Final answer:
The probability that an apartment is on the 2nd floor or has 2 bedrooms is 0.7727 or 77.27%.
Explanation:
To find the probability that an apartment is on the 2nd floor or has 2 bedrooms, we need to determine the total number of apartments that satisfy either of the conditions.
On the 2nd floor, there are 2 apartments with 1 bedroom, 2 apartments with 2 bedrooms, and 2 apartments with 3 bedrooms. This gives us a total of 2 + 2 + 2 = 6 apartments on the 2nd floor.
Out of the total distribution of apartments, there are 3 apartments with 1 bedroom, 4 apartments with 2 bedrooms, and 4 apartments with 3 bedrooms. This gives us a total of 3 + 4 + 4 = 11 apartments with 2 bedrooms.
The probability of an apartment being on the 2nd floor or having 2 bedrooms is given by:
Probability = (Number of apartments on the 2nd floor + Number of apartments with 2 bedrooms) / Total number of apartments
Probability = (6 + 11) / (6 + 1 + 1 + 2 + 2 + 2 + 1 + 2 + 4 + 1) = 17 / 22 = 0.7727 or 77.27%
In a batch of 960 calculators, 8 were found to be defective. What is the probability that a calculator chosen at random will be defective? Write the probability as a percent. Round to the nearest tenth of a percent if necessary
Answer: 0.8%
Step-by-step explanation:
Given : In a batch of 960 calculators, 8 were found to be defective.
i.e. Total calculators =960
Number of defective calculator = 8
We know that the probability of any event is given by :-
[tex]\dfrac{\text{No. of favorable outcomes}}{\text{Total outcomes}}\\\\=\dfrac{8}{960}=0.00833333333333[/tex]
In percent, [tex]0.00833333333333\times100=0.833333333333\%\\\\\approx0.8\%\ \ \ [\text{Rounding to the nearest tenth.}][/tex]
Hence, the probability that a calculator chosen at random will be defective=0.8%
Buford and Bobbie had a combined gross income of $154,900 in 2009. When filing their federal income tax return with the Married Filing Jointly filing status, they took the standard deduction of $11,400, claimed themselves as exemptions for $3650 each, and did not have any other adjustments to income. According to the following table, which income tax bracket did they fall into?
Answer:25%
Step-by-step explanation:
Choose the value of X that makes the open sentence true
30 - x^2 < 3x + 7
A 4
B 3
C 2
D 1
Answer:
Option A - 4
Step-by-step explanation:
Given : Inequality [tex]30 - x^2 < 3x + 7[/tex]
To find : Choose the value of x that makes the open sentence true ?
Solution :
We substitute the value of x from options to check which is true,
A) x=4
[tex]30 - 4^2 < 3(4) + 7[/tex]
[tex]30-16 < 12+ 7[/tex]
[tex]14< 19[/tex]
It is true.
B) x=3
[tex]30 - 3^2 < 3(3) + 7[/tex]
[tex]30-9< 9+ 7[/tex]
[tex]21< 16[/tex]
It is false.
C) x=2
[tex]30 - 2^2 < 3(2) + 7[/tex]
[tex]30-4<6+ 7[/tex]
[tex]26< 13[/tex]
It is false.
D) x=1
[tex]30 - 1^2 < 3(1) + 7[/tex]
[tex]30-1<3+ 7[/tex]
[tex]29< 10[/tex]
It is false.
Therefore, Option A is correct.
Help me please
which graph shows a triangle and it's reflection image over the x-axis?
What is the answer to. Write a polynomial equation with integer coefficients that has the given roots, x=7 and x=-5
A fisherman caught one fish that was 12 5 feet long and a second fish that was 9 4 feet long. How much longer was the first fish?
The answer is A) 3 / 20 on USA Test Prep!
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In a right triangle, one leg measures 4 inches and the other measures 6 inches. What is the length of th hypotenuse in inches
Choose all of the following that must be true for a random experiment to be binomial.
Select one or more:
A. On each trial, the event of interest either occurs or does not occur.
B. The trials are independent of one another and repeated under identical conditions.
C. The probability of occurrence is the same on each trial.
D. There is a fixed number of trials.
A binomial experiment has a fixed number of trials, all are independent and conducted under identical conditions. Only two results—success or failure—are possible with each trial, each having the same probability, fitting a binomial probability distribution.
Explanation:For a random experiment to be binomial, it must meet certain conditions. Firstly, there should be a fixed number of trials, denoted as 'n'. The results of these trials don't influence each other, meaning that the trials are independent. This signifies that the outcome of a trial, for example, the first one, does not affect the outcomes of the subsequent trials. Moreover, all these trials should be conducted under identical conditions.
In a binomial experiment, there are only two possible results, often referred to as 'success' and 'failure'. Each trial has the same probability of success, denoted as 'p'. The outcomes of a binomial experiment fit a binomial probability distribution. The random variable 'X' stands for the number of successful trials. The mean 'µ' is given by 'np', and the standard deviation 'o' by √npq. The probability of exactly 'x' successes in 'n' trials is P(X = x).
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In triangle ABC, a = 9, c = 5, and B = 120°. Find b2.
61
83.5
128.5
151
Answer:
The correct answer is 151.
Step-by-step explanation:
Given,
In triangle ABC,
BC = a = 9 unit,
AB = c = 5 unit,
m∠B = 120°,
We have to find : b² or AC²,
By the cosine law,
[tex]b^2=a^2+c^2-2ac cosB[/tex]
[tex]=9^2+5^2-2\times 9\times 5\times cos 120^{\circ}[/tex]
[tex]=81+25-90\times -0.5[/tex]
[tex]=81+25+45[/tex]
[tex]=151[/tex]
Hence, the value of [tex]b^2[/tex] is 151.
Answer:
Option D) [tex]b^2 = 151[/tex]
Step-by-step explanation:
We are given the following information in the question:
[tex]\triangle ABC\\\text{Side } a = 9\text{ units}\\\text{Side } c = 5\text{ units}\\\angle ABC = 120^{\circ}[/tex]
We have to find [tex]b^2[/tex]
The law of cosines state that if a, b and c are the sides of triangle and b is the side opposite to angle B, then,
[tex]b^2 = a^2 + c^2 - 2ac~\cos(B)[/tex]
Putting the values, we have,
[tex]b^2 = (9)^2 + (5)^2 - 2(9)(5)~\cos(120)\\\\b^2 = 81 + 25 - 90(-0.5)\\\\b^2 = 151[/tex]
Option D) [tex]b^2 = 151[/tex]
How do you multiply -5 that has an exponent of 4 but no parenthesis with 4? Please explain
The circumference of a circular hot tub at a hotel is 56.5 yards. What is the diameter of the hot tub?
To find the diameter of the circular hot tub, divide the circumference by π.
Explanation:To find the diameter of the circular hot tub, we need to use the formula for the circumference of a circle. The formula is C = πd, where C represents the circumference and d represents the diameter.
In this case, the circumference is given as 56.5 yards. So we can plug that value into the formula and solve for d: 56.5 = πd.
To isolate the variable d, we divide both sides of the equation by π. This gives us: d = 56.5/π.
Using a calculator, we can find the approximate value of d to be 18 yards.
The diameter of the hot tub is approximately 18 yards, calculated using the formula [tex]\(D = \frac{56.5}{\pi}\)[/tex] from the given circumference.
The circumference of a circle is given by the formula [tex]\(C = \pi \times D\)[/tex], where C is the circumference and D is the diameter. In this case, the circumference of the hot tub is given as 56.5 yards. So, the formula can be rearranged to solve for the diameter:
[tex]\[ C = \pi \times D \][/tex]
[tex]\[ 56.5 = \pi \times D \][/tex]
To find D, divide both sides of the equation by [tex]\(\pi\)[/tex]:
[tex]\[ D = \frac{56.5}{\pi} \][/tex]
Using the value of [tex]\(\pi \approx 3.14159\)[/tex], the diameter D is approximately:
[tex]\[ D \approx \frac{56.5}{3.14159} \approx 18 \][/tex]
Therefore, the diameter of the hot tub is approximately 18 yards.
The sum of two numbers is equal to 70. Which of the following functions can be use to find the product of the two numbers if one of the numbers is x?
a) p = x^2
b) p = x (x-70)
c) p = x (70 - x)
d) p = (x - 70)^2
Consider the graph of the linear function h(x) = –6 + x. Which quadrant will the graph not go through and why? Quadrant I, because the slope is negative and the y-intercept is positive Quadrant II, because the slope is positive and the y-intercept is negative Quadrant III, because the slope is negative and the y-intercept is positive Quadrant IV, because the slope is positive and the y-intercept is negative
The line of linear function h(x) = –6 + x is not going to enter in the second quadrant so option second will be correct.
What is a graph?The link between lines and points is described by a graph, which is a diagrammatic representation of a network.
A graph is made up of some points and the distance between two. It doesn't matter how much time the lines are or where the points are located. A node is a name for each constituent in a graph.
Given equation is h(x) = –6 + x
at x = 0 , h(x) = -6 so ( 0 , -6 ) is first point.
at x =1 , h(x) = -5 so ( 1 , -5 ) is second point.
If we draw a line by the two-point which I have attached then you can see it not going to the second quarter.
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Suppose that about 58% of the people who are murdered actually knew the person who committed the murder. suppose that a detective file in boston has 60 current unsolved murders. what is the probability that fewer than 32 victims did not know their murderer?
Final answer:
The probability that fewer than 32 out of 60 victims did not know their murderer can be found using the binomial probability formula, summing the probabilities where x ranges from 0 to 31 with a success rate of 42% for each trial.
Explanation:
To find the probability that fewer than 32 out of 60 murder victims did not know their murderer, given that 58% of victims did know their murderer, we can use the binomial probability formula. Considering that 42% (=100%-58%) of the victims did not know their murderer, we want the cumulative probability of x=0 to x=31 successes (victims not knowing the murderer) out of n=60 trials (total murder cases).
This can be calculated using a statistical program or a binomial probability table, as manually computing this would be time-consuming and complex. However, the specific steps would involve summing up the probabilities of all scenarios where the number of victims not knowing their murderer ranged from 0 to 31, factoring in the binomial coefficient, the probability of a single victim not knowing the murderer (42%), and its complement for each case.
Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces x^2+y^2=81 and z=5x^4.
Answer:
[tex]s(t)=(9 cost,9 sint , 32805 cos^4 t) , t\in (0,2\pi)[/tex]
Step-by-step explanation:
We are given that two surfaces
[tex]x^2+y^2=81[/tex]
and [tex]z=5x^4[/tex]
We have to find the parametrize the intersection of the given surfaces using cost and sin t with positive coefficient.
We know that intersection curve S(t) is given by
S(t)=(x(t),y(t),z(t)),[tex]t\in(0,2\pi)[/tex]
[tex]x^2+y^2=(9)^2[/tex]
Compare with the equation of circle [tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is center of circle and r is the radius of the circle.
The center and radius of given circle is (0,0) and 9.
[tex]x=9cost,y=9 sint[/tex]
because cost takes along x - axis and sin t takes along y- axis.
When we substitute these values then we get
[tex]81cos^2t+81sin^2t=81(cos^2t+sin^2t)=81 [/tex] ([tex]sin^2t+cos^2t)=1[/tex])
Hence, [tex]x=9 cost, y= 9sint [/tex]
Substitute the value of x in second equation of surface
[tex]z=5(9cost)^4=32805 cos^4t[/tex]
Hence, the intersection curve s(t) is given by
[tex]s(t)=(9 cost,9 sint , 32805 cos^4 t) , t\in (0,2\pi)[/tex]
Tom has r quarters. Express the value of the quarters in cents.
A diver is descending to reach the bottom of a lake. After 15 seconds, she is 90 feet below the surface of the water. If positive integers represent a distance above the surface of the lake, which integer best represents the diver’s change in position in feet per second?
dive distance traveled by time
90 feet / 15 seconds = 6
since the diver is below the surface they are changing position at -6 feet per second
A is an unknown number. When you round A to the nearest thousand you get 21000. When you round A to the nearest hundred you get 20,500
What is A
The unknown number A, when rounded to the nearest thousand and hundred, is determined to be within the range from 20500 to 20549. A can be any number within this range.
Explanation:In mathematics, when you're given that a number A, when rounded to the nearest thousand, ends up being 21000 or that when rounded to the nearest hundred, it ends up being 20500, you can infer that the unknown number A lies somewhere between two specific values. Since A rounds to 21000 when we round to the nearest thousand, this implies that A is between 20500 and 21499.
However, we also know that, when rounded to the nearest hundred, A is 20500. This implies that A is between 20450 and 20549. Comparing these two ranges, the unknown number A must lie within the common range, which is from 20500 to 20549. Therefore, the number A can be any number within this range.
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The polynomial 6x2 + 37x – 60 represents an integer. Which expressions represent integer factors of 6x2 + 37x – 60 for all values of x?
Answer with explanation:
The Given Quadratic Polynomial which can be Broken into integer factors:
[tex]\rightarrow 6 x^2 + 37 x - 60\\\\ \text{Splitting the Middle term}}\\\\ \rightarrow 6 x^2 + 37 x - 60\\\\\rightarrow 6 x^2 + 45 x-8 x - 60\\\\ \rightarrow 3x \times (2 x+15)-4 (2 x +15)\\\\\rightarrow (3 x -4)(2 x+15)[/tex]
Factors of the above Expression are:
= (3 x -4)(2 x+15)
Joe tapped his maple tree to get syrup. The tree filled 3/4 of a cup in 1/2 hour.At what rate does syrup flow from the tree?
The rate of flow of syrup from the tree will be in mixed fraction form, equal to 1 1/2.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the data mentioned in the question,
The amount of syrup obtained from the tree = 3/4 cup
The time is taken to fill 3/4 cup = 1/2 hour
Then, the rate of flow of syrup will be,
(3/4) ÷ (1/2)
3/4 × 2/1
= 6/4 = 3/2
It can also be written in mixed fraction form,
= 1 1/2
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if you are told only that you scored 80th percentile do you know from the description exactly how it wad calculated? Explain
We know that there is no universal acceptance meaning of a percentile. When someone told you that you are in the 80th percentile, the meaning of that is you have achieved the lowest score that is greater than 80 percent of the score. It is calculated by using the formula R = P/100 x (N + 1)
Final answer:
The 80th percentile represents the score below which 80% of the scores fall.
Explanation:
The 80th percentile represents the score below which 80% of the scores fall. It is calculated by finding the value at which 80% of the data is below and 20% is above. For example, if you scored in the 80th percentile on a 60-point assignment, it means that 80% of students scored equal to or below 49 points and 20% scored above.
712 divided by 8 and show work
"Find the value of the derivative (if it exists) at each indicated extremum. (If an answer does not exist, enter DNE.) f (x) = cos(πx/2)
Write 7.625 as a mixed number in simplest form
0.5,3/16,0.755/49 least to greatest
THIS IS URGENT PLZ HELP ME!!!!!!!
The graph shown is for the inequality y ≥ x. The graph has one thing wrong. What is it?
A)The shading is on the wrong side of the boundary line.
B)The boundary line should be dotted or dashed
C)The boundary line has the wrong y-intercept
D)The boundary line has the wrong slope
For the inequality y ≥ x, the boundary line should be solid, the slope should be 1, the y-intercept should be 0, and shading should be above the line. Therefore, the error could be an incorrect slope, an incorrect y-intercept, or shading below the line.
Explanation:Without seeing the graph it is difficult to determine exactly what is wrong, but based on the question and the options given, we can review the conditions of the inequality y ≥ x. For this inequality:
The boundary line should be solid, not dashed or dotted, because the inequality includes values where y is equal to x. So, choice B is incorrect. The slope of the boundary line should be 1, which is derived from the coefficient of x in the inequality (plain 'x' implies '1x'). Therefore, the slope being wrong (choice D) could be a possible error. The y-intercept of the boundary line should be 0. An incorrect y-intercept (choice C) could be another possible error. The shading should be above the line for y ≥ x (the portion where y values are greater than or equal to x values), so if the shading is below the line, choice A would be correct.Learn more about Inequality Graphing here:https://brainly.com/question/33662315
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Taryn grandmother took her family out to dinner if the dinner was 74$ and Taryn dinner was 20% of the bill how much was Taryns dinner
Given rectangular prism ABCD.
Choose all of the terms that best describe each of the sets of lines or points.
Points A, E, and J
collinear
intersecting
coplanar
noncollinear
noncoplanar
Answer: Fourth and Fifth options are correct.
Step-by-step explanation:
Since we have given two points i.e. A, E, and J
We can see from the graph that
A, E, J are non coplanar and non collinear.
Coplanar means that all the points lie in the same plane.
Collinear means that all the points lie in the same line.
But A, E, and J are neither in the same plane nor in the same line.
Hence, Fourth and Fifth options are correct.
Calculate all four second-order partial derivatives of f(x,y)=sin(2xy)
46x12=46x(10+2), find distributive property