17) After 8 years at 4% simple interest per year, your savings account earns interest of $80.00. What is the principal

The four uppercase letters of the alphabet in block style with rotational symmetry are H, I, O, and X. Rotational symmetry refers to the property of a figure or object that appears identical after being rotated around a central point by a certain angle.

In block style writing, letters are written with straight lines and sharp corners, creating a uniform and geometric appearance. H, I, O, and X are the only uppercase letters that have rotational symmetry and can be written in block style.

H has a rotational symmetry of 180 degrees, meaning it looks the same when rotated 180 degrees around its center point.

I has a rotational symmetry of 180 degrees as well, with the dot above the letter acting as its center point.

O has a rotational symmetry of 360 degrees, meaning it looks the same when rotated any number of degrees around its center point.

Lastly, X has a rotational symmetry of 180 degrees, with the intersection of the two lines acting as its center point.

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Answer: 9 miles

Step-by-step explanation: The speed of 12 miles per hour means that for every hour, Clare is 12 miles further from the starting point. 1 hour = 12 miles Since an hour is equivalent to 60 minutes, 60 mins = 12 miles We can divide both sides by 60 to find the distance travelled per minute. 1 min = 12 ÷60= 0.2 miles Multiply both sides by 45 to find the distance travelled in 45 minutes: 45 mins = 0.2(45)= 9 miles Given that the starting position is at zero, Clare's position is at 9 miles after 45 minutes.

Answer:

24% increase

Step-by-step explanation:

percent change = (new value - old value)/(old value) × 100%

A positive percent change is a percent increase.

A negative percent change is a percent decrease.

In this problem:

new value = 31

old value = 25

percent change = (31 - 25)/(25) × 100%

percent change = 24%

Since the percent change is positive, the percent change is a

24% increase

The percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the an 24% increase in the puppy's weight in 1 month.

The percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the difference between the two values (31 - 25 = 6) divided by the starting weight (25). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight in 1 month.

To explain this further, let's look at an example. If a puppy weighed 25 pounds at 4 months, and it gained 6 pounds over the course of the following month, it would weigh 31 pounds at 5 months. To calculate the percentage increase, take the difference in weight (6 pounds) and divide it by the starting weight (25 pounds). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight.

To calculate the percentage decrease, use the same steps as above, but subtract the starting weight from the final weight instead. For example, if a puppy weighed 25 pounds at 4 months and lost 6 pounds over the course of the following month, it would weigh 19 pounds at 5 months. The percentage decrease would be calculated as (25 - 19)/25 = 0.24, or a 24% decrease in the puppy's weight.

In summary, the percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the difference between the two values (31 - 25 = 6) divided by the starting weight (25). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight in 1 month.

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The key features of both equations are:

Equation 1 has a vertex at (1, -16) and opens upwards. Its axis of symmetry is x = 1

Equation 2 has a vertex at (2, 2) and opens upwards. Its axis of symmetry is x = 2.

To rewrite each equation in vertex form, we need to complete the square by adding and subtracting a constant from each equation.

y = x² - 2x - 15

y = (x - 1)² - 16

The vertex form of the equation is y = a(x - h)² + k, where (h, k) is the vertex. In this case, the vertex is (1, -16).

y = 2x² - 8x + 6

y = 2(x - 2)² + 2

The vertex form of the equation is y = a(x - h)² + k, where (h, k) is the vertex. In this case, the vertex is (2, 2).

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By using the fact that the measures ∠BAE and ∠EAC are equal, we will see that x = 20

Here we know that AE is an angle bisector of ∠BAC, this means that the measures of the two formed angles are the same ones.

Then we can write:

∠BAE = ∠EAC

Now we know that the measures of these angles are:

∠BAE = x + 30

∠EAC = 3x - 10

Replacing that in the equation above we willget:

x + 30 = 3x - 10

solving that for x, we will get:

30 + 10 = 3x - x

40 = 2x

40/2 = x

20 = x

That is the value of x.

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The central limit theorem is a statistical theory that specifies the probability distribution of a sum or average of several random variables whose distribution is not known.

It is an important theorem since it is utilized to help forecast or estimate the behavior of a specific set of data.

This theorem holds that when you take repeated samples of the same size from a population with a finite standard deviation, the means of those samples will be normally distributed, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Further more, the theorem indicates that the larger the sample size, the more closely the sample mean distribution will approximate a normal distribution.

This is why it is vital in the development and use of statistical quality control techniques, since they rely on correct assumptions about the population’s normality.

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Tyler has run 10.4 miles, which is 65% of the total distance he plans to run this week. Tyler plans to run a total of 16 miles this week.

Let's use "x" to represent the total distance that Tyler plans to run this week. According to the problem, Tyler has already run 10.4 miles, which is 65% of the total distance he plans to run. We can set up an equation to represent this information:

10.4 = 0.65x

To solve for x, we can divide both sides of the equation by 0.65:

x = 10.4 ÷ 0.65

x = 16

Therefore, the total distance that Tyler plans to run this week is 16 miles.

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Implementing multiple types of technology and thereby precluding that the failure of one system will compromise the security of information is referred to as redundancy.

Explanation:

Redundancy is the term used to describe the use of multiple components in a system to ensure that the failure of one component does not lead to system failure. Redundancy is a method of protecting computer systems against damage and disruption caused by component failure.The use of redundancy in computer systems is usually targeted at increasing system availability and lowering the likelihood of data loss.

                                       Multiple types of technology may be employed to achieve redundancy in a computer system, such as mirroring data across multiple disks, deploying standby servers, using a hot backup server, and so on. Redundancy can be implemented in numerous ways to provide reliable service and protect against system failure.

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In conclusion 39 science fiction books were sold on Thursday.

How to solve and what does algebra mean?

Let's use algebra to solve this problem. Let x be the number of science fiction books sold on Thursday. Then we know that:

86 = 8 + 2x

We can solve for x by first subtracting 8 from both sides:

78 = 2x

Then dividing both sides by 2:

x = 39

Therefore, 39 science fiction books were sold on Thursday.

Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating those symbols. It involves using letters and other symbols to represent variables and quantities in equations and formulas.

Algebra is used in a wide range of fields, including mathematics, science, engineering, and economics, and it is an essential tool for solving many real-world problems.

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Julie hourly rate of pay from the given different rates of the day with total earning of $612 is equal to $12per hour.

Total number of hours Julie works in a week is equal to,

On Sunday = 10 hours

On Monday = 10 hours

On Tuesday = 7 hours

On Wednesday = 10 hours

On Thursday = 7 hours

On Friday = 7 hours

On Saturday = 0 hours

Total hours worked in whole week is

= 10 + 10 + 7 + 10 + 7 + 7 + 0

= 51 hours

Total money earned by Julie in whole week = $612

Hourly rate of pay = Weekly earnings / Total hours worked

Substitute the value we have,

⇒ Hourly rate of pay = $612 / 51 hours

⇒ Hourly rate of pay = $12 per hour

Therefore, Julie's hourly rate of pay is $12 per hour.

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The above question is incomplete , the complete question is:

Julie works Sunday, Monday, and Wednesday for 10 hours each day. On Tuesday, Thursday, and Friday, she works 7 hours each day. She does not work on Saturday. Her weekly total earnings are $612. What is Julie's hourly rate of pay, in dollars?

the correct answer is: none of these, as only binomial distribution is applicable to this scenario.

a) This scenario follows the binomial distribution, as we are drawing marbles with replacement and interested in the number of successes (getting a blue marble) in a fixed number of trials.

b) The Poisson distribution is used to model the number of events occurring in a fixed time interval, given a certain rate of occurrence. It is not applicable in this scenario.

c) The hypergeometric distribution is used to model the probability of obtaining a certain number of successes in a sample without replacement, given a finite population of items that can be classified into successes and failures. In this scenario, we are drawing with replacement, so the hypergeometric distribution is not applicable.

d) Therefore, the correct answer is: none of these, as only binomial distribution is applicable to this scenario.

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The value of ∠FDE is 36°

An angle is a geometric figure formed by two rays, or lines that extend infinitely in opposite directions, that share a common endpoint called the vertex. The measure of an angle is determined by the amount of rotation between the two rays.

Here given a right angle ∠CDE = 90°

So, we can say that,

∠CDF + ∠FDE = ∠CDE

(2x)° + (x+9)° = 90°

(3x + 9)° = 90°

Simplify it, x = 27°

So, the value of ∠FDE = (x+9)° = (27+9)° = 36°

Therefore, the value of ∠FDE is 36°

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The angle FDE is 36°. The required answer for the given question is option (A). 36°.

Trigonometry angles are the angles provided by the trigonometric function ratios. Trigonometry is the study of the connection between angles and triangle sides. Angle values vary from 0 to 360 degrees.

An angle is a shape in geometry made by two rays or lines that stretch indefinitely in opposite directions and have a common endpoint known as the vertex. The quantity of rotation among the two rays determines the size of an angle.

From the given figure,

∠CDF + ∠FDE = 90

Thus,

(2x)+(x+9) = 90

3x + 9 = 90

3x = 81

x = 27

Then we will have that the angle FDE is:

∠FDE = (27) + 9

∠FDE = 36

The angle of FDE is 36°

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Therefore , the solution of the given problem of equation comes out to be  y=(x-12)³ and y=(x+8)³.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of a distinct algorithm that divides 12 into two parts and can be used to assess data received from y + 7, normalization in this case yields b + 7.

Here,

The following two equations show a rightward translation of the parent equation's coordinate plane graph:

=> y=(x-12)³

=> y=(x+8)³

Therefore , the solution of the given problem of equation comes out to be  y=(x-12)³ and y=(x+8)³.

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Answer:

Step-by-step explanation:

(4x - 5)(4x + 5) Option 1

16x^2 + 20x - 20x - 25

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

__________________

hope it helps ⸙

Answer:

First, we can factor out 5x²y²z from each term:

15x²y³z+25x³y²z+35x²y²z² = 5x²y²z(3y+5xz+7z)

So the fully factorized expression is:

5x²y²z(3y+5xz+7z)

Martin will have to wash 96 cars each month on average to meet his goal of washing 1,200 cars this year.

What is average ?

Average, also known as mean, is a statistical measure that represents the central value of a dataset. It is calculated by adding up all the values in the dataset and dividing by the total number of values. The average can be used to provide a general idea of the value of the dataset and to compare different datasets. There are different types of averages, including arithmetic mean, geometric mean, and median.

According to the question:
To find out how many cars Martin will have to wash each month on average, we need to first find out how many weeks there are in a year:

52 weeks/year

Then we can use this information to calculate how many cars Martin will have to wash each week:

1,200 cars/year ÷ 52 weeks/year = 23.08 cars/week

Since Martin cannot wash a fraction of a car, he will have to round up to 24 cars/week.

Finally, we can calculate how many cars Martin will have to wash each month on average:

24 cars/week x 4 weeks/month = 96 cars/month

Therefore, Martin will have to wash 96 cars each month on average to meet his goal of washing 1,200 cars this year.

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Answer:

For me it's C.

Step-by-step explanation:

the third one if you would like me to explain tell me.

The solutions to the trigonometric equations [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex] are x ≈ [tex]0.5514 + 2n\pi[/tex], where n is an integer.

Given that the equation  [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex]

To find all the solutions to the equation  [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex] ,  solve for x by isolating the cosine term and then applying the inverse cosine function.

Here are the steps to solve the equation:

Add [tex]\sqrt{30}[/tex] to both sides:

[tex]2cos(x) = \sqrt{30}[/tex]

Divide both sides by 2:

[tex]cos(x) = \sqrt{30} / 2[/tex]

Find the inverse cosine ([tex]cos^{-1}[/tex]) of both sides:

[tex]x = cos^{-1}(\sqrt{30} / 2)[/tex]

To determine the values of x in the interval [tex][0, 2\pi)[/tex] that satisfy the equation.

Evaluate [tex]cos^{-1}(\sqrt{30} / 2)[/tex] to find its approximate value.

[tex]cos^{-1}(\sqrt{30} / 2) = 0.5514[/tex] radians

Since the cosine function has a periodicity of [tex]2\pi[/tex], we can find other solutions by adding multiples of [tex]2\pi[/tex] to the initial solution.

So, the solutions in the interval  [tex][0, 2\pi)[/tex] are:

x ≈ 0.5514 radians

x ≈ [tex]0.5514 + 2\pi[/tex]

x ≈ [tex]0.5514 + 4\pi[/tex]

...

To simplify, express the solutions as:

x ≈ [tex]0.5514 + 2n\pi[/tex]

where n is an integer.

Therefore, the solutions to the trigonometric equations [tex]2cos(x) - \sqrt{30} = 0[/tex] in the interval [tex][0, 2\pi)[/tex] are x ≈ [tex]0.5514 + 2n\pi[/tex], where n is an integer.

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Rounded to three decimal places, the probability that the sample mean is between $155 and $160 is 0.072.

To find the probability that the sample mean is between $155 and $160, we will use the Central Limit Theorem. The Central Limit Theorem states that the distribution of the sample mean (with a large enough sample size) will be approximately normally distributed with the same mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Mean of the sample distribution: μ = $150
Standard deviation of the sample distribution: [tex]σ/√n = $25/√52 ≈ $3.46[/tex]
Now, we'll calculate the z-scores for $155 and $160:
[tex]Z1 = (155 - 150) / 3.46 ≈ 1.445[/tex]
[tex]Z2 = (160 - 150) / 3.46 ≈ 2.890[/tex]
Using a z-table or calculator, we can find the probability for each z-score:
[tex]P(Z1) ≈ 0.9259[/tex]
[tex]P(Z2) ≈ 0.9981[/tex]
Now, we can find the probability between the two z-scores:
[tex]P(1.445 < Z < 2.890) = P(Z2) - P(Z1) = 0.9981 - 0.9259 = 0.0722[/tex]

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The correct answer is: The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda.

What is the equation of the line?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

The y-intercept of a line of fit is the value of y when x equals 0. In the context of this problem, the y-intercept represents the amount of diet soda that the machine starts with when it is filled.

Since the y-intercept of the line of fit is −5.1, this means that the machine starts with 5.1 ounces of diet soda.

This is a reasonable value, as it is unlikely that the machine would be completely empty when it is filled.

It's important to note that the slope of the line of fit is also relevant in this context.

The slope represents the rate at which the amount of diet soda in the machine decreases over time. However, the question only asked for the y-intercept.

Hence, the correct answer is: The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda.

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Answer: 17.888543819998

Step-by-step explanation:

Answer:

17.8885

Step-by-step explanation:

find the geometric mean between 16 and 20, we need to multiply the numbers and take the square root of the result. That is:

Geometric Mean = √(16 × 20)

Geometric Mean = √320

Geometric Mean ≈ 17.8885

Therefore, the geometric mean between 16 and 20 is approximately 17.8885.

Answer: a=7.6

Step-by-step explanation:

solve for angle C:

[tex]\frac{sinc}{5} =\frac{sin120}{11}[/tex]

[tex]11sinc=5sin120[/tex]

[tex]C=23.2[/tex]

solve for A:

=180-(120+23.2)

=36.8

solve for a:

Using the law of sines

[tex]\frac{sin120}{11} =\frac{sin36.8}{a}[/tex]

[tex]asin120=11sin36.8[/tex]

[tex]a=7.6[/tex]

The coordinate of the point U that divides the line ST in the ratio 2:5 is: (12:6)

The formula for the division of line segments in the ratio m:n is

P = {[(mx2 + nx1)/(m + n)], [(my2 + ny1)/(m + n)]}

We are given the coordinates of line Segment ST as: S(10, 2) and T(17, 16)

Thus, if the ratio is 2:5, we have:

U(x, y) = {[(2*17 + 5*10)/(2 + 5)], [(2*16 + 5*2)/(2 + 5)]}

U(x, y) = (84/7), (42/7)

U(x, y) = (12, 6)

Thus, that is the coordinate of the point U that divides the line ST in the ratio 2:5.

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Answer:

x=7

Step-by-step explanation:

28/4 = 7

Answer:x=7

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total revenue from ticket sales is:

300 x £5 = £1500

The profit is the revenue minus the cost of the prize:

Profit = £1500 - £400 = £1100

Charity A receives 55% of the profit:

55% of £1100 = £605

Charity B receives 45% of the profit:

45% of £1100 = £495

Therefore, Charity A receives £605 and Charity B receives £495.

Answer:

1-

a. 19

b. -8

2-

a. -31

b. 0

c. -10.7

d. -3/7

e. 4

3-

a. -5

b. -60

c. 0

d. -1/4

4. -13/2

5. -85/18

6.  -5/12

7. -11

8. 16/11

9. -20/27

10.  26/11

11. -55/9

Step-by-step explanation:

why did i do this