Which choice is equivalent to the product below? √7/8 x √7/18

A. 3/4

B. 6/12

C. 1/2

D. 7/1

E. 7/12

If the length and width of the pen are both whole numbers the possible perimeters for the pen are 98, 52, 38, 32, and 28.

To find the possible perimeters of the pen, we first need to find all the possible length and width pairs that would give us an area of 48 square feet. Since the length and width are whole numbers, we can start by listing out all the factors of 48:

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Each of these factors represents a possible length or width of the pen, and we can find the other dimension by dividing the area (48) by the first dimension. For example, if the first dimension is 1, then the other dimension is 48/1 = 48. However, we need to make sure that the second dimension is also a whole number.

Using this method, we can find all the possible length and width pairs:

1 x 48, 2 x 24, 3 x 16, 4 x 12, 6 x 8

Now we can calculate the perimeter for each of these pairs. The perimeter is the sum of the lengths of all four sides of the pen. Since the length and width are the same for a square pen, we can use the formula:

perimeter = 2(length + width)

For each pair, we can plug in the values for length and width to get the perimeter:

1 x 48: perimeter = 2(1 + 48) = 98

2 x 24: perimeter = 2(2 + 24) = 52

3 x 16: perimeter = 2(3 + 16) = 38

4 x 12: perimeter = 2(4 + 12) = 32

6 x 8: perimeter = 2(6 + 8) = 28

Therefore, the possible perimeters for the pen are 98, 52, 38, 32, and 28.

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The sum of the expressions 2x/5 + 5/8 + x/5 - 1/4 is option b) 3x/8 + 3/8

Here we have 2x/5 + 5/8 + x/5 - 1/4

Now since we have constants as well as variables here, to add these up, we will add the constants and variables separately.

The constants are the ones with just numbers, while the variables are those terms that have the term x with them.

Hence adding up the constants will give us

5/8 - 1/4

The LCM of denominators 8, and 4 is 8

Hence, we get

5/8 - 2/8

= 3/8

Now adding the variable gives us

2x/5 + x/5

= 3x/5

Hence the sum is

3x/5 + 3/8

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Complete Question

2x/5 + 5/8 + x/5 - 1/4

a) 3x/5 + 1/8

b) 3x/5 + 3/8

c) 3x/5 + 5/8

d) 3x/5 + 7/8

It is not equal to any of the options listed: three-fifths x 1/8, three-fifths x 3/8, three-fifths x 5/8, or three-fifths x 7/8.

The expression

(2/5 * 5/8) + (1/5 * x - 1/4)

can be simplified as follows:

2/5 * 5/8 = 1/8

1/5 * x - 1/4 = (1/5 - 1/4) x = -3/20 x

So the expression becomes

1/8 + (-3/20 x) = (1/8 - 3/20 x).

This is not equal to any of the options listed: three-fifths x 1/8, three-fifths x 3/8, three-fifths x 5/8, or three-fifths x 7/8.

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The slope for the function f(t) = 3 - 3/5t at point (3/5, 2) is 5/3.

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The given function is - f(t) = 3 - 3/5t.

The data points are - (3/5, 2)

Rewrite the function -

f(t) = 3 - 3/5 t^-1

Differentiate with respect to t. Use the difference rule.

d/dt (3) - d/dt (3/5 t^-1)

Use the constant rule and the constant multiple rule.

0 - 3/5 d/dt (t^-1)

Use the power rule.

-3/5(-1)t^(-1 - 1)

3/5t^-2

Now plug in 3/5 for t on the derivative in order to find the slope at point (3/5, 2).

3/5(3/5)^-2

3/5(5/3)^2

3/5 × 25/9

5/3

Therefore, the slope value is 5/3.

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Find the slope of the graph of the function at the given point.

Function Point f(t) = 3 - 3/5t (3/5, 2)

The Earth is estimated to be around 4.54 billion years old, while the oldest known rocks found on Earth date back to about 4 billion years ago.

Determining the age of the Earth is a complex process that involves a variety of scientific disciplines. Geologists and other scientists have used a variety of methods to estimate the age of the planet, including radiometric dating, which involves measuring the decay of radioactive isotopes in rocks and other materials.

The age of the oldest known rocks found on Earth has also been determined using radiometric dating techniques. These rocks, which are primarily found in Western Greenland, have been dated to around 3.8 to 4.0 billion years old. The rocks are believed to have formed during the Hadean Eon, a period of Earth's history when the planet was still in its early stages of formation and was subject to intense meteorite bombardment.

It's important to note that the age of the Earth and the age of the oldest known rocks found on its surface are not precise measurements.

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Answer:

well um i would say $60.50

Step-by-step explanation:

The after 29 minutes 38 seconds, Jane and Kinsley will be 47 miles apart if they are moving in the exact opposite directions.

A numerical representation of the distance between two items or locations called distance. A physical length or an approximation based on other considerations in physics or common usage can be referred to as distance.

Let's suppose the at time t they are 47 miles apart.

We know, distance = speed×time

(44+51)t = 47

t = 47/95

t = 0.494 hours

t = 29 minutes 38 seconds

Thus, the after 29 minutes 38 seconds, Jane and Kinsley will be 47 miles apart if they are moving in the exact opposite directions.

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Answer:

x=0.125

Step-by-step explanation:

4/32=0.125

Answer:

28 classes

Step-by-step explanation:

84/3 = 28 classes

Answer:

28 classes didn't learn about the Holocaust

Step-by-step explanation:

If there are 84 classes and two-thirds learned about the Holocaust that means that you have to divide by three.

84 ÷ 3 = 28

Then, you can check your answer by multiplying 28 × 3 = 84

The researcher wants to determine if the number of calories burned during an hour is the same for running and walking. To conduct this investigation, the researcher would measure continuous scale data.

Continuous scale data is quantitative data that can take any numerical value within a certain range.

In this case, the researcher would measure the number of calories burned, which is a continuous variable that can have various values within a specific range (e.g., 0, 100, 200, etc.).

By measuring the calories burned for both running and walking, the researcher can compare and analyze the numerical data to determine if there is a significant difference between the two activities.

It is important to note that the type of statistical analysis required to evaluate the data would depend on the specific research design and the number of groups involved.

If the researcher is comparing only two groups (running and walking), an independent t-test may be appropriate.

On the other hand, if there are more than two groups or additional factors being considered, an analysis of variance (ANOVA) might be more suitable.

The choice of statistical analysis method would depend on the specific research question and study design.

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This how we change 23 out of 25 to a percentage

The numerator of a question is the number that appears above the bar; in this case, the numerator is 23.

The denominator is the number beneath the bar, and in this question, it is 25.

To calculate the value of a fraction, divide the numerator by the denominator.

Therefore, we must divide 23 by 25.

23/25 = 0.92

To determine the percentage, multiply the outcome by 100.

The percentage value will be obtained by multiplying 0.92 by 100.

0.92 x 100 = 92%

As a result, 92% is the answer to the question.

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To conduct a regression analysis for the given data, we'll follow the steps as outlined:

Q2.1 To test the hypothesis that X is a good predictor of Y, we need to perform a regression analysis and examine the significance of the regression model. The regression model will help us determine if there is a statistically significant relationship between the independent variable (X) and the dependent variable (Y). We will perform a hypothesis test to evaluate the significance of the regression coefficients.

Q2.2 The parameters of the linear equation are as follows:

- Slope (β₁): The slope parameter represents the change in the dependent variable (Y) for a unit change in the independent variable (X). It indicates the rate of change in Y with respect to X.

- Intercept (β₀): The intercept parameter represents the value of the dependent variable (Y) when the independent variable (X) is zero. It determines the starting point of the linear relationship between X and Y.

Q2.3 To assess the strength of the model, we can use both the regression model and correlation analysis:

- Regression Model: The strength of the model can be evaluated by examining the coefficient of determination (R²). R² represents the proportion of the total variation in the dependent variable (Y) that is explained by the independent variable (X). A higher R² value indicates a stronger relationship between X and Y.

- Correlation Analysis: We can calculate the correlation coefficient (r) between X and Y. The correlation coefficient measures the strength and direction of the linear relationship between X and Y. A value close to +1 or -1 indicates a strong linear relationship, while a value close to 0 suggests a weak relationship.

Q2.4 To show the linear line on the scatter plot graph and the linear equation, we'll plot the data points on a scatter plot and draw the best-fit line, which represents the linear equation. The linear equation can be expressed as Y = β₀ + β₁X, where β₀ is the intercept and β₁ is the slope.

Q2.5 To determine the predicted value of Y given X is 93.1, we substitute the value of X into the linear equation and calculate the corresponding Y value using the estimated slope and intercept from the regression analysis.

Q2.6 To plot the normal probability plot and the residual plot vs X, we'll analyze the normality of the residuals. The normal probability plot helps us assess whether the residuals follow a normal distribution. A straight line in the normal probability plot indicates that the residuals are normally distributed. The residual plot vs X helps us identify any patterns or deviations in the residuals, which may suggest issues with the regression model, such as heteroscedasticity or nonlinearity.

Note: To conduct a full regression analysis, including hypothesis testing, calculation of regression coefficients, and other statistical measures, we require statistical software or programming languages such as R or Python.

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Answer:

Answer:

\(\frac{2}{3}c=d\)

\(3\cdot \frac{2}{3}c=3d\)

\(2c=3d\)

\(\frac{2c}{2}=\frac{3d}{2}\)

\(c=\frac{3d}{2}\)

Answer:

Step-by-step explanation:

area of a circle = π r²

area = 3.14 (20)²

area = 3.14 (400)

area = 1256 mm²

Answer:

The slope is 1/2

Step-by-step explanation:

x-x/y-y

(7-5)/(8-4)=2/4=1/2

let me know if you can't understand

Answer:

7/36

Step-by-step explanation:

7/9* 1/4

Multiply the numerator

7*1 = 7

9*4 = 36

Put the numerator over the denominator

7/36

Answer:

Step-by-step explanation:

7/9 x 1/4 = 7/36

Answer:

y = 38

x = 18

Step-by-step explanation:

Equation 1. x + y = 56

Equation 2. x + 2y = 94​

We can use substitution

Let's create equation 3: 56 - y = x

Now using equation 3, substitute equation 2.

Equation 2 is now written as:

56 - y + 2y = 94

56 + y = 94

y = 38

Given the value of y, substitute equation 1 and find x

x + 38 = 56

x = 18

Hope this helps :)

Have a great day!

Answer:

5^6

5^6 is the same thing as

5^6=5×5×5×5×5×5

=5×5=25×5=125×5=625×5=3125×5=15625

5^6= 15625

Answer:

125 * 125

Step-by-step explanation:

do 125 x 125 = 15625

Answer:

c. equally likely events

The given statement " If A and B are n x n and invertible, then A⁻¹B⁻¹ is the inverse of AB." is true because  A and B are invertible matrices, it means that they both have an inverse (A⁻¹and B⁻¹, respectively). The product of A and B, represented by AB, is also an n x n matrix.

To show that A⁻¹B⁻¹is the inverse of AB, we must demonstrate that the product of (AB) and (A⁻¹B⁻¹) results in the identity matrix, which is an n x n matrix with 1s along the diagonal and 0s elsewhere.
To verify this, we'll multiply (AB) with (A⁻¹B⁻¹) and check if the result is the identity matrix:
(AB)(A⁻¹B⁻¹) = A(BA⁻¹)B⁻¹ (associative property of matrix multiplication)
Since B and A^-1 are inverses of each other, their product equals the identity matrix:

A(BA⁻¹)B⁻¹= AI B⁻¹(where I is the identity matrix)
Multiplying A and I doesn't change A:
AI B⁻¹= A B⁻¹
Now, A and B⁻¹are inverses of each other as well, so their product also equals the identity matrix:
A B⁻¹= I
Thus, A⁻¹B⁻¹ is indeed the inverse of AB, as the product of (AB) and (A⁻¹B⁻¹) results in the identity matrix.

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Answer: (3,-5) minimum

Step-by-step explanation:

the vertex is at the bottom so it is a minimum

Answer: Robert is correct, irrational numbers are part of real numbers.

Explanation:

In mathematics, numbers are classified into different groups or seats. In the case of real numbers, these are a broad category that includes all numbers that can be represented on a line. Moreover, this category includes smaller categories such as rational numbers, for example, 15, 2.4 or 6/2 that can be represented as fractions, as well as, irrational numbers such as \(\pi\) that cannot be fractions. In this context, Jenny is incorrect and Robert is correct because irrational numbers are also real numbers.

Coating the seed typically improves seed quality and germination rates, so the same seeding rate can be maintained even with coated seed.

To convert mass-based seeding rates to population-based establishment rates, we need to consider the area conversion factors provided:

a. Given a seeding rate of 60 lbs/acre for cereal rye, we can convert it to seeds per square foot by using the conversion factor of 1 acre = 43,560 square feet.

b. Given a seeding rate of 15 kg/ha for crimson clover, we can convert it to seeds per square meter using the conversion factor of 1 hectare = 10,000 square meters.

To convert population-based seeding rates to mass-based seeding rates, we can use the given area conversion factors:

a. Given a seeding rate of 30 plants/square foot for oats, we can convert it to pounds of seed per acre.

b. Given a seeding rate of 20 plants/square meter for hairy vetch, we can convert it to kilograms of seed per hectare.

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The null hypothesis is \(H_0:\mu=3\) and the alternative hypothesis is \(H_1:\mu > 3\)

There are two hypothesis considered in a statistical test. They are:

Formulation of null and alternative hypothesis are considered as the first step of a statistical procedure. The whole procedure, then, continues on testing whether to accept or reject these hypotheses.

Null Hypothesis is the actual hypothesis which is tested. Alternative hypothesis, as its name suggests, is the hypothesis accepted when the null hypothesis is rejected in the test carried out.

Here the sociologist is carrying out the test on the mean number of cars, \(\mu\).

So to check whether the families own more than 3 cars in average,

the null hypothesis will be ,\(\bold{H_0:\mu=3}\)  

and the alternate hypothesis will be,  \(\bold{H_1:\mu > 3}\)

So if the null hypothesis is rejected, then there is the possibility for only more than 3 cars in average.

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Rick sold 99 cans of popcorn

To find the number of popcorn cans sold by Rick,

First, we need to calculate the total number of cans sold by all the students, which is the sum of the cans sold by each student. The total number of cans sold is

76 + 84 + 119 + 81 + Rick = Total cans sold

The mean number sold is given as 91.8. So, we can write it as a equation using the mean formula,

Mean = sum of all values / total number of values

91.8 = (76 + 84 + 119 + 81 + Rick) / 5

Now, we can simplify the equation by multiplying both sides by 5 to eliminate the fraction:

5 x 91.8 = 76 + 84 + 119 + 81 + Rick

459 = 360 + Rick

Rick = 459 - 360

Rick = 99

Therefore, Rick sold 99 cans of popcorn

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Answer:the sector is 280°

Step-by-step explanation:

Answer:

Interpreting as: standard form

Input interpretation:

standard form

Definition:

The standard form of a line in the Cartesian plane is given by

ax + by = c

for real numbers a, b, c element R.

Answer:

2 , -4 , (2,0)

Step-by-step explanation:

The slope of the linear function is 2.

The y-intercept of the linear function is -4.

The solutions of the linear function are (0, -4), (1, -2), (2, 0), etc..

The graph is given below.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The linear function is y = mx + c

The linear function passes through (-2, -8) and (1, -2)

Now,

m = (-2 + 8) / (1 + 2)

m = 6/3

m = 2

The slope of the linear function is 2.

Now,

(-2, -8) = (x, y)

-8 = 2 x (-2) + c

-8 = - 4 + c

c = -8 + 4

c = -4

The y-intercept is -4.

The equation of the linear function.

y = 2x - 4

The solution of the line are (0, -4), (1, -2), (2, 0), etc..

When x = 0,

y = -4

When x = 1,

y = -2

When x = 2,

y = 0

Now,

The graph of the line is given below.

Thus,

The slope is 2.

The y-intercept is -4.

The solutions are (0, -4), (1, -2), (2, 0), etc..

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