Answer:
125
Step-by-step explanation:
[tex]25=5^2[/tex]
[tex]36=6^2[/tex]
[tex]125=5^3[/tex]
[tex]300=...[/tex]
The measure of two angles of a triangle are 31 and 128 degrees. Find the measure of the third angle.
Answer:
21°
Step-by-step explanation:
All angles in a triangle add up to 180°.
180 - 31 - 128
= 21
The measure of the third angle is 21°.
Three solid shapes, A B and C are similar. The surface area of shape A is 9cm² The surface area of shape B is 16cm² The ratio of the volume of shape B to shape C is 27:125 Work out the ratio of the height of shape A to shape B Give your answer in its simplest form.
Answer:
9:20
Step-by-step explanation:
The ratio of the surface area of similar solid is equal to the square of the ratio of their corresponding linear measures.
If the ratio of their corresponding linear measures is a:b, the surface area ratio will be (a/b)².
Therefore, (A/B )² = 9/16
square root both sides A/B = √9/√16 A/B = 3/4 A:B = 3:4
The ratio of volume of two similar solid is the ratio cube of their corresponding linear measures.
Therefore, (B/C)³ = 27/125 cube root both sides B/C = 3/5 B:C = 3:5
To make the ratio equivalent A:B:C = 9:12:20
A:C = 9:20
3. Students arrive at an ATM machine in a random pattern with an average inter-arrival time of 3 minutes. The length of transactions at the ATM machine is exponentially distributed with an average of 2 minutes. (a) What is the probability that a student arriving at the ATM will have to wait
Answer:
The probability that a student arriving at the ATM will have to wait is 67%.
Step-by-step explanation:
This can be solved using the queueing theory models.
We have a mean rate of arrival of:
[tex]\lambda=1/3\,min^{-1}[/tex]
We have a service rate of:
[tex]\mu=1/2\,min^{-1}[/tex]
The probability that a student arriving at the ATM will have to wait is equal to 1 minus the probability of having 0 students in the ATM (idle ATM).
Then, the probability that a student arriving at the ATM will have to wait is equal to the utilization rate of the ATM.
The last can be calculated as:
[tex]P_{n>0}=\rho=\dfrac{\lambda}{\mu}=\dfrac{1/3}{1/2}=\dfrac{2}{3}=0.67[/tex]
Then, the probability that a student arriving at the ATM will have to wait is 67%.
Urgent need help immediately please !
Answer:
D
Step-by-step explanation:
Select all of the following true statements if R = real numbers, I = integers, and W = {0, 1, 2, ...}.
Answer and Step-by-step explanation:
We will begin to solve this problem by defining first what the sets' elements really are.
R consists of real numbers. This means that this set contains all the numbers, rational or not.
Z is composed of whole numbers. Integers include all negative and positive numbers as well as zero (it's basically a set of whole numbers and their negated values).
W, on the other hand, has 0,1,2, and its elements are onward. Those numbers are referred to as whole numbers.
W ⊂ Z is TRUE. Z contains all the numbers as stated earlier, and W is a subset of it.
R ⊂ W is FALSE. Not all numbers are complete numbers. Complete numbers must be rational and represented fractionless. These requirements are not met by those real numbers.
0 ∈ Z is TRUE. Zero is just an integer so it is a component of Z.
∅ ⊂ R is TRUE. A set i.e null be R subset, and each and every set is a general set. Moreover, there were not single elements in a null set, so it spontaneous became a non empty set subset through description as there is no element of R.
{0,1,2,...} ⊆ W is TRUE. The set on the left is precisely what is specified in the statement for problem for W. (The bar below the subset symbol simply implies that the subset is not rigid, because the set on the left may be equal to the set on the right. Without it, the argument would be incorrect, because a strict subset needs that the two sets not be identical).
-2 ∈ W is FALSE. W's only made up of whole numbers and not their negated equivalents.
i dont understand, help?
A perfect square number can never have the digit ….. at the units place.
a :1
b :9
c :8
please tell me the answer as soon as possible
Answer:
the answer is the last option, c :8.
The commute time for people in a city has an exponential distribution with an average of 0.5 hours. What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours? Answer: (round to 3 decimal places)
Answer:
0.314 = 31.4% probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
In this question:
[tex]m = 0.5, \mu = \frac{1}{0.5} = 2[/tex]
What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours?
[tex]P(0.4 \leq X \leq 1) = P(X \leq 1) - P(X \leq 0.4)[/tex]
In which
[tex]P(X \leq 1) = 1 - e^{-2} = 0.8647[/tex]
[tex]P(X \leq 0.4) = 1 - e^{-2*0.4} = 0.5507[/tex]
So
[tex]P(0.4 \leq X \leq 1) = P(X \leq 1) - P(X \leq 0.4) = 0.8647 - 0.5507 = 0.314[/tex]
0.314 = 31.4% probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours
Compare and contrast the following piecewise
defined functions.
(-x+ 2 x<0
X+2, x<0
f(x) =
x? + 1, x>0 X + 2, x>0
g(x)=
Answer:
Both piecewise functions have a linear portion and a quadratic portion. The y-intercepts of both linear pieces are the same, 2. The quadratics are both open upward, but have different y-intercepts (one at 1, one at 2). The linear portion of the first function is decreasing, while the linear portion of the second function is increasing.
Step-by-step explanation:
Comparing and contrast of the functions are shown in below.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The given piecewise functions are;
⇒ f (x) = { - x + 2 ; x < 0
= { x² + 1 ; x > 0
Now, Comparison and contrast of the above piecewise functions are,
The similarities are;
1) Both piecewise functions are linear when x < 0.
2) Both piecewise functions are quadratic when x > 0.
3) The magnitude the slope of the linear part both function are equal.
4) The leading coefficient of the quadratic function are the same.
5) The y-intercept of the linear function are equal, therefore, the linear functions in f(x) and g(x) intersect on the y-axis.
6) The domain of the linear and quadratic functions are the same.
The contrasts (differences) in the function are;
1) The slope of the linear function of g(x) is positive and the slope of the linear function of f(x) is negative.
2) The y-intercept of the quadratic function in f(x) is +1, while the y-intercept of the quadratic function in g(x) is +2.
3) The quadratic function in f(x) and g(x) have graphs that do not intersect.
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78% of U.S. adults think that political correctness is a problem in America today. You randomly select six U.S. adults and ask them whether they think that political correctness is a problem in America today. The random variable represents the number of U.S. adults who think that political correctness is a problem in America today. Answer the questions below.
1. Find the mean of the binomial distribution (Round to the nearest tenth as needed.)
2. Find the variance of the binomial distribution. (Round to the nearest tenth as needed.)
3. Find the standard deviation of the binomial distribution. (Round to the nearest tenth as needed.)
4. Most samples of 6 adults would differ from the mean by no more than nothing. (Type integers or decimals rounded to the nearest tenth as needed.)
Answer:
Step-by-step explanation:
Let x be a random variable representing the number of U.S. adults who think that political correctness is a problem in America today. This is a binomial distribution since the outcomes are two ways. The probability of success, p = 78/100 = 0.78
The probability of failure, q would be 1 - p = 1 - 0.78 = 0.22
n = 6
a) Mean = np = 6 × 0.78 = 4.68
b) Variance = npq = 6 × 0.78 × 0.22 = 1.0
c) Standard deviation = √npq = √(6 × 0.78 × 0.22) = 1.0
d) The standard deviation is used to express the spread of the data from the mean. Therefore, most samples of 6 adults would differ from the mean by no more than 1.0
Order the numbers from least to greatest: -5, 6, and 9.
Answer: -5, 6, and 9
Step-by-step explanation:
Step-by-step explanation:
least to greatest
-5 6 9
Ethan's solution and reasoning for solving an equation are shown below: 4/2 x - 10 =30
Answer:
Step-by-step explanation:
er
Answer:
x = 20
Step-by-step explanation:
4/2x - 10 =30
Divide 4/2.
2x - 10 =30
Add 10 to both sides.
2x = 30 + 10
2x = 40
Divide 2 into both sides.
2x/2 = 40/2
x = 20
What two numbers is the square root of 74 between?
Answer:
8 and 9
Step-by-step explanation:
√64 = 8
√81 = 9
√74 falls inbetween those 2
Computer purchases: Out of 809 large purchases made at a computer retailer, 347 were personal computers, 398 were laptop computers, and 64 were printers. As a part of an audit, one purchase record is sampled at random. Round the answers to four
decimal places, as needed.
(a) What is the probability that it is a laptop computer?
(b) What is the probability that it is not a printer?
Step-by-step explanation:
personal- 347 ÷ 809 = 0.43%
lap top- 398 ÷ 809 = 0.49%
printer- 64 ÷ 809 = 0.08%
Taylor Swift wants to know the proportion of her fans who listened to her new single ME! within the first hour of it being released. In order to estimate this, she takes a sample of 150 of her fans and asks them if they listened to the song in this time period. Of the 150 fans, 135 of them (90%) responded that they did listen to the song during this time period. What is the parameter and what is its value
Answer:
The parameter is the population proportion of fans who listened to her new single and has an estimated value of 90%.
Step-by-step explanation:
The parameter is a value that corresponds to a population, while an a value that corresponds to a sample is know as statistic.
She takes a sample to estimate, with a point estimate and probably with a confidence interval around this point estimate, the true proportion of fans who listened to her new single.
This is the paramater: the population proportion of fans who listened to her new single.
Its value comes from an estimation based on the sample proportion (point estimate).
The sample proportion is 90%, so we can estimate, as there is no bias, that the population proportion is also 90%.
20 Find the area of the rectangle given that
the perimeter is 50 cm.
3m + 2
m - 5
F 32
G 7
H 46
J 9
Answer: H - 46
Step-by-step explanation:
Primeter = 2(l + w)
50 = 2{(3m+2) + (m-5)}
25 = 3m+2 +m -5
25 = 4m -3
m = 28/4 = 7
l = 3m+2 = 23 cm
w = m-5 = 2 cm
Area = l x b
= 23 x 2 = 46 sq. cm.
PLZ I NEED THIS BY THE END OF THE DAY What are at least 5 examples of math that we often do in everyday life?
Answer:
cooking ( mesurments )
gardening ( landscape )
designing ( art )
shopping for the best price ( aka money counting )
car rides ( figuring out distance and time )
sewing.
hope this helped :)
Step-by-step explanation:
Consider the ski gondola from Question 3. Suppose engineers decide to reduce the risk of an overload by reducing the passenger capacity to a maximum of 15 skiers. Assuming the maximum load limit remains at 5,000 lb, what is the probability that a group of 15 randomly selected skiers will overload the gondola
Answer:
The probability that a group of 15 randomly selected skiers will overload the gondola = (3.177 × 10⁻⁵¹)
(almost zero probability showing how almost impossible it is to overload the gondola, therefore showing how very safe the gondola is)
Step-by-step explanation:
Complete Question
A ski gondola carries skiers to the top of the mountain. If the Total weight of an adult skier and the equipment is normally distributed with mean 200 lb and standard deviation 40 lb.
Consider the ski gondola from Question 3. Suppose engineers decide to reduce the risk of an overload by reducing the passenger capacity to a maximum of 15 skiers. Assuming the maximum load limit remains at 5,000 lb, what is the probability that a group of 15 randomly selected skiers will overload the gondola.
Solution
For 15 people to exceed 5000 lb, each person is expected to exceed (5000/15) per skier.
Each skier is expected to exceed 333.333 lb weight.
Probability of one skier exceeding this limit = P(x > 333.333)
This becomes a normal distribution problem with mean = 200 lb, standard deviation = 40 lb
We first standardize 333.333 lbs
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (333.333 - 200)/40 = 3.33
To determine the required probability
P(x > 333.333) = P(z > 3.33)
We'll use data from the normal distribution table for these probabilities
P(x > 333.333) = P(z > 3.33) = 1 - P(z ≤ 3.33)
= 1 - 0.99957
= 0.00043
So, the probability that 15 people will now all be above this limit = (probability of one person exceeding the limit)¹⁵ = (0.00043)¹⁵
= (3.177 × 10⁻⁵¹)
(almost zero probability showing how almost impossible it is to overload the gondola, therefore showing how very safe the gondola is)
Hope this Helps!!!
The two figures are similar. Write a proportion to find the missing measure. Then find the value of x.
Answer:
First option is the right choice.
Step-by-step explanation:
x/95 = 15/19
x = 75
Best Regards!
Answer:
Option A
Step-by-step explanation:
Triangle ABC and DEF are similar.
Taking proportion of their sides to find the value of the unknown.
=> x/15 = 95/19
Cross Multiplying
=> 19x = 1425
Dividing both sides by 9
=> x = 75
At what point will the graph of the equations 3x +y =7&
y=1 intersect?
=======================================================
Work Shown:
Substitute y = 1 into the first equation. Basically we replace every y with 1. From here we solve for x
3x+y = 7
3x+1 = 7
3x+1-1 = 7-1 .... subtracting 1 from both sides
3x = 6
3x/3 = 6/3 .... dividing both sides by 3
x = 2
We have x = 2 pair up with y = 1. The two equations intersect at (2,1)
As a check, plugging (x,y) = (2,1) into the first equation should lead to a true statement
3x+y = 7
3(2)+1 = 7
6+1 = 7
7 = 7 and it does lead to a true statement
The graph is shown below.
Part A: A graph passes through the points (0,2), (1,3), and (2,4). Does this graph represent a linear function or a non-linear function? Explain your answer in words. Part B: Write one example of a linear function and one example of a nonlinear function. (Use x and y as the variables)
Answer:
A) linear
B) y = x is linear; y = 1/x is non-linear
Step-by-step explanation:
A) The points lie on the same straight line, so the function is linear.
__
B) Any function that has x to a power other than 1 will be non-linear.
linear function: y = x
nonlinear function: y = x^-1 = 1/x
What is the perimeter of kite WXYZ?
P=2(a+b)
Hope it helps
Answer:
C on Edge. 2 (square root of 53) +10 units
Step-by-step explanation:
Translate to an algebraic expression.
28 more than d
Answer: d + 28
Step-by-step explanation:
Answer:
d+28
Step-by-step explanation:
it is easier to remeber that you should always flip the wording so for this on "d" would be first then add the 28
Prove your work what is 1/12 of a dozen Branliest
Answer:
1/12 of a dozen is 1
Step-by-step explanation:
One dozen means 12. If you ask for 1/12 of 12, you multiply 12 and 1/12. You should get 1 as your answer.
What is the midpoint of the segment shown below?
Answer:
option a (-1,-1/2)
Step-by-step explanation:
apply mid point formula
What is the value of the expression?
8 and one-half minus 2 + 4 and three-fourths
1 and three-fourths
11 and one-fourth
13 and one-fourth
15 and three-fourths
Answer:
11 and one-fourth
Step-by-step explanation:
The given expression can be rewritten as:
[tex](8+\frac{1}{2}) -2+(4+\frac{3}{4})[/tex]
1/2 can be written as 2/4.
Solving the expression grouping integers and fractions:
[tex](8+\frac{2}{4}) -2+(4+\frac{3}{4}) =\\8+4-2+(\frac{2}{4}+\frac{3}{4}) =\\10+\frac{5}{4}=\\ 11+\frac{1}{4}[/tex]
Therefore, the value of the given expression is 11 and one-fourth.
Answer:
11 and one fourth
Step-by-step explanation:
Subtract (3x^2-x^3)-(-5x^3+2x^2+1)
Answer:
4x^3+x^2-1
Step-by-step explanation:
(3x^2-x^3)-(-5x^3+2x^2+1)
Distribute the minus sign
(3x^2-x^3)+5x^3-2x^2-1
Combine like terms
-x^3 +5x^3 + 3x^2 -2x^2 -1
4x^3+x^2-1
Answer:
your answer is [tex]4x^{3} + x^{2} -1[/tex].
Step-by-step explanation:
Distribute the negative sign in the second half of the expression by multiplying that half by a -1. this should change the signs on all the numbers. this should leave you with the addition problem: (3x^2-x^3) + (5x^3 -2x^2 -1).combine like terms by adding. -x^3 can be combined with 5x^3, but remember to follow their signs. this will give you 4x^3. the same can be done with 3x^2 and -2x^2, following their sign rules. this results in: x^2.the negative one constant does not have any like terms, so he's by himself at the end of your new equation.be sure to arrange your terms in decreasing order according to exponent, which results in your final answer.Please answer this correctly
Answer:
The median would change the most
Step-by-step explanation:
The mode will not change, because the only duplicate number is 20
The mean will change from 53.22 to 55.2 when you put 73 into the set
and the median will change from 67 to 70 when you put 73 into it
Answer:
Median
Step-by-step explanation:
Mean:
Mean of 9 numbers = 477/9 = 53
Mean of 10 numbers = 550/10 = 55
Mode:
Mode for the set of 9 numbers: 20
Mode for the setof 10 numbers when 73 is included = 20
Median:
Set of 9 numbers:
10, 20, 20 , 32, 67, 74, 76, 84, 94
Median = 67
Set of 10 numbers:
10, 20, 20 , 32, 67, 73, 74, 76, 84, 94
Median = 67+73/2 = 140/2 = 70
What is AX?
Point A is the midpoint of side XZ and point B is the
midpoint of side YZ
O2 units
O 4 units
6 units
O 8 units
5x - 7
2x-2
X + 1
B
A
N
Answer: 4 units! Just took the test!
Step-by-step explanation:
The measure of length AX is,
⇒ AX = 4 units
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Find the diagram attached. The diagram is a similar triangle.
Now, From the diagram,
⇒ XZ/XY = CA/AB
Given that;
XZ = 2x-2+2x-2
= 4x-4
And, XY =5x-7
CA = 2x-2
AB= x+1
On substituting this parameters into the formula to get x first
4x-4/5x-7 = 2x-2/x+1
cross multiply
(4x-4)(x+1) = 5x-7(2x-2)
open the parenthesis
4x²+4x-4x-4 = 10x²-10x-14x+14
4x²-4 = 10x²-24x+14
10x²-4x²-24x+14+4 = 0
6x²-24x+18 = 0
x²-4x+3 = 0
x²-3x-x+3 = 0
x(x-3)-1(x-3) =0
(x-3)(x-1) = 0
x = 3 and 1
And, Now to get length AX as;
⇒ AX = 2x-2
Substitute x = 3 into the expression,
AX = 2(3)-2
AX = 6-2
AX = 4 units
Hence, The measure of length AX is,
AX = 4 units
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URGENT!! The binomial expansion x^3-12x^2+48x-64 can be expressed as (x+n)^3. What is the value of n? A. -8 B. -4 C. 4 D. 8
Answer:
B. -4
Step-by-step explanation: