what is equivalent

2r+(t+r)2

At the bicycle manufacturer, the average cost per bicycle is $77.

To find the average cost per bicycle, we need to find the total cost of making all three bicycles and divide that by the number of bicycles.

The total cost is of the bicycles is given by -

$72 (cost of first bicycle) + $83 (cost of second bicycle) + $77 (cost of third bicycle) = $232

Now to find the average cost per bicycle, we will divide the total cost by the number of bicycles.

Hence, $232 ÷ 3 = $77

Therefore, the average cost per bicycle is $77.

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The magnitude of the x-component of this vector is 9.05m.

The angle of inclination of the vector is calculated as;

θ = 90 ⁰ - 48.4 ⁰

θ = 41.6 ⁰

The magnitude of the x-component of the vector is calculated as;

Vx = 12.1 m x cos ( 41.6 )

Vx = 9.05 m

A vector can be represented by an ordered set of numbers, called components, that indicate the magnitude and direction of the vector in a particular coordinate system. The components of a vector can be added or subtracted using vector addition and subtraction, and multiplied by a scalar (a real number) using scalar multiplication.

Vectors can be visualized as arrows in a two- or three-dimensional space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. Vectors can also be represented as matrices, which can be used to perform various operations on vectors, such as dot product and cross product.

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Complete Question:-

The given statement "A group of normal distributions can have equal arithmetic means but different standard deviations" is True  because the mean and standard deviation are two separate parameters that describe different characteristics of a normal distribution.

The mean is the measure of central tendency and represents the location of the peak of the distribution, while the standard deviation is a measure of the spread of the distribution.

Therefore, it is possible for multiple normal distributions to have the same mean, but different standard deviations. For example, consider two normal distributions with means of 50 and standard deviations of 10 and 20, respectively.

Both distributions have the same mean of 50, but different standard deviations, indicating that one distribution has a tighter cluster of data around the mean, while the other is more spread out.

Therefore, it is important to consider both the mean and standard deviation when analyzing and comparing normal distributions.

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Answer:

-2x = -3-15

-2x = -18

x = +9 :

Answer:

x=9

Step-by-step explanation:

isolate the variable by dividing each side by factors that don't contain the variable

Answer:

4

Step-by-step explanation:

if you take -6 and subtract it by 2 it equals -4

Answer:

Step-by-step explanation:x=π2,3π2

Explanation:

This can be factored as (x2+a)x2+b).⇒(sin2x+3)(sin2x-1)=0⇒

2

x

=

−

3

and

sin

2

x

=

1

⇒

sin

x

=

√

−

3

and

sin

x

=

√

1

⇒

sin

x

=

∅

and

sin

x

=

±

1

⇒

x

=

π

2

,

3

π

2

Hopefully this helps!

The volume of the cylindrical straw of diameter 6 mm and length of 270 mm is 7630.20 mm³

volume of a cylinder = πr²h

Therefore,

Hence,

radius = r = 6 / 2 = 3 mm

volume of the cylinder = 3.14 × 3² × 270

volume of the cylinder = 3.14 × 9 × 270

volume of the cylinder = 7630.2 mm³

Therefore, the volume of the straw is 7630.2 mm³

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The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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Combine like terms.

6x + 5z + 4

Step-by-step explanation:

3x = 12 - 18

3x = (- 6)

X = (-6)/3

x = (-3)

Answer:

To calculate the modified quotas for each state, we can use the divisor method. The divisor (D) is given as 1950, and the total number of seats in the legislature is 100.

To find the modified quota for each state, we divide the population of each state by the divisor and then multiply the result by the total number of seats.

Modified quotas for each state, rounded to two decimal places, using a divisor (D) of 1950:

- State A: 230.26

- State B: 267.69

- State C: 252.31

- State D: 275.90

These modified quotas represent the approximate number of seats each state would receive in the legislature based on their population, using the given divisor. The modified quotas are calculated by dividing the population of each state by the divisor and then multiplying the result by the total number of seats.

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Answer:

19.7ft

Step-by-step explanation:

o^2+a^2=h^2

\dpi{100} h^{2}=(10ft)^{2} +(17ft)^{2}

h^2=100ft^2+289ft^2

h=389ft^2−−−−−√

→19.7ft

Answer:

Step-by-step explanation:

a^2 + b^2 = c^2

where a and b are the legs of the triangle and c is the hypotenuse

so 8^2 + 12^2 = c^2

64 + 144 = c^2

208 = c^2

take the square root of both sides

c = 14.422

Answer:

12. y=30x+45

13. 135 dollars

    y=45+30(3)

    y=45+90

    y=135 dollars

14. 8 full hours

    300=45+30x

    255=30x

    x = 8.5 or 8 full hours

Answer: $200 a week for all 10 lawns. equation: y = 10x + 20

Step-by-step explanation:

1.  This means that at least one car had a speed of 4 miles per hour, which is the slowest speed observed among the 100 cars.

2.  This means that at least one car had a speed of 48 miles per hour, which is the fastest speed observed among the 100 cars.

3. In the situation of cars passing through a busy intersection, this means that half of the cars had a speed of 26 miles per hour or less.

4.  In the situation of cars passing through a busy intersection, this means that 25% of the cars had a speed of 12 miles per hour or less.

5.  In the situation of cars passing through a busy intersection, this means that 25% of the cars had a speed of 36 miles per hour or higher.

The smallest value in the data set is 4 miles per hour. In the situation of cars passing through a busy intersection, this means that at least one car had a speed of 4 miles per hour, which is the slowest speed observed among the 100 cars.

The largest value in the data set is 48 miles per hour. In the situation of cars passing through a busy intersection, this means that at least one car had a speed of 48 miles per hour, which is the fastest speed observed among the 100 cars.

The median is the middle value in the data set when arranged in ascending order. In this case, since we have 100 data points, the median would be the average of the 50th and 51st values. Looking at the given data, the median would be the average of 24 and 28, which is 26 miles per hour. In the situation of cars passing through a busy intersection, this means that half of the cars had a speed of 26 miles per hour or less.

The first quartile (Q1) represents the lower 25% of the data. To find Q1, we look for the value that separates the lowest 25% of the data. In this case, the first quartile is 12 miles per hour. In the situation of cars passing through a busy intersection, this means that 25% of the cars had a speed of 12 miles per hour or less.

The third quartile (Q3) represents the upper 25% of the data. To find Q3, we look for the value that separates the highest 25% of the data. In this case, the third quartile is 36 miles per hour. In the situation of cars passing through a busy intersection, this means that 25% of the cars had a speed of 36 miles per hour or higher.

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When the expression 8√2100x15y9 is simplified, the resulting expression is 2.6 xy(x⁷/⁸)(y¹/⁸)

We need to simplify the given expression

The expression is ⁸√2100x¹⁵y⁹

⁸√2100x¹⁵y⁹ can be written as ⁸√2100  (⁸√x¹⁵)  (⁸√y⁹)

Here the product rule is applied

(xᵃ)ᵇ = xᵃᵇ

(2100)¹/⁸ (x ¹⁵ ) ¹/⁸ (y⁹)¹/⁸

(2100)¹/⁸ (x ¹⁵/⁸ )  (y⁹/⁸)

2.6 xy(x⁷/⁸)(y¹/⁸)

Therefore, when the expression 8√2100x15y9 is simplified, the resulting expression is 2.6 xy(x⁷/⁸)(y¹/⁸)

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Answer:

x = 6

Step-by-step explanation:

Since the triangles are congruent, then corresponding sides are congruent, that is

QS = TV , substitute values

6x + 12 = 9x - 6 ( subtract 6x from both sides )

12 = 3x - 6 ( add 6 to both sides )

18 = 3x ( divide both sides by 3 )

6 = x

Answer:

x = 6

Step-by-step explanation:

x = ?

6x + 12 = 9x - 6

get the variables and numbers on different sides

6x + 12 - 6x = 12

9x - 6 + 6 = 9x

12 + 6 = 18

9x - 6x = 3x

3x = 18

divided each side by 3

3x / 3 = x

18 / 3 = 6

x = 6

well, let's move like the crab, backwards, let's start with b), then we'll do a)

b)

\({\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=2\\ y=75 \end{cases}\implies 75=ab^2 \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=5\\ y=9375 \end{cases}\implies 9375=ab^5\implies 9375=ab^{2+3}\implies 9375=ab^2 b^3\)

\(\stackrel{\textit{substituting from the 1st equation}}{9375=\underset{ab^2}{(75)} b^3}\implies \cfrac{9375}{75}=b^3\implies 125=b^3 \\\\\\ \sqrt[3]{125}=b\implies \boxed{5=b}\hspace{5em}\stackrel{\textit{we know that}}{75=ab^2}\implies 75=a5^2\implies 75=25a \\\\\\ \cfrac{75}{25}=a\implies \boxed{3=a}\hspace{5em} {\Large \begin{array}{llll} y = 3(5^x) \end{array}}\)

a)

\(\begin{cases} x=0\\ y=j \end{cases}\implies j=3(5^0)\implies j=3(1)\implies j=3 \\\\\\ \begin{cases} x=4\\ y=k \end{cases}\implies k=3(5^4)\implies k=3(625)\implies k=1875\)

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Audience reach is a metric that is used to measure of the total audience size for a specific provide platform.

Audience reach answers the question of how many people have had the opportunity to consume (i.e. read, watch, and/or hear) news coverage of whatever you're watching. This metric is based on known circulation, viewership, audience size and followers of media outlets or social media users who publish the content in question. For the audience size of the publication/social media user providing the content is identified and then this number is added to the audience size of all other outlets publishing the content to give the total audience reach.

Hence, required answer is audiance reach.

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Based on the total cost that Juan incurred to hire the roofer including the charge for parts and labor, the number of hours that was needed to complete the job was 14.50 hours.

The first thing to do is to find out the amount that went to labor:

= Final bill - cost of materials

= 1,131.5 - 450

= $681.50

Now that you have the cost of labor, you can find out the number of labor hours that were used based on the hourly rate:

= Cost of labor / Hourly rate

Solving gives:

= 681.50 / 47

= 14.5 hours

In conclusion, the number of labor hours that the roofer used to complete the work, based on the total amount charged to Juan is 14.50 hours.

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Answer:

y=9x

Step-by-step explanation:

For these x's and y's, we can notice that y is always equal to 9 times the value of x. 0 equals 9 * 0, 9 equals 9 * 1, 18 equals 9 * 2, 27 equals 9 * 3, and 36 equals 9 * 4.

We have just shown that y equals 9 times x, which is just y=9*x, or y=9x.

The measure of central tendency that is used by the professor is; Mode

A measure of central tendency is defined as a single value that attempts to describe a set of data by identifying the central position within that set of data. The types of measures of central tendency are;

1) Mean; This is defined as the average value of a given set of data.

2) Median: This is defined as the midpoint of a frequency distribution of observed values or quantities, such that there is an equal probability of falling above or below it.

3) Mode: This refers to the value in a given set of data that has highest occurrence frequency.

In this case, the professor notes that most students in his class earned a grade of b. Thus, this is the mode.

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The slope of this line is given as 1/2

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane. Calculating the slope of a line is similar to finding the slope between two different points. In general, to find the slope of a line, we need to have the values of any two different coordinates on the line.

Taking two points from the graph;

The slope of the line is calculated as

m = y₂ - y₁ / x₂ - x₁

Substituting the values into the formula above;

m = -3 - (-1) / 1 - 5

m = -2 / - 4

m = 1/2

Slope = 1/2

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Answer:

yes

Step-by-step explanation:

yes

x= y*something is proportional

x=sometting /y , will be invers proportional

Hypothesis tests can provide evidence against the null hypothesis but cannot conclusively prove it, as they can suggest if a scale might be out of calibration, but cannot demonstrate it with absolute certainty.

What are the limitations of hypothesis tests in determining the true calibration of a scale and why can't they conclusively prove the null hypothesis to be true?

It is not possible to demonstrate conclusively that the scale is in calibration using a hypothesis test. Hypothesis tests, including the one stated with H0 : μ = 9 and H1 : μ ≠ 9, can only provide evidence against the null hypothesis (H0) if the test results are statistically significant. However, hypothesis tests cannot definitively prove the null hypothesis to be true.

How does a hypothesis test help in determining the calibration of a scale?
In this scenario, a hypothesis test can help determine whether there's enough evidence to reject the null hypothesis, which would suggest that the scale may not be in calibration. However, if the test results are not statistically significant, it doesn't prove that the scale is perfectly calibrated; it only indicates that there is not enough evidence to reject the null hypothesis.
To summarize, hypothesis tests can provide evidence against the null hypothesis, but they cannot prove it conclusively. In the case of checking the calibration of a scale, a hypothesis test can suggest whether the scale might be out of calibration, but it cannot demonstrate with absolute certainty that the scale is in calibration.

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Answer: 1.5 ≤ x ≤ 5.5

Step-by-step explanation:

If the width is W and the length is L, the area of the rectangle will be:

A = W*L

In this case:

W = 2*x + 1

L = 3.

Then the area is:

A = (2*x + 1)*3 = 6*x + 3.

And we know that:

12 ≤ A ≤ 36

To find the smallest possible value of x, we assume that we have the smallest possible area: 12.

A = 12 = 6*x + 3

      12 - 3 = 6*x

       9/6 = x = 1.5

To find the largest possible value of x, we use the largest possible area, 36.

A = 36 = 6*x + 3.

      36 - 3 = 6*x

       33/6 = x = 5.5

Then we have:

1.5 ≤ x ≤ 5.5

Do you know what the answer to

Length can be between _____ and _____ units?

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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Answer:

f(6) = \(\frac{5}{22}\)

Step-by-step explanation:

To evaluate f(6) substitute x = 6 into f(x), that is

f(6) = \(\frac{5}{4(6)-2}\) = \(\frac{5}{24-2}\) = \(\frac{5}{22}\)

Answer:

8(x + 6) = 144

Step-by-step explanation:

We can start building this equation by making everything equal to 144 since the problem is representing the total number of apples:

? = 144

Next, we don't know how many apples are in each basket, so we can represent it with a variable, x.

Since 6 apples are added to each basket we will simply add 6 to the "x" amount of apples in each basket:

x + 6 = 144

Lastly, according to the scenario, we have 8 baskets, each holding "x" amount of apples plus the extra 6 that was added, so it will be multiplied:

8(x + 6) = 144