Answer:
x + 7
Step-by-step explanation:
1+7=8
2+7+9
so on
PLEASE HELP!!!! Choose the name of the angle notated by the arc.(SHOW WORK) (Will Give Brainiliest) A.TSP B.STP C.TSP
The name of the angle notated by the arc is C. TPS.
Due to the arc, P is the middle letter, so The answer is TPS.
Financial Decision Making
The daily cost of public transportation to get you to and from your current job is $5. You regularly work 8 hours a day Monday through Friday and 4 hours on Saturday. You have been offered a new job close to home where you could walk to and from work each day. The new job pays $0.75 less an hour than your current job. You will work an average of 44 hours a week. Will you make or lose money by taking the new job?
Answer:
Lose money. you lose $3 a week
Step-by-step explanation:
5*6 = 30
0.75*44=33
the kims want to visit relatives who live 800 miles from their home. if a thirty minute stop will be taken for lunch, and the average speed will be 70 miles per hour, about how long will the trip take?
The trip will take about 11.93 hours, or approximately 11 hours and 56 minutes.
What is distance?
Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance is a scalar quantity, meaning it has only magnitude and no direction.
To calculate the total time for the trip, we need to take into account the time for driving and the time for lunch.
First, let's calculate the time for driving:
Distance to be covered = 800 miles
Average speed = 70 miles per hour
Time for driving = Distance / Speed
Time for driving = 800 miles / 70 miles per hour
Time for driving = 11.43 hours
So, the driving time is approximately 11.43 hours.
Now, let's add the time for lunch. The stop for lunch is 30 minutes, which is equivalent to 0.5 hours.
Total time for the trip = Time for driving + Time for lunch
Total time for the trip = 11.43 hours + 0.5 hours
Total time for the trip = 11.93 hours
Therefore, the trip will take about 11.93 hours, or approximately 11 hours and 56 minutes.
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Circumference of 1/8th of a circle. There is 1/8 of a circle. The radius of the circle is 30 centimeters. The radius of the circle is 30 centimeters. Find the distance of the figure. Give steps
The circumference of 1/8th of a circle with a radius of 30 centimeters is 11.78 centimeters.
The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.
To find the circumference of 1/8th of a circle, we need to divide the circumference of the full circle by 8. So, the formula becomes:
C = (1/8) * 2πr
Substituting the given value of the radius, we get:
C = (1/8) * 2π(30)
Simplifying, we get:
C = (1/4) * π(30)
C = (1/4) * 30π
C = 7.5π
Approximating π as 3.14, we get:
C = 7.5 * 3.14
C = 23.55/2
C = 11.78
Therefore, the circumference of 1/8th of a circle with a radius of 30 centimeters is 11.78 centimeters.
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Complete Question:
Circumference of 1/8th of a circle. There is 1/8 of a circle. The radius of the circle is 30 centimeters. The radius of the circle is 30 centimeters. Find the distance of the figure. Give steps.
Point K is located at (7, 4) in the coordinate plane. Its image is created by the following rule: K' = Ro270°(K).
Which transformation of point K would produce the same result for K as seen in the previous question?
P.S. Pervious question
Point K is located at (7,4) in the coordinate plane. Its image is created by the following rule:
K'=Ro 270°^(k)
What are the coordinates of k'?
A. (4,-7)
B. (4, 7) This is the correct answer.
C. (7, -4)
D. (-7, 4)
After the transformation of 270° clockwise rotation we get K(7, 4)→K'(-4, 7). Therefore, option B is the correct answer.
The given coordinate point is (7, 4).
What is the transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.
Rotation of object 270° clockwise direction
The rule of rotating a figure 270 degrees clockwise is (x, y)→(-y, x)
So, K(7, 4) rotated by 270° clockwise we get K'(-4, 7).
After the transformation of 270° clockwise rotation we get K(7, 4)→K'(-4, 7). Therefore, option B is the correct answer.
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Can someone help me
Step-by-step explanation:
the answer is in the above image
Answer:
\(-12^{2}\) + 9a - 5
Step-by-step explanation:
combine like terms :
-7\(a^{2}\) - 5\(a^{2}\) = -12\(a^{2}\)
+3a - (-6a) = 9a
-9 - (-4) = -5
The graph shows the student's distance in miles from the recreation center after riding the bike x minutes.
What is the domain of the function for this situation?
A. All real numbers greater than or equal to 0 and less than or equal to 28.
B. All real numbers greater than or equal to 0 and less than or equal to 9.
C.{0,4,8,12,16,20,24,28}
D.{0,1,2,3,4,5,6,7,8,9}
Answer:
A
Step-by-step explanation:
HELP PLEASE! 50 POINTS AND WILL MARK BRAINLIEST.
Bobby charges $10. per lawn he mows, and an additional $5. per hour.
a) Find the independent and the dependent variables.
b) Write a linear function that models the wage of Bobby per lawn.
c) If Bobby work for 3.5 hours on a lawn, how much does he earn?
Answer:
a) independent = hours
dependent = wages
b ) W = 10 + 5h
c)27.50
Step-by-step explanation:
The independent variable is the one that you change which is the number of hours that it takes
The dependent variable is the variable that changes based on the independent variable. The wages depends on the hour worked so the wages are the independent variable
The wages equal the fixed cost plus the hourly rate times the number of hours where W is the wages and h is the number of hours
W = 10 + 5h
W = 10 + 5( 3.5)
= 10 + 17.5
= 27.5
Write/Describe a situation when you have to multiply a matrix by another matrix
Answer:
you multiply first row with first column and second with second so it goes
The number of hits per day on the Web site of a tool company is normally distributed with a mean of 510 and a standard deviation of 100 . a. What proportion of days have more than 650 hits? b. What proportion of days have between 580 and 650 hits? c. Find the number of hits such that only 15% of the days will have the number of hits below this number. Click the icon to view the standard normal table of the cumulative distribution function. a. The proportion of days with more than 650 hits is (Round to four decimal places as needed.) b. The proportion of days with between 580 and 650 hits is (Round to four decimal places as needed.) c. Only 15% of the days will have loss than hits
a. The proportion of days with more than 650 hits is approximately 0.0808.
b. The proportion of days with between 580 and 650 hits is approximately 0.6772.
c. The number of hits such that only 15% of the days will have fewer hits is approximately 406.36.
To solve these questions, we will use the standard normal distribution and the z-score.
a. To find the proportion of days with more than 650 hits, we need to calculate the z-score for 650 and find the area under the standard normal curve to the right of that z-score.
First, calculate the z-score:
z = (x - μ) / σ
z = (650 - 510) / 100
z = 1.4
Using the standard normal table or a calculator, we find the area to the right of the z-score 1.4 is approximately 0.0808.
Therefore, the proportion of days with more than 650 hits is 0.0808 (rounded to four decimal places).
b. To find the proportion of days with between 580 and 650 hits, we need to calculate the z-scores for 580 and 650 and find the area between these two z-scores under the standard normal curve.
First, calculate the z-score for 580:
z1 = (580 - 510) / 100
z1 = 0.7
Next, calculate the z-score for 650:
z2 = (650 - 510) / 100
z2 = 1.4
Using the standard normal table or a calculator, we find the area to the right of z1 (0.7) is approximately 0.7580, and the area to the right of z2 (1.4) is approximately 0.0808. To find the area between these two z-scores, we subtract the smaller area from the larger area:
0.7580 - 0.0808 = 0.6772
Therefore, the proportion of days with between 580 and 650 hits is 0.6772 (rounded to four decimal places).
c. To find the number of hits such that only 15% of the days will have fewer hits, we need to find the z-score that corresponds to the cumulative probability of 0.15 (15%).
Using the standard normal table or a calculator, we find that the z-score corresponding to a cumulative probability of 0.15 is approximately -1.0364.
Now, we can use the z-score formula to find the number of hits:
z = (x - μ) / σ
-1.0364 = (x - 510) / 100
Solving for x:
x - 510 = -1.0364 * 100
x - 510 = -103.64
x = 510 - 103.64
x ≈ 406.36
Therefore, the number of hits such that only 15% of the days will have fewer hits is approximately 406.36.
In summary:
a. The proportion of days with more than 650 hits is approximately 0.0808.
b. The proportion of days with between 580 and 650 hits is approximately 0.6772.
c. The number of hits such that only 15% of the days will have fewer hits is approximately 406.36.
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A snow globe is made out of regular right triangular prism that is inscribed in hemisphere with radius 12cm. help a designer to find the dimensions of maximum volume prison. state the exact answer.
Note: Find the dimensions of the prism for the case when the triangular base is on the grand circle of the hemisphere.
The maximum volume of the prism is 1728 cubic centimeters.
To find the dimensions of the prism with maximum volume, we need to consider the relationship between the volume of the prism and its dimensions.
Let's assume the base of the right triangular prism is an isosceles right triangle with legs of length 'a'. The height of the prism will be 'h'. The prism is inscribed in a hemisphere with a radius of 12 cm.
First, let's determine the relationship between 'a' and 'h'. Since the base of the prism is on the great circle of the hemisphere, the hypotenuse of the triangular base is equal to the diameter of the hemisphere, which is twice the radius. Therefore, the hypotenuse of the base is 2 * 12 = 24 cm.
By using the Pythagorean theorem, we can find 'a':
a^2 + a^2 = 24^2
2a^2 = 576
a^2 = 288
a = √288
Now, let's find the height 'h' of the prism. The height 'h' is equal to the radius of the hemisphere, which is 12 cm.
Therefore, the dimensions of the prism for maximum volume are:
Base length (a) = √288 cm
Height (h) = 12 cm
To find the maximum volume, we can use the formula for the volume of a right triangular prism:
Volume = (1/2) * a^2 * h
Substituting the values, we get:
Volume = (1/2) * (√288)^2 * 12
= (1/2) * 288 * 12
= 1728
Hence, the maximum volume of the prism is 1728 cubic centimeters.
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a surface of a reservoir has the shape of an isosceles triangle with a length of 100 m and a width of 100 m, as shown below. any vertical cross-section (as shown in blue below) is a trapezoid whose bottom side and height are both a half the length of the top side. find the volume of the reservoir.
The volume of the reservoir with an isosceles triangle surface and trapezoid cross-sections is 375,000 cubic meters.
To find the volume of the reservoir with an isosceles triangle surface and trapezoid cross-sections, we'll follow these steps:
1. Identify the dimensions of the trapezoid: Given that the top side (base) of the trapezoid is 100 m, its bottom side (smaller base) will be half of that, so 50 m. Similarly, the height of the trapezoid is half the length of the top side, so 50 m.
2. Calculate the area of the trapezoid cross-section: To find the area of a trapezoid, we use the formula A = (1/2)(b1 + b2)h, where A is the area, b1 and b2 are the lengths of the two bases, and h is the height. In our case, A = (1/2)(100 + 50)(50) = (1/2)(150)(50) = 3750 square meters.
3. Determine the length of the reservoir: The length of the reservoir is given as 100 m.
4. Calculate the volume of the reservoir: Finally, to find the volume, we multiply the area of the trapezoid cross-section by the length of the reservoir. V = A * L = 3750 * 100 = 375,000 cubic meters.
So, the volume of the reservoir with an isosceles triangle surface and trapezoid cross-sections is 375,000 cubic meters.
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There are 5 positions available in the new school. Of the applicant, 12 are men and 8 are women. In how many ways can 3 men and 2 women be chosen if they are equally considered?
There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting
What is the multiplication principle of countingThe multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.
To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).
where n is the total number of men and r is the number of men chosen
so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.
Similarly, we evaluate the number of ways to choose 2 women from the 8 women
as = ⁸C₂ = 14
Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.
220 x 14 = 3080
Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting
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PLS HELP WILL MARK BRAINLIEST
Answer:
90-degree angle
as you can see, there is clearly a 90 degree right next to it, but that doesn't tell us anything, because it has symmetry with the 3 right next to it, all that is different is that it has a longer x-axis, which will not affect our answer.
Hope this helps!
In an optical fibre, the power drops by a factor of 10 approximately every 30 km. If the transmit power is 0. 35 W, how far will a signal be transmitted before the power is attenuated to 350 μW?
Answer:
30000 kmStep-by-step explanation:
First convert the transmit power into μW, considering 1 W = 1000000 μW:
0.35 W = 0.35*1000000 μW = 350000 μWFind how many factors of 10 the power dropped:
350000 / 350 = 1000Find the distance:
1000*30 km = 30000 kmSolve -6x + 18 > -30
A. x < 2
B. x < 8
C. x > 8
D. x > 2
Answer: x < 8
P/s: if -1.x > -a => x < -a/-1
Ok done. Thank to me >:3
\( - 6x \: + \: 18 \: > \: - 30\)
We move the term "+18" to clear the unknown of the inequality.\( - 6x \: > \: - 30 \: - \: 18\)
We calculate the remainder.\( - 6x \: > \: - 48\)
We divide both sides of the inequality by "-6" to solve for the unknown.\( \boxed{x \: < \: 8}\)
Answer:\( \text{D.} \: \boxed{ \bold{x \: < \: 8}}\)
MissSpanishIf f(x) = 3x - 4 and g(x) = x + 5, then find f(x) - g(x).
Answer:
1/2
Step-by-step explanation:
Answer:
X=9/2
Step-by-step explanation:
3x-4=x+5 add like terms
2x=9 divide both sides by 2
x=9/2
Hope this helps
Help pls I’m begging pla
a professor has two lightbulbs in her garage. when both are burned out, they are replaced, and the next day starts with two working lightbulbs. suppose when both are working, one of the two will go out with probability 0.03, and we cannot lose both lightbulbs on the same day. however, when only on lightbulb works, it will burn out with probability 0.07. what is the long-run fraction of time that there is exactly one lightbulb working?
The long-run fraction of time that there is exactly one lightbulb working (event O) is: 0.228.
Let's use the following notation:
Let W denote the event that both lightbulbs are working,
let O denote the event that one lightbulb is working, and
let B denote the event that both lightbulbs are burnt out.
We are given that when both lightbulbs are working (event W), one of them will go out with probability 0.03.
Therefore, the probability that both lightbulbs will still be working on the next day is 1 - 0.03 = 0.97.
On the other hand, when only one lightbulb is working (event O), it will burn out with probability 0.07, and the other lightbulb is already burnt out.
Hence, the probability of moving from O to B is 1.
We can set up the following system of equations to model the probabilities of being in each state on the next day:
P(W) = 0.97P(W) + 0.5P(O)
P(O) = 0.03P(W) + 0.93P(O) + 1P(B)
P(B) = 0.07P(O)
Note that in the first equation, we use 0.97 because the probability of staying in W is 0.97, and the probability of moving to O is 0.5 (because there are two ways for one of the lightbulbs to go out).
Simplifying the system of equations, we get:
0.03P(W) - 0.5P(O) = 0
-0.03P(W) + 0.07P(O) - 1P(B) = 0
0P(W) - 0.07P(O) + 1P(B) = 0
Solving for P(O), we get:
P(O) = 0.3P(W)
Substituting this into the second equation, we get:
-0.03P(W) + 0.07(0.3P(W)) - P(B) = 0
Simplifying, we get:
P(B) = 0.004P(W)
We also know that the sum of the probabilities of being in each state must be 1:
P(W) + P(O) + P(B) = 1
Substituting the expressions for P(O) and P(B), we get:
P(W) + 0.3P(W) + 0.004P(W) = 1
Solving for P(W), we get:
P(W) = 0.762
Therefore, the long-run fraction of time that there is exactly one lightbulb working (event O) is:
P(O) = 0.3P(W) = 0.228.
Approximately 22.8% of the time, there will be exactly one lightbulb working.
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Find the power set for the following sets (Write 3 examples of each)
a) Two sets A & B both having any 2 elements
b) Two sets A & B both having any 3 elements
c) Two sets A & B both having any 4 elements
Given statement solution is :- a) Power set for two sets A and B with any 2 elements:
Set A: {1, 2}, Set B: {3, 4}
Power set of A: {{}, {1}, {2}, {1, 2}}
Power set of B: {{}, {3}, {4}, {3, 4}}
b) Power set for two sets A and B with any 3 elements:
Set A: {1, 2, 3}, Set B: {4, 5, 6}
Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}
c) Power set for two sets A and B with any 4 elements:
Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}
Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},
a) Power set for two sets A and B with any 2 elements:
Set A: {1, 2}, Set B: {3, 4}
Power set of A: {{}, {1}, {2}, {1, 2}}
Power set of B: {{}, {3}, {4}, {3, 4}}
Set A: {apple, banana}, Set B: {cat, dog}
Power set of A: {{}, {apple}, {banana}, {apple, banana}}
Power set of B: {{}, {cat}, {dog}, {cat, dog}}
Set A: {red, blue}, Set B: {circle, square}
Power set of A: {{}, {red}, {blue}, {red, blue}}
Power set of B: {{}, {circle}, {square}, {circle, square}}
b) Power set for two sets A and B with any 3 elements:
Set A: {1, 2, 3}, Set B: {4, 5, 6}
Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}
Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}
Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}
Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}
Set A: {red, blue, green}, Set B: {circle, square, triangle}
Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}
Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}
c) Power set for two sets A and B with any 4 elements:
Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}
Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},
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Use the given data set to complete parts (a) through (c) below. (Use α=0.05.)
1. The value of the linear correlation coefficient r is given as 0.8159. The correct option is a. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables
2. The scatterplot reveals a distinct pattern that is not a straight-line pattern.
What is the linear correlation coefficient?This is the data that we get when we try to get the existing relationship that is in existence between the variables that are used in a regression equation.
The value of r was calculated using a statistical tool online. The graph showed us it was not a straight line. The value of the r = 0.8159
The results of the test is in the attachment
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one morning, ms. simon drove directly from her home to her workplace in 242424 minutes. what was her average speed, in miles per hour, during her drive that morning?
The average speed during her drive that morning would be 43.5 miles/hr.
What is Average Speed?
Calculating average speed involves dividing the whole distance traveled by the total time it took to cover that distance.
Explanation:
Time = 24 min = 0.4 hr
Entire way = 0.6 + 15.4 + 1.4
= 17.4 miles
\(Average \ speed = \frac{Distance}{Time}\\\\Average \ speed = \frac{17.4}{0.4} \\\\Average \ speed = 43.5 miles/hr\)
Hence, The average speed during her drive that morning would be 43.5 miles/hr.
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Write down the sequence then solve
the problem.
On Monday I had 1 cup of tea, Tuesday I had 3
cups, on Wednesday I have 6 cups and on
Thursday I have 11 cups.
How many cups of tea did I have on Sunday?
1,3
38
Answer:
48.
Step-by-step explanation:
The sequence is
1, 3, 6, 11,
The differences are 2, 3, 5, 8, 12, 17
2nd difference 1 2 3 4 5
So, the next difference is 5+3 = 8 (Friday) so on that day you had 11+8 = 19 cups.
The next 2 differences are 8+4 = 12 and 12 + 5 = 17.
Saturday you had 19+12 = 31.
Sunday you had 31 + 17 = 48.
This question is 15 points and please help me! Each answer is different. Please put it in order and don't scam this is my last points thanks so much!
Answer:
What are all the opions
Step-by-step explanation:
Also I think its
1. communtive, asscotive
2. Disvision Property
3. to the left side ( I think)
Hope this helps and sorry about your points ;-;
a sauce recipe calls for 4 pounds of ground beef and you want to halve it how many ounces of ground beef do you need?
If you want to halve the recipe, you will need 32 ounces of ground beef. We can find it by multiplying.
To determine the amount of ground beef needed when halving the recipe, we need to convert pounds to ounces. There are 16 ounces in 1 pound.
Given that the original recipe calls for 4 pounds of ground beef, we can calculate the amount needed when halving the recipe by dividing it by 2.
Amount needed when halving = 4 pounds / 2 = 2 pounds.
To convert 2 pounds to ounces, we multiply it by 16:
2 pounds * 16 ounces/pound = 32 ounces.
Therefore, when you halve the recipe, you will need 32 ounces of ground beef.
In conclusion, to make half of the original recipe that calls for 4 pounds of ground beef, you will need 32 ounces of ground beef.
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The ratio 2. 5 metres to 60 centimetres can be written in the from 1:n. Find the value of n
The given ratio is 2.5 meters to 60 centimeters, and we need to express it in the form 1:n. The value of n is 4.
To find the value of n, we can start by converting both measurements to the same unit. First, let's convert 2.5 meters to centimeters. Since there are 100 centimeters in 1 meter, we can multiply 2.5 by 100 to get 250 centimeters. Now we have the ratio 250 centimeters to 60 centimeters.
To express it in the form 1:n, we need to find a common factor to divide both numbers by. In this case, we can divide both 250 and 60 by 10 to simplify the ratio. This gives us the ratio 25 centimeters to 6 centimeters. Finally, we can express this simplified ratio as 1:n. Since both numbers are divisible by 6, we can divide both 25 and 6 by 6 to get the ratio 4 centimeters to 1 centimeter.
Therefore, the value of n is 4.
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PT.2 OF MY HW IT IS UNIT RATE PLEASE HELP!
Answer:
Car 1
Step-by-step explanation:
Answer: Car 1
Step-by-step explanation:
Notice that the speed of each car is the slope of the line that represents its average speed.
Since the graph of the speed of Car 1 passes through (0,0) and (4,256), we get that its slope is:
256/4 = 64
Therefore the average speed of Car 1 is 64 mi/h.
Now, since the equation that represents the average speed of Car 2 is in slope-intercept form, we get that its slope is 55.
Therefore the average speed of Car 2 is 55 mi/h.
Answer: Car 1.
FInd the 17th term of the following sequence,2,4,6,8,16
the 17th term of the following sequence which is an AP 2,4,6,8,16 is 34.
The difference between any two successive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers.
The given sequence is an AP
as the difference between two number is same,
d= 2
a=2
n=number of terms=17
Now, by using the formula
nth term=a+(n-1) x d
Now, put the values in the formula
nth term=2+(17-1) x 2
nth term=2+16 x 2
nth term=2+32
nth term=34
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what should a good residual plot look like if the regression line fits the data well?
A good residual plot should have the points randomly scattered around the horizontal line with no discernible pattern.
This indicates that the model is well fit to the data. The residuals should also be equally distributed on either side of the horizontal line. This can be seen as the sum of the residuals being equal to 0, or mathematically expressed as the sum of the residuals (e) being equal to 0, where \(e = y - ŷ\), where y is the observed value and ŷ is the predicted value. The equation can be expressed as Σe=0.
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Spud has a problem. He knows that the roots of a quadratic function are x=3+4i and x=3−4i, but in order to get credit for the problem he was supposed to have written down the original equation. Unfortunately, he lost the paper with the original equation on it. Luckily, his friends are full of advice.
B:Hugo says, “No, no, no. You can do it that way, but that’s too complicated. I think you just start with x=3+4i and work backwards. So x–3=4i, then, hmmm… Yeah, that’ll work.” Try Hugo’s method.
Answer:
x² -6x +22 = 0
Step-by-step explanation:
You want to write the quadratic equation that has roots x = 3±4i, starting from x -3 = ±4i.
QuadraticThe next step would be to square both sides of the equation:
(x -3)² = (±4i)²
(x -3)² = 16i² = -16
(x -3)² +16 = 0 . . . . . . add 16
x² -6x +22 = 0 . . . . . expand the square