hi,
a point is given ( x; y)
standar line equation is : y = ax+b
So with (3;5) and (8;15) we have :
3a+b = 5
8a+b = 15
so :
8a+b - ( 3a +b) = 15 -5
8a +b -3a -b = 10
8a-3a = 10
5a = 10
a = 10/5
a = 2
if a = 2 so 3*2 +b = 5
6+b = 5
b = 5-6
b = -1
so let check :
8*2 + (-1) = 16 -1 = 15
and 3*2 -1 = 6-1 = 5
coordonnate works for both point, so line is y = 2x -1
6 sin θ=5 to the nearest 0.1°
The value of the equation 6 sinθ=5 for θ is 56.4 degrees
How to evaluate the equationFrom the question, we have the following parameters that can be used in our computation:
6 sinθ=5
Express the equation properly
So, we have the following representation
6 sin(θ) = 5
Divide both sides of the equation by 6
This gives
sin(θ) = 5/6
Evaluate the quotient
sin(θ) = 0.833
Take the arc sin of both sides
θ = sin⁻¹(0.833)
Evaluate
θ = 56.4
Hence, the value of the equation for θ is 56.4 degrees
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Complete question
Approximate θ in the equation, to the nearest 0.1 degrees
6 sin(θ) = 5
PLEASE HELP
The area of a rectangle in square inches is
shown below. If the length of the rectangle is
x - 4 inches, write an expression to represent
the width of the rectangle.
Your answer
A = 5x² 18x - 8
1 points
Answer:
-4x² + 14x + 8Step-by-step explanation:
It's given that, The area of a rectangle in square inches is 5x² - 18x - 8 and the length of the rectangle is x - 4 inches.
Let the width of the rectangle be x inchez
We know that area of Rectangle is calculated by,
[tex]:\implies[/tex] Length × width = area
Substituting the values we get,
[tex]:\implies[/tex] (x - 4)(x) = 5x² - 18x - 8
[tex]:\implies[/tex] x² - 4x = 5x² - 18x - 8
[tex]:\implies[/tex] x² - 5x² - 4x + 18x = -8
[tex]:\implies[/tex] -4x² + 14x = -8
[tex]:\implies[/tex] -4x² + 14x + 8 = 0
Hence, This is the required expression which represent the width of the rectangle.
Given f(x) = x³ - 6x + k, and the remainder when f(x) is divided by x - 1 is 14, then what is the value of k?
Answer: 19
Step-by-step explanation: The best way is to set this up with synthetic division (as the attached image).
Hope this helps!
Which graph shows the solution to the inequality?
The solutions of the given inequality is: x ≥ -1 or x ≤ -5, the correct number line is 2nd.
To solve the inequality |x + 3| ≥ 2, we need to consider two cases:
Case 1: (x + 3) ≥ 2
If x + 3 is greater than or equal to 2, then the absolute value of (x + 3) will also be greater than or equal to 2. Solving this case:
x + 3 ≥ 2
x ≥ 2 - 3
x ≥ -1
So, for this case, the solution is x ≥ -1.
Case 2: -(x + 3) ≥ 2
If -(x + 3) is greater than or equal to 2, then the opposite of (x + 3) will also be greater than or equal to 2. Solving this case:
-(x + 3) ≥ 2
x + 3 ≤ -2
x ≤ -2 - 3
x ≤ -5
So, for this case, the solution is x ≤ -5.
Combining the solutions from both cases, we have the final solution:
x ≥ -1 or x ≤ -5
Hence the number line showing the given inequality is 2nd.
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Identify the unit rate in each graph. Then, order the graphs by unit rate, from least to greatest.
The required rates are: Unit rate of graph K = 3, Unit rate of graph P = 0.5, and Unit rate of graph F = 1. The order from lower to greater is Graph P, graph F, graph K
How did we determine their unit rates?Step 1: As we know that Unit Rate
Step 2: Notice that the in graph K line passes through the point (1,3)
Step 3: (1,3)
It means the value of function is 3 when x= 1
Step 4: So the unit rate of graph K is, 3/1
Step 5: Simplify the expression.
3/1 = 3
Step 6: Similarly we can see that the graph P have the point (2, 1)
Step 7: So the unit rate of graph P will be 1/2
Step 8: Simplify the expression.
1/2 = 0.5
Step 9: The graph F have point (1, 1) so it have unit rate of 1/1
Step 10: Simplify the expression.
1/1 = 1
Step 11: So we have unit rate of graph K = 3, F= 1 and graph P = 0.5
Step 12: Putting them in least to greater order as,
0.5, 1, 3
It follows that;
graph P, graph F, graph K
Therefore, the required answer is,
Unit rate of graph K = 3
Unit rate of graph P = 0.5
Unit rate of graph F = 1
And the order from lower to greater is, Graph P, graph F, graph K
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workers can finish the job in days. For the first days, only workers worked on the job. Then for the next days more workers joined them. To finish the job, more workers joined them. After how many days was the whole job done?
In 20 days was the whole job done.
Let efficiency of each worker is 1 unit / day .
So, Total work = 10 x 1 x 15 = 150 units .
Now, in first 5 days 6 worker completes
= 5 x 6 x 1 = 30 units .
and, in next 3 days 8 workers completes
= 3 x 8 x 1 = 24 units .
Now, 4 more workers joined then total workers are = 12 workers .
So, amount of work left = 150 - 30 - 24 = 96 unit
Thus, the time taken by 12 workers to complete remaining work
= 96/12
= 8 days .
So, the Whole job was done in = 5 + 3 + 12 = 20 days
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The question attaches here seems to incomplete the complete question is
10 workers can finish the job in 15 days. For the first 5 days, only 6 workers worked on the job. Then for the next 3 days 2 more workers joined them. To finish the job, 4 more workers joined them. After how many days was the whole job done?
Which animal swims at a top speed of about 0.33 mile per minute? Explain how you found your answer
The animal that swims at a top speed of 0. 33 miles per minute would be the Dolphin .
How to find the animal ?To find the animal that swims at a top speed of 0. 33 miles per minute, you need to convert their top speeds in miles per hour to miles per minute.
For every 1 mile per hour, the equivalent in minutes is 0.0166667 miles per minute.
Speed of Swordfish is:
= 60 mph x 0.0166667
= 1 mile per minute
Speed of Tuna :
= 45 mph x 0.0166667
= 0. 75 miles per minute
Dolphin :
= 20 mph x 0.0166667
= 0. 33 miles a minute
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.
Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.
To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.
Let's start with the first equation:
2 + x = 5
Subtract 2 from both sides:
x = 3
Now let's move on to the second equation:
x + 1 = 4
Subtract 1 from both sides:
x = 3
Notice that we got the same value of x for both equations, so they are equivalent.
Next, let's look at the third equation:
9 + x = 6
Subtract 9 from both sides:
x = -3
Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.
Now, let's move on to the fourth equation:
x + (-4) = 7
Add 4 to both sides:
x = 11
This value of x is also different from the first two equations, so it is not equivalent to them.
Finally, let's look at the fifth equation:
-5 + x = -2
Add 5 to both sides:
x = 3
Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.
So, correct options are A, B and E.
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Complete question is:
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
- 5 + x = - 2
the temperatures at midday on march 1st in five cities are shown in the bar chart below. What is the difference in temperature between rome and munich?
The difference in temperature between Rome and Munich is given as follows:
6ºC.
How to obtain the difference in temperatures?The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.
The bar graph in the context of this problem gives the temperature for each town.
From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:
Rome: 11 ºC.Munich: 5 ºC.Hence the difference in temperature between Rome and Munich is given as follows:
11 - 5 = 6ºC.
Missing InformationThe graph is given by the image presented at the end of the answer.
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Part A: Jan INCORRECTLY
finds the surface area of the
cone using the following
work. Explain Jan's error
and find the
correct volume AND
surface area of the cone.
The volume of the cone is 2786.2 cubic meters and the surface area of the cone is 1229.51 square meters.
Given the height (h) of a cone as 22 m and the diameter (d) of its circular base as 22 m, we can find the radius (r) of the circular base using the formula:
r = d/2 = 22/2 = 11 m
Here, Jan made a mistake in the work of the surface area of the cone because she used the wrong value of slant height (l=22) in the calculation.
The volume (V) of a cone is given by the formula:
V = (1/3)πr²h
Substituting the values of r and h, we get:
V = (1/3)π(11)²(22)
V = 2786.2 cubic meters
The surface area (A) of a cone is given by the formula:
A = πr(r + l)
here l is the slant height of the cone, which can be found using the Pythagorean theorem:
l = √(r² + h²)
l = √(11² + 22²)
l = √(605)
l = 24.6
Substituting the values of r and l, we get:
A = π(11)(11 + 24.6)
A ≈ 1229.51 square meters
Therefore, the volume of the cone is 2786.2 cubic meters and the surface area of the cone is 1229.51 square meters.
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Since my uncles farmyeard apperas to be overrun with gos and chickens i asked him hom many of each did he have he responded that his dog and chicked had a total of 148 legs and 60 heads. hime mmay of each does he have
There are 14 dogs and 46 chickens in the farmyard.
The supposition that there are d dogs and c chickens.
Each chicken has two legs, but each dog has four.
Consequently, the total number of legs may be written as follows:
4d + 2c
Since we are aware that there are 148 legs in total, we can construct the following equation:
4d + 2c = 148
We may create another equation since we know that there are a total of 60 heads (dogs and chickens):
d + c = 60
Now that we have two equations with two variables, we may answer them both at the same time.
2d + 2c = 120 is the result of multiplying the second equation by two.
When we deduct this from the first equation, we obtain 2d = 28.
So, d = 14.
Reintroducing this into the second equation, we get:
14 + c = 60
So, c = 46.
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A total of 605 tickets were sold for the school play. They were either adult tickets or student tickets. There were 55 more student tickets sold than adult tickets. How many adult tickets were sold?
Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?
The amount of poster board left over will be 1275 square inches, the equation used is A = (b₁ + b₂)h/2.
To calculate the amount of poster board that will be left over after Ole cuts out a piece of poster board that is the same size as the window,
we need to find the area of the trapezoid window and subtract it from the area of the poster board.
The formula to find the area of a trapezoid is A = (b₁ + b₂)h/2, where b₁ and b₂ are the lengths of the parallel sides and h is the height.
Let's assume that the length of the top parallel side of the trapezoid is 20 inches, the length of the bottom parallel side is 10 inches, and the height is 15 inches.
Using the formula, we get A = (20 + 10) x 15 / 2 = 225 square inches. This is the area of the window.
To find the area of the poster board, we multiply the length and width, which gives 25 x 60 = 1500 square inches.
Finally, we subtract the area of the window from the area of the poster board using the equation:
1500 - 225 = 1275 square inches.
Therefore, the amount of poster board left over will be 1275 square inches.
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The complete question is
Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?
You can afford a $400 per month car payment. You've found a 5 year loan at 2% interest. How big of a loan can you afford?
The loan's Present Value for which you can afford a $400 monthly payment for a car for 5 years at 2% interest should be as big as $22,820.94.
What is the present value?The present value is the discounted monthly payments at an interest rate for a period.
The present value can be determined using an online finance calculator as follows.
N (# of periods) = 60 months (5 years x 12)
I/Y (Interest per year) = 2%
PMT (Periodic Payment) = $400
FV (Future Value) = $0
Results:
Loan size (Present Value) = $22,820.94
The sum of all periodic payments = $24,000.00
Total Interest = $1,179.06
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Please help me with this statistics question. Photo attached
a) The data in the above table about the statistics class asked the city where they live are b) Quantitative and Discrete.
b) The completion of the frequency distribution for the data is as follows:
Class Frequency
Fort Pierce 7
Port St. Lucie 6
Vero Beach 7
Sebastian 4
Okeechobee 6
Total 30
c) The completion of relative frequency and percentage distribution for the data is as follows:
Class Frequency Relative Frequency Percentage
Fort Pierce 7 0.233 23.3%
Port St. Lucie 6 0.200 20.0%
Vero Beach 7 0.233 23.3%
Sebastian 4 0.133 13.3%
Okeechobee 6 0.200 20.0%
Total 30
How the relative frequencies and percentages are computed:Class Frequency Relative Frequency Percentage
Fort Pierce 7 0.233 (7/30) 23.33% (7/30 x100)
Port St. Lucie 6 0.200 (6/30) 20.00% (6/30 x100)
Vero Beach 7 0.233 (7/30) 23.33% (7/30 x100)
Sebastian 4 0.133 (4/30) 13.33% (4/30 x100)
Okeechobee 6 0.200 (6/30) 20.00% (6/30 x100)
Total 30
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Answer Options for a):a) Time-Series
b) Quantitative and Discrete
c) Cross-Sectional Qualitative
d) Quantitative and Continuous
jasper is picking out his clothes for school he can wear a t shirt polo or sweat shirt as a top for pants khakis jeans sweat pants corduroys and short he can wear boots or tennis shoes or sandals jasper also need a jacket he has a ski and a rain coat and a wool coat how many combinations did jasper pick in total
Jasper has a total of 135 possible combinations for his outfit.
To calculate the total number of combinations that Jasper can pick for his outfit, we need to multiply the number of options for each category: tops, pants, shoes, and jackets.
For tops, Jasper has three options: t-shirt, polo, or sweatshirt.
For pants, he has five options: khakis, jeans, sweatpants, corduroys, or shorts.
For shoes, he has three options: boots, tennis shoes, or sandals.
For jackets, he has three options: ski coat, raincoat, or wool coat.
To calculate the total number of combinations, we multiply the number of options for each category:
3 (tops) × 5 (pants) × 3 (shoes) × 3 (jackets) = 135
Jasper has a total of 135 possible combinations for his outfit.
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What is the first step when factoring polynomials?
Answer:
Step-by-step explanation:
Step 1: Group the first two terms together and then the last two terms together. Step 2: Factor out a GCF from each separate binomial. Step 3: Factor out the common binomial. Note that if we multiply our answer out, we do get the original polynomial.
Answer: To find a 2 numbers that multiply to the value of C and Add to the value of b.
Step-by-step explanation: They Have to multiply to C and add to B and after that you can just continue simplifying the polynomial.
The carrying capacity of a drain pipe is directly proportional to the area of its cross section.If cylindrical pipe drain can carry 36L/sec,determine the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second .
Step-by-step explanation:
x and y are directly proportional means that
y = kx
y grows with the same factor k applied to x.
the area of a circle (the cross section of a cylindrical pipe) is
pi × r²
r being the radius (which is half of the diameter).
so, the area in terms of the diameter is
pi × (d/2)² = pi × d²/4
so, we know
36 correlates to pi × (d small)²/4
60 correlates to pi × (d large)²/4
therefore (directly proportional),
d small² = 36×4/pi
d small = 12/sqrt(pi)
d large² = 60×4/pi
d large = sqrt(4×15×4/pi) = 4×sqrt(15/pi)
the difference between large and small diameter (increase from small to large) is then
4×sqrt(15/pi) - 12/sqrt(pi)
d small = 100%
1% = 100%/100 = 12/sqrt(pi) / 100 = 12/(100sqrt(pi))
the % of the diameter increase is then
increase/1% =
(4×sqrt(15/pi) - 12/sqrt(pi)) / 12/(100sqrt(pi)) =
= (400sqrt(pi)×sqrt(15/pi) - 1200sqrt(pi)/sqrt(pi)) / 12 =
= (400×sqrt(15) - 1200) / 12 = 100×sqrt(15)/3 - 100 =
= 100×(sqrt(15)/3 - 1) = 29.09944487...% ≈ 29.1%
the diameter has to increase by about 29.1%, so that the pipe can carry 60 liters per second.
please consider : only the area of the cross section and the carrying capacity are directly proportional.
the diameter of the cross section and the area of the cross section are NOT directly proportional.
they have the pi×(d/2)² relationship.
and so, while the capacity and the cycle area both increase by the same factor, the impact on the diameter (or radius) is different.
so, for capacity and area we have
60 = k×36
k = 60/36 = 5/3 = 1.66666666...
and therefore both increase by 66.66666...%.
but because of the square relation between diameter and cross section area, the diameter only increases by 29.1%.
How many turning points are in the graph of the polynomial function?
4 turning points
5 turning points
6 turning points
7 turning points
Wendy, who is single, worked her way through college earning an annual taxable income of $12,000 in 2022. Her first job after graduation will give her a taxable income of $35,000 per year. Using the tax table, what is her marginal tax bracket in 2022 while she is still in school and what will it be when she graduates?
A. 0 percent now, 10 percent when she graduates.
B. 10 percent now and when she graduates.
C. 0 percent now and 10 percent when she graduates.
D. 12 percent now, 12 percent when she graduates.
Wendy's marginal tax brackets in 2022 while she is still in school is 12 percent and it will be also 12 percent when she graduates.
Hence the correct option is (D).
Given that Wendy is Single.
So the effective taxable income regime will be which is on the second column.
It is given that at her school days she earns a taxable income of $ 12,000.
So $12000 falls in the slab of $ 10276 - $ 41775.
So the tax rate for her in her school days is 12%.
When she will graduates the taxable per year income will be $35,000.
Clearly, $35,000 also falls into the slab of $ 10276 - $ 41775.
So the tax rate for her when she will graduate will be same 12 percent.
Hence the correct option will be (D).
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Graph by completing the square x2-2x+y2+6y-6=0
The equation in the standard form of a circle and find the centre and radius:
(x - 1)²/31 + (y + 3)²/31/3 = 1
To graph by completing the square, we need to rearrange the equation so that it has the form:
(x - h)² + (y - k)² = r²
Starting with x² - 2x + y² + 6y - 6 = 0:
First, we can factor out a 2 from the x terms and a 6 from the y terms:
2(x² - 2x) + 6(y² + 6y) - 6 = 0
Next, we need to complete the square for the x and y terms:
2(x² - 2x + 1) + 6(y² + 6y + 9) - 6 = 2(1) + 6(9)
Simplifying, we get:
2(x - 1)² + 6(y + 3)² = 62
Now we can rewrite the equation in the standard form of a circle and find the centre and radius:
(x - 1)²/31 + (y + 3)²/31/3 = 1
The centre of the circle is (1, -3), and the radius is √(31/3).
The graph is attached with the answer below.
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From a point X, the bearing of a flag pole is 280⁰, from another point Y due south of X the bearing of the flag pole is 330⁰ . if the angle of elevation of the top of the flag pole from Y is 60⁰ and the distance (X,Y) is 92km . Calculate how far Y is from the flag pole
Answer: 37km
Step-by-step explanation:
Your math teacher owns 3 pairs of pants and 3 pairs of shoes. He owns a pair of gray pants, green pants, and blue pants. He owns black shoes, brown shoes, and tan shoes. If he randomly chooses one pair of pants and one pair of shoes, what is the sample space of possible combinations of pants and shoes that he could wear on a typical school day?
Answer:
The sample space of possible combinations of pants and shoes for the math teacher is 9. These combinations include gray pants with black, brown, or tan shoes, green pants with black, brown, or tan shoes, and blue pants with black, brown, or tan shoes.
Hope its helpful
you will get 10 points for each question and help
The probability is very high and the event is very likely to occur.
option B.
What is the explanation for the probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
If the probability of a rolling a number greater than 1 on a six sided cube die is 5/6, it implies that the chances of obtaining a number greater than 1 is very high.
We will convert 5/6 to percentage to see the actual value of 5/6.
5/6 x 100%
= 83.33 %
So the value of this probability is very high and the event is very likely to occur.
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A and B are two cylinders that are mathematically similar.
The area of the cross-section
of cylinder A is 18 cm².
Work out the volume of cylinder B.
Optional working
+
18 cm²
A
Answ cm³
5 cm
B
10 cm
The volume of cylinder B can be calculated using the concept of similarity between the cylinders and the relationship between their areas and volumes. Therefore, the volume of cylinder B is approximately 135.346 cm³.
Given that cylinders A and B are mathematically similar, we can establish a ratio between their corresponding measurements. In this case, we are given the area of the cross-section of cylinder A, which is 18 cm², and the dimensions of cylinder B, which has a height of 10 cm and an unknown radius.
To find the volume of cylinder B, we need to determine the corresponding measurements of its cross-section. Since the cylinders are similar, the ratio of their areas is equal to the square of the ratio of their corresponding linear measurements.
Let's assume that the radius of cylinder B is 'r'. Since the height of cylinder B is given as 10 cm, we can calculate the area of its cross-section using the formula for the area of a circle: A = πr².
The ratio of the areas of the cross-sections of cylinders A and B can be expressed as (Area of A) / (Area of B) = 18 / (πr²).
Since the height of cylinder B is twice that of cylinder A (10 cm compared to 5 cm), the ratio of their corresponding linear measurements is 2:1.
Therefore, the ratio of the areas is (2:1)² = 4:1.
Setting up the equation, we have 18 / (πr²) = 4/1.
By rearranging the equation, we can solve for the radius 'r' of cylinder B:
18 = (4/1) * (πr²)
18 = 4πr²
r² = 18 / (4π)
r² = 4.545
r ≈ 2.132 cm
Now that we have the radius of cylinder B, we can calculate its volume using the formula for the volume of a cylinder: V = πr²h.
V = π * (2.132)² * 10
V ≈ 135.346 cm³
Therefore, the volume of cylinder B is approximately 135.346 cm³.
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help asap!!!
The tables represent hat sizes measured in inches for two baseball teams.
Cougars
21.5 24.5 22
21 22 23
22.5 24 21
22 23.5 22
23.5 22 24
Panthers
22.5 20 23.5
21 24 22
20.5 21.5 23
23 22.5 21
24 22 24.5
Which team has the largest overall size hat for their players? Determine the best measure of center to compare and explain your answer.
Panthers; they have a larger median value of 22.5 inches
Cougars; they have a larger median value of 22 inches
Panthers; they have a larger mean value of about 22 inches
Cougars; they have a larger mean value of about 22.6 inches
The correct answer is, Cougars; they have a larger median value of 22 inches.
Calculating the median and mean for each data set, we get:
Cougars:
Median = 22 inches
Mean = 22.3 inches
Panthers:
Median = 22.5 inches
Mean = 22.2 inches
Since the median of the Cougars data set is larger than the median of the Panthers data set, we can conclude that the Cougars have the largest overall size hat for their players.
Therefore, the correct answer is, Cougars; they have a larger median value of 22 inches.
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Solution for
Y= x+3
Y= 3x+1
Starting with the two equations:
Y = x + 3 (1)
Y = 3x + 1 (2)
We can solve for x and y by equating equation (1) and (2) and solving for x.
x + 3 = 3x + 1
2x = 2
x = 1
Now we can substitute x = 1 into either equation (1) or (2) to solve for y.
Using equation (1):
Y = x + 3
Y = 1 + 3
Y = 4
Therefore, the solution for the system of equations is:
x = 1, y = 4
x-y=-1
x=-9
solution problem i am having trouble trying to solve or figure out
The solution to the System of equations is x = -9 and y = 8
We have the equation x - y = -1 and the equation x = -9. We can use the second equation to substitute the value of x in the first equation and solve for y.
Given x = -9, we substitute this value into the first equation:
(-9) - y = -1
Simplifying, we have:
-9 + y = -1
To isolate y, we can add 9 to both sides of the equation:
-9 + 9 + y = -1 + 9
This gives us:
y = 8
Therefore, the solution to the system of equations is x = -9 and y = 8.
We can check this solution by substituting the values of x and y back into the original equations:
Equation 1: x - y = -1
Substituting x = -9 and y = 8:
-9 - 8 = -1
Simplifying, we have:
-17 = -1
The equation is true, so our solution is valid.It is important to note that the solution provided is derived from the given equations and standard algebraic methods.
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An electrician charges a set fee of $50 for every house call and then charges an
additional hourly rate. One day, the electrician earned a total of $400 for a 5 hour
job. Write an equation for C, in terms of t, representing the total cost of the
electrician's services if the electrician spends t hours at the house working.
Answer: C
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attempt 1 out of 2
The equation that represents the total cost is C = $50 + $70t.
What is the equation that represents the total cost?The total amount earned by the electrician is the sum of the fixed cost and the variable cost.
Total amount earned = fixed cost + variable cost
The fixed cost is the set fee he charges . The variable cost is a function of the additional hourly fee and the number of hours
The equation that represents the the total amount earned when he works for 5 hours is:
$400 = $50 + (5 x v)
$400 = $50 + 5v
$400 - $50 = 5v
$350 = 5v
v = $350 / 5
v = $70
C = $50 + $70t
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Fergus and his best friend went to a movie
and bought popcorn. They split the cost
evenly, each paying $17. How much was the
total cost of the movie and popcorn? If x
equals the total cost, choose the equation
that solves the problem.
O x/2 = 17
Ox-17 = 2
Ox+17 = 2
2x = 17
Answer:
x / 2 = 17
Step-by-step explanation:
Since we're told that there are 2 friends, they split the cost evenly, and they each paid $17 individually, we'd have to use the equation x / 2 = 17 to find the total cost.
If you were to solve, you'd find that the total cost was $34 as 2 * 17 = 34 and 34 / 2 = 17