Albert has $105 to spend, the prices varying from $80 to $180 worth delivery being one-twentieth of the price. Total cost can be modeled by the function f(c) c representing the price. Domain is:

Answer:

340 ft²

Step-by-step explanation:

perimeter of rectangle = 2 x (L+W) = 2L + 2W = 74 .....(1)

cost of two length : $1 x 2L

cost of two width: $3.50 x 2W

($1 x 2L) + ($3.50 x 2W) = $159

2L + 7W = 159 ....... (2)

(2) - (1) ...  5W = 85

W = 17

L = (74 - 2 x 17) / 2 = 20

dimension = 17 x 20 = 340 ft²

The dimensions of the rectangular lot are 162.67 feet by 325.34 feet. The perimeter equation is 2L + 2W = 74. The cost equation is L + 3.50W = 159.

Let's say the length of the rectangular lot is L feet and the width is W feet.

The perimeter of a rectangle can be defined as: 2L + 2W.

According to the question, the perimeter is 74 feet, so we can write the equation as: 2L + 2W = 74.

The cost of fencing along the two lengths is $1 per foot, so the cost for the length fencing is 1 * L dollars.

The cost of fencing along the two widths is $3.50 per foot, so the cost for the width fencing is 3.50 * W dollars.

The total cost of fencing is $159, so we can write the equation as: 1 * L + 3.50 * W = 159.

Now we have two equations:

2L + 2W = 74

L + 3.50W = 159

To solve these equations, we can use substitution or elimination method.

Let's use the elimination method:

This simplifies to: 1.50W = 244.

Divide both sides by 1.50: W = 244 / 1.50 = 162.67 feet.

Plug this value back into the first equation to find L: 2L + 2(162.67) = 74.

Simplify: 2L + 325.34 = 74.

Subtract 325.34 from both sides: 2L = -251.34.

Divide both sides by 2: L = -251.34 / 2 = -125.67 feet.

Since the dimensions of the lot cannot be negative, we discard the negative value.

Therefore, the dimensions of the lot are 162.67 feet by 325.34 feet.

Answer:

Degree of freedom = 19

Step-by-step explanation:

We are given the following information in the question:

Sample size, n = 20

For a t-test hypothesis it was claimed that the population mean is greater than 89 ​second.

1) df

Df denotes the degree of freedom.

2) Degree of freedom  = n - 1

where n is the sample size

Degree of freedom = 20 - 1 = 19

Answer:

  j = -2

Step-by-step explanation:

It usually works well to start by eliminating parentheses.

  15j +6 = 6j -12

Now you can subtract 6j from both sides to get the variable term on one side of the equation only:

  9j +6 = -12

And you can subtract 6 from both sides to get the variable term by itself:

  9j = -18

Now, dividing by the coefficient of the variable gives you the solution:

  j = -2

The solution is j = -2.

Answer:

j = -2

Step-by-step explanation:

3 (5j + 2) = 2 (3j - 6)

15j + 6 = 6j - 12

15j - 6j = - 12 - 6

9j = - 18

j = - 18/9

j = - 2

Answer:

Step-by-step explanation:

The slope of the line needs to be determined first:

[tex]m=\frac{-9+-5}{-12+-8}=\frac{-14}{-20}=\frac{7}{10}[/tex]

Now let's use that and one of the coordinates to write an equation in point-slope form:

[tex]y-5=\frac{7}{10}(x-8)[/tex]

and, simplifying,

[tex]y-5=\frac{7}{10}x-\frac{56}{10}[/tex]

Now let's multiply everything by 10 to get rid of the fractions:

10y - 50 = 7x - 56

and

-7x + 10 y = -6

Apparently, they do not like to lead with negatives, which is not uncommon:

7x - 10y = 6

So his model is not correct.

Answer:

114

Step-by-step explanation:

z = (x − μ) / σ

0.93 = (x − 100) / 15

x ≈ 114

Answer:

165 Hamburgers

Step-by-step explanation:

330 divided by 2 is 165

Answer:

Part 1) Intervals of the domain where the  graph is above the x-axis (f(x) > 0)

Part 2) location on graph where input is zero  (y-intercept)

Part 3) location on graph where output is zero  (x-intercept)

Part 4) Intervals of the domain where the  graph is below the x-axis (f(x) < 0)

Step-by-step explanation:

Verify each case

Part 1) we have

Intervals of the domain where the  graph is above the x-axis

we know that

If the graph is above the x-axis, then the value of f(x) is positive

therefore

f(x) > 0

Part 2) we have

location on graph where input is zero  

Let

x ---> the independent variable or input value

f(x) ---> the dependent variable or output value

we know that

The y-intercept is the value of f(x) (output value) when the value of x (input value) is zero

therefore

y-intercept

Part 3) we have

location on graph where output is zero  

Let

x ---> the independent variable or input value

f(x) ---> the dependent variable or output value

we know that

The x-intercept is the value of x (input value) when the value of the function f(x) (output value) is zero

therefore

x-intercept

Part 4) we have

Intervals of the domain where the  graph is below the x-axis

we know that

If the graph is below the x-axis, then the value of f(x) is negative

therefore

f(x) < 0

Answer:

Intervals of the domain where the  graph is above the x-axis (f(x) > 0)

location on graph where input is zero  (y-intercept)

location on graph where output is zero  (x-intercept)

Intervals of the domain where the  graph is below the x-axis (f(x) < 0)

Step-by-step explanation:

answer edge 2020

He used 86 pounds of type A coffee.

Step-by-step explanation:

Cost of type A coffee = $5.40 per pound

Cost of type B coffee = $4.05 per pound

Total blend made = 138 pounds

Total cost = $675.00

Let,

x represents the pounds of type A coffee

y represents the pounds of type B coffee

According to given statement;

x+y=138    Eqn 1

5.40x+4.05y=675    Eqn 2

Multiplying Eqn 1 by 4.05

[tex]4.05(x+y=138)\\4.05x+4.05y=558.90\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](5.40x+4.05y)-(4.05x+4.05y)=675-558.90\\5.40x+4.05y-4.05x-4.05y=116.1\\1.35x=116.1\\[/tex]

Dividing both sides by 1.35

[tex]\frac{1.35x}{1.35}=\frac{116.1}{1.35}\\x=86[/tex]

He used 86 pounds of type A coffee.

Keywords: linear equation, elimination method

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Answer:

7-9

Step-by-step explanation:

Sebastian goes up from 0 by 7 floors. Then, he goes down by 9.

Answer:

4 trays should he prepared, if the owner wants a service level of at least 95%.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 5

Standard Deviation, σ = 1

We are given that the distribution of demand score is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

P(X > x) = 0.95

We have to find the value of x such that the probability is 0.95

P(X > x)  

[tex]P( X > x) = P( z > \displaystyle\frac{x - 5}{1})=0.95[/tex]  

[tex]= 1 -P( z \leq \displaystyle\frac{x - 5}{1})=0.95 [/tex]  

[tex]=P( z \leq \displaystyle\frac{x - 5}{1})=0.05 [/tex]  

Calculation the value from standard normal z table, we have,  

[tex]\displaystyle\frac{x - 5}{1} = -1.645\\x = 3.355 \approx 4[/tex]  

Hence,  4 trays should he prepared, if the owner wants a service level of at least 95%.

Answer:

(-5,7) is the center

Step-by-step explanation:

Answer:

$2,940

Step-by-step explanation:

Data provided in the question:

Cost of merchandise purchased = $40,000

Cost of merchandise returned = $3,000

Terms = 2/10, n/30

Now,

The amount that will be recorded as the purchase return

= Cost of merchandise returned - Discount on cost of merchandise

= $3,000 - ( 2% of $3,000 )

= $3,000 - ( 0.02 × $3,000 )

= $3,000 - $60

= $2,940

Answer:210

Step-by-step explanation:

175+70+15=210

Answer:the original price is $210

Step-by-step explanation:

Let x represent the original price of the tent. She bought it at price that is $70 off the original price. This means that $70 was taken off the original price.The amount after the discount has been removed would be

x - 70

Judy also used a coupon for an extra $15 off. This means that the amount the Judy finally paid for the tent would be

x - 70 - 15

if Judy paid $125 for the tent, it means that

x - 70 - 15 = 125

x = 125 + 70 + 15

x = $210

Answer:

Short-Term investment: 5000$

Intermediate-Term investment: 65000$

Long-Term investment: 30000$

Step-by-step explanation:

To construct our first equation lets define sort-term bond investment as x, long-term investment as y.

So the equation is:

[tex]x*0,04+(100000-x-y)*0,05+y*0,06=5250[/tex]

From the equation it is found that:

[tex]y=25000+x[/tex]

Instead of y, if we put 25000+x the equation will be as following:

[tex]x*0,04+75000*0,05+(25000+x)*0,06=5250[/tex]

From the equation it is found that:

[tex]x=5000[/tex]

Short-Term investment is 5000$

[tex]x+25000=y[/tex]

Long-Term investment is 30000$

Rest of the money is Intermediate-Term investment 65000$

Answer:

The length of the mid-segment of the trapezoid = 7

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

Step-by-step explanation:

The mid-segment of a trapezoid is the segment that connecting the midpoints of the two non-parallel sides.

As shown in the figure the two non-parallel sides are AB and CD

∴ The mid-segment of the trapezoid = [tex]\frac{BC +AD}{2}[/tex]

From the figure: BC = 8  and AD = 6

∴ The mid-segment of the trapezoid = [tex]\frac{8+6}{2} = 7[/tex]

Answer:

The answer to your question is letter B

Step-by-step explanation:

Process

1.- Write the equation

                                   f(x) = 2x + 1

find f(2)

2.- Substitute x for 2

                                  f(2) = 2(2) + 1

3.- Simplify

                                 f(2) = 4 + 1

                                 f(2) = 5

Answer:

5

Step-by-step explanation:

2(2) + 1 = 5

Answer: The number of ways would be 36,036.

Step-by-step explanation:

Since we have given that

Number of white light bulbs = 5

Number of orange light bulbs = 6

Number of blue light bulbs = 2

Total number of light bulbs = 13

So, the number of distinct orders of light bulbs if two bulbs of the same color are considered identical.

[tex]N=\dfrac{n!}{r!}\\\\N=\dfrac{13!}{5!\times 6!\times 2!}\\\\N=36036[/tex]

Hence, the number of ways would be 36,036.

The number of different orders in which Raina can put the colored light bulbs into a string is 1,324, calculated using the formula of permutations with indistinguishable items.

The question is about the number of different possible arrangements, or combinations, of the colored light bulbs. Since all light bulbs of the same color are identical, this is a problem of permutations with indistinguishable items. The formula to calculate this is n!/(r1!*r2!*...*rn!), where n is the total number of items, and r1, r2,...,rn are the number of each type of identical items.

So in this case, there are 13 colored light bulbs in total (n=13), with 5 white light bulbs (r1=5), 6 orange light bulbs (r2=6), and 2 blue light bulbs (r3=2).

The total different orders of light bulbs can be found by calculating 13!/(5!*6!*2!) = 1,324 possibilities.

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Answer:

53

Step-by-step explanation:

Answer:

The number of cans that he will need to cover the court is 12 cans

Step-by-step explanation:

The court is in the shape of a rectangle. Its length is 54 feet and its width is 30 feet. The formula for the area of a rectangle is expressed as length × width. Therefore, the area of the wooden floor is

54×30 = 1620 square foot

Suppose each can of wood stain covers 135 square feet, the number of cans that would cover the rectangular floor of the court would be

1620/135 = 12

Answer:

Keys would have to spend $6.60 on apples for both days.

Step-by-step explanation:

Keys went to buy 5 apples and 2 oranges for $3.45 and 7 apples and 3 oranges for $4.90 .

We have to find how much money she spends on apples on both the days.

Let price of apples be x and oranges be y.

We have to make equations and solve them to find the price of oranges and apples.

5x + 2y = 3.45

7x + 3y = 4.90

Solve both these equations to find x and y.

We get x= $0.55 and y = $0.35

Key has bought 12 apples and it would cost = 12 [tex]\times[/tex] 0.55

                                           = $6.60

Explanation:

1. BF bisects ∠CBA. Given

2. ∠CBF ≅ ∠ABF. Definition of angle bisector

3. BF ≅ BF. Reflexive property

4. ∠CFB ≅ ∠AFB. Given

5. ΔCBF ≅ ∆ABF. ASA congruence postulate

6. CF ≅ FA. Corresponding parts of congruent triangles are congruent (CPCTC)

_____

Comment on the problem

It appears as though all of the congruence symbols have gone missing.

Answer:

4.08

Step-by-step explanation:

Interest I =Pnr

3 months =3/12 year = n

r = 3%

and, P = 544$

Therefore,

[tex]i = 544 \times (3 \div 100) \times (3 \div 12) \\ \: \: \: = 4.08[/tex]

Answer:

Option B) and option D) are independent events. i.e. following events are independent events:

Step-by-step explanation:

Two events would be termed as Independent events if the occurrence of one event would not affect the occurrence of other event.

Let us first consider the options having independent events.

Option B) i.e. 'a coin is flipped and a spinner is spun' is treated as neither of the events is affecting the outcome of other event. For example, assuming a coin and spinner are kept isolated, the occurrence of event of a flipping coin is not affecting the outcome of the occurrence of spinner.

The same goes with the option D) i.e. 'four number cubes are rolled at the same time', as neither of the rolling is affecting the rolling of other coin.

Now, let us consider the options having dependent events

Let us suppose one ball is drawn from a bag of balls after another ball is drawn without replacement. If there is no replacement, it logically means, after every drawn event, total number of the balls are getting decreased, hence, bringing a variation among the probability after every event, as the occurrence of next event would be dealing with the remaining of the data, instead of the data that was present before the drawn of first event. Hence, the occurrence of every event depends upon the occurrence of other event, meaning the two events will keep affecting the outcome if no replacement is made before the next event.

The same logic goes with when white marbles are drawn from a bag of marbles without replacing the marbles. If there is no replacement, it logically means, after every drawn event, total number of the white marbles and marbles are getting decreased, hence, bringing a variation among the probability after every event, as the occurrence of next event would be dealing with the remaining of the data, instead of the data that was present before the drawn of first event.

So, after all the discussion, we can safely say make a conclusion that option B) and option D) are independent events. i.e. following events are independent events:

Keywords: dependent events, independent events

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Answer:

The following statements are true:

Step-by-step explanation:

Answer:

Approx. 1.8 in.²

Step-by-step explanation:

Circumference of a circle (the pizza) = 2πr

Area of a circle = πr²

Set 2πr = 4.71 (because that's the length of bacon around the pizza) and solve for the radius "r". Then plug that "r" into the area equation πr² to find the area. You should get 1.8 square inches if I plugged them in correctly.

Answer:

Step-by-step explanation:

Set this up as a proportion.  The idea is that if we can find out the number of "no" votes based on the ratio of 5:7, then we can add the "no" votes to the number of "yes" votes to get the total number of votes.

[tex]\frac{yes}{no}:\frac{5}{7}=\frac{3710}{x}[/tex]

Cross multiply to get

5x = 25790 so

x = 5194 "no" votes.

5194 + 3710 = 8904 total votes

Answer:

[tex]x^3+2x^2-5x-6=\left(x+1\right)\left(x-2\right)\left(x+3\right)[/tex].

Step-by-step explanation:

To find [tex]\frac{x^{3} + 2 x^{2} - 5 x - 6}{x + 1}[/tex] using synthetic division you must:

Write the problem in a division-like format. To do this:

Take the constant term of the divisor with the opposite sign and write it to the left.

Write the coefficients of the dividend to the right.

[tex]\begin{array}{c|cccc}&x^{3}&x^{2}&x^{1}&x^{0}\\-1&1&2&-5&-6\\&&\\\hline&\end{array}[/tex]

Step 1: Write down the first coefficient without changes:

[tex]\begin{array}{c|rrrr}-1&1&2&-5&-6\\&&\\\hline&\1\end{array}[/tex]

Step 2:

Multiply the entry in the left part of the table by the last entry in the result row.

Add the obtained result to the next coefficient of the dividend, and write down the sum.

[tex]\begin{array}{c|rrrr}-1&1&2&-5&-6\\&&\left(-1\right) \cdot 1=-1\\\hline&{1}&{2}+\left({-1}\right)={1}\end{array}[/tex]

Step 3:

Multiply the entry in the left part of the table by the last entry in the result row.

Add the obtained result to the next coefficient of the dividend, and write down the sum.

[tex]\begin{array}{c|rrrr}{-1}&1&2&{-5}&-6\\&&-1&\left({-1}\right) \cdot {1}={-1}\\\hline&1&{1}&\left({-5}\right)+\left({-1}\right)={-6}\end{array}[/tex]

Step 4:

Multiply the entry in the left part of the table by the last entry in the result row.

Add the obtained result to the next coefficient of the dividend, and write down the sum.

[tex]\begin{array}{c|rrrr}{-1}&1&2&-5&{-6}\\&&-1&-1&\left({-1}\right) \cdot \left({-6}\right)={6}\\\hline&1&1&{-6}&\left({-6}\right)+{6}={0}\end{array}[/tex]

We have completed the table and have obtained the following resulting coefficients: 1, 1, −6, 0.

All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

Thus, the quotient is [tex]x^{2}+x-6[/tex], and the remainder is 0.

[tex]\frac{x^{3} + 2 x^{2} - 5 x - 6}{x + 1}=x^{2} + x - 6+\frac{0}{x + 1}=x^{2} + x - 6[/tex]

Now, we factor [tex]x^{2}+x-6[/tex]

[tex]\left(x^2-2x\right)+\left(3x-6\right)\\x\left(x-2\right)+3\left(x-2\right)\\\left(x-2\right)\left(x+3\right)[/tex]

Therefore,

[tex]x^3+2x^2-5x-6=\left(x+1\right)\left(x-2\right)\left(x+3\right)[/tex]

Tim has 84 more postcards than Paul.

Step-by-step explanation:

Given,

Total number of postcards = 280

Let,

Tim's share of postcards = x

Shawn's share of postcards = [tex]\frac{3}{5}\ of\ Tim's\ share[/tex] = [tex]\frac{3}{5}x[/tex]

Paul's share of postcards = [tex]\frac{2}{3}\ of\ Shawn's=\frac{2}{3}(\frac{3}{5}x)=\frac{2}{5}x[/tex]

According to given statement;

[tex]x+\frac{3}{5}x+\frac{2}{5}x=280[/tex]

Taking LCM

[tex]\frac{5x+3x+2x}{5}=280\\\\\frac{10x}{5}=280\\\\2x=280[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{280}{2}\\x=140[/tex]

Paul's share = [tex]\frac{2}{5}x=\frac{2}{5}(28)=56[/tex]

Difference = Tim's share - Paul's share

Difference = 140 - 56 = 84 cards

Tim has 84 more postcards than Paul.

Keywords: addition, fraction

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