Help with my math !!

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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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:

A) -12-4-5

B) X^2-X

Step-by-step explanation:

..

..

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.

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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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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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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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:

Step-by-step explanation:

Let the number of rooms is x.

Each room is built to hold 6 puppies, so x rooms hold 6x puppies.

The equation for this is:

And the solution is 13 rooms.

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.

The histogram for these data is given at the end of the answer.

An histogram is a graph that shows the number of times each element of x was observed.

For this problem, there are 5 classes with a range of 30, as 59.5 - 29.5 = 30, hence the class width is of:

30/5 = 6.

From the data-set, we have that:

Considering this, the histogram is given at the end of the answer.

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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]

Answer: 34

Step-by-step explanation:

1, 3, 4,5

The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x). The roots of the quadratic equation are the values of x that fulfill the equation (α, β).

It is a given that the quadratic equation has two roots. Roots might have either a real or imaginary nature.

1)m( 2m + 3) =0

2m²+3m=0

Yes it is a quadratic equation.

2) 11t² (t - 4 ) = 0

11t³-44t²=0

NO

3) 5h + h² = - 7

Yes it is a quadratic equation.

4)4b (b - 2 ) = - 8

4b²-8b +8 =0

Yes, it is a quadratic equation.

5) y² + 7y - 6 = 0

Yes it is a quadratic equation.

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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:

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:

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

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

Work Shown:

[tex]A = (x_1,y_1) = (-2,4) \text{ and } B = (x_2, y_2) = (1,0)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-1)^2 + (4-0)^2}\\\\d = \sqrt{(-3)^2 + (4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

I used the distance formula.

A slight alternative is to plot the points to form a right triangle. The hypotenuse is the segment from A to B. Then use the pythagorean theorem to find the hypotenuse. Take note how a 3-4-5 right triangle forms.

The value of the expression 2^6 × 2^2 is 8^2 * 4

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

2^6 × 2^2

Apply the product law of indices to the above expression

So, we have

2^6 × 2^2 = 2^(6 + 2)

Evaluate the sum in the above expression

So, we have

2^6 × 2^2 = 2^8

Expand the expression

So, we have

2^6 × 2^2 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

This gives

2^6 × 2^2 = 8 * 8 * 4

So, we have

2^6 × 2^2 = 8^2 * 4

Hence, the value of the expression 2^6 × 2^2 is 8^2 * 4

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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 z test statistic needed for this hypothesis test is 0.75 .

Z test is a statistical test that is conducted on data that approximately follows a normal distribution. The z test can be performed on one sample, two samples, or on proportions for hypothesis testing. It checks if the means of two large samples are different or not when the population variance is known.

NOW,

sample proportion =  p = x / n = 0.23

Test statistics

z = ( p - p0 ) / [tex]\sqrt{ p0*(1-p0)}[/tex] / n

= ( 0.23 - 0.20) /  [tex]\sqrt{ (0.20*0.80) / 100}[/tex]

= 0.75

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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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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

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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