What is the samole variance for the data given:
5,10,7,12,0,20,15,22,8,2

The domain for which functions f(x) = 2x² - 1 and g(x) = 1 - 3x are equal:{-2, 1/2}

When the functions f(x) = 2x² - 1 and g(x) = 1 - 3x are equal,

f(x) = g(x)

2x² - 1 = 1 - 3x

2x² + 3x -1 - 1 = 0

2x² + 3x - 2 = 0

We solve above quadratic equation to find the value of x.

2x² + 3x - 2 = 0

2x² + 4x - x - 2 = 0

2x(x + 2) - 1(x + 2) = 0

(x + 2)(2x - 1) = 0

x + 2 = 0    OR    2x - 1 =  0

x = -2         OR     x = 1/2

This means, for x = -2 as well as x = 1/2 the functions f(x)=2x^2−1 and g(x)=1−3x are equal.

Thus, the required domain is: {-2, 1/2}

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The number of apples that John have is 2 if Mary has 8 apples and Jahn has 1/4 the number of apples as Mary.

Therefore the answer is 2.

This is a problem based on use of fractions. A fraction is a mathematical expression that represents a part of a whole.

John has 1/4 the number of apples as Mary, which means that for every 4 apples that Mary has, John has 1 apple.

To find the number of apples John has, you would divide the number of apples Mary has by 4. In this case, Mary has 8 apples, so John would have

1/4 * 8 = 2 apples

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Answer:

1. $16-20%= 12.8 US$

2. $x-20%=x

3. >>>>>?

Step-by-step explanation:

A 20% discount means that you subtract 20% of the normal price.  Suppose the normal price is $100.  20% of this is $20.  Subtract this from $100 and you have the new price---$80.

Note that "subtracting 20%" is the same as multiplying by 0.8----the general formula is:

discount price = normal price * (1-d)   , where d is the decimal equivalent of the percentage discount.

From the example above:

discount price = normal price * (1-d) = 100(0.8)

to go the other way, simply rearrange the formula:

normal price = discount price / (1-d)

Find the midpoint of each pair of points, and then take the average of those midpoints to find the center pc. The radius r is the distance from pc to any of the given points. To find the unit normal vector n, take the cross product of any two vectors between the given points and pc.

To find the center pc, the radius r, and the unit normal vector n of the circle that goes through the three points p1=(5,0,7), p2=(1,3,6), and p3=(7,5,4) in 3D space, follow these steps:

1. Find the midpoint of each pair of points:

Midpoint of p1 and p2 = (3,1.5,6.5)

Midpoint of p2 and p3 = (4,4,5)

Midpoint of p3 and p1 = (6,2.5,5.5)

2. Take the average of the three midpoints to find the center pc:

pc = (4.33, 2.83, 6.17)

3. Calculate the radius r as the distance from pc to any of the given points:

r = √((5-4.33)2+(0-2.83)2+(7-6.17)2)

r = 2.66

4. To find the unit normal vector n, take the cross product of any two vectors between the given points and pc:

v1 = (5-4.33, 0-2.83, 7-6.17)

v2 = (1-4.33, 3-2.83, 6-6.17)

n = v1 x v2

n = (-11.67, 5.67, -7.33)

n = (-0.79, 0.37, -0.48)

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Answer:

The y-intercept is (0, 3).

The equation is not factorable.

Step-by-step explanation:

We are given the equation:

Y=4x^2-4x+3

and we are asked to graph it.

To do this, let's first find the vertex of the parabola that a quadratic equation creates.

[tex]V(-\frac{b}{2a}),f(x))[/tex]

Here, a = 4 and b = -4. So the vertex must be:

[tex]V(-\frac{-4}{2(4)},f(x))[/tex]

[tex]V(\frac{1}{2},f(\frac{1}{2}))[/tex]

[tex]V(\frac{1}{2},2)[/tex]

Next, let's find the intercepts.

[tex]x=0[/tex]

[tex]y=4(0^{2})-4(0)+3=3[/tex]

The y-intercept is (0, 3).

The equation is not factorable.

Answer: [tex]AD=33[/tex]

Step-by-step explanation:

Using the formula for the perimeter of a rectangle,

[tex]2(2z+1+3z+3)=108\\\\2(5z+4)=108\\\\5z+4=54\\\\5z=50\\\\z=10\\\\\implies BC=33 \implies AD=33[/tex]

The factored form of this polynomial x³ + 3x² - 13x - 15 will be (x - 3), (x + 5) and (x + 1).

What is factorization?

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The polynomial is given as,

⇒ x³ + 3x² - 13x - 15

Factorize the polynomial, then we have

⇒ x³ + 3x² - 13x - 15

⇒ x³ - 3x² + 6x² - 18x + 5x - 15

⇒ x²(x - 3) + 6x(x - 3) + 5(x - 3)

⇒ (x - 3)(x² + 6x + 5)

⇒ (x - 3)(x² + 5x + x + 5)

⇒ (x - 3)[x(x + 5) + 1(x + 5)]

⇒ (x - 3)(x + 5)(x + 1)

Therefore, The factored form of this polynomial x³ + 3x² - 13x - 15 will be (x - 3), (x + 5) and (x + 1).

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The  probability that x is within 1 standard deviation from its mean value is 0.68.

Probability is the measure of the likelihood of an event occurring. In statistics, it is used to describe the chance of a particular value falling within a certain range.

A standard deviation is a measure of the spread of a set of data from its mean.

Typically, 68% of the data falls within 1 standard deviation from the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.

In order to find the probability that x is within 1 standard deviation from its mean value, we need to use a normal distribution.

In a normal distribution, 68% of the data falls within 1 standard deviation from the mean.

So, in this case, the probability that x is within 1 standard deviation from its mean value is 0.68 or 68%.

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The cost of 2 pounds of cherries without the coupon would be $6.50 x 2 = $13.

With the coupon, Madeline would have to pay $13 - $1 = $12 for 2 pounds of cherries.

The expression for the cost of buying x pounds of cherries with the coupon is:

(6.5*x) - 1

Therefore , the solution of the given problem of triangle comes out to be x value of right triangle is 65° .

Due to their four sides or more, triangles are considered polygons. It has a straightforward, geometric form. A triangle is a square angle formed by the letters ABC. A singular rectangle or square is produced by Euclidean geometry when the sides are still not collinear. Triangles are polygons because they have three sides and three corners. Where three sides of a triangle come together are its corners. A triangle's angles sum up to 180 degrees.

Here,

Given :

triangle has an right angle so its 90 degree.

The triangle sum of angle is 180 degree.

Thus,

=> x + 25° + 90° = 180°

=> x + 115° = 180°

=> x = 180° -115°

=> x = 65°

Thus , x value is 65° .

Therefore , the solution of the given problem of triangle comes out to be

x value of right triangle is 65° .

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Answer:

  y = 0.4·5^x

Step-by-step explanation:

You want an exponential function y = a·b^x that passes through the points (1, 2) and (3, 50).

The given point values give two equations in two unknowns when used in the given exponential form:

  y = a·b^x

  2 = a·b^1

  50 = a·b^3

Dividing the second equation by the first, we find b:

  50/2 = (ab^3)/(ab)

  25 = b^2 . . . . . simplify

  5 = b . . . . . . . . . square root

Then the value of 'a' can be found from the first equation:

  2 = a·5

  a = 2/5 = 0.4

Using these values of 'a' and 'b', we have the exponential function ...

  y = 0.4·5^x

__

Additional comment

The exponential regression function of your calculator can tell you the same thing.

According to the information and the graph, the best place for Lois Lane to stand to receive the keys from Superman is in the middle of the Krytonite cage because it is the closest place to the point where superman is standing.

The point where Lois Lane should stand is in the middle of the cage because there he will have a better chance of receiving the Kronite keys that he has. Additionally, this point is the closest to the point where Superman is standing so he wouldn't have to go near the krionite and could throw the keys from there.

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The value of the double integral ∫r(8x 6y 48)da where r is the region: 0≤x≤3,0≤y≤4. is 864

Double integrals are a way to integrate over a two-dimensional area. In some cases, the integral of one variable function, a double integral, is defined as a limit of a Riemann sum.

Double integrals are used to calculate the area of a region, the volume under the surface, and the average value of a function of two variables over a rectangular region. In a double integral, the outer limits must be constant, but the inner limits can depend on the outer variable. This means, we must put y as the inner integration variables, as was done in the second way of computing

∬R(8x+6y+48)dA=∫04∫03(8x+6y+48)dxdy

=∫04(4x2+6xy+48x)∣03dy

=∫04(36+18y+144)dy

=∫04(180+18y)dy

=(180y+9y2)∣04

=720+144=864

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Answer:

8 and 1/3

Step-by-step explanation:

First, let's understand the situation. There is a 25 oz juice that is to be split 3 ways. To determine the amount of jucie each person gets, we will take the total amount of juice and divide it by the number of kids, 3. When we do this, we get 25/3. Since this fraction can;t be simplified into a whole number, we will need to turn 25/3 into a mixed number. To do this, we need to know how many times 3 goes into 25. 3 goes into 25 8 times with a remainder of 1. This remainder is put over 3, giving us the final answer, 8 and 1/3.

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Fitzgerald used setting in the exposition of this passage by creating atmosphere and establishing geographic context.

In The Great Gatsby, the narrator mentions that the house is located "at the very tip of the egg" and is "squeezed between two huge places" which rent for a high season price. The description of Gatsby's mansion as a "colossal affair" with a tower, marble swimming pool, and vast lawns and gardens further emphasizes Gatsby's wealth and sophistication.

By painting this picture of the setting, Fitzgerald sets the stage for the events of the story and prepares the reader to encounter the characters and conflicts that will emerge.

Hence, the setting described in this passage helps to establish the geographic context of the story and create an atmosphere for the reader.

The question seems incomplete, it must have been...

"My house was at the very tip of the egg, only fifty yards from the Sound, and squeezed between two huge places that rented for twelve or fifteen thousand a season. The one on my right was a colossal affair by any standard—it was a factual imitation of some Hotel de Ville in Normandy, with a tower on one side, spanking new under a thin beard of raw ivy, and a marble swimming pool, and more than forty acres of lawn and garden. It was Gatsby’s mansion.

How does Fitzgerald use setting in the exposition of this passage?

-He underscores the cultural differences between West Egg and East Egg.

-He introduces the reader to the themes of jealousy and undying love.

-He suggests that Gatsby is sophisticated and very wealthy.

-He creates atmosphere and establishes geographic context."

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The translated points are P' ( -2 , 3 ) and Q' ( 3 , 7 )

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the points be represented as P and Q

Now , the coordinates of point P = P ( 0 , 0 )

And , the coordinates of the point Q = Q ( 5 , 4 )

when the points are translated up 3 units and left 2 units

The coordinates of the translated point will be ( x , y ) to ( x - 2 , y + 3 )

Substituting the values in the equation , we get

The coordinates of the translated point P' = P' ( -2 , 3 )

The coordinates of the translated point Q' = Q' ( 3 , 7 )

Hence , the translated points are P' ( -2 , 3 ) and Q' ( 3 , 7 )

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If Candidate A received 36 votes, the number of votes that Candidate B received is 60 votes.

The correct option is (C)

Now, According to the question:

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

The first step is to determine the relationship between the number of votes of Candidate A and B. This can be determined by expressing the number of votes in its simplest form.

12 : 20 in its simplest form is 3 : 5

18 : 30  in its simplest form is 3 : 5

27 : 45  in its simplest form is 3 : 5

Now, determine the factor second factor of 36 if the first factor is 3.

36 / 3 = 12

Now multiply 12 by 5: 12 x 5 = 60

Hence, If Candidate A received 36 votes, the number of votes that Candidate B received is 60 votes.

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The weight of Dima in kilograms round to the nearest hundredth is: 58.51 kilograms.

A weight measuring unit: One pound equals 454 grams. One kilogram is roughly equivalent to 2.2 pounds.

One pound contains 16 ounces.

The word "poundus" means "weight" in Latin.

The £ symbol is derived from an ornate L in Libra.

We are given the weight of Dima as 129 pounds.

we know by conversion that:

1 pound= 0.453592 kilograms

Hence 129 pounds= 129×0.453592 kilograms

129 pounds=58.513368 kilograms.

Therefore, The weight of Dima in kilograms round to the nearest hundredth is: 58.51 kilograms.

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Answer:

D

Step-by-step explanation:

The correct answer is D. −0.6; for every additional hour, the length of the icicle decreases by 0.6 inches.

The slope of a line represents the rate of change of one variable with respect to the other variable. In this case, the length of the icicle (y) is changing with respect to time (x). The slope of the line represents the change in the length of the icicle (y) for every additional hour (x).

Since the icicle is melting at a rate of 0.6 inches per hour, the length of the icicle decreases by 0.6 inches for every additional hour. The slope of the line representing this relationship is -0.6. This means that for every additional hour, the length of the icicle decreases by 0.6 inches.

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Answer:

Step-by-step explanation:

The proportion of Year 13 pupils in the football club is 12/35. To convert this to a percentage, we need to multiply it by 100.

12/35 * 100 = 34.285714285714285 (approximately 34.3% when rounded to 1 decimal place)

Answer:

[tex] \frac{13}{35} \times \frac{100}{100} = 37.14\%[/tex]

There is a 68% chance that a repair claim will be between $40 and $1020.

The normal distribution is a continuous probability distribution that is symmetric around the mean, with mean and variance being the same. In this case, the mean is $530 and the standard deviation is $490. This means that the repair claims are normally distributed, with the majority of the claims being between $530-$490 and $530+$490. This gives us a range of $40-$1020.

The normal distribution is often used to describe random variables because it is the most common probability distribution. In this case, it implies that the repair claims are randomly distributed around the mean of $530. The standard deviation of $490 indicates that there is a 68% chance that a repair claim will be within one standard deviation of the mean. In this case, that means that there is a 68% chance that a repair claim will be between $40 and $1020.

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Answer: The transformation is a reflection over the line x=0. The original square OABC is reflected over the line x=0 and the only invariant point is (0,2).

Step-by-step explanation:

This transformation is a reflection over the line with equation y = 2. The original square OABC is reflected over this line, mapping point A to C and C to A, while the only invariant point is (0, 2).

Answer:

120

Step-by-step explanation:

720/6 =120

According to the problem this week Edward took 304 photographs.

A week is a unit of time typically spanning seven days, representing the time it takes for one cycle of the days of the week to be completed. Generally, a week is divided into seven days, beginning with Sunday and ending with Saturday. During a week, people usually work five days, with weekends off for leisure or relaxation.The term “week” is believed to be derived from the Germanic word “wih”, which means “turning” or “change”.

This week Edward took 304 photographs. This is calculated by taking the 320 photographs he took last week and subtracting 5% (or 16 photographs). 320 - 16 = 304.

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Answer:c=25 d=9 final answer c2+3d= 225

Step-by-step explanation:

c=25 because 5^2 is 5×5=25. D is 9 because 3×3=9. And the final answer is 25×9=225

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{c^2 + 3d}\\\mathsf{= 5^2 + 3(3)}\\\mathsf{= 5\times 5 + 3(3)}\\\mathsf{= 25 + 9}\\\mathsf{= 34}\\\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{34}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

17

Step-by-step explanation:

First you have to subtract 125-50 since we are trying to find the amount he made from selling t-shirts. That equals 85. So now we divide 85 by 5 and that gives us 85.

Answer:

Step-by-step explanation:

a._x+_=_

5x+40=125

    -40  -40

5x=85

/5

x=17

he sold 17 shirts

At the lowest temperature he could get a water and salt solution to attain, Fahrenheit set zero.

Fahrenheit is named for German scientist Daniel Gabriel Fahrenheit, who was born there in 1686 as part of the Polish-Lithuanian Commonwealth. He was the first to develop a constant, accurate method of measuring temperature. At the lowest temperature he could get a water and salt solution to attain, Fahrenheit set zero.

To assist us remember that we go from colder to hotter as we walk up the scale on our thermometer, let's label it. In other terms, a higher number of degrees Fahrenheit is hotter than a lower number.

[tex]$$\begin{aligned}& \text { Given:- } \mathrm{C}=\frac{5}{9}(\mathrm{~F}-32) \\& \Rightarrow \mathrm{F}=\frac{9}{5} \mathrm{C}+32\end{aligned}$$[/tex]

(I) If [tex]$F^{\prime}=F+1$[/tex]

[tex]$$\begin{aligned}\mathrm{C}^{\prime} & =\frac{5}{9}\left(\mathrm{~F}^{\prime}-32\right) \\\mathrm{C}^{\prime} & =\frac{5}{9}(\mathrm{~F}+1-32) \\\mathrm{C}^{\prime} & =\frac{5}{9}(\mathrm{~F}-32)+\frac{5}{9} \times 1 \\\mathrm{C}^{\prime} & =\mathrm{C}+\frac{5}{9}\end{aligned}$$[/tex]

Hence, a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of [tex]$\frac{5}{9}$[/tex] degree Celsius.

Therefore, statement I exists true.

(II) If [tex]$\mathrm{C}^{\prime}=\mathrm{C}+1$[/tex]

[tex]$$\begin{aligned}& \mathrm{F}^{\prime}=\frac{9}{5} \mathrm{C}^{\prime}+32 \\& \mathrm{~F}^{\prime}=\frac{9}{5}(\mathrm{C}+1)+32 \\& \mathrm{~F}^{\prime}=\left(\frac{9}{5} \mathrm{C}+32\right)+\frac{9}{5} \\& \mathrm{~F}^{\prime}=\mathrm{F}+\frac{9}{5} \\& \mathrm{~F}^{\prime}=\mathrm{F}+1.8\end{aligned}$$[/tex]

Therefore, a temperature increase of 1 degree Celsius exists equivalent to a temperature increase of 1.8 degrees Fahrenheit.

Therefore, statement II exists true.

[tex]$$\begin{aligned}& \text { (III) If } F^{\prime}=F+\frac{5}{9} \\& C^{\prime}=\frac{5}{9}\left(F^{\prime}-32\right) \\& C^{\prime}=\frac{5}{9}\left(F+\frac{5}{9}-32\right) \\& C^{\prime}=\frac{5}{9}(F-32)+\frac{5}{9} \times \frac{5}{9} \\& C^{\prime}=C+\frac{25}{81}\end{aligned}$$[/tex]

Therefore, a temperature increase of [tex]$\frac{5}{9}$[/tex] degree Fahrenheit exists equivalent to a temperature increase of [tex]$\frac{25}{81}$[/tex] degree Celsius.

Therefore, statement III exists false.

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Answer: 3/20

Step-by-step explanation:

3/5 x 1/4

The value of the GCF will be = 5*x = 5x

The greatest common divisor of two or more integers that are not all zero in mathematics is the biggest positive integer that divides each of the integers.

The biggest common factor is the factor that splits both numbers in half. To get the greatest common factor, first list each number's prime factors.

A set's greatest common factor (GCF) is the biggest factor that all of the numbers share. For example, the numbers 12, 20, and 24 all have two common factors: 2 and 4. The greatest is 4, hence the GCF of 12, 20, and 24 is 4. GCF is frequently used to locate common denominators.

As we have, two different terms as: 5x^3, –5x

Prime factorisation of 5x^3 = 5*x*x*x

While the prime factorisation of -5x = -1*5*x

So, the value of the GCF will be = 5*x = 5x (As only 5 and x are common in the prime factorisation of both the numbers)

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From the given figure, equation represents the Pythagorean theorem is 13²=12²+5². Therefore, option D is the correct answer.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

From the given figure, area of a largest square is 169 square units, area of a larger square is 144 square units and the area of a smaller square is 25 square units.

We know that, the area of a square is side².

Now, the side(a) of a largest square is side²=169

So, a=13 units

The side(b) of a larger square is side²=144

So, b=12 units

The side(c) of a smaller square is side²=25

Then, c=5 units

Here, a, b and c form a right angle triangle.

By using Pythagoras theorem, we get

a²=b²+c²

13²=12²+5²

Therefore, option D is the correct answer.

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