unit 7 lessen 12 cool down 12.5 octagonal box a box is shaped like an octagonal prism here is what the basee of the prism looks like
for each question, make sure to include the unit with your answers and explain or show your reasoning

Answer:

She needs 16 recipe to make 8 gallons

In domain and range of a relation, if R be a relation from set A to set B, then

• The set of all first components of the ordered pairs belonging to R is called the domain of R.

Thus, Dom(R) = {a ∈ A: (a, b) ∈ R for some b ∈ B}.

• The set of all second components of the ordered pairs belonging to R is called the range of R.

Thus, range of R = {b ∈ B: (a, b) ∈R for some a ∈ A}.

Therefore, Domain (R) = {a : (a, b) ∈ R} and Range (R) = {b : (a, b) ∈ R}

Answer:

10 years old

Step-by-step explanation:

lets break it down:

6 more means +6

four times means *4

so if her son is x years old, she is 4x+6

since we know she's 46, we know that 4x+6=46

now we just solve the equation

4x+6=46

-6 on both sides

4x=40

/4 on both sides

x=10

Answer:

n = 110

Step-by-step explanation:

Margin of Error :

Zcritical * s/ sqrt(n)

s = standard deviation = 4

Margin of Error = ±0.75

Zcritical at 95% level of confidence = 1.96

Margin of Error = Zcritical * s/ sqrt(n)

0.75 = 1.96 * 4 / sqrt(n)

0.75 = 7.84 / sqrt(n)

Take the square of both sides

0.5625 = 61.4656 / n

0.5625 * n = 61.4656

0.5625 = 61.4656

n = 61.4656 / 0.5625

n = 109.27217

About 110 samples

The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

What is Geometric sequence?

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

Given that;

In a geometric sequence,

The third term is 100 and the eighth term is 3.125.

Now,

We know that;

The nth term of geometric sequence is,

⇒ \(T_{n} = a r^{n - 1}\)

Hence, The third term is;

⇒ \(T_{3} = a r^{3 - 1} = 100\)

⇒ \(a r^{2} = 100\)   ..(i)

And, The eighth term is,

⇒ \(T_{8} = a r^{8 - 1} = 3.125\)

⇒ \(a r^{7} = 3.125\)   ..(ii)

Divide equation (ii) by (i), we get;

⇒ ar⁷ / ar² = 3.125/100

⇒ r⁷ / r² = 3125 / 100000

⇒ r⁷⁻² = 3125 / 100000

⇒ r⁵ = 3125 / 100000

⇒ r = 5/10

Thus, The common ratio of a geometric sequence will be;

⇒ r = 5 / 10

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Answer:

  (b)  3 units

Step-by-step explanation:

You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.

The dilation factor multiplies every length.

If OB is 3/4, then OB' is 4(3/4) = 3.

The length of OB' is 3 units.

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To understand this problem:

a. My first thought is to try to maximize the numerator while minimizing the denominator.

To do this, I can try to use the largest digits (9, 8, 7) in the numerator and the smallest digits (1, 2, 3) in the denominator.

b. To find the largest possible ratio for the sine of an angle, I will start by trying to use the digits 9, 8, and 7 in the numerator and digits 1, 2, and 3 in the denominator.

I will try different combinations until I find the largest possible ratio.

First, I will try 987/321. Using a calculator, I find that sin(987/321) ≈ 0.9984.

Next, I will try swapping the digits in the numerator to see if I can get a larger ratio. I will try 987/231. Using a calculator, I find that sin(987/231) ≈ 0.9999, which is larger than the previous ratio.

Finally, I will try using the digit 6 in the denominator instead of 3, since 6 is closer in value to 7 and 8 than 3. I will try 987/216. Using a calculator, I find that sin(987/216) ≈ 0.9999999955, which is even larger than the previous ratio.

Therefore, I believe that the largest possible ratio for the sine of an angle using the digits 1 through 9, each used once, is approximately 0.9999999955, and it can be obtained with the ratio 987/216.

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Answer:

3x+1=3x+1

0x=0

no solution

3x+1=3x+2

0×=1

no solution

3x+1=2x+1

x=0

X IS THE SOLUTION BTW

Using one CFL bulb for one year would cost approximately $12.62.

We have,

We already calculated the cost of electricity for using one CFL-style bulb for one year as $8.76.

Let's now calculate the cost of the bulb for one year of use.

If one CFL-style bulb lasts for 10,000 hours, then it will last for:

10,000/24 = 416.67 days or approximately 1.14 years if used for 8 hours a day.

So, for one year of use, we would need,

1/1.14 = 0.8772 or approximately 1 CFL bulb.

The cost of using one CFL bulb for one year would be the cost of the bulb ($5.58) plus the cost of electricity ($8.76) divided by the lifespan of the bulb in years (1.14).

So,

Cost of using one CFL bulb for one year

= ($5.58 + $8.76)/1.14

= $12.62

Thus,

Using one CFL bulb for one year would cost approximately $12.62.

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Just add the powers while it is multiply

-1+(-3)

= -1 - 3

= -4

So it is \(2^{-4}\)

Answer:

=-3/8-7/16

Step-by-step explanation:

If b=-3/8

y=-4/7

Then b+1/4y= - 3/8 +1/4*(-4/7)= - 3/8 +1/(-16/7) =

=-3/8-7/16

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The height of the window=  5/2  ft

The width of the window=  9/4   ft

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Let x= height

Let y= width

x+ (3/4)*2 = 4    and   y+ (3/4)*2 = 3+ (3/4)

x= 4 - 3/2 = 5/2

y+ (3/4)*2 = 3+ (3/4)

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

y=  3+ (3/4)  - 3/2  = 3- 3/4 = 9/4

So, the height of the window=  5/2  ft

     the width of the window=  9/4   ft

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The probability that they will win the World Cup is 17.01%. This result is logical because when your team lost the first game, their chances of winning the World Cup decreased.

It is used to estimate the chance of winning, the chance of drawing a particular card, or the chance of rolling a particular number. It is a measure of the potential for a certain outcome to happen.

P(win WC| lost 1st game) = P (win WC ∩ lost 1st game) / P (lost 1st game)

P (win WC ∩ lost 1st game) = P (win WC) * P (lost 1st game| win WC)

= 0.63 * 0.27

= 0.1701

P (lost 1st game) = P (lost 1st game| win WC) + P (lost 1st game| lose WC)

= 0.27 + 0.73

= 1

Therefore, the probability that your team will win the World Cup is

0.1701 / 1 = 17.01%.

This result is logical because when your team lost the first game, their chances of winning the World Cup decreased.

This is because the team that wins the championship usually wins the first game of the series 67% of the time, so if your team did not win the first game, their chances of winning the championship decreased. Therefore, the probability that they will win the World Cup is 17.01%.

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The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.

The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.

For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.

Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

So we have derived p as the result using the Power of a Power Property.

In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.

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Answer:

Hello,

Step-by-step explanation:

\(\boxed{y=-\frac{x^2}{3} }\)

Answer:

D on Edge.

Step-by-step explanation:

Got it right.

The polar equation represents the microphone the choir is using ; D. r = 2 + cos(θ)

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

It is given that a choir is performing in front of an audience. A microphone is placed in front of the choir to capture sound.

The polar equation represents the microphone the choir is using would be;

D. r = 2 + cos(θ)

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We write the linear function as f(x)=3.5x+1 for the graph.

Linear function means a linear equation. As per given statement, we need to write an equation for straight line. We are given four-point in the XY coordinate.

We use the formula line passes through two points. The required function

should be in the form f(x) =mx+b or y=mx+b

given points are (0,1) (1,4.5) , (-1,-2.5) (-2,-6)

slope of line passes through first two points is=m= (y₂-y₁)/(x₂-x₁)= 3.5

slop of last two points is = m= 3.5

hence, four points lies in the same straight line

the equation of line, y= 3.5x+b

as the line passes through (-2,-6)

                                  -6=3.5×(-2)+b

                                 b=1, b is a constant

         hence, the linear function is f(x)=y=3.5x+1

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Given: A parabola equation

Required: To find the vertex of the given parabola.

Explanation: The given equation can be written as

Now the general equation is of the form

Comparing both equations we get,

The x-coordinate of the vertex is

For the y coordinate of the vertex, put x=-3 in the equation of parabola

Hence the coordinate of the vertex is (-3,31)

Final Answer: The vertex is (3,-5).

The Intel pays $7,760 to Bally Manufacturing on August 14.

The first step in calculating what Intel Corporation pays Bally on August 14 is to determine the net price of the machinery after the trade discount and the return of $100 due to defects.

The trade discount of 40% is calculated as follows:

Discount = List price × Discount rate

Discount = $13,100 × 0.40 = $5,240

So the net price of the machinery after the trade discount is:

Net price = List price - Discount

Net price = $13,100 - $5,240 = $7,860

After Intel returns $100 of machinery, the cost of the machinery is further reduced to:

Net price after return = Net price - Return

Net price after return = $7,860 - $100 = $7,760

Since the payment terms are 3/10 EOM (end of month), Intel receives a discount of 3% if payment is made within 10 days. The 10-day period begins on August 1 and ends on August 10 (the payment due date). Since Intel pays the bill on August 14, payment is late and the 3% discount does not apply.

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

(9 × 10⁴) (1.6 × 10³) / (2 × 10⁵) ( 3 × 10⁴) (1.2 × 10⁴)

Answer:

D (13,5)

Step-by-step explanation:

X 2 3 4 5

Y 2 5 9 13

So the ordered pairs are (2,2),(3,5), (4,9), (5,13)

and the ordered pairs for the inverse are

(2,2),(5,3), (9,4), (13,5)

from which D (13,5) is found among the options.

Answer:

b

Step-by-step explanation:

The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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Answer:

Step-by-step explanation:

Purchase price (A) : $12,500

Down Payment (B): $3,000

Loan Taken (C = A - B):  $9500

D :  Interest calculation for $9,500 for 3 years P(1 + rt)

= 9500(1 + (14.5/100) * 3)

= 9500(1 + 0.145 * 3)

= 9500 * 1.435

= $13632.5

E : Interest calculation for $9,500 for 2 years P(1 + rt)

= 9500(1 + (14.5/100) * 2)

= 9500(1 + 0.145 * 2)

= 9500 * 1.29

= $12,255

Difference between D - E

= $13632.5 - $12,255

= $1377.5

Hence the answer is B i.e. $1377.5 less interest for same amount of load for 2 years vs 3 years

Step-by-step explanation:

Here's your solution

=> Base = 32 In

=> Height = 30 in

=> Area of traingle = 1/2*base *height

=> putting the value of base and height in formula

=> Area = 1/2*30*32

=> Area = 480 in sq

hope it helps

Answer:

Where is the problem?

Step-by-step explanation:

At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

From given graph we can see that

At x=2, the function in the graph is approaches to infinity.

It means function is not defined at x=2

We know that a rational function is undefined when denominator is equal to zero.

For equation 1:

f(x)= 2(x+2)/(x-2)

Equating the denominator:

x-2=0

x=2

It means function is not defined at x=2

The y-intercept is: y= -2

The function is passing through the point (1,-6).

When we substitute x=1

Hence, option 1 is true.

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Answer:

60:61.8 OR 10:10.3

Step-by-step explanation:

Cant be simplified - unless your in advanced classes. If so

10:10.3

Answer:

Step-by-step explanation:

1/3 or 0.3 or 33.333333% or 3^-1 or 3.333333 x 10^-1