a) The probability of eating at a restaurant with unsanitary conditions is 3/7. If you plan to eat at 10 different restaurants, the probability of eating at exactly 3 restaurants with unsanitary conditions is given by the binomial probability formula:
P(X = 3) = (10 choose 3) * (3/7)^3 * (4/7)^7 = 120 * (0.42857)^3 * (0.57143)^7 = 0.1437
So, the likelihood of eating at three restaurants with unsanitary conditions is 14.37%.
b) The probability of eating at 4 or 5 restaurants with unsanitary conditions can be found by summing the binomial probabilities for each case:
P(X = 4) = (10 choose 4) * (3/7)^4 * (4/7)^6 = 210 * (0.42857)^4 * (0.57143)^6 = 0.1735
P(X = 5) = (10 choose 5) * (3/7)^5 * (4/7)^5 = 252 * (0.42857)^5 * (0.57143)^5 = 0.1428
P(X = 4 or X = 5) = P(X = 4) + P(X = 5) = 0.1735 + 0.1428 = 0.3163
So, the likelihood of eating at 4 or 5 restaurants with unsanitary conditions is 31.63%.
c) The probability of eating in at least one restaurant with unsanitary conditions can be found by subtracting the probability of eating in no restaurants with unsanitary conditions from 1. The probability of eating in no restaurants with unsanitary conditions is given by the binomial probability formula:
P(X = 0) = (10 choose 0) * (3/7)^0 * (4/7)^10 = 1 * (1) * (0.57143)^10 = 0.0139
P(X >= 1) = 1 - P(X = 0) = 1 - 0.0139 = 0.9861
So, the probability of eating in at least one restaurant with unsanitary conditions is 98.61%.
d) The most likely number is 3, as it has the highest probability of occuring.
e) The data is not very variable around the most likely number, as the probability of the other numbers is relatively low.
f) Yes, this is a binomial distribution as the experiment has only two possible outcomes, "success" (eating at a restaurant with unsanitary conditions) or "failure" (eating at a restaurant with sanitary conditions) and the number of trials is fixed (10)
g) No, the likelihood of success is not always 50% in a binomial distribution. The probability of success is given by the proportion of successful trials in the population, which in this case is 3/7.
Select the story problem that this division problem represent 1/2 2/5 (Repost)
The story problem that aligns with the division problem is A. A whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the whiteboard?
How to illustrate the division problem?From the information given, it can be seen that 1/2 is divided by 2/5.
In this case, the story that aligns with it is that a whiteboard is 2/5 meter long and has an area of 1/2 square meter. How wide is the whiteboard?
In this case, the length is multiplied by width to get the area.
Therefore, the correct option is A.
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Find the zeros of polynomial function
X³-4x²-7x+5
The zeros of the polynomial function are -1.728, 0.56 and 5.167
How to solve the zeros?The polynomial function is given as:
x^3 - 4x^2 - 7x + 5
Next, we plot the graph of the polynomial
From the graph, the polynomial cross the x-axis when
x = -1.728, 0.56 and 5.167
Hence, the zeros of the polynomial function are -1.728, 0.56 and 5.167
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There are two bags containing only orange and red marbles. Bag A has 2 orange marbles and 6 red marbles. Bag B has 4 orange marbles and 16 red marbles. A marble is randomly chosen from each bag. List these events from least likely to most likely. Event 1: choosing an orange or red marble from Bag B. Event 2: choosing an orange marble from Bag B. Event 3: choosing an orange marble from Bag A. Event 4: choosing a purple marble from Bag A. Least likely Event Event, Event, X Most likely Event Ś ?
Answer:
From least to most likely:
Event 4, Event 2, Event 3, Event 1
Step-by-step explanation:
Event 1 has a 100% chance because there are only red and orange marbles in the bag.
In event 2, there are 4 orange marbles in the bag, giving us a (4/20) chance. This is 20%
In event 3, there are 2 orange marbles of 8 total, giving us an (2/8) chance. This is 25%
Lastly, there are no purple marbles in either bag, giving us a 0% chance of this occurring.
: A native wolf species has been reintroduced into a national forest. Originally 210 wolves were transplanted. After 10 years, the population had grown to 410 wolves. If the population grows exponentially, write an explicit formula for the number of wolves, where w is the number of wolves and t is the number of years.
The explicit formula that can be used to determine the number of wolves is w = 210 (1.0692^t) .
What is the explicit formula?The first step is to determine the growth rate of the wolf species.
Growth rate = [(future population / present population)^(1/number of years)] - 1
[(410 / 210)^(1/10)] - 1 = 6.92
The exponential function would have the form:
FV = P (1 + r)^t
FV = Future population P = Present populationR = rate of growtht = number of yearsw = 210 (1.0692^t)
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A concert manager counted 525 ticket receipts the day after a concert. The price for a student ticket was $10.50, and the price for an adult ticket was $18.00. The register confirms that $8,325.00 was taken in. How many student tickets and adult tickets were sold?
Answer:
150 student tickets and 375 adult tickets
Step-by-step explanation:
Let x = # of student tickets sold, and y = # of adult tickets sold.
Total of 525 tickets were sold, so the first equation is x + y = 525. The register gained $8325, so 10.50x + 18y = 8235 is the second equation.
x + y = 525
10.50x + 18y = 8325
18x + 18y = 9450
10.50x + 18y = 8325
7.5x = 1125
x = 150
150 + y = 525
y = 375
Question 2(Multiple Choice Worth 2 points)
(03.01 LC)
Assume you are working with a standard deck of 52 cards. There are 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace) in each of four suits
and spades).
What is P(Jack Heart) if you draw one card?
O
-
52
13
52
Question 3(Multiple Choice Worth 2 points)
(03.02 MC)
Answer:
Assume you are working with a standard deck of 52 cards. There are 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace) in each of four suits
and spades).
What is P(Jack Heart) if you draw one card? 13
A scientist wants an 81milliliter of saline solution with a concentration of 5% she has concentrations of 3% and 9%. How much of each solution must she use to get the desired concentration
The quantity of each concentrations of 3% and 9% needed to get the desired concentration is 54 milliliters and 27 milliliters respectively
Simultaneous equationLet
Quantity of 3% needed = xQuantity of 9% needed = yx + y = 81
0.03x + 0.09y = 81 × 5%
0.03x + 0.09y = 4.05
x + y = 81
0.03x + 0.09y = 4.05
From (1)
x = 81 - y
Substitute into0.03x + 0.09y = 4.05
0.03(81 - y) + 0.09y = 4.05
2.43 - 0.03y + 0.09y = 4.05
- 0.03y + 0.09y = 4.05 - 2.43
0.06y = 1.62
y = 1.62/0.06
y = 27
substitute y = 27 intox = 81 - y
x = 81 - 27
x = 54
Simultaneous equation:
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what is the lower quartile in the following distribution 82, 90, 66, 78, 88, 72, 60, 80 A)69 B)78 C)79 D) 85
Answer:
A) 69
Step-by-step explanation:
• First , we put the numbers of the distribution in order:
60 , 66 , 72 , 78 , 80 , 82 , 88 , 90
• Notice that the set has 8 numbers which is an even number.
Then
→ the lower quartile is the mean of the set :
60 , 66 , 72 , 78
Which is the average of the two middle numbers 66 and 72.
Then
[tex]\text{the lower quartile}=\frac{66+72}{2} = 69[/tex]
Which point lies on the circle represented by the equation x² + (y-12)² = 25²?
A. (20.-3)
B. (-7,24)
c. (0.13)
D. (-25,-13)
Answer: B
Step-by-step explanation: Trust me bro
Type 4 points found on the circumference of the following equation. Exact points only, no approximations.
(x-3)^2 +(y+2)^2+49
The points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24))
How to determine the points on the circumference of the circle?The circle equation is given as:
(x-3)^2 +(y+2)^2= 49
Rewrite as:
(y+2)^2= 49 -(x-3)^2
Take the square root of both sides
y+2= ±√[49 -(x-3)^2]
Subtract 2 from both sides
y = -2 ± √[49 -(x-3)^2]
Next, we determine the points
Set x = 3
y = -2 ± √[49 -(3-3)^2]
Evaluate
y = -2 ± 7
Solve
y = 5 and y = -9
So, we have
(x, y) = (3, 5) and (3, -9)
Set x = 8
y = -2 ± √[49 -(8-3)^2]
Evaluate
y = -2 ± √24
Solve
y = -2 - √24 and y = -2 + √24
So, we have
(x, y) = (8, -2 + √24) and (8, -2 - √24)
Hence, the points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24)
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∫[tex]\frac{xdx}{(x^{2}+4)^{3} }[/tex]
Substitute [tex]u=x^2+4[/tex] and [tex]du=2x\,dx[/tex]. Then the integral transforms to
[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \int \frac{du}{u^3}[/tex]
Apply the power rule.
[tex]\displaystyle \int \frac{du}{u^3} = -\dfrac1{2u^2} + C[/tex]
Now put the result back in terms of [tex]x[/tex].
[tex]\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \left(-\dfrac1{2u^2} + C\right) = -\dfrac1{4u^2} + C = \boxed{-\dfrac1{4(x^2+4)^2} + C}[/tex]
Two friends board an airliner just before departure time. There are only 11 seats left, 4 of which are aisle seats. How many ways can the 2 people arrange themselves in available seats so that at least one of them sits on the aisle?
The 2 people can arrange themselves in blank ways?
Using the Fundamental Counting Theorem, it is found that:
The 2 people can arrange themselves in 40 ways.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
With one people in the aisle and one in the normal seats, the parameters are:
n1 = 4, n2 = 7
With both in the aisle, the parameters is:
n1 = 4, n2 = 3
Hence the number of ways is:
N = 4 x 7 + 4 x 3 = 28 + 12 = 40.
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You deposit $4000 each year into an account earning 2% interest compounded annually. How much will you have in the account in 30 years?
The amount that will be in the account after 30 years is $162,272.32.
How much would be in the account after 30 years?When an amount is compounded annually, it means that once a year, the amount deposited and the interest already accrued increases in value. Compound interest leads to a higher value of deposit when compared with simple interest, where only the amount deposited increases in value once a year.
The formula that can be used to determine the future value of the yearly deposit of $4,000 in 30 years is : annuity factor x yearly deposit
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest raten = number of years$4000 x [{(1.02^30) - 1} / 0.02] = $162,272.32
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AB = 6cm, AC = 12cm
Calculate the length of CD.
Give your answer to 3 significant figures.
In the given diagram, the length of CD is 12.7 cm
TrigonometryFrom the question, we are to determine the length of CD
First, we will calculate the length of CB
From the Pythagorean theorem,
|CA|² = |CB|² + |BA|²
12² = |CB|² + 6²
144 = |CB|² + 36
|CB|² = 144 - 36
|CB|² = 108
|CB| = √108
|CB| = 6√3 cm
Now, to find CD
Using SOH CAH TOA
sin55° = |CB| / |CD|
sin55° = 6√3 / |CD|
|CD| = 6√3 / sin55°
|CD| = 12.7 cm
Hence, the length of CD is 12.7 cm
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what is the measure of the reference angle for a 102 degree angle? A. 78 degrees B. 68 degrees C. 57 degrees D. 12 degrees
Answer:
A. The reference angle measures 78 degrees
The tables show proportional relationships between x and y. Match each table with its constant of proportionality.
xy
1 10
2 20
3 30
xy
4 20
8 40
12 60
x y
2 15
4 30
6 45
4
12/04
10
xy
14
2 8
3 12
Which of the following expressions would simplify to be the multiplicative identity?
023.32
023.23
021
0 20
NEXT QUESTION
ASK FOR HELP
The expression that would be simplified to be a multiplicative identity is 2^0
How to determine the expression that would be simplified to be a multiplicative identity?The complete question is added as an attachment
Multiplicative identities are represented as:
a * 1 = a
This means that the definition of multiplicative identities is the product of a number and 1
From the list of options, we have
2^0
When the exponent of a non-zero number is 0, the result is 1.
This means that
2^0 = 1
Hence, the expression that would be simplified to be a multiplicative identity is 2^0
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Handre runs a paragliding and adventure touring company. For each paragliding trip (p) he takes he makes $55 and for each adventure tour (a) he makes $75. Last week, he made $2725. Write the equation to represent the relationship between the number of paragliding trips, adventure tours, and his total pay
The equation that shows the relationship between the number of paragliding trips, adventure tours, and his total pay is 55a + 75p = 2725
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let a represent the number of adventure tours and p represent the number of paragliding trip, hence:
55a + 75p = 2725
The equation that shows the relationship between the number of paragliding trips, adventure tours, and his total pay is 55a + 75p = 2725
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Find the slope and y-intercept of the line whose equation is y=6x=5
Answer:
the slope is 5 and the y intercept is 5
Step-by-step explanation:
I think that you meant to write y = 6x + 5.
y = mx + b
The number in in the m spot is the slope and the number in the b spot is the y intercept.
3
3
4
Possible inputs for the quadratic when the
output is 3 are
(Note: Fill in the least input first)
or
[tex]x {}^{(1)} = - 3 \: \: \: \: \: \: x {}^{(2)} = - 1[/tex]
Select all the terms that are like terms
Answer:
-8 x^2
1.25 x^2
1/2 x^2
Step-by-step explanation:
They are like terms because they have the same variable x^2, yx^2 is not the same because it has the variable y
Answer:
the 2nd, 3rd and 4th options (all with x²)
Step-by-step explanation:
"like terms" means the exactly same variable(s) with exactly the same exponents of these variables.
constants in the terms can be different and even have different signs.
5yx² is not "like", because of the additional y variable.
The inverse of G(x) is a function.
• A. True
• B. False
Answer: False
Step-by-step explanation:
G(x) is not a one-to-one function (since it fails the horizontal line test). Therefore, it doesn't have an inverse.
Calculate the price elasticity of supply for Bobbie's Bakery's banana bread. When the price changes by 29% the quantity supplied changes by 55%. Round your answer to two decimal places.
The price elasticity of demand is 1.90.
What is the price elasticity of demand?Price elasticity of supply measures the responsiveness of quantity supplied to changes in price of the good. It is expected that quantity supplied would be positively related to the price of the good.
Price elasticity of supply = percentage change in quantity supplied / percentage change in price
55% / 29% = 1.90
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Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire is interested in estimating the mean math SAT scores of the incoming class with 95% confidence. How large a sample should she take to ensure that the margin of error is below 29?
Using the z-distribution, it is found that she should take a sample of 46 students.
What is a z-distribution confidence interval?
The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence, by the Empirical Rule the standard deviation is found as follows:
[tex]6\sigma = 800 - 200[/tex]
[tex]6\sigma = 600[/tex]
[tex]\sigma = 100[/tex]
The sample size is n when M = 29, hence:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]29 = 1.96\frac{100}{\sqrt{n}}[/tex]
[tex]29\sqrt{n} = 196[/tex]
[tex]\sqrt{n} = \frac{196}{29}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{196}{29}\right)^2[/tex]
n = 45.67.
Rounding up, a sample of 46 students should be taken.
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Landscape artists frequently hand-draw their landscape layouts (blueprints) because this allows them more creativity and precision over their plans. Although done by hand, the layouts must be extremely accurate in terms of angles and distances.
a. A landscape artist has drawn the outline of a house. Describe three different ways to make sure the corners of the house are right angles.
b. A bench needs to be placed in the exact middle of two trees. Describe three different methods the designer can use to find out where to place the bench.
c. The landscape designer has drawn an angle on one side of the yard and wants to draw the same angle on the other side. Describe three different ways he can do this.
The information given about the landscape is illustrated below:
How to explain the landscape?a. You'll need a measuring tape, two range poles, pegs, and three people.
The first person holds the zero mark between their thumbs and fingers, the second person holds the 3m mark on the tape between their thumbs and fingers, and the third person holds the 8m. When all sides of the rope are stretched, a triangle is created, and an angle near one is a right angle.
Wrap one loop of the rope around peg A with a peg through the other loop, draw a circle on the ground, place pegs B and C where the circle crosses the base line, and place peg D half way between pegs B and C, allowing pegs D and A to form lines perpendicular to the base line, forming a right angle.
B. Method 1; Take a measurement of the distance between both trees and divide by 2 to get the midpoint.
Method 2; By use of a compass to bisect the distance between both points.
Method 3; By using a protractor to mark the 90° vertical point when placed between the two endpoints.
C The three different ways he can do this.
1) by using a protractor
2) by finding a point
3) by extending the line of the angle until it reaches the other side of the field.
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The equations of four lines are given. Identify which lines are parallel.
Line 1: y=−5x−5
Line 2: x+12y=−4
Line 3: y=−2x+4
Line 4: y+8=−15(x−9)
None of the equation of the line is parallel because there slope are not equal.
How to find lines that are parallel?Parallel line have the same slope.
Therefore, using slope intercept equation,
y = mx + b
where
m = slopeb = y-interceptHence,
y = −5x − 5 , slope = -5
x + 12y = −4; y = -1 / 3 - 1 / 12 x, slope = 1 / 12
y = −2x + 4: slope = -2
y + 8 = -15x + 135; y = -15x + 127, slope = -15
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In the geometric pattern below, n represents the number of blocks in the bottom row of each figure.
n = 1
n=2
Write a function that models the total number of blocks in terms of n.
OA f(1) = 2; f(n) = f(n-1) + 2n; for n ≥ 2
OB. f(1) = 1; f(n) = f(n-1) + 2n; for n ≥ 2
Oc f(1) = 1; f(n) = f(n-1) + n; for n ≥ 2
OD. f(1) = 2; f(n) = f(n-1) + 4n; for n ≥ 2
n=3
Find the equation of a line with a slope of 13/2
that passes through the point (−2, — 10).
Answer: [tex]y=\frac{13}{2} x+3[/tex]
Step-by-step explanation:
Remember the point-slope equation which is [tex]y-y_{1} = m(x-x_{1} )[/tex] where[tex](x_{1} , y_{1} )[/tex] is your point and [tex]m[/tex] is your slope.
Given that we substitute what you have:
[tex]y-(-10) =\frac{13}{2} (x - (-2))[/tex]
Minus and minus give us positive:
[tex]y+10 =\frac{13}{2} (x +2)[/tex]
Multiply slope into the parenthesis:
[tex]y+10= \frac{13}{2}x + \frac{13}{2}*2\\[/tex]
Calculate it:
[tex]y+10= \frac{13}{2}x +13[/tex]
Isolate the [tex]y[/tex] by subtracting 10 from both sides:
[tex]y=\frac{13}{2} x + 13 -10[/tex]
Your final equation is:
[tex]y=\frac{13}{2} x +3[/tex]
Hope this makes sense!
And here's the graph to prove that the line actually goes through the point [tex](-2,-10)[/tex]:
Please help me solve this
If the sample mean is 51,sample size is 21 , sample standard deviation is 15 and confidence level is 95% then the lower bound is 45.35 and upper bound is 56.65.
Given sample mean of 51, sample size of 21, sample standard deviation be 15 and confidence level be 95%.
We are required to find the upper bound and lower bound.
We have to use t test as the sample size is less than 30.
Margin of error is the difference between calculated figures and real figures.
Margin of error= standard deviation* critical value of t
Critical value of t at 0.05 significance level with degree of freedom 20 [21-1] is 1.7247.
Margin of error=1.7247*15/4.5826
(4.5826 is the square root of 21)
=5.6454
Upper bound=51+5.6454
=56.6454
Lower bound=51-5.6454
=45.3546
After rounding off they will be 56.65 and 45.35.
Hence if the sample mean is 51,sample size is 21 , sample standard deviation is 15 and confidence level is 95% then the lower bound is 45.35 and upper bound is 56.65.
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Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane.
y > 2x + 4
x + y ≤ 6
The solution to the system of inequalities is (0.667, 5.333)
How to graph the inequalities?The system of inequalities is given as:
y > 2x + 4
x + y ≤ 6
Next, we plot the graph of the system using a graphing tool
From the graph, both inequalities intersect at
(0.667, 5.333)
Hence, the solution to the system of inequalities is (0.667, 5.333)
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