Given the expression

Choose all the equivalent expressions as your answer.

(a) Let in the beginning Eric had 3x red pens and Kai had x blue pens

2/5 * 3x = 6x/5
Eric gave 6x/5 red pens to Kai.

Now Eric has 3x - 6x/5 = 9x/5 red pens.

Kai gave x/2 blue pens to Eric

Now Eric has a 9x/5 + x/2 = (18x + 5x)/10 = 23x/10

Now Kai has x - x/2 = x/2 blue pens.

Now Kai has total x/2 + 6x/5 = 17x/10 pens.

required fraction = (x/2)/(17x/10) = x/2 * 10/17x = 5/17

5/17 is the answer.

(b) After another round of transfer Eric has total 23x/10 - 15 pens and Kai has total 17x/10 + 15 pens.

23x/10 - 15 = 17x/10 + 15

(23x - 150)/10 = (17x + 150)/10

23x - 150 = 17x + 150

6x = 300

3x = 150

Eric had 150 pens in the beginning.

None of above options are correct.

To compute a 95% confidence interval for the proportion of adults who spend more than 20 hours a week on a home computer:

Follow these steps:

STEP 1: Determine the sample proportion (p) and sample size (n).

STEP 2:Calculate the standard error (SE) using the formula

SE = √(p(1-p)/n).

STEP 3: Determine the critical value (z) for a 95% confidence level

(1.96 for a two-tailed test).

STEP 4: Calculate the margin of error (ME) using the formula

ME = z * SE.

STEP 5: Find the confidence interval by adding and subtracting the margin of error from the sample proportion:

CI = (p - ME, p + ME).

Unfortunately, without the sample proportion (p) and sample size (n), it's not possible to compute the confidence interval.

However, once you have these values, you can follow the steps above to find the 95% confidence interval for the proportion of adults who spend more than 20 hours a week on a home computer.

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If XY = 8 and YZ = 4, the length οf XZ is 4√5 cm.

The Pythagοrean theοrem states that in a right-angled triangle, the square οf the length οf the hypοtenuse (c) is equal tο the sum οf the squares οf the lengths οf the οther twο sides (a and b) c² = a² + b².

We can use the Pythagοrean theοrem tο find the length οf the hypοtenuse XZ οf the right-angled triangle XYZ.

In this case, X is the right angle, sο XY is the adjacent side and XZ is the hypοtenuse. YZ is οn the οppοsite side. We are given that XY = 8cm and YZ = 4cm.

So, we have:

XZ² = XY² + YZ²

XZ² = 8² + 4²

XZ² = 64 + 16

XZ² = 80

Taking the square root of both sides, we get:

XZ = √80 = √(16 × 5) = √16 × √5 = 4√5

Therefore, the length of XZ is 4√5 cm.

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Complete question:

If XY=8 and YZ=4 find the length XZ

The probability of getting 2 tails is option (b) 37.5%

The event of "2 tails" can occur in three possible outcomes: {htt, tht, tth}, so the probability of getting 2 tails is the sum of the probabilities of these three outcomes.

Each toss of a fair coin is independent and has a 50% chance of landing tails. Therefore, the probability of each of these three outcomes is:

P(htt) = 1/2 × 1/2 × 1/2 = 1/8

P(tht) = 1/2 × 1/2 × 1/2 = 1/8

P(tth) = 1/2 × 1/2 × 1/2 = 1/8

So, the probability of getting 2 tails is:

P(2 tails) = P(htt) + P(tht) + P(tth) = 1/8 + 1/8 + 1/8 = 3/8

= 0.375

0.375 multiplied by 100% gives:

P(2 tails) = 37.5%

Therefore, the correct option is (b) 37.5%

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The tank will be filled in 6 minutes with the new pipes.

Let the capacity of the tank be C.

Then the rate at which the first pipe can fill the tank is C/12 per minute, and the rate at which the second pipe can fill the tank is C/15 per minute.

If the first pipe is changed with a pipe having twice of its radius, then the rate at which the new pipe can fill the tank is (2C)/12 = C/6 per minute.

If the second pipe is changed with a pipe having half of second’s radius, then the rate at which the new pipe can fill the tank is (1/2)C/15 = C/30 per minute.

Let t be the number of minutes it takes to fill the tank with the new pipes. Then we have:

(C/6 + C/30)t = C

Simplifying this equation, we get:

5Ct/30 = C

Multiplying both sides by 30/5C, we get:

t = 6 minutes

Therefore, the tank will be filled in 6 minutes with the new pipes.

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The inequality represented by the graph is 10 ≤ x ≤ 20.

Inequality is the unequal distribution of resources or opportunities among individuals or groups in a society. It can be measured in multiple ways, including income, wealth, access to education, health care, and political power. It is a major social problem, as it can lead to poverty, lack of opportunity, and even violence. The root causes of inequality are complex, but can include discrimination, unequal access to resources, and social and cultural norms. In order to address inequality, governments must create policies that provide access to resources for all individuals, regardless of their social, economic, or other backgrounds. Additionally, it is important to recognize that the effects of inequality are not limited to one group of people – everyone is affected by it in some way.

The graph shows that x must be a number between 10 and 20 (inclusive). This means that the value of x must be at least 10, but it cannot be greater than 20. This is because the graph shows that the values of x between 50 and 59 are not included in the range.

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In this scenario, a survey is being conducted to gather information about the fruit and vegetable consumption habits of a population of 200 students. The survey will help to determine the typical servings of fruits and vegetables that students consume in a day.

To ensure that the survey results are accurate and representative of the population, a random sample of students should be selected for the survey. This means that each student in the population has an equal chance of being selected for the survey. The sample size should also be large enough to ensure that the survey results are statistically significant and reliable.

Once the survey has been conducted and the data has been collected, it can be analyzed to determine the average servings of fruits and vegetables that students in the population typically consume in a day. This information can then be used to develop strategies for promoting healthy eating habits among students.

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The expression that represents the number of days until only 5% of Technetium-99m remains is approximately 3.79 days.

The given function [tex]T(d) =[/tex]  [tex]100 \cdot 2^{-2d}$[/tex]represents the percent of Technetium-99m remaining d days after the test.

To find the number of days until only 5% remains, we need to solve the following equation:

[tex]$100 \cdot 2^{-2d} = 5$[/tex]

Dividing both sides by 100, we get:

[tex]$2^{-2d}$[/tex] [tex]= 0.05[/tex]

Taking the natural logarithm of both sides, we get:

[tex]$\ln{(2^{-2d})}$[/tex] = [tex]ln(0.05)[/tex]

Using the logarithmic identity log(base a)(bⁿ) = nlog(base a)(b), we can simplify the left side as:

[tex]-2d \cdot ln(2) = ln(0.05)[/tex]

Dividing both sides by -2 ln(2), we get:

[tex]d = ln(0.05) / (-2 \cdot ln(2))[/tex]

Using a calculator, we get:

[tex]d = 3.79[/tex]

Therefore, the expression that represents the number of days until only 5% of Technetium-99m remains is approximately 3.79 days.

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Based on the given options, the correct answer is: OC. Jack interpreted the mean as the median. Half the cats weighed less than 7.96 pounds and half weighed more.

The mean is a measure of central tendency that represents the average of a set of data. It is calculated by adding up all the values in the data set and then dividing by the total number of values.

In this case, Jack interpreted the mean of 7.96 as meaning that half the cats weighed less than 7.96 pounds and half weighed more. However, this is incorrect because the mean does not necessarily divide the data set into two equal halves.

The median, on the other hand, is the middle value in a sorted list of numbers. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values.

If Jack had interpreted the median as meaning half the cats weighed less than its value and half weighed more, he would have been correct. However, he incorrectly interpreted the mean as the median.

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The answer is 15 sides

Answer:

196pie

Step-by-step explanation:

Answer:

a) The Total Expenses y (in dollars) of the College or University for t years can be modeled by an exponential function of the form:

y = ab^t                

Where "a" is the initial amount and "b" is the growth rate.

b) Using the given data, we can find the value of "a" by plugging in the first year's data into the equation:

y = ab^t

21211 = a * b^0

a = 21211

Thus, the function representing the Total Expenses y (in dollars) of the College or University after t years is:

y = 21211b^t

c) The graph of the exponential function will be an upward-sloping curve that starts at the point (0, 21211) and grows at a rate determined by the value of "b".

d) The y-intercept of the graph is (0, 21211), which represents the initial expense at the start of the first year. The function has no asymptotes. The domain of the function is all real numbers, while the range of the function is y > 21211. As t approaches infinity, the function grows without bound, which means the end behavior is that the expenses continue to increase exponentially over time.

The probability that exactly one of the two games will be won by Sally. against Martin [tex]= 0.42[/tex] or 42%.

Use the concept of probability defined as:

Probability is the ratio of:

The number of favorable outcomes to the total number of outcomes for the occurrence of an event.

Given that,

Sally plays two games against Martin.

Sally had a chance to win, tie, or drop each game.

The probability that Martin will lose against Sally is [tex]0.3[/tex].

The probability that Martin will lose against Sally in a tie is [tex]0.1[/tex].

We need to calculate the probability that Sally will win exactly one of the two games against Martin.

To calculate the probability that Sally will win exactly one of the two games against Martin:

Use a combination of probabilities.

Since there are 2 games,

So in this case:

There are 2 possible outcomes:

1. When Sally plays, she either loses the first game and wins the second one, or she wins the first game and loses the second one.
The probability of Sally winning the first game and losing the second game can be calculated,

By multiplying the probability of winning (0.3) with the probability of losing,(1 - 0.3 = 0.7).

Similarly,

2. By doubling the likelihood of losing, which is, the chance of Sally losing the first game and winning the second game,

[tex]1 - 0.3 = 0.7[/tex] with the probability of winning (0.3).

To determine the likelihood that Sally will triumph in precisely one of the two games: Add up this probability as follows:

(0.3 x 0.7) + (0.7 x 0.3)  = 0.42

Hence,

The probability that exactly one of the two games will be won by Sally against Martin = 0.42 or 42%.

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Answer:

75, 24

Step-by-step explanation:

Answer: 75, 24

Step-by-step explanation:

Let the two numbers be x and y. Then,

1. x+y=99

2. x-y=51

If you add these two equations together, you get:

2x=150

x=75

Plug in x.

75+y=99

y=24

The cost of a package containing x comic books and a poster is given by the equation y = 0.91x + 7.08.

Let's start by using the information given to form two equations. Let x be the number of comic books and let y be the cost of package.

From the first sentence, we can form the equation:

y = 7.99 + 2x

From the second sentence, we can form the equation:

y = 16.99 + 11x

Now we can use these equations to find the linear function rule that models the cost of a package containing any number of comic books.

First, we can set the two equations equal to each other since they both represent the cost of a package:

7.99 + 2x = 16.99 + 11x

Solving for x, we get:

9x = 9

x = 1

Now that we know that 1 comic book costs $4, we can substitute that value into either of the original equations to find the cost of a package with a poster and 1 comic book:

y = 7.99 + 2(1) = 9.99

So a package with a poster and 1 comic book costs $9.99.

Finally, we can use the slope of the line to find the linear function rule that models the cost of a package containing any number of comic books. We know that the slope is the change in y over the change in x, or:

m = (16.99 - 7.99)/(11 - 2) = 0.91

So the linear function rule is:

y = 0.91x + 7.08

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The given question is incomplete, the complete question is:

A store sells packages of comic books with a poster. A poster and 2 comics cost ​$7.99. A poster and 11 comics cost ​$16.99. Write a linear function rule that models the cost y of a package containing any number x of comic books.

Answer:this is the answer

Step-by-step explanation:

Answer: Using the multiple angle formula for cosine, we have:

cos 4x = 2cos^2 2x - 1

Now we need to rewrite cos 2x in terms of cos x. Again, using the multiple angle formula for cosine, we have:

cos 2x = 2cos^2 x - 1

Substituting this expression into the previous equation, we get:

cos 4x = 2(cos^2 x)^2 - 1

Simplifying the expression further, we have:

cos 4x = 2(cos^4 x) - 1

Therefore, cos 4x can be written in terms of cos x as 2(cos^4 x) - 1.

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

To solve this question we have to count which one of the options have five red square and which of the options have 7 blue squares.

By looking at the options we can see that E is the only one that matches the requirements!

We have to be careful that we are looking for 5 red squares and not 5 blue squares as our answer would be wrong.

We can find this out in the question, we see that in the question it says red and blue defining that red goes first. This is why we consider red to be 5 and blue to be 7

Hope this helps, have a lovely day! :)

Answer:

39

Step-by-step explanation:

[tex]sin(x)=\frac{10}{16}\\ x=sin^{-1} (\frac{10}{16})\\ x=38.682....\\x=39[/tex]

A box-and-whisker plot is the appropriate data display for Jace's electric-vehicle data and gas-powered vehicle data, and it will give him a visual representation of the difference between the two datasets.

The appropriate data displays for Jace's electric-vehicle data and gas-powered vehicle data would be a box-and-whisker plot. This type of plot is a graphical representation of the five-number summary of a dataset. The five-number summary consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values. It can be calculated using the following formulas:

Minimum = smallest value

Q1 = 25th percentile (the value below which 25% of the data lies)

Median = 50th percentile (the value below which 50% of the data lies)

Q3 = 75th percentile (the value below which 75% of the data lies)

Maximum = largest value

Using these formulas, Jace can calculate the five-number summary for his electric-vehicle data and his gas-powered vehicle data. He can then use these values to create a box-and-whisker plot that compares the range and shape of each dataset. The box-and-whisker plot will give him a clear visual representation of the difference between the two datasets. By comparing the range and shape of the two datasets, Jace can get a better understanding of the difference between the electric-vehicle data and the gas-powered vehicle data. From there, he can draw conclusions about the differences between the two vehicle types.

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Answer:

x = 11[tex]\sqrt{3}[/tex] , y = 33

Step-by-step explanation:

using the cosine and sine ratios in the right triangle and the exact values

cos60° = [tex]\frac{1}{2}[/tex] , sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{22\sqrt{3} }[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = 22[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 11[tex]\sqrt{3}[/tex]

and

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{22\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2y = 22[tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] = 22 × 3 = 66 ( divide both sides by 2 )

y = 33

The three numbers which add up to 180 are 90, 34 and 56.

To find the sum of three numbers as 180, we simply add the three numbers together.

In this case, the numbers are given as 128, 90, 34, 80 and 56;

We see that the three numbers whose sum is 180 are 90, 34 and 56,

Let 90 represents one quantity, 34 represents another quantity, and 56 represents yet another quantity.

When we add these three quantities together, we get the total sum of all three quantities, which is 180.

Therefore, the numbers 90, 34 and 56 adds up to 180.

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The given question is incomplete, the complete question is

Which three of these number add up to 180?  128, 90, 34, 80, 56.

To calculate Daniel's weekly pay, add his regular pay and overtime pay: Weekly pay = $1038.31.

To calculate Daniel's weekly pay, we need to determine his regular hours and his overtime hours.

Regular hours = 37 hours

Overtime hours = Total hours worked - Regular hours

Total hours worked = 9.5 + 8.5 + 10 + 10 + 10.75 = 49.75 hours

Overtime hours = 49.75 - 37 = 12.75 hours

Daniel's regular pay for 37 hours is:

$18.50/hour x 37 hours = $684.50

Daniel's overtime pay for 12.75 hours is:

$18.50/hour x 1.5 = $27.75/hour (time-and-a-half rate)

$27.75/hour x 12.75 hours = $353.81

Therefore, Daniel's weekly pay is the sum of his regular pay and overtime pay:

Weekly pay = $684.50 + $353.81 = $1038.31

Therefore, Daniel's weekly pay is $1038.31.

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Complete question:

Daniel earns $18.50 an hour, with time-and-a-half for hours worked over 37 a week. His clock hours for a week are 9. 5, 8. 5, 10, 10, and 10.75. How much is his weekly pay?

The angle AOB will be a right angle if x = 27.5

AOB will be a right angle if the angle AOB is 90°, then we can write the linear equation:

2x + 30 + 2x - 50 = 90

These are the two measures that conform AOB.

Solving that linear equation we will get:

2x + 30 + 2x -50 = 90

4x - 20 = 90

4x = 90 + 20 = 110

x = 110/4 = 27.5

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The correct answer is (c) Ali has a monthly net income of $2,088 after paying 28% in taxes.

.

To calculate Ali's net monthly income, we first need to find out the amount of tax she pays, and then we can subtract it from her annual income to get her net annual income. We'll then divide it by 12 to get her monthly net income.

Calculations: Ali's tax rate is 28%. 28% of 29,000 is 8,12029,000 - 8,120 = 20,88020,880 / 12 = 1,740

Therefore, Ali's net monthly income is $1,740. The correct answer is option D, $1,740. ($29,000 salary x 28% taxes = $8,120 in taxes annually; $8,120 / 12 months = $677 in taxes per month; $29,000 - $677 = $2,088 net monthly income).

Net income refers to the amount of money that a company or an individual has earned after deducting all the expenses and taxes from their gross income. In the context of a company, net income is also called profit, and it is an important measure of a company's financial performance.

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Corey has saved $24 and Jasper has saved $54.

Let x be the amount of money Corey has saved.

Then, we know that Jasper has saved $6 more than twice as much as Corey, which can be expressed as:

J = 2x + 6

We also know that the total amount saved by both Jasper and Corey is $78, so we can set up another equation:

J + x = 78

Now we can use these equations to solve for x, which will give us the amount of money Corey has saved:

J + x = 78 (substitute J = 2x + 6)

(2x + 6) + x = 78

3x + 6 = 78

3x = 72

x = 24

Therefore, Corey has saved $24.

To check this answer, we can substitute x = 24 into the equation we found for J:

J = 2x + 6

J = 2(24) + 6

J = 54

So Jasper has saved $54.

We can verify that $24 + $54 = $78, which matches the total amount saved by both Jasper and Corey.

In summary, Corey has saved $24 and Jasper has saved $54. It's important to remember to set up equations to represent the given information in a problem and to check our answers to make sure they are reasonable and match the given information.

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Answer:

Step-by-step explanation:

5

Answer:Option b. y = 0.

Step-by-step explanation:

A store buys paper at $15 per bundle. It then sells the bundles at a price that includes a 40% markup. The store offers a discount of To off the price of each bundle if two or more bundles are purchased. The price to purchase 3 bundles of paper is $51

$15 x 3 bundles = $45 + 40% markup = $63 - 20% discount = $51.

In short, a purchase price is the economic value, usually defined in fiat currency at a given point in time, for which a buyer purchases a product, service, or asset. The compensation paid for this value can be fiat currency or other, such as services as payment or benefits in kind.the amount of money someone pays for something .The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product. It is mostly used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.

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The probability that a randomly selected student is either female or a physics major is 27/40 or approximately 0.675.

To find the probability that a randomly selected student is either female or a physics major, we need to add the probability of selecting a female student to the probability of selecting a physics major, but subtract the probability of selecting a student who is both female and a physics major to avoid double-counting.

Let F be the event of selecting a female student, and M be the event of selecting a physics major. We are given that:

P(M) = 15/40 (15 students out of 40 are physics majors)

P(F) = 18/40 (18 students out of 40 are female)

P(F ∩ M) = 6/40 (6 students out of 40 are both female and physics majors)

To find the probability of selecting a student who is either female or a physics major, we use the formula:

P(F ∪ M) = P(F) + P(M) - P(F ∩ M)

Substituting the given probabilities, we get:

P(F ∪ M) = 18/40 + 15/40 - 6/40

Simplifying, we get:

P(F ∪ M) = 27/40

Therefore, the probability that a randomly selected student is either female or a physics major is 27/40 or approximately 0.675.

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The ratio between the areas is 4, which means that the area of the large circle is 4 times the area of the other one.

Remember that for a circle of radius R, the area is given by:

A = 3.14*R²

Here we can see that the diameter of the smaller circle is equal to the radius of the larger circle, then if R is the radius of the larger circle, the radius of the smaller one is R/2.

Then the area of the smaller circle is:

a = 3.14*(R/2)² = (1/4)*3.14*R²

The ratio between these two is:

A/a = 3.14*R²/( (1/4)*3.14*R²) = 4

That means that the area of the large circle is 4 times the area of the smaller one.

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