A bag with 12 marbles has 5 red marbles, 3 yellow marbles, and 4blue marbles. A marble is chosen from the bag at random. What is the probability that it is red? Write your answer as a fraction in simplest form.

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Explanation:

You can use the nCr formula shown below

[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]

where n = 39 and r = 1. However, you could also use the identity

[tex]_n C _{1} = n[/tex]

which basically says there are n ways to pick 1 item if you are given a choice of n items. In this specific case, we have 39 items total, and there are 39 ways to pick one item.

9514 1404 393

Answer:

  b) y=(x+6)^2-32

Step-by-step explanation:

Add and subtract the square of half the x-coefficient to put into vertex form.

  f(x) = x^2 +12x +4 . . . . . given

  y = x^2 +12x +36 +4 -36 . . . . add and subtract (12/2)^2 = 36

  y = (x +6)^2 -32 . . . . . . . . . . . write in vertex form

Answer:

Step-by-step explanation:

hope it helps

Answer:

Option D

Explanation:

The real answer would be a bit higher if you use the formula:

Area=π×r^2

Answer:

18

Step-by-step explanation:

Hope this help!!!

Have a nice day!!!

That is the same as writing [tex]10\sqrt{30}[/tex]

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Explanation:

The diagram shows that

That must mean DC = AC-AD = 60-50 = 10

We'll use this to help find BD as shown below

AD/BD = BD/DC

AD*DC = BD*BD .... cross multiply

(BD)^2 = AD*DC

BD = sqrt(AD*DC) ..... geometric mean formula

BD = sqrt(50*10)

BD = sqrt(500)

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Now apply the pythagorean theorem to find AB. Focus on triangle ABD.

(AD)^2 + (BD)^2 = (AB)^2

(AB)^2 = (AD)^2 + (BD)^2

(AB)^2 = (50)^2 + (sqrt(500))^2

(AB)^2 = 2500 + 500

(AB)^2 = 3000

AB = sqrt(3000)

AB = sqrt(100*30)

AB = sqrt(100)*sqrt(30)

AB = 10*sqrt(30)

Answer:

here u go

Step-by-step explanation:

i got 45

Answer:

Amplitude = 2

Step-by-step explanation:

The amplitude is the distance between the midline and the maximum/minimum. Because the midline is located at y=1, then the maximum and minimum are both 2 units apart from the midline. That is your amplitude.

Answer:

d. Recent observed value

Step-by-step explanation:

Exponential smoothing is technique for smoothing time series data. In exponential smoothing more recent observed values give larger weights while the weights will decline if observed values are more distant. In moving average the observations were weighted equally.

Answer:

acute and isosceles

Step-by-step explanation:

Define:

Acute - All angles have a measure of less than 90 degrees

Obtuse - has an angle with a measure of more than 90 degrees

Right - has an angle with a measure of 90 degrees

Scalene - no congruent side lengths or angles

Isosceles - two congruent sides and two congruent angles

Equilateral - all congruent sides and all congruent angles

Identify:

The triangle shown has angles that measure less than 90 degrees which means that it's an acute triangle

The triangle also has two congruent sides and two congruent angles which means that it's an isosceles triangle.

So we can conclude that the triangle can be identified as an acute isosceles

Step-by-step explanation:

If there are 3 red marbles, 5 green marbles, and 2 blue marbles, we can find the probability of finding one of them easily.

1. If we add these numbers up, we get 10, so the red marbles plus the green marbles = 8 and then there are 2 blue ones. This means that there is an 80% chance of pulling a red or a green marble. Number one is correct.

2. The probability of drawing a red marble followed by a green marble depends on each individual probability. For a red marble, that is [tex]\frac{3}{10}[/tex] = 30% chance, and a green marble is [tex]\frac{5}{10}[/tex] = 50% chance. Since we are drawing out of 20 marbles (Two sets of ten), we can conclude that the chances for red are [tex]\frac{6}{20}[/tex]; green's chances are [tex]\frac{10}{20}[/tex], and blue's chances are [tex]\frac{4}{20}[/tex]. Assuming that we draw a red marble first, there is a [tex]\frac{6}{20}[/tex] chance of that. There is a [tex]\frac{10}{20}[/tex] chance of drawing a green, so we can conclude that the probability of drawing a red marble followed by a green marble is [tex]\frac{4}{20}[/tex] ([tex]\frac{10}{20}[/tex] - [tex]\frac{6}{20}[/tex]), witch is not [tex]\frac{1}{6}[/tex]. Number two is incorrect .

3. The probability of drawing a blue marble is 20%, so the probability of not drawing a blue marble is 80%. Number three is incorrect.

4. The probability of drawing a green marble is 50% and the probabilities of red and blue combined are equal to 50% (3 red + 2 blue = 5, and their are 5 green marbles therefore 50 50 chance). Number four is correct.

Answer:

The probability of randomly drawing a red marble(red 3) and then a green (green 5) marble is [tex]\frac{1}{6}[/tex] .

The probability of drawing a green marble is the same as the probability of drawing either a red or a blue marble.

The probability of randomly drawing either a red marble or a green marble is 80%.

Answer:

The answer is "Option b"

Step-by-step explanation:

Through this context, it is determined that the p-value is much less than 0.05, which is 0.021, so the rejection of the null hypothesis at 5%. There should be enough evidence to demonstrate that now the effect of the organization was substantial on how long it has taken to solve the issue. This result is statistically important.

The correct conclusion about this data is (b) The effect of training on how long it takes to solve the problem was significant, F(2, 27) = 4.47, p < 05.

From the table, we have the following values

F = 4.467

df between group = 2

df within group = 27

To reference the result, we make use of:

F(df between group, df within group) =  F value

So, we have:

F(2, 27) = 4.47

The above result shows the F value approximated to two decimal points

Hence, the correct conclusion about this data is (b) The effect of training on how long it takes to solve the problem was significant, F(2, 27) = 4.47, p < 05.

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Answers:

x = 6

Each angle is 45 degrees

The diagram is shown below

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Explanation:

Vertical angles are always congruent

Set the two expressions equal to each other and solve for x.

5x+15 = 3x+27

5x-3x = 27-15

2x = 12

x = 12/2

x = 6

As a way to check the answer, replace x with 6 in each expression. We should get the same thing on both sides

5x+15 = 3x+27

5*6+15 = 3*6+27

30+15 = 18+27

45 = 45

Each angle is 45 degrees, so the answer is confirmed.

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The diagram is shown below. There are infinitely many ways to draw out the diagram. In the version I drew, the angles aren't vertically aligned but instead they are opposite one another in this X configuration. So the vertical angles could be vertically aligned, but they don't have to be.

In short: draw an X shape and mark any two opposite angles to form the vertical angles.

Answer:

54

Step-by-step explanation:

16.4= 16

12.8= 13

9.6= 10

14.6=15

16 + 13 +10 +15 = 54

Answer:

Kindly check explanation

Step-by-step explanation:

Using technology on the data above, the least square regression equation obtained is ;

y = 33.4528+2.7975x

Where, slope = 2.7975 ; Intercept = 33.4528

x = chirps per second, independent variable

y = temperature, predicted variable.

The Correlation Coefficient, r = 0.71

The Coefficient of determination, r² = 0.71² = 0.5041

The percentage of variation in y due to regression is the r² value, which is about 50.41%

Hence, the percentage variation in temperature due to the regression line is 50.4, while the rest is due to other factors.

Predicted temperature, y when x = 19 ;

Put x = 19

y = 33.4528+2.7975(19)

y = 86.60°

The GPA of the student, based on the given grades, is approximately 1.93.

Use the concept of probability defined as:

Given that,

Grades provided: B (13 hours), D (16 hours), C (13 hours)

Grade equivalencies: A = 4.0, B = 3.0, C = 2.0, D = 1.0, F = 0

Credit hours associated with each grade: B (13 hours), D (16 hours), C (13 hours)

To calculate GPA,

Convert grades to their point values and calculate the weighted GPA

Point values for the given grades: B (3.0), D (1.0), C (2.0)

To calculate the GPA,

First, convert each grade to its equivalent point value.

For the given grades, we have:

B (13 hours) = 3.0

D (16 hours) = 1.0

C (13 hours) = 2.0

Now, calculate the weighted GPA by multiplying the point value of each grade by the number of credit hours and then summing them up.

In this case, it would be:

(3.0 x 13) + (1.0 x 16) + (2.0 x 13) = 81

Divide the sum of the weighted grade points (81) by the total number of credit hours (13 + 16 + 13 = 42) to get the GPA:

81 / 42 = 1.93

Hence,

Rounding to two decimal places, the GPA would be approximately 1.93.

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Answer:

See Explanation

Step-by-step explanation:

Given

[tex]Reason \to Frequency[/tex]

[tex]Congestive\ heart\ failure \to 990[/tex]

[tex]Coronary\ atherosclerosis\to 1400[/tex]

[tex]Heart\ attack \to 744[/tex]

[tex]Infant\ birth\to 3800[/tex]

Solving (a): Frequency bar graph

To do this, we simply plot the reasons (on the x-axis) against the frequency (on the y-axis).

See attachment

Solving (b): Relative frequency distribution

The relative frequency is calculated as:

[tex]RF = \frac{F}{Total}[/tex]

Where

[tex]Total = 990+1400+744+3800[/tex]

[tex]Total = 6934[/tex]

So, we have:

[tex]Congestive\ heart\ failure \to \frac{990}{6934} = 0.1427[/tex]

[tex]Coronary\ atherosclerosis\to \frac{1400}{6934} = 0.2019[/tex]

[tex]Heart\ attack \to \frac{744}{6934} = 0.1073[/tex]

[tex]Infant\ birth\to \frac{3800}{6934} = 0.5481[/tex]

So, the relative distribution is:

[tex]Reason \to Frequency \to Relative\ Frequency[/tex]

[tex]Congestive\ heart\ failure \to 990 \to 0.1427[/tex]

[tex]Coronary\ atherosclerosis\to 1400 \to 0.2019[/tex]

[tex]Heart\ attack \to 744 \to 0.1073[/tex]

[tex]Infant\ birth\to 3800 \to 0.5481[/tex]

Solving (c): Relative frequency bar graph

To do this, we simply plot the reasons (on the x-axis) against the relative frequency (on the y-axis).

See attachment

Solving (d): Relative frequency Pareto chart

First, calculate the cumulative relative frequency

This is done by adding up the previous relative frequency,

So, we have:

[tex]Reason \to Relative\ Frequency \to Cumulative[/tex]

[tex]Congestive\ heart\ failure \to 0.1427 \to 0.1427[/tex]

[tex]Coronary\ atherosclerosis \to 0.2019 \to 0.2019+0.1427=0.3446[/tex]

[tex]Heart\ attack \to 0.1073\to 0.3446+0.1073 = 0.4519[/tex]

[tex]Infant\ birth \to 0.5481 \to 0.5481+4519 =1[/tex]

So, we have:

[tex]Reason \to Relative\ Frequency \to Cumulative[/tex]

[tex]Congestive\ heart\ failure \to 0.1427 \to 0.1427[/tex]

[tex]Coronary\ atherosclerosis \to 0.2019 \to 0.3446[/tex]

[tex]Heart\ attack \to 0.1073\to 0.4519[/tex]

[tex]Infant\ birth \to 0.5481 \to 1[/tex]

Next, we simply plot the reasons (on the x-axis) against the cumulative relative frequency (on the right) and the left of the Pareto chart.

See attachment

Answer:

y = 14x

Step-by-step explanation:

Use the direct variation equation, y = kx

Plug in 7 as y and 0.5 as x, and solve for k:

y = kx

7 = k(0.5)

14 = k

Plug this into the equation:

y = kx

y = 14x

So, the equation of variation is y = 14x

Answer:

arc cosine (4/5)

(the third answer)

Step-by-step explanation:

Answer:

??

Step-by-step explanation:

Answer:

77

Step-by-step explanation:

median is the middle value.

1. arrange in numerical order

65, 74, 77, 88, 92

2. cross out all outside numbers untill you find the middle value

65, 74, 77, 88, 92

3. it's 77

Answer:

(a) R = P +C

Revenue= Profit + Cost

(b) R = $6000

Step-by-step explanation:

(b) R = $4525 + $1475

        = $6000

Answer:

-54 is the answer

Step-by-step explanation:

hope you like it

Answer:

y-5 = 3/4(x+3)

Step-by-step explanation:

Answer:

c.

0.1824

Step-by-step explanation:

The computation of the decay factor is as follows;

= (1 - decrease percentage) × (1 - decrease percentage) × (1 - decrease percentage)

= (1 - 0.2) × (1 - 0.4) × (1 - 0.62)

= (0.8) × (0.6) × (0.38)

= 0.1824

hence, the decay factor is 0.1824

Therefore the option c is correct

Solution :

It is given that :

[tex]$f'(t) = (350 \ln t)'$[/tex]

       [tex]$=350(\ln t)'$[/tex]

        [tex]$=\frac{350}{t}$[/tex]

So, [tex]f(5)=350 \ln (5) \approx 563[/tex]

     [tex]$f'(5) = \frac{350}{5}$[/tex]

              [tex]=70[/tex]

The relative change is then,

[tex]$\frac{f'(5)}{f(5)}=\frac{70}{350\ \ln(5)}$[/tex]

         [tex]$=\frac{1}{5\ \ln(5)}$[/tex]

         [tex]$\approx 0.12$[/tex]

          [tex]=12\%[/tex]

This means that after 5 weeks, the revenue from the DVD sales in $563 with a rate of change of $70 per week and the increasing at a continuous rate of 12% per week.

Answer: $1260

Step-by-step explanation:

Based on the information given, Abby's gross income for the month if her sales were $12500 will be:

= $1000 + (1% × $8000) + [4% × ($12500 - $8000)]

= $1000 + (0.01 × $8000) + (0.04 × $4500)

= $1000 + $80 + $180

= $1260

Her gross income is $1260

Using trigonometry solve for h and d.

H :

Sin(60) = h/120

H = 120 x sin(60)

H = 103.9 = 104 feet

D:

Cos(60) = d/120

D = 120 x cos(60)

D = 60 feet

The correct answers:

A. D = 60 ft.

C. H = 104 ft