Work out the value of (√99 - √11)² ​

Answers

Answer 1
Answer:
4*11
Step-by-step explanation:
Answer 2

Answer: 44

Step-by-step explanation:

(√99 - √11)²

simplify the expression

(3√11 - √11)^2

collect like terms

(2√11)^2

use the properties of exponents

4 x 11

answer: 44


Related Questions

Find the
inverse of the function
y = 2x^2+2

Answers

Answer:  (It could just be the first one you did not give enough information for your question so I wasn't sure)

[tex]\sqrt{\frac{x-2}{2} } , -\sqrt{\frac{x-2}{2} }[/tex]

Step-by-step explanation:

Replace y with x:

[tex]y=2x^{2} +2[/tex]   ⇒   [tex]x=2y^{2} +2[/tex]

Subract 2 from both sides:

[tex]x-2=2y^{2} +2 -2\\[/tex]   ⇒   [tex]x-2=2y^{2}[/tex]

Divide 2 from both sides:

[tex]\frac{x-2}{2} = \frac{2y^{2} }{2}[/tex]   ⇒   [tex]\frac{x-2}{2} =y^{2}[/tex]

Square root both sides:

[tex]\sqrt{\frac{x-2}{2} } =\sqrt{y^{2} }[/tex]    ⇒  [tex]y=\sqrt{\frac{x-2}{2} }[/tex]

I hope this helps you have a bright blessed day.

PLEASE RESPOND THIS IS VERY URGENT AND ITS FOR TOMORROW.
I WILL MARK YOU AS BRAINLIEST

Giorgio fills up his car which is 60 liters.
After a certain distance, 340 deciliters remained in the tank.
How many liters did it consume?
How much did you spend if 1 liter costs € 1.45? How many liters of petrol can you buy for € 58?

My book has the answer but not step by step explanation
[ 26 liters; €37,70; 40 liters ]

Answers

The answers to all the subparts are shown:

(A) Using the conversion factor we know that the consumption of fuel was 26 liters.(B) Giorgio spends €87 on 60 liters of fuel.(C) Giorgio can buy 40 liters of fuel for € 58

What is the conversion factor?A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an equal value. For instance, 12 inches equals one foot when converting between inches and feet.

(A) So, we know that: 1 liter = 10 decilitre

Similarly, 60 liter = 600 decilitreThen, 340 decilitre = 34 liter

So, the consumption of the fuel = 60 - 34 = 26 litres.

(B) Cost of 60 liters of fuel if 1 liter is € 1.45:

60 × 1.45 = €87Giorgio spends €87 on 60 liters of fuel.

(C) Liters of fuel he could buy from € 58:

58/1.45 = 40 litresHe can buy 40 liters of fuel for € 58

Therefore, the answers to all the subparts are shown:

(A) Using the conversion factor we know that the consumption of fuel was 26 liters.(B) Giorgio spends €87 on 60 liters of fuel.(C) Giorgio can buy 40 liters of fuel for € 58

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The correct question is given below:
Giorgio fills up his car which is 60 liters. After a certain distance, 340 deciliters remained in the tank.

(A) How many liters did it consume?

(B) How much did you spend if 1-liter costs € 1.45?

(C) How many liters of petrol can you buy for € 58?

I really need help on this asp it would mean a lot

Answers

The angle at which your friend is waving at you is calculated to be 11.31° using tan theta.

What does "trigonometric function" refer to?The simplest definition of a trigonometric function is the function of an angle in a triangle, also known as a circular function. These trigonometric functions provide the relationship between the angles and sides of a triangle.

Given:

Opposite side of the triangle = 1000 m

Adjacent side of the triangle = 5000 m

We need to determine at what angle was your friend looking at you.

We know that,

tan ∅ = Opposite side/Adjacent side

         = 1000/5000

         = 0.2

∅ = 11.31°

Therefore, the angle at which your friend is waving is waving at you is found to be 11.31° .

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Look at the image. I dont get it not at all.

Answers

The fraction of the larger rectangle that is shaded is 4[tex]c^{-8}[/tex]

What fraction of the larger rectangle is shaded?

A rectangle is a two-dimensional shape that has four sides and four right angles. The opposite sides of a rectangle are parallel.

The area of a rectangle is the product of its width and its length. When multiplying numbers that have exponents, multiply the bases and add the exponents.

Area of a rectangle = length x width

Area of the larger rectangle = [tex]4c^{8}[/tex] x [tex]2c^{10}[/tex]

= (4 x 2)[tex]c^{10 + 8}[/tex]

8[tex]c^{18}[/tex]

Area of the smaller rectangle = 8c² x [tex]4c^{4}[/tex]

(8 x 4)[tex]c^{2 + 4}[/tex]

32[tex]c^{6}[/tex]

Fraction of the larger rectangle that is shaded = area of the smaller rectangle / area of the larger rectangle

32[tex]c^{6}[/tex] / 8[tex]c^{18}[/tex] = 4[tex]c^{-8}[/tex]

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134 x 0.01 what is it

Answers

i believe that it would be 1.34 :)

The logarithmic functions, f(x) and g(x), are shown on the graph.

What is the equation that represents g(x)? Explain your reasoning.

Answers

The image of the function after the translation is g(x) = log(x + 1) + 4

How to determine the equation of g(x)?

From the graph, the given parameters are:

f(x) = log(x)

From the graph, we can see that:

The graph of f(x) is translated left by 1 unitThe graph of f(x) is translated up by 4 units

This transformation is given as

g(x) = f(x + 1) + 4

Mathematically, this transformation can be represented as

(x, y) = (x + 1, y + 4)

When represented as a function, we have

g(x) = f(x + 1) + 4

Substitute the equation f(x) = log(x)

f(x + 1) = log(x + 1) + 4

So, we have the following equation

g(x) = log(x + 1) + 4

Hence, the equation of g(x) is g(x) = log(x + 1) + 4

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H name seven segments that skew to segment vw

Answers

Segments that skew to segment VW are mentioned below.

Define skew.

A deviation from the symmetrical bell curve, or normal distribution, in a set of data is referred to as skewness. The curve is said to be skewed if it is displaced to the left or right. Skew lines are two lines in three-dimensional geometry that neither cross nor are parallel. The two lines that pass through the opposing edges of a normal tetrahedron are a straightforward illustration of a pair of skew lines. A distribution is said to be "skewed right" if the tail is to the right. A distribution is said to be "skewed left" if the tail is to the left. The histogram on top represents a right-skewed distribution.

Given,

Segments that skew to segment VW are:

UZ

TY

SX

ZY

XY

TU

ST

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How many gallons of the 65% pesticide is needed to make a final solution that is 60% pesticide

Answers

we have that

the algebraic expression that represents this situation is

p(0.65)+25(0.25)=(25+p)(0.60)

solve for p

0.65p+6.25=15+0.60p

0.65p-0.60p=15-6.25

0.05p=8.75

p=175 gal

Find the output, yyy, when the input, xxx, is -1−1minus, 1.
y=y=y, equals

Answers

On observing the given line graph, we found that the value of y when x = -1 is 3.

What is a line graph?

A line graph is frequently used to display data that varies over time. It can be seen using a series of points connected by straight lines. The x-axis and the y-axis are two of its axes. The x-axis and y-axis are the names of the horizontal and vertical axes, respectively. It reflects the change in a quantity with regard to another quantity.

We are given a line graph which shows the relation between the x and y variables.

We are asked to find the value of y when x = -1.

Since it is a line graph, we can find the value just by looking into the graph as it is continuous.

So on observing the graph, x = -1 is the line between 0 and -2.

When x = -1, the corresponding y value is the point between 2 and 4 between the y-axis, which is 3.

Since each unit on the x and y axes have a value of 2, the line midway between a single unit has a value of 1.

Therefore from the line graph the value of y when x = -1 is 3.

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Write an equation in point-slope form of the line through each pair of points" (9,5) and ( 8,2)

Answers

A slope of a line is the change in y coordinate with respect to the change in x coordinate. y=3x-22  is equation in point-slope form of the line through each pair of points" (9,5) and ( 8,2).

What is Slope of Line?

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

The slope intercept form of a line is y=mx+b

where m is the slope and b is y intercept.

slope of a line passing through two points is given by

m=y₂-y₁/x₂-x₁

(9,5) and ( 8,2)

x₁=9, y₁=5, x₂=8,y₂=2

Plug in the values to get the slope.

m=2-5/8-9

m=-3/-1

m=3

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

y-5=3(x-9)

y-5=3x-27

y=3x-27+5

y=3x-22

Hence y=3x-22  is equation in point-slope form of the line through each pair of points" (9,5) and ( 8,2).

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If you work 30 hours in one week at $22/h, how much would you earn?

Answers

Answer:

660 dollars

Step-by-step explanation:

For this, you just need to multiply 30 by 22.

If you're having trouble multiplying that, you could also multiply 22 by 10 three times and then just add the outputs together to get the same answer.

Answer:

$660

Step-by-step explanation:

30 hours times $22

30x22=$660

Armand plans to save money every month for the next six months. The function f(x)=2x−1 represents the amount of money, in dollars, Armand will deposit into his savings account at the end of x months since the time he started saving. Which of the following represents the amount of money, in dollars, Armand deposits into his savings account at the end of 3 months since the time he started saving? Select all that apply.

Answers

f(x) represents the total savings for x months. If the number of months is 3, then x = 3.

f(x) = 2x - 1
f(3) = 2(3) - 1
= 6 - 1
f(3) = 5

He knows the right triangle JAM contains points J (-3,8) and M (5,4) but the Psl spilled right on his coordinates for A so he only knows that x - coordinate of A is 1. If the triangle is a right triangle, what are the possibilities for the y - coordinate of point A

Answers

Four Answers:

10.4721 approximately

1.5279 approximately

-4

16

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

Explanation:

Use the midpoint formula to find that N = (1,6) is the midpoint of J(-3,8) and M(5,4). I'm skipping steps so let me know if you need to see them.

Then draw a circle centered at N with radius NM. The equation of this circle is (x-1)^2+(y-6)^2 = 20

Plug in x = 1 and solve for y to get y = 10.4721 and y = 1.5279

These values are approximate.

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

The equation of line MJ is y = -0.5x + 6.5 where both decimal values are exact.

The slope here is m = -0.5 which has the negative reciprocal of 2, and this is the perpendicular slope.

The line perpendicular to MJ, that goes through M, is y = 2x-6

Plug in x = 1 to find that y = 2(1)-6 = -4

The line perpendicular to MJ, that goes through J, is y = 2x+14

Plug in x = 1 to find that y = 2(1)+14 = 16

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

The diagram below shows points in red of all the possible locations point A could be.

Please help me it's due tomorrow and I somehow can't understand.

Answers

LCM for 3 and 4=12
LCM for 2 and 12=24
LCM for 2 and 6=12
LCM for 12 and 9=108

14. pls help will mark brainliest to someone !!!!

Answers

The given equation is:

y - 5 = 1/2 (x-4)

On simplifying this,

⇒ y - 5 = (x - 4)/2

⇒ (y - 5) *2 = x - 4

⇒ 2y - 10 = x - 4

⇒ 2y = x - 4 + 10

⇒ 2y = x + 6

Now, let x = 0,

2y = 0 + 6

⇒ 2y = 6

⇒ y = 3

let y = 0,

x + 6 = 0

⇒ x = -6

So, two points of the given equation are (0,3) and (-6,0)

On plotting these points of the graph, we will get the line on the graph.

What is a Line?A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends. Two points on a line can be used to refer to that line.Because there are so many different geometries in modern mathematics, the definition of the geometry and the idea of a line are tightly related. In analytical geometry, for example, a line in the plane is frequently defined as the collection of points whose coordinates satisfy a given linear equation. However, in a more abstract context, such as incidence geometry, a line may be an independent object, distinct from the collection of points that lie on it.

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Identify ALL solutions to the inequality. There could be more than one selection.

Answers

The solutions to the given inequality x ≤ 6 are; -6, -3 and -10

What are the Solutions to the Inequality?

In inequalities, there are different symbols such as;

≥ which means greater than or equal to

≤ which means less than or equal to

< which means less than

> which means greater than

Now, we are given the inequality as; x ≤ 6

This means that all valid values of x must either be equal to 6 or less than 6. Thus, any value greater than 6 for x is not valid.

Looking at the options, we cans see that -6, -3 and -10 all fall within the required interval and as such they are the solutions.

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HELP ASAP!!! 50 POINTS!!

Answers

Answer:

rate of change is 3

Step-by-step explanation:

Answer:

The rate of change is 3

Step-by-step explanation:

start at (0,2)  Then go up three spaces and right 1 space.  You will be on the line again at point (1,5)

Mrs. Nguyen had 25 students in her English class. On her
birthday 1 student gave her chocolates, 12 gave her cards
and 2 gave her flowers.
QUESTION: What percentage of her students brought
something for Mrs. Nguyen on her birthday?

Answers

Answer:

60% of her students brought something for Mrs. Nguyen on her birthday.

Step-by-step explanation:

She has 25 students in her class.

12 gave her cards.

2 gave her flowers.

1 gave her chocolates.

Add them together to get 12+2+1=15.

15 students out of 25 can also be written as a fraction:

[tex]\frac{15}{25}[/tex]

This equals 0.6 as a decimal. To find the percentage multiply by 100, to get 60. Therefore 60% of her students got something for her.

A semicircular shape is cut out of the side of a rectangle as shown.
Calculate the shaded area, giving your answer in exact form.

Answers

Answer:

9 43/50cm²

Step-by-step explanation:

Required area

= 6 x 4 - ½ π 3²

= 24 - 4.5 π

= 24 - 4.5 x 3.14

= 24 - 14.13

= 9.87

= 9 43/50


44/9
Write as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.

Answers

Answer:

4.8888889

Step-by-step explanation:

44/9 is basically the same as 44 ÷ 9.

44 ÷ 9 = 4.8888889.

The 8 is terminating, and because I cannot add a line above the 8, I have placed multiple 8s.

Hope this helps!

Btw, could I get Brainliest? Thanks!

Answer:

4.88889

Step-by-step explanation:

What is the greatest common factor of 8 and 44

Answers

Answer:

GCF is 8

Step-by-step explanation:

What is the greatest common factor of 8 and 44?

8: 1, 2, 4, 8

44: 1, 2, 4, 8, 11 ....

GCF is 8

The greatest common factor of the numbers 8 and 44 is 4.

The two given numbers are 8 and 44.

The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers. The GCF of two natural numbers x and y is the largest possible number that divides both x and y without leaving any remainder.

Here, the factors of 8 and 44 are

8=2×2×2

44=2×2×11

So, the common factors are 2×2=4

Therefore, the greatest common factor of the numbers 8 and 44 is 4.

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Which ordered pair is the best estimate for the solution to the system?

Answers

The ordered pair that is the best estimate for the solution to the system is (0.5, -3.5)

Ordered Pair:

An ordered pair refers to a set of two numbers used to locate a point in a coordinate plane. Here the first point refers the x - coordinate and the second value represents the y - coordinate.

Given,

Her we have the equations,

3x - 8y = 29

3x + y = -2

Now, we need to find the solution of the system.

Here we have to use the substitution method in order to solve this one.

For that, we have to rewrite the second equation as,

y = -2 - 3x.

Now, we have to apply the value of y on the equation (1), then we get,

3x - 8(-2 - 3x) = 29

3x + 16 + 24x = 29

27x = 29 - 16

27x = 13

x = 13/27

x = 0.5

When we apply the value of x into the equation, then we get the value of y  as,

y = -2 - 3(0.5)

y = -2 - 1.5

y = -3.5

Therefore, the solution of the system is (0.5, - 3.5).

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giving brainliest!!
answer choices are:
D
A
B
C

Answers

Answer:  d

Step-by-step explanation:


Calcule A = 1 x 2° +1 x 2¹ +0×2²+1× 2¹

Answers

Answer:

1+2+0+2=5

Step-by-step explanation:

1x2° = 1

hope it helps you

branliest??

Which statement about the following sequence is true?

-10, -3, -10, -3, -10, ...

It is arithmetic.
It is geometric.
It is neither arithmetic nor geometric.

Answers

The statement about the sequence that is true is (c) It is neither arithmetic nor geometric.

How to determine the true statement?

The sequence is given as

-10, -3, -10, -3, -10, ...

Test for arithmetic sequence:

An arithmetic sequence is any seqeunce that has a common difference

The sequence -10, -3, -10, -3, -10, ... does not have a common difference

This is so because the first two terms are repeated through out

Test for geometrics equence:

A geometric sequence is any seqeunce that has a common ratio

The sequence -10, -3, -10, -3, -10, ... does not have a common ratio

This is so because the first two terms are repeated through out

Hence, the true statement is (c)


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Solve for the equation show all your work |3x-9| = 12

Answers

Answer:

x = 7 and x = -1

Step-by-step explanation:

The equation "|3x-9| = 12" can be written into two different equations:

3x-9 = 12 & 3x-9 = -12

This is because the net value inside of the absolute value will always be made positive even if it is negative. Therefore, the net value inside of the absolute value signs can also be equal to the negative of the solution.

Solve 3x-9 = 12:

Add 9 to both sides:

3x-9+9 = 12+9

3x=21

Divide both sides by 3:

3x÷3=21÷3

x=7

Solve 3x-9 = -12

Add 9 to both sides:

3x-9+9=-12+9

3x=-3

Divide both sides by 3:

3x÷3=-3÷3

x=-1

Your answer: x = 7 and x = -1

60% of 10 is what number?

Answers

Percentage is expressed in terms of 100. Thus,

60% of 10 would be expressed as

60/100 * 10

= 6

Thus, 60% of 10 is 6

My classesExample 5: The number of calories in a piece of pie is 20 less thanthree times the number of calories in a scoop of ice cream. The pieand ice cream together have 500 calories. How many calories are ineach?x = pie, y = ice creamMULTIPLE CHOICE QUESTIONx= 3y - 20x + y = 500How many calories are in a scoop of icecream?1090370250130

Answers

We will investigate the number of calories in ice cream and pie. We will define the variables as such:

[tex]\begin{gathered} x\text{ = Number of calories in pie} \\ y\text{ = Number of calories in ice-cream} \end{gathered}[/tex]

From the given data a relationhsip between the number of calories in a pie ( x ) and the number of calories in an ice-cream scoop are given by the following statement:

" The number of calories in a piece of pie is 20 less than three times the number of calories in a scoop of ice cream. "

We will go ahead and decrypt the above given statement and express it mathematically in terms of declared variables ( x and y ) as follows:

[tex]\times\text{ = 3y - 20 }\ldots\textcolor{#FF7968}{Eq1}[/tex]

The next statement gives us the combined calories in both ice-cream scoop and a pie:

" The pie and ice cream together have 500 calories. "

We will go ahead and decrypt the above given statement and express it mathematically in terms of declared variables ( x and y ) as follows:

[tex]x\text{ + y = 500 }\ldots\textcolor{#FF7968}{Eq2}[/tex]

We have two equations ( derived ) and two variables ( x and y ):

[tex]\begin{gathered} \times\text{ - 3y = -20 }\ldots Eq1\text{ } \\ x\text{ + y = 500 }\ldots Eq2 \end{gathered}[/tex]

We will solve the two equations ( Eq1 and Eq2 ) simultaneously using elimation method as follows:

[tex]\begin{gathered} x\text{ - 3y = -20 --- > }\text{\textcolor{#FF7968}{-x}}\text{ + 3y = 20} \\ \textcolor{#FF7968}{x}\text{ + y = 500} \\ =================== \\ 4y\text{ = 520 } \\ y\text{ = }\frac{520}{4} \\ \textcolor{#FF7968}{y}\text{\textcolor{#FF7968}{ = 130 calories}} \end{gathered}[/tex]

We first multiplied the ( Eq1 ) by ( -1 ) then added the modified ( Eq1 ) to ( Eq2 ) whilst eliminating ( x ) and solved for the number of calories in an ice-cream scoop ( y ) i.e 130 calories.

Then we will back substitute the value of ( y ) into ( Eq2 ) and solve for ( x ):

[tex]\begin{gathered} x\text{ + y = 500} \\ x\text{ + 130 = 500} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 370 calories}} \end{gathered}[/tex]

Therefore, the number of calories in each confectionary is as such:

[tex]\begin{gathered} \textcolor{#FF7968}{x=370}\text{\textcolor{#FF7968}{ calories in pie}} \\ \textcolor{#FF7968}{y=130}\text{\textcolor{#FF7968}{ calories in an ice-cream scoop}} \end{gathered}[/tex]

Find the product of G(x) and H(x) and write it in standard form.
G(x) = 2x + 5
H(x) = x + 4

Answers

Answer:

the product of h(x) and g(x) = 2x²+13x+20

Step-by-step explanation:

to do the product of functions you have to multiply all the values of the function by themselves with parentheses . so g(x)×h(x)= (2x+5)(x+4)

because there are parentheses being used you need to foil and thus you will get

2x(x+4)+5(x+4)

simplify and get

2x²+8x+5x+20

continue to simplify and get

2x²+13x+20

this is your answer because it is already in standard quadratic form of ax²+bx+c.

2025 cm²
[tex] \times [/tex]
2025 cm²
[tex] = [/tex]

Answers

2025 cm² × 2025 cm² = 4100625cm^4

What is Square?

A number is multiplied by itself to form a square. To describe this operation, the term "to square" is employed. For example, the square of 3 can be expressed as 32, which is the number 9, because squaring is the same as raising to the power 2, and it is indicated by a superscript 2. The notations x2 (caret) or x**2 may be used in place of x2 when superscripts are not always an option, such as in programming languages or plain text files. Quadratic is the adjective that describes squaring.

So we have to simply multiply :

2025 cm² × 2025 cm²

By multiplying we get

2025 cm² × 2025 cm² = [tex]4100625cm^{4}[/tex]

Hence, 2025 cm² × 2025 cm² =  [tex]4100625cm^{4}[/tex]

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pls help wil give brainliest Based on the excerpt, which statement best describes Humbaba's effect on the epic's plot? 1,3/5,9/25 find the 8th term What instruments of the middle ages and renaissance produced sound by using air and which did not? the international marketing manager's task is more complex than the domestic marketing manager's in part because Pluto has a diameter of 1,413 miles. What does this distance equal in kilometers?(1 mile = 1.6 kilometers)A. 12,761 kmB. 2,275 kmC. 3,476 kmD. 143,042 km The titration of a 20.0- mL sample of an H2SO4 solution of unknown concentration requires 22.47 mL of a 0.160 M KOH solution to reach the equivalence point.What is the concentration of the unknown H2SO4 solution?I am getting 0.899 no matter what I way I do it and the answer is not being accepted. What is the correct answer? the blank which are numbers that are found on the lower right hand side of the element symbole Need help asap extra points if an athlete complains of burning, tingling, or paresthesia to the fourth and fifth fingers, what structure may be damaged? an alloy steel metric 10x1.25 screw is used in a threaded hole and tightened to 20% of its proof strength of 830 mpa. determine the maximum torque that should be used if the torque coefficient on earth's surface it is approximately 10,000km from the equator to the north pole. How many kilometers is it between two parallels one degree apart There is lightning rod on the top of a building. From a location 500 feet from the base of the building, the angle of elevation to the top of the building is measured to be 36. From the same location, the angle of elevation to the top of the lightning rod is measured to be 38. Find the height of the lightning rod. To earn full credit please share a diagram and include all your work and calculations if a population of a town decreases by 5% every 3 years would it be exponential ? 280 grams - 23grams= A concession stands sells drinks and hotdogs the number of drinks sold is five more than four times the number of hotdogs sold the stands sells 500 items how many hotdogs were sold Sue learned to sing a total of 10 pieces over the course of 5 weeks of voice lessons. After 8weeks of voice lessons, how many pieces will Sue be able To sing total? For jewelry prices in a jewelry store, state whether you would expect a histogram of the data to be bell-shaped, uniform, skewed left, or skewed rightChoose the correct answer below."O UniformO Skewed rightSkewed leftO Bell shaped+ Express each number in scientific notation.1) 0.00563) 4,0855) 0.000796Standard and Scientific Notations50,41311112) 24,0104) 0.0176) 9528) 0.004 In three to five complete sentences, give a brief description of a story that would not result in stereotypes. Provide relevant textual evidence from your answers to the previous item to support your explanation.