Adding 5 bonus points to each test grade in Mrs. Matthew's class will increase the mean, median, and mode of the scores by 5 points each.
Explanation:The addition of 5 bonus points to each test grade will affect the mean, median, and mode in the following ways:
Mean: The mean is calculated by adding all the scores together and dividing by the total number of scores. If every student gets an additional 5 points, it would effectively increase the mean by 5 points.Median: The median is the middle score when all scores are listed in numerical order. If you add 5 points to each test grade, the median will also increase by 5 points because each score has increased by the same amount.Mode: The mode is the score that appears most frequently. If every score increases by 5, the mode will also increase by 5 points.So, in conclusion, adding 5 bonus points to each student's test score will raise the mean, median, and mode of the scores by 5 points each.
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I need help with this please
The ordered pair that represents the week before is given as follows:
A. (1,7).
How to define the ordered pair?The general format of an ordered pair is given as follows:
(x,y).
In which the coordinates are given as follows:
x is the x-coordinate.y is the y-coordinate.The meaning of each coordinate in this problem is given as follows:
x: chores.y: homework.For the current week, the ordered pair is given as follows:
(5,3).
For the previous week, the total number of hours was the same, that is, 5 + 3 = 8, however with x = 1 and y = 8 - 1 = 7, as only one hour was spent on chores.
Thus option A is correct.
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What fraction is a multiple of 1/9. 3/9 4/9 9/12 9/10 2/9 or 9/9
To determine which of the given fractions is a multiple of 1/9, we need to check if each fraction can be written as the product of 1/9 and another integer.
What fraction is a multiple of 1/9. 3/9 4/9 9/12 9/10 2/9 or 9/9?3/9 = 1/3, which is not a multiple of 1/9
4/9 cannot be simplified further and is therefore a multiple of 1/9
9/12 can be simplified to 3/4, which is not a multiple of 1/9
9/10 cannot be simplified further and is therefore a multiple of 1/9
2/9 cannot be simplified further and is therefore a multiple of 1/9
9/9 = 1, which is not a multiple of 1/9
Therefore, the fractions that are multiples of 1/9 are 4/9, 9/10, and 2/9.
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equation of line perpendicular to y = -4x + 3 with point 8, 1
The equation of a line that is perpendicular to the line y = –4x + 3 and passes through the point (8, 1) is y = 1/4(x) - 1
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Since the equation of this line is perpendicular to the line y = –4x + 3, the slope is given by;
Slope, m = -4
m₁ × m₂ = -1
-4 × m₂ = -1
m₂ = -1/-4
Slope, m₂ = 1/4
At data point (8, 1) and a slope of 1/4, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = 1/4(x - 8)
y = 1/4(x) - 1
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in buying ground beef for hamburgers, there are several packages from which to choose, as shown in the table below. If johannes needs 5 pounds of beef for his barbeque, what will he pay?
Johannes will need to pay $8.61 for 5 pounds of ground beef
What is the cost of the beef?Since Johannes needs 5 pounds of ground beef, and the available pounds are 1.5, 2, 3, and 3.75 pounds.
To reduce the cost, he need to select the package with the lowest cost per pound.
The cost per pound for each package is:
Package 1: $5.58 / 1.5
= $3.72 per pound
Package 2: $7.44 / 2
= $3.72 per pound
Package 3: $1.16 / 3
= $0.39 per pound
Package 4: $13.95 / 3.75
= $3.72 per pound
Therefore, the package with the lowest cost per pound is Package 3 and package 2 which will give us 5 pounds
So he can do it as:
$1.16 + $7.44
= $8.6
Or
(1 package of 3 pounds x $0.39 per pound) + (1 package of 2 pounds x $3.72 per pound)
= $1.17 + $7.44
= $8.61
Therefore, Johannes will need to pay $8.61 for 5 pounds of ground beef.
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A 20 litre solution is 85% paint and 15% thinner. Five litres of thinner is added to this solution.
What percentage of the new solution is PAINT?
Answer: 35% of thinner will be in total after the five litres is added so 85%-25% is 60% Therefore ur answer is 60%
Step-by-step explanation:
Please Help Quickly ASAP Hurry Geometry
Questions in the picture
The area of the figure, given the vertices on the coordinate plane, is 14 square units.
How to find the area ?The shoelace formula can be used to find the area. First, find the sum of the products :
= ( - 1 × 2 ) + ( -2 × - 3 ) + ( 4 × 2 ) + ( 4 × 4 ) + (1 × -2)
= 2 + 6 + 8 + 16 - 2
= 26
Then the products of the y coordinate and the x coordinates :
= ( -2 × - 2 ) + (2 × 4 ) + ( - 3 × 4 ) + ( 2 × 1) + ( 4 × -1 )
= - 2
We can then find the absolute value to be:
= | Sum 1 - Sum 2 | = | 26 - (- 2 ) | = | 26 + 2 | = 28
The area is then:
= 28 / 2
= 14 square units
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The usual price of 4 pencils was m Meihua bought 36 pencils and was given a discount of n for each pencil how much did she pay altogether
The total amount that Meihua pays for the 36 pencils is 9M - 36n
How much did she pay altogether?We know that a set of 4 pencils has a price M, then the price of each single pencil is:
P = M/4
And we also know that Meihua got a discount of n in each pencil, so the price that she pays for each pencil is:
P = M/4 - n
Now we know that she buys 36 of these, so the amount that she pays is given by the product:
amount = 36*(M/4 - n)
amount = 9M - 36n
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Riley is saving up to buy a new television. She needs a total of $1,290.78. Riley has saved $200.73 already and earns $83.85 pe
week at her job. How many weeks does Riley need to work to save enough money to buy the new television? PLEASE HELP ASAP EXTRA POINTS!!
Considering the definition of an equation and the way to solve it, the correct answer is option C: Riley need to work 13 weeks to save enough money to buy the new television.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear.
The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Weeks that Riley need to workBeing "x" the number of weeks Riley need to work, and knowing that:
The total amount that Riley requires = $1,290.78The amount of savings Riley already has = $200.73Riley's earnings per week = $83.85the equation in this case is:
200.73 + 83.85x= 1290.78
Solving:
83.85x= 1290.78 - 200.73
83.85x= 1090.05
x= 1090.05 ÷ 83.85
x=13
Finally, Riley need to work 13 weeks.
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2x^2-5x-3=0 what values of x make the equation true?
x=
x=
Which list shows all the factors of 48?
Answer:
Step-by-step explanation:
1,2,3,4,6,8,12,16,24,48
hope i helped
Write a numerical pattern that represents the rule y=x+0 starting with x=0
The pattern represents a straight line that passes through the origin with a slope of 1.
What are linear equations in two variables?The form Ax + By + C = 0 is a two-variable linear equation, where A and B are the coefficients, C is a constant term, and x and y are the two variables, with each having a degree of 1.
The numerical pattern that represents the rule y = x + 0, starting with x = 0, is:
x y
0 0
1 1
2 2
3 3
4 4
... ...
This example shows that when x increments by 1, y additionally increments by 1. Since the rule for y is y = x + 0, we can see that adding 0 to x doesn't change its value, so y is just the same as x. As a result, x and y have a linear relationship with a slope of 1 and a y-intercept of 0.
To put it another way, the pattern is a straight line with a slope of one that runs through the origin.
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PLS HELP ME!!!!!
The line plot has ______ dots plotted on it.
Answer:
Step-by-step explanation:
Okay but seriously though, you would have to write the whole question down.
help me quick and right answers only. algebra
The function that has a range of all real numbers is given as follows:
f(x) = -x + 2.
What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function, that is, all the values assumed by the independent variable x in the function.The range of a function is the set that contains all possible output values of the function, that is, all the values assumed by the dependent variable y in the function.Hence the range for each function in the context of this problem is given as follows:
f(x) = -x + 2 -> all real values.f(x) = -x²: y ≤ 0.f(x) = 2^x + 1: y ≥ 1.More can be learned about domain and range at brainly.com/question/26098895
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2. Janelle Monae obtained a $3,500.00 loan at 8.5% for one year. If the
monthly payments were $285.55, what would the interest amount be in the
first payment?
OA. $297.50
OB. $291.67
OC. $24.79
OD. $35.00
Answer:
Okay, let's think through this step-by-step:
• Janelle Monae obtained a $3,500 loan at 8.5% interest for 1 year.
• 8.5% interest for 1 year = 8.5% of $3,500 = $297.50 in interest
• The loan amount ($3,500) plus interest ($297.50) = $3,797.50 total paid back
•Monthly payments = $3,797.50 / 12 months = $285.55
• So the interest amount in the first payment is $297.50 (calculated above as 8.5% of the $3,500 loan amount)
The choices do not match this:
A. $297.50 - This is the correct choice. This is the interest amount paid over the full loan.
B. $291.67 - This is too low. Calculated interest over 1 year at 8.5% is $297.50.
C. $24.79 - This is way too low. The interest amount due is $297.50 per the working.
D. $35.00 - This is also too low and does not make sense based on the loan details provided.
In summary, to find the interest in just the first payment, we calculate:
Interest over full loan ($297.50) / Number of payments (12) = $24.79
So the interest amount in just the first monthly payment is $24.79.
But the total interest paid over the life of the loan (1 year) is $297.50.
Does this help explain the steps and reasoning? Let me know if any part of the working or explanation is unclear. I can also provide additional examples if needed.
Let me know if you have any other questions!
Step-by-step explanation:
If you have a piece of round cake that has an area of 100 square inches, and you know the piece sweeps out an angle of 50, find the radius of the cake.
If piece of cake has area of 100 in² and sweeps angle of 50°, then the radius of the cake is 15.13 inches.
The area of the piece of cake is given as 100 square inches and
The piece of cake sweeps out an angle of 50 degrees, we have to find the radius of the cake;
We know that "Area" of a sector of a circle is given as : A = (θ/360)πr²,
where A = area of the sector, θ is = angle swept by sector, and r is radius of circle,
We know that area of "piece-of-cake" is = 100 square inches and
The "angle-swept' by the piece is = 50 degrees.
Substituting the values in area of sector formula,
We get,
⇒ 100 = (50/360)πr²,
⇒ r² = (100 × 360)/(50π)
⇒ r ≈ 15.13,
Therefore, the radius of the cake is approximately 15.13 inches.
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Find the inverse of the function
The inverse of the function y-∛x/3 -1 is:
f^-1(x) = 27(x - 1)³How to calculate the inverse of the function?To find the inverse of the given function, we need to express x in terms of y. We can start by swapping the positions of x and y in the original equation:
x - ∛y/3 - 1 = 0Now, we can solve for y in terms of x:
x - ∛y/3 - 1 = 0∛y/3 = x - 1y/27 = (x - 1)^3y = 27(x - 1)^3Therefore, Therefore, the inverse of the given function is f^-1(x) = 27(x-1)³. This means that if we substitute any value of x into the inverse function, we will get the corresponding value of y that makes the original function true. Similarly, if we substitute any value of y into the original function, we will get the corresponding value of x that makes the inverse function true.
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Which ordered pair is not included in a graph of y= 2 x + 5
Mimi chose A (0,0) how did she get that answer? and is she correct.
determina el volumen cuyo diametro es de 8 y su altura de 15 cm
Answer:
3016 centímetros cúbicos.
Step-by-step explanation:
El radio del cilindro es de 8 cm y la altura es de 15 cm. Sustituya 8 por r y 15 por h en la fórmula . Simplifique. Por lo tanto, el volumen del cilindro es de alrededor de 3016 centímetros cúbicos.
A balloon filled with helium gas has a volume of 326 mL at a pressure of 1 atm. The balloon is released and reaches an altitude of 6.5 km, where the pressure is at 0.5 atm. Assuming that the temperature has remained the same, what volume does the gas occupy at the height? Answer in units of mL.
The volume of the gas at the height (i.e 6.5 Km) is 652 mL
Data obtained from the question[tex]\text{Initial volume} \ (\text{V}_1) = \text{326 mL}[/tex][tex]\text{Initial pressure} \ (\text{P}_1) = \text{1 atm}[/tex][tex]\text{Temperature = Constant}[/tex][tex]\text{Final pressure} \ (\text{P}_2) = \text{0.5 atm}[/tex][tex]\bold{Final \ volume \ (V_2) = \ ?}[/tex]The final volume of the gas can be obtained by using the Boyle's law equation as shown below:
[tex]P_1V_1 = P_2V_2[/tex]
[tex]1 \times 326 = 0.5 \times V_2[/tex]
[tex]326 = 0.5 \times V_2[/tex]
Divide both side by 0.5
[tex]V_2 = \dfrac{326}{0.5}[/tex]
[tex]\boxed{\bold{V_2 = 652 \ mL}}[/tex]
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You need a 60% alcohol solution. On hand, you have a 130 mL of a 55% alcohol mixture. You also
have 70% alcohol mixture. How much of the 70% mixture will you need to add to obtain the desired
solution?
Therefore , the solution of the given problem of unitary method comes out to be 70% alcohol combination with 130 mL of the 55% alcohol mixture.
What is a unitary method?Use the tried-and-true fundamental method, the real variables, and any useful information you learn from the broad and specific questions to complete the assignment. Customers may be given another chance to taste expression the products in response. If these improvements don't happen, we'll lose out on significant expression advances in programming understanding.
Here,
Let x represent the required amount (in mL) of the 70% alcohol mixture.
The total amount of alcohol in the final mixture would be equal to the desired 60% alcohol solution since it would be the sum of the alcohol in the 55% alcohol mixture and the alcohol in the 70% alcohol mixture.
=> 0.55 * 130 + 0.70 * x = 0.60 * (130 + x)
=> 71.5 + 0.70x = 78 + 0.60x
=> 0.10x = 6.5
=> x = 65
Therefore, to create a 60% alcohol solution, you would need to combine 65 mL of the 70% alcohol combination with 130 mL of the 55% alcohol mixture.
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the amount of money an hourly employee makes, m for working h hours can be represented by the equation m = 12.80h . what is the constant of propportionality of the equation?
The constant of proportionality of the equation would be = 12.80.
What is constant of proportionality of an equation?The constant of proportionality of an equation is the figure that represents the ratio that exists between two different variables that has direct proportional relationship.
The amount of money made by an employee is directly proportional to the number of hours they worked.
That is m directly proportional to h
The equation = m = k h. where k = 12.80 = constant of proportionality.
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You want to place stone pavers around the edges of your concrete patio. The patio is 12ft wide by 14ft long and each stone paver is 14 inches long. How many stone pavers will you need to go around the patio ( not counting the side against the house which is 14ft long)? Round to the nearest whole number
You will need 38/1.17 ≈ 32.48 stone pavers to go around the patio. Rounding to the nearest whole number, you will need 32 stone pavers.
Explain whole numbers
Whole numbers are a set of numbers that includes all natural numbers (positive integers) and zero. They are represented by the symbol "W" and do not include any fractions or decimals. Whole numbers are used in counting, measuring, and representing quantities of discrete objects or entities, and are a fundamental concept in mathematics.
According to the given information
First, let’s convert the length of the stone paver from inches to feet: 14 inches = 14/12 feet = 1.17 feet.
The perimeter of the patio is (12 + 14 + 12) feet = 38 feet. Since each stone paver is 1.17 feet long, you will need 38/1.17 ≈ 32.48 stone pavers to go around the patio. Rounding to the nearest whole number, you will need 32 stone pavers.
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help me pls I’ll give brainliest
The equation is expanding Pascal's triangle and the Binomial theorem
(x + 0.5)³ = x³/8 + 3x²/4 + 3x/2 + 1/8
(s + 4t)⁶ = s⁶ + 6s⁵(4t) + 15s⁴(4t)² + 20s³(4t)³ + 15s²(4t)⁴ + 6s(4t)⁵ + 4t⁶
(3a - 3b)⁴ = 81a⁴ - 324a³b + 486a²b² - 324ab³ + 81b⁴
(3m - 2n)⁵ = 243m⁵ - 810m⁴n + 1080m³n² - 720m²n³ + 240mn⁴ - 32n⁵
(a-4)⁵ = a⁵ - 20a⁴ + 160a³ - 640a² + 1280a - 1024
What is the binomial theorem formula?The binomial theorem formula for any positive integer n.
(x + y)n = nC0 xn + nC1 xn-1 by+ nC2 xn-2 y2 + … + nCn-1 x yn-1 + nCn x.
11) Using the Binomial Theorem, we have:
(x + 0.5)³ = C(3,0) x³(0.5)⁰ + C(3,1) x²(0.5)¹ + C(3,2) x¹(0.5)² + C(3,3) x⁰(0.5)³
= x³/2³ + 3x²/2² + 3x/2 + 1/2³
= x³/8 + 3x²/4 + 3x/2 + 1/8
12) Using Pascal's Triangle, we have:
(s + 4t)⁶ = C(6,0) s⁶(4t)⁰ + C(6,1) s⁵(4t)¹ + C(6,2) s⁴(4t)² + C(6,3) s³(4t)³ + C(6,4) s²(4t)⁴ + C(6,5) s(4t)⁵ + C(6,6) (4t)⁶
= s⁶ + 6s⁵(4t) + 15s⁴(4t)² + 20s³(4t)³ + 15s²(4t)⁴ + 6s(4t)⁵ + 4t⁶
13) Using Pascal's Triangle, we have:
(3a - 3b)⁴ = C(4,0) (3a)⁴(-3b)⁰ + C(4,1) (3a)³(-3b)¹ + C(4,2) (3a)²(-3b)² + C(4,3) (3a)(-3b)³ + C(4,4) (-3b)⁴
= 81a⁴ - 324a³b + 486a²b² - 324ab³ + 81b⁴
14)Using Pascal's Triangle, we have:
(3m - 2n)⁵ = C(5,0) (3m)⁵(-2n)⁰ + C(5,1) (3m)⁴(-2n)¹ + C(5,2) (3m)³(-2n)² + C(5,3) (3m)²(-2n)³ + C(5,4) (3m)(-2n)⁴ + C(5,5) (-2n)⁵
= 243m⁵ - 810m⁴n + 1080m³n² - 720m²n³ + 240mn⁴ - 32n⁵
15) Using Pascal's Triangle, we have:
(a-4)⁵ = C(5,0) a⁵(-4)⁰ + C(5,1) a⁴(-4)¹ + C(5,2) a³(-4)² + C(5,3) a²(-4)³ + C(5,4) a(-4)⁴ + C(5,5) (-4)⁵
= a⁵ - 20a⁴ + 160a³ - 640a² + 1280a - 1024
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The equation is expanding Pascal's triangle and the Binomial theorem ,
[tex](x + 0.5)^3= x^3/8 + 3x^2/4 + 3x/2 + 1/8[/tex]
[tex](s + 4t)^6 = s^6+ 6s^5(4t) + 15s^4(4t)^2 + 20s^3(4t)^3 + 15s^2(4t)^4+ 6s(4t)^5 + 4t^6[/tex]
[tex](3a - 3b)^4 = 81a^4 - 324a^3b + 486a^2b^2- 324ab^3 + 81b^4[/tex]
[tex](3m - 2n)^5 = 243m^5 - 810m^4n + 1080m^3n^2- 720m^2n^3 + 240mn^4- 32n^5[/tex]
[tex](a-4)^5= a^5 - 20a^4 + 160a^3 - 640a^2+ 1280a - 1024[/tex]
What is the binomial theorem formula?
The binomial theorem formula for any positive integer n.
[tex](x + y)^n = nC_0 x^n + nC_1x^{n-1} y+ nC_2 x^{n-2} y_2 + … + nC_{n-1} x y^{n-1} + nC_n x.[/tex]
11) Using the Binomial Theorem, we have:
[tex](x + 0.5)^3 = C(3,0) x^3(0.5)^0 + C(3,1) x^2(0.5)^1 + C(3,2) x^1(0.5)^2 + C(3,3) x^0(0.5)^3[/tex]
=[tex]x^3/2^3 + 3x^2/2^2 + 3x/2 + 1/2^3[/tex]
= [tex]x^3/8 + 3x^2/4 + 3x/2 + 1/8[/tex]
12) Using Pascal's Triangle, we have:
[tex](s + 4t)^6 = C(6,0) s^6(4t)^0+ C(6,1) s^5(4t)^1+ C(6,2) s^4(4t)^2 + C(6,3) s^3(4t)^3 + C(6,4) s^2(4t)^4+ C(6,5) s(4t)^5 + C(6,6) (4t)^6[/tex]
= [tex]s^6 + 6s^5(4t) + 15s^4(4t)^2 + 20s^3(4t)^3 + 15s^2(4t)^4 + 6s(4t)^5 + 4t^6[/tex]
13) Using Pascal's Triangle, we have:
[tex](3a - 3b)^4 = C(4,0) (3a)^4(-3b)^0 + C(4,1) (3a)^3(-3b)^1 + C(4,2) (3a)^2(-3b)^2 + C(4,3) (3a)(-3b)^3 + C(4,4) (-3b)^4[/tex]
= [tex]81a^4 - 324a^3b + 486a^2b^2 - 324ab^3 + 81b^4[/tex]
14)Using Pascal's Triangle, we have:
[tex](3m - 2n)^5= C(5,0) (3m)^5(-2n)^0 + C(5,1) (3m)^4(-2n)^1 + C(5,2) (3m)^3(-2n)^2+ C(5,3) (3m)^2(-2n)^3 + C(5,4) (3m)(-2n)^4 + C(5,5) (-2n)^5[/tex]
= [tex]243m^5- 810m^4n + 1080m^3n^2 - 720m^2n^3 + 240mn^4 - 32n^5[/tex]
15) Using Pascal's Triangle, we have:
[tex](a-4)^5= C(5,0) a^5(-4)^0+ C(5,1) a^4(-4)^1 + C(5,2) a^3(-4)^2 + C(5,3) a^2(-4)^3 +C(5,4) a(-4)^4 + C(5,5) (-4)^5[/tex]
= [tex]a^5 - 20a^4 + 160a^3 - 640a^2 + 1280a - 1024[/tex]
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V(d)V, left parenthesis, d, right parenthesis models Erica's vertical distance from the top of the valley (in kilometers) after walking
d
dd kilometers along the trail.
What does the statement
V
(
2
)
=
T
V(2)=TV, left parenthesis, 2, right parenthesis, equals, T mean?
The meaning of V(2) is the Erica's vertical distance after walking 2 kilometers along the trail.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The input and output variables for this problem are given as follows:
Input: number of kilometers walked along the trail.Output: vertical distance.V(2) means that the number of km is of 2, hence the meaning of V(2) is the Erica's vertical distance after walking 2 kilometers along the trail.
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The shaded area on the grid represents the part of kira's free throws that she made in the basketball practice today.
The percentage of Kira's free throws is 68%.
We have,
From the grid,
We can see that,
There are 25 boxes.
Now,
The number of shaded boxes = 17
Now,
The percentage of the shaded boxes.
= 17/25 x 100
= 17 x 4
= 68%
Thus,
The percentage of Kira's free throws is 68%.
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The complete question.
The shaded area on the grid represents the part of Kira's free throws that she made in the basketball practice today.
Find the percentage of Kira's free throws.
Felix exercises by spending 12 minutes warming up and then running for 20 minut
He has exercised a total of 240 minutes this month.
Felix has spent a total time of 11.4 hours (or 684 minutes) running this month.
HOW CAN WE CALCULATE TOTAL TIME?we can calculate the total time Felix has spent running this month.
Given:
Warm-up time: 12 minutes
Running time: 20 minutes
Total exercise time in a month: 240 minutes
Step 1: Calculate the total time spent running
Let x be the total time spent running in minutes.
According to the given information, Felix spends 12 minutes on warm-up and 20 minutes on running.
So, the equation would be:
12 + 20x = 240
Step 2: Solve for x
Subtract 12 from both sides of the equation:
20x = 240 - 12
20x = 228
Divide both sides by 20:
x = 228 / 20
x = 11.4
So, Felix has spent a total of 11.4 hours (or 684 minutes) running this month.
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The measure of arc angle QT is determined as 142 ⁰.
The measure of m∠STR is determined as 23⁰.
What is the measure of arc angle QT?The measure of angle subtended by the arc QT is calculated by applying the following formula.
Based on the angle of intersecting chord theorem, we will have the following equation.
The measure of m∠STR is calculated as;
m∠STR = ¹/₂( arc SR )
m∠STR = ¹/₂ x 46⁰
m∠STR = 23⁰
The measure of arc QT is calculated as;
m∠QST = ¹/₂( arc QT )
arc QT = 2 (m∠QST)
arc QT = 2 x 71⁰
arc QT = 142⁰
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The value 3pi/4 is a solution for the equation 3√2 sec theta +7 = 1.
A. True
B. False
Answer:
False
Step-by-step explanation:
3√2 sec(theta) + 7 = 1
3√2 sec(theta) = -6
sec(theta) = -2/√2
sec(theta) = -√2
theta = arcsec(-√2)
However, the range of secant function is [-∞, -1] U [1, ∞]. Since -√2 is not within this range, we cannot take the arcsecant of -√2. Therefore, there is no real value of theta that satisfies the equation, including 3π/4.
Therefore, the statement "The value 3π/4 is a solution for the equation 3√2 sec(theta) + 7 = 1" is False.
I hope it helps you
A suitcase is a rectangular prism whose dimensions are 2 3 foot by 1 1 2 feet by 1 1 4 feet. Find the volume of the suitcase.
The volume of the suitcase is 35/8 cubic feet or approximately 4.375 cubic feet.
What is rectangular prism?A rectangular prism is a three-dimensional solid object that has six faces, where each face is a rectangle. It is also called a rectangular parallelepiped. A rectangular prism is a type of prism because it has a constant cross section along its length.
According to question:A rectangular prism's volume V is determined by:
V = l × w × h
where l denotes the prism's length, w its width, and h its height. Here are the facts:
l = 2 3 ft
w = 1 1/2 ft
h = 1 1/4 ft
When we enter these values into the formula, we obtain:
V = (2 3 ft) × (1 1/2 ft) × (1 1/4 ft)
= (7/3 ft) × (3/2 ft) × (5/4 ft)
= 35/8 ft³
Therefore, the volume of the suitcase is 35/8 cubic feet or approximately 4.375 cubic feet.
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Un deportista se ejercita y recorre 350 metros, retrocede 125 metros avanza 80 metros. Si el punto de partida es su casa a que distancia de la misma se encuentra
The sportsman has a final distance with respect to his home equal to 305 meters.
How to determine the distance of a sportsman with respect to a home
In this problem we must the final distance of the sportsman with respect to his home. This can be determined by the following expression:
X = ∑ xₙ, for n = {1, 2, 3, ..., N}
Where the sportsman goes far away for his home for x > 0, in meters.
Now we proceed to determine the final distance:
X = + 350 m - 125 m + 80 m
X = + 305 m
The final distance of the sportsman with respect to his home is 305 meters.
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