All categories

2 years ago

The first term of an arithmetic sequence is –12 and the ninth

Mathematics

1 answer:

shtirl [24]2 years ago

8 0

Answer:

d = $\frac{7}{2}$

Step-by-step explanation:

The nth term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₉ = 16 , then

- 12 + 8d = 16 ( add 12 to both sides )

8d = 28 ( divide both sides by 8 )

d = $\frac{28}{8}$ = $\frac{7}{2}$

You might be interested in

Solve for x 8/14=x/37

Setler79 [48]

Hello there!

$\frac{8}{14}=\frac{x}{37}$

Explanation:

↓↓↓↓↓↓↓↓↓↓↓

First you had to switch sides of the equation.

$\frac{x}{37}=\frac{8}{14}$

Then you had to cancel by the common factor of 2.

$\frac{x}{37}=\frac{4}{7}$

You had to multiply by 37 from both sides of the equation.

$\frac{37x}{37}=\frac{4*37}{7}$

Simplify it should be the correct answer.

$x=\frac{148}{7}$

Answer⇒⇒⇒x=148/7

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

4 0

2 years ago

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 330 grams and a standard deviati

just olya [345]

Answer:

Weights of at least 340.1 are in the highest 20%.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 330, \sigma = 12$

a. Highest 20 percent

At least X

100-20 = 80

So X is the 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.842.

$Z = \frac{X - \mu}{\sigma}$

$0.842 = \frac{X - 330}{12}$

$X - 330 = 12*0.842$

$X = 340.1$

Weights of at least 340.1 are in the highest 20%.

3 0

2 years ago

Please help due tomorrow Fri

ch4aika [34]

5 feet is the answer

3 0

2 years ago

Read 2 more answers

Simplify the following expression: 3X(4-1) + (6+21)

Ilya [14]

Answer:

9x+27

Step-by-step explanation:

3x(4−1)+6+21

=9x+6+21

Combine Like Terms

=9x+6+21

=(9x)+(6+21)

=9x+27

3 0

2 years ago

Read 2 more answers

Mrs. Adesso wants to take her class on a trip to either the science center or natural history museum. The science center charges

BartSMP [9]

Answer:

Step-by-step explanation:

When we write expressions for the total cost of each field visit and set them equal, we find the solution to be the ratio of the difference in fixed cost to the difference in variable cost.

y = 75 +7x . . . . . cost for x students to visit the science center

y = 50 +8x . . . . cost for x students to visit the natural history museum

Subtracting the first equation from the second, we get ...

0 = -25 +x

25 = x . . . . . add 25; the number of students such that costs are equal

The cost will be the same either place for 25 students.

Additional comment

Here, the fixed cost difference is 75-50=25, and the variable cost difference is 8-7=1. The ratio of these costs is ...

$25/($1 /student) = 25 students.

This relationship only holds when the higher fixed cost is associated with the lower variable cost. Charges are such that one place caters to larger numbers of students (science center), and one prefers fewer students (natural history museum).

4 0

1 year ago