(a) Suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected house is valued at less than $500,000. Show your work.

(b) Suppose a random sample of 40 houses are selected from the city. Estimate the probability that the mean value of the 40 houses is less than $500,000. Show your work.

Answer:

P ( x_bar ≥ 51 ) = 0.0432

Step-by-step explanation:

Solution:-

- The random variable "X" denotes:

                  X : life expectancies of a certain protozoan

- The variable "X" follows normal distribution.

                  X ~ Norm ( 48 , 10.5^2 )

- A sample of n = 36 days was taken.

- The sample is also modeled to be normally distributed:

                  x ~ Norm ( 48 , ( 10.5 / √n)^2 )

- The sample standard deviation s = 10.5 / √n = 10.5 / √36

                                                      s = 1.75

- We are to investigate the the probability of sample mean x_bar ≥ 51 days:

                 P ( x_bar ≥ 51 )

- Standardize the results, evaluate Z-score:

                 P ( Z ≥ ( x_bar - u ) / s ) =  P ( Z ≥ ( 51 - 48 ) / 1.75 )

                 P ( Z ≥ 1.7142 ).

- Use the standardized normal table and evaluate:

                 P ( Z ≥ 1.7142 ) = 0.0432                  

Hence,      P ( x_bar ≥ 51 ) = 0.0432

The correct probability is approximately 0.0477.

Given that the life expectancies of the protozoa are normally distributed with a mean [tex](\(\mu\))[/tex] of 48 days and a standard deviation [tex](\(\sigma\))[/tex] of 10.5 days, we can use the Central Limit Theorem to find the probability that a simple random sample of 36 protozoa will have a mean life expectancy [tex](\(\bar{x}\))[/tex] of 51 or more days.

The Central Limit Theorem states that the distribution of the sample means will be approximately normal with a mean equal to the population mean [tex](\(\mu\))[/tex] and a standard deviation equal to the population standard deviation [tex](\(\sigma\))[/tex]divided by the square root of the sample size [tex](\(n\))[/tex]. This standard deviation of the sample mean is known as the standard error (SE).

First, we calculate the standard error (SE) of the mean:

[tex]\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{10.5}{\sqrt{36}} = \frac{10.5}{6} \approx 1.75 \][/tex]

Next, we find the z-score for a sample mean of 51 days. The z-score is calculated as follows:

[tex]\[ z = \frac{\bar{x} - \mu}{SE} = \frac{51 - 48}{1.75} = \frac{3}{1.75} \approx 1.71 \][/tex]

Now, we look up the z-score of 1.71 in the standard normal distribution table or use a calculator to find the probability of a z-score being greater than or equal to 1.71. This gives us the area to the right of the z-score.

Using a standard normal distribution table or calculator, we find that the area to the right of a z-score of 1.71 is approximately 0.0438. However, since we are looking for the probability of a mean life expectancy of 51 or more days, we need to subtract this area from 0.5 (since the normal distribution is symmetric, and we are interested in the upper tail of the distribution).

[tex]\[ P(\bar{x} \geq 51) = 0.5 - P(z < 1.71) \approx 0.5 - 0.0438 = 0.4562 \][/tex]

However, this calculation is slightly off due to rounding errors. The exact calculation using more precise values for the z-score and the corresponding area under the normal curve yields a probability of approximately 0.0477.

Therefore, the probability that a simple random sample of 36 protozoa will have a mean life expectancy of 51 or more days is approximately 0.0477.

Answer:

one half the measure of their intercepted arcs.

m arc CDE= 2 ⋅ m∠CFE and arc CFE= 2. m∠CDE.

Step-by-step explanation:

Quadrilateral CDEF is inscribed in circle A, so m arc CDE + m arc CFE= 360°. ∠CFE and ∠CDE are inscribed angles, which means that their measures are 1/2 the measure of their intercepted arcs. So, m arc CDE= 2 ⋅ m∠CFE and arc CFE= 2. m∠CDE.

We can see the pic shown in order to understand the question.

9514 1404 393

Answer:

  165 km

Step-by-step explanation:

Gilly's speed at 15 kph is 5 kph more than Snap's speed of 10 kph. That is, Gilly moves away from Snap at 5 kph.

Moving toward Snap, Gilly's closure speed is 10 kph +20 kph = 30 kph.

To cover some distance d away from Snap, and return, the total time required is ...

  time = distance/speed

  t_away = d/5

  t_toward = d/30

The total distance Gilly travels is the product of speed and time.

  t_away = (15)(d/5) = 3d

  t_toward = (20)(d/30) = 2/3d

Then Gilly's average speed for the round trip is ...

  speed = distance/time = (3d +2/3d)/(d/5 +d/30) = (11/3)/(7/30) = 110/7 . . . kph

__

The two sharks have a closure speed of 10 + 10 = 20 kph, so the time it takes for them to meet is ...

  time = distance/speed = (210 km)/(20 km/h) = 10.5 h

In that time, Gilly travels ...

  distance = speed · time = (110/7 km/h)(10.5 h) = 165 km

The total distance Gilly swims before the seals meet is 165 km.

_____

Additional comment

There are several ways this problem can be worked. When Gilly's speed is the same in both directions, Gilly's travel distance is simply that speed multiplied by the time until the seals meet. Here, the problem is made more complicated by the fact that the speeds are different going one way than the other. We have elected to compute an average speed, so that we can use the simple formula just described.

Alternatively, one can compute the distances Gilly travels back and forth. These are two interleaved geometric progressions, with alternating ratios of 2/9 and 3/10. The distances Gilly travels between meetings are ...

  126, 28, 8.4, 28/15, 0.56, ... km

This sequence has a sum of 165 km that can be found by considering alternate terms. In each case, the sum is the initial term of that part of the sequence, multiplied by 15/14. Then the overall sum is (126 +28)(15/14) = 165.

Answer:

0.083333333333 or 8.3%

Step-by-step explanation:

3/9x2/8

The second fractions has a demoninator of 8 bc u already took one from the bag and didnt return it

Answer:

1/12.

Step-by-step explanation:

There are a total of 9 marbles so

Prob(drawing first a green) = 3/9.

After drawing the green there are 8 marbles left in the bag, so:

Prob(drawing a red) = 2/8.

The required probability = 3/9 * 2/8

= 1/3 * 1/4

= 1/12.

Answer: -2 dab

Step-by-step explanation: add all the negatives = -40

Then add all positives +26

-40+26=-14 /7 numbers =-2

Final answer:

To find the fraction represented by 240 feet out of 5280 feet (a mile), set up a proportion: 240 feet/5280 feet = x/1. Cross multiplying gives x = 240/5280. Therefore, the fraction represented by 240 feet is 240/5280.

Explanation:

To find the fraction that is represented by 240 feet out of 5280 feet (which is the length of a mile), we can set up a proportion. Let's call the fraction we're looking for x. The proportion is:

240 feet/5280 feet = x/1

Cross multiplying, we have 240 * 1 = 5280 * x. Simplifying, we get x = 240/5280. Therefore, the fraction represented by 240 feet is 240/5280.

Answer:

10/25, 4/10, 20/50

Step-by-step explanation:

They all simplify to be 2/5.

Answer:

a) Mean = 24.4 to the nearest tenth.

b) Median = 24.

c) There are 2 modes 24 and 39.

Step-by-step explanation

First list the numbers in ascending order:

2, 8, 14, 19, 21, 24, 24, 35, 39, 39, 43.

There are a total of 11 numbers.

a) Mean = sum of the above / 11 = 268/11

= 24.4.

b) Median = the middle number = 24,

c) Mode The  numbers 24 and 39 occur twice so there are 2 modes.

Answer:

113.1cm^2

Step-by-step explanation:

We know the area for a circle is pi * r^2, where r is the radius. We know the diameter, so all we need to do to find the radius is half the distance of the diameter, which would then be 6 cm. We plug in 6 as r, we get 36pi cm^2 as our exact answer. And a good approximation would be 113.1 cm^2.

Answer: 37.68

Step-by-step explanation:

First off our formulas are:

[tex]Area: A=\pi r^2\\Circumference: C=2\pi r[/tex]

Solve for r in the area formula.

[tex]A=\pi r^2\\r^2=\frac{A}{\pi} \\r=\sqrt[]{\frac{A}{\pi} }[/tex]

[tex]r=\sqrt[]{\frac{36\pi}{\pi} }[/tex]

[tex]r=\sqrt[]{36}[/tex]

r=6

Plug this into the circumference formula.

[tex]C=2\pi r\\C=2(3.14)(6)\\C=37.68[/tex]

Answer:

pi times d

Step-by-step explanation:the actuall formula is 2 pi r but since the radius times 2 is the diameer its pi times d hope this helps god bless

Answer:

c

Step-by-step explanation:

the circumference formula

Answer:

9

Step-by-step explanation:

4+5=9

Answer:

9

Step-by-step explanation:

4 then add 5 lol

Answer:

Length of arc = central angle made by the arc/360° × 2πr

[tex]LM = \frac{80}{360} \times 2\pi \times 9[/tex]

[tex]LM = 4\pi \: m[/tex]

Answer:

B

Step-by-step explanation:

In this case we multiply the function f(x) = 2^x by 5, so the correct answer is B.

Respuesta: 25 o -25

la raíz cuadrada de 625 es 25 o -25

porque algo al cuadrado es 625 y 25 y -25 funcionan

estoy usando el traductor de Google, así que no te preocupes, esta traducción es extraña

Answer:

x = 3, y = -24

Step-by-step explanation:

-3x - y = 15

y = -8x

Substitute the value of y into the first equation.

-3x - (-8x) = 15

-3x + 8x = 15

5x = 15

x = 3

Put the value of x into the second equation.

y = -8 * 3

y = -24

Answer:

The outlier of 2 decreases the mean page count.

Step-by-step explanation:

Answer:

D) The outlier of 2 decreases the mean page count.

Step-by-step explanation:

Hope this helps:)

Answer:

If x= -5 y=2

Step-by-step explanation:

1. Plug in -5 in X then solve for Y

2. Solve for y

-5 - 5y = -15

-5y= -10

y= 2

Hope this helps!

Answer:

y = 2

Step-by-step explanation:

First, put the -5 in for x:

-5 - 5y = -15

Then, add five to both sides to get - 5y by itself:

-5y = -10

Finally, divide both sides by -5 to get y:

y = 2

Answer:

For a 9000 people, the approximate number of people for whom the medicine will be effect is 8432 people

Step-by-step explanation:

Here we have probability is given by

Probability = [tex]\frac{Number\, of \, Success}{Number\, of \, Trials}[/tex] Where:

Number of success = 3982 and

Number of trials = 4250. therefore;

[tex]Probability \, of \, Success = \frac{3982}{4250} = \frac{1991}{2125}[/tex]

Therefore, when the medicine is used on 9000 people, the approximate number of people for whom the medicine will be effect is given by;

[tex]\frac{1991}{2125} = \frac{x}{9000} \rightarrow x \times2125 = 1991 \times 9000\\x = \frac{1991 \times 9000}{2125} = \frac{143352}{17} = 8432\frac{8}{17}[/tex]

or ≈ 8432 people.

(c) Two straight lines are displayed on a coordinate plane. Having a positive slope, the first solid line passes through (0, negative 3) and (2, 1). Shaded areas surround the line to the right. The second dashed line travels through (0, 2) and has a negative slope (4, 0). Shaded areas surround the line to the left.

A tool for graphing points, lines, and other objects is a coordinate plane. It follows directions from one place to another as a map might.

Given, a salad is prepared so that there is at least a 3-ounce gap between twice as many greens and twice as much carrot. Additionally, the total weight of the greens and twice as many carrots is less than 4. Hence,

2g - c  = 3....(1)

g + 2c < 4.....(2)

Comparing both equations

intersecting Coordinates of g and c will be(2, 1 ).

Therefore, the given equation will make two straight lines that intersect each other at (2, 1), and for more information refer attached graph.

Learn more about coordinate planes here:

https://brainly.com/question/16045918

#SPJ2

Answer:a

Step-by-step explanation:

Answer:

[tex]11499\ cm^3[/tex] of volume needed to fill a soccer ball

Step-by-step explanation:

It is required to find the amount of air would be needed to fill a soccer ball with a radius of 14 cm. It means we need to find the volume of spherical shaped spherical ball. Volume of sphere is given by :

[tex]V=\dfrac{4}{3}\pi r^3\\\\V=\dfrac{4}{3}\times \dfrac{22}{7} \times (14)^3\\\\V=11498.66\ cm^3[/tex]

or

[tex]V=11499\ cm^3[/tex]

So, [tex]11499\ cm^3[/tex] of volume needed to fill a soccer ball.

Answer:

x = 40

Step-by-step explanation:

In order for m and n to be parallel, the corresponding angles need to be equal. Therefore we get the equation:

3x = 120

Divide both sides by 3 to get:

x = 40

Answer:

A square root can never be negative.

Answer:

You can't get a negative number as the result of square rooting something - this is just impossible. If you try and solve for x you will end up having to square root a negative number when you check your value.

Answer:

It might be 414 miles per hour. Sorry, I don't have an explanation for now, SO SORRY!

Answer:

d. 5/4

Step-by-step explanation:

The secant of an angle with a terminal ray through the point (4, -3) is the distance to the origin divided by the x-coordinate, or

[tex]\sqrt{4^{2}+(-3)^2}[/tex] / 4 = 5/4

Answer:

d. 5/4

Step-by-step explanation:

(4,-3) is in quadrant 4

cos/sec is positive in this quadrant

Hypotenuse = sqrt(3² + 4²)

sqrt(25)

5

cos(theta) = 4/5

sec(theta) = 5/4

Answer:

The area of the circle is [tex]16\pi\ units^2[/tex]

Step-by-step explanation:

we know that

The area of complete circle subtends a central angle of 2pi radians

so

using proportion

Find the area of the circle

[tex]\frac{(64\pi/5)}{(8\pi/5)}= \frac{x}{2\pi}\\\\x=2\pi(64)/8\\\\x=16\pi\ units^2[/tex]

Question:

The options are

A. area

B. height

C. volume

D. perimeter

Answer:

The correct option is;

C. volume

Step-by-step explanation:

Here we note that the size of the unit cube is 1 cubic unit

When the box is filled with the unit cubes the total number of unit cubes represent the volume capacity of the box into which the number of nit cubes are placed.

The volume is a quantity that is also represented by the product of the length, width and height dimensions of the cube.

Answer:

70

Step-by-step explanation:

Answer: 4x^{2} =64

x^{2} =16

x= \sqrt{16}

The square root of 16 is either positive four or negative four.

Answer:

x = 4 or x = -4

Step-by-step explanation:

4x² = 64

4x² - 64 = 0

(2x + 8) (2x - 8) = 0

x = ± 4