a shipping tube is shaped like a triangular prism the bases are equilateral triangles with edges of 5 in and a height of 4.3 in the tube is 14in long find the total surface area of the shipping tube

We are given the endpoints of a line PQ

We are asked to find the midpoint of line PQ.

Let us first find the distance of line PQ

Recall that the midpoint is at the halfway of the line PQ so divide the distance by 2

The expected return of the stock portfolio is 9.3%.

From the properties of stock portfolio we know that,

Expected return of a portfolio = RF + BP ( RM - RF )

E(RP) = RF + BP ( RM - RF )

RF= risk free rate =3%

RM = expected market return = 10%

BP = beta of portfolio

BP = ∑(Wi × Bi)

Wi is weight of stock i and Bi is the beta of stock i .

Wi= investment in stock / total investment

Beta of portfolio(BP)

=(0.5×1) + (0.35×0.2) + (0.33)

= 0.50 +0.07+0.33

=0.9

E(RP)

= RF + BP ( RM - RF )

= 0.03 + 0.9(0.30-0.03)

= 0.03 +0.063

= 0.093

Hence the expected rate = 0.093 × 100% = 9.3%

The stock market portfolio of an investor consists of stocks, funds, and possibly other market-traded securities. In general, cash and bond assets are often present in investment portfolios. Various assets with different sizes, industries, and other characteristics are included in a varied portfolio.

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In this expression, we can solve it by applying the distributive property

3(2y-7)

6y-21

So, factor 3 multiplies each term inside the parentheses.

2)-(x+4)

The minus outside the bracket works like a -1 multiplying it

-(x+4)

-x-4

3) For this one, remember the rule for multiplying fractions and then simplifying:

4) 6( x+1) -5(x+2)

6x+6 -5x-10

6x-5x+6-10

x-4

The number that satisfies the equation is

Doing the square root on both sides

On complex number we use the definition:

Therefore, the number that satisfies the equation is

That means that a solution is a complex number.

Complex numbers have two parts, the complex part and the real part:

Look that a and b are real coefficients, but z is a complex number because we have b multiplying i, the complex unit.

But why complex numbers are so important?

• Complex numbers can be used to solve polynomial equations, that we couldn't solve before

• Complex numbers can connect exponential function with trigonometric functions

Complex numbers are a powerful set that we can use to solve many complex problems in physics and mathematical, it may seem hard but they actually make things easier, sometimes working with complex numbers is way easier than working with real numbers.

(a). From the given table,

R(0)=226.6

R(10)=205.6

The average rate of change for the temperature from 0 minutes to 10 minutes is

(a) The average rate of change for the temperature from 0 minutes to 10 minutes is -2.1 (in degree centrigrade)

Minus sign implies that the temperature is deacreasing with increasing time

(b). Again,

R(30)=157.6

R(50)=119.6

The average rate of change for the temperature from 30 minutes to 50 minutes is

(b) The average rate of change for the temperature from 30 minutes to 50 minutes is -1.9 (in degree centrigrade)

Minus sign implies that the temperature is deacreasing with increasing time

Answer:

0, that is not possible

Step-by-step explanation:

Since she gets a discount she will always pay less

EXPLANATION

2) 812: The place of the underlined digits corresponds to UNITS.

VALUE --> 812: eight hundred twelve

In this case the answer is very simple. .

We must use the graph to find the answers.

Step 01:

Data

For x = 2 ===> y = 1

Step 02:

Direct variation equation

y = k * x

Constant of proportionality

x = 2 , y = 1

The solution is:

Constant of proportionality = k

k = 1/2

Direct variation equation

y = k * x

y = (1/2) * x

Explanation

two lines are parallel when their slopes are equal,

Step 1

convert the equation to the form

to easily find m

Hence

Step 2

Now we have this info to find the equation of the line

apply the formula

I hope this helps you

Given data:

The given triangles.

The given triangles are congruent by side-angle-side (ASA) rule.

Thus, the given triangles are congruent by ASA.

Given

Find

Exact solution by quadratic formula

Explanation

Quadratic formula is given by

here a = 1 , b = -3 and c = 1

substitute the values in quadratic formula ,

Final Answer

Therefore , the correct option is 4.

We have:

April --> -2.5

May --> Negative 2 and one-half = - 2 + 1/2 = -2.5

June --> 3.1

July --> - 1.6

Aug --> 2 and two-thirds = 2 + 2/3 = 2.67

We place them on the number line

Therefore,

June > August

April = May

May < July

May ≠ August

Answer: The true comparison is April = May

.Explanation:

we are given the following matrices

To compute

We will simply multiply the entries of G by 4 and C by 2

Thus, we will have

The final step will be to add the terms together

Thus, we will have

Find out the permutation 10P3

The parent function is:

y = x²

This is a quadratic function

The child functions are:

y = x - 4² whcih can be written as

y = x - 16

The second child function is

y = x + 3

The two child functions are linear functions while the parent function is a quadratic function.

The parent and child functions also differ in their ranges and domains

Domain = ( -∞ , ∞ )

Range = [0 , ∞ )

Domain = ( -∞ , ∞ )

Range = (-∞ , ∞ )

The difference between y = x - 4² and y = x + 3 is their intercepts on the y axis .

For y = x - 4², the y - intercept is -16

For y = x + 3, the y - intercept 3

This change is due to transformation (basically translation) on the x and y axes

We would test if np and n(1 - p) is at least 10

p = sample proportion

p = x/n

where

x = number of success

n = sample size

From the information given,

p = 41% = 41/100 = 0.41

n = 118

np = 48.38

n(1 - p) = 118(1 - 0.41) = 69.62

Both values are greater than or equal to 10. Thus, the distribution is approximately normal.

The mean of the distribution = p = 0.41

Standard deviation = √(p(1 - p)/n

By substituting the values,

standard deviation = √(0.41(1 - 0.41)/118 = √0.00205 = 0.045

We want to find P(p ≥ 0.5)

We would standardize 0.5 into a z score by applying the formula,

z = (x - mean)/standard deviation

z = (0.5 - 0.41)/0.045 = 2

From the normal distribution table, the probability value corresponding to a z score of 2 is 0.9773

P(p ≥ 0.5) = 1 - 0.9773

P(p ≥ 0.5) = 0.023

the probability that the majority (more than 50%) watched the Super Bow is 0.023

The given information is:

- Sample mean = 25.42

- Standard deviation = 14.25724

Part 1.

We have a confidence interval (C.I.) of 80%.

We need to find the z-score for this C.I., so, let's see a diagram:

We have a two-sided confidence interval. So, we need to find the z-score for a cumulative probability of 80+10=90%=0.9.

By using a standard normal table, we can see that z-score for 0.9 is:

By using an online calculator, we find the exact z-score is 1.282.

The confidence interval is given by the formula:

Where x is the mean of the sample, Zc is the z-score for the given confidence level, s is the standard deviation and n is the number of elements in the sample n=50.

By replacing the known values, we obtain:

So, the lower and upper limits are:

The margin of error is equal to half the width of the entire confidence interval, and it is also the value we add and subtract to the mean to find the confidence interval, so the margin of error is 2.585.

1. The 90% confidence interval for the mean difference between the height of trees in the park in 2009 and in 2019 is given as follows:

(11.59, 14.21)

2. The conditions for the confidence interval are of:

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 50 - 1 = 49 df, is t = 1.6766.

The remaining parameters are given as follows:

[tex]\overline{x} = 12.9, s = 5.52, n = 50[/tex]

Then the lower bound of the interval is of:

12.9 - 1.6766 x 5.52/sqrt(50) = 11.59.

The upper bound of the interval is of:

12.9 + 1.6766 x 5.52/sqrt(50) = 14.21.

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To determine the unit price for each detergent, i.e. the price per ounce, you have to divide the cost of the detergent by the number of ounces the container has.

Detergent A

Has 32 ounces

Costs $4.80

The unit price can be calculated as:

Detergent A costs $0.15/ounce

Detergent B

Has 48 ounces

Costs $5.76

The unit price can be calculated as the quotient between the price and the amount of detergent:

Detergent B costs $0.12/ounce

Detergent C

Has 128ounces

Costs $17.90

Calculate the unit price by dividing the price by the number of ounces of the container:

Detergent C costs $0.14/ounce.

The best detergent to buy is the one that has the lower unit price, so to determine which one is it you have to compare their price per ounce.

In this case, detergent B has the lower price per ounce and thus it is the best detergent to buy.

The given statement is Four less than a number is nine.

Remember that "less than" refers to subtraction. "A number" refers to a variable x. "is" refers to equality. So, the expression would be

The correct option is D

gaining 10 points cannot be represented by the number -10

-10 can represent all the given situations except gaining 10 points.

Because that will be an increase (+10), and not a decrease (-10)

Answer is: A withdrawal of $10.

Given that the baker has a total of 18 cups of flour, you know that the baker needs:

- This amount of flour for a batch of banana pancakes:

- This amount of flour for a batch of apple pancakes:

You know that the baker makes 8 batches of banana pancakes.

Let be "x" the greatest number of whole batches of apple pancakes that the baker can make.

You can set up this equation using the given data:

Now you need to solve for "x", in order to find its value:

Since the number of cups cannot be greater than 18 cups, you need to round down:

Hence, the answer is: Third option.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Jeff = 2 tens 42 ones

Victor = 3 tens 51 ones

what number is = ?

Step 02:

Jeff = 2 tens 42 ones

2 * 10 = 20

42 * 1 = 42

----------

Victor = 3 tens 51 ones

Answer:

Jeff: 62

Victor: 81

Step-by-step explanation:

Jeff has a number with 2 tens, and 42 ones. We can write out our 2 tens like this: 10 + 10 = 20

Next, he has 42 ones. This is just another way of saying '42'

So, jeff picked a number that is 20 + 42 = 62

Now, Victor. Victor has a number with 3 tens. This is saying: 10 + 10 + 10 which is 30. He has 51 ones, which is just the number 51.

So, Victor's number is 30 + 51 = 81

Answer:

Explanation:

Here, we want to find the area of the polygon

Mathematically, we have that calculated as:

where:

n is the number of sides of the polygon which is 9

b is the length of a side which is 14 cm

a is the length of the apothem which is 4 cm

Substituting the values, we have it that:

She could take

1.- {x|x Scoop}

2.- {x|x Light}

3.- {x|x Lanark}

4.- {x|x Scoop, Light}

5.- {x|x Scoop. Lanark}

6.- {x|x Light, Lanark}

The area of the figure is 24 cm²

The figure is divided into two blocks, one is rectangle having the dimensions, length as 5cm and width as 4 cm, another is a square having side of 2 cm.

The area of the figure is the summation of the area of the rectangle and the  area of the square.

area of the rectangle = length x width = 4 x 5 = 20cm²

area of the square = side² = 2² = 4cm²

area of the figure = area of rectangle + area of the square

= 20 + 4

area of the figure is 24 cm²

Therefore, the area of the figure is 24 cm²

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Shawn's age = 5 years

Ash's age = 8 years

Crystal's age = 20 years

Oscar's age = 16 years

Let Ash's age be represented by A

Let the Shawn's age be represented as S

Let the Crystal's age be represented as C

Let Oscar's age be represented as O

Ash is three years older than Shawn

A = S + 3.....................(1)

Crystal is 4 times as old as Shawn

C = 4S................................(2)

Oscar is twice as old as Ash

O = 2A.................................(3)

Altogether, their ages total 49

A + S + C + O = 49 ...............(4)

First, to get Oscar's age in terms of Shawn's age, substitute equation (1) into equation (3)

O = 2 ( S + 3)

O = 2S + 6..................(5)

Substitute equations (1), (2), and (5) into equation (4)

(S + 3) + S + (4S) + (2S + 6) = 49

S + S + 4S + 2S + 3 + 6 = 49

8S + 9 = 49

8S = 49 - 9

8S = 40

S = 40 / 8

S = 5

Shawn's age = 5 years

To get Ash's age, substitute the value of S into equation (1)

A = S + 3

A = 5 + 3

A = 8

Ash's age = 8 years

To get Crystal's age, substitute the value of S into equation (2)

C = 4S

C = 4(5)

C = 20

Crystal's age = 20 years

To get Oscar's age, substitute the value of A into equation (3)

O = 2A

O = 2(8)

O = 16

Oscar's age = 16 years

Lixin has x number of classmates and plan to buy her a birthday gift worth $36.

So basically, they need to contribute 36/x dollars each in order to buy the gift.

But 5 of them will not contribute and it cost them to add $0.24 each

So from 36/x dollars, it become (36/x + 0.24) dollars each

Multiply this individual contribution by the number of her classmates which was reduced by 5. (x - 5)

The equation will be :

Simplify the equation :

Multiply both sides by x to remove the denominator.

Rearrange and combine like terms :

Divide both sides by 0.24 to make the coefficient of x^2 become 1 :

Solve by factoring completely :

Equate both factors to 0, then solve for x :

x - 30 = 0

x = 30

x + 25 = 0

x = -25

Neglect negative value since there is no negative value for the number of persons.

The answer is x = 30

To summarize :

i Expression in terms of x :

ii Equation in x that reduces to x^2 - 5x - 750 = 0

iii Number of classmates Lixin has.

x = 30

Answer:

this is 50. i = 50

Step-by-step explanation:

hope it helps you

You have to find the equation of the linear function h(x), given that you know two points of the said function.

h(3)=-2 → this notation indicates the ordered pair (3,-2)

h(-3)=16 → this notation indicates the ordered pair (-3,16)

The first step to determine the equation of any line or linear function is to calculate its slope. To do so you have to use the following formula:

Where

(x₁,y₁) are the coordinates of one point of the line

(x,₂,y₂) are the coordinates of a second point of the line

Using the ordered pairs:

(3,-2) as (x₁,y₁)

(-3,16) as (x,₂,y₂)

Calculate the slope as follows:

So the slope of the linear function is m=-3

To determine the equation you can use the point-slope form:

Where

m represents the slope

(x₁,y₁) are the coordinates of one point of the line

I will use the point (3,-2) and the slope m=-3 to determine the equation but you can use either ordered pair to do so.

Now, what's left is to write the equation in slope-intercept form:

-Distribute the multiplication on the parentheses term:

-Pass "+2" to the right side of the equal sign by applying the opposite operation to both sides of the equal sign "-2"

The equation of the linear function is:

To find the value of h(5), you have to replace the equation of the function with x=5 and calculate the corresponding h(x) value

So: