Let [tex]W[/tex] be the random variable representing the winnings you get for playing the game. Then
[tex]W=\begin{cases}9&\text{if the sum is odd}\\4&\text{if the sum is 4 or 8}\\49&\text{if the sum is 2 or 12}\\-1&\text{otherwise}\end{cases}[/tex]
First thing to do is determine the probability of each of the above events. You roll two dice, which offers 6 * 6 = 36 possible outcomes. You find the probability of the above events by dividing the number of ways those events can occur by 36.
The sum is odd if one die is even and the other is odd. This can happen 2 * 3 * 3 = 18 ways. (3 ways to roll even with the first die, 3 ways to roll odd for the die, then multiply by 2 to count odd/even rolls)The sum is 4 if you roll (1, 3), (2, 2), or (3, 1), and the sum is 8 if you roll (2, 6), (3, 5), (4, 4), (5, 3), or (6, 2). 8 ways.The sum is 2 if you roll (1, 1), and the sum is 12 if you roll (6, 6). 2 ways.There are 36 total possible rolls, from which you subtract the 18 that yield a sum that is odd and the other 10 listed above, leaving 8 ways to win nothing.So the probability mass function for this game is
[tex]P(W=w)=\begin{cases}\frac12&\text{for }w=9\\\frac29&\text{for }w=4\text{ or }w=-1\\\frac1{18}&\text{for }w=49\\0&\text{otherwise}\end{cases}[/tex]
The expected value of playing the game is then
[tex]E[W]=\displaystyle\sum_ww\,P(W=w)=\frac{71}9[/tex]
or about $7.89.
The expected value is positive, so a player can expect to earn money in the long run, and so should play the game.
Write a function rule that gives the total cost c(p) of p pounds of sugar if each pound costs $0.59.
c(p) = 0.59p
c(p) = 59p
c(p) = p + 0.59
Answer:
c(p) = 0.59p
Step-by-step explanation:
We multiply the number of pounds of sugar, p, time the cost per pound ,.59, to get the total cost
c(p) = .59*p
Answer: c(p) = 0.59p
Step-by-step explanation:
John and his son are building a boxcar for a group competition. According to the rules of the competition, the length of the car must be 3 inches greater than its width. Also, the width of the car must be at least 2 inches greater than the radii of the wheels. When they signed up for the competition, they were given a kit containing everything they needed to build the car except for the base and the wheels. According to the rules of the competition, they must spend no more than $50. The cost of the base will be $0.50 per square inch and the cost of each of the 4 wheels will be $2.25 per inch of radius. If x represents the width of the car and y represents the radii of the wheels, then which of the following systems of inequalities can be used to determine the length and width of the car and the radii of the wheels?
The system of inequalities to determine the dimensions and budget of the boxcar, according to the given restrictions in the problem, are: x + 3 >= length, x >= y + 2, and 0.50*x*(x+3) + 4 * 2.25 * y <= 50.
Explanation:The subject of this question is Mathematics, specifically the topic of inequalities. From the problem, we can create a system of inequalities based on the restrictions specified. We are told that the length of the car must be 3 inches greater than its width, which is represented by x, so one inequality is x+3 >= length. Second, the width of the car must be at least 2 inches greater than the radii of the wheels, represented by y, so we have another inequality, x >= y + 2.
Lastly, we need to account for the monetary constraint. The cost of the base is $0.50 per square inch, so the cost is 0.50*x*(x+3), and the cost of each of the 4 wheels is $2.25 per inch of radius, so the total cost is 4 * 2.25 * y. The total spending must not exceed $50, so our final inequality is 0.50*x*(x+3) + 4 * 2.25 * y <= 50. Therefore, the system of inequalities that can be used to determine the length, width of the car and the radii of the wheels is:
x + 3 >= length
x >= y + 2
0.50*x*(x+3) + 4 * 2.25 * y <= 50
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You need 300 mL of a 65% alcohol solution. On hand, you have a 50% alcohol mixture. How much of the 50% alcohol mixture and pure alcohol will you need to obtain the desired solution?
You will need
____ mL of the 50% solution
and
______ mL of pure alcohol.
Answer:
You will need 220 mL of the 60% solution and 80 mL of pure alcohol.
Step-by-step explanation:
Let 'x' be the amount of 50% alcohol solution and y the amount of pure alcohol.
Therefore:
(0.5x + y)/300 = 0.65 ⇒ 0.5x + y = 190
x + y = 300
Solving the sistem of equations:
x = 220 and y = 080
Therefore, You will need
220 mL of the 60% solution
and 80 mL of pure alcohol.
Factor completely.
5x^2 + 10x - 40
Answer:
5(x + 4)(x - 2)
Step-by-step explanation:
Start by factoring 5 out of all three terms. We then have
5(x^2 + 2x - 8), or
5(x^2 + 2x - 8), which is in proper quadratic form.
Note that (4)(-2) = 8 and that 4 - 2 = 2, which match the 3rd and 2nd coefficients of x^2 + 2x - 8.
Thus, in completely factored form, we have 5(x + 4)(x - 2)
Answer:
5 (x -2) (x +4)
Step-by-step explanation:
5x^2 + 10x - 40
Factor out a 5
5(x^2 +2x-8)
We can then factor inside the parentheses
What two numbers multiply to -8 and add to 2
-2*4 = -8
-2+4 = 8
5 (x -2) (x +4)
Identify the two rational numbers 2.7182818459, 2.777777, square root 3, -7/3
Answer:
2.777777 and -7/3
Step-by-step explanation:
2.7182818459 cannot be written in fraction form therefore it is irrational.
2.777777 is rational because it can be written as the fraction 25/9
The square root of 3 is 1.7320508075688772, this number cannot be written as a fraction so it is irrational.
-7/3 is rational because it is already in fraction form.
Answer:
2.777777 and -7/3
Step-by-step explanation:
If a number can be defined in the form of p/q where q≠0, then it is called rational number.
If a decimal number is repeating then it is a rational number because it can be written in the form of p/q.
For example: 1.222, 3/5, 2.5, -1/2, 4.0707007...
All real numbers which are not rational numbers are called irrational numbers.
For example: 0.2357835.., √2, π.
In the given numbers,
Rational numbers = 2.777777, -7/3
Irrational numbers = 2.7182818459 and √3
Therefore the two rational numbers are 2.777777 and -7/3.
if A and B are mutually exclusive events with P(A)= 0.3 and P(B)= 0.5, then P(A and B)=
If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A and B) = 0.
Explanation:If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then P(A and B) = 0.
Mutually exclusive events are events that cannot occur at the same time. This means that if event A happens, event B cannot happen, and vice versa. Therefore, the probability of both A and B occurring together is zero.
What is the length of BC in the right triangle 9 and 12 below
The length of BC in the right triangle with sides 9 and 12 is 15.
Explanation:In a right triangle, the length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the lengths of the other two sides are given as 9 and 12. Let's label the hypotenuse as BC. We can use the Pythagorean theorem to solve for BC:
a2 + b2 = c2
92 + 122 = c2
81 + 144 = c2
225 = c2
Taking the square root of both sides, we find that the length of BC is 15 units.
If x= 6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the
equation?
Answer:
discriminant is zero (0)
Step-by-step explanation:
Actually, you have a double root here: {6, 6}: "two real, equal roots." That tells us immediately that the value of the discriminant was zero (0).
Answer:
The discriminant of the equation is zero.
Step-by-step explanation:
The given graph is a quadratic equation. If x = 6 is the only x-intercept of the graph, then the roots must be equal.
The quadratic equation will have two solutions. Here the two solutions are equal x = 6.
If the roots are equal, then the discriminant is zero.
The factors of the quadratic equation (x - 6) (x - 6)
= [tex]x^2 - 6x - 6x + 36[/tex]
= [tex]x^2 -12x + 36[/tex]
Discriminant = [tex]b^2 - 4ac[/tex]
Here a = 1, b = -12 and c = 36
Discriminant = [tex](-12)^{2} - 4.1.36[/tex]
= 144 - 144
= 0
Therefore, the answer is "The discriminant of the equation is zero."
In The Diagram Below, BD is parallel to XY, What is the value of Y?
A.73
B.97
C.83
D.87
Answer: B.97
Step-by-step explanation:
When two parallel lines are intersected by a transversal line then the sum of adjacent angles is 180°.
From the given figure , BD is parallel to XY and a transversal intersecting it making a pair of adjacent angles 83° and y°.
[tex]83^{\circ}+y^{\circ}=180^{\circ}\\\\\Rightarrow\ y^{\circ}=180^{\circ}-83^{\circ}=97^{\circ}[/tex]
Hence, the value of y= 97.
Answer:it is 83
Step-by-step explanation:
Which principle must a government follow in order to be considered a
democracy?
Step-by-step explanation:
The political equality of all citizens is an essential principle of democracy. In ademocracy, the just powers of government are based upon the consent of the governed.
D) leaders Must be selected by the citizens rather than inheriting power. (Apex)
Find the area of the equilateral triangle whose sides are 4 yd.
Answer:
The first one. 4 times square root of 3.
Step-by-step explanation:
The side of the equilateral triangle that represents the height of the triangle will have a length of because it will be opposite the 60o angle. To calculate the area of the triangle, multiply the base (one side of the equilateral triangle) and the height (the perpendicular bisector) and divide by two.
Answer:
Remember:
Triangle area= [tex]\frac{b*h}{2}[/tex]
h of equilateral triangle = [tex]\frac{\sqrt{3}}{2}*a[/tex]
Step-by-step explanation:
b=4yd
a=4yd
h = [tex]\frac{\sqrt{3}}{2}*a[/tex]
h = [tex]\frac{\sqrt{3}}{2}*4yd[/tex]
4/2=2
h= [tex]2\sqrt{3} yd[/tex]
area= [tex]\frac{b*h}{2}[/tex]
area= [tex]\frac{4 yd*2\sqrt{3} yd}{2}[/tex]
2/2=1
Finally
area= [tex]4\sqrt{3} yd^2[/tex]
Solve to get brainliest ( Need 2 people ) TIME LIMIT 8:00 MINUTES
If 12% of the number is 24, what is the number?
Good luck!
Answer:
200
Step-by-step explanation:
12% is the same thing of .12
x = the number you are trying to find
.12(x) = 24 ----- This means that 12% of x is 24.
x = 24/.12
x = 200
To solve this you must use a proportion like so...
[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]
12 is a percent and percent's are always taken out of the 100. This means that one proportion will have 12 as the part and 100 as the whole
We want to know out of what number is 24 12% of. This means 24 is the part and the unknown (let's make this x) is the whole.
Here is your proportion:
[tex]\frac{24}{x} =\frac{12}{100}[/tex]
Now you must cross multiply
24*100 = 12*x
2400 = 12x
To isolate x divide 12 to both sides
2400/12 = 12x/12
200 = x
This means that 12% of 200 is 24
Hope this helped!
~Just a girl in love with Shawn Mendes
simplify (square root 3)(5 square root 3)
[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( \sqrt{3} \right)\left( \sqrt[5]{3} \right)\implies \left( \sqrt[2]{3^1} \right)\left( \sqrt[5]{3^1} \right)\implies 3^{\frac{1}{2}}\cdot 3^{\frac{1}{5}}\implies 3^{\frac{1}{2}+\frac{1}{5}}\implies 3^{\frac{5+2}{10}}\implies 3^{\frac{7}{10}}[/tex]
The u-drive rent-a-truck company plans to spend $8 million on 280 new vehicles. Each commercial van will cost $25,000 , each small truck $30,000 , and large truck $40,000. Past experience shows that they need twice as many vans as small truck. How many of each type of vehicle can they buy?
Answer:
1 large truck, 99 small trucks and 180 commercial vans
Step-by-step explanation:
Step 1 : Write the data.
Total amount: 8,000,000
Total trucks needed: 280
Cost of commercial van (x) = $25,000
Cost of small truck (y) = $30,000
Large truck = $40,000 (from my understanding, only 1 large truck has to be bought since the amount given for commercial vans and small trucks is for each of it.
Since they need twice as many vans as small trucks, commercial van will be 2y and small truck will be y
Step 2 : Form two equations
40,000 + 25000(x) + 30000(y) = 8,000,000
25000(x) + 30000(y) = 7960,000 (equation 1)
1(large truck) + x + y =280
x + y = 279 (equation 2)
Step 3 : Find the value of y
From equation 2:
x = 279 - y
From equation 1:
25000(x) + 30000(y) = 7960,000
25000(279 - y) + 30000(y) = 7960,000
-25000y + 30000y + 6975000 = 7960000
5000y = 985000
y= 98.5 rounded off to 99 small trucks
Step 4: Find value of x
x + y = 279
y = 279 - 99
y = 180 commercial vans
Step 5: Answer how many type of each vehicle can they buy.
They can buy:
1 large truck
99 small trucks
180 commercial vans
!!
Which of the following exponential regression equations best fits the data shown below?
Answer:
The correct option is D.
Step-by-step explanation:
The general exponential regression equations is
[tex]y=ab^x[/tex] .... (1)
where, a is initial value and b is growth factor.
Using graph calculator, we get
[tex]a=3.5349151766\approx 3.53[/tex]
[tex]b=4.37391527533\approx 4.37[/tex]
[tex]R^2=0.99878148[/tex]
Put the value of a and b in equation (1), to find the exponential regression equation.
Substitute a=3.53 and b=4.37 in equation (1).
[tex]y=(3.53)(4.37)^x[/tex]
[tex]y=3.53(4.37)^x[/tex]
The exponential regression equations that best fits the data is [tex]y=3.53(4.37)^x[/tex].
Therefore the correct option is D.
A hardware store buys 300 feet of nylon rope. The store sells the rope by the inch. A customer can purchase 40 inches of the rope for $1.60. The store sells all of the rope and makes a profit of $54. How much did the store pay for the rope in dollars per inch.
Pls answer this question it’s important..
Answer:
0.025 $/in.
Step-by-step explanation:
The store bought 300 ft of rope.
1 ft = 12 in.
300 ft * 12 in./ft = 3600 in.
The store bought 3600 inches of rope.
The store sells 40 inches of rope for $1.60. We can find the selling unit price of rope in dollars per inch.
($1.60)/(40 in.) = $0.04/in.
The store sells the rope at a price of $0.04 per inch.
The store sold all the rope at $0.04/in.
3600 in. * $0.04/in. = $144
The store sold all the rope for $144.
The profit was $54 for selling ll the rope.
$144 - $54 = $90
The bought the rope for $90.
The cost is dollars per inch is
($90)/(3600 in.) = 0.025 $/in.
I Need The Answer Please Help!!
Answer:
33°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180 for ∠1, that is
∠1 = 180° - (116 + 31)° = 180° - 147° = 33°
what is the intercept for the graph of this line? 5x -3y =11
Step-by-step explanation:
[tex]5x-3y=11\\\\x-intercept\ is\ for\ y=0\\\\5x-3(0)=11\\5x-0=11\\5x=11\qquad\text{divide both sides by 5}\\x=\dfrac{11}{5}\\\\y-intercept\ is\ for\ x=0\\\\5(0)-3y=11\\0-3y=11\\-3y=11\qquad\text{divide both sides by (-3)}\\y=-\dfrac{11}{3}[/tex]
a right pyramid with a square base has a base edge length of 24 feet and slant height of 20 feet the height of the pyramid is feet
Answer:
The height of the pyramid is 16 feet.Step-by-step explanation:
Look at the picture.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=12ft,\ leg=H,\ hypotenuse=20ft[/tex]
Substitute:
[tex]12^2+H^2=20^2[/tex]
[tex]144+H^2=400[/tex] subtract 144 from both sides
[tex]H^2=256\to H=\sqrt{156}\\\\H=16\ ft[/tex]
Answer:
16 feet
Step-by-step explanation:
for edg
(3,1.5) and (5, 2.5) what is the slope of the line through these two points?
The slope of the line through given two points is [tex]\frac{1}{2}[/tex]
What is the formula of slope ?
If (x₁, y₁) & (x₂, y₂) are two given points on a line.
Then the slope of the line (m) = [tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]
What is the required slope ?Given points on a line are (3, 1.5) & (5, 2.5)
∴ Slope of the line (m) = [tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]
= [tex]\frac{2.5-1.5}{5-3}[/tex]
= [tex]\frac{1}{2}[/tex]
So, the required slope is [tex]\frac{1}{2}[/tex]
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Tyreese is using algebra tiles to solve the equation below.
2x + 5 = -x + (1)
answers
A. remove one x-tile from both sides. B. remove two x-tiles from the left side. C. add one positive x-tile to both sides. D. add two positive x-tiles to both sides.
for this case we have the following equation:
[tex]2x + 5 = -x + 1[/tex]
To resolve:
We add x to both sides of the equation:
[tex]2x + x + 5 = -x + 1 + x[/tex]
[tex]3x + 5 = 1[/tex]
We subtract 5 on both sides of the equation:
[tex]3x + 5-5 = 1-5\\3x = -4[/tex]
We divide between 3 on both sides of the equation:
[tex]x = - \frac {4} {3}[/tex]
Answer:
We add x to both sides of the equation
Answer:
The correct option is C) add one positive x-tile to both sides.
Step-by-step explanation:
Consider the provided equation.
2x + 5 = -x + 1
Now to solve the above equation first isolate the variables.
To isolate the variables add x to the both the side of the equation.
2x + 5 + x = -x + 1 + x
Now add the like terms.
3x + 5 = 1
Here we add the x tiles to the both the side of the equation.
Now consider the options.
The correct option is C) add one positive x-tile to both sides.
What will $110,000 grow to be in 9 years if it is invested today at 11%
Answer:
218,900
Step-by-step explanation:
110,000 x 11%= 12,100
12,100 x 9 = 108,900
110,000+108,900= 218,900
The future value of a present investment of $110,000 at an annual interest rate of 11% compounded for 9 years is approximately $278,984.57.
Explanation:The question is asking for the future value of a present investment of $110,000 at an annual interest rate of 11% compounded for 9 years. For such a calculation, we can use the formula for compound interest:
FV = PV * (1 + r)^n
Where,
FV is the future value of the investment PV is the present value or the initial amount invested which is $110,000 r is the annual interest rate which is 11% or 0.11 n is the number of periods the money is invested for which is 9 years
Plugging in the values, we get:
FV = $110,000 * (1 + 0.11)^9
After calculating the above expression, we find that the investment will grow to be approximately $278,984.57 after 9 years.
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Koalas absorb only 25% of the fiber they eat. A koala absorbed 10.5 ounces of fiber in one day. How many ounces of fiber did he eat that day?
42 ounces
Step-by-step explanation:In this question, it is asking how many ounces of fiber did the Koala eat that day.
In order to solve this question, we would need to gather some important information from the question.
Important Information:
Koalas absorb only 25% of fiber they eatKoala absorbed 10.5 ounces of fiber in 1 dayWith the information above, we can solve the question.
We know that koalas only absorb 25% of fiber. We also know that a koala absorbed 10.5 ounces of fiber.
This means that the 10.5 ounces is 25% of fiber. This is 1/4 of the fiber it ate.
Now, we just need to find the other 3/4.
We could just multiply 10.5 by 4 to find how much fiber it ate that day.
[tex]10.5*4=42[/tex]
When you multiply, you should get 42.
This means that the Koala ate 42 ounces of fiber that day.
I hope this helps you out.Good luck on your academics.Have a fantastic day!Answer:
42
Step-by-step explanation:
We seek the answer to the question "10.5 ounces is 25% of what number?" If we call the unknown number of ounces x, we have the equation 10.5=0.25x. Dividing both sides by 0.25, we have x=10.5/0.25=42 ounces of fiber.
Please help!
The table and the graph below each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 4,80 and 5,100 and 6,120 and 7,140. On the right of this table is a graph. The x-axis values are from 0 to 10 in increments of 2 for each grid line. The y-axis values on the graph are from 0 to 350 in increments of 70 for each grid line. A line passing through the ordered pairs 2, 70 and 4, 140 and 6, 210 and 8, 280 is drawn.
How much more would the value of y be on the graph than its value in the table when x = 12?
20
90
150
180
Answer:
180
Step-by-step explanation:
According to the table, the relationship between the x and the y value is 20, (4*20 = 80) (5*20 = 100) etc.
The graph with the points has a relationship of 35 (2*35 = 70) (4*35 = 140) etc. Therefore, you can figure out what y-value 12 would have for the table and the graph by multiplying 12 by 20 or 35 respectively.
12*20 = 240
12*35 = 420
420-240 = 180
Answer:
180
Step-by-step explanation:
Alvin throws the football to a receiver who jumps up to catch the ball. The height of the ball over time can be represented by the quadratic equation -4.9t2 + 7.5t + 1.8 = 2.1 . This equation is based on the acceleration of gravity -4.9 m/s2, the velocity of his pass is 7.5 m/s and releases the football at a height of 1.8 meters, and the height where the receiver catches the ball of 2.1 meters. Put the equation in standard form and then solve by using the quadratic equation.
Answer:
The standard form of the equation is 49t² - 75t + 3 = 0
The solution of the equations are 1.49 and 0.041
Step-by-step explanation:
* Lets explain how to solve the problem
- The standard form of the quadratic equation is ax² + bx + c = 0,
where a , b , c are constant and a can not be 0
∵ The quadratic equation is -4.9t² + 7.5t + 1.8 = 2.1
- Lets make the left hand side equal to 0
∵ -4.9t² + 7.5t + 1.8 = 2.1 ⇒ subtract 2.1 from both sides
∴ -4.9t² + 7.5t - 0.3 = 0 ⇒ multiply each term by -10
∴ 49t² - 75t + 3 = 0
* The standard form of the equation is 49t² - 75t + 3 = 0
∵ ax² + bx + c = 0
∴ a = 49 , b = -75 , c = 3
- Lets use the formula [tex]x=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex] to solve
the equation
∴ [tex]x=\frac{-(-75)+\sqrt{(-75)^{2}-4(49)(3)}}{2(49)}=1.49[/tex]
∴ [tex]x=\frac{-(-75)-\sqrt{(-75)^{2}-4(49)(3)}}{2(49)}=0.041[/tex]
* The solution of the equations are 1.49 and 0.041
A (5, 3), B (2, 1), and C (-2, 4) are the coordinates of a triangle's vertices. If the triangle is reflected over the x-axis, what are the coordinates of the image?
Answer:
A(5,3) ->A'(5,-3)
B(2,1) ->B'(2,-1)
C(-2,4) ->C'(-2,-4)
Step-by-step explanation:
If a point is reflected over the x-axis, it ends up on the opposite side of the x-axis with the same distance from the x-axis.
So what that means is the x-coordinate will stay the same and the y-coordinate will be opposite of what it was.
So if we reflect each of your points through the x-axis you will get:
A(5,3) ->A'(5,-3)
B(2,1) ->B'(2,-1)
C(-2,4) ->C'(-2,-4)
Answer:
(5,-3) (2,-1) (-2,-4)
Step-by-step explanation:
When reflection over the x-axis the rule is (x,y) becomes (x, -y)
so your x will stay the same but your y will change
a photo with a length of 3 inches and a width of 5 inches is enlarged to a poster size. the poster and the photo are similar. the length of the poster is 21 inches. what is the width of the poster? (answers there^^)
Answer:
J. 35 inches
Step-by-step explanation:
Write a proportion:
3 / 5 = 21 / x
Cross multiply:
3x = 105
Divide:
x = 35
The width of the poster is 35 inches.
The width of the poster is 35 inches.
What is the ratio proportion?Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios.
A photo with a length of 3 inches and a width of 5 inches is enlarged to poster size.
The poster and the photo are similar. the length of the poster is 21 inches.
Let x be the width of the poster.
The width of the poster is given by;
[tex]\rm \dfrac{Length \ of \ photo}{Width \ of \ photo}=\rm \dfrac{Length \ of \ poster}{Width \ of \ poster}\\\dfrac{3}{5}=\dfrac{21}{x}\\\\3 \times x =21 \times 5\\\\3x=105\\\\x=\dfrac{105}{3}\\\\x=35[/tex]
Hence, the width of the poster is 35 inches.
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What are the zeros of the function below? Check all that apply.
F(x) =x(x-2)/(x+3)(x-5)
Answer:
x = 0 and x = 2Step-by-step explanation:
[tex]\text{The domain:}\\\\(x+3)(x-5)\neq0\iff x+3\neq0\ \wedge\ x-5\neq0\\\\x\neq-3\ \wedge\ x\neq5\\\\========================\\\\f(x)=\dfrac{x(x-2)}{(x+3)(x-5)}\\\\\text{The zeros are for}\ f(x)=0\\\\\dfrac{x(x-2)}{(x+3)(x-5)}=0\iff x(x-2)=0\iff x=0\ \vee\ x-2=0\\\\x=0\in D\ \vee\ x=2\in D[/tex]
What does the line y = 2x + 5 look like?
Answer:
A line with slope 2 and y-intercept 5.
Step-by-step explanation:
y=mx+b is the slope-intercept form of a line with slope,m, and y-intercept ,b.
y=2x+5 is in this exact form.
This means y=2x+5 is a line with slope 2 and y-intercept 5.
You can graph this by first plotting the y-intercept (0,5).
You can then use the slope to find another point. Keep in my the slope=rise/run so you might want to write it as a fraction.
The slope=2/1, this means you will rise 2 units and go right 1 unit.
So if you start at (0,5) then you can find another point by going to (0+1,5+2)=(1,7).
So if you graph (0,5) and (1,7) and then connect them with a straight-edge you have graphed y=2x+5.
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Answer:
The area of the prism: 404 square feet.
Step-by-step explanation:
The idea in this exercise is to find the areas of all the geometric figures, and then add them all.
Notice that we have four consecutive rectangles, two smaller with dimension 6 ft by 8 ft and two larger with dimension 11 ft by 8 ft. Then, combined area of this four rectangles is
A_1 = 6*8 + 6*8 + 11*8+11*8 = 48+48+88+88 = 272.
For the other two rectangles, notice that their bases has the same length (11 ft). Their height can obtained using the characteristics of the prism. In this case must be 6 ft, the same length of the base of the previous smaller rectangles. The, the combined area of this rectangle is
A_2 = 6*11 +6*11 = 66 + 66 = 132.
Finally, adding those two area we get the area of the prism: 404 square feet.