(05.07 HC)
A student is assessing the correlation between the number of workers in a factory and the number of units produced daily?

Part A: Is there any correlation between the number of workers in a factory and the number of units produced daily? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indicate? (3 points)

Answer:

the third option

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

they both started at 0 and added 2 and 6 respectively

5cm

Step-by-step explanation:

volume of cube= l³

125 =l³

3root over 125 =l

l = 5

Answer:

So the length of the edge of a cube with a volume of 125 is 5.

Step-by-step explanation:

Answer:

300°

Step-by-step explanation:

That'd be 5pi/3 radians.  Note that 3pi/3 radians corresponds to 180° and that 6pi/3 corresponds to 360°.  Thus 5pi/3 is in Quadrant IV, meaning that the angle in degrees is between 270° and 360°.  

The "radians to degrees" conversion factor is (180°/pi), and so

5pi/3 radians works out to:

5pi/3 · 180°       5· 180°

----------------- = ---------- = 300°

          3 pi             3

Answer:

You mean how many centimerters are in a meter?

In that case 100.

Step-by-step explanation:

Answer:

I think the answer would be -2 . hope it helps u .

Step-by-step explanation:

11. angles 1 and 2 are vertical angles, meaning they are congruent.

angle 2=angle 1=38 degrees

14. angles 1 and 2 are supplementary angles, meaning they add to 180 degrees.

angle 1=180-angle 2=180-67=113 degrees

The type of transformation in this problem is given as follows:

Vertical translation.

The four translation rules are defined as follows:

For this problem, we have a translation of 2 units up, which is called a vertical translation.

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Answer:

I couldn't really see the height number (that had to doubled) ir really the radius but I saw 7 for the radius and 3 (×2) for the height so I did the math and the answer is 923.63

Step-by-step explanation:

i could be wrong tho, hope this helped

Answer:

923.63

Step-by-step explanation: hope this helps!!

a/ To find the limit of the expression 2 + 4 + 3i Re(z - i), we need to replace z with the limit point. Therefore, the expression will be:2 + 4 + 3i Re(z - i) = 6 + 3i Re(z - i)

We have to find the limit as z approaches i. Consider the following:

Since Re(z - i) is a real number, the limit can be found by setting Re(z - i) = 0.

Therefore, lim 2+4+3i Re(z - i) = lim 6 + 3i Re(z - i) = 6.Explanation:

b/ Given the limit lim zi / zi, we can simplify the expression by canceling zi in the numerator and the denominator. Therefore, lim zi / zi = lim 1 = 1.

Explanation:

4. Let f(x) = x3 + iy(a) The derivative of f(x) is the function f′(x). To find the derivative of f(x), we need to differentiate the real and imaginary components of f(x) separately.

Therefore, f′(x) = 3x² + iy, since the derivative of i is zero.

Explanation: (b) We must test the Cauchy-Riemann equations to see if f(x) is analytic. f(x) is said to be analytic if it meets the Cauchy-Riemann conditions. Therefore, we need to verify that the following equations are satisfied: ∂u / ∂x = ∂v / ∂y and ∂u / ∂y = -∂v / ∂x. Using the function given above, we can easily obtain its real and imaginary components. u(x, y) = x³ and v(x, y) = y. Therefore, ∂u / ∂x = 3x² and ∂v / ∂y = 1, but 3x² ≠ 1

Therefore, the Cauchy-Riemann equations are not satisfied, so f(x) is not analytic.

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Answer:

The answer is "True".

Step-by-step explanation:

The z-score value shows how often standard deviations were away from the earth. If it is 0, it is on average. The positive Z sign indicates that perhaps the raw mark is greater than the average. While z-score is equivalent to +1, for example, it is a standard deviation of 1 above average. This can be used for implementing series and also for comparing the trend of mortality among various individuals or between various periods and by using the z score we find the curve length, that's why it is correct.

we do not have enough evidence to conclude that cars get better mileage on premium gasoline. Thus, we can conclude that there is no significant difference between the mileages of cars using premium and regular gasoline.

a. What test should be used?

The test that should be used is the Two-sample t-test because we are working with two independent groups.

b. What are the hypotheses?

The null hypothesis is that there is no difference between the mileage of cars using premium and regular gasoline, while the alternative hypothesis is that there is a difference between the two mileages.

Mathematically, this can be stated as follows: Null hypothesis: µ1 = µ2Alternative hypothesis: µ1 > µ2Where µ1 is the population mean for premium gasoline and µ2 is the population mean for regular gasoline.

c. Based on the R outputs, what is your conclusion about hypotheses testing?

From the R outputs, we can see that the p-value is 0.2826. Since this value is greater than the level of significance (α) of 0.05, we fail to reject the null hypothesis. Therefore, we do not have enough evidence to conclude that cars get better mileage on premium gasoline. Thus, we can conclude that there is no significant difference between the mileages of cars using premium and regular gasoline.

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a. The test that should be used is a two-sample t-test.

b. The null hypothesis is "The population mean mileage of cars using regular and premium gasoline are equal."

The alternative hypothesis is "The population mean mileage of cars using premium gasoline is more than the population mean mileage of cars using regular gasoline."

c. We do not have enough evidence to support the claim that cars get better mileage on premium regular gas.

a. To find what test should be used.

The test that should be used is a two-sample t-test.

b. To find the hypotheses.

The null hypothesis is "The population mean mileage of cars using regular and premium gasoline are equal."

The alternative hypothesis is "The population mean mileage of cars using premium gasoline is more than the population mean mileage of cars using regular gasoline."

c. Based on the R outputs, to find the conclusion about hypotheses testing.

The sample mean of the differences in mileage for cars filled with premium and regular gasoline is 0.8. The calculated t-value is -0.59702.

The calculated p-value is 0.2826.The p-value is higher than the significance level of 0.05.

Therefore, we fail to reject the null hypothesis.

We can't conclude that the population mean mileage of cars using premium gasoline is more than the population mean mileage of cars using regular gasoline.

Hence, we do not have enough evidence to support the claim that cars get better mileage on premium regular gas.

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Answer:

$1159.69

Step-by-step explanation:

A = P (1 + r/n)^nt

A = 1000 (1 + 0.05/2)^2(3)

A = $1159.69

Answer:

a) 1/13 (or 13 depending on the factor is being applied to the dog house or applied to the shed. If its being applied to the shed like 117 * scale factor it is 1/13)

b) 10

Step-by-step explanation:

The scale factor is 13 and the height of the dog house is 10 cm.

A scale factor is defined as the ratio between the scale of a given original object and a new object.

Given that, Dave is building a doghouse that is a scale model of his shed in the farmyard, One of the windows on the shed is 117 cm wide and 130 cm high. On the doghouse the window is 9 cm wide,

a) Since, the scale factor = ratio of original scale to scale of the model.

Therefore,

Scale factor = 117 / 9 = 13

b) Since, the scale factor is 13 and the original scale of the window high is 130 cm.

Therefore, height of the doghouse = 130 / 13 = 10 cm

Hence, the scale factor is 13 and height of the dog house is 10 cm.

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Given,Test at 20% significance level whether one of the drugs is more effective than the other.

We need to calculate the absolute value of the critical value of this test, the absolute value of the calculated test statistic, and the p-value of this test.Solution:(a) The absolute value of the critical value of this test isThe level of significance is 20%.The degree of freedom is (r-1)(c-1) = (3-1)(2-1) = 2

From the chi-square table, the critical value for a chi-square distribution with 2 degrees of freedom and a level of significance of 0.20 is 3.219(i.e. critical value = 3.219)The absolute value of the critical value of this test is 3.219.(b) The absolute value of the calculated test statistic

The table is shown below:  We have, Total = 69 Test at 20% significance level whether one of the drugs is more effective than the other.To check the difference in effectiveness, we will use a chi-square goodness of fit test.

The null hypothesis H0: The two drugs are equally effective.

The alternative hypothesis Ha: One of the drugs is more effective.

The expected values of the two drugs are:  Expected Value of Drug A = (32+18) / 3 = 16 Expected Value of Drug B = (32+1) / 3 = 11 The calculations are summarized in the table below:  The formula to calculate the chi-square value is, chi-square = ∑ (O - E)2 / E The calculated value of chi-square is 6.07.The absolute value of the calculated test statistic is 6.07.(c) The p-value of this test isThe degree of freedom is (r-1)(c-1) = (3-1)(2-1) = 2

The level of significance is 20%.From the chi-square table, the p-value for a chi-square distribution with 2 degrees of freedom and a chi-square value of 6.07 is 0.047 (i.e. p-value = 0.047)The p-value of this test is 0.047.

Answer:(a) The absolute value of the critical value of this test is 3.219.(b) The absolute value of the calculated test statistic is 6.07.(c) The p-value of this test is 0.047.

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We fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that one drug is more effective than the other at the 20% level of significance.

Below is the table of values for the drugs drug A and drug B

Group A 7 10 13 15 8 7 6 10 9 11 10 11

Group B 6 12 9 11 8 8 9 12 10 14

(a) The absolute value of the critical value of this test

The absolute value of the critical value of this test is given by the formula:

[tex]`z = |zα/2|`[/tex]

where α = 0.2;

degree of freedom = `n1+n2-2` = `12+10-2` = `20`

From the standard normal table, the value of zα/2 at 0.2 is 1.645

Therefore, the absolute value of the critical value of this test is; `|1.645| = 1.645`.

(b) The absolute value of the calculated test statistic

The formula for the test statistic is given by;

[tex]`t=bar x1 -bar x2)/((s^2/n1)+(s^2/n2))`[/tex]

where `bar x1` and `bar x2` are the sample means of the two groups,

`s^2` is the pooled variance, n1 and n2 are the sample sizes of the two groups

and [tex]`s^2 = ((n1 -1) s1^2 + (n2 -1) s2^2 )/(n1 + n2 - 2)`[/tex]

Using the data given, we get:

Group A 7 10 13 15 8 7 6 10 9 11 10 11

`n1` = 12

[tex]`bar x1` = `(7+10+13+15+8+7+6+10+9+11+10+11)/12 = 9.583`[/tex]

and `s1` = 2.818

Group B 6 12 9 11 8 8 9 12 10 14

`n2` = 10

[tex]`bar x2` = `(6+12+9+11+8+8+9+12+10+14)/10 = 9.9`[/tex]

and `s2` = 2.205

[tex]`s^2` = `((12-1)2.818^2 + (10-1)2.205^2)/(12+10-2)` = `((11)(7.95)+(9)(4.86))/20` = `6.2155`[/tex]

Therefore, [tex]`t= |9.583 - 9.9| / (6.2155[(1/12)+(1/10)])`= 0.3164[/tex]

The absolute value of the calculated test statistic is 0.3164

(c) The p-value of this test is

The p-value of this test is 0.76 (rounded to two decimal places)

This indicates that the p-value is higher than the significance level, 0.2.

Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that one drug is more effective than the other at the 20% level of significance.

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Answer: the one in the bottom right

Step-by-step explanation: each month which is the x axis ( the bottom line) the y axis (line on the left) goes up by 5

so when the x axis is 1 the y axis should be at 5

Answer:

Surface area of prism = 1301 cm²

Step-by-step explanation:

A triangular pyramid has 3 rectangular sides and 2 triangular sides.

Now, we are told that the triangular side is isosceles.

This means that two of the rectangular sides which share a side with the equal side of the triangle are equal as well as the 2 triangular sides.

Surface area of prism = 2(area of triangular face) + 2(area of rectangle sharing one side with the equal side of the triangle) + (area of rectangle sharing side with the unequal side of the triangle).

Area of triangle = ½ × base × height

Area of triangle = ½ × 9 × 13 = 58.5 cm²

Since height of prism is 32 cm, then;

area of rectangle sharing one side with the equal side of the triangle = 32 × 14 = 448 cm²

area of rectangle sharing side with the unequal side of the triangle = 32 × 9 = 288 cm²

Thus;

Surface area of prism = 2(58.5) + 2(448) + 288

Surface area of prism = 1301 cm²

To indicate a strong correlation between variables, the correlation coefficient will be close to its extreme values of -1 or 1, suggesting a high degree of linear relationship between the variables.

The correlation coefficient, also known as Pearson's correlation coefficient, ranges from -1 to 1.The correlation coefficient quantifies both the magnitude and direction of the linear association between two variables, providing a measure of the strength of their relationship.

When the correlation coefficient is close to -1, it suggests a strong inverse relationship between the variables, indicating that as one variable increases, the other variable tends to decrease consistently.

On the other hand, a correlation coefficient close to 1 indicates a strong positive correlation, where an increase in one variable is associated with an increase in the other variable.

A correlation coefficient near 0, or close to 0.5, does not indicate a strong correlation between the variables. A value close to 0 suggests a weak or no linear relationship between the variables, while a value close to 0.5 indicates a moderate correlation.

Therefore, to indicate a strong correlation between variables, we look for correlation coefficients that are near -1 or 1, indicating a strong negative or positive linear relationship, respectively.

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Complete question :

From Monday through Friday, James works in the library on 2 days and in the cafeteria on another day. On Saturday and Sunday, James washes cars 50% of the days. How many days does James work in a week? What percent of the days from Monday through Friday does he work?

Answer:

4 days ;

60%

Step-by-step explanation:

From Monday to Friday

Number of days in library = 2

Number of days in cafeteria = 1

50% of days in weekends

Number of weekend days = 2

50% of 2 = 0.5 * 2 = 1 day

Total. Number of days worked = (2 +1 + 1) = 4 days

What percent of the days from Monday through Friday does he work?

Number of days workwd from. Monday to Friday = 3

Total number of days from Monday to Friday = 5

Percentage of days worked from Monday to Friday

= number of days worked / total number of days

= 3 /5 * 100%

= 0.6 * 100%

= 60%

Answer:

B.

Step-by-step explanation:

the three sticks of butter were divided among six people

Answer:

2 ≤ x ≤ 8

Step-by-step explanation:

0 ≤ 3x - 6 ≤ 18

0 ≤ 3x - 6

6 ≤ 3x

2 ≤ x

3x - 6 ≤ 18

3x ≤ 18 + 6

3x ≤ 24

x ≤ 8

Combined:

2 ≤ x ≤ 8

Answer:

2 ≤ x≤ 8

2nd option:)

Step-by-step explanation:

Answer:

s

Step-by-step explanation:

Answer:

fourth option) 5/8 lb

To determine the value of c such that the random variable cY follows a chi-squared (x²) distribution, we need to compare the moments of cY with the moments of a standard x² distribution.

The random variable Y is defined as Y = (X₁ + X₃ + X₅ + X₇)² + (X₂ + X₄ + X₆ + X₈)², where X₁, X₃, X₅, X₇, X₂, X₄, X₆, and X₈ are independent standard normal random variables.

The x² distribution is characterized by its degrees of freedom, which determine the shape and variability of the distribution. For a standard x² distribution, the degrees of freedom are equal to the number of squared independent standard normal variables that are summed together.

In this case, Y is a sum of squared independent standard normal variables. By expanding Y, we can see that it consists of two terms, each squared separately. Each term represents the sum of four independent standard normal variables. Therefore, each term follows a x² distribution with 4 degrees of freedom.

To make cY follow a x² distribution, we need to equate the degrees of freedom of cY with 4. By comparing the moments of cY with the moments of a standard x² distribution with 4 degrees of freedom, we can solve for the value of c. The moments of cY will depend on the value of c, and by setting them equal to the corresponding moments of a x² distribution, we can find the specific value of c.

In summary, to determine the value of c such that the random variable cY follows a x² distribution, we need to compare the moments of cY with the moments of a standard x² distribution. By equating the degrees of freedom and comparing the corresponding moments, we can find the value of c.

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Answer:

So the odds of flipping a coin 5 times and getting 5 heads are 1/2 ^5 (half to the power of 5). Which gives us 1/32 or just over a 3% chance.

Step-by-step explanation:

Answer:

When A is less than 0 the parabola flips downward. When A becomes larger than 1, the parabola becomes more narrow. When A becomes smaller, until 0, the parabola widens.

Step-by-step explanation:

Answer:

4/5=0.8×7=5.6

5.6 is the answer

Hey there!

4/5 × 7

= 4×7/5

= 28/5

= 5.6

Hope it helps ya!

Answer:

x= -3

Step-by-step explanation:

5x + 2 = x - 10

4x + 2 = -10

4× = 10 - 2

4x = -12

x= -3

Answer:

The rate of change is 12ft/s

Step-by-step explanation:

Given

[tex]h(t) = -16t^2 + 20t[/tex]

Required

Rate of change from when she jumps till 1/2s

The time she jumps is represented as: t = 0

So, calculate h(0)

[tex]h(t) = -16t^2 + 20t[/tex]

[tex]h(0) = -16 * 0^2 + 20 * 0 = 0[/tex]

At t = 1/2

[tex]h(t) = -16t^2 + 20t[/tex]

[tex]h(1/2) = -16 * 1/2^2 + 20 * 1/2 = 6[/tex]

Rate of change is calculated as:

[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]

In this case:

[tex]Rate = \frac{h(b) - h(a)}{b - a}[/tex]

Where

[tex](a,b) = (0,1/2)[/tex]

So, we have:

[tex]Rate = \frac{h(b) - h(a)}{b - a}[/tex]

[tex]Rate = \frac{h(1/2) - h(0)}{1/2 - 0}[/tex]

[tex]Rate = \frac{6 - 0}{1/2 - 0}[/tex]

[tex]Rate = \frac{6}{1/2}[/tex]

[tex]Rate =12[/tex]

The rate of change is 12ft/s

Ordered pair (0, 6) and  (2, 7)  satisfy both inequalities in the system and are solutions to the system.

To identify the graph that represents the given system of inequalities y > x + 5 and y ≥ 2x + 3, we need to graph the individual inequalities and find the region where they overlap.

When we plot the graph of inequality separately:

    2. y ≥ 2x + 3:

The overlapping shaded region represents the solution to the system of inequalities.

To find two ordered pairs that are solutions to the system, we can choose any points within the overlapping region. Let's select two points:

Ordered pair 1: (0, 6)

Ordered pair 2: (2, 7)

These two points satisfy both inequalities in the system and are solutions to the system.

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The correct question is given below -

Identify the graph that represents the given system of inequalities. Also identify two ordered pairs that are solutions to the system.

y > x + 5

y ≥ 2x + 3