What is the solution?



Group of answer choices

(0,-4)

(4,-3)

(0,-1)

(-2,0)

The event is randomly selecting one card from a standard deck of 52 playing cards. We need to determine the number of outcomes in this event and whether it is a simple event or not.

In a standard deck of 52 playing cards, there are 4 suits (hearts, diamonds, clubs, spades) and each suit has 13 cards (Ace, 2-10, Jack, Queen, King). Therefore, there are 52 possible outcomes or cards to choose from in this event.
Now, let's determine if this event is a simple event or not. A simple event is an event that consists of a single outcome. In this case, since we are randomly selecting one card from the deck, the event of selecting a specific card (e.g., Ace of Hearts) would be a simple event because it has a single outcome. However, if the event is defined as selecting a card of a specific suit or a card of a specific rank (e.g., selecting a heart or selecting a King), then it would not be a simple event as there are multiple outcomes associated with that event.
When randomly selecting one card from a standard deck of 52 playing cards, there are 52 possible outcomes in the event. The event of selecting a specific card, like the Ace of Hearts, would be a simple event with a single outcome. However, events defined by selecting cards of a specific suit or rank would not be simple events as they have multiple outcomes.

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The equation that must be true if A and B are independent is P(B | A) = P(B)

Two events A and B are regarded as independent in probability theory if the occurrence or non-occurrence of one event has no impact on the likelihood that the other event will occur.

The likelihood of both events A and B occurring simultaneously is equal to the product of their individual probabilities, according to the equation. This equation is valid for unrelated occurrences.

The assumption made by the equation that the occurrences are truly independent and that there is no correlation or interaction between them; must be understood. This equation would not apply if the events were interdependent, and other analysis or computations may be required to establish the joint probability of the events.

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The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. We have to find the velocity and acceleration at t = π/3 s.

Let's first find the velocity of the mass. The velocity of the mass is given by the derivative of the position of the mass with respect to time.t = π/3 s
s(t) = 300 + 16 sin t cm
Differentiating both sides of the above equation with respect to time
v(t) = s'(t) = 16 cos t cm/s

Now, let's substitute t = π/3 in the above equation,
v(π/3) = 16 cos (π/3) cm/s
v(π/3) = -8√3 cm/s

Now, let's find the acceleration of the mass. The acceleration of the mass is given by the derivative of the velocity of the mass with respect to time.t = π/3 s
v(t) = 16 cos t cm/s
Differentiating both sides of the above equation with respect to time
a(t) = v'(t) = -16 sin t cm/s²
Now, let's substitute t = π/3 in the above equation,
a(π/3) = -16 sin (π/3) cm/s²
a(π/3) = -8 cm/s²
Given, s(t) = 300 + 16 sin t cm, the height of the mass oscillating at the end of a spring. We need to find the velocity and acceleration of the mass at t = π/3 s.
Using the above concept, we can find the velocity and acceleration of the mass. Therefore, the velocity of the mass at t = π/3 s is v(π/3) = -8√3 cm/s, and the acceleration of the mass at t = π/3 s is a(π/3) = -8 cm/s².
At time t = π/3 s, the velocity of the mass is -8√3 cm/s, and the acceleration of the mass is -8 cm/s².

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15-n

15

decreased by is - (subtraction symbol)

n

Answer:

value of x = 8

Step-by-step explanation:

well here,

line x is parallel to the line measuring 18

so the two triangles are similar to each other

hence ratio of their sides are equal

so 6/ 12 = x/ 16

=》1/2 = x/16

=》 x = 16 / 2

=》 x = 8

i hope u got it

have a nice day

Answer:

x = \(\frac{16}{3}\)

Step-by-step explanation:

The outer and inner triangles are similar, thus the ratios of corresponding sides are equal, that is

\(\frac{6}{6+12}\) = \(\frac{x}{16}\) , that is

\(\frac{6}{18}\) = \(\frac{x}{16}\) ( cross- multiply )

18x = 96 ( divide both sides by 18 )

x = \(\frac{96}{18}\) = \(\frac{16}{3}\)

Standard deviation error= 3 for the average of the 36 draws from the 0-1 box.

Standard deviation error:  The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean. It tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population.

In the question it is said to find the standard error of the average of 36 draws from 0-1 box,

Probability is,  number of outcomes(n)/total number of events(t)

Probability,σ= 36/2=18

σ=18, n=36 from above

Standard deviation error= σ/\(\sqrt{n}\)

                                        =18/\(\sqrt{36}\)

                                        =18/6 =3

therefore, standard deviation error= 3.

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We know that for an object traveling with some given speed, the distance traveled is given by:

Distance = Speed*Time.

Using that relation we will find that the solution is:

1 day: Total distance = 24,900mi

          displacement = 0 mi

12 hours: Total distance = 12,450mi

                 displacement =  7,929.9 mi

To start, we need to find the speed of the Earth's equator location.

We know that it moves approximately 2,075 miles in 2 hours, then the speed is

Speed = (2,075 mi)/2h = 1,037.5 miles per hour.

Now that we know the speed, we can find the total distance traveled in one day as:

Distance traveled = (1,037.5 miles per hour)*24h = 24,900mi

Notice that the question is "How far does this location rotate in one day".

So it is not clear if it asks for total distance (24,900 mi) or displacement.

Displacement refers to the change between the initial position and the final position. Because one complete Earth's rotation happens in one day, after one day that particular location will be in the same position where it started.

Thus the final and initial positions are the same thing, and the displacement is zero.

Now we need to do the same thing for 12 hours:

Total distance traveled = (1,037 miles per hour)*12 = 12,450mi

And here we can see that the location will end on the other end of the circle, thus the displacement will be equal to the diameter of the circle that describes the motion.

Remember that for a circle of diameter D the perimeter is:

P = 3.14*D

Here the perimeter is the first total distance that we got:

24,900mi = 3.14*D

24,900mi/3.14 = D = 7,929.9 mi

Then the displacement in this case is 7,929.9 mi

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Answer:

x = 13.5

Step-by-step explanation:

2/11 = 3/(3 + x)

6 + 2x = 33

2x = 27

x = 13.5

Answer:

I dont know if this is supposed to be solved a certain way for a class, but as a bargain shopper, this is what I would do to figure out the best value.

Step-by-step explanation:

First divide $10 by 4:   10.00/4=2.5 or $2.50 per card

Then, divide $14 by 6:  14.00/6=2.3333333 so about $2.33 per card

Now, just look at the two answers and see which one is less.

If you buy 4 cards for $10, you will pay $2.50 for each card and if you buy 6 cards for $14, you will pay about $2.33 for each card. Therefore, the better value would be the 6 cards for $14.

The weight of the astronaut with gear on the moon is 80 pounds.

The pull of gravity is different on Earth than on the Moon as gravity depends on factors such as the mass of the celestial body, the radius of the celestial body, and the density of the celestial body.

The pull of gravity on Earth = 10 m/s²

Thus, Given:

Weight of object on Earth: 25 pounds

Weight is described as the product of mass and the acceleration due to gravity

Thus, 25 = 10 * mass

mass = 2.5 unit

Weight of the object on the Moon: 4 pounds

4 = 2.5 * acceleration due to gravity on the moon

Acceleration due to gravity on the moon = 1.6 m/s²

Weight of astronaut with gear on earth = 500 pounds

500 = mass * 10

mass = 50 units

Weight of astronaut with gear on earth = 50 * 1.6

= 80 pounds

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Answer:

99   (cm^2)

Step-by-step explanation:

Perpendicular to the AB segment at points D and C, the graph is divided into two triangles and a rectangle.

The area of the middle rectangle is equal to 8*9=72. The hypotenuse of the right triangle is 10cm, and one of the right sides is 9cm, so the other side is SQRT (10^2-9^2) = SQRT (19).

One side of the left triangle is 9cm long and the other side is 14-8-sqRT (19) = 6-sqRT (19) cm.

Then, add the area of the three parts.

72+9*sqrt（19）/2+9*（6-sqrt（19））/2=99    (cm^2)

Answer:

Step-by-step explanation:

The volume of a spherer is defined as

\(V=\frac{4}{3} \pi r^{3}\)

Where \(r\) is the radius and \(\pi \approx 3.14\)

According to the proble, the diameter is 20 feet. By definition of radius,

\(r=\frac{d}{2}=\frac{20ft}{2} =10ft\)

Replacing the radius in the volume formula

\(V=\frac{4}{3} \pi (10)^{3}\)

\(V=4,187 \ ft^{3}\)

Therefore, the volume of the sphere is 4187 cubic feet, approximately.

The number of square units enclosed by the polygon is 18.

First, count the number of dots that are enclosed by the polygon (including those on the boundary). There are 14 such dots.Next, count the number of dots on the boundary of the polygon. There are 8 dots on the boundary.Each of the dots on the boundary corresponds to a line segment of the polygon.

So, the perimeter of the polygon is 8 units (the length of each of these line segments).Now, we can use Pick's theorem to find the area of the polygon. Pick's theorem states that A = i + b/2 - 1, where A is the area of the polygon, i is the number of dots inside the polygon, and b is the number of dots on the boundary of the polygon.

So, plugging in the values we have: A = 14 + (8/2) - 1 = 14 + 4 - 1 = 17

Therefore, the area of the polygon is 17 square units.However, we have to remember that the dots are spaced one unit apart, horizontally and vertically.

Therefore, each square that is enclosed by the polygon has an area of 1 square unit. We counted 17 such squares, so the total area enclosed by the polygon is 17 square units.

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The best fit for explaining the growth of this particular function is option 3, polynomial.

A polynomial function is a function that can be expressed in the form of f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x + a0, where n is a non-negative integer and a0, a1, a2, ..., an are constants.

In this case, the function is 2n³, which can be expressed as f(n) = 2n³ + 0n² + 0n + 0. This is a polynomial function of degree 3, which means it is a cubic function.  ( 3)

Constant functions have the form f(x) = c, where c is a constant. Exponential functions have the form f(x) = abx, where a and b are constants and b is positive.

Linear functions have the form f(x) = mx + b, where m and b are constants. None of these functions match the form of the given function, so the best fit for explaining its growth is a polynomial function.

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Answer:

5! HOPE I HELPED

Step-by-step explanation:

Answer:

17h = 153, h = 9 (B)

Step-by-step explanation:

17h = 153

h = 153/17

h = 9

Answer to 2a: The mean of Asset A is 0.235  and the variance is 0.0123

Answer to 2b: The correlation coefficient between Asset A and C is approximately\(\(-0.670\) (Boom), \(-0.187\) (Average), \(-0.670\)\)(Bust).

2a. Mean of Asset A (Expected Value):

The mean of Asset A (E(A)) can be calculated as:

\(\[E(A) = \sum_{i} (x_i \cdot P_i)\]\)

where \(\(x_i\)\) represents the return on Asset A in each state and\(v \(P_i\)\) represents the probability of that state.

Using the given information, we have:

Boom:

\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)

Average:

\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)

Bust:

\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)

Therefore, the mean of Asset A is\(\(E(A) = 0.235\).\)

2b. Correlation Coefficient of A and C:

The correlation coefficient\((\(\rho\))\)between Asset A and C can be calculated using the formula:

\(\[\rho = \frac{{\text{{Cov}}(A, C)}}{{\sigma_A \cdot \sigma_C}}\]\)

where\(\(\text{{Cov}}(A, C)\)\) represents the covariance between Asset A and C, and \((\sigma_A\)\) and\(\(\sigma_C\)\)represent the standard deviations of Asset A and C, respectively.

Using the given information, we have:

Boom:

\(\(\text{{Cov}}(A, C) = (0.35 - 0.235) \cdot (0.10 - 0.25) = -0.017\)\)

Average:

\(\(\text{{Cov}}(A, C) = (0.20 - 0.235) \cdot (0.15 - 0.25) = -0.005\)\)

Bust:

\(\(\text{{Cov}}(A, C) = (0.05 - 0.235) \cdot (0.35 - 0.25) = -0.017\)\)

Now, we calculate the standard deviations of Assets A and C:

\(\(\sigma_A = \sqrt{{\text{{Var}}(A)}} = \sqrt{0.0123} \approx 0.1108\)\)

\(\(\sigma_C = \sqrt{{\text{{Var}}(C)}} = \sqrt{0.0517} \approx 0.2274\)\)

Finally, we can calculate the correlation coefficient:

Boom:

\(\(\rho = \frac{{-0.017}}{{0.1108 \cdot 0.2274}} \approx -0.670\)\)

Average:

\(\(\rho = \frac{{-0.005}}{{0.1108 \cdot 0.2274}} \approx -0.187\)\)

Bust:

\(\(\rho = \frac{{-0.017}}{{0.1108 \cdot 0.2274}} \approx -0.670\)\)

Therefore, the correlation coefficient between Asset A and C is approximately\(\(\rho \approx -0.670\) (Boom), \(\rho \approx -0.187\) (Average), and \(\rho \approx -0.670\) (Bust).\)

Answer to 2a: \(The mean of Asset A is \(0.235\) and the variance is \(0.0123\.\)

Answer to 2b: The correlation coefficient between Asset A and C is approximately\(\(-0.670\) (Boom), \(-0.187\) (Average), \(-0.670\)\)(Bust).

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The current, i, to the capacitor is given by i = -2e^(-2t)cos(t) Amps.

To find the current, we need to differentiate the charge function q with respect to time, t.

Given q = e^(2t)cos(t), we can use the product rule and chain rule to find the derivative.

Applying the product rule, we have:

dq/dt = d(e^(2t))/dt * cos(t) + e^(2t) * d(cos(t))/dt

Differentiating e^(2t) with respect to t gives:

d(e^(2t))/dt = 2e^(2t)

Differentiating cos(t) with respect to t gives:

d(cos(t))/dt = -sin(t)

Substituting these derivatives back into the equation, we have:

dq/dt = 2e^(2t) * cos(t) - e^(2t) * sin(t)

Simplifying further, we get:

dq/dt = -2e^(2t) * sin(t) + e^(2t) * cos(t)

Finally, rearranging the terms, we have:

i = -2e^(-2t) * sin(t) + e^(-2t) * cos(t)

Therefore, the current to the capacitor is given by i = -2e^(-2t) * sin(t) + e^(-2t) * cos(t) Amps.

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Answer:

The slope is undefined

Step-by-step explanation:

The probability is 0.4647.

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Complete statement : Two events are said to be mutually exclusive if they can not occur at the same time. Two events are said to be Independent  if the occurrence of one does not influence the probability of occurrence for the other.

What are Independent events?

Independent events are events for which the occurrence (or non-occurrence) of one event does not affect the probability of the other event occurring.

Two events are said to be mutually exclusive (or disjoint) if they cannot occur at the same time. In other words, if one event occurs, the other event cannot occur simultaneously.

For example, if we toss a coin, the events "getting a heads" and "getting a tails" are mutually exclusive. If we get a heads, we cannot get a tails at the same time.

Two events are said to be independent if the occurrence of one event does not influence the probability of occurrence of the other event. In other words, the probability of both events occurring together is equal to the product of their individual probabilities.

For example, if we roll a dice twice, the events "getting a 2 on the first roll" and "getting a 4 on the second roll" are independent. The probability of getting a 2 on the first roll is 1/6, and the probability of getting a 4 on the second roll is also 1/6. The probability of getting a 2 on the first roll and a 4 on the second roll is (1/6) x (1/6) = 1/36.

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Pizza costing $24 is being delivered to Brian's home. The change $7.72 he get if he uses two $20 bills as payment.

Given that,

Pizza costing $24 is being delivered to Brian's home.

He pays the amount in addition to the 7% sales tax and 15% tip.

In addition, he pays the delivery price of $3, which is added on after tax and tip.

We have to find how much change does he get if he uses two $20 bills as payment.

To figure out the sales tax

$24×0.07=$1.68

To figure out the tip

$24×0.15=$3.6

The Total cost=$24+$1.68+$3.6+$3=$32.28

Now, To find change we have to add the Total cost and the bill

Change=2($20)-$32.28

Change=40-32.28

Change=$7.72

Therefore, The change $7.72 he get if he uses two $20 bills as payment.

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We need to calculate the total  of the rectangular prism and divide it with the volume of single 1/3 cubes to get the number of cubes. It takes almost 25 cubes to fill the rectangular prism of given dimension.

The rectangular prism has 2.5 m length, 5 m tall and 0.75 m wide.

The total volume of the rectangular prism will be 2.5 m × 5 m × 0.75 m = 8.25 m³.

The volume of single cube will be (1/3) m³ = 0.33 m³

Now to find the number of cubes to fill the rectangular prism, we can divide the volume of the prism with the volume of single cube.

8.25 m³ / 0.33 m³ = 25 cubes.

It takes almost 25 cubes to fill the rectangular prism of dimension 2.5 m length, 5 m tall and 0.75 m wide.

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The height of the cell phone tower in feet will be 135 feet high.

The utilization of two or more additional numbers that compares is known as the ratio.

The cell tower that casts a shadow is 100 feet long.

Lia casts shadows 3 feet and 4 inches long.

If Lia is 4 feet 6 inches tall.

Let 'h' be the height of the tower. Then the height of the tower is given as,

h / 100 = (4 + 6/12) / (3 + 4/12)

h / 100 = 4.5 / 3.33

h / 100 = 1.35

h = 135 feet

The height of the cell phone tower in feet will be 135 feet high.

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It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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In inferential statistics, the objective is to determine the probability of the alternative hypothesis being true or the null hypothesis being true.

This involves using sample data to make inferences and draw conclusions about a larger population. By analyzing the data and performing statistical tests, we assess the likelihood of the alternative hypothesis or the null hypothesis being accurate.

The alternative hypothesis represents a claim or statement that contradicts the null hypothesis and suggests that there is a significant relationship or difference between variables. To determine its probability, statistical methods such as hypothesis testing and p-values are employed. These methods evaluate the strength of evidence against the null hypothesis and support the alternative hypothesis when the evidence is substantial.

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The value of x is 5.

We have,

Kite ABCD ~ kite PQRS

This means,

The ratio of the corresponding sides is equal.

Now,

AD/PS = AB/PQ

Cross multiply.

16/24 = 8/(5x - 3)

Simplify.

4/6 = 8/(5x - 3)

5x - 3 = (8 x 6) / 4

Combine like terms

5x - 3 = 12

5x = 12 + 3

Divide 3 on both sides.

5x = 15

x = 5

Thus,

The value of x is 5.

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E(U) = 4, which is an integer.

What is Linearity of expectation?

Linearity of expectation is a fundamental property of expected value that states that the expected value of a sum or difference of random variables is equal to the sum or difference of their individual expected values.

To find E(U), where U = 2X - Y - 4, we can use the properties of expected value.

First, let's find the expected values of 2X, Y, and 4 separately using the linearity of expectation:

E(2X) = 2E(X) = 2 * 6 = 12

E(Y) = 4 (given)

E(4) = 4

Now, let's calculate the expected value of U:

E(U) = E(2X - Y - 4)

Since expected value is a linear operator, we can rearrange and simplify the expression:

E(U) = E(2X) - E(Y) - E(4)

= 12 - 4 - 4

= 4

Therefore, E(U) = 4, which is an integer.

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