Select the correct answer.
If the zeros of a quadratic function are 3 and 8, what are the factors of the function?
ОА. .
(X + 8) and (x-3)
OB.
(x - 8) and (x + 3)
ОС.
(X + 8) and (x + 3)
OD
(x-8) and (x-3)

Answer:

156

Step-by-step explanation:

48*39=1872

1872 / 12=156

The area of the region consisting of all points Charlyn can see during her walk is 49sq/km.

Algebra aids in the solution of mathematical problems and enables the derivation of unknown numbers, such as interest rates, ratios, and percentages. In order to recast the equations, we can express the associated unknown values using variables from algebra.

Given that, path visible = 1km

Each Side of the boundary = 5km long

This would be the same as having a 1 km border all the way around a 5km square, thus (5+2) * (5+2) = 49 sq/km

Hence, the area of the region consisting of all points Charlyn can see during her walk is 49 sq/km.

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The area of the region consisting of all points Charlyn can see during her walk is 49sq/km.

this is a question of algebra and solution is as follows: -

Given that, path visible = 1km

Each Side of the boundary = 5km long

This would be the same as having a 1 km border all the way around a 5km square, thus (5+2) * (5+2) = 49 sq/km

Hence, the area of the region consisting of all points Charlyn can see during her walk is 49 sq/km.

Algebra

Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

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The product of (3 x 107) and (2 x 107) is 6.8694 x 10^4

To find the product of (3 x 107)and (2 x 107), we can use the distributive property of multiplication which states that the product of a number and a sum is equal to the sum of the products of the number and each term in the sum. In this case, we can multiply the numbers outside the parentheses first, and then multiply the result by the common factor of 107 to simplify the expression:

(3 x 107) x (2 x 107) = 6 x (107 x 107)

Next, we can calculate the product of 107 and 107, which is 11,449:

6 x 11,449 = 68,694

In scientific notation, this can be written as:

= 6.8694 x 10^4

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Answer:

We can rewrite this problem as:What is 38% of 288?

"Percent" or "%" means "out of 100" or "per 100", Therefore 38% can be written as  

38 /100

When dealing with percents the word "of" means "times" or "to multiply".

Finally, lets call the number of pictures we are looking for "p".

Putting this altogether we can write this equation and solve for  p  while keeping the equation balanced:

p = 38 /100 × 288

p = 10944 /100  

p = 109

Step-by-step explanation:

With the concepts of percentages and calculations, the percent decrease in the number of people who went to the pool over these four weeks is 10%

Take the base as 100 and convert the percentage to numbers and then proceed with the same.

Now, the initial number of people in the local swimming pool is 1020, after which 100 fewer went, hence 920 people

Now, 135 people more people need to be added, thus 1055 people.

Now, 137 fewer people went, so 918 people went to the pool in the four weeks.

Therefore percent decrease = Difference/No. of people in the first week * 100

Thus, the percent decrease =  102/1020*100=10%

Hence 10% of people went less in the fourth week as compared to the first week.

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Answer:

The slope of a linear model can be calculated using the formula:

m = Δy / Δx

where:

Δy = change in y (the dependent variable, in this case, total cost)

Δx = change in x (the independent variable, in this case, number of candy bars)

This is essentially the "rise over run" concept from geometry, applied to data points on a graph.

In this case, we can take two points from the table (for instance, the first and last) and calculate the slope.

Let's take the first point (3 candy bars, $6.65) and the last point (25 candy bars, $48.45).

Δy = $48.45 - $6.65 = $41.8

Δx = 25 - 3 = 22

So the slope m would be:

m = Δy / Δx = $41.8 / 22 = $1.9 per candy bar

This suggests that the cost of each candy bar is $1.9 according to this linear model.

Please note that this assumes the relationship between the number of candy bars and the total cost is perfectly linear, which might not be the case in reality.

To display formulas, one way is to press the key combination [Ctrl]+[] (grave accent).

The key combination [Ctrl]+[] is used to display formulas.

This is a useful feature for checking and editing formulas without altering the calculated values.

By pressing [Ctrl]+[], users can easily view the underlying formulas and ensure their accuracy.

This key combination provides a convenient way to switch between the formula view and the results view, enabling efficient editing and troubleshooting of complex calculations.

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Answer:

y=4

Step-by-step explanation:

4y+2+y=4y+6

4y-4y+y=6-2

y=4

hope it helps

Answer:

4

Step-by-step explanation:

The chance of the event B is 0.4 when using the probability for the two independent two event formula.

In the given question, if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then we have to find the value of p(b).

Events classified as independent do not depend on other events for their occurrence.

Event A's likelihood of happening is P(A)=0.65.

The likelihood of the two events A and B intersecting is P(A∩B)=0.26.

Given that the likelihood of the two independent events is:

P(A∩B) = P(A)⋅P(B)

Then the probability of the event B will be,

P(B) = P(A)/P(A∩B)

P(B) = 0.65/0.26

P(B) =0.4

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Answer:

3 in.

Step-by-step explanation:

volume = ⅓πr²h

⅓πr²h=12π

r²h=36

r²=9

r = 3 inches

Answer:

because of the sec,min and hours

they rotate to complete 24:00

if it's angles to complete the revolution which is always out of 360

Step-by-step explanation:

.

Answer:

$1.98

Step-by-step explanation:

6%=0.06

33*0.06=1.98

Answer: Im not sure by yes maybe

Step-by-step explanation:

Answer:

2*(4y² + 9)

Step-by-step explanation:

    8y² = 2 * 2 * 2 * y²

    18   = 2 * 3 * 3

GCF = 2

8y² + 18 = 2* 4y² + 2*9

             = 2*(4y² + 9)

Using proportions, the costs are given as follows:

a) Total Labor Cost: $2,505,600.

b) Total Product Cost: $1,950,000.

c) Total Cost = $4,455,600.

d) Cost per home = $461.77.

e) Cost per week = $99,013.33.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For item a, the labor cost is found using the earnings of the workers, as follows:

45 weeks x 5 days x 8 hours x 58 per hour x (12 + 8 + 4 workers)

Hence:

Total Labor Cost = 45 x 5 x 8 x 58 x 24 = $2,505,600.

For item b, the product cost is the cost of the boards, hence:

(175 + 150 + 50 boards) x 5,200

Total Product Cost = 375 x 5,200 = $1,950,000.

For item c, the total cost is the sum of the product cost and the labor cost, hence:

Total Cost = 2,505,600 + 1,950,000 = $4,455,600.

For item d, the cost per home is found dividing the total cost by the 9,649 homes, hence:

Cost per home = 4455600/9649 = $461.77.

For item e, the cost per week is found dividing the total cost by the 45 weeks, hence:

Cost per week = 4455600/45 = $99,013.33.

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The integral for the area of the surface obtained by rotating the curve about the x-axis and the y-axis, are:

S = ∫[3,5] 2πxe−x√(1+(e−x−xe−x)²)dx and S = ∫[3e−3,5e−5] 2π(ln(y)/y)√(1+(1/y−ln(y)/y)²)dy respectively.

To set up the integral for the area of the surface obtained by rotating the curve about the x-axis and the y-axis, we need to use the formulas for surface area of revolution.

For rotation about the x-axis, the formula is:
S = ∫2πy√(1+(dy/dx)²)dx

For rotation about the y-axis, the formula is:
S = ∫2πx√(1+(dy/dx)²)dy

Plugging in the given curve y = xe−x and the bounds 3 ≤ x ≤ 5, we get:

For rotation about the x-axis:
S = ∫[3,5] 2πxe−x√(1+(e−x−xe−x)²)dx

For rotation about the y-axis:
S = ∫[3e−3,5e−5] 2π(ln(y)/y)√(1+(1/y−ln(y)/y)²)dy

These are the integrals that need to be evaluated to find the area of the surface obtained by rotating the curve about the x-axis and the y-axis.

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Managers, goods, services, and technology are all needed in developing countries, and therefore, they provide new markets for companies that can supply these essentials.

Developing countries often have growing economies and increasing consumer demands. As these countries strive for development and improvement, they require effective management to drive their businesses and organizations. Managers play a crucial role in overseeing operations, implementing strategies, and maximizing efficiency.

Additionally, developing countries require goods and services to meet the needs of their populations. This includes basic necessities such as food, clothing, and shelter, as well as other essential products and services like healthcare, education, infrastructure development, and transportation. Companies that can provide these goods and services have an opportunity to enter new markets and cater to the demands of the growing population.

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The probability that bin 1 contains exactly 3 balls would be 0.015. Probabilities can be expressed as fractions, decimals, or percentages, and they can be used to make predictions or to quantify uncertainty.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain. For example, if the probability of it raining tomorrow is 0.3, it means that there is a 30% chance of it raining tomorrow. In addition, probability theory is a branch of mathematics that studies the probability of events, and it plays an important role in many areas such as statistics, finance, and science.

The probability that bin 1 contains exactly 3 balls out of the 10 balls placed is given by the binomial probability mass function with parameters n = 10 and k = 3, and probability of success p = 1/20. Therefore, the probability is given by:

(10 choose 3) * \((1/20)^3\) * \((19/20)^7\) = 120 * (1/8000) * \((19/20)^7\) = 120/8000 = 0.015

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The measure of the segment xy of the given right angle triangle is; 36 units

This question can be best understood if the trigonometric ratios are briefly highlighted since it has been used in the question. Cos f is given as 4/9. We know that the cos of an angle is derived as the adjacent divided by the hypotenuse. In other words, the cosine of angle f is given as;

Cos f = Adjacent / Hypotenuse

Thus;

Cos f = 4/9

From the triangle shown in the attachment, the adjacent is XW while the hypotenuse is XY. Hence, the adjacent is 16 units and the hypotenuse is unknown. Since the measurements given in the question are a ratio of the original dimensions, the relationship can be expressed as follows;

4/9 = 16/XY

Where XY is the unknown side

By cross multiplication, you now arrive at,

4XY = 9 * 16

XY = 144/4

XY = 36

Therefore, XY measures 36 units

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Using the multiplication rule, the joint probability of event A and event B is computed by multiplying the conditional probability of event A given event B by the probability of event B.

Mathematically, it can be represented as P(A and B) = P(A|B) × P(B), where P(A|B) is the conditional probability of A given B, and P(B) is the probability of B.

In other words, the multiplication rule is used to compute the probability of two events occurring together, given the probability of one event occurring and the probability of the other event occurring given the first has occurred. This rule is widely used in probability and statistics to calculate the probability of complex events, especially in cases where events are not mutually exclusive.

For example, consider a scenario where we want to calculate the probability of getting two heads when flipping two coins. Using the multiplication rule, we can calculate this probability as follows: P(Two heads) = P(Head on first flip) × P(Head on second flip given the first flip was a head) = (1/2) × (1/2) = 1/4.

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Answer: the area of the shape=25.5 cm²

Step-by-step explanation:

This shape  is composed of a rectangle and a trapezoid

The area of the rectangle= 3(4)

The area of the rectangle= 12 cm²

\(\displaystyle\\The\ area\ of\ the\ trapezoid=\frac{3+6}{2} (7-4)\\\\The\ area\ of\ the\ trapezoid=\frac{9}{2} (3)\\\\The\ area\ of\ the\ trapezoid=4.5(3)\\\\The\ area\ of\ the\ trapezoid=13.5 \ cm^2\)

The area of the shape=12+13.5

The area of the shape=25.5 cm²

To find the derivatives of the given expressions, we can apply the chain rule, which states that the derivative of a composition of functions is equal to the derivative of the outer function multiplied by the derivative of the inner function.

(a) To find the derivative of f(g(x)), we start by differentiating the outer function f with respect to the inner function g(x), and then multiply it by the derivative of the inner function g(x) with respect to x.

df/dx = df/dg * dg/dx

df/dx = cos(g(x)) * (2x)

(b) To find the derivative of g(f(x)), we differentiate the outer function g with respect to the inner function f(x), and then multiply it by the derivative of the inner function f(x) with respect to x.

dg/dx = dg/df * df/dx

dg/dx = 2f(x) * cos(x)

Hence, the derivatives are:

(a) d/dx(f(g(x))) = cos(g(x)) * (2x)

(b) d/dx(g(f(x))) = 2f(x) * cos(x)

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The interest rate your friend is charging you for the $20,000 loan is 20% per year.

The simple interest is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is the interest rate and t is time.

Given that;

The Principal P = $20,000

Accrued amount A = $40,000

Elapsed time t = 5 years

Interest rate r =?

Plug these values into the above formula and solve for the interest rate r:

\(A = P( 1 + rt )\\\\r = \frac{1}{t}( \frac{A}{P} -1 ) \\\\r = \frac{1}{5}( \frac{40000}{20000} -1 ) \\\\r = \frac{1}{5}( 2 -1 ) \\\\r = \frac{1}{5}\\\\r = 0.2 \\\\\)

Converting r decimal to R a percentage

Rate R = 0.2 × 100%

Rate r = 20% per year

Therefore, the interest rate is 20% per year.

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With a 95% probability, 62 students should be sampled to be within 0.25 drinks of the population mean.

\(\alpha\) is the level obtained by subtracting 1 from the confidence interval and dividing by 2.

So,

\(\alpha\) = (1 - 0.95) ÷ 2 = 0.25

Now, find z in the Z-table, as z has a p-value of 1 - \(\alpha\).

As a result, z has a p-value of (1 - 0.025) = 0.975

so, z  = 1.96

Now, infer M as follows:

M = z × (σ ÷ √n) where n is the sample size and is σ the population standard deviation.

When M = 1, this is n.

According to the question, the standard deviation is roughly 1.

σ = 1

M = z × (σ ÷ √n)

0. 25 = 1.96 × (1 ÷ √n)

√n = 1.96 × (1 ÷ √n)

Square both sides,

(√n)² = ((1.96 × 1) ÷ 0.25)²

n = (7.84)²

n = 61.4656

n ≈ 62

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The expression that should appear in Line 2 is "40 x 3 + 8 x 3".

Line 2: 40 x 3 + 8 x 3

In line 1, the expression "43 x 8" is given as equal to "(40+3) x 8".

To find the expression in Line 2, we need to simplify the given expression.

Simplify the expression inside the parentheses in line 1.

(40 + 3) = 43

Substitute the simplified expression back into line 1.

43 x 8 = (43) x 8

Simplify the expression in line 2.

(43) x 8 = 40 x 3 + 8 x 3

Therefore, the expression that should appear in Line 2 is "40 x 3 + 8 x 3".

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The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

Answer:

\(t = \frac{1}{2} \)

Step-by-step explanation:

\(4(t + \frac{1}{4} ) = 3\)

\( = > 4t + 1 = 3\)

\( = > 4t = 3 - 1 = 2\)

\( = > t = \frac{2}{4} = \frac{1}{2} \)

Answer:

t = \(\frac{1}{2}\)

Step-by-step explanation:

Given

4(t + \(\frac{1}{4}\) ) = 3 ← distribute parenthesis on left side

4t + 1 = 3 ( subtract 1 from both sides )

4t = 2 ( divide both sides by 4 )

t = \(\frac{2}{4}\) = \(\frac{1}{2}\)

The double points of the following conic section x' + 4xy + 3y - 2xz - 4yz + 2 = 0 is  x = 1, y = 0, z = 1

The equation that represents double points of the conic section x" + 2xy + y - 8xz - 8yz + 16 = 0 is x + y - 4z = 0

The equation of the tangent line at point P(2,0) is x - 2y - 2z = 0

The first question asks to calculate the double points of a given conic section. The conic section is represented by the equation:

x' + 4xy + 3y - 2xz - 4yz + 2 = 0

To find the double points, we need to solve the equation for the variables x, y, and z. The solution is:

x = 1, y = 0, z = 1

These values represent the double points of the conic section.

In the second question, we are again asked to calculate the double points of a conic section. The equation is:

x" + 2xy + y - 8xz - 8yz + 16 = 0

To find the double points, we need to solve the equation for the variables x, y, and z. The solution is:

x + y - 4z = 0

This equation represents the double points of the conic section.

Finally, in the third question, we are asked to calculate the tangent line at the point P(2,0) of a conic section. The equation of the conic section is:

x - 4xy - y' + 2x - 4y - 8 = 0

To find the tangent line at point P(2,0), we need to differentiate the equation with respect to x. The derivative is:

1 - 4y + 2 - 4 = -2 - 4y

At point P(2,0), the value of y is 0. Plugging in this value, we get:

-2 - 4(0) = -2

Therefore, the equation of the tangent line at point P(2,0) is:

x - 2y - 2z = 0

This equation represents the tangent line at point P(2,0) of the conic section.


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