Imagine that you are taking a multiple-choice quiz written in Faroese and must guess randomly. Each question has 5 choices and 1 correct answer. Calculate the probability that you... answer the first question incorrectly. answer the first 2 questions incorrectly. answer the first 5 questions incorrectly. answer at least 1 of the first 5 questions correctly. (Note: Enter each answer as a fraction or as a decimal rounded to the nearest thousandth.)

Answer:

1. y=3x+2

2. y=-1/2x-8

Step-by-step explanation:

1.  Find the equation of the line that passes through (1,5) and (2,8).

slope-intercept form of the line is y=mx+b

the given points are (1,5) and (2,8)

the equation for slope (m) is (y2-y1)/(x2-x1)

label the points:

x1=1

y1=5

x2=2

y2=8

substitute into the equation

m=(8-5)/(2-1)

m=3/1

m=3

the slope is 3

use slope-point form, which is y-y1=m(x-x1)

once again, substitute into the equation:

y-5=3(x-1)

do distributive property

y-5=3x-3

add 5 to both sides

y=3x+2

the equation of the first line is y=3x+2

2. Find the equation of the line that passes through (-2,-7) and (4,-10).

we are given the points (-2,-7) and (4,-10)

label the points:

x1=-2

y1=-7

x2=4

y2=-10

substitute into the equation for slope:

m=(-10--7)/(4--2)

m=(-3)/6

m=-1/2

the slope is -1/2

use slope-point form again:

y--7=-1/2(x--2)

y+7=-1/2(x+2)

do distributive property

y+7=-1/2x-1

subtract 7

y=-1/2x-8

the second equation is y=-1/2x-8

hope this helps :D

The sale price for Kendra's purchase is 51.3175 dollars.

Kendra is buying new shoes that normally cost 78.95 dollars.

She has a coupon to save 35%.

Therefore, let's calculate the sale price of her purchase.

A sale price is the discounted price at which goods or services are being sold.

The sale price is the price after the original price has been reduced by a discount.

Therefore,

sale price = 78.95 - 35% of 78.95

sale price = 78.95 - 35 / 100 × 78.95

sale price = 78.95 - 2763.25 / 100

sale price = 78.95 - 27.6325

Therefore,

sale price = 51.3175 dollars

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The statements that can be used to determine independent events are given as follows:

If two events are independent, the multiplication of the probabilities of each event is equals to the probability of both events, that is:

P(A and B) = P(A) x P(B).

Which means that the first statement is correct.

The conditional probability formula is given as follows:

P(B|A) = P(A and B)/P(A).

However, for independent events, we know that:

P(A and B) = P(A) x P(B).

Hence:

P(B|A) = P(A) x P(B)/P(A).

P(B|A) = P(B).

The same is true for the opposite, meaning that:

P(A|B) = P(A).

Meaning that the last statement is correct.

The Venn probability P(A or B) = P(A) x P(B) - P(A and B) can also be used to determine if the events are independent, when it assumes a value of zero.

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Answer:

1/22

Step-by-step explanation:

Its 1/22 because that is the total probability of your name being drawn for the prize

The surface area of the  gas tank capsule represented to 1 dp is about 9079.2 cm²

The surface area of a solid object is the area of all the faces of the object.

Part of the dimension of the gas tank obtained from a similar question on the website is; Total length of the gas tank = 85 cm

Therefore;

Radial length of the tank = (85 cm - 51 cm)/2 = 17 cm

The surface area of the tank can be found as the surface area of a composite figure. The extreme right and left part of the tank together form a sphere, while the middle portion is a cylinder. Therefore, we get;

Surface area = 4 × π × 17² + 2 × π × 17 × 51 = (1734 + 1156) × π = 2890·π

Surface area of the figure = 2890·π cm² ≈ 9079.2 cm²

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The value of the probability expression P(y|b) is 0.5 to the nearest tenth

The probability expression is given as:

P(y|b)

This is calculated using:

P(y|b) = n(y and b)/n(b)

From the complete question, we have:

P(y|b) = 1/2

Evaluate

P(y|b) = 0.5

Hence, the value of P(y|b) is 0.5

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Answer:

0.5

Step-by-step explanation:

The value of the probability expression P(y|b) is 0.5 to the nearest tenth

How to determine the value of the probability?

The probability expression is given as:

P(y|b)

This is calculated using:

P(y|b) = n(y and b)/n(b)

From the complete question, we have:

P(y|b) = 1/2

Evaluate

P(y|b) = 0.5

Hence, the value of P(y|b) is 0.5

Answer:

7.2 hours slept

Step-by-step explanation:

30%>.30

.30*24=7.2 hours

Hope this will help!

The number of red car altogether is 34

The number of blue cars altogether is 36

The  number of silver car altogether 70

The car manufacturer has parked some cars in 2 car parks .

The first car park has 60 cars.

In the ratio 1 :2:3

Therefore,

red car = 1 / 6 × 60 = 10 cars

blue car = 2 / 6 × 60 = 20 cars

Silver car = 60 - 30 = 30 cars

The second car park has 80 cars.

The ratio are

In the ratio 3:2 5

Therefore,

red cars = 3 / 10 ×80 = 24

blue cars = 2 / 10 × 80 = 16

silver cars = 5 / 10 × 80 = 40

Therefore,

The number of red car altogether is 24 + 10 = 34 red car

The number of blue cars altogether is 20 + 16 = 36 blue cars

The  number of silver car altogether is 30 + 40 = 70 silver cars

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To find the entropy of a system of N harmonic oscillators, we first need to use the expression for the partition function found in Problem 6.20:

Zh.o. = 1/(1 − e −β)

We can rewrite this as:

Zh.o. = eβ/2 / (sinh(β/2))

Using this expression for Z, we can find the entropy of the system as:

S = -k ∂(lnZ)/∂T

Simplifying this expression, we get:

S = k [ ln(Zh.o.) + (β∂ln(Zh.o.)/∂β) ]

Taking the derivative of ln(Zh.o.) with respect to β, we get:

∂ln(Zh.o.)/∂β = -hf/(kT(eβhf - 1))

Substituting this into the expression for S, we get:

S = k [ ln(eβ/2/(sinh(β/2))) - (βhf/(eβhf - 1)) ]

This expression for the entropy as a function of temperature is fairly complicated, but it gives us a way to calculate the entropy of a system of N harmonic oscillators at any temperature.


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Consequently, x = -6 and y = 0 provide the system of equations answer. The response gathering yields "(-6,0)" as the outcome.

She came back to compete in the meeting's final event, winning the knockout race. Their quick removal is the letdown. Take pride in your quick removal.

To solve this system of equations using elimination, we need to eliminate one of the variables by adding or subtracting the equations. Here's how to do it:

To find: multiply the second solution by 4.

12x - 36y = -72

Eliminate x by combining the two equations:

5x + 4y + 12x - 36y = -30 - 72

Simplify and combine like terms:

17x - 32y = -102

Solve for x:

17x = 32y - 102

x = (32/17)y - 6

Substitute this expression for x into one of the original equations, and solve for y:

5x + 4y = -30

5[(32/17)y - 6] + 4y = -30

Simplify and solve for y:

(160/17)y - 30 = -30

(160/17)y = 0

y = 0

Substitute this value for y back into either of the original equations and solve for x:

3x - 9y = -18

3x - 9(0) = -18

3x = -18

x = -6

So the solution to the system of equations is x = -6 and y = 0. Therefore, the solution set is {(-6,0)}.

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Answer:- 1/100 degrees Fahrenheit

Step-by-step explanation:

The directions say decreasing so it has to be negative, and the slope is showing how much it is decreasing every meter. y=mx+b. The mx is the slope which is where the answer is located.

To determine the coordinates of the corresponding point L' on segment S'T', we need to understand the effects of a 90° counterclockwise rotation on a point in a coordinate plane.

Let's start by visualizing the scenario. We have a line segment ST and a point L(x, y) on that line segment. To rotate the line segment 90° counterclockwise, we imagine a rotation around a point. In this case, the rotation is around the origin (0, 0) since we're not given any other specific rotation point.

To rotate a point counterclockwise 90° around the origin, we use the following formulas:

x' = -y

y' = x

Applying these formulas to point L(x, y), we can find the coordinates of the corresponding point L' on segment S'T'.

Using the formula x' = -y, we substitute the value of y with -y:

x' = -(-y) = y

Using the formula y' = x, we substitute the value of x with x:

y' = x

Hence, the coordinates of the corresponding point L' (L prime) on segment S'T' are (y, x). This means that the x-coordinate of L' is equal to the y-coordinate of L, and the y-coordinate of L' is equal to the x-coordinate of L.

In other words, if point L has coordinates (x, y), then the corresponding point L' on segment S'T' will have coordinates (y, x).

It's important to note that this transformation only applies to the coordinates of the points and not the line segment itself. The line segment is rotated while the point L moves correspondingly. The formulas used are specific to a 90° counterclockwise rotation around the origin.

By applying these formulas, you can easily find the corresponding point L' when given the coordinates of point L on segment ST.

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Statistical guidance should perform well in situations such as clinical trials and market research where rigorous data analysis and inference are necessary. Statistical methods provide a systematic approach to control biases, handle variability, and draw reliable conclusions, ensuring accurate decision-making and predictions based on the data.

Statistical methods are crucial in determining sample sizes, designing the study, and analyzing the data to draw valid conclusions about the effectiveness and safety of the treatment.

In this situation, statistical guidance should do well because it provides a systematic framework to control for biases, random variability, and confounding factors, ensuring robust and reliable results that can be generalized to a larger population.

One example where statistical guidance should perform well is in clinical trials for new drugs or treatments.

Another example is in market research and opinion polling. Statistical techniques can be used to collect and analyze data from a representative sample of the target population, allowing for accurate estimation and prediction of consumer preferences, market trends, or election outcomes.

Statistical guidance should do well in this situation because it provides methods for random sampling, hypothesis testing, and confidence interval estimation, which help minimize sampling errors and increase the reliability of the findings.

Additionally, statistical models can capture complex relationships and make accurate predictions based on the observed data.

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The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”.

Now, According to the question:

What is inequality?

A statement involving the symbols '>', '<', ' ≥', '≤' is called an inequality. For example 5 > 3, x ≤ 4, x + y ≥ 9.

(i) Inequalities which do not involve variables are called numerical inequalities. For example 3 < 8, 5 ≥ 2.

We use the equal sign "=" to say that two things are the same. However, sometimes we just want to show that something is bigger or smaller than something else. Or maybe we just want to say that two things are not equal. These cases are called inequalities.

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We need to find the angle (rounded to the nearest whole degree) of a circle that would represent the percent of students taking mathematics.

Since a complete turn around the circle has 360º, we have the following proportion:

Number of students Angle

734 360º

442 x

Then, cross multiplying the above values, we obtain:

Answer: 217º

Answer:

217°

Step-by-step explanation:

The fraction of students taking math is   442/734

 we need this same fraction of the 360 degrees in a circle

442/734 * 360 = 217°

Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

To prove:

From the figure, we observe that

The angles x and y are the alternate angles because of the transversal crossed over the two parallel lines.

So, the alternate angles are equal.

Hence, it proves that,

Answer:

The track coach set up a relay race. The race will be 2 1/2 times around the track if each runner runs 3/4 of a lap.

Step-by-step explanation:

Just use words to describe how the numbers are being used.

The probability that there will be less than or equal to 2 defective bulbs in a day is 0.6767 or 67.67%.

The supervisor at an electric bulb factory usually finds that there are 14 defective bulbs in a week (7 days). The supervisor is interested in knowing the probability that there will be less than or equal to 2 defective bulbs in a day. Using the Poisson distribution, we can calculate this probability.

The formula for the Poisson distribution is P(x) = (e^ᵃ (a=-λ) * λˣ) / x!,

where x is the number of events, e is the constant 2.71828, λ is the mean number of events, and x! is the factorial of x. In this case, λ = 14/7 = 2, since there are 14 defective bulbs in a week.

Plugging in x = 0, 1, or 2, we get P(0) = 0.1353, P(1) = 0.2707, and P(2) = 0.2707. Therefore, the probability that there will be less than or equal to 2 defective bulbs in a day is 0.6767 or 67.67%.

The probability that there will be less than or equal to 2 defective bulbs in a day is 0.6767 or 67.67%.

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Answer:

Its the second one

Step-by-step explanation:

.

Answer:

radius=d/2 = 8/2 = 4inch.

Step-by-step explanation:

area = πr²

16π(inch)². or 352/7 (inch)².

hope this helps you.

Hello There!

\(GraceRosalia\) is here to help you!

We are given that

d=8 in.

We know that the radius is 1/2 of d or r=d/2. So the radius is 4.

However, we have to find the area.

The formula for the area of a circle is:

A=\(\pi\)\(r^{2}\)

We know that r=4, so all we have to do is plug it into the formula:

A=\(\pi (4)^{2}\)

Remember that only the radius is squared.

A=\(\pi *16\)

A=50.265

Let's round to the nearest tenth:

A=50.3

Hope this helps you!

\(GraceRosalia\)

Let me know if you have any questions!

Answer:

Option A  and D

Step-by-step explanation:

A polynomial is the combined form of expression that contains variables, operations and exponents. It cannot be divided by a variable.Polynomial does not have fractional exponent.

Option A is a polynomial because it contains variables x  and y and operators like + and division

Option B is not a polynomial because it have x in the denominator . Polynomial cannot be divided by a variable.

Option C is not a polynomial because it has a fractional exponent 1/3

Option D is a polynomial because it contains variables x  and y

Answer:

If Sandy bought a soft drink for 2 dollars that's 2 dollars subtracted from the total of $12.00 spent

If we have 10 dollars and bought 5 candy bars we would divide so 10 divided by 5 = 2 so each candy bar costed $2 dollars

Answer:

1) a 2) b

Step-by-step explanation:

Answer:

\({ \rm{f(x) = - x - 1}} \\ \\{ \rm{f(6) = - 6 - 1}} \\ \\ { \rm{f(6) = - 7}}\)

Answer:

f(6) = -7

Step-by-step explanation:

It is given that x = 6. Plug in 6 for x in the given equation:

f(x) = -x - 1

f(6) = -(6) - 1

Note that when you are subtracting two negative numbers, you are really adding the two numbers:

f(6) = -(6) - 1

f(6) = -7

When x = 6, f(x) = -7

~

We know that the radius (r) is 5 m, and the rate of change of the volume (dV/dt) is 4 m^3/min. We can plug these values into the equation and solve for the rate of change of the height (dh/dt):

4 = π(5^2)(dh/dt)

dh/dt = 4/(π25)

dh/dt = 0.0507 m/min

Therefore, the height of the water is increasing at a rate of 0.0507 m/min.

To determine the rate at which the height of the water is increasing in an upright cylindrical tank, we'll use the formula for the volume of a cylinder: V = πr²h, where V is the volume, r is the radius, and h is the height.

Given:
- Radius (r) = 5 m
- Rate of filling (dV/dt) = 4 m³/min

We need to find the rate at which the height (dh/dt) is increasing.

First, let's differentiate the volume formula with respect to time (t):

dV/dt = πr²(dh/dt)

Now, plug in the given values:

4 = π(5²)(dh/dt)

Solve for dh/dt:

dh/dt = 4 / (π(25))
dh/dt ≈ 4 / (78.54)
dh/dt ≈ 0.0509 m/min

So, the height of the water is increasing at a rate of approximately 0.0509 meters per minute.

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The points on the graph of the equation represent the solution set to the equation.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is the equation as -

- x - y = 4

The given equation is -

- x - y = 4

x + y = 4

The graph of the given equation will represent a straight line. All the points on the line represent the solution set to the equation.

Therefore, the points on the graph of the equation represent the solution set to the equation.

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{Question in english -

How can i solve this?

- x - y = 4}