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2 years ago

Let f(x) = -4x + 7 and g(x) = 2x - 6. Find. (gxf)(1)

Mathematics

1 answer:

noname [10]2 years ago

6 0

Answer:

(gxf)(1) = - 12

Step-by-step explanation:

Let f(x) = -4x + 7 and g(x) = 2x - 6.

(gxf)(1) = g(1)xf(1)

but : f(1) = -4(1)+7 =7-4 = 3 and g(1)=2(1)-6 =2-6 = -4

so : (gxf)(1) = g(1)xf(1) = (-4)(3)=-12

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A researcher wishes to estimate, with 99% confidence, the population proportion of adults who think the president of their co

scoray [572]

Answer:

a. n=4148

b. n=3909

c. The sample size is smaller if a known proportion from prior study is used. The difference in sample sizes is 239

Step-by-step explanation:

a. For sample where no preliminary estimate is given, the minimum sample size is calculated using the formula:

$n=p(1-p)(\frac{z}{ME})^2$

Where:

$ME=$ Margin of error
$p=$ is the assumed proportion

#Let p=0.5, substitute in the formula to solve for n:

$n=0.5(1-0.5)\times (2.576/0.02)^2\\\\=4147.36\approx 4148$

Hence, the minimum sample size is 4148

b. If given a preliminary estimate p=0.38, we use the same formula but substitute p with the given value:

$n=p(1-p)(z/ME)^2\\\\=0.38(1-0.38)(2.576/0.02)^2\\\\=3908.47\approx3909$

Hence, the minimum sample size is 3909

c. Comparing the sample sizes from a and b:

$n_{0.5}>n_{0.38}\\\\n_{0.5}-n_{0.38}=4148-3909=239$

Hence, the actual sample size is smaller for a known proportion from prior a prior study.

8 0

3 years ago

Which expression is equivalent to 4 square root 6 divided by 3 root 2?

saw5 [17]

Answer:

$\sqrt[12]{55296}$ /2

Step-by-step explanation:

$\sqrt[4]{6}$ / $\sqrt[3]{2}$ =1.2422

$\sqrt[12]{27}$ /2=0.66 <-- not matching with the top expression.

$\sqrt[4]{24}$ /2=1.11<--not matching with the top expression.

$\sqrt[12]{55296}$ /2=1.2422<-- matches!!

$\sqrt[12]{177147}$ /3=0.91<-- not matching with the top expression.

5 0

3 years ago

A study of peach trees found that the average number of peaches per tree was 725. The standard deviation of the population is 70

TEA [102]

Answer:

She needs to sample 189 trees.

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:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

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 $1 - 0.025 = 0.975$ , so Z = 1.96.

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.

The standard deviation of the population is 70 peaches per tree.

This means that $\sigma = 70$

How many trees does she need to sample to obtain an average accurate to within 10 peaches per tree?

She needs to sample n trees.

n is found when M = 10. So

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

$10 = 1.96\frac{70}{\sqrt{n}}$

$10\sqrt{n} = 1.96*70$

Dividing both sides by 10:

$\sqrt{n} = 1.96*7$

$(\sqrt{n})^2 = (1.96*7)^2$

$n = 188.2$

Rounding up:

She needs to sample 189 trees.

3 0

3 years ago

Find all the interior angle measures of triangle ABC, if m∠A = 3x + 10, m∠B = 5x − 1, and m∠C = x. answers: m∠A = 60°, m∠B = 94°

tester [92]

Answer:

Step-by-step explanation:

Total interior angles in a triangle=180 degrees

That is: 3x + 10 + 5x - 1 + x =180

9x+9=180

9x=180-9

9x=171

x=171/9

x=19

Therefore

Angle A =67 degrees

Angle B= 94 degrees

Angle C = 19 degrees

3 0

3 years ago

Savings account A and savings account B both offer APRs of 5%, but savings account A compounds interest semiannually, while savi

Tamiku [17]

C. Savings account B because it has more compounding periods per year.

Step-by-step explanation:

Step 1:

Savings account A has an APR of 5% which compounds interest semiannually. This means that savings account A compounds twice in a year. If account A compounds 5% a time, it would compound 5(2) = 10% in a single year.

Step 2:

Savings account B also has an APR of 5% which compounds interest quarterly. This means that savings account B compounds four times in a year. If account B compounds 5% a time, it would compound 5(4) = 20% in a single year.

Step 3:

Savings account A gets an interest of 5% a year while savings account B gets an interest of 10% so account B offers a higher APR because of more compoundings in a year.

5 0

3 years ago

Read 2 more answers