Use the distributive property to write each expression as an equivalent
algebraic expression.
6(4+x)

A one-sample z-test for a population proportion requires that n po > 10 and n(1-Po) > 10 for both the sample and population proportions, Po. Additionally, each sample proportion must be less than or equal to 0.5, the sample size must be more than 10 times the population size, and the population size must be more than 10 times the sample size.

1. Calculate the sample size, n, needed for the test.

2. Check that npo > 10 and n(1 - Po) > 10 for both the sample and population proportions, Po.

3. Check that each sample proportion is less than or equal to 0.5.

4. Check that the sample size is more than 10 times the population size.

5. Check that the population size is more than 10 times the sample size.

6. Check that the population distribution is approximately normal.

A one-sample z-test for a population proportion is used to evaluate the difference between a sample proportion and a population proportion. Before conducting the test, it is important to check for independence, which is done by ensuring that certain conditions are met. First, npo > 10 and n(1-Po) > 10 must be true for both the sample and population proportions, Po. Additionally, each sample proportion must be less than or equal to 0.5, the sample size must be more than 10 times the population size, and the population size must be more than 10 times the sample size. Lastly, the population distribution must be approximately normal. These conditions must be met in order for the test to be valid and reliable. If any of these conditions are not met, the test results may be inaccurate.

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The number 480,000 in scientific notation is 4.8 * 10⁵

From the question, we have the following parameters that can be used in our computation:

Number = 480,000

Multiply the number by 1

So, we have the following representation

Number = 480000 * 1

Express 1 as 10⁵/10⁵

Som we have

Number = 480000 * 10⁵/10⁵

This gives

Number = 4.8 * 10⁵

Hence, the expression is 4.8 * 10⁵

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The numerical value of the expression 3a - 5b when a = -3 and b = -2 is 1.

Given the expression in the question;

3a - 5b

To determine the value of the expression, replace a with -3 and b with -2 for all occurrence of a and b in the expression.

3a - 5b

Plug in a = -3

3( -3 ) - 5b

Plug in b = -2

3( -3 ) - 5( -2 )

-9 -+ 10

10 - 9

Subtract 9 from 10

1

Therefore, the value of the expression is 1.

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By applying the definite integral, it can be concluded that the velocity at time t is v(t) = t² + 6t - 16, and the distance traveled during the given time interval is 36.67 meters.

Definite integral is the integral of a function whose values of the independent variables have a certain interval.

This kind of integral is frequently used for calculating the acceleration and velocity of a moving object.

a(t) = dv/dt

v(t) = ds/dt

To find the velocity at time t, we look at the given acceleration function:

    a(t) = dv/dt

2t + 6 = dv/dt

     dv = (2t + 6) dt

    v(t) = ∫(2t + 6) dt

          = t² + 6t + C

Knowing that v(0) = -16, we put this into the previous equation so we get C = -16

Now we have the velocity at the time t as follows:

v(t) = t² + 6t - 16

To find the distance traveled, we look at the velocity function:

           v(t) = ds/dt

t² + 6t - 16 = ds / dt

            ds = (t² + 6t - 16) dt

              s = ∫(t² + 6t - 16) dt

                 = 1/3t³ + 3t² - 16t + C

Then we calculate the distance traveled during 0 ≤ t ≤ 5:

s = s(5) - s(0)

  = (1/3 * 5³) + (3 * 5²) - (16 * 5) + C - 0 - 0 + 0 - C

  = 125/3 + 75 - 80

  = 125/3 - 5

  = 125/3 - 15/3

  = 110/3

  ≈ 36.67 meters.

Thus, the velocity at time t is v(t) = t² + 6t - 16, and the distance traveled during the given time interval is 36.67 meters.

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The coordinate of P that divides line AB in the ratio 4:1 is (6.6, 3.8)

An equation is an expression that shows the relationship between numbers and variables.

If a point O(x, y) divides line segment AB with endpoints A(x₁, y₁) and B(x₂, y₂) in the ratio of n:m. The coordinates of O is:

[tex]x = \frac{n}{n+m}(x_2-x_1)+x_1 \\\\y = \frac{n}{n+m}(y_2-y_1)+y_1[/tex]

Given that P(x, y) divides line AB in the ratio 4:1. The coordinates are A(1, 3) and B(8, 4). Therefore:

[tex]x=\frac{4}{4+1}(8-1) +1=6.6\ unit\\\\y=\frac{4}{4+1}(4-3) +3=3.8\ unit[/tex]

The coordinate of P is (6.6, 3.8)

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The total number of animals in the farm is given by 200

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here: The number of cows is 30 and they form 15% of the total animals on the farm.

Let the number of animals in the form be x then

15% of x=30

x=30×100/15

x=200

Hence, The total number of animals in the farm is given by 200

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3rd image is translations are rigid transformations that do not change the orientation of the original image.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.

3rd image is translations are rigid transformations that do not change the orientation of the original image.

2 and 4 are rotations and 5 is a dilation.

Hence, 3rd image is translations are rigid transformations that do not change the orientation of the original image.

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lim [f(x) - g(x)] is9.

Generally, In mathematics, a limit is a value that a function "approaches" as the input of the function "approach" some value.

More formally, given a function f(x) and a value L, we say that "the limit of f(x) as x approaches a is L" if the values of f(x) can be made arbitrarily close to L by taking x sufficiently close to a, but not equal to a.

In other words, the limit of a function describes the behavior of the function as the input gets arbitrarily close to a particular value, but doesn't necessarily equal that value

The limit of the difference between the two functions is the difference of their individual limits. So,

lim [f(x) - g(x)] = lim f(x) - lim g(x)

= 7 - (-2)

= 9.

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Emily Janson should receive the scholarship offer because she has the higher batting average over the combined junior and senior years.

The batting average of a player is calculated by dividing the number of hits they have by the total number of at-bats. This can be expressed as a formula: Batting Average = H/AB.

For Allison Fealey, her junior year batting average can be calculated by dividing the number of hits (15) by the total number of at-bats (40), which is 0.375. Emily Janson’s junior year batting average can be calculated by dividing the number of hits (74) by the total number of at-bats (204), which is 0.363

For Allison Fealey, her senior year batting average can be calculated by dividing the number of hits (79) by the total number of at-bats (254), which is 0.310. Emily Janson’s senior year batting average can be calculated by dividing the number of hits (35) by the total number of at-bats (120), which is 0.292.

When the data from the junior and senior years were combined and aggregated, Allison Fealey’s combined two-year batting average can be calculated by dividing the number of hits (94) by the total number of at-bats (294), which is 0.320. Emily Janson’s combined two-year batting average can be calculated by dividing the number of hits (109) by the total number of at-bats (324), which is 0.336.

Based on this analysis, Emily Janson should receive the scholarship offer because she has the higher batting average over the combined junior and senior years.

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The statement a(x-b)-c = ax-(ab+c) is true because it follows the rules of algebraic operations and the distributive property.

On the left side of the equation, we have a(x-b)-c.

Here, a is a constant and it is being multiplied by (x-b). According to the distributive property, we can rewrite this as:

ax-ab-c.

On the right side of the equation, we have ax-(ab+c)

Here, we have a constant a being multiplied by x and then we have another constant ab and c being subtracted, which we can also rewrite as:

ax - ab -c

As you can see, both sides of the equation are equivalent and the statement is true.

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The perimeter of a rectangle can be represented by a polynomial expression. The expression will consist of two terms, one representing the width and one representing the length. Each term will contain a variable, which is to the power of one, multiplied by a coefficient. The sum of the two terms produces the perimeter of the rectangle.

For example, if the width of the rectangle is w and the length is l, then the polynomial expression for the perimeter would be: P = w + l. This expression can also be written in expanded form as: P = w + w + l + l.

By adding more terms to this polynomial expression, the perimeter of more complex rectangles can be found. For example, if the rectangle is not a perfect square, then two additional terms can be added to the polynomial expression. One term will represent the extra width and one term will represent the extra length. By adding these two additional terms, the perimeter of the rectangle can be calculated.

In conclusion, the perimeter of a rectangle can be represented as a polynomial expression, which consists of terms that have variables raised to the power of one and are multiplied by coefficients. By adding more terms to the expression, the perimeter of more complex rectangles can be found.

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The area of the figure given, which is composed of a rectangle and two semicircles, is 154. 27 units ²

First, find the area of the rectangle in the composite shape which is :

= Length x Width

= 13 x 8

= 104 units ²

The area of a semi - circle is:

= ( π x r ² ) / 2

Seeing as there are two semi - circles, the area is:

= π x r ²  

= π x 4 ²

= 50. 27 units  ²

The area of the composite shape is therefore:

= 50. 27 + 104

= 154. 27 units ²

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So, the rate at which the area of the circular surface of the cookie dough is increasing with respect to time is 80π mm^2/min and the rate at which the height is decreasing with respect to time is  -2 mm/min.

Part A: The area of the circular surface of the cookie dough is given by A = πr^2, where r is the radius of the dough. The rate at which the area is changing with respect to time is given by dA/dt = 2πr*dr/dt. At time t, the radius is 20 mm and the rate at which it is increasing is 2 mm/min. Therefore, the rate at which the area of the circular surface of the cookie dough is increasing with respect to time is dA/dt = 2π(20 mm)(2 mm/min) = 80π mm^2/min.

Part B: The height of the dough is given by h, and the rate at which the height is decreasing with respect to time is given by dh/dt. Since the dough is retaining its cylindrical shape, the decrease in the height of the dough is exactly the opposite of the increase in the radius. At time t, the rate at which the radius is increasing is 2 mm/min, so the rate at which the height is decreasing with respect to time is dh/dt = -2 mm/min.

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So, the two balls are located on the same plane, the x-y plane, with the baseball at <3,5,0>m and the tennis ball at <-3,-1,0>m, with the vector pointing from baseball to the tennis ball is <-6,-6,0>m.

The position vector of the baseball is <3,5,0>m. The position vector of the tennis ball is <-3,-1,0>m.

The position vector of the tennis ball relative to the baseball is the vector pointing from the baseball to the tennis ball and it is calculated by subtracting the position vector of the baseball from the position vector of the tennis ball: <-3,-1,0>m - <3,5,0>m = <-6,-6,0>m

So the two balls are located on the same plane, the x-y plane, with the baseball at <3,5,0>m and the tennis ball at <-3,-1,0>m, with the vector pointing from baseball to the tennis ball is <-6,-6,0>m.

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The coldest temperature recorded in Vostok station in Fahrenheit is -89.2°F

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

The coldest temperature recorded in Vostok station in Fahrenheit is:

= -22.3 × 4

= -89.2°F

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The interest rate that Mr. Mogi borrowed the money, given the amount borrowed and the amount repaid, is 17. 8%

To find the interest rate that Mr. Mogi borrowed the money at, first find the amount he paid per year:

= Total payment / Number of years

= 20, 000 / 10

= $ 2, 000 per year

You can then use the RATE function on Spreadsheet to find the interest:

NPER = 10 years

PMT = $ 2, 000

PV = 9, 000

FV = $ 20, 000

The interest rate would be 17. 8%

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The probability (a) 6! ways; (b) 3! ways; (c) 3!2! ways. 6! = 6 x 5 x 4 = 120, 3! = 3 x 2 x 1 = 6, 3!2! = 3 x 2 x 1 x 2 x 1 = 12.

(a) In this instance, the three novels, two volumes on mathematics, and one book on chemistry can be arranged on the bookshelf in any sequence. By multiplying the number of things in each category, you can arrive at the answer: 3 novels x 2 math books x 1 chemistry book = 6. These things can be arranged in 6! (6 factorial) different ways, which is equal to 120 when multiplied by 6 x 5 x 4.

(b) In this instance, both the novels and the mathematical books must be in the same location. You can figure this out by multiplying the number of things in each category; for example, 3 novels times 1 collection of math books is 3. These things can be arranged in 3! (3 factorial) different ways, which is equal to 3 x 2 x 3.

(c) The other books may be put in any sequence, but the novels in this instance must be together. By multiplying the amount of items in each category, you can arrive at the answer: 3 novels x 2 math books and 2 x 2 chemistry books = 6. These objects can be arranged in 3!2! (3 factorial x 2 factorial) ways, which is equal to 12 when multiplied by 3 x 2 x 1 x 2 x 1.

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The true statement is " A and B must point in the same direction."

Two vectors A and B are added together to form a vector C. The relationship between the magnitudes of the vectors is given by A + B = C. Which one of the following statements concerning these vectors is true?

According to the question

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The limit does not exist because the function is not defined at (x,y) = (0,0)You can see this by plugging in (x,y) = (0,0) into the function, you get 3(0^2) * 0 / (0^2 + 0^2) = 0 / 0 which is an indeterminate form.

In Mathematics, a limit is defined as a value that a function approaches the output for the given input values. Calculus and mathematical depend on limits, which are also used to determine integrals, derivative, and continuity.

There are each limits (left- and proper limits), infinite limits, and limitations at infinity in addition to regular, two-sided limits.

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Every month of the year has

No, there is not. We do not have sufficient evidence to conclude that less than 40% of U.S. adults are aware that such an investment would result in a sum of over $100,000.

To test the hypothesis that less than 40% of U.S. adults are aware that such an investment would result in a sum of over $100,000, we can use a two-proportion z-test. The null hypothesis is that the proportion of U.S. adults who are aware of the investment's outcome is equal to or greater than 40%, and the alternative hypothesis is that the proportion is less than 40%.

The test statistic is calculated as:

z = (p1 - p2) / √(p(1-p)(1/n1 + 1/n2))

where p1 is the proportion of U.S. adults in the sample who are aware of the investment's outcome (374/1010), p2 is the proportion assumed in the null hypothesis (0.4), and n1 and n2 are the number of observations in the sample and population, respectively.

Using these values, the test statistic is:

z = (0.369 - 0.4) / √(0.4(1-0.4)(1/1010)) = -1.08

Using a two-sided test with a significance level of 0.05, we can look up the critical value in a standard normal table or using software and find that the critical value is ±1.96. Since -1.08 is between -1.96 and 1.96, we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that less than 40% of U.S. adults are aware that such an investment would result in a sum of over $100,000.

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Answer:

70

Step-by-step explanation:

The time that should take her to run each mile is approx 11.5 minutes.

Given that,

She runs 5 miles in 57 and a half minutes.

Based on the above information,

The time that should be taken by her is

= 57.5 ÷ 5 miles

= 11.5 minutes.

Therefore we can conclude that the time that should take her to run each mile is approx 11.5 minutes......

False. Undifferentiated schizophrenia is a type of schizophrenia where a person displays general symptoms of the disorder such as hallucinations and delusions, but does not meet the criteria for any of the other subtypes of schizophrenia.

A person exhibiting a mixture of schizophrenic symptoms would likely be diagnosed with schizophrenia, but not as specifically undifferentiated schizophrenia.This disorder is characterized by a mixture of positive and negative symptoms, including delusions, hallucinations, disorganized speech, disorganized behavior, lack of emotion, and social withdrawal. However, a person who exhibits a mixture of schizophrenic symptoms could have any type of schizophrenia, not just undifferentiated schizophrenia. For example, a person could have paranoid schizophrenia, disorganized schizophrenia, or catatonic schizophrenia. To diagnose schizophrenia, a doctor must analyze the patient's symptoms and determine which type of schizophrenia they have.

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Answer:

$4,200,000

Step-by-step explanation:

let x = total sales

(1/6)x = 700,000

x = 700,000(6/1) = 4,200,000

**dividing by 1/6 is the same as multiplying by 6

Answer:

-12 < -5

Step-by-step explanation:

its simple math. -12 is less than -5 because its more negative.

Answer: the diameter of the circle is about 19.8

Step-by-step explanation:

Since the length of the square is 14 units, we can use the Pythagorean theorem to find the diagonal:

14^2 + 14^2 = c^2

196 + 196 =c^2

392 = c^2

c = about 19.8

Answer:

19.8

Step-by-step explanation:

The diameter of the base of the cylinder is equal to the diagonal of the inscribed square and is equal to the hypotenuse of an equilateral triangle into which the square is divided by diagonals ... By the Pythagorean theorem, the diameter (hypotenuse) is equal to the square root of the sum of the squares of the legs and is equal to 19.8

After measuring a set of individuals, a researcher finds that Bob's score is three times greater than Jane's score. These measurements must come from a ratio scale

A ratio scale is a type of measurement scale that allows for the comparison of two or more values by using division. After measuring a set of individuals, a researcher finds that Bob's score is three times greater than Jane's score.

In this case, the researcher is comparing Bob's score to Jane's score, and the comparison involves division (Bob's score is three times greater than Jane's score).

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The sum of expression 1/2 + 2/(1/2) is obtained to be option B: 4.

What is sum?

The outcome of adding two or more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding two or more numbers together results in a new result or total.

The fractional expression is - 1/2 + 2/(1/2)

Apply the fraction reciprocal rule -

If there is a fraction in denominator then it is reciprocated and multiplied.

= 1/2 + 2/(1/2)

= 1/2 + 2(2/1)

= 1/2 + 4

Now, take the LCM and multiply it with the numerators -

= 1/2 + 4

Find the sum of the numbers -

= (1 + 8)/2

= 9/2

= 4.5

When estimated and rounded the number is equivalent to 4.

Therefore, the fractional expression results in 4.

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Estimate the sum. Round the number.

1/2 + 2/(1/2)

The sum is approximately -

A: 0

B: 4

C: -4

D: 8

Answer:

Four hundred thirdy seven and six hundred and eight thousandths.

437.068

Step-by-step explanation:

Hope it helps! =D

The number formed by these terms is 437.068.

To solve this problem, we first need to understand the place value system and what each term represents.

As per the place value system used in decimals:

- Hundreds: It is the third digit to the left of the decimal point and each unit represents 100.
- Tens: It is the second digit to the left of the decimal point and each unit represents 10.
- Ones: It is right next to the decimal point, all the digits to the left of it are the ones. Each unit represents 1.
- Hundredths: It is the second digit to the right of the decimal point and each unit represents 0.01.
- Thousandths: It is the third digit to the right of the decimal point and each unit represents 0.001.

In the given context, we know that there are 4 hundreds, 3 tens, 7 ones, 6 hundredths, and 8 thousandths.

To start, we calculate each term separately:

- 4 hundreds = 4 x 100 = 400
- 3 tens = 3 x 10 = 30
- 7 ones = 7 x 1 = 7
- 6 hundredths = 6 x 0.01 = 0.06
- 8 thousandths = 8 x 0.001 = 0.008

After evaluating each term separately, we sum them up together for the final answer:

- Sum = 400 + 30 + 7 + 0.06 + 0.008 = 437.068

Hence, the number formed by these terms is 437.068.

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Answer:

Step-by-step explanation:

8 - (-5) - 4(-7)

8- (-5) - (-28)

8 + 5 + 28

13 + 28

41

Answer:

8 - (-5) - 4(-7) = 41

Step-by-step explanation:

Given problem,

→ 8 - (-5) - 4(-7)

Let's solve the problem,

→ 8 - (-5) - 4(-7)

→ 8 + 5 - (4 × -7)

→ 13 - (-28)

→ 13 + 28

→ 41 => final answer

Hence, the answer is 41.