Dan bought a new computer for $900. Each year, the value of the computer decreased by 25% of the previous year's value. At this rate, what can Dan expect the approximate value of the computer to be after 7 years?

Answer:

theta = 24.4 degrees

Step-by-step explanation:

This is a right triangle.

sin theta = opp/ hyp

sin theta = 33/80

Take the inverse of each side

sin^-1 sin(theta) = sin^-1 (33/80)

theta =24.36197794

To the nearest tenth

theta = 24.4 degrees

Answer:

You could fit 48 cubes with side lengths of 1/3 cm inside a rectangular prism with dimensions of 1 cm X 2 2/3 cm X 2/3 cm.

Step-by-step explanation:

Answer:

4.24

Step-by-step explanation:

It is hard to explain sorry if you need it

The mean absolute deviation of the given values is 4.24

Given the values :

5, 11, 2, 7, 16

Mean = 8.2

The mean absolute deviation = Σ|x - mean| ÷ n

n = number of observations

x = observations

Mean absolute deviation :

Therefore, the mean absolute deviation of the values given is 4.24

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Answer:

5

Step-by-step explanation:

The customer paid $7.53 for the item

Markup is the difference between a product's selling price and cost as a percentage of the cost. It is given by:

[tex]Markup=\frac{selling\ price-cost\ price}{cost\ price} \\\\[/tex]

Markup = 115% = 1.15, cost price = $3.50, hence:

[tex]Markup=\frac{selling\ price-cost\ price}{cost\ price} \\\\1.15=\frac{selling\ price-3.5}{3.5} \\\\Selling\ price=\$7.53[/tex]

Hence the customer paid $7.53 for the item.

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Answer:

We conclude that the mean waiting time is less than 10 minutes.

Step-by-step explanation:

We are given that a public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes.

Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.8 minutes with a standard deviation of 2.5 minutes.

Let [tex]\mu[/tex] = mean waiting time for bus number 14.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 10 minutes      {means that the mean waiting time is more than or equal to 10 minutes}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 10 minutes    {means that the mean waiting time is less than 10 minutes}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                       T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean waiting time = 7.8 minutes

             s = sample standard deviation = 2.5 minutes

             n = sample of different occasions = 18

So, test statistics =  [tex]\frac{7.8-10}{\frac{2.5}{\sqrt{18} } }[/tex]  ~ [tex]t_1_7[/tex]

                              =  -3.734

The value of t test statistics is -3.734.

Now, at 0.01 significance level the t table gives critical value of -2.567 for left-tailed test.

Since our test statistic is less than the critical value of t as -3.734 < -2.567, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean waiting time is less than 10 minutes.

Using the t-distribution, it is found that since the test statistic is less than the critical value for the left-tailed test, it is found that there is enough evidence to support the claim that the mean is less than 10 minutes.

At the null hypothesis, it is tested if the mean is of at least 10 minutes, that is:

[tex]H_0: \mu \geq 10[/tex]

At the alternative hypothesis, it is tested if it is less than 10 minutes, that is:

[tex]H_1: \mu < 10[/tex]

We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

For this problem, the values of the parameters are: [tex]\overline{x} = 7.8, \mu = 10, s = 2.5, n = 18[/tex]

Hence, the value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{7.8 - 10}{\frac{2.5}{\sqrt{18}}}[/tex]

[tex]t = -3.73[/tex]

The critical value for a left-tailed test, as we are testing if the mean is less than a value, with a 0.01 significance level and 18 - 1 = 17 df is of [tex]t^{\ast} = -2.57[/tex]

Since the test statistic is less than the critical value for the left-tailed test, it is found that there is enough evidence to support the claim that the mean is less than 10 minutes.

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Answer: Leon was wrong by using the greatest common factor to determine that the numbers are a Pythagorean triple.

Step-by-step explanation: The numbers that Leon used in his calculations which are, 21, 28, and 35 are actually a Pythagorean triple and this can be determined by using the Pythagoras' theorem which states that,

AC² = AB² + BC²

Where AC is the longest side, and AB and BC are the other two sides.

Substituting for the given values, we now have

35² = 28² + 21²

1225 = 784 + 441

1225 = 1225

Since both sides of the equation are equal, we can conclude that the numbers form a Pythagorean triple.

However, dividing the numbers by their greatest common factor does not prove that it is a Pythagorean triple. This process cannot be successfully applied to other Pythagorean triples, and is best described as a chance event.

For example, the numbers 21, 20 and 29 are Pythagorean triples and they have no common factor. Similarly, 6, 8 and 10 are also Pythagorean triples and their greatest common factor is 2. This too is not sufficient to prove that they form a Pythagorean triple.

The only prove that is sufficient enough is to substitute the numbers into the Pythagoras theorem as stated in the calculation above, and the result must show the left hand side of the equation to be equal to the right hand side of the equation.

Answer:

it’s C tell me if I’m right or wrong

Step-by-step explanation:

Answer:

252 feet cubed

hope this helps!

Step-by-step explanation:

Answer:

k=7

Step-by-step explanation

This is the same as 12 x k = 84. To solve, put it into a division problem which is 84 divided by 12. 84 divided by 12 is 7.

Answer:

Step-by-step explanation:

The professional soccer player buys 16 acres of land.

He wants to use [tex]\frac{2}{8}[/tex] of the land to put his own soccer field and facility on.

All we have to do is find [tex]\frac{2}{8}[/tex] of 16 acres.

[tex]\frac{2}{8}[/tex] of 16 acres:

[tex]\frac{2}{8}[/tex] * 16 = 4 acres

He will need 4 acres out of the 16 acres for his soccer field and facility.

Answer: 8m+25 ≤ 65

Step-by-step explanation:

Hi, to answer this question we have to write an inequality with the information given:

The product of the number of movie tickets he will buy per month (m) and the price of each ticket (8) plus the already spent money (25) must be less or equal to his savings (65).

Mathematically speaking:

8m+25 ≤ 65

Feel free to ask for more if needed or if you did not understand something.  

Answer:

The area is 50.24

Step-by-step explanation:

Area of a circle is

A = πr²

A = 3.14 x 4²

A = 3.14 x 16

A = 50.24

Answer:

A

Step-by-step explanation:

A is the only one that intersects with the y axis at the value 3.

hope this helps :)

Answer:

The answer is the first graph!

Answer: 0.6%

Step-by-step explanation:

We have a selection of 5 numbers, in those selection we have 3 combinations of 3 consecuitve numbers (because the numbers must be in correct order).

The first 3

The 3 in the middle

the last 3.

So a contestant has 3 combinations were he wins.

Now, the number of possible combinations of the 9 numbers given is:

For the first number we have 9 options.

For the second number we have 8 options (because we already selected one)

For the last number we have 7 options (because we already selected 2 numbers)

Then the number of possible combinations is

10*9*8 = 504

The probabilty of winning will be equal to the number of combinations that the contestant has (3) divided by the total number of combinations, this is:

p = 3/504 = 0.006 or 0.006*100% = 0.6%

To find out how many 1/10's of a cantaloupe are there in 1/2 of a cantaloupe, you divide 1/2 by 1/10. The answer is 5.

To find out how many 1/10's of a cantaloupe are there in 1/2 of a cantaloupe, we can divide 1/2 by 1/10. Dividing fractions involves multiplying the first fraction by the reciprocal of the second fraction. So, we have (1/2) * (10/1) = 10/2 = 5. Therefore, there are 5 1/10's of a cantaloupe in 1/2 of a cantaloupe.

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Answer:

it the last one

Step-by-step explanation:

only the last option has all the possible combinations

Answer:

Sample space:

{Yellow Purple,

Yellow Green,

Orange Purple

Orange Green,

Red Purple,

Red Green}

Answer:

4

Step-by-step explanation:

easier answer

Answer:

4,0

Step-by-step explanation:

Answer:

i can confirm it is 4,0

Step-by-step explanation:

Answer:

4 because mode is always the number that occurs the most. If there were two sixes and two fours, then there would be two modes.

Answer:

4

Step-by-step explanation:

The mode of the data set (a set of distinct values, at least) is the value which appears the most often. In this set, that number is 4.

The equation is rearranged so that \(y\) is expressed in terms of[tex]\(x\): y= 5x - 26[/tex]

To rearrange the given equation so that x is the independent variable, you need to solve for y. Here's how you can do it step by step:

1. Start with the given equation:

[tex]\[y + 6 = 5(x - 4)\][/tex]

2. Expand the right side of the equation:

[tex]\[y + 6 = 5x - 20\][/tex]

3. Move the constant term (6) to the right side by subtracting 6 from both sides:

[tex]\[y = 5x - 20 - 6\]\\y = 5x - 26\][/tex]

Now, the equation is rearranged so that \(y\) is expressed in terms of[tex]\(x\): y= 5x - 26[/tex]

For such more question on equation

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Answer:

27,600

Step-by-step explanation:

Answer:

thursday

Step-by-step explanation:

Answer:

1,290,000

Step-by-step explanation:

Answer:

1,290,000

Step-by-step explanation:

If we are rounding to the nearest thousand, then we are finding the number in the hundredth's and rounding it.

From 1-9 If it's less than 5, round down. If it's 5 or more, round up.

At this case, it is 8 in the hundredths and nine in the thousandths. Since 8 is 5 or greater, you round it up to 1000, but the thousandth's place has a nine, which nine plus 1 is 10.

Therefore, 1,289,845 rounded up is 1,290,000.  

I hope this helped! :)

Answer:

12 cups

Step-by-step explanation:

2/5 times 12 =4 4/5

Sorry, this answer was wrong.

Answer:

(B)  [tex]y=-2x+ \dfrac{7}{6}[/tex]

Step-by-step explanation:

Given the point-slope form of the equation of a line below:

[tex]y-\dfrac{2}{3}=-2\left(x- \dfrac{1}{4}\right)[/tex]

We are required to write it in the slope-intercept form, y=mx+c.

[tex]y-\dfrac{2}{3}=-2\left(x- \dfrac{1}{4}\right)\\\\y-\dfrac{2}{3}=-2x+ \dfrac{2}{4}\\\\y=-2x+ \dfrac{2}{4}+\dfrac{2}{3}\\\\y=-2x+ \dfrac{7}{6}[/tex]

The slope intercept form is:

[tex]y=-2x+ \dfrac{7}{6}[/tex]

The correct option is B.

Answer:

b

Step-by-step explanation:

Answer:

14.2

Step-by-step explanation:

Answer:

It should be somewhere around 13.6

Step-by-step explanation:

Answer:

James has 20 more coins than Reggie

Step-by-step explanation:

Given:

Total number of coins with James and Reggie = 60

If James would agree to give 1/4 of his coins to Reggie, they would then have exactly the same number of coins

To find: number of coins with James and Reggie

Solution:

Let x denote number of coins with James and y denote number of coins with Reggie.

According to question,

[tex]x+y=60\\x-\frac{x}{4} =y+\frac{x}{4} \\x-y=\frac{2x}{4} \\x=2y[/tex]

Put [tex]x=2y[/tex] in [tex]x+y=60[/tex]

[tex]2y+y=60\\3y=60\\y=\frac{60}{3}=20\\ x=2y=2(20)=40[/tex]

So,

number of coins with James = 40

number of coins with Reggie = 20

James has 20 more coins than Reggie

Answer:

13/22

Step-by-step explanation:

The total number of crayons in the box

9 red crayons, 5 blue crayons, and 8 yellow crayons = 22

The number that are blue or yellow = 5+8 = 13

P (blue or yellow) = number that are blue or yellow / total

                             = 13/22

Answer:

13/22

Step-by-step explanation:

Total: 9 + 5 + 8 = 22

Blue or yellow: 5 + 8 = 13

P(Blue or yellow) = 13/22