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3 years ago

What is the next fraction in the sequence? Simplify your answer. 3/4, 5/8, 1/2, 3/8,

Mathematics

1 answer:

erma4kov [3.2K]3 years ago

8 0

Answer: 2/8.

Step-by-step explanation:

When we have this type of problem, the usual way to solve them is trying with known types of sequences.

I will start with the arithmetic sequence, where the difference between any two consecutive terms is a constant. And if we call this difference as D, we will have the recursive relation:

Aₙ = Aₙ₋₁ + D

To check if this sequence is an arithmetic sequence, we can take the first two terms and see the difference:

(5/8 - 3/4) = (5/8 - 6/8) = -1/8.

Now let's do the same, but with the second and third terms:

(1/2 - 5/8) = (4/8 - 5/8) = -1/8

The difference is the same, -1/8.

Now we can use the recursive relationship above and the last given term of the sequence to find the next one:

A₅ = A₄ + (-1/8)

A₅ = 3/8 - 1/8 = 2/8

Then the next fraction in the sequence was 2/8.

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Solve for x. Triangles below are similar. a) 13 b) 10 c) 4 d) 3

Reptile [31]

Answer:

the answer is 4 (option C)

Step-by-step explanation:

Since the triangles are similar, and in triangle UTV both sides are equal, we can consider QTR also has two equal sides.

therefore, the equation forms:

13x + 3 = 55

13x = 55 - 3

13x = 52

x = 52/13

x = 4

8 0

2 years ago

Sarah claims that the thickness of the spearmint gum she produces is 7.5 one-hundredths of an inch. A quality control specialist

satela [25.4K]

Answer:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

$p_v =2*P(t_{(9)}>1.539)=0.158$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

Step-by-step explanation:

Data given and notation

Data: 7.65, 7.60, 7.65, 7.7, 7.55, 7.55, 7.4, 7.4, 7.5, 7.5

We can begin calculating the sample mean given by:

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

And the sample deviation given by:

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

And we got:

$\bar X=7.55$ represent the sample mean

$s=0.103$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =7.5$ represent the value that we want to test

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

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 7.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 7.5$

Alternative hypothesis: $\mu \neq 7.5$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

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

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

P-value

The first step is calculate the degrees of freedom, on this case:

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

Since is a two sided test the p value would be:

$p_v =2*P(t_{(9)}>1.539)=0.158$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

3 0

3 years ago

Mindy, a local artist, sells a piece of art at the pizza shop for $15, and the shop takes 15 percent commission. Instead of rece

Yuliya22 [10]

In this question the first thing that needs to be determined is the commission taken by the pizza shop and the amount of money that falls in the part of Mindy.
We already know that Mindy sells the piece of art for $15 and the pizza shop takes 15% commission on it.
Then
Commission taken by the pizza shop = (15/100) * 15
   = 225/100
   = 2.25 dollars
So the pizza shop takes a commission of $2.25 from the sales of each art piece from Mindy.
Then amount that falls in Mindy's part = (15 - 2.25) dollars
   = 12.75 dollars
Now Mindy is not taking the money but taking a pizza worth rupees $12 including 5% sales tax.
Initially it looks like Mindy is making a profit of $0.75 plus the pizza worth $12. So it is a fair deal for Mindy. Now coming to the part of the pizza shop owner, we find that he also gains extra $2.25 from this deal. So it is a fair deal for both the shop keeper and Mindy.

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I think the answer the answer/question is letter C

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