help
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Step-by-step explanation:

y=4x+rx+6

y-6=4x+rxy−6=4x+rx Subtract \ 6 \ from \ both \ sidesSubtract 6 from both sides

y-6=x(4+r)y−6=x(4+r) Factor \ out \ the \ common \ term \ xFactor out the common term x

\dfrac{y-6}{4+r} =x

4+r

y−6

=x Divide \ both \ sides \ by \ 4+rDivide both sides by 4+r

Step-by-step explanation:

[tex] = (2 {a}^{ - 5} ) \times ( - 5 {a}^{9} )[/tex]

[tex] = (2 \times ( - 5)) {a}^{ - 5 + 9} [/tex]

[tex] = - 10 {a}^{4} [/tex]

The volume of the solid generated by revolving the region R bounded by

y = [tex]e^{-2x}[/tex], y = 0, x = 0, x = ln 9 around x-axis = 0.25 cubic units

Given the region R bounded by y = [tex]e^{-2x}[/tex], y = 0, x = 0, x = ln 9.

We will find the volume of the solid obtained by revolving this region around the x-axis through disc integration method.

The disc integration method is used to find the volume of a solid obtained by revolving a region around an axis parallel to x-axis.

Then, volume, V = [tex]\int\limits^0_{ln9} {y^2} \, dx[/tex]

                            = [tex]\int\limits^0_{ln9} {(e^{-2x})^2} \, dx[/tex]

                            = [tex]\int\limits^0_{ln9} {e^{-4x}} \, dx[/tex]

                            = [tex]\frac{e^{-4x}}{-4} |_{x=0\ to \ x=ln9}[/tex]

                            = [tex]\frac{e^{-4 ln9}}{-4} +\frac{1}{4}[/tex]

                            = [tex]\frac{9^{-4}+1}{4}[/tex] ≈ 0.25 cubic units

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Answer: 34

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

(3*5*7)((1)/(3) +( 1)/(5) -(1)/(7))
When you simplify this, the answer is 41.

Answer: 41

Step-by-step explanation:

0.0 65 is the probability that 30% or more of the sample will be living in poverty.

What is an probability in statistics?

P(P ≥ 0.34 ) = P ( [tex]\frac{p' - p}{\sqrt{p( 1- p )/n} }[/tex]      ≥     [tex]{\frac{0.34 - 0.30}{\sqrt{\frac{0.30 ( 1- 0.30)}{300} } } }[/tex]

            = P ( 2 ≥ 1.5119)

            = 0.0653

           = 0.0 65

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The squirrel sleeps 2548 hours more than the rabbit.

Difference of the numbers

Difference of the numbers means the result of subtracting one number from another.

Given,

If there are 52 weeks in a year,

Then we need to find how many more hours does a squirrel sleep in a year than a rabbit.

First, we have to find the sleeping pattern of squirrel  and rabbit.

A squirrel spends up to 60% of its day asleep, which means that an average squirrel sleeps for almost 15 hours each day.

Similarly, the rabbits are sleep six to eight hours each day.

So for one day,

Rabbit = 8 hours per day

Squirrel = 15 hours per day.

Then the sleeping hours for one week is

Rabbit = 8 x 7 = 56 hours

Squirrel = 15 x 7 = 105 hours

So, for 52 weeks, they spend

Rabbit = 56 x 52 = 2912

Squirrel = 105 x 52 = 5460

So, the difference is

=> 5460 - 2912

=> 2548

Therefore, the squirrel sleeps 2548 hours more than the rabbit.

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It would cost $70 to buy 40 ft of crown molding.

What is cost explain?

8 ft length costs $14

To find the cost of 1 ft length,

Divide through by 8

8ft/8 length costs $14/8

1ft costs $1.75

Now, to find the cost of 40 ft length

1ft costs $1.75

1 ft x 40 would cost $1.75

40 ft would cost $70

Therefore, it would cost $70 to buy 40 ft of crown molding.

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The true population mean is (222.52, 227.48) with a 95% confidence interval.

The critical factor for a 90% confidence interval for the true population mean is given by;

Critical factor = (x-μ)/(s/√n)

where, x = sample mean repair cost

s =  standard deviation of a sample

n = sample of stereos

μ  = critical value

⇒ P(-1.96< (x-μ)/(s/√n) < 1.96) = 0.95

⇒ P(-1.96×(s/√n) < (x-μ) < 1.96×(s/√n)) = 0.95

⇒ P(x - 1.96×(s/√n) < μ < x + 1.96×(s/√n)) = 0.95

95% confidence interval for

⇒ μ = (x - 1.96×(s/√n) , x + 1.96×(s/√n))

Here, x = 225, s  = 8.5, and n = 45

⇒ μ = (225- 1.96×(10.81/√13) , 225+ 1.96×(10.81/√13))

⇒ μ = (222.52, 227.48)

Hence, the true population mean is (222.52, 227.48) with a 95% confidence interval.

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The question seems to be incomplete the correct question would be

Calculate the 95% confidence interval for the true population mean based on a sample with x=225, s=8.5, and n=45.

Answer:

Yes

Step-by-step explanation:

If you have a graphing calculator or something similar, that could really help because all you would have to do is plug in the equation and look up the table and it would show that coordinate in there.

Answer:

20cm^3

Step-by-step explanation:

Divide 90 by 4.5.

90/4.5 = 20

We can multiply the density ratio by this quotient in order to find the volume of a sample 20x the size of the ratio's sample.

(4.5 x 20)/(1cm^3 x 20)
90g/20cm^3

In this step, let's identify the clues provided in the questions. We have:

Since we know the mass and density of titanium, we can apply the density formula to determine the volume of titanium.

Footnote: I have included the formula in case if you need to know it.

[tex]\boxed{\text{Density} = \frac{\text{Mass (Grams)}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]

To work out the volume of the titanium, we need to substitute the given clues from the question, into the formula. We have:

    [tex]\text{Density} = \dfrac{\text{Mass (Grams)}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]

When we substitute the mass and the density of titanium, we have:

    [tex]4.5 \ \text{g/cm}^{3}} = \dfrac{\text{90 grams}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]

Finally, let's simplify the equation.

    [tex]4.5 \ \text{g/cm}^{3}} = \dfrac{\text{90 grams}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]

    [tex]1 \ \text{g/cm}^{3}} = \dfrac{\text{20 grams}}{\text{Volume (cm}^{3} \text{)} }} }[/tex]

    [tex]\text{Volume (cm}^{3}) = \dfrac{\text{20 grams}}{\text{1 g/cm} ^{3} }[/tex]

    [tex]\text{Volume (cm}^{3}) = \dfrac{\text{20 grams}}{\text{1 g/cm} ^{3} } = \dfrac{20 \ \text{grams} \ \times 1 \ \text{cm}^{3} }{1 \ \text{grams}} = \boxed{20 \ \text{cm}^{3}}[/tex]

Therefore, the volume of titanium is 20 cm³.

A linear recurrence relation is a function or sequence in which each term is a linear combination of the terms that came before it.

The recurrence relation exists [tex]$T(n)=\Theta\left(3^n\right)$[/tex].

Recurrence relations are used to simplify complex problems by reducing them to an iterative process based on simpler versions of the problem.

Using the substitution method, we find out that

[tex]T(n) &=n+3 T(n-1) \\[/tex]

[tex]&=n+3(n-1)+3^2 T(n-2) \\[/tex]

[tex]&=n+3(n-1)+3^2(n-2)+3^3 T(n-3) \\[/tex]

[tex]&=\cdots \\[/tex]

[tex]&=n+3(n-1)+3^2(n-2)+\cdots+3^{n-1}(n-(n-1))+3^n T(0) \\[/tex]

simplifying the above equation, we get

[tex]$&=\frac{3^{n+1}-2 n-3}{4}+3^n T(0) \\[/tex]

[tex]&=\Theta\left(3^n\right)[/tex]

Even without doing the full calculation it is not hard to check that [tex]$T(n) \geq 3^{n-1}+3^n T(0)$[/tex], and so [tex]$T(n)=\Omega\left(3^n\right)$[/tex].

A cheap way to obtain the corresponding upper bound is by considering

[tex]$S(n)=T(n) / 3^n$[/tex], which satisfies the recurrence relation  

[tex]$S(n)=S(n-1)+n / 3^n$[/tex].

Repeated substitution then gives

[tex]$\frac{T(n)}{3^n}=\sum_{m=1}^n \frac{m}{3^m}+T(0)[/tex]

Since the infinite series [tex]$\sum_{m=1}^{\infty} \frac{m}{3^m}$[/tex] converges, this implies that [tex]$\frac{T(n)}{3^n}=\Theta(1)$[/tex] and so [tex]$T(n)=\Theta\left(3^n\right)$[/tex]

Therefore, the recurrence relation exists [tex]$T(n)=\Theta\left(3^n\right)$[/tex].

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Explanation:

The output of an absolute value is never negative.

The result of |2x+2| can never be negative, so we will have no solutions for the portion |2x+2| < 0

There will be one solution for |2x+2| = 0 as shown in the steps below

|2x+2| = 0

2x+2 = 0

2x = -2

x = -2/2

x = -1

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

Check:

|2x+2|  ≤ 0

|2(-1)+2| ≤ 0

|-2+2| ≤ 0

|0| ≤ 0

0 ≤ 0

We get a true statement at the end to fully confirm the single solution of x = -1

If you want to solve for y, then you would get y = -2x-9

This is the result after subtracting 2x from both sides. This is so we can undo the +2x that happens to the y variable.

Answer:

Infinitely many solutions (If its solved by systems of equations)

y = -2x - 9 (if you ONLY want to solve for y)

Step-by-step explanation:

Well you can solve this is 2 ways. Substitution and Elimination

SUBSTITUTION

2x + y = -9

2x+y=-9

Step 1: Solve 2x+y =−9 for y:

2x+y=−9

2x+y+−2x=−9+−2x(Add -2x to both sides)

y=−2x−9

Step: Substitute −2x−9 for y in 2x+y=−9:

2x+y=−9

2x+−2x−9=−9

−9=−9(Simplify both sides of the equation)

−9+9=−9+9(Add 9 to both sides)

Final answer -----> 0=0

ELIMINATION

2x + y = -9

2x+y=-9

Step 1: Multiply the second equation by -1, then add the equations together.

(2x + y = -9)

-1(2x+y=-9)

Which then becomes:

2x + y = -9

-2x - y = 9

Step 2: Add these equations to eliminate x:

Final answer -----> 0 = 0

Answer:  No

Explanation:

Apply the derivative

[tex]f(x) = \sqrt{x}\\\\f(x) = x^{1/2}\\\\f'(x) = (1/2)x^{-1/2}\\\\f'(x) = \frac{1}{2x^{1/2}}\\\\f'(x) = \frac{1}{2\sqrt{x}}\\\\[/tex]

Though we run into a problem since f ' (0) is undefined, due to the zero in the denominator.

Therefore, f(x) is not differentiable at x = 0.

The function is continuous, but only on the interval [tex]x \ge 0[/tex] and not over the entire set of real numbers R.

Answer:

k = 1.75

Step-by-step explanation:

5 - 4k = -7

k = 1.75, because if you subtract 4 from both sides, you are left with 1.75 = -7.

Answer:

k = 3

Step-by-step explanation:

5 - 4k = - 7 ( subtract 5 from both sides )

- 4k = - 12 ( divide both sides by - 4 )

k = 3

The marginal benefit from studying one extra hour is 5 percent.

Now,

Given:

To find: Marginal benefit on studying one hour extra.

Finding:

Now, marks scored on studying 4 hours is 80 percent and 5 hours is 85 percent.

Thus, the extra percentage that is scored is because of the 1 hour of extra studying.

The extra percentage = marginal benefit of studying extra = 85 - 80 = 5 percent.

Hence, the marginal benefit from studying one extra hour is 5 percent.

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In order to transform linear regression into polynomial regression, certain polynomial terms are added to it due to the non-linear relationship between the dependent and independent variables.

Let's say we have independent data X and dependent data Y. In the preprocessing stage, we turn the input variables into polynomial terms to some extent before feeding the data to a mode.

As a specific example of multiple linear regression, polynomial regression is a type of linear regression that estimates the connection as an nth degree polynomial. The performance can also be negatively impacted by the existence of one or two outliers since Polynomial Regression is sensitive to outliers.

The connection between the dependent and independent variables is best approximated by polynomial. It may be used for a wide range of functions. In general, polynomial suits a large range of curvature.

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Any 1 of the following transformations will work. There are others that are also possible.

translation up 4 units, followed by rotation CCW by 90°.

rotation CCW by 90°, followed by translation left 4 units.

rotation CCW 90° about the center (-2, -2).

Step-by-step explanation:

The order of vertices ABC is clockwise, as is the order of vertices A'B'C'. Thus, if reflection is involved, there are two (or some other even number of) reflections.

The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is a sequence of transformations involved, so a single rotation is probably not of interest.

If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.

If we rotate the final figure 90° CW, we find it ends up 4 units north of the starting position. So, another possible transformation is translation up 4 units + rotation 90° CCW.

Of course, rotation 90° CCW in either case is the same as rotation 270° CW.

_____

Answer:

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation i2 = −1; every complex number can be expressed in the form a + bi, where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes. For the complex number a + bi, a is called the real part and b is called the imaginary part. The set of complex numbers is denoted by either of the symbols {\displaystyle \mathbb {C} }\mathbb {C} or C. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world.[1][a]

Step-by-step explanation:

The compound inequality for the area written in terms of x is 100 ≤ 20x ≤ 1,000.

We know that, the area of rectangle is given by:

Area = Length × Breadth

Now, we will substitute the values of length as 4x and breadth as 5 in the formula:

= 4x × 5

= 20x

Now. we will substitute this value in the inequality 100 ≤ A ≤ 1,000 to get the compound inequality:

100 ≤ 20 x ≤ 1,000.

Therefore, the compound inequality for the area written in terms of x is 100 ≤ 20x ≤ 1,000.

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The gross income over the whole week upon working during the day and at night is; $449.04.

Since, the pay rates during the day and night according to the task content are; $10.05 per hour and $12.01 per hr respectively.

It then means that the total gross total income can be calculated as follows;

(10.05 × 16) + (12.01 × 24)

= 160.8 + 288.24

= $449.04.

Therefore, the gross income over the whole week upon working during the day and at night is; $449.04.

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14 is the largest integer.

Let x, x+2 & x+4 be the 3 integers.

x + 2 (x+2)= (x+4)+20

x + 2x + 4 = x + 4 + 20

3x + 4 = x + 24

3x - x = 24 - 4

2x = 20

x = 20/2

x=10 for the smallest integer.

10 + 2 = 12 for the middle integer.

10 + 4 = 14 for the largest integer.

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The sampling distribution of sample means is a mean of 79 and a standard deviation of 3.

The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation, which is also known as the square root of variance.

Given that,

Population mean,  [tex]\bar{x}[/tex] = 79

Population standard deviation, σ = 18

Sample size, n = 36

We have to determine the mean and standard deviation of a sampling distribution of sample means.

Let X denotes a random variable distributed with a mean and standard deviation of 85 and 28 respectively.

Also, if a random sample of size n is drawn from the population, then the sample mean is denoted by [tex]\bar{x}[/tex].

The sampling distribution of sample means [tex]\bar{x}[/tex] is given by:

ц [tex]\bar{x}[/tex] = ц

σ [tex]\bar{x}[/tex]  = σ/√n

Therefore, for the sample size n = 36, the sampling distribution of sample means [tex]\bar{x}[/tex] is obtained as:

ц [tex]\bar{x}[/tex] = 79

σ [tex]\bar{x}[/tex]  = 18/√36 = 3

Hence, the required sampling distribution of sample means is mean of 79 and a standard deviation of 3.

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Answer:

35:1

Step-by-step explanation:

Answer:

7 : 12

Step-by-step explanation:

the times must be of the same measure.

1 hour = 60 minutes , then

Dan : David = 35 : 60 = 7 : 12 ← in simplest form

Answer:

A) -12-4-5

B) X^2-X

Step-by-step explanation:

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