When adding the numbers in the problem shown below using the Standard Algorithm, we have to "carry."

When we do this, we carry_________ from the____________
column, and add it to the __________ column.

8 3 5
+ 4 2 1
________________

The speed of the shadow at any time while the rock is in the air is given by v(1-s) / (H-h).

By the AAA congruency theorem, the two triangles are formed and are similar. Here, the ratio of their sides must be equal, and thus -

= H/d+s = h/s

= Hs = h(d+s)

= Hs = hd + hs

= Hs - hs = hd

= s(H-h) = hd

Differentiating both sides with respect to t -

= {s' (H- h)} + {sh'} = h'

Since we know that h' = v -

= {s' (H- h)} + {sv} = v

= s'(H-h) = v - sv

= s'(H-h) = v(1-s)

= s' = v(1-s) / (H-h)

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A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.

(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.

(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.

The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.

The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.

A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

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Answer:

X intercepts: (100/3,0)

Y intercepts: (0,100)

Since the probabilities remain unchanged, events A and B are independent.

Events A and B are independent.
Mutually exclusive events cannot occur at the same time.

In this case, rolling a 1 on the first die (Event A) and rolling a 1 on the second die (Event B) can occur together, so they are not mutually exclusive.
Independent events have no effect on each other's probability.

The probability of rolling a 1 on the first die is given as 1/6.

Given that a 1 has already been rolled on the first die, the probability of rolling a 1 on the second die is still 1/6.

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As per the given limit, the sequence 0.14(4ⁿ) 5/8(4ⁿ) diverges to infinity because the terms of the sequence get larger and larger as n increases.

To determine whether the sequence 0.14(4ⁿ) 5/8(4ⁿ) converges or diverges, we need to look at what happens to the terms as n gets larger and larger. Let's first simplify the expression by factoring out the common factor of 4ⁿ:

0.14(4ⁿ) + 5/8(4ⁿ) = (0.14 + 5/8)(4ⁿ) = 0.885(4ⁿ)

Now we can see that the sequence is just a constant multiple of 4ⁿ. As n increases, the terms of the sequence get larger and larger, so the sequence diverges to infinity.

To be more precise, we can use the concept of a limit to describe the behavior of the sequence as n approaches infinity. We say that a sequence converges to a limit L if the terms of the sequence get arbitrarily close to L as we take more and more terms.

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The value of x in the equation 4 x plus 8 y equals 40 is 8.4

The equation is given as:

4 x plus 8 y equals 40

Rewrite the equation as:

4x + 8y = 40

The value of y is 0.8.

So, we have:

4x + 8 * 0.8 = 40

Divide through by 4

x + 2 * 0.8 = 10

Evaluate the product

x + 1.6 = 10

Subtract 1.6 from both sides

x = 8.4

Hence, the value of x in the equation 4 x plus 8 y equals 40 is 8.4

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i) Compute the autonomous investment, government the MPM is 0.4.

AI = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)

GM = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)

XM = 1 / (1 - 0.4) = 1 / 0.6 ≈ 1.667 (approximately)

TM = -0.35 / (1 - 0.35) ≈ -0.538 (approximately)

ii) The equilibrium income is approximately 709.52.

To compute the autonomous investment (A), government expenditure (G), export (X), and tax (T) multipliers, we need to use the following formulas:

Autonomous Investment Multiplier (AI):

AI = 1 / (1 - MPC)

where MPC is the marginal propensity to consume.

Government Expenditure Multiplier (GM):

GM = 1 / (1 - MPC)

Export Multiplier (XM):

XM = 1 / (1 - MPM)

where MPX is the marginal propensity to import.

Tax Multiplier (TM):

TM = -MPC / (1 - MPC)

Now let's calculate these multipliers using the given information:

i). Compute the multipliers:

MPC = change in consumption / change in income

Here, we can see that the consumption function is given by C = 40 + 0.35Y.

So, the MPC is 0.35.

MPM = change in imports / change in income

Here, we can see that the import function is given by M = 45 + 0.4Y.

So, the MPM is 0.4.

AI = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)

GM = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)

XM = 1 / (1 - 0.4) = 1 / 0.6 ≈ 1.667 (approximately)

TM = -0.35 / (1 - 0.35) ≈ -0.538 (approximately)

ii). Find the equilibrium income:

To find the equilibrium income, we set aggregate demand (Y) equal to aggregate supply (Y) and solve for Y.

Aggregate demand (Y):

Y = C + I + G + (X - M)

Substituting the given values, we have:

Y = (40 + 0.35Y) + (70 - 2r) + 400 + (240 - (45 + 0.4Y))

Simplifying the equation:

Y = 40 + 0.35Y + 70 - 2(0.5) + 400 + 240 - 45 - 0.4Y

Combining like terms:

Y = 745 - 0.05Y

Bringing Y terms to one side:

1.05Y = 745

Dividing both sides by 1.05:

Y = 745 / 1.05 ≈ 709.52 (approximately)

Therefore, the equilibrium income is approximately 709.52.

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Answer:

(1,-1)

Step-by-step explanation:

\( \large{ \begin{cases} y = 2x - 3 \\ y = - x \end{cases}}\)

Since both are y-isolated equation. We can combine both.

\( \large{2x - 3 = - x}\)

Since we want to solve for x-term, we need to isolate x-term.

So we move from -x which is the right side to x.

\( \large{2x - 3 + x = 0} \\ \large{3x - 3 = 0} \\ \large{3x = 3} \\ \large{x = 1}\)

But we are not done yet. Solving system of equations, you must solve for y-term as well. (Because we have to answer in ordered pairs which are (x, y))

Substitute x = 1 in any given equations but I will substitute x = 1 in y = -x

\( \large{y = - x} \\ \large{y = - 1}\)

Since we have got y-value. Therefore the answer is (1,-1)

The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51  19. 17 < 23  20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)

To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.

To indicate that the first value is less than the second value, write <.

Alternatively, to indicate that the first value is greater than the second value, write >.

Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36

To determine the direction of inequality, we need to compare the values.

We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.

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The correct question would be as

Write > or < to make each statement true.

11. -5 0

12. 9 -8

13. -7 7

14. 55 -75

15. -32 -24

16. 89 73

17. -58 -51

18. -32 4

19. 17 23

20. 18 -36​

Answer:

abigail

Step-by-step explanation:

The probability of rolling a 6 is 1/6, so you multiply by 100 to get how many times they should get a 6 and get 16.667, which abigail is the closest to

Answer:

perimeter of original rectangle *1/3  = perimeter of new rectangle

Step-by-step explanation:

The rule for perimeter is  multiply by the scale factor

perimeter of original rectangle * scale factor  = perimeter of new rectangle

perimeter of original rectangle *1/3  = perimeter of new rectangle

Answer:

i (imaginary number)

Step-by-step explanation:

\( \sqrt{ - 1} = i(imaginary \: number)\)

Answer:

E. The parameter is μmale - μfemale and the statistic is xmale - xfemale.

Step-by-step explanation:

The sample statistic is a piece of information about the individuals or objects that were selected from a given population. The sample is just a fraction of the total population. Since it is a herculean task studying an entire population, the sample forms a manageable size that allows us to have an insight into the entire population. The sample statistics are now the piece of information about the sample being studied such as the average, mean, median, or mode.  The sample statistics have to be as specific as possible of the factors being measured. In the question, we would have to obtain the mean of both the male and female genders. This gives us an insight into the population under study.

The parameter, on the other hand, is a description of the entire population being studied. For example, we might want to determine the population mean. That is the factor we seek to measure. It is represented by the sign mu (μ).  

Answer:

D

Step-by-step explanation:

Slope of the first line = (1-3)/1 = -2

The shape that we obtained will be a triangle. Then the correct option is E.

In terms of geometry, a pyramid is a polygon that is created by joining an apex and a polygonal base. A triangle known as a lateral face is formed by each base edge and apex. It has a polygonal basis and is a conic solid. There are n + 1 points, n + 1 sides, and 2n edges in a pyramid with an n-sided base. Every pyramid is dual in itself.

If the base of the pyramid is a rectangle then the pyramid is known as a rectangular pyramid.

If the pyramid is separated by slicing a rectangular pyramid perpendicular to its base. Then the shape that we obtained will be a triangle.

Then the correct option is E.

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The solution to the above algebra question is  (b) x-3, x+5.

To find the remaining factors of the polynomial x^3+4x^2-11x-30=0, we can use polynomial long division or synthetic division. However, since we are given that x+2 is a factor of the polynomial, we can use synthetic division to simplify the process.

We set up the synthetic division table as follows, using -2 as the divisor:

-2 | 1 4 -11 -30

|____-2__-4___30

| 1 2 -15 0

The bottom row of the table represents the coefficients of the quadratic polynomial obtained by dividing x^3+4x^2-11x-30 by x+2. The last term of the quadratic is 0, which indicates that x+2 is a factor of the polynomial. The remaining quadratic polynomial can be factored as:

x^2 + 2x - 15 = (x - 3)(x + 5)

Therefore, the remaining factors of the polynomial x^3+4x^2-11x-30=0 are x+2, x-3, and x+5.

The correct answer is (b) x-3, x+5.

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A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a 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.

Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.

One possible set could be 3 cm, 4 cm, and 5 cm.

To verify if this set forms a right triangle, we can apply the Pythagorean theorem.

Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.

Adding these two values together gives us 25.

Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.

It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.

There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.

These sets are known as Pythagorean triples.

Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.

In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

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Hello!

Answer:

A) Yes.

B) No.

C) Yes.

D) Yes.

Step-by-step explanation:

To find the correct solutions to this question, we can go through each choice and check for their congruency:

A) Yes. ∠8 is congruent to ∠5 because ∠5 and ∠8 are vertical angles.

B) No. ∠5 is not congruent to ∠6 because ∠5 and ∠6 are supplementary to each other.

C) Yes. ∠5 is congruent to ∠1 because corresponding angles are congruent.

D) Yes. ∠5 is congruent to ∠4 because alternate exterior angles are congruent.

A) The angle 8 should be congruent so it should be Yes.

B) The angle 6 should be congruent so it should be No.

C) The angle 1 should be congruent so it should be Yes.

D) The angle 4 should be congruent so it should be Yes.

The congruent angles are those angles in which the corresponding sides and angles should be of equal measure.

A) Yes. ∠8 is congruent to ∠5 since ∠5 and ∠8 are vertical angles.

B) No. ∠5 is not congruent to ∠6 since ∠5 and ∠6 are supplementary to each other.

C) Yes. ∠5 is congruent to ∠1 since corresponding angles are congruent.

D) Yes. ∠5 is congruent to ∠4 since alternate exterior angles are congruent.

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Answer:

-11

Step-by-step explanation:

g(-5)=-5^2+8(-5) +4

=25+-40+4

=-11

Answer:

1. Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean

2. 15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why?

The lower the standard deviation, the less dispersed the values are, meaning it is more likely to find values within a certain threshold of the mean.

So

Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean.

2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?

We have that:

\(\mu = 168000, \sigma = 40000, n = 100, s = \frac{40000}{\sqrt{100}} = 4000\)

This probability is the pvalue of Z when X = 168000 - 4000 = 164000. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{164000 - 168000}{4000}\)

\(Z = -1\)

\(Z = -1\) has a pvalue of 0.1587

15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.

Let's assume the length of the rectangle is 'l' and the width is 'w'.

From the given data, we know that each gate is 4 m wide.

Therefore, the width of the rectangle is:

Width = w + (4 m + 4 m) = w + 8 m

The perimeter of the rectangle is:

P = 2l + 2(w + 8 m) = 2l + 2w + 16 m

Now, we need to subtract the combined length of the two gates from the perimeter:

P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m

So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

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Answer:

47.900

Step-by-step explanation

45.50 plus 2.275 is 47.825 rounded is 47.9

Answer:

2 3/5 inches in a year

Step-by-step explanation:

28 1/5 - 25 3/5 = 141/5 - 128/5 = 13/5 = 10/5 + 3/5 = 2 + 3/5 = 2 3/5

The simplified form of the expression 4x(x + 1) − (3x − 8)(x + 4) is -3x^2 - 4x - 32.

To simplify the expression 4x(x + 1) − (3x − 8)(x + 4), we can expand the parentheses and combine like terms.

Expanding the first term, we get 4x^2 + 4x.

Expanding the second term, we have -(3x)(x) - (3x)(4) - (-8)(x) - (-8)(4), which simplifies to -3x^2 - 12x - (-8x) - (-32), further simplifying to -3x^2 - 12x + 8x - 32.

Combining like terms, we obtain -3x^2 - 4x - 32.

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Answer:

70% IS THE ANSWER

Step-by-step explanation:

Hope I helped.

Answer:

70%

Step-by-step explanation

0.7×100=70

Answer:

scientific notation

-6 * 10 ^ 1

Step-by-step explanation:

No Problem

Answer:

d. 1 1/8

Step-by-step explanation:

-3 -1

---- ÷ -----

8. 3

Keep, Change, Flip.

-3/8 stays the same.

Division becomes multiplication.

-1/3 becomes -3/1

-3. -3. = 9

----- × ----- ------

8. 1. = 8

9/8 = 1 1/8

Answer:

D. 1 1/8

Step-by-step explanation: