Answer:
0.12 = 12% probability that a randomly selected person likes both juices.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
We solve this question treating these events as Venn probabilities.
I am going to say that.
Event A: Like orange juice.
Event B: Like grape juice.
In a survey 125 people, 90 people liked orange juice or grape juice.
This means that:
[tex]P(A \cup B) = \frac{90}{125}[/tex]
62 people who like orange juice and 43 people who like grape juice.
This means that:
[tex]P(A) = \frac{62}{125}, P(B) = \frac{43}{125}[/tex]
What is the probability that a randomly selected person likes both juices?
This is [tex]P(A \cap B)[/tex], which is given by:
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex].
With the values in this problem:
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B) = \frac{62}{125} + \frac{43}{125} - \frac{90}{125} = \frac{62 + 43 - 90}{125} = \frac{15}{125} = 0.12[/tex]
0.12 = 12% probability that a randomly selected person likes both juices.
thirty 5 points for this answer. no links.
4(a-2) = 2(a-4) + 2a
Answer:
a = 0
Step-by-step explanation:
4(a-2) = 2(a-4) + 2a
4a - 8 = 2a - 8 + 2a
4a - 2a - 2a = -8 + 8
0 = 0
This has infinitely many solutions.
Step-by-step explanation:
Any number you put for a would work to make them equal. Feel free to try it.
6. Find the area of the segment. (the shaded region)
There are two pieces we need to find here: the area of the section of the circle, and the area of the triangle.
Area of the section of the circle:
A = pi * r^2
A = pi * 15^2
A = 225pi * 72/360 || We only need this part of the circle, not the whole thing.
A = 45pi
Area of the triangle:
A = 1/2 * a * b * sin(c)
A = 1/2 * 15 * 15 * sin(72)
A = 112.5 * sin(72)
Next, we need to subtract the area of the triangle from the area of the section of the circle.
A = 45pi - (112.5 * sin(72))
A = 112.8165 units^2 -- Feel free to round off wherever you need!
Hope this helps!! :)
What combination of transformations is shown below?
Answer:
translation then rotation
A survey of nonprofit organizations showed that online fundraising increased in the past year. Based on a random sample of 60 nonprofit organizations, the mean one-time gift donation in the past year was $75, with a standard deviation of $12. If you test the null hypothesis at the 0.05 level of significance, is there evidence that the mean one-time gift donation is greater than $70?
Answer:
The p-value of the test is 0.001 < 0.05, which means that there is evidence at the 0.05 level of significance that the mean one-time gift donation is greater than $70.
Step-by-step explanation:
Test if the mean one-time gift donation is greater than $70:
At the null hypothesis, we test if it is 70 or less, that is:
[tex]H_0: \mu \leq 70[/tex]
At the alternate hypothesis, we test if it is greater than 70, that is:
[tex]H_1: \mu > 70[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
70 is tested at the null hypothesis:
This means that [tex]\mu = 70[/tex]
Based on a random sample of 60 nonprofit organizations, the mean one-time gift donation in the past year was $75, with a standard deviation of $12.
This means that [tex]n = 60, X = 75, s = 12[/tex].
Test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{75 - 70}{\frac{12}{\sqrt{60}}}[/tex]
[tex]t = 3.23[/tex]
P-value of the test:
The p-value of the test is the probability of finding a sample mean above 75, which is a right-tailed test with t = 3.23 and 60 - 1 = 59 degrees of freedom.
Using a t-distribution calculator, this p-value is of 0.001.
The p-value of the test is 0.001 < 0.05, which means that there is evidence at the 0.05 level of significance that the mean one-time gift donation is greater than $70.
what is the median of 72 27 24 11 14 and 12
Answer: 19
Step-by-step explanation: Since there is no one middle number we have to find the mean of the two middle numbers. Once you find the mean for 24 and 11 you will see that the answer is 19.
Answer:
The median is the middle number in numerical order.
Numerical order - [tex]11,12,14,24,27,72[/tex]
There are 6 numbers.
The median is 19.
Chromium 51 is a radioactive substance used in medicine. It has a 1/2 life of 28 days. The equation for its exponential decay model is `y=a(.5)^t/28 If 10 mg is ingested by a patient, how many days before only 8 mg is still emitting radiation?
Answer:
9 days before only 8 mg is still emitting radiation.
Step-by-step explanation:
The exponential model is:
[tex]y(t) = a(0.5)^{\frac{t}{28}}[/tex]
In which a is y(0), that is, the initial quantity.
10 mg is ingested by a patient
This means that [tex]a = 10[/tex], and thus:
[tex]y(t) = 10(0.5)^{\frac{t}{28}}[/tex]
How many days before only 8 mg is still emitting radiation?
This is t for which y(t) = 8. So
[tex]y(t) = 10(0.5)^{\frac{t}{28}}[/tex]
[tex]8 = 10(0.5)^{\frac{t}{28}}[/tex]
[tex](0.5)^{\frac{t}{28}} = \frac{8}{10}[/tex]
[tex](0.5)^{\frac{t}{28}} = 0.8[/tex]
[tex]\log{(0.5)^{\frac{t}{28}}} = \log{0.8}[/tex]
[tex](\frac{t}{28})\log{0.5} = \log{0.8}[/tex]
[tex]\frac{t}{28} = \frac{\log{0.8}}{\log{0.5}}[/tex]
[tex]t = 28\frac{\log{0.8}}{\log{0.5}}[/tex]
[tex]t = 9[/tex]
9 days before only 8 mg is still emitting radiation.
If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate (in cm/min) at which the diameter decreases when the diameter is 10 cm. (Round your answer to three decimal places.)
Answer:
The diameter decreases at a rate of 0.143cm/min when it is of 10 cm.
Step-by-step explanation:
Surface area of an snowball:
An snowball has spherical format. The surface area of an sphere is given by:
[tex]S = d^2\pi[/tex]
In which d is the diameter of the sphere.
In this question:
We need to differentiate S implicitly in function of time. So
[tex]\frac{dS}{dt} = 2d\pi\frac{dd}{dt}[/tex]
Surface area decreases at a rate of 9 cm2/min
This means that [tex]\frac{dS}{dt} = -9[/tex]
At which the diameter decreases when the diameter is 10 cm?
This is [tex]\frac{dd}{dt}[/tex] when [tex]d = 10[/tex]. So
[tex]\frac{dS}{dt} = 2d\pi\frac{dd}{dt}[/tex]
[tex]-9 = 2(10)\pi\frac{dd}{dt}[/tex]
[tex]\frac{dd}{dt} = -\frac{9}{20\pi}[/tex]
[tex]\frac{dd}{dt} = -0.143[/tex]
Area in cm², so diameter in cm.
The diameter decreases at a rate of 0.143cm/min when it is of 10 cm.
Which statements are always true
about ABCD? Select all that apply.
Answer:
It doesn't show the statements so I'll create some.
Step-by-step explanation:
ABCD make a shape with 2 pairs of parallel lines.
ABCD when broken apart can create 4 triangles
Write a sine function that has a midline of 4, an amplitude of 2 and a period of 5
571
Yoko started an assignment at 8:34 AM and finished it at 9:21 AM.
How long did it take her? Give your answer in minutes.
Answer:
She started at 8:34 and finished at 9:21, with some simple math.. the answer is 47 minutes
Question 1 of 5
Select the correct answer.
Consider functions f and g, where function g is a transformation of function f.
Which statement correctly describes a transformation on the graph of function f to arrive at the graph of function g?
The graph of function f is shifted 3 units to the right.
The midline of function f is shifted 3 units down.
The graph of function f is reflected over the x-axis.
The amplitude of function f is vertically stretched by a factor of 3.
Answer:
The graph of function f is shifted 3 units to the right.
Step-by-step explanation:
Sample Answer from Edmentum
Answer:
The graph of function f is shifted 3 units to the right.
Step-by-step explanation:
Plato/Edmentum
There was a seller of horses, who sold all his horses to three people. To the first man he sold half of all his horses and a half of a horse. To the second man he sold half of what he had left and a half of a horse. To the third man he again sold half of what was left and a half of a horse. How many horses did he have at first? (No horses were harmed!)
Answer:
7
Step-by-step explanation:
3RD MAN: 1
2ND MAN: 2
1ST MAN: 4
3rd Man = 1/2+1/2 = 1
2nd Man = 1+1 = 2
1st Man = 2*2 = 4
What is the factored form of 250x3 − 16?
Answer:
Step-by-step explanation:
250x^3-16
2(125x^3-8)
2[(5x)^3-(2)^3]
2(5x-3)[(5x)^2+5x*3+(2)^2]
2(5x-3)(25x^2+15x+4)
Which expression is equivalent to (3a)-2
Answer:
1/9a2
Step-by-step explanation:
I'm not sure if there's supposed to be a list of answers, but 1/9a2 is one. Hope this helps! Let me know if there was supposed to be a list.
Answer:
removing of bracket
Step-by-step explanation:
(3a)-2
3a×(-2)
-6a
SOMEBODY PLEASE HELP I NEED THIS ASAP
Answer:
a = 1000 cm²
Step-by-step explanation:
Center square
20 * 20 = 400cm²
------------------------
Triangle side
a = (1/2)(20)(15)
a = 150
There are 4 sides
a = 4 * 150
a = 600 cm²
-----------------------
Total area
a = 400 - 600
a = 1000 cm²
PLEASE HELP IM BEING TIMED
Find the difference when we subtract 38,40,159 from the number formed by reversing its digits.
Answer:
5,670,279
Step-by-step explanation:
3,840,159 reversed is, 9,510,483 so, 9,510,483 - 3,840,159 = 5,670,279
Convert 7 pounds 3 ounces to kilograms.
Conversion ratios:
1 lb = 16 OZ
1 kg = 2.2 lb
Answer:
3.3
Step-by-step explanation:
7lb 3oz
3oz/16oz=.1875lb
7lb+.1875lb=7.1875lb
7.1875lb/2.2kg=3.27kg
I need the work and answers fast
A disc is thrown into the air with an upward velocity of 20 ft/s. It's
height h in feet after t seconds is given by the function h=-16t^2+20t+6.
1. How long will it take the disc to reach the maximum height?
2. What is the maximum height that the disc reaches?
3. How long does it take for the disc to hit the ground?
Thank you
Simplify. State any restrictions on the variables.
[tex]\frac{x^2+9x+18}{x+6}[/tex]
Answer: [tex]x+3, x \neq -6[/tex]
Step-by-step explanation:
The denominator cannot equal 0, so [tex]x \neq -6[/tex].
Simplfying,
[tex]\frac{x^2 +9x+18}{x+6}=\frac{(x+6)(x+3)}{x+6}=x+3[/tex]
What are the solutions to the quadratic equation x2-16=0
Answer:
x = -4, 4
Step-by-step explanation:
Hi there!
[tex]x^2-16=0[/tex]
Rewrite 16:
[tex]x^2-4^2=0[/tex]
The difference of squares rule states that [tex]a^2-b^2=(a+b)(a-b)[/tex]. With this, apply the difference of squares to the equation:
[tex](x+4)(x-4)=0[/tex]
The zero-product property states that if the product of two numbers is 0, then one of the numbers must be equal to zero. Set each term equal to 0 and find the solutions:
[tex]x+4=0\\x=-4[/tex]
[tex]x-4=0\\x=4[/tex]
Therefore, the solutions are -4 and 4.
I hope this helps!
Plz help me well mark brainliest if correct...???
Answer:
D) 225
Step-by-step explanation:
Given in chart. The box at column "Milk Sold" and row "Friday" has the number 225 in it. Cumulative milk sold refers to the total number of milk sold through the entire chart (from top to bottom) so far. The question is asking for how many milks were sold on Friday specifically, so we want the "Milk Sold" column.
According to the Centers for Disease control and prevention, 20.8 of high school students currently use electronic cigarettes. A high school counselor is concerned that the use of e-cigs at her school is higher.
(a) Determine the null and alternative hypotheses.
(b) If the sample data indicate that the null hypothesis should not be rejected, state the conclusion of the school counselor.
(c) Suppose, in fact, that the proportion of students at the counselor's high school who use electronic cigarettes is 0.034. Was a Type I or Type II error committed?
Answer:
H0 : p = 0.028
H1: p > 0.028
We conclude that there is not enough evidence to support the school counselor's claim they the use of electronic cigarettes in high school is higher Than 2.8%
Type 11 error
Step-by-step explanation:
H0 : p = 0.028
H1: p > 0.028
If null should not be rejected then;
We conclude that there is not enough evidence to support the school counselor's claim they the use of electronic cigarettes in high school is higher Than 2.8%
3.)
If the actual proportion is 0.034, which means 3.4%, this means it is actually higher. For failing to reject a false Null, then a type 11 error has been committed
pls help!! correct answer will be marked brainliest
Answer:
67.7
Step-by-step explanation:
Because it is the exact same as 67.7 angle n is. So it is 67.7 I went over this recently so I understand your pain!
(5) A sports drink bottle contains 16.9 fluid ounces. Andre drank 80% of the bottle. How many fluid ounces did Andre drink? Show your reasoning.
Your answer
Submit
13.52 fluid were drunk by Andre
Which is the m WZY? Need quick answers!!
Answer:
B. 55°
Step-by-step explanation:
Recall: relationship between inscribed angle and the measure of the intercepted arc [(inscribed angle = ½(intercepted arc)]
Inscribed angle = m<WZY
Intercepted arc = arc WY = 110°
Therefore:
m<WZY = ½110°)
m<WZY = 55°
50 POINTS !
PLEASE HELP ILL GIVE BRAINLIEST !! EXPLAIN YOUR ANSWER .
FAKE ANSWERS WILL GET REPORTED.
Answer:
cap it's only 5
Step-by-step explanation:
Answer:
I think she drove 65 mile.
Step-by-step explanation:
I used a piece of paper and drew a triangle. One side 25 and another 60.
Then i used the Pythagorean theorem.
Identify the two pairs of complementary angles in the figure above. Justify your answer.
Answer:
1st pair of complementary angles: ∠c + ∠d
2nd pair of complementary angles: ∠g + ∠h
Step-by-step explanation:
the two solid lines are perpendicular, creating 4 right angles
1st pair of complementary angles: ∠c + ∠d
2nd pair of complementary angles: ∠g + ∠h
450 high school freshmen were randomly selected for a national survey. Among survey participants, the mean grade-point average (GPA) was 2.96, and the standard deviation was 0.21. What is the margin of error, assuming a 70% confidence level, to the nearest hundredth
Answer:
The margin of error is of 0.01.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.7}{2} = 0.15[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.15 = 0.85[/tex], so Z = 1.037.
The margin of error is of:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation was 0.21.
This means that [tex]\sigma = 0.21[/tex]
Sample of 450:
This means that [tex]n = 450[/tex]
What is the margin of error, assuming a 70% confidence level, to the nearest hundredth?
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 1.037\frac{0.21}{\sqrt{450}}[/tex]
[tex]M = 0.01[/tex]
The margin of error is of 0.01.
What is the domain of the function y=7x-1
Answer:
Ahh I did this about a year ago but try math-way (without -) it gives the correct answers sorry I couldn't help more.