Derek ran 12 miles in 108 minutes. If he ran at a constant speed, how many minutes did it take him to run 1 mile?

The basic transformations of the parent function y=x⁵ will only generate functions that can be written in the form y=a(x-h)⁵+k because these transformations involve shifting, stretching, and compressing the graph of the parent function.

The transformation involving the horizontal shift (h) moves the graph left or right, while the vertical shift (k) moves the graph up or down. The transformation involving the vertical stretch or compression (a) changes the steepness of the graph.

By applying these transformations, we can modify the position and shape of the graph of the parent function, while still keeping it in the form y=a(x-h)⁵+k.

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| x^2 + 6x+1| = 8

There are two solutions to an absolute value equation, one positive and one negative

x^2 +6x+1 =8 and x^2 +6x + 1 =-8

We have to solve both sets of equations

x^2 + 6x +1 = 8

Subtracting 8 from each side

x^2 +6x +1 -8 =0

x^2 +6x -7 =0

Factoring

What two numbers multiply to -7 and add to 6

-1 *7 = -7

-1 +7 = 6

These are the factors that we use ( -1 and 7)

( x-1) (x+7)=0

Using the zero product property

x-1 =0 x+7 =0

x=1 x=7

Now

x^2 +6x + 1 =-8

Add 8 to each side

x^2 +6x + 1+8 =0

x^2 + 6x+9 =0

Factoring

(x+3) (x+3) =0

Using the zero product property

x+3 =0 x+3 =0

x=-3

The solutions are

x=-3, x=1 , x=-7

Step-by-step explanation:

the value of x is 8

8^(2) = 64

the value of y is 11

11^(2) = 121

x - y

= 8 - 11

= -3

Answer:

9 laps

Step-by-step explanation:

75% of something is the same as three-fourths, or multiplying by 0.75

12 x 0.75 = 9

or you can divide by 4 and then multiply by three if you know what to separate the original number into

12/4 = 3     3 x 3 = 9

Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

Answer:

y = 4x + 5

Step-by-step explanation:

4x - y = -5

-4x        -4x

-y = -4x -5

/-1    /-1   /-1

y = 4x + 5

Answer:

Y = -4x + 5

Step-by-step explanation:

-4x from both sides

-y = -4x -5

divide both side by -1

y = -4x + 5

brainliest?

Answer:

-2,-1

Step-by-step explanation:

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite (its sign is changed). If you forget the rules for reflections when graphing, simply fold your paper along the x-axis (the line of reflection) to see where the new figure will be located.

Answer:

it is -2,-1 to solve the problem take the original point and go over the x-axis to the same part but opposite side ( I hope u understand what I am saying =/

Step-by-step explanation:

first graph the original point and then reflect it across the axis you know your answer is correct if it is an equal amount of spaces from the original point or if when you fold the graph the points are lined up (hope this helps)

The equation in standard form of the Ellipse centered at the origin with vertex (-7, 0) and co-vertex (0, 5)

The standard form equation of an ellipse centered at the origin with a horizontal major axis and vertical minor axis is:(x^2/a^2) + (y^2/b^2) = 1

where "a" is the length of the semi-major axis (half of the length of the major axis) and "b" is the length of the semi-minor axis (half of the length of the minor axis).

Since the center of the ellipse is at the origin, we know that the distance from the center to the vertex (-7, 0) is equal to the length of the semi-major axis "a", which is 7. Also, the distance from the center to the co-vertex (0, 5) is equal to the length of the semi-minor axis "b", which is 5.

Therefore, we have:a = 7b = 5

Plugging these values into the standard form equation, we get:(x^2/7^2) + (y^2/5^2) = 1

Simplifying, we get:(x^2/49) + (y^2/25) = 1

This is the equation in standard form of the ellipse centered at the origin with vertex (-7, 0) and co-vertex (0, 5)

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The number of prime factors of 3×5×7+7 is 3.

To find the number of prime factors, we need to calculate the given expression:

3×5×7+7 = 105+7 = 112.

The number 112 can be factored as 2^4 × 7.

In the first step, we factor out the common prime factor of 7 from both terms in the expression. This gives us 7(3×5+1). Next, we simplify the expression within the parentheses to get 7(15+1). This further simplifies to 7×16 = 112.

So, the prime factorization of 112 is 2^4 × 7. The prime factors are 2 and 7. Therefore, the number of prime factors of 3×5×7+7 is 3.

In summary, the expression 3×5×7+7 simplifies to 112, which has three prime factors: 2, 2, and 7. The factor of 2 appears four times in the prime factorization, but we count each unique prime factor only once. Thus, the number of prime factors is 3.

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j= -2

Explanation

given

to solve for j, we need to isolate it,so

Step 1

a) apply the addition property of equality and add 47 in both sides

Step 2

now, use the division property of equality and divide both sides by 11

so, the answer is

j= -2

I hope this helps you

Answer:

A= x r^2

A= x r x r

r means radius

The value of pi() is 3.14

r^2 means radius x radius

Substitute the radius for r: A= x 7^2

Square the radius: 7 x 7= 49

Area in terms of pi(): 49

Area in terms of square inches: 153.86 in^2

Divide the diameter by 2: 12 ÷ 2= 6

Substitute the radius for r: A= x 6^2

Square the radius: 6 x 6= 36

Area in terms of pi(): 36

Area in terms of square inches: 113.04 in^2

Step-by-step explanation:

The graph that correctly solves for x in equation x^2 - 4x + 3 = x + 3 is Graph B.

To explain why Graph B is the correct solution, we need to analyze the equation and compare it to the characteristics of the graphs.

The given equation is x^2 - 4x + 3 = x + 3. To solve for x, we want to find the values of x that satisfy this equation.

Graph A: This graph shows a parabola opening upwards. It intersects the x-axis at two points, but these points do not represent the solutions to the given equation. Therefore, Graph A does not correctly solve for x in the equation.

Graph B: This graph shows a linear equation y = x. It is a straight line that intersects the x-axis at the point (1,0). This point represents the solution to the given equation because when x = 1, the equation is satisfied. Therefore, Graph B correctly solves for x in the equation.

Graph C: This graph shows a constant line y = 3. It is parallel to the x-axis and does not intersect it. This graph does not provide any solution to the equation x^2 - 4x + 3 = x + 3. Therefore, Graph C does not correctly solve for x in the equation.

Based on the analysis, Graph B is the only graph that correctly solves for x in equation x^2 - 4x + 3 = x + 3 as it intersects the x-axis at the point (1,0), which represents the solution to the equation.

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Answer:

Step-by-step explanation:

σ = sqrt [ Σ ( xi - μ )^2 / N ]

where:

σ is the standard deviation

Σ is the sum of the values

xi is the value of the i-th observation

μ is the mean of the population

N is the number of observations

First, we need to find the mean of the population:

μ = (20 + 30 + 13 + 10 + 22 + 37) / 6

μ = 132 / 6

μ = 22

Next, we can calculate the deviations of each observation from the mean:

20 - 22 = -2

30 - 22 = 8

13 - 22 = -9

10 - 22 = -12

22 - 22 = 0

37 - 22 = 15

Then, we square each deviation:

(-2)^2 = 4

8^2 = 64

(-9)^2 = 81

(-12)^2 = 144

0^2 = 0

15^2 = 225

We add up the squared deviations:

4 + 64 + 81 + 144 + 0 + 225 = 518

We divide by the number of observations and take the square root:

σ = sqrt [ Σ ( xi - μ )^2 / N ]

σ = sqrt (518 / 6)

σ ≈ 10.72

Therefore, the standard deviation of the population is approximately 10.72 dollars.

The probability that she makes correct guesses 14 times or more is 0.0582 and this probability does not seem to verify her claim

Number of tosses of coin  n = 20

probability she guesses correctly p = 0.5

Probability she guesses incorrectly q = 1- p = 0.5

P(X < A) = P( z*σ + μ < A) = P(z < (A-μ)/σ)        (1)      ( ∵ we know z = x - μ/σ)

Mean = μ  = np = 20 * 0.5 = 10

Standard deviation = σ

Standard deviation σ = √npq = √(20 *0.5*(1-0.5) = √5 = 2.236

Probability of being correct 14 times or more

P(X ≥ 14) = 1 - P(X < 13.5)      

              = 1 - P(Z < (13.5 - 10)/2.236)         (using 1)

              = 1 - P(Z < 1.57)

               = 1 - 0.9418

               = 0.0582

Here, the probability of getting 14 or more is 0.0582 and it is usually as the probability is more than 0.05. Thus this probability does not verify her claim

Problem based on normal distribution

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Answer:

(1/6)

Step-by-step explanation:

ℎ 1/6

Answer:

a^2 - 5ab

Step-by-step explanation:

[3a * (a-b)] - [2a * (a+b)]

[3a(a) - 3a(b)] - [2a(a) + 2a(b)]

3a^2 - 3ab - (2a^2) - (2ab)

3a^2 - 2a^2 - 3ab - 2ab

a^2 - 5ab

30x−9!!!!!!!!!!!!!!!!!

The comma-separated list of functions f(x) and g(x) is f(x) = x^5, g(x) = x - 9.

To express the function f(x) = (x - 9)^5 in the form f∘g, we will find two non-identity functions f(x) and g(x) such that f(g(x)) = (x - 9)^5.

Step 1: Choose a suitable function for g(x).
Let's choose g(x) = x - 9.

Step 2: Determine f(x) such that f(g(x)) = (x - 9)^5.
Since g(x) = x - 9, we can replace g(x) with (x - 9) in the f function.
Now, f(g(x)) = f(x - 9).

To obtain (x - 9)^5, let f(x) = x^5.

Step 3: Verify that f(g(x)) = (x - 9)^5.
f(g(x)) = f(x - 9) = (x - 9)^5.

Therefore, the comma-separated list of functions f(x) and g(x) is f(x) = x^5, g(x) = x - 9.

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To express the function f(x) = (x - 9)⁵ in the form f∘g, we can let g(x) be x - 9 and f(x) be x⁵. So, f∘g(x) = f(g(x)) = f(x-9) = (x-9)⁵. The functions are f(x) = x⁵ and g(x) = x - 9.

To understand this composition of functions, consider that g(x) is applied first, which results in x - 9. Then, f(x) is applied to the result of g(x), which means raising the result (x - 9) to the power of 5.

By composing these two functions, we obtain the original function f(x) = (x - 9)⁵. This is how we express the function in the form of f∘g using non-identity functions for f(x) and g(x).

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Answer:

49/250 I think I'm not sure though

Answer:

\(\frac{59}{300}\)

Step-by-step explanation:

Recall that \(\frac{x}{9}\) returns the decimal \(0.\overline{x}\). In this case, we only want the 6 repeating. We can achieve this by finding the fraction excluding the 6 and then adding the repeating fraction with the 6.

0.19 as a fraction is simply \(\frac{19}{100}\)

\(\frac{6}{9}\) returns a repeating digit 6. However, we would like the 6 to be in the thousands place. Since it's already in the tenth place, we will divide the fraction by 100 to put it in the thousands place: \(\frac{6}{9}\cdot \frac{1}{100}=\frac{6}{900}\)

Adding these two fractions, we get:

\(\frac{6}{900}+\frac{19}{100}=\frac{6}{900}+\frac{171}{900}=\frac{177}{900}=\boxed{\frac{59}{300}}\)

Answer:

Step-by-step explanation:

\(\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}\)

Answer:  The correct answer is (3x−y)(2a−b)

Step-by-step explanation:

Factor 3x(2a−b)−y(2a−b)

6ax−2ay−3bx+by

=(3x−y)(2a−b)

The equivalent expression of the rational exponent ∛a² is \((a)^{\frac{2}{3}\).

Rational exponents are exponents that are fractions, where the numerator is a power and the denominator is a root.

So rational exponents (fractional exponents) are exponents that are fractions or rational expressions.

To determine the rational exponent equivalent to the expression given, we will apply the power rule of indices as shown below.

The given expression is ;

∛a²

The rational exponent is calculated as follows;

∛a² = \((a)^{\frac{2}{3}\)

Thus, based on exponent power rule, the given expression is equivalent to ∛a² = \((a)^{\frac{2}{3}\)

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The complete question is below:

Find the equivalent expression of the rational exponent ∛a². does anyone know it

Answer:

it’s B

Step-by-step explanation:

Answer: The answer to the question is option A

Step-by-step explanation:

Answer:

(√3)/3

Step-by-step explanation:

tan ø = opp/adj

tan ø = (1/2)/((√3)/2)

tan ø = ½ * 2/(√3)

tan ø = 1/(√3) then make it rational

tan ø = (√3)/3

Answer:

1.5x = 7.5   (a)

Step-by-step explanation:

If Billy has $7.50 remaining, then he can buy x no. of boxes.

Each box costs $1.50

So, 1.5x = 7.5

Answer:

I gave you most of the answer. I'll let you check my work and find the point using the solution.

Step-by-step explanation:

The first thing we do is we divide by negative one in the first equation to get

y = -x.

-3x + 3y = -36

Plug in y = -x and get

-3x + 3(-x) = -36

= -3x - 3x = -36

This equals -6x = -36

divide both sides by -6 and you get 6. 6 is your x value

Plug 6 back in to the second equation.

-3x + 3y = -36

-3(6) + 3y = -36

-18 + 3y = -36

3y = -18

y = -6

We can say that Raymond's claim of an average typing speed of 89 words per minute may be underestimated based on the sample data collected.

In this scenario, the term "average" refers to Raymond's claimed typing speed of 89 words per minute, while "sample" refers to the 15 trials that Raymond conducted during his practice session. To determine whether there is sufficient evidence to conclude that Raymond's mean typing speed is greater than 89 words per minute, we need to conduct a hypothesis test. Our null hypothesis (H0) is that Raymond's mean typing speed is equal to 89 words per minute, while our alternative hypothesis (Ha) is that his mean typing speed is greater than 89 words per minute. We can use a one-sample t-test to test this hypothesis. Using the sample data provided, we can calculate the t-statistic as follows:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
In this case, the sample mean is 95.5, the population mean (based on Raymond's claim) is 89, the sample standard deviation is unknown, and the sample size is 15. However, since we are assuming that the population standard deviation is unknown, we will use a t-distribution with 14 degrees of freedom.
Using a t-table (or calculator), we can find the critical t-value for a one-tailed test with 14 degrees of freedom and a 1% significance level to be 2.977. If our calculated t-statistic is greater than this critical value, we can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.
Plugging in the values from our sample data, we get:
t = (95.5 - 89) / (sample standard deviation / sqrt(15))
We don't know the sample standard deviation, but we can estimate it using the sample standard deviation formula:
s = sqrt(sum((xi - x)^2) / (n - 1))
where xi is the typing speed for trial i, x is the sample mean, and n is the sample size. Using the data provided, we get:
s = sqrt((sum((xi - 95.5)^2)) / (15 - 1))
s = 9.9
Plugging this value into our t-statistic equation, we get:
t = (95.5 - 89) / (9.9 / sqrt(15))
t = 3.57
Since this calculated t-statistic is greater than our critical t-value of 2.977, we can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that Raymond's mean typing speed is greater than 89 words per minute. Therefore, we can say that Raymond's claim of an average typing speed of 89 words per minute may be underestimated based on the sample data collected.

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The change in electric potential energy of an alpha particle is:

1.3V/cm

"Information available from the question"

In a region where there is a uniform electric field, the potential, v1, is 1. 3 v at position y1=26 cm.

At position y2=28 cm , the potential, v2, is 3. 9 v.

Now, According to the question:

Calculation of magnitude:

Since  V1 is 1.3 V at position y1=26 cm. At position y2=28 cm, the potential, V2, is 3.9 V

So, We know that

\(E =\frac{V_2-V_1}{Y_2-Y_1}\)

\(E=\frac{3.9-1.3}{28-26}\)

\(E=\frac{2.6}{2}\)

E = 1.3V/cm

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