On a separate sheet of paper, graph 3x+6y=18 In the box below, enter the y value when x = 2.

The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

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Answer:

13 + 14 + 15

Step-by-step explanation:

n + (n + 1) + (n +2) =42

n + n + n + 1 + 2 = 42

3n + 3 = 42

(subtract 3 from both sides)

3n = 39

(divide both sides by 3)

n = 13

(solve)

n + (n + 1) + (n +2) =42

13 + (13 + 1) + (13 + 2) = 42

13 + (14) + (15) = 42

13, 14, 15

(Hope this helps, have a nice day!)

The first statement is false and second statement is true.

a. In a reflection, pairs of corresponding points lie on parallel lines. False.

When we consider the reflection transformation, the corresponding points lie on a single line perpendicular to the reflecting line.

The reflecting line serves as the axis of reflection, and the corresponding points are equidistant from this line.

To illustrate this, imagine a triangle ABC and its reflected image A'B'C'. The corresponding points A and A' lie on a line perpendicular to the reflecting line.

The same applies to points B and B', as well as C and C'.

Therefore, the pairs of corresponding points do not lie on parallel lines but rather on lines perpendicular to the reflecting line.

b. In a translation, pairs of corresponding points are on parallel lines. True.

When we consider the translation transformation, all pairs of corresponding points lie on parallel lines.

A translation involves shifting all points in the same direction and distance, maintaining the same orientation between them.

Therefore, the corresponding points will form parallel lines.

For example, let's consider a square ABCD and its translated image A'B'C'D'.

The pairs of corresponding points, such as A and A', B and B', C and C', D and D', will lie on parallel lines, as the entire shape is shifted uniformly in one direction.

Hence the first statement is false and second statement is true.

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Different types of integer models refer to different formulations and restrictions applied to the variables in mathematical optimization problems. Here are brief explanations of three commonly used types of integer models: total integer model, 0-1 integer model, and mixed integer model.

1. Total Integer Model: In a total integer model, all variables are required to take integer values. This means that the solution must consist of only whole numbers, without any fractional or decimal values. For example, if a variable represents the number of units to produce, a total integer model would ensure that only whole units can be produced.

2. 0-1 Integer Model: In a 0-1 integer model, the variables are binary and can only take two values: 0 or 1. This formulation is often used for decision variables that represent choices or binary decisions, such as selecting or not selecting a particular option. For example, in a facility location problem, a 0-1 integer variable can represent whether a facility is open (1) or closed (0).

3. Mixed Integer Model: A mixed integer model allows a combination of integer and continuous variables in the optimization problem. Some variables can take fractional or decimal values (continuous), while others must take integer values. This formulation is useful when there is a need to model both discrete decisions and continuous quantities in the same problem. For example, in a production planning problem, the number of machines (integer) and the amount of raw material used (continuous) can be decision variables in a mixed integer model.

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Answer: Since all the corresponding sides of two congruent polygons will be equal, their scale factor will be 1.

Step-by-step explanation:

Answer:

16/2×4−20 = 12

Step-by-step explanation:

NOTE : Make sure to review the order of operations

16/2×4−20 = (16÷2)×4-20

                  = 8×4-20

                  = 32-20

                  = 12

a) The 90% confidence interval for the population mean is approximately (21.52, 23.48).

b) The 95% confidence interval for the population mean is approximately (21.322, 23.678).

c) The 99% confidence interval for the population mean is approximately (20.926, 24.074).

To develop confidence intervals for the population mean, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

where the standard error is equal to the sample standard deviation divided by the square root of the sample size.

a) For a 90% confidence interval, we need to find the critical value corresponding to a confidence level of 90%. The critical value can be obtained from the t-distribution table with (n-1) degrees of freedom. Since the sample size is 56, the degrees of freedom is 56-1 = 55.

From the t-distribution table, the critical value for a 90% confidence interval with 55 degrees of freedom is approximately 1.671.

The standard error can be calculated as:

Standard Error = sample standard deviation / sqrt(sample size)

Standard Error = 4.4 / sqrt(56)

Standard Error ≈ 0.5882

Now we can calculate the confidence interval:

Confidence Interval = 22.5 ± (1.671 * 0.5882)

Confidence Interval = 22.5 ± 0.9816

Confidence Interval ≈ (21.52, 23.48)

b) For a 95% confidence interval, the critical value for 55 degrees of freedom is approximately 2.004 (obtained from the t-distribution table).

Standard Error = 4.4 / sqrt(56) ≈ 0.5882

Confidence Interval = 22.5 ± (2.004 * 0.5882)

Confidence Interval = 22.5 ± 1.178

Confidence Interval ≈ (21.322, 23.678)

c) For a 99% confidence interval, the critical value for 55 degrees of freedom is approximately 2.678 (obtained from the t-distribution table).

Standard Error = 4.4 / sqrt(56) ≈ 0.5882

Confidence Interval = 22.5 ± (2.678 * 0.5882)

Confidence Interval = 22.5 ± 1.574

Confidence Interval ≈ (20.926, 24.074)

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Answer

First Question

Options A and B are correct.

The correct answers that satisfy the inequality given include 1600 and 2000.

Second Question

d = 948.6 m

Explanation

We are given that

√x ≥ 40

We are then asked to pick the options that satisfy the given expressio,

To do this, we need to first square both sides

√x ≥ 40

x ≥ 1600

So, for the options, we will pick the answers that are greater than or equal to 1600

The correct answers include 1600 and 2000.

All the other options are not equal to or greater than 1600.

Second Question

We are given that the expression that gives the relationship between the distance the object falls (d) and the time taken (t) is

√d = (t) . (2.8)

√d = 2.8t

We are then asked to solve the distance a screw that falls for 11 seconds falls

√d = 2.8t

t = 11 seconds

√d = 2.8t

√d = 2.8 (11)

√d = 30.8

Square both sides

d = 948.6 m

Hope this Helps!!!

Answer:

Step-by-step explanation:

A

Answer:

y x y x y is simplified as y³

Step-by-step explanation:

Hoped this helped.

Answer:

The angle is determined by dividing 360 by the number of vertexes that it took to complete the circle. The tangent of the 100th triangle would be the same respectively.

Step-by-step explanation:

I remember learning this in kindergarten.

Answer:

45 children

Step-by-step explanation:

30% of 150=45

Answer:

45 6th graders

Step-by-step explanation:

30% of 150 is 45

Answer:

H is the height

Step-by-step explanation:

A= Area

B= Base

1/2= 0.5

Investment X earns the greater amount of interest over a period of 2 years.

Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,

SI = PRT

where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.

Let's consider that Ian invests in X, then:

Principle amount, P = $6,000
Time, T = 2 Years

Rate of Interest, R = 4.5% at simple Interest = 0.045

The interest earned is:

Interest = PRT = $6,000 × 0.045 × 2 = $540

Now, consider that Ian invests in Y, then:

Principle amount, P = $6,000
Time, n = 2 Years

Rate of Interest, R = 4% at Compound Interest = 0.04

The interest earned is:

Interest = P(1+R)ⁿ - P

            = $6,000(1+0.04)² - $6,000

            = $489.6

Since $540>$489.6, therefore, Investment X earns the greater amount of interest over a period of 2 years.

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Answer:

40

Step-by-step explanation:

Cost of the bottles of water = $0.75

Sales of the bottle= $1.05

markup Price= [(Sales of the bottle)-(Cost of the bottles of water)]/Cost of the bottles of water

= ($1.05- $0.75)/$0.75

= $0.30/$0.75

=0.40×100%

40%

=

The solution to the problem is the simplified expression: 5x³ - x² - 3x + 13.

To solve the given problem, you need to simplify and combine like terms. Start by adding the coefficients of the same degree terms.

(3x³ - x² + 4) + (2x³ - 3x + 9)

Combine the like terms:

(3x³ + 2x³) + (-x²) + (-3x) + (4 + 9)

Simplify further:

5x³ - x² - 3x + 13

In this expression, the highest power of x is ³, and the corresponding coefficient is 5. The term -x² represents the square term, -3x represents the linear term, and 13 is the constant term. The simplified expression does not have any like terms left to combine, so this is the final solution.

Remember to check for any specific instructions or constraints given in the problem, such as factoring or finding the roots, to ensure you address all requirements.

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Step-by-step explanation:

novels : cookbooks : reference books

Answer:

6 : 33 : 8

Step-by-step explanation:

cookbook = C

novel = N

reference book = R

C : N = 2 : 11

C : R = 3 : 4

C : N : R = ?

Start with C : N = 2 : 11

2 is not divisible by 2, so multiply this ratio by 3.

C : N = 6 : 33

C : R = 3 : 4 multiply by 2 to get

C : R = 6 : 8

C : N : R = 6 : 33 : 8

The correct answer is option D: The probability that an item is selected depends on the ease of selection.

Convenience sampling involves selecting items for a sample based on their easy availability or accessibility. This method does not follow the principles of statistical sampling, as it does not aim to provide a representative sample that reflects the characteristics of the entire population.

The correct answer is option D: The probability that an item is selected depends on the ease of selection. In convenience sampling, the probability of selecting an item is influenced by the ease and convenience of including it in the sample. Items that are more accessible or convenient to sample are more likely to be included, while those that are difficult to access or inconvenient may be overlooked. This leads to a nonuniform selection process, making convenience sampling nonstatistical.

Since convenience sampling does not guarantee a random or representative sample, the results obtained from such a sample may not be generalizable to the entire population. It can introduce bias and limit the external validity of the findings. Therefore, researchers often opt for other sampling methods, such as random sampling, to ensure the statistical validity and generalizability of their research.

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True, the joint probability of Y1 and Y2 taking on the value 1 simultaneously is 1/3.

The first dummy random variable is defined as follows:

Let X be the random variable representing the number on the first dice. Then, the dummy random variable Y1 is defined as:

Y1 = 1 if X is either 1, 2, or 3

Y1 = 0 otherwise

Similarly, the second dummy random variable is defined as:

Let Z be the random variable representing the number on the second dice. Then, the dummy random variable Y2 is defined as:

Y2 = 1 if Z is either 3, 4, 5, or 6

Y2 = 0 otherwise

Since Y1 and Y2 are independent, their joint probability distribution can be computed by multiplying their marginal probabilities.

P(Y1=1, Y2=1) = P(Y1=1) * P(Y2=1)

To compute P(Y1=1), we need to find the probability that X is either 1, 2, or 3. Since each face of a fair dice has an equal probability of appearing, we have:

P(X=1) = P(X=2) = P(X=3) = 1/6

Therefore,

P(Y1=1) = P(X=1 or X=2 or X=3) = P(X=1) + P(X=2) + P(X=3) = 3/6 = 1/2

Similarly, to compute P(Y2=1), we need to find the probability that Z is either 3, 4, 5, or 6. Again, since each face of a fair dice has an equal probability of appearing, we have:

P(Z=3) = P(Z=4) = P(Z=5) = P(Z=6) = 1/6

Therefore,

P(Y2=1) = P(Z=3 or Z=4 or Z=5 or Z=6) = P(Z=3) + P(Z=4) + P(Z=5) + P(Z=6) = 4/6 = 2/3

Thus,

P(Y1=1, Y2=1) = P(Y1=1) * P(Y2=1) = (1/2) * (2/3) = 1/3

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Londell needs to deliver newspapers for 24 weeks to have enough money to buy the bicycle.

Londell currently has $40 saved, and he needs a total of $400 to buy the bicycle. Each week, he earns $15 delivering newspapers.

To calculate the number of weeks Londell needs to work, we can set up an equation:

$40 (current savings) + $15 (weekly earnings) × (number of weeks) = $400 (total cost of the bicycle)

Simplifying the equation:

$40 + $15 = $400

Subtracting $40 from both sides of the equation:

$15 = $400 - $40

$15 = $360

Dividing both sides of the equation by $15:

= $360 / $15

≈ 24

Therefore, Londell will have to deliver newspapers for approximately 24 weeks to have enough money to buy the bicycle.

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Solution:

1. Since the numbers must be divisible by 2 even numbers, all odd numbers are ruled out because odd numbers are not divisible with even numbers.

In this case, the numbers that are possible are:

2. Since the numbers must be divisible by 5, it rules out a few more numbers.

In this case, the remaining numbers are:

We can clearly tell that the only number that is divisible by 8, 5, and 4 is 80.

Thus, 80 is the number.

The standard deviation of the difference \( y \) is approximately 0.583.

The mean and standard deviation of the difference, denoted as \( y \), between the ball diameters produced by the two machines can be determined based on the given information that the diameters are independently and normally distributed by \( N(8, 0.17) \).

The mean of the difference can be calculated as the difference between the means of the individual distributions:

\(\[\text{Mean of } y = \text{Mean of machine 1} - \text{Mean of machine 2}\]\)

Since both machines have the same mean of 8 (given by \( N(8, 0.17) \)), the mean of \( y \) is:

\(\[\text{Mean of } y = 8 - 8 = 0\]\)

Therefore, the mean of the difference \( y \) is 0.

To calculate the standard deviation of the difference, we can use the property that the variance of the sum or difference of independent random variables is equal to the sum of their variances.

The variance of the difference can be calculated as:

\(\[\text{Variance of } y = \text{Variance of machine 1} + \text{Variance of machine 2}\]\)

Since the variance is equal to the square of the standard deviation, we can find the standard deviation of \( y \) by taking the square root of the variance.

Given that the variance of each machine is 0.17 (given by \( N(8, 0.17) \)), the variance of \( y \) is:

\(\[\text{Variance of } y = 0.17 + 0.17 = 0.34\]\)

Taking the square root of the variance, we obtain:

\(\[\text{Standard deviation of } y = \sqrt{0.34} \approx 0.583\]\)

Therefore, the standard deviation of the difference \( y \) is approximately 0.583.

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An example of a function which is differentiable function on the real line r with exactly two roots but its derivative having 5 roots is\(f(x) = (x+2)(x-3)^2\)

The given information implies that the function f(x) has two x-intercepts and the derivative of f(x), denoted as f'(x), has five x-intercepts. Therefore, the graph of f(x) must have two local extrema (one minimum and one maximum) and the graph of f'(x) must have three local extrema (two minima and one maximum).

To construct an example of such a function, consider the following:

\(f(x) = (x+2)(x-3)^2\)

The function f(x) has two roots at x = -2 and x = 3, and its derivative is:

\(f'(x) = 3(x-3)^2 + 2(x-3)(x+2)\)

Simplifying f'(x), we get:

\(f'(x) = 5(x-3)^2 - 4(x-3)(x+2)\)

The derivative f'(x) has roots at x = -2, x = 1, x = 3, x = 5, and x = 9, implying that f(x) has local extrema at x = 1 and x = 5.

Thus, this example function satisfies the given conditions.

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As per the Maclaurin series, the value of the function is written as 2.8521

The term Maclaurin series is defined as  a function that has expansion series that gives the sum of derivatives of that function.

Here we have given that the function is \(\sum\frac{(-1)^n\pi^{2n}}{4^{2n}(2n)!}\)

And we need to find the sum of series by using the Maclaurin series as

Now, the sum of series is calculated as,

=>f(n) =  \(\sum\frac{(-1)^n\pi^{2n}}{4^{2n}(2n)!}\)

When we put the value on n = 0, then we get,

=> f(0) = [1 x 3.14]/1] =  3.14

Now, we have to put the value of the function, the value of x as 1,

Then we get,

=> f(1) = [-1 x 9.8596] / [16 x 2]

=> f(1) = -0.308

And then we have to put the value of function for the value of x as 2,

Then we get,

=> f(2) = [1 x 30.959] / [64 x 24]

=> f(2) = 0.0201

Then the sum of the series is

=> 3.14 - 0.308 + 0.0201

=> 2.8521

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The step of data storytelling that describes showing the story of the data to highlight the meaning behind the numbers is "Visuals". The correct answer is option (d).

Visuals are an important aspect of data storytelling because they can help to convey complex information in a simple and easy-to-understand way. Visuals can include graphs, charts, diagrams, and other types of visual aids that appeal to the sight and are used for effect or illustration.

By using visuals, a data analyst can help their audience to better understand the story that the data is telling and to see the patterns and trends that might not be presently alleged from the raw numbers alone.

Hence, the correct answer is option (d).

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The complete question is as follows:

A data analyst wants to tell a story with data. As a second step, they focus on showing the story of the data to highlight the meaning behind the numbers. which step of data storytelling does this describe?

a. Primary message

b. Engagement

c. Narrative

d. Visuals

The system of equations has infinite solutions, both equations represent the same line.

Here we have the following system of equations:

-3x+6y=12

2y=x+4

And we want to solve this by substitution, first, we can rewrite the first equation as:

-3x + 3*(2y) = 12

Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:

-3x + 3*(x + 4) = 12

Now we can solve this for x.

-3x + 3x + 12 = 12

12 = 12

So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).

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Answer:

(1) = 3

(2) = 7

(3) = -5

(4) = -7

(5) = -12

(6) = -19

(7) = -8

(8) = 5

(9) = 0

(10) = 0

(11) = -6

Second row:

(18) = -13

(19) = -30

(20) = -5

(21) = -46

(22) = 15

(23) = -8

(24) = -15

(25) = 0

(26) = -7

(27) = -56

(28) = -36

On Mondays at noon, the switchboard in a Minneapolis legal firm receives an average of 5.5 incoming calls. Consequently, X's standard deviation is 2.35 calls.

The current personnel can handle up to six calls in an hour, according to experience.

A Poisson distribution with an average number of calls  of 5.5 on Mondays around lunchtime can be used to model the scenario that is being given.

Thus, the following equation represents the standard deviation for the number of calls received, X:

2.35 calls make up the standard deviation of X.

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Answer:

?

Step-by-step explanation:

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