In a certain county, the mayor's office conducting a feasibility study on real estate industry. They selected a random sample of 50 selling prices of homes in a this county and found that the sample mean price was = $375,000. Assume that the population standard deviation σ is known to be $29,500. Find a 95% confidence interval for the population mean selling price of all homes in this county. (round your answers to the nearest dollar.)

Lower bound $[a]

Upper bound $[b]

Answer:

the rate of change of the water depth when the water depth is 10 ft is;  \(\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}\)

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft  is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the  rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at  a time t and r = radius of the cone shaped at a time t

Then the similar triangles  ΔOCD and ΔOAB is as follows:

\(\dfrac{h}{r}= \dfrac{20}{8}\)    ( similar triangle property)

\(\dfrac{h}{r}= \dfrac{5}{2}\)

\(\dfrac{h}{r}= 2.5\)

h = 2.5r

\(r = \dfrac{h}{2.5}\)

The volume of the water in the tank is represented by the equation:

\(V = \dfrac{1}{3} \pi r^2 h\)

\(V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h\)

\(V = \dfrac{1}{18.75} \pi \ h^3\)

The rate of change of the water depth  is :

\(\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}\)

Since the water is drained  through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

\(\dfrac{dv}{dt}= - 4 \ ft^3/sec\)

Therefore,

\(-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}\)

the rate of change of the water at depth h = 10 ft is:

\(-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}\)

\(100 \pi \dfrac{dh}{dt} = -4 \times 6.25\)

\(100 \pi \dfrac{dh}{dt} = -25\)

\(\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}\)

Thus, the rate of change of the water depth when the water depth is 10 ft is;  \(\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}\)

Answer:

the rate of change of the water depth when the water depth is 10 ft is;  

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft  is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the  rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at  a time t and r = radius of the cone shaped at a time t

Then the similar triangles  ΔOCD and ΔOAB is as follows:

   ( similar triangle property)

h = 2.5r

The volume of the water in the tank is represented by the equation:

The rate of change of the water depth  is :

Since the water is drained  through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

Therefore,

the rate of change of the water at depth h = 10 ft is:

Thus, the rate of change of the water depth when the water depth is 10 ft is;  

Step-by-step explanation:

Answer:

$8775 is the value of the investment after seven years

Answer:

863-7=856, 870-30=840, 900-55=845

Step-by-step explanation:

I think this may be the answer that is if you are to change the equations to subtraction problems, I can't see the picture so it's hard to answer.

Have a great day!

The dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ration.

To determine the amounts of the 70% protein supplement and the 20% protein ratio needed to make a 1900-pound high-grade 55% protein ration, we can set up a system of equations.

Let's assume x represents the pounds of the 70% protein supplement and y represents the pounds of the 20% protein ratio.

The total weight equation is given by:

x + y = 1900

The protein content equation is given by:

(0.70x + 0.20y) / 1900 = 0.55

Simplifying the second equation, we get:

0.70x + 0.20y = 0.55 × 1900

0.70x + 0.20y = 1045

Now, we can solve this system of equations to find the values of x and y.

Rearrange the first equation to solve for x:

x = 1900 - y

Substitute this expression for x in the second equation:

0.70(1900 - y) + 0.20y = 1045

1330 - 0.70y + 0.20y = 1045

1330 - 0.50y = 1045

-0.50y = 1045 - 1330

-0.50y = -285

y = -285 / -0.50

y = 570

Now substitute this value of y back into the first equation to find x:

x + 570 = 1900

x = 1900 - 570

x = 1330

Therefore, the dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ratio.

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Answer:dx fun fun

Step-by-step explanation:

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

Explanation:

s = 32 = sample standard deviation

n = 40 = sample size

Despite not knowing the population standard deviation (sigma), we can still use the Z distribution because n > 30. When n is this large, the student T distribution is approximately the same (more or less) compared to the standard Z distribution. The Z distribution is nicer to work with.

At 90% confidence, the z critical value is roughly z = 1.645. This can be found using either a Z table or a calculator.

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

We have these values:

Plug these values into the margin of error formula.

\(E = z*\frac{s}{\sqrt{n}}\\\\E \approx 1.645*\frac{32}{\sqrt{40}}\\\\E \approx 8.32311480156318\\\\E \approx 8.323\\\\\)

The margin of error is roughly 8.323

I rounded to 3 decimal places because z = 1.645 is rounded to 3 decimal places. If your teacher wants some other level of precision, then be sure to follow those instructions.

The range is greater for the girls and the mean is greater for the girls. So, correct option is B.

A) The statement "The range is greater for the girls" is true. The range is the difference between the highest and the lowest values in a data set.

Looking at the line plots, the highest value for the boys is 10, and the lowest is 3, giving a range of 7 hours. The highest value for the girls is 9, and the lowest is 5, giving a range of 4 hours. Therefore, the range is greater for the boys.

B) The mean is the sum of all values divided by the total number of values. To calculate the mean for the boys, we add up all the hours and divide by 10, which gives us:

(3 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 10) / 10 = 7.4 hours

To calculate the mean for the girls, we add up all the hours and divide by 10, which gives us:

(5 + 6 + 6 + 6 + 7 + 7 + 7 + 8 + 8 + 9) / 10 = 7.1 hours

Therefore, the mean for the boys is 7.4 hours and the mean for the girls is 7.1 hours, so the statement "The mean is greater for the girls".

So, correct option is B.

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Answer:

Plzzzz answer fast......

Answer:

Reflection about the y axis followed by a translation left by 2 units.

Step-by-step explanation:

There is the answer. ^

a. The probability of Mikayla drawing black pencil from the bag if each pencil is removed from the bag after it is drawn, is 2/7.

b. The probability of Mikayla drawing blue pencil from the bag if each pencil is removed from the bag after it is drawn, is 15/28.

c. The probability of Mikayla drawing cyan pencil from the bag if each pencil is removed from the bag after it is drawn, 5/28.

Mikayla has a bag of pencils with 8 black, 15 blue, and 5 cyan pencils.

Total Number of Black Pencil = 8

Total Number of Blue Pencil = 15

Total Number of Cyan Pencil = 5

Total Number of pencil = Total Number of Black Pencil + Total Number of Blue Pencil + Total Number of Cyan Pencil

Total Number of pencil = 8 + 15 + 5

Total Number of pencil = 28

a. We have to determine the probability of Mikayla drawing black pencil from the bag if each pencil is removed from the bag after it is drawn.

The Probability = Total Number of black pencil/Total Number of pencil

The Probability = 8/28

The Probability = 2/7

b. We have to determine the probability of Mikayla drawing blue pencil from the bag if each pencil is removed from the bag after it is drawn.

The Probability = Total Number of blue pencil/Total Number of pencil

The Probability = 15/28

c. We have to determine the probability of Mikayla drawing cyan pencil from the bag if each pencil is removed from the bag after it is drawn.

The Probability = Total Number of cyan pencil/Total Number of pencil

The Probability = 5/28

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The complete question is:

Mikayla has a bag of pencils with 8 black, 15 blue, and 5 cyan pencils. find the following probabilities of Mikayla drawing the given pencils from the bag if each pencil is removed from the bag after it is drawn.

a. Only black pencil left

b. Only Blue pencil left

c. Only cyan pencil left

Answer:

answer is 4.......

Step-by-step explanation:

....

Answer:

0 and -1

Step-by-step explanation:

Answer:

- 139/-3

Step-by-step explanation:

i took the test

Hello!

Out equation is: \(A=P(1+\frac{r}{n} )^t^n\)

A= 6000

P=5000

N=1

T=5

R= What we are trying to find

This means we will have \(6000=5000(1+r)^5\)

Divide both sides by 5000:

\(\frac{6000}{5000} = (1+r)^5\)

Move the power to the other side by rooting both sides:

\(\frac{6000}{5000} ^1^/^5 = 1+r\)

Subtract 1 from both sides:

\(\frac{6000}{5000} ^1^/^5 -1 = r\)

Now we just need to calculate: R = 0.03713728...

I don't know how many decimal places you can have, but I will round to 2. This will give you an Interest Rate of 3.71%.

I hope this helps! :)

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:48

Step-by-step explanation:add up all the sidees

By answering the question the answer is So the slope intercept  expression 4x + 5y = 20 in intercept form is: x/5 + y/4 = 1 

The slope-intercept form of a linear equation in mathematics is an equation of the form y = mx + b. where m is the slope of the line and b is the y-intercept, the point where the line crosses the y-axis. The slope-intercept format is a convenient way to plot equations for straight lines because it allows you to quickly see the line and determine the slope and y-intercept. The slope indicates how steep the line is, and the y-intercept indicates where the line crosses the y-axis.  

The intercept form of a linear equation in two variables (x and y) is given by

x/a + y/b = 1

where a and b are the intercepts of x and y respectively.

To convert the given expression 4x + 5y = 20 to intercept form, we need to solve for the intercepts for x and y.

For x = 0, 4x + 5y = 20 becomes

0 + 5 years old = 20

y = 4

So the y-intercept is 4.

For y = 0, 4x + 5y = 20 becomes

4x + 0 = 20

x = 5

So the x-intercept is 5.

So the expression 4x + 5y = 20 in intercept form is:

x/5 + y/4 = 1 

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Answer:

Step-by-step explanation:

The answer is c the solution will be positive because there are two negative signs

Navern's manufacturing cycle efficiency (MCE) for its elevators is: 41.4%

The formula for obtaining the manufacturing cycle efficiency is value-added time divided by the production cycle time * 100. In the data given, the process and inspection times qualify as a value-added time

Process time = 23 days

Inspection time = 13 days

Value added time = 23 + 13 = 36days

The production cycle time = Move time + process time + queue time + inspection time + wait time

= 22 + 12 + 23 + 13 + 17 days

= 87 days

So, the manufacturing efficiency time = 36/87 * 100

= 41.4%

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The function f(t) = 2cos (∏/4 t) lowest at (4,-2), (12,-2),(20,-2). The points are pl0ted in the graph.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function is  f(t) = 2cos (∏/4 t).

f(t) will be lowest when cos (∏/4 t) is lowest.

The value of cosine lies between -1 to 1.

When cos (∏/4 t) = -1, f(t) has lowest value.

Solve the equation cos (∏/4 t) = -1

cos (∏/4 t) = -1

∏/4 t =cos ⁻¹ (-1)

∏/4 t = (2n + 1)∏

t = (2n + 1)4  where n is a whole number.

The value of the function is lowest at t = 4, 12, 20.

The lowest points are (4,-2), (12,-2),(20,-2) etc.

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Answer: (4, -2) (12,-2)

Step-by-step explanation:

ACF is a 30º-60º-90º triangle because of the following:

1) Based on a theorem, in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : \(\sqrt{3}\)

1 → short leg

2 → hypotenuse

\(\sqrt{3}\) → long leg

Side length of the hexagon is the short leg of the triangle. It is 1.

r1 is the radius of the incircle in a regular hexagon. 2(r1) is the diameter of the incircle. It is also the hypotenuse of the right triangle. It is 2.

Using Pythagorean theorem.

\(a^2 + b^2 = c^2\)

\(1^2 + b^2 = 2^2\)

\(b^2 = 2^2 - 1^2\)

\(b^2 = 4 - 1\)

\(b^2 = 3\)

\(\sqrt{b^2} = \sqrt{3}\)

\(b = \sqrt{3}\)

Answer:

81

Step-by-step explanation:

25 and 27 are not perfect squares so they can not be the answer.

36 and 81 are both multiples of 3, but only 81 is not even, so the answer is 81

The solution of the compound inequality 3x + 5 > -1  or  -2x-7 > 5 is x > -2 or x < -6.

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.  

A compound inequality is an inequality that combines two simple inequalities.

Therefore,

3x + 5 > -1  or  -2x-7 > 5

Let's solve the inequality individually

3x + 5 > -1

3x > -1 - 5

3x > -6

x > -6 / 3

x > -2

Therefore,

-2x - 7 > 5

-2x > 5 + 7

-2x > 12

x > 12 / -2

x < -6

Hence,

x > -2 or x < -6

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\(~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill EF=\sqrt{(~~ 3- 2~~)^2 + (~~ 1- 3~~)^2} \\\\\\ ~\hfill EF=\sqrt{( 1)^2 + ( -2)^2} \implies \boxed{EF=\sqrt{ 5 }}\)

\(F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill FD=\sqrt{(~~ -1- 3~~)^2 + (~~ -1- 1~~)^2} \\\\\\ ~\hfill FD=\sqrt{( -4)^2 + ( -2)^2} \implies \boxed{FD=\sqrt{ 20 }} \\\\\\ D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill DE=\sqrt{(~~ 2- (-1)~~)^2 + (~~ 3- (-1)~~)^2} \\\\\\ ~\hfill DE=\sqrt{( 3)^2 + (4)^2} \implies DE=\sqrt{ 25 }\implies \boxed{DE=5} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(E(\stackrel{x_1}{2}~,~\stackrel{y_1}{3})\qquad F(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{2}}} \implies \cfrac{ -2 }{ 1 } \implies - 2 \\\\[-0.35em] ~\dotfill\)

\(F(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{3}}} \implies \cfrac{ -2 }{ -4 } \implies \cfrac{1 }{ 2 } \\\\[-0.35em] ~\dotfill\)

\(D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad E(\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} \implies \cfrac{3 +1}{2 +1} \implies \cfrac{4 }{ 3 }\)

Answer:

Hey, kevinlopez1225, your answer is Number one!

Astradele

Answer:

18 more tickets

Step-by-step explanation:

What we know:

We know that 65 Tickets is 1 Prize.

We know we have 1,282 tickets.

So if 65 tickets is one prize

then to figure out how many for twenty then we:

65 x 20 = 1300

Now to figure out how many more she needs at the least we:

1300 - 1282 = 18

So for 1 more prize she needs 18 more tickets.