While driving your rental car on your vacation in Europe, you find that you are getting 13.3 km/of gasolineWhat does this value correspond to in miles per gallon?
13.3km/L=
_mi/gal

Answers

Answer 1

The value of 13.3km/L corresponds to 30.595 miles/gal

how to find the value after conversion

The conversion required is 13.3km/L to mile/gal

converting km to miles

1km = 0.621371 miles

13.3 km = ?

cross multiplying results to

? = 13 * 0.621371 = 8.077 miles

converting L to gallons

1 liters = 0.264172

hence we have that

= 8.077 / 0.264

= 30.595

thus, 13.3km/L is equal to 30.595 miles/gal

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Related Questions

find the value of x and y

Answers

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

Identities in trigonometry

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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A circle has a center at C(2,7). The point A(8,17) lies on the circle. Which of the
following is the slope of the tangent to the circle at point A?

Answers

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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Brian says the graph shows the circle with a center (-3, 2) and a radius of 3. Mia says the graph shows all possible centers for a circle that passes through (3, -1) with a radius of 4. Which student is correct? Explain.

Answers

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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You have a bag of 12 blue marbles (numbered 1-12) and 12 red marbles (numbered 1-12). So you have 24 marbles in total (half blue and half red) with each of the numbers 1-12 appearing twice (once in each color). You draw one marble at random, replace it to the bag, mix up the marbles, and draw a second marble. Determine each of the following probabilities. P ( first marble is blue and second marble is red ) =

Answers

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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Amazon purchases an office chair for $63, and marks it up 28%.
Which equation can be used to find the selling price of the office chair?

Answers

$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.

please help! thank uu ~ :) please be correct!

Answers

Answer:

look at explanation

Step-by-step explanation:

50/50 chance

6. Julie went to a family reunion at a restaurant. In total there were 8 families that attended. The bill at the restaurant was $1,060.32. How much does each family need to pay if they split the bill evenly? (WITHOUT TIP!)​

Answers

Answer:

$132.54

Step-by-step explanation:

$1060.32 / 8 families = $132.54 / family

5 years ago the ratio of mark's age was 3:4 mark is 12 yr younger than francis how old is francis now.

Answers

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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100 Points! Algebra question. Photo attached. Find the amplitude, if it exists, and period of the function. Then graph the function. Thank you!

Answers

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

How to determine the amplitude and period of the function

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

Amplitude = APeriod = 2π/B

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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What is the slope of the line that passes through the points (2,-4) and (5, 2)? Write
your answer in simplest form.
Answer:
undefined
Submit Answer
attempt 1 out of 2

Answers

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]x_{1}, y_{1}[/tex] = (2,-4)[tex]x_{2}, y_{2}[/tex] = (5,2)

[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]

23. Solve for the missing variables.

Answers

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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(a) In the figure below, m AB = 106° and m CD =66. Find mAEB

Answers

Answer:

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

Step-by-step explanation:

Given:

arc AB = 106°

arc CD = 66°

Statement:According to angles of intersecting chords theorem, the measure of angle formed by two intersecting chords is half the sum of arcs intercepted by the angle.Mathematical form:

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

Solution:

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]

Math
82°F
Algebra 1 CC.20 Checkpoint: Quadratic equations NXG
2
x² - y + x = 16
y = 3x + 2
3x² - y + 32 = 22x
y = 2x - 16
Language arts
Decide whether each system of equations has two real solutions, exactly one real solution, or
no real solutions.
y = -x² + 6x + 12
y = -x +3

Answers

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 :)

Fill in the table using this function rule.
y=-2x+3
x
-2
-1
0
1
y
0
1
0
10
X
Ś

Answers

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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I dont get this question equation

y=0.5 (6) - 4

I know that 0.5 is equivalent to 1/2 but I just don’t get this question

Answers

The equation y = 0.5(6) - 4 is a linear equation in which y represents the value of the dependent variable and 0.5(6) - 4 represents the value of the independent variable.

To solve the equation, you first need to simplify 0.5(6) to get 3, since 0.5 is equivalent to 1/2 and multiplying 6 by 1/2 gives you 3. So the equation becomes:

y = 3 - 4

Next, you need to subtract 4 from 3 to get -1. So the solution to the equation is:

y = -1

Therefore, when the value of the independent variable is 6, the value of the dependent variable is -1.

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

your credit card has a balance of $3600 and an annual interest rate of 16%. you decide to pay off the balance over three years. if there are no further purchases charged to the card, you must pay $126.59 each month, and you will pay a total interest of $957.24. assume you decide to pay off the balance over one year rather than three. how much more must you pay each month and how much less will you pay in total interest?

Answers

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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stered comsident p43336280840
Save the expression by solating the variable Hemember to balance the equation in each step you take
2
0-6

Answers

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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A sensor is used to monitor the performance of a nuclear reactor. The sensor accurately reflects the state of the reactor with a probability of .97. But with a probability of .02, it gives a false alarm (by reporting excessive radiation even though the reactor is performing normally), and with a probability of .01, it misses excessive radiation (by failing to report excessive radiation even though the reactor is performing abnormally).
What is the probability that a sensor will give an incorrect report, that is, either a false alarm or a miss?


To reduce costly shutdowns caused by false alarms, management introduces a second completely independent sensor, and the reactor is shut down only when both sensors report excessive radiation. (According to this perspective, solitary reports of excessive radiation should be viewed as false alarms and ignored, since both sensors provide accurate information much of the time.) What is the new probability that the reactor will be shut down because of simultaneous false alarms by both the first and second sensors?


Being more concerned about failures to detect excessive radiation, someone who lives near the nuclear reactor proposes an entirely different strategy: Shut down the reactor whenever either sensor reports excessive radiation. (According to this point of view, even a solitary report of excessive radiation should trigger a shutdown, since a failure to detect excessive radiation is potentially catastrophic.) If this policy were adopted, what is the new probability that excessive radiation will be missed simultaneously by both the first and second sensors?

Answers

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%.

1. Probability of the sensor giving an incorrect report (false alarm or miss):

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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50 Points! Multiple choice algebra question. Photo attached. Thank you!

Answers

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

b) 2.5%.

How to obtain probabilities using the normal distribution?

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 z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.

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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Si un editor pone un precio de S/ 16 a un libro, se venderán 10,000 copias. Por cada dólar que aumente al
precio se dejarán de vender 300 libros. ¿Cuál debe ser el precio al que se debe vender cada libro para
generar un ingreso total por las ventas de S/ 129200?

Answers

Answer:

Step-by-step explanation:

A(2, 50°) is a point in a polar coordinate plane. Let O be the pole. 2 If B is another point in the same polar coordinate plane such that OA LOB and OB = 3 units, write down one possible answer for the coordinates of B.​

Answers

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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Determine the lengths of the missing sides x and y in the triangle below:


x =


y =


2.6 2.1 4.2 3

Answers

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

Trigonometry identities

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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What is the area of this figure

Answers

Answer: i believe it’s 68

Step-by-step explanation:

My knowledge

Can I get help, please

Answers

Answer:

  see attached

Step-by-step explanation:

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

Triangle area

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.

<95141404393>

Suppose that on January 1 you have a balance of ​$3100 on a credit card whose APR is ​17%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1
.a. Calculate your monthly payments.
b. When the card is paid​ off, how much will you have paid since January​ 1?

c. What percentage of your total payment from part​ (b) is​ interest?

Answers

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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An alcohol was made by mixing 6fl. oz. of a 20% alcohol solution and 4fl. oz. of a 5% alcohol solution. What is the concentration of the mixture?

Answers

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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please help its due today and I need a good grade on it!!!!

Answers

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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A rental company charges $75 a day and 25 cents a mile for renting a truck. Michael rents a truck for 2 days, and his bill came to $243. How many miles did he drive?

Answers

The calculated total distance he drive is 372 miles

How many miles did he drive?

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

Charges $75 a day25 cents a mile

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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5. 49% of adults say cashews are their favorite kind of nut. You randomly select 19 adults and ask
each to name his or her favorite nut. Find the probability that the number who say cashews are
their favorite nut is exactly four. (Round to the nearest thousandth as needed.)
6. According to the website nationalbikeregistry.com, at UCLA only 3% of stolen bikes are returned
to owners. If there are 335 bikes stolen at UCLA what is the probability that 12 or more stolen
bikes will be returned? (Round to the nearest thousandth as needed.)

Answers

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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Find the measure of the red arc or chord in ⊙C

Answers

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

How to find the measure of the red arc or chord in ⊙C.

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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