Evaluate.

{3 + [−5 (2−4) ÷ 2]} x 3

Answer choices:

−27
(negative 27)

−13
(negative 13)

18
(eighteen)

24
(Twenty-four)

Stefan picks up 40 bushels of apples in 12 hours.

With the helo of gabriela they do so th 6.67 hours. We can represent this in the following table:

Bulshels of apples Hours

40 6.67

We need to multiply these number by 2, so that we can know how much time it would take for Gabriella to pick 40 alone.

Bulshels of apples Hours

40 6.67

80 13.34

Now, since picking 80 together takes 13.34 hours, and we know that tefan picks up 40 in 12 hours, the other 40 where picked up by Gabriella in:

Answer: 1.34 Hours

Given data:

Amount of money invested, P = $1000

Interest rate, r = 0.0625

Total money in the account, A = 5500

Now, to find the years use simple interest rate formula that is

Therefore, t will become

Putting the values we get,

Thus, it will take 72 years for the account to reach 5500.

We know that for any number of mutually exclusive events, we have the formula:

In this case, we have that P(A)=0.60 and P(B)=0.30, then:

Therefore, P(A or B) =0.90

We can formulate an expression for the surface area of the attic like this:

The area of a triangle is given by the following formula:

Where b is the base and h is the height of the triangle.

The area of a rectangle is given by the following formula:

Where w is the width and l is the length of the rectangle.

In this case, the attic has three rectangular faces, all of them have a width of 45 ft. two of them have a length of 25 ft and one has a width of 40 ft, then we can calculate the areas of these faces like this:

By summing up these areas, we get the area of the rectangular faces:

From this expression, we can factor 45 to get:

For the two triangular faces, their height equals 15 ft and the length of the bases equals 40 ft, then their areas are:

By summing them up, we get the area of the triangular faces:

By summing the area of the rectangular faces and the area of the triangular faces, we get the expression to calculate the total surface area of the attic, like this:

Then, the net Linda draw is correct. The first term of Linda's expression 45(40+25+25) is correct. The second term of Linda's equation missing a factor of 2. The surface area of Linda's attic is 4650 square feet

The expression represents the number of COVID deaths since March 1 2020 minus 100,000 deaths.

Given the fractions 1/6 and 1/4

We need to compare between them

The two number lines will be:

By comapring between them : 1/6 < 1

Solution:

Given:

To find the product, we multiply the terms in the second parentheses by each term in the first parentheses.

Thus, we have

Hence, the product of the complex numbers is

The correct option is B

Solution

- We are told that dog treats, Barker and DogYum cost $1.95 for 3 oz and $2.10 for 3.25 oz respectively and we are required to find out which is more expensive per ounce.

- In order to find the more expensive dog treat, we need to find the cost per ounce for each item. The cost per ounce is given by the formula below:

- The dog treat with the larger cost per oz is the more expensive item.

- Thus, let us calculate the cost per oz for both items.

DogYum:

Barker:

- We can observe that Barker is marginally more expensive than DogYum. We can confirm this by simply subtracting the cost per oz for both treats.

Final Answer

The answer is:

DogYum is less expensive, per ounce

First solution

Second solution

The second equation in the second system (Equation 2.2) was formed by adding both equations in the first system.

That is;

(Equation 2.2) = (Equation 1.1) + (Equation 1.2)

The probability P of an event e can be found using the formula:

Required: The probability that the next respondent will be between 18 and 25

Number of respondents between the ages of 18 and 25 = 25

Total number of respondents :

Hence, the probability of a selecting a respondents in the age range 18 to 25 is:

Answer: 0.1256

The area, in square inches, of the painted face of the brick is; 144 in²

The area of a square is given by;

A = L²

where;

L is the length of the side of the square

The sides of a square all have the same length, and as such we just need to find the length of one side.

The length of the side of the square here is the distance between two vertices, which can be calculated as

L = √[(x₂ - x₁)² + (y₂ - y₁)²]

However, to avoid long process, since it is a square, we can use subtraction of coordinates to get the side length which is gotten by using the first 3 coordinates;

Horizontal length = (6 + 6) = 12

Thus;

Area = L² = 12² = 144 in²

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Hangalakani leaves his work for home at 3.30 PM .

Hangalakani starts his work at 7.30 am.

He works for 6.5 hours.

He then takes a lunch break for 1 hour .

He then takes tea break for about 30 minutes = 0.5  hour

Total time spent at work = 6.5 + 1 + 0. 5 = 8 hours.

So if he starts work at 7.30 then he will end at

7.30 am + 8 hours  = 3.30 pm in the afternoon .

Now the manager says that they need 246 bags while Hangalakani calculated they need 245.37 bags of cement.

The manager is correct because bags of cement are not sold as a part or decimal .  The number of bags that can be bought must be a whole number.

To learn more about work visit:

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Given:

Required:

To solve the given inequality by graphing.

Explanation:

The graph of the above inequality is,

Now, the solution is shaded in the graph.

Final Answer:

The solution by using the graph is,

ANSWER

• (g o f)(x) = ,16x² + 24x + 9

• B., the domain of g o f is all real numbers

EXPLANATION

The composition is,

This means that, to find the composition, we have to replace x with f(x) in the function g(x),

Now, replace f(x) with its expression,

We can expand this binomial squared to write it in standard form. The composition is,

As we can see, this is a polynomial function. Therefore, the domain is all real numbers.

Solution

- The solution steps are given below:

Final Answer

The answer is

The base equation of a parabola is F(X) = X^2 + C

if we make F(X+2) it means the chart will move 2 units to the left

on the other hand, if the make F(X) + 5, it means the chart will displace 5 units upwards

As a result, from the given chart, our equation would be: y = 3(x+2)^2 + 5

Coupon A gives the lower price,is $3.75 less than the price with coupon b

Explanation

Step 1

get the final price

a) Coupon A

$ 18 rebate on a $95 bycicle

so, the final price is

b) 15% off of a $95 bucycle

fint, the value for 15% of $95

so, to know the value for 15% of $95,do:

the discount for coupon b is $14.25,

hence the final price is

Hence,

Step 2

compare the prices(difference)

I hope this helps you

y = 5x ( 2x + 1)

Let the width of the rectangular box be x

Let the length be L

Let the height be H

Let the volume be y

The length of the rectangular box is 1 inch longer than twice the width (x)

L = 2x + 1

The Height is 5 inch

H = 5

The volume of a rectangular box is:

Volume = Length x Width x Height

y = LHx

y = (2x + 1) (5) (x)

y = 5x (2x + 1)

Answer:

It would take them 6 hours. Six hours is 3/5 of Herman’s required time. 6 hours is 2/3 of Rosie’s, so 3/5 +2/5= the project being complete.

a) in term

b)subtraction

c) N/A

d) 4

Explanation

a term is a single mathematical expression , it can be a number, a variable or a combination, the terms are separated by the symbols + or -

for example:

in

there are 3 expression , so

Step 1

check the expression

it has only a term ( a fractions)

so

a)the number of terms is : 1

Step 2

b)first thing to do to term 1

PEMDAS means the order of operations for mathematical expressions involving more than one operation. It stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.so

we need to P ( break the parenthesis)

to do that,

do the SUBTRACTION

Step 3

c) as there is not term 2

N/A

Step 4

simplify the expression: folloing the PEMDAS order

so

d) 4

i hope this helps you

For this problem, we are given the mean and standard deviation of a certain test. We need to determine a probability of a random sample to be in a few values.

The first value we need to determine is the probability of the random sample being below 70. The first step we need to take is to determine the z-score of this value, which can be calculated with the following expression:

For the value of 70, we have:

Now we need to find this value on the z-table, which is:

Therefore we can determine that the probability of a value to be below 70 is 6.68%.

Now we need to determine the probability of a value above 112. We need to determine the z-score once again:

The z-table only tells us values below the z-score, so we need to subtract the result from 1, which is shown below:

The probability of the value being greater than 112 is 27.25%.

Now we need to find the probability of the score to be between 85 and 115. We need to find both Z-scores:

So we need to find the two values on the Z-table and subtract them. We have:

Let's complete the transformation from ABCD to EHGF.

Let's first determine the coordinates of the two figures.

Figure ABCD:

A : -5, 2

B : -3, 4

C : -2, 4

D : -1, 2

Figure EHGF:

E : 4, 1

H : 2, 3

G : 1, 3

F : 0, 1

Reflecting ABCD over the y - axis, we get:

P (x, y) = P' (-x, y)

For ABCD:

A : -5, 2 = A' : 5, 2

B : -3, 4 = B' : 3, 4

C: -2, 4 = C' : 2, 4

D: -1, 2 = D' : 1, 2

Let's now complete the translation,

(x + S), (y + T)

Where,

S = translation at x-axis

T = translation at y-axis

We get,

A' : 5, 2 = E : 4, 1 → S, T = 4 - 5, 1 - 2 = -1, -1

B' : 3, 4 = H : 2, 3 → S, T = 3 - 4, 3 - 4 = -1, -1

C' : 2, 4 = G : 1, 3 → S, T = 1 - 2, 3 - 4 = -1, -1

D' : 1, 2 = F: 0, 1 → S, T = 0 - 1, 1 - 2 = -1, -1

Therefore, we can say that the translation is (x + _, y + _) = (x + (-1), y + (-1)) = x - 1, y - 1

Given

Distance = 30 km

Time = 1 1/2 hours = 3/2 hours

Find

rate in km per hour

Explanation

we need to find the rate in km per hour.

as we now the rate is also called a speed

so , speed = distance/time

Final Answer

Therefore, the rate of ship is 20km/hr

so , the correct option is 1.

To find the constant of proportionality of the equation y = rx, from the values of the given table, just calculate the quotient r = y/x, where x and y can be any pair of values of the table.

For x = 3 and y = 30:

r = 30/3

r = 10

Hence, the constant of proportionality is

r = 10

Since the tax on the room is given by the function:

T(x)=0.06x+45

And x(cost in dollars of the room) is given= $120, you just have to subtitue x=120 on the function

T(120)=0.06(120)+4.5

T(120)=7.2+4.5

T(120)=11.7

So, the tax in dollars would be $11.7

The exponential equation given is,

Given the points

Therefore, the values for k and b will be resolved graphically.

Let us now plot the graph using a graphical calculator

From the graph,

Final answers

If we know the confidence interval for the proportion, the point estimate will be at the center of this interval.

Then, we can calculate the point estimate p as the average between the boundaries of the interval:

The margin of error can be calculated, knowing the interval, as half the difference between the upper boundary and the lower boundary of the interval:

The margin of error is 0.04. This margin of error is also the absolute difference between any boundary of the interval and the point estimate.

If the town's population is 31,526, the best estimate for the number of people who

would support the bike lanes is to use the point estimate as the proportion:

Answer:

a) The point estimate is p=0.61

b) The margin of error is MOE = 0.04

c) The best estimate is X=19231

The given number is two hundred million thirty five.

As you can observe, this number has hundred millions, tens, and units. Specifically, it has 2 hundred million, 3 tens and 5 units. We write each part as a sum, as follows

Then we add, so the number is

Combinatorics

If Connie had only 7 pairs of shoes and she has room for 7 pairs of shoes, then she has only one way to take her shoes.

If she had 8 pairs of shoes, then she can select any group of shoes that leaves one pair out. This makes 8 possible ways to choose.

When the number of pairs of shoes goes up, then the counting gets more complex. That is when combinatorics is a useful tool.

If we have a total of n elements to select m, where the order of selection is not important, then the total number of selections is given by:

Where the sign (!) is the factorial of a number.

Connie has n=16 pairs of shoes and she will take m=7 from them, thus the number of possible ways or combinations is:

Expanding the factorial down to match the greatest factorial in the denominator:

Simplifying and calculating:

Connie can choose in 11,440 ways the shoes to choose

The first option:

A)

x² + y² = x² + 2xy + y²

is not a polynomial identity because the right side of the equation corresponds to a binomial squared, which is given by:

(x + y)² = x² + 2xy + y²

and what you have left side of the given expression is x² + y² and not (x + y)² which is totally different.

Hence, x² + y² = x² + 2xy + y² is not a polynomial identity