Find the equation of the perpendicular bisector of AB where A and B are the points (3,6) and (-3,4) respectively. Also find its point of intersection with (i) x-axis and (ii) y-axis.

Answers

Answer 1

The point of intersection with x - axis is (5/3,0) and the point of intersection with y - axis is (0,5).  

Any point on AB's perpendicular bisector, P(x,y), shall be considered. Then, PA = PB.

√(x-3)²+(y-6)² = √(x+3)²+(y-4)²

(x-3)²+(y-6)² = (x+3)²+(y-4)²

x² -6x+ 9 + y²- 12y + 36 = x² +6x+ 9 + y²- 8y + 16

12x + 4y -20 = 0

3x+ y-5 =0 ---(1)  

Consequently, 3x+y-5=0 is the equation for the perpendicular bisector of AB.

We know that the coordinates of any point on x-axis are of the form (x,0). In other words, any point on the x-axis has a y-coordinate of zero. Thus, if we enter y = 0 in (1), we get

3x -5 = 0

x = 5/3

Thus, the x-axis is cut by the perpendicular bisector of AB at (5/3, 0).

(ii) Any point's y-axis coordinates have the following format: (0,y). When we enter x = 0 in (1), we obtain

y − 5 = 0

⇒ y = 5

Thus, the y-axis is where the perpendicular bisector of AB intersects (0,5).

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Related Questions

Factor the quadratic expression completely.
-3x² +172-20=

Answers

Answer: The given quadratic expression is -3x²+172x-20. To factor this expression, we look for two numbers that multiply to -20 and add to 172.

We can start by dividing -20 by different numbers and checking if the product and the sum of the divisors equals -20 and 172 respectively.

-20/1 = -20, 1+-20 = -19

-20/2 = -10, 2+-10 = -8

-20/4 = -5, 4+-5 = -1

-20/-1 = 20, -1+20 = 19

-20/-2 = 10, -2+10 = 8

-20/-4 = 5, -4+5 = 1

We can see that the divisors that multiply to -20 and add to 172 are (x+8)(x-5)

So, we can factor the quadratic expression as:

-3x²+172x-20 = -3(x+8)(x-5)

Hope this helps!

Step-by-step explanation:

Solve the inequality. -1.5x < 7.5

Answers

Answer: x > -5

Step-by-step explanation:

-1.5x < 7.5

x > -5 (When multiplying both sides by a negative, the inequality is flipped)

[tex]-1.5x < 7.5[/tex]

Divide both sides by -1.5:

[tex]\dfrac{-1.5x}{-1.5} < \dfrac{7.5}{-1.5}[/tex]

When dividing by a negative number, the inequality sign will reverse.

Answer:

[tex]x > -5[/tex]

Given the two functions, which statement is true?
f(x) = e^x, g(x) = e^x-2

g(x) is translated down 2 units compared to f(x)
g(x) is translated right 2 units compared to f(x)
g(x) is translated left 2 units compared to f(x)
g(x) is translated up 2 units compared to f(x)

Answers

the answer is: g(x) is translated down 2 units compared to f(x)

The revenue (R) made on the sale of tickets is a function of the price (p) of each
ticket, where R(p) = -40p^2 +400p-640

Pls help!!!

Answers

The revenue is maximized when the derivative of R(p) is equal to 0.

R'(p) = -80p + 400 = 0

p = 5

What is a function?

A function is a mathematical relationship between two or more variables, where one variable (the output) is determined by the values of the other variables (the inputs). A function can be expressed as an equation, and it describes how the output changes in relation to the inputs.

Therefore, the maximum revenue is achieved when the price of each ticket is $5.

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Chase tried to evaluate an expression. Here is his work: 2(12÷2)2–14+6 = Step 1262–14+6 = Step 2236–14+6 = Step 372–14+6 = Step 472–20 = Step 552 Is Chase's work correct? PLEASE HELP FAST THIS IS FOR 6th GRADE IXL

Answers

No Chase's work is not correct. He has made a mistake in working the brackets out. The BODMAS Rule has to be used here.

We have 2(12 ÷ 2)2 – 14 + 6

Here according to the BODMAS rule which stands for Brackets  Of  Division  Multiplication  Addition  Subtraction, we will first solve the brackets.

Now any number to the left or right of the brackets without any sign in between the bracket and the number has to be multiplied by the answer we get by solving the bracket.

12 ÷ 2 = 6

Hence we get

2 X 6 X 2  -  14  +  6

Now we need to multiply.

2 X 6 X 2 = 12 X 2 = 24

Hence we get

24 - 14 + 6

Now we need to add the numbers up.

24 + 6 = 30 hence we get

30 - 14

= 16

Hence Chase's work is not correct.

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Find a2, a3, and a4.
a1=0
an=an–1+15
Write your answers as integers or fractions in simplest form.

Answers

The values of the terms are a₂ = 15, a₃ = 30 and a₄ = 45

How to determine the value of the terms?

The definition of the function is given as

a₁= 0

aₙ = aₙ₋₁ + 15

The above definitions imply that we simply add 15 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a₂ = 0 + 15

a₂ = 15

Also, we have

a₃ = 15 + 15

a₃ = 30

Lastly, we have

a₄ = 30 + 15

Evaluate the equation

a₄ = 45

Hence, the value of a₄ is 45

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Find the value of x in the acute scalene triangle that has the angles 93° and 46°

Answers

The third angle of  acute scalene triangle is  41°

Now, According to the question:

The first angle of acute scalene triangle is 93°

The second angle of  acute scalene triangle is 46°

Let the third angle of  acute scalene triangle is x

We know that:

The sum of the interior angles is always equal to 180 degrees.

Now, 93° + 46° + x = 180°

139° + x = 180°

x = 180° - 139°

x = 41°

Hence, the third angle of  acute scalene triangle is  41°

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Please help!!!!
If f(x)=-9x+13 and f(x) = -41, find x

Answers

The numerical value of x in the function f(x) = -9x + 13 when f(x) = -41 is 6.

What is the value of x in the given function?

A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.

Given the data in the question;

f(x) = -9x + 13f(x) = -41x = ?

To find the value of x, replace the occurrence of f(x) with -41 in the function and simplify.

f(x) = -9x + 13

-41 = -9x + 13

Collect like terms

9x = 41 + 13

Add 41 and 13

9x = 54

Divide both sides by 9

9x/9 = 54/9

x = 54/9

x = 6

Therefore, the input value x is 6.

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Quinn ran five times
this week for a total
distance greater than
40 miles. He says that
means he ran, on average,
more than 8 miles on
each run.
For an indirect proof,
what does he need to
assume?

Answers

We can assume linear inequality 8x>40 for x>8 for an indirect proof.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

Given,

Quinn ran total distance>40 mile

No. of times he ran=5

average distance for each run>8

also let x>8 where x=average distance for each run

Hence,

           We can assume linear inequality 8x>40 for x>8

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If Elayna bought 18 bags of topsoil and each bag contains 36 pounds, how many total bags did she buy?

Answers

Answer: To find the total weight of the bags of topsoil, you can multiply the number of bags by the weight of each bag.

18 bags * 36 pounds/bag = 648 pounds

So, Elayna bought 18 bags of topsoil which is 648 pounds in total.

Step-by-step explanation:

n engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 280 engines and the mean pressure was 6.6 lbs/square inch. assume the variance is known to be 1 . if the valve was designed to produce a mean pressure of 6.7 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve performs below the specifications? state the null and alternative hypotheses for the above scenario.

Answers

Null hypothesis: valve meets specifications. Alternative hypothesis: valve doesn't meet specifications, t-test with p-value < 0.1 to reject Null.

What is null hypothesis ?

The null hypothesis is a arithmetic theory suggesting that no statistical relationship and significance exists in a set of given, single, observed variables between two sets of observed data and measured phenomena.

To test the null hypothesis, we can use a one-sample t-test. The t-statistic for this test is calculated as:

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the population mean (6.7 lbs/square inch in this case), s is the population standard deviation (assumed to be 1), and n is the sample size (280 engines).

The p-value for this test can be calculated using the t-distribution table or a t-test calculator. If the p-value is less than the significance level of 0.1, then we can reject the null hypothesis and conclude that there is sufficient evidence that the valve performs below the specifications.

Null hypothesis: valve meets specifications. Alternative hypothesis: valve doesn't meet specifications, t-test with p-value < 0.1 to reject Null.

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Determine the exact value of cot 3pi/2

put steps please

Answers

By trigonometric functions and trigonometric formulas, the exact value of cot (3π / 2) is equal to 0.

How to determine the exact value of a trigonometric function

In this problem we have the case of trigonometric function whose exact value must be found by means of trigonometric functions and trigonometric formulas. Now we proceed to present the entire procedure:

cot (3π / 2)

1 / tan (3π / 2)

Rewrite the function in terms of fundamental trigonometric functions: (sine, cosine)

1 / [sin (3π / 2) / cos (3π / 2)]

cos (3π / 2) / sin (3π / 2)

Then, we get the following exact value:

0 / (- 1)

0

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Maggie brought $10 to the candy store. She will buy a certain amount of fudge. One pound of fudge costs $2.30. If p represents the amount of fudge, in pounds, Maggie buys, which expression

Answers

Answer: $10=2.30p

Step-by-step explanation:

Please Help me on this 3rd last question I'm on I'm a bit stuck on it it would be very amazing if you did help me.

Answers

Answer:

c

Step-by-step explanation:

How do I find the median of this trapezoid?

Answers

Answer:

23.37

Step-by-step explanation:

There ya go

:)

The total cost (in dollars) of a cell phone plan after x months can be represented by c(x) = 35x + 20. Find the inverse function. Then find the number of months
when the total cost is $1700.

Answers

The number of months when the total cost is $1700 is 48 months

What is a function?

A function can be defined as an expression, equation, law or rule that shows the relationship between two variables.

These variables are;

Dependent variableIndependent variable

From the information given, we have that;

The function for the total cost is c(x) = 35x + 20x represents the number of months

Now, substitute the values, we have;

1700 = 35x + 20

collect like terms

35x = 1700 - 20

subtract the like terms

35x = 1680

Make 'x' the subject of formula

x = 48 months

Hence, the value is 48 months

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The product of two consecutive even integers is 168. Find the integers.
What are the negative integers?

Answers

Answer:

We can use algebra to find the two consecutive even integers whose product is 168.

Let's call the first even integer x. Since it is consecutive to another even integer, the next one will be x+2. The product of these two integers is:

x * (x+2) = 168

We can solve for x by simplifying the equation:

x^2 + 2x = 168

x^2 + 2x - 168 = 0

We can factor the left side of the equation:

(x-14)(x+12) = 0

So the two solutions for x are -12 and 14.

The negative integers are -12 and -14.

The two integers that multiply to give 168 are -12 and -14, but keep in mind that they are not consecutive integers.

Which equation represents this graph? This graphic illustrates the mathematical word problem described in the accompanying text.

Answers

Answer:

Step-by-step explanation:

that a huge prob but yah

Select the correct statement in the table.
Tennis balls are traditionally sold in a cylinder which contains three balls. The volume of space in the cylinder not occupied by a
tennis ball is modeled in the following function, where r is the radius of a tennis ball, in inches.
V =
(²) (67)
477-3
Select the true statement in the table below.
-
The factor T2² represents the volume of the can.
The factor 6r represents the width of the can.
The term 41³ represents the volume of the three tennis balls.
The term (1²)(6r) represents the volume of one tennis ball.

Answers

The distance between the tennis balls and the cans is 49.46 cubic inches.

What is meant by volume?

A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

Given: Each ball has a diameter of three inches.

Three tennis balls are contained in each can, which is how they are sold.

Each can has a cylindrical shape.

We start by determining each tennis ball's volume.

Because of their spherical shape, their volume is determined by

[tex]$V=\frac{4}{3} \pi r^3$[/tex]

Where [tex]$r=\frac{d}{2}=\frac{3 \text { in }}{2}=1.5 i$[/tex] in

Replacing the radius and using [tex]$\pi \approx 3.14$[/tex], we have

[tex]$V=\frac{4}{3}(3.14)(1.5 \mathrm{in})^3=14.13 \mathrm{in}^3$$[/tex]

Therefore, the volume of each tennis ball exists 14.13 cubic inches, approximately.

Assuming that the diameter of each ball exists congruent with the diameter of the can, we contain the volume of a cylinder defined by

[tex]$V=\pi r^2 h$[/tex]

Where, r = 1.5 in and h = 3(3 in)=9 in, because each can has three balls, and the height exists the sum of all three diameters.

[tex]$V=3.14(1.5 i n)^2(9 i n)=63.59 n^3$$[/tex]

Therefore, the volume of each can exists 63.59 cubic inches, approximately.

The complete question is:

Tennis balls with a 3 inch Diameter are sold in cans of three. The can is a cylinder

A)what is the volume of one tennis ball ?

B)what is the volume of the cylinder ?

C)how much space is not occupied by the tennis balls in the can?

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25-2x≤5(2-x) pls solve w/ steps ​

Answers

Answer: X has to be greater than or equal to 15/7 for the inequality to be true.

Step-by-step explanation:

here are the steps to solve the inequality 25-2x≤5(2-x):

Start by simplifying the right side of the inequality: 5(2-x) = 10 - 5x

Now we can substitute this back into the original inequality: 25 - 2x ≤ 10 - 5x

Next, we need to combine like terms on both sides of the inequality: 25 - 7x ≤ 10

Now we'll add 7x to both sides: 25 ≤ 10 + 7x

Subtract 10 from both sides: 15 ≤ 7x

Finally, divide both sides by 7: 15/7 ≤ x

The solution set is x ≥ 15/7.

So x has to be greater than or equal to 15/7 for the inequality to be true.

Answer:

-5 ≥ x  or x ≤ -5

Step-by-step explanation:

25 - 2x ≤ 5(2 - x)

distribute the 5 to eliminate the parentheses:

25 - 2x ≤ 10 - 5x

now combine like terms:

15 - 2x ≤ -5x

15 ≤ -3x

-5 ≥ x  or x ≤ -5

the inequality symbol gets switched whenever you multiply or divide by a negative value

8.A rocket travels at an approximate speed of 7.9 kilometers per second.

Which statements about the rocket are true?

Select all that apply.

Answers

The statement below about the rocket is true:

A rocket travels at an approximate speed of 7.9 *10⁵ cm per second.

What is Unit conversion?

A statement of the connection between units that are used to alter the units of a measured quantity without affecting the value is called a conversion factor. A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).

Given, A rocket travels at an approximate speed of 7.9 kilometers per second.

Since, some unit conversion:

1 kilometer = 1000 meteres

1 kilometer = 100000 centimeteres = 10⁵ cm

1 kilometer = 10000000 milimeteres = 10⁷ mm

thus we can say that from the given options only "f" is correct that states:

A rocket travels at an approximate speed of 7.9 *10⁵ cm per second.

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if it takes you 2 hours to shape 48 baguettes, how many could you make in 30 minutes? how long would it take for you to make 1 baguette?

Answers

Answer:

12.  & 2.5mins

Step-by-step explanation:

2 hours = 120 mins for 48 baguettes.  so 120/48 = 2.5 mins per baguette

30 mins is 1/4 of 2 hours. so 12  baguettes

Two friends, Jacob and Ariana, took summer jobs. The equation y = 16. 5 x y=16. 5x represents Jacob's earnings in dollars and cents, y y, for working x x hours. Ariana earned $708 in 24 hours. How much more does Ariana earn per hour than Jacob?

Answers

Ariana earned $708 in 24 hours, so $312 more Ariana earn per hour than Jacob.

We have to find how much more Ariana earn per hour than Jacob.

The equation y = 16.5x represents Jacob's earnings in dollars and cents, y, for working x hours.

Ariana earned $708 in 24 hours.

So the value of x = 24

Now putting the value of x in equation y = 16.5x

y = 16.5 × 24

y = 396

Jacob's earnings = $396

Difference between the Ariana earning and Jacob earning = $708 - $396

Difference between the Ariana earning and Jacob earning = $312

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from a pack of cards, 2 cards are drawn in succession and the selected card is not replaced. what is the probability that both the drawn cards are diamonds? (refer to the deck of cards material shared in reference material to get better understanding of cards)

Answers

Two  cards are drawn in succession from a standard deck. The probability that both the drawn cards are diamonds is 143/2,652

Probability is defined as the ratio of the number of favorable events to the the number of possible outcomes. The probability of an event A is defined as:

P(A) = n(A)/n(S)

Where:

n(A) = number of possible ways the event A occurs

n(S) = total possible outcomes

In a standard deck, there are 52 cards. The number of diamond suit = 13 cards.

First drawn: number of diamond = 13

Hence, P1(diamond) = 13/52

In the second drawn, the number of diamonds left is 13 - 1 = 12, and total number of cards left is 52 - 1 = 51.

Hence, the probability of the second card will be a diamond is:

P2(diamond) = 12/51.

Since those 2 events are independent, the probability that both cards are diamonds is:

P(diamonds) = P1 (diamond) x P2 (diamond)

                     = (13/52) x (11/51) = 143/2,652

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3 Points

Steven rents an apartment in an all-wood building in the city suburbs. The

value of the belongings in the apartment is about $15,000. If Steven wants to

insure his belongings while renting, how much will he have to pay for

insurance per year?

Annual Premium per $100 of coverage

Brick. . Steel

Mixed

Wood

Area Building Contents Building Contents Building Contents Building Contents

rating

City 0. 39 0. 43 0. 5 0. 54 0. 55 0. 65 0. 66 0. 76

Suburb 0. 45 0. 52 0. 56 0. 63 0. 72 0. 74 083 085

Rural 0. 6 0. 69 0. 71 0. 8 0. 89 0. 91 1 | 102

O A. $150. 00

O B. $107. 50

OC. $127. 50

O D. $173. 50

Answers

Steven will have to pay $127. 50 for the insurance per year.

The correct answer is an option (C)

First, we need to find the corresponding value for the all-wood building in the city suburbs.

From given table, we will use the value 0.85 because he wishes to ensure his belongings.

Here, the value of the belongings in the apartment is about $15,000

Steven wants to insure his belongings while renting.

Now we can calculate the amount of money he will have to pay  for insurance per year as follows:

15000 × (0.85 / 100)

= 127. 50 dollars

Therefore, he will have to pay 127. 50 dollars for insurance.

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determine the minimum distance (ft) it will take for a driver going at the speed limit to come to stop at the traffic light after the traffic light turns yellow. b) what will be minimum stopping distance if the driver was going at 45 mph (5 mph over the speed limit)? express it in ft and also as % of the distance you found in part a). c) what will be the minimum stopping distance if the driver was going at 50 mph (10 mph over the speed limit)? express it in ft and also as % of the distance you found in part a). g

Answers

The minimum stopping distance is 800 ft.

Part A: The minimum stopping distance for a driver going at the speed limit (40 mph) is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (40 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 800 ft.

Part B: For a driver going at 45 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (45 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 925 ft, which is 15.6% greater than the stopping distance for the speed limit.

Part C: For a driver going at 50 mph, the minimum stopping distance is given by the equation: s = v2/2a, where s is the stopping distance, v is the speed (50 mph), and a is the deceleration rate (assumed to be 10 ft/s2). Therefore, the minimum stopping distance is 1250 ft, which is 56.3% greater than the stopping distance for the speed limit.

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simplify the expression 5^3b+2

Answers

Answer:

125b+2

Step-by-step explanation:

5^3b+2

5x5x5=125

125b+2

Cannot be simplified any futher

Nicole is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 18 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 41^{\circ} ∘ , and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 44^{\circ} ∘ . If her eyes are 1.68 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest meter if necessary.

Answers

The height of the antenna is 17m approximately to the nearest metre using the trigonometric ratio of tangent for angleof elevation 44°.

What are trigonometric ratios

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the right triangle formed by the point of Nicole's eyes E with an angle of elevation 44°, top of the roof A (90°) and the top of the antenna B,

we shall evaluate for the height of the antenna AB as follows:

tan 44° = AB/18m {opposite/adjacent}

AB = 18m × tan 44° {cross multiplication}

AB = 18m × 0.9657

AB = 17.3826m

Therefore, the height of the antenna to the nearest metre is 17 metres using the trigonometric ratio of tangent for angleof elevation 44°.

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Answer:
2 meters


I got it correct in my hw (check the photos)


also mark me brainleist

A line includes the points (0, -8) and (3, 3) find the rate of change of the line

Answers

Answer:

11/3 or 11/3x

Step-by-step explanation:

Another term for "Rate of change" is slope.

The usual slope equation is (y2-y1)/(x2-x1)

Plugging in the points we get

(3 - (-8)) / (3 - 0)

(3+8)/(3-0)

(11)/(3)

Which makes the slope 11/3 or 11/3x

What is 2/3+3/7? I CAN'T FIGURE IT OUT! Work it out!

Answers

This question is actually not that complexed!

The way we add fractions is by finding the same common denominator. A common denominator between these two fractions is 21. This is because 3x7 is 21, and 7x3 is 21, giving us a common denominator between the two. Now whenever we multiply the denominator, we have to multiply the same value to the numerator!

2/3 multiplied by 7 (Numerator and Denominator) = 14/21

3/7 multiplied by 3 (Numerator and Denominator) = 9/21

Now after we converted the denominators, we can now add! Just add straight forward, however the denominator stays the same.

14/21 + 9/21 is 23/21

After we simplify it, we would get 1 2/21 (Mixed fraction) as our final answer. Therefore the answer is 1 2/21.

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If a current of 16A flows through a wire with a resistance of 0.6 Ohms, calculate the voltage. T/F a semantic error is detected when the action that an expression describes cannot be carried out, even though that expression is syntactically correct. The Sahas were reading a best-selling novel as a family. After the first week, they checked in with each other to see how much of the book each had read The text uses the term __________ to refer to men or women who do not alter their genitalia but whose appearance and mannerisms fall within the range of what is expected from members of the opposite sex. I need help with this question please and thank you . Design a situation where the probability of one event is 1/5 and another event is 1/10 true or false? changes to external requirements, such as legislation, regulation, or industry standards, that require control changes can result in a security gap for an organization. 1-2 paragraphs Explain why college is or isn't worth the cost: What is the radial electric field at the point r = 0. 5(r1+r2)? give your answer in units of kn/c Which statement describes a characteristic of the government established by the articles of conferderation Which answer is an example of symbolism used in Part 2 of "Mowgli's Brothers"?Question 6 options:LungriTabaquiLaw of the JungleRed Flower suppose gdp consists of wheat and rice. in 2005, 20 bushels of wheat are sold at $4 per bushel, and 10 bushels of rice are sold at $2 per bushel. in 2004, the price of wheat was $2 per bushel and the price of rice was $1 per bushel. using 2004 as the base year, it follows that, for 2005,: a. nominal GDP is $100, real GDP is $50, and the GDP deflator is 50. b. nominal GDP is $50, real GDP is $100, and the GDP deflator is 200. c. nominal GDP is $100, real GDP is $50, and the GDP deflator is 200. d. nominal GDP is $40, real GDP is $100, and the GDP deflator is 50. ANS: C 22. Explain in 3 paragraphs with piece of evidence to support my understanding of at least 2 importance of having read a diversity of literature effect humanity. Find E(X) and Var(X) for a continuous random variable X with a pdf f(x) = 4x,0 < x < 1. given f(x) = 2x^2, find f(-5) 10% Rewrite the following text choosing the correct words/ phrases from the brackets. 6X1=6 One day when I got home, tired after a morning's shopping, I found that my purse had been stolen. I at once retracted my steps as far as the chemist's in.............(a/an/the) main road where I had bought some (Because/But/Therefore) medicine... there was no sign of the purse .........(on/in/at) the pavement. Luckily, there .......... (was/were/had) not much money in it, but it contained a photograph of my daughter. Later in the day, I called at the police station to enquire if they had found the purse. A policeman said, "Somebody had handed it there. If you .....(did not write/ do not write/ had not written) your address, you would not have gof it back," he added. The man was a driver who had made a note of his name and address. His address made me (to thank, thank, thanked) him. For every $\$5$ I put in my piggybank, my friend Amy puts $\$3$ in hers. We both started saving at the same time with $\$0$ in each of our piggybanks. When we broke open our piggybanks I had $\$120$ more than Amy. How much money did Amy have? Answer these please!!! which of the following forces is an example of a contact forcea) gravitational forceb) magnetic forcec) electric force d) frictional force a triangle is the shape used to represent the components of total health. rue or false