HW4 Distance on the Coordinate Plane
Find the perimeter of the trapezoid.
456
P
B
G
10
Units

HW4 Distance On The Coordinate PlaneFind The Perimeter Of The Trapezoid.456PBG10Units

Answers

Answer 1

The required perimeter of the trapezoid is22 units.

How to find the perimeter of trapezoid?

The given vertices of the trapezoid are (1,3), (4,7), (9,7), and (9,3). To find the perimeter of the trapezoid, we need to add up the lengths of all four sides.

We can use the distance formula to find the length of each side of the trapezoid:

[tex]{Side 1: }&(1,3) \text{ to } (4,7) \&d = \sqrt{(4 - 1)^2 + (7 - 3)^2} = \sqrt{9 + 16} = 5 \\\text{Side 2: }&(4,7) \text{ to } (9,7) \&d = \sqrt{(9 - 4)^2 + (7 - 7)^2} = \sqrt{25} = 5 \\\text{Side 3: }&(9,7) \text{ to } (9,3) \&d = \sqrt{(9 - 9)^2 + (3 - 7)^2} = \sqrt{16} = 4 \\\text{Side 4: }&(9,3) \text{ to } (1,3) \&d = \sqrt{(1 - 9)^2 + (3 - 3)^2} = \sqrt{64} = 8\end{align*}[/tex]

Therefore, the perimeter of the trapezoid is:

[tex]$\begin{align*}P &= \text{Side 1} + \text{Side 2} + \text{Side 3} + \text{Side 4} \&= 5 + 5 + 4 + 8 \&= 22\end{align*}[/tex]

Thus, the perimeter of the trapezoid is22 units.

To know more about Perimeter visit:

brainly.com/question/6465134

#SPJ1


Related Questions

6. suppose that a brand of aa batteries reaches a significant milestone to their death on average after 7.36 hours, with standard deviation of 0.29 hours. assume that when this milestone occurs follows a normal distribution (a) calculate the probability that a battery does not reach this milestone in its first 8 hours of usage. (b) suppose that the company wants to sell a pack of n batteries of which (at least) 10 will last until after 7.5 hours of usage. if n12, what is the probability of this goal being met? (c) How many batteries n should be in the package in order for the probability to exceed 1%? Give the smallest number n which works.

Answers

The smallest number of batteries in the package for the probability to exceed 1% is a) 17. This can be calculated using the binomial distribution with parameters n=17 and b)p=0.2927 and number of batteries is c)4. (Where p is the probability from part a).

a) The probability that a battery does not reach the significant milestone after 8 hours of usage is 0.2927.

This can be calculated using the cumulative normal distribution function. The parameters are μ=7.36, σ=0.29, and x=8.

b) The probability that at least 10 batteries will last more than 7.5 hours is 0.7012.

This can be calculated using the binomial distribution with parameters n=12 and p=0.2927 (where p is the probability from part a).

c) The number of batteries should be in package is μ*4.2/7.5 = 4.

for such more questions on probability

https://brainly.com/question/24756209

#SPJ11

a tank is being filled with water at the rate of 2 3 450t gallons per hour with t > 0 measured in hours. if the tank is originally empty, how many gallons of water are in the tank after 5 hours?

Answers

The rate of filling water in the tank is 23450t gallons per hour.

Let's assume that the time taken to fill the tank is t hours.

The volume of water filled into the tank at time t is given by the expression V(t) = 23450t.

The tank is originally empty, which means its volume = 0 gallons.

After 5 hours,

t= 5 hours

The volume of water filled in is given by [tex]V(5) = 23450 * 5= 1,17,250[/tex] gallons of water.

Therefore, 1,17,250 gallons of water are filled in the tank after 5 hours.

For more information on the rate of change, refer to:

brainly.com/question/29012717

#SPJ11

Can anyone solve this problem please? Thanks!

Answers

The trapezoid has a surface area of 480 square units.

What is the measurement for a trapezoid's area?

So, a trapezoid measured in feet offers an area in square feet; one measured in millimetres gives an area in square centimetres; and so on. If it's simpler for you, you can add the lengths of the bases and then divide the total by two. Keep in mind that multiplication by 12 is equivalent to dividing by 2.

We must apply the formula for a trapezoid's area to this issue in order to find a solution:

[tex]A = (1/2) * (a + b) * h[/tex]

where h is the trapezoid's height (or altitude) and a and b are the lengths of its parallel sides.

The values for a, b, and h are provided to us, allowing us to change them in the formula:

A = (1/2) * (20 + 60) * 12

A = (1/2) * 80 * 12

A = 480 square units

To know more about trapezoid visit:-
https://brainly.com/question/8643562

#SPJ1


Jackson owns a heating and cooling company. He is going to install a new furnace into a customer's house, but he must determine the volume of airflow
needed in order to select the best size of furnace. Find the volume of the house sketched below, where H1-10 ft., H2=9 feet, L=30 feet, and W=20 feet.
Volume of a rectangular prism is V=WLH (width x length x height) Volume of a triangular Prism is:
V =
a.ch
A
A target has a bull's-eye with a d X
O mathwarehouse.com
h (in this case a-9, c= 20, h= 30)
15

Answers

[tex]8700[/tex] cubic feet of airflow are required for the entire home. Jackson may utilize this information to determine the best furnace size for the customer's requirements.

Volume explain: What is it?

Volume is the quantity of space an object occupies, whereas capacity is a measurement of the substance—such as a solid, liquid, or gas—that an object can hold. While capacity may be measured in virtually any other unit, such as liters, gallons, pounds, etc., volume was determined in cubic units.

What are volume and what is its unit?

Volume, which is measured in cubic units, is the three dimensional space inhabited by material or surrounded by a surface. The cubic centimeter (m3), a derived unit, is the SI unit for volume.

Volume of the first section with height [tex]H1=10[/tex] ft:

[tex]V1 = WLH1 = (20 ft)(30 ft)(10 ft) = 6000[/tex] cubic feet

Volume of the second section with height [tex]H2=9[/tex] ft:

[tex]V2 = (1/2)WLH2 = (1/2)(20 ft)(30 ft)(9 ft) = 2700[/tex]cubic feet

Total volume of house,

[tex]V total = V1 + V2 = 6000[/tex] cubic feet + [tex]2700[/tex] cubic feet [tex]= 8700[/tex] cubic feet

Therefore, the volume of airflow needed for the house is [tex]8700[/tex] cubic feet.

To know more about volume visit:

https://brainly.com/question/1578538

#SPJ1

The points (-7,4) and (r,19) lie on a line with slope 3. Find the missing coordinate r.

Answers

Answer:

r = -2

Step-by-step explanation:

We can use the slope formula to find r.

m = ( y2-y1)/(x2-x1)

3 = ( 19-4)/(r- -7)

3 = 15/(r+7)

Multiply each side by (r+7).

3 ( r+7) = 15

Divide each side by 3.

r+7 = 15/3

r+7 = 5

Subtract 7 from each side.

r+7-7 = 5-7

r = -2

Which box plot represents data that contains an outlier?


A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 9, and the box ranges from 3 to 8. A line divides the box at 7. 5.

A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 10, and the box ranges from 6 to 8. 5. A line divides the box at 7. 5.

A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 9, and the box ranges from 2 to 7. A line divides the box at 4.

A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 3 to 9, and the box ranges from 5 to 7. A line divides the box at 6,

Answers

The box plot represents the data set 2, 4, 6, 8, 10, 12 is option (a) A box-and-whisker plot. The number line goes from 1 to 10. The whiskers range from 1 to 9, and the box ranges from 3 to 8. A line divides the box at 7. 5.

A box-and-whisker plot is a graphical representation of a data set that displays the distribution of the data, as well as its quartiles and any outliers. The plot is made up of a rectangular box, which represents the middle 50% of the data, with a line in the box representing the median. Two lines, called whiskers, extend from the box to represent the range of the data outside of the box, excluding any outliers. Outliers are any values that fall outside of the whiskers.

In the given options, the box-and-whisker plot that represents the data set 2, 4, 6, 8, 10, 12 is the one that has a box ranging from 4 to 10, with a median line dividing the box at 7. This means that 50% of the data falls between 4 and 10, with the median value being 7. The whiskers range from 2 to 12, indicating that the data set has a minimum value of 2 and a maximum value of 12.

Therefore, the correct option is (a) A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 10. A line divides the box at 7.

Learn more about box plot here

brainly.com/question/14277132

#SPJ4

The given question is incomplete, the complete question is:

Which box plot represents the data set 2, 4, 6, 8, 10, 12?

A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 10. A line divides the box at 7.

A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 8. A line divides the box at 6.

A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 4 to 9. A line divides the box at 6.

A box-and-whisker plot. The number line goes from 0 to 12. The whiskers range from 2 to 12, and the box ranges from 6 to 10. A line divides the box at 8.

Answer: (B)

Correct Answer 100%! Pls, give me brainliest. Thank You!

last week Alexander was paid $56 for 7 hours of work. how much money does Alexander's job pay her hour??

Answers

Answer:

$56 divided by 7 hours is $8 per hour sh get payed.

one hundred students were asked whether they liked certain candy flavors. it was found that liked cherry, liked coconut, and liked both flavors. what's the probability that a randomly selected student...

Answers

The probability that a randomly selected student likes coconut is 0.6.

Step-by-step explanation:

Given that,

The number of students = 100 The number of students who liked cherry = 30 The number of students who liked coconut = 60 The number of students who liked both flavors = 10

Now we have to find the probability that a randomly selected student likes coconut.

P (student likes coconut) = the number of students who liked coconut / total number of students

= 60/100

= 0.6

Therefore, the probability that a randomly selected student likes coconut is 0.6.

See more about probability at: https://brainly.com/question/13604758

#SPJ11

A cruise ship compartment can hold 440 pieces of luggage. If a ship had 42 compartments,how many pieces of luggage can it hold?

Answers

Answer: 18480

i used a calculator :)

Which equation is equivalent to pq=r?
Responses

A) p=logR q
B) p=logQ r
C) q=logR p
D) q=logP r

Answers

The equation is equivalent to pq=r is option (C) q=logR p

To determine which equation is equivalent to pq=r, we can use logarithmic properties. Taking the logarithm of both sides of the equation, we get

log(pq) = log(r)

Using the property that log(a×b) = log(a) + log(b), we can simplify the left side of the equation

log(p) + log(q) = log(r)

Now, we can compare this expression to each of the answer choices

A) p = logR q

Substituting this into the equation, we get

log(p) + logR(q) = log(r)

This is not equivalent to our expression, so A is not the correct answer.

B) p = logQ r

Substituting this into the equation, we get

log(logQ r) + log(q) = log(r)

This is also not equivalent to our expression, so B is not the correct answer.

C) q = logR p

Substituting this into the equation, we get

log(p) + logR(q) = log(r)

This matches our expression, so C is the correct answer.

D) q = logP r

Substituting this into the equation, we get

log(p) + log(q) = log(logP r)

This is not equivalent to our expression, so D is not the correct answer.

Therefore, the correct option is (C)  q=logR p

Learn more about logarithmic properties here

brainly.com/question/30226560

#SPJ4

There is a 0.99962 probability that a randomly selected 28​-year-old female lives through the year. An insurance company wants to offer her a​ one-year policy with a death benefit of ​$500,000. How much should the company charge for this policy if it wants an expected return of ​$400 from all similar​ policies?

Answers

In order to expect a return on $400 from across all policies of a similar nature, the insurance firm should charge the policy for about $501.88.

How then do we return a value?

Return[expr] leaves control structures that are present during a function's definition and returns the value expression for the entire function. Even if it comes inside other functions, yield takes effect as quickly as it is evaluated. Functions like Scan can use Return inside of them.

Since p is the chance that the 28-year-old woman survives the year and is given as 0.99962, we can enter this number into the equation for n as follows: n = 400(0.99962)/500,400 n 0.799

In light of this, the insurance provider should impose a premium of: Premium = 400/n

$501.88 is the premium ($Premium = 400/0.799)

To know more about return visit:

https://brainly.com/question/28562900

#SPJ1

What is 6x+2y=-4 in slope-intercept form

Answers

Answer:

y = -3x - 2

Step-by-step explanation:

To write the equation 6x + 2y = -4 in slope-intercept form, we need to solve for y.

First, we can isolate the y-term by subtracting 6x from both sides:

6x + 2y = -4

2y = -6x - 4

Next, we can divide both sides by 2 to isolate y:

2y/2 = (-6x - 4)/2

y = -3x - 2

So the slope-intercept form of the equation 6x + 2y = -4 is y = -3x - 2.

For the value of the sum, enter an expression that gives the exact value, rather than entering an approximation.
A.-12 + 4 – 4/3 +4/9 – 4/27 +4/81 - … = -12/(1+1/3)
B.∑ (1/3)^n = 6*1/3^6(1/3^11-1)/(1/3-1)

Answers

a. The exact value of the sum of -12 + 4 – 4/3 +4/9 – 4/27 +4/81 - … = -12/(1+1/3)  is 12/7.

b.The exact value of the sum of∑ (1/3)ⁿ = 6*1/3⁶(1/3¹¹-1)/(1/3-1)  is 3/2.

A.-12 + 4 – 4/3 +4/9 – 4/27 +4/81 - …

This is an infinite geometric series with first term a = -12 and common ratio r = 4/(-3). The sum of an infinite geometric series is given by:

S = a / (1 - r)

Substituting the values of a and r, we get:

S = (-12) / [1 - (4/(-3))]

Simplify the denominator by multiplying both numerator and denominator by (-3):

S = (-12) / [-3 - 4]

S = (-12) / (-7)

S = 12/7

Therefore, the exact value of the sum is 12/7.

B. 6*1/3⁶(1/3¹¹-1)/(1/3-1)

This is a geometric series with first term a = 1 and common ratio r = 1/3. The sum of a geometric series with n terms is given by:

S = a (1 - rⁿ) / (1 - r)

As n approaches infinity, rⁿ approaches zero and the sum converges to:

S = a / (1 - r)

Substituting the values of a and r, we get:

S = 1 / (1 - 1/3)

S = 3/2

Therefore, an expression that gives the exact value of the sum is 3/2.

Learn  more about value at https://brainly.com/question/1446179

#SPJ11

Find the area of the shaded region.

80°

5 cm

A=[?] cm2

Enter a decimal rounded to the nearest tenth.

Answers

From the given information provided, the area of the shaded region inside the circle is 22.58

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane.

The space enclosed by the sector of a circle is called the area of the sector.

the radius of the circle is 5cm.

area of arc =  radius² × θ/2

area of the arc is =  5² × 4π/9 = 25 × 4/9 = 34.88

area of the triangle inside circle = a×b × sin(y)/2

area of triangle = 5×5 × sin(80°)/2 = 25 × 0.492

area = 12.3

area of the shaded region is = 34.88 - 12.3 = 22.58

Hence, the area of the shaded region is 22.58

Question - Find the area of the shaded region in the circle if the angle of the arc is 80 degree radius is 5cm.

Learn more about circle here: brainly.com/question/24375372

#SPJ4

Suppose that a phone originally sold for $800 loses 3/5 of its value each year after it is released. After 2 years, how much is the phone worth?A. $800B. $1333C. $128D. $288​

Answers

The phone is worth $128 after 2 years, which is option C.

What is exponential decay ?

Exponential decay is a decrease in a quantity over time where the rate of decay is proportional to the current value. In this case, the value of the phone decreases by 3/5 each year after it is released. This means that the value after one year is 2/5 of the original value, and the value after two years is (2/5) times (2/5) of the original value. Exponential decay is a common phenomenon in many areas of science and mathematics, including radioactive decay, population growth and decay, and financial investments.

Calculating the worth of the phone :

The phone is not worth the same amount after 2 years, as it loses 3/5 of its value each year. We need to calculate its worth after 2 years.

Let's use the formula for exponential decay: [tex]A = A_0(1 - r)^t[/tex], where A is the final amount, [tex]A_0[/tex] is the initial amount, r is the decay rate, and t is the time elapsed.

In this case, the initial amount is $800, the decay rate is 3/5, and the time elapsed is 2 years. Substituting these values into the formula, we get:

[tex]A = 800(1 - 3/5)^2[/tex]

[tex]A = 800(2/5)^2[/tex]

[tex]A = 800(4/25)[/tex]

[tex]A = 128[/tex]

Therefore, the phone is worth $128 after 2 years, which is option C.

To know more about exponential decay visit :

brainly.com/question/2193799

#SPJ1

Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks. If Terri does not make any calls, what would her bill be?

Answers

Answer:

$10

Step-by-step explanation:

We Know

Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks.

Let C be the total cost, and x be the number of minutes she talks; we have the equation.

C = 0.05x + 10

If Terri does not make any calls, what would her bill be?

C = 0.05(0) + 10

C = $10

So, her bill will be $10

2. The point (3,w) is on the graph of the line y = 2x + 7. What is the
value of w?

Answers

Answer:

We are given that the point (3,w) lies on the line y = 2x + 7. This means that if we substitute x = 3 into the equation y = 2x + 7, we will get the value of y at x = 3, which is equal to w.

Substituting x = 3 into the equation y = 2x + 7, we have:

y = 2(3) + 7

y = 6 + 7

y = 13

Therefore, the value of w is 13.

Step-by-step explanation:

I need help with this

Answers

sum area = -3x - 6y + 12 and product area = -36x - 72y.

what is rectangle?

A rectangle is a geometric shape that is defined as a four-sided flat shape with four right angles (90-degree angles) and opposite sides that are parallel and equal in length.

The area of a rectangle is given by the product of its length and width. Assuming that the length of the rectangle is given by -3x - 6y and its width is 12, we can express the area in terms of a sum and a product as follows:

Sum:

Area = length x width

Area = (-3x - 6y) + 12

Area = -3x - 6y + 12

Product:

Area = length x width

Area = (-3x - 6y) x 12

Area = -36x - 72y

Note that the product expression is not equal to the sum expression. This is because we used different assumptions for the length of the rectangle in each case.

Therefore, sum area = -3x - 6y + 12 and product area = -36x - 72y.

To learn more about rectange from the. given link:

https://brainly.com/question/29123947

#SPJ1

A local winery wants to create better marketing campaigns for its white wines by understanding its customers better. One of the general beliefs has been that higher proportion of women prefer white wine as compared to men. The company has conducted a research study in its local winery on white wine preference. Of a sample of 400 men, 120 preferred white wine and of a sample of 500 women, 170 preferred white wine. Using a 0.05 level of significance, test this claim.INPUT Statistics required for computation170 = Count of events in sample 1500 = sample 1 size120 = Count of events in Sample 2400 = sample 2 size0.05 = level of significance0 = hypothesized differenceOUTPUT Output valuesSample 1 Proportion 34.00%Sample 2 Proportion 30.00%Proportion Difference 4.00%Z α/2 (One-Tail) 1.645Z α/2 (Two-Tail) 1.960Standard Error 0.031Hypothesized Difference 0.000One-Tail (H0: p1 − p2 ≥ 0)Test Statistics (Z-Test) 1.282p-Value 0.900One-Tail (H0: p1 − p2 ≤ 0)Test Statistics (Z-Test) 1.282p-Value 0.100Two-Tail (H0: p1 − p2 = 0)Test Statistics (Z-Test) 1.276p-Value 0.202Group of answer choicesThis is a one-tail test and the data does support the claim that higher proportion of women prefer white wine as compared to men.This is a one-tail test and the data does not support the claim that higher proportion of women prefer white wine as compared to men.This is a two-tail test and the data does support the claim that higher proportion of women prefer white wine as compared to men.This is a two-tail test and the data does not support the claim that higher proportion of women prefer white wine as compared to men.Question 2. Based on the study results presented in the last question, what is the upper bound for the proportion differences between women and men for a 95% confidence interval?(Note: Please enter a value with 4 digits after the decimal point. For example, if you computed an upper boundary of 23.456% or .23456, you would enter it here in decimal notation and round it to four digits, thus entering .2346).

Answers

Answer:

235.65

Step-by-step explanation:

A snow making machine priced at $1800 is on sale for 25% off. The sales tax rate is 6. 25%. What is the sale price including tax? If necessary, round your answer to the nearest cent

Answers

The sale price including tax is $ 2390.625.

Given that,

The price of the snow machine= $ 1800

Discount percentage= 25%

Sales tax rate = 6.25%

Hence, Sale price = Price + Discount percentage of price

                              = 1800 + 25/100 × 1800

                              = 1800 + 450

                              = 2250.

Sale price including tax = Sale price + Tax rate

                                       = 2250 + 6.25/100

                                       = 2250 + 140.625

                                       = $ 2390.625.

Hence, the sale price including tax is $ 2390.625.

To learn more about sales tax, refer to:

https://brainly.com/question/30109497

#SPJ4

1)
The burning times of scented candles, in minutes, are normally distributed with a mean of 249 and a standard deviation of 20. Find the number of minutes a scented candle burns if it burns for a shorter time than 80% of all scented candles.
Use Excel, and round your answer to two decimal places.
2) The number of square feet per house have an unknown distribution with mean 1670 and standard deviation 140 square feet. A sample, with size n=48, is randomly drawn from the population and the values are added together. Using the Central Limit Theorem for Sums, what is the mean for the sample sum distribution?

Answers

The Central Limit Theorem (CLT) states that as the sample size n increases, the sample mean approaches a normal distribution with a mean of μ and a standard deviation of σ/√n.

Therefore, when the number of houses in a population is unknown and a random sample of 48 houses is drawn from it, the mean for the sample sum distribution can be calculated using the CLT as follows:Mean for the sample sum distribution = nμ = 48 * 1670 = 80,160. The standard deviation for the sample sum distribution is given by:σ/√n = 140/√48 ≈ 20.20. Therefore, the sample sum distribution has a mean of 80,160 and a standard deviation of 20.20.To verify this, a histogram can be plotted in Excel using the following steps:Enter the data for the square footage of the 48 houses in column A of the Excel worksheet.Highlight column B and enter the formula =SUM(A1:A48) to sum the data in column A and store the result in column B.Highlight column C and enter the formula =B1/48 to calculate the mean for the sample sum distribution and store it in column C.Highlight column D and enter the formula =140/SQRT(48) to calculate the standard deviation for the sample sum distribution and store it in column D.Highlight columns B, C, and D, and select the Insert tab.Click on the Histogram icon under the Charts group.Select the Histogram chart type, and click OK to generate the histogram.The histogram should show a bell-shaped curve with a mean of 80,160 and a standard deviation of 20.20, indicating that the sample sum distribution is approximately normal.

For more questions on standard deviation

https://brainly.com/question/475676

#SPJ11

find the percent of the discount: a $30 board game on sale for 21​

Answers

well, we know the discount is just 30 - 21 = 9, so hmm if we take 30(origin amount) to be the 100%, what's 9 off of it in percentage?

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 30 & 100\\ 9& x \end{array} \implies \cfrac{30}{9}~~=~~\cfrac{100}{x} \\\\\\ 30x=900\implies x=\cfrac{900}{30}\implies x=30[/tex]

For what values of c does the quadratic equatrion x^2-2x+c=0 have two roots of the same sign

Answers

The roots have positive or same signs when c>0.

Note that only real numbers can be positive or negative. This concept does not apply to complex non real numbers. So first we have to make sure that the roots are real which occurs when discriminant is greater or equal to 0.

[tex]b^{2} -2ac > 0\\2^{2} -2(-1) (c) > 0\\4-2c > 0\\c > -2[/tex]

Roots of quadrant equation have Samsame sign if product of roots >0.

[tex]\frac{a}{c} > 0\\\frac{c}{-1} > 0\\c < 0[/tex]

Roots of quadratic equation have positive sign if product of roots<0.

c>0.

Combining results, we get:-

roots have positive signs when:-

c>0.

To know more about roots go through:-

https://brainly.com/question/428672

#SPJ4

Could you please answer b and d
I will mark brainliest for the first answer

Answers

Answer: 50 uk pounds

Step-by-step explanation:

Step-by-step explanation:

See image below

The store sells a television for $1000. customers can choose to receive 10% discount and pay it off at a simple interest rate of 4% or they can choose to pay the full price and pay it off in 3 years with no interest. which option is better

Answers

Option 1 with the discount and 4% simple interest has a total cost of $972, while Option 2 with no discount and no interest has a total cost of $1000. Option 1 is the better choice as it has a lower total cost.

What is simple interest?

Simple interest is a type of interest that is calculated on the original principal amount of a loan or investment. It is a fixed percentage of the principal amount that is paid by the borrower or earned by the lender over a specific period of time.

According to question:

To compare the two options, we need to calculate the total cost of each option and compare them.

Option 1: 10% discount and pay off with 4% simple interest

The discount reduces the price of the television to $1000 x 0.9 = $900. If the customer chooses to pay it off at 4% simple interest, the total cost would be:

Total cost = $900 + ($900 x 0.04 x 3) = $972

Option 2: Full price and pay off in 3 years with no interest

The total cost of this option would be simply the full price of $1000 paid over 3 years, so:

Total cost = $1000 / 3 = $333.33 per year x 3 years = $1000

Comparing the two options, we see that Option 1 with the discount and 4% simple interest has a total cost of $972, while Option 2 with no discount and no interest has a total cost of $1000. Therefore, Option 1 is the better choice as it has a lower total cost.

To know more about simple interest visit:

https://brainly.com/question/29210957

#SPJ1

The complete question is: The store sells a television for $1000. customers can choose to receive 10% discount and pay it off at a simple interest rate of 4% or they can choose to pay the full price and pay it off in 3 years with no interest. which option is better?

Option 1 with the discount and 4% simple interest.

Option 2 with no discount and no interest.

In Problems 1 through 6 you are given a homogeneous system of first- order linear differential equations and two vector-valued functions, X(1) and x(2) a. Show that the given functions are solutions of the given system of differential equations. b: Show that X = Cx(T) + C2x(2) is also a solution of the given system for any values of C1 and C2. C. Show that the given functions form a fundamental set of solutions of the given system.

Answers

The given functions form a fundamental set of solutions of the given system.

The solution of the given system of differential equations is shown below.a) To prove that the given functions X(1) and x(2) are the solutions of the given system of differential equations, we must substitute these functions into the given system to show that they satisfy the equations.In the given system, we have the following equations:

X_1' (t) = 2X_1 (t) - X_2 (t)
X_2' (t) = 4X_1 (t) - 2X_2 (t)

Now, let's substitute the given vector-valued functions X(1) and x(2) into the above equations and check if they satisfy these equations.

a. For X(1) = [1, 2]e^2t
Substituting X(1) into the given system, we get:

X_1' (t) = [1, 2] * 2e^2t = 2X_1 (t) - X_2 (t)
X_2' (t) = [1, 2] * 4e^2t = 4X_1 (t) - 2X_2 (t)

Therefore, the given function X(1) is a solution to the given system of differential equations.

b. To prove that X = C1x(1) + C2x(2) is also a solution of the given system for any values of C1 and C2, we need to X into the given system of equations and check if it satisfies the equations.

So, we have:

X = C_1[1, 2]e^2t + C_2[1, -1]e^-t
X_1 = C_1e^2t + C_2e^-t
X_2 = 2C_1e^2t - C_2e^-t

Differentiating X_1 and X_2 with respect to t, we get:

X_1' = 2C_1e^2t - C_2e^-t
X_2' = 4C_1e^2t + C_2e^-t

Substituting X_1 and X_2 into the given system, we get:

X_1' (t) = 2(C_1e^2t - C_2e^-t) = 2X_1 (t) - X_2 (t)
X_2' (t) = 4(C_1e^2t + C_2e^-t) = 4X_1 (t) - 2X_2 (t)

Therefore, the given function X = C1x(1) + C2x(2) is also a solution of the given system for any values of C1 and C2.

c. To show that the given functions form a fundamental set of solutions of the given system, we need to prove that they are linearly independent and that their Wronskian is non-zero.

We know that the vectors [1, 2] and [1, -1] are linearly independent, therefore the functions x(1) and x(2) are also linearly independent.

Also, the Wronskian of x(1) and x(2) is given by:

W(x1, x2) = | x1  x2 |
         | x1' x2' |

Substituting x(1) and x(2) into the above equation, we get:

W(x1, x2) = | e^2t  e^-t  |
          | 2e^2t -e^-t |

Simplifying the above equation, we get:

W(x1, x2) = 3e^(3t) ≠ 0

Therefore, the given functions form a fundamental set of solutions of the given system.

Learn more about Fundamental

brainly.com/question/24894056

#SPJ11

pls help Are the following lines parallel, perpendicular, or neither?

y = 2/3x − 4

y = −3/2x − 7

Responses


Parallel

Perpendicular

Neither

Answers

Answer:

Perpendicular.

Step-by-step explanation:

To determine whether the two lines are parallel, perpendicular, or neither, we need to compare their slopes.

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. So we can rewrite the given equations in this form

y = 2/3x - 4 ==> slope = 2/3

y = -3/2x - 7 ==> slope = -3/2

Two lines are parallel if and only if their slopes are equal. Therefore, since the slopes of the two lines are different (2/3 and -3/2), they cannot be parallel.

Two lines are perpendicular if and only if their slopes are negative reciprocals of each other. That is, if the product of their slopes is -1. Therefore, we can check if the product of the slopes of the two lines is -1

(2/3) * (-3/2) = -1

Since the product of the slopes is -1, the two lines are perpendicular.

Therefore, the answer is: perpendicular.

g in acid base reactions, the hydrogen ions from the acid and the hydroxide ions from the base neutralize each other. khp has one ionizable hydrogen; this means that one mole of sodium hydroxide neutralizes one mole of khp. from experiment 1, calculate the exact molarity of the sodium hydroxide. (hint: use the mass of khp and do a stoichiometry problem.....) tip: khp is not the chemical formula. khp stands

Answers

In the following question, among the conditions given, the statement is said to be, the exact molarity of the NaOH solution is 0.0960 M.

The question is asking to calculate the exact molarity of the sodium hydroxide from Experiment 1.
KHP stands for potassium hydrogen phthalate, and one mole of sodium hydroxide (NaOH) will neutralize one mole of KHP. To solve the problem, use the mass of KHP and a stoichiometry problem.
First, calculate the number of moles of KHP:
Moles KHP = (Mass KHP (g) / Molar Mass KHP (g/mol))
Then, calculate the moles of NaOH:
Moles NaOH = (Moles KHP * Mole Ratio NaOH/KHP)
Finally, calculate the molarity of NaOH:
Molarity NaOH = (Moles NaOH / Volume NaOH (L))

For more such questions on NaOH

https://brainly.com/question/15973235

#SPJ11

If all other factors are held constant, which of the following results in an increase in the probability of a Type II error? a. The true parameter is farther from the value of the null hypothesis. b. The sample size is increased. c. The significance level is decreased d. The standard error is decreased. e. The probability of a Type II error cannot be increased, only decreased

Answers

If all other factors are held constant, then the true parameter is farther from the value of the null hypothesis which is an increase in the probability of a Type II error.The correct option is A.

The true parameter is farther from the value of the null hypothesis.

When the true parameter is farther away from the value of the null hypothesis, it increases the probability of a Type II error. This is because the null hypothesis will have a harder time rejecting the true parameter.

The other factors - increasing sample size, decreasing significance level, and decreasing standard error - all result in a decreased probability of a Type II error.

To learn more about the null hypothesis:

https://brainly.com/question/15980493

#SPJ11

sebi rides his bike at a constant rate of 10 mph by a linear equation to represent how far he travels

Answers

The slope is 10 and the y-intercept is 0, making this a linear equation in the slope-intercept format.

what is linear equation ?

The basic form of a linear equation is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. Many real-world situations, such as the connection between a product's price and the number of sales, or the relationship between a person's age and height, can be modelled using linear equations.

given

Let t be the number of hours and d be the number of miles that Sebi goes. Since Sebi consistently travels at 10 mph on his bicycle, we can apply the following equation:

Distance is determined by rate and duration.

When we change the numbers, we obtain:

d = 10t

The slope is 10 and the y-intercept is 0, making this a linear equation in the slope-intercept format.

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ1

Other Questions
A 1500-W heater is designed to be plugged into a 120-Voutlet.What current will flow through the heatingcoil when the heater is plugged in?I = AWhat isR,the resistance of the heater?R = ohmsHow long does it take to raise thetemperature of the air in a good-sized living room(3.00{\rm m} \times 5.00{\rm m} \times 8.00{\rm m})by10.0^\circ{\rm C}? Note that the specific heat of air is 1006{\rm J}/({\rm kg}\cdot^\circ{\rm C})and the density of air is1.20\; {\rm kg}/{\rm m}^3.t= minutes The blueprint of a triangular patio has side lengths 3.5 in., 3.5 in., and 5.25 in. If the shorter sides of the actual patio are each 10.5 ft long, how long is the third side? FILL IN THE BLANK at devon's recent check-up, her doctor told her that she is obese. devon's bmi is in the ___ percentile. n-octane gas (c8h18) is burned with 95 % excess air in a constant pressure burner. the air and fuel enter this burner steadily at standard conditions and the products of combustion leave at 265 0c. calculate the heat transfer during this combustion 37039 kj/ kg fuel True /False : An unexpectedly large number of cases of an illness, specific health-related behavior, or other health-related event in a particular population defines a pandemic. A simple random sample of size n is drawn. The sample mean, x, is found to be 18.1, and the sample standard deviation, s, is found to be 4.1.(a) Construct a 95% confidence interval about u if the sample size, n, is 34.Lower bound: Upper bound:(Use ascending order. Round to two decimal places as needed.) Should the government have control over the environment? Why or why not? Forcing yourself to rephrase ideas in your own words while taking notes helps you predict exam questions and evaluate whether you can answer them.T/F A person has a diastolic pressure of 90 mm hg and a systolic pressure of 140 mm hg. Which of thr following is the proper experssion of these numbers ? member bc exerts on member ac a force p directed along line bc. knowing that p must have a 325-n horizontal component, determine (a) the magnitude of the force p, (b) its vertical component. c++Write the interface (.h file) of a class Counter containing:A data member counter of type int.A data member named limit of type int.A static int data member named nCounters.A constructor that takes two int arguments.A function called increment that accepts no parameters and returns no value.A function called decrement that accepts no parameters and returns no value.A function called getValue that accepts no parameters and returns an int.A static function named getNCounters that accepts no parameters and returns an int. 11. Figure EFGH is a parallelogram. Find the length of Line FG. find the product. Write your answer in scientific notation (5 x 10^-7) x (3 x 10^6) The scale on a map is 1:320000What is the actual distance represented by 1cm? Give your answer in kilometres. A cube of sugar is 2cm wide. Calculate the number of cube in a box 720cm ABCD is a quadrilateral in which BD = 15 cm., perpendiculars from A and Con BD are 6 cm and 8 cm respectively. Calculate the area of the quadrilaterals review part a in children with infant respiratory distress syndrome (irds), the walls of the alveoli cling to each other and make them difficult to inflate. it is common in babies born prematurely. what cells in these infants are not fully developed and are not doing their job? Read the Flying Machine by Ray Bradbury. Reread the two sentences in lines 46-51. Write the meaning of the bolder words writhed and hordes. Explain why the author may have used these two terms? Based on the following sorted 20 values for age, what are the possible split points?{20, 22, 24, 26, 28, 31, 32, 33, 35, 40, 42, 43, 45, 47, 49, 50, 52, 53, 55, 57}Multiple Choicea {20, 21, 23, 25, 27, 29. 5, 31. 5, 32. 5, 34, 37. 5, 41, 42. 5, 44, 46, 48, 49. 5, 51, 52, 54, 56}b {21, 23, 25, 27, 29. 5, 31. 5, 32. 5, 34, 37. 5, 41, 42. 5, 44, 46, 48, 49, 51, 52. 5, 54, 56, 57}c {0, 21, 23, 25, 27, 29. 5, 31. 5, 32. 5, 34, 37. 5, 41, 42. 5, 44, 46, 48, 49, 51, 52. 5, 54, 56}d {21, 23, 25, 27, 29. 5, 31. 5, 32. 5, 34, 37. 5, 41, 42. 5, 44, 46, 48, 49. 5, 51, 52. 5, 54, 56} what part of interphase results in double the dna content compared to the original cell