Which of the following is closest to the approximate value of 103√? A 15 B 17 C 18 D 19

The study design described is a cross-sectional study.

The study design in this scenario is a cross-sectional study. The study aims to examine the relationship between family status and school performance. The sample is selected by randomly choosing every 5th child from the list of children at the ABC elementary school. Data is collected from the school record for each child, and family status is operationalized by whether the child lives in a single-parent household, dual-parent household, or has a non-parent guardian in the household. The school performance is measured by administering a student math test and a student reading test to the child in April, with each test including 20 questions and each correct answer being worth five points.

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The equation of the trend line is given as follows:

y = 1.33x + 20.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

Two points on the line in this problem are given as follows:

(0, 20) and (15, 40).

When x = 0, y = 20, hence the intercept b is given as follows:

b = 20.

When x increases by 15, y increases by 20, hence the slope m is given as follows:

m = 20/15

m = 1.33.

Hence the function is given as follows:

y = 1.33x + 20.

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Step-by-step explanation:

Given equation

1. Rearrange it to make a the subject

2. Rearrange it to make b the subject

Answer:

see explanation

Step-by-step explanation:

(1)

P = 2a + 4b ( subtract 4b from both sides )

P - 4b = 2a ( isolate a by dividing both sides by 2 )

\(\frac{P-4b}{2}\) = a

and

(2)

P = 2a + 4b ( subtract 2a from both sides )

P - 2a = 4b ( isolate b by dividing both sides by 4 )

\(\frac{P-2a}{4}\) = b

Answer:

280m³

i hope this is help for you

The area between z = -1.84 and z = 0.68 in a standard normal distribution is approximately 0.7181, calculated using a standard normal distribution table or calculator.

To find the area between z = -1.84 and z = 0.68 in a standard normal distribution, we need to use a standard normal distribution table or a calculator. Using a standard normal distribution table, we can find the area to the left of each z-score and subtract to find the area between the two z-scores. The table gives us the area to the left of z = -1.84 as 0.0336 and the area to the left of z = 0.68 as 0.7517.

Therefore, the area between z = -1.84 and z = 0.68 is:

0.7517 - 0.0336 = 0.7181

So, the area between z = -1.84 and z = 0.68 in a standard normal distribution is 0.7181.

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a. The expected value is 14 days, the variance is 196 days^2, and the standard deviation is 14 days.

b. The probability that the number of days ahead a traveler will purchase an airline ticket is between 10 and 16 days is approximately 0.345 or 34.5%.

c. The probability that the number of days the traveler purchases the ticket is more than 9 days is approximately 0.591 or 59.1%.

Since the square root of variance is regarded as the standard deviation for the specified data set, variance and standard deviation have a relationship in statistics. The terms variance and standard deviation are defined here.

(a) To find the expected value, variance, and standard deviation of the number of days ahead of time a traveler will purchase an airline ticket, given that it follows an exponential distribution with λ = 1/14, we can use the following formulas:

Expected value (mean): E(X) = 1/λ

Variance: Var(X) = 1/λ²

Standard deviation: SD(X) = √Var(X)

Given λ = 1/14, we can calculate:

Expected value: E(X) = 1 / (1/14) = 14 days

Variance: Var(X) = 1 / (1/14)² = 196 days²

Standard deviation: SD(X) = √Var(X) = √196 = 14 days

Therefore, the expected value is 14 days, the variance is 196 days^2, and the standard deviation is 14 days.

(b) To find the probability that the number of days ahead a traveler will purchase an airline ticket is between 10 and 16 days, we can use the cumulative distribution function (CDF) of the exponential distribution.

P(10 ≤ X ≤ 16) = F(16) - F(10)

where F(x) is the CDF of the exponential distribution.

Using the formula for the CDF of the exponential distribution, we can calculate:

P(10 ≤ X ≤ 16) = \(e^{(-10/14)\) - \(e^{(-16/14)\) ≈ 0.345

Therefore, the probability that the number of days ahead a traveler will purchase an airline ticket is between 10 and 16 days is approximately 0.345 or 34.5%.

(c) Given that the number of days ahead of time a traveler will purchase an airline ticket is more than 7 days, we need to find the probability that the number of days the traveler purchases the ticket is more than 9 days.

Using conditional probability notation, we want to find P(X > 9 | X > 7).

P(X > 9 | X > 7) = P(X > 9 and X > 7) / P(X > 7)

Since X follows an exponential distribution, the exponential distribution is memoryless, meaning that P(X > a + b | X > a) = P(X > b) for any a, b > 0.

Therefore, P(X > 9 | X > 7) = P(X > 9) / P(X > 7)

Using the formula for the survival function (1 - CDF) of the exponential distribution, we can calculate:

P(X > 9) = 1 - F(9) = \(e^{(-9/14)\)

P(X > 7) = 1 - F(7) = \(e^{(-7/14)\)

So, P(X > 9 | X > 7) = \((e^{(-9/14))\) / \((e^{(-7/14)\)) ≈ 0.591

Therefore, given that the number of days ahead of time a traveler will purchase an airline ticket is more than 7 days, the probability that the number of days the traveler purchases the ticket is more than 9 days is approximately 0.591 or 59.1%.

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Answer:

8

Step-by-step explanation:

The length of one side must be less than the length of the other two sides combined.

Answer:

Where is the fourth diagram?

Answer:

D. ab=ab

Step-by-step explanation:

Communitive property of addition is a number plus a number and the number added to the first number backwards but equal the same answer. For instance (if you don't understand what I'm saying) Look at answer A in your problem, a+b=b+a that's how the communitive property works in addition. The rest of the answer choices also shows communitive property. This is why answer D does NOT show the communitive property in addition.

I'm sorry if I didn't explain right or if I'm wrong but I tried my best. Have a good day and enjoy your answer. I hope you learned something Thanks :)

"0" was the gift tax in 2018.

Gift taxes are paid by either the giver or the recipient?

A gift tax is not present. There is no gift tax because gifts up to $15,000 are tax-free.

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The quadratic equation on the graph is:

y = (x + 3)*(x - 2)

Here we can see the graph of a quadratic equation. Remember that if the zeros are h and k, then we can write the equation as:

y = a*(x - h)*(x - k)

where a is the leading coefficient.

We can see that the zeros are:

x = -3

x = 2

y = a*(x + 3)*(x - 2)

Now looking at the graph we can identify other point, like (-2, -4), replacing these values we get:

-4 = a*(-2 + 3)*(-2 - 2)

-4 = a*-4

-4/-4 = a

1 = a

So the quadratic equation is:

y = (x + 3)*(x - 2)

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In trigonometry,

if i = 10 sin α,  i at α = 30° is 5.

In trigonometry, If i = 10 sin α, and you want to find the value of i at α = 30°, you can follow these steps:
1. Substitute α with 30° in the equation: i = 10 sin(30°)
2. Calculate the sine of 30° (sin(30°) = 0.5)
3. Multiply the result by 10: i = 10 * 0.5

So, when α = 30°, i = 5.

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Answer:

You can go through your notes, go step by step of the equation to understand what you have to do

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

we have to do  Unitary method.

when x=4 then x=14

when x=1 the y=14/4

when x=21 then y=(14*6)/4

y=21

y varies directly with x, and y = 14 when x = –4. when x = –6 then value of y will be twenty one.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

In order to find the value of y at x=-6,

we will first use the line equation (with y-intercept = 0) to find the slope:

y=mx+c

(-4, 14)

14 = m(-4)

Divide both sides by -4

m = -14/4 = -3.5

Now that we have the slope value,

Now we can find the value at x = -6 by using this slope value (-3.5):

y = mx

m value is minus three point five and x value is minus six

=-3.5(-6)

=21

Hence y varies directly with x, and y = 14 when x = –4. when x = –6 then value of y will be twenty one.

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ᴇʏᴏᴀᴘᴜᴀ8ᴡ8ᴇɪᴇᴜᴇᴜɪᴇ8ᴡ8ᴡ8ǫ

Answer:

Step-by-step explanation:

Cubic centimeters is multiplying by another dimension which means volume. Squared centimeters means area.

The average speed of Amelia to complete the distance is equals to the 7.67 km/h .

Average speed : The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity. It is represented by the magnitude and does not have direction.

Average Speed = Total distance/total time taken to travelled this distance

We have, Amelia who travelled 11 kilometres in 1 hour and 45 minutes. So, Amelia's speed to travel distance of 11 km, s₁ = 11/(1 + 45/60) = 660/105

= 6.285 km/h

Then turn back and travelled same distance in 1 hour 7 minutes . So, speed at time of return , s₂

= 660/67 = 9.850 km/h

Average speed formula = (s₁ ×t₁ + s₂ × t₂) /(t₁ + t₂)

= (6.285 × 105/60 + 9.850× 67/60)/(105/60 + 67/60) = (10.998 + 10.999)/(172/60)

= 21.998/172/60

= 7.67

Hence, required speed is 7.67 km/h.

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\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

Answer:

1.

R= Number of orange juice cases.

G = Number of greapefruit juice cases.

T = Number of tomato juice cases.

Equations:

9R+10G+12T=398

6R+4G+4T=164

R+2G+T=58

2.

R=6

G=20

T=12

Step-by-step explanation:

1.

The problem is talking about three types of products and it wants us to find how many of each the factory prepares. Since this is the data we need to know, then we set them to be our variables:

R= Number of orange juice cases.

G = Number of greapefruit juice cases.

T = Number of tomato juice cases.

Next, we can use the provided information to build our equations. First, we start with the Sterilizing machine equation: 9 minutes for orange juice, 10 minutes for grape juice and 12 minutes for tomato juice. So we use the sterilizing values for each of the product, to build our first equation:

9R+10G+12T=398

next, we build the filling machine equation, so like on the previous equation, we use the provided data for filling to build the second equation:

6R+4G+4T=164

and finally we build the labeling machine equation so we get:

R+2G+T=58

so we need to solve the following system of equations:

9R+10G+12T=398

6R+4G+4T=164

R+2G+T=58

2.

The very first thing we need to do in order to solve this problem by using the Gauss-Jordan elimination method is to build our matrix based on the system of equations we got on the previous part.

\(\left[\begin{array}{cccc}9&10&12&398\\6&4&4&164\\1&2&1&58\\\end{array}\right]\)

The idea is to end up with an identity matrix on the first three columns, that will directly give us the answer to the system of equations. So we can start by dividing the first row into 9: \(\frac{R_{1}}{9}\) So we get:

\(\left[\begin{array}{cccc}1&\frac{10}{9}&\frac{4}{3}&\frac{398}{9}\\6&4&4&164\\1&2&1&58\\\end{array}\right]\)

Next, we can multiply the first row by -6 and add it to the second row to get the new second row. \(-6R_{1}+R_{2}\)

so we get:

-6   -20/3   -8   -796/3

6     4          4      164

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

0    -8/3    -4    -304/3

our matrix now looks like this:

\(\left[\begin{array}{cccc}1&\frac{10}{9}&\frac{4}{3}&\frac{398}{9}\\0&-\frac{8}{3}&-4&-\frac{304}{3}\\1&2&1&58\\\end{array}\right]\)

Next, we can subtract R3 from R1 so we get:

1   10/9   4/3   398/9

-1   -2     -1       -58

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

0    -8/9   1/3   -124/9

So the matrix looks like this now:

\(\left[\begin{array}{cccc}1&\frac{10}{9}&\frac{4}{3}&\frac{398}{9}\\0&-\frac{8}{3}&-4&-\frac{304}{3}\\0&-\frac{8}{9}&\frac{1}{3}&-\frac{124}{9}\\\end{array}\right]\)

Now, we can multiply the second row by -3/8 so we get:

\(\left[\begin{array}{cccc}1&\frac{10}{9}&\frac{4}{3}&\frac{398}{9}\\0&1&\frac{3}{2}&38\\0&-\frac{8}{9}&\frac{1}{3}&-\frac{124}{9}\\\end{array}\right]\)

Now, we can subtract: \(R_{1}-\frac{10}{9}R_{2}\) so we get:

0   -10/9   -5/3  -380/9

1      10/9    4/3   398/9

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

1        0       -1/3   2

So the matrix will now look like this:

\(\left[\begin{array}{cccc}1&0&-\frac{1}{3}&2\\0&1&\frac{3}{2}&38\\0&-\frac{8}{9}&\frac{1}{3}&-\frac{124}{9}\\\end{array}\right]\)

Next, we do the following operation: \(R_{3}+\frac{8}{9}R_{2}\)

0      8/9      4/3 304/9

0      -8/9     1/3   -124/9

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

0       0         5/3   20

So our matrix will now look like this:

\(\left[\begin{array}{cccc}1&0&-\frac{1}{3}&2\\0&1&\frac{3}{2}&38\\0&0&\frac{5}{3}&20\\\end{array}\right]\)

We next multiply R3 by 3/5 so we get:

\(\left[\begin{array}{cccc}1&0&-\frac{1}{3}&2\\0&1&\frac{3}{2}&38\\0&0&1&12\\\end{array}\right]\)

and now we do: \(\frac{R_{3}}{3}+R_{1}\)

0         0      1/3       4

1           0     -1/3      2

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

1       0          0        6

So our matrix will now look like this:

\(\left[\begin{array}{cccc}1&0&0&6\\0&1&\frac{3}{2}&38\\0&0&1&12\\\end{array}\right]\)

and now we do the following: \(R_{2}-\frac{3}{2}R_{3}\)

so we get:

0         0      -3/2     -18

0         1       3/2      38

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

0        1          0        20

for our final matrix to be:

\(\left[\begin{array}{cccc}1&0&0&6\\0&1&0&20\\0&0&1&12\\\end{array}\right]\)

so now we can retrieve the corresponding answers:

R=6

G=20

T=12

Using PEMDAS

We must first clear P which stands for Parentheses

The values in the parentheses are (12.9 -3.1)

so the first and right option is option c subtract 3.1 from 12.9

Answer:

B

Step-by-step explanation:

If you look at the graph/chart, it starts at 1,000, so half of that is 500, so you go down to 500, and go straight down to see the number of time under it (In this case, is 1 minute) so you know it is one minute

Answer:

D. 4

Step-by-step explanation:

(a) The economic loading of unit 4 and B are 11.54 MW and 138.46 MW, respectively.

To find the economic loading of the two units when the total load to be supplied by the power station is 150 MW, we need to minimize the total fuel cost. Let x be the power generated by unit 4 and y be the power generated by unit B. Then, we have:

x + y = 150 (total load)

The total fuel cost C is given by:

C = F4(x) + Fb(y)

where F4(x) and Fb(y) are the fuel costs for units 4 and B, respectively. Using the given relations, we have:

F4(x) = 0.06x^2 + 11.4x

Fb(y) = 0.07y^2 + 10y

Substituting x = 150 - y, we get:

C(y) = 0.06(150-y)^2 + 11.4(150-y) + 0.07y^2 + 10y

Expanding and simplifying, we get:

C(y) = 0.013y^2 - 3.6y + 1710

To minimize C(y), we take its derivative with respect to y and set it equal to zero:

dC/dy = 0.026y - 3.6 = 0

y = 138.46 MW

Substituting y back into x = 150 - y, we get:

x = 11.54 MW

(b) The negative value that is  -1297.5 indicates that there is a net decrease in fuel cost per hour if the load is equally shared by the two units.

To find the net increase in fuel cost per hour if the load is equally shared by the two units, we need to calculate the fuel cost for each unit when they generate half of the total load (i.e., 75 MW). Using the given relations, we have:

F4(75) = 0.06(75)^2 + 11.4(75) = 1282.5

Fb(75) = 0.07(75)^2 + 10(75) = 1312.5

Therefore, the total fuel cost is:

C = F4(75) + Fb(75) = 2595

If the load is equally shared by the two units, each unit generates 75/2 = 37.5 MW. The fuel cost for each unit is:

F4(37.5) = 0.06(37.5)^2 + 11.4(37.5) = 641.25

Fb(37.5) = 0.07(37.5)^2 + 10(37.5) = 656.25

Therefore, the total fuel cost is:

C' = F4(37.5) + Fb(37.5) = 1297.5

The net increase in fuel cost per hour is:

ΔC = C' - C = 1297.5 - 2595 = -1297.5

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Kristen is attempting to solve the equation \(0=\sqrt{6x}-x\). Hence, option b. is the correct answer.

A radical equation has no solution if the square root of a negative number is involved in the equation. The left-hand side of equation b, √(6x), is always non-negative. But the right-hand side, -x, can be negative. So, there is no value of x that can satisfy the equation.

In other words, there is no real number x that would make the left-hand side equal to the right-hand side, so equation b has no solution.

Hence, Kristen is attempting to solve equation 0 = √(6x) - x.

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The complete question is -

Kristen is solving a radical equation and determines that the equation has no solution. Which equation is Kristen attempting to solve?

a. \(\sqrt{27+6x} =x\)

b. \(0=\sqrt{6x}-x\)

c. \(\sqrt{4-x}+9=0\)

d. \(\sqrt{\frac{x}{8}} = \sqrt{90-x}\)

Answer:

1. $19.91

Step-by-step explanation: