When Q = {all perfect **squares** less than 30} and p={ all odd **numbers** from 1 to 10) Q ∩ P = { 1, 9}

**Set theory** simply means the branch of mathematical logic that deals with sets, that can be described as collections of **objects**.

It should be noted that **perfect squares** are the numbers that can be divided to give same number.

Q = {all **perfect squares** less than 30}. This will be 1, 4, 9, 16, 25

P ={ all odd **numbers** from 1 to 10}. This will be **1**, 3, 5, 7, and **9**.

In this case, the common **numbers** to set of P and Q are 1 and 9.

Therefore, the **numbers** are 1 and 9 since they're common to both sides.

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If Q = {all perfect squares less than 30} and p={ all odd numbers from 1 to 10}. Find Q ∩ P.

Provide the missing reasons for the following proof:

(In the picture)

Options

- Transitive Property of

Congruence

- Subtraction Property of

Equality

- Vertical Angles Theorem

(VAT)

- Division Property of

Equality

- Given

- Angle Congruence

Postulate

- Substitution Property of

Equality

The **missing reasons** are for the given** two triangles** VXW and VYZ are found.

The missing reasons for the following proof are -

∠XVW ≅ ∠W ; - Given∠XVW ≅ ∠ZVY ; Vertical Angles TheoremThus, the **missing reasons** are for the given** **two triangles VXW and VYZ are found.

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Evaluate (-3)^8 and (-3)^9

The **evaluation** of the **numbers** (-3)^8 and (-3)^9 will be (-3)^17.

Based on the information given, it should be noted that this illustrates that the **numbers** are raised to **power**.

In this case, it should be noted that we want to multiply the **powers**, this illustrates that we gave to add the powers. This will be:

Evaluate (-3)^8 × (-3)^9

Note that 8 + 9 = 17. Therefore,

Evaluate (-3)^8 and (-3)^9

= -3^17.

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Evaluate (-3)^8 × (-3)^9

I don’t get it I have to find the exterior angle (t+20)

**Answer:**

110

**Step-by-step explanation:**

To find the measure of the **exterior angle** we first need to find the value of t.

The sum of **interior angles** in a triangle is equal to 180° so we can write the following **equation**:

t + 10 + t + t + 20 = 180 add **like terms**

3t + 30 = 180 **subtract** 30 from both sides

3t = 150 **divide** both sides by 3

t = 50

The exterior angles and the angle represented with t + 20 make a **straight line**

and they are ** ****supplementary**** ****angles** so their sum is equal to 180

t + 20 = 70 to complete this to 180 we need 110

Alex, Cameron and Sam are all taking part in a 400 m race.

They are each running at a different constant speed.

Alex is running 12% faster than Cameron, whilst Sam is running 2% slower than Cameron.

When Alex crosses the finish line, how many metres is Sam from the finish line?

**Answer: **

**A= C + 12%C = 1.12C**

**S=.C -2%C = .98C**

**A,C and S are the speeds of Alex, Cameron and Sam**

**400 meter race**

**how far is Sam from the finish line when Alex crosses the finish line?**

**distance = speed times time**

**400 = AT where T=Alex' finish time**

**400=1.12T **

**400=CU where U = Cameron's finish time**

**400=SV where V = Sam's finish time**

**T<U<V**

**Alex' finish time is less than Cameron's finish time is less than Sam's finish time**

**if Cameron runs at 20 meters per second, finishing in 20 seconds**

**then Sam is about 50 meters from the finish line when Alex finishes**

sorry if i´m too late, hope this helps!

MANUFACTURING At a factory, molten glass is poured into molds to make

paperweights. Each mold is a rectangular prism with a height 4 inches

greater than the length of each side of its square base. Each mold holds

63 cubic inches of molten glass. What are the dimensions of the mold?

The **dimensions **of the mold are a length and width of 3 inches and a height of 7 inches.

The **volume o**f a** rectangular prism** is the space that it contains. We know that the volume of any prism is calculated by multiplying its **base area **by its height.

Given :

Let's assume that the** length** and the** width **of the "box" is x.

It is said that the height is 4 inches greater, so the height is x+4.

The **volume** of the mold is:

V = (x)(x)(x +4)

V = x²(x +4 ) using the **Distributive Property**.

V = x³ + 4x²

Since from the question we have Volume = 63 **cubic inches**

The equation we have is,

63 = x³ + 4x²

Subtracting 63 from both sides of the equation,

x³ + 4x²- 63 = 0

The **cubic equation **can be written as,

(x−3)(x²+7x+21) = 0

The solution of the **quadratic equation **(x²+7x+21) is,

x = -b ±√(b² - 4ac) / 2a

a = 1 , b =7 and c = 21

Substituting the values in the formula,

x = -7 ±√(7² - 4(1(21)) / 2(1)

x = -7 ±√-35 / 2

Hence,there are no **real solutions** to the** quadratic equation.**

There is only one **real solution **to the** **equation x = 3.

Therefore, the length and width of the rectangular prism are 3 inches and the height is x+4 = 3+4 = 7 inches.

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Please help. quickly

The** total surface area** of the triangular prism is 756 meter²

Given,

A** triangular prism** and its net.

We have to find the surface area of the triangular prism.

First we can consider the** right angled triangle.**

Height = 9 meter

Base = 12 meter

Hypotenuse = 15 meter

Area of the right angled triangle = (1/2 bh)

Here,

Area = 2 × (1/2 bh) = 2 × (1/2 × 12 × 9) = 2 × 6 × 9 = 108 meter²

Now, area of right rectangle.

**Area** of rectangle = length × breadth

Here, the breadth of the rectangle is the height of the triangle = 9 meter

Length = 18 meter

Area = length × breadth = 9 × 18 = 162 meter²

Then, area of middle **rectangle**.

Length = 18 meter

Breadth = 12 meter

Area = length × breadth = 18 × 12 = 216 meter²

Next, area of left rectangle.

Length = 18 meter

Breadth = Hypotenuse of the triangle = 15 meter

Area = length × breadth = 18 × 15 = 270 meter²

Now, lets calculate the **total surface area** of the triangular prism.

Surface Area of triangular prism = 108 + 162 + 216 + 270 = 756 meter²

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Explore Part 2

Drag the number cards to create three points that represent a proportional relationship.

Use the sketch tool if it helps you with your thinking.

Please help I give 10 pt

**Answer:**

**Step-by-step explanation:**

1,3 2,6 4,8

I hope it helps, thank you!

Form a polynomial whose zeros and degree are given.

Zeros: -7, multiplicity 1; -2, multiplicity 2; degree 3

MODE

Type a polynomial with integer coefficients and a leading coefficient of

f(x) = (Simplify your answer.)

Let p(x) be the** required polynomial.**

we are given that p(x) has a **zero **1 with **multiplicity **2

in other word, this means that (x-1) **occurs twice **as a **factor **of p(x).

Expressions with **polynomial functions** include **variables** with various degrees, non-zero **coefficients**, positive exponents (of variables), and **constants**. A **polynomial **in "b" of **degree **2 is, for **instance**, f(b) = 4b2 - 6.

Likewise, (x-3) **appears as a factor **of p(x) **once**.

we are also given that the **degree **of p(x) is 3.

So, p(x) can not have more than **3 linear factors**.

Altogether,

p(x) = k(x-1)^2 (x-3), where **constant **k ∈ R - {0}.

We may take k = 1 and get the** desired polynomial**,

p(x) = ( x-1)^2 ( x-3) = x^3 - 5x^2 +7x -3

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100 times my number is 12.6 more than 5,000.

**Answer:**

50.126

**Step-by-step explanation:**

hope this helps

The **solution **is 50.126

**What is Equation?**

**Equations **are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the **equality **of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an **equation**. The "=" sign and terms on both sides must always be present when writing an **equation**.

Given data ,

100 times my **number **is 12.6 more than 5000

Let the **number **be x

100 times the number = 100x

Now, 100x is 12.6 more than 5000

100x = 5000 + 12.6

100x = 5012.6

**Divide **by 100 on both sides , we get

x = 50.126

Hence , the **solution **is 50.126

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The personal assets and liabilities of a carpenter are listed below.

What is the carpenter's net worth?

$139,450

$145,228

$281,313

$284,678

**$139,450**

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

Explanation:

asset = an item that is either cash or can be turned into cash

liability = something that needs to be paid back (eg: truck loan)

A = total assets

A = (homeValue) + (workEquipment) + (carValue) + (investments)

A = ( $175,742 ) + ($3,365) + ($44,346) + ($61,225)

A = $284,678

B = total liabilities

B = (mortgage)+(credit card balance)+(truck loan)

B = ($76,765)+($2,055)+($66,408)

B = $145,228

C = net worth

C = A - B

C = ($284,678) - ($145,228)

C = **$139,450 which points us to ****choice A**** as the final answer.**

The** net worth** of the carpenter is $144,633.

Given that, Home value = $175,742, Mortgage = $76,765, Credit card balance = $2,055, Owned work equipment = $3,365 and Car value = $44,346.

What is the net worth?**Net worth** is the value of all the non-financial and **financial** **assets** owned by an individual or institution minus the **value** of all its outstanding **liabilities**.

Here,

Net worth = Financial **assets** - **Liabilities**

= (175,742+3,365+44,346) - (76,765+2,055)

= 223,453 - 78,820

= $144,633

Therefore, the** net worth** of the carpenter is $144,633.

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The fuel for a chain saw is a mix of oil and gasoline. The ratio of ounces of oil to gallons is 9 to 11. There are 55 gallons of gasoline. How many ounces of oil are there?

Given:

Ratio of ounces of oil to gallons of gasoline = 9 : 11

Gallons of gasoline = 55 gallons

Let's find the ounces of oil.

To find the ounces of oil, we have the equation:

[tex]\begin{gathered} \frac{\text{Ratio of ounces of oil}}{Ratios\text{ of gallons of gasoline}}=\frac{\text{Ounces of oil}}{\text{Gallons of gasoline}} \\ \\ \end{gathered}[/tex]Thus, we have:

[tex]\frac{9}{11}=\frac{x}{55}[/tex]Let x represent the ounces of oil.

Cross multiply:

[tex]\begin{gathered} 11x=9(55) \\ \\ 11x=495 \\ \\ \text{Divide both sides by 11:} \\ \frac{11x}{11}=\frac{495}{11} \\ \\ x=45 \end{gathered}[/tex]Therefore, there are 45 ounces of oil.

**ANSWER:**

**45 ounces of oil**

Find the surface area and volume of the following solids , a cylinder with radius 5 m and height 0.5 m

The radius of the cylinder is 5 m and the height is 0.5 m.

Then, the total surface area is

[tex]\begin{gathered} A=2\pi r(r+h) \\ =2\pi(5)(5+0.5) \\ =55\pi\text{ squared meter} \end{gathered}[/tex]**So, the surface area is **

Now, the volume is

[tex]\begin{gathered} V=\pi(r^2)h \\ =\pi(5)^2(0.5) \\ =39.27\text{ cubic meter} \end{gathered}[/tex]**So, the volume of the cylinder is 39.27 cubic meters. **

En una circunferencia señalamos diez puntos. ¿Cuál es la diferencia entre el número de heptágonos y el de triángulos cuyos vértices son algunos de esos puntos?

**Answer:**

ok wirrudi 123 alf8 434 21 3dis w

Find the height, if area is 24cm2 and the base is 6cm.

**Answer:**

4cm..............................

**Step-by-step explanation:**

24/6=4

4x6=24

a. Solve a³ = 11.

b. Solve c² = 27.

**Answer: a = 2.2 **

C = 5.1,-5.1

hi helpppppppppppppppppppppppppppppppppppp

**Answer:**

with what?

**Step-by-step explanation:**

1) Work out the area and the perimeter of the shape below.

10 cm

12 cm

4 cm

Diagram NOT

accurately dr

**Answer: 10 cm**

**Step-by-step explanation: because i am alwauys right about your mom**

Write an equation of the line passing through the point (2, -9) that is perpendicular to the line y=x+6.

**Answer:**

y = -x - 7

**Step-by-step explanation:**

Perpendicular to the slope m = 1 is the slope -1/m = -1.

y = m * (x - Px) + Py

y = -1 * (x - 2) + (-9)

y = -x + 2 - 9

y = -x - 7

1. consider a lottery with three possible outcomes: $125 will be received with probability 0.25, $100 will be received with probability 0.3 and $50 will be received with probability 0.45. a. what is the expected value of the lottery? b. what is the variance of the outcome? c. what would a risk-neutral person pay (at most) to play the lottery?

The** lottery's anticipated worth** is $80.

Given that,

The **probability** of receiving $125 is 0.25; the likelihood of receiving $100 is 0.3; and the likelihood of receiving $50 is 0.45.

A) EV=125*.2+100*.3+50*.5=$80

The lottery's anticipated worth is $80.

The expected value is obtained by multiplying each result by its likelihood.

The **expected value** of the lottery is then calculated by adding up all of these.

This is what we have: ;;

125(0.2) + 100(0.3) + 50(0.5) (0.5)

= 25 + 30 + 25 = $80

B) This is the formula for **variance** is shown in figure :

So, we can calculate the variance as follows:

.2*(125-80)^2+.3*(100-80)^2+.5*(50-80)^2=975

C) A risk-neutral person would pay $80 or less to play the lottery.

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**Answer:**

**Step-by-step explanation:**

Expected value of the lottery is $83.75.

Variance of the outcome is 909.6.

A risk-neutral person would pay $83.75 or less to play the lottery.

a) The expected value is obtained by multiplying each result by its likelihood.

The expected value of the lottery is then calculated by adding up all of these.

This is,

125(0.25) + 100(0.3) + 50(0.45)

= $83.75

b) we can calculate the variance as follows:

Variance=.25*(125-83.75)^2+.3*(100-83.75)^2+.45*(50-80)^2=909.6

c) A risk-neutral person would pay $83.75 or less to play the lottery.

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is (0,-4) a solution to the equation y = -10x + -4?

** Yes, it is a solution**

y = -10x + - 4

The given point: (0, -4)

**To know if it is a solution, we need to replace the y and x with the points given.**

**If the result on the left hand side is the same as the right hand side then, it is a solution**

x =0, y = -4

-4 = -10(0) + -4

-4 = 0 + (-4)

Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.

-4 = 0 - 4

-4 = -4

**The left hand side is the same as the right hand side. Hence, it is a solution**

**Answer:**

Yes it is a solution

**Step-by-step explanation:**

y = -10x + - 4

Point: (0, -4)

3. If it costs $3.50 per pound of sliced ham at the

deli and Weylan spent $2.90, how many pounds

did he buy? Round to the nearest hundredth of a

pound.

The** amount **in **pounds** of sliced ham he can buy is 083 **pounds. **

It ** costs** $3.50 per** pound** of sliced ham at the deli and Weylan spent $2.90.

The number of **pounds **of sliced ham he bought can be calculated as follows:

Hence,

3.50 dollars = 1 **pounds** of sliced ham

2.90 dollars = ?

cross multiply

**amount** of **pounds** he bought = 2.90 × 1 / 3.50

amount of **pounds** he bought = 2.90 / 3.50

amount of **pounds** he bought = 0.82857142857

amount of **pounds **he bought = 0.83 pounds

Therefore, the **amount **of pounds bought to the nearest hundredth is 0.83 **pounds.**

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What is the equation of the line that passes through the point (8, 1) and has a slope of -3/4?

**Answer:**

y-1= -(3/4)(x-8)

**Step-by-step explanation:**

y -1 =(-3/4)(x-8)

Distribute

y -1= (-3/4)x+6

Get rid of -1 by adding 1 to both sides

y=(-3/4)x+7

Hope this helps :)

the value of y is directly proportional to the value of x. when x = 20, the value of y = 16/5. the value of y is incline choice 1 when x = 50 incline choice 1:

1. 312.5

2. 1160

3. 3

4. 3200

Since y is directly **proportional **to x then the value of y is 8

In a **proportional **relationship, one variable is always equal to the constant value of the other.

It is clear that y **increases **in **proportion **to x by applying the direct proportionality formula, y = kx.

Given y is directly **proportional **to x.

Therefore y = kx

now at x = 20 , y = 16/5

∴16/5 = 20 k

or, k = 16 /100

Now at x = 50 ,

Y = 16 /100 × 50

or, y = 8

Therefore that value of y is 8.

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1. How many ways can you flip a coin and roll four-sided tetrahedron dice?

Draw the tree diagram in the space provided below.

**Answer:**

**Step-by-step explanation: I cant do the tree Diagram, however, I will help if you flip a coin (Heads or tails) The chances of it landing on heads will divide by 2 every time its heads or tails again and vise versa .**

Please only answer : The horizontal scale should be X-scale and The vertical scale should be Y-scale

Regarding the **scales **to plot the points on the table, we have that:

To find the ideal scales, we have to verify which are the **extrema **values of each variable, that is, the minimum and maximum value of each x and y.

From the table, the minimum and maximum **values of X** are given as follows:

This is a **small range** of values, hence the horizontal **scale **should be of 1.

From the same table, second column, the minimum and maximum **values of Y** are given as follows:

This is a **large **range of values, hence an ideal vertical **scale **is of 200, as then the number of traces would be almost the same as the number of traces of x.

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A car is traveling down a highway at a constant speed, described by the equation d = 65t, where d represents the distance, in miles, that the car travels at this speed in t hours.

a. What does the 65 tell us in this situation?

The car travels

miles in 1 hour.

b. How many miles does the car travel in 1.5 hours?

The car travels

miles in 1.5 hours.

c. How long does it take the car to travel 26 miles at this speed?

It takes the car

hours to travel 26 miles.

(a) 65 means the **car will travel** 65 miles in 1 hour .

(b) The car will **travel ** 97.5 miles in **1.5 hours** .

(c) The **car will take **0.4 **hours** to travel 26 miles at** his speed **.

In the question ,

it is given that

the **car is traveling** down a highway at a **constant speed**

and the **equation** representing is d =65*t

Part(a)

On comparing , the given **equation** with the equation of speed , time and distance

which is , distance = speed × time

on comparing both the **equations** , we get speed = 65 mph .

hence , 65 means the car will travel 65 miles in 1 hour .

Part(b)

substituting the value t = 1.5 hours in the **given equation** , we get

d = 65×1.5

= 97.5

hence , The **car will travel **97.5 miles in 1.5 hours

Part(c)

Substituting the value of d = 26 miles in the given equation , we get

26 = 65×t

t = 26/65

t = 0.4 hours

hence , It takes the car 0.4 hours to **travel 26 miles.**

Therefore , (a) 65 means the **car will travel** 65 miles in 1 hour .

(b) The car will **travel ** 97.5 miles in **1.5 hours** .

(c) The **car will take **0.4 **hours** to travel 26 miles at** his speed **.

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A sequence is defined by f(0) = -3, f(n) = f(n-1) + 0.5 for n ≥ 1.

1.

Write the first five terms of this sequence, starting with term 0.

2.

Write the nth term definition of this sequence.

**Answer:**

1.

f(0) = -3

f(1) = f(0) + 0.5 = -3 + 0.5 = -2.5

f(2) = f(1) + 0.5 = -2.5 + 0.5 = -2

f(3) = f(2) + 0.5 = -2 + 0.5 = -1.5

f(4) = f(3) + 0.5 = -1.5 + 0.5 = -1

2.

f(n) = 0.5n - 3

This function is linear.

Write the equation for the line that passes through the given point and is perpendicular to the given line (1,7); x - 4y = 8

The **equation** for the line that passes through the given point and is** perpendicular **to the given line is x - 4y = 3

Given : x - 4y = 8

4y = x- 8

On dividing by 4 we get;

y= x/4 - 2

This is of the form y = mx + c

Thus m in this case on comparing we get m= 1/4

We know the formula of the slope ;

y - y₁ =m ( x - x₁ )

y - 1 = 1/4 ( x- 7)

On cross multiplying we get ;

x- 4y = 3

Thus the **equation** for the line that passes through the given point and is** perpendicular **to the given line is x - 4y = 3 .

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State the transformation performed on the parent function.

For nine it should be right 6 and down 3

For ten it should be reflection on x axis and up 5

For eleven it’s a vertical stretch of 2 and down 7

For twelve it’s a vertical compression of 3/4 and right 2

For ten it should be reflection on x axis and up 5

For eleven it’s a vertical stretch of 2 and down 7

For twelve it’s a vertical compression of 3/4 and right 2

Springfield Mini Golf offers its customers a

25-round pass for $84, or they can pay

$3.25 per round. Which option has the

lesser price per round?

25 x 3.25 = 81.25 therefore paying each round separately is cheaper

84 divided by 25 = 3.36. So if they choose to pay $84 for 25-round pass they are paying $3.36 per round which is $0.11 more expensive than just paying $3.25 per round.

How important are museums to you? We asked three young people this question and this is what they told us.ChrisA lot of my friends think museums are boring but love them. I prefer ones where they move things round regularly, and bring in new things to keep it interesting I also like to have things to listen to as well as fook at. I suppose I like museums because I'm really interested in history and art. We study these subjects at college. but I've actually found out a lot more about them from museums than from my textbooks.EmilyI'm lucky because I live in New York, so there are lots of great museums for me to visit. One thing I've learnt is that you should never try to see a whole museum the first time you go. Just go to one or two rooms, and then return as often as you can to see the rest. For me, it's important that the people who work in the museum are pleasant, and happy to talk to me about the things in the exhibition. That makes a big difference.Daniel I don't go to museums much, except during my holidays in new cities. Then I make sure I spend at least a day going to the most famous ones. If it's a big museum and I don't have much time, I sometimes walk into a room and choose just five things to look at. I also take a tour if there is one, as I learn so much more from listening to the person showing us round then I do if I'm by myself.Help me find this answer.
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