suppose that 15% of people own dogs. if you pick two people at random, what is the probability that they both own a dog?

A pencil consists of a cylindrical body (10 cm long, radius 0.3 cm) with a cone-shaped eraser (1 cm slant height) and a hemisphere-shaped eraser.

A pencil consists of three main parts: a cylindrical body, a cone-shaped eraser, and a hemisphere-shaped eraser. Let's break down the dimensions of each part:

Cylindrical Body:

Length: 10 cm

Radius: 0.3 cm

Cone-shaped Eraser:

Slant height: 1 cm (assumed height of the cone)

Hemisphere-shaped Eraser:

Since the dimensions of the hemisphere-shaped eraser are not specified in detail, we'll assume a few things:

Let's assume that the hemisphere is attached to the cone in such a way that the flat surface of the hemisphere is aligned with the circular base of the cone.

We'll assume that the radius of the hemisphere is the same as the radius of the cylindrical body, which is 0.3 cm.

Please note that the actual dimensions of a pencil can vary, and these assumptions are made for the purpose of explanation.

It's worth mentioning that the cylindrical body of the pencil is the main part used for writing, while the cone-shaped and hemisphere-shaped erasers are located at the opposite end of the pencil, typically used for erasing mistakes.

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Jimmy’s total income is the sum of all the incomes which is $91838.61 .

How to determine Jimmy's income?

You should understand that total income' refers to the sum of certain incomes (in cash and, in some circumstances, in kind) of the statistical unit during a specified reference period .

Now in the given question ,

The given parameters that will help us to determine the income are

wages from accounting job,             $75,937.84;

interest,                                                   $839.40

wages from museum job,                  $14,937.92;

dividends,                                                $123.45.

Therefore Jimmy's total income is the sum of all the incomes

$(75,937.84 + 839.40 + 14,937.92 + 123.45)

Total income = $91838.61

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A. The maximum mean weight of the passengers cannot exceed 3500 lb if the gondola is filled to its capacity of 25 passengers.

B. To calculate the probability that the mean weight of 25 randomly selected skiers exceeds the maximum weight from part A, we need to use the Central Limit Theorem and standardize the sample mean using z-scores.

C. If the weight assumptions are revised so that the new capacity becomes 20 passengers, the probability that the mean weight of 20 randomly selected skiers exceeds 175 lb can be calculated by standardizing the sample mean using z-scores.

D. To assess the safety of the new capacity of 20 passengers, we need to determine the probability of exceeding the load limit of 3500 lb.

A. Let's denote the mean weight of the passengers as μ and the standard deviation as σ. We know that μ = 180 lb and σ = 38 lb. Since the gondola can carry 25 passengers, the total weight can be calculated as 25 * μ.

To ensure that the total weight does not exceed 3500 lb, we can set up the following inequality:

25 * μ ≤ 3500

Substituting the given values, we have:

25 * 180 ≤ 3500

4500 ≤ 3500

This inequality is not true, which means that the maximum mean weight of the passengers cannot exceed 3500 lb.

B. To determine the probability that the mean weight exceeds the value from part A, we need to calculate the probability distribution of the sample mean.

Now we can calculate the probability that the mean weight exceeds the value from part A, which is the maximum mean weight we found in part A. Let's denote this value as x.

P(x-bar > x) = P(x-bar > 3500 / 25)

To find this probability, we need to standardize the sample mean using z-scores. The formula for the z-score is:

z = (x - μ_x-bar) / σ_x-bar

Substituting the values, we have:

z = (x - 180) / 7.6

We can then look up the corresponding probability in the standard normal distribution table or use statistical software to find the probability.

C. The mean weight of the passengers (μ) remains the same at 180 lb, and the standard deviation (σ) remains at 38 lb. However, since the capacity has changed to 20 passengers, the sample size (n) is now 20.

μ_x-bar = μ = 180 lb

σ_x-bar = σ / √n = 38 lb / √20 ≈ 8.5 lb

Now we can calculate the probability that the mean weight exceeds 175 lb. Let's denote this value as x.

P(x-bar > x) = P(x-bar > 175)

Similarly to part B, we need to standardize the sample mean using z-scores:

z = (x - 180) / 8.5

Then, we can look up the corresponding probability in the standard normal distribution table or use statistical software to find the probability.

D. Is the new capacity of 20 passengers safe? Since the probability of overloading is (under 5%, over 50%), the new capacity (does not appear, appears) to be safe enough.

To calculate this probability, we need to find the probability that the total weight of the 20 randomly selected skiers exceeds 3500 lb. This requires considering the distribution of the sum of 20 normally distributed variables.

The total weight of the 20 skiers can be calculated as 20 * μ, where μ is the mean weight of the passengers (180 lb).

Let's denote the total weight as X. We need to calculate:

P(X > 3500)

To find this probability, we can standardize the variable X using z-scores and then look up the probability in the standard normal distribution table or use statistical software.

If this probability is less than 5%, it indicates that the probability of overloading is under 5%, suggesting that the new capacity of 20 passengers appears to be safe enough. Conversely, if the probability is greater than 50%, it suggests a high risk of overloading.

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Complete Question:

A ski gondola carries skiers to the top if a mountain. assume the weights of skiers are normally distributed with a mean of 180 lb and a standard deviation of 38 lb. the gondola has a stated compacity of 25 passengers, and the gondola is rated fir a load limit of 3500 lb

A. Given that the gondola is rated for a load limit of 3500 lb what is the max mean weight of the passengers if the gondola is filled to the capacity of 25 passengers?

B. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part A.

C. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 175 lb, which is the max weight hat does not cause the total load to exceed 3500lb

D. Is the new capacity of 20 passengers safe? Since the probability of overloading is (under 5%, over 50%) the new capacity (does not appear, appears) to be safe enough.

Since Jasmine wants to enter a career with median earnings of at least $33,500, but she doesn’t want to go to college, the occupation that fits her will be C Private detective.

It should be noted that from the information, Jasmine wants to enter a career with median earnings of at least $33,500, but she doesn’t want to go to college.

A Makeup artist earns $31,820.

A Mathematician earns $86,930.

A Private detective earns $33,750

A Massage therapist earns $33,400.

Therefore, the best occupation for her since she doesn't want to go to college and earns above $33500 is the private detective.

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Answer:

C. Private detective

Step-by-step explanation:

Answer:

4 (3 y + 2 x)^2

Step-by-step explanation:

Factor the following:

36 y^2 + 48 x y + 16 x^2

Hint: | Factor out the greatest common divisor of the coefficients of 36 y^2 + 48 x y + 16 x^2.

Factor 4 out of 36 y^2 + 48 x y + 16 x^2:

4 (9 y^2 + 12 x y + 4 x^2)

Hint: | Factor by grouping.

The coefficient of x^2 is 4 and the coefficient of y^2 is 9. The product of 4 and 9 is 36. The factors of 36 which sum to 12 are 6 and 6. So 9 y^2 + 12 x y + 4 x^2 = 4 x^2 + 6 x y + 6 x y + 9 y^2 = 2 x (3 y + 2 x) + 3 y (3 y + 2 x):

4 2 x (3 y + 2 x) + 3 y (3 y + 2 x)

Hint: | Factor common terms from 2 x (3 y + 2 x) + 3 y (3 y + 2 x).

Factor 3 y + 2 x from 2 x (3 y + 2 x) + 3 y (3 y + 2 x):

4 (3 y + 2 x) (3 y + 2 x)

Hint: | Combine products of like terms.

(3 y + 2 x) (3 y + 2 x) = (3 y + 2 x)^2:

Answer: 4 (3 y + 2 x)^2

Answer:

a

Step-by-step explanation:

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Answer:

choose   A

Step-by-step explanation:

Answer:

\(1a+2p=14\\a+p=9\\\\a=4\\p=5\)

Step-by-step explanation:

\(1a+2p=14\\a+p=9\\\\a+p=9\\a=9-p\\\\1(9-p)+2p=14\\9-p+2p=14\\9+p=14\\p=5\\\\a=9-(5)\\a=4\)

Graphing:

Slope intercept form y=mx+b

a is y, p is x

y=-2x+14

y=-x+9

Intercept at (5,4)

Answer:

x=5.8

Step-by-step explanation:

a^2+b^2=c^2

3^2+5^2=x^2

9+25 = 34

\(\sqrt{34)\) = 5.8

Answer:

\(17\sqrt{2}\)  or approximately 5.83

Step-by-step explanation:

The triangle is a right triangle so we use Pythagorean theorem to find the missing side.

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

x is the hypotenuse so that has to be the value of c but the other two sides are interchangeable.

\(3^{2} + 5^{2} = x^{2}\\\\9+25=x^{2} \\\\34=x^{2} \\\)

Square both sides to isolate the x.

\(\sqrt{34} =x\)

Simplify

\(17\sqrt{2} =x\\\)

The equilibrium price is $0 and the equilibrium quantity is 5 units.

To find the equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied and solve for the equilibrium values.

Setting Q_d = Q_s, we can equate the equations for demand and supply:

-2Q - 2Q_d = -5 + 3Q_s

Since we know that Q_d = Q_s, we can substitute Q_s for Q_d:

-2Q - 2Q_s = -5 + 3Q_s

Now, let's solve for Q_s:

-2Q - 2Q_s = -5 + 3Q_s

Combine like terms:

-2Q - 2Q_s = 3Q_s - 5

Add 2Q_s to both sides:

-2Q = 5Q_s - 5

Add 2Q to both sides:

5Q_s - 2Q = 5

Factor out Q_s:

Q_s(5 - 2) = 5

Q_s(3) = 5

Q_s = 5/3

Now that we have the value for Q_s, we can substitute it back into either the demand or supply equation to find the equilibrium price. Let's use the supply equation:

P = -5 + 3Q_s

P = -5 + 3(5/3)

P = -5 + 5

P = 0

Therefore, the equilibrium price is $0 and the equilibrium quantity is 5 units.

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Answer: Angle B

Step-by-step explanation:

Since the two shapes are similar. The angles stay with the shape. This means that angle M should correspond to angle B.

Answer: angle b .

Step-by-step explanation:

Answer:

p=6

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Step 1:

12p - 13 + 3p = 32       Equation

Step 2:

15p - 13 = 32     Add

Step 3:

15p = 45       Add 13 on both sides

Step 4:

45 ÷ 15     Divide

Answer:

p = 3

Hope This Helps :)

Answer:

5 5/6

Step-by-step explanation: umm math

Answer:

5 5/6

Step-by-step explanation:

hope it helps

its the answer above

Answer:

     9c+160

f=   ------------

          5

Step-by-step explanation:

The formula for the temperature in degrees Fahrenheit F in terms of the temperature in degrees Kelvin K is F = 9/5 (K-273)

What is temperature ?

Coldness and hotness is measured by temperature which is one of the fundamental units of measurements.

It is given that The temperature in degrees Kelvin is 273 degrees less than the temperature in degrees Celsius and generally the formula used for temperature conversion is given by :

\(\begin{aligned}\frac{C}{100}=\frac{F-32}{180}=\frac{K-273}{100}\end{aligned}\)

Now, converting Fahrenheit scale to celsius scale by comparing  Fahrenheit F and Kelvin K from above formula :

\(\begin{aligned}\frac{F-32}{180}&=\frac{K-273}{100}\\F&=\frac{9}{5}(K-273)\end{aligned}\)  

Therefore, the formula for the temperature in degrees Fahrenheit F in terms of the temperature in degrees Kelvin K is F = 9/5 (K-273)

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Answer:

Step-by-step explanation:

base b = 7

slant height = L

area of base = 49 cm²

lateral area = surface area - base area = 209 - 49 = 160 cm²

area of one lateral face = 160/4 = 40 cm²

½·b·L = 40

L = 80/7 ≅ 11.4 cm

Answer: 13 \(\frac{1}{3}\) pounds

Step-by-step explanation:

     We will set up a proportion. I will have the weight, in pounds, on the top (numerator) and the length, in inches, on the bottom (denominator).

\(\frac{12}{36} =\frac{x}{40}\)

     Cross-multiply:

36 * x = 12 * 40

36x = 480

     Divide both sides of the equation by 36:

x = 13 \(\frac{1}{3}\) pounds

Answer:

Step-by-step explanation:

First find unit weight.

1 foot = 12 inches

3 ft = 3*12 = 36 inches

3ft 4 inches = 36 + 4 = 40inches

Weight of 36 inches  long bar =   12  pounds

Weight of 1 inch bar = 12/36

\(\text{Weight of 40 inches long bar = $\dfrac{12}{36}*40$}\)

                                             = 13.3 pounds

Answer:

try 1239128981441231241

Step-by-step explanation:

myra

Answer:

3√5

Step-by-step explanation:

Hence, the square root of 45 can be expressed as, √45 = √(9 × 5) = 3√5. 45 is not a perfect square, hence, it remains within roots. The simplified radical form of the square root of 45 is 3√5.

Answer: 529.3 downloads

Explanation:

Standard version size = 2.1 MB

High quality version = 4.7 MB

The high-quality version was downloaded twice as often as the standard version

H = 2 S

The total size downloaded for the two versions = 3335 MB

H + S = 3335

We have the system:

H = 2 S (a)

H + S = 3335 (b)

Put A into B

(2S ) + S = 3335

3S = 3335

S= 3335/3

S= 1,111.67 MB

Divide the total MB of standard versions by the size of each standard version.

1,111.67 / 2.1 = 529.3 downloads

Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

47 = 2(k + 3) + 3(k - 3)

47 = 2k + 6 + 3k - 9

47 - 6 + 9 = 2k + 3k

56 - 6 = 5k

50 = 5k

k = 50/5

k = 10

Result k = 10

Answer:

50; 25; 105

Step-by-step explanation:

Sum of the angles of triange is 180, so we have 2x + x + 2*2x + 5 = 180 (x is number of degrees of second angle), if I understood word 'twice' correctly.

Next, let me solve this:

2x + x + 4x + 5 = 180

7x + 5 = 180

7x = 175

x = 25

So, second angle is 25 degrees, first is 25*2=50 degrees and third is 50*2+5=105 degrees.

Hope that this was helpful.

Answer:

\((1\frac{1}{2},1)\) - False

\((4,6)\) - True

\((18,12)\) -- False

\((0,0)\) -- True

\((2\frac{1}{2},3\frac{3}{4})\) -- True

Step-by-step explanation:

The points are

\((1\frac{1}{2},1)\) , \((4,6)\), \((18,12)\), \((0,0)\) and \((2\frac{1}{2},3\frac{3}{4})\) ---- missing from the question

Given

\(y = 1\frac{1}{2}x\)

Required

Determine if each of the points would be on \(y = 1\frac{1}{2}x\)

To do this, we simply substitute the value of x and of each point in \(y = 1\frac{1}{2}x\).

(a) \((1\frac{1}{2},1)\)

In this case;

\(x = 1\frac{1}{2}\) and \(y = 1\)

\(y = 1\frac{1}{2}x\) becomes

\(y = 1\frac{1}{2} * 1\frac{1}{2}\)

\(y = \frac{3}{2} * \frac{3}{2}\)

\(y = \frac{9}{4}\)

\(y = 2\frac{1}{4}\)

The point \((1\frac{1}{2},1)\)  won't be on the graph because the corresponding value of y for \(x = 1\frac{1}{2}\) is \(y = 2\frac{1}{4}\)

(b) \((4,6)\)

In this case;

\(x = 4\)

\(y = 6\)

\(y = 1\frac{1}{2}x\) becomes

\(y = 1\frac{1}{2} * 4\)

\(y = \frac{3}{2} * 4\)

\(y = \frac{3* 4}{2}\)

\(y = \frac{12}{2}\)

\(y = 6\)

The point \((4,6)\)  would be on the graph because the corresponding value of y for \(x = 4\) is \(y = 6\)

(c) \((18,12)\)

In this case:

\(x = 18;y = 12\)

\(y = 1\frac{1}{2}x\) becomes

\(y = 1\frac{1}{2} * 18\)

\(y = \frac{3}{2} * 18\)

\(y = \frac{3* 18}{2}\)

\(y = \frac{54}{2}\)

\(y = 27\)

The point \((18,12)\)  wouldn't be on the graph because the corresponding value of y for \(x = 18\) is \(y = 12\)

(d) \((0,0)\)

In this case;

\(x =0; y = 0\)

\(y = 1\frac{1}{2}x\) becomes

\(y = 1\frac{1}{2} * 0\)

\(y = 0\)

The point \((0,0)\)  would be on the graph because the corresponding value of y for \(x = 0\) is \(y = 0\)

(e) \((2\frac{1}{2},3\frac{3}{4})\)

In this case:

\(x = 2\frac{1}{2}\); \(y = 3\frac{3}{4}\)

\(y = 1\frac{1}{2}x\) becomes

\(y = 1\frac{1}{2} * 2\frac{1}{2}\)

\(y = \frac{3}{2} * \frac{5}{2}\)

\(y = \frac{15}{4}\)

\(y = 3\frac{3}{4}\)

The point \((2\frac{1}{2},3\frac{3}{4})\)  would be on the graph because the corresponding value of y for \(x = 2\frac{1}{2}\) is \(y = 3\frac{3}{4}\)

A. period.

This is the answer

Answer:

C

Step-by-step explanation:

The lowest number is 9

And the highest number is 18

So the range is at least 8 - 20

Answer:

C. 8-20

Step-by-step explanation:

Because if you put this in order, there will be no other number lower then eight and no other number higher then 20

Step-by-step explanation:

Principal = 250,000

Rate = 4%

Simple interest = 850,000

Time = ?

\(t = \frac{100 \times interest}{principal \times rate} \\ t = \frac{100 \times 850000}{250000 \times 4} \\ t = \frac{100 \times 85}{25 \times 4} \\ t = \frac{8500}{100} \\ t = 85years\)

The distance between Patrick and Clarissa cannot be determined as only one variable has been given in the question. Not sufficient data provided.

Using congruency, length of the missing side of the triangle =- 8.5 units.

The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. If pairings of corresponding sides and corresponding angles are equal, two triangles are said to be congruent. They are the exact same size and form. Triangles can satisfy a wide variety of congruence requirements.

In the 1st image:

The distance between Patrick and Clarissa cannot be determined as only one variable has been given in the question. Not sufficient data provided.

In the 2nd image:

Let x be the missing length of the triangle.

As the ray is an angle bisector,

Due to congruency:

11.9/7 = x/5

⇒ (11.9 × 5)/7 = x

⇒ x = 8.5 units.

Therefore, length of the missing side of the triangle =- 8.5 units.

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