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(Please answer all the questions)

The probability that exactly four out of 19 adults say cashews are their favorite nut is approximately 0.251.

The probability that 12 or more stolen bikes will be returned is approximately 0.026 (rounded to the nearest thousandth).

To solve both of these probability problems, we can use the binomial probability formula:

P(X = k) = (n C k) × p^k × (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes

n is the total number of trials

k is the number of desired successes

p is the probability of success in a single trial

(1 - p) is the probability of failure in a single trial

(n C k) represents the binomial coefficient, calculated as n! / (k! x (n - k)!)

Let's solve each problem separately:

The probability that exactly four out of 19 adults say cashews are their favorite nut can be calculated as:

P(X = 4) = (19 C 4) ⁴(0.49⁴) (0.51¹⁵)

Using the binomial probability formula, we can calculate:

P(X = 4) ≈ 0.251

Therefore, the probability that exactly four out of 19 adults say cashews are their favorite nut is approximately 0.251.

To find the probability that 12 or more stolen bikes will be returned out of 335 stolen bikes, we can use the binomial probability formula. Let's denote the probability of a stolen bike being returned as p = 0.03, the number of trials as n = 335, and the number of desired successes as k = 12 or more.

Using the complement rule, we can calculate the probability of not getting 11 or fewer successes:

P(X ≥ 12) = 1 - [P(X = 0) + P(X = 1) + ... + P(X = 11)]

To perform the calculation, summing up individual probabilities can be time-consuming. However, using statistical software or a binomial probability calculator can provide a convenient solution.

Using such a calculator, we find that the probability of 11 or fewer stolen bikes being returned is approximately 0.974. Therefore, the probability of 12 or more stolen bikes being returned is:

P(X ≥ 12) = 1 - 0.974 ≈ 0.026

Thus, the probability that 12 or more stolen bikes will be returned is approximately 0.026 (rounded to the nearest thousandth).

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The slope of the tangent to the circle at point A is -3/2.

1. The equation of a circle with center C(2, 7) is given by (x - 2)² + (y - 7)² = r², where r is the radius of the circle.

2. Since point A(8, 17) lies on the circle, we can substitute the coordinates of point A into the equation of the circle to find the value of r.

  (8 - 2)² + (17 - 7)² = r²

  6² + 10² = r²

  36 + 100 = r²

  136 = r²

  r = √136 = 2√34

3. Now that we have the radius, we can find the equation of the tangent line at point A.

  The tangent to a circle at a given point is perpendicular to the radius at that point.

  The slope of the radius can be found using the coordinates of the center and point A.

  Slope of the radius = (17 - 7) / (8 - 2) = 10 / 6 = 5/3

  The slope of the tangent line will be the negative reciprocal of the slope of the radius.

  Slope of the tangent = -1 / (5/3) = -3/5

4. However, the question asks for the slope of the tangent to the circle at point A, so we need to consider the slope of the tangent line at point A, which is the negative inverse of the slope of the radius.

  Slope of the tangent at point A = -1 / (5/3) = -3/5

5. The slope of the tangent to the circle at point A is -3/5.

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The concentration of the mixture made by mixing 6 fl. oz. of a 20% alcohol solution and 4 fl. oz. of a 5% alcohol solution will be; 14%

Consider that x represents the concentration of the mixture, hence:

(6 x 20%) + (4 x 5%) = x (4 + 6)

1.2 + 0.2 = 10x

x = 0.14 = 14%

The concentration of the mixture is made by mixing 6 fl. oz. of a 20% alcohol solution and

Thus 4 fl. oz. of a 5% alcohol solution = 14%

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The values of the missing variables are:

a = 57

b = 75

c = 96

d = 150

We have,

Angle 48 is half the intercepted arc.

So,

1/2 x c = 48

c = 48 x 2

c = 96

Now,

Similarly

Angle a = 1/2 x 114

Angle a = 57

And,

The sum of the angles in a triangle = 180

a + b + 48 = 180

57 + b + 48 = 180

b = 180 - (57 + 48)

b = 180 - 105

b = 75

Now,

Angle b = 1/2 x d

75 = 1/2 x d

d = 75 x 2

d = 150

We can also see that,

114 + c + d = 360

114 + 96 + 150 = 360

360 = 360

Thus,

The values of the missing variables are:

a = 57

b = 75

c = 96

d = 150

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The graph showing a circle with a center (-3, 2) and a radius of 3 does not represent all possible centers for a circle passing through (3, -1) with a radius of 4.

The graph represents a specific circle with its own center and radius.

To find all possible centers for a circle passing through a given point, we need to consider the locus of points equidistant from the given point.

In this case, the locus of points equidistant from (3, -1) with a radius of 4 forms another circle with a different center and radius.

The graph showing a circle with a center (-3, 2) and a radius of 3 does not represent all possible centers for a circle passing through (3, -1) with a radius of 4.

Therefore, neither student's claim is correct based on the given information.

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Answer: i believe it’s 68

Step-by-step explanation:

My knowledge

Given statement solution is:- The coordinates of point B is (3, 50°).

In the given scenario, we have point A with polar coordinates (2, 50°) and the pole O. We need to find point B such that OA is parallel to OB and OB has a length of 3 units.

Since OA and OB are parallel, they have the same angle with the positive x-axis. Therefore, the angle between OB and the positive x-axis would also be 50°.

To find the coordinates of point B, we can use the polar coordinates system, where the distance from the pole is denoted by r and the angle with the positive x-axis is denoted by θ.

Since OB has a length of 3 units, the distance from the pole (r) would be 3. The angle between OB and the positive x-axis is also 50°. Therefore, the coordinates of point B would be (3, 50°).

So, one possible answer for the coordinates of point B is (3, 50°).

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The amplitude and the period of the function f(x) = cos(5θ) are 1 and 2π/5

From the question, we have the following parameters that can be used in our computation:

f(x) = cos(5θ)

A sinusoidal function is represented as

f(x) = Acos(B(x + C)) + D

Where

So, we have

A = 1

Period = 2π/5

Evaluate

A = 1

Period = 2π/5

Hence, the amplitude is 1 and the period is 2π/5

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The percentage of vehicles that are returned with less than 30000 miles are given as follows:

b) 2.5%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 36400, \sigma = 3200[/tex]

The proportion is the p-value of Z when X = 30000, hence:

Z = (30000 - 36400)/3200

Z = -2.

Z = -2 has a p-value of 0.028 -> percentage rounded to 2.5%.

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Answer:

  see attached

Step-by-step explanation:

You want the areas of the four triangles in the figure.

The area of a triangle is given by the formula ...

  A = 1/2bh

where b is the base of the triangle, and h is its height perpendicular to the base.

Triangles A, B, C are right triangles, so their areas are easy to figure. Triangle D will be the difference between the area of the square and the areas of the other triangles.

The calculations are shown in the first attachment. Confirmation is provided by a geometry program in the second attachment.

__

Additional comment

If all you have are the coordinates of the vertices of triangle D, this method of finding its area is as good as any. There are other methods that can also be used, but they can be more trouble.

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The domain and range of the given function y = -2x + 3 are

Domain = 0, 1, 2, ,3 , 4, 5, 6

Range = 3, 1, -1, -3, -5, -7, -15

The table is given below.

We have,

y = -2x + 3

We can have domain as:

x = 0, 1, 2, 3, 4, 5, 6

For x = 0,

y = -2 x 0 + 3 = 3

For x = 1,

y = -2 x 1 + 3 = -2 + 3 = 1

For x = 2,

y = -2 x 2 + 3 = -4 + 3 = -1

For x = 3,

y = -2 x 3 + 3 = -6 + 3 = -3

For x = 4,

y = -2 x 4 + 3 = -8 + 3 = -5

For x = 5,

y = -2 x 5 + 3 = -10 + 3 = -7

For x = 6,

y = -2 x 6 + 3 = -18 + 3 = -15

The range are 3, 1, -1, -3, -5, -7, -15.

The table can be assumed as:

x         y = -2x + 3

0        3

1         1

2        -1

3        -3

4       -5

5       -7

6       -15

Thus the domain and range of the given function y = -2x + 3 are

Domain = 0, 1, 2, ,3 , 4, 5, 6

Range = 3, 1, -1, -3, -5, -7, -15

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Answer:

1/2

Step-by-step explanation:

Slope formula:

[tex] \boxed{ \purple{ \sf \: m = \frac{ y_{2} - y_{1}}{x_{2} -x_{1} } }}[/tex]

P.S. Slope is denoted by letter m

We have;

[tex] \red \implies \green{ \tt \: m = \frac{2 - ( - 4)}{5 - 2} }[/tex]

[tex] \red \implies \green{ \tt \: m = \frac{ \cancel6}{ \cancel3} }[/tex]

[tex] \red \implies \green{ \tt \: m = \frac{ 2}{ 1} = 2} [/tex]

3√2 and 3 are the values of x and y respectively from the figure.

The given diagram is a right triangle with an acute angle of 45 degrees

We need to determine the values of variables x and y.

Applying the trigonometry identity, we will have:

sin 45 = opposite/hypotenuse
sin45 = 3/x

x = 3/sin45

x = 3/(1/√2)
x = 3√2

Similarly:

tan 45 = opposite/adjacent
tan 45 = 3/y

1 = 3/y

y = 3

Hence the values of x and y from the figure is 3√2 and 3 respectively

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The calculated measure of the red arc in ⊙C is 5

From the question, we have the following parameters that can be used in our computation:

The circle

From the circle, we have

Centers = C

Also, we have

Corresponding segments are equal segments

Using the above as a guide, we have the following:

UV  = TU

Where

TU = 5

This gives

UV = 5

Hence, the value of UV is 5

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The equation of the parabola that models the cross section of the reflector is: y = (1/32)x².

To model a cross section of the reflector as a parabola that opens upward and has its vertex at the origin,

We can use the standard equation for a parabola in vertex form:

y = a(x - h)² + k

In this equation, (h, k) represents the coordinates of the vertex.

Since we want the vertex to be at the origin (0, 0), the equation becomes:

y = ax²

To determine the value of 'a,' we can use the given information that the bulb is located 8 inches from the vertex.

Since the bulb is located at the focus, we know that the distance from the vertex to the focus (f) is also 8 inches.

In a parabola, the distance from the vertex to the focus is given by the formula f = 1/(4a).

Plugging in the value of f (8) into the formula, we can solve for 'a':

8 = 1/(4a)

32a = 1

a = 1/32

Therefore, the equation of the parabola that models the cross section of the reflector is: y = (1/32)x²

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Answer:

look at explanation

Step-by-step explanation:

50/50 chance

a. Your monthly payments would be approximately $275.49.

b. When the card is paid off, you will have paid approximately $3,305.88 since January 1.

c. The percentage of your total payment that is interest is approximately 6.3%.

To calculate the monthly payments, we first need to determine the interest rate per month.

Since the APR is 17%, we divide it by 12 to get the monthly interest rate: 17% / 12 = 1.42%.

a. Monthly payments:

To pay off the credit card balance in one year (12 months), we divide the total balance by the number of months:

$3100 / 12 = $258.33 (approximately)

Therefore, your monthly payment should be approximately $258.33.

b. Total amount paid:

To calculate the total amount paid since January 1, we multiply the monthly payment by the number of months (12):

$258.33 * 12 = $3,099.96

Therefore, you will have paid approximately $3,099.96 since January 1.

c. Percentage of payment as interest:

To determine the percentage of the total payment that is interest, we subtract the initial balance from the total amount paid to find the total interest paid:

Total interest = Total amount paid - Initial balance

Total interest = $3,099.96 - $3100

Total interest = $-0.04 (approximately)

The negative value implies that the balance was paid off completely before the end of the year, resulting in a small overpayment.

As a result, there is no interest to calculate as it has been paid in full.

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You will need to pay $261.76 more each month if you want to pay off the balance in one year instead of three. However, you will save a total of $953.24 - $576 = $377.24 in interest by paying off the balance in one year instead of three.

If you decide to pay off the balance over one year instead of three, the payment amount will be higher, but the total interest paid will be lower due to the shorter repayment period.

First, let's calculate the total interest paid over three years. The total payment made over three years will be the monthly payment of $126.59 times 36 months, which is $4,553.24. The total interest paid is the difference between the total payment made and the initial balance of $3600, which is $953.24.

Now, let's consider paying off the balance over one year. The total payment made over one year will be the monthly payment of $126.59 times 12 months, which is $1,519.08. To calculate the interest paid, we can use the formula:

Total interest paid = Balance × Annual interest rate × Time

where the time is expressed in years. Plugging in the values, we get:

Total interest paid = $3600 × 0.16 × 1 = $576

Therefore, if you decide to pay off the balance over one year instead of three, you will pay an additional amount each month equal to the difference between the monthly payment for one year and the monthly payment for three years, which is:

Additional monthly payment = ($4,553.24/12) - ($1,519.08/12) = $261.76

This means that you will need to pay $261.76 more each month if you want to pay off the balance in one year instead of three. However, you will save a total of $953.24 - $576 = $377.24 in interest by paying off the balance in one year instead of three.

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Answer:

$132.54

Step-by-step explanation:

$1060.32 / 8 families = $132.54 / family

Answer

[tex]\pink\sf{y=-1}[/tex]

Step-by-step explanation

I'm assuming that this exercise is asking us to simplify the equation [tex]\sf{y=0.5(6)-4}[/tex].

We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:

[tex]\sf{y=3-4}[/tex]

And now we just simplify the last part:

[tex]\sf{y=-1}[/tex]

∴ answer: y = -1

The probability that the first marble drawn is blue and the second marble drawn is red is 1/4 or 0.25, which can also be expressed as 25%.

To determine the probability of drawing a blue marble on the first draw and a red marble on the second draw, we need to consider the total number of marbles and the number of blue and red marbles in the bag

In this case, we have a bag with 12 blue marbles and 12 red marbles, making a total of 24 marbles.

When drawing the first marble, there is a 12/24 probability of selecting a blue marble since there are 12 blue marbles out of the total 24 marbles in the bag.

After replacing the first marble back into the bag and mixing up the marbles, the probability of drawing a red marble on the second draw is also 12/24, as there are still 12 red marbles remaining out of the total 24 marbles.

To find the overall probability, we multiply the probabilities of each event since they are independent events:

P(first marble is blue and second marble is red) = P(first marble is blue)[tex]\times[/tex]P(second marble is red)

[tex]= (12/24) \times (12/24)[/tex]

[tex]= (1/2) \times (1/2)[/tex]

= 1/4.

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1. The probability that the sensor will give an incorrect report is 0.03 or 3%.

2. The probability that the reactor will be shut down because of simultaneous false alarms by both sensors is 0.0004 or 0.04%.

3. The probability that excessive radiation will be missed simultaneously by both sensors is 0.0001 or 0.01%.

The probability of a false alarm is 0.02.

The probability of a miss is 0.01.

P(false alarm or miss)

= P(false alarm) + P(miss)

= 0.02 + 0.01 = 0.03

Therefore, the probability that the sensor will give an incorrect report is 0.03 or 3%.

2. Probability of simultaneous false alarms by both sensors:

P(false alarm by both sensors)

= P(false alarm by sensor 1) * P(false alarm by sensor 2)

= 0.02 * 0.02

= 0.0004

Therefore, the probability that the reactor will be shut down because of simultaneous false alarms by both sensors is 0.0004 or 0.04%.

3. Probability of missing excessive radiation by both sensors:

P(miss by both sensors)

= P(miss by sensor 1) * P(miss by sensor 2)

= 0.01 * 0.01

= 0.0001

Therefore, the probability that excessive radiation will be missed simultaneously by both sensors is 0.0001 or 0.01%.

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The values of x and y in the figure are 3√2 and 3, respectively.

The diagram shown is a right triangle with a 45-degree acute angle.

The values of variables x and y must be determined.

Using the trigonometry identity, we get:

opposite/hypotenuse = sin 45

sin45 = 3/x

x = 3/sin45

x = 3(1/√2)

x = 3√2

Likewise,

tan 45 = opposite/adjacent

tan 45 = 3/y

1 = 3/y

y = 3

As a result, the values of x and y in the figure are 32 and 3, respectively.

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The result of the expression 20 - 6 is 14.

To solve the given expression, 20 - 6, and isolate the variable, we need to clarify whether there is an equation involved. However, in this case, the expression does not contain any variable to isolate, and it is not an equation that needs balancing. It is a straightforward arithmetic expression.

Step 1: Start with the given expression, 20 - 6.

Step 2: Evaluate the subtraction operation: 20 - 6 = 14.

Step 3: The simplified expression is now 14. However, since there is no variable present, there is no need to isolate any variable.

This means that when you subtract 6 from 20, the answer is 14. Remember that isolating a variable and balancing an equation are relevant when dealing with equations that involve variables. In this case, the expression is a simple subtraction operation, yielding a constant value of 14 as the answer.

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$63 + ($63 · 0.28) = $80.64

[tex]f = p + pm[/tex] where:

[tex]f[/tex] = final price: $80.64,

[tex]p[/tex] = original price: $63,

and [tex]m[/tex] = markup percent (in decimal): 28% → 0.28.

Answer:

Step-by-step explanation:

5 years ago the ratio of Mark's age was 3:4 mark is 12 yr younger than Francis, now Francis is currently 53 years old

Let us suppose that age of him 5 years ago was 3x and Francis's age 5 years ago was 4x. According to the given information, Mark is 12 years younger than Francis.

So, we can set up the equation: 3x + 12 = 4x.

Simplifying the equation, we have: 12 = x.

This means that 5 years ago,

Mark age = 3 * 12 = 36 years old,

Francis age = 4 * 12 = 48 years old.

Now, to find out how old Francis is now, we add 5 years to both Mark and Francis. Thus, Francis's current age is 48 + 5 = 53 years.

Therefore, Francis is currently 53 years old.

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Answer:

x² - y + x = 16 is 1 real solution

3x² - y + 32 = 22x is 2 real solutions

y = -x² + 6x + 12 is 1 real solution

Step-by-step explanation:

sorry i am unsure about rest, they do not have a value. good luck :)

Answer:

[tex]\huge\boxed{\sf \angle AEB=86 \textdegree}[/tex]

Step-by-step explanation:

arc AB = 106°

arc CD = 66°

[tex]\displaystyle \angle AEB=\frac{1}{2} (arc \ AB+arc \ CD)[/tex]

Put the given data in the above formula.

[tex]\displaystyle \angle AEB=\frac{1}{2} (106 + 66)\\\\\angle AEB=\frac{1}{2} (172)\\\\\angle AEB=86 \textdegree \\\\\rule[225]{225}{2}[/tex]

The calculated total distance he drive is 372 miles

From the question, we have the following parameters that can be used in our computation:

So, we have

Total charges = 75 * days + 0.25 * miles

For 2 days and total ot 243. we have

75 * 2 + 0.25 * miles = 243

So, we have

miles = 372

Hence, the total distance he drive is 372 miles

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