Multiply: (3√6 - √2)(4√2 - √6)​

Answer:

98cm^2

Step-by-step explanation:

The triangle is equilateral and each side is 14cm

area of triangle: h*b/2

Answer:

7 would be the closest meter when rounded 7 times 3 is 21 so its one-off but the closest you can get so the answer is 7 meters

Step-by-step explanation:

I divided 22 by three because the way to solve for the area is length times width so it'd be area divided by width for length

To find the slope of a line that includes the points (5,-2) and 6,0).​

Using the formula;

where m is the slope

x₁ = 5 y₁= -2 x₂ = 6 y₂=0

substituting the values into the formula;

m = 2/1

m=2

Hence; the slope is 2

Answer: The given polynomial is -2x³.

a) To write the polynomial in standard form, we arrange the terms in descending order of degrees:

-2x³

b) The degree of a polynomial is the highest exponent of the variable in the polynomial. In this case, the degree of the polynomial is 3.

c) The lead coefficient is the coefficient of the term with the highest degree. In this case, the lead coefficient is -2.

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Approximately 23.5% of the shoppers sampled made their visit to the store because of the coupon they received in the mail.

To calculate the percentage of shoppers who visited the store due to the coupon they received, follow these steps:

Step 1: Calculate the percentage.

Percentage = (Number of shoppers with coupons / Total number of shoppers) * 100

Step 2: Substitute the values.

Percentage = (142 / 603) * 100

Step 3: Perform the calculation.

Percentage ≈ 23.56%

Step 1: The percentage is a value representing a portion of a whole in terms of 100. In this case, we want to find the percentage of shoppers who visited the store due to the coupon they received.

Step 2: To calculate the percentage, we need two pieces of information: the number of shoppers who visited the store because of the coupon (142) and the total number of shoppers sampled (603).

Step 3: By substituting the values into the percentage formula and performing the calculation, we find that approximately 23.56% of the shoppers visited the store because of the coupon they received.

Thus, approximately 23.56% of the sampled shoppers visited the store due to the coupon they received in the mail.

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Answer:

3650

Step-by-step explanation:

just add a zero at the end

Answer: 3650 mg

Work: Mg stands for milligrams, and you need this chart to help you with this problem. On this chart, you can see that Gram is in the middle, and you need to get to milligrams (Last One.) Since Milligrams is 3 spots away to the right, you need to move the decimal point 3 spots away to the right. So, after you move the 3.65 three spots, the answer is 3650, meaning the milligrams. So, 3.65 g (Grams) is 3650 milligrams.

I hope this helps, and Happy Holidays! :)

The alternative hypothesis would be that the slope coefficient is not equal to zero, indicating that there is a linear relationship between sales and profit.

The null hypothesis for testing a linear regression model with profit as the dependent variable and sales as the independent variable is that the slope coefficient is equal to zero.

The null hypothesis for a linear regression model is usually stated as:

H0: β1=0, where β1 is the slope coefficient of the independent variable in the model.

In this case, the independent variable is sales, and the dependent variable is profit.

Therefore, the null hypothesis would be that the slope coefficient of sales (β1) is zero, indicating that there is no linear relationship between sales and profit.

The alternative hypothesis would be that the slope coefficient is not equal to zero, indicating that there is a linear relationship between sales and profit.

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Answer:

it is a function

Step-by-step explanation:

I can give you the cordinates:

(-1,1)

(2,7)

(1,-1)

(3,0)

It is a function because if you do the vertical line test you wont hit two x values twice.

The chi-square test of independence is typically used to analyze the relationship between two variables when both variables are nominal, the two variables have been measured on different individuals and the observations on each variable are within-subjects in nature. The answer is  D. all of the above

The chi-square test of independence is a statistical test that is used to determine if there is a significant association between two categorical variables. It is commonly used when both variables are nominal, meaning they consist of categories or groups rather than numerical values.

When conducting the chi-square test of independence, the data is typically collected by measuring the two variables on different individuals or units.

For example, researchers may collect data on the gender (nominal variable) and political affiliation (nominal variable) of different individuals and analyze whether there is a relationship between the two variables.

The test examines the observed frequencies of the different categories in a contingency table and compares them to the expected frequencies under the assumption of independence. If the observed and expected frequencies significantly differ, it suggests that there is an association between the two variables.

Therefore, the chi-square test of independence is applicable when both variables are nominal and the data is collected on different individuals. This allows researchers to investigate the relationship between the variables and determine if they are associated or independent.

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Answer:

r = -7

Step-by-step explanation:

-4 + 2r - 5r = 17

=> 2r - 5r = 17 + 4

=> -3r = 21

=> r = 21/(-3)

=> r = -7

Answer:

9. 81.3953% increase

10. 26.6667% decrease

Step-by-step explanation:

Hope this helps.

The rate of change of money in the account at 15 years is 20 to 2 decimal places. We can interpret this as meaning that the account balance is increasing by £20 per year at 15 years.

In mathematics, a graph is a visual representation of a set of objects, called vertices or nodes, that are connected by a set of links or edges. Graphs are commonly used to model relationships between objects, such as social networks, transportation networks, or chemical molecules.

A graph is typically represented by a set of points or dots, called vertices, and a set of lines or curves, called edges, that connect the vertices. Each edge represents a relationship between two vertices, and can be directed or undirected, weighted or unweighted, and may have additional properties such as color or shape.

a) Line A shows the best estimate for the tangent to the curve at 15 years.

b) To estimate the rate of change of money in the account at 15 years, we need to find the slope of line A at 15 years.

From the graph, we can see that line A passes through the points (15, 200) and (20, 300). Using these points, we can find the slope of line A as:

slope = (change in y) / (change in x) = (300 - 200) / (20 - 15) = 20

Therefore, the rate of change of money in the account at 15 years is 20 to 2 decimal places. We can interpret this as meaning that the account balance is increasing by £20 per year at 15 years.

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The number of subjects needed to estimate the mean number of books read per year with a certain level of confidence is calculated in different scenarios. In the first scenario, to estimate within six books with 90% confidence, the required number of subjects is determined.

In the second scenario, the number of subjects needed to estimate within three books with 90% confidence is calculated. The effect of doubling the required accuracy on the sample size is examined. Lastly, the number of subjects required to estimate within six books with 99% confidence is determined and compared to the first scenario.

(a) To estimate the mean number of books read per year within six books with 90% confidence, the required number of subjects is determined. The specific confidence level of 90% requires rounding up the number of subjects to the nearest whole number.

(b) Similarly, the number of subjects needed to estimate within three books with 90% confidence is calculated, rounding up to the nearest whole number.

(e) Doubling the required accuracy does not quadruple or quarter the sample size. Instead, it doubles the sample size.

(d) To estimate within six books with 99% confidence, the required number of subjects is calculated. This higher confidence level requires a larger sample size compared to the first scenario in part (a). Increasing the level of confidence in the estimate generally leads to a larger sample size because a higher confidence level requires more data to provide a more precise estimation. This is reasonable because higher confidence levels correspond to narrower confidence intervals, which necessitate a larger sample size to achieve.

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A discrete probability distribution is a statistical distribution that relates to a set of outcomes that can take on a countable number of values, whereas a continuous probability distribution is one that can take on any value within a given range.Therefore, the main difference between the two types of distributions is the type of outcomes that they apply to.

An example of a discrete probability distribution is the probability of getting a particular number when a dice is rolled. The possible outcomes are only the numbers one through six, and each outcome has an equal probability of 1/6. Another example is the probability of getting a certain number of heads when a coin is flipped several times.

On the other hand, an example of a continuous probability distribution is the distribution of heights of students in a school. Here, the range of heights is continuous, and it can take on any value within a given range.

The expected value of a probability distribution measures the central tendency or average of the distribution. In other words, it is the long-term average of the outcome that would be observed if the experiment was repeated many times.

For a discrete probability distribution, the expected value is computed by multiplying each outcome by its probability and then adding the results. In mathematical terms, this can be written as E(x) = Σ(xP(x)), where E(x) is the expected value, x is the possible outcome, and P(x) is the probability of that outcome.

For example, consider the probability distribution of the number of heads when a coin is flipped three times. The possible outcomes are 0, 1, 2, and 3 heads, with probabilities of 1/8, 3/8, 3/8, and 1/8, respectively. The expected value can be computed as E(x) = (0*1/8) + (1*3/8) + (2*3/8) + (3*1/8) = 1.5.

Therefore, the expected value of the distribution is 1.5, which means that if the experiment of flipping a coin three times is repeated many times, the long-term average number of heads observed will be 1.5.

Draw a vertical line and notice if the vertical line intercepts more than 2 points  in the graph.

A, if we draw a vertical line, it'll just intercept only one point of the graph. So A is function.

A is the only function here. If we draw a vertical line for other graphs, it'll intercept 2 points.

Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

Answer:

C

Step-by-step explanation

10 inches

The expressions (7x - 6y) and (3x - 5y) added together result in 10x - 11y.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Consider your square as being composed of smaller unit squares.

The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some typical units for measuring area are square cms, square feet, square inches, square meters, etc.

Draw unit squares with 1-centimeter sides in order to calculate the area of the square figures shown below. The shape will therefore be measured.

According to our question-

(7x – 6y) and (3x – 5y

Then the sum of the expressions will be

(7x – 6y) + (3x – 5y)

7x – 6y + 3x – 5y

10x – 11y

Hence, The expressions (7x - 6y) and (3x - 5y) added together result in 10x - 11y.

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The volume of the pyramid is determined as 480 m³.

option A.

The volume of a pyramid is calculated by applying the following formula as shown below;

Mathematically, the formula for the volume of a pyramid is given as;

V = ¹/₃ Bh

where;

The base area of the pyramid is calculated as follows;

B = ¹/₂Pa

where;

B = ¹/₂ x 4m x 40m

B = 80 m²

The volume of the pyramid is calculated as;

V = ¹/₃ x 80 m² x 18 m

V = 480 m³

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Answer:

Step-by-step explanation:

blah

the number is 40.

In mathematics, the system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables. In this article, you will get the definition of the system of linear equations, different methods of solving these systems of linear equations and solved examples.

If the tens digit of the number is X and the ones digit is Y then the number is equal to 10*X + Y

If you reverse the digits then the number is equal to 10*Y + X

If reversing the digits decreases the number by 36 then

10*Y + X = 10*X + Y - 36

The sum of the digits is 4 so X + Y = 4  ==>  X = 4 - Y

Substitute this value of X into the 1st equation

10*Y + (4 - Y) = 10*(4 - Y) + Y - 36

9*Y + 4 = 40 - 9*Y - 36

18*Y = 0

Y = 0

So X = 4 - 0 = 4 and the number is 40

Check:  40 - 04 = 36

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Answer:

Step-by-step explanation:

Answer:  The length of the third side is greater than 4 ft and less than 20 ft.

Step-by-step explanation:  Given that two sides of a triangle have lengths 8 ft and 12 ft.

We are to describe the possible lengths of the third side.

Let x ft be the length of the third side of the triangle.

We know that

the sum of the lengths of any two sides of a triangle is always greater than the third side.

So, we must have

Also,

and

From inequalities (i), (ii) and (iii), we get

Thus, the length of the third side is greater than 4 ft and less than 20 ft.

Answer:

-2592

Step-by-step explanation:

this doesn't seem right but its what i got

Answer:

Radius of sphere = 3 feet

Step-by-step explanation:

The volume of sphere is 36 π ft³.

We need to find the radius of sphere.

The formula used is: \(Volume\:of\:sphere=\frac{4}{3}\pi r^3\)

Putting value of volume and finding radius

\(Volume\:of\:sphere=\frac{4}{3}\pi r^3\\36\pi =\frac{4}{3}\pi r^3\\r^3=36 \pi \times \frac{3}{4\pi} \\r^3=9 \times 3\\r^3=27\\Taking\:cube\;root\:on \:both\:sides\\\sqrt[3]{r^3}=\sqrt[3]{27}\\r=3\)

So, Radius of sphere = 3 feet