a type ii error is a. rejecting the null hypothesis when it is true. b. accepting the null hypothesis when it is false. c. incorrectly specifying the null hypothesis. d. incorrectly specifying the alternative hypothesis.

The maximum angle of the incline for the car to be at rest using only friction is 38.7° if, for the car on the incline, the coefficient of static friction is 0.8 and the coefficient of kinetic friction is 0.6.

If the car is at rest on the incline, the force of gravity acting on the car down the incline is balanced by the force of static friction acting up the incline. The maximum angle \($\theta$\) of the incline is the angle at which the force of static friction is at its maximum, which is given by the product of the coefficient of static friction and the normal force.

Let's assume that the mass of the car is m and the incline makes an angle of \($\theta$\) with the horizontal. Then, the force of gravity acting on the car down the incline is given by \($mg\sin(\theta)$\), where g is the acceleration due to gravity. The normal force acting on the car perpendicular to the incline is given by \($mg\cos(\theta)$\).

For the car to be at rest on the incline, the force of static friction acting up the incline must be equal in magnitude to the force of gravity down the incline. Therefore, we have:

\($$\mu_s mg\cos(\theta) = mg\sin(\theta)$$\)

here \($\mu_s$\) is the coefficient of static friction. Simplifying this equation,

we get:

\($$\tan(\theta) \leq \mu_s$$\)

Therefore, the maximum angle \($\theta$\) of the incline is:

\($$\theta \leq \tan^{-1}(\mu_s)$$\)

Substituting the value of \($\mu_s = 0.8$\), we get:

\($$\theta \leq \tan^{-1}(0.8) \approx 38.7^{\circ}$$\)

Therefore, the maximum angle of the incline for the car to be at rest using only friction is approximately 38.7°.

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Answer:

True

Step-by-step explanation:

The coordinates of point B on segment AC such that the ratio of AB to BC is 2 : 3 is (12 / 5, 38 / 5).

In this problem we must use the concept of segment ratios and linear algebra operations to determine the location of a point within a line segment generated by two distinct points:

B(x, y) = A(x, y) + (AB / AC) · [C(x, y) - A(x, y)]

B(x, y) = (0, 4) + (2 / 5) · [(6, 13) - (0, 4)]

B(x, y) = (0, 4) + (2 / 5) · (6, 9)

B(x, y) = (0, 4) + (12 / 5, 18 / 5)

B(x, y) = (12 / 5, 38 / 5)

The coordinates of point B on segment AC such that the ratio of AB to BC is 2 : 3 is (12 / 5, 38 / 5).

The statement is incomplete, complete form is shown below:

Given that A (x, y) = (0, 4) and C (x, y) = (6, 13). What are the coordinates of point B on AC such that the ratio of AB to BC is 2 : 3.

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Answer:

x = 4

Step-by-step explanation:

Given the equation:

\(\displaystyle{4^x - 4^0 - 255=0}\)

We know that \(\displaystyle{a^0 = 1}\) where a ≠ 0. Therefore,

\(\displaystyle{4^x - 1 - 255=0}\\\\\displaystyle{4^x - 256=0}\)

Add both sides by 256, so we have:

\(\displaystyle{4^x=256}\)

Factor 256 out:

256 = 2 x 128 = 2 x 2 x 2⁶ = 2⁸

Therefore, 256 = 2⁸.

\(\displaystyle{4^x=2^8}\)

Convert to the same base:

\(\displaystyle{\left(2^2\right)^x=2^8}\\\\\displaystyle{2^{2x} = 2^8}\)

When two sides have same base, solve the equation through exponents:

\(\displaystyle{2x=8}\)

Divide both sides by 2, so we have:

\(\displaystyle{x=4}\)

Answer:

Step-by-step explanation:

You want the value of the piecewise function for various values of x.

The first step in evaluating a piecewise function is determining which domain is applicable to the value of x you have. Then you use the corresponding function, evaluating it in the usual way.

For x = -5, the applicable domain is x < -3, so the function is ...

  h(-5) = -4(-5) -18 = 20 -18

  h(-5) = 2

For x = 0, the applicable domain is -3 ≤ x < 1, so the function is ...

  h(0) = 1

For x = 1 or 4, the applicable domain is x ≥ 1, so the function is ...

  h(1) = 1 +2 = 3

  h(4) = 4 +2 = 6

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The value of the integral ∫x²dV using cylindrical coordinates is 512π / 3 .

In this case, the solid is positioned between the cylinder x² + y² = 4 and will be evaluated by using the cone z²= 16x² + 16y² .

Cylindric coordinates will be used to calculate this integral  \(\int\limits_e {x^2} \, dx\).

The distance from the origin to the point (x, y, 0) and the angle the point (x, y, 0) makes with the x-axis, respectively, are provided by the formulas.

x = r cos θ

y= r sin θ

With these coordinates, we shall characterize the solid E.

The boundary is then x² + y² = r²

The boundary also becomes r² = 4 or ( 0 ≤ θ ≤ r² )

Again z = 16r²

The original integral must now be translated into terms of these new coordinates. It is necessary to multiply the function by the Jacobian of the change in coordinates in order to ensure that the result remains the same. The value for the cylindric coordinates is r. Then

\(\int_ex^2 dx = \int\limits^{2\pi}_0\int\limits^2_0\int\limits^{16r^2}_0 r(r^2cos^2\theta)dzdrd\theta\)

\(=\int _0^{2\pi }\int _0^216r^5\cos ^2\theta drd\theta\)

\(=\int _0^{2\pi }\frac{512}{3}\cos ^2\theta d\theta\)

= 512/3 π

Hence the volume of the solid that is enclosed by the integral is given by 512/3 π .

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The pair of equation y = -3 and y = 0 has no solution .

What is equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

Equations are mathematical expressions that have two algebraic expressions on either side of an equals (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship.

When two expressions are joined by an equal sign, a mathematical statement is called an equation. An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable.

Since, the x-axis (equation y=0) does not intersect y=-7 at any point. The given pair of equations has no solution.

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when both x and y are even integers, their product xy cannot be odd

To prove the statement "If x and y are even integers, then xy is even" by contradiction, we assume the negation of the statement, which is "If x and y are even integers, then xy is not even."

So, let's assume that x and y are even integers, but their product xy is not even. This means that xy is an odd integer.

Since x and y are even, we can write them as x = 2a and y = 2b, where a and b are integers.

Now, substituting these values into the equation xy = 2a * 2b, we get xy = 4ab.

According to our assumption, xy is odd. However, we have expressed xy as 4ab, which is a product of two integers and therefore divisible by 2. This contradicts our assumption that xy is odd.

Hence, our assumption that xy is not even leads to a contradiction. Therefore, we can conclude that if x and y are even integers, then xy must be even.

This proof by contradiction demonstrates that when both x and y are even integers, their product xy cannot be odd, providing evidence for the original statement.

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The decision for this test at a .05 level of significance is not enough information to make a decision the correct answer is (d).

To make a decision for a hypothesis test, we compare the obtained test statistic (in this case, z = 1.80) with the critical value(s) based on the chosen level of significance (in this case, α = 0.05).

For a one-sample z test, if the obtained test statistic falls in the rejection region (i.e., beyond the critical value(s)), we reject the null hypothesis. Otherwise, if the obtained test statistic does not fall in the rejection region, we fail to reject the null hypothesis.

Without knowing the critical value(s) corresponding to a significance level of 0.05 and the directionality of the test (one-tailed or two-tailed), we cannot determine the decision for this test. Therefore, the correct answer is (d) There is not enough information to make a decision.

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Answer:

Explanation:

Given the expression:

This can be written as a difference of two squares. But before that, we can rewrite the expression as:

So, as a different of two squares, we write:

Answer:

Step-by-step explanation:

-1, -0.5, 1/4

Answer:

d = 3√2

Step-by-step explanation:

find the constant of variation ('k'):  F = k/d²

16 = k/3²

16 = k/9

k = 144

8 = 144/d²

d² = 144/8

d² = 18

d = √9 · √2

d = 3√2

Answer:

The answer is (-9, 5). Hope this helps.

Answer:

(x - 1)(5x - 6)

Step-by-step explanation:

Given

5x² - 11x + 6

Consider the factors of the product of the coefficient of the x² term and the constant term (ac) which sum to give the coefficient of the x- term (b)

ac = 5 × 6 = 30 and b = - 11

The factors are - 5 and - 6

Use these factors to split the x- term

5x² - 5x - 6x + 6 ( factor the first/second and third/fourth terms )

= 5x(x - 1) - 6(x - 1) ← factor out (x - 1) from each term

= (x - 1)(5x - 6)

Answer: -4.2

Step-by-step explanation:

=1-6+0.8

=-4.2

Answer:

C

Step-by-step explanation:

One man alone can finish the work in about 1.26 days, and one boy alone can finish the work in about 33.33 days.

Let the work be "1" unit, and let the rate of work of one man be "m" and that of one boy be "b". Then we can set up the following system of equations based on the given information:

8m + 12b = 1/10 (equation 1)

6m + 8b = 1/14 (equation 2)

We have two equations and two unknowns, so we can solve for "m" and "b". First, we'll simplify the equations by multiplying both sides of each equation by the least common multiple of the denominators (10*14 = 140):

112m + 168b = 14 (equation 1, multiplied by 140)

84m + 112b = 10 (equation 2, multiplied by 140)

Now we can solve this system of linear equations using either substitution or elimination. Let's use elimination by multiplying equation 2 by -12 and adding it to equation 1:

112m + 168b = 14

-84m - 112b = -120

28m + 56b = -106

Simplifying, we get:

7m + 14b = -53/2 (equation 3)

Now we can solve for "m" or "b" by using either equation 2 or equation 3. Let's use equation 3:

7m + 14b = -53/2

14m + 28b = -53

7m + 14b = -53/2

Subtracting the bottom equation from the top equation, we get:

-7m - 14b = 53/2

Multiplying both sides by -1, we get:

7m + 14b = 53/2

Adding this equation to equation 3, we get:

21m = -53/2

Solving for "m", we get:

m = -53/42 = -1.26 (rounded to two decimal places)

Now we can use equation 2 to solve for "b":

6m + 8b = 1/1

Substituting "-1.26" for "m", we get:

6(-1.26) + 8b = 1/14

Simplifying and solving for "b", we get:

b = 1/14 - (-7.56)/8 = 0.03 (rounded to two decimal places)

Therefore, one man alone can finish the work in about 1.26 days, and one boy alone can finish the work in about 33.33 days.

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Answer:

$13,400

Step-by-step explanation:

Simple Interest = principal × rate × time

principal= $9000

Rate= 12/100=0•12

Time=5years

Simple interest =PRT

= 9000× 0•12 × 5

= 5400

Total amount to be paid = 9000 + 5400

= $13400

Answer:

volume

Step-by-step explanation:

Answer:

Buy stuff and sell them at a higher price

Step-by-step explanation:

Answer:

get a job

Step-by-step explanation:

The correct answer is (1) 3/7. they can finish the ditch in (3/7) of the time that the worker takes working alone.

To solve this problem, let's assume that the worker takes 1 unit of time to complete the ditch working alone.

The worker's rate of work is 1 ditch per unit of time.

Each assistant works at a rate that is 2/3 as fast as the worker. Therefore, each assistant's rate of work is (2/3) ditch per unit of time.

When all three of them work together, their combined rate of work is the sum of their individual rates.

Worker's rate + 2 Assistants' rate = 1 + 2(2/3) = 1 + 4/3 = 7/3

Hence, they can finish the ditch in (3/7) of the time that the worker takes working alone.

Therefore, the correct answer is (1) 3/7.

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Answer:

1,2,4,5,10

1,2,3,5,6

60

Step-by-step explanation:

After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

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Answer:

58

Step-by-step explanation:

Width is 24 & Length is 12 of a rectangle.

What is rectangle short answer?

give,

Perimeter = 72

Width = 2*Length

Let P = Perimeter

Let W = Width

Let L = Length

Knowing

P = 2L + 2W = 72

W = 2L

We can rewrite everything in terms of Length

72 = 2L + 2(2L)

72 = 2L + 4L

72 = 6L

72/6 = L

12 = L

W = 2L

W = 2(12) = 24

Width is 24

Length is 12

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Answer:

3 people

Step-by-step explanation:

$11 for parking leaving $39 after paying for parking

39÷13=3

Answer:b

Step-by-step explanation:

Answer:

20.05feet

Step-by-step explanation:

Given data

Circumference= 63feet

The expression for circumference is

C= 2πr

substitute

63= 2*3.142*r

63= 6.284r

r= 63/6.284

r=10.025

Hence the diameter is

=10.025*2

=20.05feet