Express in the form
1
:
n
8
:
24

Answer: If x represents the number of hours that Ryan rides his bike, and y represents the total number of miles that he rides, we can write the equation relating x and y as:

y = 12x + 5

This is a linear equation in slope-intercept form, where the slope is 12 (the rate at which Ryan rides, in miles per hour) and the y-intercept is 5 (the number of miles Ryan has already ridden).

To predict how many minutes it will take for Ryan to ride a total of 60 miles, we can substitute y = 60 into the equation and solve for x:

60 = 12x + 5

55 = 12x

x = 55/12

To convert this to minutes, we need to multiply by 60, since there are 60 minutes in an hour:

x (in minutes) = (55/12) * 60

x (in minutes) ≈ 275

Therefore, it will take Ryan approximately 275 minutes (or 4 hours and 35 minutes) to ride a total of 60 miles.

Step-by-step explanation:

Answer:

Hello,

Step-by-step explanation:

3)

\(x^2-4x+3=0\\x^2-3x-x+3=0\\x(x-3)-(x-3)=0\\(x-3)(x-1)=0\\\\x-intercepts\ are\ x=3\ or\ x=1\)

4)

\(-x^2-8x+12=0\\x^2+8x-12=0\\(x^2+2*4x+16)-16-12=0\\\\(x+4)^2-28=0\\\\\\(x+4-2\sqrt{7} )((x+4+2\sqrt{7} )=0\\\\x-intercepts\ are \ x=-4+2\sqrt{7}\ and\ x=-4-2\sqrt{7}\\\\\)

5)

\(f(x)=-3(x-7)(x+4)\\=-3(x^2-3x-28)\\\\=-3(x^2-2*\dfrac{3}{2} *x+\dfrac{9}{4} )+\dfrac{27}{4} +84\\\\=-3(x-\dfrac{3}{2})^2+\dfrac{363}{4} \\\\\\Vertex\ is\ (\dfrac{3}{2},\dfrac{363}{4})\)

On average it take each team member to run 100 meters is 11.9125 seconds.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, Chris, Kiona, Seiko, and Dwayne each run 100 meters in a relay dod race.

Chris runs his part of the race in 12.35 seconds, Kiona takes 13.12 seconds, and Seiko takes 11.91 seconds.

a) The team wants to break the school record of 48.92 seconds.

Time taken by Dwayne = 48.92-(12.35+13.12+11.91)

= 48.92-37.38

= 11.54 seconds

So, Dwayne has taken 11.54 seconds

b) The team sets a new record of 47.65 seconds for the relay race.

Here, speed = 400/47.65

= 8.4 meter per second

So on average, 8.4 meter per second the team members run per second

c) Average = 47.65/4

= 11.9125 seconds

So, on average, the team members run 11.9125 seconds

Therefore, on average it take each team member to run 100 meters is 11.9125 seconds.

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Answer:

b

Step-by-step explanation:

=0-(-x)

=0-×-x

=0+x

=x

Answer:

c

Step-by-step explanation:

Answer:

c.

The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Based on the given data, the correct circle graph representation would be: A circle graph titled "Social Media Usage" with four sections labeled "Tweeter 17 percent", "VidTok 48 percent", "Headbook 25 percent", and "Picturegram 10 percent".

This representation aligns with the data in the table, where the number of students using each social media platform is as follows:

Tweeter: 17 percent of 500 students (85 students)

VidTok: 48 percent of 500 students (240 students)

Headbook: 25 percent of 500 students (125 students)

Picturegram: 10 percent of 500 students (50 students)

The circle graph visually represents the proportions accurately, with the largest section representing VidTok (48 percent), followed by Headbook (25 percent), Tweeter (17 percent), and finally Picturegram (10 percent). Each section's size corresponds to the relative number of students using each social media platform, as indicated in the table

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Answer:

R4ARAQuestion

Carl and Stephen and Brittney completed inQuestion

Carl and Stephen and Brittney completed in a shot put competition .Stephen's toss was 4.08 feet farther than Brittney's. Carl's toss was 2.14 shorter then Stephen's ​ a shot put competition .Stephen's toss was 4.08 feet farther than Brittney's. Carl's toss was 2.14 shorter then Stephen's ​RARRARAGG

Step-by-step explanation:

Yes, I can find the slope of a line and type the correct code. The SLOPE function will return the slope of the linear regression line that best fits the data.

The slope of a line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. The formula for finding the slope of a line is (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line.

The slope is a measure of how steep the line is. It can be positive, negative, zero, or undefined. The code for finding the slope of a line in ALL CAPS with no spaces is SLOPE.

To use this function in Excel, you need to provide the range of x-values and the range of y-values.

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The coefficient B in the partial fraction expansion is 0.To find the coefficient B in the partial fraction expansion of the Laplace transform, we can rewrite the expression as follows:

Y(s) = A/(s+1) + (Bs+C)/(s^2+9)

To determine the value of B, we need to find a common denominator for the two fractions on the right-hand side. The common denominator is (s+1)(s^2+9).

Multiplying the first fraction A/(s+1) by (s^2+9)/(s^2+9), we have:

Y(s) = A(s^2+9)/[(s+1)(s^2+9)] + (Bs+C)/(s^2+9)

Combining the fractions, we get:

Y(s) = [A(s^2+9) + (Bs+C)]/[(s+1)(s^2+9)]

Now, let's compare the numerators of the right-hand side with the denominator:

A(s^2+9) + (Bs+C) = B(s+1)(s^2+9) + C(s+1)

Expanding the right side:

A(s^2+9) + Bs^3 + Bs^2 + 9B + C = Bs^3 + Bs^2 + 9B + Cs + B + C

Matching the coefficients of the terms on both sides:

A = B

0 = B

0 = 9B + C

0 = B + C

From the second equation, we can see that B must be zero.

Therefore, the coefficient B in the partial fraction expansion is 0.

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The equation that could be solved to get the same answer is B 5(x+23)=44.5

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

WE are given that Julia correctly solved a math problem by first dividing 44.5 by 5, then subtracting 23 from the answer.

First;

44.5 /5 = 8.9

Then subtracting 23 from it

8.9 - 23

= 14.1

Therefore, we can write as 5(x+23)=44.5

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Andrew will earn a total of $230 over 10 weeks. This is calculated by multiplying the first number in the series (4) by 10, plus the second number in the series (17) multiplied by 9, plus the third number in the series (30) multiplied by 8, and so on until the 10th number in the series.

To summarize, Andrew's total earnings over 10 weeks would be:

\(4 x 10 + 17 x 9 + 30 x 8 + 49 x 7 + 74 x 6 + 109 x 5 + 154 x 4 + 209 x 3 + 274 x 2 + 349 x 1 = 230.\)

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(a) (i) Average velocity = change in displacement / change in time = 20 feet / 1 second = 20 feet per second.

(ii) Average velocity = change in displacement / change in time = 14 feet / 0.5 seconds = 28 feet per second.

(iii) Average velocity = change in displacement / change in time = 1.76 feet / 0.1 seconds = 17.6 feet per second.

(b) To find the instantaneous velocity at t = 2 seconds, we substitute t = 2 into the velocity function: v(2) = 100 - 32(2) = 100 - 64 = 36 feet per second

(a) To find the average velocity of the projectile over the given time intervals, we need to calculate the change in displacement divided by the change in time for each interval. The average velocity is a vector quantity, so we need to consider both magnitude and direction.

(i) [2,3]:

To find the average velocity over the interval [2,3], we can calculate the displacement at t = 3 and t = 2, and then divide it by the time difference.

At t = 3:

s(3) = 100 * 3 - 16 * 3^2 = 300 - 144 = 156 feet.

At t = 2:

s(2) = 100 * 2 - 16 * 2^2 = 200 - 64 = 136 feet.

Change in displacement = s(3) - s(2) = 156 - 136 = 20 feet.

Change in time = 3 - 2 = 1 second.

Average velocity = change in displacement / change in time = 20 feet / 1 second = 20 feet per second.

(ii) [2,2.5]:

Similarly, for the interval [2,2.5], we can calculate the displacement at t = 2.5 and t = 2, and then divide it by the time difference.

At t = 2.5:

s(2.5) = 100 * 2.5 - 16 * 2.5^2 = 250 - 100 = 150 feet.

At t = 2:

s(2) = 100 * 2 - 16 * 2^2 = 200 - 64 = 136 feet.

Change in displacement = s(2.5) - s(2) = 150 - 136 = 14 feet.

Change in time = 2.5 - 2 = 0.5 seconds.

Average velocity = change in displacement / change in time = 14 feet / 0.5 seconds = 28 feet per second.

(iii) [2,2.1]:

For the interval [2,2.1], we can follow the same process.

At t = 2.1:

s(2.1) = 100 * 2.1 - 16 * 2.1^2 = 210 - 72.24 = 137.76 feet.

At t = 2:

s(2) = 100 * 2 - 16 * 2^2 = 200 - 64 = 136 feet.

Change in displacement = s(2.1) - s(2) = 137.76 - 136 = 1.76 feet.

Change in time = 2.1 - 2 = 0.1 seconds.

Average velocity = change in displacement / change in time = 1.76 feet / 0.1 seconds = 17.6 feet per second.

(b) To find the instantaneous velocity at t = 2 seconds, we can use the concept of limits and algebra.

The instantaneous velocity is the limit of the average velocity as the time interval approaches zero. We can find it by taking the derivative of the position function with respect to time, which gives us the velocity function.

s(t) = 100t - 16t^2

Taking the derivative with respect to t:

v(t) = d(s(t))/dt = 100 - 32t

To find the instantaneous velocity at t = 2 seconds, we substitute t = 2 into the velocity function: v(2) = 100 - 32(2) = 100 - 64 = 36 feet per second

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Answer:

sure what do you need help on

Step-by-step explanation:

Answer:

whats the question?

Triangles HIJ and H'I'J have undergone rotation as the exact sort of transformation.

When we translate, we move a figure in any direction. When we reflect, we turn a figure or a line over. The act of rotating a figure around a point is known as rotation. Enlarging or contracting a figure is called dilation. Congruent transformations include rotations, translations, and reflections. A congruence transformation is not resizing. A figure turned over a line of reflection is called a reflection.

Translation, rotation, reflection, and dilation are the four basic forms of transformations. Get the two triangles to face in the same direction, or in the same orientation, to check if they resemble one another. You accomplish this by turning one shape so that it is in alignment with the other. A rotation is the name given to such a change.

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The speed of the water wave is 2.0 meters per second.

The speed of a wave is calculated by dividing the distance traveled by the time it takes to travel that distance. In this case, the distance traveled by the water wave is 10.0 meters, and the time taken is 5.0 seconds.

To determine the speed, we use the formula:

Speed = Distance / Time

Substituting the given values, we have:

Speed = 10.0 meters / 5.0 seconds = 2.0 meters per second

Therefore, from the given information, we can determine that the speed of the water wave is 2.0 meters per second.

This information about the speed of the water wave is useful for various purposes. It allows us to understand how quickly the wave is propagating through the medium. It also helps in analyzing wave behavior, such as interference, reflection, or refraction, and studying the characteristics of the medium through which the wave is traveling. Additionally, the speed of the wave can be used in calculations involving wave frequencies, wavelengths, and periods.

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Step-by-step explanation:

You can factor out a '10' from each of the terms

10 ( -6 + 6n^2 + 5 n^3 )        

If you meant    - 60 n + 60 n^2 + 50 n^3

   you can factor out a 10 n

     10n ( -6 + 6n + 5n^2)

As described in statistics the mean standard deviation of the headway is 0.890

what is the statistics ?

The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to a problem in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.

solution:

P(0.995 ≤ x ≤ 1.445) = F(1.445) - F is the given mean value (0.995).

The distribution's cdf is

f(x) = { (1 - 1/x⁶ , x > 1) (0. x ≤ 1)

F(1.445) = 1 - (1/(1.445)⁶)

F(0.995) = 0

Now, using the values of F(1.445) and F(0.995) in P( 0.995 ≤ x ≤ 1.445) to get F(1.445) - F(0.995):

P( 0.995 ≤ x ≤ 1.445)

=1 - (1/(1.445)⁶) - 0

=0.890

Therefore the mean value of standard deviation is 0.890

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The limit doesn't exist.

The value that a function (or sequence) approaches when the input (or index) gets closer to a particular value is known as a limit. Calculus and mathematical analysis are impossible without limits, which are also required to determine continuity, derivatives, and integrals.

In addition to being closely related to limit and direct limit in category theory, the idea of a limit of a sequence is further generalized to include the concept of a limit of a topological net.

A function's limit is typically expressed in formulas as

\(\lim_{x \to c } F(x) = L\)

It is typically used to assign values to specific functions at locations where none are defined while maintaining consistency with existing values.

\(F(x) = -x+8 ,x\leq 0\)

\(F(x) = 4x+9 , if x > 0\)

\(\lim_{x \to 0^{+} } F(x) = \lim_{n \to 0^{+} } (4x+9) = 9\)

\(\lim_{x \to 0^{-} } F(x) = \lim_{x \to 0^{-} } (-x+8) =8\)

\(\lim_{x \to 0^{+} } F(x) \neq \lim_{x \to 0^{-} } F(x)\)

So limit doesn't exist

For limit to exist

\(\lim_{x \to 0^{+} } F(x) = \lim_{x \to 0^{-} } F(x) = \lim_{x \to 0} f(x)\)

must be satisfied

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Answer:

Step-by-step explanation:

Put ' - 3' whre 'x' is and compute the answer

f(-3) = 3 (-3) - 7

      = -9 - 7 = - 16

Answer:

Below

Step-by-step explanation:

This IS basically an experiment with  15 hits out of 45 at-bats

   15/45 = .333    or  33.3 %  experimental probability

Answer:

--------------------------------------

Given:

Find the experimental probability.

Probability of getting a hit is:

1. (A)  Section titles  (lines starting with %% followed by a space and then a title).

2. (B)  Automatically pause code execution at the start of each section when running a script. (This is not a purpose of code in the MATLAB Editor.)

3. All these functions operate element-wise on each element of the matrix X and return a matrix of the same size.

The source of the section headers in the resulting document when publishing a script from the MATLAB Editor is:

a. Section titles (lines starting with %% followed by a space and then a title).

The statement that is not true about the purpose of code in the MATLAB Editor is:

b. Automatically pause code execution at the start of each section when running a script. (This is not a purpose of code in the MATLAB Editor.)

3. The commands that return a matrix of the same size as x, given a non-scalar matrix X, are:

a. mean(x)

b. sin(x)

c. log(x)

d. sum(x)

e. std(x)

f. sqrt(x)

All these functions operate element-wise on each element of the matrix X and return a matrix of the same size.

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The correct answer is B i.e. Standard Error of the Mean (SE) = σ / √(n)

The measure of the variability of the sample means, also known as the standard error of the mean, can be calculated using the formula:

Standard Error of the Mean (SE) = σ / √(n)

sigma is the population standard deviation,

n is the sample size.

The standard error of the mean represents the variability or dispersion of the sample means obtained from repeated samples of size n from a population. It indicates how much the sample means are likely to differ from the true population mean.

The smaller the standard error of the mean, the less variability is expected among the sample means, indicating a more precise estimate of the population mean.

Therefore, the correct answer is B i.e. Standard Error of the Mean (SE) = σ / √(n)

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Given question is incomplete, the complete question is below

A measure of variability of the sample means xbar in repeated samples of n observations randomly selected from a given population is

a. s

b. σ/√(n)

c. s/√(n)

d. σ

Answer:

The formula is \(a_n = 3n-2\)

The 14th term is 40, in other words, \(a_{14} = 40\)

========================================================

Explanation:

The given sequence is 1, 4, 7, 10, ...

Subtract each adjacent term:

This shows that each term is increasing by 3. This is the common difference, so d = 3.

The first term is \(a_1 = 1\)

The nth term of the arithmetic sequence is...

\(a_n = a_1 + d(n-1)\\\\a_n = 1 + 3(n-1)\\\\a_n = 1 + 3n-3\\\\a_n = 3n-2\\\\\)

As a check, let's plug in say n = 3 to find that:

\(a_n = 3n-2\\\\a_3 = 3(3)-2\\\\a_3 = 9-2\\\\a_3 = 7\\\\\)

The third term is 7, which matches with the sequence given to us. I'll let you confirm the other values.

-----------

We'll repeat this idea but now for n = 14 to find the 14th term of the sequence.

\(a_n = 3n-2\\\\a_{14} = 3(14)-2\\\\a_{14} = 42-2\\\\a_{14} = 40\\\\\)

The 14th term is 40.

You can make a table of values to help confirm the answer. In the first column you'll have the values of n (1,2,3,...) all the way up to 14. The second column will consist of the sequence 1, 4, 7, 10, ... each time going up by 3 until you reach the 14th term of 40.

(30+6)+(40+7)=86

add all those steps and see what you get

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

Area is 16 square unites

Since it is a cube..

length of one side should be

\( \sqrt{16} \)

so one side length is 4 units

Now..volume of a cube is x^3

so,

volume = 4^3

= 64 cubic units

Answer: 64

Step-by-step explanation: First I noticed that the cube had 6 faces which meant it was a square. The area of the square units was 16. So the perimeter is 4 because 4 multiplied by 4 is 16. Then I multiplied 4 three times because the formula for this type of shape is V = whl (volume = width, height, and length). 4 multiplied by 4 is 16. 16 multiplied by 4 is 64. This is how I got my answer. Hope it helps!

Answer:

Step-by-step explanation:

the equation is y=mx+b

the b part is the y-intercept

so in your equation... the y=intercept would be 7/6

We want to find the slope of the line that connects points C' and D'. We will find that the slope is -3/7.

First, we start with the points:

Now we create points C' and D' by translating points C and D to the left by 6 units, this means that we need to subtract 6 in the x-value of each point, so we will have:

And we know that if a line passes through points (x₁, y₁) and (x₂, y₂) the slope is given by:

\(a = \frac{y_2 - y_1}{x_2 - x_1}\)

Then the slope that connects points C' and D' is:

\(a = \frac{5 - 8}{2 - (-5)} = \frac{-3}{7}\)

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