A college student is taking two courses. The probability she passes the first course is 0.67. The probability she passes the second course is 0.7. The probability she passes at least one of the courses is 0.79. Give your answer to four decimal places. a. What is the probability she passes both courses
Answer:
0.58 = 58% probability she passes both courses
Step-by-step explanation:
We can solve this question treating the probabilities as a Venn set.
I am going to say that:
Event A: She passes the first course.
Event B: She passes the second course.
The probability she passes the first course is 0.67.
This means that [tex]P(A) = 0.67[/tex]
The probability she passes the second course is 0.7.
This means that [tex]P(B) = 0.7[/tex]
The probability she passes at least one of the courses is 0.79.
This means that [tex]P(A \cup B) = 0.79[/tex]
a. What is the probability she passes both courses
This is [tex]P(A \cap B)[/tex].
We use the following relation:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
So
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.67 + 0.7 - 0.79 = 0.58[/tex]
0.58 = 58% probability she passes both courses
Determine whether the given procedure results in a binomial distribution. If not, state the reason why?
Rolling a single "loaded die 19 times, keeping track of the numbers that are rolled.
a. Not binomial: the trials are not independent.
b. Not binomial: there are more than two outcomes for each trial.
c. Procedure results in a binomial distribution.
d. Not binomial: there are too many trials.
Answer:
b. Not binomial: there are more than two outcomes for each trial.
Step-by-step explanation:
Binomial probability distribution:
We need
Fixed number of trials.
Independent trials.
Each trial can be reduced to a yes/no proposition.
Rolling a single "loaded die 19 times, keeping track of the numbers that are rolled.
There are six possible outcomes(1,2,3,4,5,6), so cannot be reduced to a yes/no proposition, and the answer is given by option b.
Amy and two of her friends eat lunch at a restaurant. Their bill, including tax, comes to $27.63. They decide to split the bill equally. Amy wants to leave a 20% tip for her portion. What is the total amount Amy should pay, including tip? Round to the nearest cent.
A chemist examines 17 sedimentary samples for lead concentration. The mean lead concentration for the sample data is 0.268 cc/cubic meter with a standard deviation of 0.069. Determine the 80% confidence interval for the population mean lead concentration. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
The critical value that should be used in constructing the confidence interval is T = 1.337.
The 80% confidence interval for the population mean lead concentration is between 0.246 and 0.29 cc/cubic meter.
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 17 - 1 = 16
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 16 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.8}{2} = 0.9[/tex]. So we have T = 1.337, which is the crical value.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.337\frac{0.069}{\sqrt{17}} = 0.022[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 0.268 - 0.022 = 0.246 cc/cubic meter
The upper end of the interval is the sample mean added to M. So it is 0.268 + 0.022 = 0.29 cc/cubic meter
The 80% confidence interval for the population mean lead concentration is between 0.246 and 0.29 cc/cubic meter
find the area of the shaded region under the
standard normal curve. If convenient, use technology to find the area
Answer
The area of the shaded region under the standard normal curve is 0.4834.
Step-by-step explanation:
A random variable X is said to have a normal distribution with mean, µ and variance σ².
Then , is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z N (0, 1).
The distribution of these z-variates is known as the standard normal distribution.
Compute the area under the curve between -2.13 and 0 as follows:
Thus, the area of the shaded region under the standard normal curve is 0.4834.
A 2.5-kg bag of grass seed covers an area of 1200 m2. How much seed is needed to cover a square park with side length 500 m?
Answer:
520.83 k g of seed
Step-by-step explanation:
Answer:
A #2.5#-#kg# bag of grass seed covers an area of #1200# #m^2#. How much seed is needed to cover a square park with side length #500# #m#?
Step-by-step explanation:
can you answer this
Answer:
B. 7ab²c
Step-by-step explanation:
The GCF of 21a²b^4c and 49ab²c³ is
7ab²c
Answer:
The correct answer is b.
A fish tank has 12 angelfish .out of every 8 fish 3 are angelfish. how many fish are in the tank?
12 fishes are in the tank
A fish tank has 12 angelfish .out of every 8 fish 3 are angelfish. how many fish are in the tank?
Answer:
Step-by-step explanation:
12angelfish(8fish/3angelfish)=32 fish
find the value of x. (geometry)
Answer:
18.02 units
Step-by-step explanation:
A twin-engined aircraft can fly 816 miles from city A to city B in 4 hours with the wind
and make the return trip in 6 hours against the wind. What is the speed of the wind?
Answer:
,mnl.khvmfjdrykytdd7ir rvrtuy
Step-by-step explanation:
Create and manipulate a data frame.
i) Create a `data.frame` named `my.trees` that has the following columns: - `
Girth = c(10.3, 10.6, 10.8, 13.5, 13.7, 13.8, 14.0)` - `
Height = c(70, 65, 63, 72, 81, 83, 66)` - `
Volume = c(10.3, 10.3, 10.2, 16.4, 18.8, 19.7, 15.6)`
ii) Extract the second observational unit.
iii) Extract the `Height` column referring to it by name.
iv) Print out a data frame of all the observations except for the firt observation.
Please answer! will mark brainilest eight tenths plus nine tenths equals
Answer:
it equals 17 tenths
Step-by-step explanation:
Answer:
the answer will be 0.7 for sure
Step-by-step explanation:
for the steps
the question is given as eight tenths i.e 0.8 and another is given nine tenth i.e 0.9
so when you calculate (add) both
0.8+0.9
gives
0.7
Please help i need to help
Answer:
4.25
Step-by-step explanation:
Step 1: 23-(17-12)²+6.25
Step 2: 23-5²+6.25
Step 3: 23-25+6.25
Chris works at a jewelry store, and he earns 4% commission on all sales that he makes. If Chris's jewelry sales total $1,370, how much will he earn in commission?
A portable basketball hoop is on sale for 25% off the original price of $142. What is the sale price?
Carla is fundraising for her school. She buys t-shirts for $7.50 each and then she sells the t-shirts with a markup of 150%. What is the selling price of each t-shirt?
Dinner costs $22.50. Apply sales tax of 9.5%. Then add a 20% tip to the after tax bill. What is the final cost of dinner?
Find the interest earned on a $125 investment at a 7.5% simple interest rate for 6 months? Use the formula I = Prt
Find the total account balance for a $400 investment that earns a 6% simple interest rate over a 5 year period. Use the formula I = Prt.
Sweatshirts are on sale for 35% off the regular price, x. What expression can be used to find the sale price of a sweatshirt.
Answer in order.
Consider the following hypothesis test. H0: μ ≥ 55 Ha: μ < 55 A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use α = 0.01.
(a) x = 54 and s = 5.3 Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
State your conclusion.
(b) x = 53 and s = 4.6
Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
(c) x = 56 and s = 5.0
Find the value of the test statistic.
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
Answer:
Step-by-step explanation:
Given that:
[tex]H_o: \mu \ge 55 \ \\ \\ H_1 : \mu < 55[/tex]
(a) For x = 54 and s = 5.3
The test statistics can be computed as:
[tex]Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }[/tex]
[tex]Z = \dfrac{54-55}{\dfrac{5.3}{\sqrt{36}} }[/tex]
[tex]Z = \dfrac{-1}{\dfrac{5.3}{6} }[/tex]
Z = -1.132
degree of freedom = n - 1
= 36 - 1
= 35
Using the Excel Formula:
P-Value = T.DIST(-1.132,35,1) = 0.1326
Decision: p-value is greater than significance level; do not reject [tex]\mathbf{H_o}[/tex]
[tex]Conclusion: \ There \ is \ insufficient \ evidence \ to \ conclude \ that \[/tex] [tex]\mu < 55[/tex]
b
For x = 53 and s = 4.6
The test statistics can be computed as:
[tex]Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }[/tex]
[tex]Z = \dfrac{53-55}{\dfrac{4.6}{\sqrt{36}} }[/tex]
[tex]Z = \dfrac{-2}{\dfrac{4.6}{6} }[/tex]
Z = -2.6087
degree of freedom = n - 1
= 36 - 1
= 35
Using the Excel Formula:
P-Value = T.DIST(-2.6087,35,1) =0.0066
Decision: p-value is < significance level; we reject the null hypothesis.
[tex]Conclusion: \ There \ is \ sufficient \ evidence \ to \ conclude \ that[/tex] [tex]\mu < 55[/tex]
c)
For x = 56 and s = 5.0
The test statistics can be computed as:
[tex]Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }[/tex]
[tex]Z = \dfrac{56-55}{\dfrac{5.0}{\sqrt{36}} }[/tex]
[tex]Z = \dfrac{56-55}{\dfrac{5.0}{\sqrt{36}} }[/tex]
Z = 1.2
degree of freedom = n - 1
= 36 - 1
= 35
Using the Excel Formula:
P-Value = T.DIST(1.2,35,1) = 0.88009
Decision: p-value is greater than significance level; do not reject [tex]\mathbf{H_o}[/tex]
[tex]Conclusion: \ There \ is \ insufficient \ evidence \ to \ conclude \ that \[/tex] [tex]\mu < 55[/tex]
7. Find the Value of x. SHOW YOUR WORK OR NO CREDIT!!!!!
Answer:
x=21.9317121994
Step-by-step explanation:
You just look at the half triangle and use the Pythagorean Theorem. One side of the triangle is 9 (half of 18), the other is 20, so you find the hypotenuse.
9²+20²=x²
81+400=x²
481=x²
√481=x
x=21.9317121994
Find the measure of angle 1
A. 90
B. 110
C. 180
Answer:
90°
Step-by-step explanation:
I need help with this can someone help
My work:
3x4=12
12+12=24
6-4=2
2+2+2=6
24÷6=4
Your answer:
4
Hope this helps!
-Alex
Answer:
18.
Step-by-step explanation:
3 x 4 = 12, 12 times 12 equals 144, 6 - 4 equals 2, and 2 times 2 times 2 is 8, and 144 / 8 = 18.
Why does paying off the highest interest rate credit card first make the most mathematical sense?
Answer:
Paying off the highest interest rate credit card first makes the most mathematical sense because it will save you more money and allow you to redirect funds to other financial goals faster. Paying off the highest interest rate first is better because this way you get to avoid financial problems and avoid having to pay too much money of interest since the card with the highest interest rate is usually the one that will cause you the most financial pain.
You treat your friend to lunch. The food bill was $30.24. A 7% sales tax will be added and you want to leave a 20% tip.
a. Find the sales tax.
b. Find the tip.
c. Find the total amount you pay for lunch.
Answer:
a. $2.12
b. $6.45
c. $38.81
Step-by-step explanation:
a.
I'll convert 30.24 and 7% into fractions.
756/25 * 7/100
Cross cancel 756 and 100 (GCF is 4)
189/25 * 7/25
Convert above into a single fraction
(189 * 7)/(25 * 25)
Multiply 189 by 7, then 25 by 25.
1323/625
Divide, then round to the nearest cent
$2.1168 ≈ $2.12 in sales tax
b.
Like before, I'll convert $32.26 ($30.24 + $2.12) and 20% into fractions.
1613/50 * 1/5
Multiply 50 by 5.
1613/250
Divide, then round to the nearest cent.
$6.452 ≈ $6.45 in tip money
c.
This is probably the simplest part of the 3. Just add $30.24 + $2.12 + $6.45.
$30.24 + $2.12 + $6.45
$32.36 + $6.45
You pay a total of $38.81 for lunch.
What is - 0.9 as a decimal
Answer: -0.9 as a decimal is -0.9
but if you meant as a fraction, then it's -9/10
Step-by-step explanation:
Answer:
0.9
Step-by-step explanation:
There Are Several Ways To Write 0.9.
1) 0.9
2)0.90
3)9/10
4)90/100
Hope this was able to help you!
-TheAnimeCatUwU
#LearnWithBrainly
A family of 4 bought 6 bags of peanut
Answer:
24
Step-by-step explanation:
Um. I guess you just multiply 6 x 4 and you get 24
Pls help me answer the question attached
Answer:
A.
Step-by-step explanation:
(2/3)*6.75=4.5
Math 7th grade... help pls thanks
Answer:
35
Step-by-step explanation:
1 bracelet costs $7
5 bracelets is 7*5=35
As we can see with the numbers they gave us every bracelet costs 7 dollars, 1 =7, 2=14 and so on. With this information we can just take the number 5 and multiply it by 7 which would equal 35. Or you could add 7 to 21 and then 7 to 28. Whichever one works for you.
Hope this helped
Mr. Alpert’s house has 40 windows. Kids playing baseball outside the house broke 10% of the windows.
Answer:
Step-by-step explanation:
Number of windows broken = 10% of 40
[tex]= \frac{10}{100}*40\\= 4[/tex]
Answer:
4 windows are broken
Step-by-step explanation:
Gabin takes care of the management of the electricity department of a DIY store. He contacts his wholesaler for an order of electrical products. The wholesaler tells him that the net purchase price will be E7,825, to which must be added a purchase charge of E 325 1. Indicate how to obtain the purchase cost. 2. Calculate the cost of purchasing electrical products.
Answer:
I have no clue.,...
.....
how many miles per hour does it take to go 160 miles in 4.5 hours
HI i need help i will give brainliest to correct answer.
Answer:
Top picture: 1/3
middle picture: 1
bottom picture: 1/2
Step-by-step explanation:
rise over run
The sum of eight and twice a number is 42
Answer:
8 + 2n = 42
Step-by-step explanation:
the sum of eight: ___+ 8
and twice(2) a number(could be any variable but for now i choose n): 2n + 8
is 42 (literally mean it equals 42): 2n + 8 = 42