Salaries of 40 college graduates who took a statistics course in college have a mean x of $60.600. Assuming a standard deviation of $13,553 construct a 90% confidence level for estimating the population mean u

Answer:

Width is 5.

Length is 11.

Step-by-step explanation:

Let the width be x.

x = width

The length is 6 feet longer.

x + 6 = length

Area is

length × width

Area is 55 (given)

55 = x(x+6)

Use distributive property.

55 = x^2 + 6x

Set equal to 0 and factor to solve. See image.

We have to toss out a solution that doesn't make sense. A measure of a side of a rectangle cannot be negative.

see image.

Answer:

the answer is 1.06

Step-by-step explanation:

1.06 x 4 = 4.24

Answer:

always true , because 120+60=180

Points A, B, and C are collinear then the possibility of AB will be equal to 4.7. Hence, option A is correct.

Points that are parallel to or within a single line are referred to as collinear points. In Euclidean space, two or more points have been shown to be collinear if they are situated on a line that is either close to or far from another.

As per the given information in the question,

The case is that when B is in between A and C, which means A, B, and C are collinear.

So,

AB + BC = AC

AB + 8.5 = 13.2

AB = 13.2 - 8.5

AB = 4.7

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Answer: A residual is the difference between the observed value of a dependent variable and the predicted value based on a given model. In this case, the manager of the water park has produced a least squares regression equation of the form y = -3110 + 51.2x, where y is the number of customers entering the park and x is the daily high temperature. This equation can be used to predict the number of customers based on a given temperature.

On the day in question, the high temperature was 93F and 1700 customers entered the park. Using the given equation, we can predict the number of customers that would be expected based on this temperature:

y = -3110 + 51.2x

= -3110 + 51.2 * 93

= -3110 + 4768.6

= 1658.6

The residual for this observation is the difference between the observed value of 1700 and the predicted value of 1658.6, which is 1700 - 1658.6 = 41.4. This is the residual for this observation.

The dimensions of the box with a volume of 4096 cm³ that has a minimal surface area are 16cm×16cm×16 cm.

A solid object's surface area is a measurement of the overall space that the object's surface takes up. It is also known as the overall area of a three-dimensional shape's surface. The formula to calculate surface area is S = 2(xy+yz+zx) where x is length, y is width and z is the height of the object.  

Given the volume is 4096 cm³.

Then, V = xyz = 4096. Deriving the value of z from this, we get z = 4096/xy. Substitute value of z in S = 2(xy+yz+zx), we get,

[tex]\begin{aligned}S&=2\left(xy+y\times\frac{4096}{xy}+x\times\frac{4096}{xy}\right)\\&=2\left(xy+\frac{4096}{x}+\frac{4096}{y}\right)\\&=2xy+\frac{8192}{x}+\frac{8192}{y}\\&=2xy+8192\left(\frac{1}{x}+\frac{1}{y}\right)\end{aligned}[/tex]

Differentiating S with respect to x, we get,

[tex]\frac{dS}{dx}=2y-\frac{8192}{x^2}[/tex]

Equating this to zero and multiplying with x² we get,

[tex]\begin{aligned}2y-\frac{8192}{x^2}&=0\\2x^2y-8192&=0\\x^2y&=\frac{8192}{2}\\x^2y&=4096\end{aligned}[/tex]

Differentiating S with respect to y, we get,

[tex]\frac{dS}{dy}=2x-\frac{8192}{y^2}[/tex]

Equating this to zero and multiplying with y² we get,

[tex]\begin{aligned}2x-\frac{8192}{y^2}&=0\\2xy^2-8192&=0\\xy^2&=\frac{8192}{2}\\xy^2&=4096\end{aligned}[/tex]

Dividing x²y by xy², we get,

[tex]\begin{aligned}\frac{x^2y}{xy^2}&=\frac{4096}{4096}\\\frac{x}{y}&=1\\x&=y\end{aligned}[/tex]

Substitute x = y in x²y = 4096, we get,

[tex]\begin{aligned}y^3&=4096\\y&=16=x\end{aligned}[/tex]

Then, the z value is

[tex]\begin{aligned}z &= \frac{4096}{16\times 16}\\&=16\end{aligned}[/tex]

The required answer is 16cm×16cm×16 cm.

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Answer:

1) 12ft

2) 8ft

3) 6 ft

4) 3ft

5)

Answer:

1. 12ft

2. 8ft

3. 6ft

4. 4ft

5. The diameter and radius of the circles are proportional by a factor of 1.5 because 12/8 = 1.5 and if I multiply circle B's radius by a factor of 1.5 I will get the radius of Circle A as is with the diameter.

6.

A- (3/7)(21) = x

B- x approximately equals 9

Step-by-step explanation:

Circumference formula

C= 2(pi)r

z equals circumference of circle q

Q = 7

P = 3

Z = 21

(P/Q)(Z) = x

Therefore (3/7)(21) = 9

We can prove this by using the Circumference formula

C= 2(pi)r

C=2(pi)1.5

C= 3(pi)

C= 9.4247...

Rounded = 9

hope this helps!!

It will take 220.8 hour, Teresa to knit 265 squares

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

Given that the relationship between the number of hours Teresa spends

knitting and the number of squares she completes for a blanket.

We need to find the hours does it take Teresa to knit 265 squares.

Now Based on the equivalent ratios  we have;

Teresa's Knitting /Completed Squares

10/12 = x / 265

Thus, Now cross multiplication we get;

x = 265(10/12)

x = 220.8

The answer is 220.8

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We would expect 198 of the intervals to contain the mean.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data

Given that Mary wishes to estimate the mean height of women aged 18-24.

picks a sample of 100

Women aged between 18 and 24 and constructs a 99% confidence interval for the population mean.

If Mary were to repeat this procedure 200 times in total, she would obtain

200 different confidence intervals.

A confidence interval of a parameter gives an interval in which the parameter is expected to be found. Because the interval either contains or doesn't contain the parameter, the probability is either 0 or 100%, which is not helpful.  A 95% CI says that if we construct 100 intervals, 95% will contain the parameter. That is a true percentage, not a confidence. We don't know which 95, however, since the parameter is still unknown or unknowable.

I would expect 99%×200 or 198 of the intervals to contain the mean.

Hence, would expect 198 of the intervals to contain the mean.

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Answer:

$3893.97

Step-by-step explanation:

5000 = x (1 + 0.05/365)^365 * 5

5000 = x ( 1 + 0.000137)^1825

5000 =  x (1.000137)^1825

5000 = 1.284036 x

1.284036 / 1.284036 x = 5000 / 1.284036

x = 3 893.97182

x = 3 893.97

Answer:

$3,894.07

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula and solve for P:

[tex]\implies 5000=P\left(1+\dfrac{0.05}{365}\right)^{365 \times 5}[/tex]

[tex]\implies 5000=P\left(1.000136986...\right)^{1825}[/tex]

[tex]\implies P=\dfrac{5000}{\left(1.000136986...\right)^{1825}}[/tex]

[tex]\implies P=3894.070588...[/tex]

Therefore, the amount you would need to deposit in an account now in order to have $5,000 in the account in 5 years time is $3,894.07.

a) Making x the subject of the formula in terms of r is; x = (r + 1)/r

b) Solving for r and x gives; r = 5/3 and x = 8/5

a) We are given that;

r = 1/(x - 1)

We are asked to make x the subject of the formula in terms of r. Thus;

Multiply both sides by (x - 1) to get;

rx - r = 1

r + 1 = xr

x = (r + 1)/r

b) We are given that;

xr + ²/₃ = 2r

Put (r + 1)/r for x to get;

r(r + 1)/r + ²/₃ = 2r

r + 1 + ²/₃ = 2r

1 + ²/₃ = r

r = 5/3

Put 5/3 for r into the x equation to get;

x = ((5/3) + 1)/(5/3)

x = (8/3)/(5/3)

x = 8/5

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The equation for converting gain in decibels to a linear scale is dB → gain-multiplier: [tex]g=2^{\frac{d}6} }[/tex]

gain-multiplier → dB: [tex]6*log_{2} g[/tex]

The decibel is used in a wide range of applications. Decibels are especially used when referring to power or a derived measure, which values can vary in a wide range. The most prominent usage of decibels is in sound volume. So, for example, a sound of 0dB is barely hearable, whereas a vacuum cleaner on average has 75dB and a rock concert reaches about 110 dB.

Practical version-

dB → gain-multiplier: [tex]g=2^{\frac{d}6} }[/tex]

gain-multiplier → dB: [tex]6*log_{2} g[/tex]

So if we set that 0 dB gain as 1.0 factor, and -∞ dB gain is 0.0 factor, it means that (if we are considering voltage gain as in a mixing desk fader) :

gain = 20.0*log10(factor)

therefore :

factor = 10^(gain/20.0)

If, as described in a comment, the 0 dB gain is at 0.65 factor, it means the ref is 0.65.

gain in dB = 20*log10(factor/0.65)

factor = 0.65*10^(gain/20.0)

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Answer:

B

Step-by-step explanation:

To determine how much data is enough to estimate the average weight of this population with a 95% confidence and an error not superior to 15 grams, we would need to use a statistical sample size calculator or consult a statistical table. Factors that would need to be considered include the desired confidence level, the desired margin of error, and the standard deviation of the population.

Using a sample size calculator, we can input these values and determine the required sample size. For example, with a 95% confidence level, a margin of error of 15 grams, and a standard deviation of 87 grams, the required sample size would be approximately 38 children. This means that we would need to measure the weight of at least 38 male children who are 10 weeks old in order to estimate the average weight of the population with a 95% confidence and an error not superior to 15 grams.

It is important to note that this is just an estimate and the actual sample size may vary depending on the specific characteristics of the population being studied. Additionally, it is always a good idea to consult with a statistician or other expert to ensure that the appropriate sample size is used in any statistical analysis.

The equations that model the total cost of the meal are:

A. x = 3 * 4 + 29

C. x = 41

We know that the family has 4 members and they buy:

Then the total cost is the $29 for the dinner plate plus four times the $3 for the dessert, this is:

x = $29 + $4*3

x = $29 + $12

x  = $41

Then the correct options are A and C.

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The value of x in the triangles is 24.5

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

The triangle

On the triangle, we have the following ratio

7 + x : x = 27 : 27 - 6

Evaluate the difference

7 + x : x = 27 : 21

Express as fraction

This gives

x/(x + 7) =21/27

So, we have

27x = 21(x + 7)

Expand

27x - 21x = 147

So, we have

6x = 147

Evaluate

x = 24.5

Hence, the value of x is 24.5

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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Answer:

Step-by-step explanation:

es posible que desee cambiar a la sección de negocios del sitio web porque es posible que puedan responderle mejor

The equation of the cubic polynomial is f(x) = x³ - x² -9x + 9.

What is a polynomial function?

Polynomial functions are defined for all values of x and have a finite number of roots (x-values at which the function is equal to 0). The roots of a polynomial function can be found by solving the equation f(x) = 0.

By using the given table, we can plot the points on the graph and we can draw a graph

• Fitted coefficients:

a = 9

b = -9

c = -1

d = 1

Then we can prepare the polynomial as

y = 9 - 9x - x² + x³

Now write down in the standard form, we get

f(x) = x³ - x² -9x + 9

Hence, the equation of the cubic polynomial is f(x) = x³ - x² -9x + 9.

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Answer:

No, because with Y- represents the reading time & X-Representing the TV time. The two variables are being effected by the age of te viewer/reader

Step-by-step explanation:

The change represents growth and rate of increase is 4.2%

Exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change.

Given that, an exponential function y = 970(1.042)ˣ

When the growth rate is greater than 1, then the function represents a growth.

The general form equation is:

y(x)= a(1+r)ˣ such that r is the growth percent.

So,

1+r = 1.042

r = 0.042

r = 4.2%

Hence, the growth rate is 4.2%

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Answer:

[tex]85 \sqrt{5} [/tex]

Step-by-step explanation:

30/4=7.4

30/5=6

6/3=2

Alex went to the moves 4 times that year.

12,000g

Since there are 1,000 grams per kilogram, that means:

1 kg = 1,000 g

2kg = 2,000g

3kg = 3,000g

And so on until we get to 12 kilograms:

12kg = 12,000g

12,000g

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer:

12000 gram

Step-by-step explanation:

step 1:

[tex]1 kg=1000g\\12kg = x[/tex]

step 2:

do a criscross multiplication to find x.

[tex]x*1kg=1000g*12 kg[/tex]

step 3:

devide both sides by 1kg

[tex]x=(1000g*12kg)/1kg[/tex]

step 4:

cancel units tha exist on both the numerator and the denominator.(in our case cancel kg)

[tex]x=(1000kg*12)/1[/tex]

Step 5: simplify

[tex]x=12000g[/tex]

The "method is least square" is a least-squares fitting of a simple regression model minimizes the sum of the squares of the perpendicular distances from the data points to the regression line.

The term linear regression refers the predictive method to predict or estimate the values of a dependent quantitative variable denoted by y with the help of other independent variables denoted by x1,x2,x3 by using one of many methods like that of ordinary least squares.

Here we need to find what is the method for a least-squares fitting of a simple regression model minimizes the sum of the squares of the perpendicular distances from the data points to the regression line.

As per the definition of the linear regression, we have know that a least-squares fitting of a simple regression model  which minimizes the sum of the squares of the perpendicular distances from the data points to the regression line.

Here we have to take the square for the number to fit into the given interval.

So, this is known as method for least square and it does not use the sum of perpendicular distances between the points and the ‘estimated regression equation’ does not used to minimize.

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Triangle ABC is equilateral and hence proved.

According to the question,

Let ABC be a triangle

And the given points A1, B1, and C1 are on its sides BC, AC, and AB respectively

Since according to the first equality says that A1, B1, and C1 are not the midpoints and just normal points on the lines.

According to what equality says that ΔABC = ΔA1B1C1 because the sides are in proportion.

Let us consider 3 more triangles = ΔAB1C1, ΔBC1A1, and ΔCA1B1

Now, these above-mentioned triangles will also be similar due to the proportionality insides.

Which results in ⇒ ∠A = ∠B = ∠C due to the phenomenon of corresponding angles of triangles.  

Therefore, Triangle ABC is equilateral and hence proved.

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Statistic value t=2.27

p-value: < 0.00001

To obtain information on the corrosion-resistance properties of a certain type of steel conduit a random sample of 45 specimens was taken and buried for two years.

The study variable is:

X: Max. penetration of a steel conduit.

The data of the sample

n= 45

sample mean X[bar]= 52.9

sample standard deviation S= 4.2

The conduits are manufactured to have a true average penetration of at most 50 mills, symbolically: μ ≤ 50

The hypothesis is:

H₀: μ ≤ 50

H₁: μ > 50

α: 0.05

To choose the corresponding statistic to use to study the population mean, the variable must have a normal distribution. There is no available information to check this, so I'll just assume that the variable has a normal distribution and, since the population variance is unknown and the sample is small, the statistic to use is a Student t.

Under the null hypothesis, the critical region and the p-value are one-tailed.

Critical value: [tex]t_{n- 1;1-\alpha} =t_{44;0.95} =1.68[/tex]

Rejection rule:

Reject the null hypothesis when t ≥ 1.68

t= [tex]\frac{52.9-50}{\frac{4.2}{\sqrt{45} } }[/tex]

t= 2.9-0.626 = 2.27

If the calculated value is greater than the critical value, the decision is to reject the null hypothesis.

p-value:

P(t ≥ 2.27) = 1 - P(t < 2.27) = < 0.00001.

The p-value is less than α so the decision is to reject the null hypothesis.

Since the null hypothesis was rejected, then the population average of the penetration of the conduits specimens is greater than 50 mils. It is not recommendable to use these conduits.

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Therefore ,the linear function that best describes the scatterplot relating the number of books in the library is y = 10 + 8x

Two separate but related concepts are referred to as linear functions in mathematics: A polynomial function of degree 0 or 1 is referred to as a linear function in calculus and related fields if its graph is a straight line.

Here,

The points given on the scatterplot are (0,10),(4,42),(8,74) & (12,106)

By putting in the points in the given linear functions

y = 8 − 10x

y = 8 + 10x

y = 10 − 8x

y = 10 + 8x

Thus ,the  linear function which best satisfy the points given on the scatterplot is  y = 10 + 8x

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Answer:

y = 10 + 8x

Step-by-step explanation:

we can find the y-intercept first, by observing the point at which x=0, (0,y)

when x = 0, y = 10. The y-intercept is 10.

Let's find the slope. Given the 2 points (0, 10) and (4, 42), we can use the slope calculating formula:

[tex]m(slope)=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

we have:

m = (42-10)/(4-0)

m = 32/4

m=8.

we have y = 8x + 10 (slope-intercept form), which is equal to y = 10 + 8x (unofficial confusing form.)

Hope this helped!

The required value of x  for y = 25 is 32.4

What is a linear function?

A polynomial function of degree 0 or 1 that has a straight line as its graph is said to be linear.

A linear function is given by:

y = mx + b

where:

The slope, or m, indicates how much y changes when x changes by one, or the rate of change.

b is the y-intercept, which is also known as the function's starting point and is the value of y at x = 0.

From the given graph, the line passes through points (32,25) and (48,50), then the slope of the line is given by:

m = (50-25)/(48-32) = 25/16 = 1.6

Then, y = 1.6x + b

For points (48,50) then,

or, 50 = 1.6*48 + b

or, 50 = 76.8 + b

or, b = 50 - 76.8 = -26.8

Then, the equation will be

y = 1.6x - 26.8

So, for y = 25 then x becomes

25 = 1.6x - 26.8

or, 1.6x = 25 + 26.8

or, 1.6x = 51.8

or, x = 32.4

Hence, the required value of x is 32.4.

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Answer: x>2

Step-by-step explanation:

To solve for x, we want to use inverse operations to isolate x.

[tex]-\frac{x}{2} < -1[/tex]            [multiply both sides by -2]

[tex]x > 2[/tex]