A bag contains 2 red, 5 blue, and 2 white marbles. Find the probability of randomly picking a red marble, keeping the marble, and then picking a blue marble.


A) 7/8

B) 10/81

C) 5/36

D) 1/9

Answer:

Step-by-step explanation:

It’s (1,4)

The numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾. The third option is correct.

The ordering of numbers refers to arranging numbers in a specific sequence based on their magnitude or value. The ordering of numbers is determined by their relative values. Comparisons are made between numbers to determine their position in the order.

12⅝ = 101/8 = 12.645

12.62 = 12.62

√146 = 12.0830

12.39 = 12.39

12¾ = 51/4 = 12.75

Therefore, the numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾.

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Answer:

He needs to get $178 to average at least $150.

Step-by-step explanation:

105, 132, 165, 170, and 178 has an average of 150.

Answer:

C≈25.13cm

Step-by-step explanation:

C=πd=π·8≈25.13274cm

d=2r

C=2πr

(hope this helps)

Step-by-step explanation:

area of a cicle is π\(r^{2}\)

the diameter is twice as long as the radius so the radius would have a length of 4 cm.

π\(4^{2}\)=50.27

Hope that helps :)

The position of the particle at which it turns around is approximately 0.995 meters.

x = 2.0 t^2 - 0.90 t^3

To find out at what position the particle turns around, we need to find the turning point or point of inflection.

This can be done by taking the second derivative of the position function and finding when it is zero.

Second derivative:

dx^2/dt^2 = 4.0 - 5.4t

At the turning point, the second derivative is zero.

dx^2/dt^2 = 0 = 4.0 - 5.4t

=> t = 0.7407 s

Substituting t = 0.7407 s in the original position function, we can find the position at which the particle turns around.

x = 2.0(0.7407)^2 - 0.90(0.7407)^3

≈ 0.995 m

Therefore, the position of the particle at which it turns around is approximately 0.995 meters.

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The mean of the number of drivers expected not to be wearing seatbelts is approximately 4.35, the variance is approximately 15.62, and the standard deviation is approximately 3.95 and they expect to stop approximately 4.35 cars before finding a driver whose seatbelt is not buckled.

a. To find the mean, variance, and standard deviation of the number of drivers expected not to be wearing seatbelts, we can model the situation using a geometric distribution.

Let's define a random variable X that represents the number of cars stopped until the first driver without a seatbelt is found. The probability of a driver not wearing a seatbelt is given as p = 0.23.

The mean (μ) of a geometric distribution is given by μ = 1/p.
μ = 1/0.23 ≈ 4.35

The variance (σ^2) of a geometric distribution is given by σ^2 = q/p^2, where q = 1 - p.
σ^2 = (0.77)/(0.23^2) ≈ 15.62

The standard deviation (σ) is the square root of the variance.
σ = √(15.62) ≈ 3.95


b. The expected number of cars they expect to stop before finding a driver whose seatbelt is not buckled is equal to the reciprocal of the probability of success (finding a driver without a seatbelt) in one trial. In this case, the probability of success is p = 0.23.

Expected number of cars = 1/p = 1/0.23 ≈ 4.35

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so we can say that statement b is also False.The mean of the first distribution is -2, while the mean of the second distribution is 6. As a result, the two normal distributions are not centered at the same place.

'

The statement "The two normal distributions have the same spread" is false, and the statement "The two normal distributions are centered at the same place" is false as well.Explanation:Normal Distribution: A normal distribution is a statistical distribution that is symmetric about its mean, showing that data near the mean is more frequent in occurrence than data far from the mean. To describe the distribution of data, it is frequently utilized, and it is frequently utilized in inferential statistics.A normal distribution is defined by two parameters: its mean (μ) and its standard deviation (σ). The mean (μ) is the center of the distribution, while the standard deviation (σ) indicates how spread out the data is from the mean of the distribution.The spread of a distribution is determined by its standard deviation (σ). The standard deviation is the measure of dispersion, which shows how much the data deviates from the mean. As a result, the standard deviation (σ) determines the spread of the normal distribution.Here are the given parameters of the two normal distributions:Distribution 1:Mean = -2Standard deviation = 3.7Distribution 2:Mean = 6Standard deviation = 3.7According to the parameters of the two normal distributions mentioned above, we may deduce that the two normal distributions have the same standard deviation. The spread of the distributions is measured by the standard deviation (σ), therefore we can say that statement a is False.However, the mean of the two normal distributions is not the same, so we can say that statement b is also False.The mean of the first distribution is -2, while the mean of the second distribution is 6. As a result, the two normal distributions are not centered at the same place.

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Answer:

Mario brought 5 magazines

Step-by-step explanation:

If you just add $12.60 and $2.25 together then keep adding $2.25 until you get to $23.85, you'll get your answer.

So like,  

(1) 12.60 + 2.25 = 14.85

(2) 14.85 + 2.25 = 17.1

(3) 17.1 + 2.25 = 19.35

(4) 19.35 + 2.25 = 21.6

(5) 21.6 + 2.25 = 23.85  

So the total would be 5. Mario bought 5 magazines.

The equation to model this situation is Hannah = 1 4/5 * 7 2/3 miles.

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

This means that

Hannah = 1 4/5 * Jamil

So. we have

Hannah = 1 4/5 * 7 2/3 miles.

Evaluate

Hannah = 13 4/5 miles.

Using the above as a guide, we have the following:

The equation is

Hannah = 1 4/5 * 7 2/3 miles.

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Answer:

mean height of girls = 1.48 metres

Step-by-step explanation:

total height of all students = 1.515 x 32 = 48.48

total height of boys = 1.56 x 14 = 21.84

Total girls = 48.48 - 21.84 = 26.64

32 students - 14 boys = 18 girls

mean height of girls = 26.64/18 = 1.48 metres

Answer:

Step-by-step explanation:

I have no idea

Answer:

3(x+3)^2=12

Step-by-step explanation:

3x^2-18x+15

(3x^2+18x)+15

3(x^2+6x)+15

3(x^2+6x+9)+15-27

3(x+3)^2-12

3(x+3)^2=12

Hope this helps!

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The value of length PB is 2cm

Similar triangles have the same corresponding angle measures and proportional side lengths. This means that the corresponding angles of similar triangles are equal.

And also the ratio of corresponding sides of similar triangles are equal.

Therefore ;

3/9 = PB/ 6

represent PB by x

3/9 = x/6

18 = 9x

divide both by 9

x = 18/9

x = 2cm

Therefore the value of length PB is 2

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Answer:13.8 is the best answer i could get

Step-by-step explanation:1,077 multiply that × 13.8 =14,862

Answer:

24.4

Step-by-step explanation:

14² + 20² = c²

196 + 400 =  596

√596 = 24.4

When, bisecting diagonal of length 8 inch bisects the diagonal is equal halves then the length of the bisected diagonal is 8.66 inch.

In kite, one diagonal is bisects the other diagonal in two equal halves.

Let x and (8-x) be the lengths of the two parts of the bisecting diagonal.

Let y be the length of the bisected diagonal in half.

The legs of a right triangle with hypotenuse 5 are then x and y.

\(5^2=y^2+x^2\\\\y^2=5^2-x^2...i\)

The legs of a right triangle with hypotenuse 7 are (8-x) and y.

\(7^2=(8-x)^2+y^2\\\\y^2=7^2-(8-x)^2....ii\)

Equating both the equations i and ii,

\(5^2-x^2=7^2-(8-x)^2\\\\25-x^2=49-(64+x^2-16x)\\\\25-x^2=49-64-x^2+16x\\\\25=-15+16x\\\\40=16x\\\\x=2.5\)

substitute x in eq. i,

\(y^2=25-2.5^2\\\\y^2=25-6.75\\\\y^2=18.25\\\\y=4.33\)

Hence, the length of bisected diagonal is 2(4.33)=8.66 inch.

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The correct answer: C) do not reject the null hypothesis and conclude that the mean IQ is not greater than 100.

The null hypothesis, H0: μ ≤ 100, is tested against the alternative hypothesis, Ha: μ > 100, to determine whether the mean IQ of employees in an organization is greater than 100. The sample size is 30 and the computed value of the test statistic is t29 = -2.42.

At the 5% level of significance, we have a one-tailed test with critical region in the right tail of the t-distribution. For a one-tailed test with a sample size of 30 and a significance level of 5%, the critical value is 1.699.

Since the computed value of the test statistic is less than the critical value, we fail to reject the null hypothesis and conclude that the mean IQ is not greater than 100.

Option C is therefore the correct answer: do not reject the null hypothesis and conclude that the mean IQ is not greater than 100.

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The difference in elevation between the dead sea and the mount everest is; 9277 m

We are told that the dead sea in the Middle East is 429 m below sea level.

Now, since it is below sea level, the elevation will be expressed as negative. Thus, it can be expressed as -429m.

The peak of Mount Everest in Asia is 8848 m above sea level. Since it is above sea level, the elevation can be expressed as positive.

Thus;

Difference in elevation = 8848 - (-429)

= 8848 + 429

= 9277 m

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Answer:

The answer is  

20x + 17.5

Step-by-step explanation:

Multiply the 5 by the numbers inside the parenthesis.

5 x 4x

5 x 3.5

a. The volume of the fully-inflated balloon is 288π cubic inches.

b. The volume of the half-inflated balloon is 144π cubic inches.

c. The radius of the half-inflated balloon is about 5 inches.

Part 1:

a. The volume of the fully-inflated balloon can be calculated using the formula for the volume of a sphere: V = (4/3)πr^3, where r is the radius of the balloon. Since the diameter is given, we can divide it by 2 to find the radius.

Given that the diameter is 12 inches, the radius is 12/2 = 6 inches. Plugging this value into the volume formula, we have:

V = (4/3)π(6^3) = (4/3)π(216) = 288π cubic inches.

Part 2:

b. To find the volume of the half-inflated balloon, we need to calculate the new radius after half of the air is let out. Since the balloon remains a sphere, the ratio of the new radius to the original radius is equal to the cube root of the ratio of the new volume to the original volume.

The new volume is half of the original volume, which is 288π/2 = 144π cubic inches. Let's denote the new radius as r'. Then we have:

(4/3)π(r'^3) = 144π.

Dividing both sides by (4/3)π, we get:

r'^3 = 108.

Taking the cube root of both sides, we find:

r' = ∛108 ≈ 4.779 inches.

Part 3:

c. The radius of the half-inflated balloon is approximately 4.779 inches. Rounded to the nearest whole number, it is 5 inches.

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c = 11.05 ≈ 11 cm. When the diagonal length for the rectangular prism is given is to the nearest whole unit, the correct answer is B.

A quantity known as length has the ability to calculate approximate distance between two areas. In addition to height the breadth, it creates an object's length. Children will learn about length in math lessons to help them solve practical challenges both inside and outside of the classroom. the length or width that is possible to measured; a thing's greatest or longest dimension. 10 feet in length. Table of Metric units, Metric System Table: The length characteristic. The quantity or measurement between two points is the definition of length. In other words, a geometric arrangement or object's largest two or highest three dimensions.

given

Start by calculating the length of the base's diagonal using the Pythagorean theorem:

a² + b² = c²

Fill in the equation with the length and width:

8² + 3² = c²

64 + 9 = c²

73 = c²

c ≈ 8.54 cm

Using our estimated diagonals for the base and the height, we can now determine the prism's diagonal's length. Apply the same formula:

(8.54)² + 7² = c²

73 + 49 = c²

122 = c²

√122 = c

c = 11.05 ≈ 11 cm. When the diagonal length for the rectangular prism is given is to the nearest whole unit, the correct answer is B.

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The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

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The missing parts are solved using ratio and are given as follows:

15) DE is derived as 6

16) BE is derived as 4.5

17) CE is derived as: 16

The missing parts of the geometric shapes above are derived using ratio or proportion.

15)

Where AB = 12 and DB = 9 and AC = 8

Thus,

DB/AB = DE/AC

⇒ 9/12 = DE/8

First, we can simplify 9/12 by dividing the numerator and denominator by 3 to get:

3/4 = DE/8

To solve for DE, we can cross-multiply by multiplying both sides of the equation by 8:

3/4 * 8 = DE

DE = 6

Therefore, the solution to the equation is DE = 6.

16)

Since, DE =6, AC = 9, and CE = 3 ; we can say that:

AC/DE = BE/CE
⇒ 9/6 = BE/3

irst, we can simplify 9/6 by dividing the numerator and denominator by 3 to get:

3/2 = BE/3

To solve for BE, we can cross-multiply by multiplying both sides of the equation by 3:

3/2 * 3 = BE

BE = 4.5

Therefore, the solution to the equation is BE = 4.5.



17)

Where

DE = 6 AC = 8 and BE = 12

AC/DE = CE/BE

⇒ 8/6 = CE/12

First, we can simplify 8/6 by dividing the numerator and denominator by 2 to get:

4/3 = CE/12

To solve for CE, we can cross-multiply by multiplying both sides of the equation by 12:

4/3 * 12 = CE

CE = 16

Therefore, the solution to the equation is CE = 16.

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Overall, the testing facility concluded that the brush tee would be a better option for golfers looking to improve their drives.

An independent golf equipment testing facility compared the difference in the performance of golf balls hit off a brush tee to those hit off a 4 yards more tee. A'Air Force One DFX driver was used to hit the balls, with an average swing speed of 100 miles per hour. The testing facility wanted to determine which tee would perform better and whether it would be beneficial to golfers to switch to a different tee.

The two different types of tees were the brush tee and the 4 Yards More tee. The brush tee is designed with bristles that allow the ball to be suspended in the air, minimizing contact between the tee and the ball. This design is meant to reduce spin and allow for longer and straighter drives. On the other hand, the 4 Yards More tee is designed to be more durable than traditional wooden tees, and its design is meant to create less friction between the tee and the ball, allowing for longer drives.

The testing results showed that the brush tee was able to create longer and straighter drives than the 4 Yards More tee. This is likely due to the brush tee's design, which allows for less contact with the ball, minimizing spin and creating longer and straighter drives.

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Answer:

72

Step-by-step explanation:

The closest answer is 11.49% (option C). Offer lower yields compared to lower-rated bonds like BB, which carry higher default risk and higher yields.

To calculate the yield on a seven-year AA-rated bond issued by Harrington Horticulture Co., we need to consider several factors:

1. Real Risk-Free Rate (r*): 2.8%

2. Expected Inflation: 8% for the next two years, then 7% thereafter

3. Maturity Risk Premium (MRP): 0.1% per year of maturity (7-year bond = 0.1 * (7-1)% = 0.6%)

4. Liquidity Premium (LP): 1.05%

5. Default Risk Premium (DRP) for AA-rated bonds (based on the table)

Let's calculate the yield:

Yield = Real Risk-Free Rate + Expected Inflation + Maturity Risk Premium + Liquidity Premium + Default Risk Premium

Yield = 2.8% + (8% + 8% + 7%) + 0.6% + 1.05% + (AA-rated DRP from the table)

Without the specific value for the AA-rated DRP, we cannot provide the exact yield. However, based on the given options, the closest answer is 11.49% (option C).

Regarding the statement about interest rates:

In theory, the yield on a bond with a longer maturity is expected to be higher than the yield on a bond with a shorter maturity. This is because longer-term bonds are exposed to more uncertainties and risks over an extended period, leading investors to demand higher returns.

The statement about the yield on an AAA-rated bond being higher than the yield on a BB-rated bond is incorrect. Higher-rated bonds, such as AAA, typically have lower default risk and, therefore, offer lower yields compared to lower-rated bonds like BB, which carry higher default risk and higher yields.

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The complete question is:<The real risk-free rate (r*) is 2.8% and is expected to remain constant. Inflation is expected to be 8% per year for each of the next two years and 7% thereafter. The maturity risk premium (MRP) is determined from the formula: 0.1 (t - 1)%, where t is the security's maturity. The liquidity premium (LP) on all Harrington Horticulture Co.'s bonds is 1.05%. The following table shows the current relationship between bond ratings and default risk premiums (DRP): Harrington Horticulture Co. issues seven-year, AA-rated bonds. What is the yield on one of these bonds? Disregard cross-product terms; that is, if averaging is required, use the arithmetic average. 5.25% 12.54% 11.49% 11.94% Based on your understanding of the determinants of interest rates, if everything else remains the same, which of the following will be true? In theory, the yield on a bond with a longer maturity will be higher than the yield on a bond with a shorter maturity. The yield on a AAA-rated bond will be higher than the yield on a BB-rated bond>