What value of b completes f(x)=2x^2+bx+74 If the vertex is (-6,2)

Answer:

-1/6

Step-by-step explanation:

24x=-4

X=-4/24

X=-2/12

X=-1/6

The probability that a white ball was transferred from bag b into bag a given that a black ball was drawn from bag a is approximately 0.5760.

Let us denote the events as follows,

A represents the ball drawn from bag a is black

B represents the ball transferred from bag b to bag a is white

Probability of event B given that event A has occurred is P(B|A).

Using Bayes' theorem ,

P(B|A) = P(A|B) × P(B) / P(A)  __(1)

P(A|B) = Probability of drawing a black ball from bag a given that a white ball was transferred from bag b to bag a.

P(A|B)

= (3/5)× (5/9) + (4/9)× (4/9)

= 43/81

P(B) = Probability of transferring a white ball from bag b to bag a

       = 5/9

P(A) = Probability of drawing a black ball from bag a.

Using the law of total probability,

P(A) = P(A|B) ×P(B) + P(A|B') × P(B')

Here, B' represents the event that a black ball was transferred from bag b to bag a.

P(B') = 4/9

P(A|B')

= (3/5) × (4/9) + (2/5) × (5/9)

= 22/45

Now,

P(A)

= (43/81) ×(5/9) + (22/45)× (4/9)

= 0.512

Substitute all the values into Bayes' theorem,

P(B|A)

= (43/81) ×  (5/9) / (0.512)

≈ 0.5760

Therefore, the required probability of transferring a ball from one bag to another is approximately 0.5760.

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The above question is incomplete, the complete question is:

Bag a contains 2 white and 3 black balls. Bag b contains 5 white and 4 black balls. One ball is drawn at random from bag b and is placed unseen in bag a. If the ball drawn from bag a is black, find the probability that a white ball was transferred from bag b into bag a?

Answer:

8√3

Step-by-step explanation:

pythagoras theorem

16^2=8^2+p^2

p= √(16^2-8^2)

= 8√3

Answer:

P = 8√3

Step-by-step explanation:

Apply the Pythagoras Theorem:

\(\displaystyle{\text{opposite}^2+\text{adjacent}^2=\text{hypotenuse}^2}\)

Commonly written as:

\(\displaystyle{a^2+b^2=c^2}\)

From the attachment, we know that opposite = 8 and hypotenuse = 18. Solve for the adjacent (P). Therefore:

\(\displaystyle{8^2+P^2=16^2}\\\\\displaystyle{64+P^2=16^2}\)

Subtract 64 both sides to isolate P:

\(\displaystyle{P^2=16^2-64}\\\\\displaystyle{P^2=256-64}\\\\\displaystyle{P^2=192}\)

Square root both sides:

\(\displaystyle{\sqrt{P^2} = \sqrt{192}}\\\\\displaystyle{P=\sqrt{192}}\)

192 can be factored as 8 x 8 x 3. Therefore:

\(\displaystyle{P=\sqrt{8 \times 8 \times 3}}\\\\\displaystyle{P = 8\sqrt{3}}\)

Thus, P = 8√3

Answer: 53

Step-by-step explanation:

It's already ordered from least to greatest so find the number in the middle. That would be 52 and 54.

Find the mean/average of 52 and 54.

(52+54)/2=106/2=53

Answer:

3,6,12,24,48,96 ,192 ,384

Step-by-step explanation:

The conclusions that can be made about the two distributions are:

Options A and D are correct.

The means-to-MAD ratio is found by dividing the mean of a dataset by its Mean Absolute Deviation (MAD).

We have that in Data Set 1, the means-to-MAD ratio is 54/4 = 13.5, and in Data Set 2, the means-to-MAD ratio is 60/2 = 30.

Since the means-to-MAD ratio in Data Set 1 is 13.5 and in Data Set 2 is 30, we can conclude that the two distributions are not similar.

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Answer: (1, -10)

Step-by-step explanation:

Substituting the coordinates of each of the points into the given inequalities, we see that (1, -10) is the only point that results in two true statements.

To solve the given probability questions, we can use the properties of the normal distribution.

Given that the per capita consumption of bottled water is approximately normally distributed with a mean of 30.5 gallons and a standard deviation of 13 gallons, we can calculate the probabilities using the z-score.

a. To find the probability that someone consumed more than 31 gallons of bottled water, we need to calculate the area under the normal curve to the right of 31. We can use the z-score formula:

z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

Calculating the z-score:

z = (31 - 30.5) / 13 = 0.0385

Using a standard normal distribution table or a calculator, we can find the probability corresponding to this z-score. The probability of z > 0.0385 is approximately 0.4801.

Therefore, the probability that someone consumed more than 31 gallons of bottled water is approximately 0.4801.

b. To find the probability that someone consumed between 25 and 35 gallons of bottled water, we need to calculate the area under the normal curve between these two values. We can calculate the z-scores for both values:

For 25 gallons:

z1 = (25 - 30.5) / 13 = -0.4231

For 35 gallons:

z2 = (35 - 30.5) / 13 = 0.3462

Using the standard normal distribution table or a calculator, we can find the probabilities corresponding to these z-scores. The probability of -0.4231 < z < 0.3462 is approximately 0.4357.

Therefore, the probability that someone consumed between 25 and 35 gallons of bottled water is approximately 0.4357.

c. To find the probability that someone consumed less than 25 gallons of bottled water, we need to calculate the area under the normal curve to the left of 25. We can calculate the z-score:

z = (25 - 30.5) / 13 = -0.4231

Using the standard normal distribution table or a calculator, we can find the probability corresponding to this z-score. The probability of z < -0.4231 is approximately 0.3372.

Therefore, the probability that someone consumed less than 25 gallons of bottled water is approximately 0.3372.

d. To find the value of gallons of bottled water consumed by 90% of people, we need to find the z-score that corresponds to a cumulative probability of 0.90. From the standard normal distribution table or using a calculator, we find that the z-score is approximately 1.2816.

Using the z-score formula, we can solve for x:

1.2816 = (x - 30.5) / 13

Rearranging the equation, we find:

x - 30.5 = 1.2816 * 13

x - 30.5 = 16.6518

x ≈ 47.15

Therefore, 90% of people consumed less than approximately 47.15 gallons of bottled water.

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Answer:

195

Step-by-step explanation:

So -79 + x = 116

then x = 116 + 79 = 195

Answer:

The sum of two consecutive integers will always be an odd number.

Step-by-step explanation:

-79 + x = 116

x = 116 + 79 = 195

195 is the answer

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The probability of hitting the bull's-eye all three times when throwing darts can be calculated using the multiplication rule of probability as P(3 hits) = p x p x p = \(p^3\),

where p is the probability of hitting the bull's-eye on each throw.

When throwing darts at a dart board, the probability of striking the bull's-eye is affected by many factors, such as the player's skill, the distance from the board, the type of dart used, and so on.

However, assuming that the probability of hitting the bull's-eye is the same for each throw and independent of previous throws;

We can calculate the probability of hitting the bull's-eye all three times using the multiplication rule of probability.

Suppose the probability of hitting the bull's-eye on each throw is p. Then, the probability of missing the bull's-eye on each throw is 1 - p.

The probability of hitting the bull's-eye all three times can be calculated as follows:

P(3 hits) = p x p x p = \(p^3\)

For example, if p = 0.05 (or 5%), then the probability of hitting the bull's-eye all three times would be:

P(3 hits) = 0.05 x 0.05 x 0.05 = 0.000125 or 0.0125%

This means that the chance of hitting the bull's-eye all three times is very low, and it would require a lot of skill and luck to achieve such a feat.

However, the probability of hitting the bull's-eye at least once in three throws would be much higher, and it would depend on the player's skill and consistency.

Overall, the probability of hitting the bull's-eye all three times is quite low, and it is more likely that a player will hit it once or twice or miss it altogether.

Nonetheless, the thrill of the game lies in the challenge and the unpredictability of each throw, making darts a popular game of skill and chance.

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The diameter of the bike's tire is 2.325 inches.

Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by it.  If we open a circle and make a straight line out of it, then its length is the circumference. It is usually measured in units, such as cm or unit m.

A mountain bike tire completes 15 revolutions and travels 146 feet.

Now,

1 revolution of a tire is equal to the circumference of the tire.

Since we have 15 revolutions, we should take 15C=146

where C=πd where π is pi (use 3.14 or the pi symbol).

Our equation is:

20πd=146.

Then solve for d:

20 × 3.14 × d = 146

62.8d = 146

d = 146/62.8

d = 2.325 inches.

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In hypothesis testing, a Type 1 error occurs when we reject a null hypothesis that's actually true. In other words, we conclude that there's a significant effect or difference when there is not one. The probability of making a Type 1 error is denoted by the symbol alpha( α).

A Type 2 error, on the other hand, occurs when we fail to reject a null hypothesis that's actually false. In other words, we conclude that there's no significant effect or difference when there actually is one. The probability of making a Type 2 error is denoted by the symbol beta( β).

In general, Type 1 errors are considered more serious than Type 2 errors because they lead to false positive results and can have negative consequences, similar as making incorrect opinions or wasting coffers. still, the inflexibility of the consequences depends on the specific situation.

The chances of Type 1 and Type 2 errors are related to the significance position( α) and the power( 1- β) of the hypothesis test, independently. The significance position( α) is the probability of making a Type 1 error and is generally set at 0.05 or 0.01. .

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Answer:

The answer is A.

Step-by-step explanation:

You have one solution where the lines intersect, which is (-7, 6)

Answer: :)

Step-by-step explanation:

To classify the triangle as acute, right, or obtuse, we need to determine the measure of the largest angle in the triangle. We can use the Law of Cosines to find the angles of the triangle:

c^2 = a^2 + b^2 - 2ab cos(C)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

For this triangle, we have:

c = 12

a = 6

b = 9

Using these values in the Law of Cosines, we get:

12^2 = 6^2 + 9^2 - 2(6)(9)cos(C)

144 = 117 - 108cos(C)

27 = 108cos(C)

cos(C) = 0.25

To find angle C, we can take the inverse cosine (cos^-1) of both sides:

C = cos^-1(0.25)

C ≈ 75.5°

Now we can classify the triangle based on its largest angle:

- If C is less than 90 degrees, then the triangle is acute.

- If C is exactly 90 degrees, then the triangle is right.

- If C is greater than 90 degrees, then the triangle is obtuse.

In this case, since C ≈ 75.5°, which is less than 90 degrees, we know that this triangle is an acute triangle.

9514 1404 393

Answer:

  36

Step-by-step explanation:

The parallel lines divide the segments proportionally.

  GH/HI = GK/KJ

  GH = HI(GK/KJ) = 48(30/40)

  GH = 36

Answer:

3. 72= (x)+(x+1)+(x+2) where x= the smallest number

72=3x+3

-3        -3

69=3x

/3   /3

x=23

x+1=24

x+2=25

smallest is 23

4. 48= (x)+(x+2)+(x+4)

48= 3x+6

-6        -6

42=3x

/3    /3

x=14

x+2=16

x+4=18

smallest is 14

5. all erasers were the same cost

25= 4x+5 (x= cost of erasers)

-5         -5

20=4x

/4   /4

x=5

each cost  $5

6. b= boxes

22= b/2 +7

-7            -7

15=b/2

multiply both sides by 2 to cancel the denominator

30=b

30 boxes originally

7. 40= total

8= left

2= balls given to each

x=number of friends

40= 2x+8

-8         -8

32=2x

/2   /2

x=16

she has 16 friends

8.  12= left

a= total allowance

12= (a/2) +4

-4            -4

8= a/2

multiply both sides by 2 to cancel the denominator

a= $16

she had an allowance of $16

9.  4 (2) = amount that her four children recieved

10=amount she took for herself

x= original

x= 4(2) + 10

x= 8 +10

x=18

she started with 18 candies

10. a= age

244= 400 - 2a

-400 -400

-156= -2a

/-2     /-2

a= 78

they are 78 years old

11. c= comic books

36=  c/2 + 16

-16           -16

20=c/2

multiply both sides by 2 to cancel the denominator

c=40

she started with 40 comic books

12.  b= students in buses

472= 9b + 4

-4             -4

468=9b

/9     /9

b= 52

52 students went in each bus

13. h= hats

17= h/2 +5

-5          -5

12=h/2

multiply both sides by 2 to cancel the denominator

h=24

she had 24 hats on monday

14. p= pies the club made

60= (p+4)/5

multiply both sides by 5 to cancel the denominator

300=p+4

-4         -4

p= 296

the club made 296 pies

Step-by-step explanation:

The ratio that compares the number of jackets without caps to the number of jackets with caps is 6:12, or simplified as 1:2.

Libby has a total of 18 jackets, and out of those, 6 do not have caps. To find the ratio, we compare the number of jackets without caps to the number of jackets with caps.

Out of the 18 jackets, the remaining 12 jackets must have caps since 6 jackets do not have caps. Therefore, the ratio of jackets without caps to jackets with caps is 6:12, or simplified as 1:2.

This means that for every jacket without a cap, there are two jackets with caps. The ratio 1:2 represents the relationship between the two quantities.

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To calculate the sample standard deviation for the given data set (-12, -10, 14, -10, 14, -10), we need to follow a series of steps. Once the calculation is performed, the value should be rounded to one decimal place.

To find the sample standard deviation, we first calculate the mean of the data set. Summing up all the values and dividing by the total number of values gives us the mean. In this case, the sum is -12 + (-10) + 14 + (-10) + 14 + (-10) = -14, and there are 6 values, so the mean is -14/6 ≈ -2.33.

Next, we calculate the difference between each data point and the mean, and square each difference. The squared differences are (-12 - (-2.33))^2, (-10 - (-2.33))^2, (14 - (-2.33))^2, (-10 - (-2.33))^2, (14 - (-2.33))^2, and (-10 - (-2.33))^2.

Summing up these squared differences and dividing by the number of values minus 1 (since it's a sample) gives us the sample variance. Taking the square root of the sample variance yields the sample standard deviation.

Performing the calculations and rounding to one decimal place will give us the final result for the sample standard deviation.

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The statement that the pack() function uses ipadx to force external space horizontally is True.

To elaborate, the pack() function is a geometry manager in the Tkinter library for Python. It is responsible for organizing and placing widgets within a container, such as a window or a frame. The ipadx option in the pack() function allows you to add additional horizontal padding (external space) around the widget.

This helps in visually separating the widget from other elements within the same container, making the user interface more readable and user-friendly.

Therefore, the pack() function utilizes the ipadx option to create external horizontal space around a widget, making it easier for users to interact with the interface.

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The solution is, the finally discounted price is 71.5.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

sale price = 90

15% discount, so, the price = 90* 85%

                                            =76.5

now, after 5 discount, price became = 76.5 - 5

                                                             = 71.5

Hence, The solution is, the finally discounted price is 71.5.

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Answer:

slope - (2x)

y-intercept - (-1)

Step-by-step explanation:

-8x + 4y = - 4

4y = 8x - 4

y = 2x - 1

An expression that represent the combined inventory of the two stores include the following: B. 7/2(g²) - 4/5(g) + 15/4.

In Mathematics, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value.

Next, we would add the two (2) given polynomials as follows;

Polynomial = 1/2(g²) + 7/2 + 3g² - 4/5(g) + 1/4

By rearranging and collecting like-terms, we have the following:

Polynomial = [1/2(g²) + 3g²] - 4/5(g) + [1/4 + 7/2]

Polynomial = 7/2(g²) - 4/5(g) + 15/4

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Answer:

500=D 100=M

Step-by-step explanation:

I hope that helps :D

Answer:

The correct answer is D: 6y = 42 - 2x

Step-by-step explanation:

By definition, two lines are perpendicular if and only if their slopes are negative reciprocals of each other.

If we transform 6y = 42 - 2x into its slope-intercept form, y = mx + b:

6y = 42 - 2x

6y = -2x + 42

Divide both sides by 6 to isolate y:

\(\frac{6y}{6} = \frac{-2x + 42}{6}\)

y = \(-\frac{1}{3}x + 7\)

Its slope, - 1/3 is the reciprocal of the given question's slope, 3.

Therefore, the correct answer is D, 6y = 42 - 2x

Answer:

B

Step-by-step explanation:

If you think of it as a graph the y intercept is -430, meaning that after 0 minutes it's at -430 (it started at -430).

Because you multiply the number of minutes by 38, that means it ascends by 38 meters every minute.

Answer:

15 19/60

Step-by-step explanation:

-7 2/3 + (- 5 1/2) + 8 3/4 =

23/3 +(- 11/10) +35/4 =

LCM of 3,4 and 10 = 60

460/60 + (- 66/60) + 525/60 =

460+525= 985 - 66 = 919

919/ 60 = 15 19/60

The solution to the equation 8log₂(7p - 5) - 4 = 28 is p = 3.

To solve the equation 8log₂(7p - 5) - 4 = 28, we can follow these steps:

Add 4 to both sides of the equation:

8log₂(7p - 5) = 32

Divide both sides by 8:

log₂(7p - 5) = 4

Rewrite the equation in exponential form:

2^4 = 7p - 5

Simplifying:

16 = 7p - 5

Add 5 to both sides:

21 = 7p

Divide both sides by 7:

p = 3

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