the length of a rectangle is three times the width. Determine the dimensions that will give a total area of 27 meters

Answer:

C. 15/16

Step-by-step explanation:

A. Divide by 3

B. Divide by 5

C. Can't divide by anything.

D. Divide by 4

Answer:

C

Step-by-step explanation:

21/24 = 7/8

35/40 = 7/8

7/8 ≠ 15/16

14/16 ≠ 15/16

28/32 = 7/8

Answer:

68.26

Step-by-step explanation:

The symbol σ represents standard deviation. 1 standard deviation (in both directions) under a normal distribution= 68.26

Answer:

68%.

Step-by-step explanation:

The 68-95-99.7 rule (also know as the Empirical Rule) states that 68% of the data lies within 1 standard deviation of the mean. 95% of the data lies within 2 standard deviations of the mean. 99.7% of the data lies within 3 standard deviations of the mean.

According to the diagram, the area shaded shows data within 1 standard deviation of the mean (one standard deviation to the left, and one to the right). That means that 68% of the data is within the shaded area.

Hope this helps!

Find Q

Not safe

Apply Pythagorean theorem

PR²=4²+15²=16+225=241

Answer:

a) not safe

b) 15.5 ft (nearest tenth)

Step-by-step explanation:

Tan trig ratio

\(\sf \tan(\theta)=\dfrac{O}{A}\)

where:

Given:

Substituting the given values into the formula and solving for x:

\(\implies \sf \tan(x)=\dfrac{4}{15}\)

\(\implies \sf x=\tan^{-1}\left(\dfrac{4}{15}\right)\)

\(\implies \sf x=14.9^{\circ}\:(nearest\:tenth)\)

As 14.9° is not between 18° and 27°, the roof is not safe.

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

Pythagoras’ Theorem

\(\sf a^2+b^2=c^2\)

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substituting the given values into the formula and solving for PR:

\(\implies \sf 15^2+4^2=PR^2\)

\(\implies \sf 225+16=PR^2\)

\(\implies \sf PR^2=241\)

\(\implies \sf PR=\sqrt{241}\)

\(\implies \sf PR=15.5\:ft\:(nearest\:tenth)\)

Answer:\(96cm^2\\\)

Step-by-step explanation:

64= \(x^3\\\)

\(\sqrt[3]{64} =4\)

So a side is 4, and surface area of one side is 4x4 = \(16cm^2\)

cude has 6 faces, 16*6 = \(96cm^2\\\)

Answer:

96 cm²

Step-by-step explanation:

If the side of a cube is a, then volume = a³

There are six surfaces for a cube and each surface has an area of a²
So total surface area = 6a²

Since we are given volume = 64 cm³, each side must be ∛64 = 4 cm

So total surface area = 6 x 4² = 6 x 16 = 96 cm²

Answer:

2664.8

Step-by-step explanation:

Answer: 3.20 hours

Step-by-step explanation:

Hi, to answer this question, first we have to convert the kilometers into miles:

Since: 1 mile = 1.61 km

For 350km:

350 /1.61 = 217.39 miles  

Next, we have to apply the next formula:

Replacing with the values given:

Time = 217.39 mi / 68 mi/h = 3.20 hours

Feel free to ask for more if needed or if you did not understand something  

Parallel lines have the same slopes.

So if line s has a slope of -3/2, line t also has a slope of -3/2.

The vector 2x + y is equal to (2 + 5√3/2, 5/2), and its direction is approximately 19.11° with respect to the positive x-axis.

To determine 2x + y, we need to perform vector addition. Given that the vectors x and y have magnitudes of 2 and 5, respectively, and there is an angle of 30° between them, we can use trigonometry to find their components.

For vector x:

x = 2(cos(0°), sin(0°)) = (2, 0)

For vector y:

y = 5(cos(30°), sin(30°)) = (5 * cos(30°), 5 * sin(30°)) = (5 * √3/2, 5 * 1/2) = (5√3/2, 5/2)

Now, we can perform vector addition:

2x + y = (2, 0) + (5√3/2, 5/2) = (2 + 5√3/2, 0 + 5/2) = (2 + 5√3/2, 5/2)

Therefore,

2x + y = (2 + 5√3/2, 5/2).

To determine the direction of 2x + y, we can calculate the angle it forms with the positive x-axis using the arctan function:

θ = arctan((5/2) / (2 + 5√3/2))

Using a calculator, we find that θ ≈ 19.11°.

Hence, the direction of 2x + y is approximately 19.11° with respect to the positive x-axis.

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The regression equation for predicting y from x in the given set of data is y = 1.909x + 2.227. This equation represents the line of best fit that minimizes the sum of squared residuals between the predicted values and the actual values of y based on the corresponding values of x.

To find the regression equation, we use the method of least squares to fit a line to the data points. The equation takes the form of y = mx + b, where m is the slope (coefficient of x) and b is the y-intercept. Using the given set of data, we calculate the slope (m) and the y-intercept (b) to determine the regression equation.

By applying the formulas for m and b:

m = (nΣxy - ΣxΣy) / (nΣx² - (Σx)²)

b = (Σy - mΣx) / n

where n is the number of data points, Σxy is the sum of the products of x and y, Σx and Σy are the sums of x and y respectively, and Σx² is the sum of the squares of x.

By substituting the values from the given data set into these formulas, we obtain the values for m and b. The resulting regression equation for predicting y from x in this case is y = 1.909x + 2.227. This equation represents the line that best fits the data points and can be used to estimate or predict the value of y for any given x within the range of the data.

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Answer: C

Step-by-step explanation:

For a, the initial height of the ball is 1.5 meters. For b, the maximum height of the ball is 51.5 meters. For c, the ball hits the ground again after approximately 10.0743 seconds.

a. The initial height of the ball can be determined by finding the value of h(0) in the given function.

h(t) = -2t^2 + 20t + 1.5

To find the initial height, we substitute t = 0 into the equation:

h(0) = -2(0)^2 + 20(0) + 1.5

    = 0 + 0 + 1.5

    = 1.5 meters

Therefore, the initial height of the ball is 1.5 meters.

b. The maximum height of the ball can be determined by finding the vertex of the parabolic function. The vertex of a quadratic function in the form ax^2 + bx + c is given by (-b/2a, f(-b/2a)), where f(x) represents the function.

In this case, a = -2, b = 20, and c = 1.5. Therefore, the x-coordinate of the vertex can be found using -b/2a:

x = -20 / (2 * -2)

 = -20 / -4

 = 5

To find the maximum height, substitute x = 5 into the equation:

h(5) = -2(5)^2 + 20(5) + 1.5

    = -2(25) + 100 + 1.5

    = -50 + 100 + 1.5

    = 51.5 meters

Therefore, the maximum height of the ball is 51.5 meters.

c. The ball hits the ground when its height becomes 0. We can find the time at which this happens by setting h(t) equal to 0 and solving for t.

0 = -2t^2 + 20t + 1.5

To solve this quadratic equation, we can either factor it or use the quadratic formula. Factoring may not be possible in this case, so let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values a = -2, b = 20, and c = 1.5 into the formula, we get:

t = (-20 ± √(20^2 - 4(-2)(1.5))) / (2 * -2)

 = (-20 ± √(400 + 12)) / (-4)

 = (-20 ± √412) / (-4)

The square root of 412 is approximately 20.297, so we have:

t = (-20 ± 20.297) / (-4)

Using both the positive and negative square root, we get two solutions:

t1 = (-20 + 20.297) / (-4) ≈ -0.0743 seconds

t2 = (-20 - 20.297) / (-4) ≈ 10.0743 seconds

Since time cannot be negative in this context, the ball hits the ground again after approximately 10.0743 seconds.

The initial height of the ball is 1.5 meters. The maximum height of the ball is 51.5 meters. The ball hits the ground again after approximately 10.0743 seconds.

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Both functions decrease at (-1, 2)

The complete question is added as an attachment

The polynomial function f(x) is represented by the graph.

From the graph, the polynomial function decreases at (-2, 2)

The absolute function is given as;

f(x) = =5|x + 1| + 10

The vertex of the above function is

Vertex = (-1, 10)

Because a is negative (a= -5), the vertex is a maximum.

This means that the function decreases at (-1, ∞)

So, we have

(-2, 2) and (-1, ∞)

Combine both intervals

(-1, 2)

This means that both functions decrease at (-1, 2)

See attachment 2 for the number line that represents the interval where both functions are decreasing

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Jordan's average rate over the last 2 hours of her trip is 9 miles/hour.

To find Jordan's average rate over the last 2 hours of her trip,

we need to calculate the distance she traveled during that time period.

We know that Jordan was initially 20 miles away from her house and after 4 hours, she was 38 miles away. Therefore, she traveled a distance of 38 miles - 20 miles = 18 miles in the first 4 hours.

To find her average rate over the last 2 hours, we divide the distance traveled in those 2 hours by the time taken. The distance traveled in the last 2 hours is 18 miles (since she traveled 18 miles in the first 4 hours), and the time taken is 2 hours.

Average rate = Distance / Time

Average rate = 18 miles / 2 hours

Average rate = 9 miles per hour

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it is seen that if the number of people in the group is n = 23, the probability that at least two people will have the same birthday is at least 1/2.

Let P(A) be the probability that in a randomly selected group of n people, at least two people have the same birthday.

If we assume that the year has 365 days, then the number of ways to select n people with different birthdays is n x (n-1) x (n-2) x ... x (n-364).

the probability of selecting n people with different birthdays is P(A') = n(n - 1)(n - 2)...(n - 364)/365nThen, the probability that at least two people in a group of n have the same birthday is given by P(A) = 1 - P(A').

We need to find the smallest value of n such that P(A) ≥ 1/2.Let's solve for this.Let us find n such that P(A) ≥ 1/2.

By using the complement rule, 1-P(A') = P(A).Then:1 - n(n - 1)(n - 2)...(n - 364)/365n ≥ 1/2n(n - 1)(n - 2)...(n - 364)/365n ≤ 1/2(2)n(n - 1)(n - 2)...(n - 364) ≤ 365n/2Now, take the natural logarithm of both sides and simplify as follows:ln[n(n - 1)(n - 2)...(n - 364)] ≤ ln[365n/2]nln(n) - ln[(n - 1)!] - ln[(n - 2)!] - ... - ln[2!] - ln[1!] ≤ ln[365n/2]

Therefore, we need at least 23 people in the group for the probability of two or more people having the same birthday to be at least 1/2.

This is because n = 23 is the smallest number for which the inequality holds, and therefore, it is the smallest number of people required to ensure that the probability of two or more people having the same birthday is at least 1/2.

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Answer:

1) (x - 9)(x + 2)  ==> trinomials

2) (s + z) (3m - 2n)  ==> factorising by parts

3) (x + 2)(5x + 3)  ==> factorising with a leading coefficient

4) 9y²(3y² - 2)  ==> GCF

5) (4m - 12)(4m + 12)  ==> DoPS

Step-by-step explanation:

1). Find multiples of -18 that add up to -7

Multiples of -18 : (only one number can be negative, because positive*negative = negative)

1, 18 or 3, 6 or 2, 9

Only one pair adds up to -7 which is -9 + 2

Hence ==> (x - 9)(x + 2)

2). Find the common things between the terms and factorise it out  

3m(s + z) - 2n(s + z)

Since the terms inside the brackets are the same, you simplify it to:

(s + z) (3m - 2n)

3). Multiply the first coefficient with the last coefficient: 5(6) = 30

Find two numbers that multiply to 30 and add up to the middle coefficient -13.

Multiples of 30 are: 1, 30 or 2, 15 or 3, 10 or 5,6, but only one pair would add to -13 and that is 3 and 10

So the next step is to write it in this form: 5x² + 10x + 3x + 6

Factorise: 5x(x + 2) + 3(x + 2)

(x + 2)(5x + 3)

4). Find the greatest common factor within 27y⁴ and 18y², which is 9y²

9y²(3y² - 2)

5). Square root each number: √16 = 4 and √144 = 12

(4m - 12)(4m + 12)

Answer:

ms finch

Step-by-step explanation:

.

Answer:

This is your answer ☺️☺️☺️

The solution is Option D.

x = { 1 , 2 , 3 }

y = { 150 , 300 , 450 }

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be A

Now , the points given be P ( x₁ , y₁ ) , Q ( x₂ , y₂ ) and R ( x₃ , y₃ )

where  P ( x₁ , y₁ )  = P ( 5 , 750 )

and Q ( x₂ , y₂ ) = Q ( 6 , 900 )

and R ( x₃ , y₃ ) = R ( 7 , 1050 )

Now , the slope of the line is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 900 - 750 ) / ( 6 - 5 )

              = 150

Therefore , the slope is 150

Now , the equation of line is

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 750 = 150 ( x - 5 )

y - 750 = 150x - 750

Adding 750 on both sides of the equation , we get

y = 150x

Therefore , the equation of line is y = 150x

And , when x = 1

y = 150

when x = 2

y = 2 x 150

  = 300

when x = 3

y = 3 x 150

  = 450

Hence , the table will be

x = { 1 , 2 , 3 }

y = { 150 , 300 , 450 }

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Here's the explanation :

we know,

\( \boxed{\sin( \theta) = \frac{opposite \: \: side}{hypotenuse} }\)

so,

\( \sin(k) = \dfrac{11}{61} \)

hence, option b. is correct

Answer:

29

Step-by-step explanation:

3 x 8 = 54 - 25 = 29

Answer:

tan(y) = 8/6

Step-by-step explanation:

Tangent of measurement is the opposite side of focused measurement to the adjacent side of focused measurement.

In this problem, we are given with focused measurement of y; hence, tan(y).

Find the opposite side of focused measurement, the opposite side of measurement y is 8 ft.

Find the adjacent (the side that connects between right angle to the focused measurement) of focused measurement, the adjacent side of measurement y is 6 ft.

Since tan(y) = opposite of measurement y to adjacent of measurement y. Hence, tan(y) = 8/6

The probability that exactly one of the computers will be defective is 0.141

To calculate the probability of exactly one defective computer being selected out of four computers, we can use the binomial distribution formula

P(X = k) = (n choose k) × p^k × (1 - p)^(n - k)

where P(X = k) is the probability of exactly k successes (in this case, one defective computer), n is the total number of trials (in this case, four computers being selected), p is the probability of success (in this case, the probability of selecting a defective computer), and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n.

The probability of selecting a defective computer is 4/15, since there are 4 defective computers out of 15 in total. Therefore, the probability of selecting exactly one defective computer out of four is:

P(X = 1) = (4 choose 1) × (4/15)^1 × (11/15)^3

= 4 × 4/15 × 1331/3375

= 0.141

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The given question is incomplete, the complete question is:

A computer retail store has 15 personal computers in stock. A buyer wants to purchase 4 of them. Unknown to either the retail store or the buyer, 4 of the computers in stock have defective hard drives. Assume that the computers are selected at random. What is the probability that exactly one of the computers will be defective?

Answer: 28282

Step-by-step explanation:

I think

The Paint Process is out of control if more than two samples indicate it. if two or fewer samples indicate an issue, it indicates that the process is under control.

Based on the information provided, the number of samples indicating that the Paint Process is out of control cannot be determined without the actual data. The options A) >2, B) 2, C) 1, and D) 0 are insufficient to draw a conclusion regarding the number of out-of-control samples.

To assess whether the Paint Process is out of control, it is necessary to analyze the specific data samples obtained from the process. Various statistical techniques, such as control charts, can be used to monitor process performance and identify any instances where the process is deviating from its desired specifications.

If you can provide the actual Paint Data Sample, including the relevant parameters and measurements, I can assist you in analyzing the data and determining the number of samples indicating an out-of-control Paint Process.

To determine if the Paint Process is out of control, we need to analyze the data samples. The given options suggest that we should look at the number of samples indicating an out-of-control process. If more than two samples show signs of being out of control, it suggests that the Paint Process is not within acceptable limits.

However, if two or fewer samples indicate an issue, it indicates that the process is under control. Unfortunately, the provided information about the Paint Data Sample is missing, so we cannot accurately determine the number of samples indicating an out-of-control process. To make a conclusive assessment, we would need access to the actual Paint Data Sample.

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Answer:

Step-by-step explanation:

Put them in your calculator. I think you'll find 2.95 is larger by 0.001

Do it like this 2.95 - 2.949 = 0.001

Direct labor efficiency variance = $6,100 F.

Given that

Standard labor-hours per unit of output     8.5 hours

Standard labor rate                                     $12.30 per hour

Standard labor hours allowed                          6,800 hours (800 units *                                         8.5 hours allowed)

The following data pertain to operations concerning the product for the last month:

Actual hours worked  6,300 hours

Actual total labor cost  $74,970

Actual output                  800 units

We can determine the labor efficiency variance using the following equation:

1. Direct labor efficiency variance = (Standard hours allowed - Actual labor hours) * Standard rate

2. Direct labor efficiency variance = (6,800 hours - 6,300 hours) * $12.20

3. Direct labor efficiency variance = $6,100 F

The variance is favorable as the actual labor hours used are less than the standard hours allowed.

Hence the answer is Direct labor efficiency variance = $6,100 F.

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Answer:

The equation that models the amount of money she could raise is written as:

t = 25c

Step-by-step explanation:

Rachel is selling gift cards to raise money for her swim team. Each gift card costs $25.00. If c represents the number of gift cards she sells, , which equation models the amount of money she could raise?

Let t represent the total amount collected

Each gift card costs $25.00.

If c represents the number of gift cards she sells

The equation that models the amount of money she could raise is written as:

t = $25 × c

t = 25c

Answer:

a) 2f(x) = 4x - 2

b) f(2x) = 4x - 1

Explanation:

Given function:

a) 2f(x)

2f(x) = 2(2x - 1)

       = 4x - 2

b) f(2x)

f(2x) = 2(2x) - 1

       = 4x - 1