Conditional Probability

A card is chosen at random from a standard deck. What is the probability that the card is a spade or a king, given that it is black?

Find each probability as a fraction (in simplest form), decimal, and percent.

The range is $14.

The interquartile range is $8.5.

The mean absolute deviation is $4.

The Data set of the admission prices are: [tex]20, 20, 16, 12, 15, 25, 11[/tex]

The range = Maximum value - Minimum value

The range = $25 - $11

The range = $14

To get interquartile range, we will calculate first and third quartiles.

Arranging data in order, we get: [tex]11, 12, 15, 16, 20, 20, 25[/tex]

The first quartile is the median of the lower half of the data which is:

= (11+12)/2

= $11.5

The third quartile (Q3) is the median of the upper half of the data which is:

(20+20)/2

= $20

IQR = Q3 - Q1

IQR = $20 - $11.5

IQR = $8.5

To find the mean absolute deviation, we will calculate the mean.

Mean = sum of values / number of values

Mean = ($11 + $12 + $15 + $16 + $20 + $20 + $25) / 7

Mean = $17

|$11 - $17| = $6

|$12 - $17| = $5

|$15 - $17| = $2

|$16 - $17| = $1

|$20 - $17| = $3

|$20 - $17| = $3

|$25 - $17| = $8

MAD = Sum of absolute deviations / Number of values

MAD = (6 + 5 + 2 + 1 + 3 + 3 + 8) / 7

MAD = 4

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Answer:

Maybe add a picture

Step-by-step explanation:

i can solve it with a picture

Answer:

972

Step-by-step explanation:

Answer:

x = -18.4

Step-by-step explanation:

3-8x=95-3x

add 3x to both sides

3-5x=95

subtract 3 from both sides

-5x=95-3

-5x=92

divide both sides by -5

x=-18.4

The required function be  y = 5000 - 250x.

Given that,

Amount of saving = $5000

Amount of withdraw and spend = $250

Number of months = x

If the total money in Ken's savings account after x number of months is represented by y,

Then, to calculate the entire amount in his savings account after x number of months, the program deducts 250x from the beginning amount of $5000.

Therefore, The function be,

y = 5000 - 250x

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The 95% confidence interval for the true proportion of all nannies who work for a celebrity is approximately 0.0145 to 0.0613.

In this case, we have a random sample of 528 in-home childcare providers (nannies) and we want to estimate the proportion of nannies who work for a celebrity.

To do this, we calculate the sample proportion (p-hat) by dividing the number of nannies working for a celebrity by the total sample size.

Here we have

Sample size (n) = 528

Number of nannies working for a celebrity (x) = 20

First, we calculate the sample proportion (p-hat), which is the proportion of nannies working for a celebrity in the sample:

=> p-hat = x / n = 20 / 528

Next, we calculate the standard error (SE) using the formula:

SE = √(p-hat × (1 - p-hat)) / n)

SE = √((20 / 528) × (1 - 20 / 528) / 528)

Now, we can calculate the margin of error (ME) using the critical value associated with a 95% confidence level.

Since we have a large sample size, we can use the z-value:

z-value for a 95% confidence level ≈ 1.96

ME = z-value × SE

Finally, we can calculate the confidence interval:

Confidence Interval = p-hat ± ME

Substituting the values:

Confidence Interval = [ 20 / 528) ± (1.96×√(20 / 528)×(1 - 20 / 528) / 528) ]

Simplifying:

Confidence Interval ≈ 0.0379 ± 0.0234

Therefore,

The 95% confidence interval for the true proportion of all nannies who work for a celebrity is approximately 0.0145 to 0.0613.

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Answer:

x2+2x−132x2+16

Step-by-step explanation:

First, let's simplify the expression by combining like terms:

x - 7x^2 + 8 - x^2 - x + 6x^2 + 8

= -7x^2 + 5x^2 - x^2 + x + 16

= -x^2 + 2x + 16

Now we need to factor the quadratic expression -x^2 + 2x + 16. We can use the quadratic formula or complete the square to find the roots, but it turns out that the expression doesn't factor nicely. However, we can rewrite it as -(x^2 - 2x - 16) and then use the quadratic formula to find the roots of the expression inside the parentheses:

x = (-(-2) ± sqrt((-2)^2 - 4(-16)))/(2(1))

x = (2 ± sqrt(68))/2

x = 1 ± 2sqrt(17)/2

x = 1 ± sqrt(17)

So we have:

-x^2 + 2x + 16 = -(x - (1 + sqrt(17)))(x - (1 - sqrt(17)))

Therefore, the expression is equal to -x^2 + 2x + 16, which corresponds to the option:

x^2 + 2x - 13 / 2x^2 + 16

The expected value is 0.8, variance is 0.48, and standard deviation is 0.693 with the given probability.

a. The probability of getting one success in two trials with p=0.4 is given by the binomial probability formula:

f(1) = 2C1 * (0.4)^1 * (0.6)^1 = 0.48

b. The probability of getting zero successes is:

f(0) = 2C0 * (0.4)^0 * (0.6)^2 = 0.36

c. The probability of getting two successes is:

f(2) = 2C2 * (0.4)^2 * (0.6)^0 = 0.16

d. The probability of at least one success is:

P(at least one success) = 1 - P(no success)

= 1 - f(0)

= 1 - 0.36

= 0.64

e. The expected value of a binomial distribution with n trials and probability of success p is given by:

E(X) = np

In this case, n = 2 and p = 0.4, so:

E(X) = 2 * 0.4 = 0.8

The variance of a binomial distribution is given by:

Var(X) = np(1-p)

So:

Var(X) = 2 * 0.4 * 0.6 = 0.48

The standard deviation is the square root of the variance:

SD(X) = sqrt(Var(X)) = sqrt(0.48) = 0.693.

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Let's use x to represent the cost of one orange and y to represent the cost of one lemon. We can then set up a system of two equations:16x + 13y = 9.29 19x + 6y = 9.05 These equations represent the total cost of buying a certain number of oranges and lemons in two different scenarios.

To understand why we need two equations, let's consider the first equation: 16x + 13y = 9.29

This equation tells us that if we buy 16 oranges and 13 lemons, the total cost will be $9.29. But we don't know the individual prices of oranges and lemons yet. That's where the second equation comes in: 19x + 6y = 9.05

This equation tells us that if we buy 19 oranges and 6 lemons, the total cost will be $9.05. Again, we don't know the individual prices yet.

By setting up a system of equations, we can solve for x and y, which represent the prices of oranges and lemons, respectively.

One way to solve this system is by elimination. We can multiply the first equation by 19 and the second equation by -16, which will allow us to eliminate y:

304x + 247y = 176.51
-304x - 96y = -144.8

Adding these two equations together gives: 151y = 31.71
Dividing both sides by 151, we get: y = 0.21
Now we can substitute this value of y into one of the original equations to solve for x. Let's use the first equation:
16x + 13(0.21) = 9.29
16x + 2.73 = 9.29
16x = 6.56
x = 0.41

So the cost of one orange is $0.41 and the cost of one lemon is $0.21.

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The first step is to calculate the total area of 600 bricks.

Area of one brick = 12 inches x 18 inches = 216 square inches

Area of 600 bricks = 600 x 216 = 129,600 square inches

Next, we need to convert the height of the wall from feet to inches since the area of the bricks is in square inches.

10 feet = 120 inches

Now, we can divide the total area of the bricks by the height of the wall to find the length of the wall.

Length of the wall = Area of 600 bricks / Height of the wall
Length of the wall = 129,600 square inches / 120 inches
Length of the wall = 1080 inches

Finally, we can convert the length of the wall back to feet by dividing by 12 since there are 12 inches in a foot.

Length of the wall = 1080 inches / 12 inches/foot
Length of the wall = 90 feet

Therefore, the length of the wall is 90 feet.

To solve this problem, we need to use the formula for calculating area which is length x width. We also need to convert units from feet to inches and vice versa as necessary to ensure we are working with the same units throughout the problem.

The length of the wall is 90 feet.

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Given that QT is the perpendicular bisector of PR.The bisector of any line segment divides it into two equal parts, each of which has the same measure.To begin, let's define a few terms.

Angle bisector - An angle bisector is a line or segment that divides an angle into two equal parts.The given figure is shown below: We are given QT is the perpendicular bisector of PR. That means QT is perpendicular to PR and it bisects it. That is, it divides it into two equal halves.Suppose, PR = 2xFrom the given information, we know that the perpendicular bisector QT divides PR into two equal halves.

So,PQ = QR

Now, In right triangle

TPQ,QT² = TP² + PQ²QT² = TP² + QR² (since PQ = QR)QT² = TP² + (2x)² (since PQ = QR = 2x)QT² = TP² + 4x²

Also, In right triangle

TRQ,QT² = TR² + QR²QT² = TR² + (2x)²QT² = TR² + 4x²

We now have two equations:

QT² = TP² + 4x² QT² = TR² + 4x²

The above two equations can be equated:

TP² + 4x² = TR² + 4x²TP² = TR²

Thus, we can say that

TP = TRLet TP = TR = a

By Pythagoras theorem in right angled triangle

TPQ,TP² + PQ² = TQ²a² + (2x)² = QT²a² + 4x² = QT²

The answer is 4x² + a² = QT².

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In both cases, the estimates depend on the specific characteristics of the box and the probabilities associated with each draw.

To estimate the chance that the sum of the draws will be more than 1,500, we need to know the distribution of values in the box and their probabilities. Without this information, we cannot provide a specific estimate.

(b) Similarly, to estimate the chance that the ticket [3] will be drawn fewer than 90 times, we need to know the distribution of values in the box and their probabilities. Without this information, we cannot provide a specific estimate.

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The value of Tan θ is -5/12

Given that 8 Sin θ = 4 + Cos θ, we need to find Tan θ,

So,

8 Sin θ = 4 + Cos θ

Dividing by Cos θ,

8 Sin θ / Cos θ = (4 + Cos θ) / Cos θ

8 Tan θ = 4 Sec θ + 1

Squaring both sides,

64 Tan² θ = 16 Sec² θ + 1 + 8 Sec θ

64 Tan² θ - 16 Tan θ + 1 = 16 (1 + Sec² θ)

48 Tan² θ - 16 Tan θ - 15 = 0

4 Tan θ(12 Tan θ + 5) -3(Tan θ + 5) = 0

(12 Tan θ + 5) (4 Tan θ - 3) = 0

Tan θ = 3/4 or Tan θ = -5/12

Since Tan θ = 3/4 does not satisfy the equation so Tan θ = -5/12

Hence the value of Tan θ is -5/12

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Answer:

The angle between building 1 and building 3 at building 2 is not a right angle, and hence, the buildings do not form a right triangle.

Step-by-step explanation:

The value of x is equal to 0.8603 units.

In order to determine the adjacent side (value of x), we would apply the law of tangent because the given side lengths represent the opposite side and angles of a right-angled triangle.

tan(θ) = Opp/Adj

Where:

Based on the information provided in the image, we can logically deduce the following parameters:

Adj = x units.

Opp = 8.3 units.

By substituting the parameters into the tangent ratio formula, we have the following;

Tan16 = 8.3/x

x = 3tan16

x = 0.8603 units.

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So the equation of the parabola in standard form is y = (5/4)x^2 - (7/4)x + 2.

One way to approach this problem is to use the standard form of the equation for a parabola, which is y = ax^2 + bx + c. We can set up a system of three equations using the three points given and solve for the coefficients a, b, and c.

Starting with the point (-2, 18):

18 = a(-2)^2 + b(-2) + c

18 = 4a - 2b + c

Using the point (0, 2):

2 = a(0)^2 + b(0) + c

2 = c

Using the point (4, 42):

42 = a(4)^2 + b(4) + c

42 = 16a + 4b + c

Substituting c = 2 into the second equation, we get:

2 = 2

This is always true, so it doesn't provide any additional information.

Substituting c = 2 into the first and third equations, we get:

18 = 4a - 2b + 2

42 = 16a + 4b + 2

Simplifying each equation:

9 = 2a - b

20 = 4a + b

Solving this system of equations, we get:

a = 5/4

b = -7/4

Substituting these values for a and b, and c = 2, into the standard form equation for a parabola, we get:

y = (5/4)x^2 - (7/4)x + 2

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it takes Lindiwe's teacher 300 seconds to walk to her classroom and the break is 50 minutes long.

To convert 3 km to meters we multiply by 1000 (since there are 1000 meters in 1 km).

3 km = 3,000 meters

Therefore, Lindiwe walks 3,000 meters from home to school during weekdays.

3.2 To convert 5 minutes to seconds, we multiply by 60 (since there are 60 seconds in 1 minute).

5 minutes = 5 x 60 = 300 seconds

Therefore, it takes Lindiwe's teacher 300 seconds to walk to her classroom.

To find the length of Lindiwe's break, we subtract the start time from the end time:

11:20 - 10:30 = 0:50

The break is 50 minutes long.

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The approximate volume of the sphere is 606.25 cm³, which is closest to option D. 606 cm³.

To find the approximate volume of a sphere, we'll use the formula:
Volume = (4/3) × π × r³
Given that the sphere has a diameter of 10.5 cm, we can find its radius by dividing the diameter by 2:
Radius (r) = Diameter / 2 = 10.5 cm / 2 = 5.25 cm
Now, we can plug the radius into the volume formula:
Volume = (4/3) × π × (5.25 cm)³
Volume ≈ (4/3) × 3.14 × (144.703125 cm³)
Volume ≈ 4.1867 × 144.703125 cm³
Volume ≈ 606.25 cm³
The approximate volume of the sphere is 606.25 cm³, which is closest to option D. 606 cm³.

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The required arc made by the angle ∠UQT in the given circle is arc UT.

Given the diagram of circle, which is marked with different line segments.

Arc is the part of the circle. Diameter is the line passing through the centre of the circle, radius of the circle is the line segment between centre and other point on the circle, the chord is the line segment  points on the circle and diameter is the biggest chord, tangent is the line segment which intersect the circle at only one point and that point is known as point of tangency and secant is the line segment which cuts the circles.

That implies, the arc made by the angle  ∠UQT is arc UT.

Therefore, the required arc made by the angle ∠UQT in the given circle is arc UT.

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According to the information, the cuboid in the image is missing 3 faces of the following dimensions 1 face of 1 * 4, 1 face of 1 * 3 and 1 face of 3 * 3.

To complete the cuboid we must take into account that there are already three of its faces. Therefore, we must identify which faces are missing. As we know, cuboids are three-dimensional figures that have 6 faces. Another characteristic of non-regular cuboids is that they have pairs of equal faces.

Based on the information above, we can infer that the missing sides of this cuboid have the same dimensions as the existing sides on the graph. Therefore, the following sides would be missing:

Additionally, to know the surface of the area we must count the number of squares that the figure has in total, in this case it would be 38 squares, so the area is 38 units²

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The volume of the space inside the cylinder that is not filled with the right cone is 640π m³

Volume is the total space occupied by a solid shape.

To calculate the volume of the space inside the cylinder that is not filled with the right cone, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence the right option is A. 640π m².

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Answer:

the other day I dey bro you doing today I hope

The expected value for a student to spend on lunch each day is $7.09.

To calculate the expected value for a student to spend on lunch each day based on the survey data,

we need to find the average amount spent by each student.

We can calculate the expected value by summing up the products of the number of students and the amount spent on lunch for each category, and then dividing by the total number of students:

Expected value = [tex](2 * 10 + 1 * 8 + 2 * 6 + 3 * 5 + 8 * 4 + 11 * 3 + 10 * 2.59 + 13 * 5.11 + 10 * 5.18 + 10 * 9.07) / 50[/tex]

Expected value = [tex](20 + 8 + 12 + 15 + 32 + 33 + 25.9 + 55.21 + 51.8 + 90.7) / 50[/tex]

Expected value = $354.71 / 50

Expected value ≈ $7.09

Therefore, based on the survey data, the expected value for a student to spend on lunch each day is approximately $7.09.

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The height of prism B based on the information given will b 22cm.

Prisms are transparent optical elements that have at least two flat surfaces and refract light. They are usually made of glass or plastic and are used in a variety of optical applications, including scientific experiments, photography, and surveying. Prisms come in a variety of shapes and sizes, including triangular, rectangular, and pentagonal.

From the information, it should be noted that the surface area of prism A will be

= 60 × 2 + 7+ 384

= 576cm²

The surface area of prism A will be:

48 + 10h + 8h + 6h = 576

48 + 24h = 576

h = 528 / 24

h = 22cm

The height is 22cm

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The right triangular prisms shown have the same surface area. Find the height of prism B.

Prism A:

Height: 24 cm

Base: a right triangle with legs 3 cm and 20 cm

Depth: 6 cm

Prism B:

Height: ?

Base: a right triangle with legs 8 cm and 20 cm

Depth: 3 cm

Both prisms have the same surface area.

Option d) He uses the bottom of the Protractor to draw a Straight line connecting the mark he made with the vertex.

The correct step to complete the drawing of a 50° angle is:

Step 4: He uses the bottom of the protractor to draw a straight line connecting the mark he made with the vertex.

In this step, Jimmy will connect the mark he made at 50° on the protractor with the vertex of the angle using a straight line. This line will complete the angle and ensure that it measures 50°. By connecting the mark with the vertex, Jimmy will have successfully drawn a 50° angle.

After completing Step 4, he can proceed to Step 5, which involves drawing arrows on both ends of the line to indicate that they are rays.

Therefore, the correct answer is option d) He uses the bottom of the protractor to draw a straight line connecting the mark he made with the vertex.

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The correct answer is (c) Reject the null hypothesis. There is enough evidence to oppose the car manufacturer's claim.

The null hypothesis (H0) is that the true average speed is 145 mph, and the alternative hypothesis (H1) is that the average speed is not 145 mph.

Using a z-test, we can calculate the z-score as [tex](150-145)/(19 \sqrt(87)),[/tex]which is approximately 3.67.

For a two-tailed test at the 1% significance level, the critical z-scores are -2.576 and 2.576.

Since the calculated z-score is beyond this range, we can reject the null hypothesis.

Therefore, there is enough evidence to oppose the car manufacturer's claim.

The correct answer is (c) Reject the null hypothesis. There is enough evidence to oppose the car manufacturer's claim.

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Answer:

150(2)^t

Step-by-step explanation:

The function that represents the worth, w(t), of the basketball at any given time, t, can be written as:

w(t) = 150(2)^t

where t is the number of years since the basketball was collected.

This function uses the formula for exponential growth, where the value of the basketball doubles each year. The initial value of the basketball is $150, and the value is multiplied by 2 for each year that passes. Therefore, after one year, the basketball is worth $300 (2 times $150), after two years it is worth $600 (2 times $300), and so on.

By plugging in different values of t, we can calculate the worth of the basketball at any given time.