In order to test a new drug for adverse reactions, the drug was administered to 1,000 tests subjects with the following results: 60 subjects reported that their only adverse reaction was a loss of appetite, 90 subjects reported that their only adverse reaction was a loss of sleep, and 80 subjects reported no adverse reactions at all. If this drug is released for general use, what is the probability that a person using the drug will Suffer a loss of appetite

The equation of the parabola having vertex at (1,4) and passing through the point (3,8) is y = (x - 1)² + 4 .

There are different methods to find the equation of a parabola,

We use the standard form of the equation of a parabola:

which is : y = a(x - h)² + k;

Where (h, k) = vertex and a = constant which determines shape and orientation of parabola.

we know that, vertex of the parabola is (1, 4),

So, we substitute h = 1 and k = 4 in the equation above:

we get,

⇒ y = a(x - 1)² + 4,

Now, To determine the value of a,

We know that parabola passes through point (3, 8).

So, we substitute x = 3 and y = 8 in the equation above,

We get,

⇒ 8 = a(3 - 1)² + 4,

⇒ 8 = 4a + 4

⇒ 4a = 4

⇒ a = 1

Substituting this value of "a" in equation for parabola,

We get,

⇒ y = (x - 1)² + 4,

Therefore, the equation of the parabola y = (x - 1)² + 4.

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The given question is incomplete, the complete question is

Find equation of parabola with the vertex at (1,4) and passes through the point (3,8).

Answer:

16.167

Step-by-step explanation:

17×0.049= 0.833

17-0.833= 16.167

Answer:

16.167

Step-by-step explanation:

percentage decreased by 4.9% (percent) of its value = 16.167

hope this helps! :)

Based on the given information and calculations, the decision regarding the null hypothesis is to reject it.

To determine whether the null hypothesis H0: π ≤ 0.70 can be rejected based on the sample of 100 observations with a sample proportion of p = 0.75, we can perform a one-sample proportion test.

First, let's define the significance level α = 0.05.

The decision rule for a one-sample proportion test is as follows:

If the test statistic falls in the rejection region, reject the null hypothesis.

If the test statistic does not fall in the rejection region, fail to reject the null hypothesis.

To determine the rejection region, we need to calculate the critical value.

The critical value corresponds to the value beyond which we reject the null hypothesis. Since H1: π > 0.70, we are conducting a right-tailed test.

Using a significance level of α = 0.05 and the normal distribution approximation for large sample sizes, we can calculate the critical value as:

Z_critical = Zα

where Zα is the Z-value corresponding to the upper α (0.05) percentile of the standard normal distribution.

Now, let's calculate the critical value using a standard normal distribution table or a statistical software. Zα = 1.645 (rounded to two decimal places).

Next, we can calculate the test statistic, which is the standard score for the observed sample proportion.

Z_test = (p - π) / sqrt(π(1 - π) / n)

where p is the sample proportion, π is the hypothesized population proportion, and n is the sample size.

Plugging in the values, we get:

Z_test = (0.75 - 0.70) / sqrt(0.70(1 - 0.70) / 100)

Finally, we compare the test statistic Z_test with the critical value Z_critical to make a decision.

If Z_test > Z_critical, we reject the null hypothesis.

If Z_test ≤ Z_critical, we fail to reject the null hypothesis.

Based on the calculated test statistic and the critical value, we can make a decision regarding the null hypothesis.

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Answer:

14 cm

Step-by-step explanation:

The maximum area of a rectangle (actually square) with a perimeter of 14 can have is 12.25 cm².  So the smallest perimeter a rectangle of 12 cm² i just a little below 14 cm, namely 4sqrt(12) = 13.86 cm.

Answer:

Hey there!

Your answer is c)

Answer:

2√5

Step-by-step explanation:

The triangle that's shown on the page is a special isosceles right triangle with angle measures of 45° - 45° - 90°

Since one of the side length that sees 45° angle measure is 2√5 the other also has to be equal to this value so the answer is 2√5

Answer:

3 = 0.25 + 0.5d

Step-by-step explanation:

Given that:

Amount charged per hour = $2

Time left before inserting $d = 15 minutes

Total time after inserting $d = 3 hours

Total time of 3 hours = time left by previous driver + hours purchased with $d

$2 = 1 hour

$d = x

2x = d

x = d/2 ; 0.5d

Since 15 minutes is left before inserting $d

15 minutes to hour ; 15/60 = 0.25

Total time of 3 hours = time left by previous driver + hours purchased with $

3 = 0.25 + 0.5d

Answer:

I think this is right 5 is x=30

Step-by-step explanation:

4 is a because 2x=6 can simple to x=3

and 5 is x=30

The number of years that it will take for the Valence of the account to be $6500 = 6.9 years

Annual simple interest is defined as the amount of money that is being paid to an individual who invested a specific amount of money for a period of time.

The principal amount = $4000

The rate for earnings= 9%

The simple interest= $6500 - 4000 = 2500

Time = X

Using the formula:

Simple interest = P ×T×R/100

Make T the subject of formula;

T = Simple interest × 100/ P × R

T = 2500 × 100/ 4000× 9

T = 250000/36000

T = 6.9 years

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Answer:

False.

Cones have a single circular base, while polyhedrons (such as prisms or pyramids) can have multiple bases.

Answer:

true

Step-by-step explanation:

Answer:

x=-2, x=5

Step-by-step explanation:

it just is

Answer:

y=x-2

Step-by-step explanation:

the line is linear with a slope of 1/1

the y int is -2

plug into y=mx+b

y=x-2

Cindy will need 19.5 cups of water to make lemonade with 13 lemons.

To find out how many cups of water Cindy will need, you can use the following formula:

cups of water = (lemons ÷ 2) × 3

Plug in the number of lemons that Cindy is using:

cups of water = (13 ÷ 2) × 3

Simplify the equation:

cups of water = 6.5 × 3

Multiply:

cups of water = 19.5

Therefore, Cindy will need 19.5 cups of water to make lemonade with 13 lemons.

Here is the answer formatted with HTML:

Cindy will need 19.5 cups of water to make lemonade with 13 lemons.

To find out how many cups of water Cindy will need, you can use the following formula:

cups of water = (lemons ÷ 2) × 3

Plug in the number of lemons that Cindy is using:

cups of water = (13 ÷ 2) × 3

Simplify the equation:

cups of water = 6.5 × 3

Multiply:

cups of water = 19.5

Therefore, Cindy will need 19.5 cups of water to make lemonade with 13 lemons.

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Answer:

Step-by-step explanation:

hi

Answer:

15

Step-by-step explanation:

you have to take 98 away from 113.

Answer:

X= 15

Step-by-step explanation:

The x-intercept is (9, 0) and the y-intercept is (0, -3).

To find the x-intercept, we substitute y = 0 into the equation x - 3y = 9:

x - 3(0) = 9

x = 9

Therefore, the x-intercept is (9, 0).

To find the y-intercept, we substitute x = 0 into the equation x - 3y = 9:

0 - 3y = 9

-3y = 9

y = -3

Hence, the y-intercept is (0, -3).

The x-intercept is (9, 0) and the y-intercept is (0, -3) for the line represented by the equation x - 3y = 9.

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We want to find the value of a sum, given that we need to remove some values of that given sum.

We will see that the value of the sum is  6.471

--------------------

We start with the sum:

S = 1 + 2 + 3 + ... + 150

And we want to remove all the multiples of 3 and 7.

To do that, we need to find the values of k and c such that

3*k = 150

k = 150/3 = 50

Then we have 50 multiples of 3 in that sum that must be removed.

Now we can do the same for the multiples of 7:

7*c = 150

c = 150/7 = 21.4

Rounding to the next whole number we get 21, meaning that there are 21 multiples of 7 in that sum (where the multiples of 7 and 3 together are counted twice, so we need to add them again)

Then the sum will be:

S = 1 + ... + 150 - 3*(1 + ... + 50) - 7*(1 + ... + 21) + 7*(3 + 6 + 9 + 12 + 15 + 18 + 21)

Now we just need to perform that sum, we will get:

S = 11,325 - 3*1275 - 7*231 + 588 = 6,471

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DOE is a statistical tool for analyzing reliability issues, while productivity is a measure of efficiency. Designs of experiments (DOE) is a statistical technique used in Six Sigma to collect, analyze, and interpret data.

It is a structured and organized method for determining whether there is a statistical correlation between two variables. DOE helps in identifying potential reliability problems and weaknesses in a product or process by systematically varying the factors and observing their impact on the output.

Productivity is a measure that broadly defines the efficiency of a process or system. It is calculated by dividing the output by the input. On the other hand, the quality-productivity ratio refers to the relationship between the quality and productivity of a product or process. It can be represented by the ratio of quality cost divided by production cost or the ratio of yield divided by total planned units.

In summary, DOE is a statistical tool for analyzing reliability issues, while productivity is a measure of efficiency. The quality-productivity ratio assesses the relationship between quality and productivity by considering factors such as quality cost, production cost, and yield.

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Answer:

Step-by-step explanation:

Change from rectangular to spherical coordinates: In spherical coordinates, (0, 3, -3) is (3, π/2, 5π/4) and In spherical coordinates, (-6, 6, 6√2) is (√108, π/4, π/2).

In spherical coordinates, a point in three-dimensional space is represented by three coordinates: ρ (rho), θ (theta), and φ (phi).

For part (a), we can use the following formulas to convert from rectangular to spherical coordinates:

ρ = √(x^2 + y^2 + z^2)

θ = arctan(y/x)

φ = arccos(z/ρ)

Plugging in the values (0, 3, -3), we get:

ρ = √(0^2 + 3^2 + (-3)^2) = 3

θ = arctan(3/0) = π/2 (since x = 0 and y > 0)

φ = arccos((-3)/3) = 5π/4 (since z < 0)

Therefore, in spherical coordinates, (0, 3, -3) is (3, π/2, 5π/4).

For part (b), we can use the same formulas to convert from rectangular to spherical coordinates:

ρ = √(x^2 + y^2 + z^2)

θ = arctan(y/x)

φ = arccos(z/ρ)

Plugging in the values (-6, 6, 6√2), we get:

ρ = √((-6)^2 + 6^2 + (6√2)^2) = √108

θ = arctan(6/(-6)) = π/4 (since x < 0 and y > 0)

φ = arccos((6√2)/√108) = π/2

Therefore, in spherical coordinates, (-6, 6, 6√2) is (√108, π/4, π/2).

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C) f is decreasing for x<0 because f′(x)<0 for x<0. , we can conclude that the function f is decreasing for x<0 because f′(x)<0 for x<0.

The derivative of f is f′(x)=x2−a2=(x−a)(x+a).

This implies that f′(x)<0 when x<−a or x>a. From the derivative, we can deduce that f is decreasing for x<0 because f′(x)<0 for x<0.

The derivative of the function f is f′(x)=x2−a2=(x−a)(x+a), where a is a positive constant. This means that the derivative is negative when x<−a or x>a. We can use this information to determine the behavior of the function. Since the derivative is negative when x is less than zero, we can conclude that the function f is decreasing for x<0 because f′(x)<0 for x<0.

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Answer:

I think 15 or 25

Step-by-step explanation:

If you divide 75 by 5 then you get 15. So if you plant 5 seeds per pot then you will need 15 pots to plant all of the seeds.

Also,

If you divided 75 by 3 it =25

An expression is defined as a set of numbers, variables, and mathematical operations. The statements that are true are 1, 3, and 5.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

For the given expression 4x + 9 - y(6x + 7), the following things are can be written,

Thus, the statements that are true are:

Hence, the statements that are true are 1, 3, and 5.

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Answer:

it should be 5.5

Step-by-step explanation:

cross multiply and solve as an equation

The p-value is 0.01, which means that it is very rare to observe a test statistic that is equal to or more extreme than the one that was actually observed. SO the option a is correct.

In the given question, in a hypothesis test for population proportion, we calculated the p-value is 0.01 for the test statistic, we have to find which statement of the p-value is correct.

The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

If the null hypothesis is correct, the p-value is the likelihood that a test statistic will be equal to or more extreme than the one that was actually observed. Given that the null hypothesis is correct in this situation, the p-value of 0.01 indicates that it is extremely unusual to see a test statistic as dramatic as the one that was actually seen. This shows that the alternative hypothesis is more likely to be correct and that the null hypothesis is probably not true.

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Answer: 1 tablespoon

Step-by-step explanation:

The gift wrap needed by Damarcus = total surface area of a rectangular box = 1,048 in.².

Total surface area (TSA) = 2(wl+hl+hw), where:

The amount of gift wrap needed to cover the whole box = total surface area of the rectangular box

l = 20 in.

w = 8 in.

h = 13 in.

Plug in the values into the formula for total surface area of a rectangular box:

TSA = 2(8×20 + 13×20 + 13×8)

TSA = 1,048 in.²

Therefore, the gift wrap needed by Damarcus = total surface area of a rectangular box = 1,048 in.².

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Answer:

B

Step-by-step explanation:

half × base × height

height × length

Answer: B

Step-by-step explanation:

Triangle)

25 - 7 = 18

\(A=\frac{1}{2}(b)(h)\\A=\frac{1}{2}(18)(17)\\A=153cm^2\)

Rectangle)

\(A=b(h)\\A=7(17) = 119cm^2\)

Total)

\(153+119=272 cm^2\)