Answer:
5x3 y(5xy-4)
5x3y ×1xy
5x4y2
Answer:
[tex]5 {x}^{3} y[/tex]
step by step
[tex]5 {x}^{3} y(2x + 3y - 4) \\ = 10 {x}^{3}y + 15 {x}^{3} y + 20 {x}^{3} y \\ = 5 {x}^{3} y[/tex]
Find the missing side lengths help please?
Answer:
Step-by-step explanation:
Answer:
y=2, x=4
Step-by-step explanation:
sin60=2sqrt3/x
so x = 2sqrt3/sin60
and x=4
for the value of y, use pythagorean theorem to get
16=y^2+12
which gives you y=2
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
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
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.
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.
A, B, and C are points of tangency. CQ = 5, PQ = 10, and PR = 14. What is the perimeter
of the triangle PQR?
*see attachment for diagram
Answer:
Perimeter = 38
Step-by-step explanation:
Recall: when two tangents are drawn to meet at a point outside a circle, the segments of the two tangents are congruent.
Given,
CQ = 5
PQ = 10
PR = 14
Perimeter of ∆PQR = RC + CQ + QB + BP + PA + AR
CQ = QB = 5 (tangents drawn from an external point)
BP = PQ - QB
BP = 10 - 5 = 5
BP = PA = 5 (tangents drawn from an external point)
AR = PR - PA
AR = 14 - 5 = 9
AR = RC = 9 (tangents drawn from an external point)
✔️Perimeter of ∆PQR = RC + CQ + QB + BP + PA + AR
= 9 + 5 + 5 + 5 + 5 + 9
Perimeter = 38
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.
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 milkAccording 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]
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
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].
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]The maximum and minimum values of a quadratic function are called as_______of the function.
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.
Whats The Correct Answer?!
Answer: the correct answer is D 0.05
Step-by-step explanation:
Answer:
0.02 m/s
Step-by-step explanation:
42/50 meters in 26/30 minutes,
26/30 minutes = 52 seconds
so in 1 second, 42/50 ÷ 52
= 42/50 × 1/52
= 21/1300
= 0.02 (approximately)
Answered by GAUTHMATH
add:7ab,8ab,-10ab,-3ab
Answer:
2ab
Step-by-step explanation:
7ab+8ab+(-10ab)+(-3ab)=
=15ab-13ab= 2ab
Answer:
2ab
Step-by-step explanation:
7ab+8ab+-10ab+-3ab
Factor out ab
ab(7+8-10-3)
ab(2)
2ab
what describes shoe size?
a. natural number
b. integer
c. rational number
d. real number
Find the lateral surface area and volume of the solid object.
Answer:
See answers below
Step-by-step explanation:
Lateral surface area of a cone is expressed as:
L = πr√h²+r²
Given that
r = 11.5/2 = 5.75cm
h=16.6cm
L = 3.14(5.75)√16.6²+5.75²
L = 18.055√275.56+33.0625
L = 18.055*17.56
L=317.0458cm²
Volume = 1/3πr²h
Volume = 1/3π(5.75)²(16.6)
Volume = 1,723.34975/3
Volume = 574.45cm³
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:
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 :)
Which of the following rational functions is graphed below?
Answer:
D. F(x) = [tex]\frac{1}{(x+4)}^{2}[/tex]
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.
Select the correct answer from the drop-down menu.
Answer:
-60 60 30 -30 one of it is answer
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
Ophelia is making homemade spaghetti sauce by combining 48 oz of tomato paste with 6 cups of water.how many ounces of tomatoes paste are needed for every cup of water show your work.
Answer:
8 ounces of tomato paste for each cup of water.
Step-by-step explanation:
Just divide 48 / 6 to get 8 oz of tomato paste per cup of water.
Hope this helps!
Work Shown:
48 oz of tomato paste = 6 cups of water
48/6 oz of tomato paste = 6/6 cups of water
8 oz of tomato paste = 1 cup of water
In short, we divide both values by 6 so that the "6 cups" becomes "1 cup". We can say the unit rate is 8 oz of tomato paste per cup of water.
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]
A game consists of tossing three coins. If all three coins land on heads, then the player wins $75. If all three coins land on tails, then the player wins $45. Otherwise, the player wins nothing. On average, how much should a player expect to win each game
Answer:
On average, a player should expect to win $15.
Step-by-step explanation:
The expected value in an event with outcomes:
x₁, x₂, ..., xₙ
Each with probability:
p₁, ..., pₙ
is given by:
Ev = x₁*p₁ + ... +xₙ*pₙ
In this case we have 3 outcomes:
player wins $75 = x₁
player wins $45 = x₂
player does not win = x₃
Let's find the probabilities of these events.
player wins $75)
Here we must have the 3 coins landing on heads, so there is only one possible outcome to win $75
While the total number of outcomes for tossing 3 coins, is the product between the number of outcomes for each individual event (where the individual events are tossing each individual coin, each one with 2 outcomes)
Then the number total of outcomes is:
C = 2*2*2 = 8
Then the probability of winning $75 is the quotient between the number of outcomes to win (only one) and the total number of outcomes (8)
p₁ = 1/8
Win $45:
This happens if the 3 coins land on tails, so is exactly equal to the case above, and the probability is the same:
p₂ = 1/8
Not wining:
Remember that:
p₁ + p₂ + ... + pₙ = 1
Then for this case, we must have:
p₁ + p₂ + p₃ = 1
1/8 + 1/8 + p₃ = 1
p₃ = 1 - 1/8 - 1/8
p₃ = 6/8
Then the expected value will be:
Ev = $75*1/8 + $45*1/8 + $0*6/8 = $15
On average, a player should expect to win $15.
What is 2/11 as a decimal rounded to 3 decimal places?
Answer: The answer is 0.182
Hope this help :)
a. A contest entrant has a 0.002 probability of winning $12,165. If this is the only prize and the fee is $35, then find the expected value of winning the contest.
b. The probability of winning a lottery is 0.125, what is the probability of winning at least once in twelve trials?
Part (a)
If you win $12165, then you really net 12165-35 = 12130 dollars when you consider the ticket fee. So this is the true amount of money you win, or take home at the end of the day. This is before taxes.
Multiply 0.002 with 12,130 to get 0.002*12130 = 24.26
We'll use this later so let A = 24.26
The chances that you don't win are 1 - 0.002 = 0.998 which multiplies with -35 to indicate you lost $35 in playing the game. So we get B = 0.998*(-35) = -34.93
Lastly, add the values of A and B to get the expected value:
A+B = 24.26 + (-34.93) = -10.67 is the expected value.
On average, you expect to lose about $10.67 for any time you play the game.
Answer: -10.67 dollars===========================================================
Part (b)
0.125 is the probability of winning so 1-0.125 = 0.875 is the probability of losing.
Let's say you get really unlucky and lose 12 times in a row. Assuming each trial (aka case when you play the game) is independent, this would mean the probability of such an event is (0.875)^12 = 0.2014172, which is approximate.
Subtract that from 1 to get the probability of winning at least once
1 - (0.875)^12 = 1 - 0.2014172 = 0.7985828
which is also approximate. If we rounded to three decimal places, then it would be 0.799; I'm picking three decimals since 0.125 is to three decimal places. Round however you need to if otherwise.
Answer: 0.799 (approximate)A housing official in a certain city claims that the mean monthly rent for apartments in the city is less than $1000. To verify this claim, a simple random sample of 47 renters in the city was taken, and the mean rent paid was $941 with a standard deviation of $245. Can you conclude that the mean monthly rent in the city is less than $1000
Answer:
The p-value of the test is 0.053, which is more than the standard significance level of 0.05, and thus it cannot be concluded that the mean monthly rent in the city is less than $1000.
Step-by-step explanation:
A housing official in a certain city claims that the mean monthly rent for apartments in the city is less than $1000.
At the null hypothesis, we test if the mean is of at least $1000, that is:
[tex]H_0: \mu \geq 1000[/tex]
At the alternative hypothesis, we test if the mean is less than $1000, that is:
[tex]H_1: \mu < 1000[/tex]
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used.
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
1000 is tested at the null hypothesis:
This means that [tex]\mu = 1000[/tex]
To verify this claim, a simple random sample of 47 renters in the city was taken, and the mean rent paid was $941 with a standard deviation of $245.
This means that [tex]n = 47, X = 941, s = 245[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{941 - 1000}{\frac{245}{\sqrt{47}}}[/tex]
[tex]t = -1.65[/tex]
P-value of the test and decision:
The p-value of the test is found using a left-tailed test(test if the mean is less than a value), with t = -1.65 and 47 - 1 = 46 df.
Using a t-distribution calculator, the p-value is of 0.053.
The p-value of the test is 0.053, which is more than the standard significance level of 0.05, and thus it cannot be concluded that the mean monthly rent in the city is less than $1000.
