Suppose A and B are independent events. If P(A)= 0.4 and P(B) = 0.85, what is P(A and B)?

A. 0.17

B. 0.51

C. 0.68

D. 0.34

Answer:

0.9830 = 98.30%

Step-by-step explanation:

Answer:

7x+10

Step-by-step explanation:

2x(3x)+1x(x+10)

6x+1x+10

7x+10

Example:

Carbon-14 has a radioactive half-life of 5,730 years. Use the radioactive decay equation to find the age of a fossil that contains 20% of its original carbon-14.

\(\begin{array}{|l|c|} \cline{1-2}& \\ \text{Substitute the known values into the} & 0.2A_0 = A_0(0.5)^{\frac{t}{5730}}\\\text{equation} & \\ \cline{1-2}& \\\text{Isolate the exponential expression} & 0.2 = (0.5)^{\frac{t}{5730}}\\ & \\ \cline{1-2} & \\\text{Rewrite into log form} & \log_{0.5}(0.2) = \frac{t}{5730}\\ & \\ \cline{1-2}\end{array}\)

\(\begin{array}{|l|c|} \cline{1-2}& \\ \text{Isolate the variable} & 5730\log_{0.5}(0.2) = t\\& \\ \cline{1-2}& \\ \text{Use the }\underline{\text{chan}}\text{g}\underline{\text{e}} \ \underline{\text{of}} \ \underline{\text{base}}\text{ formula to} & 5730\frac{\log(0.2)}{\log(0.5)} = t\\ \text{rewrite the logarithmic expression and solve} & \\ \text{for t} & 13,304.64798\approx t\\ & \\ \cline{1-2}\end{array}\)

The fossil is approximately 13 thousand years old.

Side note: carbon-14 decays into nitrogen-14 and a beta particle.

====================================================

Question: How long will it take $2,000 to double if it is deposited in an account with an interest rate of 5% compounded continuously?

When interest is compounded continuously, the equation \(A = Pe^{rt}\) represents the balance, A, after t years, where r is the rate of   interest   and P is the beginning balance or   principal   .

Twice $2,000 is $4,000. Substitute these variables into the compound interest formula, isolate the exponential expression and solve for t.

\(A = Pe^{rt}\\\\4000 = 2000e^{0.05t}\\\\4000/2000 = e^{0.05t}\\\\2 = e^{0.05t}\\\\\text{Ln}(2) = \text{Ln}(e^{0.05t})\\\\\text{Ln}(2) = 0.05t\\\\\frac{\ln(2)}{0.05} = t\\\\13.8629 \approx t\)

In about   13.86   years, the amount doubles.

x = 20/7

x = 2  6/7

Hi there !

6x - 9 - 2(1 - x) = x + 9

6x - 9 - 2 + 2x = x + 9

6x + 2x - x = 9 + 9 + 2

8x - x = 20

7x = 20

x = 20/7

x = 2  6/7

Good luck !

Answer:

5r = 7.50

Step-by-step explanation:

As, the cost of 1 ruler = r

So, r times 5 ruler will give u the cost of 5 rulers, which is 7.50

So, 5r = 7.50

Answer:

Here is the answer

Step-by-step explanation:

36 = 3x2x3x2

8 = 2x2x2

42 = 7x3x2

Answer:

10.8

Step-by-step explanation:

Answer:

\(\frac{30meters}{second}\)

600meters

Step-by-step explanation:

Use conversion factors that represent 1.  You can cross cancel wods just like numbers.

\(\frac{108km}{1hour}\) · \(\frac{1hour}{60 minutes}\) · \(\frac{1minute}{60seconds}\) ·\(\frac{1000meters}{1 km}\)

\(\frac{108000meters}{3600seconds}\)

\(\frac{30meters}{second}\)

\(\frac{30meters}{second}\) ·\(\frac{20seconds}{1}\)

600 meters

Helping in the name of Jesus.

Answer:

a. 95%

Step-by-step explanation:

We solve this question, using z score formula.

Z score formula = (x - μ)/σ/√n

where x is the raw score

μ is the population mean

σ is the population standard deviation.

n is number of samples

For z1, where x1 = 460, μ = 500, σ = 20, n = 140

z score formula = (460 - 500)/ 20

= -40/20

= -2

We find the probability of the z score using the z score table.

P(x = 460) = P(z = -2)

= 0.02275

For z2, where x2 = 540, μ = 500, σ = 20

z score formula = (540 - 500)/20

= 40/20

= 2

We find the probability of the z score using the z score table.

P(x = 540) = P(z = 2)

= 0.97725

The probability that the cargo containers will weigh between 460 pounds and 540 pounds is calculated as:

= 460 < x < 540

= P(z = 2) - P(z = -2)

= 0.97725 - 0.02275

= 0.9545

Converting to percentage

0.9545 × 100

= 95.45%

Therefore,the percentage of the cargo containers will weigh between 460 pounds and 540 pounds is 95%

The answer is C)

The car travels 63 mph(Miles Per Hours).

252/4 = 63

378/6 = 63

504/8 = 63

630/10 = 63

Hope Helps you

The rate of change of traveling of the car is 63 miles every 1 hour.

A

Distance = 252 miles

Time = 4 hours

= 252 / 4

= 63 miles per hour

B

Distance = 378 miles

Time = 6 hours

= 378 / 6

= 63 miles per hour

C

Distance = 504 miles

Time = 8 hours

=504 / 8

= 63 miles per hour

D

Distance = 630 miles

Time = 10 hours

= 630/10

= 63 miles per hour

Therefore, the rate of change of traveling of the car is 63 miles every 1 hour

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Answer:

2 solutions

Step-by-step explanation:

The absolute value of m makes us break this equation apart into two cases:

4(m) = -20 and 4(-m) = -20

Answer:

49

Step-by-step explanation:

25²-24²

625-576

=49

use calculator lah dehh

Answer: i think hes correct

Step-by-step explanation:

Only so many prints could be made, each sent to one theater at a time.

Thus, option (C) is correct.

Before the blockbuster era, movie distribution was limited by the number of physical film prints that could be made. Each film had a limited number of copies, and these prints had to be physically shipped to individual theaters. This process took time and limited the number of theaters that could screen a movie simultaneously.

As a result, it was harder for pre-blockbuster-era moviegoers to see movies as soon as they were released because the films were not as widely available in theaters right after their release.

This distribution constraint was a significant factor in controlling the release and accessibility of movies in the pre-blockbuster era.

Thus, option (C) is correct.

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The Consumer Price Index for the year 2 be 116.11.

This is calculated by adding together a sampling of product prices from a previous year.

We then add together the current prices of the same products and divide the total of current prices by the old prices, then multiply the result by 100.

Given data

Year 1 = $9

Year 2 = $10.45

Year 2 / Year 1 = $10.45 / $9.00

Year 2 / Year 1= 1.6111

CPI for year 2 = 1.61 x 100

CPI for year 2 = 116.11

Therefore, the Option D is correct.

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Answer: (a) 13 (b) 1

Step-by-step explanation: The absolute value of -6 is 6. That equal 6 plus 7 which is 13. In the second equation, add -6 and 7 first. That is 1 and the absolute value of 1 is 1.

Answer:

A.13 b.-1

Step-by-step explanation:

a 6+7=13

b 6- -7=-1

The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping

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

4x³ - 2x² + 8x - 4

Group the expression in 2's

So, we have

(4x³ - 2x²) + (8x - 4)

Factorize each group

2x²(2x - 1) + 4(2x - 1)

So, we have

(2x² + 4)(2x - 1)

Hence, the factored expression is (2x² + 4)(2x - 1)

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Answer:

Step-by-step explanation:

Given

Find A - B by substitution

The statement which best describes the data given is C) The data can be modeled by a quadratic function.

Given a data,

The numbers of customers that visited a store each hour for several hours after the store opened at 8 am are shown in the table.

It is clear that the number of customers increases to 18 for the first 4 hours and then decreases to 0 after 9 hours.

So this data cannot be modeled by a linear function or an exponential function.

Also since the number of customers arriving is not constant, this cannot be expressed as constant function.

So it is quadratic function.

Hence the correct option is c.

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Answer:

sin of 52 radians = 0.98662759204

Step-by-step explanation:

Answer: 0.98

Step-by-step explanation:

Approximately 1, you shouldn't have to answer 0.988 etc on the test.

Answer:15

Step-by-step explanation: 20 divided by 8=2.5 x 6=15

Let 'x' represent the number of students tickets.

Let 'y' represent the number of adults tickets.

Two equations will be formed from the statements.

We were told that the total number of tickets sold is 9536 tickets.

The total cost of the tickets is $56,878.

Given that tickets are selling for students $5(under 18) and for Adults $11(18+).

Let us now combine the two equations and solve for x and y using the substitution method.

Solving for x and y

Isolate x for x + y = 9536

x = 9536 - y

Substitute x = 9536 - y into equation 2

Simplify

Solve for y

For x = 9536 - y

The solution to the system of equations is,

Hence, the number of tickets sold are

Answer:

The 95% confidence interval is   \(0.6428 < \sigma < 1.0954\)

Step-by-step explanation:

From the question we are told that

   The sample size is  n = 29

    The sample standard deviation is \(s = 0.81\)

  Generally the 95% confidence interval to estimate the true standard deviation  is mathematically represented as  

                      \(\sqrt{\frac{(n- 1)s^2 }{ X^2_( \frac{\alpha }{2 } , n-1)} } < \sigma < \sqrt{\frac{(n- 1)s^2 }{ X^2_(1- \frac{\alpha }{2 } , n-1)} }\)

Generally from the  chi -distribution table  the critical value of \(\frac{\alpha }{2}\) at a degree of freedom of  \(df = 29 - 1 = 28\)  is  

            \(X^2 _{\frac{\alpha }{2} , 28 } =44.46079184\)

Generally from the  chi -distribution table  the critical value of \(1 - \frac{\alpha }{2}\) at a degree of freedom of  \(df = 29 - 1 = 28\)  is  

             \(X^2 _{(1 - \frac{\alpha }{2}) , 28 } = 15.30786055\)

So

                 \(\sqrt{\frac{(29- 1)0.81^2 }{ 44.46079184 } } < \sigma < \sqrt{\frac{(29- 1)0.81^2 }{15.315.307860551 }\)

=>              \(0.6428 < \sigma < 1.0954\)

Answer:

Step-by-step explanation:

47.50 + 4x = 65.90

Solution :

a).

Given :

R = 0.636, \($S_x = 99$\), \($S_y=113, M_x=108, M_y=129$\)

Here R = correlation between the two variables

        \($S_x , S_y$\) =  sample standard deviations of the distance and travel time between the two train stops, respectively.

      \($M_x, M_y$\) = means of the distance and travel between two train stops respectively.

The slope of the regression line is given by :

Regression line, \(b_1\)  \($=R \times \left(\frac{S_y}{S_x}\right)$\)

                            \($=0.636 \times \left(\frac{113}{99}\right)$\)

                            = 0.726

Therefore, the slope of the regression line \(b_1\) is 0.726

The equation of the regression line is given by :

\($\overline {y} = b_0+b_1 \overline x$\)

The regression line also has to pass through the two means. That is, it has to pass through points (108, 129). Substituting these values in the equation of the regression line, we can get the value of the line y-intercept.

The y-intercept of the regression line \($b_0$\) is given by :

\($b_0=M_y-(b_1 \times M_x)$\)

  = 129 - (0.726 x 108)

  = 50.592

Therefore, the equation of the line is :

Travel time = 20.592 + 0.726 x distance

b).\(\text{ The slope of the line predicts that it will require 0.726 minutes}\) for each additional mile travelled.

The intercept of the line, \($b_0$\) = 0.529 can be seen as the time when the distance travelled is zero. It does not make much sense in this context because  it seems we have travelled zero  distance in 50.529 minutes, but we could interpret it as that the wait time after which we start travelling and calculating the distance travelled and the additional time required per mile. Or we could view the intercept value as the time it takes to walk to the train station before we board the train. So this is a fixed quantity that will be added to travel time. It all depends on the interpretation.

c). \($R^2=0.404$\)

This means that the model accounts for around 40.4% variation in the travel time.

In the given similar triangles below, we have to find the measure of Dwrite. Triangle 1, ABC, is similar to Triangle 2, DEF. The two triangles are similar because their corresponding angles are congruent and their sides are proportional.

In order to find the measure of Dwrite, we can use the concept of proportionality. The sides of similar triangles are proportional to each other.

This means that if we know the ratio of the sides of one triangle, we can use that ratio to find the corresponding sides of the other triangle. We can use this property to find the value of Dwrite.

To start, let's write down the ratio of the sides of Triangle 1 and Triangle 2. We can choose any two corresponding sides to do this, but we'll choose AB and DE because they are easiest to measure: AB/DE = 6/8.5We know that the measure of AB is 6, so we can solve for the measure of DE: DE = AB x (DE/AB)DE = 6 x (8.5/6)DE = 8.5Now we know that the measure of DE is 8.5.

We can use this to find the measure of Dwrite. We know that DE and Dwrite are corresponding sides of Triangle 2 and Triangle 1, respectively.

So we can write a proportion using the ratio of DE to Dwrite: DE/Dwrite = 8.5/xWe know that DE is 8.5, so we can substitute that in:8.5/Dwrite = 8.5/Now we can solve for x by cross-multiplying:8.5x = 8.5Dwrite = 1Therefore, the measure of Dwrite is 1.

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using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

Answer:g=0 is not the solution

Step-byd-step explanation:

-1 1/2 is a negative number and 0 is not negative

Answer:

g=0

Step-by-step explanation:

happy to help ya :)

Answer:

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

Step-by-step explanation:

We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams.

The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2.

The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3.

The difference between sample means is Md=-9.4.

\(M_d=M_1-M_2=33.4-42.8=-9.4\)

The estimated standard error of the difference between means is computed using the formula:

\(s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{2.2^2}{26}+\dfrac{4.3^2}{26}}\\\\\\s_{M_d}=\sqrt{0.186+0.711}=\sqrt{0.897}=0.9473\)

The critical t-value for a 99% confidence interval is t=2.678.

The margin of error (MOE) can be calculated as:

\(MOE=t\cdot s_{M_d}=2.678 \cdot 0.9473=2.537\)

Then, the lower and upper bounds of the confidence interval are:

\(LL=M_d-t \cdot s_{M_d} = -9.4-2.537=-11.937\\\\UL=M_d+t \cdot s_{M_d} = -9.4+2.537=-6.863\)

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

In this way, we can calculate the individual duration of each one and the duration time, knowing that the sample means:

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is -11.937 and -6.863.

We have to calculate a 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams. The sample 1 (Fiberglass), of size n1=26 has a mean of 33.4 and a standard deviation of 2.2. The sample 2 (Carbon), of size n2=26 has a mean of 42.8 and a standard deviation of 4.3. The difference between sample means is Md=-9.4.

\(Sm_d= \sqrt{\frac{\sigma^2_1}{n_1} +\frac{\sigma^2_2}{n_2}} = \sqrt{(0.186)+(0.711) }= 0.9473\)

The critical t-value for a 99% confidednce interval is t=2.678. The margin of error (MOE) can be calculated as:

\(MOE=t*8M_d = (2.678)(0.9473)= 2.537\)

Then, the lower and upper bounds of the confidence interval are:

\(LL= M_d-t*SM_d = -9.4-2.537= -11.937\\UL= M_d+t*SM_d= -9.4+2.537= -6.863\)

The 99% confidence interval for the difference between the true average load for the fiberglass beams and that for the carbon beams is (-11.937, -6.863).

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