A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 224 cars owned by students had an average age of 5.06 years. A sample of 233 cars owned by faculty had an average age of 7.19 years. Assume that the population standard deviation for cars owned by students is 3.42 years, while the population standard deviation for cars owned by faculty is 2.81 years. Determine the 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty. Step 2 of 3 : Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.

9514 1404 393

Answer:

  (5, 6) is (h, k)

Step-by-step explanation:

Vertex form is an instance of the transformation of parent function f(x) = x². It is vertically scaled by a factor of 'a', and translated so the vertex is point (h, k). That is, the transformed vertex is h units right and k units up from that of the parent function (0, 0).

Parent:

  f(x) = x^2

Transformed:

  f(x) = a(x -h)^2 +k

__

When you compare the form to your specific instance, you need to pay attention to what it is that you're comparing. As the attachment shows, ...

Hence the vertex is (h, k) = (5, 6). The second attachment shows this on a graph.

The dimensions length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet.

Volume=lbh

lbh=500 cubic feet

h=500/lb

Surface area S=lb+2bh+2lh...(1) {rectangular tank has no top}

S=lb+2b(500/lb)+2l(500/lb) {substituting the value of h in 1}

S=lb+1000/l+1000/b { partially differentiating S with respect to l and b}

for S to be minimum dS/dl=0 and dS/db=0

dS/dl= b-1000/l^2

dS/dl=0

b=1000/l^2...(2)

dS/db= l-1000/b^2

dS/db=0

l=1000/b^2

l=1000/(1000/l^2)^2 {substituting the value of b from 2}

l=(1000 x l^4)/(1000000)

1000000/1000=l^4/l

1000=l^3

l=10  feet

b=1000/l^2

b=1000/100=10  feet

lbh=500

h=500/(10x10(

h=5  feet

S=10x10+2x5x10+2x10x5

S=300 square  feet

Length is 10 feet, width is 10 feet and height is 5 feet and the smallest possible surface area is 300 square feet of the  rectangular tank.

To know more about partial derivative:

https://brainly.com/question/14782333

#SPJ4

Answer:

The area of the circle is [tex]1\pi[/tex] or approximately 3.14 [tex]km^2[/tex]

Step-by-step explanation:

The formula to find the area of a circle is [tex]\pi r^2[/tex], where [tex]r[/tex] represents the radius of the circle. In this case, the area would be [tex]1^2*\pi[/tex] = [tex]\pi[/tex] ≈ 3.14 [tex]km^2[/tex].

The equation of the line that passes through the points (-4, -6) and (9, 2) is

y = (8/13)x - 46/13.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The line passes through points (-4, -6) and (9, 2).

Let the equation of the line y = mx + c.

Now,

m = (2 + 6) / (9 + 4) = 8/13

(-4, -6) = (x, y)

-6 = (8/13) x -4 + c
-6 = -32/13 + c

c = -6 + 32/13

c = (-78 + 32)/13

c = -46/13

Thus,

The equation of the line is y = (8/13)x - 46/13.

Learn more about equation of a line here:

https://brainly.com/question/23087740

#SPJ1

The area of the circle is A. 3 square units

The formula for determining the area of a circle is expressed as;

A = πr² or 1/4πd²

Given that;

Also, the formula for calculating the radius of a circle is given as;

Radius = diameter/2

Substitute the value, we have;

Radius = 2/2

Radius = 1

Substitute the value into the formula

Area, A = 3. 14 × (1)²

Find the square

Area, A = 3. 14 square units

Hence, the value is 3 square units. Option A

Learn more about area here:

https://brainly.com/question/25292087

#SPJ1

The complete question

Estimate the area of the circle, given the diameter as 2 unit. Round to the nearest whole number. A) 3 square units B) 6 square units C) 9 square units D) 12 square units

Answer:

gay

Step-by-step explanation:

gayayayayayayaydyfyfaygaygagya

Answer:

y = - 3

Step-by-step explanation:

Call the line y = a + bx (d)

Since d go through (-7;-3) so -7 = a - 3b (1)

Since d go through (8;-3) so 8 = a - 3b (2)

From (1) and (2), we have equations: [tex]\left \{ {{a - 3b = -7} \atop {a - 3b = 8}} \right.[/tex]

Solve the equations, we have [tex]\left \{ {{a = 0} \atop {b = -3}} \right.[/tex]

Answer:

25.9%

Step-by-step explanation:

10/22 x 12/21 = 25.9%

Answer:

74

Step-by-step explanation:

You subtract 43 from 12 you get 31 then you add 43 and 31 you get 74 bye

Answer:

c=35 degrees

Step-by-step explanation:

Its a right angle triangle which is equal to 90 degrees

so 43 +12=55 degrees.

90-55=35 degrees

c=35 degrees

It looks like there may be a typo in the function you provided. It appears that you meant to write "f(x) = 80(0.5)^x", which would represent the distance after a pendulum begins swinging, where x is the number of swings.

This function indicates that the distance traveled by the pendulum decreases by half with each swing. For example, after the first swing, the distance traveled would be 80(0.5)^1 = 40 units. After the second swing, the distance traveled would be 80(0.5)^2 = 20 units. And so on.

The exponent x in the function represents the number of swings, so the distance traveled by the pendulum can be calculated by plugging in the desired value of x into the function. For example, to calculate the distance traveled after 10 swings, we can plug in x = 10:

f(10) = 80(0.5)^10 = 0.390625 units

This indicates that the pendulum has traveled a distance of approximately 0.39 units after 10 swings.

Answer:

c

Step-by-step explanation:

the theoretical guess would be a 50/50 split for heads and tail, but tails was landed on less than 50 times, so heads landed more. the answer would be c. hope this helps

The Greatest Common Factor (GCF) for 75 and 105, notation CGF(75,105), is 15. Explanation: The factors of 75 are 1,3,5,15,25,75; The factors of 105 are 1,3,5,7,15,21,35,105.

THANKS!

FROM CAMBRIDGE UNIVERSITY

:)

The highest common factor (HCF) of 75 and 105 is 15.

The factor of a number is a number that can divide another number perfectly without any remainder.

A similar question was answered here: https://brainly.com/question/19039202

The number of bottles of mustard they went through is given by the equation A = 1/6 of the bottle

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of bottles of mustard be represented as A

Now , the equation will be

The amount of ketchup used by Camille's Snack Shack = ( 1/4 ) of the bottle

Now , the amount of bottle of mustard used = ( 2/3 ) of the bottle of ketchup

Substituting the values in the equation , we get

The number of bottles of mustard used A = ( 2/3 ) of ( 1/4 ) of the bottle

On simplifying the equation , we get

The number of bottles of mustard used A = ( 2/3 ) x ( 1/4 )

The number of bottles of mustard used A = ( 1/6 ) of the bottle

Therefore , the value of A is 1/6

Hence , the number of bottles is 1/6

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

It is A because it is only $40.000 so therefore it is A.

Answer:

circumference of the base

Step-by-step explanation:

Given that

The height of the cylinder is 10 inches

And, the 8 inches show the circumference of the base or the circumference of the circle

So,

C = 2r π

or

8 = 2r π

So, the 8 inches represent the same as shown above

Hence, the last option is correct

Answer:

circumference of the base.. D

Step-by-step explanation:

ANSWER D OPTION D

Point C is tangent to the circle and will be a right angle which is 90 degrees.

The three inside angles of a triangle need to equal 180.

X = 180-90-64 = 26

X = 26 degrees

Answer:

I believe it to be A.

Answer:

y = 312x + 2

Step-by-step explanation:

According to y = mx + b, m stands for slope and b stands for y-intercept. Let us find the y-intercept. To find the y-intercept, the x should be zero in (x, y).

(x, y)

(0, 2) ---> y-intercept (b)

Now that we have found the y-intercept, we will now find the slope by using its formula.

Slope formula:-

m = y2 - y1 / x2 - x1

Pick two random (x, y). I will pick the first and last pairs.

(0, 2) and (4, 1250)

Now plug these two pairs in the formula.

m = y2 - y1 / x2 - x1

m = 1250 - 2 / 4 - 0

m = 1248 / 4

m = 312

This means that the slope (m) is 312. Now put that in y = mx + b form.

y = mx + b

y = 312x + 2

Both of the forms are the same. Hope this helps, thank you :) !!

16 full days will be covered by the 785.7 pounds of food.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique.

We typically utilize this technique for math calculations.

This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

We are able to locate the missing value using the unitary technique.

This technique allows us to calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units.

According to our question-

1 pound of food will last = 1/48.5 day

Pounds equal 785.7*(1/48.5) = 785.7

= 785.7/48.5

= 16.2

Only full days will be counted, therefore

We'll only count up to 16.

So, the 785.

16 days will pass after 7 days.

The 785.7 pounds of food will therefore be plenty for 16 full days.

learn more about unitary method click here:

https://brainly.com/question/24587372

.

#SPJ4

The length of base ON of trapezoid LMNO is 17 units

We know that the median theorem of trapezoid, which states that the median of a trapezoid is parallel to each base. Also, the length of the median equals one-half the sum of the lengths of the two bases.

Consider the following diagram of trapezoid LMNO with bases LM and ON , and Median PQ.

Given that the equations for the bases and median of trapezoid LMNO .

PQ = t +6, LM = t +3 and ON = 3t – 7

From above theorem,

PQ = 1/2 (LM + ON)

t + 6 = 1/2 ( t + 3 + 3t - 7)

2(t + 6) = 4t + 3 - 7

2t + 12 = 4t - 4

4t - 2t = 12 + 4

2t = 16

t = 8 units

So, ON = 3t - 7

ON = 3(8) - 7

ON = 24 - 7

ON = 17 units

Learn more about the trapezoid here:

https://brainly.com/question/29193735

#SPJ4

Solution of the equation is x = 3 ± i that is a complex number where 3 is the real part and i is the imaginary part.

The equation of two-degree polynomial having one variable is called quadratic equation.

The solution of a quadratic equation is either real or complex. We use quadratic equation formula for solution whenever we cannot expand, and factoring a given two-degree polynomial equation.

given equation, x² = 6x -10

                x²-6x +10 =0

This equation cannot be expanded so we need to write the formula for quadratic equation to solve it.

we know that standard form of a quadratic equation is given by

ax² + bx +c = 0

where a is the coefficient of x², b is the coefficient of x and c is the constant.

the solution of the equation is given by x = -b ± √ (b² - 4ac) / 2a

Now, the solution for the above equation is x = 6 ± √ (6² - 4×1×10) / 2×1

                                                                     x = 6 ± √ (36 -40) / 2

                                                                x = 6 ± √-4 / 2

                                                   as        √-4 = √-1 ×2

                                                            x = 6 ± 2 √-1 /2  

                                        divide both numerator and denominator by 2

                                              x = 3± i     as √-1 = i

this is the solution in (a + bi) form a = 3 and b = 1

To learn more about quadratic equation visit:

https://brainly.com/question/29011747

#SPJ1

As you can see, we turned the fraction 10100 into its decimal representation, 0.1, in a single simple computation.

Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.

With 100 as the denominator, decimal fractions in the hundredth place are written. We shall discover how each square is split into 100 equal sections in this section. A tenth is a portion that is just partially shaded. The fraction is expressed as 1/100 in decimal form.

To know more about fractions visit:

brainly.com/question/10354322

#SPJ4

The actual length of the car based on the model will be 350 inches.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Since the ratio of the model car was 2:35. If the model is 20 inches long, the actual length of the car will be:

= 20 ÷ 2/35

= 20 × 35/2

= 350 inches.

Learn more about ratio on:

brainly.com/question/2328454

#SPJ1

Complete question

The ratio of the model car was 2:35. If the model is 20 inches long. then what would be the actual length of the car??

Answer:

Step-by-step explanation:

.

.

.

.

Answer:

The area left is equal to about 2686 [tex]ft^{2}[/tex] (if we will round to the nearest whole number).

Step-by-step explanation:

The area of the backyard that will be left will equal to the area of his backyard minus the area of the circular pool. So we can write it as...

The area left = (area of the backyard) - (area of the pool)

The area left = [tex]60 * 50 - \pi (20 / 2)^{2}[/tex]

The area left = [tex]3000 - 100\pi[/tex]

The area left ≅ 2686 [tex]ft^{2}[/tex]

Answer:

Your answer is C

Step-by-step explanation:

3(4)-1 = 11

Answer:

d.   8

Step-by-step explanation:

3x − 1 = 11

add 1 to both sides

3x = 12

Divide both sides by 3

x = 4

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

2x = 2*4 = 8

Answer:

tony

Step-by-step explanation:

his fraction is the greatest meaning that it's also the lowest

The given two functions are said to be equal functions if and only if both it's domain and range are equal.

In mathematics we use functions to show the relation between two objects.

They are used in various aspects of real life. The domain of a function is known as all the possible input values which can be given to the function.

The range of the function is the set of all the possible outputs which can be obtained from a function. We also have co-domain of a function which can be defined as the set of outputs for a relation or function , it can be equal to the range.

To learn more about  functions

brainly.com/question/29756953

#SPJ4

The members voted 2 more for mars than earth.

The Solar System has at least eight planets: the terrestrial planets Mercury, Venus, Earth and Mars, and the giant planets Jupiter, Saturn, Uranus and Neptune.

Given here, Mars has 8 votes while earth has 6 votes

Thus difference in votes is =8-6

                                              = 2

Hence, Mars got two more members than earth

Learn more about the solar system here:

https://brainly.com/question/12075871

#SPJ1

Answer:

Step-by-step explanation:

A scatter plot is a chart type that is normally used to observe and visually display the relationship between variables. It is also known as a scattergram, scatter graph, or scatter chart