Complete the steps to identify all potential rational roots of f(x) = 3x2 – x – 4.

Values of p are factors of
.
Values of q are factors of
.

Use the drop-down menus to complete the solution to the equation cosine (start fraction pi over 2 end fraction minus x) = start fraction start root 3 end root over 2 end fraction for all possible values of x on the interval [0, 2pi].

Using trigonometric identities, the solution to the equation \(cos(\frac{\pi }{2}-x) = \frac{\sqrt{3} }{2}\) for all possible values of x on the interval [0, 2π].

What are trigonometric identities?

Trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.

\(cos(\frac{\pi }{2}-x) = \frac{\sqrt{3} }{2} \\\\cos(x)cos\frac{\pi }{2}+sin(x)sin \frac{\pi }{2} = \frac{\sqrt{3} }{2}\\\\cos(x)(0)+sin(x)(1) = \frac{\sqrt{3} }{2}\\\\sin(x) = \frac{\sqrt{3} }{2}\\\\x = \frac{\pi }{3}, \frac{2\pi }{3}\)

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Answer: 24 days

Step-by-step explanation:

Takes her 4 days to read 1/2 of a 200 page book, or 100 pages.

4 days = 100 pages

X days = 600 pages

24 days = 600 pages

Answer: 22.5625

Step-by-step explanation: 4.75^2 squared is the same thing

Hey there! I'm happy to help!

Sum means to add. Let's call our number n.

n+15

We multiply this whole thing by 6.

6(n+15)

And this is -42.

6(n+15)=-42

We use distributive property to undo the parentheses.

6n+90=-42

We subtract 90 from both sides.

6n=-132

We divide both sides by 6.

n=-22.

Have a wonderful day! :D

The $3 per unit subsidy will increase consumer surplus, decrease producer surplus, and increase total surplus. The $8 price floor will decrease consumer surplus, increase producer surplus, and decrease total surplus.

(a) To find the effect of a $3 per unit subsidy, we need to compare the equilibrium price and quantity before and after the subsidy. In the absence of the subsidy, the equilibrium price is determined by setting the demand equation equal to the supply equation:

7 - 0.5P = -2 + P

Solving for P, we find the equilibrium price P_eq = $5. The equilibrium quantity can be obtained by substituting this price back into either the supply or demand equation:

Q_eq = -2 + P_eq = -2 + 5 = 3 units

With the $3 per unit subsidy, the supply equation becomes Q = -2 + P - 3 = -5 + P. The new equilibrium price and quantity are determined by setting the demand equation equal to the new supply equation:

7 - 0.5P = -5 + P

Solving for P, we find P_subsidy = $6. The equilibrium quantity can be obtained by substituting this price back into the supply equation:

Q_subsidy = -5 + P_subsidy = -5 + 6 = 1 unit

To calculate the effects on consumer surplus (CS), producer surplus (PS), and total surplus (TS), we need to compare the areas of the relevant triangles. Before the subsidy, CS is the area above the demand curve and below the equilibrium price, PS is the area below the supply curve and above the equilibrium price, and TS is the sum of CS and PS. After the subsidy, CS expands, PS contracts, and TS increases.

(b) To find the effect of a $8 price floor, we need to compare the equilibrium price and quantity before and after the price floor. In the absence of the price floor, the equilibrium price and quantity remain the same as calculated in part (a): P_eq = $5 and Q_eq = 3 units.

With the $8 price floor, the market price cannot fall below $8. If the price floor is above the equilibrium price, it does not have any effect on the market. In this case, the price floor is below the equilibrium price, so it becomes binding. The new equilibrium price and quantity are determined by setting the supply equation equal to the price floor:

-2 + P_floor = 8

Solving for P_floor, we find P_floor = $10. The equilibrium quantity remains the same as Q_eq = 3 units.

To calculate the effects on CS, PS, and TS, we compare the areas of the relevant triangles. Before the price floor, CS is the area above the demand curve and below the equilibrium price, PS is zero because no units are being supplied, and TS is equal to CS. After the price floor, CS contracts, PS expands to include the entire area below the price floor and above the equilibrium quantity, and TS decreases.

In conclusion, the $3 per unit subsidy increases consumer surplus, decreases producer surplus, and increases total surplus. On the other hand, the $8 price floor decreases consumer surplus, increases producer surplus, and decreases total surplus. These effects can be visualized by comparing the areas of the relevant triangles in each scenario.

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To find the orthogonal projection of a vector onto a subspace, we can use the formula:

projᵥ(u) = A(AᵀA)⁻¹Aᵀᵤ,

where A is a matrix whose columns span the subspace, and u is the vector we want to project.

In this case, the subspace W is spanned by the vector v = [0, 0, 0, 1].

Let's calculate the orthogonal projection of u onto W using the formula:

A = [v]

The transpose of A is:

Aᵀ = [vᵀ].

Now, let's substitute the values into the formula:

projᵥ(u) = A(AᵀA)⁻¹Aᵀᵤ

= v⁻¹[vᵀ]u

= [v][(vᵀv)⁻¹vᵀ]u

Substituting the values of v and u:

v = [0, 0, 0, 1]

u = [1, 0, 0, 0]

vᵀv = [0, 0, 0, 1][0, 0, 0, 1] = 1

[(vᵀv)⁻¹vᵀ]u = (1⁻¹)[0, 0, 0, 1][1, 0, 0, 0] = [0, 0, 0, 1][1, 0, 0, 0] = [0, 0, 0, 0]

Therefore, the orthogonal projection of u onto the subspace W is [0, 0, 0, 0].

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Given the following function::

We will find the interval on which the function will be concave down

We need to find the critical points (Minimum, Maximum or Inflection )

We will find f'(x) and f''(x):

From f'(x) = 0 ⇒ we will get the minimum and the maximum points:

From, f''(x) = 0 ⇒ we will get the inflection points

So, we can conclude the following:

There is two inflection points x = 0, x = 2

And the function has a minimum at x = 3

So, as x > 2 the function will be concave up

So, the function from x = 0 to x = 2, will be concave down

So, the answer will be: C. (0, 2)

A z-score represents the number of standard deviations a data point is away from the mean. A score that is 2.5 standard deviations below the mean would have a z-score of -2.5 that is option D.

A z-score is a statistical measure that indicates how many standard deviations a particular data point is away from the mean of a distribution. It is calculated using the formula:

z = (x - μ) / σ

Where:

z is the z-score,

x is the value of the data point,

μ is the mean of the distribution, and

σ is the standard deviation of the distribution.

If a score is 2.5 standard deviations below the mean, it means that the value of x is 2.5 times the value of σ below the mean. In other words, it is located in the left tail of the distribution.

Since the z-score represents the number of standard deviations away from the mean, a score that is 2.5 standard deviations below the mean would have a z-score of -2.5. The negative sign indicates that the score is below the mean.

So, if we substitute the values into the z-score formula:

z = (x - μ) / σ

-2.5 = (x - μ) / σ

This equation represents the z-score being -2.5, indicating that the score is 2.5 standard deviations below the mean.

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The probability that it is a hardcover or a reference book  will be 0.37. in other words, the probability is the number that shows the happening of the event.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes,

Event H; Selected base is hardcover

R;Selected book is a reference book

\(\rm P(H)= 0.28 \\\\ P(R)=0.22 \\\\\)

P(H∩R)=0.13

The probability that it is a hardcover or a reference book;

P(H∪R)=P(H)+P(R)-P(H∩R)

P(H∪R)=0.28+0.22-0.13

P(H∪R)=0.37

Hence, the probability that it is a hardcover or a reference book will be 0.37.

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The number of years it would take Becky to double the amount invested is 10 years.

The rule of 70 is a rule of thumb that is used to know the number of years it would take an investment to double at the interest rate. The formula entails dividing 70 by the interest rate.

Rule of 70 = 70 / interest rate

70 / 7 = 10 years

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Answer:

Step-by-step explanation:

The function for this case would be:

If we need the money to double, the return rate should be 100%:

Answer:

\(\displaystyle \frac{\pi}{3}\)  radians

Step-by-step explanation:

As an equilateral triangle has all angles congruent to each other, each angle is measured 60°

To convert from degrees to radians, we multiply by π/180

Hence, \(\displaystyle 60^\circ*\frac{\pi}{180}=\frac{60\pi}{180}=\frac{\pi}{3}\)

The total area of the solid figure is 90 square inches + 27sqrt(3) / 4 square inches.

To find the total area of the solid figure, we need to determine the areas of each face and then add them together.

The solid figure consists of a rectangular prism with dimensions 3" x 3" x 6" and a pyramid on top with an equilateral triangle base.

First, let's find the area of the rectangular prism. The rectangular prism has two identical square faces with side length 3" and four rectangular faces with dimensions 3" x 6". The total area of the rectangular prism can be calculated as:

Area of the square faces: 2 * (3" * 3") = 2 * 9 square inches

Area of the rectangular faces: 4 * (3" * 6") = 4 * 18 square inches

Total area of the rectangular prism: 2 * 9 + 4 * 18 = 18 + 72 = 90 square inches.

Next, let's find the area of the triangular pyramid. The base of the pyramid is an equilateral triangle with side length 3". The height of the pyramid is 3". The formula to find the area of an equilateral triangle is (sqrt(3) / 4) * (side length)^2. Plugging in the values, we have:

Area of the triangular pyramid: (sqrt(3) / 4) * (3" * 3") * 3" = (sqrt(3) / 4) * 9 * 3 = (sqrt(3) / 4) * 27 = 27sqrt(3) / 4 square inches.

Now, we can find the total area of the solid figure by adding the area of the rectangular prism and the area of the triangular pyramid:

Total area = Area of rectangular prism + Area of triangular pyramid

Total area = 90 square inches + 27sqrt(3) / 4 square inches.

Thus, the total area of the solid figure is 90 square inches + 27sqrt(3) / 4 square inches.

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The average credit card debt for a public school teacher is μ = 14,975 pesos and the standard deviation is σ = 5,650 pesos.

Find the probability that the teacher owes at least 6,740 pesos.

Let X be the random variable representing the credit card debt that a public school teacher has.

Then, X ~ N(14975, 5650) which means that X is normally distributed with a mean 14,975 and a  standard deviation of  5650.

Find the probability that the teacher owes at least 6,740 pesos.

This can be represented as P(X ≥ 6740).

Use the z-score formula which is given by z = (X - μ) / σ,

where X is the credit card debt, μ is the mean, σ is the standard deviation and z is the z-score corresponding to X.

So, substituting the given values,

z = (6740 - 14975) / 5650= -0.8912 (approx)

Using the z-table, the probability corresponding to this z-score is P(Z ≤ -0.8912) = 0.1866 (approx).

Therefore,P(X ≥ 6740) = 1 - P(X < 6740)= 1 - P(Z ≤ -0.8912) = 1 - 0.1866= 0.8134 (approx).

Hence, the probability that the teacher owes at least 6,740 pesos is approximately 0.8134.

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\(\frac{1}{4}x + 2 = -3 + \frac{1}{2} x\)

First, we will take \(\frac{1}{4}\)x to the right hand side of the equation, and -3 to the left hand side. In doing so, their signs will change (that is, they will be subtracted from the side that they are moved to).

2 -(-3) = \(\frac{1}{2} x - \frac{1}{4} x\)

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

\(\frac{1}{4} x = 5\)

Now, we will multiply both sides by 4, so as to find x.

\(\frac{1}{4} x\) x 4 = 5 x 4

x = 20

Therefore, x = 20.

Answer:

-4/7 - 7.83673469388x

Step-by-step explanation:

-4/7 + 2/7x - 14x × 4/7

2/7x - 14x

-4/7 + -13.7142857143x × 4/7

-4/7 -7.83673469388x

The value of x  for The quadrilateral which is a trapezoid is if the top is 21 and the bottom is 27 is option 2 that is 5.

Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides.

From the given diagram, the expression below is true:

2(5x - 1) = 21 + 27

Expand

10x - 2 = 48

10x = 48 + 2

10x = 50

Divide both sides by 10

10x.10 = 50/10

x = 5

Hence the value of x is 5

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The value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

The history of pi dates back thousands of years, and over time, various civilizations have attempted to calculate its value with varying degrees of accuracy. One of the most inaccurate versions of pi was recorded by the ancient Babylonians around 2000 BC.

The Babylonians calculated the value of pi as 3.125, which is off by more than 6% from the actual value. It is believed that the Babylonians arrived at this value by using a rough approximation of a circle as a hexagon. They measured the perimeter of the hexagon and divided it by the diameter to get their approximation of pi.

This value was later refined by the ancient Egyptians and Greeks, who were able to calculate pi with greater accuracy. The Greek mathematician Archimedes, for instance, was able to calculate pi to within 1% accuracy by using a method of exhaustion.

It wasn't until the development of calculus in the 17th century that mathematicians were able to derive an exact formula for pi. Today, the value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

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the function y = f(x) that satisfies the given conditions is y = 2x^3 - x^2 - 5x + C2, where C2 is a constant that can take any real value.

First, integrate y' with respect to x to find the first derivative y:

∫(y') dx = ∫(12x - 2) dx

y = 6x^2 - 2x + C1

Next, integrate y with respect to x to find the function f(x):

∫y dx = ∫(6x^2 - 2x + C1) dx

f(x) = 2x^3 - x^2 + C1x + C2

To determine the specific values of C1 and C2, we use the given condition that the line y = -x + 5 is tangent to the graph at x = 1.

Since the tangent line has the same slope as the function f(x) at x = 1, we can equate their derivatives:

f'(1) = -1

Taking the derivative of f(x), we have:

f'(x) = 6x^2 - 2x + C1

Substituting x = 1 and equating f'(1) to -1, we can solve for C1:

6(1)^2 - 2(1) + C1 = -1

6 - 2 + C1 = -1

C1 = -5

Now we have the values of C1 and C2. Plugging them back into the equation for f(x), we obtain the final function:

f(x) = 2x^3 - x^2 - 5x + C2

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A major disadvantage of correlations is that they cannot make a cause-and-effect statement.

Correlations are statistical measures that describe the size and direction of a relationship between variables.

Correlations are expressed as numbers. Correlations establish that relationships exist but do not explain if the change in one variable is caused by the change in another variable's value.

The disadvantages of correlations include:

Thus, a major disadvantage of correlations is that they cannot make a cause-and-effect statement.

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Answer:

-a+9c-2

Step-by-step explanation:

4a+7c-2-5a+2c

Collect like terms

=4a-5a+7c+2c-2

= -a+9c-2

Therefore: a. The current ratio is approximately 1.68. b. The quick ratio is approximately 0.80. a. Current ratio times is approximately $6,229.68. b. Quick ratio times is approximately $2,968.00.

To calculate the current ratio and quick ratio for SDJ, Inc., we'll use the following formulas:

Current Ratio = Current Assets / Current Liabilities

Quick Ratio = (Current Assets - Inventory) / Current Liabilities

Given the information:

Net Working Capital = $3,710

Current Liabilities = $5,500

Inventory = $4,440

a. Current Ratio:

Current Assets = Net Working Capital + Current Liabilities

Current Assets = $3,710 + $5,500 = $9,210

Current Ratio = Current Assets / Current Liabilities

Current Ratio = $9,210 / $5,500

Current Ratio ≈ 1.68

b. Quick Ratio:

Quick Ratio = (Current Assets - Inventory) / Current Liabilities

Quick Ratio = ($9,210 - $4,440) / $5,500

Quick Ratio ≈ 0.80

a. Current ratio times:

Current Ratio times = Current Ratio * Net Working Capital

Current Ratio times = 1.68 * $3,710

Current Ratio times ≈ $6,229.68

b. Quick ratio times:

Quick Ratio times = Quick Ratio * Net Working Capital

Quick Ratio times = 0.80 * $3,710

Quick Ratio times ≈ $2,968.00

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Answer:

48 wings

Step-by-step explanation:

12:3 is the ratio. So multiply both of it by 4. Then it would be 48:12

Answer:

48 chicken wings

Step-by-step explanation:

If Bao can eat 12 chicken wings in 3 minutes and 12 minutes is 3 minutes times 4, then the answer would be 12 chicken wings times 4, so 12 times 4, which is 48, so the answer would be 48 chicken wings.

Answer:

x =149

Step-by-step explanation:

Answer:

X=149

Step-by-step explanation:

77+72=149

The probability that a randomly selected child takes more than two minutes to eat a donut given that the child has already been eating the donut for more than 1.5 minutes is approximately 0.5714 or 57.14%.

To calculate the probability that a randomly selected child takes more than two minutes to eat a donut given that the child has already been eating the donut for more than 1.5 minutes, we need to find the conditional probability.

Let's denote:

A = Event that a child takes more than two minutes to eat a donut

B = Event that a child has already been eating the donut for more than 1.5 minutes

We want to calculate P(A|B), which represents the probability of event A occurring given that event B has already occurred.

The time it takes a child to eat a donut is uniformly distributed between 0.5 and 4 minutes, inclusive. Since the distribution is uniform, the probability density function (PDF) is constant within the interval.

To find P(A|B), we need to consider the intersection of events A and B, which corresponds to the portion of the time interval where both conditions are satisfied. In this case, the intersection is the interval from 2 minutes to 4 minutes.

The length of the entire time interval is 4 - 0.5 = 3.5 minutes.

The length of the intersection interval is 4 - 2 = 2 minutes.

Therefore, P(A|B) = (length of intersection interval) / (length of entire interval) = 2 / 3.5 ≈ 0.5714.

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Answer: Not reasonable

Answer:

No, it isn't a reasonable scale.

Step-by-step explanation:

if the scale is 1in=4in then  12 by 24 paper should equal a 48 by 96 painting. That is not the case since the painting is 48 by 120.

A more appropriate scale for a 1=4 ratio would be 12 by 30.

I hope this helps!

To show that (x)^0 for all x in the interval of convergence, we need to select the correct answer option among (a), (b), and (c), which provide explanations for why (x)^0 holds true.

The correct answer is (a) "(x)^0 because of explanation here and 0 for all x." However, the explanation is missing from the given options, so we cannot determine the specific reasoning behind it. In general, any non-zero number raised to the power of 0 is equal to 1. Therefore, (x)^0 is equal to 1 for all x, regardless of the specific function or expression. This is a fundamental property of exponentiation and holds true for any valid value of x within the interval of convergence.

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Answer:

7.626

Step-by-step explanation: thousandths place is 3 from the decimal point

\(7.6258\) rounded to the nearest thousandths would be written as:

\(\fbox{7.626}\)

The 5 in the thousandths place would be rounded to 6 because the digit in the ten thousandths place is 8. If the digit is over 5, it is rounded away from zero.