Suppose that the functions g and are defined for all real numbers x as follows. g(x) = 2x ^ 2; h(x) = x - 3 Write the expressions for (h - g)(x) and (hg)(x) and evaluate (h + g)(- 1) .

Answer:

Answer to your question ; f(t) = 55 = 4t

Vector v can be written as the sum of two vector components, \(v_x = -5i\)  and \(v_y = 6j\)

To write vector v as the sum of two vector components, we need to decompose it into two vectors along different directions.

v = -5i + 6j

w = 3i + 4j

We can decompose vector v into two components, one along the x-axis and the other along the y-axis.

Let's denote the component along the x-axis as \(v_x\) and the component along the y-axis as \(v_y.\)

The x-component, \(v_x,\) represents the projection of vector v onto the x-axis and can be found using the dot product of v and the unit vector i:

\(v_x = v . i = (-5i + 6j) . i = -5i . i + 6j . i = -5\)

Similarly, the y-component, \(v_y,\) represents the projection of vector v onto the y-axis and can be found using the dot product of v and the unit vector j:

\(v_y = v . j = (-5i + 6j) . j = -5i . j + 6j . j = 6\)

Now, we can write vector v as the sum of its components:

\(v = v_x + v_y = -5i + 6j\)

So, vector v can be written as the sum of two vector components: -5i along the x-axis and 6j along the y-axis.

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Answer:

y = -6x + 8

Step-by-step explanation:

\begin{bmatrix}6x+y=8\\ y=-6x+8\end{bmatrix}

I don't know why it came out like this

No, the conditions for inference are not met. The Large Counts Condition is not satisfied because the number of successes (6) is less than 10.

To determine if the conditions for inference are met in this scenario, we need to consider a few key conditions: the 10% condition, the randomness condition, and the Large Counts Condition.

The 10% condition: This condition states that the sample size should be no more than 10% of the population size. In this case, the sample size is 10 (the number of times the penny was spun), and we don't have information about the population size. However, since the proportion of times the penny lands tails up is not likely to be affected by the sample size of 10, we can assume that the 10% condition is met.

The randomness condition: This condition requires that the sample is randomly selected from the population. If the student followed the instructions and spun the penny 10 times, recording the number of times it landed tails side up, and there was no bias in the way the spins were performed, we can assume that the randomness condition is met.

The Large Counts Condition: This condition is related to the number of successes and failures in the sample. It states that both the number of successes and failures should be at least 10. In this case, the student recorded 6 tails side up out of 10 spins. Since 6 is less than 10, the Large Counts Condition is not met.

Based on these conditions, we can conclude that the conditions for inference are not fully met. The 10% condition and the randomness condition are likely met, but the Large Counts Condition is not satisfied. This means that we should be cautious when making inferences about the true proportion of tails up based on this sample. It may not be appropriate to construct a confidence interval or perform statistical inference in this case due to the violation of the Large Counts Condition.

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Answer:

The area of the triangle:

=1/2×base×height

=1/2×2×2

=2 units²

2 units² is the right answer.

Answer:

Area = 2

Step-by-step explanation:

A= base x height/2

base = 2

height = 2

2 x 2 = 4

4/2 = 2

Hope this helps! Have a great day/night

Answer:

8x=42 where x is hourly cost

so x = 21/4

6*x = 63/2 $

Step-by-step explanation:

Answer:

The solution would be to solve two equations simultaneously.

Step-by-step explanation:

The solution would be to solve two equations simultaneously.

So let X = ml of 8 % SOLUTION and Y = ml of 20 % SOLUTION

We know that X + Y must = 60 ml.

So first equation is X + Y = 60

The second equation is the statement of the problem

0.2 X + 0.08 Y = 0.1 x 60 = 6

Second equation reduces to

0.2 X + 0.08 Y = 6

Solve the two equations for X and Y and you have your answer.

Answer: -11 ÷ 4; 11 ÷ (-4); \(\frac{-11}{4}\); \(\frac{11}{-4}\)

Step-by-step explanation:

A negative divided by a negative is a positive.

A positive divided by a negative or a negative divided by a positive is a negative.

The standard form of the equation for the circle is\((x - 4)^2 + (y - 3)^2 = 2.\)

To find the standard form of the equation for the circle, we need to determine the center and radius of the circle using the given information.

The center of the circle can be found by taking the average of the x-coordinates and the y-coordinates of points A and B.

Center:

x-coordinate = (3 + 5) / 2 = 4

y-coordinate = (2 + 4) / 2 = 3

The center of the circle is (4, 3).

Next, we need to find the radius of the circle.

The radius is the distance between the center of the circle and any point on its circumference.

In this case, we can use the distance formula between the center (4, 3) and point B (5, 4).

Radius:

\(r = \sqrt{((5 - 4)^2 + (4 - 3)^2)}\)

= \(\sqrt{(1 + 1)}\)

\(=\sqrt{(2)}\)

The radius of the circle is \(\sqrt{(2).}\)

Now we can write the standard form of the equation for the circle, which is:

\((x - h)^2 + (y - k)^2 = r^2\)

Plugging in the values we found:

\((x - 4)^2 + (y - 3)^2 = 2\)

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Answer:

There is obviously only 1 10x10 square. If we start with a 9x9 square in the top left corner, we can move it down 1, across 1 and back up 1, so there are 4 possible 9x9 squares.

For 8x8 we can move down 1, then 2 and we can move across 1 or 2 so that's 9 possible 8x8 squares.

For 7x7 we can go down 3 and across 3, so that's 4x4=16 possible squares.

The pattern is now clear the total number if squares is 1+4+9+16+…+100.

There's a formula for this, which I had to look up, but any the sum of the first n squared is 1/6n(n+1)(2n+1)1/6n(n+1)(2n+1), so the total number of squares is 10x11x21/6=5x11x7=385.

Answer:

see below

Step-by-step explanation:

y = a cos ( bx)

The amplitude is |a|

y = -2cos (3x) so the amplitude is |-2| = 2

The period is  2pi/b

period is  2pi/3

the answer is C I think im pretty sure

Answer:

Step-by-step explanation:

$100x0.5x1=$5

there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.

answer is D. None of the above.

To test if there is significant evidence to claim that the variance of the battery life population is different than 4 hours2, we can use a chi-square test.This is how the test statistic is computed:

X2 = (n-1)*(s2/σ2)

where n is the sample size, s2 is the sample variance and σ2 is the population variance.

In this case, n = 16, s2 = 3.25 and σ2 = 4

X2 = (16-1)*(3.25/4) = 12.1875

The critical value of X2 with 15 degrees of freedom and α = 0.05 is 24.996. Therefore, since 12.1875 < 24.996, we fail to reject the null hypothesis, and there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.

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The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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Answer: 3/4

Step-by-step explanation:

Both 81 and 108 are divisible by 27

\(area = \pi \times {r}^{2} \\ area = 3.142 \times {6.1}^{2} \\ area = 3.142 \times 37.21 \\ area = 116.91 {mm}^{2} \)

a) Yes given statment concluded from the ANOVA test

b) No given statment cannot concluded from the ANOVA test

c) No given statment cannot concluded from the ANOVA test

d) Yes given statment concluded from the ANOVA test

a) On average, people in the middle class agree with the new government policies to a different extent than people in the upper class.

Can conclude: Yes, this can be concluded from the ANOVA test, as the null hypothesis was rejected in Test 2, indicating that there is a significant difference between at least two levels of socio-economic class.

b) All of the socio-economic classes are different in relation to the average extent of voter agreement with the new government policies.

Cannot conclude: No, this cannot be concluded from the ANOVA test, as Test 3 did not reject the null hypothesis, indicating that there is no significant interaction effect between age group and socio-economic class.

c) All of the socio-economic classes are the same in relation to the average extent of voter agreement with the new government policies.

Cannot conclude: No, this cannot be concluded from the ANOVA test, as Test 2 rejected the null hypothesis, indicating that there is a significant difference between at least two levels of socio-economic class.

d) At least one of the socio-economic classes is different to the rest in relation to the average extent of voter agreement with the new government policies.

Can conclude: Yes, this can be concluded from the ANOVA test, as Test 2 rejected the null hypothesis, indicating that there is a significant difference between at least two levels of socio-economic class.

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The statements that will be true about parallelogram ABCD are: A, B, D, and E.

Properties of a Parallelogram -

Diagonals of a parallelogram bisect each other into congruent segments.

Opposite angles and sides of a parallelogram are always congruent.

Alternate interior angles are always congruent in measure.

Thus, the following would be true of parallelogram ABCD:

AP ≅ CP (congruent segment's of a bisected diagonal)

BC ≅ AD (congruent opposite sides)

∠CAD ≅ ∠ACB (congruent angles)

∠BPC ≅ ∠APD (congruent angles)

Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.

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The rate of change of the perimeter of this rectangle is equal to 2 feet per second.

The rate of change of the area of this rectangle is equal to 20 feet per second.

Mathematically, the perimeter of a rectangle can be calculated by using this formula;

P = 2L + 2W

Where:

The rate of change for the perimeter of this rectangle is given by:

P = 2L + 2W

Differentiating with respect to t, we have:

dP/dt = 2dl/dt + 2dw/dt

Substituting the given parameters into the formula, we have;

dP/dt = 2(3) + 2(-2)

dP/dt = 6 - 4

dP/dt = 2 feet per second.

For the rate of change of the area of this rectangle, we have:

dA/dt = ldw/dt + wdl/dt

dA/dt = 8(-2) + 12(3)

dA/dt = -16 + 36

dA/dt = 20 feet per second.

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The travelled distance of the traveller is equal to 195 kilometers.

According to the statement of the problem, a traveller already walked a third part of his trail and if he travels the half of his trail, then the half of his trail shall be covered. Mathematically, the travelled distance shall be described by following expression:

x = d / 3

x + 65 = d / 2

Where:

Now we proceed to determine the travelled distance:

d / 3 + 65 = d / 2

d / 2 - d / 3 = 65

3 · d - d = 390

2 · d = 390

d = 195

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Answer:

The answer is 16.90 because 52.50 minus 35.5 is 16.90.

The length of z in the triangle is 97 inches.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the side z of the triangle XYZ using sine law as follows:

a / sin A = b / sin B = c / sin C

Hence,

500 / sin 117 = z / sin 10

cross multiply

500 sin 10 = z sin 117

divide both sides by sin 117

z = 500 sin 10  / sin 117

z = 86.8240888335 / 0.89100652418

z = 97.4410774411

Therefore,

z = 97 inches

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Answer: $227,226.51

Step-by-step explanation:

First, we need to convert the period to weeks.

9 1/2 years = 9.5 years

1 year = 52 weeks

9.5 years = 494 weeks

Next, we can use the formula for the future value of an annuity:

FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)

where:

PMT = payment amount per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values:

PMT = $300

r = 0.055 (5.5% expressed as a decimal)

n = 52 (compounded weekly)

t = 9.5 years = 494 weeks

FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)

FV = $227,226.51

Therefore, the future value of the annuity is approximately $227,226.51.

Answer:

6.2 (Approximated).

Step-by-step explanation:

12x-7 > 67

Add 7 to both sides.

12x > 74

Divide 12 from both sides.

12/12x > 74/12

Final answer

x > 6.2 (approximately)

The amount of cost to carpet the entire rectangular living room floor of the cabin is given by A = $ 420

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangular living room be A

The scale factor is 1 cm of graph = 4 feet

Now , the length of rectangular floor be L = 5 cm

So , the length of the rectangular floor L = 20 feet

And , the width of the rectangular floor W = 3.5 cm

So , the width of the rectangular floor W = 14 feet

The cost per unit area of carpet = $ 1.50

The area of rectangular floor = L x W

On simplifying , we get

The area of rectangular floor = 20 x 14 = 280 feet²

Now , the cost to carpet 280 feet² of living room = 280 x cost per unit area of carpet

The amount of cost to carpet the entire living room floor = 280 x 1.5

The amount of cost to carpet the entire living room floor = $ 420

Hence , the cost to carpet the living room is $ 420

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The complete question is :

If carpet cost s $1.50 per square foot including the cost of installation how much would it cost to carpet the entire living room floor of the cabin shown at the right?

Given that,

The water level of a lake rose by 1 2/3 in. during a 3 1/3 week-long wet spell. We need to find the average rate at which the water level changed every week. It is a problem based on the concept of ratio. So,

\(R=\dfrac{1\dfrac{2}{3}}{3\dfrac{1}{3}}\\\\=\dfrac{\dfrac{5}{3}}{\dfrac{10}{3}}\\\\=\dfrac{5}{3}\times \dfrac{3}{10}\\\\=\dfrac{1}{2}\)

So, the average rate at which the water level changed every week is 1/2 inches/week.