Answers
Answer:
y=-1/2x+-1
Step-by-step explanation:
try desmos with this equation.
y=mx+b
m=the slope which is -1/2. It goes down 1 it is negative because it is going down, and to the right 2.
b=y-intercept meaning the point which the line crosses the line y .-1
Related Questions
five brothers of 4, 9, 11, 13 and 16 years respectively, receive an inheritance of 1,500,000, the will stipulated that that amount must be shared by the heirs so that, placed the shares in a bank, they would result in equal capitalized amounts, when each one reached 21, could raise his share. Knowing that the bank charges an interest rate of 9% per year, what is the amount of each share?
Answers
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Answer:
Youngest to oldest:
160,406.86246,805.83293,230.01348,386.58451,170.72Step-by-step explanation:
At 9% interest per year, the present value of 1 at age 20 is ...
p(a) = 1.09^(a-20)
Adding the present values for the different ages, we get a total of about 2.35528984846. Dividing the inheritance by that amount gives the multiplier for each of the present value numbers. The result is the list of shares shown above. At age 20, each brother will inherit about 636,864.29.
__
Additional comment
This is the sort of question that suggests the use of a graphing calculator or spreadsheet for doing the tedious number crunching.
(We assume the bank pays 9% per year, rather than charges 9% per year.)
Name this triangle by its sides and angles. This is a(n) ____________________ triangle.
A.obtuse, isosceles
B.right, scalene
C.obtuse, scalene
D.right, isosceles
Answers
Answer:
right scalene
Step-by-step explanation:
Since all three sides have different lengths , this is a scalene triangle
(isosceles means two sides have the same lengths and equilateral means all three sides have the same length)
We have a right angle indicated by the box in the corner
A record store owner finds that 20% of customers entering her store make a purchase. One morning 180 people, who can be regarded as a random sample of all customers, enter the store.
a. What is the mean of the distribution of the sample proportion of customers making a purchase?
b) What is the variance of the sample proportion?
c) What is the standard error of the sample proportion?
d) What is the probability that the sample proportion is less than 0.15?
Answers
Answer:
a) 0.2
b) 0.0009
c) 0.0298
d) 0.0465 = 4.65% probability that the sample proportion is less than 0.15.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
20% of customers entering her store make a purchase.
This means that [tex]p = 0.2[/tex]
180 people
This means that [tex]n = 180[/tex]
a. What is the mean of the distribution of the sample proportion of customers making a purchase?
By the Central Limit Theorem, [tex]\mu = p = 0.2[/tex].
b) What is the variance of the sample proportion?
The standard deviation is:
[tex]s = \sqrt{\frac{0.2*0.8}{180}} = 0.0298[/tex]
Variance is the square of the standard deviation, so:
[tex]s^2 = (0.0298)^2 = 0.0009[/tex]
c) What is the standard error of the sample proportion?
As found in the previous item, 0.0298.
d) What is the probability that the sample proportion is less than 0.15?
This is the p-value of Z when X = 0.15. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.15 - 0.20}{0.0298}[/tex]
[tex]Z = -1.68[/tex]
[tex]Z = -1.68[/tex] has a p-value of 0.0465.
0.0465 = 4.65% probability that the sample proportion is less than 0.15.
The automatic opening device of a military cargo parachute has been designed to open when the parachute is 185 m above the ground. Suppose opening altitude actually has a normal distribution with mean value 185 and standard deviation 32 m. Equipment damage will occur if the parachute opens at an altitude of less than 100 m. What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes
Answers
Answer:
0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.
Step-by-step explanation:
For each parachute, there are only two possible outcomes. Either there is damage, or there is not. The probability of there being damage on a parachute is independent of any other parachute, which means that the binomial probability distribution is used to solve this question.
To find the probability of damage on a parachute, the normal distribution is used.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Probability of a parachute having damage.
The opening altitude actually has a normal distribution with mean value 185 and standard deviation 32 m, which means that [tex]\mu = 185, \sigma = 32[/tex]
Equipment damage will occur if the parachute opens at an altitude of less than 100 m, which means that the probability of damage is the p-value of Z when X = 100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{100 - 185}{32}[/tex]
[tex]Z = -2.66[/tex]
[tex]Z = -2.66[/tex] has a p-value of 0.0039.
What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes?
0.0039 probability of a parachute having damage, which means that [tex]p = 0.0039[/tex]
5 parachutes, which means that [tex]n = 5[/tex]
This probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.0039)^{0}.(0.9961)^{5} = 0.9807[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.9807 = 0.0193[/tex]
0.0193 = 1.93% probability that there is equipment damage to the payload of at least one of five independently dropped parachutes.
A company that produces DVD drives has a 12% defective rate. Let X represent the number of defectives in a random sample of 55 of their drives.
Required:
a. What is the probability the sample will contain exactly 8 defective drives?
b. What is the probability the sample will contain more than 8 defective drives?
c. What is the probability the sample will contain less than 8 defective drives?
d. What is the expected number of defective drives in the sample?
Answers
Answer:
a) 0.1287 = 12.87% probability the sample will contain exactly 8 defective drives
b) 0.2092 = 20.92% probability the sample will contain more than 8 defective drives.
c) 0.6621 = 66.21% probability the sample will contain less than 8 defective drives.
d) The expected number of defective drives in the sample is 6.6
Step-by-step explanation:
For each DVD, there are only two possible outcomes. Either it is defective, or it is not. The probability of a DVD being defective is independent of any other DVD, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
A company that produces DVD drives has a 12% defective rate.
This means that [tex]p = 0.12[/tex]
Let X represent the number of defectives in a random sample of 55 of their drives.
This means that [tex]n = 55[/tex]
a. What is the probability the sample will contain exactly 8 defective drives?
This is [tex]P(X = 8)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{55,8}.(0.12)^{8}.(0.88)^{47} = 0.1287[/tex]
0.1287 = 12.87% probability the sample will contain exactly 8 defective drives.
b. What is the probability the sample will contain more than 8 defective drives?
This is:
[tex]P(X > 8) = 1 - P(X \leq 8)[/tex]
In which:
[tex]P(X \leq 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{55,0}.(0.12)^{0}.(0.88)^{55} = 0.0009[/tex]
[tex]P(X = 1) = C_{55,1}.(0.12)^{1}.(0.88)^{54} = 0.0066[/tex]
[tex]P(X = 2) = C_{55,2}.(0.12)^{2}.(0.88)^{53} = 0.0244[/tex]
[tex]P(X = 3) = C_{55,3}.(0.12)^{3}.(0.88)^{52} = 0.0588[/tex]
[tex]P(X = 4) = C_{55,4}.(0.12)^{4}.(0.88)^{51} = 0.1043[/tex]
[tex]P(X = 5) = C_{55,5}.(0.12)^{5}.(0.88)^{50} = 0.1450[/tex]
[tex]P(X = 6) = C_{55,8}.(0.12)^{6}.(0.88)^{49} = 0.1648[/tex]
[tex]P(X = 7) = C_{55,7}.(0.12)^{7}.(0.88)^{48} = 0.1573[/tex]
[tex]P(X = 8) = C_{55,8}.(0.12)^{8}.(0.88)^{47} = 0.1287[/tex]
So
[tex]P(X \leq 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.0009 + 0.0066 + 0.0244 + 0.0588 + 0.1043 + 0.1450 + 0.1648 + 0.1573 + 0.1287 = 0.7908[/tex]
[tex]P(X > 8) = 1 - P(X \leq 8) = 1 - 0.7908 = 0.2092[/tex]
0.2092 = 20.92% probability the sample will contain more than 8 defective drives.
c. What is the probability the sample will contain less than 8 defective drives?
This is:
[tex]P(X < 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)[/tex]
With the values we found in b.
[tex]P(X < 8) = 0.0009 + 0.0066 + 0.0244 + 0.0588 + 0.1043 + 0.1450 + 0.1648 + 0.1573 = 0.6621[/tex]
0.6621 = 66.21% probability the sample will contain less than 8 defective drives.
d. What is the expected number of defective drives in the sample?
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
In this question:
[tex]E(X) = 55(0.12) = 6.6[/tex]
The expected number of defective drives in the sample is 6.6
Which correlation best describes the data below. no correlation weak positive weak negative strong positive
Answers
Find the area of the plot of land shown below.
Answers
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Answer:
3070.06 square inches
Step-by-step explanation:
The area of the left triangle can be found using Heron's formula:
s = semiperimeter = (53+71+58)/2 = 91
area = √(s(s -53)(s -71)(s -58)) = √2282280 ≈ 1510.72
The area of the right triangle can be found using the trig formula ...
area = 1/2ab·sin(C)
area = 1/2(55)(71)sin(53°) ≈ 1559.34
Then the total area is ...
1510.72 +1559.34 = 3070.06 . . . . . square inches
Find x. Round your answer to the nearest tenth of a degree.
Answers
Answer: x=52.6°
Step-by-step explanation:
To find the value of x, we have to use our SOHCAHTOA. We can eliminate sine and cosine because both uses hypotenuse, which is not labelled. Therefore, we use tangent.
[tex]tan(x)=\frac{17}{13}[/tex]
To find x, we want to use inverse tangent.
[tex]x=tan^{-1}(\frac{17}{13} )[/tex] [plug into calculator]
[tex]x=52.6[/tex]
Now, we know that x=52.6°.
write your answer in simplest radical form
Answers
Answer:
c = 4√2
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 30
Opposite = 2√2
Hypothenus = c =?
We can obtain the value of c by using the sine ratio as illustrated below:
Sine θ = Opposite / Hypothenus
Sine 30 = 2√2 / c
½ = 2√2 / c
Cross multiply
c = 2 × 2√2
c = 4√2
Therefore, the value of c is 4√2.
5√48-4√27-2√108+√147
Answers
Answer:
[tex]3\sqrt{3}[/tex]
Step-by-step explanation:
The tires Mary wants to buy for her car cost $100 per tire. A store is offering the following deal. Buy a tire and get the 4th tire for 75% off! Mary will buy 4 tires using the deal. A sales tax of 8% will be charged after applying the discount. How much money will Mary saveby using the deal instead of paying the full price for all 4 tires?
Answers
she saved $162
hope it helps
In each figure below, find m<1 and m<2 if a is parallel to b. You don't have to show work.
please help i need this by tonight will give brainliest
Answers
Answer:
m <5 = 71 degrees.
m <8 = 109 degrees.
The volume of a gas with a pressure of 1.2 atm increases from 1.0 L to 4.0 L. What is the final pressure of the gas, assuming constant temperature?
(a) 1.2 atm
(b) 0.30 atm
(c) 3.3 atm
(d) 4.8 atm
(e) 1.0 atm
Answers
Answer:
(b) 0.30 atm
Step-by-step explanation:
Given data
Initial pressure= 1.2atm
Initial volume= 1.0L
Final volume= 4.0L
Final pressure= ???
Let us apply the gas formula to find the Final pressure
P1V1= P2V2
Substitute
1.2*1= x*4
Divide both sides by 4
1.2/4= x
x= 0.3atm
Hence the final pressure is 0.3 atm
Solve the following system of equations and show all your work y=2x^2 y=3x-1
Answers
Answer:
( 1/2 ; 1/2 ) and ( 1 ; 2 )
Step-by-step explanation:
y = 2x².............1
y = 3x-1............2
2x²=3x-1
2x²-3x+1 = 0
(2x-1)(x-1) = 0
x = 1/2 or x = 1
y = 1/2 or y = 2
are ratios 2:3 and 8:12 equalvelent to eachother
Answers
Answer:
2:3 is equal to 8:12
Step-by-step explanation:
2:3
To get the first number to 8
8/2 = 4
Multiply by all terms 4
2*3 : 3*4
8:12
2:3 is equal to 8:12
8:12 = 8/12
= 2/3
= 2:3
Therefore 2:3 and 8:12 are equalent to each other.
Answered by Gauthmath must click thanks and mark brainliest
which expression is equivalent to c^2 - 4 / c + 3 /
Answers
Step-by-step explanation:
[tex] \frac{ {c}^{2} - 4 }{c + 3} [/tex]
[tex] \frac{(c - 2)(c + 2)}{(c + 3)} [/tex]
Suppose that a customer is purchasing a car. He conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. He conducts this experiment 15 times on each car and records the number of miles driven.
Car 1 Car 2
214 220
245 221
239 244
224 225
220 258
295 259
Describe each data set, that is determine the shape, center, and spread
i. Sample mean for Car 1
ii. Sample mean for Car 2
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data :
Car 1 Car 2
214 220
245 221
239 244
224 225
220 258
295 259
Ordered data:
Car 1 : 214, 220, 224, 239, 245, 295
Sample mean = ΣX/ n ; n = sample size = 6
Sample mean = 1437 / 6 = 239.5
Median = 1/2(n+1)th term = 1/2(7) = 3.5th term
Median = (3rd + 4th) /2 = (224 + 239) /2 = 231.5
Sample standard deviation; √(Σ(x - xbar)²/n-1 ) = 29.60 (using calculator)
Car 2 : 220, 221, 225, 244, 258, 259
Sample mean = ΣX/ n ; n = sample size = 6
Sample mean = 1427 / 6 = 237.833
Median = 1/2(n+1)th term = 1/2(7) = 3.5th term
Median = (3rd + 4th) /2 = (225 + 244) /2 = 234.5
Sample standard deviation; √(Σ(x - xbar)²/n-1 ) = 18.21 (using calculator)
If a system including the quadratic equation representing the parabola and a linear equation has no solution, which linear equation could be the second equation in the system? A. 1/2x=y+4 B. 2x-y=0 C.y=6 D.y=2x+6
Answers
9514 1404 393
Answer:
D. y=2x+6
Step-by-step explanation:
The line cannot intersect the parabola if it has a y-intercept greater than 5 and a suitable slope. The only sensible answer choice is ...
y = 2x +6
Answer:
D. y = 2x + 6.
Step-by-step explanation:
The required equation would not intersect the parabola at any point.
The only one to fit that is D.
Base conversion. Perform the following conversion
675_10= ?___6
Answers
Answer:
3043 (base 6)
Step-by-step explanation:
216 36 6 1
3 0 4 3
216* 3 = 648
6*4 = 24
1*3 = 3
648+24+3 = 675
Help please. For the hign school basketball game, it costs $8 for every 4 tickets. Complete the table below showing the cost and the number of tickets.
Answers
Answer:
$2 for 1 ticket, 7 tickets for $14, $18 for 9 tickets, 10 tickets for $20
Step-by-step explanation:
Since we know that it $8 for 4 tickets, we can simplify the ratio down to 2:1, meaning that each ticket is $2.
You're welcome and good luck with your classes young one
What is the value of |-6|—|6|-(-6)?
The solution is
Answers
Answer:
6
Step-by-step explanation:
|-6| = 6
|6| = 6
- -6 = +6
so, we have
6 - 6 + 6 = 6
Identify the first 4 terms in the arithmetic sequence given by the explicit formula ƒ(n) = 8 + 3(n – 1).
Answers
Step-by-step explanation:
simple formula application :
a1 = 8 + 3×(1-1) = 8
a2 = 8 + 3×(2-1) = 11
a3 = 8 + 3×(3-1) = 14
a4 = 8 + 3×(4-1) = 17
...
Find the missing side of the triangle
Answers
Answer:
x = 7[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Pytago:
[tex]7^2 + 7^2 = x^2\\x = \sqrt{7^2 + 7^2} \\x = 7\sqrt{2}[/tex]
Step-by-step explanation:
In a right triangle, you can find the leg of the triangle by using the Pythagorean theorem.
[tex]a^2+b^2=c^2[/tex]
In this case, we have [tex]7^2+7^2=c^2[/tex], or
[tex]c^2=98[/tex]
[tex]\sqrt{98}[/tex]≅[tex]9.9[/tex]
What is the output of the function: f(x)=2x+5, if the input is 3?
Answers
Answer:
2*3+5=11
Step-by-step explanation:
Answer:
[tex]\boxed {\boxed {\sf 11}}[/tex]
Step-by-step explanation:
We are given the following function and asked to find the output if the input is 3.
[tex]f(x)= 2x+5[/tex]
The input is what is plugged into the function and its variable is x. The output is the result of plugging in the input and its variable is y.
Substitute 3 in for x,
[tex]f(3)= 2(3)+5[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Multiply 2 and 3.
[tex]f(3)= 6+5[/tex]
Add.
[tex]f(3)= 11[/tex]
If the input is 3, then the output is 11.
1 calculate the weight of a dog on the earth and on the moon if it has a mass of 28kg
Answers
To solve the problem.
W=m×g
W=28×10
W=280.
The weight of a dog on the surface of earth is 280N.
Answer:
274.68N and 45.36N respectively
Step-by-step explanation:
Weight of any object is the mass in kilograms(kg) multiplied by the gravity in meter per square second(m/s^2). The gravity on earth is 9.81m/s^2 and on moon is 1.62m/s^2...so since the gravity varies the weight of the dog will also vary. The wight on earth would be 28kg multiplied by 9.81m/s^2 which would be 274.68N and the weight on moon would be 28kg multiplied by 1.62m/s^2 which would be 45.36N.
Emily, Yani and Joyce have a total of 3209 stickers. Yani has 2 times
as many stickers as Joyce. Emily has 279 more stickers than Yani. How
many more stickers does Emily have than Joyce?
Answers
Answer:
279+x
Step-by-step explanation:
Emily + Yani + Joyce=3209 stickers
if Yani has 2 times as many stickers as Joyce:this statement states that Joyce has x stickers and Yani has 2x stickers because x multiplied by 2"Emily has 279 more stickers than Yani":therefore the equation for Emily will be ;279+2xhow many stickers does Emily have than Joyce:
(279+2x)-(x)
279+2x-x
=279+x
Juan had 5 candy bars for himself and 4 friends to share with after lunch. Then three other friends joined them. Juan divided the 5 candy bars equally with all of his friends. How much did each person get?
Answers
Answer:
5/8
Step-by-step explanation:
There are 5 people when 3 more join for a total of 8 people
5 candy bars divided by 8 people
Take the candy bars and divide by the people
5/8
Please help explanation if possible
Answers
Answer:
17.3
Step-by-step explanation:
14.4 x 1.2
= 17.28
= 17.3 ( approximately )
The scores on an entrance exam to a university are known to have an approximately normal distribution with mean 65% and standard deviation 7.1%. What is the standardized score for a student who scores 60% on this test?
A. -0.70
B. 0.70
C. 1.88
D. -1.88
Answers
A store has x packages of 4 markers and y packages of 12 markers. The store has a total of 192 markers in
stock. If there are 21 packages of 4 markers in the store, how many packages of 12 markers are there?
Answers
Sh363gdbzej3yve truly urban urge Heydyeh hdye
