Find the approximate area of the shaded region below, consisting of a square with a circle cut out of it. Use 3.14 as an approximation for PI


A. 856 square feet


B. 86 square feet


C. 314 square feet


D. 214 square feet

Answer:

[tex]\frac{(x^2\times x^4)^3}{x^8}[/tex] [tex]=x^{10}[/tex]

Step-by-step explanation:

1.

Power of the same base multiply by adding their exponent.

Example: [tex]a^m\times a^n = a^{(m+n)}[/tex]

2.

Power of the same base divide by subtracting their exponent.

Example:[tex]a^m \div a^n = a^{(m-n)}[/tex]

3.

Find power of a power we may multiple the exponent.

Example:[tex](a^m)^n = a^{mn}[/tex]

4.

[tex]\frac{(x^2\times x^4)^3}{x^8}[/tex]

[tex]=\frac{(x^6)^3}{x^8}[/tex]   [ using multiplication rule]

[tex]=\frac{(x^{18})}{x^8}[/tex]  [ using power of power rule]

[tex]=x^{18-8}[/tex]  [ Using division rule]

[tex]=x^{10}[/tex]

Answer:

wait time in order = 0,1,4,3,0,1,3,3,3,2

Step-by-step explanation:

We need to make a table for easy computation of wait time for each customer.

Customer    Arrival   Time taken      Checkout      Wait

Serial no.       time     for checkout      time             time

1                        1              4                    1+4=    5        0

2                       4             4                    4+5=    9       5-4=   1

3                       5             4                    9+4=   13       9-5=  4

4                       10            4                    13+4=  17       13-10=3

5                       20           3                    20+3= 23      0

6                       22            3                   23+3= 26      23-22=1

7                       23            5                   26+5= 31       26-23=3

8                       28            1                    31+1=   32      31-28=3

9                       29            5                   32+5= 37      32-29=3

10                     35                                                        37-35=2

Answer:

The probability that a person is willing to commute more than 25 miles is 0.2865.

Step-by-step explanation:

Exponential probability distribution is used to define the probability distribution of the amount of time until some specific event takes place.

A random variable X follows an exponential distribution with parameter m.

The decay parameter is, m.

The probability distribution function of an Exponential distribution is:

[tex]f(x)=me^{-mx}\ ;\ m>0, x>0[/tex]

Given: The decay parameter is, [tex]\frac{1}{20}[/tex]

X is defined as the distance people are willing to commute in miles.

Compute the probability that a person is willing to commute more than 25 miles as follows:

[tex]P(X>25)=\int\limits^{\infty}_{25} {\frac{1}{20} e^{-\frac{1}{20}x}} \, dx \\=\frac{1}{20}|20e^{-\frac{1}{20}x}|^{\infty}_{25}\\=|e^{-\frac{1}{20}x}|^{\infty}_{25}\\=e^{-\frac{1}{20}\times25}\\=0.2865[/tex]

Thus, the probability that a person is willing to commute more than 25 miles is 0.2865.

Step-by-step explanation:

Infinitely many equations can be written that will be equal to 100.

x + y = 100

2x - y = 100

and many more..

Answer:

Mass of the liquid in the tank will be [tex]1.45\times 10^8kg[/tex]

Step-by-step explanation:

We have given volume of tar [tex]V=3.20\times 10^5gallon[/tex]

1 gallon = 3.785 liter

So [tex]3.20\times 10^5gallon=3.20\times 10^{5}\times 3.785=12.112\times 10^5liter[/tex]

Specific gravity = 1.2

Density of water [tex]=1000kg/m^3[/tex]

We know that specific gravity [tex]=\frac{density\ of\ liquid}{density\ of\ water}[/tex]

[tex]1.2=\frac{density\ of\ liquid}{density\ of\ water}[/tex]

Density of liquid [tex]=1200kg/m^3[/tex]

So mass of liquid = volume × density

= [tex]12.112\times 10^5\times 1200=1.45\times 10^8kg[/tex]

So mass of the liquid in the tank will be [tex]1.45\times 10^8kg[/tex]

Answer:

(a) P (Both vehicles are available at a given time) = 0.81

(b) P (Neither vehicles are available at a given time) = 0.01

(c) P (At least one vehicle is available at a given time) = 0.99

Step-by-step explanation:

Let A = Vehicle 1 is available when needed and B = Vehicle 2 is available when needed.

Given:

The availability of one vehicle is independent of the availability of the other, i.e. P (A ∩ B) = P (A) × P (B)

P (A) = P (B) = 0.90

(a)

Compute the probability that both vehicles are available at a given time as follows:

P (Both vehicles are available) = P (Vehicle 1 is available) ×

                                                              P (Vehicle 2 is available)

                                  [tex]P(A\cap B)=P(A)\times P(B)[/tex]

                                                  [tex]=0.90\times0.90\\=0.81[/tex]

Thus, the probability that both vehicles are available at a given time is 0.81.

(b)

Compute the probability that neither vehicles are available at a given time as follows:

P (Neither vehicles are available) = [1 - P (Vehicle 1 is available)] ×

                                                                   [1 - P (Vehicle 2 is available)]

                                    [tex]P(A^{c}\cap B^{c})=[1-P(A)]\times [1-P(B)]\\[/tex]

                                                       [tex]=(1-0.90)\times (1-0.90)\\=0.10\times0.10\\=0.01[/tex]

Thus, the probability that neither vehicles are available at a given time is 0.01.

(c)

Compute the probability that at least one vehicle is available at a given time as follows:

P (At least one vehicle is available) = 1 - P (None of the vehicles are available)

                                                          [tex]=1-[P(A^{c})\times P(B^{c})]\\=1-0.01.....(from\ part\ (b))\\ =0.99[/tex]

Thus, the probability that at least one vehicle is available at a given time is 0.99.

Answer:

[tex]R = 59x[/tex]

Step-by-step explanation:

We are given the following in the question:

Cost per unit = $59

Let x units of product be sold.

We have to write an expression the amount of money received (revenue R) from the sale of x units of the product.

Revenue:

Revenue =

[tex]\text{Unit Cost}\times \text{Units sold}\\R = 59x[/tex]

is the required expression of revenue.

The water level in the bowl is rising at a rate of approximately 0.00269 meters per second when the water is 4 meters deep.

Let's address each part of the problem:

a. To find the volume of water in a hemispherical bowl of radius "a" to a depth "h," we can use the formula for the volume of a spherical cap. The volume of a spherical cap is given by:

V = (1/3)πh^2(3a - h)

In this case, "a" is the radius of the hemisphere, and "h" is the depth of the water.

So, the volume of water in the bowl is:

V = (1/3)πh^2(3a - h)

b. To find how fast the water level in the bowl is rising, we can use related rates. Let's denote the radius of the water-filled hemisphere as "R" (which is equal to "a" since it's the same hemisphere), and the depth of the water as "h."

Given that water is running into the bowl at a rate of 0.2 cubic meters per second, we can express the change in volume with respect to time:

dV/dt = 0.2 m^3/sec

We want to find dh/dt, the rate at which the water level is rising when the water is 4 meters deep.

We have the formula for the volume of water in the hemisphere from part (a):

V = (1/3)πh^2(3a - h)

Differentiate both sides of this equation with respect to time (t):

dV/dt = (1/3)π(2h)(dh/dt)(3a - h) - (1/3)πh^2(d(3a - h)/dt)

Now, plug in the values we know:

dV/dt = 0.2 m^3/sec

h = 4 m

a = 5 m

Now, solve for dh/dt:

0.2 = (1/3)π(24)(dh/dt)(35 - 4) - (1/3)π(4^2)(d(3*5 - 4)/dt)

0.2 = (8/3)π(dh/dt)(15 - 4) - (16/3)π(d(15 - 4)/dt)

0.2 = (8/3)π(11)(dh/dt) - (16/3)π(d(11)/dt)

0.2 = (88/3)π(dh/dt) - (16/3)π(0)

Now, solve for dh/dt:

(88/3)π(dh/dt) = 0.2

dh/dt = 0.2 / [(88/3)π]

Now, calculate dh/dt:

dh/dt ≈ 0.00269 meters per second

for such more question on hemispherical bowl

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Final answer:

To find the volume of water in a hemispherical bowl, subtract the volume of the upper portion of the hemisphere from the volume of the entire hemisphere. Therefore, the volume of the water in the hemispherical bowl is (2/3)πa³ - (1/3)π(h²)(3a - h).

Explanation:

To find the volume of water in a hemispherical bowl, we need to consider the shape of the bowl. The volume of a hemisphere is given by the formula V = (2/3)πr³, where r is the radius of the hemisphere. However, we only need to find the volume of the water in the bowl, not the entire bowl. To do this, we can subtract the volume of the upper portion of the hemisphere that is not filled with water.

Let's break down the steps:

Therefore, the volume of the water in the hemispherical bowl is (2/3)πa³ - (1/3)π(h²)(3a - h).

Answer:

the line equation is 2*x - y = 3

Step-by-step explanation:

for the line equation in implicit form

A*x + B*y = C

then if the point (x=4,y=5) belong to the line

4*A + 5*B = C

and  if the point (x=7,y=11) belong to the line

7*A + 11*B = C

then since we can choose C freely , we set C=1 for simplicity , then

4*A + 5*B = 1 → B= (1-4*A)/5

7*A + 11*B = 1

7*A + 11*(1-4*A)/5  = 1

7*A - 44/5*A + 11/5 = 1

-9/5*A = -6/5

A= 2/3

B= (1-4*A)/5 = (1-4*2/3)/5 = -1/3

therefore

2/3*x - 1/3*y = 1

2*x - y = 3

Answer:The statement is true

Step-by-step explanation:

This is an implication, then if we by starting from the premise we can get to the conclusion, then the implication is true. First let us remember that a given set of n vectors, say [tex]\{u_1,\ldots, u_n\}[/tex] is l.i (linearly independent), by definition if the only solution to [tex]\alpha_1\cdot u_1 + \cdots + \alpha_n\cdot u_n = \textbf{0}, is (\alpha_1, \ldots, \alpha_n)= \textbf{0}\in \mathcal {R}^n, \mathcal {R}[/tex] the set of real numbers, that is the only linear combination equal to the null vector is the null combination, all the scalars must be zero. And since it is a definition it is  if and only if.

Then if we say that the premise is true, then u4 is not a linear combination of {u1,u2,u3}, this means there do not exist [tex]\alpha_1, \alpha_2, \alpha_3 \in \mathcal{R}[/tex] not all zero, such that, [tex]\alpha_1\cdot u_1+ \alpha_2\cdot u_2+ \alpha_3\cdot u_3=u_4[/tex] which is equivalent to say that for every [tex]\alpha_1, \alpha_2, \alpha_3,\alpha_4 \in \mathcal{R}[/tex] with

[tex]\alpha_1\cdot u_1 + \alpha_2\cdot u_2+ \alpha_3\cdot u_3+ \alpha_4\cdot u_4 = \textbf{0}[/tex] implies [tex]\alpha_1= \alpha_2= \alpha_3= \alpha_4=0[/tex], then the given set is linearly independent as by definition and just as it is stated in the conclusion, therefore the affirmation is true.

Answer:

The diameter was [tex]d=\frac{45}{\pi }[/tex] in.

Step-by-step explanation:

The arc of a circle is given by

[tex]s=r\theta[/tex]

where

s = arc length

r = radius of the circle

θ = measure of the central angle in radians.

From the information given

s = 4 in

θ = 32º

To find the diameter of the original​ pizza, we use the formula of the diameter of a circle

[tex]d=2r[/tex]

First, we need to convert the angle to radians

[tex]\theta=32\º \cdot \frac{\pi}{180\º} =\frac{8\pi }{45}[/tex]

Next, solve for r from the arc formula

[tex]r=\frac{s}{\theta} =\frac{4}{\frac{8\pi }{45}} =\frac{45}{2\pi }[/tex]

Then, we use the diameter of a circle formula

[tex]d=2r=2(\frac{45}{2\pi })=\frac{45}{\pi }[/tex]

Answer:

The systems of equation is CONSISTENT

Step-by-step explanation:

The detailed steps using crammers rule to ascertain the CONSISTENCY is as shown in the attached file

Answer:

The sample standard deviation of 5.95.9 inches differs from the population standard deviation of 5.25.2 inches because of their formulas for calculating it.

Step-by-step explanation:

We are given the​ heights, in​ inches, of the starting five players on a college basketball team ;

68, 73, 77, 75 and 84

Now whether we treat this data as sample data or population data, the mean height would remain same in both case because the formula for calculating mean is given by ;

     Mean = Sum of all data values ÷ No. of observations

     Mean = ( 68 + 73 + 77 + 75 + 84 ) ÷ 5 = 75.4 inches

So, numerically, the sample mean of 75.4 inches is the same as the population mean.

Now, coming to standard deviation there will be difference in both sample and population standard deviation and that difference occurs due to their formulas;

Formula for sample standard deviation = [tex]\frac{\sum (X_i - Xbar)^{2} }{n-1}[/tex]

           where, [tex]X_i[/tex] = each data value

                       X bar = Mean of data

                        n = no. of observations

Sample standard deviation = [tex]\frac{ (68 - 75.4)^{2} +(73 - 75.4)^{2}+(77- 75.4)^{2}+(75- 75.4)^{2}+(84 - 75.4)^{2} }{5-1}[/tex]    

                                           = 5.9 inches

Whereas, Population standard deviation = [tex]\frac{\sum (X_i - Xbar)^{2} }{n}[/tex]

   = [tex]\frac{ (68 - 75.4)^{2} +(73 - 75.4)^{2}+(77- 75.4)^{2}+(75- 75.4)^{2}+(84 - 75.4)^{2} }{5}[/tex] = 5.2 inches .

So, that's why sample standard deviation of 5.95.9 inches differs from the population standard deviation of 5.25.2 inches only because of formula.

To calculate the initial trust fund deposit for three children of diverse ages, you create an equation reflecting the present value of the future payouts for each child at ages 18 and 21. The equation of value here models the required single investment with respect to the annual interest rate.

The problem presented, concerning setting up a trust fund for three children aged 1, 3, and 6, involves future value of lump sum investments, compound interest, and time value of money. Using an equation of value approach, the equation for the single investment Z made today that will pay each child X at age 18 and Y at age 21 can be modeled as follows:

where r represents the annual interest rate. This equation reflects the present value of the future payouts for each child. The term (1+r)years until payout is used to calculate the present value of each future payment. The equation adds up these present values for each child to calculate the initial trust fund deposit (Z).

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Answer: Breed for black-haired pigs

Step-by-step explanation:

Now according to the statement, the farmer catches  wild pigs and mostly are brown.

Since black hair is dominant over brown and also black and brown are dominant over red,  this implies that red is the least dominant color meaning if breeding occurs, there would be less chance of getting red colored pigs.

She wants to breed either black or red haired pigs and since black is more dominant so she should breed the black ones with the brown ones or with themselves so she would eventually get pure-breeding herd i.e. of black color.

(a) Assuming that Q satisfies the differential equation Q' = -rQ, determine the decay constant r for carbon-14. (b) Find an expression for Q(t) at any time t, if Q(0) = Qo. (c) Suppose that certain remains are discovered in which the current residual amount of carbon-14 is 20% of the original amount. Determine the age of these remains.

Answer:

a) r = (In 2)/(t1/2) = (In 2)/5730 = 0.000121/year

b) Q(t) = Q₀ (e^-rt)

c) Are of the 20% remnant of Carbon-14 = 13301.14 years.

Step-by-step explanation:

Q' = -rQ

Q' = dQ/dt

dQ/dt = -rQ

dQ/Q = -rdt

Integrating the left hand side from Q₀ to Q₀/2 and the right hand side from 0 to t1/2 (half life, t1/2 = 5730 years)

In ((Q₀/2)/Q₀) = -r(t1/2)

In (1/2) = -r(t1/2)

In 2 = r(t1/2)

r = (In 2)/(t1/2) = (In 2)/5730 = 0.000121 /year

b) Q' = -rQ

Q' = dQ/dt

dQ/dt = -rQ

dQ/Q = -rdt

Integrating the left hand side from Q₀ to Q(t) and the right hand side from 0 to t.

In (Q(t)/Q₀) = -rt

Q(t)/Q₀ = e^(-rt)

Q(t) = Q₀ (e^-rt)

c) Q(t) = Q₀ (e^-rt)

Q(t) = 0.2Q₀, t = ? and r = 0.000121/year

0.2Q₀ = Q₀ (e^-rt)

0.2 = e^-rt

In 0.2 = -rt

-1.6094 = - 0.000121 × t

t = 1.6094/0.000121 = 13301.14 years.

Hope this Helps!

Radiocarbon dating is a method used in archeological research to determine the age of artifacts based on the ratio of carbon-14 to the original amount. This technique is limited to time periods of 50,000 years or more.

Radiocarbon dating is an important tool in archeological research that allows scientists to determine the age of wood, plant remains, and other artifacts. This method is based on the fact that some wood or plant remains contain residual amounts of carbon-14, a radioactive isotope of carbon. By measuring the ratio of carbon-14 to the original amount, scientists can accurately determine the age of these remains. Radiocarbon dating is limited to time periods of 50,000 years or more.

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Answer:

(1) The probability that the technician tests at least 5 computers before the 1st defective computer is 0.078.

(2) The probability at least 5 computers are infected is 0.949.

Step-by-step explanation:

The probability that a computer is defective is, p = 0.40.

(1)

Let X = number of computers to be tested before the 1st defect is found.

Then the random variable [tex]X\sim Geo(p)[/tex].

The probability function of a Geometric distribution for k failures before the 1st success is:

[tex]P (X = k)=(1-p)^{k}p;\ k=0, 1, 2, 3,...[/tex]

Compute the probability that the technician tests at least 5 computers before the 1st defective computer is found as follows:

P (X ≥ 5) = 1 - P (X < 5)

              = 1 - [P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)]

              [tex]=1 -[(1-0.40)^{0}0.40+(1-0.40)^{1}0.40+(1-0.40)^{2}0.40\\+(1-0.40)^{3}0.40+(1-0.40)^{4}0.40]\\=1-[0.40+0.24+0.144+0.0864+0.05184]\\=0.07776\\\approx0.078[/tex]

Thus, the probability that the technician tests at least 5 computers before the 1st defective computer is 0.078.

(2)

Let Y = number of computers infected.

The number of computers in the company is, n = 20.

Then the random variable [tex]Y\sim Bin(20,0.40)[/tex].

The probability function of a binomial distribution is:

[tex]P(Y=y)={n\choose y}p^{y}(1-p)^{n-y};\ y=0,1,2,...[/tex]

Compute the probability at least 5 computers are infected as follows:

P (Y ≥ 5) = 1 - P (Y < 5)

             = 1 - [P (Y = 0) + P (Y = 1) + P (Y = 2) + P (Y = 3) + P (Y = 4)]               [tex]=1-[{20\choose 0}(0.40)^{0}(1-0.40)^{20-0}+{20\choose 1}(0.40)^{1}(1-0.40)^{20-1}\\+{20\choose 2}(0.40)^{2}(1-0.40)^{20-2}+{20\choose 3}(0.40)^{3}(1-0.40)^{20-3}\\+{20\choose 4}(0.40)^{4}(1-0.40)^{20-4}]\\=1-[0.00004+0.00049+0.00309+0.01235+0.03499]\\=1-0.05096\\=0.94904[/tex]

Thus, the probability at least 5 computers are infected is 0.949.

Answer:

Step-by-step explanation:

First let's identify decision variables:

X1 - acres of corn

X2 - acres of tobacco

Bradley needs to maximize the profit, MAX = 300X1 + 520X2

The Bradley family owns 410 acres, X1+X2≤410

Each acre of corn costs $105,  each acre of tobacco costs $210

The Bradleys have a budget of $52,500

So 105X1 +210X2≤52,500

There is a restriction on planting the tobacco - 100acres

X2≤100

Also, since outcomes can be only positive, X1X2 ≥0

So, what we have:

MAX = 300X1 + 520X2

X1+X2≤410

105X1 +210X2≤52,500

X2≤100

X1X2 ≥0

To maximize profit, the Bradleys can formulate a linear programming model based on the costs and profits of each crop, subject to budget and government constraints.

Linear programming model formulation:

Answer:

The probability that more than 10 parts will be defective is 0.99989.

Step-by-step explanation:

Let X = a part in the shipment is defective.

The probability of a defective part is, P (Defect) = p = 0.03.

The size of the sample is: n = 1000.

Thus, the random variable [tex]X\sim Bin(1000, 0.03)[/tex].

But the sample size is very large.

The binomial distribution can be approximated by the Normal distribution if the following conditions are satisfied:

Check the conditions:

[tex]np=1000\times0.03=30>10\\n(1-p)=1000\times(1-0.03)=970>10[/tex]

Thus, the binomial distribution can be approximated by the Normal distribution.

The sample proportion (p) follows a normal distribution.

Mean: [tex]\mu_{p}=0.03[/tex]

Standard deviation: [tex]\sigma_{p}=\sqrt{\frac{p(1-p)}{n} } =\sqrt{\frac{0.03(1-0.03)}{1000} } =0.0054[/tex]

Compute the probability that there will be more than 10 defective parts in this shipment as follows:

The proportion of 10 defectives in 1000 parts is: [tex]p=\frac{10}{1000}=0.01[/tex]

The probability is:

[tex]P(p>0.01)=P(\frac{p-\mu_{p}}{\sigma_{p}}> \frac{0.01-0.03}{0.0054}) =P(Z>-3.704)=P(Z<3.704)[/tex]

Use the standard normal table for the probability.

[tex]P(p>0.01)=P(Z<3.704)=0.99989[/tex]

Thus, the probability that more than 10 parts will be defective is 0.99989.

There are

[tex]5! = 5\cdot 4 \cdot 3 \cdot 2 = 120[/tex]

possible arrangements of 5 students. So, if you pick a particular one, you'll have a probability of 1/120 to guess the correct one.

The probability of getting the order used in the spelling bee is 1/120 or approximately 0.0083.

The probability of randomly selecting an order and getting the order used in the spelling bee is 1 divided by the number of possible orders. To find the number of possible orders, we use the concept of permutations. If there are 5 students participating in the spelling bee, there are 5 factorial (5!) possible orders. So the probability is 1/5! which is equal to 1/120 or approximately 0.0083.

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Answer:

After 167 miles the Budget rental deal would be better than the U-haul deal

Step-by-step explanation:

Let x be the number of miles.

Considering the U-haul plan the cost can be expressed as:

[tex]u=29.95+0.28x[/tex]

Consider the Budget rental plan the cost can be expressed as:

[tex]b=34.95+0.25x[/tex]

For the Budget rental plan to be better than the U-haul plan the relation between the two cost equation will be:

[tex]b<u[/tex]

Substitute the equations of u and b and solve for x:

[tex]b<u\\34.95+0.25x<29.95+0.28x\\34.95-29.95<0.28x-0.25x\\5<0.03x\\0.03x>5\\x>166.67\approx167[/tex]

So after 167 miles the Budget rental deal would be better than the U-haul deal.

After approximately 167 miles, Budget Truck rental becomes a cheaper option than U-Haul for Bryce and Lauren's move.

To find the point at which Budget Truck rentals becomes cheaper than U-Haul, we must set up the cost equation for each company and solve for the number of miles (m) that makes them equal. For U-Haul, the cost (C) is given by C = 29.95 + 0.28m, and for Budget it’s C = 34.95 + 0.25m.

Setting these two equations equal, we get: 29.95 + 0.28m = 34.95 + 0.25m.

We then solve for m: 0.03m = 5. Subtracting 29.95 from both sides, then dividing by 0.03 gives: m ≈ 167 miles.

So, after 167 miles, Budget Truck becomes the cheaper option.

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Answer:

Step-by-step explanation:

The formula for finding the sum of the measure of the interior angles in a regular polygon is expressed as (n - 2) × 180.

Where

n represents the number of sides of the polygon.

5a) The polygon has 11 sides. Therefore, sum of angles is

(11 - 2) × 180 = 1620

The measure of each angle is

1620/11 = 148.3°

b) n = 24

Therefore, sum of angles is

(24 - 2) × 180 = 3960

The measure of each angle is

3960/24 = 165°

5a) n = 7

Therefore, sum of angles is

(7 - 2) × 180 = 900

The measure of each angle is

900/7 = 128.6°

5b) n = 10

Therefore, sum of angles is

(10 - 2) × 180 = 1440

The measure of each angle is

1440/10 = 144°

Final answer:

Events B and D are disjoint; events B and C, A and C, B and D are independent; events A and B, A and C, and B and D are neither disjoint nor independent.

Explanation:

The pairs of events that are disjoint (have no intersection) are:

Events B and D are disjoint because if the white die is odd (event B), then it cannot match with the red die (event D).

Events A and D are disjoint because if the sum of the dice is 7 (event A), then the dice cannot match (event D).

The pairs of events that are independent are:

Events B and C are independent because the outcome of one die does not affect the outcome of the other die.

Events A and C are independent for the same reason.

The pairs of events that are neither disjoint nor independent are:

Events A and B are neither disjoint nor independent. If the white die is odd (event B), it is still possible for the sum of the dice to be 7 (event A).

Events A and C are also neither disjoint nor independent. If the sum of the dice is 7 (event A), it is still possible for the red die to have a larger number showing than the white die (event C).

Events B and D are neither disjoint nor independent. If the white die is odd (event B), it is still possible for the dice to match (event D).

Answer:Yes (A can occur when B occurs)

Step-by-step explanation: Independent events are events that are not determined by the occurrence of another. In this case EVENT A CAN OCCUR AS EVENT B OCCURS.

Justification: Landing on tails after tossing a coin and landing on a Five (5) after rolling the DIE Landing on Six (6) after rolling a DIE and landing on tails after tossing a coin.

Independent probabilities can occur together,they don't depend on each other.

Answer:

The standard deviation of given probability distribution is 0.8292

Step-by-step explanation:

We are given the following in the question:

              q:        0          1          2

Probability:    0.25     0.25    0.50

Formula:

[tex]E(q) = \displaystyle\sum q_ip(q_i)\\=0(0.25) + 1(0.25) + 2(0.50) = 1.25[/tex]

[tex]E(q^2)= \displaystyle\sum q_i^2p(q_i)\\=0^2(0.25) + 1^2(0.25) + 2^2(0.50) = 2.25[/tex]

Variance =

[tex]\sigma^2 = E(q^2) = (E(q))^2\\= 2.25- (1.25)^2\\=0.6875\\\sigma = \sqrt{0.6875} = 0.8292[/tex]

Thus, the standard deviation of given probability distribution is 0.8292

The standard deviation of a random variable can be calculated using the formula: √∑(xi-μ)2 ⋅ P(xi) . We find the mean (μ) by multiplying each value of q by its corresponding probability and summing them up. Next, we calculate the squared difference between each value of q and the mean, multiplied by their respective probabilities. Finally, we take the square root of this value to obtain the standard deviation.

The standard deviation of a random variable can be calculated using the formula:

\sqrt{\sum (x_i - \mu)^2 \cdot P(x_i)}

First, we need to find the mean (μ) of the probability distribution. The mean can be calculated by multiplying each value of q by its corresponding probability and summing them up:

μ = (0 × 0.25) + (1 × 0.25) + (2 × 0.5) = 0.5

Next, we calculate the squared difference between each value of q and the mean, multiplied by their respective probabilities:

(0 - 0.5)^2 × 0.25 + (1 - 0.5)^2 × 0.25 + (2 - 0.5)^2 × 0.5 = 0.5

Finally, we take the square root of this value to obtain the standard deviation:

√0.5 ≈ 0.7071

Therefore, the standard deviation of the random variable q is approximately 0.7071.

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Answer:the equation representing his daily salary is

s = 100 + c

Step-by-step explanation:

Let s represent the Salary that Martins earns per day.

Let c represent the commission that Martins earns on his sales on that day.

He earns $100 per day, plus

any commission on his sales. Since

his daily salary in dollars depends on the amount of commission, then an equation to represent his daily salary would be

s = 100 + c

Answer: you need to add each side .45+45+90=180

Step-by-step explanation:

Answer:

(-2.95,0)

x = -2.95 is the zero of the function.                                                      

Step-by-step explanation:

We are given the function:

[tex]f(x) = 1.5x + 3(x-3) + 5.5(x+7)[/tex]

We have to find the zero of the function.

Zero of function:

We can find zero of the function in the following manner:

[tex]f(x) = 1.5x + 3(x-3) + 5.5(x+7) = 0\\1.5x + 3x -9 + 5.5x + 38.5 = 0\\(1.5x + 3x + 5.5x) + (38.5-9) = 0\\10x + 29.5 = 0\\10x = -29.5\\x = -2.95[/tex]            

Thus, x = -2.95 is the zero of the function.        

Answer:

[tex] P(T>1) = e^{-\frac{1}{10}}= e^{-0.1}= 0.9048[/tex]

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

[tex]P(X=x)=\lambda e^{-\lambda x}[/tex]

Solution to the problem

For this case the time between breakdowns representing our random variable T is exponentially distirbuted [tex] T \sim Exp (\mu = 10)[/tex]

So on this case we can find the value of [tex]\lambda[/tex] like this:

[tex] \lambda = \frac{1}{\mu} = \frac{1}{10}[/tex]

So then our density function would be given by:

[tex]P(T)=\lambda e^{-\frac{t}{10}}[/tex]

The exponential distribution is useful when we want to describe the waiting time between Poisson occurrences. If we assume that the random variable T represent the waiting time between two consecutive event, we can define the probability that 0 events occurs between the start and a time t, like this:

[tex]P(T>t)= e^{-\lambda t}[/tex]

And on this case we are looking for this probability:

[tex] P(T>1) = e^{-\frac{1}{10}}= e^{-0.1}= 0.9048[/tex]

Answer:

P(A)= 0.606 and P(B)= 0.237

Step-by-step explanation:

Since A and B are independent

P(A ∩ B) = P(A) *  P(B) → P(B) = P(A ∩ B) / P(A)

and also

P(A ∪ B)=  P(A) + P(B) -  P(A ∩ B)

P(A ∪ B) =  P(A) + P(A ∩ B) / P(A) -  P(A ∩ B)

[P(A ∪ B) +  P(A ∩ B) ]* P(A) =  P(A)² + P(A ∩ B)

P(A)² - [P(A ∪ B) +  P(A ∩ B) ]* P(A) + P(A ∩ B) = 0

P(A)² - [ 0.626+0.144] * P(A) + 0.144 =0

P(A)² - 0.77* P(A) + 0.144 =0

thus

P(A)₁= 0.606 or P(A)₂= 0.1647

for P(A)₁→ P(B)₁ = P(A ∩ B) / P(A)₁ = 0.144/0.606 = 0.237

thus  P(A)₁ > P(B)₁ → correct

for P(A)₂→ P(B)₂ = P(A ∩ B) / P(A)₂ = 0.144/0.1647= 0.8743

thus  P(A)₂ < P(B)₂ → incorrect

therefore

P(A)= 0.606 and P(B)= 0.237