7

Consider the following table. Find the corresponding percent discount and fill in the blank.

A discount percent is a percent of change. Use the percent of change formula: (change in price

Note: Write your answer using the percent sign (%) as the example shows.

Original Price Sale Price

$90 $54

$79 $75. 84

$50 $20

$51 $47. 84

The expression when solved for a = 8 is 26

Algebraic expressions are defined as mathematical expressions that are made up of terms, variables, constants, coefficients, and factors.

Also, algebraic expressions are seen as expressions that consist of mathematical operations.

These mathematical operations are;

From the information given, we have;

(–4a – 6) + a2 for a = 8

Now, substitute the value of a as 8 in the expression, we have;

(-4(8) - 6) + (8)^2

find the square

-32 - 6 + 64

Add the values

26

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The heavy marble using a two-pan balance, the minimum number of weighings required is two.

Here's how you can do it:

Divide the eight marbles into two groups of four.

Weigh the two groups against each other.

If the two groups weigh the same, the heavy marble is one of the remaining four marbles. Proceed to step 3.

If one group weighs more, the heavy marble is in that group. Proceed to step 3.

Divide the four marbles from the heavier group into two groups of two.

Weigh the two groups of two against each other.

If the two groups weigh the same, the heavy marble is one of the remaining two marbles. Proceed to step 5.

If one group weighs more, the heavy marble is in that group. Proceed to step 5.

Weigh the remaining two marbles against each other.

The heavier marble is the heavy marble.

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a. Using a significance level of α = 0.01, the critical values for a two-tailed test are ±2.576.

b. To determine whether to reject or fail to reject the null hypothesis, we compare the test statistic (-3.25) to the critical values. Since -3.25 is less than -2.576, we can reject the null hypothesis at the 0.01 significance level. This means we have evidence to support the claim that p = 3/5.

What is significance level?

Significance level, denoted as alpha (α), is the probability threshold used to determine whether a statistical hypothesis is rejected or not. It represents the maximum level of Type I error that a researcher is willing to accept.

A test statistic is a numerical value calculated from a sample of data that is used in hypothesis testing to determine whether to reject or fail to reject a null hypothesis.

The test statistic is compared to a critical value to make this determination. The critical value is a threshold value determined by the level of significance and the degrees of freedom of the sample.

If the test statistic falls within the rejection region determined by the critical value, the null hypothesis is rejected. If the test statistic falls outside the rejection region, the null hypothesis is not rejected.

a. Using a significance level of α = 0.01, the critical values for a two-tailed test are ±2.576.

b. To determine whether to reject or fail to reject the null hypothesis, we compare the test statistic (-3.25) to the critical values. Since -3.25 is less than -2.576, we can reject the null hypothesis at the 0.01 significance level. This means we have evidence to support the claim that p = 3/5.

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Answer:

28.5

Step-by-step explanation:

7 times 18

plus 45

divided by 6(2x3)

Answer:

B) 175

Step-by-step explanation:

Same thing as before:

To get from 1.4 to 7 and to get from 7 to 35, you have to multiply by 5.

To get from 35 to the next sequence, you also have to multiply by 5.

35·5

=175

Hope this helps! :)

Answer:

7=1.4n

n=7÷1.4

n=5

next term =35×5

=175 B

Answer:

8

Step-by-step explanation:

3.2 times 1.8 is 5.76. so you just add up their powers to get answer

The answer will be 5.76x 108

We are given,(3.2 x 103)(1.8 x 105)

Now, (3.2 x 1.8) (103 x 105)

5.76 x 108

the researcher can conclude that private hospitals pay more than government-owned hospitals based on the sample data.

To test whether private hospitals pay more than government-owned hospitals, we can use a two-sample t-test with equal variances.

The null hypothesis is that there is no difference in mean salary between the two groups:

H0: μprivate = μgovernment

The alternative hypothesis is that private hospitals pay more than government-owned hospitals:

Ha: μprivate > μgovernment

We can use a significance level of 0.01, which corresponds to a critical value of t = 2.364 (with degrees of freedom = 898).

First, we need to calculate the pooled standard deviation:

Sp = sqrt(((n private - 1)s^2private + (n government - 1)s^2government) / (n private + n government - 2))

where n private and n government are the sample sizes, s^2private and s^2government are the sample variances, and s^2pooled is the pooled variance.

Plugging in the values, we get:

Sp = sqrt(((100-1) * 186^2 + (800-1) * 176^2) / (100 + 800 - 2)) = 176.43

Next, we calculate the test statistic:

t = (x(bar)private - x(bar)government) / (Sp * sqrt(1/n private + 1/n government))

where x(bar)private and x(bar)government are the sample means.

Plugging in the values, we get:

t = (26,800 - 25,400) / (176.43 * sqrt(1/100 + 1/800)) = 3.14

Since our test statistic (3.14) is greater than the critical value (2.364), we reject the null hypothesis and conclude that private hospitals pay more than government-owned hospitals at a significance level of 0.01.

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Since 23² is less than 12² + 20², we can conclude that the values 12, 20, and 23 do not create a right triangle.

To determine if the values 12, 20, and 23 create a right triangle, we can use the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

So, we can calculate:

12² + 20² = 144 + 400 = 544

23² = 529

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The prediction for the number of passwords in which the first character is a number is given as follows:

139 passwords.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The passwords have the first character chosen as follows:

Hence the probability of a number is given as follows:

p = 10/(10 + 26)

p = 10/36

p = 5/18.

Out of 500 passwords, the expected number is then given as follows:

E(X) = 500 x 5/18

E(X) = 139 passwords.

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The standard deviation for the given sample data is 2.83.

To calculate the standard deviation, we first need to calculate the mean of the sample data:

Next, we calculate the deviation of each data point from the mean:

Then, we square each deviation:

Next, we calculate the sum of squared deviations:

To calculate the variance, we divide the sum of squared deviations by the sample size minus one:

Finally, we calculate the standard deviation by taking the square root of the variance:

Therefore, the standard deviation for the given sample data is 2.83. This tells us how spread out the data points are from the mean, with most data points being within 2.83 units of the mean.

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Considering a number of 100 trials, the experimental probability of heads should be close to the theoretical probability of 1/2 = 50%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

A fair coin is equally as likely to come up heads or tails, hence the theoretical probability of heads is given as follows:

1/2 = 0.5 = 50%.

For a large number of trials, such as 100 trials, the experimental probability is expected to be close to the theoretical probability, hence it should also be close to 50%.

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(x, y) → (-x, -y) represents a rotation 180° clockwise.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

Rotation is the flipping of a figure about a point. Translation is the movement of a point either up, down, left or right in the coordinate plane. Dilation is the increase or decrease in the size of a figure.

(x, y) → (x - 7, y + 2) represents a translation 7 units left and 2 units to the up.

(x, y) → (-x, -y) represents a rotation 180° clockwise.

(x, y) → (x + 3.5, y + 3.5) represents a translation 3.5 units right and 3.5 units to the up.

(x, y) → (-x, y) represents a reflection over the y-axis

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The value of the triple integral is 72π.

To evaluate this triple integral in cylindrical coordinates, we first need to express the region E using cylindrical coordinates.

The cylinder x² + y² = 16 can be expressed in cylindrical coordinates as r² = 16, or r = 4. The planes z = -5 and z = 4 define a region of height 9.

So, the region E can be expressed in cylindrical coordinates as:

4 ≤ r ≤ 4

-5 ≤ z ≤ 4

0 ≤ θ ≤ 2π

The integrand √(x² + y²) can be expressed in cylindrical coordinates as r, so the integral becomes:

∭E√x²+y²dV = ∫0²π ∫4⁴ ∫-5⁴ r dz dr dθ

Note that the limits of integration for r are from 0 to 4, which means we are only integrating over the positive x-axis. Since the integrand is an even function of x and y, we can multiply the result by 2 to get the total volume.

The integral with respect to z is easy to evaluate:

∫₋₅⁴ r dz = r(4 - (-5))

= 9r

So the triple integral becomes:

∭E√x²+y²dV = 2 ∫0^2π ∫4⁴ 9r dr dθ

= 2(9) ∫0^²π 4 dθ

= 72π

Therefore, the value of the triple integral is 72π.

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In regression analysis, the variable that is being predicted is called the dependent variable or response variable. It is the outcome variable that is being measured or predicted based on the values of other variables, which are referred to as independent variables or predictors.

The independent variables are used to explain the variation in the dependent variable and to determine the strength and direction of their relationship.

Regression analysis is a statistical method that is used to estimate the relationship between the dependent variable and one or more independent variables by fitting a line or curve through the data points. The resulting regression equation can then be used to predict the value of the dependent variable based on the values of the independent variables.

The quality of the regression model is evaluated by measuring the goodness of fit, which measures how well the model fits the data, and by examining the significance of the coefficients, which measures the strength and direction of the relationship between the variables

. Overall, regression analysis is a powerful tool that is widely used in many fields to understand and predict the relationship between variables.

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The image of (−2, 6) after a dilation by a scale factor of 1/2 centered at the origin is (-1, 3)

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 1/2 centered at the origin as follows:

Ordered pair A (-2, 6) → Ordered pair A' (-2 × 1/2, 6 × 1/2) = Ordered pair A' (-1, 3).

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Answer:

-2

Step-by-step explanation:

This graph is a graph of f, that states it is equal to g'. We're graphing the first derivative, so that means g(3) is the integral of f, or the area under the curve. g'(3) is just asking for the y value that corresponds to the x value of f, because f and g' are equal.

g = ∫f

g' = f

And by extension,

g'' = f'

Because we're looking at a graph of f, finding f' is just finding the slope at f(3). Rise over run, -2 over 1, so g''(x) = f'(x) = -2

This dynamic programming algorithm will help you find the optimal solution for the coin-changing problem using the fewest number of coins.

To optimally solve the coin-changing problem for an arbitrary denomination set {d1, d2, ..., dk} and make up a value 'v' using the fewest number of coins, you can use a dynamic programming algorithm. Here's the step-by-step explanation:

1. Create an array 'dp' of length 'v+1' and initialize all elements with infinity (except dp[0], which should be 0, as you need 0 coins to make up a value of 0).
2. Sort the denomination set in ascending order.
3. Iterate through the denomination set using a variable 'coin' from d1 to dk.
4. For each 'coin', iterate through the 'dp' array starting from the index 'coin' up to 'v' using a variable 'i'.
5. In the inner loop, for each 'i', update the value of dp[i] with the minimum between dp[i] and 1 + dp[i-coin].
6. After the loops, the value of dp[v] will be the minimum number of coins needed to make up the value 'v'. If dp[v] is still infinity, then it's not possible to make up the value 'v' using the given denomination set.

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Answer:

A is the correct answer. x = 3.

Step-by-step explanation:

[tex] {49}^{x + 4} = {7}^{5x - 1} [/tex]

[tex] {7}^{2(x + 4)} = {7}^{5x - 1} [/tex]

[tex]2x + 8 = 5x - 1[/tex]

[tex]3x = 9[/tex]

[tex]x = 3[/tex]

the third side must be greater than 8 and less than 16.

To determine the range of possible lengths for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

So, for a triangle with sides of 4 and 12, the third side must satisfy:

12 - 4 < third side < 12 + 4

which simplifies to:

8 < third side < 16

what is triangle?

A triangle is a geometric shape with three sides and three angles. It is formed by connecting three non-collinear points in a plane. The sum of the interior angles of a triangle is always 180 degrees, and there are various types of triangles based on their side lengths and angle measures.

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If the point (3, -2) were reflected across the y-axis what would be the new y-coordinate is same as before, which is -2.

If a point (x, y) is reflected across the y-axis, its x-coordinate becomes its opposite (-x), while its y-coordinate remains the same.

In this case, the point is (3, -2). If we reflect this point across the y-axis, its x-coordinate will become its opposite, which is -3. The new coordinates of the reflected point will be (-3, -2).

Therefore, the new y-coordinate is still -2, as the point is only being reflected across the y-axis and not moving up or down in the y-direction. The change is only in the x-coordinate, which becomes its opposite.

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The confidence interval is (0.451, 0.549).

To find the confidence interval, we need to use the formula:

Confidence interval = sample proportion +/- margin of error

where the margin of error is calculated as:

Margin of error = z* (standard error)

The standard error is the standard deviation of the sampling distribution of the proportion, which is calculated as:

Standard error = [tex]\sqrt{p*(1-p)/n}[/tex]

where p is the sample proportion and n is the sample size.

The z-value corresponding to a 95% confidence level is 1.96.

Using the given information, we have:

Sample proportion (p) = 0.50

Sample size (n) = 400

Margin of error = 0.052 * 0.5 = 0.026

Standard error = [tex]\sqrt{0.5(1-0.5)/400}[/tex] = 0.025

Z-value for 95% confidence level = 1.96

So the confidence interval is:

0.50 +/- 1.96 * 0.025

= 0.50 +/- 0.049

Therefore, the confidence interval is (0.451, 0.549) or 45.1% to 54.9%. We can say with 95% confidence that the true proportion of respondents who agree with the statement lies between 45.1% and 54.9%.

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The difference in the Beatles length is 1 / 10 centimeters.

We have,

The lengths of Beetles are 4/5 cm and 7/10 cm.

So, the difference in the beetles length can be calculated as

difference between the beetles length = 4 / 5 - 7 / 10

                                                                 = 8 - 7 / 10

                                                                  = 1/10 cm

Thus, the difference in beetles length is 1/10 cm.

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It is true that every invertible square matrix can be written as a product of elementary matrices. because, it depends on whether you are talking about invertible square matrices or all square matrices.

An elementary matrix is a matrix that can be obtained from the identity matrix by performing a single elementary row operation (such as swapping two rows, multiplying a row by a scalar, or adding a multiple of one row to another).

Moreover, any matrix that can be expressed as a product of elementary matrices is invertible.

However, not every square matrix is invertible, and so not every square matrix can be written as a product of elementary matrices. For example, the zero matrix cannot be written as a product of elementary matrices since it is not invertible.

So, it depends on whether you are talking about invertible square matrices or all square matrices.

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Step-by-step explanation:

Right triangles obey Pythagorean theorem :

?^2  = 2^2 + 9^2

?^2 = 85

? = sqrt 85  ft

Answer:

85ft

Step-by-step explanation:

Answer:

Original price is $274

Step-by-step explanation:

Let

x = Original price of calculator ($)

Percentage decrease = [tex]\frac{Original Price - New Price}{Original Price}[/tex]× [tex]100[/tex]%

                              31% = [tex][\frac{x - 189.06}{x}][/tex] × [tex]100[/tex]%

                              [tex]\frac{31}{100}[/tex]  = [tex]\frac{x - 189.06}{x}[/tex]

                             0.31 = [tex]\frac{x - 189.06}{x}[/tex]

Cross-multiplication is applied:

                       [tex](0.31)(x)[/tex] = [tex](1)(x - 189.06)[/tex]

  Distributive Law is applied to expand the brackets or parentheses:

                            [tex]0.31x[/tex] = [tex]x - 189.06[/tex]

Like terms are brought together. At the same time, the unknown variable

x is isolated and made subject of the equation:

                          [tex]189.06[/tex] = [tex]x - 0.31x[/tex]

                          [tex]189.06[/tex] = [tex]0.69x[/tex]

                                [tex]x[/tex]  = [tex]\frac{189.06}{0.69}[/tex]

∴ x = Original price of the calculator = $274

G. One sample t-test for a proportion.

E. Two sample t-test for means independent.

A. In scenario 1, the nutrition major is interested in comparing the mean IQ scores of two groups: those who like Ovaltine and those who don't. Since the sample size of the group who don't like Ovaltine is small (n=5), it's not appropriate to use a z-test. Instead, a one-sample t-test for a mean can be used to compare the mean IQ scores of those who like Ovaltine to a hypothesized population mean (which could be the population mean IQ score, assuming that Ovaltine preference doesn't affect IQ).

B. In scenario 2, the engineering major is interested in comparing the means of two independent groups (oak wood beams and elm wood beams) with equivalent standard deviations. Since the sample sizes are both 50 and the standard deviation of the population is unknown, a two-sample t-test for means can be used to compare the means of the two groups.

C. In a matched pairs difference in means scenario, each subject in a sample is paired with another subject based on some characteristic that affects the outcome of the study (such as age, weight, or gender). In this scenario, the difference in scores between each pair of subjects is calculated, and a one-sample t-test can be used to determine whether the average difference between the two groups is statistically significant.

D. In a two-sample z-test for means scenario, the researcher is interested in comparing the means of two independent groups with known population variances. This type of test is rarely used in practice since population variances are usually unknown.

E. In a two-sample t-test for means independent scenario, the researcher is interested in comparing the means of two independent groups with unknown population variances. This is the most commonly used test for comparing the means of two independent groups.

F. In a one-sample z-test for a proportion scenario, the researcher is interested in testing whether a sample proportion is significantly different from a hypothesized population proportion.

G. In a one-sample t-test for a proportion scenario, the researcher is interested in testing whether a sample proportion is significantly different from a hypothesized population proportion when the sample size is small and/or the population variance is unknown.

H. In a two-sample z-test for the p1-p2 scenario, the researcher is interested in comparing two proportions in two independent groups with known population variances.

I. If none of the above tests are appropriate for a particular scenario, then another type of test (such as a chi-square test or ANOVA) may be needed.

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The price that maximizes annual revenue is $17.86 per bushel, which should be charged by the farmers; The quantity of corn that can be sold per year at 67,786 bushels per year; the farmers' resulting revenue will be  $1,210,392.96 per year.

To find the price that maximizes annual revenue, we need to differentiate the revenue function with respect to the price and set it equal to zero:

Revenue = pq = (6,600,000q^1.3)q

= 6,600,000q^2.3

dRevenue/dp = q

Setting dRevenue/dp = 0, we get q = 0, which is not a valid solution. Therefore, we need to consider the endpoints of the feasible range, which is q >= 13,000.

At q = 13,000, we have p = 6,600,000*13,000^(-0.3) ≈ $17.86 per bushel.

At q → ∞, we have p → 0.

So, the price that maximizes annual revenue is $17.86 per bushel, which should be charged by the farmers.

The quantity of corn that can be sold per year at that price is given by

q = (p/6,600,000)^(1/1.3)

= (17.86/6,600,000)^(1/1.3)

≈ 67,786 bushels per year.

The farmers' resulting revenue will be Revenue = p*q

= $17.86 * 67,786

≈ $1,210,392.96 per year.

Therefore, the price that maximizes annual revenue is $17.86 per bushel, which should be charged by the farmers; The quantity of corn that can be sold per year at 67,786 bushels per year; the farmers' resulting revenue will be  $1,210,392.96 per year.

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The probability that the mean weight of a sample of twenty freshmen will be greater than 145 pounds is 0.138.

The probability is determined using the central limit theorem and the formula for the standard error of the mean:

where;

Data given;

σ = 12.3 pounds; n = 20

SE = 12.3/√20

SE = 2.75 pounds.

The sample mean is then standardized using the z-score formula:

z = (x - μ) / SE

z = (145 - 142) / 2.75

z = 1.09

Using a calculator, the probability of a z-score greater than 1.09 is 0.138.

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Answer:

2(1/2)(3)(4) + 2(4) + 2(5) + 2(3)

= 12 + 8 + 10 + 6 = 36 square feet