Cara computes the mean and variance for the set 87, 46, 90, 78, and 89. She finds the mean to be 78. Her steps for finding the variance are shown below.
Variance squared = StartFraction (87 minus 78) squared + (46 minus 78) squared + (90 minus 78) squared + (78 minus 78) squared + (89 minus 78) squared Over 5 EndFraction
Variance squared = StartFraction (9) squared minus (32) squared + (12) squared + 0 squared + (11) squared Over 5 EndFraction
Variance squared = StartFraction 81 minus 1,024 + 144 + 0 +121 Over 5 EndFraction
Variance squared = StartFraction negative 678 Over 5 EndFraction = negative 135.6
What is the first error Cara made in computing the variance?

Answer:

78,732

Step-by-step explanation:

a_1 = 4

a_2 = 12

a_2/a_1 = 12/4 = 3

a_1 = 4

a_2 = 4 * 3 = 4 * 3^1 = 12

a_3 = 4 * 3 * 3 = 4 * 3^2 = 36

a_n = 4 * 3^(n - 1)

For n = 10:

a_10 = 4 * 3^(10 - 1) = 4 * 3^9 = 4 * 19,683 = 78,732

Final answer:

The formula for the nth term of a geometric sequence is a(n) = [tex]\[ a_n = a_1 \times r^{(n-1)} \][/tex], where a(n) is the nth term, a(1) is the first term, and r is the common ratio. In this case, the first term is 4 and the second term is 12. By using the formula, the calculated tenth term is 78,732. Therefore, the correct answer is C.

Explanation:

The formula for the nth term of a geometric sequence is given by:

[tex]\[ a_n = a_1 \times r^{(n-1)} \][/tex]

where:

- [tex]\( a_n \)[/tex] is the nth term,

- [tex]\( a_1 \)[/tex] is the first term,

- [tex]\( r \)[/tex] is the common ratio,

- [tex]\( n \)[/tex] is the term number.

In this case, the first two terms are given as 4 (which is [tex]\( a_1 \)[/tex]) and 12 (which is [tex]\( a_2 \)[/tex]).

The common ratio ([tex]\( r \)[/tex]) can be found by dividing the second term by the first term:

[tex]\[ r = \frac{a_2}{a_1} = \frac{12}{4} = 3 \][/tex]

Now, you can use this common ratio in the formula to find the 10th term [tex](\( a_{10} \))[/tex]):

[tex]\[ a_{10} = 4 \times 3^{(10-1)} \][/tex]

[tex]\[ a_{10} = 4 \times 3^9 \][/tex]

[tex]\[ a_{10} = 4 \times 19683 \][/tex]

[tex]\[ a_{10} = 78,732 \][/tex]

So, the correct answer is: C) 78,732

Answer: x = -9, x = 115

Step-by-step explanation:

when x = -9 :

5(-9) + 40

-45 + 40

= -5

when x = 15

5(15) + 40

75 + 40

= 115

Answer:

X = -5, 40, 115

Step-by-step explanation:

when x = 0-9

5(0-9) + 40

-45 + 40

= -5

when x = 0T =0

5(0) + 40

0 + 40

= 40

when x = 015=15

5(15) + 40

75 + 40

= 115

Answer:

Therefore both Ken and Billy ran the same amount of the training course.

Step-by-step explanation:

i) Billy was going to [tex]\frac{3}{4}[/tex] th of the training course.

ii) Ken was going to run [tex]\dfrac{1}{2}[/tex] of the training course.

iii) Billy finished [tex]\frac{1}{3}[/tex] of his run Therefore Billy finished only [tex]\frac{1}{3} \times \frac{3}{4} = \frac{3}{12} = \frac{1}{4}[/tex] of the training course.

iv) Ken finished [tex]\dfrac{1}{2}[/tex] of his run Therefore Billy finished only [tex]\dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}[/tex] of the training course.

v) Therefore both Ken and Billy ran the same amount of the training course.

Step-by-step explanation:

15x + 21= 3 (5x + 7)

Therefore, greatest common factor is (5x + 7)

Answer:

The answer 180=3x+90

Answer:

A   =  90,312.5 square feet is the maximum area.

Step-by-step explanation:

Here, the shape of the enclosure  = Rectangle

Now, 3 sides of the rectangle needs to be fenced.

Total length of the fencing wire  = 1000 ft

Let us assume the length of the enclosure = L

The width of the enclose = W

According to question:

The length to fenced = Perimeter of the rectangle - 1 side of Enclosure

⇒ 1000  =  2 (L + W) - L

or, 1000 = L +  2 W

or, L  = 1000 - 2 W  .... (1)

Now, as we need to MAXIMIZE the area of the enclosure:

Area of the enclosure  = L x W    =  (1000 - 2 W) x  W

Now simplifying the area expression, we get:

[tex]A(w) = 1000 w - 2w^2[/tex]

This is a parabola that opens downward so there is a maximum point.

The vertex of the parabola is (h,k) where h is the "maximizing number" and k is the maximum area.

Use the fact that h   =   -b/2 a

h   =    -850/(2*[-2])

h  =   -850/(-4)

h   =   212.5 would be the length of all four sides if it were not for the barn

Therefore you have an extra 212.5 feet

Add the 212.5 feet to the opposite side(length) to get 425 feet.

You have a rectangle that is 212.5 feet by 425 feet by 212.5 feet by "the barn".

The width is 212.5 feet which maximizes the area.

A  =   l w

A  =  425*212.5

A   =  90,312.5 square feet is the maximum area.

Answer:

Answer is: C - hope it helps you!

Answer:

y=3x+-7

Step-by-step explanation:

the standard form is y=mx+b

m being the slope and b being the y intercept

Answer:309.799

Step-by-step explanation:293.08

14.00 =309.799

+ 2.719

Answer:

x=6

Step-by-step explanation:

2x+(4x+3)=39

2x+4x+3=39

6x+3=39

6x=39-3

6x=36

x=36÷6

x=6

Solving the system of equations y = 4x + 3 and 2x + y = 39, we first substitute y from the first equation into the second. Simplifying, we find x = 6. Substituting x = 6 into the first equation, we find y = 27. Therefore, the solution is x = 6, y = 27.

To find the answer to this system of linear equations using substitution method, we first need to make y the subject of the first equation. From y = 4x + 3, we then substitute y in the second equation, thereby getting 2x + 4x + 3 = 39.

After simplifying, the combined equation becomes 6x + 3 = 39. We then isolate x by subtracting 3 from both sides, giving 6x = 36, and therefore x = 6.

To find y, substitute x = 6 into the first equation, y = 4x + 3. Thus, y = 4*6 + 3, which gives y = 27.

So, for the equations y = 4x + 3 and 2x + y = 39, the solution is x = 6, y = 27.

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Answer:

EF = 6m.

Step-by-step explanation:

Given that:

1) All the edges of the pyramid in the model have length 12m.

So, AB = 12m

2) E is the middle of AT, F is the middle of BT

So, EF is a line segment connecting the midpoints of ΔATB

So, by applying The Triangle Mid-segment Theorem

EF // AB and EF = 0.5 AB

So, EF = 0.5 AB = 0.5 * 12 = 6m

====================================

The Triangle Mid-segment Theorem:

The line segment connecting the midpoints of any two sides of a triangle has the following properties:

1) The line segment will be parallel to the third side.

2) The length of the line segment will be a half of the length of the third side.

[tex](7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6) = 8x^3+5x^2+2x+3[/tex]

Solution:

Given that we have to perform the indicated operation

Given polynomial is:

[tex](7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6)[/tex]

Polynomial addition\subtraction is similar to arithmetic addition\subtraction

Add\subtract the terms of coefficients with same variable with same exponent

For example: [tex]x^3 -2x^3 = -x^3[/tex]

To subtract Polynomials, first reverse the sign of each term we are subtracting

Which means, reverse the sign of each term in second bracket

[tex]\rightarrow (7x^3 + 11x^2 + 4x + 9)-(-x^3 + 6x^2 + 2x+6)\\\\\rightarrow (7x^3 + 11x^2 + 4x + 9)+x^3 - 6x^2 - 2x-6\\\\\text{Remove the parenthesis in first bracket }\\\\\rightarrow 7x^3 + 11x^2 + 4x + 9+x^3 - 6x^2 - 2x-6\\\\\text{Group the similar terms }\\\\\rightarrow 7x^3+x^3+11x^2-6x^2+4x-2x+9-6\\\\\text{Combine the similar terms }\\\\\rightarrow 8x^3+5x^2+2x+3[/tex]

Thus the given operation is performed

Answer: 0.112485

Step-by-step explanation: Look below for an attached explanation

Hope this helps!

To find 0.06 divided by 0.5334, multiply both numbers to convert them into whole numbers and then perform long division. The result of the division is approximately 0.1125.

The question asks for the division of two decimal numbers, specifically 0.06 divided by 0.5334. To divide these decimals, you can use long division or a calculator. Here's how to divide them step-by-step using long division:

In this case, 0.06 divided by 0.5334 is approximately 0.1125.

This type of math problem is common in various science calculations, such as determining the concentration of a solution in chemistry or the rate of a reaction in physics.

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Answer:

300

Step-by-step explanation:

22% means 22 of 100

for every 100 persons 22 voted

for every x persons 66 voted.lets do the math to find what is the x

[tex] \frac{22}{100} = \frac{66}{x} [/tex]

[tex]x = \frac{66 \times 100}{22} [/tex]

x=300

Answer: 300

Step-by-step explanation:

we know that 22% is the same as 22/100 ( 22 over 100). We are trying to find the whole, which means we are already given the part which is 66. how can we get from 22 to 66? 22 multiples by 3 = 66 do the same to the bottom 100 multiplied by 3 is 300.

Answer: 2

Step-by-step explanation:

to find this you use the equation

y2-y1

--------

x2-x1

so with your points tuat would be

5+3/4-0 (it becomes a plus bc two negatives= a positive

8/4=2

Step-by-step explanation:

9/8 × (-7/3) =

9 × -7 = -63

8 × 3 = 24

-63/24 simplify

-21/8

Answer:

34.246

Just divide both numbers

Answer:

[tex]\large\boxed{y=\dfrac{1}{4}x^2-x-4}[/tex]

Step-by-step explanation:

The equation of a parabola in vertex form:

[tex]y=a(x-h)^2+k[/tex]

(h, k) - vertex

The focus is

[tex]\left(h,\ k+\dfrac{1}{4a}\right)[/tex]

We have the vertex (2, -5) and the focus (2, -4).

Calculate the value of a using [tex]k+\dfrac{1}{4a}[/tex]

k = -5

[tex]-5+\dfrac{1}{4a}=-4[/tex]        add 5 to both sides

[tex]\dfrac{1}{4a}=1[/tex]           multiply both sides by 4

[tex]4\!\!\!\!\diagup^1\cdot\dfrac{1}{4\!\!\!\!\diagup_1a}=4[/tex]

[tex]\dfrac{1}{a}=4\to a=\dfrac{1}{4}[/tex]

Substitute

[tex]a=\dfrac{1}{4},\ h=2,\ k=-5[/tex]

to the vertex form of an equation of a parabola:

[tex]y=\dfrac{1}{4}(x-2)^2-5[/tex]

The standard form:

[tex]y=ax^2+bx+c[/tex]

Convert using

[tex](a-b)^2=a^2-2ab+b^2[/tex]

[tex]y=\dfrac{1}{4}(x^2-2(x)(2)+2^2)-5\\\\y=\dfrac{1}{4}(x^2-4x+4)-5[/tex]

use the distributive property: a(b+c)=ab+ac

[tex]y=\left(\dfrac{1}{4}\right)(x^2)+\left(\dfrac{1}{4}\right)(-4x)+\left(\dfrac{1}{4}\right)(4)-5\\\\y=\dfrac{1}{4}x^2-x+1-5\\\\y=\dfrac{1}{4}x^2-x-4[/tex]

Answer:

yes

Step-by-step explanation:

Answer:

3x + 1 <-5 is x<−2

5x-1> 29 is x>6

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x<−2

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

x>6

Final answer:

To solve the compound inequality 3x + 1 < -5 OR 5x - 1 > 29, solve each inequality separately. The solution is all real numbers that are either less than -2 or greater than 6.

Explanation:

To solve the compound inequality 3x + 1 < -5 OR 5x - 1 > 29, we need to solve each inequality separately and then find the union of the two solutions, since the word 'OR' indicates that a solution to either inequality will satisfy the compound inequality.

Solving the first inequality:

3x + 1 < -5

Solving the second inequality:

5x - 1 > 29

The solution to the compound inequality is the set of all real numbers that are either less than -2 or greater than 6.

Answer: 0.766 = x/12

Final answer:

The correct equation for the triangle is determined by the context provided, which may involve setting up proportions or using trigonometric ratios such as the tangent. Without specific information from a diagram or narrative of the triangle, the correct equation cannot be identified.

Explanation:

The correct equation based on the triangle shown is determined by setting up a mathematical relationship (proportion or equation) that represents the situation described in the diagram or narrative associated with the triangle. Without the specific diagram or narrative details, it is impossible to determine the correct equation. However, generally, if you are given the lengths of sides in different units (for example, feet and inches), you would set up a proportion like

1 foot/12 inches = x feet/y inches

and then cross-multiply to solve for x or y.

If you are dealing with trigonometric functions and are given an angle, you may use a function like sine, cosine, or tangent to find a relationship between the sides. The correct equation could include the tangent ratio if the triangle is right-angled and you have the lengths of the opposite and adjacent sides to the given angle:

tan(theta) = opposite/adjacent

Answer:

Volume= 3*4*6= 72 cubic feet

Step-by-step explanation:

Whenever finding volume of a simple rectangular prism like that one, simply multiply the Length of one side by the Height of the prism by the Width of the front face and you will get your solution. Length=6 ft, Height=3 ft, Width=4 ft. Hence, V=L*W*H or V=6*4*3=72 cubic feet.

We are given a painter can paint 350 square feet in 1.25 hours.

We want to figure out the painting rate in square feet per hour. “Per hour” means for every 1 hour.

To find this, an equation like 350 = 1.25h (h for hours) can be set up. To solve, the only thing we need to do is divide by 1.25 to get h alone:

350/1.25 = 1.25h/1.25 or 280 = h

The painter can paint 280 square feet per 1 hour.

Each month for 9 months, Jordan buys 2 sports books. How many more sports books does he need to buy before has bought 25 sports books?

Jordan needs to but 7 more sports book

From given,

Each month for 9 months, Jordan buys 2 sports books

Thus for one month he buys 2 sports books

For, 9 months, number of books is bought is given as:

[tex]\text{Number of books bought in 9 months } = 9 \times 2 = 18[/tex]

Thus, in 9 months he has bought 18 books

He needs to buy 25 sports books

Therefore, remaining books to be bought = 25 - 18 = 7

Thus he needs to buy 7 more books to have 25 of them

True, [tex]f(x)[/tex] is a function.

a = –2 and b = 3

Solution:

Given equations are

3a – b = –9 – – – – (1)

–3a – 2b = 0  – – – – (2)

To solve these equations by elimination method.

Elimination method means eliminating one variable to find the other variable.

Add equation (1) with equation (2), we get

3a – b + (–3a – 2b) = –9 + 0

⇒ 3a – b – 3a – 2b = –9

Combine like terms together.

⇒ 3a – 3a – b – 2b = –9

⇒ 0 – 3b = –9

⇒ – 3b = –9

Divide by (–3) on both sides, we get

⇒ b = 3

Substitute b = 3 in equation (1), we get

(1) ⇒ 3a – b = –9

⇒ 3a – 3 = –9

Add 3 on both sides of the equation,

⇒ 3a = –6

Divide 3 on both sides of the equation

⇒ a = –2

Hence, a = –2 and b = 3.

Answer:

3x-7y=14

Step-by-step explanation:

7y=3x-14

3x-7y=14

Answer:

37.41

Step-by-step explanation:

multiply 4.30 by 10 to get 43

then make it a decimal =0.43

after that multiply it by 13

0.43 times 13 = 5.59

subtract 5.59 from 43

Answer:

The equation of a line through (5 -3) that is parallel to y = 1/2 x+3 is

y = - 2 x  + 7

Step-by-step explanation:

Let us assume the slope of the line whose equation we need to find is m 1.

The line parallel to the needed line  is:   y=1/2x+3

Comparing it with the general form: y = m x + C

we get m 2 = 1/2

Now, as Line 1 is Perpendicular to Line 2.

⇒ m 1 x m 2  = -1

⇒ m 1 x ( 1/2)  = -1

⇒ m 1  = - 2

Also, the point son the line 1 is given as: (x,y)  = (5,-3)

Put the value of point and Slope in y = m x + C to find the value of Y- INTERCEPT.

we get: -3 = (-2) (5) +  C

or, C = -3 + 10 = 7

⇒ C = 7

The general line equation is given as:  y = m x + C

Substituting  the values of C and m, we get:

y = - 2 x  + 7

Hence, the equation of a line through 5 -3 that is parallel to y = 1/2 x+3 is

y = - 2 x  + 7

Answer:

18

Step-by-step explanation:

2(x - 5) + 4 = 30

2x - 10 + 4 = 30

2x - 6 = 30

2x = 36

x = 18

Answer:

18

Step-by-step explanation:

2(x-5)+4=30

2(x-5)=30-4

2(x-5)=26

x-5=26/2

x-5=13

x=13+5

x=18

Answer:$135

Step-by-step explanation: you divide it and get that answer

Answer:

$135

Step-by-step explanation:

90×1.5= 135 Hope this helps