A rectangle has a perimeter of 48 inches. If twice the length decreased by three is equal to three times the width, then find the length and width.

1. Write a system of equations that will solve the problem
2. Define your variables
3. Solve the problems SHOW YOUR WORK
4. Sketch a graph of your solution

Answer:

The difference between factoring x4+9x2+8 and factoring x2+9x+8 is that the first equation is a fourth degree polynomial, while the second equation is a second degree polynomial. The first equation can be factored into (x2 + 3)(x2 + 8), while the second equation can be factored into (x + 8)(x + 1).

The value of the integral ∫x²dV using cylindrical coordinates is 512π / 3 .

In this case, the solid is positioned between the cylinder x² + y² = 4 and will be evaluated by using the cone z²= 16x² + 16y² .

Cylindric coordinates will be used to calculate this integral  [tex]\int\limits_e {x^2} \, dx[/tex].

The distance from the origin to the point (x, y, 0) and the angle the point (x, y, 0) makes with the x-axis, respectively, are provided by the formulas.

x = r cos θ

y= r sin θ

With these coordinates, we shall characterize the solid E.

The boundary is then x² + y² = r²

The boundary also becomes r² = 4 or ( 0 ≤ θ ≤ r² )

Again z = 16r²

The original integral must now be translated into terms of these new coordinates. It is necessary to multiply the function by the Jacobian of the change in coordinates in order to ensure that the result remains the same. The value for the cylindric coordinates is r. Then

[tex]\int_ex^2 dx = \int\limits^{2\pi}_0\int\limits^2_0\int\limits^{16r^2}_0 r(r^2cos^2\theta)dzdrd\theta[/tex]

[tex]=\int _0^{2\pi }\int _0^216r^5\cos ^2\theta drd\theta[/tex]

[tex]=\int _0^{2\pi }\frac{512}{3}\cos ^2\theta d\theta[/tex]

= 512/3 π

Hence the volume of the solid that is enclosed by the integral is given by 512/3 π .

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Answer:

394

Step-by-step explanation:

because 14,203 divided by 36 is 394.527777778 but the complete number of necklaces he can make is 394.

a firm in a purely competitive industry is currently producing 1,000 units per day at a total cost of $700 then average total cost is $ 0.61

The average total cost is calculated as the total cost divided by the number of outputs. The firm's ATC at these three levels of production will be:

1. 1,000 units per day at a total cost of $700.

ATC = Total cost/output

ATC = $700/1000

ATC = $0.58

2. If the firm produced 500 units per day, its total cost would be $450.

ATC = Total cost/output

ATC = $450/500

ATC = $0.45

3. If it produced 700 units per day, its total cost would be $425.

ATC = Total cost/output

ATC = $425/700

ATC = $0.61

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Answer:

22

Step-by-step explanation:

it is false that that when the direction of bias is towards love it means that the error causes the true measure of association to be overestimated

A Measurement process is biased if it systematically overstates or understates the true value of the measurement

Systematic error due to difference in accuracy or completeness of recall to memory of past or experience is the most associated with recall bias.

Positive association is biased toward the null null value it means that the error causes the true value of association to be underestimated

but in the given given question the statement states that when the direction of the bias is toward the null it means that the error causes the true measure of association to be overestimated which is false

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The exponential growth function's estimate of the monthly percentage rate is; log 3/ 3.

We will employ the exponential function, as indicated, to determine the monthly percentage rate;

P(t) = P(0)e∧(rt)

Enter the following parameters into the calculation to obtain the rate "r".

P(t) = P(0)e∧(rt)

3P(0) = P(0)e∧(rt)

3 = e∧(rt)

Taking log both sides.

log 3 = (rt)

r = log 3 / 3

r = 0.366

r = 36.6%

Consequently, the exponential growth function's estimate of the monthly percentage rate compounded continuously is; log 3/ 3.

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Answer: the answer is ln(2)/3

Step-by-step explanation:

The simplified expression is [tex]\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex].

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.

The given statement is "7-radical 7 over10+radical 3".

Write the statement in mathematical form and simplify:
[tex]\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\\\\\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\times\frac{10 - \sqrt{3}}{10 -\sqrt{3}}\\\\\frac{(7 - \sqrt{7})(10-\sqrt{3})}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex]

Hence, the simplified expression is [tex]\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex].

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Yes there was an error made and it is a type II error

What is type i and ii error in Hypotheses testing?

A Type I mistake in statistics is a false positive finding, whereas a Type II error is a false negative finding.

The possibility of making these mistakes is inherent in hypothesis testing since making a statistical choice always entails some level of uncertainty.

The significance level, or alpha (), determines the likelihood of a Type I mistake, whereas beta () determines the likelihood of a Type II error. These dangers can be reduced by carefully designing the layout of your study.

Comparison of Type I and Type II errors

Considering your minor symptoms, you decide to get checked for COVID-19. There are two mistakes that could happen:

False positives of type I are when a test indicates you have a coronavirus when you don't.

False negative type II errors occur when the test results indicate that you don't have coronavirus but in fact you have.

The null and alternate hypotheses are provided below for the scenario:

H0: The average amount of tooth whitening achieved by toothpaste is four shades.

Ha: The average amount of colors your teeth lighten after using toothpaste is less than four.

H0: µ = 4

Ha: µ < 4

While we reject the null hypothesis when it is true, we made a type I error, according to the definition.

The failure to reject the null hypothesis when the null hypothesis is false is what is referred to as a type II error .

In the hypothetical situation, it is said that the average number of shades that toothpaste whitens teeth is three. This implies,

There are less than four hues. This proves that the null hypothesis is untrue.

This indicates that when the null hypothesis is false, we are unable to reject it.

It is a type II error as a result.

Yes, a type II error.

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The average sample of 10 plantings tree-planting time is two hours- P-value = 0.251453

The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees, shrubs, and so on to be used for the project-P-value = 0.251453

We are unable to reject the null hypothesis and accept it because the p value is higher than the significance level.

As a result, we draw the conclusion that the average tree-planting time is two hours.

Hypothesis:

In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.

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Answer: f(x) = -1/2(x+3)

Example: g(x) = -1/2(-x-3)

This function is a dilation and a reflection of the parent function f(x) because when graphed, the two functions have the same shape but are reflected over the y-axis and are half the size of the original.

Answer:

40

Step-by-step explanation:

280 divided by 7

The regression equation of the formula regarding tuition will be given as y = 34000 - 2300x.

Regression method of writing an equation is used to show relation between two variables. The two variables include an independent variable and a dependent variable. The dependent variable is related to the independent variable and their relation and changes can be shown with the help of regression model. According to the question

the charge for tuition = $32000

Charge deduced from tuition per year = $2300

So we assume the tuition cost as y and the number of years as x.

The regression equation will be

y = 34000 - 2300x

where y is the tuition cost and x is the number of years in school and y is dependent variable and x is independent variable.

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Answer: B. Angle Bisector

Why: the line from D to be is intersecting or bisecting the 90 degree angle

The sample standard deviation of the following dataset is dev = $22.4 : $96, $125, $80,$110, $75, $100,8121.

The square root of the variance of a random variable, sample, mean ,statistical population, data set, or probability distribution is that variable's standard deviation. Although less robust in practice, it is algebraically simpler than the average absolute deviation.The fact that the standard deviation is expressed in the same unit as the data, as opposed to the variance, is a useful characteristic of the statistic.

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Answer: h = 70

Step-by-step explanation: We just need to take 14 timed 5 and we will get h.  

14 = h/5 because it is divided so to get rid of it we multiply by 5

70=h

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Answer:

25

Step-by-step explanation:

knowing that 80 is 4/5 of 100, we need to find the number that is 5/4 of 20. That number is 25. This can be proven by calculating that 20/25 and 80/100 both can be simplified to 4/5.

The required are of shaded region for the given question is 20.7 cm^2.

A circle is partitioned into two areas, specifically the significant area, and the minor area. A bigger piece of the circle involved by the radii and the significant circular segment is supposed to be a significant area. A more modest part involved by two radii and a minor circular segment is known as the minor area.

We have,

∠BOC = 2π/5, radius = 6 cm, OA = 2 cm, DC = 2 cm

OD = 6 - 2 = 4 cm,

We know that

Area of triangle = OA×OD×sin(2π/5)/2

A = 2×4×0.475/2 = 1.9 sq. cm

And

Area of sector = (π/5)/2π ×πr^2

Area of sector = π(6)^2/5

Area of sector = 22.6  sq. cm

Area of shaded region = 22.6 - 1.9 = 20.7  sq. cm

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An expression that would represent the number of frames he has left for him to make would be = X = n - ⅔.

A fraction is an expression that is used to represent the part of a whole structure or an object such as the wooden frame.

The total number of wooden frames to be made= n.

The number of frames that Mr. Brown has made= ⅔

The number that is left to be made = X

But, n = ⅔ + X

To find X, make X the subject of formula;

X = n - ⅔.

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Why you lie you say 30 but give a 15

The possible amount of time that it could take Wyatt to husk 72 dozen ears of corn is 4 to 6 hours.

What are time and work?

Time is the span of any action or work that occurs or is ongoing. Work is a task or series of activities carried out to accomplish a specific goal.

Given, Wyatt can husk anywhere from  12 to  18 dozen ears of corn per hour.

Thus, to find the time taken to husk 72 dozen ears of corn,

the maximum time = 72/12 =6 hours

And, the minimum time =  72/18 =4 hours

Thus, depending on his speed, Wyatt takes anywhere from  4  to 6 hours to husk  72 dozen ears of corn.

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Answer:

To find the answers you just need to multiply each value by 3. This is as we are given the information that y is equal to 3x. If we know this and we know the values of x we can easily work out the output (y)!!

We can also see a pattern of +3 going upwards!!

Hope this helps, have a great day!

The number of packages that can be wrapped with 12 feet of ribbon is 24.

For the stated question.

Total length of the ribbon = 12 feet.

Ribbon required to wrap a one box = 1/2 foot.

Number of boxes = Total length / required ribbon for one box

Number of boxes = 12/ (1/2)

Number of boxes = 12 x 2

Number of boxes = 24

Thus, the number of packages that can be wrapped with 12 feet of ribbon is 24.

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True, A P-value of 0.07 is less than that significance requirement of 0.1, suggesting that there is sufficient evidence to conclude that people who have a significant other are happier than single people.

The hypothesis being examined was that those who have a significant other are happier on average than those who do not. To test this hypothesis, data from a sample size of persons were collected and evaluated to compute the P-value.

The P-value of 0.07 was determined to be less than the level of significance established at 0.1, implying that there is sufficient evidence to support the hypothesis that persons with a significant other are happier on average than solitary people.

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Answer:yes

Step-by-step explanation: 2/8=4

4/1=4 since both of them equal 4 they are equivalent

The equation of the ellipse in the graph, with center at (0, 0), and semi  major and minor axis of 3 and 2 can be presented as follows;

[tex]\dfrac{x^2}{2^2} +\dfrac{y^2}{3^2 } = 1[/tex]

An ellipse is the locus of a point that moves such that the sum of the distance from two points is constant.

The standard form of the equation of an ellipse can be presented as follows;

[tex]\dfrac{(x - h)^2}{b^2} + \dfrac{(y - k)^2}{a^2} = 1[/tex]

Where;

(h, k) = The coordinates of the center of the ellipse

a = The semi major axis

b = The semi minor axis

From the attached graph the coordinates of the center of the ellipse is; (0, 0)

The semi major axis, a  = 3

The semi minor axis, b = 2

Therefore;

[tex]\dfrac{(x - 0)^2}{2^2} + \dfrac{(y - 0)^2}{3^2} = 1[/tex]

The equation of the ellipse in standard form is therefore;

[tex]\dfrac{x^2}{2^2} + \dfrac{y ^2}{3^2} = 1[/tex]

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y=2x/3-2  is the required slope-intercept form of the line

The coordinate of points where the line intersects at the x-axis is (-3,0) and at the y-axis is (0,-2) now from there two points we can find slope if line that is

slope=y₂-y₁/x₂-x₁=(-2-0)/(0-(-3))

slope =-2/3

with one point (0,-2) and slope we can find the slope-intercept form that is y=mx+c

where m is slope and c is intercept on the y-axis

y=2x/3-2 this is the slope-intercept form and by simplifying it we get

3y=2x-6

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The margin of error for the population mean is 5.601

What does the term "margin of error" mean?

Your results will deviate by how many percentage points from the actual population value, according to your margin of error. It is described as a very small percentage that is allowed for error in calculations.

Given c = 0.95

The significance level is obtained as follows:

alpha = 1 - c

alpha = 1 - 0.95

alpha = 0.05

Also, it is given that n = 150 and sigma = 35 .

The critical value of Z distribution at 0.05 level of significance can be computed in MS Excel using + NORMS INV (alpha/2) function as follows:

Thus, [tex]Z_{0.005/2}=1.96[/tex]

Now, the margin of error can be computed as follows: ME = Critical Value x Standard Error

[tex]Z_{0.005/2}*\frac{sigma}{\sqrt{n} } \\= 1.96 * \frac{35}{\sqrt{150} } \\= 5.601[/tex]

Thus, the margin of error for the population mean is 5.601

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