3|x + 3| = 12

A. x = 1
B. x = 1 or x = -4
C. x = 1 or x = -7
D. no solution exist

Answer:

Choice A

Step-by-step explanation:

The population after 105 minutes is 282651.0114.

What is exponential growth?

Exponential growth is the process by which quantity rises over time. It occurs when a quantity's instantaneous rate of change with regard to time is proportionate to the quantity itself.

Here, we have

Given: The count in a bacteria culture was 200 after 15 minutes and 1500 after 40 minutes. Assuming the count grows exponentially.

Exponential growth is modeled by the equation: P(t) = P₀\(e^{kt}\)....(1)

where P(t) is the population at time t, P₀ is the initial population and k is the growth rate.

Given

200 after 15 minutes

Now, we put the values in equation (1) and we get

200 = P₀\(e^{15k}\)...(2)

Also, 1500 after 40 minutes

1500 = P₀\(e^{40k}\)...(3)

Now, we divide equation(3)by (2) and we get

1500/200 = \(e^{40k}\)/\(e^{15k}\)

15/2 = \(e^{25k}\)

Now, we take a log and we get

ln(15/2) = 25k

k = ln(15/2)/25

k = 0.0805

Now, we put the value of k in equation(2) and we get

200 = P₀\(e^{15(0.0805)}\)

Initial size of the culture P₀ = 59.702

Now, we find the doubling period:

f(t) = 2P₀

We know that f(t) = P₀\(e^{kt}\).

2P₀ = P₀\(e^{kt}\)

\(e^{kt}\) = 2

Now, we take a log and we get

ln(2) = kt

t = ln(2)/k

t = ln(2)/0.0805

t = 8.600

The time taken to doubling period is 8.600 minutes.

Population after 105 minutes:

f(t) = P₀\(e^{kt}\)

f(t) = 59.702\(e^{0.0805*105}\)

f(t) = 282651.0114

Hence, the population after 105 minutes is 282651.0114.

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Answer:

x = 42.67

Step-by-step explanation:

x + 2x + 7 + 45 = (3 - 2) * 180

3x + 52 = 180

   - 52       - 52

3x = 128

/ 3    / 3

x = 42.67

Answer:

Step by step explanation::

Answer:

the price will decrease by 4148

the price of the next model will be 29852

Answer:

C

Step-by-step explanation:

lol

All the functions a to d have a period of 2π

From the question, we have the following parameters that can be used in our computation:

The functions

A sinusoidal function is represented as

f(x) = Asin(B(x + C)) + D

Where

Period = 2π/B

In the functions (a to d), we have

B = 1

So, we have

Period = 2π/1

Evaluate

Period = 2π

Hence, all the functions have a period of 2π

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The smaller number is -17, and the quadratic equation that can be used to find it is\(x^2 + x - 272 = 0.\)

The correct answer would be \(x^2 + x - 272 = 0.\)

To find the quadratic equation that can be used to find the smaller number, we can set up the equation using the given information. Let's assume that the smaller number is x.

Since the product of two consecutive integers is 272, we can express this as an equation: x(x + 1) = 272.

Expanding the equation, we have:

\(x^2 + x = 272.\)

To find the quadratic equation, we need to rearrange the equation in the standard form, which is\(ax^2 + bx + c = 0\). In this case, we have:

\(x^2 + x - 272 = 0.\)

Therefore, the correct quadratic equation that can be used to find the smaller number is\(x^2 + x - 272 = 0.\)

This equation can be solved by factoring, completing the square, or using the quadratic formula. Factoring may not be straightforward in this case since 272 does not have obvious factors, so let's use the quadratic formula to find the solutions.

The quadratic formula states that for an equation of the form \(ax^2 + bx + c = 0\), the solutions for x can be found using the formula:

x = (-b ± √\(\sqrt{(b^2 - 4ac)}\)) / (2a).

For the equation\(x^2 + x - 272 = 0,\)we have a = 1, b = 1, and c = -272. Substituting these values into the quadratic formula, we get:

x = (-(1) ± \(\sqrt{((1)^2 - 4(1)(-272))) / (2(1)).}\)

Simplifying further, we have:

x = (-1 ±\(\sqrt{ (1 + 1088)) / 2.}\)

x = (-1 ± \(\sqrt{1089)}\) / 2.

Since we are looking for the smaller number, we take the negative square root:

x = (-1 -\(\sqrt{ 1089}\)) / 2

Calculating the value, we have:

x = (-1 - 33) / 2.

x = -34 / 2.

x = -17.

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Answer:

-24

Step-by-step explanation:

Answer-24

Step-by-step explanation:

3 x -4 x 2

6 x -4 =

-24

The kind of error where a bank misses an opportunity to make a loan to someone who would have repaid it is known as a Type II error or a false negative.

1. Type II error: When a bank fails to grant a loan to an individual who would have been capable of repaying it, it is considered a Type II error or a false negative. This means that the bank incorrectly rejects a potentially profitable opportunity.

2. Loan evaluation process: Banks assess various factors before approving a loan, such as credit history, income stability, debt-to-income ratio, and collateral. These factors help determine the borrower's creditworthiness and ability to repay the loan.

3. Probability of error: The bank's decision-making process involves setting thresholds or cutoff points for different criteria. If the borrower's profile falls below these thresholds, the loan may be denied. However, these thresholds are not infallible and can lead to errors.

4. Factors contributing to error: There can be several reasons why a bank might miss an opportunity to grant a loan to someone who would have repaid it. Some potential factors include overly strict evaluation criteria, outdated or incomplete data, limited access to information, or human error in the decision-making process.

5. Impact and mitigation: Type II errors can result in missed business opportunities for the bank and potential benefits for the borrower. To minimize these errors, banks can continually refine their loan evaluation processes, adopt advanced data analysis techniques, leverage technology for more accurate assessments, and regularly update their risk models. Additionally, ensuring proper training and supervision of loan officers can also reduce the likelihood of such errors.

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The domain and the range of the graph given will be 0 ≤ x ≤ 95 and 0 ≤ y ≤ 20.

Given is a graph, we need to find the domain and the range of the graph given,

So,

The domain is all the input values that mean all the values of x,

Here we see the values of x are lies between 0 to 95, so the domain is 0 ≤ x ≤ 95

And the range is all the output values that mean all the values of y,

Here we see the values of y are lies between 0 to 20, so the range is 0 ≤ x ≤ 20.

Hence the domain and the range of the graph given will be 0 ≤ x ≤ 95 and 0 ≤ y ≤ 20.

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The equation used to represent the distance between two points A and B is AB  =  x Cos 28°

The equation can be defined as a mathematical statement made up of expressions. The length of the line that connects two points is known as the distance between the two points. A triangle is a closed shape with 3 sides, 3 angles and 3 vertices. Triangle is a 2- dimensional figure.

As per the given question,

Let the hypotenuse be x

The two points A and B are on the base of the triangle so,

Base - length = AB

The distance between the two points is

⇒   cos Θ   =   base / hypotenuse

where,      base = AB

                hypotenuse = x

⇒   cos Θ   =   AB / x

⇒   AB   =   x cos Θ      →   1

Substitute Θ  =  28 in 1,

⇒   AB = x cos 28°

Therefore, AB = x cos 28° is the equation used to represent the distance between two points A and B.

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The complete question is

When θ = 28° , which equation can be used to find the distance from point a to point b?

If a group consists of 10 kids and 2 adults, the number of ways are there to form the line are 2 * 10!. So, correct option is C.

To form a line with an adult at the front and an adult at the back, we need to consider the positions of the 10 kids within the line. The two adults are fixed at the front and back, so we have 10 positions available for the kids.

To calculate the number of ways to arrange the kids in these positions, we can use the concept of permutations. Since each position can be occupied by a different kid, we have 10 options for the first position, 9 options for the second position, 8 options for the third position, and so on, until the last position, where only 1 kid remains.

Therefore, the number of ways to form the line is:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 10!

However, the problem also mentions that there are 2 adults, so we need to consider the arrangements of the adults as well. Since there are only two adults, there are 2 ways to arrange them in the line (adult at the front and adult at the back or vice versa).

Therefore, the total number of ways to form the line is:

2 x 10! = 2 * 10!

Hence, the correct option is b. 2 * 10!, which accounts for both the arrangements of the kids and the adults.

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The circumference of the circle is 26.38 inches and the area of the circle is 55.39 square inches, both rounded to the nearest hundredth.

The diameter of a circle is the distance across the circle passing through its center. In this problem, the diameter of the circle is given as 8.4 inches. We can use the formula for the circumference and the area of a circle in terms of its diameter to find the solutions.

First, we can find the radius of the circle by dividing the diameter by 2. So, the radius is 8.4/2 = 4.2 inches.

To find the circumference of the circle, we can use the formula:

C = πd

where d is the diameter. Substituting the value of d = 8.4 inches and π = 3.14, we get:

C = 3.14 x 8.4 = 26.376

Therefore, the circumference of the circle is 26.38 inches (rounded to the nearest hundredth).

To find the area of the circle, we can use the formula:

A = πr²

where r is the radius. Substituting the value of r = 4.2 inches and π = 3.14, we get:

A = 3.14 x (4.2)² = 55.3896

Therefore, the area of the circle is 55.39 square inches (rounded to the nearest hundredth).

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Answer 315 people.

Step-by-step explanation:

Answer:

315

Step-by-step explanation:

45% is part of the 700 people who vote for a political party at the upcoming election.

Step 1. Use \(\frac{part}{whole} =\frac{part}{whole}\) where 45% is part of the 700 people

Answer: \(\frac{45}{100} =\frac{?}{700}\)

Step 2. Divide 45 by 100

Answer: 0.45

Step 3. Multiply it by 700

Answer: 315

so 315 people were planning to vote for a political party

Using Direct Variation, the value of n = 26

An equation is an expression that shows the relationship between two or more numbers and variables.

We need to Write y = kx based on the conditions stated.

Replace with: -18 = k x 3

Turn the sides around: k × 3 = -18

Now Subtract the coefficient of the variable from both sides of the equation:

k = 26 compute the product or quotient.

Write the function's equation as;

y = 26x

Replace with:

n = 26 × 4

n = 104; compute the product or quotient.

Response: n = 26

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\(x + 2y = 0\)

\(x - y = 9\)

Subtract the second equation from the first equation :

\((x + 2y) - (x - y) = 0 - 9\)

\(x + 2y - x + y = - 9\)

\(x - x + 2y + y = - 9\)

Collect like terms

\(0 + 3y = - 9\)

\(3y = - 9\)

Divide both sides by 3

\( \frac{3y}{3} = \frac{ - 9}{3} \\ \)

\(y = - 3\)

Now it's time to find the value of x so put the y value in one of the above equations to find the value of x :

\(x = - 2 \times y\)

\(x = - 2 \times ( - 3)\)

\(x = 6\)

Thus the solution is :

\(s = (6 \: , - 3)\)

Answer:

2,600

Step-by-step explanation:

Answer:

it is 2,600.00

Step-by-step explanation:

The expression 12a and 24ab can be rewritten by factoring out the common factor 12a, resulting in 12a(0+2b), 12a(1+2b), 12ab(0+2), and 12ab(1+24ab).

To rewrite the given expression using a common factor, we identify the largest common factor between the terms. In this case, the common factor is 12a. By factoring out 12a from each term, we distribute it to the terms within the parentheses. This allows us to simplify the expression and combine like terms.

The resulting expressions are equivalent to the original expression and have the common factor 12a factored out.

This technique of factoring out common factors is useful for simplifying algebraic expressions and identifying patterns within them.

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The linear approximation for the expression indicated as per the attached question is given by:

\(L\left ( x \right );\)

\(L\left ( x \right )=f\left ( a \right )+f{}'\left ( a \right )\left ( x-a \right )\).

\(f\left ( x \right )=\sin ^{2}x,\, \, a=2\pi\)

\(f\left ( 2\pi \right )=\sin ^{2}2\pi =0\)

\(f{}'\left ( x \right )=\frac{\mathrm{d} }{\mathrm{d} x}\left [\sin ^{2}x \right ]\)

\(=2\sin x\times \frac{\mathrm{d} }{\mathrm{d} x}\left [\sin x \right ]\)

\(=2\sin x\times \cos x\)

\(=\sin 2x\)

\(f{}'\left ( 2\pi \right )=\sin \left (2\times 2\pi \right ) =0\)

\(L\left ( x \right )=f\left ( 2\pi \right )+f{}'\left ( 2\pi \right )\left ( x-2\pi \right )\)

\(=0+0\left ( x-2\pi \right )\)

= 0

Step 2 : \(f\left ( x \right )=x+x^{4},\, \, a=0\)

f (0) = - + 0⁴ = 0

\(f{}'\left ( x \right )=\frac{\mathrm{d} }{\mathrm{d} x}\left [x+x^{4} \right ]\)

\(=\frac{\mathrm{d} x}{\mathrm{d} x}+\frac{\mathrm{d} }{\mathrm{d} x}\left [x^{4} \right ]\)

= 1 + 4x³

f' (0) = 1 + 4 x 0³

= 1

L (x) = f(0) + f' (0) (x-0)

= 0 + 1 * x

= x

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400 grams of gasoline corresponds to a volume of approximately 601.50 mL when spilled into the puddle of water.

To determine the volume of gasoline spilled, we can use the given density of gasoline and the mass of the spilled gasoline.

Mass of gasoline = 400 grams

Density of gasoline = 0.665 g/mL

We can use the formula:

Density = Mass / Volume

Rearranging the formula to solve for Volume, we have:

Volume = Mass / Density

Substituting the values into the formula, we get:

Volume = 400 grams / 0.665 g/mL

To obtain the volume in milliliters (mL), we divide the mass by the density.

Volume = 601.50 mL

Therefore, 400 grams of gasoline corresponds to a volume of approximately 601.50 mL when spilled into the puddle of water.

It is important to note that gasoline and water do not mix due to their differing polarities.

Gasoline, being a non-polar liquid, is less dense than water, causing it to float on the surface.

This characteristic makes it important to take necessary precautions in handling and cleaning up gasoline spills to prevent environmental contamination and ensure safety.

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Basically, we are given the diagonal of the square to be 13.5 feet. We need to find the side length of the square.

The formula that relates diagonal and side length of a square is:

Where

d is the diagonal

s is the side length

We substitute and find our answer:

The side length is about 9.5 feet

Answer choice B

Answer:

The answer would be 342

Step-by-step explanation:

Multiply 19 by 18 and you get 342

Answer:

Square root of 37, about 6.08

Step-by-step explanation:

Pythagorean Theorem: a^2 + b^2 = c^2

18^2 + b^2 = 19^2

324 + b^2 = 361

b^2 = 37

b= sqrt37

b about equal to 6.08

Answer : by reversing the order of integration, we obtained the integral ∫[3 to 4] 2/3 * 64^(3/2) * e^(x^4) dx. However, this integral cannot be evaluated analytically.

To reverse the order of integration, we need to rewrite the given integral by interchanging the order of integration and the limits of integration.

The original integral is:

∫[0 to 64] ∫[3 to 4] √y * 3e^(x^4) dx dy

Let's reverse the order of integration:

∫[3 to 4] ∫[0 to 64] √y * 3e^(x^4) dy dx

Now, we can evaluate the integral by integrating with respect to y first and then integrating with respect to x.

∫[3 to 4] ∫[0 to 64] √y * 3e^(x^4) dy dx

Integrating with respect to y:

∫[3 to 4] [∫[0 to 64] √y * 3e^(x^4) dy] dx

The inner integral becomes:

∫[0 to 64] √y * 3e^(x^4) dy = 2/3 * (y^(3/2)) * e^(x^4) | [0 to 64]

                            = 2/3 * (64^(3/2)) * e^(x^4) - 2/3 * (0^(3/2)) * e^(x^4)

                            = 2/3 * 64^(3/2) * e^(x^4)

Substituting this result back into the outer integral:

∫[3 to 4] 2/3 * 64^(3/2) * e^(x^4) dx

Now, we can evaluate the integral with respect to x:

2/3 * 64^(3/2) * ∫[3 to 4] e^(x^4) dx

Unfortunately, the integral with respect to x in this form does not have a standard closed-form solution. Therefore, we cannot evaluate it analytically.

In summary, by reversing the order of integration, we obtained the integral ∫[3 to 4] 2/3 * 64^(3/2) * e^(x^4) dx. However, this integral cannot be evaluated analytically.

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The ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88

For given question,

We have been given the unit conversion.

A traditional unit of length in Japan is the ken

and 1 ken = 1.97 m

We need to find the the ratios of (a) square kens to square meters.

First we find the square of 1 ken.

⇒ 1 square kens = (1.97 m)²

⇒ 1 square kens = 1.97 × 1.97 m²

⇒ 1 square kens = 3.88 m²                  ..................(1)

And 1 square meters = 1 m²                 ................. (2)

Now we take the ratio of square kens to square meters.

From (1) and (2),

⇒ 1 ken² / 1 m² = 3.88 / 1

⇒ 1 ken² / 1 m² = 3.88

Therefore, the ratios of (a) square kens to square meters (1 ken² / 1 m²) is 3.88

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Answer: 1.C 2.B

Step-by-step explanation:

An equation that matches the table include the following: y = x + 5.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 5)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1.

At data point (0, 5) and a slope of 1/, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 1(x - 0)

y - 5 = x

y = x + 5

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Proportion should a 10% cream be mixed with a 1% cream of the same active ingredient to make a 3% cream  the proportion in which the 10% cream should be mixed with the 1% cream to make a 3% cream is X:Y = 1:3.5, which can be approximated as X:Y = 2:7.

To determine the proportion in which a 10% cream should be mixed with a 1% cream to make a 3% cream, we can again use the concept of weighted averages.

Let's assume we mix X parts of the 10% cream with Y parts of the 1% cream.

The equation for the weighted average can be written as:

(Percentage A * Weight A) + (Percentage B * Weight B) = Desired Percentage * Total Weight

In this case, the equation would be:

(10% * X) + (1% * Y) = 3% * (X + Y)

Simplifying the equation, we get:

0.1X + 0.01Y = 0.03X + 0.03Y

Rearranging the terms, we have:

0.03X - 0.1X = 0.03Y - 0.01Y

-0.07X = 0.02Y

Dividing both sides by 0.02Y, we get:

(-0.07X) / (0.02Y) = 1

Simplifying further:

-3.5X = Y

Therefore, the proportion in which the 10% cream should be mixed with the 1% cream to make a 3% cream is X:Y = 1:3.5, which can be approximated as X:Y = 2:7.

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Answer:

48

Step-by-step explanation:

13 + 22 + 29 = 64

64/x = 4/3

x = 48