5 times 10 divided by 4

Answer:

85.71 %

Step-by-step explanation:

26-14=12

12/14= 0.8571

0.8571x100= 85.71

Answer:

A change from 14 to 26 represents a positive change (increase) of 85.7142857143%

Step-by-step explanation:

Use the formula:

New - Old / Old x 100%

In other words, new(26) minus old(14) divided by old(14) time 100%

14 is the old value and 26 is the new value. In this case we have a positive change (increase) of 85.7142857143 percent because the new value is greater than the old value.

10 maybe? I don't really know but maybe 10 will be right?????

Answer:

C.  -18

Step-by-step explanation:

Scalar Product (Dot Product) of two vectors

\(\displaystyle \vec{a} \cdot \vec{b}=\sum_{i=1}^na_ib_i\)

\(\textsf{If }\: \vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k} \quad \textsf{and } \quad \vec{b}=b_1\hat{i}+b_2\hat{j}+b_3\hat{k}\)

\(\textsf{then }\quad \vec{a} \cdot \vec{b}=a_1b_1+a_2b_2+a_3b_3\)

Given:

⇒ v₁ · v₂ = (3 · 2) + (-4 · 6)

⇒ v₁ · v₂ = 6 + (-24)

⇒ v₁ · v₂ = 6 - 24

⇒ v₁ · v₂ = -18

The symbol that should be used is the division symbol. On the other hand, in the result the whole number represents the number of curtains, while the fraction represents a fraction of the next curtain.

Given :

The numerator: Number above.

The denominator: Number below.

A whole number: Optional element.

The number of curtains the tailor can make is equal to the total fabric divided by the fabric required for one curtain. Based on this, the symbol should be ÷.

= 18 1/2 ÷ 2 3/4

The whole number represents the number of curtains. The division of the total fabric and the total fabric required for one curtain will include a whole number and a fraction. In this situation, the whole number represents the number of curtains that can be made from the total fabric.

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Answer:

its c

Step-by-step explanation:

Answer:

Option 1

Step-by-step explanation:

The equations in the options are in the slope-intercept form (y= mx +c, where m is the slope and c is the y-intercept).

In the graph, the line cuts through the y-axis at y= -2. Thus, c= -2 and the 2nd option can be eliminated.

The slope can be found using the formula below.

\(\boxed{\text{slope}=\frac{y_1-y_2}{x_1-x_2} }\)

Let's choose 2 points on the line: (0, -2) and (-2, 4)

Slope

\(=\frac{4-(-2)}{-2-0}\)

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

\(=\frac{6}{-2}\)

= -3

The equation of the line is thus y= -3x -2.

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All are required assumptions about the error term.

In regression analysis, there are several assumptions that need to be met regarding the error term :

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Answer:a

Step-by-step explanation:

The amount of interest a single deposit earns for the period of one year is equal to your initial investment multiplied by this yield.

Compound interest may be computed using the formula FV = P*(1+R/N)(N*T), where FV is the loan or investment’s future value, P is the original principle amount, R is the yearly interest rate, N is the number of times interest is compounded each year, and T is the period in years.

The amount of interest earned on a single deposit over a year is equal to your initial investment multiplied by this return. As an example: After a year, $1,000 invested at a 5.00% annual effective return yields $50.00 in interest. $1,000.00 x 5.00% = $50.00.

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Answer:

C. 2x^2 + 3x - 1

is the answer

The pitch of the roof is 0.3.

Pitch:

The pitch can be expressed numerically as a fraction. The pitch fraction represents a certain amount of vertical rise over the entire span.

Here it is given that the rise in the roof is 3.6m and a rum of 12m,

We have to find the pitch of the roof.

As is already given in the statement that the slope of a roof is called its pitch.

By this we get the slope:

Slope = 3.6/12

= 3/10

= 0.3

Therefore we get the pitch of the roof at 0.3.

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By factoring the quadratic equation 4x^2 = 59x + 153, we obtain the solutions x = 3/4 and x = -51.

To solve the quadratic equation by factoring, we need to rewrite the equation in the form of ax^2 + bx + c = 0, where a, b, and c are coefficients.

Given the equation 4x^2 = 59x + 153, we need to rearrange it to bring all the terms to one side of the equation, so it becomes 4x^2 - 59x - 153 = 0.

Now, we can try to factor the quadratic expression 4x^2 - 59x - 153. To do this, we look for two binomials in the form (px + q)(rx + s) that, when multiplied, result in the given quadratic expression.

We need to find two numbers, p and q, such that pq = 4 and ps + qr = -59. Similarly, we need to find two numbers, r and s, such that rs = -153 and ps + qr = -59.

After some trial and error or by using factoring techniques, we find that the factors of 4 are 1 and 4, and the factors of -153 are -3 and 51.

So, we can rewrite the quadratic expression as (4x - 3)(x + 51) = 0.

Now, using the zero product property, we set each factor equal to zero and solve for x:

4x - 3 = 0, which gives x = 3/4.

x + 51 = 0, which gives x = -51.

Therefore, the solutions to the quadratic equation 4x^2 = 59x + 153 are x = 3/4 and x = -51.

In summary, by factoring the quadratic equation 4x^2 = 59x + 153, we obtain the solutions x = 3/4 and x = -51.

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Answer:10

Step-by-step explanation:

10

square root of 100 is 10 because 10×10=100

Kristen is attempting to solve the equation \(0=\sqrt{6x}-x\). Hence, option b. is the correct answer.

A radical equation has no solution if the square root of a negative number is involved in the equation. The left-hand side of equation b, √(6x), is always non-negative. But the right-hand side, -x, can be negative. So, there is no value of x that can satisfy the equation.

In other words, there is no real number x that would make the left-hand side equal to the right-hand side, so equation b has no solution.

Hence, Kristen is attempting to solve equation 0 = √(6x) - x.

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The complete question is -

Kristen is solving a radical equation and determines that the equation has no solution. Which equation is Kristen attempting to solve?

a. \(\sqrt{27+6x} =x\)

b. \(0=\sqrt{6x}-x\)

c. \(\sqrt{4-x}+9=0\)

d. \(\sqrt{\frac{x}{8}} = \sqrt{90-x}\)

Simplifying this expression will give you the slope of the tangent line to the polar curve at θ = π/3.

What is derivative?

The derivative provides information about the slope or steepness of a curve at various points and can be used to find critical points, determine the concavity of a function, and solve optimization problems. The derivative is denoted using various notations, such as f'(x), dy/dx, or df/dx, depending on the context and notation conventions.

To find the slope of the tangent line to the polar curve r = 5 + 2θ at the point specified by θ = π/3, we need to determine the derivative of the polar curve with respect to θ and evaluate it at θ = π/3.

The polar curve r = 5 + 2θ can be expressed in Cartesian coordinates as x = (5 + 2θ) * cos(θ) and y = (5 + 2θ) * sin(θ).

Now, let's find the derivative of y with respect to x using the chain rule:

dy/dx = (dy/dθ) / (dx/dθ)

To find dy/dθ and dx/dθ, we differentiate the expressions for y and x with respect to θ:

dy/dθ = d/dθ [(5 + 2θ) * sin(θ)] = (2 + 2θ) * sin(θ) + (5 + 2θ) * cos(θ)

dx/dθ = d/dθ [(5 + 2θ) * cos(θ)] = (2 + 2θ) * cos(θ) - (5 + 2θ) * sin(θ)

Now, we can calculate the derivative of y with respect to x:

dy/dx = [(2 + 2θ) * sin(θ) + (5 + 2θ) * cos(θ)] / [(2 + 2θ) * cos(θ) - (5 + 2θ) * sin(θ)]

To find the slope of the tangent line at θ = π/3, substitute θ = π/3 into the expression for dy/dx:

dy/dx = [(2 + 2(π/3)) * sin(π/3) + (5 + 2(π/3)) * cos(π/3)] / [(2 + 2(π/3)) * cos(π/3) - (5 + 2(π/3)) * sin(π/3)]

Simplifying this expression will give you the slope of the tangent line to the polar curve at θ = π/3.

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As a result, for the same data set, a 99% confidence interval would have a greater margin of error than a 90% confidence interval.

Answer: If a 90% confidence interval is constructed based on a sample of data, and it is 74% + 3%, a 99% confidence interval based on this same sample of data would have a larger margin of error and probably a different center.

What is a confidence interval? A confidence interval is a statistical technique used to establish the range within which an unknown parameter, such as a population mean or proportion, is likely to be located. The interval between the upper and lower limits is called the confidence interval. It is referred to as a confidence level or a margin of error.

The confidence level is used to describe the likelihood or probability that the true value of the population parameter falls within the given interval. The interval's width is determined by the level of confidence chosen and the sample size's variability. The confidence interval can be calculated using the standard error of the mean (SEM) formula

.A 90% confidence interval indicates that there is a 90% chance that the interval includes the population parameter, while a 99% confidence interval indicates that there is a 99% chance that the interval includes the population parameter.

When the level of confidence rises, the margin of error widens. The center, which is the sample mean or proportion, will remain constant unless there is a change in the data set. Therefore, alternative A is the correct answer.

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The rate of change of z with respect to t is given by [9e^t - e^(2t) - e^(-t)] / (e^(2t) + (9 - e^(-t))^2).

To use the chain rule to find dz/dt, we first need to find the partial derivatives of z with respect to x and y.

∂z/∂x = 1/(1 + (y/x)^2) * (y/x^2) = y/(x^2 + y^2)
∂z/∂y = -1/(1 + (y/x)^2) * (1/x) = -x/(x^2 + y^2)

Now we can apply the chain rule:

dz/dt = ∂z/∂x * dx/dt + ∂z/∂y * dy/dt

Substituting in the given values:

dx/dt = e^t
dy/dt = e^(-t)

x = e^t
y = 9 - e^(-t)

∂z/∂x = y/(x^2 + y^2) = (9 - e^(-t)) / (e^(2t) + (9 - e^(-t))^2)
∂z/∂y = -x/(x^2 + y^2) = -e^t / (e^(2t) + (9 - e^(-t))^2)

Substituting these into the chain rule formula:

dz/dt = [(9 - e^(-t)) / (e^(2t) + (9 - e^(-t))^2)] * e^t + [-e^t / (e^(2t) + (9 - e^(-t))^2)] * e^(-t)

Simplifying:

dz/dt = [9e^t - e^(2t) - e^(-t)] / (e^(2t) + (9 - e^(-t))^2)

Therefore, the rate of change of z with respect to t is given by [9e^t - e^(2t) - e^(-t)] / (e^(2t) + (9 - e^(-t))^2).

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Answer: (x - 5)^2 + (y - 7)^2 = 50

Step-by-step explanation:

The general equation for a circle is (x - a)^2 + (y - b)^2 = r^2 where (a, b) is the centre

Use Pythagoras to find r^2

r^2 = (5 - -2)^2 + (7 - 8)^2

= 7^2 + (-1)^2

= 50

So the circle is (x - 5)^2 + (y - 7)^2 = 50

According to the chi square test, yes and at alpha 0.05 there is a significant difference in music preferred by the three restaurants' customers.

The term chi square test refers a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large.

Here we have given that a researcher is interested in whether a significant trend exists regarding the popularity of certain music played at restaurants. a random sample of 50 customers from each of three restaurants is selected. the customers are asked to indicate which of three music types: country, jazz, and classical they preferred

And we need to find results deviate significantly from what would be expected due to chance.

While we reading the given question, we know that a researcher is interested in whether a significant trend exists regarding the popularity of certain music played at restaurants.

And the number of samples = 50

When we convert it into the percentage then we get,

=> 50/1000

=> 0.05

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To determine which method can be used to prove the similarity of the given triangles, use SAS, SSS, and AA.

To determine which method can be used to prove the similarity of the given triangles, let's briefly discuss each method:

a) SAS~ (Side-Angle-Side Similarity): If two sides of a triangle are proportional to two sides of another triangle, and their included angles are congruent, then the triangles are similar.

b) SSS~ (Side-Side-Side Similarity): If all three sides of a triangle are proportional to the corresponding sides of another triangle, then the triangles are similar.

c) AA~ (Angle-Angle Similarity): If two angles of a triangle are congruent to two angles of another triangle, then the triangles are similar.

Unfortunately, I cannot see the given triangles in your question, but based on the provided information, you can use these explanations to determine which method (SAS~, SSS~, or AA~) can be used to prove their similarity. If none of these methods apply, then similarity cannot be proved for the triangles.

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Answer:8

Step-by-step explanation

Answer:

\(\frac{4}{8}\)=\(\frac{50}{100}\)

Step-by-step explanation:

6 students can be seated in a row of 6 chairs in 121 ways.

Given,

Number of students = 6

Number of chairs = 6

We have to find the number of ways the students can be seated in a row.

Here,

Jack insists on sitting in the first chair.

So, 1 way of sitting for jack.

Next,

5 students and 5 chairs are there.

So they can sit in;

5! = 120 ways

Therefore,

Total number of way of sitting is 120 + 1 = 121 ways.

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Answer:  b

Step-by-step explanation:

I think

Answer:

Steve was correct in his statement.

Step-by-step explanation:

According to standard notation, opening bracket ( \([\) ) represents the lower bound of a set so that elements of the set are equal or greater than lower bound. In addition, closure parenthesis ( \()\) ) represents the upper bound of a set so that element of the set are less than upper bound.

In consequence, Steve was correct in his statement.

The maximum height of the stone is 45 meters. It would take 1 second to reach its maximum height

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

The height (h) of the stone after x seconds is given by:

h(x) = -5(x - 1)² + 45

h(x) = -5(x² - 2x + 1) + 45 = -5x² + 10x + 40

h(x) = -5x² + 10x + 40

The maximum height is at h'(x) = 0, hence:

h'(x) = -10x + 10

-10x + 10 = 0

10x = 10

x = 1

h(1) = -5(1 - 1)² + 45

h(1) = 45

The maximum height of the stone is 45 meters

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This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.

The confidence interval estimate of the population means examination score can be calculated using the sample mean and the margin of error. The margin of error depends on the level of confidence and the sample size.

For example, if a sample of 100 applications provided a sample mean score of 80, and a 95% confidence level is used, the confidence interval estimate of the population mean examination score would be:

Margin of error = (critical value) x (standard error)

The critical value for a 95% confidence level with 99 degrees of freedom is 1.984. The standard error can be calculated using the formula:

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

If the standard deviation of the examination scores is known, it can be used in the formula. If not, the sample standard deviation can be used as an estimate.

Assuming a sample standard deviation of 10, the standard error would be:

\(Standard\  error = \frac{10} { \sqrt{(100)}} = 1\)

Therefore, the margin of error would be:

Margin of error = 1.984 x 1 = 1.984

The confidence interval estimate of the population means examination score would be:

80 ± 1.984, or between 78.016 and 81.984.

This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.

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The 95% confidence interval for the population mean examination score would be between 72.23 and 77.77, to the

nearest whole number.

To determine the confidence interval estimate of the population mean examination score based on a sample mean

provided to the nearest whole number, we need to know the sample size and the level of confidence.

Assuming a normal distribution and a level of confidence of 95%, we can use the following formula to calculate the

confidence interval estimate:

Confidence interval = sample mean +/- (critical value) x (standard error)

The critical value can be found using a t-distribution table or a calculator, based on the sample size and degrees of

freedom (n-1). For a sample size of 30 or more, we can use the z-score instead of the t-score.

The standard error is the standard deviation of the sample divided by the square root of the sample size.

For example, if a sample of 50 applications provided a sample mean of 75, and the standard deviation was 10, the

standard error would be 10/sqrt(50) = 1.41.

Assuming a level of confidence of 95%, the critical value for a sample size of 50 and degrees of freedom of 49 would be 1.96.

Therefore, the confidence interval estimate would be:

75 +/- 1.96 x 1.41 = 75 +/- 2.77

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The investment's expected return is 5.95%.

The expected return of an investment is calculated by multiplying the probabilities of each possible return by their respective returns and summing them up. In this case, Gautney Enterprises has provided the probabilities and returns for the investment. By applying the formula, we find that the expected return is 5.95%.

To calculate the standard deviation, we need to determine the variance first. The variance is computed by taking the difference between each possible return and the expected return, squaring those differences, multiplying them by their respective probabilities, and summing them up. Once we have the variance, the standard deviation is simply the square root of the variance. The standard deviation measures the degree of risk associated with an investment.

In this scenario, the expected return of the investment is 5.95%, but we need to consider the standard deviation as well to assess the risk. If the standard deviation is high, it indicates a greater level of uncertainty and potential volatility in returns. A low standard deviation implies a more stable investment.

Without the specific values for each return and their respective probabilities, we cannot calculate the exact standard deviation. However, Gautney Enterprises should compare the calculated expected return and the associated standard deviation to their risk tolerance and investment objectives. If the expected return meets their desired level of return and the standard deviation aligns with their risk appetite, they may consider investing in this security.

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Answer:

\(c.\hspace{3}x=12\)

Step-by-step explanation:

Isosceles triangles are a type of triangles in which two of their sides have an identical length. It should be noted that the angles opposite the sides that are the same length are also the same. This means that these triangles not only have two equal sides, but also two equal angles.

You can solve this problem using different methods, I will use pythagorean theorem. First take a look at the picture I attached.  As you can see:

\(x=2a\)

And we can find a easily using pythagorean theorem:

\((\sqrt{45} )^{2} =3^{2} +a^{2}\)

Solving for a:

\(a^{2} =(\sqrt{45} )^{2} -3^{2} \\\\a^{2} =45-9\\\\\)

\(a^{2} =36\\\\a=\sqrt{36} \\\\a=6\)

Therefore:

\(x=2a\\\\x=2(6)\\\\x=12\)

The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.

To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.

In this case, a = 25, so b = (1/2)(70) = 35.

Expanding (ax + b)^2, we have:

(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2

= 25x^2 + 70x + 1225.

Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.

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