Solve the inequality. | 7 + 8x | > 5
Absolute ^value^
20 POINTS!

Answer:

d

Step-by-step explanation:

You are asking a question trying to suggest whether it can be done later

The Volume of the solid formed by the curves y = 4x³ , y = 4x, x ≥ 0 ; about the x axis is 64π/21  .

In the question ,

it is given that ,

the given curves are y = 4x³ , y = 4x, x ≥ 0 ,

we have to find the volume about x axis ,

the region formed by the given curves about x axis is shown below in the figure .

So , the Volume of the required region is

V = \(\int\limits^1_0 {\pi [(4x)^{2} - (4x^{3} )^{2} }] \, dx\)

On simplification ,

we get ,

V = \(\pi \int\limits^1_0 { [16x^{2} - 16x^{6} }] \, dx\)

V = π[ x³/3 - x⁷/7 ]¹₀

= 16π( 1/3 - 1/7 - 0 - 0)

= 16π((7 - 3)/21)

= 64π/21

Therefore , the required Volume is 64π/21   .

The given question is incomplete , the complete question is

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 4x³ , y = 4x, x ≥ 0 ; about the x-axis  .

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Answer:

ind the slope of the original line and use the point-slope formula  y − y 1 = m ( x − x 1 )

to find the line parallel to  x + 4y = 28 .

Step-by-step explanation:

Answer:

It would be like counting up fives

Step-by-step explanation:

Answer:

It would be going up by 5 every time.

brainliest pls

Step-by-step explanation:

If a skier travels 4700 feet up a ski lift whose angle of inclination is 30°​, how high above his starting level is the​ skier is 2350 feet.

Given data:

Distance = 4700 feet

Angle of inclination = 30°​

Now let determine the height by  formulating an equation which will help us to find the height

4700 × sin 30°

Where:

Sin 30° = 0.5 or 1/2

Hence,

Height :

Height = 4700 feet × 0.5

Height = 2350 feet

So,

Height = 2350 feet above the starting level

Therefore we can conclude that the skier is 2350 feet above the starting level.

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Dimension of the extended stage is; length = 6 m and width = 2x m

Area of the rectangular outdoor = length x width

New area = area of the outdoor + area of the extended stage

              = 216 + 12x

               = 6(36 + 2x)

New area = 6 (36 + 2x)

So that;

The dimension of the rectangular outdoor = 36 x 6

i.e length = 36 m and width = 6 m

So that the dimension of the extended stage = length x width

                                    = (6 x 2x) m

i.e length = 6 m and width = 2x m

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Answer:

It can be any measure

Step-by-step explanati

The correct option R avg(x) =  100 - 5x, shows the average revenue function.

For the given question;

The revenue function is given by the equation,

R(x) = 100x - 5x²

Let the

Let the total revenue be 'x'.

Then,

Average revenue function = revenue function/ total revenue

Average revenue function = (100x -5x²)/x

Average revenue function = 100 - 5x

Thus, the average revenue function is given by the equation 100 - 5x.

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Answer:

the answer is 40 hope this helps you

Answer:

Q+D = 65, multiply both sides by 2525Q + 25D = 162525Q + 10D = 950  subtract to get            15D = 675               D = 675/15 = 135/3 = 45 dimes               Q = 65-45 = 20 quarters25(20) + 10(45) = 500+450 = 950

Answer:

12.93

Step-by-step explanation:

26.49-13.56= 12.93

It will take 12.93 seconds Michael to run the second leg of the race.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that Spencer ran the first leg of a relay in 13.56 seconds. Michael ran the second leg.

Therefore, the total time it took both boys to run the race was 26.49 seconds.

Now we have to calculate the difference;

26.49-13.56= 12.93

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The maximum displacement is 5 centimeters.

The time required for one oscillation is π seconds.

The frequency is 1 / π Hz.

Equation to model the motion of the object is x(t) = 5 × cos(2t)

The maximum displacement from equilibrium can be determined by observing that the object is pulled down 5 centimeters from its rest position.

In simple harmonic motion, the amplitude represents the maximum displacement from equilibrium.

The period of oscillation is given as π seconds.

The period (T) is the time required for one complete oscillation.

The frequency (f) is the reciprocal of the period and represents the number of oscillations per unit time.

Thus, the frequency is the inverse of the period: f = 1 / T.

To model the motion of the object, we can use the equation for simple harmonic motion:

x(t) = A×cos(ωt + φ)

A = 5 centimeters (maximum displacement),

T = π seconds (period),

f = 1 / π Hz (frequency).

To find ω, we can use the relation ω = 2π / T:

ω = 2π / π = 2 radians/second.

The equation to model the motion of the object is:

x(t) = 5 × cos(2t)

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tile will it take to cover the pedestal, including the bottom is 288 square feet

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Answer:

Concept:

Doubling the dimensions of a prism will increase the new area by 4 times the original area

Tripling the the dimensions of the prism will increase the new area by 9 times the original area

Quadrupling will increase the new area by 16 times the original area

Given that the original area given is

The new area therefore will be

Hence,

The final answer will be

The required probability of Jackie planting a tulip followed by a hyacinth is 0.1684.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

To determine the probability that Jackie plants a tulip followed by a hyacinth, we can use the formula for conditional probability:

P(tulip and hyacinth) = P(tulip) × P(hyacinth | tulip).

First, we'll find the probability of Jackie choosing a tulip on the first pick: P(tulip) = 8/30 (there are 8 tulips out of 30 total bulbs in the box).

Next, we'll find the probability of Jackie choosing a hyacinth on the second pick, given that she chose a tulip on the first pick:

P(hyacinth | tulip) = 12/29 (there are 12 hyacinths remaining out of 29 total bulbs remaining in the box).

Finally, we'll multiply these two probabilities together to find the overall probability:

P(tulip and hyacinth) = 8/30 × 12/29 = 16/95 = 0.1684.

So the required probability is 0.1684.

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Answer:

C. 8x²+x+3.

Step-by-step explanation:

A and B are not polynomials as they contain a division (A) and a square root (B).

D is a monomial ( just one term).

oc.8x²+x+3

Step-by-step explanation:

Which of the following is a polynomial?

OA. 5+x2²/X

OB. √x+2x-1

OC. 8x²+x+3

OD. 7x

Answer:

15 yards

Step-by-step explanation:

the length of fencing required for the rectangular garden is

2( 4 \(\frac{1}{2}\) + 3)

= 2 × 7 \(\frac{1}{2}\)

= 15 yards

The explicit formula of the function s(n) is s(n) = 2n

The domain and the range of h(n)

Given that

h(n) is the number of houses

The possible values of n and h(n) are whole numbers

So, we have

The values of h(5) and h(11)

Based on the patterns in the sequence, we have

h(n) = n

So, we have

h(5) = 5

h(11) = 11

The explicit function of h(n)

In (b), we have

h(n) = n

The values of s(4) and s(7)

Given that

s(n) is the number of segments

Based on the patterns in the sequence, we have

s(n) = 2n

So, we have

s(4) = 8

s(7) = 14

The growth pattern of s(n)

Above, we have

s(n) = 2n

The above equation is a proportional equation

This means that

The growth pattern of s(n) is linear, with a constant rate of change

The explicit function of s(n)

Above, we have

s(n) = 2n

Hence, the explicit of s(n) is s(n) = 2n

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Answer:

32,000

Step-by-step explanation:

10% of 320,000 is 32,000

Answer:

The perimeter of the track is of 317 meters.

Step-by-step explanation:

Perimeter:

The perimeter of a figure is the sum of all its dimensions.

In this question:

The track is composed by two straights of 80m, and two half circles with a diameter of 50m.

Perimeter of a circle:

The perimeter of a circle with diameter d is of:

\(P = \pi d\)

Track:

Two half circles, each with a diameter of 50m, plus two straight lines of 80m. So

\(P = \frac{2\pi}{2}(50) + 2*80) = 50\pi + 160 = 50*3.14 + 160 = 317\)

The perimeter of the track is of 317 meters.

The slope of the line for the given condition is 10.

A line's slope is defined as the ratio of the change in y coordinates to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

Given the graph for the pool being filled with water,

in the graph, the x-axis represents the number of minutes,

the y-axis represents the gallons of water filled,

equation of line is y = mx + c

c is the y-intercept = 2

where m is the slope of the line,

m = (y₂ - y₁)/(x₂ - x₁)

or slope of the line also shows the rate of change,

a given rate of change is  10 gallons per minute

so 10 is the slope of the line

m = 10

equation is y = 10x + 2

Hence slope is 10.

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Answer:

$1.25

Step-by-step explanation:

Sara saved $12.50 for five weeks, and her brother saved $13.75 for five weeks. To find out how much more her brother saved, we can subtract Sara's savings from her brother's savings:

$13.75 - $12.50 = $1.25

Therefore, her brother saved $1.25 more than Sara did over the course of five weeks.

Answer:

(5x + 3)(25x^2 - 15x + 9)

Step-by-step explanation:

This is a "sum of two cubes" We just memorize how to factor a sum of cubes (and a difference of two cubes) Someone else discovered it, we just have to recognize it and use a pattern to factor.

First, 125 is a perfect cube. It is 5^3. Also, 27 is 3^3. Obviously, x^3 is a cube. So the given problem could be (5x)^3 + 3^3

It will factor into a binomial (5x + 3) and a trinomial (5x)^2 - (5x)(3) + 3^2

You can see the binomial is the same as the problem but without the exponents. The other factor, the trinomial has the first term, the 5x but squared. The second term of the trinomial is the two terms of the problem, multiplied together and without any exponents, 5x•3, so 15x. The last term of the trinomial is the second term of the binomial, 3, but squared, so 3^2, thats 9. Theres a memory tool called SOAP that can help you memorize the adding and subtracting in the factors. SOAP stands for Same, Opposite, Always Positive. The 5x + 3 has that + bc the original problem has a + . Thats the Same. The trinomial has a - thats the Opposite of the original problem. The last + is always a +, so thats the Always Positive.

a. The absolute value of a number is the distance of the number from zero on a number line. It is always a non-negative value, meaning that it is either zero or a positive number. It is denoted by two vertical bars surrounding the number, like |x|.

b. The absolute value of -109 is the distance of -109 from zero on a number line. Since -109 is 109 units away from zero, the absolute value of -109 is 109. Therefore, |-109| = 109.

c. First, we need to evaluate |-7|, which is the absolute value of -7. The distance of -7 from zero on a number line is 7 units, so |-7| = 7. Therefore, the expression |-7| - 2 is equivalent to 7 - 2, which is equal to 5. Therefore, |-7| - 2 = 5.

Answer:

In basic mathematics, pi is used to find the area and circumference of a circle. Pi is used to find area by multiplying the radius squared times pi. So, in trying to find the area of a circle with a radius of 3 centimeters, π32 = 28.27 cm.

Answer:

Succinctly, pi or π is the ratio of the circumference of any circle to the diameter of that circle.

Have A Nice Day!!!!!!

:))))))

Answer:

Step-by-step explanation:

a) The formula for the regression function is:

Maintenance Cost = 54.7757 + 120.689 x Age of Car

b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.

c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:

Y = a + bX ± tα/2 * SE

where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.

Plugging in the values, we get:

Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442

Y = 923.167 ± 26.010

Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.

d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.

To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.

Answer:

It all depends on the food they are going for, just like humans, mice have instincts. For example, if you were falling forward, which foot would you put out? Most likely the opposite one. I hope this helps you!

Step-by-step explanation:

Using hypotheses testing,

In both cases, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that mice show a preference towards one paw over the other.

We have,

(a)

To test whether the data suggest that mice show a preference towards one paw over the other, we can use a one-sample proportion test.

The null hypothesis (H0) is that the proportion of mice that use their right paw is 0.5 (indicating no preference towards one paw over the other).

The alternative hypothesis (Ha) is that the proportion of mice that use their right paw is different from 0.5 (indicating a preference towards one paw over the other).

We can use a significance level (alpha) of 0.05.

To conduct the test, we can calculate the test statistic using the formula:

z = (p - 0.5) / √(0.5 x 0.5 / n)

where p is the proportion of mice that use their right paw, and n is the sample size.

Using the given data, we have:

p = 18/48 = 0.375

n = 48

Plugging in the values, we get:

z = (0.375 - 0.5) / √(0.5 x 0.5 / 48) = -1.714

Using a standard normal distribution table or calculator,

We can find the p-value associated with this test statistic.

The p-value is the probability of observing a test statistic as extreme as -1.714 or more extreme, assuming the null hypothesis is true.

The p-value for this test is 0.0869.

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.

This means that we do not have sufficient evidence to conclude that mice show a preference towards one paw over the other, based on the given sample.

(b)

With the new dataset of 480 observations, we can still conduct a similar analysis using a one-sample proportion test.

However, since each mouse was measured 10 times, the observations are no longer independent.

Therefore, we need to use a different test that accounts for the dependency between observations, such as McNemar's test.

McNemar's test is a test of the marginal homogeneity of a two-way table, where the same subjects are measured twice on a binary outcome.

In this case, we can create a 2x2 contingency table of the number of times each mouse used their right or left paw, and conduct a McNemar's test on this table.

The null hypothesis for McNemar's test is that there is no difference in the proportions of mice that use their right or left paws.

The alternative hypothesis is that there is a difference.

To conduct the test, we can calculate the test statistic using the formula:

chi-squared = (|b-c|-1)² / (b+c)

where b is the number of mice that used their right paw more often, and c is the number of mice that used their left paw more often.

Using the given data, we have:

b = 214

c = 244

Plugging in the values, we get:

chi-squared = (|214-244|-1)² / (214 + 244) = 2.417

Using a chi-squared distribution table or calculator with 1 degree of freedom (since we have a 2x2 table), we can find the p-value associated with this test statistic.

The p-value is the probability of observing a test statistic as extreme as 2.417 or more extreme, assuming the null hypothesis is true.

The p-value for this test is 0.119.

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.

This means that we do not have sufficient evidence to conclude that there is a difference in the proportions of mice that use their right or left paws, based on the new dataset.

Thus,

In both cases, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that mice show a preference towards one paw over the other.

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