Michelle can swim 4 laps in 6 minutes and 12 seconds. If michelle swims at the same pace, how long would it take her to swim 10 laps?

The scale ratio is therefore 1:5 miles per inch

The connection between distances on the map and their equivalent distances on the ground is expressed by the scale ratio. Here, one inch on the chart corresponds to five miles on the Earth. We must represent this connection as a fraction using the same units in order to calculate the scale ratio:

5 miles per inch.

By reducing both the numerator and denominator by one inch, we may simplify the following fraction:

1/5 of a mile per inch

The scale ratio is therefore 1:5 miles per inch. This implies that the comparable distance on the ground is 5 units long for every 1 unit of distance indicated on the map (1 inch) (5 miles).

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Answer:

[tex]24\pi \: {cm}^{2} [/tex]

Step-by-step explanation:

Given:

A cone

h (height) = 4 cm

r (radius) = 3 cm

Find: A (surface area) - ?

In order to find the surface area, we have to know the length of the slant height first (use the Pythagorean theorem):

[tex] {l}^{2} = {r}^{2} + {h}^{2} [/tex]

[tex] { l}^{2} = {3}^{2} + {4}^{2} = 9 + 16 = 25[/tex]

[tex]l > 0[/tex]

[tex]l = \sqrt{25} = 5 \: cm[/tex]

Now, we can find the surface area:

[tex]a(surface) = \pi {r}^{2} + \pi \times r \times l[/tex]

[tex]a(surface) = \pi \times {3}^{2} + \pi \times 3 \times 5 = 9\pi + 15\pi = 24\pi \: {cm}^{2} [/tex]

Answer:

6

Step-by-step explanation:

he needs 6 points to score over the last nine holes

Kevin needs to score 8.5 strokes per hole for the last nine holes to get back to an even par.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

We can find the total number of strokes Kevin needs to score over 18 holes to reach an even par.

If the par score for 18 holes is 72,

and Kevin scored 4 over par on the first nine holes

= 9 × 4 = 36 extra strokes.

Now, if the par score for the last nine holes is x, then we have:

4 + x + x + x + x + x + x + x + x = 72

4 + 8x = 72

8x = 68

x = 8.5

Therefore, Kevin needs to score 8.5 strokes per hole for the last nine holes to get back to an even par.

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By answering the presented questiοn, we may cοnclude that In summary, equatiοn the vertex fοr f(x) = -(x - 1)² + 5 is a maximum, while the vertex fοr g(x) = (x + 2)² - 3 is a minimum.

A mathematical equatiοn is a fοrmula that links twο statements and uses the equals sign (=) tο indicate equality. In algebra, an equatiοn is a statement that demοnstrates the equality οf twο mathematical expressiοns. The equal sign divides the variables 3x + 5 and 14 in the equatiοn 3x + 5 = 14, fοr instance.

f(x) = a(x - h)² + k

f(x) = -(x - 1)² + 5

= -1(x - 1)² + 5

g(x) = (x + 2)² - 3

In summary, the vertex fοr f(x) = -(x - 1)² + 5 is a maximum, while the vertex fοr g(x) = (x + 2)² - 3 is a minimum.

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The first and third quartiles of x are 269.625 and 330.375 respectively.

The interquartile range is 61.11.

To get the first (Q1) and third (Q3) quartiles of a normally distributed dataset, use the following formulas:

Q1 = μ – (.675)σ

Q3 = μ + (.675)σ

μ -  denotes the population mean

σ - denotes the population standard deviation.

The first quartile represents 25% of a dataset and the third quartile represents 75% of a dataset.

Using Mean and Standard Deviation, we need to determine Quartiles

Assume we have a normally distributed dataset with and = 45.

The first and third quartiles of the dataset can be calculated using the following formulas:

Q1 = μ – (.675)σ = 300 – (.675)*45 = 269.625

Q3 = μ + (.675)σ = 300 + (.675)*45 = 330.375

This means that 25% of all values in the dataset are less than 269.625 and 75% of all values in the dataset are less than 330.375.

We may also calculate the interquartile range using these numbers:

IQR = Q3 - Q1 = 330.375 - 269.265

IQR = 61.11

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The total number of possible outcomes when flipping a coin three times is 8, since there are two possible outcomes for each flip (heads or tails).

Combination is a way of selecting items from a set where order does not matter. Combinations are written as a set of n distinct objects taken r at a time, where n is the total number of objects and r is the number of objects taken.

Of these 8 outcomes, 3 include exactly one head. These are the outcomes HHT, HTH, and THH.

The total number of possible outcomes is calculated using the formula 2ⁿ, where n represents the number of flips. In this case, n = 3, so the total number of outcomes is 2³ = 8.

To find the number of outcomes with exactly one head, we can use the formula nCr, which stands for n choose r.

This formula is used to calculate the number of combinations of r elements that can be chosen from a set of n elements.

In this case, n = 3 (the number of flips) and r = 1 (the number of heads).

This gives us 3C1 = 3, which is the number of outcomes with exactly one head.

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Answer:

The probability that the first grape candy chosen is not among the first two is:

P(not grape in first two) = (1 - 0.26) × (1 - 0.26) = 0.5764

Therefore, the probability that the first grape candy chosen will be at least the third candy chosen is:

P(grape candy chosen third or later) = 1 - P(not grape in first two) = 1 - 0.5764 = 0.4236

So, the answer is 0.4236, which is closest to 0.424. Therefore, the correct option is:

0.424

The deduction that is optional is C. Retirement plan deductions.

When contributing to a retirement plan like a 401(k) or an Individual Retirement Account (IRA), you receive deductions from your taxable income. Essentially, whatever amount of money contributed towards the retirement fund can be subtracted from your total annual income.

Consequently, the entire amount cannot then be seized for taxation purposes. Let's say, for instance that you earn $50,000 annually and contribute $5,000 into your account; this would imply your taxable revenue reduces to $45,000.

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Options for this question are:

The p-value of the test statistic is given as follows:

0.0606

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, we are testing if the proportion is greater than a value, hence we have a right-tailed test.

As we have a right-tailed test, the p-value is one subtracted by the p-value of z = 1.55, hence:

1 - 0.9394 = 0.0606

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Game 1 required 3.5 hrs and game 2 required 4 hrs

mr.Abenezer can spend only 50 hrs per week

he can make 13 games per week

so he'll make 6 games which requires 3.5 hrs and 7 games of which requires 4 hrs for maximize profits.



Triangles QNR and RMQ are congruent

PQR is an isosceles triangle, by extension PQ = PR.

Considering the triangles QNR and RMQ:

Given that angle MRQ = angle NQR.

Likewise, angle RQM = angle RQN (since they are vertically opposite angles).

Consequently, angle MRQ = angle RQM + angle NQR = angle RQN + angle NQR = angle RNQ.

Hence, two pairs of angles that are equal:

angle MRQ = angle RNQ

angle RMQ = angle RQN

Also, PQ = PR, and for M and N are on PQ and PR at the same time, then, MQ = NR.

Through the angle-side-angle (ASA) congruence criterion, we can conclude that triangles QNR and RMQ are congruent.

Therefore, we have proved that triangles QNR and RMQ are congruent.

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There are 48 ways to order this model of car. The correct option is A

We need to multiply the number of options for each feature to get the total number of ways to order this particular car:

   4 color choices

   2 options (manual or automatic) for the transmission

   Audio system: 6 choices

We can multiply these figures in order to find the total number of ways by applying the counting principle to multiplication:

4 × 2 × 6 = 48

Therefore, there are 48 ways to order this model of car.

Therefore, The correct option is A

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Find x, so that 7x + 2, 5x + 7 and 2x - 1 form an arithmatic sequence

Answer:

x=2

Step-by-step explanation:

Simple ratio:

44/88=x/4

Simplify:

1/2=x/4

Cross multiply:

4=2x

x=2

Answer:

x = 2

Step-by-step explanation:

If y varies directly with x then:

[tex]\boxed{y \propto x \implies y=kx}[/tex]

where k is the constant of variation.

Given y = 88 when x = 44:

[tex]\implies 88=44k[/tex]

Solve for k by dividing both sides by 44:

[tex]\implies \dfrac{88}{44}=\dfrac{44k}{44}[/tex]

[tex]\implies 2=k[/tex]

[tex]\implies k=2[/tex]

Therefore, the equation is:

[tex]\boxed{y=2x}[/tex]

To find the value of x when y = 4, substitute y = 4 into the equation and solve for x:

[tex]\implies 4=2x[/tex]

[tex]\implies \dfrac{4}{2}=\dfrac{2x}{2}[/tex]

[tex]\implies 2=x[/tex]

Therefore, the value of x when y = 4 is x = 2.

The value of the given function at f(-6) is -14.

A function in mathematics is a relationship between a set of inputs (the domain) and a set of outputs (the range), where each input corresponds to one specific outcome. Equations, tables, diagrams, and verbal descriptions can all be used to depict functions. They are frequently represented by the notation f(x), where x is the input variable and f is the name of the function. In many branches of mathematics, science, and engineering, functions are fundamental ideas that are used to simulate real-world occurrences and address issues in a variety of applications.

The give function is f(x) = 3x + 4.

Substitute the value of x = -6 to obtain the value of f(-6):

f(-6) = 3(-6) + 4

f(-6) = -18 + 4

f(-6) = -14

Hence, the value of the given function at f(-6) is -14.

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The value of P(A n B) where A and B are independent event is 5/36

From the question, we have the following parameters that can be used in our computation:

P(A) =1/3 and P(B) =5/12,

where A and B are independent event

Since the events are independent, then we have

p(A and B) = p(A) * p(B)

Substitute the known values in the above equation, so, we have the following representation

P(A n B) = 1/3 * 5/12

Evaluate

P(A n B) = 5/36

Hence, the solution is 5/36

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The dimension of the rectangular of a norman window will be 1.6803*3.3606.

What is the area of Rectangle?

In any quadrilateral which have equal and parallel opposite sides is considered to be a rectangle. It is also called as a polygon with four sides and the four angles that are all 90 degrees each. A rectangle is a shape with only two dimensions. The product of the length and the breadth calculates its area. The length of the diagonals of any rectangle are equal in length. Thus, the length of the diagonals can be calculated easily using the Pythagoras theorem where, the diagonal is considered to be the hypotenuse.

Let r represents the radius, and b be the breadth.

Then, perimeter = 3.14*r+2r+2b = 12

For the dimension needed for the most light to enter we need to maximize the area.

Hence, area of the window : area of the semicircle + area of the rectangle

= [tex]\frac{3.14*r^2}{2} + 2rb[/tex]

= [tex]12r - (\frac{3.14+4}{2}) r^2[/tex]

A'(r) = 0

Therefore, [tex]r=\frac{12}{3.14+4}[/tex] which is nearly equal to 1.6803m

From this value of r we can calculate the value of b to be;

b= 1.6803m

Thus, a= 3.606m

Thus the required dimension is : 1.6803*33606

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The measure of angle R,if R is a point of tangency is 37°.

We have been given a diagram of a circle. We are asked to find the measure of angle R.

Since QR is the tangent of our given circle, so measure of angle Q will be 90 degrees as radius is perpendicular to tangent at point of tangency.

We will use angle sum property to solve for angle R as:

53 + 90 + R = 180

R = 180 - 143

R = 37°

Therefore, based on the information, it should be noted that the measure of angle R,if R is a point of tangency is 37°.

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Answer:

y = (5/7)x + (75/7)

Step-by-step explanation:

If you ever find yourself in a math class where you have to write the equation of a line that goes through a certain point and has a certain slope, don't panic. There is a simple formula that can help you out. It's called the point-slope form and it looks like this:

y - y1 = m (x - x1)

It may look scary, but it's actually pretty easy to use. All you have to do is plug in the values that you know and solve for the ones that you don't. For example, let's say you have a line that passes through the point (-1, 10) and has a slope of 5/7. You can use the point-slope form to write the equation of the line like this:

y - 10 = (5/7) (x - (-1))

See? That wasn't so bad. Now you can simplify the equation by distributing the 5/7 and adding 10 to both sides. You get:

y = (5/7)x + (75/7)

And that's it! You have written the equation of the line in slope-intercept form, which is another way of writing the equation of a line. You can check your answer by plugging in the values of x and y from the original point and seeing if they make the equation true. If they do, you're good to go. If not, you made a mistake somewhere and you should go back and fix it.

Congratulations! You have learned how to use the point-slope form to write the equation of a line. Now you can impress your math teacher and your friends with your skills.  Remember, with great power comes great responsibility.

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

1. The policy has a $3,000 deductible clause, which means that Jasper must pay the first $3,000 of his expenses before the insurance company begins to cover the remaining expenses.

2. Jasper should expect to receive $13,270 from the insurance company.

His total out of pocket expense will be $5,730.

3. Other policies may have offered Jasper additional protection, such as disability income benefits. This would have helped him while he was unable to work due to his injury.

4. Based on the information given, the health care insurance coverage that Jasper had appears to be adequate, given his circumstances.

The deductible clause is used by insurance companies to reduce the risk of paying out large amounts of money for small claims and to spread out the cost of insurance among policyholders.

1. The policy provisions as they relate to deductibles, co-insurance, and internal limits are as follows: The policy has a $3,000 deductible clause, which means that Jasper must pay the first $3,000 of his expenses before the insurance company begins to cover the remaining expenses. The co-insurance clause means that the insurance company will cover 80% of the remaining expenses and Jasper will be responsible for the remaining 20%.

The internal limits for hospital room and board and surgical fees are $180 and $1,500, respectively. This means that the insurance company will only cover up to $180 per day for hospital room and board and up to $1,500 for surgical fees.

2. Jasper should expect to receive $13,270 from the insurance company. He must pay $3,000 out of his own pocket to meet the deductible, and he will also be responsible for the remaining 20% of the expenses not covered by the insurance company, which amounts to $2,730.

This means that his total out of pocket expense will be $5,730.

3. Other policies may have offered Jasper additional protection, such as disability income benefits. This would have helped him while he was unable to work due to his injury.

4. Based on the information given, the health care insurance coverage that Jasper had appears to be adequate, given his circumstances.

The policy provides enough coverage to cover the majority of his medical expenses and the deductible and co-insurance amounts are reasonable. In addition, the internal limits for hospital room and board and surgical fees are within reasonable limits.

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The expression for y is y = (-1/4)(cos 8x + 2 cos 4x) + C, where C is the constant of integration.

What is integration?

Integration is a fundamental concept in calculus that involves finding the antiderivative of a function

To find y, we need to integrate the given expression with respect to x:

∫ dy/dx dx = ∫ 5 cos² 4x sin 4x dx

y = ∫ cos² 4x sin 4x d(4x) (using u-substitution, where u = 4x)

y = ∫ cos² u sin u du

Now, we can use the identity cos²θ = (1/2)(1 + cos2θ) to simplify the integral:

y = ∫ (1/2)(1 + cos2u) sin u du

y = (-1/4)(cos2u - 2 cos u) + C (using integration by substitution)

y = (-1/4)(cos2(4x) - 2 cos 4x) + C

y = (-1/4)(cos 8x + 2 cos 4x) + C

Therefore, the expression for y is y = (-1/4)(cos 8x + 2 cos 4x) + C, where C is the constant of integration.

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Answer:

1. greatest common factor is 6x

2.3v^2

Answer:

6x and 3v²

Step-by-step explanation:

The greatest common factor of 30x² and 24x is 6x, because 30x²+24x=6x(5x+4)

The greatest common factor of 15v² and 12v² is 3v²

Answer: Mean = 89.67

Step-by-step explanation:

Step 1:

Calculate the sum of integers, then divide by the number (N) of scores:

Sum of scores = 538

538 ÷ 6 = 89.67

Step 2:

89.67 - 85 = 4.67

89.67 - 86 = 3.67

89.67 - 84 = 5.67

89.67 - 88 = 1.67

99 - 89.67 = 9.33

96 - 89.67 = 6.33

Step 3:

Avg = Sum / N

4.67 + 3.67 + 5.67 + 1.67 + 9.33 + 6.33 = 31.34

Avg = 31.34 / 6 = 5.223

Step 3; 2: 5

We can estimate that the population of the town will reach 30000 in the year 2032.

What is Population?

In the context of statistics and demography, a population refers to the total group of individuals, objects, or events that share some common characteristic of interest. This characteristic can be anything that is measurable, such as age, gender, income, education, location, or behavior.

The population of the town is given by the function:

P(t) = [tex]20000(1.06)^{t}[/tex]

We want to find the value of t such that P(t) = 30000. So we can set up the equation:

[tex]20000(1.06)^{t}[/tex] = 30000

To solve for t, we can divide both sides by 20000 and then take the natural logarithm of both sides:

ln[tex](1.06)^{t}[/tex] = ln(3/2)

Using the property of logarithms that ln(a^b) = b*ln(a), we can simplify the left-hand side:

t*ln(1.06) = ln(3/2)

Finally, we can solve for t by dividing both sides by ln(1.06):

t = ln(3/2) / ln(1.06)

Using a calculator, we find that t is approximately 11.94 years after the year 2020. So the population of the town will reach 30000 people approximately 11.94 years after the year 2020. To find the year, we can add 11.94 to 2020:

2020 + 11.94 = 2031.94

Therefore, we can estimate that the population of the town will reach 30000 in the year 2032.

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the width of the rectangle is less than 13. However, we don't know the exact value of the width without additional information.

How to determine?

In a rectangle, the width refers to the shorter side and the length refers to the longer side. Let's use "w" to represent the width of the rectangle.

According to the problem, the length of the rectangle is 8 more than twice its width, which can be written as:

length = 2w + 8

The problem also tells us that the length is less than 34, so we can write an inequality:

length < 34

Substituting the first equation into the inequality, we get:

2w + 8 < 34

Subtracting 8 from both sides, we get:

2w < 26

Dividing both sides by 2, we get:

w < 13

So the width of the rectangle is less than 13. However, we don't know the exact value of the width without additional information.

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Answer: it is A  (The mean is about 57.4, and it represents the average number of students who left school early.)

Step-by-step explanation:

first you add all of the numbers then you get 689. then divide by 12 and you get 57.4

if the bias of the estimator is 5, the expected value of the estimator is equal to the true value of the parameter plus 5.

What is unbiased estimator?

An unbiased estimator is a statistical estimator that, on average, provides an estimate of a parameter that is equal to the true value of the parameter being estimated. In other words, an unbiased estimator does not systematically overestimate or underestimate the true value of the parameter. More formally, an estimator θ is said to be unbiased for a parameter θ* if the expected value of θ is equal to θ*.

If θ is an unbiased estimator for θ, then we have E(θ) = θ, which means that the expected value of the estimator is equal to the true value of the parameter being estimated.

Now, if B(θ) = 5, it means that the estimator is biased, and the expected value of the estimator deviates from the true value of the parameter by a constant amount of 5.

To find E(θ), we can use the formula:

E(θ) = θ + B(θ)

Substituting B(θ) = 5, we get:

E(θ) = θ + 5

Therefore, if the bias of the estimator is 5, the expected value of the estimator is equal to the true value of the parameter plus 5.

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In set-builder notation, the same set can be expressed as {x|x (N and 4<x<10)}, which reads as "the set of all x such that x is a natural number and 4 < x < 10."

How to solve the question?

a. The set of natural odd numbers greater than 2, but less than 11 can be expressed using the roster method as {3, 5, 7, 9}. The set includes all the odd natural numbers between 2 and 11, excluding the endpoints, since 2 is not odd, and 11 is not less than 11.

b. The set {x|x (N and 4<x<10)} can be expressed using the roster method as {5, 6, 7, 8, 9}. The set includes all the natural numbers greater than 4 and less than 10, since x is a natural number (N) and satisfies the condition 4 < x < 10.

In set-builder notation, the same set can be expressed as {x|x (N and 4<x<10)}, which reads as "the set of all x such that x is a natural number and 4 < x < 10." The vertical bar separates the description of the elements of the set (the condition) from the set itself.

The roster method and set-builder notation are both ways of describing sets, but the roster method lists all the elements of a set, while the set-builder notation describes the properties or conditions that define the set. Both methods are useful in different situations and depend on the specific context and the purpose of the set description.

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Your complete question is :-

express each set using the roster method.

a. the set of the natural odd numbers greater than 2, but less than 11

b.{x|x (N and 4