Consider this equation. (4x)1/3 - x = 0 The first step in solving this equation is to ___The second step is to ____ Solving this equation for x initially yields _____ Checking the solutions shows that _____

Answer:

The zeros are 0, 4, 6.

The y-intercept is 0.

Step-by-step explanation:

f(x) = x^3 - 10x^2 + 24x

x^3 - 10x^2 + 24x = 0

x(x^2 - 10x + 24) = 0

x(x - 4)(x - 6) = 0

x = 0 or x - 4 = 0 or x - 6 = 0

x = 0 or x = 4 or x = 6

y-intercept:

Since x = 0 is a root, that means that the point (0, 0) is part of the function. That makes the y-intercept 0.

You can also solve for the y-intercept by letting x = 0 in the function and solving for f(0).

Let x = 0.

f(0) = 0^3 - 10(0^2) + 24(0)

f(0) = 0

y-intercept: 0

The total cost of producing 8 widgets is $34.

In Mathematics and Geometry, the standard form of a quadratic function is represented by the following equation;

ax² + bx + c = 0

Next, we would create a system of equation by using the data points provided above;

a(2)² + b(2) + c = 16

4a + 4b + c = 16    .....equation 1.

a(4)² + b(4) + c = 18

16a + 4b + c = 18    .....equation 2.

a(10)² + b(10) + c = 48

100a + 10b + c = 48    .....equation 3.

By solving the system of equations simultaneously, the values of a, b, and c are as follows;

a = 1/2

b = -2

c = 18

Therefore, the required quadratic function in standard form is given by;

ax² + bx + c = 0

c(x) = 1/2(x)² - 2x + 18

For the total cost of 8 widgets, we have:

c(8) = 1/2(8)² - 2(8) + 18

c(8) = 1/2 * 64 - 16 + 18

c(8) = 32 - 16 + 18 = 34

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Complete Question:

Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x. The company also discovered that it costs $16 to produce 2 widgets, $18 to produce 4 widgets, and $48 to produce 10 widgets.

Find the total cost of producing 8 widgets.

Based on the two-tangent theorem, the value of x is calculated in the circle as: x = 2.

Based on the two-tangent theorem, if two tangents are drawn from a circle to meet each other at any point outside the circle, then the lengths of the tangents are congruent to each other, that is, they are equal.

Therefore, we would create the following equation based on the two-tangent theorem:

20x + 6 = 10x + 26

Combine like terms:

20x - 10x = -6 + 26

10x = 20

Divide both sides by 10:

10x/10 = 20/10

x = 2

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Answer:

1) 4^2 = 16

2) 4^(-2)= 2

3) 3^4 x 3^2 = 3^6  = 729

6) x^5/x^2 = x^3

7) (2^5)^3 = 2^15 = 32768

8) (x^2)^3 = x^6

Answer: 16, 16, 6³the 3 above is a 6, x³, 6³this 3 above is also a five, x³ The 3 above is a 5

Step-by-step explanation: the exponents above are adding and the regular numbers are multipling.

For the transformation at -78 °C, appropriate reagents include lithium aluminum hydride (LiAlH4) and diethyl ether.

At -78 °C, certain chemical reactions require the use of specific reagents to achieve the desired transformation. One commonly used reagent is lithium aluminum hydride (LiAlH4), which acts as a strong reducing agent. It is capable of reducing various functional groups, such as carbonyl compounds, to their corresponding alcohols.

Diethyl ether is typically employed as a solvent to facilitate the reaction and ensure efficient mixing of the reactants. Researchers often utilize this low temperature for reactions involving sensitive or reactive intermediates, as it helps control the reaction and prevent unwanted side reactions.

The use of LiAlH4 and diethyl ether provides a reliable combination for achieving the desired transformation at this temperature, enabling chemists to manipulate and modify compounds in a controlled manner.

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Answer:

a. (x+y)=-7

a.(x-y)= 1

b. 9-16= -7

Answer:

sine (78°) = 714 / side c

side c = 714 / sine (78°)

side c = 714 /  0.97815

side c = 729.95

Step-by-step explanation:

"Yes, there is." The coordinates of point P are either (11/4, 63) or (73/52, 36), depending on the chosen value of x.

We can use the distance formula to find the distance between R and P, and between P and S:

Distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the values, we get:

RP = √((x - (-3))² + (y - 1)²)

SP = √((x - 4)² + (y - 3)²)

Now, we can set up an equation based on the given ratio of RP to SP:

RP/SP = 5/4

We can substitute the expressions we just derived for RP and SP into this equation:

√((x - (-3))² + (y - 1)²) / √((x - 4)² + (y - 3)²) = 5/4

Squaring both sides of the equation to eliminate the square roots, we get:

((x - (-3))² + (y - 1)²) / ((x - 4)² + (y - 3)²) = 25/16

Expanding the squares and simplifying, we get:

41x² - 146x - 191y² + 1210y + 2900 = 0

For simplicity, let's solve for y:

y = (73x + 2900)/191

Now we can substitute this expression for y into one of the original equations:

RP = √((x - (-3))² + ((73x + 2900)/191 - 1)²)

Simplifying this expression, we get:

RP = √(1049x² - 12212x + 36010)/191

We want RP to be 5x units long, so we can set up the equation:

√(1049x² - 12212x + 36010)/191 = 5x

Squaring both sides, we get:

Expanding the square and simplifying, we get:

1044x² - 12212x + 36010 = 0

Now we can solve for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1044, b = -12212, and c = 36010. Plugging in these values, we get:

x = (-(-12212) ± √((-12212)² - 4(1044)(36010))) / 2(1044) x = (12212 ± √(5924688)) / 2088 x = (12212 ± 3864) / 2088

This gives us two possible values for x:

x = 11/4 or x = 73/52

Now we can substitute each value of x back into the expression we derived for y:

y = (73x + 2900)/191

For x = 11/4, we get:

y = (73(11/4) + 2900)/191 = 63

So one possible set of coordinates for P is (11/4, 63).

For x = 73/52, we get:

y = (73(73/52) + 2900)/191 = 36

So another possible set of coordinates for P is (73/52, 36).

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The purpose of controlling is to monitor performance and take corrective action as needed to ensure that objectives are met.

Performance refers to how effective or successful someone or something is in doing something. The capacity of a corporation to adopt optimal organization with the goal of providing a product or service that satisfies the expectations of consumers and customers determines business performance, which is strongly related to commercial effectiveness. Employee Engagement and Productivity are Improved by Performance Management. Employees who are actively involved in their work environments stay longer and produce better outcomes. Increasing employee engagement is essential to increasing output and maximizing return on investment.

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v + w and v - w are orthogonal.

To show that v + w and v - w are orthogonal, we need to show that their dot product is zero.

We have:

(v + w) . (v - w) = ||v||^2 - ||w||^2

Now, since ||v|| = ||w||, we can simplify this to:

(v + w) . (v - w) = 0

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Answer:

9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

9

Answer: 2.48%

..................................................

Therefore, h(x, y) = 49x^3 - 294x^2y + 441xy^2 - 252x^2 + 252xy - 588y^2 + 294x - 252y - 1764.

To find h(x, y) = g(f(x, y)), we first need to evaluate f(x, y) and then use the result as input for g(t).
Starting with f(x, y), we have:
f(x, y) = 7x - 6y - 42
Next, we need to use this as input for g(t), which is defined as:
g(t) = t^2*t
Substituting f(x, y) for t, we get:
g(f(x, y)) = (7x - 6y - 42)^2*(7x - 6y - 42)
Simplifying this expression, we can expand the square and get:
h(x, y) = 49x^3 - 294x^2y + 441xy^2 - 252x^2 + 252xy - 588y^2 + 294x - 252y - 1764
Therefore, h(x, y) = 49x^3 - 294x^2y + 441xy^2 - 252x^2 + 252xy - 588y^2 + 294x - 252y - 1764.

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Answer:184yards

Step-by-step explanation:

First of all, the formulae for finding the perimiter is 2xlength + 2xwidth

which can also be written as 2l + 2w

solution:

=2l + 2w

=2x33 + 2x59

=66 + 118

= 184

Therefore the perimeter of the rectangle is 184yards.

Given, the function is f(x,y,z)=5+yxz+g(x,z)Here, we need to find the directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) . The directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is 0.

Using the formula of the directional derivative, the directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is given by

(f(x,y,z)) = grad(f(x,y,z)).v

where grad(f(x,y,z)) is the gradient of the function f(x,y,z) and v is the direction vector.

∴ grad(f(x,y,z)) = (fx, fy, fz)

                       = (∂f/∂x, ∂f/∂y, ∂f/∂z)

Hence, fx = ∂f/∂x = 0 + yzg′(x,z)fy

                = ∂f/∂y

                = xz and

fz = ∂f/∂z = yx + g′(x,z)

We need to evaluate the gradient at the point (3,0,3), then

we have:fx(3,0,3) = yzg′(3,3)fy(3,0,3)

                             = 3(0) = 0fz(3,0,3)

                             = 0 + g′(3,3)

                             = g′(3,3)

Therefore, grad(f(x,y,z))(3,0,3) = (0, 0, g′(3,3))Dv(f(x,y,z))(3,0,3)

                                                 = grad(f(x,y,z))(3,0,3)⋅v

where, v = (0,4,0)Thus, Dv(f(x,y,z))(3,0,3) = (0, 0, g′(3,3))⋅(0,4,0)   = 0

The directional derivative of f at the point (3,0,3) along the direction of the vector (0,4,0) is 0.

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Answer: 4,700

Step-by-step explanation: 678 is above 650, meaning it is closer to 700 than it is 600

so rounding this makes it 4,700

unless you meant it as a decimal which 4.678 would result in 4.68 since the 8 before 7 would round up the 7 to an 8 making it 4.68

Hope this helps ^_^

Answer:

It's 4,700.

Step-by-step explanation:

When rounding to the nearest hundred, we use the following rules:

1) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

2) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.

3) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

Answer:

C = 5b + 3m

Step-by-step explanation:

Answer:

5b + 3m

Step-by-step explanation:

If b represents the cost of a book, then 5b will represent the cost of 5 books

If m represents the cost of a magazine, then 3m will represent the cost of 3 magazines.

To create an expression for the total cost, add these terms together:

5b + 3m

So, the expression for the total cost is 5b + 3m

Answer:

6 days

Step-by-step explanation:

Because they do not support survival and reproduction, undesirable features are chosen against and inherited less frequently over time.

By examining the connection between natural selection and evolution, Darwin's theory of evolution is examined. Controlling natural selection in an interactive population will help you achieve this. Each species displays.

For instance, while some beetles are brown, others are green. Not every member of a population will live long enough to reproduce. Those that do pass on their traits to their progeny.

Evolution and Natural Selection A species' members do not all resemble one another. Each species displays. For instance, while some beetles are brown, others are green. Not every member of a population will live long enough to reproduce. Those that do pass on their traits to their progeny.

Because they do not support survival and reproduction, undesirable features are chosen against and inherited less frequently over time.

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Critical values of the function f(θ) = 2cos(θ) +(sin(θ))² on the interval 0≤ θ < 2π is 0 and π.

Therefore, the answer is 0 and π.

f(θ) = 2cos(θ) +(sin(θ))²

f'(θ) = -2sin(θ) +2sin(θ)cos(θ)

Critical values of f are points at which f' is zero or not defined.

For all values of θ, we can find that f'(θ) is defined.

f'(θ) = 0

-2sin(θ) +2sin(θ)cos(θ) = 0

cos(θ) - 1 = 0 or sin(θ) = 0

cos(θ) = 1

θ = nπ, n = 0, 1, 2, ...

sin(θ) = 0

θ = nπ, n = 0, 1, 2, ...

Therefore in the interval 0 ≤ θ < 2π, critical values are 0 and π.

2π is not there as it is not included in the interval.

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Answer:

1.1

Step-by-step explanation:

Answer:

3 terms

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is the part of the circle to reflect the education pie.

25% of the circle is:

The integral Pπ/4 tan4(0) sec²(0) de is equal to 0. The integral Pπ/4 tan4(0) sec²(0) de can be evaluated using the following steps:

1. Use the identity tan4(0) = (4tan²(0) - 1).

2. Substitute u = tan(0) and du = sec²(0) de.

3. Use integration in the following formula: ∫ uⁿ du = uⁿ+1 / (n+1).

4. Substitute back to get the final answer.

Here are the steps in more detail:

We can use the identity tan4(0) = (4tan²(0) - 1) to rewrite the integral as follows:

∫ Pπ/4 (4tan²(0) - 1) sec²(0) de

We can then substitute u = tan(0) and du = sec²(0) de. This gives us the following integral:

∫ Pπ/4 (4u² - 1) du

We can now integrate using the following formula: ∫ uⁿ du = uⁿ+1 / (n+1). This gives us the following:

Pπ/4 (4u³ / 3 - u) |0 to ∞

Finally, we can substitute back to get the final answer:

Pπ/4 (4∞³ / 3 - ∞) - (4(0)³ / 3 - 0) = 0

Therefore, the integral Pπ/4 tan4(0) sec²(0) de is equal to 0.

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Researchers conducted a study and obtained  the p-value is 0.30, which is higher than the common significance level of 0.05. This means that there is not enough evidence to reject the null hypothesis, but it does not mean that the null hypothesis is accepted.

Hence this statement is false.

When researchers conduct a study and obtain a p-value, they use it to make a decision regarding the null hypothesis.

However, a high p-value does not provide evidence to accept the null hypothesis.

Instead, it indicates that there is not enough evidence to reject the null hypothesis.
1. Researchers start with a null hypothesis (H0), which is a statement that there is no effect or relationship between variables being studied.

They also have an alternative hypothesis (H1), which is a statement that there is an effect or relationship between variables.
2. They collect data and perform statistical tests to calculate the p-value, which represents the probability of observing the test results (or more extreme results) assuming the null hypothesis is true.
3. The p-value is then compared to a pre-determined significance level (alpha), commonly set at 0.05 or 5%.

If the p-value is less than the significance level, researchers reject the null hypothesis in favor of the alternative hypothesis.
4. In this case, the p-value is 0.30, which is higher than the common significance level of 0.05.

This means that there is not enough evidence to reject the null hypothesis, but it does not mean that the null hypothesis is accepted.
5. Instead, researchers should say that they "fail to reject" the null hypothesis, meaning they cannot confidently conclude that the alternative hypothesis is true based on the data and analysis.

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Answer:

d. y=8x

Step-by-step explanation:

since y = the number of legs and spiders = x

each spider has 8 legs

so y = 8*x

which is y=8x

Answer:

About 11.4

Step-by-step explanation:

There are 3.78541178 liters in a gallon.

Round that up to the nearest 100 and you get 3.8

Multiply 3.8 by 3.

You get 11.4

$592 is the minimum cost in dollars for a fair to be included in the highest 3% of domestic airfares. Using the concept of probability -

Probability is a mathematical discipline that concerns with numerical figures of how probable an occurrence is to occur or how probably a statement is to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Mean – 385 per ticket

Standard Deviation - 110

Now,

P (Z > x ) = 0.03

Value of z to the cumulative probability of 0.03 from the normal distribution table is 1.88

P(x - u / (standard deviation) > x - 385/110) = 0.03

That is, (x - 385/110) = 1.88

Therefore, x = 1.88 ×( 110+385)

= 591.91 or $592

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