Will pick brainliest! I need help with this, actual effort in answering is much appreciated.
Answer:
option 2
Step-by-step explanation:
4^2=16/8=2. 4^2=16/16=1. 2-1=1
A county environmental agency suspects that the fish in a particular polluted lake have elevated mercury levels. To confirm that suspicion, five striped bass in that lake were caught and their tissues tested for the presence of mercury. For the purposes of comparison, four striped bass in an unpolluted lake were also caught and tested. The fish tissue mercury levels in mg/kg are given below. (Note: You may wish to use Excel for this problem.) Sample 1 (polluted lake) Sample 2 (unpolluted lake) 0.580 0.382 0.711 0.276 0.571 0.570 0.666 0.366 0.598a. Construct the 95% confidence interval for the difference in the population means based on these data.b. Test, at the 5% significance level, whether the data provide sufficient evidence to conclude that fish in the polluted lake have elevated levels of mercury in their tissue.c. Do your answers to (a) and (b) agree or disagree? Explain.
Answer:
a. The 95% confidence interval for the difference between means is (0.071, 0.389).
b. There is enough evidence to support the claim that the fish in this particular polluted lake have signficantly elevated mercury levels.
c. They agree. Both conclude that the levels of mercury are significnatly higher compared to a unpolluted lake.
In the case of the confidence interval, we reach this conclusion because the lower bound is greater than 0. This indicates that, with more than 95% confidence, we can tell that the difference in mercury levels is positive.
In the case of the hypothesis test, we conclude that because the P-value indicates there is a little chance we get that samples if there is no significant difference between the mercury levels. This indicates that the values of mercury in the polluted lake are significantly higher than the unpolluted lake.
Step-by-step explanation:
The table with the data is:
Sample 1 Sample 2
0.580 0.382
0.711 0.276
0.571 0.570
0.666 0.366
0.598
The mean and standard deviation for sample 1 are:
[tex]M=\dfrac{1}{5}\sum_{i=1}^{5}(0.58+0.711+0.571+0.666+0.598)\\\\\\ M=\dfrac{3.126}{5}=0.63[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{5}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}\cdot [(0.58-(0.63))^2+...+(0.598-(0.63))^2]}\\\\\\ s=\sqrt{\dfrac{1}{4}\cdot [(0.002)+(0.007)+(0.003)+(0.002)+(0.001)]}\\\\\\ s=\sqrt{\dfrac{0.015}{4}}=\sqrt{0.0037}\\\\\\s=0.061[/tex]
The mean and standard deviation for sample 2 are:
[tex]M=\dfrac{1}{4}\sum_{i=1}^{4}(0.382+0.276+0.57+0.366)\\\\\\ M=\dfrac{1.594}{4}=0.4[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{3}\cdot [(0.382-(0.4))^2+(0.276-(0.4))^2+(0.57-(0.4))^2+(0.366-(0.4))^2]}\\\\\\ s=\sqrt{\dfrac{1}{3}\cdot [(0)+(0.015)+(0.029)+(0.001)]}\\\\\\ s=\sqrt{\dfrac{0.046}{3}}=\sqrt{0.015}\\\\\\s=0.123[/tex]
Confidence interval
We have to calculate a 95% confidence interval for the difference between means.
The sample 1, of size n1=5 has a mean of 0.63 and a standard deviation of 0.061.
The sample 2, of size n2=4 has a mean of 0.4 and a standard deviation of 0.123.
The difference between sample means is Md=0.23.
[tex]M_d=M_1-M_2=0.63-0.4=0.23[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{0.061^2}{5}+\dfrac{0.123^2}{4}}\\\\\\s_{M_d}=\sqrt{0.001+0.004}=\sqrt{0.005}=0.07[/tex]
The critical t-value for a 95% confidence interval is t=2.365.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_{M_d}=2.365 \cdot 0.07=0.159[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M_d-t \cdot s_{M_d} = 0.23-0.159=0.071\\\\UL=M_d+t \cdot s_{M_d} = 0.23+0.159=0.389[/tex]
The 95% confidence interval for the difference between means is (0.071, 0.389).
Hypothesis test
This is a hypothesis test for the difference between populations means.
The claim is that the fish in this particular polluted lake have signficantly elevated mercury levels.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0[/tex]
The significance level is 0.05.
The sample 1, of size n1=5 has a mean of 0.63 and a standard deviation of 0.061.
The sample 2, of size n2=4 has a mean of 0.4 and a standard deviation of 0.123.
The difference between sample means is Md=0.23.
[tex]M_d=M_1-M_2=0.63-0.4=0.23[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{0.061^2}{5}+\dfrac{0.123^2}{4}}\\\\\\s_{M_d}=\sqrt{0.001+0.004}=\sqrt{0.005}=0.07[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.23-0}{0.07}=\dfrac{0.23}{0.07}=3.42[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-1=5+4-2=7[/tex]
This test is a right-tailed test, with 7 degrees of freedom and t=3.42, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t>3.42)=0.006[/tex]
As the P-value (0.006) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the fish in this particular polluted lake have signficantly elevated mercury levels.
c. They agree. Both conclude that the levels of mercury are significnatly higher compared to a unpolluted lake.
In the case of the confidence interval, we reach this conclusion because the lower bound is greater than 0. This indicates that, with more than 95% confidence, we can tell that the difference in mercury levels is positive.
In the case of the hypothesis test, we conclude that because the P-value indicates there is a little chance we get that samples if there is no significant difference between the mercury levels. This indicates that the values of mercury in the polluted lake are significantly higher than the unpolluted lake.
Wyoming fisheries contend that the mean number of cutthroat trout caught during a full day of fly-fishing on the Snake, Buffalo, and other rivers and streams in the Jackson Hole area is 4.0. To make their yearly update, the fishery personal asked a sample of fly-fishermen to keep a count of the number caught during the day. The numbers were: 4, 4, 3, 2, 6, 8, 7, 1,9, 3, 1, and 6. At the 0.05 significance level, can we conclude that the mean number caught is greater than 4.0?
Answer:
[tex]t=\frac{4.5-4}{\frac{2.680}{\sqrt{10}}}=0.59[/tex]
The degrees of freedom are given by:
[tex] df =n-1= 12-1=11[/tex]
And the p value would be:
[tex]p_v =2*P(t_{11}>0.59)=0.567[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean area is not significantly different from 4
Step-by-step explanation:
We have the following data given:
4, 4, 3, 2, 6, 8, 7, 1,9, 3, 1, and 6
The sample mean and deviation from these data are:
[tex]\bar X=4.5[/tex] represent the sample mean
[tex]s=2.680[/tex] represent the sample deviation
[tex]n=10[/tex] sample size
[tex]\mu_o =4[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to verify
We want to verify if the true mean is equal to 4, the system of hypothesis would be:
Null hypothesis:[tex]\mu =4[/tex]
Alternative hypothesis:[tex]\mu \neq 4[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the the info we got:
[tex]t=\frac{4.5-4}{\frac{2.680}{\sqrt{10}}}=0.59[/tex]
The degrees of freedom are given by:
[tex] df =n-1= 12-1=11[/tex]
And the p value would be:
[tex]p_v =2*P(t_{11}>0.59)=0.567[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean area is not significantly different from 4
Which equation is equivalent to One-fourth + x =Negative StartFraction 5 over 4 EndFraction? Select all that apply.
Options:
(A)x = StartFraction 6 over 4 EndFraction
(B)x = Negative StartFraction 6 over 4 EndFraction
(C)x minus one-fourth = negative StartFraction 5 over 4 EndFraction
(D)x = negative three-halves
(E)x = negative three-fourths
Answer:
(B)x = Negative StartFraction 6 over 4 EndFraction
[tex]-\dfrac{6}{4}[/tex]
(D)x = negative three-halves
[tex]-\dfrac{3}{2}[/tex]
Step-by-step explanation:
We want to determine which fraction is equivalent to
[tex]\dfrac{1}{4}+x=-\dfrac{5}{4}\\$First, we collect like terms$\\x=-\dfrac{5}{4}-\dfrac{1}{4} \\\\=\dfrac{-5-1}{4}\\=-\dfrac{6}{4}\\x=-\dfrac{6}{4}[/tex]
This value of x is the result in Option B.
Reducing [tex]-\dfrac{6}{4}[/tex] to its lowest form:
[tex]-\dfrac{6}{4}=-\dfrac{3}{2}[/tex] which is Option D.
Therefore, the correct options are: B and D
I don’t know how to do this, what’s the area?
Answer:
Hello!
Step-by-step explanation:
To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.
So,you have to multiply.
Hope this helps.
Some of the stock in a winery has been found to be infected by Brettanomyces. You independently sample 80 barrels from the winery, and find that 28 of them are infected. Carry out a hypothesis test to evaluate the claim that half of the wine barrels are infected. What is closest to the p-value that you obtain
Answer:
Step-by-step explanation:
If half of the wine barrels are infected, it means that the proportion of infected wine is 0.5
We would set up the hypothesis test.
For the null hypothesis,
p = 0.5
For the alternative hypothesis,
p < 0.5
Considering the population proportion, probability of success, p = 0.5
q = probability of failure = 1 - p
q = 1 - 0.5 = 0.5
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 28
n = number of samples = 80
P = 28/80 = 0.35
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.35 - 0.5)/√(0.5 × 0.5)/80 = - 2.68
From the normal distribution table, the area below the test z score in the left tail 0.0037
Therefore,
p value = 0.0037
Assuming a significance level of 0.05, therefore,
Since alpha, 0.05 > than the p value, 0.0037, then we would reject the null hypothesis.
100 thousands equal to ---lakhs
Answer:one lakh....
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thnk me...
Answer:
1 Lakh = 100 Thousands
Step-by-step explanation:
here it is ill mark you as brainliest if the answer is correct.
Answer:
A = 1168.67 cm²
Step-by-step explanation:
[tex]A=2\pi rh+2\pi r^{2}[/tex] Use this equation to find the surface area
[tex]A=2\pi (6)(25)+2\pi (6)^{2}[/tex] Multiply
[tex]A=2\pi (150)+2\pi (36)[/tex] Multiply
A = 942.48 + 226.19 Add
A = 1168.67 cm²
Answer:
1169.14cm2
Step-by-step explanation:
The surface area is that area which you can feel. Now there are two circles one at the top and one at the bottom.
These areas are expressed as;
π×r2 { remember area of a circle}.
Therefore for the two areas we have twice the area of once since they are the same. Hence we have:
2×π×r2.
Secondly, there is still another area we haven't talked about yet. It's the area you feel at the side and this area curls into a circular fashion.
Now let's assume the two circles are the top and bottom are knocked off , we would have a shape that looks like a rectangle.
Now area of a rectangle is the multiplication of both sides. In this case the side would be the height,h and the circumference of the circle since the rectangle forms into a circle when she try to join both edges together.
Hence the area of this Shape would be;
2πr{circumference} × h=2πrh
Hence the total surface area would be;
2πr2 + 2πrh.
Substituting the giving values we have;
Note: to obtain raduis,r ; we divide the diameter by 2.
2 × 22/7 × 6^2 + 2 × 22/7 × 6× 25
2×22/7(36+150)
44/7(186)= 8184/7
=1169.1429cm2
=1169.14cm2{ to 2 decimal place}
A bird of species? A, when? diving, can travel six times as fast as a bird of species B top speed. If the total speeds for these two birds is 224 miles per hour
Answer:
Maximum speed of bird A is [tex]192\,\,\frac{mi}{h}[/tex]
Maximum speed of bird B is [tex]32\,\,\frac{mi}{h}[/tex]
Step-by-step explanation:
This is a problem with two unknowns: Max speed of bird A (we name that "A"), and max speed of bird B (we call that "B"). Now we can create two equations with these two unknowns, based on the info provided:
Equation 1): based on the phrase "bird A can travel six times as fast as bird B" we write:
[tex]A=6\,*\, B\\A=6B[/tex]
Equation 2): based on the phrase; "the total speeds for these two birds is 224 miles per hour", we write:
[tex]A+B=224\,\,\frac{mi}{h}[/tex]
Now, we use the first equation to substitute A in the second equation, ad then solve for the unknown B:
[tex]A+B=224\,\,\frac{mi}{h}\\(6B)+B=224\,\,\frac{mi}{h}\\7B=224\,\,\frac{mi}{h}\\B=\frac{224}{7} \,\,\frac{mi}{h}\\B=32\,\,\frac{mi}{h}[/tex]
Now we can solve for the other unknown "A" using the substitution equation and the value of B we just found:
[tex]A=6B\\A=6\,(32\,\,\frac{mi}{h})\\A=192\,\,\frac{mi}{h}[/tex]
For the transformation to be a translation, which statements must be true? Select four options.
Answer:
BD = DB'
CG = GC'
m∠EFA = 90°
The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC'.
Step-by-step explanation:
Hope this helps
Correct me if this is wrong
(x + y )(x 2 - xy + y 2 )
Answer:
[tex]x^3+y^3[/tex]
Step-by-step explanation:
[tex](x+y)(x^2-xy+y^2)= \\\\x(x^2)+x(-xy)+x(y^2)+y(x^2)+y(-xy)+y(y^2)= \\\\x^3-x^2y+xy^2+x^2y-xy^2+y^3= \\\\\boxed{x^3+y^3}[/tex]
Hope this helps!
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Solution,
Radius=2 m
Area =pi r^2
= 3.142*(2)^2
=12.568 m^2
hope it helps
Good luck on your assignment
At a gas station, 50% of the customers use regular gas, 30% use mid-grade gas and 20% use premium gas. Of those customers using regular gas, only 30% fill their tanks. Of those customers using mid-grade gas, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. What is the probability that the next customer will request mid-grade gas and fill the tank
Answer:
The probability that the next customer will request mid-grade gas and fill the tank is 0.1800
Step-by-step explanation:
In order to calculate the probability that the next customer will request mid-grade gas and fill the tank we would have to make the following calculation:
probability that the next customer will request mid-grade gas and fill the tank= percentage of the people using mid-grade gas* percentage of the people using mid-grade gas that fill their tanks
probability that the next customer will request mid-grade gas and fill the tank= 30%*60%
probability that the next customer will request mid-grade gas and fill the tank= 0.1800
The probability that the next customer will request mid-grade gas and fill the tank is 0.1800
find the mean of x,2x,3x,4x,5x
Answer:
Mean = 3x
Step-by-step explanation:
Mean = [tex]\frac{SumOfObservations}{No. OfObservations}[/tex]
Mean = [tex]\frac{x+2x+3x+4x+5x}{5}[/tex]
Mean = [tex]\frac{15x}{5}[/tex]
Mean = 3x
The mean, also known as the average of x, 2x, 3x, 4x, and 5x is 3x as per the concept of Simplifying.
To find the mean of x, 2x, 3x, 4x, and 5x, we need to add up all the values and divide by the total number of values.
In this case, we have five values.
Mean = (x + 2x + 3x + 4x + 5x) / 5
Simplifying the numerator:
Mean = (15x) / 5
Mean = 3x
Therefore, the mean of x, 2x, 3x, 4x, and 5x is 3x.
The mean, also known as the average, represents the central tendency of a set of values. In this case, the mean is 3x, which indicates that on average, the values x, 2x, 3x, 4x, and 5x are three times the value of x.
To learn more about the mean;
brainly.com/question/13451489
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Please help! Will give Brainliest!
Steps 1-4 in attachment (#4 below)
Step 4: Use the equation you wrote in Step 3. Write the equation for the graph of g(x) that has also been shifted right 1 unit.
Answer:
g(x) = 2|x|g(x) = -2|x|g(x) = -2|x| -3g(x) = -2|x-1| -3Step-by-step explanation:
1) Vertical stretch is accomplished by multiplying the function value by the stretch factor. When |x| is stretched by a factor of 2, the stretched function is ...
g(x) = 2|x|
__
2) Reflection over the x-axis means each y-value is replaced by its opposite. This is accomplished by multiplying the function value by -1.
g(x) = -2|x|
__
3) As you know from when you plot a point on a graph, shifting it down 3 units subtracts 3 from the y-value.
g(x) = -2|x| -3
__
4) A right-shift by k units means the argument of the function is replaced by x-k. We want a right shift of 1 unit, so ...
g(x) = -2|x -1| -3
An artist is trying to choose 5 covers for children’s books. There are 10 different covers to choose from. How many ways can the artist choose covers? (It’s a permutation and combination kind of problem)
Answer:
252
Step-by-step explanation:
The order of the books isn't important, so we'll use combinations.
The number of ways to choose 5 books from 10 is:
₁₀C₅ = 10! / (5! (10 − 5)!)
₁₀C₅ = 10! / (5! 5!)
₁₀C₅ = 10×9×8×7×6 / (5×4×3×2×1)
₁₀C₅ = 252
which of the following expressions is equal to 2X^2 +8
Answer:
The question is not clear.
Step-by-step explanation:
Normally it helps to rewrite 8 as
8 = 2 * 2 * 2 = 2³
However the question is not clear.
There are no following expressions given...
By 2X^2 +8,
do you mean 2*x² + 8, or do you mean 2*x^(2 + 8)
or did you perhaps mean 2^(x+8)
Next time, please add a picture.
Answer:
(2x-4i)(x+2i)
What is the area of triangle ABC?
3 square units
0 7 square units
11 square units
15 square units
[tex]the \: answer \: is \: 7 \: square \: units \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
On a number line, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with number a. For example b= 11/4 when a= -11/4
A) b=-a
B) -b=-a
C) b-a=0
D) b(-a)=0
Answer:
B and A
Step-by-step explanation:
So based on the facts given, we know that b and a both have the same abasolute value. It does not matter whether a or b is negative or positive.
The height of a cylinder is twice the radius of its base.
What expression represents the volume of the cylinder, in
cubic units?
4pix2
2pix3
pix2+2x
2+pix3
Answer:
The answer is 2pix3 or [tex]2\pi x^3\\[/tex]
Step-by-step explanation:
This problem brothers on the mensuration of solid shapes, a cylinder.
we know that the expression for the volume of a cylinder is
[tex]volume= \pi r^2h\\[/tex]
let the radius r of the base be= x
and the height h of the cylinder be = 2x
we can now solve the expression that represents the volume of the cylinder, in cubic units.
[tex]volume= \pi *x^2*2x\\volume= \pi *2x^3\\\\volume= 2\pi x^3\\[/tex]
Which property is illustrated by the expression 5(4+2)=20+10
Answer:
distributive property
Step-by-step explanation:
The distributive property tells you ...
a(b+c) = ab +ac
5(4+2) = 5·4 +5·2 = 20 +10
[tex]\text{It would most likely be the distributive property}\\\\\text{In the equation:}\\\\5(4+2)=20+10\\\\\text{You would see that you can distribute the 5 into the variables inside }\\\text{the parenthesis}\\\\\text{In which it is set up in that particular way in order to do so}[/tex]
Suppose a box of Cracker Jacks contains one of 5 toy prizes: a small rubber ball, a whistle, a Captain America decoder ring, a race car, or a magnifying glass. Each prize is equally likely to be in a box. Question 1. How many boxes of Cracker Jacks would you expect to buy until you obtain a complete set of prizes
Answer:
11.42 boxes
Step-by-step explanation:
For the first box bought, there is a 100% chance of getting a unique toy (since you still don't have any). E₁ = 1.
After that, there is a 4 in 5 chance of getting a unique toy from the next box, the expected number of boxes required is:
[tex]E_2 = (\frac{4}{5})^{-1} = 1.25[/tex]
For the next unique toy, there is now a 3 in 5 chance of getting it:
[tex]E_3 = (\frac{3}{5})^{-1} = 1.67[/tex]
Following that logic, there is a 2 in 5 chance of getting the 4th unique toy:
[tex]E_4 = (\frac{2}{5})^{-1} = 2.5[/tex]
Finally, there is a 1 in 5 chance to get the last unique toy:
[tex]E_5 = (\frac{1}{5})^{-1} = 5[/tex]
The expected number of boxes to obtain a full set is:
[tex]E=E_1+E_2+E_3+E_4+E_5\\E=1+1.25+1.67+2.5+5\\E=11.42\ boxes[/tex]
Using the information given, select the statement that can deduce the line segments to be parallel. If there are none select none. When m<7=m<4
Answer:
Option (2). None
Step-by-step explanation:
A quadrilateral ABCD has been given with a property,
m∠7 = m∠4
Option (1). AB║ DC
For AB║DC, angle 7 and angle 3 should measure the same.
(By the property of alternate angles)
Therefore, by the given property we can not deduce AB║DC.
Option (3). AD║BC
For AD║BC, angle 7 and angle 3 must be equal in measure.
(By the property of alternate angles)
Therefore, by the given property we can not deduce AD║DC
Option (2). None will be the answer.
Solve for x in the diagram below.
Answer:
x = 20
Step-by-step explanation:
The three angles form a straight line so they add to 180 degrees
x+ 100 +3x = 180
Combine like terms
100+4x= 180
Subtract 100 from each side
100+4x-100= 180-100
4x= 80
Divide each side by 4
4x/4 = 80/4
x = 20
Answer:
[tex]x = 20 \: \: degrees[/tex]
Step-by-step explanation:
Angles in a straight line = 180 degrees
[tex]x + 3x + 100 = 180 \\ 4x + 100 = 180 \\ 4x = 180 - 100 \\ 4x = 80 \\ \frac{4x}{4} = \frac{80}{4} \\ x = 20 \: \: degrees[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Is a sinusoid a function whose values repeat based on position of a point that moves around a circle
Answer:
yes
Step-by-step explanation:
One way to describe a sine function is that it is the y-coordinate of a point on the unit circle that is θ radians counterclockwise from the x-axis:
y = sin(θ)
__
Another way to describe the sine function is that it is the solution to the differential equation for undamped "simple harmonic motion."
y'' + y = 0; y'(0) = 1, y(0) = 0
y = sin(x)
Answer:
True
Step-by-step explanation:
A (-5,2) B (0,-5) C (5,1) D (7,5)
Answer:
C
Step-by-step explanation:
You roll a die with the sample space S = {1, 2, 3, 4, 5, 6}. You define A as {1 ,4, 6}, B as {1, 3, 4, 5, 6}, C as {1, 5}, and D as {2, 3, 5) 5}. Determine which of the following events are exhaustive and/or mutually exclusive
Exhaustive Mutually exclusive
a. A and B (Click to select) (Click to select)
b. A and C Click to select) (Click to select)
c. A and D (Click to select) (Click to select)
d. Band C (click to select) (click to select)
Answer:
Step-by-step explanation:
Recall that two events A,B are called mutually exclusive if and only if [tex]A\cap B = \emptyset [/tex] (their intersection is empty). They are exhaustive if they are mutually exclusive and their union is the sample space.
Based on this
a) Note that [tex]A\cap B = \{1,6\}[/tex], so they are not mutually exclusive nor exhaustive.
b) [tex]A\cap C = \{1\}[/tex] so they are not mutually exclusive nor exhaustive.
c) [tex]A\cap D = \emptyset [/tex], so they are mutually exclusive. Note that [tex]A\cup D = \{1,2,3,4,5,6\}=S[/tex]. Then they are exhaustive.
d) [tex]B\cap C = \{1,5\}[/tex], so they are not mutually exclusive nor exhaustive.
the sum of 3 consecutive even integers is 228
Here we will use algebra to find three consecutive integers whose sum is 228. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 228. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) = 228
To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 228
3X + 3 = 228
3X + 3 - 3 = 228 - 3
3X = 225
3X/3 = 225/3
X = 75
Which means that the first number is 75, the second number is 75 + 1 and the third number is 75 + 2. Therefore, three consecutive integers that add up to 228 are 75, 76, and 77.
75 + 76 + 77 = 228
We know our answer is correct because 75 + 76 + 77 equals 228 as displayed above.
Answer:
74, 76, 78
Step-by-step explanation:
The numbers are even and consecutive so they are 2x, 2x+2 and 2x+4 because any number multiplied by 2 is always even and they are even CONSECUTIVE,. So 2 and 4
Now their sum is given as 228 so,
2x+2x+2+2x+4= 228
6x+6= 228
6x= 228-6= 222
x= 222/6
= 37
So the numbers are:
2x= 37*2= 74
2x+2= 74+2= 76
2x+4= 74+4= 78
3) If you know the volume of a prism and the area of the base of the prism, what other information
can you find about the prism?
Answer:
I could find out the surface area and it's capacity
A 48 meter antenna mast is stabilized by a 52 meter guy wire How far from the base of the mast is the guy wire secured to the ground A 20m B 50m C 60m D 100m
Answer:
A) 20m
Step-by-step explanation:
52^2 - 48^2 = b^2
√2704 - √ 2304 = √400
b^2 = √400 = 20
As this is Pythagoras as we do not have any 2nd angle measure.
if it was trigonometry we could use 90 degree as part of the sum
48/ sin(?)x90 = 52
Then try other angle by deducting angle shown from 90
m/sin (?) x 90 = 52 etc.
But to guarantee you would find the base you could use tan.