10,000 individuals are divided evenly into two groups. The treatment group is given a vaccine and the control group is given a placebo. 95 of the 5,000 individuals in the treatment group developed a disease. 125 of the 5,000 individuals in the control group developed a particular disease. A research team wants to determine whether the vaccine is effective in decreasing the incidence of disease.


Required:

Does sufficient evidence exist to conclude that the proportion of developing a disease in individuals given the vaccine is less than that of individuals given a placebo?

Accumulate $48,000 by July 1, 2032, Carla Vista must invest the initial amount of $19,000 at an annual interest rate of approximately 5.25%.

To determine the exact annual rate of interest, we can use the concept of compound interest and the formula for calculating the future value of an investment. In this case, we have the present value (PV) of $19,000, the future value (FV) of $48,000, and the time period of 10 years.

Using a financial calculator or spreadsheet software, we can input these values and solve for the annual interest rate (i). The formula to calculate the future value is:

FV = PV * (1 + i)^n

Where:

FV = Future value

PV = Present value

i = Annual interest rate

n = Number of years

Rearranging the formula to solve for i:

i = (FV / PV)^(1/n) - 1

Plugging in the given values, we have:

i = ($48,000 / $19,000)^(1/10) - 1

Evaluating this expression using a financial calculator or spreadsheet, we find the exact annual interest rate required for Carla Vista to accumulate $48,000 by July 1, 2032.

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√27 is greater than √95/2. So the sign 'Greater than' will be used to satisfy this statement: √27  > √95/2

In the given question, we have to put the appropriate sign of inequality so that statement becomes True. First, we will have to calculate the roots of both √27 and √95/2.

Calculating,  => √27  =  5.19

and,  => √95/2 = 4.87

Comparing the square roots of both √27 and √95/2 we can clearly see that √27 is greater than √95/2. So, we get √27 > √95/2                    

Hence, the sign used to make the statement true will be of 'Greater than' such that √27 > √95/2

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Answer:

\(s(u(3)) = 84\)

Step-by-step explanation:

\(u(t) = 8t - 14 \\ u(3) = 8(3) - 14 \\ u(3) = 24 - 14 \\ u(3) = 10 \\ \\ s(u(3)) = {(u(3))}^{2} - 16 \\ s(u(3)) = {(10)}^{2} - 16 \\ = 100 - 16 \\ = 84\)

Answer:

It’s c. 78cm

Step-by-step explanation:

This might be hella late

Answer:

C-78

Step-by-step explanation:

Answer:

289m2

Step-by-step explanation:

The mathematical formula  for the area of the triangle is:

base x height / 2

a. The PDF (probability density function) of an exponential random variable X with expected value λ is given by:

f(x) = λ * e^(-λ*x), for x > 0

Therefore, for an exponential random variable with an expected value of 0.5, the PDF would be:

f(x) = 0.5 * e^(-0.5*x), for x > 0

b. The graph of the PDF of an exponential random variable with an expected value of 0.5 is a decreasing curve that starts at 0 and approaches the x-axis, as x increases.

c. The CDF (cumulative distribution function) of an exponential random variable X with expected value λ is given by:

F(x) = 1 - e^(-λ*x), for x > 0

Therefore, for an exponential random variable with an expected value of 0.5, the CDF would be:

F(x) = 1 - e^(-0.5*x), for x > 0

d. The graph of the CDF of an exponential random variable with an expected value of 0.5 is an increasing curve that starts at 0 and approaches 1, as x increases.

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The slope is -40, and the Y intercept is 83. The equation would be Y= -40x + 83.

You can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

To calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation with 10% interest compounded monthly, we can break down the problem into two parts:

Calculate the accumulated balance after 15 years of regular deposits:

We can use the formula for the future value of a regular deposit:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV is the future value (accumulated balance)

P is the regular deposit amount

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

P = $125.00 (regular deposit amount)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 15 (number of years)

Plugging the values into the formula:

FV = $125 * ((1 + 0.10/12)^(12*15) - 1) / (0.10/12)

Calculating the expression on the right-hand side gives us the accumulated balance after 15 years of regular deposits.

Calculate the balance after an additional 5 years of accumulation:

To calculate the balance after 5 years of accumulation with monthly compounding, we can use the compound interest formula:

FV = P * (1 + r/n)^(nt)

where:

FV is the future value (balance after accumulation)

P is the initial principal (accumulated balance after 15 years)

r is the interest rate per period (10% per annum in this case)

n is the number of compounding periods per year (12 for monthly compounding)

t is the number of years

Given the accumulated balance after 15 years from the previous calculation, we can plug in the values:

P = (accumulated balance after 15 years)

r = 10% = 0.10 (interest rate per period)

n = 12 (number of compounding periods per year)

t = 5 (number of years)

Plugging the values into the formula, we can calculate the balance after an additional 5 years of accumulation.

By following these steps, you can calculate the balance in Connor's account after 15 years of regular deposits and an additional 5 years of accumulation.

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Answer:

6.2

Step-by-step explanation:

6.231 to the 10th

Answer:

He will spend about $6.23

Step-by-step explanation:

You just multiply 9.3 and .67 and get 6.231 rounded to 6.23

Answer:

27

Step-by-step explanation:

0.45 divide by 60 and you get 27

Answer:

27

Step-by-step explanation:

x/60 = 45/100

if you write it out, cross multiply then solve for x

 Answer: functions graphically because they were, after all, just sets of points in the plane. Then in ... However, of these two answers, only x = −2 fits in the domain x < 1 for this piece. This means the only x-intercept for the x < 1 region of the x-axis is (−2,0). ... use the formula f(x) = x − 3, so the point on the graph (1,f(1)) is (1,−2).

\(5 \frac{1}{4} + 1 \frac{3}{8} \)

Lets solve it

\(5 \frac{1}{4} + 1 \frac{3}{8} \)

\( \frac{21}{4} + \frac{11}{8} \)

Taking the LCM of both denominator which is 8

\( \frac{42 + 11}{8} \)

\( \frac{53}{8} \)

Hey ! there

Answer:

Step-by-step explanation:

In this question we are given with two whole fraction . And we are asked to simplify them by adding .

Solution : -

Step 1 : Converting the fractions into improper fraction :

\(\dashrightarrow \: \qquad \: \dfrac{21}{4} + \dfrac{11}{8} \)

Step 2 : We know that L.C.M of 4 and 8 is 8. So,

\(\dashrightarrow \: \qquad \: \dfrac{42 + 11}{8} \)

Step 3 : Adding 42and 11 :

\(\dashrightarrow \: \qquad \: \dfrac{53}{8} \)

Step 4 : Converting it in form of whole fraction :

\(\dashrightarrow \: \qquad \blue{\underline{\boxed{\frak{ \:6 \dfrac{5}{8} }}}} \quad\bigstar\)

The value of tan(θ) is approximately 0.88.

To find the value of tan(θ) when the distance from the point (1,0) to the point (0.75, 0.66) along the circumference of the unit circle, we'll first find the angle θ using the given points.

1. Since we're given points on the unit circle, we know their coordinates represent the cosine and sine values, i.e., (cos(θ), sin(θ)) = (0.75, 0.66).

2. Now, we need to find the value of tan(θ), which can be calculated using the formula: tan(θ) = sin(θ) / cos(θ).

3. Plugging in the values we have: tan(θ) = 0.66 / 0.75.

4. Performing the calculation, we get: tan(θ) ≈ 0.88.

5. Therefore, the value of tan(θ) when the distance from the point (1,0) to the point (0.75, 0.66) along the circumference of the unit circle is approximately 0.88.

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Answer:

Reduce by cancelling common factors.

The simplified expression of this problem is -2/3

\(-\frac{2}{3}(-0.6)\)

Answer:

-2/3

Step-by-step explanation:

Answer:

A. 85%

   135%

B.15%

C.24 gallons

Step-by-step explanation:

A.

B.80-12=68.00    80X15%=12.00

C.6x4=24

Answer:

The answer for this question is :s = 12.806248474866 cm

Step-by-step explanation:

All possible calculations are as :

height h = 10 cm

slant height s = 12.806248474866 cm

side length a = 16 cm

perimeter of base P = 64 cm

lateral edge length e = 15.099668870541 cm

1/2 side length r = 8 cm

volume V = 853.33333333333 cm3

lateral surface area L = 409.7999511957 cm2

base surface area B = 256 cm2

total surface area A = 665.7999511957 cm2

side face slope m = 1.25

side face angle θ = 51.34019174591 °

Answer:

It’s option A, Choi’s option A

Step-by-step explanation:

a. The probability of drawing a red ball from Box 1 is 30%.

b. If a red ball is drawn from Box 1, the probability of drawing another red ball from Box 2 on the second round is 60%.

c. If the first draw from Box 1 was black, the conditional probability of drawing a red ball from Box 3 on the second draw is 80%.

d. The probability of drawing two red balls at both draws, without any prior information, is 46%.

e. The probability of drawing a red ball at the first draw and a black ball at the second draw, without any prior information, is 21%.

a. The probability of drawing a red ball from Box 1 can be calculated by dividing the number of red balls in Box 1 by the total number of balls in Box 1. Therefore, the probability is 3/(3+7) = 3/10 = 0.3 or 30%.

b. Since a red ball was drawn from Box 1, we only consider the balls in Box 2. The probability of drawing a red ball from Box 2 is 6/(6+4) = 6/10 = 0.6 or 60%. Therefore, the probability of drawing another red ball when the first ball drawn from Box 1 is red is 60%.

c. If the first draw from Box 1 was black, we only consider the balls in Box 3. The probability of drawing a red ball from Box 3 is 8/(8+2) = 8/10 = 0.8 or 80%. Therefore, the conditional probability of drawing a red ball from Box 3 when the first ball drawn from Box 1 was black is 80%.

d. Before any draws, the probability of drawing two red balls at both draws can be calculated by multiplying the probabilities of drawing a red ball from Box 1 and a red ball from Box 2. Therefore, the probability is 0.3 * 0.6 = 0.18 or 18%. However, since there are two possible scenarios (drawing red balls from Box 1 and Box 2, or drawing red balls from Box 2 and Box 1), we double the probability to obtain 36%. Adding the individual probabilities of each scenario gives a total probability of 36% + 10% = 46%.

e. Before any draws, the probability of drawing a red ball at the first draw and a black ball at the second draw can be calculated by multiplying the probability of drawing a red ball from Box 1 and the probability of drawing a black ball from Box 2 or Box 3. The probability of drawing a red ball from Box 1 is 0.3, and the probability of drawing a black ball from Box 2 or Box 3 is (7/10) + (2/10) = 0.9. Therefore, the probability is 0.3 * 0.9 = 0.27 or 27%. However, since there are two possible scenarios (drawing a red ball from Box 1 and a black ball from Box 2 or drawing a red ball from Box 1 and a black ball from Box 3), we double the probability to obtain 54%. Adding the individual probabilities of each scenario gives a total probability of 54% + 10% = 64%.

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Answer:

33

Step-by-step explanation:

Answer:

m<ADX = 38

m<DAB = 104

m<AYC = 104

Step-by-step explanation:

1. Diagonals of a rhombus bisect each other at right angles, so angles AXD, AXB, CXD, CXB are all right angles and AX and CX, DX and BX are congruent.

<AXD ≅ <CXD ≅ <AXB ≅ CXB

AX ≅ CX

DX ≅ BX

By SAS, triangles AXD, CXD, AXB, and CXB are congruent. Since corresponding parts of congruent triangles are congruent, <ADX ≅ <CDX, m<ADX = m<CDX, m<ADX = 38.

2. Consecutive angles of a rhombus are supplementary. Since <DAB and <ADC are corresponding angles in rhombus ABCD, m<DAB + m<ADC = 180, m<DAB + 76 = 180, m<DAB = 104.

3. Diagonals of a rhombus bisect the angles, so in rhombus ABCD, AC bisects <DAB and <BCD. By definition of angle bisectors, m<XAD = m<XAB.

m<XAD = m<XAB

m<XAD + m<XAB = m<DAB

2m<XAD = m<DAB

2m<XAD = 104

m<XAD = 52

Since interior angles of a triangle add up to 180, m<XAY + m<AYC + m<YCA = 180.

m<XAY + m<AYC + m<YCA = 180

52 + m<AYC + 24 = 180

m<AYC = 104

Answer:

Jacksons Tip: $2.31

Total: $17.71

It is stated that the population mean is 3.37, which represents the average GPA of all students at the university in that year.

In the given scenarios:

American households' Halloween spending:

Sample Mean: $58 per household

Claimed Population Mean: $52

In this case, the sample mean represents the average spending per household obtained from the survey conducted in 2008 on 1,500 households. This sample mean is $58. It is a representative value calculated from the data collected in the sample of households.

On the other hand, the claimed population mean refers to the average spending per household in the entire population of American households. In this case, it is claimed or known that the population mean is $52, which represents the average Halloween spending in 2007.

The researchers conducted the survey in 2008 to determine if there was any change in Halloween spending compared to the claimed population mean of $52.

Average GPA of students at a private university:

Sample Mean: 3.59

Claimed Population Mean: 3.37

Here, the sample mean is the average GPA calculated from the data collected in the survey on a sample of 203 students from the university in the spring semester of 2012. The sample mean is 3.59, representing the average GPA of the sampled students.

The claimed population mean, on the other hand, refers to the average GPA of all students at the private university in 2001. It is stated that the population mean is 3.37, which represents the average GPA of all students at the university in that year.

The survey conducted in 2012 aimed to determine if there was any change in the average GPA compared to the claimed population mean of 3.37 in 2001.

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Answer:

C

Step-by-step explanation:

since the dilatation is centred at the origin then multiply the coordinates of the point by scale factor of \(\frac{1}{3}\)

(- 3, 6 ) → (\(\frac{1}{3}\) (- 3), \(\frac{1}{3}\) (6) ) → (- 1, 2 )

Using the z table, the probability that a standard normal random variable will be between 0.3 and 3.2 is 0.3814.

In the given question,

We have to find that the probability that a standard normal random variable will be between 0.3 and 3.2 .

We firstly learn about a standard normal random variable which is expressed with a mean and standard deviation.

Since we have to find the probability that a standard normal random variable will be between 0.3 and 3.2 .

So The probability should be

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

From the standard value of z

P(0.3<z<3.2)=0.9993−0.6179

Simplifying

P(0.3<z<3.2)=0.3814

Hence, the probability that a standard normal random variable will be between 0.3 and 3.2 is 0.3814.

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Answer:

see image

Step-by-step explanation:

You are multiplying x² - 4x + 4 and 6x + 3.

This is set up like:

6x + 3(x² - 4x + 4)

To solve this, we want to multiply each term that is outside of the parentheses with each term that is inside of the parentheses.

Let's start with 6x.

6x • x² = 6x³

6x • -4x = -24x²

6x • 4 = 24x

These numbers will be in the first blank row.

Now, let's move onto 3.

3 • x² = 3x²

3 • -4x = -12x

3 • 4 = 12

These numbers will be in the second blank row.

Now let's write all these numbers together.

6x³ - 24x² + 24x + 3x² - 12x + 12

Combine like terms, pay attention to the exponent.

6x³ - 21x² + 12x + 12

Refer to the completed table below.

Hope this helps!

the probability P(X<-2), we use the cumulative distribution function F(x) = 0 for x < -2. We plug in -2 for x in the function to get F(-2) = 0.

a. P(X<1.8) = .25(1.8) + .5 = .95

b. P(X>-1.5) = .25(-1.5) + .5 = .375

c. P(X<-2) = 0

d. P(-1.5<X<2) = .25(2) + .5 - (.25(-1.5) + .5) = .875

a. For the probability P(X<1.8), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in 1.8 for x in the function to get F(1.8) = 0.25(1.8) + 0.5 = 0.95. Therefore, P(X<1.8) = 0.95.

b. For the probability P(X>-1.5), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in -1.5 for x in the function to get F(-1.5) = 0.25(-1.5) + 0.5 = 0.375. Therefore, P(X>-1.5) = 0.375.

c. For the probability P(X<-2), we use the cumulative distribution function F(x) = 0 for x < -2. We plug in -2 for x in the function to get F(-2) = 0. Therefore, P(X<-2) = 0.

d. For the probability P(-1.5<X<2), we use the cumulative distribution function F(x) = 0.25x + 0.5 for -2 <= x < 2. We plug in -1.5 and 2 for x in the function to get F(-1.5) = 0.25(-1.5) + 0.5 = 0.375 and F(2) = 0.25(2) + 0.5 = 0.95. Therefore, P(-1.5<X<2) = 0.95 - 0.375 = 0.875.

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Answer:

Explanation:

Here, we want to find the derivative of the given function

To do this, we are going to use the product rule

Mathematically, we have the product rule as follows:

where:

We proceed as follows to find the unit derivatives:

We put together the final answer as follows:

According to unitary method, the total number of fruits in the basket is (8/7) times the difference between the total number of fruits and 5.

To find out the total number of fruits in the basket, we need to add up the number of apples, bananas, and oranges. So, the equation we can use is:

total fruits = number of apples + number of bananas + number of oranges

total fruits = 5 + (5/8)x + (1/4)x

Notice that we used "x" to represent the total number of fruits. Now we can simplify the equation by finding a common denominator for the fractions:

total fruits = 5 + (5/8)x + (2/8)x

total fruits = 5 + (7/8)x

So, we have an equation for the total number of fruits in the basket in terms of "x". To solve for "x", we can subtract 5 from both sides of the equation:

(7/8)x = total fruits - 5

And then, we can multiply both sides by 8/7 to isolate "x":

x = (8/7)(total fruits - 5)

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Complete Question:

Mike made a fruit basket. Of a total fruit, 5 were apples, 5/8 were bananas and 1/4 were oranges. How many pieces of fruit does mike have in his basket.

The event that had the most improved attendance is the Chorus Performance. The amount of change in the number of tickets sold is 20.

There are three different events whose ticket sales have been provided in the table:

Spring Play, Chorus Performance, and Band Concert.

The table shows the number of tickets sold on opening night and closing night of each event along with the amount of change. The students want to find out which event had the most improved attendance.

Based on the data given in the table, the event that had the most improved attendance is the Chorus Performance. The reason is that it has the highest amount of change in the number of tickets sold from the opening night to the closing night.

The amount of change in the number of tickets sold for the Chorus Performance is 20. On the opening night, the number of tickets sold was 40 while on the closing night, the number of tickets sold was 60.

Therefore, we can say that the attendance for Chorus Performance has improved the most.

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Complete Question : Coudnt find

The event which had the most improved attendance given the ticket sales would be Spring Play with 30 more tickets sold.

The amount of change, which indicates how much the attendance improved, can be calculated by subtracting the Opening Night Ticket Sales from the Closing Night Ticket Sales for each event.

For the Spring Play, the amount of change is:

= 230 - 200

= 30

For the Chorus Performance, the amount of change is:

= 60 - 40

= 20

For the Band Concert, the amount of change is:

= 110 - 100

= 10

Therefore, the event that had the most improved attendance was the Spring Play with an increase of 30 tickets sold.

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The question is:

The students want to know which event had the most improved attendance. Give your answer as one of the three events.