Answer:
[tex]\fbox{\begin{minipage}{14em}Number of subsets: 16\\Number of proper subsets: 15\end{minipage}}[/tex]
Step-by-step explanation:
Given:
The set A = {5, 13, 17, 20}
Question:
Find the number of subsets of A
Find the number of proper subsets of A
Simple solution by counting:
Subset of A that has 0 element:
{∅} - 1 set
Subset of A that has 1 element:
{5}, {13}, {17}, {20} - 4 sets
Subset of A that has 2 elements:
{5, 13}, {5, 17}, {5, 20}, {13, 17}, {13, 20}, {17, 20} - 6 sets
Subset of A that has 3 elements:
{5, 13, 17}, {5, 13, 20}, {5, 17, 20}, {13, 17, 20} - 4 sets
Subset of A that has 4 elements:
{5, 13, 17, 20} - 1 set
In total, the number of subsets of A: N = 1 + 4 + 6 + 4 + 1 = 16
The number of proper subsets (all of subsets, except subset which is equal to original set A): N = 16 - 1 = 15
Key-point:
The counting method might be used for finding the number of subsets when the original set contains few elements.
The question is that, for a set that contains many elements, how to find out the number of subsets?
The answer is that: there is a fix formula to calculate the total number ([tex]N[/tex]) of subsets of a set containing [tex]n[/tex] elements: N = [tex]2^{n}[/tex]
With original set A = {5, 13, 17, 20}, there are 4 elements belonged to A.
=> Number of subsets of A: N = [tex]2^{4} = 16[/tex]
(same result as using counting method)
Brief proof of formula: N = [tex]2^{n}[/tex]
Each element of original set is considered in 2 status: existed or not.
If existed => fill that element in.
If not => leave empty.
For i.e.: empty subset means that all elements are selected as not existed, subset with 1 element means that all elements are selected as not existed, except 1 element, ... and so on.
=> From the point of view of a permutation problem, for each element in original set, there are 2 ways to select: existed or not. There are [tex]n[/tex] elements in total. => There are [tex]2^n}[/tex] ways to select, or in other words, there are [tex]2^{n}[/tex] subsets.
Hope this helps!
:)
The sum of two consecutive even integers is at most 400. The pair of integers with the greatest sum is 196 and 198.
Answer:
Step-by-step explanation: If the sum of two equal even numbers is 400, the numbers will be 200+200. Therefore the largest possible consecutive even numbers which have a sum of 400 or less are 198 and 200 which have a sum of 398.
i guss this would be helpful :]
Answer:
Step-by-step explanation:
3y-y please can you work it out
What’s the correct answer for this question?
Answer:
D.
Step-by-step explanation:
In the attached file
Die A has 4 red faces and 2 black faces. Die B has 2 red faces and 4 black faces. A coin is flipped once. If it were heads, only die A is used (die B is discarded). If it were tails, only die B is used (die A is discarded). We do not get to know which die was chosen.
a) The first roll of the chosen die gives red. What is the probability that the second roll (with the same die) will be red?
b) The first two rolls of the die were both red. What is the probability that the third roll (with the same die) will be red?
Answer:
a) 5/9
b) 1/3
Step-by-step explanation:
a) P(Die A or Die B) = P(red and red with Die A) + P(red and red with Die B)
= 4/6 × 4/6 + 2/6×2/6
= 5/9
b) P(Die A or Die B) = P(red and red and red with Die A) + P(red and red and red with die B)
= 4/6×4/6×4/6 + 2/6×2/6×2/6
= 1/3
g You run a regression analysis on a bivariate set of data ( n = 14 ). With ¯ x = 27.7 and ¯ y = 26.5 , you obtain the regression equation y = 0.495 x − 14.914 with a correlation coefficient of r = 0.39 . You want to predict what value (on average) for the response variable will be obtained from a value of 110 as the explanatory variable. What is the predicted response value?
Answer:
Predicted response value = 39.536
Note that this predicted response value will most likely be far from the actual response value because the correlation coefficient of the regression equation used (r = 0.39) is too far away from 1.
Step-by-step explanation:
The response variable is the dependent variable (y) whose value is obtained from the expression involving the independent variable (x).
For this question, although the correlation coefficient, r = 0.39, is far from 1, the regression equation is
y = 0.495x - 14.914
The predicted response value will be obtained from the explanatory variable and the regression equation
x = 110
y = 0.495x - 14.914
y = (0.495×110) - 14.914 = 39.536
Note that this predicted response value will most likely be far from the actual response value because the correlation coefficient of the regression equation used (r = 0.39) is too far away from 1.
Hope this Helps!!!
find the value of the expression :1/216^-2/3 + 1/256^-3/4 + 1/243^-1/5
Answer:
103
Step-by-step explanation:
A number to the power of a negative exponent, means 1 divided by that same number to the power of the positive exponent.
1/(216^(-2/3)) + 1/(256^(-3/4)) + 1/(243^(-1/5))
Break it apart into three pieces.
1/(216^(-2/3))
216^(2/3) = 36
1/(256^(-3/4))
256^(3/4) = 64
1/(243^(-1/5))
243^(1/5) = 3
So...
1/(216^(-2/3)) = 36
1/(256^(-3/4)) = 64
1/(243^(-1/5)) = 3
Add the numbers gives:
36 + 64 + 3 = 103
The highest rated of the four European cities under consideration: This can be done by multiplying factor and importance and summing for each city. A: 8050: Highest rating B: 6450 C: 7150 D: 7950
Answer:
The question is not complete, as the table containing the data is missing, but I found a matching table that can be used to answer the question.
The Question is:
Which is the highest rated, of the four European cities under consideration, using the table.
The correct answer is: City A is the highest rated European city.
Step-by-step explanation:
The highest rated European city can be found by multiplying the factor and the importance of the factors, and summing up their final values. the cty with the highest number is the one with the highest rated city. Having this in mind, let us calculate the ratings for each of the cities as follows:
City A:
(70 × 20) + (80 × 20) + (100 × 20) + (80 × 10) + (90 × 10) + (65 × 10) + (70 × 10) = 1400 + 1600 + 2000 + 800 + 900 + 650 + 700 = 8050
City B:
(70 × 20) + (60 × 20) + (50 × 20) + (90 × 10) + (60 × 10) + (75 × 10) + (60 × 10) = 1400 + 1200 + 1000 + 900 + 600 + 750 + 600 = 6450
City C:
(60 × 20) + (90 × 20) + (75 × 20) + (65 × 10) + (50 × 10) + (85 × 10) + (65 × 10) = 1200 + 1800 + 1500 + 650 + 500 + 850 + 650 = 7150
City D:
(90 × 20) + (75 × 20) + (90 × 20) + (65 × 10) + (70 × 10) + (70 × 10) + (80 × 10) = 1800 + 1500 + 1800 + 650 + 700 + 700 + 800 =7950
Therefore, from the ratings computed above, City A with a rating of 8050, is the highest rated, while City B with a rating of 6450, is the lowest rated.
Data on U.S, Work-Related fatalities by cause follow (The World Almanac,2012)Cause of Fatality Number of Fatalities Transportation Incidents 1795 Assaults and violent acts 837 Contacts with objects and equipment 741 Falls 645 Exposure to harmful substances 404 Fires and explosions 113 Assume that a fatality will be randomly chosen from this population. a. What is the probability the fatality resulted froma fall? b. What is the probability the fatality resulted from a transporation incident? c. What cause of fatality is least likely to occur? What is th probability the fatality resulted from this cause?
Answer:
a) Probability the fatality resulted from a fall = 0.1422
b) Probability the fatality resulted from a transportation incident = 0.3958
c(i) The cause of fatality that is least likely to occur is fatality due to fires and explosions with the lowest number of fatalities, 113.
c(ii) Probability that the fatality resulted from fires and explosions = 0.0249
Step-by-step explanation:
Data on U.S, Work-Related fatalities by cause follow (The World Almanac, 2012)
Cause of Fatality | Number of Fatalities Transportation Incidents | 1795
Assaults and violent acts | 837
Contacts with objects and equipment | 741
Falls | 645
Exposure to harmful substances | 404
Fires and explosions | 113
Total number of fatalities = 1795+837+741+645+404+113 = 4,535
Assume that a fatality will be randomly chosen from this population.
a. What is the probability the fatality resulted from a fall?
The probabilty of an event is given mathematically as the number of elements in that event divided by the Total number of elements in the sample space.
P(E) = n(E) ÷ n(S)
Probability the fatality resulted from a fall = (645/4535) = 0.14223 = 0.1422
b. What is the probability the fatality resulted from a transportation incident?
Probability the fatality resulted from a transportation incident = (1795/4535) = 0.39581 = 0.3958
c(i) What cause of fatality is least likely to occur?
The cause of fatality that is least likely to occur is the cause of fatality with the lowest frequency or number of fatalities. And this is fatality due to fires and explosions with the lowest fatalities of 113
c(ii). What is the probability the fatality resulted from this cause?
This is the probability that the fatality resulted from fires and explosions.
Probability that the fatality resulted from fires and explosions = (113/4535) = 0.02492 = 0.0249
Hope this Helps!!!
HELP! the function f(x)=200/x+10 models the cost per student of a field trip when x students go on the trip. how is the parent function f(x)=1/x transformed to create the function f(x)=200/x+10
Answer:
stretch of 200 shift up 10 units
Step-by-step explanation:
f(x)=1/x to 200/x+10
Multiply by 200 means a stretch of 200
f(x) = 200/x
Now shift up 10 units
f(x) = 200/x + 10
Answer:
It moves up 10 units
Step-by-step explanation:
f(x) =1/x to 200/x + 10
= 200/x
If we shift up 10 units, we get:
f(x) = 200/x + 10
Hope this helps!
Please answer this correctly
Answer: 207^2 + 9km^2 = 216km^2
Step-by-step explanation:
(my explanation is wrong)
All you want to do is break this figure up into rectangles and triangles.
I see 3 rectangles and 1 triangle.
Three Rectangles:
The bottom one has the dimension of 5 and 20. 5 x 20 = 100 km^2
The middle one has the dimensions of 5+4 and 7. 9 x 7 = 63 km^2
The top one has the dimensions of 4 and 11. 4 x 11 = 44 km^2
Add them all up to get 207km^2
One Triangle:
We can see at the bottom rectangle that the left side is 5 and the right side is 3 + x. X being our missing height of the triangle. The height equals 2.
The triangle now has the dimensions of 2 and 6. 2 x 6 = 12. Then divide by 2 to get 6 km^2
Answer:
216 km²
Step-by-step explanation:
To solve this, you have to divide the figure into different parts. I divided the parts up into four sections. I will work on the parts in numerical order.
1. At the top of the rectangle, it is marked 4 km. On the left side, it is marked 11 km. This is the length and width.
A = lw
A = 11 × 4
A = 44 km²
2. On the left side of this rectangle, it is marked 7 km. At the top it is marked 5 km, but there is a portion that does not have a measurement (the part with a different color than the rest. Because this line is also part of rectangle 1, we know that the line is 4 km. Adding up the two numbers gives you 9 km.
4 + 5 = 9
A = lw
A = 7 × 9
A = 63 km²
3. On the left side, it is marked 5 km. On the bottom, it is marked 20 km.
A = lw
A = 20 × 5
A = 100 km²
4. This is one is a bit more tricky. This is a triangle, so we have to find the base and the height. The base is 6 km. You have to figure the height. Look at the picture with the red lines.
The red line on the right side has a length of 17 + 3 + x = 20 + x. The length is 20 + x because there is a portion of the line that is missing.
The red lines on the left side have a length of 5 + 7 + 11 = 23. The two side should be equal so
23 = 20 + x
x = 3
Now, you have the height. Use the equation for area of a triangle to solve.
A = 1/2bh
A = 1/2(3)(6)
A = 1/2(18)
A = 9 km²
Now you have to add up all the areas to find the total area.
44 km² + 63 km² + 100 km² + 9 km² = 216 km²
What are the zeroes of the polynomial x(x²+4x-12)
Answer:
x= 0, 2, -6
Hope this helps!
Goods available for sale are $40000, beginning inventory is $16000, ending inventory is $20000, the cost of goods sold $50000, what is the inventory turnover
Answer:
2.78Step-by-step explanation:
Inventory turn over is the same as the inventory turn over ratio. Inventory turn over is defined simply as the ratio of the cost of goods that was sold (net sales) to the average inventory at the selling price.
Inventory turn over = Cost of goods/average inventory
Cost of goods sold = $50000
Average inventory = beginning of inventory + ending inventory/2
Average inventory = $16000+$20000/2
Average inventory = $36000/2
Average inventory = $18000
Inventory turn over = $50000/$18000
Inventory turn over= 2.78
Can someone help me with this I’m sorry I really just don’t know
Answer:
15
Step-by-step explanation:
Because the two triangles are similar:
[tex]\dfrac{LN}{30}=\dfrac{6}{30-18} \\\\\\\dfrac{LN}{30}=\dfrac{6}{12} \\\\\\LN=30\cdot \dfrac{1}{2}=15[/tex]
Hope this helps!
A hospital claims that the proportion, , of full-term babies born in their hospital that weigh more than pounds is . In a random sample of babies born in this hospital, weighed over pounds. Is there enough evidence to reject the hospital's claim at the
Complete question is:
A hospital claims that the proportion, p, of full-term babies born in their hospital that weigh more than 7 pounds is 36%. In a random sample of 170 babies born in this hospital, 56 weighed over 7 pounds. Is there enough evidence to reject the hospital's claim at the level of significance?
Answer:
Yes, there is enough evidence to reject the claim.
Step-by-step explanation:
We are given;
n = 170
x = 56
So, will use one sample proportion test to solve this.
p^ = x/n
p^ = 56/170
p^ = 0.3294
Since the proportion, p, of full-term babies born in their hospital that weigh more than 7 pounds is 36%.
Thus;
Null Hypothesis H0: p ≠ 0.36
Alternative Hypothesis Ha: p = 0.36
Formula for test statistic = (p^ - p)/√(p(1 - p)/n)
This gives;
Test statistic = (0.3294 - 0.36)/√(0.36(1 - 0.36)/170)
Test statistic = -0.8311
From z-table and online z-calculator, the p - value is 0.203.
level of significance is; α = 0.05
Now, Since the p value < α, we reject the null hypothesis .
Thus, the claim is true
Borland, Inc., has a profit margin of 5.6 percent on sales of $13.6 million. If the firm has debt of $6.4 million and total assets of $9.8 million, what is the firm’s ROA?
Answer:
ROA = 7.77 percent
Step-by-step explanation:
Borland, Inc., has a profit margin of 5.6 percent on sales of $13.6 million
Thus, profit = 5.6% of $13.6 million
profit = 5.6 / 100 * $13.6 million = $0.7616 million
Profit is same as net income
Formula for ROA (return on asset) = net income/ total asset
total asset as given = $9.8 million
Thus, ROA = $0.7616/ $9.8 = 0.0777
ROA in percentage = 0.0777*100 = 7.77
Thus, ROA is 7.77 percent .
Observe the expression below and select the true statement(s).
3y(7 + 2x) + 9ry - 10
The "(7 + 2x)" in the first term is a factor.
The "9" in the second term is a coefficient.
The "By" in the first term is a factor.
The "10" in the third term is a coefficient.
The "2" in the first term is a constant.
The "x" in the second term is an exponent
Answer: The 9 in the second term is a coefficient that is true. I think that is the only thing that is true. There may be one more thing that is true.
The 10 in the third term is not a coefficient.
The 2 is not a constant
the x is not an exponent.
those are the ones that I'm sure about.
Please correct anything if i'm wrong.
:)
Suppose a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%. A cell phone company has reason to believe that the proportion is 30%. Before they start a big advertising campaign, they conduct a 99% CL hypothesis test. Their marketing people survey 150 households with the result that 43 of the households have three cell phones.
Required:
a. Is the actual percentage of households different from 30%?
b. Set up the hypothesis test.
c. What is the success for this problem?
d. Calculate the p-value.
e. Draw conclusion.
Answer:
We conclude that the actual percentage of households is equal to 30%.
Step-by-step explanation:
We are given that a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%.
Their marketing people survey 150 households with the result that 43 of the households have three cell phones.
Let p = proportion of households that have three cell phones NOT known.
So, Null Hypothesis, [tex]H_0[/tex] : p = 30% {means that the actual percentage of households is equal to 30%}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 30% {means that the actual percentage of households different from 30%}
The test statistics that would be used here One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of households having three cell phones = [tex]\frac{43}{150}[/tex] = 0.29
n = sample of households = 150
So, the test statistics = [tex]\frac{0.29-0.30}{\sqrt{\frac{0.30(1-0.30)}{150} } }[/tex]
= -0.27
The value of z test statistic is -0.27.
Also, P-value of the test statistics is given by;
P-value = P(Z < -0.27) = 1 - P(Z [tex]\leq[/tex] 0.27)
= 1 - 0.6064 = 0.3936
Now, at 1% significance level the z table gives critical value of -2.58 and 2.58 for two-tailed test.
Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the actual percentage of households is equal to 30%.
1/4+3/8+1/2+5/8+7/8
Answer: 1/4+3/8+1/2+5/8+7/8
= 21/8
Hope this helps :)))
Answer:
21/8
Step-by-step explanation:
Please answer this correctly
Answer:
342 square meters
Step-by-step explanation:
Consider the length of j;
[tex]j * 9 * 9 = 405,\\j = 405 / 81,\\j = 5 meters[/tex]
Applying the volume of a rectangular prism formula length * width * height = volume, we noted that 9, 9, and j corresponded to the length, width, and height of the rectangular prism and made it equivalent to the volume. Doing so, we solved for j. Now let us solve for the surface area;
[tex]Area of 1st Face = 5 * 9 = 45,\\Area of 2nd Face = 9 * 9 = 81,\\Area of 3rd Face = 5 * 9 = 45,\\\\Surface Area = 2 * ( 45 ) + 2 * ( 81 ) + 2 * ( 45 ) = 342 square meters[/tex]
Opposite faces are equal in terms of their area, so by finding the area of 3 faces, we multiply their area each by 2 to result in the total surface area!
Any help would be great
Answer:
2/3
Step-by-step explanation:
[tex]\dfrac{12}{18}= \\\\\\\dfrac{6\times 2}{6\times 3}= \\\\\\\dfrac{2}{3}[/tex]
Hope this helps!
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]\frac{12}{18}=\frac{x}{3}[/tex]
[tex]18x=12 \times 3[/tex]
[tex]18x=36[/tex]
[tex]\frac{18x}{18y} =\frac{36}{18}[/tex]
[tex]x=2[/tex]
[tex]=\frac{2}{3}[/tex]
Which figure has two bases and one lateral face that is rectangular? cone cylinder rectangular prism rectangular pyramid
Answer: Cylinder
Step-by-step explanation:
Two bases first: that rules out cone and rectangular pyramid.
One lateral face: the only one with that is cylinder.
Hope that helped,
-sirswagger21
The figure which has two bases and one lateral face that is rectangular is, ''Cylinder.''
What is mean by Triangle?Any triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The shape have two bases and one lateral face that is rectangular.
We know that;
In a Cylinder,
It is a three-dimensional solid that contains two parallel bases connected by a curved surface.
And, The bases are usually circular in shape. The perpendicular distance between the bases is denoted as the height “h” of the cylinder and “r” is the radius of the cylinder.
Thus, The figure which has two bases and one lateral face that is rectangular is, ''Cylinder.''
Learn more about the triangle visit;
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What sequence is generated by the function f(n+1)=f(n)-2 for f(1)=10
Answer:
-3
Step-by-step explanation:
nu
a. Write the equation of a line through the points (-4,- 10) and (8,5) in slope-intercept form.
b. Write the equation in standard form Ax+By = C, where A, B, and C are integers and A>0.
ents
Thoquution
Answer:
5x - 4y = 20
Step-by-step explanation:
First find slope
(5- -10)/(8- -4) = 15/12 = 5/4
(y - 5) = 5/4 (x - 8), multiply everything by 4 so you don't have fractions
4y - 20 = 5x - 40
5x - 4y = 20
Given that f(x)=x^2+4x-32f(x)=x
2 +4x−32 and g(x)=x-4g(x)=x−4, find (f+g)(x)(f+g)(x) and express the result in standard form.
Answer:
So your question was not very clear but with (f+g) im guessing thats f(x)+g(x)
So first we add them x^2+4x-32 + x-4 then we will get x^2 + 5x - 36
Then we need to multiply both
(x^2+5x-36)(x^2+5x-36)
=
(x^2+5x-36)^2
The only reason im not solving it out is because it yields large numbers and you might not understand.
Two fair coins are flipped at the same time What is the probability that both display tails?
1/8
1/4
1/3
1/2
Answer:
Step-by-step explanation:
Your answer would be 1/2.
Because they are 2 coins and each have a probability of landing on tails.
The probability that both display tails are 1/2.
We have given that,
Two fair coins are flipped at the same time
We have to determine the, what is the probability that both display tails.
What is the probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
Because they are 2 coins and each has a probability of landing on tails.
To learn more about the probability visit:
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Jose runs a factory that makes stereo tuners. Each S100 takes 8 ounces of plastic and 4 ounces of metal. Each FS20 requires 4 ounces of plastic and 6 ounces of metal. The factory has 312 ounces of plastic, 372 ounces of metal available, with a maximum of 20 S100 that can be built each week. If each S100 generates $7 in profit, and each FS20 generates $13, how many of each of the stereo tuners should Jose have the factory make each week to make the most profit
Answer: Jose should have the factory make 50 FS20 stereo tuners and 14 S100 stereo tuners each week to make the most profit
Step-by-step explanation:
Since each S100 takes 8 ounces of plastic and 4 ounces of metal. Each FS20 requires 4 ounces of plastic and 6 ounces of metal. And the factory has 312 ounces of plastic, 372 ounces of metal available, then,
For plastic
8 ounces + 4 ounces = 12 ounces
The number of stereo tuners it can produce will be
312/12 = 26 stereo tuners
For metal
4 ounces + 6 ounces = 10 ounces
The number of stereo tuners it can produce will be
372/10 = 37.2 = 37 approximately
Since FS20 generate more profit than S100, let assume that Jose produces 50 FS20 by consuming
4 × 50 = 200 ounces of plastic
6 × 50 = 300 ounces of metal
The remaining plastic will be
312 - 200 = 112
The remaining plastic will be
372 - 300 = 72
Divide 112 by 8 in order to make S100
112/8 = 14
Also 72/4 = 18.
Therefore, Jose should have the factory make 50 FS20 stereo tuners and 14 S100 stereo tuners each week to make the most profit
Solving an Equation Using Algebra Tiles
Arrange the tiles on both boards to find the value of x.
What is the value for x when solving the equation
-x+ (-1) = 3x + (-5) using algebra tiles?
O x= -1
O x= 1
OX= 2
O x=3
Board sum: (-x) + (-1) = 3x + (-5)
Reset
The tiles are ready for moving
Done
Intro
Answer:
[tex]\boxed{ \ x = 1 \ }[/tex]
Step-by-step explanation:
hi,
-x+(-1)=3x+(-5)
<=>
-x-1=3x-5
<=>
3x+x = -1+5 = 4
<=>
4x=4
<=>
x=1
thanks
The value of x when solving the equation -x+ (-1) = 3x + (-5) is 1
Algebraic expression:Algebraic expression is a union of terms by the operations such as addition, subtraction, multiplication, division, etc
-x + (-1) = 3x + (-5)
The value of x can be found as follows:
-x + (-1) = 3x + (-5)
Let's open the parenthesis, Therefore,
-x - 1 = 3x - 5
-x - 3x = -5 + 1
-4x = -4
divide both sides by -4
-4x / -4 = -4 / -4
x = 1
learn more on algebra here: https://brainly.com/question/22817831?referrer=searchResults
Only answer if you know geometry or if you know this
Answer:
SAS
Step-by-step explanation:
the angles are congruent, and the 2 pairs of sides are proportional.
200/150 is 4/3 and 320/240 is 4/3 as well.
therefore Side-Angle-Side
At the Rowlett Holiday Parade
there were a total of 51 floats. If
7 of those floats were from
sports teams, what percent
were NOT sports teams?
Answer:
[tex] p =\frac{7}{51}= 0.1372[/tex]
And then the probability that is NOT from sport temas using the complement rule is given by:
[tex] q = 1-p =1- \frac{7}{51}= 0.8627[/tex]
And if we convert that into % we got:
[tex] 0.8627 *100= 86.27\%[/tex]
Approximately 86.27% of the floats were NOT sports teams
Step-by-step explanation:
For this case we can begin finding the % of floats that were from sport tems using the Laplace definition of probability given by:
[tex]p = \frac{Possible}{Total}[/tex]
And replacing we got:
[tex] p =\frac{7}{51}= 0.1372[/tex]
And then the probability that is NOT from sport temas using the complement rule is given by:
[tex] q = 1-p =1- \frac{7}{51}= 0.8627[/tex]
And if we convert that into % we got:
[tex] 0.8627 *100= 86.27\%[/tex]
Approximately 86.27% of the floats were NOT sports teams
A credit card company monitors cardholder transaction habits to detect any unusual activity. Suppose that the dollar value of unusual activity for a customer in a month follows a normal distribution with mean $250 and variance $2400.
(a) What is the probability of $250 to $294 in unusual activity in a month? Round your answer to four decimal places (e.g. 98.7654) P-0.4861
(b) What is the probability of more than $294 in unusual activity in a month? Round your answer to four decimal places (e.g. 98.7654) P 0.0139
(c) Suppose that 10 customer accounts independently follow the same normal distribution. What is the probability that at least one of these customers exceeds $294 in unusual activity in a month? Round your answer to four decimal places (e.g. 98.7654)
Answer:
Step-by-step explanation:
Let x be the random variable representing the dollar value of unusual activity for a customer in a month. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 250
σ = √variance = √2400 = 48.99
a) the probability of $250 to $294 in unusual activity in a month is expressed as
P(250 ≤ x ≤ 294)
For x = 250,
z = (250 - 250)/48.99 = 0
Looking at the normal distribution table, the probability corresponding to the z score is 0.5
For x = 294
z = (294 - 250)/48.99 = 0.9
Looking at the normal distribution table, the probability corresponding to the z score is 0.8159
Therefore,
P(250 ≤ x ≤ 294) = 0.8159 - 0.5 = 0.3159
b) the probability of more than $294 in unusual activity in a month is expressed as
P(x > 294) = 1 - P(x < 294)
P(x > 294) = 1 - 0.8159 = 0.1841
c) since n = 10, the formula becomes
z = (x - µ)/(σ/n)
z = (294 - 250)/(48.99/√10) = 2.84
Looking at the normal distribution table, the probability is 0.9977
Therefore, the probability that at least one of these customers exceeds $294 in unusual activity in a month is
1 - 0.9977 = 0.0023
