A cash register contains $10 bills and $50 bills with a total value of $1080. If there are 28 bills total, then how many of each does the register contain?

Answer:

Mean weight = 19 pounds

Step-by-step explanation:

From the question given above, the following data were obtained:

17, 11, 21, 24, 22

Number of data (n) = 5

Mean weight =?

The mean of a set of data is the value obtained by adding all the data together and dividing the result obtained by the total number of data. Thus, the mean can be obtained as follow:

Summation of data = 17+ 11 + 21 + 24 + 22

= 95

Number of data = 5

Mean = Summation of data / Number of data

Mean = 95 / 5

Mean weight = 19 pounds

Therefore, the mean weight of the data is 19 pounds

Answer:

-------------------------

Apply the Triangle Inequality Theorem.

It states that:

We'll take the sum of two shortest sides and compare with the longest:

It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.

The matching answer choice is e).

The value in the data set varies from 12 by an Average of 4.

The mean of the data set is 12 and the mean absolute deviation is 4.

Option 1: Each value in the data set varies from 12 by exactly 4.

This statement cannot be concluded based on the given information. The mean absolute deviation measures the average distance between each data point and the mean. It does not imply that each value varies by exactly 4 from the mean.

Option 2: Each value in the data set varies from 12 by an average of 4.

This statement is true. The mean absolute deviation of 4 indicates that, on average, each data point deviates from the mean by 4 units. It does not necessarily mean that each value varies by exactly 4, but the average deviation is indeed 4.

Option 3: No values in the data set are less than 8 or greater than 16.

This statement cannot be determined based on the given information. The mean and mean absolute deviation do not provide information about the specific values in the data set. It is possible for some values to be less than 8 or greater than 16 while still maintaining a mean of 12 and a mean absolute deviation of 4.

Option 4: Half of the values in the data set are 8, and half of the values in the data set are 16.

The  value in the data set varies from 12 by an average of 4.

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The average slope of the climb is approximately 0.404.

To find the average slope of the climb, we need to calculate the change in elevation divided by the horizontal distance covered.

Change in elevation = Final elevation - Initial elevation = 1943 ft - 875 ft = 1068 ft

Horizontal distance covered = 2645 ft

Average slope = Change in elevation / Horizontal distance covered = 1068 ft / 2645 ft

Using a calculator or dividing these values, we find that the average slope is approximately 0.404 to the nearest hundredth.

The average slope of the climb is approximately 0.404. This means that for every 1 foot of horizontal distance covered, the hiker ascends approximately 0.404 feet in elevation.

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The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.

Total number of Outfit Combinations:

There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.

No of favourable options:

As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .

Probability = Number of favourable outcomes/Total no. of combinations

Probability = 1/8

Probability = 0.125 or 12.5%

Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

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Answer:

\(\frac{x}{30}=\frac{2.70}{10}\)

Step-by-step explanation:

The ratio of cost to ounces must be constant.

The cost of 30 ounces of organic blueberries will be;

⇒ x = $8.1

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The cost for 10 ounces of organic blueberries = $2.70.

Now,

Since, The cost for 10 ounces of organic blueberries is $2.70.

Hence, The cost for 1 ounces of organic blueberries = $2.70/10

                                                                                 = $0.27

So, The cost for 30 ounces of organic blueberries = 30 × $0.270

                                                                              = $8.1

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The distance between point T (-5, 1) and point I (-1, 1) is 4 units.

To find the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is:

Distance = √((x2 - x1)² + (y2 - y1)²)

Let's apply this formula to find the distance between point T (-5, 1) and point I (-1, 1):

x1 = -5, y1 = 1 (coordinates of point T)

x2 = -1, y2 = 1 (coordinates of point I)

Plugging these values into the formula, we have:

Distance = √((-1 - (-5))² + (1 - 1)²)

        = √(4² + 0²)

        = √(16 + 0)

        = √16

        = 4

Therefore, the distance between point T (-5, 1) and point I (-1, 1) is 4 units.

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Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

a) The mean of the data-set is of 2.

b) The range of the data-set is of 4 units, which is of around 4.3 MADs.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:

Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)

Mean = 2.

The range is the difference between the largest observation and the smallest, hence:

4 - 0 = 4.

4/0.93 = 4.3 MADs.

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Answer:

y=2

Step-by-step explanation:

the image and preimage are 6 units apart so thhe line of reflection is in the middle at 3 units and is a line that is paralel to the x-axis

y=2

Answer: 4

Step-by-step explanation:

Answer:4

2+2=4 if I have two apples and pick up two more I now have 4 total

Answer:

Step-by-step explanation:

x=2

so 7*2= 14

therefore the answer is 14

Answer:

x=27x

Step-by-step explanation:

x=27.x

find- x-?

x=27x

The quotient of the given complex number is 7/13 - 15/13i

Given the division expression

(10 – 4i) ÷ (5 + i).

This can also be expressed as:

10-4i/5+i

On rationalizing, we will have:

10-4i/5+i * 5-i/5-i

50-10i-20i-4(-1)/25-(-1)

50-30i+4/26

54-30i/26

27/13 - 15/13i

Hence the quotient of the given complex number is 7/13 - 15/13i

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Answer: D \(\frac{23}{13} - \frac{15}{13} i\)

Step-by-step explanation:

Answer:

81=1/2h×9,

81=1/18h

1458h=1

h=1/1458

Answer:

h=1/ 1458

hope it is helpful to you

Answer: n=30

Step-by-step explanation:

first, you subtract 3, as 'and' refers to addition and the opposite is subtraction. this gives you 60.

then you divide by 2, which gives you 30.

if you want, you can input 30 into the equation the situation creates, which is 63 = 2n + 3. input 20 makes 2(30) + 3, which is 60 + 3, which is 63.

a) Mean for the first year of the contract: $63,500

The standard deviation for the first year of the contract: $2,000.

b) Mean for the second year of the contract: $65,405.

The standard deviation for the second year of the contract: $60.

We have,

To find the mean and standard deviation for the first year of the contract, we can use the given information and the properties of the normal distribution.

Given:

The mean salary for professors in the previous year = $62,000

Standard deviation in the previous year = $2,000

Raise in the first year = $1,500

Mean for the first year of the contract:

The mean salary for the first year can be obtained by adding the raise to the previous mean:

Mean = Previous Mean + Raise

Mean = $62,000 + $1,500

Mean = $63,500

The standard deviation for the first year of the contract:

Since each professor receives the same raise, the standard deviation remains the same:

Standard Deviation = $2,000

Therefore, for the first year of the contract, the mean salary is $63,500, and the standard deviation remains $2,000.

Now,

In the second year of the contract, each professor receives a 3% raise based on their salary during the first year of the contract.

To find the mean and standard deviation for the second year, we can use the given information and the properties of the normal distribution.

Mean for the second year of the contract:

To calculate the mean for the second year, we need to add a 3% raise to the mean salary of the first year:

Mean = Mean of the first year + (3% * Mean of the first year)

Mean = $63,500 + (0.03 * $63,500)

Mean = $63,500 + $1,905

Mean = $65,405

The standard deviation for the second year of the contract:

Since each professor receives a raise based on their salary from the first year, the standard deviation also increases. To calculate the standard deviation, we multiply the standard deviation from the first year by the percentage increase:

Standard Deviation = Standard Deviation of the first year * (Percentage Increase / 100)

Standard Deviation = $2,000 * (3 / 100)

Standard Deviation = $2,000 * 0.03

Standard Deviation = $60

Therefore, for the second year of the contract, the mean salary is $65,405, and the standard deviation is $60.

Thus,

a) Mean for the first year of the contract: $63,500

The standard deviation for the first year of the contract: $2,000.

b) Mean for the second year of the contract: $65,405.

The standard deviation for the second year of the contract: $60.

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Answer:

The cost of the bottle of drink is P4.85. The refund for an empty bottle is 25 thebe.

To express the refund as a percentage of the cost of the drink, we need to convert the refund to the same unit as the cost of the drink.

1 thebe = 0.038 Philippine pesos (as of June 2023)

25 thebe = 0.95 Philippine pesos

Therefore, the refund for an empty bottle is 0.95/4.85 x 100% = 19.59%

So the refund for an empty bottle is 19.59% of the cost of the bottle of drink.

hope it helps you.....

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This means that 5% of the 10-1/2-month-old baby boys in the reference population weigh 16.7 pounds or less, and 95% of these baby boys weigh 16.7 pounds or more.

The determination is based on the definition of a percentile. A percentile is a value below which a certain percentage of the data falls. So, in this case, if a weight of 16.7 pounds is at the 5th percentile for 10-1/2-month-old baby boys, then 5% of the baby boys in the reference population have a weight of 16.7 pounds or less. This also means that the remaining 95% of the baby boys in the reference population have a weight of more than 16.7 pounds.

The calculation of percentiles is based on the ranking of the data set. The data is first sorted in ascending order and then divided into 100 equal parts, with each part representing a percentile. The value at each percentile is the value below which a certain percentage of the data falls.

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Answer:

x=4.2. If you divide 12.6 by 3, you get 4.2

Answer: =6 hope that helps

Answer:

8.604 in.

Step-by-step explanation:

We can use the formula for compound interest to find the height of domino #9:

A = P(1 + r)^n

where A is the final amount, P is the initial amount, r is the growth rate, and n is the number of compounding periods. In this case, P is the height of domino #0, r is 15% or 0.15, and n is 9 (since we want to find the height of domino #9).

Substituting the given values:

A = 3.00 in * (1 + 0.15)^9

Simplifying:

A = 3.00 in * 2.86797199

A ≈ 8.604 in

Therefore, the height of domino #9 is approximately 8.604 inches.

The complete frequency table for the following set of data is below:

Interval: Tally Frequency

0 - 2. |||||. 5

3 - 5. |. 1

6 - 8. |||||. 5

9 - 11. |||. 3

12 - 14. ||||| |||. 8

A frequency table is a table which shows the number of times an event occurred in an experiment.

Frequency is the number of times an event occurred in an experiment.

Tally is used to record the number of times an event occurred by using marks.

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The weight range for the farmer's chickens is between 57 and 64 grams for roughly 29.85% of them.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given,

μ = Mean = 55.8

σ = Standard deviation = 7.5

x = 57 or 64

The z-score is the value decreased by the mean, divided by the standard deviation.

z₁ = (x - μ)/σ

z₁ = (57 - 55.8)/7.5

z₁ = 0.16

z₂ = (x -μ)/σ

z₂ = (64 - 55.8)/7.5

z₂ = 1.09

Determine the corresponding probability using the normal probability table in the appendix.

P(Z<0.16) is given in the row starting with 0.1 and in the column starting with .06 of the standard normal

probability table in the appendix.

P(Z < 1.09) is given in the row starting with 1.0 and in the column starting with .09 of the standard normal probability table in the appendix.

P(57≤ X ≤64) = P(0.16 < Z < 1.09)

= P(Z < 1.09) − P(Z < 0.16)

= 0.8621 0.5636

= 0.2985

= 29.85%

Thus about 29.85% of the farmer's hens have a weight between 57 grams and 64 grams.

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The ramp rises 8.79 inches from the lowest point on the ground to the nearest hundredth.

A right angle triangle has a 90 degree angle as one of its angles. Trigonometric ratios can be used to determine the sides. The length of the fiberboard becomes the hypotenuse of the right triangle that is so constructed. As a result, the ramp rises 8.79 inches from the ground at its tallest point to the closest hundredth.

The opposite side of the right triangle is the height of the ramp that is created.

Hence,

sin 19° = opposite / hypotenuse

sin 19° = h / 27

cross multiply

h = 27 × sin 19°

h = 27 × 0.32556815445

h = 8.79034017034

h = 8.79 inches.

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With a monthly repayment of $809.49, the total interest on the car loan will be $5,569.67.

We assume that there are monthly repayments and compounding interest on the car loan.

With periodic repayments and compounding interest, the total interest paid on the car loan will be as shown by the car loan calculator.

Car loan = $43,000

Down payment = $0

Fixed Annual Percentage Rate (APR) = 4.9%

Loan term = 5 years

Car Loan Calculator with monthly Repayment:

Payment = $809.49/month

Interest Paid =$5,569.67

Total Paid = $48,569.67

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Answer: Straight lines that do not intersect or overlap each other.

The equivalent expression to  4√3 is  √48 or 6.928.

An equivalent expression is an expression that has equal value to the original given expression.

From the given expression, we can determine its equivalent expression as follows;

The given expression = 4√3

We can square 4 and multiply it by 3 and enclose all with the square root.

4√3 = √(4² x 3 )

= √ ( 16 x 3 )

= √ ( 48 )

= 6.928

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Answer:

Number Standard Power of 10 Factors of 10 Exponential

700 7 x 10² 7 x 10² 7 x 100 7 x 10²

9,000 9 x 10³ 9 x 10³ 9 x 1000 3² x 10³

80,000 8 x 10⁴ 8 x 10⁴ 8 x 10000 2³ x 10⁴

Explanation:

To write the numbers in a standard form, we need to identify the first digit, and then count the number of digits after that number.

For example, 700 can be written as 7 x 10²

Because the first digit is 7 and there are 2 zeros after the 7.

So, 9,000 is 9 x 10³

80,000 is 8 x 10⁴

Then, if we write the number using a power of 10, we will have the same results as the standard form, because the number has only one digit that is different from zero.

On the other hand, if we will use factors of 10 to express the number, we will use numbers like 10, 100, 1000, and so we get:

700 = 7 x 100

9,000 = 9 x 1,000

80,000 = 8 x 10,000

Finally, for the exponent form, we can write the numbers in the same way as the standard form but we will factorize the number 9 and 8 as follows:

9 = 3² because 3 x 3 = 9

8 = 2³ because 2 x 2 x 2 = 8

Therefore, the exponent form is:

700 = 7 x 10²

9,000 = 3² x 10³

80,000 = 2³ x 10⁴

So, the complete table is:

Number Standard Power of 10 Factors of 10 Exponential

700 7 x 10² 7 x 10² 7 x 100 7 x 10²

9,000 9 x 10³ 9 x 10³ 9 x 1000 3² x 10³

80,000 8 x 10⁴ 8 x 10⁴ 8 x 10000 2³ x 10⁴