Option D, 4.1 is the correct answer. The mean baseball score is 4.1 given the table of values of baseball scores and score number of students. This can be obtained by using the formula for mean.
Calculate mean for the data:Mean can be obtained by the formula,
Mean = [tex]\frac{sum\ of\ observations}{total\ number\ of\ observations}[/tex]
Sum of basketball scores = 0×1 + 1×2 + 2×5 + 3×3 + 4×6 + 5×7 + 6×9
= 0 + 2 + 10 + 9 + 24 + 35 + 54
total number of basketball scores = 1 + 2 + 5 + 3 + 6 + 7 + 9 = 33
Mean = [tex]\frac{0+2+10+9+24+35+54}{33}[/tex] = 4.06 ≈ 4.1
Hence the mean baseball score is 4.1 given the table of values of baseball scores and score number of students. Option D, 4.1 is the correct answer.
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Exercise 21 1. A girl moves from a point P on a bearing of 060° to a point Q, 40m away. She then moves from the point Q, on a bearing of 120° to a point R. The bearing of P from R is 255, Calculate, correct to three significant figures, the distance between P and R.
Therefore , the answer is the distance between P and R is 12,2m.
How far is that?Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending point.
Here,
Using the sine rule, sin a/A = sin b/B in this instance, we can determine the distance between P and R.
Sin angle PQR/PR is equal to Sin angle QRP/PQ.
We are aware that the QRP angle is 45° because:
Since it is an alternative interior angle, angle NPR is 75°.
Since 75° – 60° = 15, the angle QPR would be 15°.
As a result, angle QRP would be 45° since 180° – 120° – 15° = 45°.
When we know the angle QRP, we can quickly calculate the PR by entering the values into a calculator.
Sin 120°/RP = Sin 45°/10
RP = sin(120,10) sin(45,45),
=root 6 × 5
= 12.2m(3s.f) (3s.f)
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Niquelle places signposts along a trail that is 4 1/2 miles long. The signposts divide the
trail into sections that are 3/4 mile long. How many sections does Niquelle create
along the trail?
Using Simple division, Number of sections that Niquelle create along the trail is 6 sections.
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.
The other operations are multiplication, addition, and subtraction. Simply write the first fraction, the division symbol (), and the second fraction to divide a fraction. For instance, your issue could be 3/4 5/8. Use horizontal rather than diagonal lines to conveniently divide each fraction's numerator (top number) and denominator (bottom number).
Partitive division and quotative division are the two types of division. In some circumstances, one form may be more beneficial than the other.
Length of the trail = 4 1/2 miles long = 9/2 miles
The signposts divide the trail into sections that are 3/4 mile long.
Number of sections that Niquelle create along the trail = 9/2 miles ÷ 3/4
⇒ 9/2 × 4/3
⇒ 6 sections
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Identify the value of x that makes each pair of ratios equal
5:15 and x:3
The ratio for 5 / 15 based on the information is 1:3. The value of x is 1.
How to illustrate the ratio?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
This simply indicates that you're dividing the variable A by B. Let us say for instance, the ratio will be 3/10 if A is 3 and B is 10.
The ratio for 5 / 15 will be:
= 5 / 15
= 1 / 3
= 1:3
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A is the midpoint of segment bouded by (-2, 3) & (6, -1). B is a point at 3/4 of distance from (4, 3) to (0, -3). Find the equation of AB.
The equation of line segment AB, whose endpoints are A(x, y) = (2, 1) and B(x, y) = (1, - 1.5), is P(x, y) = (1 - k) · (2, 1) + k · (1, - 1.5), for 0 ≤ k ≤ 1.
How to derive the equation of a line segment
In this problem we need to determine the equation that described the line segment AB, whose endpoints are points within other two line segments. The location of a point can be found by means of the following formula:
P''(x, y) = P(x, y) + k · [P'(x, y) - P(x, y)], 0 ≤ k ≤ 1
Where:
P(x, y), P'(x, y) - Endpoints of line segment.k - Length ratio.P''(x, y) - Endpoint within line segment.First, determine the locations of endpoints A and B:
A(x, y) = (- 2, 3) + 0.5 · [(6, - 1) - (- 2, 3)]
A(x, y) = (- 2, 3) + 0.5 · (8, - 4)
A(x, y) = (- 2, 3) + (4, - 2)
A(x, y) = (2, 1)
B(x, y) = (4, 3) + 0.75 · [(0, - 3) - (4, 3)]
B(x, y) = (4, 3) + 0.75 · (- 4, - 6)
B(x, y) = (4, 3) + (- 3, - 4.5)
B(x, y) = (1, - 1.5)
Second, derive the equation of line segment AB:
P(x, y) = A(x, y) + k · [B(x, y) - A(x, y)]
P(x, y) = (2, 1) + k · [(1, - 1.5) - (2, 1)]
P(x, y) = (1 - k) · (2, 1) + k · (1, - 1.5), for 0 ≤ k ≤ 1.
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The rectangle on the right is a scaled copy of the rectangle on the left. Identify the
scale factor. Express your answer as a whole number or fraction in simplest form.
3
7
7/3
The scale factor of the rectangle and its copy is [tex]\frac{2}{3}[/tex].
What is scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
The rectangle on right hand side is the scaled copy of the original rectangle. The scaled version of the rectangle is given as follows:
[tex]\frac{42}{63} \text{ and } \frac{15}{\frac{45}{2} } = \frac{30}{45}[/tex]
Rationalize the factors to find the scale factor.
Rationalize the factor [tex]\frac{42}{63}[/tex] by multiplying and dividing by 45.
[tex]\frac{(42)(45)}{(63)(45)}[/tex]
[tex]\frac{1890}{2835}[/tex]
Rationalize [tex]\frac{30}{45}[/tex] by multiplying and dividing by 63.
[tex]\frac{(30)(63)}{(45)(63)}[/tex]
[tex]\frac{1890}{2835}[/tex]
Scale factor = [tex]\frac{1890}{2835} = \frac{2}{3}[/tex]
Hence the scale factor of the rectangle and its copy is [tex]\frac{2}{3}[/tex].
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A circle has a radius of 11 ft. Find the radian measure of the central angle θ that intercepts an arc of length 9 ft. Do not round any intermediate computations, and round your answer to the nearest tenth.
The radian measure of the central angle θ is 5.4 radians.
Find the radian measure of the central angle θ that intercepts an arc of length 9 ft.The radian measure of a central angle is the ratio of the arc length to the radius of the circle. To calculate the radian measure of the central angle, we must divide the length of the arc (9 ft) by the radius of the circle (11 ft). 9ft/11ft = 0.818181818Therefore, the radian measure of the central angle θ is 0.818181818. To convert this value to a decimal to the nearest tenth, we must multiply the value by 10 and round to the nearest tenth.0.818181818 x 10 = 8.18181818Rounding to the nearest tenth, the radian measure of the central angle θ is 8.2.The radian measure of the central angle of a circle can be found using the formula θ = s/r, where s is the length of the arc and r is the radius of the circle. In this case, s = 9 ft and r = 11 ft, so θ = 9/11.To find the radian measure of the central angle, we need to convert the fraction 9/11 into decimal form, which yields 0.818181818....To convert this decimal into radians, we can multiply it by 2π and get 5.06544 radians. Finally, to round this answer to the nearest tenth, we can round 5.06544 to 5.1 radians.Therefore, the radian measure of the central angle θ that intercepts an arc of length 9 ft on a circle with a radius of 11 ft is 5.1 radians.To learn more about The radian measure of the central angle refer to:
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A blue parallelogram has a height of 6 inches and a base of 10 inches. a scale of 2:1 was applied to the blue parallelogram to create a green parallelogram. what is the area of the green parallelogram? Provide explanation/show work!
the area of the green parallelogram will be 15inch².
What is Area of Parallelogram?
The region in a two-dimensional plane that a parallelogram occupies is known as its area. A parallelogram is a form with four sides with two geometry dimensions. Because the opposing sides are equal and parallel, so it is a unique quadrilateral example. The space bounded by the four sides of a parallelogram is known as its area. A parallelogram's area is calculated as the sum of its length and height.
A blue parallelogram has a height of 6 inches and a base of 10 inches.
a scale of 2:1 was applied to the blue parallelogram to create a green parallelogram.
So the height will be half and the base ill also be.
For the green parallelogram will be 3 inch and 5 inch.
The area will be 3*5 = 15inch²
Hence, the area of the green parallelogram will be 15inch².
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Write an equation of the line that passes through each pair of points (9,2) (-2,6)
y = (-4/11)x + 5.27 is the equation that passes through each pair of points (9,2) (-2,6).
What is equation?A group of numbers and variables without an equal sign are known as a numerical expression. A set of numbers and variables with an equal sign is referred to as an equation.
Once you are familiar with these terms, you will realise that an equation is just two expressions joined by an equal sign. You can also write expressions, equations, and simplify equations.
To find an equation of the line that passes through each pair of points (9,2) (-2,6) we need to find slope and convert it to y-intercept form
Slope formula = y - y₁ = m(x - x₁)
Putting the values in the formula we get
2 - 6 = m(9 - (-2))
-4 = m(11)
m = -4/11
As we have found slope, we can find the slope intercept form i.e.
y - 2 = -4/11(x -9)
y = (-4/11)x + 3.27 + 2
y = (-4/11)x + 5.27
Thus, y = (-4/11)x + 5.27 is the equation that passes through each pair of points (9,2) (-2,6)
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3 / 3/4=, 5 / 3/4=, 8 / 4/7=, 6 / 3/5=, 2 / 5/8=, and 4 / 8/9= simplify them all
On simplifying the values obtained for the fractions are - 3 / 3/4= 4, 5 / 3/4= 6.66, 8 / 4/7= 14, 6 / 3/5= 10, 2 / 5/8= 3.2 and 4 / 8/9= 4.5.
What is fraction?
In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
The first fraction is 3/(3/4).
The denominator will reciprocate.
Simplify, the fraction -
3 × 4/3 = 4
The second fraction is 5/(3/4).
The denominator will reciprocate.
Simplify, the fraction -
5 × 4/3
20/3 = 6.66
The third fraction is 8/(4/7).
The denominator will reciprocate.
Simplify, the fraction -
8 × 7/4 = 14
The fourth fraction is 6/(3/5).
The denominator will reciprocate.
Simplify, the fraction -
6 × 5/3 = 10
The fifth fraction is 2/(5/8).
The denominator will reciprocate.
Simplify, the fraction -
2 × 8/5
16/5 = 3.2
The sixth fraction is 4/(8/9).
The denominator will reciprocate.
Simplify, the fraction -
4 × 9/8
9/2 = 4.5
Therefore, the values of fractions are 4, 6.66, 14, 10, 3.2 and 4.5.
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Use the formula d = ( r − c ) t to find c if d = 12 , r = 7 , and t = 2 .
Answer:
30=(12-c)5
30=60-5c multiply 12 and c by 5
-30=-5c Subtract 60 from 30
-30 ÷ -5= c divide -30 by -5
c=6
What are the features of the quadratic function graphed in the figure?
Vertex (3, -4) with x-intercepts (1, 0), (5, 0), and (0, 5) and an axis of symmetry of 3. As a result, choice B is the right response.
In a graph, what exactly is a vertex?
A node of a graph, or one of the points on which the graph is defined and which may be connected by graph edges, is known as a "vertex" and is a mathematical term for this type of point.The following are some characteristics of the quadratic function:The curve's bottommost point, or vertex, is situated halfway along the curve. The point's x-coordinate is 3 and its y-coordinate is -4. The quadratic's x-axis intersection points are (1, 0) and (5, 0), and its y-axis intersection point is (0,5).The right response is, therefore, option B.
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Full Question-
What characteristics can you see in the graph of the quadratic function in the figure? Options for question 14: A: The vertex is at (-4,3), the y-intercept is at (5,0), the x-intercepts are at (0,1) and (0,5), and the symmetry axis is at (-4,3) B: The vertex is at (-3,-4), the y-intercept is at (0,5), the x-intercepts are at (1,0) and (5,0), and the symmetry axis is at (3); C: Vertex: (3, -4), y-intercepts: (1, 0), and (5, 0), x-intercept: (0, 5), axis of symmetry: (3 D) Axis of symmetry is at x = -3, vertex is at (-3,4), y-intercept is at (0,5), and x-intercepts are at (1,0) and (5,0).
What is the properties of (10c - 4) + 11d?
Answer:
10c-4+11d Welcome :D
Step-by-step explanation:
You randomly select a letter from the letters A, B, C, D, E and flip a coin. The table represents the sample space, where H represents the coin landing heads up and T represents landing tails up. What is the probability of selecting the letter “C” or the coin landing tails up?
To find the probability of selecting the letter "C" or the coin landing tails up, we need to calculate the probability of each event individually and then add the probabilities of the two events together.
The probability of selecting the letter "C" is:
1/5
This is because there are 5 letters in total, A, B, C, D, and E, and "C" is one of them, so the probability of selecting "C" is 1/5.
The probability of the coin landing tails up is:
1/2
This is because there are two possible outcomes when flipping a coin, heads or tails, and since the coin is fair, the probability of getting heads or tails is 1/2.
To find the combined probability of the two events we need to add them together using the rule of "or" in probability which is defined as:
P(A or B) = P(A) + P(B) - P(A and B)
However in this case A and B are mutually exclusive events, meaning they can't happen at the same time. There is no way to have "C" and coin landing tails up at the same time. Then we don't have to subtract P(A and B)
Therefore, the probability of selecting the letter "C" or the coin landing tails up is:
1/5 + 1/2 = 2/5 + 1/2 = 7/10
So the probability of selecting the letter "C" or the coin landing tails up is 7/10
Sallu car has an average fuel economy of 28 miles per gallon the capacity of the fuel tank is 16
The number of miles Sallu car will travel with 16 gallons fuel capacity if he travelled 28 miles per gallon is 448 miles.
How many miles can a full tank capacity travel?If Sallu car can travel 28 miles using 1 gallon of fuel;
then, Sallu car will travel x miles using 16 gallons of fuel.
Based on the given task content; we can solve the task using the concept of ratio.
A ratio is a number representing a comparison between two named things.
It also refers to the relative magnitudes of two quantities usually expressed as a quotient.
Equate the ratio of miles travelled to gallons of fuel used
28 miles : 1 gallon = x miles : 16 gallons
28/1 = x / 16
28 × 16 = x × 1
448 = x
Therefore, Sallu car will travel 448 miles using 16 gallons of fuel.
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Ed’s birthday is less than 16 days away.
Part A
Ann writes the inequality d ≤ 16, where d equals the number of days, to represent this scenario.
Choose the best explanation for Ann’s error.
A.
Ann should have used 16d because it is less than 16 days away. B.
Ann should have switched the inequality symbol to greater than or equal to. C.
Ann should have switched the inequality symbol to not include 16 as a possible choice. D.
Ann should have used the not equals sign to compare the two sides of the inequality.
Part B
Select the correct inequality symbol to complete the inequality.
d
Choose...
16
Ann should have switched the inequality symbol to not include 16 as a possible choice. The correct answer would be an option (C).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
As per the question, we have been given that Ed's birthday is less than 16 days
away and that Ann writes the inequality
d ≤ 16, where d equals the number of days, to represent this.
Thus, He should have switched the inequality symbol to not include 16 as a possible choice.
Hence, the correct answer would be an option (C).
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Pleas HELP MEEEEEEE :CCC
Answer: 15,24,plan A
Step-by-step explanation: you will need to use the 15 from 150 to see which one costs less because 24+ 15= 39 so its obvious that plan B costs less then plan A the next step is pretty easy because they both cost 24 at the same time but its obvious that plan A costs more so your answer for each of them is
Select the correct answer from each drop-down menu.
How are line segments and rays alike? How are they different?
Both a ray and a line segment
is
✓. A ray is
but a line segment
Both a ray and a line segment have two endpoints . A ray is bounded on one side , but a line segment is not bounded on either side.
What is the difference between a ray and a line?Line extends forever in both directions. 1. Ray starts at one point and continues on forever in one directionA line is a straight path on a plane that extends forever in both directions with no endpoints. A line segment is part of a line that has two endpoints and is finite in length. A ray is a line segment that extends indefinitely in one direction.A line is a simple geometric shape that extends in both the directions, but a line segment has two defined endpoints. Both the figures are also different from a ray, as a ray has only one endpoint and extend infinitely in one direction.To learn more about difference between a ray and a line refers to:
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Solve the following problem using the substitution method. Please make sure to show all of your work.
6x - 3y = 1
y = -2x - 5
Answer:
x=-7/6, y=-8/3. (-7/6, -8/3).
Step-by-step explanation:
6x-3y=1
y=-2x-5
-------------
6x-3(-2x-5)=1
6x+6x+15=1
12x+15=1
12x=1-15
12x=-14
x=-14/12=-7/6
y=-2(-7/6)-5=7/3-5=7/3-15/3=-8/3
Jorge's trip takes the same amount of time as Zahara's but he traveled a shorter distance. Does Jorge drive faster or slower Zahara's dad
Answer: Slower
Step-by-step explanation:
Speed is a measure of how quickly an object moves, and it is calculated as distance traveled divided by time. Since Jorge and Zahara's dad traveled the same amount of time but Jorge traveled a shorter distance, it can be inferred that Zahara's dad traveled at a faster speed.
Another way to understand this is that, if Jorge and Zahara's dad were driving at the same speed, they would have traveled the same distance in the same amount of time. However, since Jorge traveled a shorter distance than Zahara's dad, it can be inferred that Jorge was driving at a slower speed.
Answer:
Step-by-step explanation:
Lines l and m are parallel find m<2
Answer: m<5 = 142°
Step-by-step explanation:
For which addition equation can you make a 10 to add?
24+14=
7+25=
76+3=
26+14=
isabella is building a fort.The base is 78 inches wide by 92 inches long. what is the area of the base in square inches show your work
The area of a rectangle is found by multiplying the length by the width.
To find the area of the base of Isabella's fort, we will use the following formula:
Area = length x width
We are given that the base of the fort is 78 inches wide and 92 inches long. So we can plug these values into the formula:
Area = 78 inches x 92 inches = 7176 square inches
Therefore, the area of the base of Isabella's fort is 7176 square inches.
The dimensions of the rectangular pool shown below are 60 yards by 30
yards. A fence will be built around the outside of the deck. The ratio of the
dimensions of the pool to the dimensions of the fence is How many yards
of fence should be purchased to enclose the deck?
60 Yards
30 Yards
A. 270 yards
B. 540 yards
C. 200 yards
D. 312 yards
540 yards should be purchased to enclose the deck and option B is correct.
What is rectangle?A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides.
A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
Pools dimension = 1:3
Length = 60 × 3
= 180
Breadth= 30 × 4
= 90
Perimeter of rectangle = 2(l+b) = 2(90+180)
P = 2(270) = 540 yards
Thus, 540 yards should be purchased to enclose the deck and option B is correct
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What is the equation in slope intercept form of the line that passes through the y-intercept (0, -4) and has a slope of 5?
O y = 5x + 28
O y = 5x + 4
O y = 5x-4
O y = 5x-28
The equation in slope-intercept form of the line that passes through the point (0, -4) and has a slope of 5 is y = 5x - 4.
What is slope intercept form ?The form of a line's slope intercept is one of the most common ways to represent a line's equation. The slope intercept formula can be utilized to find a line's equation given its slope and y-intercept for a straight line ( the y-coordinate of the point where the line intersects the y-axis). For a line to exist, every point along the line must be satisfied by its equation. This straight line equation, which is represented as, can be resolved in a number of ways.
1. Slope-intercept form
2. Two-point form
3. Intercept form
4. Point slope form
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Write the inequality using interval notation.
A person has to be taller than 55 inches but shorter than 70 inches to ride the Twirly
Swirly ride at an amusement park.
The inequality using interval notation is given as 55 < x < 70
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
Inequalities are used to show that an expression containing numbers and variables are not equal.
Interval notation involves using parentheses for opened ends and square brackets for closed ends.
Let x represent the allowed height to ride at an amusement park. A person has to be taller than 55 inches but shorter than 70 inches, hence:
55 < x < 70
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Find the equation of the line that passes through the point (6,-2) and is parallel to the line 5x+3y
Answer: y=(-5/3)x+8
Step-by-step explanation: earrange 5x+3y=6 in slope intercept form
y=mx=b
5x+3y=6
3y=6-5x
y=2-(5x)/3
then slope for a line parallel is -5/3
Use point slope form y-y1=m(x-x1)
plug un values of (x,y) = (6,-2)
and m=-5/3
y-y1=m(x-x1)
y-(-2)=(-5/3)(x-6)
y+2=(-5/3)x+10
y=(-5/3)x+10-2
y=(-5/3)x+8 <-- solution
You put $600 in an account. The account earns $31 simple interest in 10 months. What is the annual interest rate? need % answer
The annual interest rate that yields $31 from $600 in 10 months is 6.2%
What is an interest earned on an amount?An interest is the amount earned by placing a sum of money in a savings account or in an investment.
The principal amount you put in the account, P = $600
The amount (interest) earned in 6 months, I = $31
The duration over which the interest of $31 is earned, T = 10 months
The annual interest rate is found as follows;
The annual interest rate is the interest rate per year
The number of months in a year = 12 months
The formula for the simple interest, I, is presented as follows;
I = P·R·T
Where;
I = The simple interest earned
P = The principal amount saved in the account
R = The annual interest rate
T = The time duration the amount was saved in years
12 months = 1 year
Therefore; 10 months = (1/12) × 10 year = (5/6) year
The time, T, of 10 months = (5/6) year
31 = 600 × R × (5/6)
R = 31/(600 × (5/6)) = 0.062
0.062 in percentage is 0.062 × 100 = 6.2%
The annual interest rate, R = 6.2%
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Todd made $12,800 in interest by placing $40,000 in a savings account with simple interest for 4 years. What was the interest rate?
Answer: The interest rate is 0.16 or 16% ✅
Step-by-step explanation:
The interest rate is the percentage of the principal (the initial amount of money) that is paid as interest over a certain period of time. To find the interest rate in this scenario, we can use the formula:
Interest = Principal x Interest Rate x Time
In this case:
Interest = $12,800
Principal = $40,000
Time = 4 years
So we can set up the equation:
12800 = 40000 x Interest Rate x 4
To find the interest rate, we can divide both sides of the equation by 40000 x 4, which gives us:
12800 / (40000 x 4) = Interest Rate
We can simplify this fraction:
0.16 = Interest Rate
So the interest rate is 0.16 or 16%.
When Todd made $12,800 in interest by placing $40,000 in a savings account with simple interest for 4 years, the interest rate was 7.5%.
Simple interest is a formula for calculating the amount of interest that will be charged on a sum of money at a specific rate and during a specific time frame.
In contrast to compound interest, where the interest of one year's principal is added to the principal of the following year to calculate the interest, the principal sum in the case of simple interest stays the same.
Simple Interest = [tex]$ \frac{ \text P \times \text R \times \text T}{100}[/tex]
where,
P = Principal,
R = Rate of Interest in % per annum, and
T = Time, in years
Here given that,
Todd made $12,800 in interest, i.e. Simple Interest = 12,800
By placing $40,000 in a savings account, i.e. Principal = 40,000
with simple interest for 4 years, i.e. Time = 4 years
To find, interest rate
Substitute the data into the simple interest formula
[tex]$ \Rightarrow 12,800 = \frac{40,000 \times \text R \times 4}{100}[/tex]
[tex]$ \Rightarrow \text R = \frac{ 12,000 \times 100}{40,000 \times 4}[/tex]
[tex]$ \Rightarrow \text R = \frac{1,200,000}{160,000}[/tex]
⇒ R = 7.5%
Thus, the interest rate was 7.5%.
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In 1986 one of the first video games, the Nintendo, sold for $180. Similar to many items, its value depreciated over time. the function that models how its value has changed over times is: f(x) = 3x^2 - 40x +180,
1. The number shows the video game sold in 1986at $180.
2. The function f(x) = 3x² - 40x +180 which clearly resemble the standard vertex form.
3. The vertex of the given parabola is, (h, k) = (6.667, 46.667)
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x) = 3x² - 40x +180
1. For f(0) put x= 0 we get
f(0) = 3(0)² - 40(0) +180
f(0) = 180
So, the number shows the video game sold in 1986 at $180.
2. We know that the standard form of the parabola is y=ax²+bx+c.
Also we have f(x) = 3x² - 40x +180 which clearly resemble the standard vertex form.
3. Comparing the given equation with y = ax² + bx + c, we have
a = 3, b = -40, and c = 180.
So, x-coordinate is, h = -b/2a = - (-40)/ 2(3)
h= 40/6 = 6.667
and, y-coordinate is, k = 3(6.667)² - 40(6.667) +180 = 46.667.
So, The vertex of the given parabola is, (h, k) = (6.667, 46.667)
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For a certain kind of plaster work, 1.1 cu yd of sand are needed for every 100 sq yd of surface. How much sand will be needed for 280 sq yd of surface
cu yd of sand will be needed for 280 sq yd of surface.
308 cubic yards of sand will be needed for 280 square yards of surface.
How to find the cubic yards?If 1.1 cubic yards of sand are needed for every 100 square yards of surface, we can find the amount of sand needed for 280 square yards of surface using the proportion:
1.1 cu yd / 100 sq yd = x cu yd / 280 sq yd
To find the value of x, we can cross-multiply and solve for x:
1.1 cu yd * 280 sq yd = x cu yd * 100 sq yd
x = 1.1 cu yd * 280 sq yd / 100 sq yd
x = 308 cu yd
So, 308 cubic yards of sand will be needed for 280 square yards of surface.
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