Answer:
a. P(X=50)= 0.36
b. P(X≤75) = 0.9
c. P(X>50)= 0.48
d. P(X<100) = 0.9
Step-by-step explanation:
The given data is
x 25 50 75 100 Total
P(x) 0.16 0.36 0.38 0.10 1.00
Where X is the variable and P(X) = probabililty of that variable.
From the above
a. P(X=50)= 0.36
We add the probabilities of the variable below and equal to 75
b. P(X≤75) = 0.16+ 0.36+ 0.38= 0.9
We find the probability of the variable greater than 50 and add it.
c. P(X>50)= 0.38+0.10= 0.48
It can be calculated in two ways. One is to subtract the probability of 100 from total probability of 1. And the other is to add the probabilities of all the variables less than 100 . Both would give the same answer.
d. P(X<100)= 1- P(X=100)= 1-0.1= 0.9
URGENT!! EASY IM DUMB MY LAST QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
18. Using the diagram below as reference, write a paragraph proof to prove that the symmetric property of congruence exists for any two angles. (IMAGE BELOW)
Given: ∠A is congruent to ∠B
Prove: ∠B is congruent to ∠A
Plan: Show that ∠A and ∠B have the same measure, thus ∠B and ∠A have the same measure under symmetry for equality. Conclude with ∠B being congruent to ∠A.
Answer:
Below.
Step-by-step explanation:
Since A is congruent to B, you can conclude that B is congruent to A by the Reflexive Property of Congruence.
Please help me with this question, I need it to pass the class!!
Answer:
cos(20°)
Step-by-step explanation:
The "cofunction" is the function having the same value for the complement of the angle that this function has for the angle.
The cofunction of sine is cosine. The complement of 70° is 90° -70° = 20°.
sin(70°) = cos(20°)
I need the answers for 21 and 22
Answer:
21.b
22.c
Step-by-step explanation:
idk how to explain it lol I did mental math
Dustin is buying carpet for the living room. How many square feet of carpet will he need to buy?
Complete Question:
Dustin is buying carpet for the living room. If the length of the room is 21 ft and the width
is 11 ft, how many square feet of carpet does he need to buy?
Answer:
231 ft²
Step-by-step explanation:
==>GIVEN:
Length of room (L) = 21 ft
Width of room (W) = 11 ft
==>REQUIRED:
Square feet of carpet to be bought = area of the rectangular room
==>SOLUTION:
The room to be covered with carpet is rectangular in shape. In order to ascertain the square feet of carpet to be bought, we need to calculate the area of the room by using the formula for area of rectangle.
Thus, area of rectangle (A) = Length (L) × Width (W)
A = 21 × 11
A = 231 ft²
Square feet of carpet to be bought = 231 ft²
What’s the correct answer for this?
Answer:
D.
Step-by-step explanation:
Volume of cylinder = base area × height
25.5 = A × 4.8
A = 25.5/4.8
A = 5.3 inch ²
nancy will arrive at the hotel on July 8, and will stay three nights. What date will Nancy check out of the hotel?
Answer:
july 11
Step-by-step explanation:
Mr. Dylan asks his students throughout the year to record the number of hours per week they spend practicing math at
home. At the end of the year, he creates a scatter plot that models the relationship between exam score and time spent
practicing. Which line of best fit will give Mr. Dylan the most accurate linear equation in order to make predictions about
this relationship?
Answer:
see the attachment
Step-by-step explanation:
A "line of best fit" generally has about as much data above the line as below it. If the data has any trend, it generally follows the trend.
The best choice here is B.
Answer:Answer:
see the attachment
Step-by-step explanation:
A "line of best fit" generally has about as much data above the line as below it. If the data has any trend, it generally follows the trend.
The best choice here is B.
Step-by-step explanation:
A study conducted at a certain high school shows that 72% of its graduates enroll at a college. Find the probability that among 4 randomly selected graduates, at least one of them enrolls in college.
Answer:
[tex] P(X \geq 1) =1-P(X<1) =1-P(X=0) [/tex]
And we can use the probability mass function and we got:
[tex]P(X=0)=(4C0)(0.72)^0 (1-0.72)^{4-0}=0.00615[/tex]
And replacing we got:
[tex] P(X \geq 1) = 1-0.00615 = 0.99385[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of graduates who enroll in college", on this case we now that:
[tex]X \sim Binom(n=4, p=0.72)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
We want to find the following probability:
[tex] P(X \geq 1)[/tex]
And we can use the complement rule and we got:
[tex] P(X \geq 1) =1-P(X<1) =1-P(X=0) [/tex]
And we can use the probability mass function and we got:
[tex]P(X=0)=(4C0)(0.72)^0 (1-0.72)^{4-0}=0.00615[/tex]
And replacing we got:
[tex] P(X \geq 1) = 1-0.00615 = 0.99385[/tex]
What sit he shape of the cross section formed when’s. Cone intersects a plane as shown in the drawing?
Give me a reason why tok
Answer: Option D.
Step-by-step explanation:
Here we see the cross-section of a cone when it is cut by a plane that is parallel to the base of the cone.
As the plane is parallel to the base, we expect to see a figure that has the same shape as the base ( a circle) (you can think that over the plane we have a smaller cone, and the base of that cone also must be circular)
So the correct option is D.
Which number best represents the location of the point on the line?
X
-4.44
-T
11
3
_V17
RETRY
Answer:
- 11 over 3 Just did it on edg 2021
Does this table represent a function? Why or why not?
A.
B.
C.
D.
Answer:C
Step-by-step explanation:
the x value 5 corresponds to two difference y-values.
Which of the following sequence of transformations takes point J(9, 1) to J'(-3, 7)?
Answer:
Translate point J 12 units down and 6 units right.
Benjamin deposits $3,000 into each of two savings
accounts. The first savings account pays 5% interest
compounded annually. The second savings account
pays 5% simple interest annually. If Benjamin makes
no other deposits or withdrawals, what will be the
difference between the interest earned by the two
savings accounts after 4 years?
Answer:
So I have never stepped foot into this. But I have experience from this. So for the first one we can use the compound intrest formula - A = P(1+r/n)^nt so if we do that we get.
A = 3000(1+0.05/1)^1*4
So then we get A is equal to 3646.52
The next one we need to calculate
A = P (1 + rt)
So now we do A = 3000(1+0.05*1)
A = 3000*1.05 = 3150. We add them together and we get 6796.52.
So we subtract 6000 from that. He earned
796.52 dollars
Adam drew a line that was 6 4/10 inches long. If he drew a second line that was 2 2/3
inches longer, what is the length of the second line? Answer as a mixed number.
Answer:
The length of the second line is [tex]9\frac{1}{15}[/tex] inches
Step-by-step explanation:
Given
Length of first line = [tex]6\frac{4}{10}[/tex] inches
Length of second line = [tex]2\frac{2}{3}[/tex] inches longer
Required
Length of second line.
Let the length of the second line be represented by x.
From the question, x is [tex]2\frac{2}{3}[/tex] inches longer than the first line;
This implies that:
[tex]x = 2\frac{2}{3} + 6\frac{4}{10}[/tex]
Convert both fractions to improper fractions
[tex]x = \frac{8}{3} + \frac{64}{10}[/tex]
Take LCM
[tex]x = \frac{80 + 192}{30}[/tex]
[tex]x = \frac{272}{30}[/tex]
Convert to mixed fraction
[tex]x = 9\frac{2}{30}[/tex]
Reduce fraction to lowest term
[tex]x = 9\frac{1}{15}[/tex]
Hence, the length of the second line is [tex]9\frac{1}{15}[/tex] inches
for each sequence find the first 4 terms and the 10th term n+5 , , , , ...,
Answer:
10,15.20.25
Step-by-step explanation:
+5 in each number
5×100+4×10+6×1+2×(110)+8×(11000)
What is the number written in standard form?
Answer: 8.059
Explanation: It's the digit times the column heading.
Researchers want to know about the true proportion of adults with at least a high school education. 1000 adults are surveyed, and 710 of them have at least a high school education. Create a 95% confidence interval for the true population proportion of adults with at least a high school education. Interpret this interval in context of the problem.
Answer:
The 95% confidence interval for the true population proportion of adults with at least a high school education is (0.6819, 0.7381). This means that we are 95% sure that the true proportion of adults in the entire population surveyed with at least a high school education is (0.6819, 0.7381).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 1000, \pi = \frac{710}{1000} = 0.71[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.71 - 1.96\sqrt{\frac{0.71*0.29}{1000}} = 0.6819[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.71 + 1.96\sqrt{\frac{0.71*0.29}{1000}} = 0.7381[/tex]
The 95% confidence interval for the true population proportion of adults with at least a high school education is (0.6819, 0.7381). This means that we are 95% sure that the true proportion of adults in the entire population surveyed with at least a high school education is (0.6819, 0.7381).
Use the substitution and to rewrite the equations in the system in terms of the variables and . Solve the system in terms of u and v . Then back substitute to determine the solution set to the original system in terms of x and y.
-3/x+4/y=11
1/x-2/y=-5
Answer:
x = -1 and y = 1/2
Step-by-step explanation:
Let u = 1/x, and v = 1/y
Then the pair of equations
-3/x + 4/y = 11
1/x - 2/y = -5
Can be written as
-3u + 4v = 11 .................................(1)
u - 2v = -5......................................(2)
From (2)
u = 2v - 5 .......................................(3)
Substituting (3) into (1)
-3(2v - 5) + 4v = 11
-6v + 15 + 4v = 11
-6v + 4v = 11 - 15
-2v = -4
v = 4/2 = 2
Substituting this value of v in (3)
u = 2v - 5
u = 2(2) - 5
= 4 - 5
= -1
That is
u = -1, v = 2
Since u = 1/x, and v = 1/y, we have
1/x = -1
=> x = -1
And
1/y = 2
=> y = 1/2
Therefore
x = -1 and y = 1/2
Using the definition of the derivative, find f prime (x ). Then find f prime (1 ), f prime (2 ), and f prime (3 )when the derivative exists.
Step-by-step explanation:
We need the function f(x) to be able to determine the required.
Suppose we were given a function
f(x) = y
f'(x) represents the first derivative of the function f(x) = y.
f'(1) represents the value of the first derivative of the function f(x) = y after replacing x by 1.
f'(5) represents the value of the first derivative of the function f(x) = y after replacing x by 5.
Example: Suppose f(x) = x² + 3x, find
f'(x), f'(1), and f'(5).
f'(x) = 2x + 3
f'(1) = 2(1) + 3 = 5
f'(5) = 2(5) + 3 = 13
X and Y are both standard normal random variables (mean = 0, standard deviation = 1), statistically independent of each other. Using the DATA IN THE ATTACHED FILE, estimate the probability that X and Y are both positive and that their sum is less or equal to 1. This probability is
Answer:
The probability that X and Y are both positive and that their sum is less or equal to 1 0.64.
Step-by-step explanation:
It is provided that the random variables X and Y follows a standard normal distribution.
That is, [tex]X,Y\sim N(0, 1)[/tex]
It is also provided that the variables X and Y are statistically independent of each other.
Compute the probability that X and Y are both positive and that their sum is less or equal to 1 as follows:
The mean and standard deviation of X + Y are:
[tex]E(X+Y)=E(X)+E(Y)=0+0=0\\\\SD(X+Y)=\sqrt{V(X)+V(Y)+2Cov(X,Y)}=\sqrt{1+1+0}=\sqrt{2}[/tex]
The probability is:
[tex]P(X+Y\leq 1)=P(X+Y<1-0.50)\ [\text{Apply continuity correction}]\\[/tex]
[tex]=P(X+Y<0.50)\\\\=P(\frac{(X+Y)-E(X+Y)}{SD(X+Y)}<\frac{0.50-0}{\sqrt{2}})\\\\=P(Z<0.354)\\\\=0.63683\\\\\approx 0.64[/tex]
*Use the z-table.
Thus, the probability that X and Y are both positive and that their sum is less or equal to 1 0.64.
sarah can complete a project in 90 minutes and her sister betty can complete it in 120 minutes if they both work on the project at the same time how long will it take them to complete the project
Answer:
It will take them approximately 51.43 minutes to complete the project together
Step-by-step explanation:
This is what is called a "shared job" problem.
The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.
So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project
Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.
We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).
Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.
In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:
[tex]\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min[/tex]
So it will take them approximately 51.43 minutes to complete the project together.
1. OSHA is an agency responsible for workplace safety, read its rule and sketch a diagram that shows the proper relationship between the ladder, wall and ground
Completed Question
1. OSHA is an agency responsible for workplace safety, read its rule and sketch a diagram that shows the proper relationship between the ladder, wall and ground .
Rule: Non-self-supporting ladders, which must lean against a wall or other support, are to be positioned at such an angle that the horizontal distance from the top support to the foot of the ladder is about the 1/4 working length of the ladder.
2. Calculate the angle that the ladder makes with the ground using a trigonometric ratio.
3. If a ladder is x feet long, how high up a wall can it safely reach?
4. Would a 51-foot ladder be long enough to climb a 50-foot wall?
Answer:
(a)See attachment
(b)75.52 degrees
(c)[tex]Height ,h=\dfrac{x\sqrt{15}}{4} $ feet[/tex]
(d) NO
Step-by-step explanation:
Part 1
Let the length of the ladder =x
Since by the given rule, Horizontal Distance =[tex]\dfrac14$ of the length of the ladder[/tex]
Horizontal Distance = [tex]\dfrac14x[/tex]
In the sketch of the problem attached below,
The length of the ladder=ACHorizontal distance =BCPart 2
From Triangle ABC
[tex]\cos C=\dfrac{BC}{AC} \\\cos C=\dfrac{x/4}{x} \\\cos C=\dfrac{1}{4}\\ C=\arccos \dfrac{1}{4}\\C \approx 75.52^\circ[/tex]
The angle that the ladder makes with the ground is 75.52 degrees.
Part 3
If the ladder is x feet long
Using Pythagoras theorem in Triangle ABC below
[tex]x^2=(x/4)^2+h^2\\h^2=x^2-\dfrac{x^2}{16}\\ h^2=\dfrac{15x^2}{16}\\h=\sqrt{\dfrac{15x^2}{16}} \\h=\dfrac{x\sqrt{15}}{4}$ feet[/tex]
Part 4
If x=51 feet
[tex]Height ,h=\dfrac{51\sqrt{15}}{4}$ = 49.38 feet[/tex]
Therefore, a 51 feet ladder would not be enough to climb a 50 feet wall as it would violate the safety rule.
7. How much alcohol must be added to 480 grams of hand sanitizer that is 24% alcohol to
make it a hand sanitizer that is 40% alcohol? Correct your answer to the nearest whole
number
Answer:
the amount of alcohol to be added is 128 grams
Step-by-step explanation:
Given that:
The initial mass of the hand sanitizer = 480 grams
The initial strength of the hand sanitizer = 24 %
The new strength of the hand sanitizer = 40%
The objective here is to determine the final amount of alcohol that is to be added to get the new strength of the alcohol
First; let's find the mass of alcohol in the initial hand sanitizer;
SO;
= 24 % of 480
[tex]=\dfrac{24}{100}*480[/tex]
= 115.2 grams
If y should represent the mass of the alcohol added to have 40%; we have
The new amount of the alcohol to be[tex](115.2 + y) \ grams[/tex]
The new amount of the hand sanitizer will be[tex](480 + y) grams[/tex]
∴
For the new strength of sanitizer:
40 % of (480 + y) = (115.2 + y)
[tex]0.4 *(480 + y) = (115.2 + y) \\ \\ 192 + 0.4 y = 115.2 + y \\ \\ y (1 - 0.4) = 192 - 115.2 \\ \\ y= \dfrac{76.8}{0.6} \\ \\ y = 128 \ grams[/tex]
Thus ; we can conclude that the amount of alcohol to be added is 128 grams
Please answer this correctly
Answer:
Area of the figure = 254.5 cm²
Step-by-step explanation:
Area of rectangle = Length × Width
Area of triangle = 1/2(base × Height)
Dividing the figure into parts for convenience
So,
Rectangle 1 (the uppermost):
4 × 6 = 24 cm²
Rectangle 2 (below rectangle 1):
15 × 8 = 120 cm²
Rectangle 3 (with rectangle 2):
11 × 4 = 44 cm²
Triangle 1 :
1/2(7 × 19) = 133/2 = 66.5 cm²
Now adding up all to get the area of the figure:
Area of the figure = 24 + 120 + 44 + 66.5
Area of the figure = 254.5 cm²
For each of the following research scenarios, decide whether the design uses a related sample. If the design uses a related sample, identify whether it uses matched subjects or repeated measures.
1. You are interested in a potential treatment for compulsive hoarding. You treat a group of 50 compulsive hoarders and compare their scores on the Hoarding Severity scale before and after the treatment. You want to see if the treatment will lead to lower hoarding scores. The design described__________a, b, or c________.
a. uses a related sample - repeated measures
b. uses a related sample - matched subjects
c. does not use a related sample
2. John Caccioppo was interested in possible mechanisms by which loneliness may have deterious effects of health. He compared the sleep quality of a random sample to lonely people to the sleep quality of a random sample of nonlonely people. The design described______a, b, or c_______.
a. does not use a related sample
b. uses a related sample (repeated measures)
c. uses a related sample (matched subjects)
Answer:1. uses a related sample - repeated measures
2. . does not use a related sample--a
Step-by-step explanation:
Question 1.
step1 A repeated measure design is a design which measures a given sample repeatedly over a given time using different conditions or related measures.
step 2:In the treatment for compulsive hoarding, Here, measures are taken two times ie before and after treatment on the same 50 hoarders which shows a repeated measure, also the design is a within related sample of the same 50 hoarders to give measurement at different conditions of treatment for high and low hoarding scores so the design describes a related sample - repeated measures
Question 2:
step 1 ; An unrelated sample occurs when Samples being measured do not depend on each other
Step 2; 1st Sample for comparison by John are random lonely people and Second Sample are random non lonely people. so the two samples are independent on each other and will give different measurement based on quality of sleep. So the design does not use a related sample
what is the greatest common factor of 36 and 90?
Answer:
18
Step-by-step explanation:
The greatest common factor is 18. All of the common factors are: 1, 2, 3, 6, 9, 18.
Answer:
There is only one greatest common factor of 36 and 90 which is 18. There are also a number of common factors including 1, 2, 3, 6, 9, 18.
Step-by-step explanation:
A random sample pulled 43 catfish from a large lake. They were marked and released. A second sample pulled out 88 catfish. Seventeen had been marked. Calculate the estimated population
Answer: 114
Step-by-step explanation: You have 43 new catfish then you catch 88 but 17 of them have already been marked so you do not want to count those in the estimated population again because they have already been counted so you take 88 minus 17 and you get 71 new fish. So then you add the first new sample of fish 43 and then you add the second new sample of fish 71 and then you get 114
Rebecca Pearson is a widow and needs to take care of the expenses in her household. Her budget is below.
Find her net monthly cash flow. (Assume 1 month = 4 weeks)
Income Expenses
Salary: $2300/month
Rent: $1090/month
Groceries: $200/week
Utilities: $125/month
Car Insurance: $525 semiannually
Gasoline: $25/week
Miscellaneous: $200/month
Phone: $50/month
Hey there!
First, let's take all of the expenses and change the ones that aren't monthly into monthly.
Groceries: $800/month
Car insurance: $87.5/month
Gasoline: $100/month
Now, let's add together all of our expenses
1090+800+125+87.5+100+200+50=2452.5
Now, we subtract that from her salary.
2300-2452.5=-152.5
Therefore, Rebecca's net monthly cash flow is -$152.5. She should spend a bit less on groceries, not do so much miscellaneous, find a place that charges less rent, drive less, etc. so she isn't spending more than she earns.
I hope that this helps! Have a wonderful day!
Chris Evans drives 300 miles per week in his Honda Civic that gets 22 miles per gallon of gas. He
is considering buying a new fuel-efficient car for $20,000 (after trade-in of your Honda Civic)
that gets 50 miles per gallon. Insurance prerniums for the new car and old care are $900 and
$500 per year respectively. If he decides to keep his car, he will need to spend $1200 on repairs
per year. Assume gas costs $3.50 per gallon over a 5-year period,
a, what is the cost of the old car?
b. what is the cost of the new car?
Answer:
old car $20,909new car: $29,960Step-by-step explanation:
At 300 miles per week, Chris drives 300×52 = 15,600 miles per year. His gas cost can be figured as ...
(5 years)×(miles per year)÷(miles/gallon)×($ per gallon) = $273,000/(miles per gallon)
__
a) old car cost = repair cost + gas cost + insurance cost
= 5($1200) + $273,000/22 + 5($500) ≈ $20,909 . . . over 5 years
__
b) new car cost = purchase cost + gas cost + insurance cost
= $20,000 + $273,000/50 +5($900) = $29,960 . . . over 5 years
determine whether these two functions are inverses.
Answer:
Yes,these two functions are the inverse of each other.
Step-by-step explanation:
They way of finding if two functions ([tex]f(x)\,\,and\,\,g(x)[/tex] ) are the inverse of each other is by studying if their composition renders in fact the identity. That is, we see if:
[tex]f(x) \,o \,g(x)=f(g(x))=x[/tex]
in our case:
[tex]f(g(x))=\frac{1}{g(x)+4} -9\\f(g(x))=\frac{1}{(\frac{1}{x+9} -4)+4}-9\\f(g(x))=\frac{1}{\frac{1}{x+9} }-9\\f(g(x))={x+9} -9\\f(g(x))=x[/tex]
The composition does render the identity, therefore, these two functions are indeed the inverse of each other
