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andrey2020 [161]

2 years ago

14

Chris spent half of his money on a pair of headphones. Then he spends half of his remaining money of recordable CDs. Finally, he

spent his remaining $12.75 on a book. How much money did Chris have to begin with?

2 answers:

otez555 [7]2 years ago

4 0

I think the answer would be $50.50

kompoz [17]2 years ago

4 0

Assume that Chris began with m dollars in his pocket.

Half of that, or m/2, went to purchase a pair of headphones.

Half of that, or (1/2)(m/2), or m/4, went to purchasing CDs. By now Chris has spent (1/2 + 1/4) of his money: (3/4)m. He had (1/4)m left, and that (m/4) = $12.75.

Solve this for m:
$12.75
m = ------------ = $5 (answer).
(1/4)

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Match each set of vertices with the type of quadrilateral they form.

Serjik [45]

Only correct the first one.

Please, see the graph in the attached file.

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noncongruent ←→ C(7,6), D(7,3)
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nonperpendicular ←→ C(6,3), D(5,1)
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(in blue)

3) a square ←→ A(3,3), B(2,5),
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5 0

2 years ago

From Statistics and Data Analysis from Elementary to Intermediate by Tamhane and Dunlop, pg 265. A thermostat used in an electri

Leviafan [203]

Answer:

$t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The p value for this case is given by:

$p_v =2*P(t_{(9)}>2.32)=0.0455$

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

Step-by-step explanation:

Information given

data: 202.2 203.4 200.5 202.5 206.3 198.0 203.7 200.8 201.3 199.0

We can calculate the sample mean and deviation with the following formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$\sigma=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=201.77$ represent the sample mean

$s=2.41$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =200$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic

$p_v$ represent the p value for the test

Hypothesis to test

We want to determine if the true mean is equal to 200, the system of hypothesis are :

Null hypothesis: $\mu = 200$

Alternative hypothesis: $\mu = 200$

The statistic for this case is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

The statistic is given by:

$t=\frac{201.77-200}{\frac{2.41}{\sqrt{10}}}=2.32$

The degrees of freedom are given by:

$df=n-1=10-1=9$

The p value for this case is given by:

$p_v =2*P(t_{(9)}>2.32)=0.0455$

For this case since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 200 F.

4 0

1 year ago

Leticia charges $8 per hour to babysit. She babysat Friday night for 4 hours,

JulsSmile [24]

For this case we have that the variable "x" represents the number of hours that Leticia uses to take care of children on Saturday.

IF on Friday I use 4 hours ($ 8 each) and on Saturday "x" hours ($ 8 each) obtaining a profit of $ 72, we have the following equation:

$8 (4 + x) = 72$

We apply distributive property:

$32 + 8x = 72\\8x = 72-32\\8x = 40\\x = \frac {40} {8}\\x = 5$

So, on Saturday she spent 5 hours.

Answer:

$8 (4 + x) = 72\\x = 5$

6 0

1 year ago

Read 2 more answers

Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27\pi

anyanavicka [17]

Question:

Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27\pi27π27, pi cm^3 3 start superscript, 3, end superscript of melted purple liquid. The radius of the cone is 333 cm. What is the height of the cone?

Answer:

The height of the cone is $9 \ cm$

Explanation:

It is given that the radius of the cone is $3 \ cm$

The volume of the cone is $27\pi$

The height of the cone can be determine using the formula,

$V=\frac{1}{3} \pi r^{2} h$

Substituting the values $V=27 \pi$ and $r=3$ , we get,

$27 \pi=\frac{1}{3} \pi(3)^{2} h$

Multiplying both sides by 3, we have,

$81 \pi= 9\pi h$

Dividing both sides by $9 \pi$ , we have,

$9=h$

Thus, the height of the cone is $9 \ cm$

4 0

2 years ago

Suppose we want to choose 2 objects, without replacement, from the 5 objects pencil, eraser, desk, chair, and lamp. (a)How many

BigorU [14]

Answer:

a) 20 ways

b) 10 ways

Step-by-step explanation:

When the order of selection/choice matters, we use Permutations to find the number of ways and if the order of selection/choice does not matter, we use Combinations to find the number of ways.

Part a)

We have to chose 2 objects from a group of 5 objects and order of choice matters. This is a problem of permutations, so we have to find 5P2

General formula of permutations of n objects taken r at time is:

$nPr=\frac{n!}{(n-r)!}$

Using the value of n=5 and r=2, we get:

$5P2=\frac{5!}{(5-2)!} =20$

Therefore, we can choose 2 objects from a group of 5 given objects if the order of choice matters.

Part b)

Order of choice does not matter in this case, so we will use combinations to find the number of ways of choosing 2 objects from a group of 5 objects which is represented by 5C2.

The general formula of combinations of n objects taken r at a time is:

$nCr=\frac{n!}{r!(n-r)!}$

Using the value of n=5 and r=2, we get:

$5C2=\frac{5!}{2!(5-2)!} =10$

Therefore, we can choose 2 objects from a group of 5 given objects if the order of choice does not matters.

3 0

2 years ago

Read 2 more answers