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Vinil7 [7]
2 years ago
9

An arithmetic sequence is defined by its 1st term a1 = 7 and the sum of the first 10 terms s10 = 25. Find the difference d of th

e sequence.
Mathematics
1 answer:
VARVARA [1.3K]2 years ago
3 0

Step-by-step explanation:

difference is 1.8

hope it is correct

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What is the are of a hexagon with a radius of 5 inches?
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The area of a hexagon with a radius of 5 inches is 86.603. 
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3 years ago
Use the distributive property to write the next step in simplifying the equation. Use the asterisk symbol (*) to represent multi
Maksim231197 [3]

Given:

The equation is:

x(4+5)=54

To find:

The next step in simplifying the equation by using distributive property.

Solution:

Distributive property: According to this property if a, b and c are three real numbers, then

a(b+c)=ab+ac

We have,

x(4+5)=54

Using the distributive property, we get

x(4)+x(5)=54

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4x+5x=54

Therefore, the next step of the simplification is 4x+5x=54.

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6 0
3 years ago
Tim and Cynthia leave Cynthia's house at the same time. Tim drives north and Cynthia drives west. Tim's average speed is 10 mph
RSB [31]

Answer:

  54.2 mph

Step-by-step explanation:

Since the drivers leave at the same time and travel in directions 90° from each other, their separation speed can be found using the Pythagorean theorem. Let c represent Cynthia's average speed. Then (c-10) will represent Tim's average speed. Their combined separation speed is 70 miles per hour, so we can write ...

  70² = c² +(c -10)²

  4900 = 2c² -20c +100 . . . . eliminate parentheses

  c² -10c -2400 = 0 . . . . . . . . divide by 2; put in standard form

  (c -5)² -2425 = 0 . . . . . . . . . rearrange to vertex form

  c = 5 ±5√97 . . . . . . . . . . . . solve for c, simplify radical

  c ≈ 54.244 ≈ 54.2 . . . . . . . use the positive solution

Cynthia's average speed was 54.2 miles per hour.

6 0
3 years ago
When we test Upper H 0​: muequals0 against Upper H Subscript a​: mugreater than​0, we get a​ P-value of 0.03. a. What would the
Anastasy [175]

Answer:

(a) The null hypothesis will be rejected.

(b) Type I error

(c) The null hypothesis will not be rejected. The error is type II error.

Step-by-step explanation:

The hypothesis provided is:

H_{0}: \mu = 0\\ H_{a} : \mu > 0

The p-value of the test obtained is 0.03

(a)

Decision rule for hypothesis testing, based on p-value, states that if the p-value is less than the significance level (α) then the null hypothesis is rejected and vice versa.

The significance level is α = 0.10

Then,

p-value = 0.03 < \alpha  = 0.10

Thus, the null hypothesis will be rejected.

Conclusion:

The null hypothesis is rejected stating that the value of μ is more than 0.

(b)

If the decision in​ (a) is an​ error, i.e. the null hypothesis is rejected when in fact it is true, this type of error is known as type I error.

(c)

The significance level is α = 0.01

Then,

p-value = 0.03 > \alpha  = 0.01

Thus, the null hypothesis will not be rejected.

Conclusion:

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If this decision is an error, i.e. the null hypothesis was not rejected when in fact it is false, this type of error is known as type II error.

3 0
3 years ago
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