The new Play Station 5 is price at 500$. For Christmas, it is priced at 420$. What is the percent change?

Answer:

An impossible event has a probability of 0. A certain event has a probability of 1.

This will increase the probability of rejecting a false null hypothesis and accepting a true alternative hypothesis.The political advisor should ensure proper sampling, increase the alpha level, and have a larger sample size to reduce the risk of making a Type II error. A type II error is when a null hypothesis is accepted when it is false.

Suppose a political advisor is interested in the proportion of the vote an opponent will receive. If he samples voters randomly and tests hypotheses regarding p, the population proportion, he should do the following to reduce his risk of making a Type II error:To reduce the risk of making a Type II error, a political advisor interested in the proportion of the vote an opponent will receive, if he samples voters randomly and tests hypotheses regarding p, the population proportion should ensure that he has a larger sample size for testing. A larger sample size can help in making his results statistically significant and that the results are a true representation of the population.Proper sampling can also help to reduce the risk of a Type II error. Random sampling of the voters ensures that there is no bias in the selection process, which can skew the results. A random sample of voters is a fair representation of the population, and results obtained from a random sample are more likely to be accurate. This reduces the likelihood of a Type II error.The advisor should also increase the alpha level to reduce the risk of a Type II error. By increasing the alpha level, he is lowering the rejection region, which will reduce the likelihood of a Type II error. This will increase the probability of rejecting a false null hypothesis and accepting a true alternative hypothesis.The political advisor should ensure proper sampling, increase the alpha level, and have a larger sample size to reduce the risk of making a Type II error. A type II error is when a null hypothesis is accepted when it is false.

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Hydrostatic weighing uses the statistic known as density to predict the percentage of body fat.

Hydrostatic weighing, also known as underwater weighing or densitometry, is a method used to estimate body composition by measuring the density of an individual's body.

The principle behind hydrostatic weighing is that fat tissue is less dense than lean tissue, such as muscle and bone.

During a hydrostatic weighing test, the individual is submerged in water while their body volume is measured. By comparing the weight on land with the weight in water, the density of the body can be calculated.

The measured density is then used in equations or regression models to estimate the percentage of body fat.

The statistic of density is crucial in this process because it represents the ratio of an individual's mass to their volume.

By accounting for the density of fat and lean tissue, hydrostatic weighing provides an estimate of body fat percentage based on the differences in density between these components.

It is worth noting that while hydrostatic weighing has been widely used as a reference method for body composition assessment, more modern techniques such as dual-energy X-ray absorptiometry (DXA) and bioelectrical impedance analysis (BIA) have gained popularity due to their convenience and accessibility.

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The solution to the given differential equation \(y'' + 2y' - 3y = 0\), with initial conditions \(y(0) = 2\) and \(y'(0) = 0\) by applying Laplace transform is \(y(t) = e^{(-3t)} + 3e^t\)

To solve the given differential equation \(y'' + 2y' - 3y = 0\) using the Laplace transform, we'll first apply the Laplace transform to the equation. Let Y(s) represent the Laplace transform of y(t), denoted as Y(s) = L[y(t)].

Applying the Laplace transform to the equation, we get:

\(s^2Y(s) - sy(0) - y'(0) + 2sY(s) - 2y(0) - 3Y(s) = 0\)

Substituting the initial conditions y(0) = 2 and y'(0) = 0, the equation becomes:

\(s^2Y(s) - 2s + 2 + 2sY(s) - 6 - 3Y(s) = 0\)

Rearranging the terms, we have:

\((s^2 + 2s - 3)Y(s) = 4s - 4\)

Now, solving for Y(s), we divide both sides of the equation by (s^2 + 2s - 3):

\(Y(s) = (4s - 4) / (s^2 + 2s - 3)\)

Now, we need to decompose the right side of the equation into partial fractions. Factoring the denominator, we have:

\(Y(s) = (4s - 4) / ((s + 3)(s - 1))\)

To find the partial fraction decomposition, we assume:

\(Y(s) = A / (s + 3) + B / (s - 1)\)

Multiplying both sides by (s + 3)(s - 1), we get:

\(4s - 4 = A(s - 1) + B(s + 3)\)

Expanding and simplifying:

\(4s - 4 = As - A + Bs + 3B\)

Equating coefficients of like terms:

4s - 4 = (A + B)s - A + 3B

From the coefficients of the terms involving 's', we have:

A + B = 4 (coefficient of 's')

-A + 3B = -4 (constant term)

Solving these equations, we find A = 1 and B = 3.

Substituting these values back into the partial fraction decomposition:

\(Y(s) = 1 / (s + 3) + 3 / (s - 1)\)

Now, taking the inverse Laplace transform of Y(s) using the table of Laplace transforms, we find:

\(y(t) = e^{(-3t)} + 3e^t\)

Therefore, the solution to the given differential equation \(y'' + 2y' - 3y = 0\), with initial conditions \(y(0) = 2\) and \(y'(0) = 0\) by applying Laplace transform is \(y(t) = e^{(-3t)} + 3e^t\).

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Answer:

Step-by-step explanation:

a linear equation is of degree 1.

It is of degree 2 so it is not a linear equation.

Answer:

78 is a solution

Step-by-step explanation:

The given equation is b/13 = 6

Therefore, by applying the multiplication property of equality, we have by multiplying both sides by 13, we have;

b/13 × 13 = 6 × 13

The 13 in the denominator of b/13 divides the 13 in the multiplicand to give 1, and we get the following equation

b/13 × 13 = b × 1

Therefore;

b/13 × 13 = b × 1  = 6 × 13 = 78

b × 1 = 78

By the multiplicative identity property of '1', we get;

b × 1 = 1 × b = b

∴ b × 1 = b = 78

b = 78

∴ 78 is a solution of the equation.

Answer:

No solution

Step-by-step explanation:

\(y=-2x+1\)

\(4x+2y=-1\)

The first equation is set up in slope-intercept form but the second equation isn't. So first set up the second equation in slope-intercept form.

\(4x+2y=-1\)

Divide everything by 2

\(2x+y=-\frac{1}{2}\)

Solve for y

\(y=-2x-\frac{1}{2}\)

Both equations have the same slope but different y-intercepts which means that there is no solution

Answer:

AE

Step-by-step explanation:

Because it intersects with EJ.

Whereas skew lines are those that do not inersect and not parallel with each other.

Hope it helps :)

Answer: AE

Step-by-step explanation:

Answer:

3 1 4 7 9 3 8

Step-by-step explanation:

Answer: 52 = 2, 4, 13, 52

Step-by-step explanation:

Answer:

Step-by-step explanation:

I assume the figures are parallelograms, then

1). KL = MJ and

12x - 22 = 7x - 2

12x - 7x = 22 - 2

5x = 20

x = 4

2). m∠RQT + m∠QTS = 180°

(The picture is not clear and I might be wrong about coefficients by x for ∠RQT and ∠QTS)

(3x + 5)° + (9x - 17)° = 180°

12x - 12 = 180

12x = 192

x = 16

The equation which is used to find the number of chocolates candy in the jar is given by 18 + 24 + 19 + n = 82 , the number of chocolate candy in the jar is equal to 21.

Number of strawberry candy in the jar = 18

Number of cherry candy in the jar = 24

Number of lime flavored candies = 19

Let 'n' be the number of chocolate candy in the jar

Total number of candy in the jar = 82

Equation used to represent the given condition is :

18 + 24 + 19 + n = 82

⇒ 61 + n = 82

⇒ n = 82 - 61

⇒ n = 21

Therefore, the equation required to represent the number of chocolate candy is 18 + 24 + 19 + n = 82 and the value of n is equal to 21.

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We are looking for the value of t when d(t) equals 250. So:

\(d(t)=250\\-16t^2+400t=250\)

So let's solve for t. The best way to do this is by using the Quadratic Formula. This evaluates quadratic equations. Quadratic equations are trinomials with a degree of two.

\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\-16t^2+400t=250\\-16t^2+400t-250=250-250\\-16t^2+400t-250=0\\\\t=\frac{-400\pm\sqrt{400^2-4(-16)(-250)}}{2(-16)}\\t=\frac{-400\pm\sqrt{160000-4(4000)}}{-32}\\t=\frac{-400\pm\sqrt{160000-16000}}{-32}\\t=\frac{-400\pm\sqrt{144000}}{-32}\\t=\frac{-400\pm379.47}{-32}\\t=\frac{-20.53}{-32},\frac{-779.47}{-32}\\t=0.641,24.36\)

So the projectile will be at a height of 250ft at 0.641 seconds and 24.36 seconds.

Answer:

Rate me 1 star if wrong but its answer A

Step-by-step explanation:

Answer:

The probably need to sell 340 more

Step-by-step explanation:

1500divided by25 is 60. So they have sold 60. 10,000 divided by 25 is 400, so they need to sell 400 cups to reach their goal.

A p-value for correlation which is statistically significant implies the correlation is due to random chance. The correct solution to this is False.

A p-value for correlation which is statistically significant implies that it is unlikely that the observed correlation is due to random chance alone. In other words, it suggests that there is evidence to support the presence of a true correlation between the two variables being studied. The p-value is a measure of the strength of evidence against the null hypothesis (i.e., that there is no correlation between the two variables), and a smaller p-value indicates stronger evidence against the null hypothesis.

Interpretation of the intercept: The intercept in a linear regression model represents the value of the dependent variable when all independent variables are equal to zero. It is the value of the dependent variable when there is no effect of the independent variable(s) on it. For example, in a regression model predicting height based on age, the intercept would represent the expected height of a person at age zero (which is not a realistic scenario).

Interpretation of a residual: A residual is the difference between the actual observed value of the dependent variable and the predicted value of the dependent variable based on the regression model. It represents the part of the dependent variable that the model was not able to explain. A positive residual means that the actual value is greater than the predicted value, while a negative residual means that the actual value is smaller than the predicted value.

Interpretation of r-squared: R-squared is a measure of how much of the variation in the dependent variable is explained by the independent variable(s) in the regression model. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data. Specifically, it represents the proportion of the total variation in the dependent variable that is explained by the independent variable(s) in the model. For example, if r-squared is 0.75, it means that 75% of the variability in the dependent variable is explained by the independent variable(s) in the model.

Interpretation of the slope: The slope in a linear regression model represents the change in the dependent variable that is associated with a one-unit increase in the independent variable, holding all other variables constant. It reflects the average change in the dependent variable for each unit change in the independent variable. For example, in a regression model predicting height based on age, the slope would represent the average change in height for each additional year of age.

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Answer:

1. 38.3 x 10^5

2. 6.67 x 10^9

3. 4.48 x 10^4

Step-by-step explanation:

4.2 X 10 ^6 - 1.2 X 10^5 - 2.5 x 10^5

For the above question, we need to make the exponents equal

=> 42 x 10^5  -  1.2 x 10^5  -  2.5 x  10^5

SInce, all the exponents are equal, we can now add and subtract the normally.

=> (42 - 1.2 -2.5) x 10^5

=> (42 - 3.7) x 10^5

=> 38.3 x  10^5

So, the answer to the 1st question is 38.3 x 10^5

Next question:

=> 3.3 x 10^9 + 2.6 x 10^9 +7.7 x 10^8

=>  we need to make the exponents equal

=> 3.3 x 10^9 + 2.6 x 10^9 + .77 x 10^9

=> All the exponents are equal, we can now add and subtract the normally.

=> (3.3 + 2.6 + .77) x 10^9

=> 6.67 x 10^9

=> So the answer to the 2nd question is 6.67 x 10^9

Next question,

=> 8 X 10^4 - 3.4 x 10^4  - 1.2 x 10^3

=> we need to make the exponents equal

=> 8 x 10^4 - 3.4 x 10^4 - .12 x 10^4

=> All the exponents are equal, we can now add and subtract the normally.

=> (8 - 3.4 - .12) x 10^4

=> 4.48 x 10^4

=> So the answer to the 3rd question is 4.48 x 10^4

The solutions to the expressions are:

\(4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5\)=\(38.3\times 10^5\)

\(3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8\) = \(6.67\times 10^9\)

\(8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3\) = \(4.48 \times 10^4\)

\(4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5\)

Combine like terms:

\(4.2 \times 10^6 - (1.2+2.5) \times 10^5\)

\(4.2 \times 10^6 - 3.7 \times 10^5\)

\(42 \times 10^5 - 3.7 \times 10^5\)

\((42-3.7)\times 10^5\)

\(38.3\times 10^5\)

\(3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8\)

Convert all terms with same power:

\(3.3 \times 10^9 + 2.6 \times 10^9 + 0.77 \times 10^9\)

\((3.3+2.6+0.77) \times 10^9\)

\(6.67\times 10^9\)

\(8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3\)

\(8.0 \times 10^4 - 3.4 \times 10^4 - 0.12 \times 10^4\)

\((8.0-3.4-0.12) \times 10^4\)

\(4.48 \times 10^4\)

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Answer:

X=4

I’m pretty sure

Answer:

x=32

Step-by-step explanation:

Answer:

  (d)  219.80 ft

Step-by-step explanation:

The side opposite the angle is given, and we want to find the side adjacent. The relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(20°) = (80 ft)/(distance to sculpture)

This rearranges to ...

  distance to sculpture = (80 ft)/tan(20°) ≈ 219.80 ft

Answer:

The volume of the rectangular prism in cubic inches is;

Explanation:

Given the figure in the attached image;

The edge length of each cube is 1/2 in.

so, the height of the rectangular prism which has two cubes is;

The length and width of the rectangular prism is;

Recall that the volume of a rectangular prism can be calculated using the formula;

substituting the values;

Therefore, the volume of the rectangular prism in cubic inches is;

The probability of an event is a number describing the chance that the event will happen. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1.

An event that is certain to happen has a probability of 1.

Answer:

85

Step-by-step explanation:

i useed the formula LxWxH

i came up with 85

5x5x3.5

\(\\ \sf\longmapsto x+40=90\)(Complementary)

\(\\ \sf\longmapsto x=90-40\)

\(\\ \sf\longmapsto x=50\)

Now

\(\\ \sf\longmapsto y+40=180\)

\(\\ \sf\longmapsto y=180-40\)

\(\\ \sf\longmapsto y=140\)

Now

\(\\ \sf\longmapsto x+y=140+50=190\)

The sum of any tetracontadigon's interior angles is 7200 degrees.

Answer:

It will take the ant 10 minutes to reach its hole.

Step-by-step explanation:

The partial fraction decomposition is:

\((14x + 34) / (x^2 + 6x + 5) = 14/(x+5) + 5/(x+1)\)
This can be helpful in evaluating integrals or simplifying complicated rational expressions.

To express the given rational function in terms of partial fractions, we first need to factor the denominator. We can see that x^2 + 6x + 5 factors to (x+5)(x+1).

Next, we need to determine the form of the partial fractions. Since the denominator has distinct linear factors, we can write the partial fraction decomposition as:

\((14x + 34) / (x^2 + 6x + 5) = A/(x+5) + B/(x+1)\)

where A and B are constants that we need to solve for.

To solve for A and B, we can multiply both sides by the denominator and simplify:

14x + 34 = A(x+1) + B(x+5)

Setting x = -1, we get:

14(-1) + 34 = A(-1+1) + B(-1+5)
-14 + 34 = 4B
B = 5

Setting x = -5, we get:

14(-5) + 34 = A(-5+1) + B(-5+5)
-56 = -4A
A = 14

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Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:

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

Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years

In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.

For the simple interest option, the interest is calculated using the formula:

I = P * r * t

Where:

I is the total interest earned

Using the given values, we can calculate the interest earned with simple interest:

I = 3000 * 0.03 * 7
I = 630

Now, let's calculate the total amount earned with the compound interest option.

Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:

r = 0.03/12

t = 7 * 12

Using these values, we can calculate the total amount with compound interest:

\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)

A ≈ 3,729.19

To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:

Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19

Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

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The surface area of the rectangular prism is 88 square inches.

Given that:

Length, L = 6 inches

Width, W = 2 inches

Height, H = 4 inches

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

SA = 2(6 x 2 + 2 x 4 + 4 x 6)

SA = 2 (12 + 8 + 24)

SA = 2 x 44

SA = 88 square inches

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