sarah and thomas are going bowling. the probability that sarah scores more than 175 is 0.6, and the probability that thomas scores more than 175 is 0.2. their scores are independent. round your answers to four decimal places, if necessary. (a) find the probability that both score more than 175. (b) given that thomas scores more than 175, the probability that sarah scores higher than thomas is 0.2. find the probability that thomas scores more than 175 and sarah scores higher than thomas. part: 0 / 20 of 2 parts complete

Answer:

standard form

Step-by-step explanation:

Answer: 1 solution

Step-by-step explanation:

-8(-8x-6)= -2x+7

64x + 48 = -2x +7

66x =  -41

x = -41/66

we have that

The three solutions of the equation y = -2x - 1 are (–2, 3), (1, –3), and (2, –4).

To find the solutions, we substitute different values of x into the equation and solve for y.

For the first solution, when x is –2, we have y = -2(-2) - 1 = 3. Therefore, the first solution is (-2, 3).

For the second solution, when x is 1, we have y = -2(1) - 1 = -3. Thus, the second solution is (1, -3).

For the third solution, when x is 2, we have y = -2(2) - 1 = -4. Hence, the third solution is (2, -4).

These three points satisfy the equation y = -2x - 1, and therefore, they are the solutions of the equation. They represent coordinate pairs (x, y) where the equation holds true.

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Answer:

-6n-4+3<17

-6n-1<17

-6n<17+1

-6n<18

DIVIDE BOTH SIDE WITH THE COEFFICIENT OF n WHICH IS (-6)

-6n =18

-6 -6

n= -3

Answer:

Step-by-step explanation:

AB

away fram house

2km 4mins

rate: 1km\minute

BC

away from house

5km 6mins

rate:0.83km\minute

CD

niether

0km 9mins

no rate

DE

toward house

6km 15mins

0.4km\minute

The position of point S after dilating will be half of the original. The dilated point S' has been shown below.

What is dilation?

Using a modification known as dilation, an object can be resized. Through dilatation, the objects can be resized or enlarged. This transformation results in a shape that is a perfect replica of the original image. The form's dimensions do vary, though. An expansion or contraction of the original form is required for a dilatation. This shift is referred to as a scale factor.

We are given a graph showing position of point S.

Now, on dilating the point by a scale factor of \(\frac{1}{2}\), we get that the point will be located at half of the original.

The point has been located and attached in the image below.

Hence, the required solution has been obtained.

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Answer:

44 :

Step-by-step explanation:

77/175 = 0.44

0.44x100

Answer:

(3, -4)

Step-by-step explanation:

Lines are intersecting at points (3, -4).

So, the solution of the given system of equations is (3, -4).

Hope it helps you in your learning process.

Answer:

14.42

Step-by-step explanation:

17.00 x .80  20% off means price is 80% (or .80) of price

=13.6

13.6 x .06 = .82 sales tax

13.60 + .82 = 14.42 sales price plus sales tax

The total amount of loan needed to buy the car is 3,639.1

The first step is to calculate the tax rate= 3999 × 9/100= 3999 × 0.09= 359.91= 3999 + 359.91= 4,358.91

The next step is to calculate the down payment= 3999 × 18/100= 3999  × 0.18= 719.82

The total amount of loan can be calculated as follows= 4,358.91 - 719.82= 3,639.1

Hence the amount of the loan is 3,639.1

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Answer: A & D

Step-by-step explanation: parallel lines never touch. if you graph all the equations, lines A & D don't touch each other.

Answer:

x=1

Step-by-step explanation:

Answer: A.Spreads: The weights of the tigers are more spread out.

B.Centers:The leopards have a lower median weight than the tigers

Step-by-step explanation:

On analyzing the dot plots, we find that the weight of Leopards are more spread out and the weight of Leopards has a lower median than Tiger.

Median is a statistical measure that determines the middle value of a dataset listed in ascending order. The measure divides the lower half from the higher half of the dataset.

Median of Weight of Leopard = 50 kg

Median of Weight of Tiger = 125 kg

This implies that the Leopards have a lower median weight than Tigers.

What is spread of data?

Spread describes the variation of the data. One of the measures of spread is range.

Range of weight of Leopards= 40 kg

Range of weight of Tigers = 90 kg

This implies that the weight of Tigers are more spread out.

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The location of the x value of R' after using the translation rule is 28

The translation rule is given as:

(x + 4, y - 7)

The pre-image of R is located at (24, -13)

Rewrite as

R = (24, -13)

When the translation rule is applied, we have:

R' = (24 + 4, -13 - 7)

Evaluate

R' = (28, -20)

Remove the y coordinate

R'x = 28

Hence, the location of the x value of R' after using the translation rule is 28

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Liams wage is 9. 20 pounds per hour, he receives 15% pay rise. To calculate Liam's new wage after a 15% pay rise, add 15% of his old wage to the old wage. The new wage is £10.58.

New wage = Old wage + (Old wage * Percentage increase)

Liam's old wage is £9.20. To find the pay rise amount, multiply his old wage (£9.20) by the percentage increase (15% or 0.15). The pay rise amount is £1.38. Adding this pay rise amount to his old wage gives the new wage: £9.20 + £1.38 = £10.58.

Therefore, Liam's new wage after a 15% pay rise is £10.58.

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Answer:

The answer would be x =10

Step-by-step explanation:

Fill in 10

You welcome

The value of x in the figure ABCD is 10.

We know that rhombuses are a particular type of quadrilateral in Euclidean geometry. It is a unique instance of a parallelogram in which the diagonals meet at a 90-degree angle and all sides are equal.

Since the side lengths of a rhombus are equal, so the lengths of AB and DC are equal.

Now, 3x - 11 = x + 9

i.e. 3x - x = 9 + 11

i.e. 2x = 20

i.e. x = 10

Therefore the value of x in the figure ABCD is 10.

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Exact length of polar curve is √10/3[\(e^{6\pi }\)−1]

Given,

r = e3θ, 0 ≤ θ ≤ 2π

Now,

exact length of the polar curve,

The length of the polar curve :

∫√(r²+(drdθ)²)dθ

Here,

dr/dθ  = 3e3θ

Substitute the values in the formula,

∫√((e3θ)²+(3e3θ)²)dθ

∫√((e3θ)2+9(e3θ)2)dθ

Further,

=√10∫e3θdθ

= √10/3[\(e^{6\pi }\)−\(e^{0}\)]

∴\(e^{0} = 1\)

= √10/3[\(e^{6\pi }\)−1]

Thus the exact length of the polar curve is √10/3[\(e^{6\pi }\)−1] .

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Answer:

minutes

Step-by-step explanation:

Answer

-10,-7,0,98,145

Step-by-step explanation:

Integers are whole numbers negative or positive.

Hope that helped :)

Answer:

y = -2x + 9

Step-by-step explanation:

1) Use the equation y = mx + c (m being gradient and c being y-intercept)

2) Substitute all the values to get 7 = -2(1) + c

3) Solve to get c:

4) Final answer: y = -2x + 9

Answer:

B.) x + (x + 16) = 90

2x+16=90

2x=90-16

x=74/2

x=37

Answer:

number 2 in the left

Step-by-step explanation:

The probability of rolling an odd number or rolling a 2 on a fair six-sided die is the fraction 2/3

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes

A fair six-sided die has faces numbered 1 to 6, and there are only three numbers that are odd numbers, which are 1, 2, and 3.

so;

probability of rolling an odd number = 3/6

probability of rolling a 2 = 1/6

probability of rolling an odd number or a 2 = 3/6 + 1/6

probability of rolling an odd number or a 2 =4/6

probability of rolling an odd number or a 2 = 2/3

In conclusion, 2/3 is the resulting fraction for the probability of rolling an odd number or rolling a 2 on a fair six-sided die.

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The mean and standard deviation for the number of defective bolts in a total of 400 bolts is 40 and 6.32 (approx), respectively.

The mean and standard deviation for the number of defective bolts in a total of 400 bolts if the probability of defective bolt is 0.1 can be calculated using Poisson distribution.

Poisson distribution is used to predict the number of events that occur over a specified interval of time when the probability of an event occurring is known.

The formula for calculating the mean (μ) and standard deviation (σ) is given as follows:
μ = λσ = √λ
Where λ = np, where n is the number of trials and p is the probability of success.

Here, the probability of a defective bolt is 0.1. So the probability of a non-defective bolt is 0.9. The total number of bolts is 400, so the expected number of defective bolts can be calculated as follows:
μ = λ = np = 400 x 0.1 = 40

The mean number of defective bolts is 40. The standard deviation can be calculated as follows:
σ = √λ = √40 = 6.32 (approx)

The standard deviation is 6.32 (approx).

Therefore, the mean and standard deviation is 40 and 6.32 (approx), respectively.

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The statistics are as follows:

- Test Statistic: The calculated test statistic is approximately 1.02.

- P-value: The P-value associated with the test statistic of 1.02 is approximately 0.154.

- Confidence Interval: The 95% confidence interval for the difference in proportions is approximately -0.0186 to 0.0786.

To solve the problem completely, let's go through each step in detail:

1. Test Statistic:

The test statistic can be calculated using the formula:

z = (p1 - p2) / √[(p_cap1 * (1 - p-cap1) / n1) + (p_cap2 * (1 - p_cap2) / n2)]

We have:

p1 = 0.55 (proportion in the first poll)

p2 = 0.53 (proportion in the second poll)

n1 = 630 (sample size of the first poll)

n2 = 1010 (sample size of the second poll)

Substituting these values into the formula, we get:

z = (0.55 - 0.53) / √[(0.55 * (1 - 0.55) / 630) + (0.53 * (1 - 0.53) / 1010)]

z = 0.02 / √[(0.55 * 0.45 / 630) + (0.53 * 0.47 / 1010)]

z ≈ 0.02 / √(0.0001386 + 0.0002493)

z ≈ 0.02 / √0.0003879

z ≈ 0.02 / 0.0197

z ≈ 1.02 (rounded to two decimal places)

Therefore, the test statistic is approximately 1.02.

2. P-value:

To find the P-value, we need to determine the probability of observing a test statistic as extreme as 1.02 or more extreme under the null hypothesis. We can consult a standard normal distribution table or use statistical software.

The P-value associated with a test statistic of 1.02 is approximately 0.154, which means there is a 15.4% chance of observing a difference in proportions as extreme as 1.02 or greater under the null hypothesis.

3. Confidence Interval:

To estimate the difference in proportions with a 95% confidence interval, we can use the formula:

(p1 - p2) ± z * √[(p_cap1 * (1 - p_cap1) / n1) + (p_cap2 * (1 - p_cap2) / n2)]

We have:

p1 = 0.55 (proportion in the first poll)

p2 = 0.53 (proportion in the second poll)

n1 = 630 (sample size of the first poll)

n2 = 1010 (sample size of the second poll)

z = 1.96 (for a 95% confidence interval)

Substituting these values into the formula, we get:

(0.55 - 0.53) ± 1.96 * √[(0.55 * (1 - 0.55) / 630) + (0.53 * (1 - 0.53) / 1010)]

0.02 ± 1.96 * √[(0.55 * 0.45 / 630) + (0.53 * 0.47 / 1010)]

0.02 ± 1.96 * √(0.0001386 + 0.0002493)

0.02 ± 1.96 * √0.0003879

0.02 ± 1.96 * 0.0197

0.02 ± 0.0386

The 95% confidence interval for the difference in proportions is approximately (0.02 - 0.0386) to (0.02 + 0.0386), which simplifies to (-0.0186 to 0.0786).

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