The time it takes Susan to drive to work each day is normally distributed with a mean of 42 minutes and a standard deviation of 4 minutes.



Approximately what percent of workdays does it take Susan between 38 and 46 minutes to drive to work?




50%



68%



95%



99. 7%

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\( {3}^{ \sqrt{6} } \times {3}^{ \sqrt{4} } = \)

\( {3}^{ \sqrt{6} } \times {3}^{2} = \)

\( {3}^{ \sqrt{6} + 2 } = {3}^{2 + \sqrt{6} } \)

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Among the given options, the only variable that is a discrete random variable is a) the number of patients in a hospital.

a. the number of patients in a hospital

A discrete random variable is a variable that can only take on a finite or countably infinite set of distinct values. In this case, the number of patients in a hospital can only be whole numbers (e.g., 0, 1, 2, 3, etc.), which is a countable set of values. Therefore, it is a discrete random variable.

b. the average amount of electricity consumed

The average amount of electricity consumed is not a discrete random variable but a continuous random variable. It can take on any real number value within a certain range, and it is not restricted to specific distinct values.

c. the amount of paint used in repainting a building

The amount of paint used in repainting a building can be measured in continuous quantities (e.g., liters or gallons). It is not restricted to specific distinct values, and therefore, it is not a discrete random variable.

d. the average weight of female athletes

Similar to the average amount of electricity consumed, the average weight of female athletes is not a discrete random variable but a continuous random variable. It can take on any real number value within a certain range and is not restricted to specific distinct values.

Among the given options, the only variable that is a discrete random variable is a) the number of patients in a hospital.

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X = 38

2x is equal to the angle next to the x + 66 angle because ℓ1 ∥ ℓ2 is parallel so:

2x + x + 66 = 180 -- combine like terms

3x + 66 = 180 -- subtract 66 from both sides

3x = 114 -- divide by 3 on both side

x = 38

Answer:

x = -3, y = -7

Step-by-step explanation:

Eliminate the equal sides of each equation and combine.

Solve 2x - 1 = 3x + 2 for x.

-x - 1 = 2

-x = 3

x = -3

Evaluate y when x = -3

y = 3 (-3) + 2

y = -7

(-3, -7)

good luck, i hope this helps :)

Answer:

they do be right, give them brain

Step-by-step explanation:

The sale price of the green beans represents a decrease of 16.67% compared to the original price of the beans.

To find the percent increase or decrease in the price of a can of green beans during the sale, we need to compare the sale price with the original price.

During the sale, the green beans were sold at a rate of 3 cans for $1.25, or approximately 41.67 cents per can:

Sale price per can = $1.25 / 3 = $0.4167 ≈ 41.67 cents

The original price of a can of green beans was 50 cents.

To find the percent increase or decrease in the price, we can use the following formula:

Percent increase or decrease = ((New value - Old value) / Old value) x 100%

Substituting the values, we get:

Percent increase or decrease = ((0.4167 - 0.5) / 0.5) x 100%

Percent increase or decrease = (-0.0833 / 0.5) x 100%

Percent increase or decrease = -16.67%

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We were told that the salary, t years after 2015 is given by the function,

S(t) = 3100t + 56000

When considering 2017, the number of years, t from 2015 is 2017 - 2015 = 2

We would substitute t = 2 into the function and find S(2)

Thus,

S(2) = 3100 x 2 + 56000 = 6200 + 56000 = 62200

When considering 2020, the number of years, t from 2015 is 2020 - 2015 = 5

We would substitute t = 2 into the function and find S(2)

Thus,

S(5) = 3100 x 5 + 56000 = 15500 + 56000 = 71500

Thus, we can say that

when

x1 = 2, y1 = 62200

when x2 = 5, y2 = 71500

Recall,

slope or average rate of change = (y2 - y1)/(x2 - x1)

average rate of change = (71500 - 62200)/(5 - 2) = 9300/3

average rate of change = 3100

The last option is correct

Answer:

cd

Step-by-step explanation:

The solution range for the given function inequality is x > 25.

A function is a relation between a dependent and independent variable. Mathematically, we can write -

y = f(x) = ax + b

Given is the function inequality as -

- 3(2x - 5) < 5(2 - x)

The given function inequality is -

- 3(2x - 5) < 5(2 - x)

- 6x - 15 < 10 - 5x

- 6x + 5x < 10 + 15

- x < 25

x > 25

Therefore, the solution range for the given function inequality is x > 25.

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Answer:

0

Step-by-step explanation:

.21 is closer to 0 than to 1

After rounding to the nearest whole number, we get;

⇒ 0

We have to given that;

A number is,

⇒ 0.21

And, Round 0.21 to the nearest whole number.

Since, We know that;

Whole numbers are defined from 0 to infinity.

Here, Number is, 0.21

Which is written as,

⇒ 0 < 0.21 < 1

Hence, 0.21 is closer to 0.

So, After rounding to the nearest whole number, we get;

⇒ 0

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The indicated angle measures are m∠PRQ = 52 degrees and m∠QRS  = 46°.

The indicated angles can be found as follows:

m∠PRS = 98°

Therefore,

m∠PRS = m∠PRQ + m∠QRS

m∠PRQ = 3x - 8

m∠QRS  = 2x + 6

Therefore,

m∠PRS = 3x - 8 + 2x + 6

m∠PRS = 5x - 2

98 = 5x - 2

98 + 2 = 5x

100 = 5x

divide both sides by 5

x = 100 / 5

x = 20

Therefore,

m∠PRQ = 3(20) - 8 = 60 - 8 = 52°

m∠QRS  = 2(20) + 6 = 40 + 6 = 46°

Therefore, the indicated angle measures are as follows:

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(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R'  is 1/2

(B) Coordinates of Δ P"Q"R"

P" (-4,0)

Q"(-3,1)

R"(1,-2)

(C) Triangles PQR and P"Q"R" are not congruent.

Given

ΔPQR is transformed into ΔP'Q'R'

Coordinates of P, Q, R are

P (8,0),

Q(6,2)

R(-2,-4)

Coordinates of P'Q'R' are

P′(4, 0)

Q′(3, 1)

R′(−1, −2)

(A) By Distance formula we can find the distance between P Q and P'Q'

Distance formula = \(D = \sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

Where D = Distance between two points

from distance formula we can write that

PQ = \(\sqrt{(6-8)^{2} +(2-0)^{2} } = \sqrt{4+4} =2 \sqrt{2}\)

Similarly

P'Q'= √2

PQ /P'Q' = 2

hence the scale factor of dilation is 1/2 (Compression)

(B )The Coordinates of Reflection about y axis can be written for a point

(x,y) as (-x,y)

So the Coordinated of Δ P"Q"R" can be written as

P" (-4,0)

Q"(-3,1)

R"(1,-2)

(C) ΔPQR  and ΔP"Q"R" are similar triangles but they are not  congruent because their sides  are not equal in size.

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Where 12 samples of 100 printed circuit boards were tested and the number of defective boards in each sample is provided, a control chart that should be constructed to monitor the process is the p-chart.

The p-chart, also known as the proportion chart, is used to monitor the proportion of nonconforming items in a sample. In this case, the number of defective printed circuit boards in each sample can be used to calculate the proportion of defective boards.

To construct the p-chart, you would calculate the proportion of defective boards for each sample by dividing the number of defective boards by the total number of boards in that sample. Then, you can plot these proportions on the control chart to monitor the process over time.

The p-chart helps to identify any shifts or trends in the proportion of defective boards, allowing the quality assurance department to take appropriate actions to maintain or improve the process quality.

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Given the parameter values n, δ, A₀, and k₀, the endogenous technological progress A(t) can be calculated using a recursive formula. The value of physical capital k(t) can also be determined using a separate recursive formula. The specific values depend on additional parameters not provided.

To compute the value of the endogenous technological progress A(t) at time t, we can use the following recursive formula:

A(t+1) = (1 - δ) * A(t) + n * k(t)^θ

where:

- A(t) represents the value of technological progress at time t.

- δ is the depreciation rate, which is 0.1 in this case.

- n is the exogenous growth rate of technological progress, which is 0.01 in this case.

- k(t) is the value of physical capital at time t.

- θ is the elasticity of output with respect to capital, which is not provided in the given information.

To compute k(t), we can use the following formula:

k(t+1) = (1 - δ) * k(t) + i(t)

where:

- k(t) represents the value of physical capital at time t.

- δ is the depreciation rate, which is 0.1 in this case.

- i(t) is the investment at time t.

Since the investment i(t) is not given in the provided information, we cannot determine the exact values of A(t) and k(t) for each time period. However, we can use the given initial values to compute their values for the initial time period (t = 0).

Using the provided initial values:

A(0) = 5

k(0) = 10

We can substitute these values into the recursive formulas to compute A(1) and k(1):

A(1) = (1 - 0.1) * 5 + 0.01 * 10^θ

k(1) = (1 - 0.1) * 10 + i(0)

The values of A(1) and k(1) can then be used to compute A(2) and k(2), and so on, by iteratively applying the recursive formulas. The specific values of A(t) and k(t) for each time period would depend on the values of θ and the investment i(t), which are not provided.

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The expected value of the number of games played is 5.5 games, and the variance is 1.25.

To find the expected value of the number of games played, we need to consider all the possible ways the match can end. Since the match is a best of 7, one team needs to win at least 4 games. The possible outcomes are:

Team A wins in 4 games: AAAA

Team A wins in 5 games: AABAA or ABAAA

Team A wins in 6 games: ABAABA, ABABAA, or ABBAAA

Team A wins in 7 games: ABABABA, ABABAB, ABBABAA, or ABBABAAA

Similarly, we can list the possible outcomes for Team B winning in 4, 5, 6, or 7 games. However, since both teams are equally likely to win each game, the probability of each outcome is the same. Therefore, the expected value of the number of games played is:

E(X) = (41/8) + (52/8) + (63/8) + (72/8) = 5.5 games

To find the variance, we need to first calculate the squared deviation from the expected value for each outcome. For example, for the outcome AABAA, the deviation is (5-5.5) = -0.5, and the squared deviation is (-0.5)^2 = 0.25. We can then multiply each squared deviation by the probability of that outcome and sum them up,

Var(X) = (1/8)(4-5.5)^2 + (2/8)(5-5.5)^2 + (3/8)(6-5.5)^2 + (2/8)(7-5.5)^2

= 1.25

Therefore, the expected value of the number of games played is 5.5 games, and the variance is 1.25.

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Answer:

Unknown, Solve for x or y?

Step-by-step explanation:

You need to elaborate on your answer... sorry.

In the meantime, here is Microsoft Math Solver, With your equations:

https://mathsolver.microsoft.com/en/solve-problem/x-y%20%3D%20%203

You can use this tool next time :)

Have a great day,

Nate

Thus, the test for homogeneity follows the same procedures as the test for independence because the assumptions for performing the chi-square test for independence and chi-square test for homogeneity are the same.

The procedures for the chi-square test of homogeneity are the same as for the chi-square test of independence. The data is different for both tests. Tests of independence are used to determine whether there is a significant relationship between two categorical variables from the same population. One population is segmented based on the value of two variables. So there will be a column variable and a row variable.

The chi-square test of homogeneity of proportions can be used to compare population proportions from two or more independent samples, determining whether the frequency counts are distributed identically among different populations.

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Hi There!

Remember, the quotient of means we divide.

In order to find the quotient of -54/9, we should divide -54 by 9:

-6 Is our answer.

Hope you could understand.

Have an awesome day!

-Starry

Answer:

To determine which function eventually grows faster, we need to look at their growth rates as x approaches infinity.

For function f(x), the growth rate is 8x, which means that as x gets larger, f(x) gets larger at a rate of 8 times x.

For function g(x), the growth rate is 1.2x, which means that as x gets larger, g(x) gets larger at a rate of 1.2 times x.

Since 8x grows faster than 1.2x as x approaches infinity, we can conclude that function f(x) grows faster than function g(x) in the long run.

Therefore, function f(x) eventually outgrows function g(x).

Answer:

x ≈ 14.4

Step-by-step explanation:

using the cosine ratio in the right triangle

cos59° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{x}{28}\) ( multiply both sides by 28 )

28 × cos59° , then

x ≈ 14.4 ( to the nearest tenth )

JL, LK, JK are the smallest angle of a triangle is located across from its smallest side. The biggest side is on the other side of the biggest side.

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Answer:

D

Step-by-step explanation:

6Hello there. To solve this question, we'll have to remember some properties about parallelograms.

Given the parallelogram RODY, and the measure of the angles as functions of a variable x:

We have to determine the measure of the angle R.

For this, we'll have to remember the following property about parallelograms:

The sides with one and two lines have the same measure, respectively.

Now imagine the following angles:

And that we move this triangle to the other side, that is:

With this, you notice that the angles might be supplementary, or mathematically it is the same as:

We also know that the angle at R might be:

When we moved the triangle, we now have that:

So the measure of the angle at O will be:

In the end, we reached the equation we need to solve:

Plugging the measures in function of x, we get

Add the values

Subtract 20º on both sides of the equation

Divide both sides of the equation by a factor of 16

Now, to find the measure of the angle R, simply plug the value of x:

This is the answer we were looking for.

is:

With this, you notice that the angles might be supplementary, or mathematically it is the same as:

Using the above system of equations, we can find the values of a, b for other vectors:

\($$\begin{aligned}\text { (b) } & a=-0.5, b=3.5 \quad \Rightarrow \quad a \boldsymbol{v}_{1}+b \boldsymbol{v}_{2}=-0.5\langle 2,-1,1\rangle+3.5\langle-3,1,2\rangle=\boxed{\mathrm{(b)}\ (3,-1,5)} \\\text { (c) } & a=2, b=-1 \quad \Rightarrow \quad a \boldsymbol{v}_{1}+b \boldsymbol{v}_{2}=2\langle 2,-1,1\rangle -\langle-3,1,2\rangle=\boxed{\mathrm{(c)}\ (7,-3,0)}\end{aligned}$$\)

We have given the following vectors:

\($$\begin{aligned}\text { (a) } & \boldsymbol{v}_{1}=\langle 2, -1,1\rangle, \quad \boldsymbol{v}_{2}=\langle-3,1,2\rangle, \quad \boldsymbol{a}=\langle a_{1}, a_{2}, a_{3}\rangle \\\text { (b) } & \boldsymbol{v}_{1}=\langle 2,-1,1\rangle, \quad \boldsymbol{v}_{2}=\langle-3,1,2\rangle, \quad \boldsymbol{a}=\langle-0.5,1.5,-1.5\rangle \\\text { (c) } & \boldsymbol{v}_{1}=\langle 2,-1,1\rangle, \quad \boldsymbol{v}_{2}=\langle-3,1,2\rangle, \quad \boldsymbol{a}=\langle2,2,2\rangle\end{aligned}$$\)

The sum of the given vectors:

\($$a \boldsymbol{v}_{1}+b \boldsymbol{v}_{2}=(2,-1,1)$$\)

We need to determine the values of scalars a and b, then we will find the values of given vectors. Using the above equation and equating the corresponding components of the vectors, we get the following system of linear equations:

\($$\begin{aligned}2 a-3 b &=2 \\a+b &=-1 \\a+2 b &=1\end{aligned}$$\)

Adding the 1st and 3rd equations, we get

\($$3 a-b=3$$\)

Multiplying the 2nd equation by 2 and subtracting it from the above equation, we get

\($$a=5$$\)

Substituting a=5 in the 2nd equation, we get b=4. Hence

\($$a \boldsymbol{v}_{1}+b \boldsymbol{v}_{2}=5\langle 2,-1,1\rangle+4\langle-3,1,2\rangle=\boxed{\mathrm{(a)}\ (13,-5,-4)}$$\)

Again using the above system of equations, we can find the values of a, b for other vectors:

\($$\begin{aligned}\text { (b) } & a=-0.5, b=3.5 \quad \Rightarrow \quad a \boldsymbol{v}_{1}+b \boldsymbol{v}_{2}=-0.5\langle 2,-1,1\rangle +3.5\langle-3,1,2\rangle=\boxed{\mathrm{(b)}\ (3,-1,5)} \\\text { (c) } & a=2, b=-1 \quad \Rightarrow \quad a \boldsymbol{v}_{1}+b \boldsymbol{v}_{2}=2\langle 2,-1,1\rangle -\langle-3,1,2\rangle=\boxed{\mathrm{(c)}\ (7,-3,0)}\end{aligned}$$\)

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Answer:

-3

Step-by-step explanation:

1 × -3 = -3

-3 × -3 = 9

9 × -3 = -27

-27 × -3 = 81

81 × -3 = -243

The pattern is that each number is multiplied by -3, and 1 × -3 = -3.

To cover a 75.2 square foot wall, approximately 7.52 gallons of paint will be needed. This can be determined using proportional relationship , unit conversion and cross-multiplication to solve the given problem.

To solve the problem of determining how many gallons of paint will cover a 75.2 square foot wall, we can consider the following three strategies:

1. Proportional relationship: We can establish a proportional relationship between the amount of paint and the area of the wall. In this case, the ratio of gallons of paint to square feet of wall area is constant.

Using this ratio, we can set up a proportion: 4 gallons / 40 square feet = x gallons / 75.2 square feet. Solving this proportion will give us the required amount of paint.

2. Unit conversion: Since we know that 4 gallons of paint cover 40 square feet, we can calculate the amount of paint needed per square foot.

Dividing 4 gallons by 40 square feet gives us the rate of 0.1 gallons per square foot. Multiplying this rate by the area of the 75.2 square foot wall will give us the required amount of paint.

3. Direct ratio: We can also solve this problem by using a direct ratio. The ratio of square feet between the two walls is 75.2 square feet / 40 square feet.

We can set up a direct ratio with the amount of paint needed as the unknown: 4 gallons / 40 square feet = x gallons / 75.2 square feet. Solving this ratio will give us the amount of paint required.

Using any of these three strategies, we can determine the number of gallons of paint needed to cover the 75.2 square foot wall.

To determine the number of gallons of paint needed to cover a 75.2 square foot wall, we can use the concept of proportionality.

Let x represent the unknown number of gallons of paint needed to cover the 75.2 square foot wall. The proportion can be set up as follows:

4 gallons / 40 square feet = x gallons / 75.2 square feet

To solve this proportion, we can use cross-multiplication:

4 * 75.2 = 40 * x

300.8 = 40x

Dividing both sides by 40, we find:

x = 300.8 / 40

x ≈ 7.52 gallons

Therefore, approximately 7.52 gallons of paint will cover the 75.2 square foot wall.

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Answer:

\(the \: two\: numbes \: are : \\ 7.777 \: and \: - 2.099\)

Step-by-step explanation:

\(let \: the \: two \: numbers \: be : x \: and \: y \\ x + y = 5.678.....eq(1) \\ x - y = 9.876 .....eq(2)\\ x = 9.876 + y....from \: eq(2) \\ y = 5.678 - x....frm \: eq(1) \\ eq \:...y \: in \: terms \: o f\: x : \\ x = 9.876 + 5.678 - x \\ 2x = 15.554 \\ x = 7.777 \\ y = 5.678 - x = y = 5.678 - 7.777 \\ y= - 2.099.\)