Using the general addition rule, p(F or G) = 0.667.
What is sample space?
In probability theory, the set of all feasible outcomes or outcomes of an experiment or random trial is referred to as the sample space. The sample points, or potential ordered outcomes, are listed as elements in the set used to represent the sample space.
Let,
S = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
F = {8, 9, 10, 11, 12, 13}
G = {12, 13, 14, 15}
n(S) = number of elements in set S are 12.
n(F) = 6
n(G) = 4
n(F and G) = common elements in F and G = 2
n(F or G) = n(F) + n(G) - (F and G)
n(F or G) = 6 + 4 - 2
n(F or G) = 8
Now, using the general addition rule,
P(F or G) = P(F) + P(G) - P(F and G)
Here,
P(F) = n(F)/n(S) = 6/12 = 1/2
P(G) = n(G)/n(S) = 4/12 = 1/3
P(F and G) = n(F and G)/n(S) = 2/12 = 1/6
⇒ P(F or G) = 1/2 + 1/3 - 1/6
= 5/6 - 1/6
= 4/6
⇒ P(F or G) = 0.667
Hence, using the general addition rule, P(F or G) = 0.667.
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A restaurant's delivery person can determine the number of miles he can drive in x hours by the function f (x) = x2 + 3x. the number of gallons of gasoline that the delivery person uses for driving y miles can be determined by the function g of y is equal to y over 22 period if the delivery person works an 8-hour shift, how many gallons of gasoline will he need in his tank?
Given that the delivery person works an 8-hour shift, he needs 4 gallons of gasoline in his tank.
A function is defined as the expression that relates a independent variable with a dependent variable. To evaluate a function is to substitute the value of the independent variable and then calculate the function value.
Given that the delivery person works an 8-hour shift, substitute x = 8 to the function of y.
y = f(x) = x² + 3x
y = 8² + 3(8)
y = 88
To determine the amount of gasoline needed, substitute the value of y to the function of g of y.
g = y / 22
g = 88 / 22
g = 4
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The Tran family and the Campbell family each used their sprinklers last summer. The water output rate for the Tran family's sprinkler was 35 L per hour. The water output rate for the Campbell family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1925 L. How long was each sprinkler used?
The time in hours for the Tran family's sprinkler will be 30 hours.
The time in hours for the Campbell family's sprinkler will be 35 hours.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The water output rate for the Tran family's sprinkler was 35 L per hour.
The water output rate for the Campbell family's sprinkler was 25 L per hour.
And, The families used sprinklers for a combined total of 65 hours, which is resulting in a total water output of 1925 L.
Now,
Let time in hours for the Tran family's sprinkler = t
And, The time in hours for the Campbell family's sprinkler = 65 - t
So, We can formulate by the given condition,
⇒ 35t + 25 (65 - t) = 1925
Solve for t as;
⇒ 35t + 25 (65 - t) = 1925
⇒ 35t + 1625 - 25t = 1925
⇒ 10t + 1625 = 1925
⇒ 10t = 1925 - 1625
⇒ 10t = 300
⇒ t = 30
Thus, The time in hours for the Tran family's sprinkler = t
= 30 hours
And, The time in hours for the Campbell family's sprinkler = 65 - t
= 65 - 30
= 35 hours.
Therefore, we get;
The time in hours for the Tran family's sprinkler will be 30 hours.
The time in hours for the Campbell family's sprinkler will be 35 hours.
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The equation is y=
Graph of f(x)= |x|
The equation from the given graph is y=-2/3 x²+5.
From the given graph the vertex is (h, k)=(0, 5).
What is quadratic equation of graph?A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.
The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.
Here, point on the given line from the graph is (3, -1)
Put (x, y)=(3, -1) and (h, k)=(0, 5) in y = a(x - h)² + k, we get
-1=a(3-0)²+5
⇒ 9a=-6
⇒ a=-2/3
Now, y=-2/3(x-0)²+5
y=-2/3 x²+5
Hence, the equation from the given graph is y=-2/3 x²+5.
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Pls help me ! for this question
Answer:
f = 3cm g = 16cm
Step-by-step explanation:
Area of ABCE = 60cm²
Area of ABCD = 48cm²
60 - 48 = 12
Area of ADE = 12cm²
A to D = 3cm
f = 3cm
g = 16cm
A helicopter leaves A and flies 40 miles due east. Then the helicopter flies
10 miles due south and arrives at B. Work out the bearing of B from A.
The bearing of the helicopter from B to A is 75.96 degrees
How to determine the bearing of the helicopter from B to AInformation from the question
A helicopter leaves A and flies 40 miles due east
the helicopter flies
10 miles due south
Work out the bearing of B from A = ?
The bearing from B to A is worked using SOH CAH TOA
The direction of movements describes a right angle triangle of
opposite = 40 miles
adjacent = 10 miles
The bearing is calculated using tan, TOA let the angle be x
tan x = Opposite / Adjacent
tan x = 40 / 10
tan x = 4
x = arc tan 4
x = 75.96 degrees
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Julio is running in a 13.1 mile race. There are water stops every 2.75 miles along the route from the beginning of the race. What is the distance between the last water stop and the end of the race?
There is 2.1 miles distance between the last water stop and the end of the race.
Total miles Julio will run = 13.1 miles
Distance at which water stops are location = 2.75
Total number of water stops in full race of 13.1 miles = 13.1 / 2.75
=4.764
so , there are 4 stops in the runs for drinking water every 2.75 miles
Distance from starting point of race and last water stops = 4 × 2.75 = 11 miles
Distance between the last water stop and the end of the race = 13.1 - 11
= 2.1 miles
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2: The probability of a $2 winner in a particular state lottery is 1 in 10, the probability of a $5 winner is 1
in 50, and the probability of a $10 winner is 1 in 500.
a) What is the probability of getting either a $2, or $5, or $10 winner?
b) What is the probability of getting a $2 winner?
c) If you buy 50 lottery tickets, what is the probability that you will get at least one $5 winner?
d) If you buy 500 lottery tickets, what is the probability that you will get at least one $10 winner? B
The probability of each event will be
a. 0.122
b. 0.1
c. 0.64
d. 0.63
Probability of a $2 winner is 1 in 10
Probability of a $5 winner is 1 in 50
Probability of a $10 winner is 1 in 500
The formula to find probability is
1. no. of favorable outcomes / total no. of favorable outcomes
OR
2. P(A) = n(A)/n(S)
where
P(A) is the probability of an event “A”
n(A) is the number of favorable outcomes
n(S) is the total number of events in the sample space
Now we will use formula to find probability of different events happening
a. To find the probability of getting either a $2, or $5, or $10 winner we
will find probability of $2 , $5 and $10 and add them together.
1/10 + 1/50 + 1/500 = 0.122
b. The probability of getting a $2 winner will be
1/10 = 0.1
c. The probability of getting no $5 winner is (49/50)^50 = 0.36
So the probability of getting $5 winner will be 1 - 0.37 = 0.64
d. The probability of getting no $10 winner is (499/500)^500 = 0.37
And we can take probability of total no. of outcomes as 1.
So the probability of getting $10 winner will be 1 - 0.37 = 0.63
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Paula bought p packages of 5 rolls of tape. Then, she bought 4 individual rolls of tape. Which expression shows how many total rolls of tape Paula bought? SOLVE AND I'll MARK BRAINST AHAHAHHA
Y=5p+3
Y equals the total amount of tape rolls
P is for the number of packages there are.
Hope this helped!
:)
Answer:
Y=5p+4
Y equals the total amount of tape rolls
P is for the amount of packages there are
Step-by-step explanation:
7. What number multiplied by 2/3 has a product
of 1? (Example 2) it's saying 4/6 is wrong what do i do
Answer:
3/2
Step-by-step explanation:
To multiply fraction×fraction, you multiply top×top and bottom×bottom.
2/3 × 3/2
= 6/6
= 1
The 3/2 is called the reciprocal. Take the number in the problem and flip it over to find the reciprocal.
A triangle has interior angles of 50°, 55°, and 75° with side lengths of 3.1 m, 3.2 m, and 4.0 m. A second
triangle has side lengths of 10.3 m, 10.5 m, and 12.0 m. What must the interior angles of the second triangle
be for the two shapes to be similar?
The interior angles of the second triangle will be 50°, 55°, and 75° respectively.
What are similar triangles?
If the corresponding angles and sides of two triangles are congruent, then the two triangles are said to be similar.
In other words, similar triangles have the same shape but may differ in size.
Given, a triangle has interior angles of 50°, 55°, and 75° with side lengths of 3.1 m, 3.2 m, and 4.0 m.
And, a second triangle has side lengths of 10.3 m, 10.5 m, and 12.0 m.
The corresponding sides of both triangles are 3.1 m, 3.2 m, and 4.0 m with 10.3 m, 10.5 m, and 12.0 m respectively.
Then, the angles of both triangles are also corresponding to each other.
So we get, the interior angles of the second triangle will be 50°, 55°, and 75° respectively.
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what condition or conditions must hold true for the sampling distribution of the sample mean to be normal when the sample size is less than 30?
When the sample size is smaller than 30, the following requirements must be met for the sampling distribution of the sample mean to be considered normal:
The data values should be symmetrical in the sample.No outliers should be in sample data .If these conditions are satisfied then the sampling distribution of the sample mean to be normal when sample size is less than 30.
A statistic's sampling distribution is a form of probability distribution produced by selecting several random samples of a predetermined size from the same population. You may better comprehend the variations in a sample statistic by using these distributions.
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a store increased the original price of a shirt by a certain percent and then decreased the new price by the same amount. given that the resulting price was 84% of the original price, by what percent was the price increased and decreased?
A retailer raised a shirt's original price by a certain percentage before lowering it by the same percentage. The price was increased and decreased by 40% as the final cost was 84% of the initial cost.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Here,
Let's say the shirt originally cost Rs 100, and we're adding t% to the price.
The new price of the shirt is therefore 100 + (t/100 * 100) = Rs. 100+t after the initial t% increase.
The price is then reduced by t%.
Cost of a new shirt: (100 + t) - (t/100)
[100+t] = (100+t)
[1-(t/100] = [(100+t)/100]
therefore, the final price is equal to 84% of Rs 100, or Rs 84.
10000 - t^2 = 84.
t^2 = 1600
t = 40
The price was thus raised and lowered by 40%.
The original price of a shirt was increased by a specific percentage before being decreased by the same percentage by the retailer. As the final price was 84% of the initial price, the price was both increased and decreased by 40%.
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Graph the line that represents a proportional relationship between d and t with the property that an increase of 5 units in t corresponds to an increase of 8 units in d.
What is the unit rate of change of d with respect to t? (That is, a change of 1 unit in t will correspond to a change of how many units in d?)
The unit rate is
?
Graph the relationship.
The unit rate of change , d with respect to t is = 1.6 .
In the question,
it is given that , the relationship between d and t is proportional
also given that " increase of 5 units in t corresponds to increase of 8 units in d ".
which is represented as 5t = 8d
Divide both sides of the equation 5t = 8d by "5" ,
t = 8/5d
t = 1.6d
next we plot the graph of t = 1.6d
we see that the above equation is a proportional linear equation
and A proportional linear equation is represented as
t = md , Where m represents the unit rate .
So , after comparing , we get
m = 1.6
Therefore , The unit rate of change of d with respect to t is 1.6 .
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Will give u brainliest!
Answer:6 is the correct answer
Step-by-step explanation:
Because 16 + 20 equals 36 and the sq root of 36 is 6. So you chose the correct answer.
Answer:
6
Step-by-step explanation:
[tex]\sqrt{16+20}[/tex]
[tex]\sqrt{36}[/tex]
6
PLEASE HELP!
4) The "random walk theory of stock prices holds that price movements in disjoint time periods are independent of each other. Suppose that we record only whether the price is up or down each year, and that the probability that our portfolio rises in price in any one year is 0.65.
a) What is the probability that the portfolio goes up for 3 consecutive years?
b) What is the probability that the portfolio's value moves in the same direction (either up or down) for 3 consecutive years?
c) What is the probability that the portfolio's value goes up for at least 1 of 3 years?
Part (a)
Each year is independent of any other. This allows us to simply multiply the probability values for each increase. Recall that P(A and B) = P(A)*P(B) if and only if events A & B are independent.
(0.65)*(0.65)*(0.65) = (0.65)^3 = 0.274625
Answer: 0.274625=========================================
Part (b)
We calculated the probability of an increase for each of the 3 years back in part (a). Let's calculate we have a decrease 3 times in a row.
0.65 is the probability of increase for any given year, which makes 1-0.65 = 0.35 the probability of decrease for any given year.
Therefore (0.35)^3 = 0.042875 represents the probability of 3 decreases in a row.
Add this result to what we got in part (a)
0.274625+0.042875 = 0.3175
This is done because we could have 3 increases OR 3 decreases (pick one). Think of it like this P(A or B) = P(A) + P(B) where A & B are mutually exclusive events.
Answer: 0.3175=========================================
Part (c)
In the previous part we calculated 0.042875 as the probability of 3 decreases in a row.
1-0.042875 = 0.957125 is the probability of at least one increase. Note how the events "no increases" and "at least one increase" are complementary events. They are opposite. One or the other must happen, which allows us to subtract from 1.
You can think of it like this
P(no increases) + P(at least one increase) = 1
P(at least one increase) = 1 - P(no increases)
Answer: 0.957125Side note: none of the final answers have been rounded.
What is an equation of the line that passes through the points (3,-3) and (3,-6)
Answer:
x = 3
Step-by-step explanation:
You want the equation of the line through points (3, -3) and (3, -6).
Vertical lineThe two points have the same x-value, indicating the line through them is a vertical line. That will have an equation of the form x = c.
The x-value of the given points is 3, so the equation is ...
x = 3
__
Additional comment
We note that the answer box is pre-filled with "y =". There is no "y =" equation that will go through these points. The slope is undefined, so the slope-intercept form of the equation cannot be used.
Solve for x.
2/x^2−4 − 1/x+2 = 3/x−2
In regards to the question above, the solution for the equation is x=-2(1+2x)/x^2-4.
What is the equation known as?A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. Equations come in two varieties: identities and conditional equations.
How to solve this:
2/x^2-4 -1/x+2=3/x-2
collecting like terms
2/x^2-4 -1/x+2 -3/x-2=0
Divides through by:
x^2-42 -1(x-2) -3(x+2)/x^2-4=0
Remove bracket: 2-x+2-3x-6/x^2-4
Lastly, collecting like terms:
2+2-6-x-3x/x^2-4-2-4x/x^2-4
=-2(1+2x)/x^2-4
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Write 30 000 000 in standard form.
Answer:
3×10^7
Step-by-step explanation:
Write 30 000 000 in standard form.
=3×10,000,000
=3×10^7
Step-by-step explanation:
this is
3.0 × 10⁷
as 30 000 000 has 7 zeroes (7 sequential and continuously increasing powers of 10 starting with 10¹).
and the first non-zero digit is 3.
an inverted cone is partially filled with water, as shown below. the radius of the inverted cone is 16 mm. the height of the inverted cone is 18 mm. if the volume of the water is increasing at a rate of 548 cubic mm per hour, what is the rate, in mm per hour, at which the height of the water is changing when the height of the water is 2 mm?
The rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2
Given data,
A partially filled inverted cone contains water. The inverted cone has a 16 mm radius. The inverted cone is 18 mm in height. if the water's volume is growing at a pace of 548 cubic millimeters per hour.
The rate in mm per hour at which the height of the water is changing when the height of the water is 2 mm;
r/h = 16/18
= 8/9
r = 8h/9
The volume of the cone is;
v = [tex]\frac{1}{3}\pi r^2h[/tex]
v = [tex]\frac{1}{3}\pi (8h/9)^2h[/tex]
v = [tex]\frac{64}{243}\pi h^3[/tex]
Now, differentiating concerning x;
[tex]\frac{dv}{dt}[/tex]= [tex]\frac{d}{dt}[/tex] [tex]\frac{64}{243}\pi h^3[/tex]
[tex]\frac{dv}{dt}[/tex]= 64π/243*[tex]\frac{d}{dt}[/tex] h³
[tex]\frac{dv}{dt}[/tex]= [tex]\frac{64}{81}\pi h^2\frac{dh}{dt}[/tex]
We have;
[tex]\frac{dv}{dt}[/tex]= 548 and h = 2mm
[tex]\frac{dh}{dt} = \frac{548*81}{256\pi }[/tex]
[tex]\frac{dh}{dt}[/tex] = 55.19
[tex]\frac{dh}{dt}[/tex] = 55.2mm per hour.
Hence, the rate in mm per hour at which the height of the water is changing when the height of the water is 2mm is 55.2
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0.25 in standard form
Answer:
2.5 × 10^-1
step-by-step explanation:
To get to standard form, you must move the decimal to the right one place so the number before it is not a 0. Because you move the decimal, you must add the second part of the equation so that the value does not change.
Answer:
02.5 but the 0 at the beginning isn't significant so 2.5
Step-by-step explanation:
because to find the standard form you move the decimal point so that there is only one non-zero digit in front of the decimal point.
how many whole numbers lie between
[tex] \sqrt{8} \: and \: \sqrt{80} [/tex]
The volume of the triangular prism is 12.5 m³. The length is 2.5 m and the base is 2 m. What is the width?
Answer:
(4) 5 m
Step-by-step explanation:
You want the length of side x of a right triangular prism with base edge lengths of 2.5 m and 2 m, and a volume of 12.5 m³.
VolumeThe volume of the prism is given by the formula ...
V = Bh
where B is the area of the base:
B = 1/2bh . . . . where b and h are the leg dimensions of the right triangle
Using these formulas together, we have ...
V = 1/2(2.5 m)(2 m)x
12.5 m³ = 2.5x m²
Dividing by 2.5 m², we find x to be ...
(12.5 m³)/(2.5 m²) = x = 5 m
The dimension labeled x has length 5 meters.
each other.
с
D
1. The volume of box A is 64 cubic inches. The circumference of a regulation baseball is at least 9 inches but no more
than 9.25 inches. Can a baseball fit in box A? Explain.
2. Box B has a surface area of 216 square inches. What is the ratio of the side length of box B to the side length of box
A?
3. The ratios of the side lengths of B to A, C to B, and D to C are the same. How much more space do the boxes
occupy when stored separately in a closet than when they are stacked inside each other in the closet?
1.) Yes,it will fit because volume of the base ball is 13.36 cubic inch and the volume of box is 64 cubic inch which greater than the volume of baseball .
2) The ratio of the side length of box B to the side length of box
A is 1.472 inche : 6 inch.
What is cube ?
A Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron.
What is circumference?
The circumference is the distance that surrounds a circle. We can measure the circumference of the earth by measuring the distance that we will have to walk all the way around the world.
To check whether the baseball is will till in the box we will check the maximum value of circumference.
⇒ [tex]2\pi r[/tex] = 9.25
⇒ [tex]r = \frac{9.25}{2\pi}[/tex]
⇒[tex]r = 1.472 in.[/tex]
Volume of the baseball [tex]= \frac{4}{3} \pi x^{3}[/tex]
[tex]= \frac{4}{3}\times \pi\times (1.472)^3 in^3[/tex]
[tex]= 13.36\ in^3 < 64 \ in^3\\[/tex]
So, it will fit inside the box.
2.)[tex]\sqrt[3]{216} = 6 \ (\therefore V = a^3)[/tex]
The length of each side of the box is 6 inches.
and the ratio of the side length of box B to the side length of box
A:
1.472 in : 6 inches
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Find the perimeter of this semi-circle
with diameter, d = 84cm.
Give your answer as an expression in
terms of π.
The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:
= 48π + 42
What is the equation for a semicircle?The area of a circle, A, is calculated using the formula A = pi * r2, where r is the circle's radius. Since we already know that a semicircle is half of a circle, we can easily divide that equation by two to determine the area of a semicircle. As a result, A = pi * r2/2 is the formula for calculating the area of a semicircle.
How do you calculate the circumference of a half-semicircle?With the aid of the following formula, we can determine a semicircle's perimeter: The semicircle's perimeter is equal to r + 2r units, where r is the radius of the semicircle.
According to the given data:Diameter of the semi-circle = 84cm
Now,
the circumference of the semi-circle = πr + 2r
Substituting the value of r in the given formula:
the circumference of the semi-circle = πr + 2r
= πr + 2r
= 48π + 42
The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:
= 48π + 42
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1 . 10. A life insurance company found that among its last 200 claims, there were six dozen smokers. What is the ratio of smokers to nonsmokers in this group of claimants? Write in lowest terms
2. A woman threw 60 darts and hit the target a dozen times. What is her ratio of hits to misses? Write in lowest terms
3. . While watching television for one week, a consumer group counted 1240 acts of violence and 40 acts of kindness. What is the violence to kindness ratio for television, according to this group. Write in lowest terms
Answer for No.2
Answer: 1/4
Step-by-step explanation:
Hits = 12
Misses = 60-12 = 48
Ratio of hits to misses = 12/48 = ¼
So the answer is 1/4.
in a particular game, a fair die is tossed. if the number of spots showing is either four or five, you score 1 point. if the number of spots showing is six, you score 4 points. and if the number of spots showing is one, two, or three, you score 0. you are going to play the game twice. what is the probability that you score 4 points both times?
1/36 is the probability that you score 4 points both times.It is the likelihood of scoring four points twice.
1/6 * 1/6 =1/36
The probability of an event occurring is measured by its probability. It determines the probability of an event. The probability calculation is P(E) = Number of Favourable Outcomes/Total Outcomes.A game is a formalized form of play that is frequently done for amusement or fun but can also serve as a teaching game tool.
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when two pipes fill a pool together, they can finish in 4 hours. if one pipe fills half of the pool and then the other takes over and finishes filling the pool, the pool will fill in 9 hours. how long would it take each pipe to fill the pool if it were working alone?
Time taken by pipe 1 to fill the pool is 6 and by pipe 2 is 12.
Here we have to find the time taken by each pipe to fill the pool.
Formula to find the work:
w = r × t
where
w = is the work done
r = is the rate of work done
t = is the time taken to do the work
For pipe 1 working alone to fill 1 pool, the work done is 1
w1 = r1 t1
1 = r1 × t1
t1 = 1/r1
For pipe 2 working alone to fill 1 pool, the work done is 1;
w2 = r2 t2
1 = r2 × t2
t2 = 1/r2
From the question, it would take 9 hours if each pipe took turns filling half the pool. That is;
t1/2 + t2/2 = 9
t1 + t2 = 18
However, if both pipes worked together, it would take 4 hours for each pipe. That is;
w1 + w2 = w
r1t1 + r2t2 = 1
4r1 + 4r2 = 1
r1 + r2 = 1/4
As we know from the above:
r1 = 1/t1 and r2 = 1/t2
So;
1/t1 + 1/t2 = 1/4
(t2 + t1)/ t1 t2 = 1/4
t1 + t2 = 18
So
t1 t2 = 72
The only factors of 72 that satisfy the conditions
t1 + t2 = 18
t1 . t2 = 72
are 6 and 12.
Therefore, pipe 1 will take 6 hours, and pipe 2 will take 12 hours.
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Wyatt is deciding between two different movie streaming sites to subscribe to. Plan A costs $19 per month plus $0.50 per movie watched. Plan B costs $13 per month plus $1.50 per movie watched. Let A represent the monthly cost of Plan A if Wyatt watches x per month, and let B represent the monthly cost of Plan B if Wyatt watches a movies per month. Write an equation for each situation, in terms of x, and determine the number of monthly movies watched, x, that would make the two plans have an equal monthly cost.
Equations representing the total costs for plan A and B are A = 19 + 0.50x and B = 13 + 1.5x, respectively, where x is the number of movies watches.
Cost of both the plans will be equal for 6 movies.
What is a linear equation?A linear function is defined as a function that has either one or two variables without exponents.
Given that, Wyatt is deciding between two different film streaming sites to subscribe to, plan A costs $19 per month plus $0.50 per film watched, plan B costs $13 per month plus $1.50 per film watched.
According to question,
A = 19 + 0.50x and
B = 13 + 1.5x
For costs being equal, we have,
A = B
19 + 0.50x = 13 + 1.5x
x = 6
Hence, for 6 films the costs of both the plans will be equal and equation for both the plans are A = 19 + 0.50x and B = 13 + 1.5x
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Consider a window the shape of which is a rectangle of height h surmounted by a triangle having a height t that is 0.9 times the width w of the rectangle. if the cross-sectional area is a, determine the dimensions of the window which minimize the perimeter.
The cross-sectional area is (h × w ) + ((1 ÷ 2) × 0.9 × w²) and the dimensions of the window which minimize the perimeter is (A - [tex]c_{0}[/tex][tex]w_{0}^{2}[/tex]) ÷ [tex]w_{0}[/tex] = 2√A[tex]c_{1}[/tex]([tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex]) = 0.60592√A.
height of rectangle = h
height of the triangle = t
T = 0.9
width of the rectangle = w
The formula of Cross-sectional area is,
A = h × w + (1 ÷ 2)T × w
A = (h × w ) + ((1 ÷ 2) × 0.9 × w²)
Perimeter,
P = w + (2 × h) + 2√(T² + (w ÷ 2)²)
P = w + (2 × h) + 2√((0.9)² + (1 ÷ 2)²)
P = 2h + 2√((0.9)² + (1 ÷ 2)² + 1) × w
Therefore, [tex]C_{0}[/tex] = 0.9 ÷ 2, [tex]C_{1}[/tex] = 2, [tex]C_{2}[/tex] = 2√((0.9)² + (1 ÷ 2)² + 1)
minP=[tex]c_1[/tex]h+[tex]c_2[/tex]w
A = (h × w) + [tex]c_{0}[/tex]w²
substituting h = (A - [tex]c_{0}[/tex]w²) ÷ hw in P,
P = [tex]c_1[/tex]w + ([tex]c_1[/tex](A - [tex]c_{0}[/tex]w²) ÷ w)
Differentiating both sides,
(dP ÷ dw) = -2[tex]c_{0}[/tex][tex]c_{1}[/tex] + [tex]c_{2}[/tex] - ([tex]c_{2}[/tex](A - [tex]c_{0}[/tex]w²) ÷ w²) = 0
[tex]w_{0}[/tex] = (√[tex]c_{1}[/tex]A ÷ (√[tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex])) = 0.962445√A
and consequently,
[tex]h_{0}[/tex] = (A - [tex]c_{0}[/tex][tex]w_{0}^{2}[/tex]) ÷ [tex]w_{0}[/tex] = 2√A[tex]c_{1}[/tex]([tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex]) = 0.60592√A
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Figure E is dilated from point D, the center of dilation
The figure that is a dilation of figure E is the figure F
What is dilation?Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.
How to determine the dilated figure?The graph represents the given parameter
From the figure, we have the original shape to be figure E
The center point of figure E is the origin
This means that a line drawn from the origin that passes through point E must pass through the same point on the shape
From the figure, the line passes through the same point on figure E and F
Hence, figure F is a dilation of figure
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