I have to pick one answer for each!!

Answer:

Step-by-step explanation:

The Mean Value Theorem says that for continuous and differentiable function f(x) on the interval ( a, b ) there is number c ∈ ( a, b ) that

f'(c) = \(\frac{f(b)-f(a)}{b-a}\) ....... (1)

~~~~~~~~~~~~~~~~

f(5) = 44

f(0) = - 1

5 - 0 = 5

f'(x) = 2x + 4 ⇒ f'(c) = 2c + 4

2c + 4 = \(\frac{44+1}{5}\)

2c + 4 = 9 ⇒ c = \(\frac{5}{2}\) (D).

The "central-tenet" in his system was : (d) Workers should earn "higher-wages" and work "shorter-hours", which creates new pool of consumers with income and leisure to purchase car.

Henry Ford's system, known as Fordism, was characterized by the belief that by paying workers higher wages and reducing their working hours, they would have the means and leisure time to become consumers of the products they were producing, particularly automobiles.

Ford implemented the 8-hour workday and a $5 daily wage for his workers, which was significantly higher than the prevailing wages at the time. This approach aimed to increase the purchasing-power of workers and stimulate consumer demand, ultimately benefiting the economy as a whole.

Therefore, the correct option is (d).

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The given question is incomplete, the complete question is

Henry Ford is known for refining the assembly line and the Model T. He also adopted an attitude that came to be known as Fordism. What was a central tenet in his system?

(a) Workers could easily tolerate working on an assembly line, so they should be paid lower wages and work longer hours.

(b) Workers should be drawn from a pool of immigrant labor, which was cheaper and willing to tolerate the grueling work of an assembly line.

(c) Workers should earn lower wages and work shorter hours, since they were easily replaced on the assembly line.

(d) Workers should earn higher wages and work shorter hours, creating a new pool of consumers with the income and leisure to purchase a car.

To identify the slope and y-intercep of a line, you need to write the equation in slope intercpet form:

m is the slope

b is the y-intercept (the value of y when the line cross the y-axis)

To write the equation in slope-intercept form, leave the variable y in one side of the equation.

-Substract 7x in both sides of the equation:

-Divide both sides of the equation into 2:

Answer: (2;3).

Step-by-step explanation:

\(\displaystyle\\\left \{ {{4x=-3y+17} \atop {3x-4y=-6}} \right. \ \ \ \ \left \{ {{4x+3y=17\ |*4} \atop {3x-4y=-6\ |*3}} \right. \ \ \ \ \left \{ {{16x+12y=68} \atop {9x-12y=-18}} \right. \\Let's\ sum \ up\ these\ equations:\\25x=50\ |:25\\x=2.\\4*2=-3y+17\\8+3y=17\\3y=9\ |:3\\y=3.\)

Answer:

6x²-x-15

degree: second

leading coefficient : 6 , -1

constant : -15

Step-by-step explanation:

(2x + 3) (3x – 5)=

6x²+9x-10x-15=

6x²-x-15

degree: second

leading coefficient : 6 , -1

constant : -15

In summary: Sequence 1 has no term out of increasing order. Sequence 2 has the first term out of increasing order at position 2. Sequence 3 has the first term out of increasing order at position 7. Sequence 4 has the first term out of increasing order at position 4. Sequence 5 has the first term out of increasing order at position 3.

1 5 78 99 101 202 400: This sequence is in increasing order throughout, so there is no term that breaks the increasing pattern.

5 2 7 90 85 80 72: The sequence starts with 5, then decreases to 2 (out of increasing order) at position 2.

5 6 9 10 14 21 20: The sequence is increasing until position 6, where it reaches 21. However, the next term, 20, is lower than the previous term, 21 (out of increasing order) at position 7.

3 7 10 9 8 14 17: The sequence starts with 3 and increases until position 3 (10). However, at position 4, the next term, 9, is lower than the previous term, 10 (out of increasing order).

5 77 25 45 22 94 58 99: The sequence is increasing until position 2, where it reaches 77. However, at position 3, the next term, 25, is lower than the previous term, 77 (out of increasing order).

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Answer:

7,460,000

Step-by-step explanation:

6 makes the 5 go up to 6

Answer:

x = 45 Yes

Step-by-step explanation:

x+3x+2x+90= 360°

6x= 270

x=45

A= 2x = 90°

so yes both A and B makes 90° so they should be parallel

walking = biking + 1.5 hour

biking speed = 9 mph + walking speed

route = 6 miles

6/w = 6/(w + 9) - 3/2

Solving for w:

108 = -3w^2 - 27w ==> 3w^2 + 27w + 108 = 0 ==> x^2 + 9x + 36 = 0

Answer:

Both are correct

Step-by-step explanation:

Jared and Nicole both have found the correct value and will get the same solution to the system of equations.

Given information:

Jared found that  for one equation and substituted  for y in the other equation.

Nicole found  for the one equation and substituted  for x in the other equation.

So, there are two equations. Based on the question, the equation should be,

and .

Now, Jared and Nicole have found the value of one variable from one equation and have put it in the other equation.

This method is the substitution method which is used to find the solution of the system of equations.

Therefore, Jared and Nicole both have found the correct value and will get the same solution to the system of equations.

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The three factors that need to be taken into account when determining the sample size are the margin of error, level of confidence, and standard deviation.

To determine the sample size required to estimate the mean with a given level of confidence, we need to consider three factors. The first factor is the margin of error, which is the maximum distance between the sample mean and the true population mean that can be tolerated and is denoted by E.

The second factor is the level of confidence, which is the probability that the true population mean lies within the margin of error of the sample mean. This is denoted by (1-α), where α is the level of significance. Therefore, the level of confidence is 1 - α.

The third factor is the population standard deviation (σ) or the variance (σ²). If the population standard deviation is not given, we can use the sample standard deviation as an estimate. However, if the population size is greater than 30 and the distribution is normal, the sample mean can be used to estimate the population mean. On the other hand, if the population size is less than or equal to 30, the sample mean can be used to estimate the population mean only if the population distribution is normal.

Therefore, it is crucial to consider the distribution of the population when deciding if the sample mean can be used to estimate the population mean.

In summary, the three factors that need to be taken into account when determining the sample size required to estimate the mean with a given level of confidence are the margin of error, level of confidence, and population standard deviation (σ) or the variance (σ²). It is essential to understand each of these factors to accurately determine the required sample size.

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Answer:

f(x) = -(x + 8)(x -14)

= -(x2 - 112 - 6x)

= -x2 + 6x + 112 --- (1)

We know the graph of an equation y = ax2 + bx + c where a ≠ 0 is a parabola. The parabola opens upwards if a > 0 and opens downwards if a < 0. The vertex of the parabola is the point where the axis and parabola intersect. Its x coordinate x = -b/2a and its y coordinate is found out by substituting x = -b/2a in the parabola equation.

The parabola given in the problem statement has a negative coefficient of x2 and hence it is a parabola which opens downwards. Also for the equation

a = -1, b = 6 and c = 112. Therefor the x-coordinate of the vertex is

x = -b/2a

= -(6)/[2(-1)]

= 3

Substituting the value of x = 3 in equation (1) we get,

Now y = -(3)2 + 6(3) + 112

= -9 + 18 + 112 = 121

So the vertex point coordinates are (3, 121) and the y value is 121.

The graph below verifies the vertex point.

vertex of the graph

What is the y-value of the vertex of the function f(x) = -(x + 8)(x - 14)?

Summary:

The y-value of the vertex of the function f(x) = -(x + 8)(x - 14) is 121.

Answer: The lowest possible product would be -6724 given the numbers 82 and -82.

We can find this by setting the first number as x + 164. The other number would have to be simply x since it has to have a 164 difference.

Next we'll multiply the numbers together.

x(x+164)

x^2 + 164x

Now we want to minimize this as much as possible, so we'll find the vertex of this quadratic graph. You can do this by finding the x value as -b/2a, where b is the number attached to x and a is the number attached to x^2

-b/2a = -164/2(1) = -164/2 = -82

So we know one of the values is -82. We can plug that into the equation to find the second.

x + 164

-82 + 164

82

Step-by-step explanation: Hope this helps.

If the multiplicity of the roots was 3, the curve would still be tangent to the x-axis at -3 and 3, but the curve would cross the x-axis.

The graph below is the graph of the equation f(x) = 0. The equation is graphed on the x-y plane. To determine the multiplicity of the roots, one needs to look at the graph closely.

The multiplicity of the roots of a polynomial function is a way of determining the behavior of the function as it approaches a particular point on the x-axis. In particular, it tells us how quickly the function approaches zero at that point.

The graph shows a curve that intersects the x-axis at -3 and 3. At these two points, the curve is tangent to the x-axis. Since the curve is tangent to the x-axis at these points, this means that the roots are repeated.

The multiplicity of the roots of f(x) = 0 is 2. This means that the curve touches the x-axis at -3 and 3, but doesn't cross it. This is because the roots are repeated.

If the multiplicity of the roots was 3, the curve would still be tangent to the x-axis at -3 and 3, but the curve would cross the x-axis.

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Answer:

The polar form of the rectangular coordinates (0, 6√3) with a positive value of r, over the interval 0 ≤ θo < 27 and in terms of radians, is (6√3, 1.58).

Step-by-step explanation:

To convert the rectangular coordinates (0, 6√3) to polar form, we can use the following formulas:

r = √(x^2 + y^2)

θ = tan^(-1)(y/x)

Substituting the given values, we get:

r = √(0^2 + (6√3)^2) = 6√3

θ = tan^(-1)((6√3)/0) = π/2

However, note that the angle θ is not well-defined since x=0. We can specify that the point lies on the positive y-axis, which corresponds to θ = π/2 radians.

Thus, the polar form of the rectangular coordinates (0, 6√3) is:

r = 6√3

θ = π/2

To express the angle θ in terms of θo, where 0 ≤ θo < 27 and in radians, we can write:

θ = π/2 = (π/54) × 54 ≈ (0.0292) × 54 ≈ 1.58 radians

Therefore, the polar form of the rectangular coordinates (0, 6√3) with a positive value of r, over the interval 0 ≤ θo < 27 and in terms of radians, is (6√3, 1.58).

Answer:

A. 25

Step-by-step explanation:

1- See the length of XA

2- Divide length by 2

3- 50 divided by 2 equals 25

Answer:

Freind it's answer is B.25

Step-by-step explanation:

First you have to prove that the triangle XYZ and AYZ are congruent.

There we have YZ in common...

Angles XYZ and AYZ are given congruent...

Also angles XZY and AZY are given 90 degrees.....

Hence, Triangle XYZ is congruent to triangle AYZ....

So,XZ=AZ(Congruent Parts of Congruent Triangle)

Now,we have XZ+AZ=XA

So,XZ+AZ=50cm

=2XZ=50 or 2AZ=50

Hence,AZ=25cm

Here's your answer friend ...

Don't forget to follow....

The probability that the sample proportion will differ from the population proportion by greater than 4% is 0.990.

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

µ = p

The standard deviation of this sampling distribution of sample proportion is:

σ = √p(1-p)/n

The information provided is:

p = 0.14

n = 41

As the sample size is large, i.e n = 411 > 30. the central limit theorem can be used to approximate the sampling distribution of sampling proportion.

Compute the values of P(p^ - p >0.04) as follows:

P(p^ - p < 0.04) = P(p^-p/σ > 0.04/√0.14(1-0.14)/411

= P(Z>2.33)

= 0.990

Thus the probability that the sample proportion will differ from the population proportion by greater than 4% is 0.990

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Answer:

a. 2(^3 sqrt 3) - ^3 sqrt 18

Step-by-step explanation:

got it right on edge

\(\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}\)\(\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}\)\(2(\sqrt[3]{3})-\sqrt[3]{18}\) option (A)  is Correct.

The problem can be solved by following steps.

The expression given is \(\frac{6-3(\sqrt[3]{6})}{\sqrt[3]{9}}\)

So , The first step we will do is Rationalize the figure

= \(\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }}{\sqrt[3]{9}*\sqrt[3]{9} }\)

The product of radicals with the same index equals the radical of the product:\(\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9*9^2} }\)

Simplify using exponent with same base

\(a^{n}*a^{m} = a^{a+m}\)

= \(\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9^1+^2} }\)

Calculate the sum or difference: \(\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {\sqrt[3]{9^3} }\)

Simplify the radical expression: \(\frac{6-3(\sqrt[3]{6})*3 {\sqrt{9^2} }} {{9} }\)

Calculate the power : \(\frac{6-3(\sqrt[3]{6})*3 {\sqrt[3]{3} }} {{9} }\)

Cross out the common factor: \(\frac{6-3(\sqrt[3]{6})*3 {\sqrt[3]{3} }} {{3} }\)

Factor Greatest Common Factors : \(\frac{3*2\sqrt[3]{3}-\sqrt[3]{18} }{3}\)\(3*2\sqrt[3]{3}-\sqrt[3]{18}}\)

Reduce the fraction : \(2\sqrt[3]{3}-\sqrt[3]{18}}\)

Hence the First option is correct

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If -4 is a zero with multiplicity 1, then (x + 4) is a factor of the polynomial. Similarly, if 1 is a zero with multiplicity 2, then (x - 1)^2 is a factor of the polynomial. Therefore, we can write the polynomial in factored form as:

f(x) = a(x + 4)(x - 1)^2

where "a" is a constant that we need to determine.

To find "a", we use the fact that f(0) = -12. Substituting x = 0 into the equation above, we get:

f(0) = a(0 + 4)(0 - 1)^2

-12 = -4a

Solving for "a", we get:

a = 3

Therefore, the polynomial is:

f(x) = 3(x + 4)(x - 1)^2

Note that this polynomial has a zero at x = -4 (with multiplicity 1), a zero at x = 1 (with multiplicity 2), and f(0) = -12.

The part of exponent, x, will have the value 7/4 according to the expression of exponent.

As we see the base on both sides is same, concerning this we can equate the exponents for equal values on Left Hand Side and Right Hand Side of the equation.

5x + 9 = 9x + 2

Rearranging the equation for like terms on each side

9x - 5x = 9 - 2

Subtracting the values in each side of the equation to find the value of x

4x = 7

Rearrange the formula

x = 7/4

Hence, the value of x will be 7/4.

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Answer:

315

Step-by-step explanation:

→ Substitute the first equation into the second

a + 21a = 330

→ Simplify

22a = 330

→ Solve for a

a = 15

→ Multiply answer by 21

15 × 21 = 315

Answer:

12

Step-by-step explanation:

3x+5+49=90

3x+54=90

3x=90-54

3x=36

3x/36/3

x=12

In a wheel game with eight equally spaced sectors, Keisha's chances of winning a reward on both spins are 1/16.

Probability—the possibility that an occurrence will happen—is calculated by dividing here the same number of favorable outcomes by the total number of possible outcomes. A coin toss serves as the most simple instance. If you flip a coin, there are only two possible outcomes: heads or tails.

The spinners will get a reward each everytime she lands on white. She will spin the wheel twice.

Here, there are two instances of such color white in the wheel, and there are a total of eight sectors. the likelihood that white will appear in the spin for the first time is,

P = 2/8

P = 1/4

The second case's circumstances are the same. In this instance, the outcomes including both wheel revolutions are independent of one another.

According to the product rule, the likelihood that a white sector will both spin and emerge is,

P = 1/4 * 1/4

P = 1/16

In a wheel game with eight equally spaced sectors, Keisha has a 1/16 chance of winning a reward on both spins.

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The complete question is-

Keisha is playing a game using a wheel divided into eight equal sectors, as shown in the diagram. Each time the spinner lands on white, she will win a prize. If she spins this wheel twice, what is the probability she will win a prize on both spins? Please show all steps!

Answer:

The second option

Step-by-step explanation:

Since root 16 is an integer (4), the second option produces the fraction 4/5 which is rational.

75% of the beads are green in color.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Chase ordered a set of beads

He received 4,000 beads in all.

3,000 of the beads were green.

We need to find the  percentage of the beads were green of 4000.

x/100×4000=3000

40x=3000

Divide both sides by 40

x=75%

Hence, 75% of the beads are green in color.

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