A sprinkler sprays water a distance of 10.2 m in a circular pattern How much area does the sprinkler cover in one complete rotation? Use 3.14 for n and round to the nearest tenth.​

Answer:

y = 25x + 40

Step-by-step explanation:

Using the formula, y = mx + b we can find out what this equation would be.

m = the rate of change/slope

b = the y- intercept

25 per month is telling us that this is the rate of change.

Since the $40 is only paid once, you can tell that this is the y intercept.

The equation will look like:

y = 25x + 40

On a graph it would look like:

Let the total cost of a gym membership be y, with the number of months as x.

The total cost would be 40 dollars, the initial fee, plus 25 times the number of months (x).

y = 40 + 25x

a. The labor productivity ratio for Mack's guitar fabrication shop is $30 per labor hour, and the multi-factor productivity ratio is $0.3647 per dollar.

b. If option 1 is implemented, the new productivity level would be $0.424 per dollar, and if option 2 is implemented, the new productivity level would be $0.427 per dollar.

a. The labor productivity ratio for Mack's guitar fabrication shop is $30 per labor hour. The multi-factor productivity ratio for Mack's guitar fabrication shop is $0.3647 per dollar.

To calculate the labor productivity ratio, we divide the total output value ($240 per guitar) by the total labor hours required (2 labor hours per guitar). Thus, the labor productivity ratio is $240 / 2 = $120 per labor hour.

To calculate the multi-factor productivity ratio, we divide the total output value ($240 per guitar) by the sum of labor, materials, and overhead costs per guitar ($9 labor cost + $38 materials cost + $4,200 overhead cost). Thus, the multi-factor productivity ratio is $240 / ($9 + $38 + $4,200) = $0.3647 per dollar.

b. If Mack's guitar fabrication shop decides to implement Darren Funk's option 1 to improve the multi-factor productivity, the new productivity level would be $0.424 per dollar. This is obtained by increasing the sales price by 15%, resulting in a new output value of $276 per guitar, while keeping the labor, materials, and overhead costs unchanged.

If Mack's guitar fabrication shop decides to implement Darren Funk's option 2 to improve the multi-factor productivity, the new productivity level would be $0.427 per dollar. This is achieved by improving the quality so that only 15% of the guitars are defective, reducing the scrapped percentage from 22% to 15%, while again keeping the labor, materials, and overhead costs unchanged.

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Answer:

Step-by-step explanation:

A and B are the side lengths. C is the hypotenuse (the longest side).

For triangle A)

a^2+b^2=c^2

(it won't let me add exponents but you get the point)

4^2+2^2=c^2

8+4=c^2

12=c^2

c=square root of 12

For B)

a^2+b^2=c^2

2^2+5^2=c^2

4+10=c^2

After solving, it doesnt

add up to 45

The probability that a randomly selected first-year teacher makes less than $20,000 a year is approximately 0.0071.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

To solve this problem, we can use the normal distribution and the standard normal distribution table (also known as the z-table).

Let X be the salary of a first-year teacher. We are given that X is approximately normally distributed with a mean (average) of mu = $27,989 and a standard deviation of sigma = $3250. We want to find the probability that a randomly selected first-year teacher makes certain salaries.

A. Between $20,000 and $30,000 a year

To find the probability that a first-year teacher makes between $20,000 and $30,000 a year, we need to standardize the interval using the z-score formula:

z1 = (20000 - mu) / sigma = (20000 - 27989) / 3250 = -2.45

z2 = (30000 - mu) / sigma = (30000 - 27989) / 3250 = 0.63

Using a standard normal distribution table or calculator, we can find that the probability of a random variable being between z1 and z2 is approximately 0.8461.

Therefore, the probability that a randomly selected first-year teacher makes between $20,000 and $30,000 a year is approximately 0.8461.

B. Less than $20,000 a year

To find the probability that a first-year teacher makes less than $20,000 a year, we need to standardize this value using the z-score formula:

z = (20000 - mu) / sigma = (20000 - 27989) / 3250 = -2.45

Using a standard normal distribution table or calculator, we can find that the probability of a random variable being less than z is approximately 0.0071.

Therefore, the probability that a randomly selected first-year teacher makes less than $20,000 a year is approximately 0.0071.

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Answer:

= 42m²

Step-by-step explanation:

The ratio of two similar hexagons is 3:7

where the smaller correspond to 3

And

the bigger correspond to 7

where the area of the smaller haxagon is 18

so if 3 = 18m²

then 7 = ?

therefore

\( \frac{7}{3} \times 18 \\ = 42 {m}^{2} \)

therefore the area of the bigger hexagon is 42m²

Analysing the data and evaluating the claims about the duration of flavor, we use analysis of variance (ANOVA) to compare the mean flavor intensities of the four gums.

Let's assume we have the following hypothetical data for the flavour intensity ratings:

Participant 1: Gum A: 7,Gum B: 6,Gum C: 8,Gum D: 7

Participant 2: Gum A: 6,Gum B: 5,Gum C: 7,Gum D: 6

Participant 3: Gum A: 8,Gum B: 7,Gum C: 9,Gum D: 8

Participant 4: Gum A: 7,Gum B: 6,Gum C: 8,Gum D: 7

Participant 5: Gum A: 6,Gum B: 5,Gum C: 7,Gum D: 6

We have 5 participants who each chewed 4 different types of gum (A, B, C, D) over 4 days. The flavor intensity ratings were recorded after 2 hours of chewing, ranging from 1 to 9.

To analyze the data and evaluate the claims about the duration of flavor, we can use analysis of variance (ANOVA) to compare the mean flavor intensities of the four gums. ANOVA helps determine if there is a statistically significant difference in the mean flavor intensities among the groups.

Here are the steps to conduct ANOVA:

Set up hypotheses:

Null hypothesis (H₀): The mean flavor intensities of the four gums are equal.

Alternative hypothesis (Hₐ): The mean flavor intensities of the four gums are not equal.

Calculate the sum of squares:

Calculate the total sum of squares (SST) by summing the squared differences between each observation and the overall mean.

Calculate the between-group sum of squares (SSB) by summing the squared differences between each group mean and the overall mean, weighted by the number of observations in each group.

Calculate the within-group sum of squares (SSW) by summing the squared differences between each observation and its respective group mean.

Calculate the degrees of freedom:

Degrees of freedom between groups (dfB) = Number of groups - 1

Degrees of freedom within groups (dfW) = Number of observations - Number of groups

Calculate the mean squares:

Mean square between groups (MSB) = SSB / dfB

Mean square within groups (MSW) = SSW / dfW

Calculate the F-statistic:

F-statistic = MSB / MSW

Determine the critical value or p-value:

Using the F-statistic and degrees of freedom, you can look up the critical value from an F-distribution table or use statistical software to calculate the p-value.

Compare the obtained F-value with the critical value or p-value:

If the obtained F-value is greater than the critical value (or if the p-value is less than the significance level, often 0.05), reject the null hypothesis and conclude that there is a significant difference in the mean flavor intensities among the gums.

If the obtained F-value is less than the critical value (or if the p-value is greater than the significance level), fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference in the mean flavor intensities among the gums.

By following these steps, you can perform an ANOVA analysis to evaluate the claims about the duration of flavor and determine if there is a significant difference in the mean flavor intensities among the four different gums.

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The 1st and the 3rd are the distributions where the median the best measure of center

The median represents the central value in a dataset that is organized in ascending or descending order. If there are an even number of data points, the median can be calculated as the mean of the two middle values.

This method is much less prone to influence by extreme values when compared to other methods such as the mean. Hence, it is considered a more reliable measure of center particularly for datasets with outliers.

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Answer:

.7

Step-by-step explanation:

because you see here that under tennis you see 7 and yeah sometimes I am not all right I am sure

Answer: 0.25

Step-by-step explanation:

It's 0.25 because the total is 28 and if you divide 7 from 28, you get 4, to make sure this is correct we should multiply 4 by 7 and that is 28. Since it's asking how many people prefer tennis more than the other sports in decimal form, 7/28 is equivalent to 1/4 and 1/4 is equivalent to 0.25 since 1/4 x 4 is 1 and 0.25 x 4 is also 1.

The correct option is:(–[infinity], 2) ∪ (2, [infinity])The function `g(x) = (x² + 3x)/(x² + x – 6)`, for x < 3, and the function `g(x) = log2(x + 5)`, for x ≥ 3.

We can see that the function is piecewise.Therefore, to find the domain of a piecewise function, we must determine the domain of each piece and then join the two domains to find the domain of the entire piecewise function. 1. For the first part of the piecewise function, g(x) = (x² + 3x)/(x² + x – 6) is undefined for x = -2 and x = 3. So, the domain of the first piece is (–[infinity], -2) ∪ (-2, 3) ∪ (3, [infinity]).2.

For the second part of the piecewise function, g(x) = log2(x + 5) is defined for all x ≥ -5. Therefore, the domain of the second piece is [-5, [infinity]).Since we are looking for the domain of the entire piecewise function, we need to find the intersection of the domain of each piece: (–[infinity], -2) ∪ (-2, 3) ∪ (3, [infinity]) ∩ [-5, [infinity]) = (–[infinity], -2) ∪ (-2, 3) ∪ (3, [infinity]).The domain of the entire piecewise function is (–[infinity], -2) ∪ (-2, 3) ∪ (3, [infinity]), which can be expressed as (–[infinity], 2) ∪ (2, [infinity]).Hence, the option `(–[infinity], 2) ∪ (2, [infinity])` describes the domain of the given piecewise function.

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Answer:

Can be C or D

Step-by-step explanation:

Janice and her 4 friends means there are 5 people in total.

She will divide them and so beads will be left which means no remainder.

so we have to look for a number divisible by 5

480 and 240 both are divisible by 5

In general, any symmetrical object will have a net torque of zero if the axis of rotation is through its center of mass.

It seems that the list of examples is missing from your question, so I'll provide a general explanation of situations where the net torque is zero. Please feel free to provide a list of examples for a more specific answer.

A net torque of zero about an axis perpendicular to the page and extending from the center means that the total clockwise torque is equal to the total counterclockwise torque. This can occur when:

1. There are no external forces acting on the system, so there is no torque.
2. The external forces are acting along the line of the axis, causing no rotation and hence no torque.
3. The clockwise and counterclockwise torques cancel each other out, resulting in a net torque of zero.

Some examples of objects that have a net torque of zero about the axis perpendicular to the page and extending from the center of the object are a sphere, a cube, a cylinder, and a cone.

Please provide the list of examples you'd like me to evaluate, and I'll be glad to help you determine which have a net torque of zero.

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Answer:

Answer is C

Step-by-step explanation:

-Non terminating

-Non repeating

So it's irrational. You can find out which decimal are irrational by seeing if they end or if they repeat with a number. 2.9 terminates, 17 terminates, and 3/11 (0.2727...) doesn't terminate but repeats, so they're all rational

Answer:

\(\frac{3x^2}{(x+2)(x-4)}\)

Step-by-step explanation:

Before adding the fractions we require them to have a common denominator.

Multiply numerator/ denominator of first fraction by x - 4

Multiply numerator/ denominator of second fraction by x + 2

= \(\frac{x(x-4)}{(x+2)(x-4)}\) + \(\frac{2x(x+2)}{(x+2)(x-4)}\) ← expand and simplify numerators, leaving common denominator

= \(\frac{x^2-4x+2x^2+4x}{(x+2)(x-4)}\)

= \(\frac{3x^2}{(x+2)(x-4)}\)

The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.

To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.

Let x be the number of acres of corn and y be the number of acres of soybeans.

1. Total acre constraint: x + y ≤ 6,000

2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501

3. Labor constraint: 0.75x + y ≤ 5,250

The objective function to maximize is the profit function: P(x,y) = 75x + 40y

Now, we will use the Solver to find the maximum profit:

Step 1: Set up a spreadsheet with the constraints and the objective function.

Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.

Step 3: Set the objective function by selecting the cell with the profit function.

Step 4: Choose "Max" for the objective.

Step 5: Add the constraints by selecting the corresponding cells.

Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.

After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83

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sin(2t) = 2(79)cos(t). cos(2t) = √(1 - 79^2) - 79^2. tan(2t) = (2(79)cos(t))/((√(1 - 79^2) - 79^2).

To find the exact value of sin(2t), cos(2t), and tan(2t) algebraically without solving for t, we can use trigonometric identities.

Let's start with sin(2t). By using the double-angle identity for sine, we have:

sin(2t) = 2sin(t)cos(t)

Since t is in quadrant I, both sin(t) and cos(t) are positive. Therefore, we can substitute sin(t) = 79 into the equation:

sin(2t) = 2(79)cos(t)

Moving on to cos(2t), we can use the double-angle identity for cosine:

cos(2t) = cos^2(t) - sin^2(t)

Substituting sin(t) = 79 and cos(t) = √(1 - sin^2(t)) = √(1 - 79^2) into the equation, we get:

cos(2t) = √(1 - 79^2) - 79^2

Finally, let's find tan(2t) using the identity:

tan(2t) = sin(2t)/cos(2t)

Substituting the values we found for sin(2t) and cos(2t):

tan(2t) = (2(79)cos(t))/((√(1 - 79^2) - 79^2)

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Answer:

Step-by-step explanation:

The implied utilization of the resources in the process can be calculated by dividing the demand rate by the total capacity of the resources. In this case, the total capacity is 1.1 + 0.93 = 2.03 clients per hour. Therefore, the implied utilization is 0.75 / 2.03 = 0.369 (or 36.9%).

The implied utilization represents the proportion of the available capacity that is being utilized to meet the demand. In this scenario, approximately 36.9% of the total capacity is being utilized to serve the clients. This indicates that there is still some unused capacity available in the process.

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Answer:

6

Step-by-step explanation:

3÷1/2

You would flip the denominator and numerator and multiply it by the first number.

3×2/1

6/1

6

Hope this helps!!!

Answer:

$401.47

Step-by-step explanation:

1st year: 300+6%=318

2nd Year: 318+6%= 337.08

3rd Year: 337.08+6%= 357.30

4th Year: 357.30+6%= 378.74

5th Year= 378.74+6%= 401.47

Answer:

If the simple interest is 6% then A is $90.00 and B is $390.00.

Step-by-step explanation:

Answer:

f(x)=x^3 - 13x^2 + 40x + 17

Step-by-step explanation:

x-0=0    x-5=0       x-8=0

  x=0        x=5           x=8

y=x(x-5)(x-8)+b  ==> b is what's going to be used to find the equation so that

                                y=17 when x=0

17=0(0-5)(0-8)+b  ==> plugin 0 for x and 17 for y

17=0*(-5)*(-8)+b  ==> simplify

17=0+b  ==> anything multiplied by 0 is 0.

b=17  

Hence, the equation is:

y=x(x-5)(x-8)+17  ==> expand this equation

y=x*(x-5)(x-8) + 17

y=x*(x(x - 8) - 5(x - 8)) + 17  ==> distribute x-8 to x and -5

y=x*(x*x - 8x - 5x - (8)(-5)) + 17  ==> distribution property

y=x*(x^2 - 13x - (-40)) + 17   ==> simplify

y=x*(x^2 - 13x + 40) + 17  ==> subtracting a negative number is equivalent to

                                              adding a positive number

y=x^3 - 13x^2 + 40x + 17 ==> multiply x with x^2, 13x, and 40 using the

                                              distribution property.

Answer: f(x)=x^3 - 13x^2 + 40x + 17

Answer: Okay, lets explain.

Step-by-step explanation:Since 0, 5 & 8 are given as the zeros of the required 3rd degree polynomial f(x), therefore, one may take it as ; f(x) =k (x-0)(x-5)(x-8)

= k(x³−13x²+40) …. .. .(1) . Since f(10) = 17 (given), it implies 17 = k(1000 -1300 + 400) = 100 ==> k = 17/100 = 0.17 . Put this value of k in eq(1) and get the required polynomial.

Answer:

-8

Step-by-step explanation:

-21-(-13)

=-21+13

=-8 is the answer......

Answer:

\(-8\)

Step-by-step explanation:

\(-21 - (-13)\)is the same as \(-21+13\), so the answer is \(-8\).

The measure of ∠CFE is 40°

To solve for triangle ∠CEF, we know that

Parallel to DE is BC

Arc length BD = 58°

Arc length DE = 142°

We can then draw a diameter across the center of the circle and give it a name as the first step. The diameter in this situation is line ZT.

The arcs BD and DE are split in half by the line ZT.

Which is:

Arc SC = 1/(1/2(arc BC) = 1/(58)

Arc SC = 29°

142 = 1/2(arc DE) + arc TE

Arc TE = 71°

Sum of the angles of a semicircle is 180 degrees: Arc SC + Arc CE + Arc TE

29° + Arc CE + 71° = 180°

Arc CE + 100° = 180°

Arc CE = 180-100

Arc CE = 80°

Angle inscribed equals half of angle intercepted

CFE = 1/2 of Arc CE

<CFE = 1/2(80)

< CFE = 40°

The above answer is based on the full question below;

In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer

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Answer:

normal force decreases

Step-by-step explanation:

N=mgcosθ, and cosine decreases as theta increases

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Answer:

A) decreases

Step-by-step explanation:

As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.

They are related as u^T transposes of each other. v and v^T u are scalar values that represent the dot product of u and v. uv^T and vu^T are matrices of size n x n that represent the outer product of u and v.

If u and v are vectors in R^n, then:

u^T v and v^T u are related as transposes of each other. Specifically, if

u = [u_1, u_2, ..., u_n]^T

and v = [v_1, v_2, ..., v_n]^T

then:

u^T v = v^T u

= u_1 * v_1 + u_2 * v_2 + ... + u_n * v_n

So, u^T v and v^T u are scalar values that represent the dot product of u and v.

uv^T and vu^T are related as transposes of each other. Specifically, if u = [u_1, u_2, ..., u_n]^T and v = [v_1, v_2, ..., v_n]^T

then:

uv^T = [u_1 * v_1, u_1 * v_2, ..., u_1 * v_n;

u_2 * v_1, u_2 * v_2, ..., u_2 * v_n;

...;

u_n * v_1, u_n * v_2, ..., u_n * v_n]

vu^T = [v_1 * u_1, v_2 * u_1, ..., v_n * u_1;

v_1 * u_2, v_2 * u_2, ..., v_n * u_2;

...;

v_1 * u_n, v_2 * u_n, ..., v_n * u_n]

So, uv^T and vu^T are matrices of size n x n that represent the outer product of u and v.

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Answer:

  0.98

Step-by-step explanation:

You want the decay factor for the decay of 207.19 grams of I-131 to 191.26 grams in 4 days.

The second attachment shows where the decay factor fits in an exponential function. Writing the function as ...

  f(t) = ab^t

we have ...

  f(3) = 207.19 = ab^3

  f(7) = 191.26 = ab^7.

Then the ratio of these numbers is ...

  f(7)/f(3) = (ab^7)/(ab^3) = b^4 = (191.26)/(207.19)

Taking the fourth root, we have the decay factor:

  b = (191.26/207.19)^(1/4) ≈ 0.98

The decay factor for the given data is about 0.98.

<95141404393>

Answer:

2 x -2 + 5

-4 + 5

1 = y

Step-by-step explanation:

Plug in the value of X and do the equation.

Answer:

y = 1

Step-by-step explanation:

When x = -2 :

y = 2x + 5

y = 2(-2) + 5

y = -4 + 5

y = 1

Answer:

a - b

Step-by-step explanation:

Assuming you mean:  \((a^\frac12-b^\frac12)(a^\frac12+b^\frac12)\)

Apply Difference of Two Squares formula \((a-b)(a+b)=a^2-b^2\):

\(\implies (a^\frac12-b^\frac12)(a^\frac12+b^\frac12)=(a^\frac12)^2-(b^\frac12)^2\)

Apply the exponent rule \((a^b)^c=a^{bc}\) :

\(\implies (a^\frac12)^2-(b^\frac12)^2=a^1-b^1=a-b\)

Therefore, the r value alone is not enough to infer causality, regardless of its magnitude.

The correlation coefficient, also known as the Pearson correlation coefficient or Pearson's r, is a measure of the strength and direction of the linear relationship between two continuous variables. It is expressed as a number between -1 and 1, where -1 indicates a perfect negative correlation (meaning that as one variable increases, the other decreases), 1 indicates a perfect positive correlation (meaning that as one variable increases, the other also increases), and 0 indicates no correlation. The value of the correlation coefficient provides information about how closely the two variables are related, but it does not establish causality.

The r value alone is not enough to infer causality. A high correlation coefficient suggests a strong relationship between two variables, but causality means that one variable is causing the changes in the other variable and requires a causal mechanism and a demonstration of a temporal relationship between the variables.

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9514 1404 393

Answer:

  18.42

Step-by-step explanation:

The "rate of change" in a linear equation is the coefficient of the variable. Here, the variable is "g" and its coefficient is 18.42.

The value that represents the rate of change is 18.42.