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4 years ago

Determine ƒ(a + h) for ƒ(x) = 2x3.

Mathematics

1 answer:

DedPeter [7]4 years ago

4 0

Answer:

see explanation

Step-by-step explanation:

To evaluate f(a + h) substitute x = a + h into f(x)

f(a + h)

= 2(a + h)³

= 2( a³ + 3a²h + 3ah² + h³ ) ← distribute

= 2a³ + 6a²h + 6ah² + 2h³

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Rectangle divided into four rectangles. The perimeters of rectangle #1, #2, #3, #4 are 10 cm, 20 cm, 28 cm and 18 cm respectivel

notsponge [240]

Answer:

Perimeter of big rectangle = 38 units

Step-by-step explanation:

Let the sides of rectangle (1) = a and c cm

Sides of rectangle (2) = b and c cm

Sides of rectangle (3) = b and d cm

Sides of rectangle (4) = a and d cm

Perimeter of (1) = 2(length + width)

2(a + c) = 10

a + c = 5 ---------(1)

Perimeter of (2) = 2(b + c)

2(b + c) = 20

b + c = 10 -------(2)

Perimeter of (3) =2(b + d)

2(b + d) = 28

b + d = 14 --------(3)

Perimeter of (4) = 2(a + d)

2(a + d) = 18

a + d = 9 -------(4)

Since perimeter of the big rectangle = 2(a + b + c + d)

By adding equations (1) + (2) + (3) + (4),

(a + c) + (b + c) + (b + d) + (a + d) = 5 + 10 + 14 + 9

2(a + b + c + d) = 38

Therefore, perimeter of the rectangle ABCD = 38 units

7 0

3 years ago

The triangular prism and the triangular pyramid shown have the same base and the same height. Use the drop-down menus to complet

Mila [183]

A triangular prism Vol. = area (A) of the triangular base × height (h) of prism
A triangular pyramid V = A × 1/3 h
So since they have same base A and h, the V of the pyramid will be exactly 1/3 the V of the prism

3 0

3 years ago

Read 2 more answers

The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tail

olganol [36]

Answer:

Two tailed test

Parameter tested= population standard deviation

Step-by-step explanation:

1) Important concepts

The chi-square test if the standard deviation of a population is equal to a given value. We can conduct the test two-side or a one-side.

For the case of two-side we want to check if the population deviation is equal to some value or no. And for the case of one-side we want to check if the population devition is higher or lower than a given value.

The system of hypothesis are:

$\sigma=\sigma_o$ Null hypothesis

$\sigma \neq \sigma_o$ Alternative hypothesis

That's when we use the two sided version but we can have other's alternative hypothesis if we use one-side test:

$\sigma < \sigma_o$ Alternative hypothesis

$\sigma > \sigma_o$ Alternative hypothesis

The test statistic to check the hypothesis is:

$t=(N-1)(\frac{s}{\sigma_o})^2$

For this special case the value of $\sigma_o =99$

Where N represent the sample size and s is the sample standard deviation. The ratio $\frac{s}{\sigma_o}$ is important since allows to compare the ratio of the sample standard deviation to the specified value. If this ratio is different from 1, we will have evidence that we can reject the null hypothesis.