcomes by the number of total outcomes.

The percentage is calculated as the multiplication of the relative frequency by 100%.

From the table given by the image at the end of the answer, the total number of people in the survey is of:

77 + 128 = 134 + 71 = 205.

The percentage for item a is then calculated as follows:

95/205 x 100% = 46.34%.

The relative frequency for item b is then calculated as follows:

134/205 = 0.6537.

The joint frequencies are found completing the table, considering the sums for the rows and columns, as follows:

The table is given by the image shown at the end of the answer.

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Answer: -d + 3.5

Step-by-step explanation:

Expand the brackets to

-5d + 4d +3.5

Add similar elements/ like terms

= -d +3.5

The simplified form of the given expression, [tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }[/tex] is equal to [tex]4x^{9}[/tex]

What are Exponents?

What is the Product of Powers rule?

In this question, the expression is  [tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }[/tex]  ------(1)

Multiplying the values in the numerator, we get

[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-5} \times x^{-3} }[/tex]

Now, the values in the denominator can be simplified using the Product of Powers rule.

The formula for the Product of Powers rule is given as, [tex]x^{m} \times x^{n} =x^{m+n}[/tex]

Simplifying the given expression using the Product of Powers rule, we get

[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-5+(-3)} }\\\implies \frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-8} }[/tex]     -----(2)

The formula for the Quotient of Powers rule is given as, [tex]\frac{x^{m} }{x^{n} } =x^{m-n}[/tex]

Simplifying the expression in (2) using the Quotient of Powers rule, we get

[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=4x^{1-(-8)} \\\implies \frac{4x \times 1}{x^{-5} \times x^{-3} }=4x^{9}[/tex]

Therefore, the simplified form of the given expression is [tex]4x^{9}[/tex]

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Check the picture below.

Answer:

Step-by-step explanation:

-1

Answer:

-11

Step-by-step explanation:

Equation:

5+x=-6

The equation for the line we want to get is:

y = -x + 3

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular of the product between the slopes of the two lines is -1.

Here we want to find a line perpendicular to the one that passes through  the line with Y(1,3) and Z(-3,-1), the slope of that line is:

a = (-1 - 3)/(-3 - 1) = 1

Then the slope of a perpendicular line, a', is:

a'*1 = -1

a' = -1

Then our line is like:

y = -1*x + b

To find the value of b, we use the fact that this line passes through (1, -4), then we will get:

-4 = -1*1 + b

-4 + 1 = b

-3 = b

So the linear equation is:

y = -x + 3

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The expression fraction with negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 is simplified to give 8

The fraction: negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 is written in words

Rewriting the fraction

-4( (2 - ∛8 * 6) / 5)

The equation is simplified as

= -4( (2 - ∛8 * 6) / 5)

= -4( (2 - 2 * 6) / 5)

= -4( (2 - 12) / 5)

= -4( (-10) / 5)

= -4( -2)

= 8

Option C, 8 is the correct answer

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The closest to the approximate value of ✓103 is E. 10.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

It should be noted that the expression is the square root of 103. This will give 10.1

Therefore, this will be 10. The correct option is E

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Complete question

Which of the following is closest to the approximate value of ✓103√? A 15 B 17 C 18 D 19 E. 10

The expressions that are equivalent to the expression y + y + y + 3z are 3y + 3z and 3(y + z)

From the question, we have the following parameters that can be used in our computation:

y + y + y + 3z

To start with, expressions that are equivalent are expressions that have equal values when evaluated

Using the above as a guide, we have the following:

Evaluate the like terms in y + y + y + 3z

So, we have the following representation

y + y + y + 3z = 3y + 3z

Factor out 3 from the expression

So, we have the following representation

y + y + y + 3z = 3(y + z)

Hence, the equivalent expressions of y + y + y + 3z are 3y + 3z and 3(y + z)

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5% of $1100 = 55

Year given = 7

So, 55 × 7 = 385

She would get after 7 years all total  = (1100 + 385) = $1485

Step-by-step explanation:

y = 2/3x + 7

Multiply both sides by 3 to get rid of the fraction 2/3

3y = 2x +21

subtract 2x from both sides

3y - 2x = 21

Answer ofc is 3x - 2y = 21

Please rate if you get the answer right.

Answer: the answers should be B and D

Step-by-step explanation:

so basically, this is just simplifying

B is the correct answer because the numerator 12, when divided by 4 is 3, and the denominator 32, when also diving by 4, is eight. This makes the two fractions equivalent.

Same goes for D, for if you diving the numerator and denominator by 2, you get answer choice D

it’s kind of a trial and error type problem and you have to test out all possibilities

hope this helps!

Answer:

B and D

Step-by-step explanation:

12/32 (if you divide them both by three) does not equal 4/10

12/32 fully simplified is 3/8

12/32 - subtracting is not simplifying, therefore, 10/30 is not correct

12/32 - both divided by two, a common factor, is 6/16, therefore, this answer is correct

12/32 - both of them divided by three equals 4/10.7 (rounded up to the nearest tenth), therefore, 4/9 is not a correct answer

12/32 - both divided by six equals 2/5.3 (rounded down to the nearest tenth), therefore, 2/6 is not a correct answer

Answer:

can 3x+3x+3x =9x if so what is the value of x?

It's possible 3x+3x+3x=9

=3*(3x) =9

3^(x+1) =3^(2x)

Quadratic equation :The maximum height reached by Alonzo's ball will be 9m.

What is a quadratic equation?

The equation whose highest degree of the variable used in the equation is 2 and has 2 roots, is called quadratic equation.

Here the quadratic equation of the path of Chase's ball is given by y = - 4x²+ 5x+ 7
To compare the height of both paths followed by the ball
we have to first calculate the height of the path of Chase's ball.
the path of Chase's ball is f(x)=-4x²+ 5x+ 7
The function will have the highest value when f'(x) will be 0.
f'(x)=-8x+5
f'(x)=0
⇒-8x+5=0
⇒-8x=-5
⇒x=5/8
at x=5/8, function value is
f(x)=-4x²+ 5x+ 7
=-4(5/8)²+ 5(5/8)+ 7
=-4(25/64)+(25/8)+7
=(-25/16)+25/8+7
=8.5625
There maximum value of f(x) is 8.5625.
The maximum height reached by Chase's ball will be 8.5625m.
From the graph of the path of Alonzo's ball, it is clear that
The maximum height reached by Alonzo's ball will be 9m.
As 8.5625m < 9m
Alonzo's baseball will reach greater height.

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Complete Question:
Chase and Alonzo stand next to each other and throw baseballs in the air. The path of Chase's ball is described by the equation y = - 4x²+ 5x+ 7. The path of Alonzo's ball is shown by the graph. In each function, x is the horizontal distance the ball travels in meters, and y represents its height. Whose baseball reaches a greater height?
A. Both baseballs reach the same height.
B. Chase's baseball
C. Alonzo's baseball
D) Non of these

Answer:

Alonzo's baseball

whompwhompwhompwhopwhompwhompwhompwhompwhompwhompwhompwhompwhompwhompwhomp

Step-by-step explanation:

Answer:

The average rate of change of f(x)= 4x^2 + 3x on the interval [1,5] is 18.

The total miles that Laney walked is 11 2/3 miles.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this situation, Laney walks 2 1/3 miles to school from her house and rides the bus home and she attended school five days last week.

The total miles that Laney walked will be:

= 2 1/3 × 5

= 7/3 × 5

= 35/3

= 11 2/3 miles

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Answer:  -45x + 111 or -3(15x-37)

Step-by-step explanation:

Instead of :6 (8-3x )− 3 (9x−1 )+ 60

54 - 18x = −27x − 3 + 60

54 - 18x = −27x + 57

-18x = -27x + 3

9x = 3

x= 1/3

Corrected :

6 (8-3x )− 3 (9x−1 )+ 60

First Simplify : 54 - 18x -27x - 3 + 60

Combine Like terms Like 54, - 3, and 60 : 111 - 18x -27x

Combine Like Terms Like -18x and -27x : 111 -45x

Rearrange It So The Variable Is First : -45x + 111

So, the answer is -45x + 111 or if you want you can still simplify it by finding the common factor which you will get -3(15x-37)

Corrections : The friend is wrong because he turned the equation into an inequality instead of simplifying it. He turned the equation into an inequality by adding an equal sign in the middle then he tried to solve it like how you solve inequalities.

P.S : So, correct me if I am wrong but i will try my best to answer. Hope it helps.

Answer:

6 days

Step-by-step explanation:

total is 445

first day charge is 145

so, 445-145 = 300

second day onwards its 60.

so, 300/60 = 5 days

so total 5+1 = 6 days.

I hope I helped you

The probability distribution that the number of U.S. adults who favor the use of unmanned drones by police agencies is

​ (a) exactly​ three :-= 0.251

(b) at least​ four:-= 0.445

(c) less than eight:-= 0.994

What is probability distribution?

The probabilities of any random occurrence are determined by the probability distribution. It is sometimes described as a collection of potential results from any random experiment depending on the underlying sample space. A set of real numbers, a set of vectors, or a set of any other things might make up these settings. It is a component of statistics and probability.

The outcome of an experiment whose results cannot be anticipated is known as a random experiment. Imagine that we can't foresee whether a coin will land on its head or its tail when we throw one. An outcome is a potential outcome of a random experiment. The collection of results is known as a sample point.

X ~ Bin ( n , p)

Where n = 12 , p = 0.28

Binomial probability distribution is

P(X) = nCx * px * ( 1 - p)n-x .

a)

P(X = 3) = 12C3 * 0.283 *  ( 1 - 0.28)9

= 0.251

b)

P(X >= 4) = 1 - P(X <= 3)

= 1 - [ P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) ]

= 1 - [ 12C0 * 0.280 *  ( 1 - 0.28)12 +12C1 * 0.281 *  ( 1 - 0.28)11 +12C2 * 0.282 *  ( 1 - 0.28)10 +12C3 * 0.283 *  ( 1 - 0.28)9 ]

= 0.445

c)

P(X < 8) = 1 - P(X >=8)

= 1 - [ P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) ]

= 1 - [ 12C8 * 0.288 *  ( 1 - 0.28)4 +12C9 * 0.289 *  ( 1 - 0.28)3 +12C10 * 0.2810 *  ( 1 - 0.28)2 +

12C11 * 0.2811 *  ( 1 - 0.28)1 +12C12 * 0.2812 *  ( 1 - 0.28)0 ]

= 0.994

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The interest rate, to the nearest hundredth of a percent, that would be required in order for Mohal to end up with $1,110 would be = 4.2%

The interest rate of an investment is defined as the rate at which an individual receives stipulated amount of money for a period of time over the investment made.

The amount for investment (P) = $830

The time for investment(T) = 8 years

The simple interest yield(SI) = $1,110 -830 = 280

The rate(R) = x%

using the formula;

Simple interest = P×T×R/100

Make R the subject of formula;

R= SI ×100/P×T

R= 280×100/830×8

R= 28000/ 6,640

R= 4.2%

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(b) System B is likely to experience a smaller increase in the average time in queue.

As utilization increases, the length of time in line grows more quickly. So a 5% increase in utilization has a larger effect from 90% to 95% than from 80% to 85%.

When you use something, you use it, whether it's a tool—like when you write something down with a pen—or a talent or skill—like the speed you use when you run a race. Utilization is the act of using something, such as using your voice to sing a song. It may be necessary for a team to use a gym for practices until the rain stops.

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