Going into the final​ exam, which will count as two​ tests, Brandi has test scores of 75, 80, 74, 63, and 92. What score does Brandi need on the final in order to have an average score of​ 80?

Answer: the wire should be cut into 12 cm and 28 cm

Step-by-step explanation:

All sides of a square is equal.

The perimeter of a square is the distance around the square.

Let L represent the length each side of one of the squares. Then the perimeter of this square is 4L.

The length of a side of one square is to be 4 longer than length of a side of the other. This means that the length of each side of the other square is L + 4

The perimeter of the other square would be 4(L + 4) = 4L + 16

Since the piece of wire is 40 cm long, then

4L + 4L + 16 = 40

8L = 40 - 16 = 24

L = 24/8 = 3

The perimeter of the first square is

4L = 4 × 3 = 12

The perimeter of the second square is

4L + 16 = 4 × 3 + 16= 28

Final answer:

To make two squares with one side being 4 cm longer than the other, a 40 cm wire should be cut into pieces of 12 cm and 28 cm.

Explanation:

The question concerns cutting a 40 cm long piece of wire into two pieces to form two squares, where the length of a side of one square is 4 cm longer than the length of a side of the other square. Let's denote the length of the side of the smaller square as x cm. Thus, the side of the larger square will be x + 4 cm. Since the perimeter of a square is four times its side length, the total length of wire used for the smaller square will be 4x cm, and for the larger square will be 4(x + 4) cm.

Combining the total length of both squares, we have:

4x + 4(x + 4) = 40

This simplifies to:

8x + 16 = 40

Subtracting 16 from both sides, we get:

8x = 24

Dividing both sides by 8, we find:

x = 3

Therefore, the side of the smaller square is 3 cm, and the side of the larger square is 7 cm. To find out how long each piece of wire must be cut, we calculate the perimeters:

Smaller square wire length: 4(3) = 12 cm

Larger square wire length: 4(7) = 28 cm

So the wire should be cut into one 12 cm piece and one 28 cm piece.

Answer:

8 ounces of each must be mixed to make 16 ounces of a 10%solution.

Step-by-step explanation:

The careful analysis and detailed calculation is as shown in the attached file.

Answer: I will pick B

Step-by-step explanation:

Because it's a logical explanation

Answer:

Room 1.

Step-by-step explanation:

The note on room 3 is true.  So The notes on room 1 and room 2 are untrue.

If the lion is in  room 1 that would make the note on room 1 untrue  - so both room 1 and room 2 notes would be untrue.

Also if the lion  is in room 2  that would make both room 1 and room 2 notes true.

So the lion must be in room 1.

72 squares can be cut from a rectangular piece of leather measuring 4 feet by two-thirds of a yard

Solution:

Given, 4-inch by 4-inch squares can be cut from a rectangular piece of leather measuring 4 feet by two-thirds of a yard

Therefore,

Area of square = 4 x 4 = 16

Thus area of square to be cut is 16 square inches

Rectangular piece of leather measuring 4 feet by two-thirds of a yard

Convert feet to inches

1 feet = 12 inch

4 feet = 4 x 12 = 48 inches

Also,

1 yard = 36 inch

Given is a two-thirds of a yard

[tex]\frac{2}{3} \times 36 = 24\ inches[/tex]

Thus area of rectangular piece of leather is:

[tex]Area = 48 \times 24 = 1152\ square\ inches[/tex]

Total number of squares cut is given as:

[tex]\text{Total number of squares cut} = \frac{\text{area of leather}}{\text{ area of square}}[/tex]

Thus we get,

[tex]\text{Total number of squares cut} = \frac{1152}{16} = 72[/tex]

Thus 72 squares can be cut from a rectangular piece of leather measuring 4 feet by two-thirds of a yard

Answer:

72

Step-by-step explanation:

Step-by-step explanation:

The given sequence:

[tex]\dfrac{1}{2}+1+\dfrac{3}{2}+2+ ...[/tex]

Here, first term (a) = [tex]\dfrac{1}{2}[/tex], common difference(d) =[tex]1-\dfrac{1}{2}=\dfrac{1}{2}[/tex] and

the number of terms (n) = 25

The given sequence are in AP.

To find, the value of [tex]S_{25}[/tex] = ?

We know that,

The sum of nth terms of an AP

[tex]S_{n}=\dfrac{n}{2}[2a+(n-1)d][/tex]

The sum of 25th terms of an AP

[tex]S_{25}=\dfrac{25}{2}[2(\dfrac{1}{2})+(25-1)(\dfrac{1}{2})][/tex]

⇒ [tex]S_{25}=\dfrac{25}{2}[1+(24)(\dfrac{1}{2})][/tex]

⇒ [tex]S_{25}=\dfrac{25}{2}[1+12][/tex]

⇒ [tex]S_{25}=\dfrac{25}{2}[13][/tex]

⇒ [tex]S_{25}=\dfrac{325}{2}[/tex]

∴ [tex]S_{25}=\dfrac{325}{2}[/tex]

The value of the expression is [tex]0.25[/tex]

Explanation:

The expression is [tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}$[/tex]

Since, the base of the expression is the same. Then, by "product rule", when multiplying two powers that have the same base, you can add the exponents.

Thus, we have,

[tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}=\left(\frac{1}{2}\right)^{4-2}$[/tex]

Adding the exponents, we have,

[tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}=\left(\frac{1}{2}\right)^{2}$[/tex]

Applying exponent rule, [tex]$\left(\frac{a}{b}\right)^{c}=\frac{a^{c}}{b^{c}}$[/tex], we have,

[tex]$\left(\frac{1}{2}\right)^{2}=\frac{1^{2}}{2^{2}}$[/tex]

Simplifying, we get,

[tex]\frac{1}{4}[/tex]

Dividing, we have,

[tex]0.25[/tex]

Thus, the value of the expression is [tex]0.25[/tex]

Answer:

1/10 of pizza

Step-by-step explanation:

Let x represent size of equal pieces.      

We have been given that a pizza is cut into five pieces. Four of the pieces are the same size, and the fifth size is 0.5 the size of each of the others.

This means that size of small piece would be half the size of other pieces, that is [tex]\frac{x}{2}[/tex].

Since the pizza is divided in 5 pieces, so we will divide [tex]\frac{x}{2}[/tex] by 5 as:

[tex]\frac{\frac{x}{2}}{5}=\frac{x}{2\cdot5}=\frac{x}{10}=\frac{1}{10}x[/tex]

Therefore, the smallest piece is 1/10 of the pizza.

Answer:

There are 5 apples in the best bundle Charlie can afford

Step-by-step explanation:

If the utility function is u(xa, xb) , where xa represent the quantity of apples and xb is the quantity of bananas then we want to choose the quantity of bananas and apples that maximises the utility of Charlie for the same budget restriction ( get the most benefit for the same money).

The budget restriction is

$4* xa + $2* xb = $40

then

u(xa, xb) =xa*xb

4*xa + 2*xb = 40  → xb = (40 - 4*xa)/2 = 20 - 2*xa

replacing in the utility function

u(xa, xb) =xa* (20 - 2*xa) = 20*xa - 2*xa²

the maximum of this function is obtained when the derivative of the utility function with respect to xa is 0 . Thus

du/dxa = 20 - 4*xa = 0 → xa = 20/4 = 5

then for

xa=5 apples

xb=20 - 2*xa = 20 - 2*5 = 10 bananas

Charlie maximises his utility  . Therefore there are 5 apples in the best bundle Charlie can afford

To determine the best bundle Charlie can afford, we need to maximize his utility function u(xa, xb) = xaxb subject to his income and the prices of apples and bananas. The maximum value of xa represents the number of apples in the best bundle Charlie can afford, which is 5.

To determine the best bundle Charlie can afford, we need to maximize his utility function u(xa, xb) = xaxb subject to his income and the prices of apples and bananas. Let's denote the quantity of apples as xa and the quantity of bananas as xb. Since Charlie's income is $40, we have 4xa + 2xb ≤ 40. Using this inequality, we can find the maximum value of xa, which represents the number of apples in the best bundle Charlie can afford.

To solve for xa, we rearrange the inequality:

Now, let's look at the utility function u(xa, xb) = xaxb. To maximize the utility function, we take the derivative of u with respect to xa and set it equal to zero.

Since xb is in the denominator, its value should be greater than zero. Therefore, the best bundle Charlie can afford will have the maximum value of xa such that 4xa + 2(could be anything greater than 0) ≤ 40. Solving for xa, we get xa ≤ 5.

Hence, Charlie can afford a maximum of 5 apples in the best bundle.

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Answer:

COPD

Step-by-step explanation:

COPD is a lung disease caused by tobacco use and other factors

Answer:

The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are [tex]x=1\pm i\sqrt{7}[/tex].

Step-by-step explanation:

Consider the provided information.

Algebra's fundamental theorem states that: Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers.

Now consider the provided equation.

[tex]2x^2-4x+16=0[/tex]

The degree of the polynomial equation is 2, therefore according to Algebra's fundamental theorem the equation have two complex roots.

Now find the root of the equation.

For the quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are: [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Substitute [tex]a=2,\:b=-4,\:\ and \ c=16[/tex] in above formula.

[tex]x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:2\cdot \:16}}{2\cdot \:2}[/tex]

[tex]x_{1,\:2}=\frac{4\pm \sqrt{16-128}}{4}[/tex]

[tex]x_{1,\:2}=\frac{4\pm \sqrt{-112}}{4}[/tex]

[tex]x_{1,\:2}=\frac{4\pm 4i\sqrt{7}}{4}[/tex]

[tex]x_{1,\:2}=1\pm i\sqrt{7}[/tex]

Hence, the fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are [tex]x=1\pm i\sqrt{7}[/tex].

Answer:

2.21936352 feet

Step-by-step explanation:

420334*5280 (thats feet in a mile) divided by 1000000000

Yo sup??

Average shoulder width=total lenght / number of people

since we want it in inches therefore

Final answer=Average shoulder width*63360

=420334*63360/1,000,000,000

=26.62 inches

Hope this helps

Answer:

1 .  60!=8.31*[tex]10^{81}[/tex] ways

The rows and number of barns are related in that if we want to get the number of ways the cows and horse can be arranged

Step-by-step explanation:

At the county fair,animals are judged for the quality of their breeding and health.The animal pens are arranged in an array,with one animal in each pen .A barn can hold at most 10 rows of pens and at most 6 pens in each row ,with room for people to walk around them.What different ways can the planners of county fair arrange the pens for the horses and cows in the same barn? How the quantities given in the problem relate to each other?

if there are 10 ros and 6 barns. the number of ways animsls can be arrganged becomes

10 *6=60

60

look for 60 factorials, the number of ways

60!=8.31*[tex]10^{81}[/tex] ways

2.Permutation means arrangement . The rows and number of barns are related in that if we want to get the number of ways the cows and horse can be arranged , it makes it possible

For example find the number of ways 12 cows and 18 horses can be arranged in the barns.

we have the number of animals to be=12+18=30

60P30=60[tex]\frac{60!}{960-30)!} =\frac{60!}{30!}[/tex]

31.37*10^48 ways

Final answer:

The planners at the county fair can arrange the animal pens in various ways as long as the total number does not exceed 60, based on a maximum of 10 rows and 6 pens per row. This problem is one of combinatorics, requiring the counting and arranging of objects within given constraints.

Explanation:

The question involves arranging animal pens within a barn that can accommodate at most 10 rows of pens and up to 6 pens per row for animals like horses and cows at a county fair. This is fundamentally a problem of combinatorics, a branch of mathematics dealing with the counting, arrangement, and combination of objects. To determine the different arrangements possible for placing the pens, we would consider the combinations that do not exceed the given maximums for rows and pens per row.

The total number of pens that can fit in the barn is found by multiplying the maximum number of rows by the maximum number of pens per row, which gives us 10 rows × 6 pens per row = 60 pens as the upper limit. Therefore, the planners could arrange the pens in a variety of ways, including all rows filled with 6 pens, fewer rows with 6 pens, or more rows with less than 6 pens each, as long as the total number of pens does not exceed 60.

The quantities given in the problem relate to one another as constraints in a two-dimensional array. The planners have the flexibility to decide how many rows and pens per row to use without exceeding the maximum capacity of the structure. This scenario underscores the practical application of mathematical principles in planning and logistics.

Answer:

The width of path is 1.5 m                                        

Step-by-step explanation:

We are given the following in the question:

Field:

Length = 45 m

Width = 35 m

Area of filed =

[tex]\text{Area} = \text{Length}\times \text{Width} = 45\times 36 = 1620[/tex]

The area of rectangular field the is 1620 square meter.

Area of path = 234 m

Let x be the width of path.

Area of field without path = 1620 - 234 = 1386 square meter.

Now, dimensions of field without path is:

Length = [tex]45 -x - x = 45 -2x[/tex]

Width = [tex]36 -x - x = 36 - 2x[/tex]

[tex]\text{Area} = \text{Length}\times \text{Width}[/tex]

Thus, we can write:

[tex](45-2x)(36-2x) = 1386[/tex]

[tex]1620 - 90x - 72x + 4x^2 = 1386\\4x^2 - 162x + 234 = 0\\2x^2 - 81x + 117 = 0\\(2x - 3)(x - 39) = 0\\x = 1.5, x = 39[/tex]

We cannot take the width as 39 m, thus, the width of path is 1.5 m.

Answer:

$4200

Step-by-step explanation:

450 - 240 = 210 this is the amount of her commissions for the week.

we are looking for x = sales for the week

x * .05 = 210

x = 210/.05

x = 4200

Answer:c 4200

Step-by-step explanation:

Answer:

  2 1/2

Step-by-step explanation:

Each term is 1/2 added to the previous term. The first term is -3/2, so the first 9 terms of the sequence are ...

  -3/2, -1, -1/2, 0, 1/2, 1, 1 1/2, 2, 2 1/2

a9 is 2 1/2.

I'm pretty sure the answer to

a1=−32

an=an−1+12

is 5/2

Answer:

10 years

40 years

Step-by-step explanation:

let present ag e of son=x

5 years ago age of son=x-5

5 years ago age of man=7(x-5)=7x-35

present age of man=7x-35+5=7x-30

after 5 years

age of son=x+5

age of man=7x-30+5=7x-25

also 7x-25=3(x+5)

7x-25=3x+15

7x-3x=15+25

4x=40

x=10

age of son=10 years

age of man=7*10-30=70-30=40 years

Final answer:

By creating equations from the given information and solving them, it was found that the man is currently 40 years old, and his son is 10 years old.

Explanation:

Let's solve the problem using algebra. Suppose the current age of the man is M years and the current age of his son is S years.

According to the problem, 5 years ago, the age of the man was 7 times the age of his son. Therefore, M - 5 = 7(S - 5).

After 5 years, the age of the man will be 3 times the age of his son from now. Therefore, M + 5 = 3(S + 5).

Solving these equations:

M - 5 = 7S - 35

M + 5 = 3S + 15

Simplifying both:

M = 7S - 30

M = 3S + 10

Equating both equations we get:

7S - 30 = 3S + 10

4S = 40

S = 10

Substituting the value of S in the first equation:

M = 7*10 - 30 = 40

Therefore, the man is currently 40 years old, and his son is 10 years old.

Answer:

A) zero; cannot

Step-by-step explanation:

In line with the principle of rational expectations, expectation errors are unpredictable. The expectations of all available information will not differ from the optimal projections.The word optimal projection is inexorably intertwined with the best guess in rational expectations theory.

Answer:

Sample

Step-by-step explanation:

The part or portion of a population is called as sample. The given data represents a sample because a questionnaire is given to the selected 40 college students for collecting response on athletic participation rather to all of the college students. Thus, the questionnaire is given to a part of population. So, the given data represents a sample.

Answer:

Z=4

Step-by-step

You just add 2.05 to 1.95 to get z alone

Answer: Z=4

Step-by-step explanation:

Add 2.05 and 1.95 and you get 4.

If you subtract 2.05 from 4 you get 1.95

Answer:

43

Step-by-step explanation:

We have the following data:

Total number of hikers: 136

Minimum: 9 days

Q1 : 18 days

Median: 21 days

Q3: 28 days

Maximum: 56 days

Using the 1.5 Interquartile rule means:

Left boundary: Q1 - 1.5 × IQR

Right boundary: Q3 + 1.5 × IQR

We first calculate the IQR (Interquartile Range): Q3 - Q1

⇒ 28 - 18 = 10

Right boundary: 28 + 1.5 × 10

= 28 + 15

= 43

Hence the right boundary is 43.

Answer:

A. 15, 20, and 25

Step-by-step explanation:

Note that 3-4-5 is a pythagorean triple via following:

[tex]\sqrt{ (3^2 + 4^2 )} = 5^2[/tex]

Dividing 15, 20, and 25 by 5 nets you the pythagorean triple 3-4-5.

Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of 4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment?  

$450.71

____________________________

*100% CORRECT ANSWERS

Question 1

A family is purchasing a house and needs to finance a $195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 years and making monthly payments. What is the monthly payment?

$1082.84    

Question 2

A family is purchasing a house and needs to finance a 195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 years and making monthly payments. What is the total amount the family will pay back to the bank (to the nearest dollar)?

$389,822    

Question 3

Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of 4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment?  

$450.71

Step-by-step explanation:

[tex]PV = FV \div (1+i)^n[/tex]

Here FV = $83870

i = 6.8% = 0.068

[tex]n = \frac{226}{365}[/tex] =0.62

Therefore,

[tex]PV=\frac{83870}{(1+0.068)^{0.62}}[/tex]

     =$80517.91

Therefore the present value = $ 80517.91

Answer:

The answer to your question is There is only one solution (0, -2)

Step-by-step explanation:

Data

Equation 1     x - y = 2

Equation 2    x + y = -2

Solve for y

Equation 1          y = x -2

                          y = x - 2

Equation 2         y = - x - 2

See the graph below

These lines cross in point (0 ,-2), that is the only solution.

If the lines have not crossed, they were parallel lines.

Answer:

P = 2(5W + W)

Step-by-step explanation:

P = 2(L +W)

L = 5W

P = 2(5W + W)

P = 10W + 2W

P = 12W

Answer:

the least is 40

Step-by-step explanation:

if u multiply each money amount times the amount they bought you get the awnser

Answer: $116.99

Step-by-step explanation:

By using compound interest formula which said:

A = P ( 1 + r/n )^(n×t)

P=Principal= 1000

r=rate=4/100

n=1

t= 4

Apply the above formula

A = P ( 1 + r/n )^(n×t)

A = 1000(1 + 0.04/1)^(1 × 4)

A= 100(1.04)^4

A= 100 × 1.17

A = 116.99

Answer:

Ben

Step-by-step explanation:

Ben has an absolute advantage in making of pizza because he can make five pizzas in one hour which is a greater quantity compared to Sam that makes four pizzas in one hour.

The true statement is: d. The conclusion is incorrect because the range is limited to the set of positive real numbers.

The function is given as:

[tex]\mathbf{f(x) =2x}[/tex]

The above function implies that:

The above highlights mean that: Geraldine's claims are incorrect.

Because y increases or decreases by 2, when x increases or decreases by 1

In other words, the value of y does not get doubled or halved.

Hence, both statements are incorrect

Read more about range at:

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