The length of a rectangle is 4 yards longer than its width. If the perimeter of the rectangle is 52 yards, find its length and width.

the probability of a standard normal random variable being greater than 1.84 is approximately 0.0336.

We can use the central limit theorem to answer this question. The central limit theorem states that if we have a large enough sample size, the distribution of sample means will be approximately normal, even if the population distribution is not normal. The sample mean is given by:

X = μ

where X is the sample mean, μ is the population mean, and n is the sample size.

In this case, we have a sample size of n = 40, and we want to know the probability that the sample mean is greater than 25 minutes. We can standardize the sample mean using the standard error of the mean, which is given by:

SE = σ / sqrt(n)

where σ is the population standard deviation. In this case, σ = 15.4 minutes, so:

SE = 15.4 / sqrt(40) = 2.44 minutes

We can then calculate the z-score for the sample mean:

z = (X - μ) / SE = (25 - 20.5) / 2.44 = 1.84

Using a standard normal distribution table or calculator, we can find that the probability of a standard normal random variable being greater than 1.84 is approximately 0.0336. This means that the probability of a random sample of 40 people having a mean commute time that is greater than 25 minutes is approximately 0.0336, or 3.36%.

In summary, we used the central limit theorem to approximate the distribution of sample means, calculated the standard error of the mean and the z-score for the sample mean, and used a standard normal distribution table or calculator to find the probability of the sample mean being greater than 25 minutes.

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it is true that  0.5% of 200 is 10.

True.

To find 0.5% of a number, we need to multiply the number by 0.5/100, which can be simplified to 5/100 or 1/20. This is because "percent" means "per hundred", so 0.5% is equivalent to 0.5 per 100 or 0.5/100.

Multiplying the number by 5/100 is the same as multiplying it by 0.5/100, so it will give us the correct result.

For example, if we want to find 0.5% of 200, we can multiply 200 by 5/100 or 0.5/100:

\(0.5% of 200 = 200 \times 5/100 = 10\)

Therefore, it is true that  0.5% of 200 is 10.

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According to the given information, the sample period should be from 2010-2020.

a) Model specification

The model specification based on the scenario above is as follows:

SDF= f(T, TI, NL)

Where: SDF= Sustainable Development Framework

T= Tourism

TI= Technological innovation

NL= National leadership

b) Justification for the selection of the dependent and independent variables model:

Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.

Independent variables:

The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.

The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.

c) Justification for the selection of the sample period:

The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.

Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.

The sample period should be from 2010-2020.

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Answer:

Step-by-step explanation:

According to the order of operations, you need to take care of what's inside the () first. Do this by flipping the second fraction upside down and then multiplying it by the first one:

\(\frac{1}{10}*\frac{5}{2}=\frac{5}{20}=\frac{1}{4}\)

Now you have

\(\frac{1}{4} -\frac{3}{4}=-\frac{2}{4}=-\frac{1}{2}\)

The sides of the triangle are approximately 3, 8.44, and 6.46 the angles opposite these sides are approximately 25 degrees, 110 degrees, and 45 degrees.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle.

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms.

To solve the triangle, we can use the law of sines or the law of cosines to find the lengths of the other sides, and then use the angle sum property of triangles to find the remaining angle.

We are given that a = 110 degrees and b = 25 degrees, and one side is 3 and opposite angle to 3 is angle B. Let's call the length of side 3 as b.

To solve this triangle, we can use the Law of Sines and the fact that the angles in a triangle add up to 180 degrees.

First, let's find angle C:

Angle C = 180 - angle A - angle B

Angle C = 180 - 110 - 25

Angle C = 45 degrees

Now, we can use the Law of Sines to find the lengths of sides b and c:

b/sin(B) = c/sin(C)

3/sin(25) = c/sin(45)

Solving for c, we get:

c = (3*sin(45))/sin(25)

c ≈ 6.46

To find side a, we can use the Law of Cosines:

a² = b² + c² - 2bc*cos(A)

a² = 3² + 6.46² - 2(3)(6.46)*cos(110)

a ≈ 8.44

So the lengths of the sides are:

a ≈ 8.44

b = 3

c ≈ 6.46

And the angles are:

A ≈ 110 degrees

B = 25 degrees

C = 45 degrees

Therefore, the sides of the triangle are approximately 3, 8.44, and 6.46 the angles opposite these sides are approximately 25 degrees, 110 degrees, and 45 degrees.

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question is - solve the given triangle and find all the angles and sides of the triangle.

Answer:

f(x) = 12x³ + 11x² - 43x + 21

Step-by-step explanation:

given the product of factors

(4x - 3)(3x² + 5x - 7)

multiply each term in the second factor by each term in the first factor, that is

4x(3x² + 5x - 7) - 3 (3x² + 5x - 7) ← distribute parenthesis

= 12x³ + 20x² - 28x - 9x² - 15x + 21 ← collect like terms

= 12x³ + 11x² - 43x + 21

then the polynomial is

f(x) = 12x³ + 11x² - 43x + 21

Answer:35

Step-by-step explanation:

The volume of a cylinder is calculated by multiplying the area of its base by its height. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height.

The volume of a cone is calculated by multiplying the area of its base by its height and then dividing by 3. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height.

Since Sonequa’s two containers have equal radii and equal heights, it can be concluded that the volume of the cylinder is three times the volume of the cone. This means that if Sonequa fills the cone with water and pours it into the cylinder, she will need to repeat this process three times to fill the cylinder completely.

So, the claim that is most likely to be supported using the result of Sonequa’s investigation is: “The volume of a cylinder with the same radius and height as a cone is three times greater than the volume of the cone.”

The correct answer is d. we can see the range of values.

Sorting data allows us to arrange the data points in ascending or descending order, which helps us easily identify the minimum and maximum values in the dataset. By observing the range, we can determine the span or spread of the data, providing insights into the variation between the smallest and largest values.

While options a, b, and c are also benefits of sorting data, they are not specific to sorting alone. Frequency distribution, determining shape, and analyzing center and variability can be done using various statistical techniques and measures, such as histograms, measures of central tendency, and measures of dispersion. However, sorting data directly aids in visualizing the range, making option d the most appropriate choice.

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The length of B’C’ for the triangle A’B’C' is 7.5 cm if a dilation maps triangle ABC onto A’B’C'.

A triangle is a three-sided polygon that has three angles, three vertices, and three sides. It is a basic geometric shape that is often studied in mathematics and geometry. Triangles come in different shapes and sizes, but the sum of their interior angles always adds up to 180 degrees. Triangles can be classified based on their sides and angles, such as equilateral, isosceles, scalene, acute, right, or obtuse.

Here,

We can use the property that the ratio of corresponding sides of similar triangles is equal to the scale factor of dilation. In this case, we have:

AC/A'C' = BC/B'C'

Substituting the given values:

24/6 = 30/B'C'

Simplifying:

4 = 30/B'C'

Multiplying both sides by B'C':

4B'C' = 30

Dividing both sides by 4:

B'C' = 7.5

Therefore, B'C' is 7.5 cm.

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Complete question:

A dilation maps triangle ABC onto triangle A’B’C if AC = 24 cm A’C =6 cm and BC= 30 cm then B’C’ equals?

Answer:

The answer for the Area of the shape is

1357in²

Step-by-step explanation:

cut the shape into rectangle and another rectangle

then,Area of the shape =Area of small rectangle +Area of big Rectangle)

A=L×B+L×B

A=25×1015×75

A=250+1125

A=1357in²

the area of the region between the graph of y = 64 − x^3 and the x-axis over the interval [2, 4] is 68 square units.

What is a Graph?

A graph is a visual representation of the relationship between two or more variables on the axes.

To find the area of the region between the graph of the function y = 64 − x^3 and the x-axis over the interval [2, 4], we can use the limit process by approximating the area using rectangles and taking the limit as the width of the rectangles approaches zero.

The first step is to divide the interval [2, 4] into smaller subintervals. Let's choose n subintervals, each with a width of Δx = (4 - 2)/n. This will give us n+1 points: x0 = 2, x1, x2, ..., xn-1, xn = 4.

Within each subinterval, we can choose a representative point, xi*, to evaluate the function y = 64 − x^3. The height of the rectangle corresponding to the ith subinterval will then be the function value at that representative point, which is y(xi*).

The area of the ith rectangle is given by A_i = y(xi*) * Δx.

To find the total area, we sum up the areas of all the rectangles:

A_total = A_1 + A_2 + ... + A_n.

Using the limit process, we can find the area by taking the limit as n approaches infinity:

A_total = lim(n→∞) [A_1 + A_2 + ... + A_n].

To evaluate this limit, we need to express it as a definite integral. Recall that the definite integral of a function f(x) over an interval [a, b] is given by:

∫[a,b] f(x) dx.

In our case, the definite integral that represents the area can be written as:

A_total = ∫[2,4] (64 - x^3) dx.

To compute this integral, we can use standard techniques for integration. Integrating the function 64 - x^3 gives us:

A_total = [64x - (x^4)/4] evaluated from x = 2 to x = 4.

Plugging in the limits, we have:

A_total = [64(4) - (4^4)/4] - [64(2) - (2^4)/4].

Simplifying the expression, we get:

A_total = [256 - 64] - [128 - 4].

Calculating further, we find:

A_total = 192 - 124.

Therefore, the area of the region between the graph of y = 64 − x^3 and the x-axis over the interval [2, 4] is 68 square units.

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The probability that not more than 5 graduates plan to pursue a graduate degree is 0.0191.

Given Information

Percentage of college graduates that plan on pursuing a graduate degree=50%

Number of graduates selected=14

Let us consider the event that a college graduate plans on pursuing a graduate degree as a success.

The probability of getting success is p = 0.50

Let X denotes the event of success.

We have, n = 14.

Then,

X∼Bin(14,0.50).

The pmf of X is given as,

\(P(X)= ^nC_xP^x(1-P)^n^-^x\\\\P(X)= ^1^4C_x(0.50)^x(0.50)^1^4^-^x\)

The probability that not more than 5 graduates plan to pursue a graduate degree can be computed as,

P(X≤5)=5∑¹⁴Cₓ(0.50)x(0.50)¹⁴⁻ˣ

=0+0.00001+0.00012+0.00081+0.00396+0.01425

P(X≤5)=0.01914

Hence, the probability that not more than 5 graduates plan to pursue a graduate degree is 0.0191.

The probability that exactly 7 of the college graduates plan to pursue a graduate degree can be computed as,

P(X=7)=¹⁴C₇(0.5)⁷(0.5)⁹

P(X=7)=0.08395

Therefore, the probability that exactly 7 of the college graduates plan to pursue a graduate degree is 0.0840.

The probability that at least 9 but not more than 14 of the college graduates plan to pursue a graduate degree can be computed as,

P(9≤X≤14)=14∑x=9 ¹⁴Cₓ(0.50)x(0.50)¹⁴⁻ˣ

P(9≤X≤14)=0.18889+0.19833+0.16227+0.10142+0.04681+0.01505

P(9≤X≤14)=0.71277

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The probability of the horse winning the race is 4/11 or approximately 0.36 or 36%.

The odds in favor of a horse winning a race is expressed as a ratio of the number of favorable outcomes to the number of unfavorable outcomes. In this case, the odds in favor of the horse winning the race is 4:7.

This means that for every 4 favorable outcomes, there are 7 unfavorable outcomes.

To determine the probability of the horse winning the race, we can use the formula:

Probability = favorable outcomes / total outcomes

In this case, the total number of outcomes is the sum of the favorable and unfavorable outcomes, which is 4 + 7 = 11.

Therefore, the probability of the horse winning the race is:

Probability = 4 / 11

This means that the horse has a probability of approximately 0.36 or 36% of winning the race.

In summary, the odds in favor of a horse winning a race of 4:7 means that there are 4 favorable outcomes for every 7 unfavorable outcomes.

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Answer:

99   (cm^2)

Step-by-step explanation:

Perpendicular to the AB segment at points D and C, the graph is divided into two triangles and a rectangle.

The area of the middle rectangle is equal to 8*9=72. The hypotenuse of the right triangle is 10cm, and one of the right sides is 9cm, so the other side is SQRT (10^2-9^2) = SQRT (19).

One side of the left triangle is 9cm long and the other side is 14-8-sqRT (19) = 6-sqRT (19) cm.

Then, add the area of the three parts.

72+9*sqrt（19）/2+9*（6-sqrt（19））/2=99    (cm^2)

The equation that could be used to find the amount of life insurance sold after x years is:

P = 231.5 * (1 + 0.0963)^x

Let P be the total amount of life insurance sold after x years. We know that in 1950, the total amount of life insurance sold was $231.5 billion. Since then, the annual increase has been estimated at 9.63%.

To find the amount of life insurance sold after x years, we can use the following formula:

P = 231.5 * (1 + 0.0963)^x

Here, (1 + 0.0963) represents the factor by which the total amount of life insurance sold increases each year. We raise this factor to the power of x, which represents the number of years since 1950, to find the total increase in the amount of life insurance sold. We then multiply this increase by the initial amount of life insurance sold in 1950, which was $231.5 billion, to get the total amount of life insurance sold after x years.

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We know that the time is inversely proportional to the work.

Let t₁ is the time taken by Jeff and t₂ is the time taken by Jeff's dad.

We know that the formula:

Given:

Therefore,

Hence, it took Jeff's dad 12hours to wash the car himself.

Answer:

24 minutes

Step-by-step explanation:

The Dimensions of the wall are given as:

8ft × 5ft = 40ft² or 40 square feet

We are told that: You can paint 75 square feet of a surface every 45 minutes.

Hence:

75 ft² = 45 minutes

40 ft² = x minutes

Cross Multiply

75 ft² × x = 40 ft² × 45 minutes

x = 40 ft² × 45 minutes/75 ft²

x = 24 minutes

Therefore, It will takes you 24 minutes to paint a wall with dimensions 8ft × 5 ft

If a student is ranked in the 85th percentile on their college entrance exams, it means that they scored better than 85% of the other students who took the same exam.

In other words, only 15% of the students who took the exam scored higher than this student. This is a good achievement and suggests that the student is likely to be competitive in the college application process.

A percentile is a statistical metric that shows the proportion of a dataset's values that are equal to or lower than a given value. For instance, the dataset's 75th percentile implies that 75% of the values are equal to or lower than that number.

In the case of the request for the "percentile 100 words," it appears to be a misunderstanding or an incomplete query. In order to produce a useful response, the term "percentile" often needs more details, such as the dataset or the particular value of interest. Could you please elaborate on your point or make your inquiry more clear?

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Answer:

Step-by-step explanation:

Perimeter

Area

Answer: See below

Step-by-step explanation:

To find the square root of a number is the same as squaring the answer.

In this perticular example, the square root of 35 is +6 and -6.

As I said before, the square root of a number is the same as squaring the answer. That means, we square +6 and -6.

(6)²=36

(-6)²=36

It is clear that when you square 6 and -6, you get 36. This is because a positive×positive=positive, and negative×negative=positive.

That's why square root 36 equals +6 and -6.

Answer A negitive number times a negitive number will give you a positive number.

Step-by-step explanation:

-6 multiplied by -6= 36

6 multiplied by 6= 36

The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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Since LMNO is a parallelogram, opposite angles are congruent, which means that angle L is congruent to angle N and angle M is congruent to angle O.

Since angles L and M are adjacent angles in a parallelogram, they are supplementary, which means that their sum is 180 degrees. Therefore, the sum of the measures of angles L and M is:

L + M = 180 degrees.

Answer: 180 degrees

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

So and L and M add up to 180 degrees.

Answer:

The renters have to pay 1.5 months rent before moving in (first month plus security deposit) so we can write the following equation to represent the situation:

1.5

m

=

1725

where

m

is the amount of one month's rent.

Using algebra

1.5

m

1.5

=

1725

1.5

1.5

m

1.5

=

1150

m

=

1150

The monthly rent is $1,150.

Step-by-step explanation:

Answer:

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The ratio of the weight of a semi-truck trailer tire compared to the weight of a mobile home will be 51: 52.

The utilization of two or more additional numbers that compares is known as the ratio.

The weight of the semi-truck trailer tire is 102 pounds.

The weight of the mobile home is 104 pounds.

The ratio of the weight of a semi-truck trailer tire to a mobile home is given as.

Ratio = 102 / 104

Ratio = 51 / 52

Ratio = 51: 52

The ratio of the weight of a semi-truck trailer tire to a mobile home will be 51: 52.

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Can you make a cross product from a scalar and a vector? Ex: A x (B*C)
No, you cannot make a cross product from a scalar and a vector. Cross product is only defined for two vectors. In your example, if A is a scalar and B and C are vectors, the operation A x (B*C) is not valid since cross product requires both operands to be vectors.

How can a scalar triple product be reorganized and still be equivalent?
The scalar triple product of three vectors A, B, and C is defined as (A x B) • C. It can be reorganized in several ways while still being equivalent:
1. (B x C) • A
2. (C x A) • B
3. (B x A) • C = -(A x B) • C
4. (C x B) • A = -(B x C) • A
5. (A x C) • B = -(C x A) • B

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If the pond now contains 320 gallons of water, number of weeks it has been since the pond was at full capacity is 5 week.

Given that, a full pond containing 625 gallons of water begins losing its water at a rate of 20% per week.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here, number of gallons water being used for x weeks is

625-320=305 gallons

Now, number of gallons of water used in a week= 20% of 305

= 20/100 ×305

= 0.2 ×305

= 61 gallons

So, number of weeks = x=305/61

= 5

Therefore, if the pond now contains 320 gallons of water, number of weeks it has been since the pond was at full capacity is 5 week.

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Answer:

5

Step-by-step explanation:

Look that guys answer is better

Answer

Option C is correct.

8.0 × 10³ miles = 8 thousand miles.

Explanation

The number given in scientific notation is

8.0 × 10³ miles

= 8.0 × 1000 miles

= 8000 miles

= 8 thousand miles.

Hope this Helps!!!

Answer:

4(6) + 4(5) + 4(4) = 24 + 20 + 16 = 60 ft^2

Answer:

John and Shawn spent the same number of hours after \(4\) weeks.

Step-by-step explanation:

Number of hours already completed by John to his volunteer project \(=40\) hours

Number of hours spent by John each week to his volunteer project \(=5\) hours

Number of hours spent by Shawn each week to his volunteer project \(=15\) hours

Suppose John and Shawn spent the same number of hours after \(x\) weeks.

Therefore,

\(40+5x=15x\)

\(40=15x-5x\\40=10x\)

\(x=4\) weeks.

So,

John and Shawn spent the same number of hours after \(4\) weeks.