12 5/8-7 4/5
Simplify the expression above. Which of the following is correct?

O -4 33/40
O -5 7/40
O -5 1/3
O -4 7/40

The definite integral is [tex]$$\left(r^{\wedge} 3\right) /\left(\text { sqrt }\left(4+r^{\wedge} 2\right)\right) d r$$[/tex] [tex]=0.116[/tex].

As per given data,

Definite Integral helps to find the area of a curve in a graph. It has limits, which are the start and the endpoints, within which the area under a curve is calculated. The limit points can be taken as [a, b], to find the area of the curve f(x), with respect to the x-axis.

Here,

∫ = Integration symbol

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus, ∫ab f(x) dx is read as the definite integral of f(x) with respect to dx from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

Consider the following integral:

[tex]$$\int_0^1 \frac{r^3}{\sqrt{4+r^2}} d r$$[/tex]

The objective is to evaluate the integral, using substitution method.

Let [tex]$u=4+r^2 \rightarrow r^2=u-4$[/tex]

[tex]$$\begin{aligned}& d u=2 r d r \\& r d r=\frac{d u}{2}\end{aligned}$$[/tex]

when [tex]$r=0$[/tex], then [tex]$u=4$[/tex]

When [tex]r =1[/tex], then [tex]u=5[/tex]

Use the above details to evaluate the integral.

[tex]& =\frac{1}{2}\left[\frac{2 u^{\frac{3}{2}}}{3}-8 \sqrt{u}\right]_4^5 \\& =\left[\frac{u^{\frac{3}{2}}}{3}-4 \sqrt{u}\right]_4^5 \\& =0.116 \\& =\frac{5^{\frac{3}{2}}}{3}-4 \sqrt{5}-\frac{4^{\frac{3}{2}}}{3}+8 \\& =0.11585 \\& \left.=\left[\frac{5^{\frac{3}{2}}}{3}-4 \sqrt{5}\right]^{-}\left(\frac{4^{\frac{3}{2}}}{3}-4 \sqrt{4}\right)\right][/tex]

[tex]$$& \int_0^1 \frac{r^3}{\sqrt{4+r^2}} d r=\int_0^1 \frac{r^2}{\sqrt{4+r^2}}(r d r) \\& =\int_4^5 \frac{(u-4)}{\sqrt{u}}\left(\frac{d u}{2}\right) \\& =\frac{1}{2} \int_4^5 \frac{(u-4)}{\sqrt{u}} d u \\& =\frac{1}{2} \int_4^5\left(\sqrt{u}-\frac{4}{\sqrt{u}}\right)^{d u} \\[/tex]

[tex]& =\left[\frac{u^{\frac{3}{2}}}{3}-4 \sqrt{u}\right]_4^5 \\& =0.116 \\& =\frac{5^{\frac{3}{2}}}{3}-4 \sqrt{5}-\frac{4^{\frac{3}{2}}}{3}+8 \\& =0.11585 \\& \left.=\left[\frac{5^{\frac{3}{2}}}{3}-4 \sqrt{5}\right]^{-}\left(\frac{4^{\frac{3}{2}}}{3}-4 \sqrt{4}\right)\right][/tex]

Therefore, the evaluated integral is 0.116.

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There is percent decrease of 30%

50 pounds to 35 pounds

Original amount = 50 pounds

New amount= 35 pounds

Since, New amount is less than the original amount, this is a percentage of decrease.

Change in amount = 35 -50

Change in amount = -15 pounds

Substitute the given values we have;

% change = (change/original value) x 100

% change = -(15/50) x 100

% change = - 30%

Therefore, there is percent of decrease which is 30%.

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Finding a line equation that can roughly represent the data is your goal. the best-fit line or regression line.

A mathematical equation is a formula that connects two statements using the equal sign (=) to signify equivalence.  For instance, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematically, the connection between two phrases on either side of a letter is stated. The symbol doubles as the sole variable most of the time. for illustration, 2x - 4 = 2.

given

Perfect or exact lines are not present in real-world data sets.

Your task is to identify a line equation that can roughly reflect the data. The regression line or line of best fit is what we refer to as here.

You might draw a line by eye from the graph, choose some random integers, and do this.

Finding a line equation that can roughly represent the data is your goal. the best-fit line or regression line.

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The perimeter of the rectangle is 19.93 meter and the area of the rectangle is 22.22 sq. meter.

Here one side of the rectangle is 3( 3/10 ) and the other side is 6 (2/3 ) meter respectively.

Perimeter of the rectangle is 2 ( l + w ) and the Area of the rectangle is (l)*(w), where l is the length and w is the width of the rectangle.

Perimeter = 2(3 3/10 + 6 2/3) = 2(3.3 + 6.666667) = 2(9.96667) = 19.93334 meters

To find the area of a rectangle, we multiply the length by the width. The area of a rectangle with side lengths of 3 3/10 meters and 6 2/3 meters is:

Area = (3 3/10) * (6 2/3) = 3.3 * 6.666667 = 22.222222 square meters

Note that you can convert the mixed numbers to decimals, since it's more convenient to work with decimals when solving arithmetic problems.

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Answer:

x = 7

Step-by-step explanation:

given f(x) = 3x - 1 and f(x) = 20, then equate the right sides to find x

3x - 1 = 20 ( add 1 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Answer: x = 7

Step-by-step explanation:

f (x) = 20 eq_i

f (x) = 3x - 1 eq_ii

eq_i = eq_ii

20 = 3x - 1

3x = 20 + 1

x = 21 ÷ 3

x = 7 answer

hope that helps...

Answer:

ab-ac

Step-by-step explanation:

a(b-c)=ab-ac

[tex]d-2=23[/tex]

Add 2 to both sides:

[tex]d-2+2=23+2[/tex]

[tex]\fbox{d = 25}[/tex]

Logarithm is a mathematical operation that is the inverse of exponentiation. It is denoted by log b (x), which means the logarithm of x to base b.

For example, log2 8 = 3, since 23 = 8. Logarithm is useful in solving equations that involve exponential terms.

The properties of logarithm are:

1. log b 1 = 0: This property states that the logarithm of 1 is zero for any base b.

2. log b b = 1: This property states that the logarithm of any base b is 1.

3. log b (xy) = log b (x) + log b (y): This property states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the two numbers. For example, log2 (8x32) = log2 8 + log2 32 = 3 + 5 = 8.

4. log b (x/y) = log b (x) - log b (y): This property states that the logarithm of the quotient of two numbers is equal to the difference of the logarithms of the two numbers. For example, log2 (8/32) = log2 8 - log2 32 = 3 - 5 = -2.

5. log b c = clog b (c): This property states that the logarithm of a number c to the base b is equal to c times the logarithm of b. For example, log2 32 = 32log2 2 = 5.

These properties of logarithm are very useful in solving mathematical problems involving exponential terms.

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To graph 3-dimensional coordinates, you will need a 3-dimensional graph or plot. As with 2-dimensional coordinates, each point is labeled with three coordinates (x, y, z). You can then plot the point on a 3-dimensional graph by connecting the x, y and z coordinates with 3 lines.

1. Determine the coordinates of the point you want to plot.

2. Draw 3 axes on a graph paper or use a 3D graph on your computer.

3. Label each axis with the corresponding coordinate (x, y, z).

4. Plot the point by connecting the corresponding coordinates with 3 lines.

5. Add labels to the point to indicate which point it is and what the coordinates are.

To graph 3-dimensional coordinates, you will need a 3-dimensional graph or plot. As with 2-dimensional coordinates, each point is labeled with three coordinates (x, y, z). You can then plot the point on a 3-dimensional graph by connecting the x, y and z coordinates with 3 lines.

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Answer:

66, 68, 70, 72

Answer:

66 68 70 72

Step-by-step explanation:

it is what it is

The rate of change of y with respect to x will be equal to 8 when there is a linear relationship between x and y.

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another. The relationship defining how one quantity changes in relation to the change in another quantity is given by the rate of change formula.

The rate of change is given by the formula:

Here, the value of points are (-2.5,-30) and (-1,-18)

Now, substituting these values in the formula, we get

Rate of change=

= 8

Hence, the rate of change of the y with respect to x will be equal to 8 when there is a linear relationship between x and y.

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The required representation of given number line is x ∈ (-10,  ∞).

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities, is at the core of social justice theories. However, because it frequently means different things to different people, it is prone to confusion in public discourse.

We have number line,

By using baby curve method.

The representation of the line is ,

Let the line is x axis

Then

x ≥-10

x ∈ (-10,  ∞)

Thus, the required inequality is  (-10,  ∞).

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Answer:

  (d)  24,057

Step-by-step explanation:

Starting with 11 bacteria in a culture that triples in size every hour, you want to know the number grown in the 7th hour.

In hour 0, we have 11, and the growth factor per hour is 3. That means the population can be modeled by ...

  p = 11·3^t

where t is in hours.

In the 7th hour, the population will grow to 11·3^7 = 24,057.

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Answer:

Your Domain Will be (6,-12,-6,20)

Your Range will Be 36

Sorry i dont have work shown i just remember doing this problem and just gave answers glad to help and stay safe

Answer:

Domain: {6, -12, -6, 20}

Range: {0, -16 , 10 , -7}

Step-by-step explanation:

Domain and Range:

Domain: In the set of ordered pairs, domain is all the x-values.

Range: In the set of ordered pairs, range is all the y-values

Domain: {6, -12, -6, 20}

Range: {0, -16 , 10 , -7}

So, on solving the question we can say here, in equation we have, (10x - 20) = 7x + 4; 3x = 24; x = 8

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here, in equation we have,

(10x - 20) = 7x + 4

3x = 24

x = 8

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Answer:

We can start by using algebra to represent the given information in the problem in terms of variables. Let x be the cost of each candy bar. Then we can write the following equation:

3 + 7x = 31

This equation states that the total cost of the soft drink and the candy bars is $31, and the cost of the candy bars is 7 times the cost of each candy bar.

Now we can solve for x, the cost of each candy bar:

3 + 7x = 31

7x = 31 - 3

7x = 28

x = 28/7

x = 4

Each candy bar cost $4.

We can also check this by substituting this value back into the original equation to see if it is true:

3 + 7(4) = 31

3 + 28 = 31

31 = 31

This confirms that the cost of each candy bar is $4.

Step-by-step explanation:

The range of the given constant function y = -5 is {-5}.

The range of a function is the set of all possible output values (y-values) that the function can produce for any input value (x-value).

y = -5 is a constant function, which means that the output value is always equal to -5 for any input value, the range of this function would be the set of real numbers that contain only the value -5.

So the range of y = -5 is {-5}.

A constant function is a special kind of function that always returns the same output value regardless of the input value.

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The depreciation Straight Line Method charges a fixed depreciation amount on an annual basis for the duration of an asset. The original cost is the basis for computing the annual depreciation, which is constant year over year. This approach is additionally referred to as the "Original Cost method" or the "Fixed Instalment method."

What is straight line method answer?

  The value of an asset is steadily decreased via the Straight Line Method (SLM) of Depreciation until it reaches its scrap value. Depreciation is subtracted from the asset's value on an annual basis in a specified amount.

Why is the straight-line approach used?

The straight line approach is popular with accountants because it is simple to apply, produces fewer errors during the asset's lifetime, and costs the same amount for each accounting period.

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Answer:

1) The trick to making these fractions equivalent is to make sure they have the same denominator. to do this you need to know your multiplication facts. These are the multiples when you multiply two numbers together.

2) Since 24 is the largest denominator, you need the smallest denominator into 24ths, which you do by multiplying 8 x 3, giving you 24.

3) Whatever you do to the denominator, you do to the numerator, so multiply 5 x 3, which is 15.

4) New fraction for 5/8 becomes 15/24.

5) So 5/8 is equivalent. to 15/24.

Step-by-step explanation:

5/8 = x/24

5 x 3 = 15

8 x 3 24

Proof: Reduce 15/24 by dividing 3 into both numbers (15÷3) and (24÷3) = 5/8.

The types of stakeholders are internal, external, Primary and secondary

Stakeholders are a group that expresses interest in the firm and whose activities, whether professional or personal, have an impact on its operations. The four types of stakeholders can be noted as -

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Answer: 25,000

Step-by-step explanation: 125,000 x 0.2 = 25,000

Answer:

Exact Form:

r=√143.36346562,    −√143.36346562

Decimal Form:

r

=

11.97344835

…

,

−

11.97344835

…

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The area of the partial circle with a radius of 8 cm = 150.72 [tex]cm^{2}[/tex], then the we can use  [tex]\pi =3.14[/tex] value.

The circle is missing 1/4, so the area of it is just 3/4 of the whole area of the circle.

Area of a circle is the region occupied by the circle in a two-dimensional plane.

It can be determined easily using a formula, A = [tex]\pi r^{2}[/tex] , (Pi r-squared) where r is the radius of the circle.

The unit of area is the square unit, such as [tex]m^{2}[/tex], [tex]cm^{2}[/tex], etc.

Area of Circle = [tex]\pi r^{2}[/tex] or [tex]\frac{\pi d^{2} }{4}[/tex], square units. where π = 22/7 or 3.14.

Area of a circle,

A = [tex]\pi r^{2}[/tex]      (Equation-1)

Where,

r = radius

Given that,

r = 8cm

We can substitute equation-1,

A = [tex]\pi 8^{2}[/tex] cm * cm

A = [tex]64\pi[/tex] [tex]cm^{2}[/tex]

So,

We can write,

Whole one quarter,

[tex]\frac{4}{4} -\frac{1}{4}[/tex] [tex]=\frac{3}{4}[/tex]

We can get,

= [tex]\frac{3}{4} *64\pi[/tex]

= 48[tex]\pi[/tex]

We can substitute [tex]\pi =3.14[/tex] value,

Then,

= 48 * 3.14

= 150.72 [tex]cm^{2}[/tex]

Therefore,

The area of the partial circle with a radius of 8 cm = 150.72 [tex]cm^{2}[/tex], then the we can use  [tex]\pi =3.14[/tex] value.

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The smaller sail boat's height, x, is 10.5 inches.

Congruence describes two triangles that have the same number of sides and angles on each side.

The two sails in the hypothetical situation have the same sides, and their proportions are:

7/8 = x/12

x = 12.7 / 8

x = 10.5

Thus, the smaller sail boat's height, x, is 10.5 inches.

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The complete question is-

Hays build model sailboats as a hobby. The dimensions of the sailboats are given. What is the height, x, of the smaller sailboat's sail? Enter your answer, as a decimal, in the box. x = in. Two sailboats with sails that are right triangles.  The top angle on the sails are marked congruent to each other. The smaler sail has a a height of x and a base of 7 inches. The lareger sail has a height of 12 inches and a base of 8 inches.

The amount that Pham will have to pay back is $8,602.80

The formula to calculate the compound interest is:

A = P(1 + r/n)^nt

Where A is the amount of the loan including interest, P is the principal or the initial amount borrowed, r is the interest rate, t is the number of years the loan is taken out for and n is the number of times the interest is compounded per year.

In this case, we know that:

P = $6,000

r = 6% (expressed as 0.06)

t = 72/12 = 6 (since the loan is for 72 months, or 6 years)

n = 1 (the interest is compounded annually)

So the formula becomes:

A = 6000(1 + 0.06)⁶

A = 6000(1.06)⁶

A = 6000 * 1.4338

A = $8,602.80

Therefore, Pham will have paid back $8,602.80, including interest, if he pays off the loan in 72 months.

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To enlarge a triangle by a scale factor greater than 1, identify the center of enlargement, multiply the coordinates of each point by the scale factor, connect the new points, and check the side lengths will be greater.

To enlarge a triangle with a center of enlargement, you can use the following steps:

It's important to note that in order to keep the triangle congruent during the dilation, the center of enlargement must be the centroid of the triangle and the scale factor should be the same for all the points of the triangle.

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On solving the provided question, we can say that the money they would raise if they sell 1000 tickets will be given the equation that is  y = 24R/10

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the money they would raise if they sell 1000 tickets

will be given the equation that is

M = 24/10R

y = 24R/10

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The additive inverse of 11 /- 25 is -11 /+ 25. This means that the two numbers have opposite signs and the same absolute value.

The additive inverse of a number is the number that, when added to the original number, results in a sum of zero. In other words, the two numbers have opposite signs and the same absolute value. For example, the additive inverse of 11 /- 25 is -11 /+ 25. This is because when adding 11 /- 25 and -11 /+ 25 together, the negative and positive signs cancel each other out and the absolute values add up to zero. The same concept applies to all numbers, not just integers. For example, the additive inverse of 4.7 is -4.7. When 4.7 and -4.7 are added together, the sum is 0. As such, the additive inverse of any number can be calculated by changing the sign of the number and leaving the absolute value the same.

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Answer:

Slope intercept form is y = -x+7

Standard form is x+y = 7

Both forms represent the same line, just written in different ways of course.

The graph is shown below.

=====================================================

Explanation:

Let's check the answer you got.

The equation -1x+y=1 is the same as -x+y = 1

Plug the coordinates of the first point into this equation

-x+y = 1

-3+4 = 1

1 = 1

The first point is on the line -x+y = 1

Repeat similar steps for the other point

-x+y = 1

-(-1)+8 = 1

1+8 = 1

9 = 1

The two sides don't match up. We need the same number on both sides to get a true equation. The false equation tells us that (-1,8) is not on the line -x+y = 1.

In short, this rules out -x+y = 1 being the answer.

The next section will show one way to find the answer.

--------------------------------

First we'll need the slope of the line through (3,4) and (-1,8)

[tex](x_1,y_1) = (3,4) \text{ and } (x_2,y_2) = (-1,8)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{8 - 4}{-1 - 3}\\\\m = \frac{4}{-4}\\\\m = -1\\\\[/tex]

Then I'll use the y = mx+b template to find b. For the (x,y), use either point given to you. I'll use (3,4).

So,

y = mx+b

4 = -1*3+b

4 = -3+b

4+3 = b

7 = b

b = 7

We found that m = -1 and b = 7.

We go from y = mx+b to y = -1x+7 aka y = -x+7 which is the answer in slope intercept form.

To convert to standard form Ax+By = C, add x to both sides. The goal is to get the variable terms to one side, and the constant isolated on its own side.

y = -x+7

y+x = -x+7+x

x+y = 7 is the answer in standard form

--------------------------------

Check:

Plug (x,y) = (3,4) into the equation to see if we get a true result.

x+y = 7

3+4 = 7

7 = 7

That works out. Now do the other pair of coordinates (-1,8).

x+y = 7

-1+8 = 7

7 = 7

That works as well. The answers are fully confirmed to be correct.

If you wanted, you can use the equation y = -x+7 as the way to check the answer. It's up to you which you prefer better if it's slope-intercept or standard form.

Yet another way to check the answer is to use a graphing tool like GeoGebra. It's something I use all the time. See the screenshot diagram below.