Which is the graph of the function f(x) = x³ + x² + x + 1?

A toy manufacturer wants to know how many new toys children buy each year. A sample of 305 children was taken to study their pur

Harrizon [31]

Answer:

The 80% confidence interval for the mean number of toys purchased each year is between 7.5 and 7.7 toys.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.8}{2} = 0.1$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.1 = 0.9$ , so Z = 1.28.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.28\frac{1.5}{\sqrt{305}} = 0.1$

The lower end of the interval is the sample mean subtracted by M. So it is 7.6 - 0.1 = 7.5

The upper end of the interval is the sample mean added to M. So it is 7.6 + 0.1 = 7.7

The 80% confidence interval for the mean number of toys purchased each year is between 7.5 and 7.7 toys.

8 0

3 years ago

What is the nth term?

kumpel [21]

Let $a_k$ denote the kth term of the sequence. Then

$a_k=a_1+d(k-1)$

where d is the common difference between consecutive terms in the sequence and a₁ is the first term.

The sum of the first n terms is

$S_n=\displaystyle\sum_{k=1}^na_k=a_1+a_2+\cdots+a_{n-1}+a_n$

From the formula for $a_k$ , we get

$S_n=\displaystyle\sum_{k=1}^n(a_1+d(k-1))=a_1\sum_{k=1}^n1+d\sum_{k=1}^n(k-1)$

$S_n=\displaystyle na_1+d\sum_{k=0}^{n-1}k$

$S_n=na_1+\dfrac{d(n-1)n}2$

$S_n=\dfrac n2(2a_1-d+dn)$

So we have $d=-5$ , and $2a_1-d=16$ so that $a_1=\frac{11}2$ .

Then the nth term in the sequence is

$a_n=\dfrac{11}2-5(n-1)=\boxed{\dfrac{21-10n}2}$

7 0

3 years ago

Suzanne has a student loan balance of $25,904 with an average interest rate of 6.8 percent. Use the student loan repayment calcu

Alex_Xolod [135]

Since the problem is requiring us to use the loan repayment calculator and here is what the calculator gave:

Loan Balance: $25,506.00

Adjusted Loan Balance: $25,506.00

Loan Interest Rate: 6.80%

Loan Fees: 0.00%

Loan Term: 10 years

Minimum Payment: $0.00

Monthly Loan Payment: $293.52

Number of Payments: 120 months

Cumulative Payments: $35,223.07

Total Interest Paid: $9,717.07

It is projected that you will need an annual salary of a minimum $35,222.40 to be capable to have enough money to repay this loan. This approximation assumes that 10% of your gross monthly income will be keen to repaying your student loans. This resembles to a debt-to-income ratio of 0.7. If you use 15% of your gross monthly income to repay the loan, you will need an annual salary of only $23,481.60, but you may experience some financial difficulty. This corresponds to a debt-to-income ratio of 1.1.

8 0

3 years ago

Suppose S and T are mutually exclusive events. Find P(S or T) if P(S) = 65% and P(T) = 7%.

Diano4ka-milaya [45]

When you have two mutually exclusive events, to find the probability of one or another, you add the probabilities.
65+7=72
Final answer: B

5 0

2 years ago

Read 2 more answers

Identify the parent function for the function g(x) = x + 4 based on its function rule. Then graph g and identify the transformat

N76 [4]

The graph of the function is linear and translation down 4 units. Thus option A is a correct option.

According to the statement

We have to find that the transformation of the parent function that it represents.

So, For this purpose, we know that the

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.

From the given information:

The given function is a g(x) = x + 4.

From this it is clear that the the function is a linear and the there is a some addition of the number to make graph linear.

then we can say that the The graph is linear and translation down 4 units.

So, The graph of the function is linear and translation down 4 units. Thus option A is a correct option.

Learn more about function here

brainly.com/question/4025726

#SPJ9

8 0

1 year ago