The original value of the house when it was purchased was $450,000.
Let us assume the original value of the house was x. This means that the house has increased by 38% from x to become $621,000.
In order to find the original value therefore, you can use the formula:
Original value + (Original value x Increase) = Current price
x + (38% × x) = 621,000
1.38x = 621,000
x = 621,000 / 1.38
= $450,000
In conclusion, the original value was $450,000.
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Final answer:
The original purchase price of the house was $450,000.
Explanation:
To find the original value of the house before it increased in value, we must first understand that the current value represents 138% of the original value, since the house has increased in value by 38%. This is because the original value is 100%, and the increase is 38%, making the total 138%. Therefore, the equation to find the original purchase price (which we can call 'P') is:
P * 138% = $621,000
We can rewrite this as:
P * 1.38 = $621,000
To solve for P, we divide both sides of the equation by 1.38:
P = $621,000 / 1.38
Now, doing the division:
P = $450,000
So, the house was originally purchased for $450,000 before it increased by 38% to its current value of $621,000.
Factor x^2 +11xy+30y^2
Answer:
(x+5y)(x+6y)
Step-by-step explanation:
A bucket contains five green tennis balls, two yellow tennis balls, six red tennis balls, and eight blue tennis balls. Tony removes for tennis balls, without replacement from the bucket shown. What is the probability that Tony removes one yellow, one green ,one blue,and then one more blue tennis ball?
Answer:
The probability that Tony removes one yellow, one green ,one blue,and then one more blue tennis ball is 0.0039.
Step-by-step explanation:
We are given that a bucket contains five green tennis balls, two yellow tennis balls, six red tennis balls, and eight blue tennis balls.
As we know that, Probability of an event = [tex]\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}[/tex]
Number of green tennis balls = 5
Number of yellow tennis balls = 2
Number of red tennis balls = 6
Number of blue tennis balls = 8
Total number of tennis balls = 5 + 2 + 6 + 8 = 21
{Now it should be notes that Tony removes for tennis balls, without replacement from the bucket means that every time the total number of remaining balls available for selecting will be one less}.
Now, Probability that Tony removes one yellow = [tex]\frac{2}{21}[/tex]
Probability that Tony removes one green = [tex]\frac{5}{20}[/tex]
Probability that Tony removes one blue = [tex]\frac{8}{19}[/tex]
Probability that Tony removes one blue again = [tex]\frac{7}{18}[/tex]
SO, final probability is = [tex]\frac{2}{21} \times \frac{5}{20} \times \frac{8}{19} \times \frac{7}{18}[/tex]
= [tex]\frac{2}{513}[/tex]
= 0.0039
An equation was created for the line of best fit from the actual enrollment data. It was used to predict the dance studio enrollment values shown in the table below:
Analyze the data. Determine whether the equation that produced the predicted values represents a good line of best fit.
A. No, the equation is not a good fit because the sum of the residuals is a large number.
B. No, the equation is not a good fit because the residuals are all far from zero.
C. Yes, the equation is a good fit because the residuals are not all far from zero.
D. Yes, the equation is a good fit because the sum of the residuals is a small number.
Answer:
B. No, the equation is not a good fit because the sum of the residuals is far from zero. Should be your answer
Step-by-step explanation:
Have a nice day :)
No, the equation is not a good fit because the sum of the residuals is far from zero.
What is Equation?Two or more expressions with an Equal sign is called as Equation. An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
An equation was created for the line of best fit from the actual enrollment data. which was used to predict the dance studio enrollment values shown in the table.
We need to check whether the equation that produced the predicted values represents a good line of best fit.
No, the equation is not a good fit because the sum of the residuals is far from zero.
A line of best fit is meant to compensate for positive and negative deviation in a matter that balances them. A large residual values' sum shows that they are not balanced.
Hence, No, the equation is not a good fit because the sum of the residuals is far from zero.
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Keith opened an investment account where he is paid 8% annual interest, compounded semi-annually. He wants to have $7,000 in the investment account in 3 years. What is the number of periods for this investment?
Answer:
6 periods
Step-by-step explanation:
The investment is compounded semi-annually which means it is compounded twice in a year. Period of investment is 3 years. So, number of periods compounded is 3 multiplied by 2 that is 6 periods.
Rate would be 8% divided by 2 that is 4%.
Initial investment can be calculated usinf spreadsheet function as =PV(rate,nper, pmt, FV)
Where,
rate is 0.04
nper is 6
pmt is 0
FV is 7,000
So, initial investment is $5,532.20.
It is negative as it is a cash outflow.
Which statement is correct regarding the measurements of the parallelogram?
The base is 6 and the height is 3. so the area is 6(3) - 18 square units.
The base is 8 and the height is 3, so the area is a(3) - 24 square units.
The base is 8 and the height is 4, so the area is 3(4) - 32 square units.
The base is 8 and the height is 6, so the area is a = 48 square units.
Answer:
The first one is correct
Step-by-step explanation:
You can multiply the base and perpendicular height to find the area.
-9-(-4) what is the answer to this equation.
Answer:
-5
Step-by-step explanation:
Answer:
The answer is -5
Step-by-step explanation:
Find the value of 1/3 divided by 1/2
When dividing two fractions, it is important to know to multiply the first fraction by the reciprocal of the second fraction.
Reciprocal means basically a flipped fraction. 2/3 as a reciprocal is 3/2, etc.
1/3 / 1/2= 1/3 x 2/1=2/3
A triangle has a perimeter of 10.2 kilometers. Two of the sides measure 3.4 kilometers and 3.4 kilometers. What is the length of the third side?
Answer:
3.4
Step-by-step explanation:
3.4+3.4= 6.8
10.2-6.8=3.4
Consider the following data set:
7.8, 0.6, 1.9, 5, 5.7, 0.7, 1.6, 5.9
Work out the IQR.
Answer:
Population size:8
Lower quartile (xL): 0.925
Upper quartile (xU): 5.85
Interquartile range (xU-xL): 4.925
Step-by-step explanation:
Answer:
4.65
Step-by-step explanation:
7.8, 0.6, 1.9, 5, 5.7, 0.7, 1.6, 5.9
Sort the data
0.6, 0.7, 1.6, 1.9, 5, 5.7, 5.9, 7.8
Q1: (0.7+1.6)/2
= 1.15
Q3: (5.7+5.9)/2
= 5.8
IQR = 5.8 - 1.15
= 4.65
Mekala has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Mekala's Jumble has 4 44 techno songs, 2 22 country songs, and 3 33 jazz songs on it. Mekala plans to listen to 270 270270 songs.
Answer:Close to 60 country songs but probably not exactly 60 country songs.
Step-by-step explanation:
Mekala player Jumble has 4 techno songs, 2 country songs, and 3 jazz songs on it.
Represent this songs in ratio format
Ratio of techno songs,to country songs,to jazz songs= 4: 2 : 3
Total number of songs is unknowns ,let it be represented by x
total number of songs is therefore 4 x, 2 x, and 3 x.
Total number of songs that Mekala plans to Listen = 2 70
Then , 4 x + 2 x + 3 x= 270
9 x = 270
Dividing both sides by 9, we get
x = 30
So, Number of techno songs = 4 × 30= 120
Number of country songs = 2 × 30= 60
Number of jazz songs = 3 × 30= 90
Answer:
Close to 60 country songs but probably not exactly 60 country songs
Step-by-step explanation:
Mark knows that his yard is 214 times as long as it is wide. Which equation shows the length, in feet, of the fence that goes all the way around the yard if Mark measures the width as w feet?
Answer:
Length in feet is equal to [tex]\frac{2P}{6.5}[/tex], where P is the perimeter
Step-by-step explanation:
Let the width (W) of the yard be "X"
[tex]W = w[/tex]
Then the length(L) of the yard will be
[tex]2\frac{1}{4} * w[/tex]
[tex]L = \frac{9}{4} *w[/tex]
The perimeter of the yard will be equal to the sum of twice the length and width of the yard
Thus,
[tex]P = 2 W + 2L\\[/tex]
Substituting the given values in above equation, we get -
[tex]P = 2 w + 2 (\frac{9}{4})w\\P = 2w + 4.5 w\\P = 6.5w[/tex]
Thus, width in terms of perimeter is equal to
[tex]w = \frac{P}{6.5}[/tex]
Length in feet is equal to [tex]\frac{2P}{6.5}[/tex]
4/3 x 3.14 x 13^3
What is the answer
Answer:
(4/3) x 3.14 x (13^3) = 9198.1066666... (repeating decimal)
Step-by-step explanation:
The result of multiplication is: 4/3 x 3.14 x 13³ =9198.11.
Here, we have,
given that,
4/3 x 3.14 x 13³
now, we have to multiply the terms.
so, we get,
4/3 x 3.14 x 13³
=4/3 x 3.14 x 13 x 13 x 13
=4/3 x 3.14 x 2197
=4/3 x 6898.58
=27594.32 /3
=9198.11
Hence, The result of multiplication is: 4/3 x 3.14 x 13³ =9198.11.
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(x+4y=5
- 1-2x + 5y = 16
Answer:
x,y( 27/13 ,43/13)
Step-by-step explanation:
x=5-4y
•1-2x+5y=16
1-2(5-4y)+5y=16
y=27/13
x=5-4y
x=5-4×27/13
x=-43/13
4x3 + x2 - 8x - 2 by grouping
Solve for Y
Just checking my answer to see if I’m right,
Thx! :D
The restaurant served 220 sandwiches, 120tacos, and 160 salads for lunch. What is the ratio of salads to total number of lunches sold? * 5 points 5 to 11 8 to 25 6 to 8
Answer:
8 to 25
Step-by-step explanation:
The total number of lunches sold i
220+120+160 =500
We want the ratio of salads to total lunches
salads: lunches
160: 500
Divide each side by 20
160/20 : 500/20
8:25
Let x denote the courtship time for a randomly selected female–male pair of mating scorpion flies (time from the beginning of interaction until mating). suppose the mean value of x is 120 min and the standard deviation of x is 110 min (suggested by data in the article
Complete Question:
a) Is it plausible that X is normally distributed?
b) For a random sample of 50 such pairs, what is the (approximate) probability that the sample mean courtship time is between 100 min and 125 min?
Answer:
a) It is plausible that X is normally distributed
b) probability that the sample mean courtship time is between 100 min and 125 min is 0.5269
Step-by-step explanation:
a)X denotes the courtship time for the scorpion flies which indicates that is a real - valued random variable, and since normal distribution is a continuous probability distribution for a real valued random variable, it is plausible that X is normally distributed.
b) Probability that the sample mean courtship time is between 100 min and 125 min
[tex]\mu = 120\\n = 50[/tex]
[tex]P(x_{1} < \bar{X} < x_{2} ) = P(z_{2} < \frac{x_{2}- \mu }{SD} ) - P(z_{1} < \frac{x_{2}- \mu }{SD})[/tex]
[tex]SD = \sqrt{\frac{\sigma^{2} }{n} } \\SD = \sqrt{\frac{110^{2} }{50} } \\SD = 15.56[/tex]
[tex]P(100 < \bar{X} <125 ) = P(z_{2} < \frac{125- 120 }{15.56} ) - P(z_{1} < \frac{100- 120 }{15.56})\\P(100 < \bar{X} <125 ) = P(z_{2} < 0.32 ) - P(z_{1} < -1.29)[/tex]
From the probability distribution table:
[tex]P(z_{2} < 0.32 ) = 0.6255\\ P(z_{1} < -1.29) = 0.0986[/tex]
[tex]P(100 < \bar{X} <125 ) = 0.6255 - 0.0986\\P(100 < \bar{X} <125 ) =0.5269[/tex]
An account earns simple interest. $300 at 4% for 3 years, what is the interest earned
Answer:
$36
Step-by-step explanation:
You are going to want to use the simple interest formula for this. The one below is modified for solving the interest earned.
[tex]I = Prt[/tex]
I = interest amount
P = principal amount
r = interest rate (decimal form)
t = time (years)
First, change 4% into a decimal:
4% -> [tex]\frac{4}{100}[/tex] -> 0.04
Now, plug the values into the equation:
[tex]I=300(0.04)(3)[/tex]
[tex]I=36[/tex]
The interest earned is $36
What is the reasonable estimate of the probability that ragin Cajun score 30 more points in their next football game
Answer:
Step-by-step explanation:
What percent of 300 is 51
Answer:
17
Step-by-step explanation:
300:51*100 =
(300*100):51 =
30000:51 = 588.24
Now we have: 300 is what percent of 51 = 588.24
Question: 300 is what percent of 51?
Percentage solution with steps:
Step 1: We make the assumption that 51 is 100% since it is our output value.
Step 2: We next represent the value we seek with $x$x.
Step 3: From step 1, it follows that $100\%=51$100%=51.
Step 4: In the same vein, $x\%=300$x%=300.
Step 5: This gives us a pair of simple equations:
$100\%=51(1)$100%=51(1).
$x\%=300(2)$x%=300(2).
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
$\frac{100\%}{x\%}=\frac{51}{300}$
100%
x%=
51
300
Step 7: Taking the inverse (or reciprocal) of both sides yields
$\frac{x\%}{100\%}=\frac{300}{51}$
x%
100%=
300
51
$\Rightarrow x=588.24\%$⇒x=588.24%
Therefore, 17% of 300 is 51
Answer:
Answer 17%
Step-by-step explanation:
Solution for 300 is what percent of 51:
300:51*100 =
(300*100):51 =
30000:51 = 588.24
588.24 as a percentage is 17%
I hoped this helped and remember to stay safe!!!(a) Suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected house is valued at less than $500,000. Show your work.
(b) Suppose a random sample of 40 houses are selected from the city. Estimate the probability that the mean value of the 40 houses is less than $500,000. Show your work.
Answer:
a. 0.71
b. 0.9863
Step-by-step explanation:
a. The mean of the distribution is given as $403,000 and the standard deviation is $278,000.
-To estimate the probability that a randomly selected house has a value less than $500,000:
[tex]P(X<500,000)=P(X=0)+P(X=500)\\\\=0.34+0.37\\\\=0.71[/tex]
Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71
b. -since 40 is larger than or equal to 30, we assume normal distribution.
-The probability can therefore be calculated as:
[tex]P(\bar X)=P(z<\frac{\bar X-\mu}{\sigma/\sqrt{n}})\\\\=P(z<\frac{500-403}{278/\sqrt{40}})\\\\=P(z<2.2068)\\\\=0.986336\\\\\approx 0.9863[/tex]
Hence, the probability that the mean value of the 40 houses is less than $500,000 is 0.9863
To estimate the probability that a house is valued less than $500,000, we count the bars below that value on the histogram. To estimate the probability that the mean value of 40 houses is less than $500,000, we use the Central Limit Theorem to calculate the z-score.
Explanation:(a) To estimate the probability that the selected house is valued at less than $500,000, we need to find the area under the histogram below the value of $500,000. Looking at the histogram, we see that there are 3 bars below $500,000. Each bar represents a count of houses, so we add up the counts of those 3 bars. The estimated probability is given by:
Estimated Probability = (Count of houses valued less than $500,000) / (Total count of houses)
(b) To estimate the probability that the mean value of the 40 houses is less than $500,000, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of the sample mean approaches a normal distribution with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. We can then calculate the z-score for $500,000 using the formula:
z = (x - mean) / (standard deviation / sqrt(sample size))
Once we have the z-score, we can find the estimated probability using a standard normal distribution table or calculator.
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PROBLEM 1
Evaluate the expression 9 – z when z = 4.
What’s the answer
Answer:
[tex](9 - 4) \\ ( {3}^{2} - {2}^{2}) \\ (3 - 2)(3 + 2) \\ 1 \times 5 = 5 [/tex]
hope this helps you.
I need help asap :):);)
Answer: The third option.
Step-by-step explanation:
This is an equation because it has an equals sign that can be solved for, making it an equation.
Answer:
x + 3 = 12
Step-by-step explanation:
This is an equation because it contains an equal sign, if it does not contain an equal sign then it is an expression.
3[tex]\sqrt{16}[/tex] + [tex]\sqrt{-9}[/tex]
Simplify the expression. Write your answer as a complex number.
Answer:
Step-by-step explanation:
hello :
let: A = 3√16+√-9
16=4² and -9 = 9i² =(3i)² .... ( i² = -1)
√16 =√4² = 4 and √-9 = √9i²= √(3i)² ± 3i
A= 12 ± 3i
Seventy-five percent of consumers prefer to purchase electronics online. You randomly select 88 consumers. Find the probability that the number of consumers who prefer to purchase electronics online is (a) exactly five, (b) more than five, and (c) at most five.
Answer:
Step-by-step explanation:
Find attached the solution
If 2^2х = 2^3, what is the value of х?
Answer:
19
Step-by-step explanation:
if x=3
Answer:
x = 2
Evaluate the powers.Divide both sides by 4. Solution should be x = 2Which statement is true about the values of the ones and tenths digit in 346.68? A. The value of the ones digit is 6 more then the value of the tenths digit. B. The value of the ones digit is the same as the value of the tenths digit. C. The value of the ones digit is 6 times as many as the value of the tenths digit. D. The value of the ones digit is 10 times as many as the value of the tenths digit,
Answer:
B. The value of the ones digit is the same as the value of the tenths digit.
Step-by-step explanation:
346.68
From the above digit, the value of one is 6 and the value of tenth is 6.
3 = hundred
4 = ten
6 = unit
6 = tenth
8 = hundredth
The unit is the same for ones.
From the above we can see that unit and tenth have the same value.
So, therefore, the answer is:
B. The value of the ones digit is the same as the value of the tenths digit.
What is the value of x in this equation? 4x + 2 – 23(92 + 92x) = 7
Answer:
-707/704
Step-by-step explanation:
4x + 2 - 2116 - 2116x = 7
-2112x = 2121
x = 2121/-2112 = -707/704
Answer:
x= 2121/-2112 = -707/704 = -1.00426136
Step-by-step explanation:
4x + 2 – 23(92 + 92x) = 7
Eliminate the 2 by substracting both side by -24x - 23(92+92x) = 5
2. Discriminate by multiplying -23 with 92 and -23 with 92x
4x - 2116 -2116x = 5
3. Add 2116 both sides to eliminate -2116
4x -2116x = 2121
4. combine 4x-2116x together
-2112x = 2121
5. Divide both sides with -2112
x= 2121/-2112 = -707/704 = -1.00426136
HELP THIS IS DUE IN 5 MINSSSSS! Mr. Viviano would like to report to the principal the smaller measure of center between the mean and the median for the distribution of test scores of his AP Calculus class.
The test scores are as follows: 60, 65, 70, 75, 80, 80, 85, 85, 90, 95, 100.
What is the number that he will report?
Answer:
The median. 80 because the mean is 80.454545
Step-by-step explanation:
Can you please help me this is 6th grade stuff
Answer:
116
Step-by-step explanation: You would have to split the figure into a square and a triangle as you can see in the picture. You then find the area of each figure.
Area of Square : 8 * 8 = 64
Area of Triangle : 8 * 13 /2 = 52
Then, you add the areas of both figures together to get 116.