Answer:
(a) The value of a is 53.35.
(b) The value of a is 38.17.
(c) The value of a is 26.95.
(d) The value of a is 25.63.
(e) The value of a is 12.06.
Step-by-step explanation:
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{55-22}=\frac{1}{33}[/tex]
Here, 22 < X < 55.
(a)
Compute the value of a as follows:
[tex]P(X\leq a)=\int\limits^{a}_{22} {\frac{1}{33}} \, dx \\\\0.95=\frac{1}{33}\cdot \int\limits^{a}_{22} {1} \, dx \\\\0.95\times 33=[x]^{a}_{22}\\\\31.35=a-22\\\\a=31.35+22\\\\a=53.35[/tex]
Thus, the value of a is 53.35.
(b)
Compute the value of a as follows:
[tex]P(X< a)=\int\limits^{a}_{22} {\frac{1}{33}} \, dx \\\\0.95=\frac{1}{33}\cdot \int\limits^{a}_{22} {1} \, dx \\\\0.49\times 33=[x]^{a}_{22}\\\\16.17=a-22\\\\a=16.17+22\\\\a=38.17[/tex]
Thus, the value of a is 38.17.
(c)
Compute the value of a as follows:
[tex]P(X\geq a)=\int\limits^{55}_{a} {\frac{1}{33}} \, dx \\\\0.85=\frac{1}{33}\cdot \int\limits^{55}_{a} {1} \, dx \\\\0.85\times 33=[x]^{55}_{a}\\\\28.05=55-a\\\\a=55-28.05\\\\a=26.95[/tex]
Thus, the value of a is 26.95.
(d)
Compute the value of a as follows:
[tex]P(X\geq a)=\int\limits^{55}_{a} {\frac{1}{33}} \, dx \\\\0.89=\frac{1}{33}\cdot \int\limits^{55}_{a} {1} \, dx \\\\0.89\times 33=[x]^{55}_{a}\\\\29.37=55-a\\\\a=55-29.37\\\\a=25.63[/tex]
Thus, the value of a is 25.63.
(e)
Compute the value of a as follows:
[tex]P(1.83\leq X\leq a)=\int\limits^{a}_{1.83} {\frac{1}{33}} \, dx \\\\0.31=\frac{1}{33}\cdot \int\limits^{a}_{1.83} {1} \, dx \\\\0.31\times 33=[x]^{a}_{1.83}\\\\10.23=a-1.83\\\\a=10.23+1.83\\\\a=12.06[/tex]
Thus, the value of a is 12.06.
Eighty-five percent of the people that use the Internet order something online. Find the probability that only 7 of 10 Internet users will order something online
Answer:
the probability that 7 out 10 Internet users will order something online is 0.78 or 78%
Step-by-step explanation:
Given that:
Internet users who order something online = 85%
To find:
Probability that 7 out of 10 Internet users will order something online ?
Solution:
This problem is of binomial distribution of probability.
where, p = 0.85
q = 1-p = 0.15
r = 7 and
n = 10
Formula is given as:
[tex]P(x = r) = _nC_r q^{n-r}p^r[/tex]
Putting all the values:
[tex]P(x = 7) = _{10}C_7 0.15^{10-7}\times 0.85^7\\P(x = 7) = _{10}C_3 0.15^{3}\times 0.85^7\\P(x = 7) = 10\times 9 \times 8 \times 0.15^{3}\times0.85^7\\P(x = 7) = 720 \times .0034 \times0.32\\P(x = 7) = 0.78[/tex]
So, the probability that 7 out 10 Internet users will order something online is 0.78 or 78%.
Michelle, a student studying music, randomly sampled fellow music majors and asked whether they listen to music while they study. The resulting confidence interval for the proportion of music students who listen to music while studying is (0.09,0.26). What is the margin of error?
Answer:
The margin of error of this confidence interval is MOE=0.085.
Step-by-step explanation:
The confidence interval bounds are usually calculated from a sample statistic substracting (for the lower bound) or adding (for the upper bound) the margin of error. This margin of error depends on the confidence level, the standard deviation and the sample size.
Then, if the lower and upper bound are calculated this way, we can calculate the margin of error as:
[tex]LB=p-MOE\\\\UB=p+MOE\\\\UB-LB=(p+MOE)-(p-MOE)=2\cdot MOE\\\\\\MOE=\dfrac{UB-LB}{2}=\dfrac{0.26-0.09}{2}=\dfrac{0.17}{2}=0.085[/tex]
11- In
how many ways 3 mathematics books, 4 history books ,3
chemisidy books and a biology books can be arranged
on an Shelf so thet all books of the same subjects are
together!
Answer: 20,736
Step-by-step explanation:
Math and History and Chemistry and Biology and Subjects
3! x 4! x 3! x 1! x 4! = 20,736
What steps would you take to determine if these figures are similar? Check all that apply. Use a scale factor of 2. Multiply the vertices of polygon ABCD by One-half. Translate the intermediate image 4 units down. Perform two different dilations. Reflect the intermediate image.
Answer:
Well I took it"s Reflect the intermediate image. and Multiply the vertices of polygon ABCD by One-half.
Step-by-step explanation:
Answer:
2 and 5 or B and E
Step-by-step explanation:
i did it on edge! ; )
Find the circumference of a circle with a radius of 15 centimeters. Round your answer to the nearest centimeter
Answer:
94 cm
Step-by-step explanation:
The formula for finding the circumference of a circle is;
Circumference = 2πr
where π = [tex]\frac{22}{7}[/tex] or 3.14 and
r = radius
Here radius is 15 cm so;
Circumference = [tex]2 * \frac{22}{7} * 15[/tex]
= [tex]\frac{660}{7}[/tex]cm
= 94.28cm
= 94 cm ( rounded to the nearest centimetre )
Which of the following are exterior angles? Check all that apply.
Answer:<5 and <4 are exterior angles
Step-by-step explanation:
Because they are the only ones outside it they are the only ones that are exterior angles!
<!> Brainliest is appreciated! <!>
Answer:
for AL Its 3 and 4
How many ways can a 4-person subcommittee be selected from a committee of 6 people? (B) How many ways can a president comma vice dash president comma secretary comma and treasurer be chosen from a committee of 6 people?
Answer:
A) 360
B) 360
Step-by-step explanation:
Part A)
Given that there are a total of 6 people and 4 person subcommittee is to be selected.
Number of ways to select 1st person = 6
Now, 1 person is selected, total persons left are 5
Number of ways to select 2nd person = 5
Now, 1 person is selected, total persons left are 4
Number of ways to select 3rd person = 4
Now, 1 person is selected, total persons left are 3
Number of ways to select 4th person = 3
So, total number of ways = 6[tex]\times[/tex]5[tex]\times[/tex]4[tex]\times[/tex]3 = 360
Part B)
Given that there are a total of 6 people in the committee
Number of ways to select president = 6
Now, 1 person is selected, total persons left are 5
Number of ways to select vice president = 5
Now, 1 person is selected, total persons left are 4
Number of ways to select secretary = 4
Now, 1 person is selected, total persons left are 3
Number of ways to select treasurer = 3
So, total number of ways = 6[tex]\times[/tex]5[tex]\times[/tex]4[tex]\times[/tex]3 = 360
which graph is the solution to lx| > 10? HELP PICTURE INCLUDED
Answer:
Its the first answer choice.
Step-by-step explanation:
Its open circle because the sign is just greater than. And since x is an absolute value, the negative sign doesnt matter so, it points to the right of 10 and to the left of -10.
Help me pls pls pls pls
Answer:
Inequality Form:
x≥130
Step-by-step explanation:
isolate the variable by dividing each side by factors that don’t contain the variable.
In her last semester at SPC, Polly Hedron needs to take Statistics, Composition 2, Ethics, and Physics. Because Polly is registering early, she has 14 choices for her section of Statistics, 12 choices for her section of Composition, 11 choices for her section of Ethics, and 18 choices for her section of Physics. From how many possible schedules can Polly choose? (You may presume that none of these sections interfere with each other)
Answer:
Polly can choose 33264 schedules.
Step-by-step explanation:
None of these sections interfere with each other, so:
For each statistics choice, there are 12 composition choices.
For each composition choice, there are 11 section of Ethics choices.
For each section of Ethics choice, there are 18 Physics choises.
There are 14 statistics choices.
From how many possible schedules can Polly choose?
14*12*11*18 = 33264
Polly can choose 33264 schedules.
which expression defies the arithmetic series 10 + 7 + 4 ... for six terms?
Answer:
[tex]a_n = 10-3(n - 1)[/tex]
10 + 7 + 4 + 1 + -2 + -5
Step-by-step explanation:
Explicit Arithmetic Formula: [tex]a_n = a_1 + d(n-1)[/tex]
To find d, take the common difference between 2 numbers.
To find the other terms of the sequence, plug them into the explicit formula or subtract 3 from the given numbers.
How many meters are in 18,200 milliliter
Answer:
18.2 :)
Have a great day!!!
The cube of a number is less than five times the square of the number. For what set of numbers is this true?
(–ꝏ, 5)
(5, ꝏ)
(–ꝏ, 0) U (0, 5)
(–ꝏ, 5) U (5, ꝏ)
Answer:
(–ꝏ, 0) U (0, 5)
Step-by-step explanation:
The relation can be written as ...
x³ < 5x²
x³ -5x² < 0
x²(x -5) < 0
This is not true for x = 0. It is true for x < 5, otherwise. Then the solution set is ...
x ∈ {(–ꝏ, 0) U (0, 5)}
Answer:
C
Step-by-step explanation:
got it right on edge
how to simplify -8+5w=27
Answer:
w=7
Step-by-step explanation:
1. -8+5w=27
2. add 8 to both sides: 8+-8+5w=27+8
3. Simplify: 5w=35
4. Divide both sides by 5: 5w/5=35/5
5. w=7
Hope This Helps :)
Answer:
w = 7
Step-by-step explanation:
-8 + 5w = 27
Add 8 on both sides.
-8 + 5w + 8 = 27 + 8
5w = 35
Divide both sides by 5.
5w/5 = 35/5
w = 7
hey one more for my friend :)
Answer:
Third graph from the top
Step-by-step explanation:
A proportional relationship is a straight line that goes through the point (0,0)
Answer:
The third graphStep-by-step explanation:
The third straight graph, since a proportion is a relationship in which a second variable is changed by a same value all the time (linear).
Hope this helps, if not, tell me and I shall try again
Consider the matrices. A=⎡⎣⎢4−3−578−2⎤⎦⎥ and B=⎡⎣⎢−27−35−12⎤⎦⎥ What is the result of A−B? Enter your answer by filling in the boxes.
hello
[tex]A-B=\left[\begin{array}{cc}4-(-2)&7-5\\-3-7&8-(-1)\\-5-(-3)&-2-2\end{array}\right] \\\\=\left[\begin{array}{cc}4+2&2\\-10&8+1\\-5+3&-4\end{array}\right] \\\\=\left[\begin{array}{cc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]
hope this helps
Using matrices A and B, the result of A-B is
[tex]A-B=\left[\begin{array}{ccc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]
Given :
Two matrices A and B. We need to subtract both matrix
Lets find out A-B
Given matrices A and B are
[tex]A=\left[\begin{array}{ccc}4&7\\-3&8\\-5&-2\end{array}\right] \\B=\left[\begin{array}{ccc}-2&5\\7&-1\\-3&2\end{array}\right][/tex]
When we subtract A-B we need to subtract the corresponding elements in that matrix
[tex]A-B=\left[\begin{array}{ccc}4&7\\-3&8\\-5&-2\end{array}\right] -\left[\begin{array}{ccc}-2&5\\7&-1\\-3&2\end{array}\right]=\left[\begin{array}{ccc}4-(-2)&7-5\\-3-7&8-(-1)\\-5-(-3)&-2-2\end{array}\right] \\A-B=\left[\begin{array}{ccc}6&2\\-10&9\\-2&-4\end{array}\right][/tex]
The above is the resultant matrix .
Learn more: brainly.com/question/12579158
What is the equation of the graphed line written in
standard form?
O 2x - y = -4
O 2x - y = 4
O y = 2x – 4
O y=x-4
Answer:
2x-y=4
Step-by-step explanation:
Standard form of a line: Ax+by=c
Use slope intercept form: y=mx+b
slope= 2
y=2x-4
Add 4 to both sides.
y+4=2x
subtract y from both sides.
4=2x-y
Rotate the equation
2x-y=4
Answer:
2x-y=4
Step-by-step explanation:
y=2x-4 is the slope intercept.
y-2x=-4
-2x+y=-4
2x-y=4
In a test of the effectiveness of garlic for lowering cholesterol, 47 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes (beforeminusafter) in their levels of LDL cholesterol (in mg/dL) have a mean of 2.7 and a standard deviation of 17.8. Construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.
We have,
To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:
CI = X ± (Z * (σ/√n))
where:
CI is the confidence interval
X is the sample mean
Z is the critical value corresponding to the desired confidence level (90% confidence level corresponds to Z = 1.645 for a large sample size)
σ is the population standard deviation
n is the sample size
Given that the sample mean X of the net change in LDL cholesterol is 2.7, the standard deviation (σ) is 17.8, and the sample size (n) is 47, we can calculate the confidence interval as follows:
CI = 2.7 ± (1.645 * (17.8/√47))
Calculating the standard error (SE):
SE = σ/√n = 17.8/√47 ≈ 2.587
Substituting the values into the confidence interval formula:
CI = 2.7 ± (1.645 * 2.587)
Calculating the upper and lower bounds of the confidence interval:
Upper bound = 2.7 + (1.645 * 2.587) ≈ 7.199
Lower bound = 2.7 - (1.645 * 2.587) ≈ -1.799
Therefore, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199.
Interpreting the confidence interval:
Since the confidence interval contains both positive and negative values, it suggests that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.
The interval includes zero, indicating that there is a possibility that the mean net change in LDL cholesterol after the garlic treatment could be zero (no change).
However, it is important to note that further studies or a larger sample size may be needed to draw more definitive conclusions.
Thus,
The 90% confidence interval for the mean net change in LDL cholesterol after the garlic treatment is approximately -1.799 to 7.199, suggesting that the effectiveness of garlic in reducing LDL cholesterol is not statistically significant.
Learn more about confidence intervals here:
https://brainly.com/question/32546207
#SPJ4
The 90% confidence interval suggests that the true mean net change in LDL cholesterol after the garlic treatment lies between -1.57 and 6.97 mg/dL. Since the interval contains both positive and negative values, it indicates that the garlic treatment may or may not be effective in reducing LDL cholesterol.
What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?To construct a 90% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment, we can use the formula:
CI = mean ± (Z * (standard deviation / √n))
Here, n represents the sample size (47), Z is the critical value corresponding to a 90% confidence level (Z = 1.645 for a 90% confidence level), and the mean is 2.7 with a standard deviation of 17.8.
Plugging in the values:
CI = 2.7 ± (1.645 * (17.8 / √47))
CI = 2.7 ± (1.645 * (17.8 / 6.856))
CI = 2.7 ± (1.645 * (2.596))
CI = 2.7 ± 4.270
CI = 2.7 + 4.270 ; CI = 2.7 - 4.270
CI = 6.97 ; CI = -1.57
Thus, the 90% confidence interval estimate for the mean net change in LDL cholesterol after the garlic treatment is approximately (-1.57, 6.97).
The confidence interval suggests that the effectiveness of garlic in reducing LDL cholesterol is inconclusive. The interval spans both positive and negative values, indicating that the true mean change in LDL cholesterol could be anywhere within this range. Further research or a larger sample size might be needed to draw a more definitive conclusion about the effectiveness of garlic in lowering LDL cholesterol.
Read more about confidence interval here: https://brainly.com/question/20309162
#SPJ1
Which of the following points is NOT a solution of the inequality y ≥ Ixl + 3?
A. (-3, 0)
B. (-3, 6)
C. (0, 4)
Hey there!
To solve this, we need to plug each of our answer options into the inequality and see if it is true. Which ever one doesn't make the inequality true when plugged in is the answer.
OPTION A
(x,y)=(-3,0)
We plug our values into the inequality.
0≥ I-3I+3
You may have noticed the bars surrounding the negative three.. If you didn't know, this is called absolute value. Absolute value is how far the number is from 0 on the number line. -7 is 7 away from 0 on a number line, so the absolute value of -7 is 7. The absolute value of 7 is 7. The absolute value of 0 is 0. Absolute value is signified by these bars. Le'ts finish evaluating.
0≥6
As you can see, zero is not greater than or equal to six. So, option A is false.
Since A is not a solution, we already know that that is the answer, so we don't even need to check B and C. But, we can still evaluate them if you want.
OPTION B
6≥I-3I+3
6≥6
This is true.
OPTION C
4≥I0I+3
4≥3
This is also true.
Therefore, the answer is A. (-3,0)
Have a wonderful day!
pls help me pls pls pls
Answer: 1x + 2y = 4
Step-by-step explanation:
The equation of the line is y = -1/2x + 2.
First, let's make 4 on one side of the equation. First, bring x to the left. y + 1/2x = 2. Then multiply the whole equation by two. Thus, 1x + 2y = 4.
Hope it helps <3
A jar contains 5 brown marbles, 3 yellow marbles, 4 red marbles, 6 blue marbles, and 2 orange marbles. A marble is chosen and replaced. Then another marble is chosen. What is the likelihood that a brown marble AND a red marble were chosen? A: 9/20 B: 1/2 C: 1/20 D: 0
Answer:
1/20
Step-by-step explanation:
5 brown marbles, 3 yellow marbles, 4 red marbles, 6 blue marbles, and 2 orange marbles = 20 marbles
P( brown) = brown / total = 5/20 = 1/4
Replace
5 brown marbles, 3 yellow marbles, 4 red marbles, 6 blue marbles, and 2 orange marbles = 20 marbles
P( red) = red / total = 4/20 = 1/5
P( brown, replace, red) = 1/4 * 1/5 = 1/20
Find the least number which is exactly divisible by 72 and 108
Step-by-step explanation:
2 is the answer because:
72/2=36
108/2=54
Answer:
2
Step-by-step explanation:
Well divisible means the lowest numbers it can be divided by.
So we can make a chart.
72 - 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
108 - 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
So besides 1, 2 is the lowest divisible number between 108 and 72.
If x ∥ y and y ∥ z, then _____
Answer:
x ║ z
Step-by-step explanation:
Lines parallel to the same line are parallel to each other.
x and z are both parallel to y, so are parallel to each other:
x ║ z
The side, s, of a square with area A square feet is given by the formula s = square root A. Find the perimeter of a square with an area of 36 square feet. ______________ ft
Answer:
24 feet.
Step-by-step explanation:
The side of the square = √36 = 6 feet.
The square has 4 equal sides so the perimeter = 4*6 = 24 feet.
Not sure of how to solve this
Answer:
undefined
Step-by-step explanation:
Using the slope formula
m = (y2-y1)/ (x2-x1)
and the given points
m = ( 8 - -1)/( 2-2)
= (8+1) / 0
We cannot divide by 0 so the slope is undefined
Domain and range of T
Answer:
Let's list out the points that belong to T. They are T{(-1, -4), (2, 2), (2, -3)}.
The domain is all of the x values. Therefore the domain is {-1, 2}.
The range is all of the y values. Therefore the range is {-4, -3, 2}.
We don't use ( ) or [ ] because T is a discrete relation.
4(x+1)=16 HELP MEEEEEE
Answer:
4(x + 1) = 16
x + 1 = 4 (Divide equation by 4)
x = 3 (subtract 1)
Answer:
x = 3
Step-by-step explanation:
4(x + 1)=16
Expand the brackets.
4x + 4 = 16
Subtract 4 on both sides.
4x + 4 - 4 = 16 - 4
4x = 12
Divide both sides by 4.
4x/4 = 12/4
x = 3
Hurry!! Determine the intervals for which the function shown below is decreasing.
Answer:
everywhere except between 2 and 5
(between -inf and 2 and between 5 and inf)
Step-by-step explanation:
**Hello !** I need help to do that algebra homework. I don't really know how that website works, so just tell me how much points you want if your answer is good and i'll give them to your with a lot of pleasure. Here is the homework : Thank you so much for your help ! :)
Answer:
y = √(900 -x²); see below for a graph
Step-by-step explanation:
The high point (30 ft) is the radius of the circle, so the equation is ...
x² +y² = 30²
Subtract the x-term and take the square root to find y.
y² = 30² -x²
y = √(30² -x²) = √(900 -x²)
The graph is shown in the attachment.
_____
Comment on "how that website works"
We don't know what web site you're referring to, but the one I like is Desmos. It only takes a few minutes to learn to graph the equation here.
You don't even need to solve for y to get the desired graph. You can simply specify that y ≥ 0.
Ahmad makes compost by mixing 0.5 kg of sand with 2 kg of peat. Write the ratio of sand to peat. Give your answer in its simplest form.
Answer:
0.5kg
2kg
0.7kg
b668_*;
fxjiezncy
gcjoxfj
vxfhb