A research scholar wants to know how many times per hour a certain strand of virus reproduces. The mean is found to be 10.2 reproductions and the population standard deviation is known to be 2.4. If a sample of 907 was used for the study, construct the 85% confidence interval for the true mean number of reproductions per hour for the virus. Round your answers to one decimal place

Answer:

Step-by-step explanation:

in order to simplify this equation we are going to have to subtract 12c from 20c, 22r from 15r, 65p from 75p, and 70e from 50e:

20c - 12c = 8c

15r - 22r = -7r

75p - 65p = 10p

70e - 50e = -20e

Now we are going to put all the answers into the equation again:

8c + (-7r) + 10p + (-20e)

Answer:

Her monthly allowance is $25

Step-by-step explanation:

20% Of 25 is 5

Answer:

Autumn's monthly allowance is $25.

Step-by-step explanation:

5 x 5 = 25

To check: 25 x 0.20 = 5

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Answer:

  correct answer is marked

Step-by-step explanation:

You can work with the letters in the similarity statement, or you can work with the diagram.

The corresponding sides are ...

  AC and BC

  AE and BD

  CE and CD

If you choose a pair on the left of this list, the proportion is written using the corresponding pair on the right of this list. Using the first two lines, we can write ...

  AC/AE = BC/BD . . . . matches the first choice

Answer:

The answer is 9

Step-by-step explanation:

1080 divided by 120 = 9

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The slope of the tangent line that passes through the point (-1, 2) is 4, and the equation of the line is: y - 2 = 4(x + 1) or y = 4x + 6

To find the slope of the tangent line to a circle, we first need to find the equation of the circle.

Given the center and radius, the equation of a circle can be written as:

(x + 5)^2 + (y - 3)^2 = 17

Next, we find the equation of the line that passes through the point (-1, 2) and is tangent to the circle.

We can use the slope-point form of the equation of a line:

y - 2 = m(x + 1)

where m is the slope of the line.

To find the value of m, we need to find the slope of the line that is tangent to the circle at the point (-1, 2).

The slope of a tangent line to a circle at a point is equal to the derivative of the equation of the circle at that point.

Taking the partial derivatives of x and y in the equation of the circle, we get:

2(x + 5)dx + 2(y - 3)dy = 0

Rearranging and solving for the slope:

dy/dx = -(x + 5)/(y - 3)

Evaluating the slope at the point (-1, 2), we get:

dy/dx = -(−1 + 5)/(2 − 3) = 4

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Answer:

GA =34

Y = 61

Step-by-step explanation:

GA= GENERAL ADMISSION =$10

Y= YOUTH =$8

GA+Y= 95

GA=95-Y

10GA+8Y=828

10(95-Y)+8Y=828

950-10Y+8Y=828

-2Y= 122 MULTIPLY BY (-1)

2Y= 122

Y= 61

GA= 34

There were 61 youth tickets sold and 34 general admission tickets

Answer:

C

Step-by-step explanation:

Just because I think that's the one ^^

Answer:

A) 110° and 109°

Step-by-step explanation:

Hope this helps.

The required number of different distances possible is given as 36.

Given that,
In a board game, the distance a player travels is equal to the sum of the numbers shown when two 6-sided dice are tossed.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
1 dice have 6 outcomes
2 dice have 6 outcomes,
Number of possible combination = 6 × 6 = 36

Thus, the required number of different distances possible is given as 36.

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Answer:

∠JKL = 159

∠JKM = 43

∠MKL = 116

Step-by-step explanation:

Step 1: Define a equation for the angles

∠JKL = ∠JKM +∠MKL

Step 2: Substitute the values in for the angles

(10x - 11) = (43) + (8x-20)

Step 3: Solve for x

10x - 11 = 43 + 8x - 20

2x = 34

x = 17

Step 4: Substitute x = 17 back into angle to solve

∠JKL = 10(17) - 11

          =170 - 11

           =159

∠JKM = 43

∠MKL = 8x - 20

          = 8(17) - 20

           = 136 - 20

           =116

Answer:

17=x

JKM =43

MKL =  116

JKL= 159

Step-by-step explanation:

JKM + MKL = JKL

43+ 8x-20 = 10x-11

Combine like terms

23+8x = 10x-11

Subtract 8x from each side

23 +8x-8x = 10x-8x-11

23 = 2x-11

Add 11 to each side

23+11 = 2x-11+11

34 = 2x

Divide by 2

34/2 = x/2

17=x

JKM =43

MKL =  8x-20 = 8*17 -20 = 116

JKL= 10x-11 = 10*17 -11 = 159

Answer:

Balance at the age of 20 will be $1455966.46

Step-by-step explanation:

Formula to calculate the final amount is,

\(A=P(1+\frac{r}{n})^{nt}\)

Where A = Final amount

P = Principal amount or amount invested

A = Final amount

r = Rate of interest

n = Number of compounding in a year

If Jason invested $200 in an account for 4 years with rate of interest 223%.

P = $200

r = 223%

n = 365

t = 4 years

A = \(200(1+\frac{2.23}{365})^{(4\times 365)}\)

A = \(200(1.0061096)^{1460}\)

A = $1455966.46

Therefore, balance amount in Jason's account at the age of 20 will be $1455966.46.

Answer:

16 deliveries

Step-by-step explanation:

238 ≤ 10d + 78

160 ≤ 10d

16 ≤ d

Thus, he needs to make at least 16 deliveries to make at least $238 in one day.  Any less than 16 deliveries will cause him to fall short of his goal and any more than 16 deliveries will cause him to exceed his goal.

The solution to the linear system is c = -6 and d = 3.

To solve the linear system using the elimination strategy, we can eliminate one variable by adding or subtracting the equations. Let's solve the first linear system:

(1) 12c + 28d = 12

(2) -20c + 16d = 168

To eliminate one variable, we can multiply equation (1) by 5 and equation (2) by 3, which will result in opposite coefficients for 'c'. This will allow us to eliminate 'c' when adding the equations together:

(1) 60c + 140d = 60

(2) -60c + 48d = 504

Now, we can add the equations:

(60c + 140d) + (-60c + 48d) = 60 + 504

188d = 564

d = 564/188

d = 3

Substituting the value of 'd' back into equation (1):

12c + 28(3) = 12

12c + 84 = 12

12c = 12 - 84

12c = -72

c = -72/12

c = -6

The solution to the linear system is c = -6 and d = 3.

Now let's analyze the second linear system:

(1) 7x - 3y = 43

(2) 7x - 3y = 13

By comparing the two equations, we can see that they have the same coefficients for both 'x' and 'y', and the constant terms on the right side are different. This means the lines represented by the equations are parallel and will never intersect.

The linear system has no solution.

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Answer:

36

Step-by-step explanation:

Answer:

On a number line, negative five and positive five are the same distance from zero.

Step-by-step explanation:

Answer:

On a number line, negative five and positive five are the same distance from zero.

Step-by-step explanation:

because 5 is to 5 hops to the right and -5 id 5 hops to the left

\(\boxed{y}=\cfrac{1}{2}x-4\\\\ y=-2x+1 \end{cases}\qquad \qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{\stackrel{\boxed{y}}{\cfrac{1}{2}x-4}~~ = ~~-2x+1} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( \cfrac{1}{2}x-4 \right)~~ = ~~2(-2x+1)}\implies x-8=-4x+2\implies 5x-8=2\)

\(5x=10\implies x=\cfrac{10}{5}\implies \blacktriangleright x=2 \blacktriangleleft \\\\\\ \stackrel{\textit{we know that}}{y==\cfrac{1}{2}x-4}\implies y=\cfrac{1}{2}(2)-4\implies \blacktriangleright y = -3 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (2~~,~~-3)~\hfill\)

Answer:

y=8x+8

Step-by-step explanation:

Slope Intercept form: y=mx+b

m=slope

b=y-intercept.

so if you put them together using what we have, you get y=8x+8

Answer:

a) -6 mpg.

b) 2.77 mpg

c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

Step-by-step explanation:

To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Gas mileage A: Mean 36, standard deviation 6, sample of 50:

So

\(\mu_A = 36, s_A = \frac{6}{\sqrt{50}} = 0.8485\)

Gas mileage B: Mean 42, standard deviation 8, sample of 50:

So

\(\mu_B = 42, s_B = \frac{8}{\sqrt{50}} = 1.1314\)

Distribution of the difference:

Mean:

\(\mu = \mu_A - \mu_B = 36 - 42 = -6\)

Standard error:

\(s = \sqrt{s_A^2+s_B^2} = \sqrt{0.8485^2+1.1314^2} = 1.4142\)

A. Find the point estimate.

This is the difference of means, that is, -6 mpg.

B. Find the margin of error

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.95}{2} = 0.025\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.

Now, find the margin of error M as such

\(M = zs = 1.96*1.4142 = 2.77\)

The margin of error is of 2.77 mpg

C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)

The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg

The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg

The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).

Step-by-step explanation:

Let's solve all of them,

A. getting paid $35 for walking dogs, then spending $10 on games

=$35-$10

=$25

B. getting paid $25 for walking dogs, then spending $25 on games

=$25-$25

=$0

C. getting paid $20 for walking dogs, then spending $5 on games

=$20-$5

=$15

D. getting paid $15 for walking dogs, then spending $10 on games

=$15-$10

=$5

Here,

Option B. matches with the above situation.

So,

Option B. is the correct answer.

Answer:

here's the answer to your question

Answer:

for B : he spend 30 minutes jogging and 45 minutes riding his bike

Step-by-step explanation:

75-15=60

60/2=30

jogging (x) =30

30+15=45

riding bike (y) =45

hopefully it help you

Number of boxes: 2262

Number of packages of pencils: 29

Number of Erasers in Each Box: 26

1) Considering that we want to know the greatest number of identical boxes She could pack, then we need to find out the LCM (Least Common Multiple) of 78 and 87 to get the greatest number of identical boxes.

2) Pencils and erasers:

Let's find out the Least Common Multiple of 78 and 87.

Divide by prime numbers.

Repeat it down when it's not divisible.

At the end multiply the prime numbers to the right.

Dividing by prime numbers we'll get the: 3 x 2 x 13 x 29 = 2262 identical boxes for pencils and erasers.

2.2) The number of boxes:

2262

Number of packages of pencils in Each Box: 2262: 78= 29

Number of packages of erasers in Each box: 2262: 87 =26

3) Hence, the answer is:

Number of boxes 2262

Number of packages of pencils in Each Box: 2262 : 78= 29

Number of packages of erasers in Each box: 2262: 87 =26

If you were standing near the ocean, your elevation would be 0 feet above sea level.

Elevation above sea level refers to the height of a location above the sea level. It is typically measured in meters or feet. Elevation is important because it can affect the local climate and weather patterns, as well as the availability of resources such as water.

A location with a high elevation may have a cooler climate and less available water, while a location with a low elevation may have a warmer climate and more available water.

This means that if you are standing near the ocean, you would be at sea level and therefore you would be at 0 feet above sea level.

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Answer: where is the answer choices

Step-by-step explanation:

Answer:

0.6429

Step-by-step explanation:

Let, s = play a sport

c = participate in a club

P(s) = 0.14

P(s n c) = 0.09

probability that a student participates in

a club given that they also play a sport = P(c | s)

P(c | s) = P(c n s) / P(s)

P(c | s) = 0.09 / 0.14

P(c | s) = 0.64285

= 0.6429

The required proportion for the given case is 36/100 = x/150.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

The given statement is as below,

36% of 150

Suppose the required number is x.

Then, the equivalent form of the given statement is,

36% of 150 = x

=> 36% × 150 = x

=> 36/100 × 150 = x

=> 36/100 = x/150

Hence, the required proportion to to be used to solve the problem is 36/100 = x/150.

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Answer:

z(w-x) =y

Step-by-step explanation:

w=x + y/z

Subtract x from each side

w-x=x-x + y/z

w-x = y/z

Multiply each side by z

z(w-x) = y/z *z

z(w-x) =y

Step-by-step explanation:

y = -1/2 X + 1/4

comparing with y = mx+c

m = -1/2 and m is slop

henve slope = -1/2

Answer:

F(2)=4*-2+7=-1

F(-3)=9*-2+7=-11

F(0)=0*-2+7=7

Step-by-step explanation:

Answer:

Therefore, the correct statements are A, B, and E.

Explanation:

Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.

To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀

.

- The component form of −4⇀

is obtained by multiplying each component of ⇀

by –4. Therefore, −4⇀

= ⟨–8, –12⟩. This means that statement A is true.

- The magnitude of −4⇀

is obtained by multiplying the magnitude of ⇀

by 4. The magnitude of ⇀

is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀

is 4√13. This means that statement B is true.

- The direction of −4⇀

is opposite to the direction of ⇀

because the scalar –4 is negative. This means that statement C is false.

- The vector −4⇀

is in the third quadrant because its components are both negative. This means that statement D is false.

- The direction of −4⇀

is 180° greater than the inverse tangent of its components because it is opposite to ⇀

. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀

is 180° + tan^(-1)(3/2). This means that statement E is true.

Therefore, the correct statements are A, B, and E.

Answer:

B it originally cost 12000

Step-by-step explanation:

the depriciation factor is  0.75^t and the original value was 12000

Answer:

(2) The motorcycle cost $12,000 when purchased.

Step-by-step explanation:

\(V(t)=12000(0.75)^t\)

\(V(0)=12000(0.75)^0=12000\)

\(V(1)=12000(0.75)^1=9000\)

\(V(2)=12000(0.75)^2=6750\)

etc.

⇒ Initial cost = $12,000

⇒ The motorcycle's value is decreasing by 25% each year.