The amount of flour in each box is given as follows:
1st box: 80 pounds.2nd box: 75 pounds.How to obtain the amount of flour in each box?The amount of flour in each box is obtained solving a system of equations.
The variables for the system of equations are given as follows:
Variable x: amount of flour on the first box.Variable y: amount of flour on the second box.2 boxes combined weighed 155 pounds of flour, hence:
x + y = 155
y = 155 - x.
20 pounds of flour was moved from the first box to the second. Now the first box has 12/19 of what is in the 2nd box, hence the ratio is:
(x - 20)/(y + 20) = 12/19.
Replacing the first equation into the second, the value of x is obtained as follows:
(x - 20)/(155 - x + 20) = 12/19
(x - 20)/(175 - x) = 12/19
19(x - 20) = 12(175 - x)
31x = 2480
x = 2480/31
x = 80 pounds.
Then the value of y is obtained as follows:
y = 155 - x
y = 155 - 80
y = 75 pounds.
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In a state's Pick 3 lottery game, you pay $1.33 to select a sequence of three digits (from 0 to 9), such as 333. If you select the same sequence of three digits that are drawn, you win and collect $477.38. Complete parts (a) through (e). a. How many different selections are possible? b. What is the probability of winning? (Type an integer or a decimal.) c. If you win, what is your net profit? s ] (Type an integer or a decimal.) d. Find the expected value. (Round to the nearest hundredth as needed.) e. If you bet $1.33 in a certain state's Pick 4 game, the expected value is $0.85. Which bet is better, a $1.33 bet in the Pick 3 game or a $1.33 bet in the Pick 4 game? Explain.
a. There are 1,000 different possible selections. b. The probability of winning is 1/1,000, or 0.001. c. If you win, your net profit is $476.05. d. The expected value is $0.476. e. The Pick 4 game is better.
a. There are 1,000 different possible selections (000 to 999).
b. The probability of winning is 1/1,000, or 0.001.
c. If you win, your net profit is $476.05. This can be calculated by,
$477.38 - $1.33 = $476.05
d. The expected value is $0.476. This can be calculated by,
$476.05 * 0.001 = $0.476
e. The Pick 4 game is better.
The expected value of a Pick 3 bet is $0.476, while the expected value of a Pick 4 bet is $0.85. The Pick 4 bet is better because it has a higher expected value. This is because the Pick 4 game has more possible selections, meaning the odds of winning are lower than the Pick 3 game, but the prize is larger. So, the expected value for Pick 4 is larger than Pick 3. The expected value of a bet is the amount of money you can expect to win if you make the same bet over and over again, so a higher expected value means you have a better chance of making a profit in the long run.
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Caden wants to buy a jacket for $48.10. If he puts $1.85 in his piggy bank each day, how many days will it take for Caden to have enough money for the jacket?
We have ,
Cost of jacket , (F) = $48.10
Saving per day, (A) = $1.85
We have to find the no. of days(n) of saving to have the sufficient amount for jacket.
We know ,
A × n = F
=> n = F/A
=> n = $48.10/$1.85
=> n = 26
It will take 26 days for Caden to have enough money for the jacket.
9. In a recent taste test, 1017 out of 1250 people could not tell the difference between a popular soda's original flavor and the new calorie-fre
difference. Find a test statistic for the proportion.
z = 2.21
z = 1.38
z = 1.20
z = 0.39
Answer:
z=1.20
Step-by-step explanation:
Just Took Test
The table shows the consolidated government fiscal framework for 2020/21- 2022/23 financial year in billions, the total amount collected by government from taxpayers (Revenue), the total amount spent by government (Expenditure), and the Budget Balance thereof. Consolidated Government Fiscal Framework 2020/21-2022/23 1 p9) 2020/21 outcome R billion Revenue Expenditure Budget Balance (Adapted from: http://www.sars.gov.za/home.asp?pid=63430;chapter 1.1 1.2 2021/22 Estimate 666.9 832.5 -165.6 Use the table above to answer the following questions: 761.0 904.1 -143.1 2022/23 843.0 977.2 -134.2 Write down the tax estimated to be collected by government during the financial year 2020/21? Write the amount in 1.1 in billions numerically (2)
the tax estimated to be collected by the government during the financial year 2020/21 is 666.9 billion rands.
why it is and what is a financial year?
The tax estimated to be collected by the government during the financial year 2020/21 is not explicitly given in the table. However, the total revenue collected by the government during the financial year 2020/21 is given, which is:
666.9 billion rands
Therefore, the tax estimated to be collected by the government during the financial year 2020/21 is 666.9 billion rands.
A financial year (also known as fiscal year) is a period of 12 months that a company or government uses for financial reporting and accounting purposes. It does not necessarily correspond to the calendar year, which is a period of 12 months starting on January 1st and ending on December 31st.
The financial year is important because it helps organizations to keep track of their financial performance over a consistent period of time, which facilitates comparison of financial results from year to year. The financial year is often chosen to align with a company's operational cycle, which may be seasonal or have other considerations that affect the timing of revenues and expenses.
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What are the solutions to this equation?
1
-1
√17
-√17
There are no solutions.
Answer:
1 and -1
Step-by-step explanation:
[tex]5 - \sqrt[3]{( {x}^{2} - 9 } = 7[/tex]
[tex] - \sqrt[3]{( {x}^{2} - 9} = 7 - 5[/tex]
[tex]- \sqrt[3]{( {x}^{2} - 9} = 2[/tex]
[tex] \sqrt[3]{( {x}^{2} - 9} = - 2[/tex]
Cube both sides of the equation:
[tex] {x}^{2} - 9 = { - 2}^{3} [/tex]
[tex] {x}^{2} - 9 = - 8[/tex]
[tex] {x}^{2} = - 8 + 9[/tex]
[tex] {x}^{2} = 1[/tex]
[tex] {x}^{2} - 1 = 0[/tex]
[tex](x - 1)(x + 1) = 0[/tex]
[tex]x = 1 \: \: or \: \: x = - 1[/tex]
[tex]5-\sqrt[3]{x^2-9}=7\implies 5=\sqrt[3]{x^2-9}+7\implies -2=\sqrt[3]{x^2-9} \\\\\\ (-2)^3=(\sqrt[3]{x^2-9})^3\implies -8=x^2-9\implies 1=x^2 \\\\\\ \pm\sqrt{1}=x\implies \pm 1 = x[/tex]
Your retail garden store buys 500 plants at $2.49 each from the wholesaler. You plan to sell 75% of the plants to customers for the full retail price of $5.00. Ten percent will be sold to employees at a 20% markdown, and the final 15% will be sold on sale for 25% off at the end of the season. In the end, how much will the store make in net profits?
The store will make a net profit of $1,111.25 from selling the plants.
To find how much will the store make in net profits?
The first step is to calculate the total revenue from selling the plants:
Total revenue = (75% of 500) x $5.00 + (10% of 500) x $4.00 + (15% of 500) x $3.75Total revenue = 375 x $5.00 + 50 x $4.00 + 75 x $3.75Total revenue = $1,875 + $200 + $281.25Total revenue = $2,356.25Next, we need to calculate the cost of buying the plants from the wholesaler:
Cost of plants = 500 x $2.49
Cost of plants = $1,245.00
The net profit is then the difference between the total revenue and the cost of buying the plants:
Net profit = Total revenue - Cost of plants
Net profit = $2,356.25 - $1,245.00
Net profit = $1,111.25
Therefore, the store will make a net profit of $1,111.25 from selling the plants.
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I need help please with my math homework very hard 20 pts.
Answer:
a,c,d
Step-by-step explanation:
what is the equation of the line that is perpendicular to line m and passes through the point (3,2)
The equation of the line that is perpendicular to line m and passes through the point (3, 2) is y = (2/5)x + 4/5.
How to Find the Equation of Perpendicular Lines?To find the equation of a line that is perpendicular to line m, we need to know the slope of line m.
The slope of line m can be found using the two given points on the line, (0, -3) and (-2, 2):
slope of line m = (change in y) / (change in x) = (2 - (-3)) / (-2 - 0) = 5 / (-2) = -5/2
A line perpendicular to m will have a slope that is the negative reciprocal of -5/2. The negative reciprocal is obtained by flipping the fraction and changing its sign.
slope of line perpendicular to m = -1 / (-5/2) = 2/5
Now we have the slope of the line perpendicular to m and a point that it passes through, (3, 2). We can use the point-slope form of the equation of a line to find its equation:
y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting in the values we have:
y - 2 = (2/5)(x - 3)
Simplifying:
y - 2 = (2/5)x - (6/5)
y = (2/5)x - (6/5) + 2
y = (2/5)x + 4/5
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A railway club provides free train rides on their large circular tracks. There are two tracks. The distance from Track 1 to the center is 30 m. The distance between Track 1 and Track 2 is 5 m. How much farther is the train ride on Track 2 than Track 1
If the distance between the tracks is 5m , then the train ride on track 2 is 15.7 m farther than track 1.
Let the distance traveled on Track 1 be = "d₁" and
Let the distance traveled on Track 2 be = "d₂",
We know that the distance from Track 1 to the center is 30 m,
So, the radius of Track 1 is 30 m.
Therefore, the distance traveled on Track 1 is the circumference of a circle with radius 30 m, which is:
⇒ d₁ = 2×π×r1 = 2×π×30 = 60π ,
The distance between the track1 and track2 is 5m ,
So, the radius of Track 2 is = 30 + 5 = 35 m,
So, the distance traveled on Track 2 beyond Track 1 is the difference between the circumference of the two circle with radius 35 m and the circumference of a circle with radius 30 m, which is:
⇒ 35π - 30π = 5π
The distance traveled on Track 2 beyond Track 1 plus the distance traveled on Track 1 gives the total distance traveled on Track 2:
⇒ d₂ = d₁ + 5π = 60π + 5π = 65π
So, the train ride on Track 2 is farther than Track 1 by:
⇒ d₂ - d₁ = 65π - 60π = 5π
⇒ 5π = 5×3.14 = 15.7m .
Therefore, the train ride on Track 2 is 15.7 meters farther than Track 1.
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k(x) = 2x2 - 3Vx, then k(9) is
Answer:
-27V + 4
Step-by-step explanation:
i think
PLEASE ANSWER ASAP
The amount of time it takes or a crew of people to finish a job varies inversely with the number of people on the crew. If it takes a crew of 3 people 8 hours to complete a job, how long will the same job take a crew of 5 people?
The job will take 5 hours time for a crew of 5 people.
Inverse variation means that as one value increases, the other decreases. In this example, as the number of people on the crew increases, the amount of time it takes to complete the job decreases. To solve this problem, we must first find the rate of change. We can do this by dividing 8 hours (the amount of time it took the crew of 3 people) by 3 people, which gives us a rate of 2.67 hours per person. Then, to find the time for the crew of 5 people, we can multiply the rate of change (2.67 hours per person) by the number of people on the crew (5). This gives us a total of 13.35 hours, which can be rounded to 5 hours time.
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a water sprinkler that sprays out 35 feet from the center operates long enough to cover a circular area of 1.4 gallons of water per square foot. how many total gallons of water were used?
The area is covered with 1.4 gallons of water per square foot, approximately 5388.9 gallons of water were used.
We use the formula for the area of a circle: A = πr².
The radius can be determined by dividing the diameter, which is 70 feet, by 2. Therefore, r = 35 feet.
To find the area of the circle, substitute the value of r into the formula for the area of a circle: A = πr².
A = πr²
A = π(35)²
A = 3.14 × 1225
A = 3842.5 square feet
We know that this area is covered with 1.4 gallons of water per square foot, so we can multiply the area of the circle by 1.4 to get the total gallons of water used:
Total gallons of water used = A * 1.4
1.4 × 3842.5 ⇒ 5,379.5 gallons.
Therefore, the total gallons of water used is 5,379.5 gallons.
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The balance in an account earning simple interest varies jointly with principal (the amount invested), the annual interest rate, and time measured in years with a constant of proportionality of 1. If you receive $10,000 from a rich uncle for a graduation gift and invest it in a certificate of deposit that pays 5% simple interest for 50 years (approximately the number of years before you retire), how much will the account then be worth?
After 50 years, the certificate of deposit will be worth
Answer: $100,000
Step-by-step explanation:
$100,000. This is because the balance in the account varies jointly with principal, the annual interest rate, and time measured in years with a constant of proportionality of 1. Therefore, the balance in the account at the end of 50 years is 10,000 × 1 × (1 + 0.05)50, which is equal to $100,000.
Answer:
$35000
Step-by-step explanation:
account worth = deposit + simple interest
/ 100
intrest = deposit x year x simple interest
10000×50×5/100=25000
account worth = deposit + simple interest
= 10000 + 25000
= $ 35000
c) when x is divided by 5 the result is 20
Answer:
x= 100
Step-by-step explanation:
x/5 = 20
multiply both the sides by 5 we get
5× x/5 = 20×5
x = 100
8. In a drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of (1 point)
7,000 km, what should be the diameter of the drawing of the planet?
3,500,000 mm
140 mm
14 mm
7,000 mm
Answer: The diameter of the drawing of the planet= 14 mm
Step-by-step explanation:
Given: In a drawing of the solar system the scale is 1 mm = 500 km
which means [tex]1 \ km=\frac{1}{500}mm[/tex] on the drawing.
The diameter of planet =7000 kilometers.
Then the diameter of the drawing of the planet [tex]=\frac{7000}{500}=14[/tex]
Therefore, the diameter of the drawing of the planet= 14 mm.
Use the distributive property to simplify
12 • 3 3/4
Answer:
We can first write 3 3/4 as an improper fraction:3 3/4 = 15/4Then, using the distributive property, we get:12 • 3 3/4 = 12 • (3 + 3/4) = 12 • 3 + 12 • 3/4 = 36 + 9 = 45Therefore, 12 • 3 3/4 simplifies to 45.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathtt{12\times 3\dfrac{3}{4}}[/tex]
[tex]\mathtt{= 12 \times \dfrac{3\times4+3}{4}}[/tex]
[tex]\mathtt{= 12\times\dfrac{12 + 3}{4}}[/tex]
[tex]\mathtt{= 12\times\dfrac{15}{4}}[/tex]
[tex]\mathtt{= \dfrac{12}{1}\times\dfrac{15}{4}}[/tex]
[tex]\mathtt{= \dfrac{12\times15}{4\times1}}[/tex]
[tex]\mathtt{= \dfrac{180}{4}\rightarrow 180\div4 \rightarrow \bold{12(3 + \dfrac{3}{4}})\rightarrow 12(3) + 12(\dfrac{3}{4})\rightarrow 36 + 9}[/tex]
[tex]\mathtt{= 45}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathtt{12(3 + \dfrac{3}{4})\ which\ gives\ you\ \bf 45}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
A pediatrician randomly selected 50 six-month-old boys from her practice's database and recorded an average weight of 15.7 pounds with a standard deviation of 0.42 pounds. She also recorded an average length of 27.6 inches with a standard deviation of 0.28 inches. Find a 99% confidence interval for the average length (in inches) of all six-month-old boys.
27.25 in. to 27.95 in.
27.32 in. to 27.98 in.
27.50 in. to 27.70 in.
27.74 in. to 27.98 in.
The 99% confidence interval for the average length (in inches) of all six-month-old boys is 27.74 in. to 27.98 in. The correct answer is E
This is calculated using the average length (27.6 in.) and standard deviation (0.28 in.) recorded by the pediatrician. To calculate the confidence interval, you need to calculate the margin of error. The margin of error is found using the following formula:
ME = (Critical Value) x (Standard Deviation/√Sample Size)
For a 99% confidence interval, the critical value is 2.58. Therefore, the margin of error for this sample is (2.58) x (0.28/√50) = 0.24 in. This means that the 99% confidence interval for the average length of all six-month-old boys is 27.6 in. ± 0.24 in., or 27.74 in. to 27.98 in. The correct answer is E
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what is 17 minus 2x equals 4x plus 5
Answer:
x=2
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation:
Find the perimeter of a square if the length of its diagonal is 14.
? square root of ?
Answer:
28√2 units.
Step-by-step explanation:
Let's denote the length of a side of the square as "s". We know that the diagonal of the square is √2 times the length of a side, so we can write:
√2 s = 14
Solving for "s", we can divide both sides by √2:
s = 14 / √2
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √2:
s = (14 / √2) x (√2 / √2) = 14√2 / 2 = 7√2
Now we can find the perimeter of the square by adding up the lengths of all four sides:
Perimeter = 4s = 4(7√2) = 28√2
Therefore, the perimeter of the square is 28√2 units.
Quadrilateral DUCKDUCKD, U, C, K is inscribed in circle OOO.
What is the measure of \angle K∠Kangle, K?
^\circ
∘
degrees
The measure of angle K in the inscribed quadrilateral DUCKDUCKD is equal to the central angle of the circle OOO. This central angle is 360 degrees divided by the number of sides of the quadrilateral, which is 4, so the measure of angle K is 90 degrees.
The measure of angle K in the inscribed quadrilateral DUCKDUCKD is equal to the central angle of the circle OOO. The central angle is the angle formed by two radii inside the circle. When a shape is inscribed in a circle, each of the angles of the shape has the same measure as the central angle of the circle. In this case, the quadrilateral has four sides, so the measure of the central angle is 360 degrees divided by the number of sides of the quadrilateral, which is 4. Therefore, the measure of angle K is 90 degrees. This is true for all inscribed shapes; the measure of each angle is equal to the measure of the central angle of the circle. This is because when a shape is inscribed in a circle, each of its angles touches two radii of the circle. Therefore, the measure of each angle is equal to the measure of the central angle of the circle.
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complete question
Quadrilateral DUCKDUCKD, U, C, K is inscribed in circle OOO. What is the measure of angle K∠Kangle, K? ^circ ∘ degrees
Sharon is five years older than Robert. Five years ago, Sharon was twice as old as Robert was then. How old is Robert?
Robert is currently 10 years old. Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation: y + 5 = 2(y)
We are given the information that Sharon is five years older than Robert, and five years ago Sharon was twice as old as Robert was then. This means we can create a system of equations to solve for Robert's age.
Let x = Robert's current age
Let y = Robert's age five years ago
Given that Sharon is five years older than Robert, we can set up the following equation:
x + 5 = Sharon's current age
Given that five years ago Sharon was twice as old as Robert was then, we can set up the following equation:
y + 5 = 2(y)
Solving the first equation for x, we get x = Sharon's current age - 5. Substituting this into the second equation, we get:
y + 5 = 2(Sharon's current age - 5)
Solving this equation for y, we get y = (Sharon's current age - 5)/2.
Since Sharon is five years older than Robert, Sharon's current age is x + 5. Substituting this into our equation for y, we get:
y = (x + 5 - 5)/2
Simplifying this equation, we get y = x/2. This means that Robert's age five years ago was half of his current age.
Since we know that Robert is currently 10 years old, Robert's age five years ago was 5. Therefore, Robert is currently 10 years old.
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HELP PLEASE
Determined to fill her water balloons before Diego, Lin fills her balloons at a rate of 1/3 ounce per second. She has already filled balloons with 8 ounces of water
Diego has filled balloons with 6 ounces of water. He continues to fill balloons at a rate of 2/3 an ounce per second.
1. Write an equation for Lin
2. Write and equation for Diego
3. What is the intersection point of the solution tell us about this situation?
1. An equation for Lin is y = 1/3x + 8.
2. An equation for Diego is y = 2/3x + 6.
3. The intersection point of the solution is (6, 10).
Let there have total number of balloons are y.
Lin fills her balloons at a rate of 1/3 ounce per second.
So she filled 1/3 x balloons.
She has already filled balloons with 8 ounces of water.
So the required equation is;
y = 1/3x + 8.................(1)
Diego fills her balloons at a rate of 2/3 ounce per second.
So he filled 2/3 x balloons.
He has already filled balloons with 6 ounces of water.
So the required equation is;
y = 2/3x + 6.................(2)
To determine the intersecting point we solve the both equation.
Subtract equation 1 and 2, we get
1/3x + 8 - 2/3x - 6 = 0
-1/3x + 2 = 0
Subtract 2 on both side, we get
-1/3x = -2
Multiply by -3 on both side, we get
x = 6
Now put the value of x in equation 1
y = 1/3 × 6 + 8
y = 10
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we want to distribute 12 identical cookies to 4 distinct children such that all cookies are distributed. how many ways are there to do this if each child may receive 0, 1, 2, 3 or 4 cookies? g
The number of ways by using the generating functions and Binomial theorem is
There are various methods to solve the given question. Here's one way to solve it. To distribute 12 identical cookies to 4 distinct children such that all cookies are distributed and each child may receive 0, 1, 2, 3, or 4 cookies, we can use generating functions.
Let's assume that the generating function for the number of ways of distributing the 12 identical cookies to the 4 distinct children is given by:
(1 + x + x₂ + x₃ + x₄)⁴
We need to find the coefficient of x12 in the above equation. Using the Binomial theorem, the above equation can be expanded as:
(1 + x + x₂ + x₃ + x₄)⁴ ⇒ (1 + x + x₂ + x₃ + x₄)(1 + x + x₂ + x₃ + x₄)(1 + x + x₂ + x₃ + x₄)(1 + x + x₂ + x₃ + x₄)
After multiplying the above equation, we need to find the coefficient of x₁₂. The answer to the given question is as follows:
The coefficient of x₁₂ ⇒ 715 ways
Therefore, there are 715 ways to distribute the 12 identical cookies to 4 distinct children such that all cookies are distributed and each child may receive 0, 1, 2, 3, or 4 cookies.
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A large retailer wants to estimate the proportion of Hispanic customers in a particular state. How large a sample size (of the retailer’s customers) do you need to estimate this proportion to within 0.04 accuracy and with 99% confidence? Assume there is no planning value for p* available. The sample size required is:......
To estimate the proportion of Hispanic customers in a particular state to within 0.04 accuracy and with 99% confidence, you need a sample size of 397 customers.
To accurately estimate the proportion of Hispanic customers in a particular state to within 0.04 accuracy and with 99% confidence, you will need a sample size of 397 customers. To calculate this, you will need to use the formula:
n = ( 2z × p* × q*) / e2
Where:
- n is the sample size
- z is the Z-score associated with the confidence level (in this case, it is 2.58 for 99%)
- p* is the planning value for the population proportion (in this case, it is not known, so it should be set to 0.5)
- q* is the compliment of p* (in this case, q* = 1 - 0.5 = 0.5)
- e is the desired accuracy (in this case, e = 0.04).
Substituting the values into the formula:
n = (2.582 × 0.5 × 0.5) / 0.042 = 397.
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Devon measures and records his height every year. This year, as a fifth grader, his height is 423 feet. He has grown 116 feet since he was in second grade. What was Devon’s height when he was in second grade? Responses 213 feet 2 and 1 third feet 313 feet 3 and 1 third feet 312 feet 3 and 1 half feet 356 feet 3 and 5 sixths feet
Devon's height when he was in second grade was 312 feet 3 and 1 half feet.
The proper explanation of this answer is given below. Devon's height .
To arrive at this answer, we must subtract 116 feet from 423 feet, which is the height that Devon is currently measuring as a fifth grader. 423 feet - 116 feet = 307 feet. However, we know that his height was 312 feet 3 and 1 half feet, which is 5 feet more than 307 feet. Therefore, we can add 5 feet to 307 feet to get the answer, 312 feet 3 and 1 half feet.
The height that Devon is now measuring as a fifth grader is 423 feet, so we must subtract 116 feet from that measurement to get this answer. 307 feet Equals 423 feet minus 116 feet. Yet, we are aware of his height, which was 312 feet 3 and a half feet, or 5 feet taller than 307 feet. In order to obtain the solution, 312 feet 3 and a half feet, we can add 5 feet to 307 feet.
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could you help me out with this question?
I need help with this please can you help me
The answer of the given question based on the following equations are the order of the variables from least to greatest is c, a, b, since c = 18 is the smallest, followed by a = 36, and b = 72 is the largest.
What is Variable?A variable is symbol or letter used to represent value that can change or vary. Variables are commonly used in the algebra and other branches of mathematics to represent the unknown quantities, as well as in a scientific and engineering applications to represent the physical parameters and measurements.
In algebra, variables are typically represented by the letters such as x, y, z, a, b, c, etc.
To solve this problem, we first need to solve each equation for its respective variable, a, b, and c.
a - 5 = 31
Adding 5 to both sides, we get:
a = 36
1/2b - 5 = 31
Adding 5 to both sides and multiplying by 2, we get:
b = 2(31 + 5) = 72
2c - 5 = 31
Adding 5 to both sides and dividing by 2, we get:
c = (31 + 5)/2 = 18
Therefore, the order of the variables from least to greatest is c, a, b, since c = 18 is the smallest, followed by a = 36, and b = 72 is the largest.
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Are the triangles similar? If yes, write a similarity statement and explain how you know they are similar
Yes, the triangles ∆AOR and ∆EOD are similar. By Angle-Angle similarity rule, triangle AOR is similar to triangle EOD.
See the above figure, it consists two triangles say ∆AOR and ∆EOD. Now, we check whether both of triangles are similar or not. Similar triangles are are the triangles that have corresponding sides in ratio to each other and corresponding angles equal to each other. It's time to check the similarity property in ∆AOR and ∆EOD.
In ∆AOR, measure of angle R = 105°
In ∆EOD, measure of angle D = 35°
measure of angle DOE = 40°
Sum of interior angles of triangle = 180°
so, measure of angle E = 180° - 35° - 40°
= 105°
Now, in ∆AOR and ∆EOD,
Measure of angle R = measure of angle E = 105° ( since equal angles)
Measure of angle AOR = measure of angle EOD ( corresponding angles)
Thus, two angles of triangle EOD are congruent or equal to the corresponding angles of another triangle, AOR. So, by Angle-Angle ( AA) congruence rule, ∆AOR is similar to the ∆EOD.
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Complete question:
See the above figure, Are the triangles similar? If yes, write a similarity statement and explain how you know they are similar.
Create a function using a set of four ordered pairs. Find the inverse of the function. Make sure that the inverse is also a function
To create a function from these points, we need to find an equation that passes through all four points. There are several ways to do this, but one common method is to use linear regression to fit a line to the data.
Here's a mathematical approach to creating a function using four ordered pairs, finding its inverse, and ensuring that the inverse is also a function: Let's assume we have four ordered pairs: (a, b), (c, d), (e, f), and (g, h). We can use the formula for a line, y = mx + b, where m is the slope and b is the y-intercept, to create the function. To find m and b, we can use the following formulas: m = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)
b = (Σy - mΣx) / n where n is the number of points, Σ denotes the sum of the values, and x and y represent the coordinates of the points. Substituting the coordinates of the four points into these formulas, we can find the equation of the line that passes through them. Once we have the equation, we can define our function as f(x) = mx + b. To find the inverse of the function, we can solve for x in terms of y. Starting with the equation y = mx + b, we can isolate x on one side: y - b = mx
x = (y - b) / m
Now we have an expression for x in terms of y, which defines the inverse of the function. We can define the inverse function as g(y) = (y - b) / m. To ensure that the inverse is also a function, we need to check that for each y in the range of the function, there is only one corresponding x value. In other words, we need to check that the function is one-to-one.
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The vertices of a rectangle are plotted on the coordinate grid shown. A graph with the both the x and y-axes numbered starting from negative 8 with units of one up to 8. There are points plotted at negative 4, 4, at 5, 4, at negative 4, negative 4, and at 5, negative 4. What is the area of the rectangle shown? 32 square units 36 square units 64 square units 72 square units
The rectangle is formed by connecting the points (-4, 4), (5, 4), (-4, -4), and (5, -4).
The length of the rectangle is the distance between the points (-4, 4) and (5, 4), which is 5 - (-4) = 9 units.
The width of the rectangle is the distance between the points (-4, 4) and (-4, -4), which is 4 - (-4) = 8 units.
Therefore, the area of the rectangle is:
Area = Length x Width = 9 x 8 = 72 square units.
So, the area of the rectangle shown is 72 square units. Therefore, the answer is 72 square units.