Find the principle value of each of the following to the nearest minute:

Arccos (0.333)

The inverse cosine function to find the measures of the = arccos(-sqrt)

What is measure of angles?

Angle measure can be defined as the measure of the angle formed by the two rays or arms at a common vertex.

To find the measures of the angles of a triangle, you can use the Law of Cosines, which states that the square of the length of a side of a triangle is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of the other two sides and the cosine of the angle opposite the side in question.

In this case, we are given the coordinates of the vertices of the triangle and we want to find the measures of the angles. To do this, we can use the distance formula to find the lengths of the sides of the triangle and then use the Law of Cosines to find the cosines of the angles.

The distance formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
where d is the distance between the two points with coordinates (x1, y1, z1) and (x2, y2, z2).
Using this formula, we can find the lengths of the sides of the triangle as follows:
PR = sqrt((4 - 1)^2 + (0 - 2)^2 + (2 - 3)^2) = sqrt(9 + 4 + 1) = sqrt(14)
PQ = sqrt((3 - 1)^2 + (4 - 2)^2 + (2 - 3)^2) = sqrt(4 + 4 + 1) = sqrt(9)
QR = sqrt((4 - 3)^2 + (0 - 4)^2 + (2 - 2)^2) = sqrt(1 + 16 + 0) = sqrt(17)
Now we can use the Law of Cosines to find the cosines of the angles:
cos A = (PR^2 + PQ^2 - QR^2) / (2 * PR * PQ)
= (14 + 9 - 17) / (2 * sqrt(14) * sqrt(9))
= (-4) / (2 * sqrt(14) * sqrt(9))
= -2 / (sqrt(14) * sqrt(9))

cos B = (QR^2 + PQ^2 - PR^2) / (2 * QR * PQ)
= (17 + 9 - 14) / (2 * sqrt(17) * sqrt(9))
= (2) / (2 * sqrt(17) * sqrt(9))
= 1 / (sqrt(17) * sqrt(9))

cos C = (QR^2 + PR^2 - PQ^2) / (2 * QR * PR)
= (17 + 14 - 9) / (2 * sqrt(17) * sqrt(14))
= (12) / (2 * sqrt(17) * sqrt(14))
= 6 / (sqrt(17) * sqrt(14))

Finally, we can use the inverse cosine function to find the measures of the angles:
A = arccos(-2 / (sqrt(14) * sqrt(9)))
= arccos(-2 / (2 * sqrt(7) * sqrt(3)))
= arccos(-1 / sqrt(7) * sqrt(3))
= arccos(-sqrt)

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Answer:

70

Step-by-step explanation:

1 million = 10 hundred thousands because 100,000 x 10 = 1,000,000

Answer:

you answer is 7 1/25

Step-by-step explanation:

0.04 ---> 1/25

7 ---> 7

7 + 1/25 = 7 1/25

Although part of your question is missing, you might be referring to this full question: Which of the following statements regarding the expansion of (x + y)^n are correct?

By expanding the exponential expressions, the answers are option A, B, and D.

The exponential expressions: (x + y)^n

Which means that we multiply the polynomial (x + y) by itself n times.

Option A.

This statement is true, because there is only one x in the original polynomial, and we multiply it by itself n times, then we can have only one term equal to x^n (or y^n).

Option B.

This statement is true, because if we multiplicate the variables by themselves n times, then the degree of the term also has to be n. Since for a term: (x^a)*(y^b) the degree is a + b; then it always be a + b = n.

Option C.

This statement is false, because of the same reasons in Option B.

Option D.

This statement is true, because in the original polynomial the coefficients of y and x are the same, then in the expansion the coefficients of the reflected terms like (x^a)*(y^b) and (x^b)*(y^a) are equal.

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On solving the provided question, by the given information we can say that Momentum is a vector quantity.

A physical quantity that only has magnitude is known as a scalar quantity. such as distance, speed, mass, density, etc. However, vector quantities—which include displacement, velocity, acceleration, force, and mass—are physical quantities that have both magnitude and direction.

Momentum is a vector quantity.

It is directed and has a magnitude. According to Isaac Newton's second law of motion, the force pushing a particle has an equal and opposite effect on the time rate at which its momentum changes. Consider Newton's laws of motion.

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9 x (46+70) 5 - 32 (40 - 219) = 11428

Using the BODMAS rule, we solve the brackets first,

9 x (46+70) 5 - 32 (40 - 219)

= 9 x 116 x 5 - 32 x -179

Next, we solve the multiplication signs

9 x 116 x 5 - 32 x -179

= 5520 - ( -5728)

Solving the subtraction sign, we get

5520 - ( -5728)

= 11428

Hence, the answer is 11428

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The probability of choosing a red or a blue marble is 0.475.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.

Main body:

number of red marbles =19

number of blue marbles = 19

number of yellow marbles = 42

total number of balls = 19+19+42

                                   =80

probability of choosing a red or a blue marble = 19+19

P(red or blue ) = 38/80

                        = 0.475

hence the probability of choosing a red or a blue marble is 0.475.

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The payoff matrix that Gabriel and Nia use demonstrates the zero-sum between two players by showing each person's earnings as a function of both of their choices.

The reward matrix or payoff matrix is a double-entry table, similar to another Table, that holds all of the payments made by one player to the other for each selected strategy. Since one player's payment equals the other player's gain, the game is referred to as zero-sum.

The example case scenario can be used to demonstrate the calculation in the payout matrix above;

If the row player has n strategies and the column player has m strategies, the matrix must have n & m cells and contain a total of 2 n m reward values. The row player's name appears in a payment matrix to the left of the matrix, while the column player's name appears above the matrix. Since one player's payment equals the other player's gain, the game of payout matrix is referred to as zero-sum.

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there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.

answer is D. None of the above.

To test if there is significant evidence to claim that the variance of the battery life population is different than 4 hours2, we can use a chi-square test.This is how the test statistic is computed:

X2 = (n-1)*(s2/σ2)

where n is the sample size, s2 is the sample variance and σ2 is the population variance.

In this case, n = 16, s2 = 3.25 and σ2 = 4

X2 = (16-1)*(3.25/4) = 12.1875

The critical value of X2 with 15 degrees of freedom and α = 0.05 is 24.996. Therefore, since 12.1875 < 24.996, we fail to reject the null hypothesis, and there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.

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The descending order of the polynomial is (x³ + 8y³)

The term polynomial in algebra is defined as  an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division

Here we have given that (x+2y)(x²−2xy+4y²)

And we have to multiply the polynomial and write your answer in descending order.

Here we have the polynomial (x+2y)(x²−2xy+4y²).

Now, we have to use the identity

=> a³ + b³ = ( a² − ab + b² ) ( a + b ) ,

Now, we have to apply these identity one the given polynomial, then we get,

=> ( x + 2y ) ( x² − 2xy + 4y² )

=> (x³ + ( 2 y )³) = (x³ + 8 y³) .

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The average value of the given function on the given interval is = 7/2 and 6.25 respectively

What is Average?

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

(a) f(x) = x2 – 8x + 10

f = 1/b-a [tex]\int\limits^b_a {f(n)} \, dx[/tex]

f = 1/5-2 [tex]\int\limits^5_2 {x^{2} -8x+10} \, dx[/tex]

Here, a=2

b=5

f(x) =x2 – 8x + 10

f = 1/3 (x³/3 - 8x²/2+10x)5/2

f = -25/9 -20/9

f = -45/9

= -5

Mean Value Theorem

If f(x) = continous on (a, b)

If f(x) = differentiable on (a, b)

Then f(c) = f(b) -f(a)/b-a

were c∈ (a,b)

Here, f(c) = f(-5)-f(2)/5-2

f(c) = -5+2/3

f(c) = -1 ......................(1)

Here, f(x) = x²-8x+10

f(c) = c²-8c+10

f(x) = 2c-8...................(2)

equating 1&2

2c -8 = -1

2c = -1 +8

c = 7/2

c∈ (2,5)

(b) f(x) = Vx on [1, 16]

f = [tex]\sqrt{x}[/tex] on (1 ,16)

f= 1/b-a [tex]\int\limits^b_a {f(n)} \, dx[/tex]

f = 1/16-1 [tex]\int\limits^6_1 {\sqrt{x} } \, dx[/tex]

f = ( 2x (3/2)/45)₁¹⁶

f = 128/45-2/45

f = 126/45

= 14/5

Mean Value Theorem

f(x) = [tex]\sqrt{x}[/tex]

f(c) =[tex]\sqrt{c}[/tex]

f(c) = 1/2[tex]\sqrt{c}[/tex]....................(1)

we know that

f(c) = f(b)-f(a)/b-a

f(c) = f(16)-f(1)/16-1

f(c) = [tex]\sqrt{16}[/tex] -[tex]\sqrt{1}[/tex]/15

f(c) = 4-1/15

= 3/15.....................(2)

Equating (1) and (2)

1/2[tex]\sqrt{c}[/tex] = 3/15

2[tex]\sqrt{c}[/tex] = 15/3

2[tex]\sqrt{c}[/tex] = 5

[tex]\sqrt{c}[/tex] = 5/2

c = (5/2)²

=25/4

c≅ 6.25

6.25 = (1 ,16)

The average value of the given function on the given interval is = 7/2 and 6.25 respectively

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By dividing, we find The number that does not have 8 as a factor is C. 36502.

A factor of a number is a positive integer that divides evenly into the number. For example, the factors of 6 are 1, 2, 3, and 6.

Division is a mathematical operation that involves dividing one number (the dividend) by another number (the divisor) to determine the quotient, which is the result of the division.

to check whether 8 is a factor of 25424, you can divide 25424 by 8:

25424 / 8 = 3178

Since the result is an integer, 8 is a factor of 25424.

To check whether 8 is a factor of 15000, you can divide 15000 by 8:

15000 / 8 = 1875

Since the result is an integer, 8 is a factor of 15000.

To check whether 8 is a factor of 36502, you can divide 36502 by 8:

36502 / 8 = 4562.75

Since the result is not an integer, 8 is not a factor of 36502.

To check whether 8 is a factor of 10008, you can divide 10008 by 8:

10008 / 8 = 1251

Since the result is an integer, 8 is a factor of 10008.

Therefore, the number that does not have 8 as a factor is C. 36502.

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Answer:

Below

Step-by-step explanation:

This is a right triangle

the two legs are equal and the hypotenuse is 32 ft

Here is a way to calculate the answer with Pythagorean theorem

  32 ^2 = L^2 + L^2

512 = L^2

L = sqrt (512) = 22.6 ft

As per the exponential growth function, the cost of the same goods and services in January 1, 2013 is $291.54

Exponential growth function:

In statistics, exponential growth function mean  a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

Given,

The amount of goods and services that costs $200 on January 1, 1997 costs $230.16 on January 1, 2006.

Here we need to estimate the cost of the same goods and services on January 1, 2013 and also assume the cost is growing exponentially. Round your answer to the nearest cent.

Here we know that the value of

Cost on 1997 = $200

Cost on 2006 = $230.16

So, the time difference is

=> 2006 - 1997 = 6

And the amount difference is

=> $30.16

So, based on the exponential growth function, the cost of goods and services at the time of 2013 is

=> 200 + ( 1 + 30.16)⁶

=> 200 + 91.54

=> 291.54

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If other factors are held constant, sets of data that would produce the largest value for an independent-measures t statistic is the two samples both have n =30, with sample variances of 20 and 25

In a T test, the T statistic is used to help you decide whether to accept or reject the null hypothesis.

You utilize it in a manner that is quite similar to using a Z-score. When you don't know the population standard deviation or have a limited sample size, you use the t statistic.

You employ the T statistic with a p value while performing a hypothesis test. Your results' likelihood of being the result of chance is indicated by the p-value. Typically, in statistics, you use a T Test with a T Statistic rather than a Z score because you don't know much about the population.

To have larger t value , Combined standard deviation should be less

Therefore, n should be large and standard deviation should be less

Hence , The two samples both have n=30, with sample variances of 20 and 25 will provide us larger t-statistics

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Answer: [tex]y=-\frac{1}{2} x-3[/tex]

Step-by-step explanation:

[tex]3x+6y=-18[/tex]

[tex]-3x[/tex]             [tex]-3x[/tex]

[tex]6y=-3x-18[/tex]

[tex]\frac{6y}{6} =\frac{-3x}{6} -\frac{18}{6}[/tex]

[tex]y=-\frac{1}{2 } x-3[/tex]

According to the given charges, the mean of the sum would be as follows $1,692.5 and the difference of the amount of money earned by Jennie and Paul would be $-232.5

Mean:

In statistics, mean refers the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers

Given,

As Jennie charges $200 per passenger for a sunset sailing tour on her catamaran, while Paul charges $250 per passenger. we can define the amount of money each person earns per cruise as a random variable.

Here we need to find the mean and the difference of the amount of money earned by Jennie and Paul.

Let us consider x be the amount earned by Jennie and y be the amount earned by Paul.

While we looking into the given question , we have identified the value of the following,

=> Money earned by Jennie(A) = 200x

=> Money earned by Paul(B) =  250 X

Here the value of μ = $730 and σ = $ 192.62 for Jennie

And the value of Paul is μ = $962.5 and σ = $253.425

Then the mean of the sum is calculated as,

=> 730 + 962.5 = 1292.5

Similarly, the difference of the amount of money is calculated as,

=> -232.5

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Answer:

D) On average, Jennie makes $232.50 less than Paul in a typical cruise.

Step-by-step explantion

Answer:

isnt it 72

Step-by-step explanation:

since it is that kind of triangle

The number of pizzas delivered to a customer who pays $ 80 is 7 pizzas

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the number of pizzas be x₁ = 2

Let the cost of 2 pizzas be y₁ = $ 25

So , the first point A ( x₁ , y₁ ) = A ( 2 , 25 )

Now ,

Let the number of pizzas be x₂ = 5

Let the cost of 5 pizzas be y₂ = $ 58

So , the second point B ( x₂ , y₂ ) = B ( 5 , 58 )

Therefore , the slope of the 2 points is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 58 - 25 ) / ( 5 - 2 )

Slope m = 33 / 3

Slope m = 11

Therefore , the equation of the line is given by

y - y₁ = m ( x - x₁ )

Substitute the value of m in the equation , we get

y - 25 = 11 ( x - 2 )

y - 25 = 11x - 22

Adding 25 on both sides of the equation , we get

y = 11x + 3

So , the equation of line is y = 11x + 3

Now , the customer pays $ 80 , so to find the number of pizzas the customer gets can be calculated by substituting the value of y = 80

And ,

y = 11x + 3

80 = 11x + 3

Subtracting 3 on both sides of the equation , we get

11x = 77

Divide by 11 on both sides of the equation , we get

x = 7 pizzas

Therefore , the number of pizzas is 7 pizzas

Hence ,

The number of pizzas delivered to a customer who pays $ 80 is 7 pizzas

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Answer:

y = [tex]\frac{7}{5}[/tex] x + 4

Step-by-step explanation:

Perpendicular slopes are opposite reciprocals.  

So the slope is 7/5  

Us the slope and the point to find the y intercept

m = 7/5

x = -5

y = -3

y= mx + b

-3 = (7/5)(-5) + b

-3 = -7 + b  Add 7 to both sides

4 = b

y = mx + b

y = 7/5 x + 4

The equation of the line is y+1/2=3(x-2) when a line with a slope of 3 and passes through the points (2, -1/2).

Given that,

We have to find what is the equation describes a line with a slope of 3 and passes through the points (2, -1/2).

We know that,

The equation of the line is represented by (y-y₁)=m(x-x₁)

Here,

Point (2,-1/2)

Slope is 3.

Substitute in the equation,

(y-(-1/2)=3(x-2)

(y+1/2)=3(x-2)

Therefore, The equation of the line is y+1/2=3(x-2) when a line with a slope of 3 and passes through the points (2, -1/2).

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Answer:

the observed value of 9 is 13 units lower than the predicted value of 22.

Step-by-step explanation:

A residual is the difference between the observed value of a data point and the predicted value of that data point based on a given model. In a regression analysis, the residual is calculated using the formula e = y - y', where y is the observed value, y' is the predicted value, and e is the residual.

In this case, we are given the point (4,9) and the regression equation y = 5x + 2. Plugging in the value x = 4 into the regression equation, we get:

y' = 5(4) + 2 = 22

Since we are also given that the observed value of the point (4,9) is 9, we can plug these values into the formula for the residual to calculate the residual:

e = 9 - 22 = -13

Therefore, the residual e when x = 4 is -13. This means that the observed value of 9 is 13 units lower than the predicted value of 22.

1. Completing the percentage table about the payment for a pair of jeans bought by Terese at a clothing store is as follows:

Dollar Amount      Percentage

                              % off the

                         original amount

$75                         25%

2. The coupon gives Terese 25% off the original amount.

3. The amount Terese paid for the jeans (before tax) was $56.25.

4. The number of yellow candies in the bag is 15.

5. In the Math test, Blair, who answered 27 questions correctly out of 35, scored 77 percent.

6. The true statement about the amount of money Jeffrey has concerning Louis is A. Jeffry has $66.

Cost of a pair of jeans = $75

Coupon value = $18.75

Amount paid = $56.25

The coupon percentage = 25% ($18.75/$75 x 100)

Yellow candy = 25%

The total number of candies in the bag = 60

The number of yellow candy = 15 (60 x 25%)

The total number of questions = 35

The number of questions answered correctly = 27

Percent scored by Blair = 77% (27/35 x 100)

The amount of money Louis has = $110

The percentage of Louis' money that Jeffry has = 60%

The amount Jeffry has = $66 ($110 x 60%)

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Both the inequalities (- 3 > 1 - 3 = 3)  and  (1 < 3 - 3 < 1) are false.

We have the following integers -

- 3, 1 and 3.

The given inequality are -

- 3 > 1 - 3 = 3

1 < 3 - 3 < 1

- 3 > 1 - 3 = 3

- 3 > - 2 = 3

Which is false.

1 < 3 - 3 < 1

1 < 0 < 1

Which is false.

Therefore, both the inequalities (- 3 > 1 - 3 = 3)  and  (1 < 3 - 3 < 1) are false.

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Answer:

The difference is multiplied by 4 can be represented as 4 (x - 1/2) According to the question, 4 (x - 1/2) = 5 x - 1/2 = 5/4 x = 5/4 + 1/2 x = (5 + 2)/4 x = 7/4 Therefore, the number is 7/4.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Im assuming the question is to write this into actual numbers,

answer: 4(5-x)

The ordered pair which is a solution to the system of linear equations (0,2).

In mathematics, a system of linear equations refers to a collection of one or more linear equations which involve the same variables. In order to solve the system of linear equations, multiply each equation by a constant such as the coefficient of one variable becomes the same.

Hence, multiply 2x + 3y= 6 by 3 and –3x + 5y = 10 by 2.

3 (2x + 3y= 6)

6x + 9y = 18

2(–3x + 5y = 10)

-6x + 10 y = 20

Adding the two equations

6x + 9y = 18

-6x + 10 y = 20

19y = 38

y = 2

Substitute y in either of the equations:

2x + 3(2)= 6

2x = 6 – 6 = 0

x = 0

Hence, the solution is (0, 2)

The ordered pair (0,0) is not a solution as it will invalid the given linear equation.

Note: The question is incomplete. The complete question probably is Which ordered pair is a solution to the system of linear equations? 2x + 3y= 6 and –3x + 5y = 10.  (0,2) (2,0) (3,2) (2,3)

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The maximum number of poles required to drive the load is 8.

full load speed = 120*f/p

850 = 120*60/p

p = 120*60/850

p = 8.47

since no. of poles are even so

p = 8

if number pole p = 8

synchronous speed Ns = 120*f/p = 120*60/8 = 900RPM

SLIP = (Ns - N)/Ns

s = (900-850)/900

s = 0.056

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the interval, the function returns zero (-6,-2)  –6 < x < –2

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

The given f(x) = (x + 2)(x + 6)

In this function, a quadratic equation is represented (vertical parabola open upward)

The vertex stands for a minimum.

the use of a graphing tool

view the attached image

x=-6 and x=-2 are the x-intercepts.

Point: the y-intercept

The point is called the vertex.

The range ——-> is the domain. (-∞,∞) (All real numbers) (All real numbers)

The range is in the range [-4,].

x -6 or x > -2 make the function positive.

For the interval, the function returns zero (-6,-2)  –6 < x < –2

Hence, the interval, the function returns zero (-6,-2)  –6 < x < –2

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Answer:

[tex]y=2^x-5[/tex]

Step-by-step explanation:

The y-intercept occurs when x = 0.

Therefore, substitute x = 0 into each equation to find its y-intercept.

[tex]\begin{aligned}\implies y&=(-4)^0\\&=1\end{aligned}[/tex]

[tex]\begin{aligned}\implies y&=2^0-5\\&=1-5\\&=-4\end{aligned}[/tex]

[tex]\begin{aligned}\implies y&=3^0+4\\&=1+4\\&=5\end{aligned}[/tex]

[tex]\begin{aligned}\implies y&=(0)^{-4}\\&=0\end{aligned}[/tex]

Therefore, the exponential function that has a y-intercept of (0, -4) is:

[tex]\large\boxed{y=2^x-5}[/tex]

Correct option is C

The plot of normal distributions A and B

A has the larger standard deviation

Standard Deviation

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

The name standard deviation for SD came from Karl Pearson. I would guess no more than that he wanted to recommend it as a standard measure. If anything, I guess that references to standardization either are independent or themselves allude to SD.

Mean

In statistics, the mean is one of the measures of central tendency, apart from the mode and median. Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set. The mean, median and mode are the three commonly used measures of central tendency.

Normal Distribution

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graphical form, the normal distribution appears as a bell curve.

The plot of normal distributions A and B

A has the larger standard deviation

Correct option is C

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