Explain me that excersice step by step please3x((2x3)^-1x1/2^3)^-1x(3x2^2)^-2
Answer:
Begin by simplifying the phrases within the brackets, beginning with the innermost brackets:
(2 x 3)^-1 = 1/6 (because 2 x 3 = 6, and the negative exponent flips the fraction)
1/2^3 = 1/8 (because 2^3 = 8)
So, (2x3)^-1x1/2^3 = 1/6 x 1/8 = 1/48
Next, simplify the expression outside the parentheses:
(3x2^2)^-2 = 1/(3x2^2)^2 = 1/(3^2 x 2^4) = 1/36 x 1/16 = 1/576
Now, substitute the simplified terms back into the original expression and simplify:
3x(1/48)x(1/576) = 1/768
So the final answer is 1/768.
Select the correct answer from each drop-down menu.
Based on the two triangles shown, what can be concluded?
An angle opposite the longest side of a triangle is the side
The two triangles shows that an angle opposite the longest side of a triangle is the largest angle
Making conclusions from the two triangles shownFrom the question, we have the following parameters that can be used in our computation:
The two triangles
From the triangles we have the largest angles to be
C = 117.3 and E = 93 degrees
The lennths opposite these sides aere
AB = 6 and DF = 11.94
These lengths are the longest segments on their respective triangles
This means that an angle opposite the longest side of a triangle is the largest angle
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will mark brainlist for anyone who do step by step correctly and make sure it's not no other answers that is not on the answer choice.
An image of a rhombus is shown.
What is the area of the rhombus?
224 cm2
120 cm2
112 cm2
60 cm2
Answer:224cm^2
Step-by-step explanation:
Formula for the area of a parallelogram is base x height (b x h) so we do 14x16 which is 224.
A gift bag is shaped like a rectangular prism and has a volume of 1152 cubic inches.
The volume of the gift bag is given as 1152 cubic inches.
Since it is shaped like a rectangular prism, we can write the formula for its volume as V = l × w × h, where l, w, and h are the length, width, and height of the rectangular prism, respectively.
To determine the dimensions of the gift bag, we need more information such as the ratio of its length, width, and height or any one of its dimensions. If we assume one of the dimensions, say, the length is L inches, then we can write the volume as V = L × w × h. Solving for w × h, we get w × h = V/L = 1152/L.
We can then use this equation along with the fact that the gift bag is a rectangular prism to find the other dimensions. For example, if the width is W inches, then we have h = 1152/(L × W) and the volume can be expressed as V = L × W × 1152/(L × W) = 1152.
Similarly, if the height is H inches, then we have w = 1152/(L × H) and the volume can be expressed as V = L × 1152/(L × H) × H = 1152.
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topic 3 providing lines are parallel
21
21. in the figure, provided line n and line m are parallel the values of x and y are
x = 7
y = 24
How to find x and y21. When line m and line n are parallel then using corresponding angle theorem we have that:
7y - 23 + 8x - 21 = 180
7y - 8x = 180 + 23 - 21
7x - 8x = 182
Also
8x - 21 + 23x - 16 = 180
8x + 23x = 180 + 21 + 16
31x = 217
x = 217 / 31
x = 7
using vertical angle theorem we have:
7y - 23 = 23x - 16
plugging in the value of x
7y - 23 = 23 * 7 - 16
7y - 23 = 145
7y = 145 + 23
7y = 168
y = 24
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Explain why one-twelfth interest every month on an initial one pound will give you (1 + (1/12))¹² pounds at the end of the year
One-twelfth interest every month on an initial one pound will give (1 + (1/12))¹² pounds at the end of the year due to the compounding effect of interest.
How to find the formula for compound interest?The interest rate of investment of one-twelfth per month means that for every pound invested, one-twelfth of that amount will be added as interest at the end of the month. Therefore, at the end of the first month, the initial investment of one pound will earn an additional interest of (1/12) pound, making the total amount of money to be 1+(1/12) pounds.
At the end of the second month, the new amount of money will earn another one-twelfth of interest, which will be added to the previous total. Therefore, the new total amount of money will be (1+(1/12))+(1/12) = (1+(2/12)) pounds, which can be simplified to (1+(1/6)) pounds.
By the end of the twelfth month, the initial one pound investment will have earned twelve one-twelfth interests, which can be calculated as (1+(1/12)[tex])^12[/tex] pounds, using the formula for compound interest. This simplifies to (1+1/12[tex])^12[/tex] pounds or (1.0833[tex])^12[/tex] pounds, which is approximately equal to 2.613 pounds.
Therefore, an initial investment of one pound with a one-twelfth interest rate per month will earn a total of (1+(1/12)[tex])^12[/tex] pounds or approximately 2.613 pounds by the end of the year.
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Given that f is continuous on [1, 5] and differentiable on the interval (1,5), with f'(x) ≤ 23, for all x, and f(1) = 4. Find the largest possible value for f(5).
We are given that f is continuous on [1, 5], differentiable on (1, 5), and f'(x) ≤ 23 for all x. We want to find the largest possible value for f(5). the largest possible value for f(5) is found to be 96.
We can apply the Mean Value Theorem (MVT) here, which states that if a function is continuous on [a, b] and differentiable on (a, b), there exists a number c in the interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a). In this case, a = 1, b = 5, and f(1) = 4.
Since f'(x) ≤ 23 for all x, we know that f'(c) ≤ 23. Plugging into the MVT equation, we have:
[tex]f'(c) = (f(5) - f(1))/(5 - 1) ≤ 23, f'(c) = (f(5) - 4)/4 ≤ 23[/tex]
To find the largest possible value for f(5), we assume f'(c) is equal to its maximum, 23: 23 = (f(5) - 4)/4. Solving for f(5), we get: f(5) = 4 + 4 * 23 = 4 + 92 = 96. So, the largest possible value for f(5) is 96.
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The graph of the function p(x) is represented below. On the same set of axes, sketch the function p(x + 2).
A graph of the function p(x) and the function p(x + 2) is shown below.
How to determine the factored form of a quadratic equation?In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided above, we can determine the value of a as follows:
f(x) = a(x - h)² + k
0 = a(-3 - 0)² + 4
0 = 9a + 4
a = -4/9
Therefore, the required quadratic function is given by:
f(x) = a(x - h)² + k
p(x) = y = -4/9(x - 0)² + 4
p(x + 2) = -4/9(x + 2)² + 4
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Doors&Windows, Inc. Makes, you guessed it, doors and windows. Each day, Doors&Windows orders 6,150 linear feet of framing material and has a few staff member who are able to work a collective 600 hours. For each window, Doors&Windows profits $40 requiring 6 labor hours and 30 linear feet of framing material. For each table, Doors&Windows profits $90 requiring 10 labor hours and 120 linear feet of framing material. Due to the availability of glass, they can only produce a maximum of 70 windows. When formulating this problem as a linear programming model, what are the decision variables?
Decision variables in Doors&Windows linear programming model.
How to formulate linear programming?The decision variables in the linear programming model for this problem are the number of windows (W) and the number of tables (T) that Doors&Windows should produce to maximize their profit while meeting the constraints. The objective function to maximize would be the total profit, which can be expressed as 40W + 90T. The constraints include the available linear feet of framing material (6150) and labor hours (600), which can be written as 30W + 120T ≤ 6150 and 6W + 10T ≤ 600, respectively. Additionally, the maximum number of windows that can be produced (W ≤ 70) due to glass availability is also a constraint. These decision variables and constraints can be used to create a linear programming model to optimize Doors&Windows' production and profit.
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A surveyor at an intersection noticed that over the past 24 hours, 318 cars turned left, 557 turned right, and 390 went straight. Based on the activity of the past 24 hours, what fraction is closest to the probability that the next car will turn left?
probability that the next car will turn left, we need to divide the number of cars that turned left by the total number of cars that passed through the intersection in the past 24 hours. This will give us a fraction that represents the likelihood of a car turning left.
Using the numbers provided, the total number of cars that passed through the intersection in the past 24 hours is:
318 (cars turned left) + 557 (cars turned right) + 390 (cars went straight) = 1265
So, the probability of the next car turning left is:
318 (cars turned left) ÷ 1265 (total number of cars) = 0.251 (rounded to three decimal places)
This means that there is a 25.1% chance that the next car will turn left at the intersection.
As a surveyor, it is important to be able to analyze data and calculate probabilities to make informed decisions. Understanding the probability of different outcomes can help to plan for future events and anticipate potential issues.
In this case, knowing the probability of a car turning left can help to inform traffic flow and reduce congestion at the intersection.
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You are shopping for a King & Queen size mattress, each of which are shaped like a rectangle. The Queen is 16 inches longer than it is wide. The King is 20 inches wider than the Queen, but has the same length. The area of the King-sized mattress is 1,600 in² larger than the Queen. Find the Area of both mattresses
The area of the King-sized mattress is 4,800 square inches and the area of the Queen-sized mattress is 3,200 square inches.
To find the dimensions of the Queen-sized mattress, let x be the width. Then, the length of the mattress is x + 16. The area of the Queen-sized mattress is x(x + 16) = x² + 16x.
Since the King-sized mattress has the same length as the Queen-sized mattress, its length is x + 16. Also, its width is 20 inches wider than the Queen-sized mattress, so its width is x + 16 + 20 = x + 36. Therefore, the area of the King-sized mattress is (x + 16)(x + 36) = x² + 52x + 576.
The area of the King-sized mattress is 1,600 square inches larger than the area of the Queen-sized mattress. So, we can set up the following equation:
x² + 52x + 576 - (x² + 16x) = 1600
Simplifying this equation, we get:
36x + 576 = 1600
36x = 1024
x = 28
Therefore, the width of the Queen-sized mattress is 28 inches and the length is 44 inches. So, its area is 3,200 square inches.
The width of the King-sized mattress is 28 + 36 = 64 inches and the length is 44 inches. So, its area is 4,800 square inches.
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In ΔPQR, the measure of ∠R=90°, the measure of ∠P=26°, and PQ = 8. 5 feet. Find the length of QR to the nearest tenth of a foot
In ΔPQR, the length of QR is approximately 4.1 feet to the nearest tenth of a foot.
In ΔPQR, given that ∠R=90°, ∠P=26°, and PQ=8.5 feet, you want to find the length of QR to the nearest tenth of a foot.
Step 1: Since ∠R is a right angle (90°), we can use trigonometric ratios to find QR. First, let's find ∠Q. We know that the sum of angles in a triangle is 180°, so ∠Q = 180° - (∠P + ∠R) = 180° - (26° + 90°) = 64°.
Step 2: Now that we have all the angles, we can use the sine formula to find QR. We'll use the sine of ∠P (26°) and the given side PQ (8.5 feet) as our reference. The sine formula is:
QR = (PQ * sin(∠P)) / sin(∠Q)
Step 3: Plug in the known values:
QR = (8.5 * sin(26°)) / sin(64°)
Step 4: Calculate the sine values and the division:
QR = (8.5 * 0.4384) / 0.8988 ≈ 4.1326
Step 5: Round the answer to the nearest tenth of a foot:
QR ≈ 4.1 feet
In ΔPQR, the length of QR is approximately 4.1 feet to the nearest tenth of a foot.
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1)You have a monthly income of $2,800 and you are looking for an apartment. What is the maximum
amount you should spend on rent?
2)You have a monthly income of $1,900 and you are looking for an apartment. What is the maximum
amount you should spend on rent?
3)An apartment you like rents for $820. What must your monthly income be to afford this apartment?
4)An apartment you like rents for $900. What must your monthly income be to afford this apartment?
5)An apartment rents for $665/month. To start renting, you need the first and last month's rent, and a
$650 security deposit.
Using Rule of thumb,
The maximum amount you should spend on rent for an income of $2,800 is $840 (30% of $2,800).The maximum amount you should spend on rent for an income of $1,900 is $570 (30% of $1,900).To afford an $820/month apartment, your monthly income must be at least $2,733.33 (30% of $2,733.33).To afford a $900/month apartment, your monthly income must be at least $3,000 (30% of $3,000).To start renting the apartment, you would need $1,980 for first and last month's rent plus a $650 security deposit.1) A common rule of thumb is to spend no more than 30% of your income on rent. Therefore, the maximum amount you should spend on rent is:
$2,800 x 0.3 = $840
2) Using the same rule of thumb, the maximum amount you should spend on rent is:
$1,900 x 0.3 = $570
3) To afford an $820/month apartment, you should aim to spend no more than 30% of your income on rent:
$820 = 0.3x
x = $2,733.33
So your monthly income must be at least $2,733.33 to afford the apartment.
4) Following the same reasoning, your monthly income must be at least:
$900 = 0.3x
x = $3,000
5) To start renting, you need to pay first and last month's rent, plus a $650 security deposit, for a total of:
$665 x 2 + $650 = $1,980
So you would need $1,980 to start renting the apartment.
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The am between two number exceeds their gm by 2 and the gm exceed the hm by 1.8 find the number
The unknown number x = (6.1 ± sqrt(6.
How to find the unknown numberLet's call the two numbers x and y.
We are given:
AM (Arithmetic Mean) between x and y exceeds their GM (Geometric Mean) by 2:
(x + y)/2 - sqrt(xy) = 2
GM between x and y exceeds their HM (Harmonic Mean) by 1.8:
sqrt(xy) - 2xy/(x+y) = 1.8
We can solve for one variable in terms of the other from the second equation and substitute into the first equation to solve for the remaining variable. Let's solve for y in terms of x from the second equation:
sqrt(xy) - 2xy/(x+y) = 1.8
sqrt(xy)(x+y) - 2xy = 1.8(x+y)
sqrt(xy)x + sqrt(xy)y - 2xy = 1.8x + 1.8y
sqrt(xy)(x+y-1.8) = 0.2x + 0.8y
x+y-1.8 = (0.2/0.8)sqrt(xy)(x+y-1.8)
x+y-1.8 = 0.25sqrt(xy)(x+y-1.8)
4x + 4y - 7.2 = sqrt(xy)(x+y)
Now we can substitute this expression for sqrt(xy)(x+y) into the first equation and solve for x:
(x + y)/2 - sqrt(xy) = 2
(x + y)/2 - (4x + 4y - 7.2)/4 = 2
2(x + y) - (4x + 4y - 7.2) = 8
12.2 = 2x + 2y
6.1 = x + y
Now we can substitute x + y = 6.1 into the expression we derived for sqrt(xy)(x+y) to solve for sqrt(xy):
4x + 4y - 7.2 = sqrt(xy)(x+y)
4x + 4y - 7.2 = sqrt(xy)(6.1)
sqrt(xy) = (4x + 4y - 7.2)/6.1
Finally, we can substitute both x + y = 6.1 and sqrt(xy) = (4x + 4y - 7.2)/6.1 into the equation sqrt(xy) - 2xy/(x+y) = 1.8 and solve for y:
sqrt(xy) - 2xy/(x+y) = 1.8
(4x + 4y - 7.2)/6.1 - 2xy/6.1 = 1.8
4x + 4y - 7.2 - 12.2xy = 11.38
4x + 4y - 11.38 = 12.2xy
4x + 4(6.1 - x) - 11.38 = 12.2xy (substituting x + y = 6.1)
xy = 4.08
Now we know that xy = 4.08, and we can use this to solve for x and y:
y = 6.1 - x
xy = 4.08
x(6.1 - x) = 4.08
6.1x - x^2 = 4.08
x^2 - 6.1x + 4.08 = 0
We can solve for x using the quadratic formula:
x = (6.1 ± sqrt(6.
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Jaoan reads that themass of an average elephant's brain is 3 4/10 kilograms greater than an average man's brain. How many kilograms is an average elephant's brain?
Answer:
Step-by-step explanation:
Let's call the mass of an average man's brain "m."
According to the problem, the mass of an average elephant's brain is 3 4/10 kilograms greater than an average man's brain. We can write this as:
mass of elephant's brain = m + 3 4/10
To find out how many kilograms an average elephant's brain weighs, we need to know the value of "m." However, this information is not given in the problem.
Therefore, we cannot determine the exact mass of an average elephant's brain.
The volume of a cylinder is 336m3 . what is the volume of a cone with the same radius and height?
Q=1/6p^2
p= 13. 6 correct to 3 significant figures.
By considering bounds, work out the value of q to a suitable degree of accuracy.
Give a reason for your answer.
+
The value of Q, taking into account the significant figures is 30.8.
To work out the value of Q given the value of p, we can substitute the value of p into the equation Q = (1/6) × p².
Given p = 13.6, we can calculate Q as follows:
Q = (1/6) × (13.6)²
Q = (1/6) × 184.96
Q = 30.826666...
Now, let's consider the significant figures of the given value of p, which is 13.6 (3 significant figures).
Since the value of p has 3 significant figures, we should round our final answer for Q to 3 significant figures as well.
Considering the value of Q to a suitable degree of accuracy, we can round our answer to three significant figures, which gives us:
Q = 30.8
Therefore, the value of Q, taking into account the significant figures, is 30.8.
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What is the measure of angle A? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. m∠A=° Right triangle A B C, with right angle C B A. Side A B is three centimeters, side B C is four centimeters, and side C A is five centimeters.
The measure of angle A is given as follows:
m < A = 53.13º.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.Angle A is opposite to a side of length 4 cm, while the hypotenuse is of 5 cm, hence it's measure is obtained as follows:
sin(A) = 4/5
m < A = arcsin(4/5)
m < A = 53.13º.
Missing InformationWe have a right triangle, in which the side length opposite to angle A is BC = 4, while the hypotenuse is CA = 5.
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The preimage and image of WXYZ are shown. Use coordinate notation to describe the translation.
The image of WXYZ moves two unit to the right and 5 unit down. The coordinate is (x+2, y-5).
The polar system of coordinates is a coordinate system with two dimensions in which the location of each point can be determined by its distance from the origin, a fixed point, and its angle from the polar axis, also known as the polar axis of rotation. A ray beginning at the origin and extending outward at a set angle, typically 0 degrees or horizontal, is how the polar axis is typically depicted. The image of WXYZ moves two unit to the right and 5 unit down. The coordinate is (x+2, y-5).
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It is typical for the person who is most difficult to convince in an argument to say that everyone else is stubborn. group of answer choices displacement sublimation projection rationalization regression
"It is typical for the person who is most difficult to convince in an argument to say that everyone else is stubborn." refers projection (option c).
To understand projection in mathematical terms, we can think of it as a function f(x), where x represents the individual's own thoughts or emotions. The output of the function, f(x), represents the projection of these thoughts or emotions onto someone else.
In the case of arguments, the person who is most difficult to convince may have a high value of x, indicating that they are feeling stubborn. However, instead of accepting this feeling, they project it onto others, resulting in a high value of f(x) for those around them.
Projection is just one example of the many defense mechanisms that humans use to protect themselves from unpleasant thoughts or emotions. Understanding these mechanisms can help us to better navigate difficult situations, including arguments, and improve our communication skills.
Hence the correct option is (c).
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Chris bought 5 tacos and 2 burritos for $13. 25.
Brett bought 3 tacos and 2 burritos for $10. 75.
The price of one taco is $
The price of one burrito is $
Answer:
Let's start by assigning some variables to the unknowns:
Let's call the price of one taco "t".
Let's call the price of one burrito "b".
With these variables, we can write two equations based on the information given in the problem:
5t + 2b = 13.25 (equation 1)
3t + 2b = 10.75 (equation 2)
We now have two equations and two variables. We can use algebra to solve for t and b. One way to do this is to eliminate b by subtracting equation 2 from equation 1:
(5t + 2b) - (3t + 2b) = 13.25 - 10.75
Simplifying this equation, we get:
2t = 2.5
Dividing both sides by 2, we get:
t = 1.25
So the price of one taco is $1.25.
Now that we know the price of one taco, we can substitute this value into one of the equations to solve for b. Let's use equation 1:
5t + 2b = 13.25
Substituting t = 1.25, we get:
5(1.25) + 2b = 13.25
Simplifying this equation, we get:
6.25 + 2b = 13.25
Subtracting 6.25 from both sides, we get:
2b = 7
Dividing both sides by 2, we get:
b = 3.5
So the price of one burrito is $3.5.
Therefore, the price of one taco is $1.25 and the price of one burrito is $3.5.
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can yall help me with this and this is due today!
a) The experimental probability of rolling an even number is given as follows: 12/25.
b) The theoretical probability of rolling an even number is given as follows: 1/2.
c) With a large number of trials, there might be a difference between the experimental and the theoretical probabilities, but the difference should be small.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The number of trials in which an even number is rolled is given as follows:
88 + 69 + 83 = 240.
Hence the experimental probability is given as follows:
240/500 = 12/25.
For each roll, 3 out of 6 numbers are even, hence the theoretical probability is given as follows:
p = 3/6
p = 1/2.
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Frank wants to paint his room in the
school colors of maroon and white. The floor and ceiling will be white, and all the walls will be maroon. The door will also be white. If one gallon of paint covers 400 sq ft, how many gallons of each color will he need?
A. 1 gallon white,1 gallon maroon
B. 1 gallon white,2 gallons maroon
C. 2 gallon white,2 gallons maroon
D. 2 gallon white,3 gallons maroon
To determine how many gallons of white and maroon paint Frank will need, we need to calculate the total square footage for each color. Here's a step-by-step explanation:
1. Determine the square footage of the floor and ceiling that will be painted white. Since they are the same size, we can calculate the area of one and multiply it by 2.
2. Determine the square footage of all the walls that will be painted maroon. Calculate the area of each wall and sum them up.
3. Determine the square footage of the door that will be painted white. Subtract this value from the total maroon wall area.
4. Divide the total square footage of the white and maroon surfaces by 400 sq ft (coverage of one gallon) to find out how many gallons are needed for each color.
After calculating the areas and the number of gallons needed, compare the results with the given options (A, B, C, or D). Keep in mind that we don't have the specific dimensions for Frank's room, but following these steps will help you solve the problem once you have the necessary measurements.
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A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
He concludes that she is not running fast enough to exceed her fastest time.
What errors did the coach make? Check all that apply.
He used an incorrect time ratio converting hours to minutes.
His units do not cancel.
He used an incorrect distance ratio converting miles to feet.
He incorrectly concluded that she is not running fast enough.
He cannot determine her average rate in miles per hour after only 15 minutes.
In a case whereby A bike wheel is 26 inches in diameter the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters) the the diameter is 660.4mm
How can the diameter be calculated?Note; the bike man do not make any calculation, so we can not know mat be he make any mistake.
Since the bike wheel is 26 inches in diameter then we can calculate the diameter of the bike wheel through the multiplication of the two numbers.
Diameter in milimeters = ( 26.0 x 25.4)
Diameter in milimeters = 660.4 mm.
Hence diameter of the bike wheel in millimeters will be 660.4.
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Write the standard form of the equation of the circle with the given characteristics. Endpoints of a diameter: (0, 0), (8, 6)
The standard form of the equation of the circle with the given characteristics is[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]
To get the equation of the circle using the endpoints of a diameter, we have to use the standard form :
[tex](x - h) ^{2} + (y - k)^{2} = {r}^{2} [/tex]
In which (h, k) represents the middle point of the circle and r as the radius. so, we need to find the midpoint of the diameter using the endpoints (0, 0) and (8, 6).
Midpoint = ((0+8)/2, (0+6)/2) = (4, 3)
Next, we need to calculate the radius by using the distance formula to calculate the distance between the center and one of the diameter endpoints.
[tex] {r}^{2} = {(8 - 4)}^{2} + {(6 - 3)}^{2} = {4}^{2} + {3}^{2} = 16 + 9 = 25[/tex]
Now, substituting the values of (h, k) and
[tex] {r}^{2} [/tex] into the standard form equation to get the equation:
[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]
Therefore, the standard form equation of the circle with the given characteristics is
[tex] {(x - 4)}^{2} + {(y - 3)}^{2} = 25[/tex]
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The standard form of the given question is (x - 4)² + (y - 3)² = 25, under the condition endpoints of a diameter: (0, 0), (8, 6).
In order To write the standard form of the equation of a circle with endpoints of a diameter (0, 0), (8, 6), we first need to find the center and radius of the circle.
The diameter comprises the midpoints of the center of the circle. The midpoint of (0, 0) and (8, 6) is ((0+8)/2, (0+6)/2) = (4,3). Center point of the circle is (4,3).
Diameter = 2× radius
. The distance between (0, 0) and (8, 6) is √((8-0)² + (6-0)²)
= √(64+36)
= √100
= 10.
Then, the radius of the circle is 10/2 = 5.
Then,
(x - h)² + (y - k)² = r²
here
(h,k) = center of the circle
r = radius.
Staging in this equation
h=4,
k=3
r=5
(x - 4)²+ (y - 3)² = 25
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A store sells four ears of sweetcorn for one dollar how much will nine ears cost
Nine ears of sweetcorn will cost $2.25 at this store.
To determine the cost of nine ears of sweetcorn, given that four ears cost one dollar, you can follow these steps:
1. Determine the cost of one ear of sweetcorn: Since four ears cost one dollar, we can calculate the cost per ear by dividing the total cost by the number of ears: $1 / 4 ears = $0.25 per ear.
2. Calculate the cost of nine ears: Multiply the cost of one ear by the number of ears desired: $0.25 per ear × 9 ears = $2.25.
So, nine ears of sweetcorn will cost $2.25 at this store.
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Marcia drew a plan for a rectangular piece of material that she will use for a blanket. Three of the vertices are (-1.3, -3.5), (-1.3, 1.4), and (3.9,1.4) . What are the coordinates of the fourth vertex?
The coordinates of the fourth vertex is (3.9, 6.3,0).To find the coordinates of the fourth vertex, we can use the fact that opposite sides of a rectangle are parallel and equal in length.
We can find the length and slope of one side of the rectangle and then use that information to find the coordinates of the fourth vertex.
Let's start by finding the length and slope of the side connecting (-1.3, -3.5) and (-1.3, 1.4). The length of this side is the difference between the y-coordinates, which is:
1.4 - (-3.5) = 4.9
Since this side is vertical, its slope is undefined.
Next, let's find the length and slope of the side connecting (-1.3, 1.4) and (3.9, 1.4). The length of this side is the difference between the x-coordinates, which is:
3.9 - (-1.3) = 5.2
Since this side is horizontal, its slope is 0.
Since opposite sides of a rectangle are equal in length, the length of the side connecting (-1.3, 1.4) and (3.9, 1.4) must also be 4.9. We can use this length to find the y-coordinate of the fourth vertex, which is:
1.4 + 4.9 = 6.3
Now we know that the fourth vertex has coordinates (x, 6.3). To find the x-coordinate, we can use the length of the vertical side connecting (-1.3, -3.5) and (-1.3, 1.4), which is also 5.2. The x-coordinate of the fourth vertex is:
-1.3 + 5.2 = 3.9
Therefore, the coordinates of the fourth vertex are (3.9, 6.3,0).
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Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.
Maximize: f(x, y, 2) = xyz
Constraint: × + y + z - 6 = 0
f = _____
To use Lagrange multipliers, we need to set up the Lagrangian function, Therefore, the maximum value of f(x,y,2) = xyz subject to the constraint x+y+z-6=0 is f(2,2,2) = 8.
L(x,y,z,λ) = xyz + λ(x+y+z-6)
Then we need to find the critical points of L by setting its partial derivatives equal to zero:
∂L/∂x = yz + λ = 0
∂L/∂y = xz + λ = 0
∂L/∂z = xy + λ = 0
∂L/∂λ = x + y + z - 6 = 0
Solving this system of equations, we get:
x = y = z = 2
λ = -4
This critical point satisfies the constraint, since 2+2+2-6 = 0. To check whether it is a maximum or minimum, we need to use the second partial derivative test:
∂²L/∂x² = 0, ∂²L/∂y² = 0, ∂²L/∂z² = 0
∂²L/∂x∂y = z, ∂²L/∂x∂z = y, ∂²L/∂y∂z = x
The Hessian matrix is:
| 0 z y |
| z 0 x |
| y x 0 |
At the critical point (2,2,2), the Hessian matrix is:
| 0 2 2 |
| 2 0 2 |
| 2 2 0 |
The eigenvalues of this matrix are -4, -4, and 8. Since the eigenvalues are not all positive or all negative, we cannot conclude whether the critical point is a maximum or minimum.
Therefore, the maximum value of f(x,y,2) = xyz subject to the constraint x+y+z-6=0 is f(2,2,2) = 8.
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B. It will be a curve.
C. It will be a line.
D. There is no way to tell.
The given equation on a graph can be described best as C. It will be a line.
Why would this be a line ?The given equation is a linear equation because it has the form y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation can be rewritten as:
y = 3x + 15 - 64
y = 3x - 49
Since it's a linear equation, it will represent a straight line on the graph that can be found by using the equation and some values of x, to find values of y and then plotting them.
In conclusion, the best answer is C. It will be a line.
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The full question is:
An equation is given to be 3x + 15 = 64
What will this be on a graph ?
A. It will be irregular
B. It will be a curve.
C. It will be a line.
D. There is no way to tell.
Catherine talks on the phone for 3/4 of an hour every night. How many hours dose she talk on the phone is one week. No decimals pls!
Answer: 5 1/4
Step-by-step explanation: 3/4 times 7/1 equals 5.25
Turn the decimal to a fraction and get 5 1/4
