Step-by-step explanation:
1. 84 cm^2
2. 616 cm^2
3. 2496 cm^2
Given:
A triangle
l (length) = 12 cm
w (width) is 2 cm less than 3/4 of its length
Find: A (area) - ?
First, let's find the width of the rectangle according to the given information:
[tex]w = (\frac{3}{4} \times 12) - 2 = 9 - 2 = 7 \: cm[/tex]
Now, we can find the area:
[tex]a = w \times l[/tex]
.
2. Given:
A circular clock
C (circumference) = 88 cm
π = 22/7
Find: A (area) - ?
[tex]c = 2\pi \times r[/tex]
First, let's find the radius of the clock:
[tex]2 \times \frac{22}{7} \times r = 88[/tex]
[tex] \frac{44}{7} \times r = 88[/tex]
Multiply both sides of the equation by 7 to eliminate the fraction:
[tex]44r =616[/tex]
Divide both parts of the equation by 44 to make r the subject:
[tex]r = 14[/tex]
Now, we can find the area:
[tex]a = \pi {r}^{2} [/tex]
[tex]a = \frac{22}{7} \times {14}^{2} = 616 \: {cm}^{2} [/tex]
.
3. Given:
A rectangle
l (length) = 52 cm
P = 200 cm
Find: A (area) - ?
First, let's find the width of the rectangle (the perimeter is equal to the sum of all side lengths):
P = 2l + 2w
2w = P - 2l
2w = 200 - 2 × 52
2w = 96 / : 2
w = 48 cm
Now, we can find the area:
A = w × l
A = 48 × 52 = 2496 cm^2
The half life of a drug in the body is 3 hours. (a) By what factor, b , is the amount of drug in the body multiplied by for each passing hour?
Therefore, for every passing hour, the amount of drug in the body is multiplied by approximately 0.7937 or 79.37% based on factor.
The half-life of a drug refers to the amount of time it takes for the concentration of the drug in the body to decrease by half. In this case, with a half-life of 3 hours, we can assume that the concentration of the drug in the body decreases by 50% every 3 hours.
To determine the factor by which the amount of drug in the body is multiplied for each passing hour, we can use the formula:
[tex]b = 0.5^(1/t)[/tex]
where b: factor by which the amount of drug in the body is multiplied for each passing hour, and t: half-life of the drug in hours. Substitute t = 3 hours into formula gives:
[tex]b = 0.5^(1/3) = 0.7937[/tex]
Therefore, for every passing hour, the amount of drug in the body is multiplied by approximately 0.7937 or 79.37%. This means that after one hour, the amount of drug in the body is reduced to 79.37% of its original amount, after two hours it is reduced to 62.86% (0.7937^2), after three hours it is reduced to 50%, and so on.
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leah peeled 175 oranges in 7 hours at that rate how many ornages would she peel in 12 min
Answer:
The answer is 5
Step-by-step explanation:
You divide 175 divided by 7 to find the hourly rate of how many oranges Leah peels. 60 minutes are in a hour. So 12 times 5 is 60. If 175 divided by 7 is 25. And that's hour much she peels in an hour. You divide it by five to find the 12 minute rate, because 12 times 5 is 60 that is equivalent to your hourly rate.
Answer:
Step-by-step explanation:
--> If 7 hrs= 175 oranges
1 hr= 175/7=25
1hr= 60 minutes
So, leah can peal 25 oranges in 60 mins.
Let the number of oranges peeled in 12 mins be x.
60x=25*12
x= 25*12/60
x=300/60
x=5
Leah can peel 5 oranges in 12 minutes,
I need help with the last question
The definite integrals associated with the piecewise function have the following values:
Case 1: 1.5
Case 2: - 2 + 0.5π
Case 3: 5.5
How to determine the definite integral of a function
In this problem we find the representation of a piecewise function formed by four parts, whose definite integrals must be determined by means of the following formulas:
[tex]I = \int\limits^b_a {f(x)} \, dx[/tex]
Graphically speaking, the definite integral is equal to the area below the curve.
Case 1
I = 0.5 · 2² - 0.5 · 1²
I = 1.5
Case 2
I = - 2 · 1 + 0.5π · 1²
I = - 2 + 0.5π
Case 3
I = - 0.5 · 0.5 · 1 + 0.5 · 1.5 · 3 + 1 · 3
I = - 0.25 + 2.75 + 3
I = 5.5
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4
The temperature at 4 P.M. was 53 degrees Fahrenheit. The temperature dropped
3 degrees each hour from 4 P.M. to 9 P.M. Which equation below accurately
represents the temperature at 9 P.M.?
the temperature at 9 P.M. is 38 degrees Fahrenheit, and the equation that represents this temperature is T(9) = 53 - 3(9-4).
How to determine the temperature ?
To determine the temperature at 9 P.M., we need to calculate how much the temperature drops from 4 P.M. to 9 P.M. We know that the temperature drops 3 degrees per hour, and since there are 5 hours between 4 P.M. and 9 P.M., the temperature will have dropped 3 x 5 = 15 degrees.
Therefore, to calculate the temperature at 9 P.M., we need to subtract 15 degrees from the temperature at 4 P.M.:
Temperature at 9 P.M. = Temperature at 4 P.M. - 15
Substituting the given temperature of 53 degrees Fahrenheit at 4 P.M.:
Temperature at 9 P.M. = 53 - 15 = 38 degrees Fahrenheit
Thus, the equation that accurately represents the temperature at 9 P.M. is:
T(9) = 53 - 3(9-4)
Simplifying the equation:
T(9) = 53 - 15
T(9) = 38
In conclusion, the temperature at 9 P.M. is 38 degrees Fahrenheit, and the equation that represents this temperature is T(9) = 53 - 3(9-4).
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whats the total amount
Answer: The answer is 4.64$
Step-by-step explanation:
9 pencils is 2.25$. and we have 2.39$ for the notebook. 2.25 + 2.39 = 4.64
In 2012, the population of a city was 5.94 million. The exponential growth rate was 3.77% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 9 million?
d) Find the doubling time.
The exponential growth function can be written as P0 * [tex]e^(rt)[/tex] where P0 is the initial population, r is the annual growth rate expressed as a decimal, t is the time in years, and e is the mathematical constant e. To estimate the population in 2018, we need to find the value of P(t) when t = 6 (since 2018 is six years after 2012).
What is an exponential growth function?An exponential growth function is a mathematical function that models the growth of a quantity at an exponential rate over time.
a) The exponential growth function can be written as:
P(t) = P0 * [tex]e^(rt)[/tex]
where P0 is the initial population, r is the annual growth rate expressed as a decimal, t is the time in years, and e is the mathematical constant e (approximately equal to 2.71828).
In this case, P0 = 5.94 million, r = 0.0377 (3.77% expressed as a decimal), and t is the time in years. Therefore, the exponential growth function for this city is:
P(t) = 5.94 * [tex]e^(0.0377t)[/tex]
b) To estimate the population in 2018, we need to find the value of P(t) when t = 6 (since 2018 is six years after 2012). So, we plug in t = 6 into the exponential growth function:
P(6) = 5.94 * [tex]e^(0.0377 * 6)[/tex] ≈ 7.58 million
Therefore, the estimated population of the city in 2018 was 7.58 million.
c) To find when the population of the city will be 9 million, we need to solve the exponential growth function for t when P(t) = 9. So, we plug in P(t) = 9 into the exponential growth function:
9 = 5.94 * [tex]e^(0.0377t)[/tex]
Divide both sides by 5.94:
1.516835016835017 = [tex]e^(0.0377t)[/tex]
Take the natural logarithm of both sides:
ln(1.516835016835017) = 0.0377t
Solve for t:
t ≈ 8.39
Therefore, the population of the city will reach 9 million approximately 8.39 years after 2012, which is around 2020.
d) The doubling time is the amount of time it takes for the population to double. We can use the exponential growth function to find this time by solving for t when P(t) = 2P0 (twice the initial population):
2P0 = P0 * [tex]e^(rt)[/tex]
Divide both sides by P0:
2 = [tex]e^(rt)[/tex]
Take the natural logarithm of both sides:
ln(2) = rt
Solve for t:
t = ln(2) / r
Substituting r = 0.0377, we get:
t = ln(2) / 0.0377 ≈ 18.38
Therefore, the doubling time for the population of this city is approximately 18.38 years.
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What is the slope of the line graphed below?
m=
-5 (0,-5)
(3, 1)
5
X
The slope of the line passing through A(0,-5) and B(3,1) is 2.
what is slope?
In mathematics, slope is a measure of how steep a line is. It is the ratio of the change in the y-coordinates to the change in the x-coordinates between two points on the line.
The slope formula is given by:
slope = (change in y)/(change in x)
The change in y is the difference between the y-coordinates of two points on the line, while the change in x is the difference between the x-coordinates of the same two points. The slope is a single number that represents the degree of steepness of the line.
To find the slope of the line passing through two given points A(0,-5) and B(3,1), we can use the slope formula:
slope = (change in y)/(change in x)
We first need to find the change in y and the change in x between the two points:
change in y = y-coordinate of B - y-coordinate of A
= 1 - (-5)
= 6
change in x = x-coordinate of B - x-coordinate of A
= 3 - 0
= 3
Now, we can substitute these values into the slope formula:
slope = (change in y)/(change in x)
= 6/3
= 2
Therefore, the slope of the line passing through A(0,-5) and B(3,1) is 2.
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In 2010 Bolivia had a population of 10.5 million with a Growth Rate of 1.6 %.
Growing Continuously what is the Population in 2030?
the population of Bolivia in 2030, if it continues to grow at a rate of 1.6% continuously, will be approximately 14.45 million.
To solve this problem, we need to use the formula for continuous compounding, which is:
[tex]A = Pe^(rt)[/tex]
Where:
A = the final amount
P = the initial amount
r = the annual growth rate (as a decimal)
t = the number of years
We know that Bolivia had a population of 10.5 million in 2010 and a growth rate of 1.6%, or 0.016 as a decimal. We want to find the population in 2030, which is 20 years after 2010.
So, we plug in the values into the formula:
[tex]A = 10.5 million * e^(0.016 * 20)[/tex]
Using a calculator, we get:
[tex]A = 10.5 million * e^(0.32)[/tex]
A = 10.5 million * 1.3775
A = 14.45 million
Therefore, the population of Bolivia in 2030, if it continues to grow at a rate of 1.6% continuously, will be approximately 14.45 million.
Continuous compounding is a mathematical concept used to calculate the growth of a quantity that grows at a constant rate over time. It is different from simple interest, which is calculated based on a fixed rate over a certain period of time. In continuous compounding, the growth rate is applied infinitely many times over an infinite time period, resulting in exponential growth. The formula we used is a standard formula for continuous compounding, and it can be used to calculate the growth of various quantities, such as population, money, or investments.
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Your car battery dies in the school parking lot and you need a "jump" using jumper
cables in order to get your car started. Magically, mystically, we just know that 18% of
the students who drive to school carry jumper cables. You will randomly stop students
until you find the needed jumper cables. What is the probability that the 4th or 5th
student you stop is the first to have the cables?
The probability that the 4th or 5th student you stop is the first to have the jumper cables is 0.2417 or about 24.17%.
how to find probability of 4th or 5th student?This is an example of a negative binomial probability problem, where we want to know the probability of obtaining a certain number of failures before obtaining a certain number of successes in a series of independent trials. In this case, the "success" is finding a student with jumper cables, and the "failure" is finding a student without jumper cables.
Let p be the probability of success (finding a student with jumper cables) on any given trial, which is 0.18 according to the problem. Let k be the number of successes we want to obtain, which is 1 in this case (since we only need to find one student with jumper cables). Let x be the number of trials it takes to obtain k successes, which is either 4 or 5 in this case.
Then, the probability of finding the first student with jumper cables on the 4th or 5th stop is:
P(X = 4 or X = 5) = P(X = 4) + P(X = 5)
We can calculate these probabilities using the negative binomial distribution formula:
[tex]P(X = x) = (x-1) choose (k-1) * p^k * (1-p)^{x-k}[/tex]
For x = 4:
[tex]P(X = 4) = (4-1) choose (1-1) * 0.18^1 * (1-0.18)^{4-1} = 0.1778[/tex]
For x = 5:
[tex]P(X = 5) = (5-1) choose (1-1) * 0.18^1 *(1-0.18)^{5-1} = 0.0639[/tex]
So, the probability of finding the first student with jumper cables on the 4th or 5th stop is:
P(X = 4 or X = 5) = 0.1778 + 0.0639 = 0.2417
Therefore, the probability that the 4th or 5th student you stop is the first to have the jumper cables is 0.2417 or about 24.17%.
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Mrs. Williams wants to determine which year-end celebration to choose for the students. She wants student input, so she needs to choose a sample of 20 students from the school. Which of the samples shown is a random sample? Select two answers.
Answer: make sure to add options.
Solve the triangle: a=100, b=90, a 29 degrees If it is not possible, say so.
It is not possible to solve the triangle with the given information.
What is Triangle ?
A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry and is widely used in mathematics, science, and engineering. Triangles can be classified in different ways based on their side lengths, angle measures, and other properties.
To solve a triangle, we need at least three pieces of information, including at least one side length. In this case, we have the side lengths a=100 and b=90, and the angle opposite side a is 29 degrees. However, we don't have enough information to find the remaining angles and side lengths of the triangle.
We can use the Law of Cosines and the Law of Sines to solve a triangle, but we need at least one more piece of information. For example, if we had the length of side c or another angle, we could solve the triangle.
Therefore, It is not possible to solve the triangle with the given information.
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A radio station had 172 tickets to a concert. They gave away 3 times as many tickets to listeners as to employees. How many tickets did they give away to employees?
The radio station gave away 43 tickets to employees, and they gave away 3 times as many tickets (3x) to listeners, which is 3 * 43 = 129 tickets. We can calculate it in the following manner.
Let's assume that the radio station gave away "x" tickets to employees.
According to the problem, they gave away three times as many tickets to listeners as to employees. So the number of tickets given to listeners would be 3x.
We know that the total number of tickets given away is 172. Therefore, we can set up an equation based on this:
x + 3x = 172
Simplifying and solving for x, we get:
4x = 172
x = 43
Therefore, the radio station gave away 43 tickets to employees, and they gave away 3 times as many tickets (3x) to listeners, which is 3 * 43 = 129 tickets.
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Does anyone know what they mean by this?
Step-by-step explanation:
The vertical line exactly between them x = -1 is the axis of rotation
Pedro's car completes 2.2 laps for every 2 laps Noor's car completes. a. How many laps does Pedro's car complete when Noor's car completes 100 laps?
B) Pedro's car completes what percent of the number of laps that Noor's car completes?
a) Pedro's car completes 110 laps while Noor's car completes 100 laps.
b) Pedro's car completes 110% of the number of laps that Noor's car completes.
What do laps mean?A lap refers to a complete circuit or rotation around a racetrack or other designated course. It is a standard unit of distance used in racing and other related sports. The length of a lap can vary depending on the specific track or course being used. In general, completing more laps than your competitors in a race is an indication of better performance and can help you win the race.
According to the given informationa)We can start by setting up a proportion to represent the relationship between the number of laps Pedro's car completes and the number of laps Noor's car completes:
2.2 laps / 2 laps = x laps / 100 laps
We can solve for x by cross-multiplying:
2.2 laps * 100 laps = 2 laps * x laps
220 laps = 2x
Dividing both sides by 2, we get:
x = 110 laps
b)If Pedro's car completes 2.2 laps for every 2 laps Noor's car completes, then we can find the ratio of the number of laps Pedro's car completes to the number of laps Noor's car completes as follows:
2.2 laps / 2 laps = 1.1
This means that Pedro's car completes 1.1 laps for every 1 lap Noor's car completes.
To find the percentage that Pedro's car completes compared to Noor's car, we can multiply this ratio by 100:
1.1 * 100 = 110%
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If f(x)=2x² + 4x-14 and g(x) = -x³ + 15x then what is (f+g)(3)?
Answer:
soln;Here
Given,
f(x)=2x² + 4x - 14
g(x)= x³ + 15x
(f + g)(3)= ?
Now,
(f + g)(3) = f(3) + g(3)
=2×3³- 14 + 3³ + 15 × 3
=2 × 27 - 14 + 27 + 45
= 54 - 14 + 27 + 45
= 54 - 14 + 7
=61 - 14
= 47..
Hence the value of f + g)(3)= 47
Indiana Company began a construction project in 2024 with a contract price of $161 million to be received when the project is completed in 2026. During 2024, Indiana incurred $36 million of costs and estimates an additional $86 million of costs to complete the project. Indiana recognizes revenue over time and for this project recognizes revenue over time according to the percentage of the project that has been completed.
The percentage of the project that has been completed 29.5%.
What is percenatge?
Percentage is a way of expressing a fraction or a portion of a whole as a number out of 100. The word "percent" comes from the Latin phrase "per centum", which means "by the hundred".
Based on the information given, Indiana Company began a construction project in 2024 with a contract price of $161 million to be received when the project is completed in 2026. During 2024, Indiana incurred $36 million of costs and estimates an additional $86 million of costs to complete the project.
Indiana Company recognizes revenue over time and for this project recognizes revenue over time according to the percentage of the project that has been completed. This means that Indiana Company will recognize a portion of the revenue each year based on the percentage of the project that has been completed.
To calculate the percentage of the project that has been completed, we need to divide the total costs incurred by Indiana Company by the estimated total costs of the project.
Total costs incurred in 2024 = $36 million
Estimated total costs of the project = $36 million + $86 million = $122 million
Therefore, the percentage of the project that has been completed in 2024 is:
Percentage of project completed = Total costs incurred / Estimated total costs
Percentage of project completed = $36 million / $122 million
Percentage of project completed = 0.295 or 29.5%
Based on this calculation, Indiana Company can recognize 29.5% of the total contract price as revenue for 2024.
Revenue recognized in 2024 = 29.5% x $161 million
Revenue recognized in 2024 = $47.5 million
So, Indiana Company can recognize $47.5 million in revenue for 2024. However, it is important to note that this is only an estimate and the actual revenue recognized may differ based on the progress of the project.
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Calculate the area of the shape below
The shape given below consists of a rectangle and a triangle, and its area is 91 m²
Based on the image, we can see that the shape is composed of a rectangle and a triangle.
In order to find the width of rectangle we have to subtract the height of the triangle from the total length:
9m - 4m = 5 m .
Area of Rectangle:
Length = 13 m
Width = 5 m
Area of Rectangle = Length x Width
= 13 m x 5 m
= 65 m²
Triangle:
Base = 13 m
Height = 4 m
Area of Triangle = (1/2) x Base x Height
= (1/2) x 13 m x 4 m
= 26 m²
Total area of the shape = Area of Rectangle + Area of Triangle
= 65 m² + 26 m²
= 91 m²
Therefore, the area of the shape is 91 square meters (m²)
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Find the missing side lengths. Leave your answers and radicals in the simplest form.
Answer:
u = 12;
v = 6
Step-by-step explanation:
Use trigonometry:
[tex] \tan(60°) = \frac{6 \sqrt{3} }{v} [/tex]
Use the property of proportion to find v:
[tex]v = \frac{6 \sqrt{3} }{ \tan(60°) } = \frac{6 \sqrt{3} }{ \sqrt{3} } = 6[/tex]
Use the Pythagorean theorem to find u:
[tex] {u}^{2} = {v}^{2} + ( {6 \sqrt{3}) }^{2} [/tex]
[tex] {u}^{2} = {6}^{2} + ( {6 \sqrt{3}) }^{2} = 36 + 36 \times 3 = 36 + 108 = 144[/tex]
[tex]u > 0[/tex]
[tex]u = \sqrt{144} = 12[/tex]
I NEED THIS ANSWER TO THIS QUESTION!!
In order to have $140,000 in 20 years, you should deposit $371 each month.
$89,040 of the $140,000 comes from deposits and $50,960 comes from interest.
How to calculate the periodic deposit (payment)?In Mathematics and Financial accounting, the periodic deposit (payment) for an investment can be calculated by using the following mathematical equation (formula):
[tex]FV=PMT(\frac{(1+\frac{r}{n})^{nt} -1}{\frac{r}{n} })[/tex]
Where:
P represents the periodic deposit (payment).r represents the interest rate.FV represents the future value.t represents the time or number of years.n represents the number of periodic deposits.By substituting the given parameters into the formula for the periodic deposit (payment), we have:
[tex]140,000=PMT(\frac{(1+\frac{0.0425}{12})^{12 \times 20} -1}{\frac{0.0425}{12} })[/tex]
140,000(0.0425/12) = PMT(1.33613612561)
495.8333333333 = PMT(1.33613612561)
PMT = 495.8333333333/1.33613612561
PMT = $371.0949 ≈ $371.
For the amount that comes from deposits, we have:
Total deposit = $371 × 12 × 20
Total deposit = $89,040
For the amount that comes from interest, we have:
Interest = $140,000 - $89,040
Interest = $50,960.
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write an equation of the line that passes through the given point and has the given slope. (1, -5); slope -3/2
Answer: 4 ft 2 in i believe <3
Step-by-step explanation:
find exact value by using half angle
sin 75 degrees
Answer: [tex]\frac{\sqrt{6}+\sqrt{2} }{4}[/tex]
Step-by-step explanation:
Half angle formula for sine is
sin([tex]\frac{x}{2}[/tex])=[tex]\sqrt{1-cosx}/2[/tex]
If x is 150, then sin 75=[tex]\sqrt{1-cos150}/2[/tex] =[tex]\sqrt{1-\frac{cos(180-30)}{2} }[/tex]=[tex]\sqrt{1+cos30}/2[/tex]
=[tex]\sqrt{(1/2)+(\sqrt{3}/4)}[/tex] =[tex]\frac{\sqrt{6}+\sqrt{2} }{4}[/tex]
PLEASE HELP
Which statement is true?
Responses
Interior angles should all be congruent, so neither of these pictures show parallel lines.
Same side interior angles are supplementary so picture i shows parallel lines.
Same side interior angles are supplementary so picture ii shows parallel lines.
It doesn't look like any lines will intersect, so both pictures i and ii are parallel lines.
A summary of two stocks is shown. 52W high 52W low Name of Stock Symbol High Low Close 37.18 29.39 Zycodec ZYO 39.06 32.73 34.95 11.76 7.89 Unix Co UNX 16.12 12.11 15.78 Last year, a stockholder purchased 40 shares of Zycodec at its lowest price of the year and purchased 95 shares of Unix at its highest price of the year. If the stockholder sold all shares of both stocks at their respective closing price, what was the overall gain or loss? The overall loss is $604.30. The overall gain is $604.30. The overall loss is $660.35. The overall gain is $660.35.
Answer:
The overall gain is $604.30.
Step-by-step explanation:
A summary of two stocks is shown.
52W high 52W low Name of Stock Symbol High Low Close
37.18 29.39 Zycodec ZYO 39.06 32.73 34.95
11.76 7.89 Unix Co UNX 16.12 12.11 15.78
Last year, a stockholder purchased 40 shares of Zycodec at its lowest price of the year and purchased 95 shares of Unix at its highest price of the year. If the stockholder sold all shares of both stocks at their respective closing price, what was the overall gain or loss?
The overall loss is $604.30.
The overall gain is $604.30.
The overall loss is $660.35.
The overall gain is $660.35.
Got It Right.
Answer: Don't use the other message below it's AI generated..
Step-by-step explanation:
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
The two equations that are true for the value x = -2 and x = 2 are x² - 4 = 0 and 4x² = 16.
For x = -2, substituting into equation 1 gives:
(-2)² - 4 = 0
4 - 4 = 0
Adding x = -2 to equation 2 results in:
4(-2)² = 16
4(4) = 16
For x = 2, substituting into equation 1 gives:
(2)² - 4 = 0
4 - 4 = 0
Adding x = -2 to equation 2 results in:
4(2)² = 16
4(4) = 16
Therefore, the equations is true.
The equation 3x² + 12 = 0 is not true for either x = -2 or x = 2 since substituting either value into the equation yields a non-zero result.
The equation 2(x - 2)² = 0 is only true for x = 2, but not for x = -2, since substituting x = -2 yields a non-zero result.
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fifteen thousand raffle tickets are sold. One first prize of $3000, two second prizes of $750, and three third prizes of $300 each will be awarded, with all winners selected randomly. If you purchased one ticket, what are your expected gross winnings?
if you purchased one ticket, your expected gross winnings are $0.36.
what is gross winnings ?
Gross winnings refer to the total amount of money won before any taxes or fees are deducted. In other words, it is the total amount of money won by an individual in a lottery or other type of game of chance, without taking into account any deductions that may be made
In the given question,
To calculate the expected gross winnings, we need to multiply the probability of winning each prize by the value of the prize and then add up these values.
First, let's find the probability of winning each prize:
First prize: There is only one first prize, and there are 15,000 tickets sold, so the probability of winning the first prize is 1/15,000.
Second prize: There are two second prizes, so the probability of winning a second prize is 2/15,000.
Third prize: There are three third prizes, so the probability of winning a third prize is 3/15,000.
Now we can calculate the expected gross winnings:
First prize: The probability of winning the first prize is 1/15,000, and the value of the prize is $3,000, so the expected value of the first prize is (1/15,000) x $3,000 = $0.20.
Second prize: The probability of winning a second prize is 2/15,000, and the value of each prize is $750, so the expected value of a second prize is (2/15,000) x $750 = $0.10.
Third prize: The probability of winning a third prize is 3/15,000, and the value of each prize is $300, so the expected value of a third prize is (3/15,000) x $300 = $0.06.
Now we can add up these value to find the total expected gross winnings:
$0.20 + $0.10 + $0.06 = $0.36
Therefore, if you purchased one ticket, your expected gross winnings are $0.36.
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Anyone know what this might be?
Answer:
y ≈ 13,9
Step-by-step explanation:
Use trigonometry:
[tex] \tan(60°) = \frac{y}{8} [/tex]
Cross-multiply to find y:
[tex]y = 8 \times \tan(60°) = 8 \times \sqrt{3} = 8 \sqrt{3} ≈13.9[/tex]
Answer:
y ≈ 13.9
Step-by-step explanation:
using the tangent ratio in the right triangle
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{8}[/tex] ( multiply both sides by 8 )
8 × tan60° = y , then
y ≈ 13.9 ( to the nearest tenth )
In a roll of 50 pennies, there are 12 dated 1977. If a penny is drawn at random, what is the probability that it is dated 1977?
The probability of drawing a penny dated 1977 is 0.24 or 24%.
What is Probability:Probability is a branch of mathematics that deals with the study of random events. It is used to measure the likelihood or chance of a particular event occurring.
Probability is expressed as a fraction or a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.
The probability of drawing a penny dated 1977 can be found by dividing the number of pennies dated 1977 by the total number of pennies.
Here we have
Total number of pennies = 50
Number of pennies dated 1977 = 12
Probability of drawing a penny dated 1977
= Number of pennies dated 1977 / Total number of pennies
= 12 / 50
= 0.24
Therefore,
The probability of drawing a penny dated 1977 is 0.24 or 24%.
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An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots), Imagine that such a die is roiled twice in
succession and that the face values of the two rolls are added together, This sum is recorded as the outcome of a single trial of a random experiment
Compute the probability of each of the following events.
Event A: The sum is greater than 9.
Event B: The sur is not divisible by
Write your answers as fractions.
A sum is divisible by 3 if and only if both of the dice rolls are either 1 and 2 or 2 and 1, or both of the dice rolls are either 1
How to solve the problem?
To solve this problem, we first need to determine the total number of possible outcomes when rolling the die twice. Each roll has six possible outcomes, so the total number of outcomes when rolling the die twice is 6 x 6 = 36.
Next, we can create a table to list all possible outcomes and their corresponding sums:
Die 1 Die 2 Sum
1 1 2
1 2 3
1 3 4
1 4 5
1 5 6
1 6 7
2 1 3
2 2 4
2 3 5
2 4 6
2 5 7
2 6 8
3 1 4
3 2 5
3 3 6
3 4 7
3 5 8
3 6 9
4 1 5
4 2 6
4 3 7
4 4 8
4 5 9
4 6 10
5 1 6
5 2 7
5 3 8
5 4 9
5 5 10
5 6 11
6 1 7
6 2 8
6 3 9
6 4 10
6 5 11
6 6 12
Using this table, we can calculate the probability of each event:
Event A: The sum is greater than 9.
There are four possible outcomes where the sum is greater than 9: 10, 11, and 12. The probability of getting each of these outcomes is:
P(sum = 10) = 3/36
P(sum = 11) = 2/36
P(sum = 12) = 1/36
Therefore, the probability of Event A is:
P(Event A) = P(sum = 10) + P(sum = 11) + P(sum = 12)
= (3/36) + (2/36) + (1/36)
= 6/36
= 1/6
Event B: The sum is not divisible by 3.
A sum is divisible by 3 if and only if both of the dice rolls are either 1 and 2 or 2 and 1, or both of the dice rolls are either 1
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
What point do these two lines Have in common? The answer choices are (3,3) (2,4) (2,5) (0,3)
Answer:
3,3,0,3
Step-by-step explanation:
because it's right
For each of the figures, write an absolute value equation that has the following solution set. x={-5, -1}
After answering the presented question, we can conclude that This equation also has solutions x = -5 and x = -1: |x + 5| - |x + 1| = 4
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
[tex]|x + 3| - 2 = 0\\|x + 3| = 2\\x + 3 = 2 or x + 3 = -2\\x = -5 or x = -1\\|x + 2| + 4 = 1\\|x + 2| = -3\\|x + 5| - |x + 1| = 4\\[/tex]
This equation also has solutions x = -5 and x = -1:
|x + 5| - |x + 1| = 4
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For the given figure the absolute value equation | [tex]x+3[/tex] | = [tex]2[/tex] has the solution set x={[tex]-5,-1[/tex]}.
What is the absolute value equation?An absolute value equation is an equation that involves an absolute value expression. An absolute value expression is denoted by enclosing the expression inside vertical bars, like this: |expression|. The absolute value of a real number x is defined as:
|x| = x if x is non-negative (i.e.,[tex]x\geq 0[/tex])
|x| = -x if x is negative (i.e., [tex]x < 0[/tex])
A quadratic equation is a second-degree polynomial equation of the form:
[tex]ax^{2} +bx +c = 0[/tex]
where a, b, and c are constants, and x is the variable. The highest power of the variable x is[tex]2[/tex], which means that the equation represents a curve called a parabola. The constant a is called the leading coefficient and determines the shape and direction of the parabola.
According to the given information
An absolute value equation with solution set x={[tex]-5,-1[/tex]} can be written as:
| [tex]x+3[/tex] | = [tex]2[/tex]
To see why this equation has the given solution set, we can substitute [tex]-5[/tex] and [tex]-1[/tex] for x and check that they satisfy the equation:
| [tex]-5+3[/tex] | = [tex]2[/tex], which is true since |[tex]-2[/tex]| = [tex]2[/tex]
| [tex]-1+3[/tex] | = [tex]2[/tex] which is also true since |[tex]2[/tex]| = [tex]2[/tex]
Therefore, the absolute value equation | [tex]x+3[/tex] | = [tex]2[/tex] has the solution set x={[tex]-5,-1[/tex]}.
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