which expression represents the perimeter of
8x - 43
5x+12

Percentage of data within 2 population standard deviations of the mean is 68%.

To calculate the percentage of data within two population standard deviations of the mean, we need to first find the mean and standard deviation of the data set.

The mean can be found by summing all the values and dividing by the total number of values:

Mean = (20*2 + 22*8 + 28*9 + 34*13 + 38*16 + 39*11 + 41*7 + 48*0)/(2+8+9+13+16+11+7) = 32.68

To calculate standard deviation, we need to calculate the variance first. Variance is the average of the squared differences from the mean.

Variance = [(20-32.68)^2*2 + (22-32.68)^2*8 + (28-32.68)^2*9 + (34-32.68)^2*13 + (38-32.68)^2*16 + (39-32.68)^2*11 + (41-32.68)^2*7]/(2+8+9+13+16+11+7-1) = 139.98

Standard Deviation = sqrt(139.98) = 11.83

Now we can calculate the range within two population standard deviations of the mean. Two population standard deviations of the mean can be found by multiplying the standard deviation by 2.

Range = 2*11.83 = 23.66

The minimum value within two population standard deviations of the mean can be found by subtracting the range from the mean and the maximum value can be found by adding the range to the mean:

Minimum Value = 32.68 - 23.66 = 9.02 Maximum Value = 32.68 + 23.66 = 56.34

Now we can count the number of data points within this range, which are 45 out of 66 data points. To find the percentage, we divide 45 by 66 and multiply by 100:

Percentage of data within 2 population standard deviations of the mean = (45/66)*100 = 68% (rounded to the nearest percent).

Therefore, approximately 68% of the data falls within two population standard deviations of the mean.

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The sum of the given two vectors A and B is found to be R = 3i + 3j. The magnitude of vector R is found to be 3√2 and its direction is 45°.

The sum of the two vectors A and B is given by: R = A + B

Here, vector A = i + 4j And, vector B = 2i - j

Now, to find R, we will add the respective components of the two vectors, i.e,

R = (i + 4j) + (2i - j)

= 3i + 3j

The magnitude of vector R is given by the formula:

|R| = \(\sqrt{(R_x^2 + R_y^2)}\)

Substituting the values,

|R| = √(3² + 3²) = √18 = 3√2

The direction of vector R is given by the formula:

θ = tan⁻¹(\(R_y/R_x\))

θ = tan⁻¹(3/3)

θ = 45°

Therefore, the magnitude of vector R is 3√2 and its direction is 45°.

The sum of the given two vectors A and B is found to be R = 3i + 3j. The magnitude of vector R is found to be 3√2 and its direction is 45°.

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Answer:

Blue box is 9

Orange box is 2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

1+1=2

Answer:

The answer is "6000".

Step-by-step explanation:

It seems to be a total of 30 buddies there. Every column has 10 seats so that the 10 pals are now in a row. Of all the other 20 buddies, 10 are on the following row. And we have ten friends remaining and that they are sitting in the next row.

Therefore the possibility of sitting is:

\(30 \times 20 \times 10 = 6000\)

Answer:

35

Step-by-step explanation:

equation: 17+2x=87

Answer: nothing it’s a variable

The exact values of c in increasing order are: c = (10 - sqrt(7)) / 3, (10 + sqrt(7)) / 3

To verify that Rolle's Theorem can be applied to the function f(x) = x³ - 10x² + 31x - 30 on the interval [2, 5], we need to check if the following conditions are satisfied:

Let's check each condition:

f(x) = x³ - 10x² + 31x - 30 is a polynomial function and is continuous for all real values of x. So, it is continuous on [2, 5].

To check the differentiability, we need to find f'(x):

f'(x) = 3x² - 20x + 31.

The derivative f'(x) exists and is continuous for all real values of x. So, f(x) is differentiable on (2, 5).

Now, let's evaluate f(2) and f(5):

f(2) = (2)³ - 10(2)² + 31(2) - 30 = -10

f(5) = (5)³ - 10(5)² + 31(5) - 30 = 95

Since f(2) = -10 is not equal to f(5) = 95, we can conclude that Rolle's Theorem can be applied to the function f(x) = x³ - 10x² + 31x - 30 on the interval [2, 5] after differentiable.

To find the values of c in the interval (2, 5) such that f'(c) = 0, we need to solve the equation f'(c) = 3c² - 20c + 31 = 0.

Using quadratic formula:

c = (-(-20) ± sqrt((-20)² - 4(3)(31))) / (2(3))

c = (20 ± sqrt(400 - 372)) / 6

c = (20 ± sqrt(28)) / 6

c = (20 ± 2sqrt(7)) / 6

c = (10 ± sqrt(7)) / 3

The values of c in the interval (2, 5) such that f'(c) = 0 are:

c = (10 + sqrt(7)) / 3

c = (10 - sqrt(7)) / 3

Therefore, the exact values of c in increasing order are: c = (10 - sqrt(7)) / 3, (10 + sqrt(7)) / 3.

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Incomplete question:

Verify that Rolle's Theorem can be applied to the function f(x) = x³ - 10x² +31x-30 on the interval [2, 5]. Then find all values of c in the interval such that f' (c) = 0.

Enter the exact answers in increasing order.

To enter √a, type sqrt(a)

c = ?

The point e. x = 5, y = 0 satisfies the two linear constraints simultaneously. We have two linear constraints which are given as;

2x + 5y ≤ 10 (Equation 1)

10x + 6y ≤ 42 (Equation 2)

We need to find the point which satisfies both equations. Let us plug in the values one by one to check which one satisfies the two equations simultaneously.

a. x= 6, y = 2

In Equation 1:2x + 5y = 2(6) + 5(2) = 17

In Equation 2:10x + 6y = 10(6) + 6(2) = 66

Thus, this point does not satisfy equations 1 and 2 simultaneously.

b. x=6, y=4

In Equation 1:2x + 5y = 2(6) + 5(4) = 28

In Equation 2:10x + 6y = 10(6) + 6(4) = 72

Thus, this point does not satisfy equations 1 and 2 simultaneously.

c. x=2, y = 1

In Equation 1:2x + 5y = 2(2) + 5(1) = 9

In Equation 2:10x + 6y = 10(2) + 6(1) = 26

Thus, this point does not satisfy equations 1 and 2 simultaneously.

d. x=2, y = 6

In Equation 1:2x + 5y = 2(2) + 5(6) = 32

In Equation 2:10x + 6y = 10(2) + 6(6) = 52

Thus, this point does not satisfy equations 1 and 2 simultaneously.

e. x = 5, y = 0

In Equation 1:2x + 5y = 2(5) + 5(0) = 10

In Equation 2:10x + 6y = 10(5) + 6(0) = 50

Thus, this point satisfies both equations simultaneously.

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Answer:

\(\frac{2}{10}\) lies between 0 and 1.

Step-by-step explanation:

We must have in mind that given average weight of a newborn panda is a non-integer rational number, such that lies between two integer rational number. In other words, this number must satisfy the following condition:

\(n < \frac{a}{b} < n +1\), \(n, a, b \in \mathbb{N}_{O}\)

\(\mathbb{N}_{O} = \mathbb{N}\,\cup\,{\{0\}}\)

Which is now developed mathematically to deduce a useful expression to find integers:

1) \(n < \frac{a}{b} < n +1\) Given

2) \(n \cdot 1 < \frac{a}{b} < n\cdot 1 + 1\) Modulative property

3) \(n \cdot (b\cdot b^{-1}) < a\cdot b^{-1} < n \cdot (b\cdot b^{-1}) + b\cdot b^{-1}\) Existence of Multiplicative inverse/Definition of division.

4) \((n\cdot b)\cdot b^{-1} < a\cdot b^{-1}< [(n+1)\cdot b] \cdot b^{-1}\) Commutative, Associative and Distributive properties.

5) \(n\cdot b < a < (n+1)\cdot b\) Compatibility with Multiplication/Existence of Multiplicative Inverse/Modulative Property/Result.

If we know that \(a = 2\) and \(b = 10\), the following inequation is formed:

\(10\cdot n < 2 < 10\cdot (n+1)\)

It is quite evident to conclude that \(\frac{2}{10}\) lies between 0 and 1.

Step-by-step explanation:

x² + 9x < -20

x² + 9x + 20 < 0

(x + 4)(x + 5) < 0

Therefore -5 < x < -4 / (-5,-4)

The probability that a teacher can teach in any department is 2/3.

To find the probability that a teacher can teach in any department,

find the proportion of teachers who teach the whole spectrum of courses taught in a department, which is denoted by x.

Let's denote the proportion of teachers who can teach their favorite courses by y.

The joint density function of x and y is given by

\(f(x,y) = 2(x+y), 0 < x < 1, 0 < y < 1, and x + y < 1\)

To find the probability that a teacher can teach in any department, integrate the joint density function over the region where x > y:

\(P(x > y) = \int\int(x > y) f(x,y) dxdy\)

Split the integration into two parts: one over the region where y varies from 0 to x, and another over the region where y varies from x to 1:

\(P(x > y) = \int[0,1]\int[0,x] 2(x+y) dydx + \int[0,1]\int[x,1-x] 2(x+y) dydx\\P(x > y) = \int[0,1] x^2 + 2x(1-x) dx\\= \int[0,1] (2x - x^2) dx\\= [x^2 - x^3/3]_0^1\)

= 2/3

Therefore, the probability that a teacher can teach in any department is 2/3.

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Answer:

C

Step-by-step explanation:

it is because the hours spent by training will determine the pay at the end of the month.

therefore it's independent that's y it is the domain.

Answer:

x = 20

Step-by-step explanation:

these angles are supplementary, which means they add up to 180°

using this, you can make the following equation:

6x + 60 = 180

subtract 60 from both sides of the equation

6x + 60 - 60 = 180 - 60

6x = 120

divide both sides of the equation by 6

6x/6 = 120/6

x = 20

In observational studies, the variable of interest The correct answer is (a) is not controlled.

The variables are measured as they occur naturally, without any manipulation or intervention by the researcher. Therefore, the variable of interest is not controlled in observational studies.

Observational studies are used in situations where it is not feasible or ethical to conduct controlled experiments, such as in studies of the effects of environmental exposures or lifestyle factors on health outcomes. In these studies, the researcher cannot control the exposure or intervention and must rely on observational data to draw conclusions about the relationship between the exposure and the outcome.

The other options are not correct because:

b. If the variable of interest is controlled, then the study is a controlled experiment, not an observational study.

c. The variable of interest can be numerical or categorical in observational studies.

d. The variable of interest does not have to be numerical in observational studies, as it can also be a categorical variable

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If in 1990 the cost of tuition at a state university was 4300 during the next eight years that tuition rose 4% each year.  the equation is A = $4300 (1+0.04)^t and the tuition is $5,231.61.

Using this formula to find the tuition

A = P (1+ r)^t

The equation is:

A = $4300 (1+0.04)^t

Where:

A =Amount = ?

P = Principal = $4300

r = rate = 4%

t = time =?

Now let find the tuition in 1995

A = P (1+ r)^t

A =Amount = ?

P = Principal = $4300

r = rate = 4%

t = time =  (1995 - 1990) = 5 years

Let plug in the formula

A = $4300 (1+0.04)^5

A = $4300 (1.04)^5

A = $5,231.61

Therefore the equation is A = $4300 (1+0.04)^t and the tuition is $5,231.61.

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The complete question is:

In 1990 the cost of tuition at a state university was 4300 during the next eight years that tuition rose 4% each year.  Write an equation to model the amount of  tuition  (in dollars) for t years after 1990. Then find the tuition in 1995

The assessment value of the house will be $97,200.

The fair market value of a house refers to its calculated selling price under current market conditions. Assessed value is used by government tax assessors to determine how much property taxes a new homeowner may anticipate to pay.

Both fair market value and tax-assessed value contribute to determining a home's worth.

FMV is a fictitious value derived by estimating how much a buyer and seller would likely agree on under "normal" conditions. In contrast, market value is the price at which a property will actually sell.

As per the data given in the questions,

We have,

The market value of the home = $135,000

For finding the market value of the house, we simply multiply the market value by the assessment rate:

So, the market value will be: $135,000 * 0.72 = $97,200.

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Answer:

(x - -3/10) + 1=10 so it is 9.3

Step-by-step explanation:

Answer:

C. Each person will receive between 3 and 4 liters

Step-by-step explanation:

because if you divide 27 by 8 you'll get 3.375

Answer:

x = 49

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{DN}{KJ}\) = \(\frac{DG}{KM}\) , substitute values

\(\frac{5}{35}\) = \(\frac{8}{x+7}\) ( cross- multiply )

5(x + 7) = 280 ( divide both sides by 5 )

x + 7 = 56 ( subtract 7 from both sides )

x = 49

Answer:

3 5/6 cups of flour

Step-by-step explanation:

You want the total amount so we add both fractions together.

1 1/2 + 2 1/3

I prefer to convert both to an improper fraction and then convert back to a mixed number, so;

1 1/2 = whole number (1) x denominator (2), add numerator (1), = 3, put this over the old denominator (2) = 3/2

2 1/3 = whole number (2) x denominator (3), add numerator (1), = 7, put this over the old denominator (3) = 7/3

Now we add the 2 improper fractions, so we have to convert them both to a common denominator. The LCM of 2 and 3 is 6, so it will be over 6.

3/2 = to get from 2 to 6, you multiply by 3, numerator (3) x 3 = 9, over 6 = 9/6.

7/3 = to get from 3 to 6, you multiply by 2, numerator (7) x 2 = 14, over 6 = 14/6.

9/6 + 14/6 = 23/6

Now we change back into a mixed number, how many times do 6 go into 23? 3 (6x3=18), as 4 would be 24.

So our whole number is 3

What is left goes over our denominator (6): 23 - 18 = 5.

So your answer is 3 5/6 cups of flour.

Using the Pigeonhole Principle, it can be shown that in a set of n positive integers, none exceeding 2n, there is at least one integer that divides another integer.

We can prove this statement by contradiction using the Pigeonhole Principle.

Suppose we have a set of n positive integers, none of which exceed 2n, and assume that no integer in the set divides another integer.

Consider the prime factorization of each integer in the set. Since each integer is at most 2n, the largest prime factor in the prime factorization of any integer is at most 2n.

Now, let's consider the possible prime factors of the integers in the set. There are only n possible prime factors, namely 2, 3, 5, ..., and 2n (the largest prime factor).

By the Pigeonhole Principle, if we have n+1 distinct integers, and we distribute them into n pigeonholes (corresponding to the n possible prime factors), at least two integers must share the same pigeonhole (prime factor).

This means that there exist two integers in the set with the same prime factor. Let's call these integers a and b, where a ≠ b. Since they have the same prime factor, one integer must divide the other.

This contradicts our initial assumption that no integer in the set divides another integer.

Therefore, our assumption must be false, and there must be at least one integer in the set that divides another integer.

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The question requires us to find the speed of the plane at the time when the angle of elevation is θ = π/3 and is decreasing at a rate of -dθ/dt = π/4 rad/min.

Given, the altitude of the plane is h = 4 km.

We need to find the speed of the plane. Let v be the speed of the plane. The angle of elevation θ between the plane and the tracking telescope on the ground is given by:

\tan \theta = \frac{h}{d}

\Rightarrow \tan\theta = \frac{h}{v t}

where d = vt is the distance traveled by the plane in time t. Differentiating both sides with respect to time t,

we get:

\sec^2 \theta \cdot \frac{d\theta}{dt} = \frac{h}{v}\cdot \frac{-1}{(v t)^2} \cdot v

Substituting the given values θ = π/3, dθ/dt = π/4, and h = 4 km = 4000 m,

we get:

\Rightarrow \frac{3}{4}\cdot \frac{16}{v^2} \cdot \frac{\pi}{4} = \frac{\pi}{4}\cdot \frac{1}{v}

\Rightarrow \frac{3}{4} = \frac{1}{v^2}

\Rightarrow v^2 = \frac{16}{3}

\Rightarrow v = \sqrt{\frac{16}{3}}

\Rightarrow \boxed{v = \frac{4\sqrt{3}}{3}\text{ km/min}}

Therefore, the plane is traveling at a speed of 4√3/3 km/min when the angle of elevation is π/3 and is decreasing at a rate of π/4 rad/min.

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Answer:

−7x−5y=4 - 7 x - 5 y = 4. Rewrite in slope-intercept form. Tap for more steps... The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is ...

Step-by-step explanation:

Answer:

134

Step-by-step explanation:

26% of 515

.26 x 515 = 133.9 I cannot have .9 of a person.  Round to 134

Supplementary angles are two angles whose measures add up to 180°. If An angle is 134.2 then other angles are 22.9.

Supplementary angles are two angles whose measures add up to 180°

Supplementary angles are those that add up to 180.

supplementary angle: x

an angle: x+134.2

and together they must measure 180:

x+x+134.2 = 180

2x+134.2=180

2x=180-134.2

2x=45.8

x=22.9

This is the supplementary angle the other angle is 22.9+134.2 = 157.1

Thus the the angle of each is 22.9.

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Answer:

20

Step-by-step explanation:

First, let's find how much she spent on the expensive calculators

40 times $16400= $656,000

Now, lets find how much money she had for the cheap calculators.

$774,000- $656,000=$118000

Now that we have her budget (money remaining) for the cheaper calculators, lets divide that by the price for each individual calculator.

$118000/$5900=20

If you like my answer, please mark me as a brainliest! (I am new to this community.)

Answer:

The answer to your problem is, 63

Step-by-step explanation:

How to find area of a trapezoid:

Area = \(\frac{a+b}{2}\)h

Base = 10

Height = 7

Base = 8

We would need to use our formula to find our answer:

Area = \(\frac{a+b}{2}\)h  = \(\frac{10+8}{2}\)×7 =

18 / 2 = 8

8 x 7

= 63

Thus the answer to your problem is, 63