The rectangle has a perimeter of 62 millimeters. What is its area?

Answer: To match the shapes produced by the slice through the triangular prism, we need to consider the orientation of the slice relative to the prism. Here are the matching options:

A. Perpendicular to the base: Rectangle

B. Parallel to the base: Triangle with dimensions equal to the base

C. Diagonal from vertex to vertex: Triangle with unknown dimensions

The woman plans to save $1,000,000 by depositing $500 each month into an ordinary annuity with a 4.3% annual interest rate. The explanation will calculate the number of years it will take for her to retire.

To determine the number of years it will take for the woman to retire, we need to calculate the future value of the annuity and find the time it takes to reach or exceed $1,000,000.The future value of an ordinary annuity can be calculated using the formula:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the annuity

P is the monthly deposit ($500)

r is the monthly interest rate (4.3% / 12 = 0.03583)

n is the number of months

We can rearrange the formula to solve for n:

n = log(1 + (FV * r) / P) / log(1 + r)

Substituting the given values, we have:

n = log(1 + (1,000,000 * 0.03583) / 500) / log(1 + 0.03583)

Calculating this expression, we find that the woman will be able to retire in approximately 232.94 months. Since we are looking for the number of years, we divide this value by 12:

n = 232.94 / 12 ≈ 19.41

Therefore, it will take approximately 19.41 years for the woman to save $1,000,000 and retire.

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Answer:

725 x0.05=36.25

Step-by-step explanation:

when finding percentage move the decimal over two places, making 5 0.05

16250 many different three-letter words—including nonsense words—have different letters in the next position.

Given that,

We have to find how many different three-letter words—including nonsense words—have different letters in the next position.

We know that,

The number of alphabets are 26

First letter has 26 choices.

Second letter can not be same has first letter so 25 choices.

Third letter can not be same has second letter so 25 choices.

So,

Total words = 26×25×25=16250

Therefore, 16250 many different three-letter words—including nonsense words—have different letters in the next position.

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Answer:

The number of the exponential is 3

Step-by-step explanation:

10^-2×10^5

According to the law when the base are equal you pick one then add the power when it is multiplication when it is division, you subtract the power

10^-2+5=10^3

Pls make answer as brainlist

Part (d) is correct.

i.e. The variance of the random variable associated with this given experiment is 2.4510.

What is Binomial experiment?

It is an experiment with a set number of independent trials, each having the same chance of success and the two outcomes of success or failure. A binominal distribution can be used to describe the likelihood of a certain number of successes.

Given that,

No. of independent trials ( n ) = 10

Probability of success in each trail ( p ) = 0.43

∴ probability of failure in each trial ( q ) = 0.57

we can find the variance of a binomial experiment by using the formula i.e. npq.

∴ Variance = npq

                  = 10 × 0.43 × 0.57

                  = 2.4510.

Hence, part (d) matches with the answer.

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The statement is not true for spherical geometry. Because the sum of the angles in a triangle in spherical geometry is not equal to 180 degrees.

"Information available from the question"

In the question:

In Euclidean geometry the sum of the angles in a triangle equals 180 degrees.

We have to identify that this is true for spherical geometry also;

Now, According to the question:

In a Euclidean space, the sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn). A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides.

The sum of the angles of a spherical triangle is not equal to 180°. A sphere is a curved surface, but locally the laws of the flat (planar) Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees.

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Butt Koko, this is the solution:

Original price = 19.99

Sale price = 15.99

Discount = 19.99 - 15.99 = 4.00

We can use Direct Rule of Three to calculate the percent of discount, this way:

Price Percent

19.99 100

4.00 x

___________________

4 * 100 = 19.99 * x

400 = 19.99x

x = 400/19.99

x = 20.01

The approximate percent discount on the frisbee is 20%

The length of the base, of a triangle of 114.31 square kilometers, is 16.1 kilometers.

To find the length of the base of a triangle, we can use the formula for the area of a triangle:

A = (1/2)bh ; where A is the area, b is the base, and h is the height.

We are given the area and the height, so we can plug those values into the formula and solve for the base:
A = (1/2)bh
114.31 = (1/2)b(14.2)
228.62 = 14.2b
b = 228.62/14.2
b = 16.1 km

Therefore, the length of the base of the triangle is 16.1 kilometers.

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If an acute angle increases, then its supplement decreases.

To give you a short quick answer, the supplement is going to have to decrease or get smaller.

Example

Suppose the acute angle is 10 (anything under 90 will do).

Then the supplement is going to be 180 - 10 = 170

Now suppose the acute angle increase to 50 degrees.

That means the supplement will go from 180 - 50 = 130

Conclusion

As the acute angle gets bigger, the supplement gets smaller. This is an important idea to get clear. Bigger and Smaller or More or Less can be ugly little words, so anytime you come across them, pay attention. It will make your life in science so much easier

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The graph of the linear relationship is represented by the equation y = 3x - 5

An equation is an expression relating two or more numbers and variables.

The standard form of a linear equation is:

Ax + By = C

where A, B and C are constants

The slope - intercept form of a linear equation is:

y = mx + b

Where m is the rate of change(slope) and b is the y intercept.

The graph of the linear relationship was plotted using the points from the table. The graph is attached

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Answer: i believe Z=115 and Y=30

Step-by-step explanation: again im sorry if its wrong. but im pretty sure theyre not.

The length ratio is 1/72, and the width ratio is approximately 0.014.

Let's convert the measurements to a common unit for easier comparison. Since the dimensions of the field are given in yards, let's convert the dimensions of the foosball table to yards.

The foosball table dimensions are:

Length = 30 inches = 30/36 yards = 5/6 yards

Width = 55 1/2 inches = 55.5/36 yards = 1.54 yards (rounded to two decimal places)

The soccer field dimensions are:

Length = 60 yards

Width = 110 yards

Now, let's calculate the ratios of the corresponding dimensions:

Length ratio = (Foosball table length) / (Soccer field length)

= (5/6) / 60

= 5/360

= 1/72

Width ratio = (Foosball table width) / (Soccer field width)

= 1.54 / 110

= 0.014

Thus, the length ratio is 1/72, and the width ratio is approximately 0.014.

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The complete question si as follows:

Jason wants to determine if his foosball table is a dilation of his school's soccer field. The dimension of the table are 30 inches by 55 1/2 inches, and the dimensions of the field are 60 yards by 110 yards. Is the table a dilation? Explain.

The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

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Answer:

The answer is $82.88.

Step-by-step explanation:

Too complicated. Will do explanation later.

Answer: You're correct :3

Step-by-step explanation:

15% of 78.93 ≈ 11.84

78.93 - 11.84 = 67.09

20% of 78.93 ≈ 15.79

67.09 + 15.79 = 82.88

You're correct!

Thanks for the free points btw. :p

If you're gonna write. just write the numbers and equations...

a. To find the probability that daily sales will fall between 2,500 and 3,000 gallons, we need to find the proportion of the total area under the probability distribution curve that lies between 2,500 and 3,000 gallons. Since the distribution is uniform, the probability density function is constant over the interval [2,000, 5,000] and equals 1/(5,000 - 2,000) = 1/3,000. Thus, the probability of selling between 2,500 and 3,000 gallons is:

P(2,500 ≤ X ≤ 3,000) = (3,000 - 2,500) / (5,000 - 2,000) = 0.1667

Therefore, the probability that daily sales will fall between 2,500 and 3,000 gallons is approximately 0.1667 or 16.67%.

b. To find the probability that the service station will sell at least 4,000 gallons, we need to find the proportion of the total area under the probability distribution curve that lies to the right of 4,000 gallons. This can be computed as:

P(X ≥ 4,000) = (5,000 - 4,000) / (5,000 - 2,000) = 0.3333

Therefore, the probability that the service station will sell at least 4,000 gallons is approximately 0.3333 or 33.33%.

c. Since the distribution is continuous, the probability of selling exactly 2,500 gallons is zero. This is because the probability of any single point in a continuous distribution is always zero, and the probability of selling exactly 2,500 gallons corresponds to a single point on the distribution curve.

*IG:whis.sama_ent*

Answer:

8 is the length

Step-by-step explanation:

The length of AD is 9 units from the given right triangle ABC.

A right angled triangle is a triangle with one of the angles as 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle is called a right triangle.

Given right triangle ABC with altitude BD drawn to hypotenuse AC.

Given that, AB = 18 and AC = 36

Using Pythagoras theorem

AC²=AB²+BC²

⇒ 36²=18²+BC²

⇒ BC²=1296-324

⇒ BC²=972

⇒ BC=31.18 units

We know that, area of a triangle =1/2 × Base × Height

= 1/2 × 31.18 × 18

= 280.62 square units

Now, area of a triangle ABC with base AC and height BD

That is, Area = 1/2 ×36×BD

⇒ 18BD=280.62

⇒ BD=280.62/18

⇒ BD=15.6

Consider ΔBDA

AB²=AD²+BD² (Pythagoras theorem)

18²=x²+15.6²

⇒ x²=18²-15.6²

⇒ x=9 units

Therefore, the length of AD is 9 units from the given right triangle ABC.

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Answer:

8:31

Step-by-step explanation:

all of them are equal with 1:4 except 8:31

Answer:

$43071

Step-by-step explanation:

Commission = 5.6%

So $2,412 represents 5.6% of total value of sold vacation packages

Image the numbers as ratios:

$2,412 : 5.6%

X : 100%

To get from 5.6% to 100% you can divide by 5.6 and then multiply by 100

So to find X you do:

(2,412 / 5.6)*100 = 43071.428…

Now round the answer to nearest dollar:

43071.428… = $43071 (to nearest dollar)

(a) A nonzero vector orthogonal to the plane through points P, Q, and R is <9, -7, -4>.

(b) The area of triangle PQR is 6.5 square units.

Consider the three given points P(1, 0, 1), Q(-2, 1, 3), and R(3, 2, 5). To find a nonzero vector orthogonal to the plane formed by these points, we can use the cross product of two vectors lying on the plane. Let's call PQ the vector from P to Q, and PR the vector from P to R. Taking the cross product of these two vectors gives us a vector perpendicular to the plane. The resulting vector is <9, -7, -4>, which is orthogonal to the plane through points P, Q, and R.

To calculate the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR. The magnitude of the cross product represents the area of the parallelogram formed by these two vectors, and since we are interested in the triangle, we divide this area by 2. The magnitude of the cross product is 13, so the area of triangle PQR is 6.5 square units.

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Since our calculated t score of 14.4 is much larger than the cutoff t score of 2.131, we can reject the null hypothesis and conclude that the mean creativity score of the current statistics class is significantly different from the mean creativity score of the rest of the university students.

The null hypothesis in this scenario is that the mean creativity score of the current statistics class is not significantly different from the mean creativity score of the rest of the university students, which is 40.

We can use a one-sample t-test to test this hypothesis, where the test statistic is calculated as:

t = (sample mean - population mean) / (sample standard error)

where the sample standard error is calculated as:

standard error = population standard deviation / sqrt(sample size)

Plugging in the given values, we have:

t = (47 - 40) / (5 / sqrt(16)) = 14.4

To find the cutoff t score at the 5% level of significance with 15 degrees of freedom (16 students - 1), we can use a t-distribution table or a calculator. Using a table, we find that the cutoff t score is 2.131.

Therefore, since our calculated t score of 14.4 is much larger than the cutoff t score of 2.131, we can reject the null hypothesis and conclude that the mean creativity score of the current statistics class is significantly different from the mean creativity score of the rest of the university students.

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Answer:

(a) 4.875 minutes

(b) 1.86 minutes

Step-by-step explanation:

The length of fence = 150 feet.

Rate of painting by Tyler = 11ft/min

Rate of painting by Benito = 15ft/min

(a) Let after time t minutes  both have painted equal number of feet.

As Taylor has already painted 19.5 feet. So,

\(15t=19.5+11t\)

\(\Rightarrow 4t=19.5\)

\(\Rightarrow t=\frac{19.5}{4}\)

\(\Rightarrow t=4.875\) minutes.

(b)The length of fencs to be painted by Tylor=150-19.5=130.5 feet.

So. time taken by Tylor to finish the painting

\(=\frac{130.5}{11}=11.86\) minutes.

Time taken by Benito to finish the painting

\(=\frac{150}{15}=10\) minutes

Here, tome taken by Benito is less, so Benoto finishes first.

Benoto will get the time to rest for 11.86-10=1.86 minutes.

Vertical angulation refers to the angle at which the x-ray beam is directed when taking dental radiographs. It is an important factor in obtaining clear and accurate images.

In both the paralleling and bisecting techniques, the group of answer choices remains the same. However, the vertical angulation is generally greater for images taken with the paralleling technique compared to the bisecting technique.

This is because the paralleling technique requires the x-ray beam to be directed more vertically in order to capture the entire tooth structure on the film. On the other hand, the bisecting technique involves angling the x-ray beam downward to intersect the imaginary bisector between the long axis of the tooth and the film.

Therefore, the vertical angulation differs depending on which technique is being used.

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Taillamps should be visible from a distance of 500 feet.

Taillamps are an essential safety feature of any vehicle, serving to alert other drivers of its presence, especially in low light or adverse weather conditions. The visibility distance required for taillamps is 500 feet. This specification ensures that the taillamps can be easily seen by drivers approaching from behind, allowing them ample time to react and adjust their driving accordingly. Maintaining a clear visibility distance helps to prevent accidents and promotes overall road safety.

The specific requirement of a 500-feet visibility distance for taillamps is established to provide a reasonable buffer zone for drivers to react and maintain a safe distance. This distance allows drivers to anticipate the actions of the vehicle in front and make necessary adjustments to their speed and following distance. It also helps in avoiding sudden braking or rear-end collisions, contributing to safer road conditions for all motorists.

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We were told that the salary, t years after 2015 is given by the function,

S(t) = 3100t + 56000

When considering 2017, the number of years, t from 2015 is 2017 - 2015 = 2

We would substitute t = 2 into the function and find S(2)

Thus,

S(2) = 3100 x 2 + 56000 = 6200 + 56000 = 62200

When considering 2020, the number of years, t from 2015 is 2020 - 2015 = 5

We would substitute t = 2 into the function and find S(2)

Thus,

S(5) = 3100 x 5 + 56000 = 15500 + 56000 = 71500

Thus, we can say that

when

x1 = 2, y1 = 62200

when x2 = 5, y2 = 71500

Recall,

slope or average rate of change = (y2 - y1)/(x2 - x1)

average rate of change = (71500 - 62200)/(5 - 2) = 9300/3

average rate of change = 3100

The last option is correct

Answer:

6.27 minutes

Step-by-step explanation:

1/10 of 2.1 is 0.21 and 2.1+0.21=2.31 and if there final time is 3.96 then to find the original time you must add them 2.31+3.96=6.27

The measure of length PQ will be 22 units.

A triangle's third side is stated to be parallel to the line segment uniting its two midpoints, and it is also half as long as the third side.

Given:

PQ = 5x + 62, and MN = 6x-4

Now, using Mid- Point Theorem

PQ= 1/2 MN

-5x+ 62 = 1/2( 6x - 4)

-5x+ 62 = 3x - 2

-5x- 3x = -2 - 62

-8x = -64

x= 8

PQ= 5x+ 62 = -5(8) + 62 = -40 + 62 = 22

Hence, the measure of PQ is 22 units.

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Answer:

60%

Step-by-step explanation:

27/45 = .6

.6 = 60%