Find the sum of 2x² – 5x + 2 and 3x² + 2x.

Answer:

2,087,000,000 583,000 3,000,000

Step-by-step explanation:

You're taking the decimal point of 2.087 and moving it to the right nine times, getting you 2,087,000,000.

The same applies to 5.83 x 10^5, moving the decimal point to the right five times, getting you 583,000.

3 x 10^6 -> 3,000,000

The producer's surplus if the supply function for pork bellies is s(q)=q^(5/2)+ 3q^(3/2)+50 by assuming supply and demand are in equilibrium at q = 9 is approximately $18.20.

To find the producer's surplus, we need to first determine the market price at the equilibrium quantity of 9 units.

At equilibrium, the quantity demanded is equal to the quantity supplied:

d(q) = s(q)

q^(3/2) = 9^(5/2) / (3*50)

q^(3/2) = 81/2

q = (81/2)^(2/3)

q ≈ 7.55

The equilibrium quantity is approximately 7.55 units. To find the equilibrium price, we can substitute this value into either the demand or supply function:

p = d(7.55) = s(7.55)

p = (9^(5/2)) / (3*(7.55^(3/2)) * 50)

p ≈ $1.71 per unit

Now we can find the producer's surplus. The area of the triangle formed by the supply curve and the equilibrium price is equal to the producer's surplus:

Producer's surplus = (1/2) * (9^5/2) * (1/50) * (1.71 - 0)

Producer's surplus ≈ $18.20

Therefore, the producer's surplus is approximately $18.20.

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Answer:

3.25

Step-by-step explanation:

Divide 48.75 by 15

Answer: 3.25

Step-by-step explanation:

48.75/15= 3.25

Answer:

0.02a

Step-by-step explanation:

Since 0.02 is equal to 2 cents, he would get 0.02a annually. This is because a represents the income from interest and 0.02 is the amount of money made for interest.

Answer:

X = 20

Step-by-step explanation:

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Answer:

\({20}^{o} \)

Step-by-step explanation:

hint alternate angles are equal,

the angle portrayed in the diagram are alternate angles ,ie equal,

for an equation equating the two angles then solve for x

ie,

\(3x = 2x + 20 \\ 3x - 2x = 20 \\ x = 20\)

32b+12

32 and 12 is both divisible by 4 so divide them by 4 and the answers in parentheses

4(8b+3)

Answer:

14.176 mm

Step-by-step explanation:

16=\(\pi\)\(r^{2}\)

r=2.25733052

C=2\(\pi\)r

C= 14.176mm

Answer:

side: 4 metres

perimeter: 16 metres

Step-by-step explanation:

Let's first find the area of this rectangle.

The area of a rectangle is denoted by A = lw, where l is the length and w is the width. Here, the length is l = 6.4 and the width is w = 2.5. Plug these in:

A = lw

A = 6.4 * 2.5 = 16 metres squared

We want to find the side of a square with area 16. Suppose the side length is x. The area of a square is denoted by A = x * x = x², so set this equal to 16:

x² = 16

x = √16 = 4

Thus, the side length is 4 metres.

The perimeter of a square is denoted by P = 4s, where s is the side length.

Here the side length is 4 metres, as we found, so:

P = 4s = 4 * 4 = 16

Hence the perimeter is 16 metres.

When a point falls outside of control limits in statistical process control, the probability is quite high that the process is experiencing special cause variation.

In statistical process control (SPC), control limits are used to define the range within which a process is expected to operate under normal or common cause variation. Common cause variation refers to the inherent variability of a process that is predictable and expected.

On the other hand, special cause variation, also known as assignable cause variation, refers to factors or events that are not part of the normal process variation. These are typically sporadic, non-random events that have a significant impact on the process, leading to points falling outside of control limits.

When a point falls outside of control limits, it indicates that the process is exhibiting a level of variation that cannot be attributed to common causes alone. Instead, it suggests the presence of specific, identifiable causes that are influencing the process. These causes may include equipment malfunctions, operator errors, material defects, or other significant factors that introduce variability into the process.

Therefore, when a point falls outside of control limits in statistical process control, it is highly likely that the process is experiencing special cause variation, which requires investigation and corrective action to identify and address the underlying factors responsible for the out-of-control situation.

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Answer:

1-2

Step-by-step explanation:

Answer:

Option (D)

Step-by-step explanation:

If a function f(x) is represented on a graph and we follow the transformation as,

f(x) → \(k.f(x)\)

1). If k ≥ 1, graph of the parent function f(x) will be stretched vertically by a factor k.

That means the transformed graph will be narrower.

2). If 0 < k < 1, graph will be vertically compressed or the transformed function will show a wider graph.

Following this rule,

f(x) → \(\frac{1}{2}.f(x)\) shows k = \(\frac{1}{2}\) [Since 0 < \(\frac{1}{2}\) < 1]

Therefore, transformed form will be wider.

Option (D) will be the answer.

Answer:

3•10^3 is 3,000, so the answer is 9,000

Answer:

5 and 6

Step-by-step explanation:

The square root of 25 is 5 and the square root of 36 is 6. 33 falls between those

Answer:

I think on this one you use: y1-y1/x2-x1 then you get your answer, and remember the number on top is your X and the number on the bottom is your Y.

Step-by-step explanation:

The two numbers are approximately (3.583, 1.990) and (3.062, -1.990).

1. Let's assume the two numbers as x and y.

We are given two conditions:

1st condition: The sum of two numbers is 9.

x + y = 9

2nd condition: The sum of their squares is 45.

x² + y² = 45

To solve this system of equations, we can use the method of substitution. Rearrange the first equation to express x in terms of y:

x = 9 - y

Substitute this value of x into the second equation:

(9 - y)² + y² = 45

Expanding and simplifying:

81 - 18y + y² + y² = 45

2y² - 18y + 36 = 0

Divide the equation by 2 to simplify:

y² - 9y + 18 = 0

Factorize the quadratic equation:

(y - 3)(y - 6) = 0

Setting each factor to zero, we get:

y - 3 = 0   or   y - 6 = 0

Solving for y:

y = 3   or   y = 6

Now substitute these values back into the equation x + y = 9 to find x:

For y = 3, x + 3 = 9, x = 6

For y = 6, x + 6 = 9, x = 3

Therefore, the two numbers are (3, 6) or (6, 3).

2. Let's assume the two numbers as x and y.

We are given two conditions:

1st condition: The difference of the cubes of two numbers is 37.

x³ - y³ = 37

2nd condition: The sum of their squares is 25.

x² + y² = 25

Again, we can use the method of substitution to solve this system of equations. Rearrange the first equation to express x in terms of y:

x³ = y³ + 37

x = \((y^3 + 37)^{1/3}\)

Substitute this value of x into the second equation:

\([(y^3 + 37)^{1/3}]^2 + y^2 = 25\)

Simplifying:

y² + \(37^{2/3}\) + y² = 25

2y² = 25 - \(37^{2/3}\)

2y² = 25 - 17.074

2y² ≈ 7.926

y² ≈ 3.963

y ≈ ±1.990

Now substitute these values back into the equation x³ - y³ = 37 to find x:

For y ≈ 1.990, x³ - (1.990)³ = 37

x³ - 7.920 = 37

x³ ≈ 44.920

x ≈ ∛(44.920)

x ≈ 3.583

For y ≈ -1.990, x³ - (-1.990)³ = 37

x³ + 7.920 = 37

x³ ≈ 29.080

x ≈ ∛(29.080)

x ≈ 3.062

Therefore, the two numbers are approximately (3.583, 1.990) and (3.062, -1.990).

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If we use 8 tins of red paint, we would need 12 tins of blue paint to obtain the desired purple paint mixture.

To determine how many tins of blue paint are needed when using 8 tins of red paint:

The given ratio is: 3 tins of blue paint to 2 tins of red paint.

It is given that purple paint is obtained by mixing 3 tins of blue and 2 tins of red paint.

Let "x" represents the number of tins of blue paint needed.

We can set up the proportion as:

3/2 = x/8

2x = 3 * 8

2x = 24

x = 24/2

x = 12

Therefore, if we use 8 tins of red paint, we would need 12 tins of blue paint to obtain the desired purple paint mixture.

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Based on the provided graph, the correct statement is that nearly "200 of the cancer cases reported in the U.S. are attributable to smoking".

The graph visually represents statistical data or relationships between variables by drawing lines or bars that connect data points or present information in a graphical format. In this case, the graph likely shows the attribution of cancer cases to smoking in the U.S.

Smoking is a dangerous practice that is known to be one of the leading causes of cancer worldwide. The link between smoking and cancer is well-established, with tobacco smoke containing various harmful chemicals that can damage DNA and increase the risk of developing cancer. It is estimated that nearly 25% of all cancer cases can be attributed to smoking.

The graph likely presents data indicating the number of cancer cases attributable to smoking in the U.S. Based on the information provided, the graph suggests that nearly 200 cancer cases in the U.S. can be directly linked to smoking.

Therefore, the correct statement is that nearly 200 of the cancer cases reported in the U.S. are attributable to smoking.

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The sample standard deviation is approximately 5.61 and sample variance is approximately 31.46.

To compute the range of a sample,

we subtract the minimum value from the maximum value.

Range = Maximum value - Minimum value

For the given sample,

the minimum value is 15 and the maximum value is 34.

Range = 34 - 15 = 19

The range of the sample is 19.

To compute the interquartile range (IQR) of a sample, we need to find the difference between the third quartile (Q3) and the first quartile (Q1).

IQR = Q3 - Q1

To calculate the quartiles,

we first need to arrange the data in ascending order:

15, 20, 20, 24, 25, 27, 30, 34

The sample size is 8,

so the median (Q2) will be the average of the fourth and fifth values:

Q2 = (24 + 25) / 2 = 24.5

To find Q1, we take the median of the lower half of the data:

Q1 = (20 + 20) / 2 = 20

To find Q3, we take the median of the upper half of the data:

Q3 = (27 + 30) / 2 = 28.5

Now we can calculate the interquartile range:

IQR = 28.5 - 20 = 8.5

The interquartile range of the sample is 8.5.

To compute the sample variance, we use the formula:

Variance = Σ\([(x - X)^2]\) / (n - 1)

where Σ represents the sum of, x is each data value, X is the mean, and n is the sample size.

First, let's calculate the mean (X):

X = (24 + 20 + 25 + 15 + 30 + 34 + 27 + 20) / 8 = 24.625

Now we can calculate the sample variance:

Variance = \([(24 - 24.625)^2 + (20 - 24.625)^2 + (25 - 24.625)^2 + (15 - 24.625)^2 + (30 - 24.625)^2 + (34 - 24.625)^2 + (27 - 24.625)^2 + (20 - 24.625)^2]\) / (8 - 1)

Variance = 31.46

To compute the sample standard deviation,

we take the square root of the sample variance:

Standard deviation = √(Variance) = \(\sqrt{(31.46}\)) ≈ 5.61

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Answer: See below.

Step-by-step explanation:

1) x=49

2) x=-16

3) x=6/11

4) x=3

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Answer:

1)  x = 49

2)  x = -16

3)  x = ⁶/₁₁

4)  x = 3

Step-by-step explanation:

72 = x - (-23)

Apply rule -(-a) = a :

⇒ 72 = x + 23

Subtract 23 from both sides:

⇒ 72 - 23 = x + 23 - 23

⇒ 49 = x

⇒ x = 49

-5x - (7 - 4x) = 9

Apply rule -(a - b) = -a + b :

⇒ -5x - 7 + 4x = 9

Collect and combine like terms:

⇒ -5x + 4x - 7 = 9

⇒ -x - 7 = 9

Add 7 to both sides:

⇒ -x - 7 + 7 = 9 + 7

⇒ -x = 16

Divide both sides by -1:

⇒ -x ÷ -1 = 16 ÷ -1

⇒ x = -16

8x + 6 = 3(4 - x)

Distribute:

⇒ 8x + 6 = 12 - 3x

Add 3x to both sides:

⇒ 8x + 6 + 3x = 12 - 3x + 3x

⇒ 11x + 6 = 12

Subtract 6 from both sides:

⇒ 11x + 6 - 6 = 12 - 6

⇒ 11x = 6

Divide both sides by 11:

⇒ 11x ÷ 11 = 6 ÷ 11

⇒ x = ⁶/₁₁

¹/₂(4x - 16) = -2

Distribute:

⇒ 2x - 8 = -2

Add 8 to both sides:

⇒ 2x - 8 + 8 = -2 + 8

⇒ 2x = 6

Divide both sides by 2:

⇒ 2x ÷ 2 = 6 ÷ 2

⇒ x = 3

The conjugate of a complex number with a real part of -5 and an imaginary part of 4i is represented by :

C) -5 - 4i.

The conjugate of a complex number with a real part of -5 and an imaginary part of 4i can be found by changing the sign of the imaginary part. In this case, the imaginary part is 4i, so the conjugate will have a negative sign for the imaginary part.

The conjugate of the complex number is given by -5 - 4i. This means that if we have a complex number of the form -5 + 4i, its conjugate will be -5 - 4i. The conjugate of a complex number is important in various mathematical operations, such as complex number multiplication and division, as it helps simplify the expressions and eliminate the imaginary parts when needed.

Among the given options, option C) -5 - 4i represents the conjugate of the complex number with a real part of -5 and an imaginary part of 4i.

The correct question should be :

Which of the following expressions represents the conjugate of a complex number with a real part of -5 and an imaginary part of 4i?

A) 5

B) 4i

C) -5 - 4i

D) -5 + 4i

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Answer:

Answers

Step-by-step explanation:

1.) 4 weeks = 28 days

12 x 4 = 48 in

2.) 13.95 ÷ 4 = 4.65

3.) 9 ÷ 4 = $2.25 per pound

4.) yes, 4 x 4 = 16, 9 x 4 = 36

Can i get a brainiest if right? Have a good day! I hope this helps

The expression in the format "5(blank space 1) + (blank space 3)(blank space 4) + 8(blank space 7)" represents a mathematical expression with three terms. To create the expression with the given conditions, we can use the following format:

5(blank space 1) + (blank space 3)(blank space 4) + 8(blank space 7)

Here are four options for each blank space:

Option 1:

Blank space 1: x

Blank space 3: 2

Blank space 4: y

Blank space 7: z

So the expression would be:

5x + 2y + 8z

Option 2:

Blank space 1: a

Blank space 3: 3

Blank space 4: b

Blank space 7: c

So the expression would be:

5a + 3b + 8c

Option 3:

Blank space 1: m

Blank space 3: 4

Blank space 4: n

Blank space 7: p

So the expression would be:

5m + 4n + 8p

Option 4:

Blank space 1: r

Blank space 3: 1

Blank space 4: s

Blank space 7: t

So the expression would be:

5r + s + 8t

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Value of x is 2 and value of k is 0.999.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.

Given Data

At t=0, Water Volume is 3,000 Litres

The volume of water in the tank equals t hours later.

As it is also stated, there is x% less water in the tank at the conclusion of every hour than there was at the beginning.

After an hour, the amount of water is equal to 3,000 - = 3,000 - 30 x

Water consumption after two hours = (3,000 - 30 x) - (3,000 - 30 x)

×= (3,000 - 30 x) (3,000 - 30 x)

Also,

= 288120

⇒300000 - 3000 x - 3000 x + 30 x²

= 288120

⇒ 30 x ² - 6,000 x + 11880= 0

When we multiply both sides by 30, we get

⇒ x² - 200 x + 396=0

reducing the quadratic equation to factors

(x -198)(x-2) = 0

x = 198,

x = 2

Which suggests that x = 2 might be the answer to this equation.

Also,

V₁ = 3000- 30(2)

V₁ = 3000 - 60

V₁ = 2940

k = \(\frac{2940}{3000}\)

k = 0.999(approximately)

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Answer:

-1

Step-by-step explanation:

Answer:

steps below

Step-by-step explanation:

(a) first green: 8/23 AND 2nd green: 7/22

AND: multiplication.. 8/23 x 7/22 = 28/253 ≈ 0.11 (11%)

(b) 15/23 x 8/22

Answer:

55x + 148/24

Explanation:

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.

1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:

$223 / 1.70 = $131.18

2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:

$131.18 x 1.25 = $163.98

3. Calculate the price of a Suite room for check-in on Friday and Saturday:

$163.98 x 1.70 = $278.50

The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.

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