What is the mode of the following numbers?
9,8, 7, 1,1

The probability that the sample mean would be higher than 88.4 or smaller than 84.4 is 0.85582

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ = 86

sample size, n = 140

standard deviation, σ  = 11

The probability

P(z > 88.4) + P(z < 84.4)

z score for z < 88.4

z = (88.4 - 86) / 11

= 0.21818 p value = 0.41364

z score for z < 84.4

z = (84.4 - 86) / 11

=  -0.14545

p value for z < -0.14545 = 0.44218

The probability required = 0.41364 + 0.44218 = 0.85582

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y is inversely proportional to the square of x, here y in terms of x is 2/5.

From the given problem y is inversely proportional to the square of x.  

A table of values for x and y is shown.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

From the table:

(a) As we know that, y is inversely proportional to the square of x,

Here k is proportionality constant.

y∝1/x²

y= k/x²

4=k/1²

k=4

So, y in terms of x is y=4/x²

(b) Putting the value of y=25, we get:

25=4/x²

x²=4/25

x=2/5

Therefore, y is inversely proportional to the square of x, here y in terms of x is 2/5.

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Answer:

Step-by-step explanation:

Get the same denominator by multiplying 4/9 by 2/2 and 1/2 by 9/9 to get 8/18-9/18=-1/18

The two negative signs can become an addition to make -1/9+2/5 which can be rewritten as 2/5-1/9. We make them the same denominator and subtract to get 13/45.

The value for the given expression  [tex]\alpha ^{2} + \beta ^{2}[/tex] will be [tex](\alpha +\beta )^{2}-2\alpha \beta[/tex].

What are Algebraic Identities?

Algebraic identities are algebraic equations that hold true for any value of each of their variables. In factoring polynomials, they are also used.

As we know, [tex](a+b)^{2} = a^{2} +2ab + b^{2}[/tex]  then,

For the given question, [tex](\alpha +\beta )^{2} = \alpha ^{2} +2\alpha \beta + \beta ^{2}[/tex]

Now, subtracting [tex]2\alpha \beta[/tex] on both sides then, we get

or, [tex](\alpha +\beta )^{2}-2\alpha \beta = \alpha ^{2} +2\alpha \beta + \beta ^{2}-2\alpha \beta[/tex]

or, [tex](\alpha +\beta )^{2}-2\alpha \beta = \alpha ^{2} + \beta ^{2}\\[/tex]

or, [tex]\alpha ^{2} + \beta ^{2}=(\alpha +\beta )^{2}-2\alpha \beta[/tex]

That's how the value  [tex]-2\alpha \beta[/tex] comes.

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The translated absolute value function graphed is defined as follows:

y = |x - 3| + 5.

The absolute value function, of vertex (h,k), is defined by the following piecewise rule, depending on the input of the function:

In this problem, the coordinates of the vertex are given as follows:

Hence the vertex is given by the following point:

(3,5).

Then the equation graphed is defined by the rule presented as follows:

y = |x - 3| + 5.

Which is a translation of 3 units right and 5 units up of the standard absolute value function.

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Answer:

1256.64

Step-by-step explanation:

Step-by-step explanation:

-(10x + 2) > 5x - 1 - 8x

combine x terms on right side:

-(10x + 2) > -3x - 1

remove ()'s from left side:

-10x - 2 > -3x - 1

add 10x to both sides:

-10x - 2 + 10x > -3x - 1 + 10x

-2 > 7x - 1

add 1 to both sides:

-2 + 1 > 7x - 1 + 1

-1 > 7x

divide both sides by 7:

-1/7 > 7x /7

-1/7 > x or x < -1/7

in interval notation: (-∞, -1/7)

I need help too on this one

Answer:

you lowest tempeture in the mesosphere is -96

Step-by-step explanation:

Answer:

87c

Step-by-step explanation:

Answer:

Bag a, by 85 grams!

Step-by-step explanation:

1) Work out the weight of bag a

1 banana is 140 grams so to find out 8 you have to multiply them

140 x 8 = 1120

Bag a = 1120 grams

2) Work out the weight of bag b

1 pineapple weight 345 grams so to find out 3 you have to multiply them just like above

345 x 3 = 1035

Bag b = 1035

3) Find the difference

Bag a is 1120 grams and bag b is 1035

To find out out by how much you just have to subtract them

1120 - 1035 = 85

Hope this helps, have a great day!

Answer:

The picture is not Clear. Please provide a better view of the question.

Step-by-step explanation:

The speed of the wind is 50 mile per hour  .

In the question ,

it is given that

the speed of the plane is [tex]=[/tex] 200 miles per hour .

let the speed of the wind is = "w"

So ,the speed of the plane with wind is [tex]=[/tex] 200 + w

and the speed of the plane against  wind is [tex]=[/tex] 200 - w

we know that , distance [tex]=[/tex] speed × time

the plane flew "500 miles" with wind ,

which means ,

500 [tex]=[/tex] (200 + w) × t      .....(1)

and the plane flew 300 miles against the wind ,

which means ,

300 [tex]=[/tex] (200 - w) × t       ......(2)

adding both the equations ,

we get

800 [tex]=[/tex] t ( 200 [tex]+[/tex] w [tex]+[/tex] 200 - w)

800 = t × 400

t = 2

Substituting  , t = 2 in 500 [tex]=[/tex] (200 + w) × t      

we get

500 = (200 + w) × 2

500/2 = 200 + w

250 = 200 + w

w = 250 - 200

w = 50

Therefore , The speed of the wind is 50 mile per hour  .

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Answer:

A $1.20

Step-by-step explanation:

Answer:   A) $1.20

Step-by-step explanation:   To get 10% of a number, you just need to divide by 10, so 12 ÷ 10 = 1.2.

2x^2+6x

2(-5)^2+6(-5)

2(25)+6(-5)

50+6(-5)

50+(-30)

50-30

20

The geometric system has a length of f = 4 cm and a length of g = 6 cm.

Herein we find a geometric system formed by two rectangles, the rectangle ABCD has an area of 60 square centimeters and the rectangle APQD has an area of 24 square centimeters. The area of a rectangle is equal to the product of the lengths of its base (b) and its height (h), both in centimeters.

First, describe the area formulas for the rectangles ABCD and APQD, both in square centimeters:

Rectangle ABCD

(g + 9) · f = 60        (1)

Rectangle  APQD

g · f = 24                 (2)

Where:

Second, use distributive property in (1):

By (1):

g · f + 9 · f = 60

Third, use substitution by (2) on (1) and determine the value of f:

(2) in (1):

24 + 9 · f = 60

9 · f = 36

f = 4

Fourth, determine the value of g:

By (2):

g = 24 / f

g = 24 / 4

g = 6

The lengths of f and g are 4 and 6 centimeters, respectively.

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The length of the line segment with points (-5, 5) (3, -1) is 10 units

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points  (-5, 5) and (3, -1) is calculated as follows

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

d =√{(-5 - 3)² + (5 - -1)²}

d =√{64 + 36}

d = √100

d = 10 units

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The equation of the line that passes through the points  (9,2) and (3,4) is x + 3y = 15  and the graph  is shown below .

In the question ,

it is given that

the required line passes through the points (9,2) and (3,4)

in order to find the equation of  line we first need to find slope .

so , the slope(m) will be

m = (4-2)/(3-9)

m = 2/(-6)

m = -1/3

The equation of the line passing through the point (3,4) having slope -1/3 is

y - 4 = (-1/3)(x - 3)

3(y - 4) = -1(x - 3)

3y - 12 = -x + 3

x + 3y = 12 + 3

x + 3y = 15

the graph of the line is drawn below .

Therefore ,The equation of the line that passes through the points  (9,2) and (3,4) is x + 3y = 15  .

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answer:

(1,3)

step-by-step explanation:

desmos.

The value of x will be equal to 7 for the given slope of 2 for the line.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

Given that the points (4, -3) and (x, 3) lie on the same straight line. The slope of the line is 2.

The slope of the line is calculated by the formula,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

2 = ( 3 + 3 ) / ( x - 4)

2(x-4) = 6

2x - 8 = 6

2x = 8 + 6

2x = 14

x = 14 / 2

x = 7

Therefore, the value of x will be equal to 7 for the given slope of 2 for the line.

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The curve is laid out from point to point, the last deflection angle of circular curve is 26.5°

In the given question we have,

Radius of circular curve (R) = 225 ft

intersection or central angle in circular curve (I or delta) = 55°

separtion between stakes alaong arc = 50 ft

Angle of deflection is measured from tangent at PC or PT to any point .

deflection angle formula

deflection angle = (Lc /L)(I/2)

where, Lc is long chord and L is lenth of arc , I is central angle

first we find out the value of Lc and L

using formula , R = Lc / 2sin(I/2)

Lc = 225× 2 sin(55°/2) = 208 ft

L = R × I ×π/180°

L = 225 × 3.14 ×55/180 = 215.8 ~ 216 ft

put all the vales in deflection angle formula we get ,

deflection angle= (208/216)(55°/2) = 26.48° ~ 26.5°

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Answer: Width = 7 inches, Length = 14 inches

Step-by-step explanation:

Let the width be [tex]w[/tex]. Then, the length is [tex]2w[/tex].

Using the formula for the perimeter of a rectangle,

[tex]2(w+2w)=42\\\\w+2w=21\\\\3w=21\\\\w=7\\\\\implies 2w=14[/tex]

maximum height = 32ft

Given function  h(t) = -16t^2+40t+7

known data:

[tex]h{0}[/tex] = 7 ft

[tex]v_{0}[/tex] = 40 ft/s

we equate the first derivation to zero

and solve for time.

h(t) = -16t^2 + 40t+7

[tex]\frac{dh}{dt} (t)[/tex] = -32t+40 = 0

t = [tex]\frac{40}{32}[/tex] = 1.25s

second derivative and evaluate:

[tex]\frac{d^{2}h}{dt^{2}}[/tex] [tex]\frac{}{}(t)[/tex] = -32

the maximum height of the rocket with the respect to

the ground can be obtained by evaluating the function

h(1.25) = - 16[tex](1.25)^{2}[/tex]+40(1.25)+7 = 32 ft

therefore the rocket reaches maximum height at  h = 32ft.

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The statements which are as a result of corresponding parts of congruent triangles being congruent are:

1) EFGH is a rectangle.

The above statements is not true in general. EFGH is a quadrilateral with opposites sides are equal, it may be rectangle in some cases but it is not always be a rectangle.

2). EFGH has 4 congruent sides.

The above statement is also false. EFGH has two opposite sides are congruent.

3). Diagonal FH bisect angles EFG and EHG.

The above statement is true. Triangle EFH and FGH both are isosceles triangles and hence they both have equal angles for the equal sides. Thus, it is true in all cases.

4). Diagonal FH is perpendicular to side Fe.

The above case is not true in general.

5). Angle FEH is congruent to angle FGH.

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Answer:

(7,5)

Step-by-step explanation:

[tex]-3y+4x=13 \implies -15y+20x=65 \\ \\ -5y-6x=-67 \implies 15y+18x=201 \\ \\ \therefore 38x=266 \implies x=7 \\ \\ \implies -3y+4(7)=13 \implies y=5 \\ \\ \therefore (7,5)[/tex]

1.

The slope intercept form is y=mx+b

4x-3y=2

subtract 4x from both sides

3y=2+(-4x)

Divide by 3

y=2/3+(-4x/3)

simplify:

y=2/3-4x/3

reorder:

y=-4/3x+2/3

slope= -4/3, y intercept= 2/3

2.

In the same way,

3x+2y=-3

2y=-3-3x

y=-3/2 - 3x/2

y+3/2=-3x/2

y=-3x/2-3/2

y=-3/2x-3/2

slope=-3/2, y intercept= -3/2

I hope this helped you.

Answer:

I believe the unit price would be $2.97

Step-by-step explanation:

Hope this helps! :))
Please let me know if its incorrect.

Answer:

Step-by-step explanation:

5 1/2 +2x = 25

25- 5 1/2 = 2x

19 1/2 = 2x

x = 9.75

It took him about 9.75 weeks to lose at least 25 pounds.

Answer:

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

It took Mr. Henry at least 10 weeks to lose 25 pounds.

The leading coefficients and parabolic equations, considering the vertices, are given as follows:

1. a = 7/4, y = 7/4(x - 4)² - 1.

2. a = -2, y = -2(x + 1)² + 2.

The equation of a parabola with vertex given by (h,k) is presented as follows:

y = a(x - h)² + k.

In which a is the leading coeffiicent.

For item 1, the coordinates of the vertex is given as follows:

(4,-1).

Hence:

h = 4, k = -1, and the equation is:

y = a(x - 4)² - 1.

When x = 6, y = 6, hence the leading coefficient is calculated as follows:

6 = a(6 - 4)² - 1

4a = 7

a = 7/4.

Thus the equation is:

y = 7/4(x - 4)² - 1.

For item 2, the vertex is:

(-1,2).

Hence:

y = a(x + 1)² + 2.

When x = 0, y = 0, hence the leading coefficient is calculated as follows:

0 = a(0 + 1)² + 2

a = -2.

Hence the equation is:

y = -2(x + 1)² + 2.

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