Answer:
The equation of the perpendicular bisector of the segment AB is [tex]y = x - 2[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
Perpendicular lines and slopes:
If two lines are perpendicular, the multiplication of their slopes is -1.
Equation of the perpendicular bisector of the segment AB.
Equation of a line that passes through the midpoint of segment AB and is perpendicular to AB.
Midpoint of segment AB:
Mean of their coordinates x and y. So
(1+7)/2 = 4
(5-1)/2 = 2
So (4,2).
Slope of segment AB:
When we have two points, the slope between them is given by the change in y divided by the change in x.
In segment AB, we have points (1,5) and (7,-1). So
Change in y: -1 - 5 = -6
Change in x: 7 - 1 = 6
Slope: -6/6 = -1
Equation of the perpendicular bisector:
The slope, multiplied with the slope of segment AB, is -1. So
[tex]-1m = -1[/tex]
[tex]m = 1[/tex]
So
[tex]y = x + b[/tex]
Passes through (4,2), which means that when [tex]x = 4, y = 2[/tex]. So
[tex]y = x + b[/tex]
[tex]2 = 4 + b[/tex]
[tex]b = -2[/tex]
So
[tex]y = x - 2[/tex]
12 gallons to 36 gallons. Percent change?
I guess it is 200%
Hope it is correct
Answer:
200.00%Step-by-step explanation:
Here i will show you how to calculate the Percent Change from 12 to 36.
Basically, we are trying to find the change from 12 to 36 in terms of percent. We do this in three steps:
1) Find the difference between 12 and 36 as a number.
2) Divide the result from Step 1 by the starting number 12.
3) Multiply the result you got on step two by 100 to get it in terms of percent.
this can be shotenn sown with a simple formulatso, to find the percent change from 12 to 36, we use this formula:
((Y-X)/X)*100 = Percent Change
X is the starting number 12, and Y is the ending number 36 that it changed to. When we enter these numbers into the formula, we get:
((36-12)/12)*100 = 200.00%
there fore you answer is
200.00%A flying disc was originally marked at 5$ and has been sold at $3.50. What was the percent of discount?
Answer:
30%
Step-by-step explanation:
Percentage discount
[tex] = \frac{discount}{original \: price} \times 100\% \\ = \frac{5 - 3.50}{5} \times 100\% \\ = 30\%[/tex]
☆ Discount= original price -selling price
(1) The ratios 18:3 and 6:1 are equivalent. Why?
Answer:
Because if you take 18:3 and divide both sides by 3, you will get 6:1
Step-by-step explanation:
Because 18:3 divided by 3 on both sides equals 6:1, also 6:1 times 3 on both sides equals 18:3.
Can u help me please
Im pretty sure its D
Answer:
The answer is D
Step-by-step explanation:
A polling company is trying to estimate the percentage of adults that consider themselves happy. A confidence interval based on a sample size of 180 has a larger than desired margin of error. The company wants to conduct another poll and obtain another confidence interval of the same level but reduce the error to one-third the size of the original sample. How many adults should they now interview
Answer:
They should interview 1620 adults now.
Step-by-step explanation:
Margin of error of a confidence interval:
The margin of error of a confidence interval has the following format:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which z is related to the confidence level, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this question:
z wont change, neither will [tex]\sigma[/tex]
We want to increase n as such the margin of error is reduced to one third.
We have that the margin of error is inversely proportional to the square root of the size of the sample, which means that for the margin of error to be reduced to one third, the sample size has to be multiplied by [tex]3^2 = 9[/tex]. So
180*9 = 1620
They should interview 1620 adults now.
8) The relationship between a figure and it's scale copy is proportional.
True or False?
Step-by-step explanation:
i think True
99% wrong 1% right
solve 5y - 2 = 3y + 14
Answer: y=8
Step-by-step explanation:
Answer:
Y = 8
Step-by-step explanation:
Can someone help me please im so confused
Answer:
it is either the dice or the cups
Step-by-step explanation:
Answer:
cups
Step-by-step explanation:
i might be wrong
Please answer I really need help
Answer:
8
Step-by-step explanation:
its somethings difficult
PLS HELP !!! Dwight has a total of 55 nickels and quarters that total $8.75. How many of each coin
does he have?
Answer:
25 nickle and 30 quarters
Step-by-step explanation:
30 time .25 is 7.5 and 25 times .05 is 1.25 so yea thats it
Answer:
25 nickels 30 quarters
Step-by-step explanation:
What is greater than 525.06 but less than 525.6?
|x|=5
Solve for x
|x| = -5
Solve for x
Answer:
Step-by-step explanation:
For |x|=5, x can be either 5 or -5.
For |x|=-5, absolute value cannot be negative, so it is no solutions.
a car is 180 inches long. a truck is 75 percent longer than thr car. how long is the truck
Answer:
315
Step-by-step explanation:
180+((75/100)x180)=
180+(3/4 x 180)=
180+135=
315
Answer:
315 inches
Step-by-step explanation:
180 × .75 = 135
What is the area of this figure?
Enter your answer as a decimal
Answer:
176.00 cm^2
Hope you got the answer.
Find the values of x and y
help me plz!!
Answer:
24=5y+3y
8y=24
y=3
x+x+9y+5=90
2x+9(3)+5=90
2x=58
x=29
Step-by-step explanation:
Gerber Product's Gerber Mixed Cereal for Baby contains, in each serving, 60 calories and 11 grams of carbohydrates.† Gerber Mango Tropical Fruit Dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.† If you want to provide your child with 340 calories and 75 grams of carbohydrates, how many servings of each should you use?
Answer:
2 servings of Gerber Mixed Cereal for Baby and 3 servings of Gerber Mango Tropical Fruit Dessert should be used.
Step-by-step explanation:
Given that Gerber Product's Gerber Mixed Cereal for Baby contains, in each serving, 60 calories and 11 grams of carbohydrates, while Gerber Mango Tropical Fruit Dessert contains, in each serving, 80 calories and 21 grams of carbohydrates, and you want to provide your child with 340 calories and 75 grams of carbohydrates, in order to how many servings of each you should use, the following calculation has to be made:
(80 x 5) + (60 x 0) --- (21 x 5) + (11 x 0) = 400 --- 105
(80 x 4) + (60 x 1) --- (21 x 4) + (11 x 1) = 380 --- 95
(80 x 3) + (60 x 2) --- (21 x 3) + (11 x 2) = 360 --- 85
(80 x 2) + (60 x 3) --- (21 x 2) + (11 x 3) = 340 --- 75
Therefore, 2 servings of Gerber Mixed Cereal for Baby and 3 servings of Gerber Mango Tropical Fruit Dessert should be used.
Although five of John's answers were incorrect, 90% of his answers were correct. How many questions did John answer in all?
Answer:
John answered 50 questions.
Step-by-step explanation:
Although five of John's answers were incorrect, 90% of his answers were correct.
This means that 5 is 100 - 90% = 10% of the total number of questions, n. So
[tex]0.1n = 5[/tex]
[tex]n = \frac{5}{0.1}[/tex]
[tex]n = 50[/tex]
John answered 50 questions.
Classify the triangle with the given side lengths as 1,13,13
Answer:
isosceles triangle
Step-by-step explanation:
Given a population mean of 27.1 with a standard deviation of 8.4 and a sample size of 10, answer these questions:
Part A: What is the standard deviation of the sampling distribution of x? Show your work
Part B: what does the sample size need to be if you want the standard deviation of the sampling distribution of c to be2.8? Show your work.
Answer:
Step-by-step explanation:
The mean of the sampling distribution is equal to the mean of the population. Therefore, we use the standard deviation of the sampling distribution of the means formula.
The standard deviation of the sampling distribution of the means is 2.656.
With a new population standard deviation of 2.8, the sampling size, n, is 9.
Radon is a naturally occurring gas and is the second leading cause of lung cancer in the United States. It comes from the natural breakdown of uranium in the soil and enters buildings through cracks and other holes in the foundations. Found throughout the United States, levels vary considerably from state to state. Several methods can reduce the levels of radon in your home, and the Environmental Protection Agency ecommends using one of these if the measured level in your home is above 4 picocuries per liter. Four readings from Franklin County, Ohio, where the county average is 9.32 picocuries per liter, were 5.2, 13.8, 8.6, and 16.8.
Required:
a. Find the mean step-by-step.
b. Find the standard deviation step-by-step.
Answer:
a) mean = 11.1
b) Standard Deviation = 5.191
Step-by-step explanation:
Given the data in the question;
x = 5.2, 13.8, 8.6, and 16.8
sample n = 4
so;
x ( x - mean)²
5.2 34.81
13.8 7.29
8.6 6.25
16.8 32.49
∑ 44.4 80.84
a) Mean
Mean = total sum of the sample divided by the sample size
mean = ∑x / n
we substitute
mean = 44.4 / 4
mean = 11.1
b)
Standard Deviation is the Square root of variance;
Variance = ∑(x-mean)² / n - 1
we substitute from the above table
Variance = 80.81 / 4 - 1
Variance = 80.81 / 3
Variance = 26.94667
now since Standard Deviation is the Square root of variance;
Standard Deviation = √Variance
Standard Deviation = √26.94667
Standard Deviation = 5.191
Pat said that the amount of money he has in his pocket is greater than or equal to $5.75 but less than $13.00. Which number line shows the amount of money Pat might have?
10. A random sample of 10 fibers is taken from a collection of 92 fibers that consists of 43 fibers of polymer A, 17 fibers of polymer B, and 32 fibers of polymer C. a. What is the probability that the sample does not contain any fibers of polymer B
Answer:
0.1150 = 11.50% probability that the sample does not contain any fibers of polymer B
Step-by-step explanation:
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
Fibers are chosen without replacement, which means that we use the hypergeometric distribution.
92 fibers means that [tex]N = 92[/tex]
Sample of 10 means that [tex]n = 10[/tex]
No polymeter B which means that [tex]x = 0[/tex]
17 fibers of polymeter B which means that [tex]k = 17[/tex]
a. What is the probability that the sample does not contain any fibers of polymer B
This is P(X = 0).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,92,10,17) = \frac{C_{17,0}*C_{75,10}}{C_{92,10}} = 0.1150[/tex]
0.1150 = 11.50% probability that the sample does not contain any fibers of polymer B
The probability that the sample does not contain any fibers of polymer B is 0.123
The given parameters are:
n = 92
A = 43
B = 17
C = 32
The probability of selecting a sample that contains polymer B is:
[tex]p = \frac{17}{92}[/tex]
[tex]p = 0.185[/tex]
Using binomial probability, we have:
[tex]P(x) = ^nC_x * p^x *(1 - p)^{n -x}[/tex]
The probability that a selection of 10 fibers do not contain polymer B is then calculated as:
[tex]P(0) = ^{10}C_0 * 0.185^0 *(1 - 0.185)^{10 -0}[/tex]
This gives
[tex]P(0) = 1 * 1 *(0.815)^{10}[/tex]
Evaluate the product
[tex]P(0) = 0.123[/tex]
Hence, the probability that the sample does not contain any fibers of polymer B is 0.123
Read more about probability at:
https://brainly.com/question/25870256
Worl
10.
9. A bottle contains 3.5 liters of water. A second
bottle contains 3,750 milliliters of water. How
many more milliliters are in the larger bottle
than in the smaller bottle?
Math Explain how units of length and
Answer:
250 milliliters
Step-by-step explanation:
3.5 liters = 3.5 × 1000 milliliters=3500milliliters
3750-3500 = 250 milliliters
A cruise cost £4500 and you have to pay a 30% deposit. What is the deposit and what is the balance.
Answer:
$5350
Step-by-step explanation:
What is the square root of 25
Answer:
5
Step-by-step explanation:
5 square, which means 5 multiplied by 5 gives you 25
Answer:
the square root of 25 is 5
Help pls I will give brainliest
Answer:
Least: 14%
Next: 0.15
Next: 1/5
Next: 24%
Greatest: 27/100
Step-by-step explanation:
If you put them all into decimal form they are:
.14, .15, .20, .24, .27
hello twngan sus puntos!!
Answer:
2029jjajvdjsjsvdghsjsjbs
Answer:
Answer:
Step-by-step explanation:
Thanks for free points!
como se llama la figura geométrica que tiene 6 caras 12 aristas 8 vertises
Answer:
hexaedro
ahí esta la respuesta
Circle 20% of these lollipops there are 10 lollie pops
Answer:
20% of 10 is 2
Step-by-step explanation:
What is 8z + x -5 - 9z + 2 written in simplest form
Answer:
Hope this helps :D
Step-by-step explanation:
The simplified form of the given expression is x-z-3.
The given expression is 8z + x -5 - 9z + 2.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is written in simplified form is as follows
Group the like terms
8z - 9z + x -5 + 2
= -z+x-3
= x-z-3
Hence, the simplified form of the given expression is x-z-3.
To learn more about an expression visit;
https://brainly.com/question/28170201.
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