Find the missing length on this triangle
Answer:
Step-by-step explanation:
This is a geometric means problem where 60, the side common to both the triangles, is the geometric mean. Set it up like this:
[tex]\frac{36}{60}=\frac{60}{x}[/tex] and cross multiply to get
36x = 3600 so
x = 100
An election ballot asks voters to select three city commissioners from a group of six candidates. If your aunt and father are running, what is the probability that either your aunt or your father will become a city commissioner
Answer:
0.8 = 80% probability that either your aunt or your father will become a city commissioner.
Step-by-step explanation:
The candidates are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
6 candidates, which means that [tex]N = 6[/tex]
2 are the aunt and father, which means that [tex]k = 2[/tex]
3 are chosen, which means that [tex]n = 3[/tex]
What is the probability that either your aunt or your father will become a city commissioner?
Probability of at least one of them being chosen, which is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,6,3,2) = \frac{C_{2,0}*C_{4,3}}{C_{6,3}} = 0.2[/tex]
Then
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.2 = 0.8[/tex]
0.8 = 80% probability that either your aunt or your father will become a city commissioner.
find the missing variables
The triangle on the image is a right triangle which means we can use trigonometry to untangle its mysteries.
We have a side an and angle from that we can compute anything.
We will first compute x, we do so by taking the cosine of an angle,
[tex]\cos(45)=\frac{5\sqrt{2}}{x}[/tex]
[tex]x=\frac{5\sqrt{2}}{\cos(45)}=\frac{5\sqrt{2}}{\frac{\sqrt{2}}{2}}=\frac{10\sqrt{2}}{\sqrt{2}}=\boxed{10}[/tex]
Then we can also compute y, simply by using pythagorean theorem,
[tex]10^2=y^2+(5\sqrt{2})^2[/tex]
[tex]y=\pm\sqrt{100-50}=\pm\sqrt{50}=\boxed{5\sqrt{2}}[/tex].
So triangle has sides [tex]5\sqrt{2},5\sqrt{2},10[/tex] which is also known as equilateral triangle.
Hope this helps :)
According to The Wedding Report, Inc., the mean cost for a wedding in the United States is $28732 (as of November 2008). Suppose the cost for a wedding is normally distributed with a standard deviation of $1500, and that a wedding is selected at random. Use the appropriate Excel function to calculate each of the following. (Note - Part (e) can be done by hand.)
(a) Find the probability that the wedding costs less than $22000.
(b) Find the probability that the wedding costs more than $32000.
(c) Find the probability that the wedding costs between $25000 and $30000.
(d) Find Q1 (the 25th percentile) and Q3 (the 75th percentile).
(e) Find the IQR for the wedding costs.
(f) The top 10% of weddings cost more than how much?
Answer:
Following are the solution to the given points:
Step-by-step explanation:
[tex]X = \text{cost of wedding}\sim \text{Normal}\ (\mu = 28732, \sigma= 1500)\\\\[/tex]
For point a:
[tex]Probability\ = 0.00000359\\\\ \text{(Using Excel function:} =NORMDIST(22000,28732,1500,1)).[/tex]
For point b:
[tex]Probability \ = 0.014678\\\\\text{(Using Excel function:} =1-NORMDIST(32000,28732,1500,1))\\\\[/tex]
For point c:
[tex]Probability\ = 0.794614436 \\\\[/tex]
[tex]\text{(Using Excel function:} \\=NORMDIST (30000,28732,1500,1)-NORMDIST(25000,28732,1500,1))\\\\[/tex]
For point d:
[tex]Q_1 = 27720.26537 \\\\\text{(Using Excel function:} =NORMINV(0.25,28732,1500)) \\\\Q_3 = 29743.73463 \\\\\text{(Using Excel function:} =NORMINV(0.75,28732,1500)).[/tex]
For point e:
[tex]IQR = Q_3 - Q_1 = 29743.73463 - 27720.26537 = 2023.469251.[/tex]
For point f:
[tex]Top\ 10\% = 30654.32735 \\\\\text{(Using Excel function:} =NORMINV(0.9,28732,1500)).[/tex]
what describes shoe size?
a. natural number
b. integer
c. rational number
d. real number
ASAP HELP: If a sample proportion is 0.55, which range of possible values best describes an estimate for the population parameter?
A. (0.55, 0.6)
B. (0.4, 0.7)
C. (0.4, 0.69)
D. (0.5, 0.59)
Answer:
B.(0.4,0.7)
Step-by-step explanation:
We are given that
Sample proportion
[tex]\hat{p}=0.55[/tex]
We have to find the range of possible values which describes best an estimate for the population parameter.
Estimate for the population parameter
[tex]\hat{p}\pm Z(SE)[/tex]
A.(0.55,0.6)
Difference between 0.55 and 0.55=0
Difference between 0.55 and 0.6=0.05
Difference between 0.55 and 0.55 is not equal to difference between 0.55 and 0.6.
Hence, option A is wrong.
B.(0.4,0.7)
Difference between 0.55 and 0.4=0.15
Difference between 0.55 and 0.7=0.15
Difference between 0.55 and 0.4 is equal to difference between 0.55 and 0.7.
Hence, option B is correct.
C. (0.4,0.69)
Difference between 0.55 and 0.4=0.15
Difference between 0.55 and 0.69=0.14
Difference between 0.55 and 0.4 is not equal to difference between 0.55 and 0.69.
Hence, option C is not correct.
D.(0.5,0.59)
Difference between 0.55 and 0.5=0.05
Difference between 0.55 and 0.59=0.04
Difference between 0.55 and 0.5 is not equal to difference between 0.55 and 0.59.
Hence, option D is not correct.
CHOOSE THE EQUIVALENT STATEMENT.
If a parallelogram has congruent diagonals, then it is a rectangle.
A. If a parallelogram is not a rectangle, then it does not have congruent diagonals.
B. If parallelogram does not have congruent diagonals, then it is a rectangle.
C. If a parallelogram is a rectangle, then it does not have congruent diagonals.
Answer: A. If a parallelogram is not a rectangle, then it does not have congruent diagonals.
Subtract.
8 over 9 minus 1 over 3
Answer:
5 over 9
Step-by-step explanation:
multiplayer both sides of the second fraction by 3, then you have 3 over 9. So the problem becomes 8-3=5
Write a linear equation representing the information shown in the table.
A) y = –2∕5x – 5
B) y = –5∕2x – 5
C) y = 5∕2x – 5
D) y = 2∕5x – 5
Answer: C
Step-by-step explanation:
There are many ways to find the linear equation that matches the table, but let's do it so that we find the slope and y-intercept.
Based on the first entry (0,-5), we know that the y-intercept is -5.
To find slope, we take any two points and plug them into this [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]. We'll use the first two points.
[tex]m=\frac{0-(-5)}{2-0} =\frac{5}{2}[/tex]
Now, we know the slope is [tex]\frac{5}{2}[/tex].
The only equation that has the same slope and y-intercept that we found is C.
Which two values of x are roots of the polynomial below? x2 + 3x - 5
Answer:
Step-by-step explanation:
The roots are the values of x for which x² + 3x - 5 = 0.
Quadratic formula:
x = [-3±√(3²-4(1)(-5))]/(2·1) = [-3±√29]/2
If the graphs of the linear equations in a system are the same line, what does that mean about the possible solution or solutions of the system?
A. There is exactly one solution.
В.
There is no solution.
C. There are infinitely many solutions.
D. The lines in a system cannot graph as the same line.
Answer:
C. There are infinitely many solutions.
Step-by-step explanation:
If the graphs of linear equations are the same line, then any point (solution) on one line is automatically a point on the "other" line. For example,
[tex]\begin{array}{l} x + y =10 \\ 2x + 2y =20 \end{array}[/tex]
The graphs of these "two" equations is only one line, x + y =10. The point [tex](5, 5)[/tex]is on "both" lines.
8.7 cm
9.6 cm
Find the volume of cylinder. Round to the nearest hundredth. A. 570.69 cm^3 B. 760.92 cm^3 C. 1,141.38 cm^3 D. 2,282.76 cm^3
9514 1404 393
Answer:
A. 570.69 cm³
Step-by-step explanation:
The volume is given by the formula ...
V = πr²h
The radius is half the diameter, so is 4.35 cm. Then the volume is ...
V = π(4.35 cm)²(9.6 cm) = 181.656π cm³ ≈ 570.69 cm³
Determine the number positive real zeros of the polynomial below. (Type answer in as a whole number)f(x)=x^5+3x^2-4x+2
Answer:
The number of positive real zeros is 2 or 0
Step-by-step explanation:
Given
[tex]f(x)=x^5+3x^2-4x+2[/tex]
Required
Number of positive real zeros
Using Descartes rule of signs;
We write out the signs in front of each term;
Sign = + + - +
Count the number of times the sign alternate; i.e. from positive to negative and from negative to positive
From positive to negative, we have: 1 (i.e. + - )
From negative to positive, we have: 1 (i.e. - +)
Add up the count
[tex]count = 1+1[/tex]
[tex]count = 2[/tex]
Hence, the number of positive real zeros is 2 or 0
A survey of North Albion students found that they favoured Avengers: EndGame to Black Panther to Mulan in a ratio of 8:7:3. If 754 students were surveyed, how many preferred each movie?
Answer:
Avengers: Endgame ≈ 335
Black Panther ≈ 293
Mulan ≈ 126
Step-by-step explanation:
8+7+3=18
754/18 = 41.88888889
8*41.88888889 ≈ 335
7*41.88888889 ≈ 293
3*41.88888889 ≈ 126
335+293+126=764
please help me with this on the image
Answer: For flour it is 360g
3 eggs
900ml of milk
Step-by-step explanation:
Answer:
First, find the amount of ingredient for one pancake:
240 ÷ 8 = 30g of plain flour per pancake2 ÷ 8 = 0.25 eggs per pancake600 ÷ 8 = 75 ml of milk per pancakeMultiply that amount by 12 to find the amount needed for 12 pancakes:
30 x 12 = 360g of plain flour0.25 x 12 = 3 eggs75 x 12 = 900 ml of milkThe radius of a sphere is 3 inches. Which represents the volume of the sphere?
A) 120 cubic inches
B) 367 cubic inches
C) 647 cubic inches
D) 817 cubic inches
What is the simplified form of the following expression? Assume X=0
5v10x/3x^3
Answer:
firth root of 810x cubed /3x
The maximum and minimum values of a quadratic function are called as_______of the function.
Rudy Banks has won $5000 to attend university. If he invests the money in an
account at 12% per annum, compounded monthly, how much can he draw monthly
for the next 3 years?
Answer:
$7153.84
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Compounded Interest Rate Formula: [tex]\displaystyle A = P(1 + \frac{r}{n})^{nt}[/tex]
P is principle amountr is raten is compound ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 5000
r = 12% = 0.12
n = 12
t = 3
Step 2: Find Interest
Substitute in variables [Compounded Interest Rate Formula]: [tex]\displaystyle A = 5000(1 + \frac{0.12}{12})^{12(3)}[/tex][Exponents] Multiply: [tex]\displaystyle A = 5000(1 + \frac{0.12}{12})^{36}[/tex](Parenthesis) Add: [tex]\displaystyle A = 5000(1.01)^{36}[/tex]Evaluate exponents: [tex]\displaystyle A = 5000(1.43077)[/tex]Multiply: [tex]\displaystyle A = 7153.84[/tex]Which of the following rational functions is graphed below?
Answer:
D. F(x) = [tex]\frac{1}{(x+4)}^{2}[/tex]
Which of the following is equivalent to the expression below?
8^11•8^x
A. 8^x-11
B. 8^11x
C. 8^11+x
D. 8^11-x
Answer:
C
Step-by-step explanation:
[tex] \sf {a}^{c} \times {a}^{b} = {a}^{b + c} \\ \sf = {8}^{11} \times {8}^{x} \\ \sf = {8}^{11 + x} (c)[/tex]
Help please:))
2. When shipping ice cream, melting is understandably a big concern. You will notice that ice cream is not generally packaged in a cube-shaped container. A standard container of ice cream contains 1 L, or 1000 cm3 of ice cream,
a. What would be the optimal dimensions (radius and height) to minimize surface area?
b. What would the surface area be?
C. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.
Answer:
a) Because this asks about the radius and height, I assume that we are talking about a cylinder shape.
Remember that for a cylinder of radius R and height H the volume is:
V = pi*R^2*H
And the surface will be:
S = 2*pi*R*H + pi*R^2
where pi = 3.14
Here we know that the volume is 1000cm^3, then:
1000cm^3 = pi*R^2*H
We can rewrite this as:
(1000cm^3)/pi = R^2*H
Now we can isolate H to get:
H = (1000cm^3)/(pi*R^2)
Replacing that in the surface equation, we get:
S = 2*pi*R*H + pi*R^2
S = 2*pi*R*(1000cm^3)/(pi*R^2) + pi*R^2
S = 2*(1000cm^3)/R + pi*R^2
So we want to minimize this.
Then we need to find the zeros of S'
S' = dS/dR = -(2000cm^3)/R^2 + 2*pi*R = 0
So we want to find R such that:
2*pi*R = (2000cm^3)/R^2
2*pi*R^3 = 2000cm^3
R^3 = (2000cm^3/2*3.14)
R = ∛(2000cm^3/2*3.14) = 6.83 cm
The radius that minimizes the surface is R = 6.83 cm
With the equation:
H = (1000cm^3)/(pi*R^2)
We can find the height:
H = (1000cm^3)/(3.14*(6.83 cm)^2) = 6.83 cm
(so the height is equal to the radius)
b) The surface equation is:
S = 2*pi*R*H + pi*R^2
replacing the values of H and R we get:
S = 2*3.14*(6.83 cm)*(6.83 cm) + 3.14*(6.83 cm)^2 = 439.43 cm^2
c) Because if we pack cylinders, there is a lot of space between the cylinders, so when you store it, there will be a lot of space that is not used and that can't be used for other things.
Similarly for transport problems, for that dead space, you would need more trucks to transport your ice cream packages.
What is 2/11 as a decimal rounded to 3 decimal places?
Answer: The answer is 0.182
Hope this help :)
8. (3 points) Consider the largest cylinder that can be fit inside the sphere. What fraction of the volume of a sphere does this cylinder occupy?
ʕ•ﻌ•ʔ[tex]\huge\bold\pink{hello!!!}[/tex]ʕ•ﻌ•ʔ
HERE IS UR ANSWER
_____________________
The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter. The volume V of a sphere is four-thirds times pi times the radius cubed. The volume of a hemisphere is one-half the volume of the related sphere.
An isosceles right triangle has a hypotenuse that measures 4√2 cm. What is the area of the triangle?
Answer:
It would be B. 16 centimeters^2
Step-by-step explanation:
The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $16 and $30 per share.
What is the probability that the stock price will be:_______
a) More than $25? (Round your answer to 4 decimal places.)
b) Less than or equal to $18? (Round your answer to 4 decimal places.)
Answer:
a) 0.3571 = 35.71% probability that the stock price will be more than $25.
b) 0.1429 = 14.29% probability that the stock price will be less than or equal to $18.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Uniformly distributed between $16 and $30 per share.
This means that [tex]a = 16, b = 30[/tex]
a) More than $25?
[tex]P(X > x) = \frac{30 - 25}{30 - 16} = 0.3571[/tex]
0.3571 = 35.71% probability that the stock price will be more than $25.
b) Less than or equal to $18?
[tex]P(X < 18) = \frac{18 - 16}{30 - 16} = 0.1429[/tex]
0.1429 = 14.29% probability that the stock price will be less than or equal to $18.
A political candidate has asked his/her assistant to conduct a poll to determine the percentage of people in the community that supports him/her. If the candidate wants a 3% margin of error at a 90% confidence level, what size of sample is needed
Answer:
A sample size of 752 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
If the candidate wants a 3% margin of error at a 90% confidence level, what size of sample is needed?
We have no estimate of the proportion, so we use [tex]\pi = 0.5[/tex].
The sample size is n for which M = 0.03. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645*0.5[/tex]
[tex]\sqrt{n} = \frac{1.645*0.5}{0.03}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645*0.5}{0.03})^2[/tex]
[tex]n = 751.67[/tex]
Rounding up:
A sample size of 752 is needed.
Write an expression (or equation) that represents the number of square feet
of wallpaper you will need if the height of the family room is x feet, with a
length and width that are each 3 times the height of the room. The family
room has 1 door, which is 3 feet wide and 7 feet tall.
Answer: Given
room height is x feet
room length is 3x feet
room width is 3x feet
a door 3 ft wide by 7 ft tall
Find
The net area of the wall, excluding the door
Solution
The area of the wall, including the door, is the room perimeter multiplied by the height of the room. The room perimeter is the sum of the lengths of the four walls.
... gross wall area = (3x +3x +3x +3x)·x = 12x²
The area of the door is the product of its height and width.
... door area = (7 t)×(3 ft) = 21 ft²
Then the net wall area, exclusive of the door is ...
... net wall area = gross wall area - door area
... net wall area = 12x² -21 . . . . square feet
Select the correct answer from the drop-down menu.
Answer:
-60 60 30 -30 one of it is answer
Use the information below to complete the problem: p(x) = (1)/(x + 1)
and q(x) = (1)/(x - 1)
Perform the operation and show that it results in another rational expression.
p(x) - q(x)
Given:
The functions are:
[tex]p(x)=\dfrac{1}{x+1}[/tex]
[tex]q(x)=\dfrac{1}{x-1}[/tex]
To find:
The rational expression for [tex]p(x)-q(x)[/tex].
Solution:
We have,
[tex]p(x)=\dfrac{1}{x+1}[/tex]
[tex]q(x)=\dfrac{1}{x-1}[/tex]
Now,
[tex]p(x)-q(x)=\dfrac{1}{x+1}-\dfrac{1}{x-1}[/tex]
[tex]p(x)-q(x)=\dfrac{(x-1)-(x+1)}{(x+1)(x-1)}[/tex]
[tex]p(x)-q(x)=\dfrac{x-1-x-1}{x^2-1^2}[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]p(x)-q(x)=\dfrac{-2}{x^2-1}[/tex]
Therefore, the required rational expression for [tex]p(x)-q(x)[/tex] is [tex]\dfrac{-2}{x^2-1}[/tex].
