8. Cost Comparison

Dean is planning to purchase a new Nissan Altima which costs $26,865. He has saved up $3,200 to put toward it. He is thinking about getting a loan for it from his credit union, but he could also keep driving his beat-up old car for a while longer and save up cash for the new one.



Possibility Two: Saving Up

You've already calculated the total Dean would spend on the car if he gets the loan, and also the total he would spend on the car if he saves up for it. Use those two numbers to determine how much less he would pay for the car by saving up for it instead of getting the loan.

The given amounts of money will be written as £5.37, £2.04 and £15.70 respectively. The solution has been obtained by using denominations of money.

What is denomination?

The term "denomination" refers to the units of measure that are used to categorize various financial products such as coins and paper money. Every country has different denomination.

We are given three different amounts of money in words which are to be written in denominations.

So,

a. Five pounds and thirty seven pence = £5.37

b. Two pounds and four pence = £2.04

c. Fifteen pounds and seventy pence = £15.70

Hence, the amounts in their denominations have been obtained.

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Answer:

$179.1

Step-by-step explanation:

Total area to be painted = 2,250 sq.ft

area covered by per gallon of paint = 250 sq.ft

Hence, gallons of paint required to paint 2,250 sq.ft is...

2250/250 = 9

so, 9 gallons of paint are required to paint 2,250 sq.ft

cost per gallon of paint = $19.90

so, cost of 9 gallons is...

19.90*9 = 179.1

The total money that Kathy will spend for painting the outside of her house is $179.1.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given is the Kathy who is painting the outside of her house. Its area is 2,250 square feet. Each gallon of paint covers 250 square feet and costs $19.90.

Area of the outer house = [A] = 2250 ft²

Area covered by 1 gallon of paint = [a] = 250 ft²

Therefore, the total gallons of paint needed = (2250/250) = 9 gallons.

Cost of 9 gallons of paint will be = 19.90 x 9 = 179.1

Therefore, the total money that Kathy will spend for painting the outside of her house is $179.1.

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The most reasonable explanation for why Medera received zero calls between 3pm and 5pm is that she turned the phone off while playing in a soccer game.

Number is an abstract concept used to count or measure something. It is present in many aspects of our lives, from counting the number of people in a room to measuring a distance between two points. Numbers are also used to represent information and to quantify facts. We use numbers in mathematics, science, engineering, business, and many other fields. Numbers are also used in everyday life, such as for telling time, counting items, and measuring distances.

The most reasonable explanation for why Medera received zero calls between the hours of 3pm and 5pm is that Medera turned the phone off while playing in a soccer game. This can be seen by looking at the histogram, which shows that there were zero calls received around this time, while Medera was likely playing in the game. The graph also shows that Medera usually receives a cluster of calls at certain times. This is also evidence that she turned her phone off while playing in the game, as it would be unlikely that she would receive no calls if her phone was still on. Additionally, it is unlikely that Medera's phone can only receive 22 calls a day, as this would be an unusually low limit. Furthermore, it is unlikely that Medera lost her phone for two hours, as this would not explain why there were zero calls received. Therefore, the most reasonable explanation for why Medera received zero calls between 3pm and 5pm is that she turned the phone off while playing in a soccer game.

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The hours when no calls were received were most likely when Madera turned off the phone while practising soccer.

According to the question,

Madera, a middle school student, got phone calls from 10 a.m. to 10 p.m. on one Saturday.

From the scenarios presented, the one that would suggest this would be when Medera turned off his phone while playing soccer. This is because, her phone was turned off, it was not receiving any phone signal, which meant that no inbound calls were received during that time. Medara lost her phone for two hours, but even though she didn't have it with her, the phone was still on and connected to a network, indicating that calls were still streaming.

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The simplified form of the given expression is 25 x² y ²⁶.

What is the simplified form of the expression?

Simplifying expressions mean rewriting the same algebraic expression in a compact form such that there are no like terms.

What are the exponent rules?

The different Laws of exponents used to solve the above mentioned question are:

\(x^{m}.x^{n} = x^{m+n} \\\frac{x^{m} }{x^{n} } = x^{m-n} \\(x^{m})^{n} } = x^{mn }\)

According to the given question.

We have an expression (5xy⁷)²(y⁴)³

To simplify the above expression we use the exponent rules.

Therefore,

(5xy⁷)²(y⁴)³

(5² x² y²×⁷) (y ⁴׳)

(25 x² y¹⁴ ) (y¹²)

25 x² y¹⁴⁺¹²

25 x² y ²⁶

Therefore, the simplified form of the given expression is  25 x² y ²⁶

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Answer:

We conclude that:

Option D i.e. m∠DAB = m∠BCD is correct option.

Step-by-step explanation:

We know that a Parallelogram is a quadrilateral with two pairs of parallel sides.

We also know that the opposite angles of a parallelogram are equal.

Given

From the figure:

It is clear that m∠DAB is the opposite angle of m∠BCD.

Thus,

m∠DAB = m∠BCD  ∵ opposite angles of a parallelogram are equal.

Therefore, we conclude that:

Option D i.e. m∠DAB = m∠BCD is correct option.

To solve for the volume of a rectangular prism, we could use the following formula:

\(V=l*w*h\)

Although we typically use this formula to solve for the volume, we could also use it to determine any of the variables above. All we have to do is rearrange the equation to isolate what we need to find.

We're given:

First, rearrange the volume formula to isolate width (w):

\(V=l*w*h\)

⇒ Divide both sides by \(l*h\):

\(\dfrac{V}{l*h}=\dfrac{l*w*h}{l*h}\\\\\dfrac{V}{l*h}=w\\\\w=\dfrac{V}{l*h}\)

⇒ Plug in the given values for V, l and h:

\(w=\dfrac{1144}{8*13}\\\\w=11\)

Therefore, the box is 11 ft wide.

The box is 11 ft wide.

Answer:

(A) 11 ft.

Step-by-step explanation:

got it right

To find the number of dimes and quarters, you have 17 dimes and 34 quarters in your pocket , when there are 51 coins in your pocket.

To solve this problem, we can set up a system of equations using the given information. Let's use "d" to represent the number of dimes and "q" to represent the number of quarters.

We know that there are 51 coins in total, so we can write the equation: d + q = 51.

We also know that the total value of the coins is $10.20, which can be expressed as 10d + 25q (since dimes are worth 10 cents and quarters are worth 25 cents). So our second equation is: 10d + 25q = 1020.

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

Rearrange the first equation to solve for d: d = 51 - q.

Substitute this expression for d in the second equation: 10(51 - q) + 25q = 1020.

Simplify and solve for q: 510 - 10q + 25q = 1020.

Combine like terms: 15q = 510.

Divide both sides by 15: q = 34.

Now substitute this value back into the first equation to solve for d: d + 34 = 51.

Subtract 34 from both sides: d = 17.

Therefore, you have 17 dimes and 34 quarters.

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Answer: 3/-4

Hope it helps!

Answer:5

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

If you try to divide the highest 4-digit number (9999) by some number 10 or over, you will always get a number that is more than 2 digits

Answer:

x= 14.0 (nearest tenth)

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer: The exact answer is 3.61 weeks, so the "about" answer is 4 weeks.

Step-by-step explanation:

b = $85 + w (10+8)

b = 85 + w (18)

b = 85 + 18w

b is the total amount need in the bank account, so $150.

$150 = $85 + 18w

$150 - $85 = $85 - $85 + 18w

$65 = 18w

$65 / 18 = 18w / 18

3.611 weeks = w

So, it will take about 4 weeks to get $150 in his bank account.

Hope this helps!

Simplify the expression

Put b=150

For the graphed function, it is found that:

I. a) The domain of the function is [0,12].

I. b) The domain represents the time in hours that the temperature was observed.

II. a) The range of the function is [-2,4].

II. b) The range represents the temperatures observed.

III. a) The function is decreasing on the interval [0,3].

III. b) On this interval, the temperatures are falling.

The domain of a function is composed by the set containing all the input values of the function.

In the graphed function, the input is the time in hours, hence the domain is given by the following interval:

[0,12].

The range of the function is composed by the set containing all the output values of the function.

In the graphed function, the output is the temperature, hence the range is given by the following interval:

[-2,4].

The function is decreasing when the graph is moving right and down, hence the interval in which the temperatures are falling are given as follows:

[0,3].

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Answer:

I love you sweetheart I want to look and love you

Answer:

slope- 1/4

y intercept- 1

ACF is a 30º-60º-90º triangle because of the following:

1) Based on a theorem, in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : \(\sqrt{3}\)

1 → short leg

2 → hypotenuse

\(\sqrt{3}\) → long leg

Side length of the hexagon is the short leg of the triangle. It is 1.

r1 is the radius of the incircle in a regular hexagon. 2(r1) is the diameter of the incircle. It is also the hypotenuse of the right triangle. It is 2.

Using Pythagorean theorem.

\(a^2 + b^2 = c^2\)

\(1^2 + b^2 = 2^2\)

\(b^2 = 2^2 - 1^2\)

\(b^2 = 4 - 1\)

\(b^2 = 3\)

\(\sqrt{b^2} = \sqrt{3}\)

\(b = \sqrt{3}\)

Answer:

the answer would be 375 miles.

Brainliest please?

The linear regression equation that represents this set of data is given by:

y = 30x + 854.6.

The predicted calendar year in which the number of new cases would reach 1141 is:

2020.

The format of the linear regression equation is given as follows:

y = mx + b.

In which the coefficients are listed as follows:

The equation is built inserting the points given on the table into a linear regression calculator.

The points from the table given by the image at the end of the answer are given as follows:

(0, 856), (1, 871), (2, 924), (3, 961), (4,961).

Inserting these points into a calculator, the equation is given as follows:

y = 30x + 854.6.

The predicted calendar year in which the number of new cases would reach 1141 is 2011 + integer part of x, when y = 1141, hence:

1141 = 30x + 854.6

x = (1141 - 854.6)/30

x = 9.54.

Hence during the year of 2020.

The table is given by the image shown at the end of the answer.

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The solution in interval notation is; (-∞,  49/2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To solve the equation 5/16x - 7/4 < 3/4x + 21/2, we can simplify both sides:

5/16x - 7/4 < 3/4x + 21/2

Combining like terms:

5/16x  -3/4x  < 21/2 + 7/4

8/16x < 49/4

1/2x < 49/4

Simplifying the fraction;

x < 49/2

Therefore, the solution in interval notation is (-∞,  49/2).

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242 inches

Step-by-step explanation:

with an 11 inch diameter, a single spiral of the wires circumference is about 22 inches. with this we can multiply 22 by 11 and assume its 242 inches long

Answer: 50% decrease

Step-by-step explanation:

50% of 310 = 155

310-155=155

50% decrease :)

ANSWER: 50% decrease

SOLUTION:

50% of 310 = 155

310-155=155

So in all the answer is.......

50% decrease  :)))))

-XOXOXO:)

angle FEB = angle ABE ( Alternate Interior Angles )

angle FEB = 4x = angle ABE

x + 4x + 65° = 180° ( sum of the Angles On the same line is equal to 18° )

or, 5x = 180° - 65°

or, x = 115/5

or, x = 23

The value of x is 23°.

4x = 4(23) = 92°.

b) We have 25% support the changes, therefore solve:

where p =25% = 0.25

So

Need 54 people but already have 50, then:

Answer: 4

The answer choice which represents the rewritten form of; 2,290,000 in scientific notation is; 2.29 × 10⁶.

The scientific notation of a number is the form of the number such that only one digit appears before the decimal and the rest of the place value is represented by exponents of 10.

Hence, since the highest place value in the number is million; it follows that the science notation representation is; 2.29 × 10⁶.

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A) If the change in b results in a smaller feasible region, then the optimal objective value will either remain the same or increase.

B)  If the change in b results in a larger feasible region, then the optimal objective value may remain the same or decrease.

In linear programming, the objective is to minimize or maximize an objective function subject to certain constraints. One common constraint is that the solution must be in the feasible region, which is defined by the set of all solutions that satisfy the constraints.

Recall that the constraints are given by Ax >= b, where A is a matrix of coefficients and x is a vector of variables. If we increase one component of b, say bi, then the set of solutions that satisfy the constraints will change. Specifically, any solution that previously satisfied Ax >= b may no longer satisfy the constraints, since the left-hand side of the inequality is fixed while the right-hand side has increased. In other words, the feasible region may shrink or shift in response to the change in b.

Now let's consider the effect on the optimal objective value. Recall that the objective function is given by cx, where c is a vector of coefficients. The optimal objective value is the minimum (or maximum) value of cx over all solutions in the feasible region. If we increase one component of b, then the optimal objective value may or may not change, depending on the specifics of the problem.

To see why, let's think about what happens to the feasible region. As we noted above, the feasible region may shrink or shift in response to the change in b. If the optimal solution was previously at the boundary of the feasible region, then it may no longer be feasible, and the optimal objective value will increase. On the other hand, if the optimal solution was previously in the interior of the feasible region, then it may still be feasible, and the optimal objective value will remain the same.

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Answer:

Step-by-step explanation:

y = -3

Answer:

Id say D but im noot 100% positive so im sorry if its wrong

Step-by-step explanation:

The graph that represents the solution to the linear inequality −3x − 3y ≥ 6 is given as follows:

The graph shows a solid line, which passes through a point (-2,0) and a point (0,-2), with shading below the line.

The graph is presented at the end of the answer.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

The inequality for this problem is given as follows:

−3x − 3y ≥ 6

In slope-intercept format, we have that:

3y ≤ -3x + 6

y ≤ -x - 2.

Hence the intercepts are:

Due to the equal sign, the graph is a solid line, and the shading is below the line, as the inequality is the amounts lower than the line.

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Answer:

First part representing requirements for the length x>=5 ft

Second part yes

Step-by-step explanation:

Well, the formula for finding the area of a rectangle is l x w. In the question, it states that the pen must be 4 ft wide and to fit his requirements of the pen being at the minimum 20 ft^2 we have this inequality 4x>=20 which we must solve and we get x>=5 which means that this represents all of the possible lengths for the play space. For the second part, we know that to fufill Judah's requirements for square ft., our length must be greater than or equal to 5. Last time I was doing math, I'm pretty sure 5 1/2>5 which thus can be accepted as a length value, still meeting the requirements of at least 20ft^2 space for the play space.

These two equations form a system that can be solved to find the values of x and y, representing the number of children and adults, respectively, who played on that day.

The correct system of equations to model this scenario is:

x + y = 414 (Equation 1)

9x + 12y = 3780 (Equation 2)

In this system, x represents the number of children and y represents the number of adults who played that day.

Equation 1 represents the total number of customers, which is 414. It states that the sum of the number of children (x) and the number of adults (y) is equal to 414.

Equation 2 represents the total cost of the games played. Since the cost for a child's game is $9 and the cost for an adult's game is $12, we multiply the number of children (x) by $9 and the number of adults (y) by $12. The equation states that the total cost, which is $3780, is equal to the sum of these individual costs.

Together, these two equations form a system that can be solved to find the values of x and y, representing the number of children and adults, respectively, who played on that day.

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