grant is rolling a standard six sided number die eight times. how many outcomes are possible

Answer:

ita A

Step-by-step explanation:

You can calculate the monthly payments for a 10-year fixed loan at 5.0% on a balance of $275,325 by plugging the values into the amortization formula: M = P [r(1+r)^n] / [(1+r)^n – 1]. Perform the calculations and compare the result to the answer choices.

This question falls under the category of financial mathematics, specifically loan repayment calculations. When calculating a fixed loan, we typically use an amortization formula to find our monthly payment. The formula we use is: M = P [r(1+r)^n] / [(1+r)^n – 1], where M is our monthly payment, P is the principal loan amount (in this case $275,325), r is our monthly interest rate (annual rate of 5% divided by 12), and n is the number of payments (or the number of months, in this case, 10 years or 120 months).

Plugging in these numbers, we get M = $275,325[0.004167(1+0.004167)^120] / [(1+0.004167)^120 – 1].

After performing these calculations, you will get the monthly payment for this 10-year fixed loan. Compare this number to the choices given to get your answer.

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The correct answer is: a. The population will fall below 1,200,000 around the year 2024.

To determine when the city's population will fall below 1,200,000, we need to use the formula for exponential decay:

[tex]P(t) = P_0 \cdot (1 - r)^t[/tex]

where:

-  P(t)  is the population at time  t .

-  P₀  is the initial population.

-  r  is the rate of decrease (expressed as a decimal).

-  t  is the number of years.

Given:

- Initial population,  P₀ = 1,405,233

- Rate of decrease,  r = 1.1% = 0.011

- Final population,  P(t) = 1,200,000

We need to find  t  such that:

[tex]1,200,000 = 1,405,233 \cdot (1 - 0.011)^t[/tex]

First, we divide both sides by 1,405,233:

[tex]\frac{1,200,000}{1,405,233} = (0.989)^t[/tex]

Next, we calculate the left-hand side:

[tex]\frac{1,200,000}{1,405,233} \approx 0.854[/tex]

So we have:

[tex]0.854 = (0.989)^t[/tex]

To solve for  t , we take the natural logarithm of both sides:

[tex]\ln(0.854) = \ln((0.989)^t)[/tex]

Using the properties of logarithms, we can bring down the exponent:

[tex]\ln(0.854) = t \cdot \ln(0.989)[/tex]

Now, solve for  t :

[tex]t = \frac{\ln(0.854)}{\ln(0.989)}[/tex]

Let's calculate this:

[tex]\ln(0.854) \approx -0.157 \\\\ \ln(0.989) \approx -0.011 \\\\ t = \frac{-0.157}{-0.011} \approx 14.27[/tex]

Since 14.27 years from 2010 is approximately in 2024:

[tex]2010 + 14.27 \approx 2024[/tex]

So the population will fall below 1,200,000 around the year 2024.

The correct answer is: a. 2024

Answer:

A. Figure A

Step-by-step explanation:

We are given the figure WXYZ.

It is required to find the final figure after [tex]T_{2,7}D_{0,2}[/tex].

Now, [tex]D_{0,2}[/tex] means to dilate the figure by 2 units and [tex]T_{2,7}[/tex] means to translate it by 2 units to the left/right and seven units up/down.

As we have to apply [tex]T_{2,7}D_{0,2}[/tex] to the figure.

This means that first dilation is applied and then translation.

Since, the all the figures are dilated. We focus on the translations.

We can see that, only figure A is translated 2 units to the right and 7 units upwards.

So, option A is correct.

Answer:

the answer is (D)

Step-by-step explanation:

Final answer:

To divide $80 between two men so that 1/4 of one person's share equals 1/6 of the other's share, each man will receive $40 and $60, respectively.

Explanation:

To divide $80 between two men so that 1/4 of one person's share equals 1/6 of the other's share:

Let x be one person's share and y be the other person's share.

Set up the given ratio: 1/4x = 1/6y.

Solve the ratio equation to find x and y: 1/4x = 1/6y can be simplified to x = $40 and y = $60.

To find the area of a rhombus with diagonals of 500 yards and 800 yards, use the formula (d1 * d2) / 2 and convert the result to square miles.

Given: The diagonals of the rhombus are 500 yards and 800 yards.

Formula: The area of a rhombus can be calculated using the formula: Area = (d1 * d2) / 2, where d1 and d2 are the diagonals of the rhombus.

Calculation: Area = (500 * 800) / 2 = 200,000 square yards.

Conversion: To convert square yards to square miles, divide the area by 3,097,600 (number of square yards in a square mile).

Final Result: The area of the rhombus is approximately 0.0646 square miles.

Answer: The standard deviation of the sample will be 11.6.

The standard deviation of the population will be 12.31.

Step-by-step explanation:

Mr Smith's math class scores : 61, 67, 81, 83, 87, 88, 89, 90, 98, 100

Number of terms,N = 10

[tex]Mean=\mu =\frac{\text{sum of all the terms}}{\text{total number of terms}}[/tex]

[tex]\mu =\frac{61+67+81+83+87+88+89+90+98+100}{10}=\frac{844}{10}=84.4[/tex]

Standard deviation of the sample:

[tex]\sigma=\sqrt{\frac{1}{N}\sum_{i=1}^n(x_i-\mu )^2}=\sqrt{\frac{1}{10}(1364.4)}=11.68[/tex]

Standard deviation for the population:

[tex]\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^n(x_i-\mu )^2}=\sqrt{\frac{1}{9}(1364.4)}=12.31[/tex]

The standard deviation of the sample will be 11.6.

The standard deviation of the population will be 12.31.

Answer:

The largest number of gift bags that can be packed is:

9

Step-by-step explanation:

To find The largest number of gift bags that can be packed, we need to find the greatest common divisor of these numbers.

Listing the prime factorization's for each number:

171 = 3 x 3 x 19

63 = 3 x 3 x 7

27 = 3 x 3 x 3

As we can clearly see from the prime factorization the greatest common factor of these numbers is 9(3×3)

The largest number of gift bags that can be packed is:

9

Answer:

for the first and second questions the answers are

Field hockey players                   basketball players

mean:66                                      mean:72

mode:66                                      mode:72

median: 66                                  median:72

range:10                                      range:7

Step-by-step explanation:

1. For the Field Hockey Players

The mean height is 68 inches, the mode is 66 inches, the median is 66 inches, and the range is 15 inches.

2. For the Basketball Players:
The mean is approximately 67 inches, the median is 67 inches, the modes are 63 inches and 72 inches, and the range of the heights is 11 inches

3. All 10 basketball players are shorter than the tallest field hockey player.

3b. the overlapping heights are: 60 in., 64 in., 65 in., 66 in., 67 in., 68 in., 69 in., 72 in., and 74 in.

Field Hockey Players:

The data is sort as follows

60, 60, 64, 64, 65, 65, 65, 66, 66, 66, 66, 66, 66, 66, 67, 67, 67, 68, 68, 68, 68, 69, 69, 70, 72, 72, 72, 73, 75, 75.

Now let's calculate the measures of center and variability:

Mean (Average): Add up all the heights and divide by the total number of heights. We then round the answer to the nearest whole number.

Mean

= (60 + 60 + 64 + 64 + 65 + 65 + 65 + 66 + 66 + 66 + 66 + 66 + 66 + 66 + 67 + 67 + 67 + 68 + 68 + 68 + 68 + 69 + 69 + 70 + 72 + 72 + 72 + 73 + 75 + 75) / 30

= 2040 / 30

= 68 inches (rounded to the nearest whole number).

Mode: This is the height that occurs most frequently.

From the sorted list, we can see that 66 inches appears 8 times, which is more than any other height, so Mode = 66 inches.

Median: This is the middle height when all the heights are listed in ascending order. If there is an even number of heights, as in this case, the median is the average of the two middle heights.

Here, the 15th and 16th heights are both 66 inches, so Median = (66 + 66) / 2 = 66 inches.

Range: This is the difference between the tallest (maximum) and shortest (minimum) players.

Range = Maximum - Minimum = 75 inches - 60 inches = 15 inches.

So, for the field hockey players, the mean height is 68 inches, the mode is 66 inches, the median is 66 inches, and the range is 15 inches.

Basketball Player Heights

The data is sort as follows

63, 63, 64, 64, 66, 67, 68, 72, 72, 74.

Mean (Average): The mean is calculated by adding all the numbers together and then dividing by the number of numbers.

Mean

= (63 + 63 + 64 + 64 + 66 + 67 + 68 + 72 + 72 + 74) / 10

= 673 / 10

= 67.3 inches.

Median: The median is the middle number in a sorted, ascending list. If there are an even number of observations, the median is the average of the two middle numbers.

In our list, since we have 10 numbers, an even number, the median is the average of the 5th and 6th numbers.

Median = (66 + 67) / 2 = 66.5 inches.

Mode: The mode is the number that appears most frequently in a data set.

From our list, we can see that the numbers 63 and 72 both appear the most (2 times each). So, this data set has two modes: 63 inches and 72 inches.

The range is calculated by subtracting the smallest number in a set from the largest number.

In your data set, the smallest number (the minimum) is 63 inches and the largest number (the maximum) is 74 inches.

So, Range = Maximum - Minimum = 74 - 63 = 11 inches.

So, for this data set, the mean is approximately 67.3 inches, the median is 66.5 inches, the modes are 63 inches and 72 inches, and the range of the heights is 11 inches.

3. First, let's identify the tallest field hockey player. Considering all heights given for field hockey players, the tallest field hockey player is 75 inches.

Now, let's look at the basketball player heights. We have 10 basketball player heights in total: 68 in., 64 in., 63 in., 63 in., 72 in., 74 in., 60 in., 66 in., 65 in., and 69 in.

From this, we can see that all 10 basketball players are shorter than 75 inches. So, all 10 basketball players are shorter than the tallest field hockey player.

3b. The overlapping heights are those that appear in both basketball and field hockey teams. Looking at both sets, the overlapping heights are: 60 in., 64 in., 65 in., 66 in., 67 in., 68 in., 69 in., 72 in., and 74 in.

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There are 4 cups of water in a bottle containing 32 fluid ounces.

We have,

The number of cups in a bottle of water depends on the conversion rate from fluid ounces to cups.

1 cup is equivalent to 8 fluid ounces.

To find the number of cups in a bottle containing 32 fluid ounces of water, we can divide the total number of fluid ounces by the conversion rate:

So,

= 32 fluid ounces / 8 fluid ounces per cup

= 4 cups

Therefore,

There are 4 cups of water in a bottle containing 32 fluid ounces.

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Answer:

The correct answer is A. A fairly strong positive correlation

Step-by-step explanation:

Scatter Plot : A graph of plotted points that show the relationship between two sets of data.

Now, the points of the scatter plot are going up this shows the increase in the data points so we can say the correlation is positive.

Now, the direction of the scatter plots is to the right. So, we can say that the correlation is strong correlation.

Hence, the correct answer is A. A fairly strong positive correlation

Answer:

the Correct Option is A : fairly strong positive correlation

Step-by-step explanation:

Scatter Plot is a graph that is graphed using points and which shows the relationship between two sets of data. Only used to show correlation.

As given the points of the scatter plot are going up this implies the increment in one set of data with respect to other so we can say here correlation is positive. And  the direction of the scattered points is to the right. So, it reflects that the correlation is strong correlation.

Thus, the Correct Option is A : fairly strong positive correlation

Answer:

14.21

Step-by-step explanation:

Answer:

x = - 16, x = 9

Step-by-step explanation:

[tex]x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}[/tex]

Ignore the "A" ^

v² + 7v - 144 = 0

a = 1, b = 7, c = - 144

[tex]x=\frac{-7±\sqrt{7^{2} -4(1)(-144)} }{2(1)}[/tex]

[tex]x=\frac{-7±\sqrt{49 +576} }{2}[/tex]

[tex]x=\frac{-7±\sqrt{625} }{2}[/tex]

[tex]x=\frac{-7+25}{2}[/tex] and [tex]x=\frac{-7-25}{2}[/tex]

[tex]x=\frac{18}{2}[/tex] and [tex]x=\frac{-32}{2}[/tex]

x = 9 and x = - 16