Given:
The two points are P(14,16) and Q(21,19).
M is the midpoint of the segment PQ.
To find:
The distance between P and Q, and find the coordinates of point M.
Solution:
Distance between P(14,16) and Q(21,19) is
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
\(d(P,Q)=\sqrt{(21-14)^2+(19-16)^2}\)
\(d(P,Q)=\sqrt{(7)^2+(3)^2}\)
\(d(P,Q)=\sqrt{49+9}\)
On further simplification, we get
\(d(P,Q)=\sqrt{58}\)
\(d(P,Q)=\sqrt{58}\)
The midpoint of P and Q is M. So, the coordinates of the midpoint are:
\(M=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\)
\(M=\left(\dfrac{14+21}{2},\dfrac{16+19}{2}\right)\)
\(M=\left(\dfrac{35}{2},\dfrac{35}{2}\right)\)
\(M=\left(17.5,17.5\right)\)
Therefore, the distance between P and Q is \(\sqrt{58}\) and the midpoint of P and Q is \(M=\left(17.5,17.5\right)\).
someone help me please and thank you
Answer: i know what school ur from my school page looks the same (we in CCA) XDD
anyways this question is very vague. but i think its c.
Step-by-step explanation:
again its very vague but i tried i think its c
The repeating decimal, 0.27, is converted to the fraction 0.27 =
What is the value of x in the fraction?
Answer:
The value of x is 11
Step-by-step explanation:
problem solving/data analysis additional topics in math heart of algebra passport to advanced mathematics
Problem Solving and Data Analysis, Heart of Algebra, and Passport to Advanced Mathematics are three additional topics in math that are part of the SAT Math section. These topics cover various concepts and skills that are essential for solving complex mathematical problems and analyzing data effectively.
Problem Solving and Data Analysis: This topic focuses on the ability to interpret and analyze real-world scenarios, solve problems using quantitative reasoning, and apply mathematical models to data. It includes concepts such as ratios, proportions, percentages, statistics, data interpretation, and data representation.
Heart of Algebra: This topic emphasizes algebraic concepts and skills, particularly those related to linear equations, linear inequalities, and systems of linear equations. It involves understanding and solving equations, manipulating algebraic expressions, graphing linear functions, and solving word problems using algebraic methods.
Passport to Advanced Mathematics: This topic builds upon the foundational algebraic skills and extends into more advanced mathematical concepts. It covers topics such as quadratic equations, exponential and logarithmic functions, radicals and rational exponents, polynomial operations, and complex numbers. It also involves solving higher-order equations, understanding function transformations, and applying algebraic concepts in various contexts.
These topics are important for SAT Math because they assess a student's ability to apply mathematical knowledge and problem-solving strategies to real-world situations. Familiarity with these topics enables students to analyze data, reason quantitatively, solve complex algebraic problems, and make connections between different mathematical concepts.
In conclusion, Problem Solving and Data Analysis, Heart of Algebra, and Passport to Advanced Mathematics are key topics in the SAT Math section. Mastering these topics is essential for achieving a high score on the SAT and for developing strong problem-solving and data analysis skills in mathematics.
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Find specific solution of the following differentila equation y' = 2y for y(0) = 3. Write an expression: y(x)=3
The specific solution to the given differential equation, y' = 2y, with the initial condition y(0) = 3 is y(x) = 3e^(2x). This solution can be expressed in two lines as y(x) = 3e^(2x).
To solve the differential equation y' = 2y, we can separate the variables by dividing both sides by y and dx, yielding 1/y dy = 2 dx. Integrating both sides, we obtain ∫(1/y) dy = ∫2 dx. The integral of 1/y with respect to y gives us ln|y|, and the integral of 2 with respect to x gives us 2x. Therefore, we have ln|y| = 2x + C, where C is an arbitrary constant.
Next, we can solve for y by exponentiating both sides of the equation. Taking the exponential function of ln|y| gives us |y| = e^(2x + C). Since e^C is a positive constant, we can write |y| = Ce^(2x), where C = e^C. Now we consider the initial condition y(0) = 3, which implies that when x is 0, y is 3. Substituting these values into the equation, we have |3| = Ce^(2 * 0), leading to 3 = Ce^0. Therefore, C = 3, and our specific solution is y(x) = 3e^(2x), which satisfies the initial condition y(0) = 3.
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What would be the opportunity cost of spending $90,000 on advertising but only producing 12,000 units? Potential sales (before advertising) of 12,000 units, Price of $16, Fixed costs of $48,000, Variable costs $8, Advertising $90,000 Assume advertising multiplier is (30,000+ advertising)/30,000
$76,800
$576,000
$192,000
−$191,936
$768,000
The opportunity cost of spending $90,000 on advertising but only producing 12,000 units can be calculated by comparing the benefits of the advertising investment to the potential alternative uses of that money.
First, let's calculate the total cost of producing 12,000 units. Fixed costs amount to $48,000, and variable costs are $8 per unit, resulting in a total cost of $48,000 + ($8 × 12,000) = $144,000.
Next, we need to calculate the potential sales revenue without advertising. With a price of $16 per unit, the potential sales revenue would be $16 × 12,000 = $192,000.
Now, let's calculate the potential sales revenue after advertising. The advertising multiplier is given as (30,000 + advertising) / 30,000. In this case, the multiplier would be (30,000 + 90,000) / 30,000 = 4.
Therefore, the potential sales revenue after advertising would be $192,000 × 4 = $768,000.
The opportunity cost is the difference between the potential sales revenue after advertising ($768,000) and the potential sales revenue without advertising ($192,000), which is $768,000 - $192,000 = $576,000.
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Plz need help like rn What is m
Answer:
measure of angle p=
94
Step-by-step explanation:
ok 5 sided polygon= 540
so put all of those equal to 540
need to find x first
540=132+(4x-10)+(5x-11)+128+(4x+2)
simplify and combine like terms
x=23
now plug in for angle p
(4(23)+2)
94
Solve the following equation for the variable. 2m – 3 =23
m =
What was the FIRST step?
Answer:add 3
Step-by-step explanation:
On saturdays, cars arrive at sami schmitt's scrub and shine car wash at the rate of 6 cars per fifteen minute interval. Using the poisson distribution, the probability that five cars will arrive during the next five minute interval is.
The probability that five cars will arrive during the next thirty minute interval is 0.0361
What is probability?
Probability is a way of calculating how likely something is to happen. Numerous things are difficult to forecast with absolute confidence.
Main Body:
Let X = number of cars arriving at Sami Schmitt's Scrub and Shine Car Wash.
The average number of cars arriving in 15 minutes is 6.
The average number of cars arriving in 1 minute is = 6/15 = 2/5
The average number of cars arriving in 5 minutes is, (2/5)*5 = 2
The random variable X follows a Poisson distribution with parameter λ = 2.
The probability mass function of X is:
P(X=\(x\)) = \((e^{-2} 2^{x} )/x!\) , x = 0,1 ,2 ,3...
Compute the probability that 5 cars will arrive in 5 minutes as follows:
P(X=5) =\((e^{-2} 2^{5} )/5!\)
P (X= 5) = 0.0361
Hence probability is 0.0361
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2x^2 - 16x + 13 in the form a(x-b)*2+c?
Answer:
y=2(x−4)2−19
Step-by-step explanation:
PLS BRAINLIEST
after selling a total of 60 items, you have made a total of $450. how many cases and t-shirts were sold?
54 t-shirts and 6 cases were sold, as determined by solving the simultaneous equations of the total revenue made and the total number of items sold, which were $450 and 60.
We can assign variables to represent the number of T-shirts and cases sold. Let x be the number of T-shirts sold and y be the number of cases sold. We can then express the given information as a system of simultaneous equations:
7x + 12y = 450x + y = 60which gives us the following value for y:
x + y = 60y = 60 - xPlugging the value into the first equation, we have:
7x + 12(60 - x) = 4507x + 12*60 - 12x = 4505x = 12 * 60 - 450 = 270X = 270/5X = 54Therefore, we sold 54 T-shirts.
Meanwhile, the following number of cases have been sold:
y = 60 - xy = 60 - 54y = 6So the number of t-shirts sold is 54, and the number of cases sold is 6.
This question should be provided as:
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one container is filled with a mixture that is 30% acid a second container is filled with the mixture that is 50% acid the second container is 50% larger than the first and the two containers are emptied into a third container what percent of acid is in the third container
Answer:
42%
Step-by-step explanation:
x is for the volume of the container
the amount filled in the first container=0.30x
the volume of the first container + 50% of the second=(x+x*50%)=1.5 x
the amount of acid in the second container= 1.5x * 50%=0.75x
total amount of acid in the third one =0.3x+0.75x=1.05x
total solution : x+1.5x=2.5x
percentage=1.05x/2.5x= 0.42 or 42%
it is known that amounts of money spent on clothing in a year by college students follow a normal distribution with a mean of $340 and a standard deviation of $50. what is the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year?
The required probability for randomly selected students spend between $300 and $400 on clothing in a year is equal to 0.6730 or 67.30% (approximately ).
For a normal distribution with a mean (μ) of $340
And a standard deviation (σ) of $50.
Let X be the amount of money spent on clothing by a randomly chosen student.
Probability that a randomly chosen student will spend between $300 and $400 on clothing in a year,
P(300 < X < 400)
Standardize the distribution by converting the given values to z-scores, using the formula,
z = (X - μ) / σ
For the lower limit, we have,
z1 = (300 - 340) / 50 = -0.8
For the upper limit, we have,
z2 = (400 - 340) / 50 = 1.2
Area under the standard normal distribution curve between these two z-scores.
Standard normal distribution table
Probabilities, or use the properties of the normal distribution to calculate it as,
P(-0.8 < Z < 1.2)
= P(Z < 1.2) - P(Z < -0.8)
Using a standard normal distribution table we have,
P(Z < 1.2) ≈ 0.8849
P(Z < -0.8) ≈ 0.2119
Substituting these values in the above equation, we get,
P(-0.8 < Z < 1.2)
≈ 0.8849 - 0.2119
≈ 0.6730
Therefore, the probability that a randomly chosen student will spend between $300 and $400 on clothing in a year is approximately 0.6730 or 67.30%.
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10 records in her collection. Now she has 12 records. What is the percent increase of her collection?
10 records in her collection. Now she has 12 records. The percentage increase of her collection is by 20%.
Percentage:
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is usually represented by the percent sign "%", although 'it is abbreviated "pct.", "pct.", and sometimes "pc". Percentage is a dimensionless number (pure number); it is unmeasured Unit.
Example :
If 50% of the total number of pupils in a class are boys, this means that 50 out of 100 pupils are boys. If there are 500 students, 250 of them are men.
According to the Question:
We can use the rule of three to solve this problem.
If 100% is 10 records, the percentage of 12 records:
= 12 × 100%/10
= 120%
Then if subtracted 120% -100%, there will be a difference of 20%, i.e. 12 is 20% more, i.e. his collection has increased by 20%.
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if msbetween = 54.2 and mswithin = 27.9, what is the value of fobt?
fobt ≈ 1.945. This is the calculated value of the F-statistic for the given data.
The fobt, also known as the F-statistic, is used in statistical analysis to assess the significance of differences between groups or treatments. It is calculated by dividing the mean square variation between groups (MSbetween) by the mean square variation within groups (MSwithin).
In this case, we are given MSbetween = 54.2 and MSwithin = 27.9. To find fobt, we use the formula fobt = MSbetween / MSwithin. Substituting the given values, we have fobt = 54.2 / 27.9.
Dividing these two values gives us fobt ≈ 1.945. This is the calculated value of the F-statistic for the given data. The significance of this value depends on the context and the specific analysis being performed. Generally, the fobt value is compared to a critical value or p-value to determine if the observed differences between groups are statistically significant.
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The volume of a cone that has a radius of 3mm and a hight of 6mm is equal to the volume of a cylinder that has a height of 2mm what is the radius of the cylinder
The volume of a shape is the amount of space in the shape
The radius of the cylinder is 3 mm
How to determine the radiusThe given parameters of the cone are:
Radius = 3mm
Height = 6mm
The volume of the cone is:
\(V =\frac 13\pi r^2h\)
So, we have:
\(V =\frac 13\pi * 3^2 * 6\)
The volume of a cylinder is:
\(V= \pi r^2h\)
The height is:
Height = 2 mm
So, we have:
\(V= \pi r^2 * 2\)
The volumes are equal.
So, we have:
\(\pi r^2 * 2 = \frac 13\pi * 3^2 * 6\)
Divide the common factors
\(r^2 = \frac 13 * 3^2 * 3\)
Evaluate the products
\(r^2 = 9\)
Take the square roots of both sides
\(r = 3\)
Hence, the radius of the cylinder is 3 mm
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You can buy 5 pens for $3.75 What is the price for 1 pen?
Answer: 0.75
Step-by-step explanation:
3.75/5 = 0.75$
Plzzzzzzzzhellpppppppmeeee please! We will be besties if ur2 help me!
21. Solve the equation with variables on both sides: 12y = 2y − 10
a. y=−10 b. y=10 c. y=−1 d. y=1
22. Solve the equation using inverse operations. 4x+5 = 6x−9
Answer:
Answer:
d. y=-1; x=7
Step-by-step explanation:
Please help me I need help
If the diameter of a circle is doubled, the circumference of the new circle is..
A. 1/4 of the circumference of the original circle
B. 1/2 of the circumference of the original circle
C. The same as the circumference as the original circle
D. 2 times the circumference of the original circle
E. 4 times the circumference of the original circle
Answer:
D
Step-by-step explanation:
Let's call the original diameter x. Then, the circumference would be xπ. If the diameter is 2x, the circumference is 2xπ. 2xπ / xπ = 2 so the answer is D.
Answer:
D. 2 times the circumference of the original circle
Step-by-step explanation:
The circumference of a circle is represented by the formula C = 2(r)pi (where is r is the radius), which can also be written as C = (d)pi, where d is the diameter, (since 2r is equivalent to d). If the diameter is doubled, the original equation can be rewritten as C = 2(d)pi. Therefore, the circumference of the new circle is double the original circle.
You can plug in a sample number to further prove this point. Pretend r = 3 so d = 6. C = 6pi. Now when the diameter is doubled, d = 12 and C = 12pi which is double 6pi.
So the answer is D. 2 times the circumference of the original circle
Determine the required value of the missing trokakilify to make the distribution a discrete probataility diettisufteon
The required value of the missing probability to make the distribution a discrete probability distribution is given as follows:
P(X = 4) = 0.22.
How to obtain the required value?For a discrete probability distribution, the sum of the probabilities of all the outcomes must be of 1.
The probabilities are given as follows:
P(X = 3) = 0.28.P(X = 4) = x.P(X = 5) = 0.36.P(X = 6) = 0.14.Hence the value of x is obtained as follows:
0.28 + x + 0.36 + 0.14 = 1
0.78 + x = 1
x = 0.22.
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What if a fence painting competition allowed pairs to compete? If Ben Rogers can paint the fence in 8 min on his own and Johnny Miller can paint it in 6 min, then how long would it take them working together?
If Ben can paint a single coat of the fence in 8 min, then how much of the fence could Ben paint in 1 min?
If Johnny can paint a single coat of the fence in 6 min, then how much of the fence could Johnny paint in 1 min?
If Ben and Johnny work together to paint a single coat of the fence, then let t represent the amount of time they each spend painting. What operation should be used to set up an equation that represents how long they would take to paint a single coat of the fence?
Solve the equation for t. How long will it take Ben and Johnny to paint the fence? Round your answer to the nearest tenth of a minute.
Answer:
I'm confused on what it's asking
Step-by-step explanation:
A plane takes off and climbs steadily for 15 minutes until it reaches 30,000 feet. It travels at that altitude for 2 hours until it begins to descend to land, which takes 15 minutes at a constant rate
A six-sided die with sides labeled 1 through 6 will be rolled once. Each number is equally likely to be rolled.
What is the probability of rolling a number greater than 2?
Write your answer as a fraction in simplest form.
Please Helppp
Answer:
2/3
Step-by-step explanation:
The numbers greater then 2 are 3, 4, 5, 6
That's four numbers that are greater then two.
or 4/6, then you just reduce it by dividing by two on the top and bottom
4/2 =2
6/2 = 3 so the answer is 2/3
please help ill mark brainliest
For a recent paint job, Josh mixed red and white paint to make two different shades of pink. When the job was done, Josh ended up with leftover paint: 5 gallons of dark pink paint (80% red) and 4 gallons of light pink paint (30% red). Josh wants to make a medium pink color (50% red) to paint his daughter's bedroom. He will need 3 gallons to completely cover the walls. How much of each of the leftover paints should Josh mix to achieve his desired color?
? gallons of dark pink paint
? gallons of light pink paint
Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.
To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.
Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.
The total amount of paint needed is 3 gallons, so we have the equation:
x + y = 3
The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:
(80/100)x + (30/100)y = (50/100)(x + y)
Simplifying this equation, we get:
0.8x + 0.3y = 0.5(x + y)
Now, we can solve this system of equations to find the values of x and y.
Let's multiply both sides of the first equation by 0.3 to eliminate decimals:
0.3x + 0.3y = 0.3(3)
0.3x + 0.3y = 0.9
Now we can subtract the second equation from this equation:
(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)
-0.5x = 0.9 - 0.5x - 0.5y
Simplifying further, we have:
-0.5x = 0.9 - 0.5x - 0.5y
Now, rearrange the equation to isolate y:
0.5x - 0.5y = 0.9 - 0.5x
Next, divide through by -0.5:
x - y = -1.8 + x
Canceling out the x terms, we get:
-y = -1.8
Finally, solve for y:
y = 1.8
Substitute this value of y back into the first equation to solve for x:
x + 1.8 = 3
x = 3 - 1.8
x = 1.2
Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.
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Question 2 (5 points)
(01.01 LC)
Which of the following describes a situation in which the total distance a ball travels is zero meters from its starting point? (5 points)
a
The ball first bounces up to a height of 4 meters, and then falls 2 meters towards the ground.
b
The ball first bounces up to a height of 2 meters, and then falls 2 meters towards the ground.
c
The ball first bounces up to a height of 2 meters, and then falls 4 meters towards the ground.
d
The ball first bounces up to a height of 4 meters, and then falls 0 meters towards the ground.
The situation is which the total distance traveled is of zero is given by:
b. The ball first bounces up to a height of 2 meters, and then falls 2 meters towards the ground.
How to calculate the total distance?The total distance can be calculated by the subtraction of the final position by the initial position.
Hence, the total distance traveled will be of zero when the object ends at the same place it started, and the only option in which this happens is given by:
b. The ball first bounces up to a height of 2 meters, and then falls 2 meters towards the ground.
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Please help to find the answer to a b and c please
Answer:
a) 5p (or 5q)
b) 5p ( or 5q)
c) 10p (or 10q)
Step-by-step explanation:
We will use the following information for solving and using the given figure
In a regular hexagon all six sides are equalPreliminary computation
We have \(\overrightarrow{AB} = \overrightarrow{BC}\)
Therefore 4p + q = 5p
5p = 4p + q
5p-4p = q
p = q
\(\overrightarrow{AB} = 4p + q = 4p + p = 5p = 5q\\\)
So each side is 5p in length which is also equal to 5q since p = q
Part a
\(\overrightarrow{AO} = \overrightarrow{OA} = \overrightarrow{AB} = 5p\) (same as 5q)
Part b
\(\overrightarrow{OB} = \overrightarrow{OA} = 5p\) (same as 5q)
Part c
\(\overrightarrow{EB} = 2 \cdot \overrightarrow{OB} = 2 \cdot 5p = 10p\) (also 10q)
Question 5
3 pts
In 1995, you bought a baseball card for $50 that you expect to increase in value 5% each
year for the next 10 years. Write an exponential growth equation
and
estimate the value of the baseball card in 2002
Mr. Walker is looking at the fundraiser totals for the last five years.
A 2-column table with 5 rows. The first column is labeled year with entries 1, 2, 3, 4, 5. The second column is labeled total (in dollars) with entries 896, 925, 880, 963, 914.
How does the mean of the totals compare to the median?
The median is $1.60 greater than the mean.
The mean is $1.60 greater than the median.
The median is $2.82 greater than the mean.
The mean is $2.82 greater than the median.
Answer:
the median is $1.60 greater than the mean
Answer:
a
Step-by-step explanation:
assume that 20 parts are checked each hour and that x denotes the number of parts in the sample of 20 that require rework. parts are assumed to be independent with respect to rework. a. if the percentage of parts that require rework remains at 1%, what is the probability that hour 10 is the first sample at which x exceeds 1?
Answer:
what
Step-by-step explanation:
The probability that hour 10 is the first sample at which x exceeds 1 is 0.0086.
Let X denotes the number of parts in the sample of 20 that require rework. We can model the number X of parts in a random sample of 20 that require rework with a binomial distribution \($X\sim B(20,0.01)$\). We want to find the probability that the first sample at which X exceeds 1 occurs at hour 10. To do this, we need to compute two probabilities:
- The probability that in the first 9 samples, no sample has more than 1 part needing rework.
- The probability that in the 10th sample, there are at least 2 parts needing rework.
To compute the first probability, we use the binomial distribution with n=20 and p=0.01, and note that each of the first 9 samples is independent. Thus, the probability that no sample in the first 9 has more than 1 part needing rework is
\($$P(X\le 1)^9 = \left(\binom{20}{0}(0.01)^0(0.99)^{20} + \binom{20}{1}(0.01)^1(0.99)^{19}\right)^9 \approx 0.435$$\)
To compute the second probability, we just use the binomial probability mass function with n=20 and p=0.01:
\($$P(X\ge 2) = 1 - P(X=0) - P(X=1) \approx 0.0198$$\)
Finally, we can multiply these probabilities to get the desired probability:
\($P(\text{first sample with } X > 1 \text{ is at hour } 10) = 0.435\times 0.0198 \approx \boxed{0.0086}.$\)
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7 1/2 divided by 3/4 =
Answer:
10
Step-by-step explanation:
\(7 \frac{1}{2} \div \frac{3}{4} \\ \)
\( \frac{15}{2} \div \frac{3}{4} \\ \)
\( \frac{15}{2} \times \frac{4}{3} \\ \)
\( \frac{60}{6} = 10 \\ \)