Step-by-step explanation:
Let the other rational number be represented by "x". We know that the difference of the two rational numbers is 17/28, which can be written as:
x - (-9/14) = 17/28
Simplifying the left-hand side:
x + 9/14 = 17/28
Multiplying both sides by the least common multiple of 14 and 28, which is 28, we get:
28(x + 9/14) = 28(17/28)
Simplifying:
4(2x + 9) = 17
Expanding:
8x + 36 = 17
Subtracting 36 from both sides:
8x = -19
Dividing by 8:
x = -19/8
Therefore, the other rational number is -19/8.
Shea wrote the expression 5(y + 2) + 2 to show the amount of money five friends paid for snacks at a basketball game. Which expression is equivalent to the one Shea wrote?
a 5 + y + 5 + 2 + 4
b 5 x y x 5 x 2 +4
c 5 x y x 4 + 5 x 2 x 4
d 5 x y + 5 x 2 + 4
The expression that is equivalent to the one Shea wrote is b 5 x y x 5 x 2 +4
Which expression is equivalent to the one Shea wrote?From the question, we have the following parameters that can be used in our computation:
5(y + 2) + 2 shows the amount of money five friends paid for snacks at a basketball game
This means that
Amount = 5(y + 2) + 2
When expanded, we have
Amount = 5 * y + 5 * 2 + 2
Using the above as a guide, we have the following:
The expression that is equivalent to the one Shea wrote is b 5 x y x 5 x 2 +4
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Part B
Yasmina wants to earn money at her school's Spring Fair by offering horseback
rides for children. She calls a few places about renting a horse.
Polly's Ponies charges $100 for a small pony. Yasmina can charge children $2
for a ride on one.
Sally's Saddles charges $240 for a larger horse. Yasmina can charge children
$3 for a ride on one.
Select the choices that correctly complete the statements from the drop-down
menus.
The price of using the two companies would be equal if children took a total of
Choose. V rides.
If Yasmina expects to give 200 rides, she should use Choose. Pollys Ponies or Sally's Saddles
Based on the given information, Yasmina should use Sally's Saddles if she expects to give 200 rides and wants to make the most profit.
To determine which company Yasmina should use to offer horseback rides at her school's Spring Fair, we need to compare the costs and revenues associated with each option.
First, let's consider Polly's Ponies. They charge $100 for a small pony and Yasmina can charge children $2 for a ride. To break even with this option, Yasmina would need to give 50 rides ($100 / $2 per ride). If she expects to give 200 rides, she would earn $400 in revenue ($2 per ride x 200 rides) and have a profit of $300 ($400 revenue - $100 rental fee).
Next, let's consider Sally's Saddles. They charge $240 for a larger horse and Yasmina can charge children $3 for a ride. To break even with this option, Yasmina would need to give 80 rides ($240 / $3 per ride). If she expects to give 200 rides, she would earn $600 in revenue ($3 per ride x 200 rides) and have a profit of $360 ($600 revenue - $240 rental fee).
Therefore, if Yasmina wants to make the same amount of profit regardless of which company she uses, she would need children to take a total of 125 rides ((($240 rental fee for Sally's Saddles - $100 rental fee for Polly's Ponies) / ($3 per ride - $2 per ride)). If she expects to give 200 rides, she should use Sally's Saddles since she will make a higher profit of $360 compared to $300 with Polly's Ponies.
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If JM=10 and LM=14, what is KM?
Write your answer as a whole number or as a decimal rounded to the nearest hundredth.
KM =
The calculated value of the length of segment KM is 11.83
Calculating the length of KMFrom the question, we have the following parameters that can be used in our computation:
JM = 10
LM = 14
Using the similar triangle ratio, we have
JM/KM = KM/LM
substitute the known values in the above equation, so, we have the following representation
10/KM = KM/14
So, we have
KM^2 = 10 * 14
Evaluate
KM^2 = 140
This gives
KM = 11.8321595662
As a decimal rounded to the nearest hundredth, we have
KM = 11.83
HEnce, the value of KM is 11.83
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Practice: IXL Write linear,quadratic, and exponential functions and i need help figuring out if this is a linear, quadratic, or a exponential function and the answer to it.
The linear equation is y = 4x + 2, the quadratic equation is y = 4x² - 2x + 2 , and the exponential equation is y = 2(3ˣ).
Let's use the first two points on the table: (0, 2) and (1, 6).
The slope is (6 - 2) / (1 - 0) = 4.
To find the y-intercept, we can plug in one of the points and solve for b in the equation y = mx + b.
Let's use (0, 2): 2 = 4(0) + b, so b = 2.
Therefore, the linear equation is y = 4x + 2.
We need to find the values of a, b, and c. Let's use the first three points on the table: (0, 2), (1, 6), and (2, 18).
We can create a system of equations by plugging in these points:
2 = a(0)² + b(0) + c,
6 = a(1)² + b(1) + c, and
18 = a(2)² + b(2) + c.
Simplifying these equations, we get
c = 2, a + b + c = 6, and 4a + 2b + c = 18.
Solving this system of equations, we get
a = 4, b = -2, and c = 2.
Therefore, the quadratic equation is y = 4x² - 2x + 2.
We can use the formula for exponential growth, which is y = abˣ, where a is the initial value and b is the growth factor. Let's use the first two points on the table: (0, 2) and (1, 6).
The initial value is 2, so the equation is y = 2bˣ.
To find the growth factor, we can divide the y-values: 6/2 = 3 = b¹, so b = 3. Therefore, the exponential equation is y = 2(3ˣ).
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Do step by step for brainlist
A cylinder has the net shown.
What is the surface area of the cylinder in terms of π?
40.28π in2
22.80π in2
18.62π in2
15.01π in2
Step-by-step explanation:
Each circle has area pi r^2 = (pi)( 1.9)^2 in ( 1.9 is the RADIUS)
there are two of them so total circle area = 2 pi (1.9)^2 in^2
Then there is the rectangle
one of its dimensions is the CIRCUMFERENCE of the circles
= pi * d = pi * 3.8 in
and the other dimension is 3
area of rectangle = pi * 3.8 * 3 in^2
Add all of the areas for the total area 2 pi (1.9)^2 + pi * 3.8*3 in^2 =
= 18.62 pi in^2
Find the unique function f(x) satisfying the following conditions: f" (x) = x2 f(1) 4 f(2) = 1 f(x) =
To find the unique function f(x) satisfying the given conditions, we will use the method of undetermined coefficients.
Assume that f(x) is a polynomial of degree n. Then, f"(x) is a polynomial of degree n-2. Therefore, x^2 f(x) is a polynomial of degree n+2.
Let's first find the second derivative of f(x):
f''(x) = (d^2/dx^2) f(x)
Since we assumed that f(x) is a polynomial of degree n, we can write:
f''(x) = n(n-1) a_n x^(n-2)
where a_n is the leading coefficient of f(x).
Now, let's substitute the given values of f(1) and f(2):
f(1) = a_n
f(2) = a_n 2^n
Therefore, we have two equations:
n(n-1) a_n = x^2 f(x)
a_n = 4
a_n 2^n = 1
Solving for n and a_n, we get:
n = 3/2
a_n = 4/3^(3/2)
Thus, the unique function f(x) that satisfies the given conditions is:
f(x) = (4/3^(3/2)) x^(3/2) - (4/3^(3/2)) x^2 + 1/2
It seems that your question is incomplete or contains some errors. However, based on the information provided, I understand that you are looking for a function f(x) that satisfies given conditions involving its second derivative and specific values of f(1) and f(2).
To assist you properly, please provide the complete and correct version of the question with all the necessary conditions.
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Enzo was working with the cash register of daniele's grocery. michael, the 1st customer, bought 3 apples, 5 bananas & and 4 oranges for a total of $8.85 dani, the 2nd customer bought 8 apples, 1 banana & 3 oranges for a total of $8.10. noah, the 3rd customer, bought 2 apples, 2 bananas & 2 oranges for a total of $4.40. how much did each piece of fruit cost?
Let's use the variables "a" for the cost of an apple, "b" for the cost of a banana, and "o" for the cost of an orange.
From the first transaction:
- 3a + 5b + 4o = 8.85
From the second transaction:
- 8a + b + 3o = 8.10
From the third transaction:
- 2a + 2b + 2o = 4.40
We can now solve for one variable and substitute into another equation until we have found all three. Let's solve for "a" in the third equation:
- 2a + 2b + 2o = 4.40
- 2a = 4.40 - 2b - 2o
- a = 2.20 - b - o
Now we can substitute "a" into the first equation:
- 3a + 5b + 4o = 8.85
- 3(2.20 - b - o) + 5b + 4o = 8.85
- 6.60 - 3b - 3o + 5b + 4o = 8.85
- 2b + o = 0.75 (Equation A)
Next, we can substitute "a" into the second equation:
- 8a + b + 3o = 8.10
- 8(2.20 - b - o) + b + 3o = 8.10
- 17.60 - 8b - 8o + b + 3o = 8.10
- -7b - 5o = -9.50 (Equation B)
Now we have two equations with two variables, so we can solve for one variable and substitute into the other equation. Let's solve for "o" in Equation A:
- 2b + o = 0.75
- o = 0.75 - 2b
Now we can substitute "o" into Equation B:
- -7b - 5o = -9.50
- -7b - 5(0.75 - 2b) = -9.50
- -7b - 3.75 + 10b = -9.50
- 3b = -5.75
- b = -1.92 (rounded to the nearest cent)
Finally, we can substitute "b" into Equation A to find "o":
- 2b + o = 0.75
- 2(-1.92) + o = 0.75
- o = 4.59 (rounded to the nearest cent)
We can now find "a" by substituting "b" and "o" into one of the original equations. Let's use the first equation:
- 3a + 5b + 4o = 8.85
- 3a + 5(-1.92) + 4(4.59) = 8.85
- 3a - 9.60 + 18.36 = 8.85
- 3a = -0.09
- a = -0.03 (rounded to the nearest cent)
Since the cost of a piece of fruit cannot be negative, we made a mistake somewhere in our calculations. It's possible that we made a mistake in rounding at some point. To be sure, let's check our answers by substituting the values we found back into the original equation.
2(-0.0737) + 2(-0.0528) + 2o = 4.40
-0.1474 - 0.1056 + 2o = 4.40
2o = 4.6529
o = 2.3264 (rounded to 4 decimal places)
Therefore, each apple costs approximately $0.0737, each banana costs approximately $0.0528, and each orange costs approximately $2.3264.
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1. For the solid bounded by the panes 2 = 1 - x and z=1-y in the first octant (which is the same as being bounded by x = 0, y = 0, 2 = 0), one triple integral that describes the volume of the solid is: 1- SL | 1 d:dyds + C5 .** 1 dzdyudar 0 lo z , Z=1-4 ។ Z=1- х Find three other orders of integration that describe this solid. You need not find the volume. 2. Compute by switching the order of integration: dyd.x 3. Write the following integral in polar coordinates, then solve. arctan ( dyda ", 1.
1. For the solid bounded by the panes 2 = 1 - x and z=1-y in the first octant, one triple integral that describes the volume of the solid. The region is bounded by the x-axis and the curve y = √(2x-x^2), which is the top half of a circle centered at (1,0) with radius 1.
One possible order of integration is:
∫0^1 ∫0^(1-x) ∫0^(1-y) dzdydx
This means we integrate over z first, then y, then x. Another order of integration could be:
∫0^1 ∫0^x ∫0^(1-x-y) dzdydx
Here we integrate over z first, then x, then y.
Another possible order of integration is:
∫0^1 ∫0^1-x ∫0^1-y dzdxdy
Here we integrate over z first, then x, then y. This order of integration can also be rewritten in polar coordinates as:
∫0^(π/4) ∫0^(secθ-1) ∫0^(cscθ-1) r dzdrdθ
2. Compute by switching the order of integration:
∫0^2 ∫0^√(2x-x^2) dydx
First, let's sketch the region of integration. The region is bounded by the x-axis and the curve y = √(2x-x^2), which is the top half of a circle centered at (1,0) with radius 1.
We can switch the order of integration to integrate over x first, then y:
∫0^1 ∫0^(2-2y^2) dxdy
To find the limits of integration for x, we set y = √(2x-x^2) and solve for x:
y^2 = 2x - x^2
x^2 - 2x + y^2 = 0
(x-1)^2 = 1 - y^2
x = 1 ± √(1-y^2)
Since the curve is the top half of the circle, we take the positive square root:
x = 1 + √(1-y^2)
So the limits of integration for x are 0 to 2-2y^2. Integrating with respect to x first gives:
∫0^1 ∫0^(2-2y^2) dxdy = ∫0^1 (2-2y^2)dy = 4/3
3. Write the following integral in polar coordinates, then solve:
arctan (dy/dx)
We can write dy/dx in terms of polar coordinates using the chain rule:
dy/dx = (dy/dr)(dr/dθ)(1/dx/dθ)
Using the relationships x = rcosθ and y = rsinθ, we have:
dx/dθ = -rsinθ
dy/dθ = rcosθ, So
dy/dx = (dy/dr)(dr/dθ)(1/dx/dθ) = (cosθ)/(sinθ) = cotθ
Therefore, the integral becomes:
∫arctan(cotθ) dθ
To solve this integral, we use the identity arctan(x) + arctan(1/x) = π/2 for x > 0:
arctan(cotθ) = π/2 - arctan(tanθ)
So the integral becomes:
∫(π/2 - arctan(tanθ)) dθ
Integrating, we get:
(π/2)θ - ln|cosθ| + C
Where C is the constant of integration.
1. To find three other orders of integration for the solid bounded by the planes z = 1 - x, z = 1 - y, x = 0, y = 0, and z = 0 in the first octant, we can rearrange the given triple integral, which is given as:
∫∫∫_D dz dy dx
Now, we can find three other orders of integration:
a) ∫∫∫_D dx dz dy
b) ∫∫∫_D dy dx dz
c) ∫∫∫_D dy dz dx
2. To compute the volume of the solid by switching the order of integration, we can rewrite the given integral ∫∫ dy dx as: ∫∫ dx dy
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if 4y= 2.6,find the value of 20y + 3
Answer:
16
Step-by-step explanation:
4y = 2.6
y = 0.65
20y + 3
= 20 × 0.65 + 3
= 13 + 3
= 16
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The slant height if the cone is 13 cm. What is the volume of a cone having a radius of 5 cm and a slant height of 13 cm.
Thus, the volume of cone for the given slant height and radius is found as: 314 cu. cm.
Explain about the slant height of cone:The distance from a cone's apex to its outer rim is referred to as the segment's slant height. It is corresponding to the hypotenuse's length of a right triangle that creates the cone.
Given data:
slant height of cone l = 13 cm
radius r = 5 cm
Let h be the height
So, using Pythagorean theorem, find height.
l² = h² + r²
h² = l² - r²
h²= 13² - 5²
h² = 169 - 25
h = 12 cm
volume of a cone = 1/3 *π*r²*h
volume of a cone = 1/3 *3.14*5²*12
volume of a cone = 3.14*25*4
volume of a cone = 314 cu. cm
Thus, the volume of cone for the given slant height and radius is found as: 314 cu. cm.
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A baker paid $15. 05 for flour at a store that sells flour for $0. 86 per pound.
How many pounds of flour did the baker buy? :)
The baker bought approximately 17.5 pounds of flour.
Let's use algebra to solve the problem. Let x be the number of pounds of flour that the baker bought. We know that the cost of the flour is $15.05 and the price per pound is $0.86. So we can set up the equation:
$15.05 = $0.86 x
To solve for x, we can divide both sides by $0.86:
x = $15.05 ÷ $0.86
x ≈ 17.5
Therefore, the baker bought approximately 17.5 pounds of flour.
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Tina collects cans to recycle at the supermarket. Last week, on
Wednesday and Thursday, she collected 37 cans each day. On Tuesday, Friday,
Saturday, and Sunday, she collected 43 cans each day. Tina gets 5 cents for every can
she recycles.
а
How much money did Tina get for her cans last week?
Tina received $12.30 for recycling her cans last week.
How to calculate the money Tina get ?To find how much money Tina got for her cans last week, we need to find the total number of cans she collected and then multiply that by 0.05 (since she gets 5 cents per can).
On Wednesday and Thursday, Tina collected 37 cans each day, for a total of 2 x 37 = 74 cans.
On Tuesday, Friday, Saturday, and Sunday, she collected 43 cans each day, for a total of 4 x 43 = 172 cans.
The total number of cans collected is 74 + 172 = 246 cans.
To find the total amount of money Tina received, we multiply 246 by 0.05, which gives us:
246 x 0.05 = $12.30
Therefore, Tina received $12.30 for recycling her cans last week.
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A statistics class weighed 20 bags of grapes purchased from the store. The bags are advertised to contain 16 ounces, on average. The class calculated the 90% confidence interval for the true mean weight of bags of grapes from this store to be (15. 875, 16. 595) ounces. What is the sample mean weight of grapes, and what is the margin of error?
The sample mean weight is 15. 875 ounces, and the margin of error is 16. 595 ounces.
The sample mean weight is 16. 235 ounces, and the margin of error is 0. 360 ounces.
The sample mean weight is 16. 235 ounces, and the margin of error is 0. 720 ounces.
The sample mean weight is 16 ounces, and the margin of error is 0. 720 ounces
0.180 is the sample mean weight of grapes, and what is the margin of error
The sample mean weight is the midpoint of the confidence interval:
sample mean = (lower limit + upper limit) / 2 = (15.875 + 16.595) / 2 = 16.235
Therefore, the sample mean weight of grapes is 16.235 ounces.
The margin of error is half of the width of the confidence interval:
margin of error = (upper limit - sample mean) = (16.595 - 16.235) / 2 = 0.180
Therefore, the margin of error is 0.180 ounces.
So the correct answer is: "The sample mean weight is 16.235 ounces, and the margin of error is 0.180 ounces."
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Lillian deposits $430 every month into an account earning an annual interest rate of 4. 5% compounded monthly. How much would she have in the account after 3 years, to the nearest dollar? Use the following formula to determine your answer
Lillian would have approximately $14,599 in her account after 3 years, to the nearest dollar.
To find out how much Lillian would have in her account after 3 years, we need to use the future value of a series formula, which is:
[tex]FV = P \frac{(1 + r)^nt - 1)}{r}[/tex]
where:
FV = future value of the series
P = monthly deposit ($430)
r = monthly interest rate (annual interest rate / 12)
n = number of times interest is compounded per year (12)
t = number of years (3)
First, we need to find the monthly interest rate by dividing the annual interest rate (4.5%) by 12:
[tex]r =\frac{0.045}{12} = 0.00375[/tex]
Now we can plug the values into the formula:
[tex]FV = 430 \frac{(1 + 0.00375)^{12x3} - 1)}{0.00375}[/tex]
Calculating the future value:
[tex]FV = 430\frac{(1.127334 - 1) }{0.00375} = 430 \frac{0.127334}{ 0.00375} = 430 (33.955)[/tex]
[tex]FV =14,598.65[/tex]
So, Lillian would have approximately $14,599 in her account after 3 years, to the nearest dollar.
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Mr Mensah starts a job with an
annual salary of € 6400. 00 which increases by
€ 240. 00 every year After working for eight years
Mr Mensah is promoted to a new post with an
annual salary of ¢ 9500. 00 which increases by
€ 360. 00 every year Calculate
i) Mr. Mensah's Salary in the fifteenth year of service
ii) Mensah's total earnings at the end the fifteenth
year of service
Mr. Mensah's total earnings at the end of the fifteenth year of service is €1920.00 + €2520.00 = €4440.00.
To calculate Mr. Mensah's salary in the fifteenth year of service, we need to determine the pattern of salary increase over the years.
We know that Mr. Mensah's salary starts at €6400.00 and increases by €240.00 every year for the first eight years. After that, he is promoted to a new post with an annual salary of €9500.00, which increases by €360.00 every year.
Let's break it down:
For the first eight years, the salary increases by €240.00 per year:
After 1 year: €6400.00 + €240.00 = €6640.00
After 2 years: €6640.00 + €240.00 = €6880.00
...
After 8 years: €6400.00 + (8 * €240.00) = €6400.00 + €1920.00 = €8320.00
From the ninth year onwards, the salary increases by €360.00 per year:
After 9 years: €9500.00 + €360.00 = €9860.00
After 10 years: €9860.00 + €360.00 = €10220.00
...
After 15 years: €9500.00 + (7 * €360.00) = €9500.00 + €2520.00 = €12020.00
Therefore, Mr. Mensah's salary in the fifteenth year of service is €12,020.00.
To calculate Mr. Mensah's total earnings at the end of the fifteenth year of service, we need to sum up his salaries from year 1 to year 15.
For the first eight years, the total earnings can be calculated as follows:
Total earnings = (Salary in year 1 + Salary in year 2 + ... + Salary in year 8) = 8 * €240.00 = €1920.00
From the ninth year onwards, the total earnings can be calculated as follows:
Total earnings = (Salary in year 9 + Salary in year 10 + ... + Salary in year 15) = 7 * €360.00 = €2520.00
Therefore, Mr. Mensah's total earnings at the end of the fifteenth year of service is €1920.00 + €2520.00 = €4440.00.
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colleen's photo is 9 inches long and 7 inches wide. is it larger or smaller than ali's photo? explain how you know.
By calculations, Colleen's photo is smaller than Ali's photo
Determining if Colleen's photo larger or smaller than Ali's photo?From the question, we have the following parameters that can be used in our computation:
Area of Ali's photo = 91 square inches.
For Colleen's photo, we have
9 inches by 7 inches
This means that
Area of Colleen's photo = 9 * 7 square inches.
Evaluate
Area of Colleen's photo = 63 square inches.
63 square inches is lesser than 91 square inches
This means that Colleen's photo is smaller than Ali's photo
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A company claims that the mean monthly residential electricity consumption in a certain region is more than 880 kiloWatt-hours (kWh). You want to test this claim. You find that a random sample of 64 residential customers has a mean monthly consumption of 900 kWh. Assume the population standard deviation is 124 kWh. At a = 0. 01, can you support the claim? Complete parts (a) through (e)
(a) State the null and alternative hypotheses.
Null Hypothesis: The mean monthly residential electricity consumption in the region is less than or equal to 880 kWh.
Alternative Hypothesis: The mean monthly residential electricity consumption in the region is greater than 880 kWh.
(b) Determine the test statistic.
We need to use a one-tailed t-test because the alternative hypothesis is one-tailed.
t = (x - μ) / (σ / √n) = (900 - 880) / (124 / √64) = 2.581
(c) Find the p-value.
Using a t-table or a calculator, we can find the p-value associated with a t-value of 2.581 and 63 degrees of freedom: p-value = 0.007
(d) State the conclusion.
The p-value is less than the significance level of 0.01, which means that we reject the null hypothesis. We have enough evidence to support the claim that the mean monthly residential electricity consumption in the region is more than 880 kWh.
(e) Interpret the conclusion in the context of the problem.
Based on the sample data, we can conclude that the mean monthly residential electricity consumption in the region is likely to be greater than 880 kWh. However, we cannot say for sure whether this conclusion would hold true for the entire population.
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The height of lava fountains spewed from volcanoes cannot be measured directly. Instead, their height in meters can be found using the equation
where y represents the height, g is 9.8, and t represents the falling time of the lava rocks. Find the height in meters of a lava rock that falls for 3 seconds.
I need help with this problem.
Please and thank you.
Answer:
Step-by-step explanation:
Look at the intersection of madison street and peachtree street. describe the angles on the north side of the intersection as either supplementary or complementary explain your reasoning.
The angles on the north side of the intersection are complementary angles because complementary angles are two angles whose measures add up to 90 degrees. At the intersection of Madison Street and Peachtree Street, the north side of the intersection forms a right angle (90 degrees).
Any angle on the north side of the intersection must be complementary to the right angle, meaning its measure must be less than 90 degrees.
For example, if we consider the angle formed by Madison Street and the north side of the intersection, it is less than 90 degrees and therefore complementary to the right angle formed by the intersection. Similarly, if we consider the angle formed by Peachtree Street and the north side of the intersection, it is also less than 90 degrees and complementary to the right angle formed by the intersection.
Therefore, all angles on the north side of the intersection are complementary to the right angle formed by the intersection.
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Question 1. 4. The survey results seem to indicate that Imm Thai is beating all the other Thai restaurants among the voters. We would like to use confidence intervals to determine a range of likely values for Imm Thai's true lead over all the other restaurants combined. The calculation for Imm Thai's lead over Lucky House, Thai Temple, and Thai Basil combined is:
We know that when you have this data, you can proceed with calculating the confidence intervals to determine IMM Thai's lead.
Hi there! The survey results seem to indicate that IMM Thai is indeed ahead of the other Thai restaurants among the voters.
To determine a range of likely values for IMM Thai's true lead over Lucky House, Thai Temple, and Thai Basil combined, you would need to calculate confidence intervals.
Unfortunately, I cannot provide specific calculations without the necessary data (sample size, mean, standard deviation, etc.).
Once you have this data, you can proceed with calculating the confidence intervals to determine IMM Thai's lead.
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20. MP MODELING REAL LIFE The dot plot shows the lengths of earthworms.
.:
:
15 16 17 18 19 20 21 22 23 24 25 26 27 28
Length
a. Find and interpret the number of data values on the dot plot.
b. How can you collect these data? What are the units?
c. Write a statistical question that you can answer using the
dot plot. Then answer the question. PLS HELP
To find the quotient of 4. 082 and 10,000, move the decimal point 4. 082_places to the_
The quotient of the given division is 0.4082, under the condition that dividend is 4.082 and divisor is 10,000.
The count of zeros in 10,000 is 4, then we have to transfer the decimal point four places to the left to divide by 10,000. Here, we have to relie on the basic principles involved in division.
Then, in order to find the quotient of 4.082 and 10,000, we have to divide 4.082 by 10,000. To perform this, we expand the number by moving the decimal point forward of 4.082.
That is,
[tex] \frac{4.082 }{10000} [/tex]
= 0.4082
The quotient is 0.4082
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Find the moment of inertia about the y-axis of the
first-quadrant area bounded by the curve y=9−x^2
and the coordinate axes find ly (answer as a fraction)
To find the moment of inertia about the y-axis of the first-quadrant area bounded by the curve y=9−x^2 and the coordinate axes, we can use the formula:
I = ∫y² dA
where I is the moment of inertia, y is the distance from the y-axis to the infinitesimal element of area dA, and the integral is taken over the first-quadrant area.
To set up the integral, we need to express y in terms of x for the curve y=9−x². Solving for y, we get:
y = 9 - x²
The area element dA is given by:
dA = y dx
Substituting y in terms of x, we get:
dA = (9 - x²) dx
Now we can express the moment of inertia as an integral:
I = ∫y² dA
= ∫(9 - x²)² dx (limits of integration: x = 0 to x = 3)
To evaluate the integral, we can expand the integrand using the binomial theorem:
I = ∫(81 - 36x² + x⁴) dx
= 81x - 12x³ + (1/5)x⁵ (limits of integration: x = 0 to x = 3)
Finally, we can substitute the limits of integration and simplify:
I = (81(3) - 12(3)³ + (1/5)(3)⁵) - 0
= 243 - 108 + 27
= 162
Therefore, the moment of inertia about the y-axis is 162 units^4.
To find the moment of inertia (Iy) about the y-axis for the first-quadrant area bounded by the curve y = 9 - x^2 and the coordinate axes, we need to integrate the expression for the moment of inertia using the limits of the region.
The curve intersects the x-axis when y = 0, so:
0 = 9 - x²
x² = 9
x = ±3
Since we're in the first quadrant, we're interested in x = 3.
The moment of inertia about the y-axis is given by the expression Iy = ∫x²dA, where dA is the area element. In this case, we'll use a vertical strip with thickness dx and height y = 9 - x². Therefore, dA = y dx.
Now, let's integrate Iy:
Iy = ∫x²(9 - x²) dx from 0 to 3
To solve this integral, you may need to use polynomial expansion and integration techniques:
Iy = ∫(9x² - x⁴) dx from 0 to 3
Iy = [3x³/3 - x⁵/5] from 0 to 3
Iy = (3(3)³/3 - (3)⁵/5) - (0)
Iy = (81 - 243/5)
Iy = (405 - 243)/5
Iy = 162/5
So the moment of inertia about the y-axis for the first-quadrant area bounded by the curve y = 9 - x^2 and the coordinate axes is Iy = 162/5.
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The volume of a cone 69,120π cm cubed. The diameter of the circular base is 96 cm, what is the height of the cone?
Answer:
h = 30 cm
Step-by-step explanation:
Given:
V (volume) = 69,120π cm^3
d (diameter) = 96 cm (r (radius) = 0,5 × 96 = 48 cm
Find: h (height) - ?
[tex]v = \frac{1}{3} \times \pi {r}^{2} \times h[/tex]
[tex] \frac{1}{3} \times \pi \times {48}^{2} \times h = 69120\pi[/tex]
Multiply the whole equation by 3 to eliminate the fraction:
[tex]2304\pi \times h = 69120\pi[/tex]
[tex]h = 30[/tex]
The sum of two integers is 21. The second integer is three more than the twice the first integer. Find both of the integers
Answer:
what integer?
Step-by-step explanation:
more detail please?
13, 9, 17, 12, 18, 12, 17, 7, 16, 19
so what is the Mean Median_____ Range
Which recursive formula defines the sequence of f(1)=6, f(4)=12, f(7)=18
The recursive formula for this sequence is f(n) = f(n-3) + 6n - 18.
How did get the formula?We can use the method of finite differences to find a possible recursive formula for this sequence.
First, let's compute the first few differences:
f(4) - f(1) = 6
f(7) - f(4) = 6
Since the second differences are zero, we can assume that the sequence is a quadratic sequence. Let's write it in the form f(n) = an^2 + bn + c. We can solve for the coefficients using the given values:
f(1) = a(1)^2 + b(1) + c = 6
f(4) = a(4)^2 + b(4) + c = 12
f(7) = a(7)^2 + b(7) + c = 18
Solving for a, b, and c, we get:
a = 1
b = 5
c = 0
Therefore, the recursive formula for this sequence is f(n) = f(n-3) + 6n - 18.
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1. Given the function: f(x)=-2x+7 and g(x)=5x-16
Find the function for h(x)=f(x)+g(x)
The function h(x) can be represented by -3x-9 .
Linear Equation
An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=7x+6. Where:
m= the slope.
b= the constant term that represents the y-intercept.
For the given example: m=7 and b=6.
The question gives two linear equations that represent two functions: f(x)=-2x+7 and g(x)=5x-16.
For solving this you should sum both equations. See below
h(x)=f(x)+g(x)
h(x)=-2x+7 +5x-16
h(x)=-3x-9
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Find the volume of this cone.
Round to the nearest tenth.
7in
4in
The volume of the cone is 117.3 (Round to the nearest tenth).
To find the volume of this cone with a height of 7 inches and a radius of 4 inches, and round to the nearest tenth, follow these steps:
1. Use the formula for the volume of a cone: V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height.
2. Plug in the given values: V = (1/3)π(4²)(7)
3. Calculate the volume: V = (1/3)π(16)(7) = (1/3)(112π)
4. Multiply and round to the nearest tenth: V ≈ 117.3 cubic inches
So, the volume of this cone is approximately 117.3 cubic inches.
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