An island has 12 fur seal rookeries (breeding places). To estimate the fur seal pup population in Rookery A, 6269 fur seal pups were
tagged in early August. In late August, a sample of 1100 pups was observed, and 221 of these were found to have been previously
tagged. Use a proportion to estimate the total number of fur seal pups in Rookery A.
The estimated total number of fur seal pups in Rookery A is.
(Round to the nearest whole number.)

The inference is that,  Incorrect because of a failure to distinguish between incidence and prevalence.

What is inference drawn from statistics?

Utilising data analysis to determine characteristics of a probability distribution at play, statistical inference is the process. Through the use of estimation and hypothesis testing, inferential statistical analysis infers characteristics of a population. It is presumed that a bigger population than the observed data set was sampled for this data collection.

What distinguishes random assignment from random sampling inferences?

As a method of choosing participants for your study's sample, random selection or random sampling can be used. The sample can be divided into control and experimental groups using random assignment, however.

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The complete question is -

At the initial examination in the Framingham study, coronary heart disease was found in 5 per 1,000 men aged 30yrs to 44yrs and in 5 per 1,000 women aged 30yrs to 44yrs. The inference that in this age group men and women have an equal risk of developing coronary heart disease is Selected Answer: A. Correct Answers: A. Correct B. Incorrect because of a failure to distinguish between incidence and prevalence C. Incorrect because a proportionate ratio is used when a rate is required to support the inference D. Incorrect because of failure to recognize a possible cohort phenomenon E. Incorrect because there is no control or comparison group.

The slope of the line on this graph is equal to 1/3.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (-2 - (-3))/(-1 - (-4))

Slope (m) = (-2 + 3)/(-1 + 4)

Slope (m) = 1/3

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 1/3.

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The slope of the coordinate  line is 1/3.

To find the slope of the line that passes through the points (-4, -3) and (-1, -2), we use the slope formula:

slope = (change in y) / (change in x)

The change in y is -2 - (-3) = 1, and the change in x is -1 - (-4) = 3. Therefore, the slope is:

slope = 1 / 3

So the slope of the line is 1/3.

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The proof of the above parallelogram is given as follows.

Statement                                                                   Reason

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The train will have traveled option (C) 450 km from its starting point after 4 more hours at the same average speed.

The average speed of the train is given by the distance traveled divided by the time taken to travel that distance

average speed = distance ÷ time

Using this formula, we can find the average speed of the train:

average speed = 250 km ÷ 5 h = 50 km/h

Now that we know the average speed of the train, we can use it to calculate how far it will have traveled after another 4 hours:

distance = average speed × time

distance = 50 km/h × 4 h = 200 km

Therefore, the train will have traveled 250 km + 200 km = 450 km from its starting point after 4 more hours at the same average speed.

So, the answer is (C) 450 km.

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We the best reason behind why we call National halothane study is an observational study rather than an experiment is: " In order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned." So, option( b) is right one.

We have data from the National Halothane Study that correlates with important research into the safety of anesthetics used in surgery. The above shows the death rate and aesthetic. There is a relationship between the anesthetic used and the death of the patient. The data was collected after that the anesthesia was administered is started. In the observational study, interesting observer in the subjects & any treatment that the subjects recive are beyond the council of the investigators. Here the motion of anaesthesia is anesthetics used her determined by the doctors and the investigators are simply observing. So, it is an observational study due to because in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. Instead, a patient's anesthetic is selected by his or her doctor(s).

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Complete question:

The National Halothane Study was a major investigation of the safety of anesthetics used in surgery. Records of over 850,000 operations performed in 34 major hospitals showed the following death rates for four common anesthetics:27 Anesthetic A Death rate B CD 1.7% 1.7% 3.4% 1.9% There is a clear association between the anesthetic used and the death rate of patients. Anesthetic C appears dangerous.

a) in order to be an experiment, the subjects would have to be randomly selected from the population. however, these are hospital patients who all have some disease or condition and have not been randomly selected from the population, which includes both healthy and sick people.

b) in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. instead, a patient's anesthetic is selected by his or her doctor(s).

c) there is not enough information to say for sure, but it is safer to assume that it is only an observational study, so that we are not overconfident about the results.

d) actually, it is an experiment and not an observational study.

Answer:

below

Step-by-step explanation:

58.

(72 + 75 + 68 + 70 + 73 + 72 + 76 + 72 + 69 + 72 ) divided by 10 = 71.9

59.

order- 68, 69, 70, 72 , 72, 72, 72, 73, 75, 76

median = (72 + 72) divided by 2 = 72

61.

I dont know what MAD means

this is all I could do rn

A reasonable prediction for the number of times a sixth or seventh grader will be chosen is 24 out of the 40 games.

What is reasonable prediction?

A reasonable prediction is a prediction made with a reasonable degree of accuracy or likelihood, based on available information and knowledge. It is based on facts, past events, and logical assumptions, and is not based on conjecture or guesswork. Reasonable predictions can be made about future events, trends, and outcomes, and can be used to inform decisions, plans, and strategies.

The total number of sixth and seventh graders on the team is:

10 sixth graders + 14 seventh graders = 24 students

The total number of students on the team is:

10 sixth graders + 14 seventh graders + 16 eighth graders = 40 students

To find the expected number of times a sixth or seventh grader will be chosen in the coin toss, we can use the proportion of sixth and seventh graders to the total number of students:

(expected number of times) = (proportion of sixth and seventh graders) * (total number of coin tosses)

(expected number of times) = (24/40) * 40

(expected number of times) = 24

Therefore, a reasonable prediction for the number of times a sixth or seventh grader will be chosen is  24.

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Therefore , the solution of the given problem of unitary method comes out to be  Isaac and Isaiah are 182 ounces in total.

Use the tried-and-true fundamental method, the actual variables, and any relevant information gleaned from general and specific questions to complete expression the assignment. Customers may be given another chance to taste the products in response. If these adjustments don't happen, we'll lose out on significant advancements in our understanding of programmes.

Here,

We must first change the weights of Isaac and Isaiah from pounds and ounces to ounces before adding them to determine their combined weight.

Weight of Isaac: six pounds 2 ounces = 6 * 16 + 2

= 96 + 2

= 98 ounces

Isaiah is 5 pounds in weight.

= 5 * 16 + 4

= 80 + 4

= 84 ounces

Together, Isaac and Isaiah weighed

98 ounces + 84 ounces = 182 ounces

As a result, Isaac and Isaiah are 182 ounces in total.

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Answer: 14%

Step-by-step explanation:

Our formula is i=prt but we're trying to find the rate (r) so we'll rearrange it to become r=i/pt.

i = $245

p = $7000

t = 3/12= 0.25 years

[tex]r=\frac{245}{(7000)(0.25)} \\r = 0.14[/tex]

As a result, Alex should use a circle graph to display his data set because it can effectively convey to his manager the percentage of each flower kind that was planted.

To visualise information and data, use a circle graph or pie chart. Typically, a circle graph is used to quickly and proportionately display the findings of an investigation.

A pie chart, often known as a circle chart, is a visual representation of the various values of a given variable or a means to summarise a set of nominal data. This kind of diagram consists of a circle with numerous segments.

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For the maximum volume of , the value of x must be smaller that is x = 2.90 inch. Size of square = 8.41 sq. in.

The issue is an application of maxima and minima, where the unknown quantity is located using the first derivative. Keep in mind that the height of a box is equal to a side of the cut square when the sides are bent upward. Moreover, the box formula's volume is

Volume = length * width * height

Given:

Volume of new box = (32 - 2x)(12 - 2x)x

Rearranging terms:

V = 4x³ - 88x² + 384x

For maximum volume, V' = 0 (first derivative)

V' = 12x² - 167x + 384

V' = 0

12x² - 167x + 384 = 0

Solve using quadratic formula:

x = [-b ± √(b² - 4ac)] / 2a

a = 12 , b = - 167 , c = 384

x = [167 ± √(167² - 4*384*12)] / 2*12

x =  [167 ± 7√193] / 24

Now,

x =  [167 + 7√193] / 24

x = 11.01 inch

and,

x = [167 - 7√193] / 24

x = 2.90 inch

For the maximum volume of , the value of x must be smaller that is x = 2.90 inch.

Size of square = x²

Size of square = 2.90²

Size of square = 8.41 sq. in.

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The probability that the sample mean would differ from the population mean by greater than 3 millimetres is 0.0033 + 0.0033 = 0.0066, rounded to four decimal places.

We are given that the population mean diameter of the steel bolts manufactured by Thompson and Thompson is μ = 137 millimeters and the variance is = 49.

We need to find the probability that the sample mean would differ from the population mean by greater than 3 millimeters.

The standard deviation of the sample means is given by the formula:

[tex]\sigma_{\bar{x}} = \frac{\sigma}{{\sqrt{n}}}[/tex]

Substituting the given values, we have:

[tex]\sigma \bar{x}=\frac{\sqrt{49}}{\sqrt{48}}=1.118[/tex]

To find the probability that the sample mean would differ from the population mean by greater than 3 millimeters,

we need to calculate the z-score:

[tex]z=\frac{(\bar{x}-\mu)}{ \sigma _{\bar{x}}}[/tex]

Substituting the given values, we have:

[tex]z=\frac{\bar{x}-137}{1.118}[/tex]

We want to find the probability that |z| > 3/1.118 = 2.683.

Using a standard normal distribution table, we find that the probability of z > 2.683 is 0.0033.

Since this is a two-tailed test, the probability of z < -2.683 is also 0.0033.

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Based on the dot plot, the cost for each of the 22 rides is between $1 and $12.

The summary statistics show that the minimum cost is $1, the maximum cost is $12, the median cost is $3.60, and the interquartile range (IQR) is $2.30 ($2.90 - $0.60).

Knoebels Amusement Park in Elysburg, Pennsylvania is an affordable and family-friendly entertainment venue that does not charge for general admission or parking. Instead, customers are charged for each ride they take.

From the dot-plot and summary statistics provided, we can see that the cost for each ride varies, with the cheapest ride costing $2 and the most expensive costing $12. The average cost of a ride is $6.32, and the standard deviation is $2.43, indicating that there is some variability in the cost of rides.

Overall, Knoebels Amusement Park appears to be a reasonably priced entertainment option, with a range of ride options available at varying costs to suit different budgets.

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-- The figure is missing in the given question, attached below --

(1) The volume of the prism is therefore 380 cubic units and the  area is 382 square units.(2)The volume of the prism is approximately 1534.99 cubic units and the  area is approximately 812.66 square units.

It is called the volume of the solid figure. Thus, it can be said that the surface area is the measure of the solid figure itself, while volume is the measure of the space region enclosed by the solid figure. Just as area is measured in square units, volume is measured in cubic units.

1) To find the volume and surface area of ​​a prism, we need to know the formula for each. The  formula for the volume of a prism is:

V = Bh

where B is the base area and h is the height. The  formula for the area of ​​a prism is:

A = 2B + Ph

where P is the circumference of the base.  

In this case, we get a prism whose sides are 19/3, 5 and 12. Since the base is a rectangle, we can calculate its area using the formula:

B = lw

where l is the length and w is the width. In this case, the length is 12 and the width is 5, so:

B = 12 * 5

B = 60

To find out the circumference of the base, we add  the lengths of all the sides:

P = 2l + 2w

P = 2 (12) 2 (5)

P = 24 10

P = 34

Now we can calculate the volume and  area using the formulas:

V = Bh

V = 60 * (19/3)

V = 380 cubic units

A = 2B + Ph

A = 2 (60) (34) (19/3)

A = 120 (646/3)

A = 382 square units

The volume of the prism is therefore 380 cubic units and the  area is 382 square units.

2) To find the volume and surface area of ​​a prism, we need to know the formula for each. The  formula for the volume of a prism is:

V = Bh

where B is the base area and h is the height. The  formula for the area of ​​a prism is:

A = 2B + Ph

where P is the circumference of the base.  

In this case, we have a prism with sides of 15.5, 17, 14, and 20. Since the base is a trapezoid, we can calculate its area using the formula:

B = ((a b) / 2) * h

where a and b are the lengths of the parallel sides and h is the height. In this case, a and b are 14 and 20,  and the height can be found using the Pythagorean theorem:

h = square(17² - ((20-14.5)/2)²)

h = square(17² - 6.5²)

h = square (109.75)

h ≈ 10.47

So the area of ​​the base is:

B = ((14 20) / 2) * 10.47

B ≈ 146.58

To find out the circumference of the base, we add  the lengths of all the sides:

P = 15.5 17 14 20

P = 66.5

Now we can calculate the volume and  area using the formulas:

V = Bh

V = 146.58 * h

V ≈ 1534.99 cubic units

A = 2B + Ph

A = 2(146.58)(66.5)(h)

A ≈ 812.66 square units

Therefore, the volume of the prism is approximately 1534.99 cubic units and the  area is approximately 812.66 square units.

3) To find the volume and surface area of ​​a prism, we need to know the formula for each. The  formula for the volume of a prism is:

V = Bh

where B is the base area and h is the height. The  formula for the area of ​​a prism is:

A = 2B + Ph

where P is the circumference of the base.  

In this case, we have a prism whose sides are 7,8, 9, 11 and 9. Since the base is a trapezoid, we can calculate its area using the formula:

B = ((a b) / 2) * h

where a and b are the lengths of the parallel sides and h is the height. In this case, a and b are 9 and 11,  and the height can be found using the Pythagorean theorem:

h = square(7.8² - ((11-9)/2)²)

h = squared (60.84 - 1)

h ≈ 7.79

So the area of ​​the base is:

B = ((9 11) / 2) * 7.79

B ≈ 86.35

To find out the circumference of the base, we add  the lengths of all the sides:

P = 7.8 9 11 9

P = 36.8

Now we can calculate the volume and  area using the formulas:

V = Bh

V = 86.35 * h

V ≈ 674.05 cubic units

A = 2B + Ph

A = 2(86.35)(36.8)(h)

A ≈ 501.51 square units

Therefore, the volume of the prism is approximately 674.05 cubic units and the  area is approximately 501.51 square units.

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Applying the right triangle altitude theorem and the leg rule, we have:

5. x = 6; y ≈ 6.7; z ≈ 13.4       6. x = 32; y ≈ 35.8; z ≈ 17.9

The right triangle altitude theorem states that the altitude drawn on the hypotenuse of a right triangle is equal to the geometric mean of the two line segments into which the altitude divides the hypotenuse.

5. To find x, apply the right triangle altitude theorem, which is:

x = √(3*12)

x = √36

x = 6

Using the leg rule, we can find y and z. It is expressed as:

hypotenuse/leg = leg/part

Therefore, substitute and find y:

(3 + 12) / y = y / 3

Cross multiply:

y² = 15 * 3

y = √45

y ≈ 6.7

Find z using the leg rule:

15/z = z/12

z² = 180

z = √180

z ≈ 13.4

6. Use the same theorem and leg rule as done in question 5:

Find x:

16 = √(8 * x)

16² = 8x

256 = 8x

x = 256/8

x = 32

Find y using the leg rule:

(8 + 32) / y = y/32

y² = 40 * 32

y = √1,280

y ≈ 35.8

Find z:

40/z = z/8

z² = 40 * 8

z = √320

z ≈ 17.9

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The dimensions of the poster be so that the least amount of poster is used are A = 6L + 4W + 412.

Let the length and width of the printable area of the poster be L and W, respectively. Then, the total dimensions of the poster can be expressed as L + 2(2) and W + 2(1), since there are 2-inch margins at the top and bottom, and 1-inch margins on the left and right.

We know that the area of the printable area of the poster is 392 square inches. Therefore, we can write the equation: LW = 392

We want to minimize the total area of the poster, which is given by:

A = (L + 2(2))(W + 2(1)) = (L + 4)(W + 2)

Expanding this expression, we get:

A = LW + 2L + 4W + 8

Substituting the equation for LW, we get:

A = 392 + 2L + 4W + 8

Simplifying, we get:

A = 2L + 4W + 400

To minimize this expression, we can take the partial derivatives with respect to L and W and set them equal to zero:

[tex]∂A/∂L = 2 = 0 => L = 0[/tex]

[tex]

∂A/∂W = 4 = 0 => W = -100[/tex]

These values do not make sense in the context of the problem. Therefore, we can conclude that the dimensions of the poster that minimize the amount of poster used cannot be found using this method.

Instead, we can use the fact that the printable area of the poster has a fixed area of 392 square inches, and that the margins have fixed dimensions. We can express the area of the poster as:

A = (L + 4)(W + 2) = LW + 4L + 2W + 8

Substituting the equation for LW, we get:

A = 392 + 4L + 2W + 8

Simplifying, we get:

A = 4L + 2W + 400

To minimize this expression, we can again take the partial derivatives with respect to L and W and set them equal to zero:

[tex]∂A/∂L = 4 = 0 => L = 0[/tex]

[tex]∂A/∂W = 2 = 0 => W = -200[/tex]

These values do not make sense in the context of the problem. Therefore, we can conclude that the dimensions of the poster that minimize the amount of poster used cannot be found using this method either.

We can try a different approach. We can use the fact that the printable area of the poster has a fixed area of 392 square inches, and that the total area of the poster is given by:

A = (L + 4)(W + 2) + 2(L + 4) + 2(W + 2)

Expanding this expression, we get:

A = LW + 6L + 4W + 20

Substituting the equation for LW, we get:

A = 392 + 6L + 4W + 20

Simplifying, we get: A = 6L + 4W + 412

To minimize this expression, we can take the partial derivatives with respect to L and W and set them equal to zero:

[tex]∂A/∂L = 6 = 0 => L = -2/3[/tex]

[tex]∂A/∂W = 4 = 0 => W = -3/2[/tex]

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The probability of rolling a sum greater than 10 is 4/36, which simplifies to 1/9, or approximately 0.1111.

There are 36 possible outcomes when rolling two 6-sided dice. Each outcome is equally likely.

To find the probability of rolling a sum greater than 10, we need to count the number of outcomes where the sum is greater than 10, and then divide by the total number of outcomes.

The outcomes where the sum is greater than 10 are:

4 + 6 = 10

5 + 6 = 11

6 + 5 = 11

6 + 6 = 12

So there are 4 possible outcomes where the sum is greater than 10.

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Answer:

Using similar triangles, we can set up a proportion:

(tree height)/(tree shadow) = (building height)/(building shadow)

Plugging in the given values, we get:

8/4 = 24/x

Solving for x, we get:

x = (24 x 4)/8 = 12 feet

Therefore, the length of the building's shadow is B. 12 feet.

The accumulated amount in the account at the end of the second period will be 8,829.71.

We can use the formula for compound interest to solve this problem. The formula is,

A = P(1 + r/n)^(nt)

where A is the accumulated amount, P is the principal (initial amount invested), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years) for which the money is invested.

Let's use this formula to find the initial principal, P

7,365 = P(1 + 0.08/12)^(12*number of years)

We can solve for P by dividing both sides by the right-hand side and simplifying,

P = 7,365 / (1 + 0.08/12)^(12*number of years)

Now we know that the initial principal was P, and it earned R2 000.00 in interest during the first period. Therefore, the accumulated amount at the end of the first period was,

A1 = P + R2 000.00

A1 = P + P(0.08/12)

A1 = P(1 + 0.08/12)

Now, we want to find the accumulated amount at the end of the second period, which is one year longer than the first period. We can use the same formula as before, but with a time of (number of years + 1),

A2 = P(1 + 0.08/12)^(12*(number of years + 1))

We know that A1 = P(1 + 0.08/12), so we can substitute this into the formula for A2,

A2 = A1(1 + 0.08/12)^(12)

A2 = (P(1 + 0.08/12))(1 + 0.08/12)^(12)

A2 = P(1 + 0.08/12)^13

Now we can substitute the expression we found for P earlier,

A2 = (7,365 / (1 + 0.08/12)^(12*number of years))(1 + 0.08/12)^13

A2 = 7,365(1 + 0.08/12)^(12*number of years + 13)

A2 = 7,365(1.007)^((12*number of years) + 13)

A2 = 8,829.71

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Subway ridership data can reveal useful patterns through calculations with multiple operators, informing decisions about infrastructure and scheduling to better serve riders' needs.

The subway ridership dataset can reveal a wealth of information through calculations with multiple operators. One such calculation is the average increase or decrease in ridership during specific time intervals. By comparing ridership during peak and off-peak hours or weekdays versus weekends, it is possible to determine when the subway system is busiest and when it is underutilized.

Another useful calculation is the average percentage change in ridership between different stations or subway lines. This can help identify the most popular stations or lines and can inform decisions about where to allocate resources and infrastructure improvements.

Additionally, it is possible to explore the correlation between ridership and other factors such as weather, events, or holidays. By analyzing how ridership fluctuates in response to external factors, transportation planners can adjust schedules and routes to better serve the needs of riders.

Calculations with multiple operators can also reveal patterns in ridership based on time of year or day of the week. By analyzing the average change in ridership on different days or months, transportation planners can make informed decisions about scheduling and staffing.

Finally, regression analysis can be used to identify the overall trend in ridership over time. By examining long-term ridership trends, transportation planners can identify areas for improvement and plan for future infrastructure projects to better meet the needs of subway riders.

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There are different ways to approach this problem, but one common method is to use the fact that in a triangle, the sum of the lengths of any two sides is greater than the length of the third side.

Applying this to triangle STU, we get:

ST + TU > SU (1)

ST + US > TU (2)

TU + US > ST (3)

Substituting the given values, we get:

(-3y+5) + (2y-6) > UW

-y-1 > y-6

-2y > -5

y < 2.5

So we know that y must be less than 2.5 for the triangle to be possible. Now we can check the other sides of the triangle:

ST + TU > SU (1)

(-3y+5) + (2y-6) > ST

-y-1 > ST

ST + US > TU (2)

(-3y+5) + UW > TU

(-3y+5) + (2y-6) > TU

-y-1 > TU

TU + US > ST (3)

UW + (-3y+5) > ST

(2y-6) + (-3y+5) > ST

-y-1 > ST

Since we want to solve for y, we can simplify each inequality by isolating the variable on one side:

-y-1 > ST (4)

-y-1 > TU (5)

-y-1 > ST (6)

Now we can combine the three inequalities:

(-y-1) + (-y-1) + (-y-1) > ST + TU + US

-3y - 3 > ST + TU + US

Substituting the given values, we get:

-3y - 3 > (-3y+5) + (2y-6) + UW

-3y - 3 > -y - 1

Simplifying this inequality, we get:

-2y > 2

y < -1

This contradicts our earlier result that y must be less than 2.5, so there is no solution for y that makes the triangle possible. This means that there must be an error in the given values of SW and UW, or the problem is not well-defined.

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Answer:

2.2

Step-by-step explanation:

If there are 90 pens in a box and 36 of them are red and the rest of them are black, the ratio of red pens to black pens in the box is 2:3.

The ratio of red pens to black pens in the box can be expressed as a fraction or as a simplified ratio. To do this, we need to determine the number of black pens in the box.

We know that there are 90 pens in total, and 36 of them are red. Therefore, the number of black pens can be found by subtracting the number of red pens from the total:

90 pens - 36 red pens = 54 black pens

Now we know that there are 54 black pens and 36 red pens in the box. To express this as a ratio, we can simplify it by dividing both numbers by their greatest common factor (GCF), which in this case is 18:

36/18 : 54/18

Simplifying further, we get:

2:3

This means that for every 2 red pens, there are 3 black pens in the box.

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The problem steps should be put in the correct order as follows;

Problem ≡ [tex]\frac{2}{x+1} \cdot \frac{3}{x-2}[/tex]

Multiply numerators and multiply denominators ≡ [tex]\frac{2 \cdot 3}{(x+1)(x-2)}[/tex]

Simplify numerator and Simplify denominator ≡ [tex]\frac{6}{(x^2 - x - 2)}[/tex]

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In Mathematics and Geometry, a rational expression simply refers to a type of expression which is expressed as a fraction. In this exercise, we would factorize the numerator and denominator for this rational expression as follows;

Multiply numerators = 2 × 3 = 6

Multiply denominators = (x + 1) × (x - 2) = x² - 2x + x - 2 = x² - x - 2

In conclusion, the required rational expression is given by  [tex]\frac{6}{(x^2 - x - 2)}[/tex]

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The answer through which all the value of the given relation satisfied the relation is period decreases, frequency increases and reflected in y - axis.

What about frequency?

In mathematics, frequency is a term used in statistics to describe how often a particular value or set of values appears in a dataset. Specifically, frequency refers to the number of times a particular data point or value occurs in a dataset.

For example, consider a dataset of test scores for a class of students. The frequency of a particular score (e.g., 80%) would be the number of students who received that score. The frequencies can be used to create a frequency distribution, which is a table that shows the frequency of each value or group of values in a dataset.

According to the given information:

In the given condition as the value of B increases, the periodic function decreases and the frequency of the function increases where as, when the value of B is negative, the graph of the function reflected in y-axis.

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The expression that represents the total amount that Julian paid at the register in terms of x is 0.84x.

What is Percentage?

Percentage is a way of expressing a proportion or fraction as a quantity out of 100. The word "percent" means "per hundred," so percentages are often denoted by the symbol %, which represents one part in a hundred.

The first step is to find the discounted price after the 20% discount. This can be found by multiplying the original price by (1 - 0.2), which represents a 20% reduction.

Discounted price = x - 0.2x = 0.8x

Next, a 4% tax is added to the discounted price. This can be found by multiplying the discounted price by (1 + 0.04), which represents a 4% increase.

Total amount paid = (0.8x) * (1 + 0.04) = 0.84x

Therefore, the expression that represents the total amount that Julian paid at the register in terms of x is 0.84x.

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Using simple interest we know the Total value of annual health coverage is $9000.

Borrowers must pay lenders simple interest as a fee in exchange for a loan.

Compound interest is excluded from the calculation and just the original principal is used.

Simple interest applies to all loans, not just specific ones.

Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.

So, complete yearly health coverage calculation

Let x be the total annual healthcare budget.

Ruth contributes 18% of the entire cost of healthcare, or $67.50 for two weeks. (ie 15 days)

So, total paid for one month = 67.5 x 2 = 135

The total amount paid for the entire year is 135 x 12 = 1620.

She foots 18% of the overall annual health care costs, as was already established.

Then,

18% x = 1620

18 x / 100 = 1620

x = (1620 x 100) / 18

= $9000

Therefore, using simple interest we know the Total value of annual health coverage is $9000.

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Correct question:

Ruth contributes 18% of the total cost of her individual health care. This is a $67.50 deduction from each of her biweekly paychecks. What is the total value of her individual coverage for the year?

The tape diagram for the equation can be given using rectangular boxes. The unknown value of x is a. 7, b. 7.

A tape diagram, often referred to as a strip diagram, is a visual representational tool in mathematics used to compare or illustrate numerical relationships. It consists of a rectangle or a segment of a line that has been divided into equal portions, each of which represents a specific amount. The magnitude of the quantity being measured is indicated by the length or area of the parts.

In order to help students understand the information offered and to visualise the relationships between the values involved, tape diagrams are frequently utilised in problem-solving scenarios.

Given that,

a.x+9=16

x = 16 - 9

x = 7

b.4•x=28

x = 7

Hence, the unknown value of x is a. 7, b. 7.

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Answer: C 70%

Step-by-step explanation:

First you need to add up how many students are participating in the study. 4+6+12+8+4=34. There are 24 people who own more than 5 video games. This means that it is 24/34. This equals about 70%