A bag contains four green gum balls , three blue gum balls , and two red gum balls , all the same size and shape A. What is the probability of choosing a red gum ball

The relative frequencies of this data by row is

          150 cc    180 cc

Black 0.43         0.57

Blue   0.47         0.53

Red   0.55          0.45

The table of values is given as:

          150 cc    180 cc

Black 18              24

Blue   15              17

Red   26              21

Calculate the row total.

          150 cc    180 cc    Total

Black 18              24          42

Blue   15              17           32

Red   26              21           47

Divide each element by the row total

          150 cc    180 cc

Black 0.43         0.57

Blue   0.47         0.53

Red   0.55          0.45

Hence, the relative frequencies of this data by row is

          150 cc    180 cc

Black 0.43         0.57

Blue   0.47         0.53

Red   0.55          0.45

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The solution to the given differential equation dy/dx = e^(x+1)/y, with the initial condition y = 2 when x = 0, is y = sqrt(e^(2x+2) + 3).

1. Begin by separating the variables in the differential equation: dy/y = e^(x+1) dx.

2. Integrate both sides of the equation with respect to their respective variables. The integral of dy/y is ln|y|, and the integral of e^(x+1) dx is e^(x+1).

3. Applying the initial condition y = 2 when x = 0, we have ln|2| = e^1 * C, where C is the constant of integration.

4. Solve for C by evaluating ln|2| = e * C, which gives C = ln|2|/e.

5. Substitute the value of C back into the integral to obtain ln|y| = e^(x+1) * ln|2|/e.

6. Exponentiate both sides to eliminate the natural logarithm: |y| = e^(x+1) * ln|2|/e.

7. Remove the absolute value by considering y > 0, which gives y = e^(x+1) * ln|2|/e.

8. Simplify further by noting that ln|2|/e is a constant, let's denote it as A for simplicity. Hence, y = A * e^(x+1).

9. Since the question asks for the solution in terms of y, we can rewrite the equation as y = sqrt(e^(2x+2) + 3), by substituting A^2 = 1 + 3 and simplifying the exponent.

10. Therefore, the solution to the given differential equation is y = sqrt(e^(2x+2) + 3).

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The Solution:

The question says:

8 packages of batteries cost $10.50

We are required to find how much 6 packages would cost.

So, the cost of 6 packages of batteries would be

Therefore, the cost of 6 packages of batteries would be $7.88

Answer:

5 hours lifeguarding and two hours babysitting.

Step-by-step explanation:

5(20) = 100

10(2) = 20

100 + 20 = 120

Solution

The volume of a sphere is

Where radius = diameter/2

radius = 5.6/2 = 2.8 cm

Hence, the correct option is D

In the event that linear regression is required, we have two options: (1) change the delay column 2) ignore them.

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

Given,

You want to run a regression to predict the probability of a flight delay, but there are flights with delays of up to 12 hours that are really messing up your model.

I immediately think of grouping delays into ranges such as those under 40 minutes, those between 40 minutes and 2 hours, those between 2 hours and 10 hours, and those above 10 hours. But doing so requires the use of a classification model, such as logistic regression. We frequently consider whether there will be a delay rather than how long it might last when thinking about delays. In the event that linear regression is required, we have two options: (1) change the delay column 2) ignore them.

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The hypothesis that is typically used to test the claim is the null hypothesis, which asserts that the average time spent by students studying for a midterm exam is indeed 3 hours. The alternative hypothesis would be that the average time spent is either greater or less than 3 hours.

The null hypothesis is usually denoted as H0 and the alternative hypothesis as Ha. In this case, we can write:

H0: The average time spent by students studying for a midterm exam is 3 hours.

Ha: The average time spent by students studying for a midterm exam is not 3 hours.

To test this hypothesis, a statistical test can be performed, such as a t-test or a z-test, depending on the sample size and the population parameters. The results of the test will determine whether the null hypothesis can be rejected or not. If the null hypothesis is rejected, it means that there is evidence to suggest that the average time spent studying is different from 3 hours. If the null hypothesis is not rejected, it means that there is not enough evidence to suggest that the average time spent studying is different from 3 hours.

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a. The solution to the system is shown in the graph given below, which is (3, 8).

b. Plugging in the values of x and y into each equation, both sides of each equation are balanced.

To find the solution to a system of equations, plot both equations on a coordinate plane, then find the coordinates of the point where the two lines intersect, which is the solution.

a. Given the system, 3y = x + 21 and y + 2/3x = 10, the image below show each line where 3y = x + 21 is represented as the blue line, and y + 2/3x = 10 is represented as the red line.

The lines of both equations intersect at point (3, 8) which shows that the solution of the system is solved graphically as (3, 8).

b. 3y = x + 21 --> eqn. 1

y + 2/3x = 10 --> eqn. 2

Substitute x = 3 and y = 8 into equation 1:

3(8) = 3 + 21

24 = 24 [true]

Substitute x = 3 and y = 8 into equation 2:

8 + 2/3(3) = 10

8 + 2 = 10

10 = 10 [true]

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Answer

$660

Step-by-step explanation:

0.70 * 3 = 2.10

1.15 * 2 = 2.30

2.1 + 2.3 = 4.4

4.4 * 150 = 660

Answer: The dividend yield on Stock A = 0.04

Step-by-step explanation:

Given: quarterly dividend = $0.15 per share

Annual dividend per share = 4 x 0.15 = $0.6  [1 year = 4 quarters]

Stock's price per share = $0.15

The computation of dividend is given by :-

Dividend yield = (annual dividend per share) divided by (the stock's price per share).

Here, Dividend yield = (0.6) ÷ 15 =  0.04

Hence, the dividend yield on Stock A = 0.04

Answer:

-2 is the answer

Step-by-step explanation:

In the down question i.e (5t+2)° answer is one as anything to the power zero is one so we have fond the value of 5 is one t is one and 2 is also one

By putting the value of t

we have ,

(2t-4)

=(2x1-4)

=2-4

= -2

Answer:

y = 9x - 5

Step-by-step explanation:

The slope is already given, so we just need to find the y-intercept.

Plug in 9 for m, 1 for x, and 4 for y in the equation y = mx + b.

4 = 9(1) + b

b = -5

Now that we know the y-intercept, we can construct the equation of the line.

y = 9x - 5

The probability that the insurance representative will sell a policy to three out of four prospective clients is 0.0256.

The probability that the insurance representative sells to more than two prospective clients is 0.0272.

To calculate the probability that the insurance representative will sell a policy to a specific number of prospective clients out of four, we can use the binomial probability formula.

The binomial probability formula is given by:

P(X = k) = \((n C k) * p^k * (1 - p)^(n - k)\)

Where:

P(X = k) is the probability of exactly k successes (selling a policy) out of n trials (appointments).

(n C k) represents the combination or "n choose k" which calculates the number of ways to choose k successes out of n trials.

p is the probability of success on a single trial (probability of making a sale).

(1 - p) is the probability of failure on a single trial (probability of not making a sale).

Using this formula, we can calculate the probability of selling a policy to three out of four prospective clients.

Probability of selling a policy to three clients:

P(X = 3) = (4 C 3) * (0.20)^3 * (1 - 0.20)^(4 - 3)

Calculating:

P(X = 3) = 4 * 0.008 * 0.80

P(X = 3) = 0.0256

To calculate the probability that she sells to more than two clients, we need to sum the probabilities of selling to three clients and selling to all four clients.

Probability of selling to more than two clients:

P(X > 2) = P(X = 3) + P(X = 4)

Substituting the values:

P(X > 2) = \(0.0256 + (4 C 4) * (0.20)^4 * (1 - 0.20)^(4 - 4)\)

Calculating:

P(X > 2) = 0.0256 + 1 × 0.0016 × 1

P(X > 2) = 0.0272

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The concentration of E. coli in the fermenter at 35°C under these oxygen transfer limitations is approximately 0.067 g/L.

To solve this problem, we can use the concept of oxygen transfer and the given values to calculate the expected concentration of E. coli in the fermenter.

The equation that relates the specific rate of oxygen consumption (Qo) and the volumetric oxygen transfer coefficient (kLa) is given by:

Qo = kLa × (C' - C)

Where:

Qo is the specific rate of oxygen consumption (10 mmol/gcell-hr in this case).

kLa is the volumetric oxygen transfer coefficient (30 h^(-1) in this case).

C' is the equilibrium dissolved oxygen concentration in the fermentation broth in mg/L (7.3 mg/L in this case).

C is the actual dissolved oxygen concentration in the fermentation broth in mg/L (0.2 mg/L in this case).

We can rearrange the equation to solve for C, which is the concentration of E.coli:

C = C' - (Qo / kLa)

Now, plug in the given values:

C = 7.3 - (10 / 30)

C = 7.3 - 0.3333

C = 6.9667 mg/L

The concentration of E. coli is given in g/L, and since 1 g = 1000 mg, we convert the value:

C = 0.67 g/L

Therefore, the concentration of E. coli in the fermenter at 35°C under these oxygen transfer limitations is approximately 0.067 g/L.

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Answer:

Step-by-step explanation:

It is going to be:

Answer:

58

Step-by-step explanation:

20+12= 32

it is a 90 degree angle so

90-32=58

58 is closest to 60

Answer:

16

Step-by-step explanation:

The required, Mmusi borrowed R3000 from Aggie as per the given conditions.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan.

Amount = Principal [1 + rate×time]

Let's call the amount Mmusi borrowed from Aggie "P".

After two years, he has to pay back
= P + P * 18% * 2
= P + 0.18 * P * 2
= P + 0.36P
= 1.36P

So if he has to pay back R4080, we can set up an equation to solve for P:

1.36P = 4080

To find P, we can divide both sides by 1.36:

P = 4080 / 1.36 = 3000

So Mmusi borrowed R3000 from Aggie.

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Answer:

where is the sequence?

#carryinlearning

Answer:

( -4 , 16 )

Step-by-step explanation:

1/2x + 18 =  5/2x + 26

-8 = 4/2x

-4 = x

so the lines cross at -4 x  so, then plug that number into either equation to see what y is

y = 1/2(-4) + 18

y = 16

Answer:

-4

Step-by-step explanation:

4/6 - 3/6p=16/6

Multiply each side by 6

4 - 3p = 16

Subtract 4 from both sides

-3p = 12

Divide both sides by -3

p = -4

Answer:

-4

Step-by-step explanation:

   \(\sf \dfrac{4}{6}-\dfrac{3}{6}p=\dfrac{16}{6}\)

To find the value of 'p', isolate 'p',

         \(\sf \dfrac{-3}{6}p=\dfrac{16}{6}-\dfrac{4}{6}\\\\\)

                 \(\sf = \dfrac{12}{6}\)

                  = 2

             \(\sf p = 2* \dfrac{6}{-3}\\\\ p = 2 *(-2)\\\\p = -4\)

Answer:

29

Step-by-step explanation:

conjugate of a+ib=a-ib

conjugate of 2-5i=2+5i

(2+5i)(2-5i)=2²-(5i)²=4-25i²=4-25(-1)=4+25=29

Answer:

29

i had the same question and 29 was the right answer

The limit of the function as x approaches 0 is 0.  So the answer is 0.

The limit of the function as x approaches 0 is given by:
lim x→0 8 − 8 cos(x) 4

To find the limit, we can use the fact that lim x→0 cos(x) = 1. This means that the limit of the function as x approaches 0 is:
lim x→0 8 − 8(1) 4

Simplifying the expression, we get:
lim x→0 8 − 8 4

= lim x→0 0 4

= lim x→0 0

= 0

Therefore, the limit of the function as x approaches 0 is 0.  So the answer is 0.

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Answer:

1) 0.3

2) 12

3a) 5/6

3b) 4/5

Step-by-step explanation:

1) There are;

12 white balls, 6 green balls and 2 red balls.

Total number of balls = 12 + 6 + 2 = 20

Probability of selecting a green ball at random = 6/20 = 3/10 = 0.3

2) we are told that number of marbles is 28 marbles.

Now, theoretical probability of drawing a blue marble = 3/7

This fraction is; number of favorable outcomes/number of possible outcomes.

Thus;

Number of blue marbles = 3/7 × 28 = 12 blue marbles

3a) theoretical probability is what we expect to happen.

There are 5 numbers less than 6 in the table.

Thus;

Theoretical probability of getting a number less than 6 in the next throw = 5/6

3b) Experimental probability is what actually happens.

Number of times a number less than 6 appears = 6 + 4 + 7 + 11 + 12 = 40 times

There was a total of 50 trials. Thus;

Experimental probability of getting a number less than 6 in the next throw = 40/50 = 4/5

Answer:

I think 2

Step-by-step explanation:

6-2is 4 8-6 2 both have common 6 and 2 multiple of 6is 2

Answer: left by 4 units and down 4 units

Step-by-step explanation: up and right is positive and left and down are negative

Using the normal distribution, it is found that 95% of babies born in Danaville have a healthy birthweight.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation are given, respectively, by:

\(\mu = 3.4, \sigma = 0.6\)

The proportion with a healthy weight is the p-value of Z when X = 4.6 subtracted by the p-value of Z when X = 2.2, hence:

X = 4.6:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (4.6 - 3.4)/0.6

Z = 2.

Z = 2 has a p-value of 0.975.

X = 2.2:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (2.2 - 3.4)/0.6

Z = -2.

Z = -2 has a p-value of 0.025.

0.975 - 0.025 = 0.95.

0.95 = 95% of babies born in Danaville have a healthy birthweight.

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Answer:

Step-by-step explanation:

1). SSS property of congruence.

2). SAS property of congruence.

3). SSS property of congruence.

4). SAS property of congruence.

5). SSS property of congruence.

6). SAS property of congruence.

7). SAS property of congruence.

8). SSS property of congruence.

9). SAS property of congruence.

10). SSS property of congruence.

11). N

12). SSS property of congruence.

Se ha demostrado mediante la aplicación de definiciones y teoremas algebraicos que la expresión algebraica (a + b)³ es igual a a³ + 3 · a² · b + 3 · a · b² + b³.

En esta pregunta debemos demostrar mediante definiciones y teoremas algebraicos la igualdad expresada en el enunciado puesto que los polinomios pueden ser analizadas por medios exclusivamente algebraicos:

En consecuencia, se ha demostrado mediante definiciones y teoremas algebraicos que la expresión algebraica (a + b)³ es igual a a³ + 3 · a² · b + 3 · a · b² + b³.

El enunciado está incompleto y muestra severas deficiencias en la explicación del punto. Una forma correcta y completa sería la siguiente:

Demuestre que (a + b)³ = a³ + 3 · a² · b + 3 · a · b² + b³.

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Step-by-step explanation:

Hey there!

We know that the slope intercept is; y = mx+b.

Where "m" represents the slope. And "b" represents the y-intercept.

Example:

If the question is as; y = 3x +8

Then your slope of the slope intercept form is "3" where as "8" is y-intercept.

So, the variable"m" represents the slope.

Hope it helps...

Step-by-step explanation:

Hey there!

We know that the slope intercept is; y = mx+b.

Where "m" represents the slope. And "b" represents the y-intercept.

Example:

If the question is as; y = 3x +8

Then your slope of the slope intercept form is "3" where as "8" is y-intercept.

So, the variable"m" represents the slope.

Hope it helps...