Answer:
a. The theoretical probability of drawing a spade from a standard deck of cards is 13/52, which reduces to 1/4, or 0.25, or 25%.
b. The theoretical probability of drawing a face card (jack, queen, or king) from a standard deck of cards is 12/52, which reduces to 3/13, or approximately 0.231, or 23.1%.
c. The theoretical probability of drawing a non-face card from a standard deck of cards is 40/52, which reduces to 10/13, or approximately 0.769, or 76.9%.
d. The theoretical probability of drawing a black jack from a standard deck of cards is 2/52, which reduces to 1/26, or approximately 0.038, or 3.8%.
e. The theoretical probability of drawing a red or black card from a standard deck of cards is 52/52, which reduces to 1/1, or 100%.
f. The theoretical probability of drawing a red face card from a standard deck of cards is 6/52, which reduces to 3/26, or approximately 0.115, or 11.5%.
you are given f(x) = x + 3 and g(x) = 2x + 1
find g[g(-3)
find f[g(x)]
find g[f(x)]
Answer:
Step-by-step explanation:
f(x) = x + 3
g(x) = 2x + 1
g(g(-3)) = g(-5) = -9
f(g(x) = f(2x + 1) = 2x + 1 + 3 = 2x + 4
g(f(x) = g(x + 3) = 2(x + 3) + 1 = 2x + 7
X<= -5 or x >= 3 which answer represents the inequality in interval notation
The inequality x ≤ -5 or x ≥ 3 in interval notations is (-∞, -5] ∪ [3, ∞)
Inequality is the relationship between two expressions or values that are not equal to each other
The inequality x ≤ -5 or x ≥ 3 represents the solution set of all real numbers less than or equal to -5 or greater than or equal to 3.
The interval notation of the given inequality is (-∞, -5] ∪ [3, ∞)
The closed brace means the number is included and open bracket doesnot includes a number
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please help me with my geometry i cant fail this class or i’ll have to move out of my parents house :(
The length of the arcs are calculated to the nearest hundredth as:
12. 14.03 meters 13. 6.91 meters
How to Find the Length of an Arc?The formula used to find the length of a an arc is: length of arc = ∅/360 * 2πr, where ∅ is the central angle measure and r is the radius of the circle.
Length of arc XW:
∅ = m<XZW = 180 - 113
∅ = 67 degrees
r = 24/2 = 12 meters
Plug in the values:
length of arc XW = 67/360 * 2 * π * 12 ≈ 14.03 meters
Length of arc XW:
∅ = m<YVU = 180 - 67 - 80
∅ = 33 degrees
r = 24/2 = 12 meters
Plug in the values:
length of arc YVU = 33/360 * 2 * π * 12 ≈ 6.91 meters
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g(n)=−50−15ng, left parenthesis, n, right parenthesis, equals, minus, 50, minus, 15, n
Complete the recursive formula of
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g(n)g, left parenthesis, n, right parenthesis.
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g(1)=g, left parenthesis, 1, right parenthesis, equals
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g(n)=g(n−1)+g, left parenthesis, n, right parenthesis, equals, g, left parenthesis, n, minus, 1, right parenthesis, plus
The recursive formula of g(n) g(1) = -50 and g(n) = g(n-1) - 15
g(n) = g(n-1) - 15
Start with the given formula: G(n) = -50 - 15n
To find the recursive formula, we need to find the value of g(n) in terms of g(n-1).
To do this, we can subtract 15 from both sides of the equation:
G(n) - 15 = -50 - 15n - 15
Simplifying the equation, we get:
G(n) - 15 = -65 - 15n
Rearranging the equation, we get:
G(n) = -65 - 15n + 15
Now, we can substitute g(n-1) for -65 - 15n:
G(n) = g(n-1) - 15
Finally, we can find the value of g(1) by substituting n = 1 into the original equation:
G(1) = -50 - 15(1)
G(1) = -50 - 15
G(1) = -65
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Complete question is also attached below:/
G(n)=−50−15n complete the recursive formula of g(n)
g(1)=
g(n)=g(n−1) +=
Enter values to write the function that matches the graph shown.
Answer:
The roots of this function are at -4 and -1.
f(x) = (2x + 8)(-2x - 2)
= (2x + 8)(-2x + (-2))
At a certain intersection, the light for eastbound traffic is red for 15 seconds, yellow for 5 seconds, and green for 30 seconds. What is the probability that the light is red? Using the binomial distribution, what is the probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light?
The Probability that exactly three out of the next eight eastbound cars that arrive randomly at the light will be stopped by a red light is approximately 0.268.
The probability that the light is red is given by the ratio of the time the light is red to the total cycle time:
P(red) = 15 / (15 + 5 + 30) = 0.375
Using the binomial distribution, the probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light is:
P(X = 3) = (8 choose 3) * (0.375)^3 * (0.625)^5
where (8 choose 3) is the binomial coefficient, which represents the number of ways to choose 3 cars out of 8. Evaluating this expression gives:
P(X = 3) = (8 choose 3) * (0.375)^3 * (0.625)^5
= (8! / (3! * 5!)) * (0.375)^3 * (0.625)^5
= 56 * 0.052734375 * 0.1787109375
≈ 0.268
Therefore, the probability that exactly three out of the next eight eastbound cars that arrive randomly at the light will be stopped by a red light is approximately 0.268.
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a) (i) 830 + 50 gives the same answer as x + 100
Work out the value of x.
X =
(ii) What is the value of 830 + 50?
A coach can take 50 people.
(iii) How many coaches would be needed to transport 830 people?
b) Jayne needs to hire 13 coaches.
Each coach costs £450 to hire.
Work out the total cost of hiring 13 coaches. £
Total marks: 6
The value of x is 780 and 830 + 50 equals 880
The number of coaches is 17 and the total cost is £5850
Calculating the value of x.From the question, we have the following parameters that can be used in our computation:
830 + 50 gives the same answer as x + 100
This means that
830 + 50 = x + 100
So, we have
x = 830 + 50 - 100
Evaluate
x = 780
Also, we have
830 + 50 = 880
So, the value of x is 780 and 830 + 50 equals 880
Calculating the number of coachesHere, we have
People = 830
People per coach = 50
So, we have
Coaches = 830/50
Evaluate
Coaches = 16.6
Approximate
Coaches = 17
The total cost of hiring 13 coaches is
Cost = 450 * 13
Evaluate
Cost = 5850
Hence, the number of coaches is 17 and the total cost is £5850
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5.2 Given that cos 20° = p Without using a calculator, write EACH of the following in terms p: 5.2.1 5.2.2 5.2.3 cos 200° sin(-70°) sin 10°
The trigonometric ratio in terms p are
cos 200 = -p
- sin 70 = -p.
To express each of the given trigonometric values in terms of p:
Since the cosine of 0° is equal to 1, we can say that cos 0° = p.
cos 200°: Using the identity
cos(180° + θ) = -cos(θ), we can rewrite
cos 200° = -cos(180° + 20°).
Since cos 20° = p, we can express cos 200° as -p.
sin(-70°): Using the identity
sin(-θ) = -sin(θ), we can rewrite
sin(-70°) as -sin(70°)
=- sin (90- 20)
= - cos 20
= -p
sin 10°: Since sin 10° is not related to p, we cannot express sin 10° in terms of p.
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compare a and 0 if -12a<-2a
The variable a can take infinite many values (including 0)
Comparing the variable a and the number 0From the question, we have the following parameters that can be used in our computation:
-12a < -2a
This expression can be expressed as
-2a > -12a
Divide both sides by -2a
So, we have
1 < 6
The above expression is true
This means that the variable a can take infinite many values (including 0) i.e. 0 is a subset of a
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Factoring Polynomials Formative
QUESTION 1
Solve the following by factoring:
y³ - 6y² = 0
[tex]y^3 - 6y^2 = 0\\y^2(y-6)=0\\y^2=0 \vee y-6=0\\y=0 \vee y=6[/tex]
A recent random survey of 100 individuals in Michigan found that 78 drove to work alone. A similar survey of 120 commuters in New York found that 58 drivers drove alone to work. Find the 95% confidence interval for the difference in proportions
The 95% confidence interval for the difference in proportions is approximately 0.0957 to 0.4977.
To find the 95% confidence interval for the difference in proportions between Michigan and New York commuters who drove alone to work, we can use the formula:
CI = (p1 - p2) ± Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))
Where:
p1 and p2 are the proportions of Michigan and New York commuters who drove alone to work, respectively.
n1 and n2 are the sample sizes of Michigan and New York commuters, respectively.
Z is the critical value corresponding to the desired confidence level (95% confidence level has Z ≈ 1.96).
Given:
Michigan: p1 = 78/100 = 0.78, n1 = 100
New York: p2 = 58/120 = 0.4833, n2 = 120
Plugging in the values:
CI = (0.78 - 0.4833) ± 1.96 * sqrt((0.78 * (1 - 0.78) / 100) + (0.4833 * (1 - 0.4833) / 120))
CI = 0.2967 ± 1.96 * sqrt(0.006456 + 0.004074)
CI = 0.2967 ± 1.96 * sqrt(0.01053)
CI ≈ 0.2967 ± 1.96 * 0.1026
CI ≈ 0.2967 ± 0.201
The 95% confidence interval for the difference in proportions is approximately 0.0957 to 0.4977.
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Which of the word problems exemplify a linear function?
A. Angie's swimming classes required $50 enrollment fee and $10 safeguard
insurance cost each month.
B. Ken's car value depreciates by about 20% in the first year and then at estimated
15% each year following the first year.
C. A candy manufacturing business began its venture with 1,200 packets of candy
varieties. Then, 3,600 and 10,800 packets on the 2nd and 3rd days respectively.
D. The area of a triangular yard that has a right angle.
The word problem that exemplifies a linear function is
- Angie's swimming classes required a $50 enrollment fee and a $10 safeguard insurance cost each month.
Option A is the correct answer.
We have,
A linear function is a mathematical model that represents a relationship between two variables that is a straight line.
In this problem,
The cost of Angie's swimming classes is a linear function of the number of months.
The enrollment fee of $50 is a fixed cost that does not depend on the number of months, and the safeguard insurance cost of $10 per month is a variable cost that increases linearly with the number of months.
Thus,
The word problem that exemplifies a linear function is
- Angie's swimming classes required a $50 enrollment fee and a $10 safeguard insurance cost each month.
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Find the length of the hypotenuse of the right triangle.
Answer:
The length of the hypotenuse is 100.
Step-by-step explanation:
To find the length of the hypotenuse, we use the following formula:
c=[tex]\sqrt{a^2+b^2}[/tex]
c=[tex]\sqrt{28^2+96^2}[/tex]
c=[tex]\sqrt{10,000}[/tex]
c=100
Therefore, the length of the hypotenuse is 100.
please help asap i’m stuck
Answer:
10%
Step-by-step explanation:
P(reading paper 'given' that they are <40)
= P(reading paper AND < 40) / P(< 40)
= (4/80) / (40/80)
= 4/40
=1/10
=0.1
=10%
(Worth 100 Brainly points)After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the
rainbow is the shape of a parabola.
The equation for this parabola is y=-x² + 36
1.Create a table of atleast 4 values of the function that includes two points of intersection between the airplane and the rainbow
2.What is the domain and range of the rainbow? Explain what the domain and range represent.Do all of the values make sense in the situation. Why or why not.
3.what are the x and y intercepts of the rainbow. Explain what each intercept represents.
1) Equation for the parabola y = - x² + 36.
2) A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table of at least four values for the function.
The points of intersection will be: (0,36) and (4, 20)
Table of values for a linear function and the parabola
x linear function parabola y = - x² + 36
0 36 (0)² + 36 = 36
1 32 - (1)² + 36 = 35
2 28 - (2)² + 36 = 32
3 24 -3² + 36 = 27
4 20 -4² + 36 = 20
It is a linear function because the rate of change is constant: for each increase of 1 unit in x, there is a decrease of 4 units in y: ⇒ slope = - 4
Remember to include the two points of intersection in your table. Analyze the two functions; they are there (0,36) and (4, 20)
Answer the following reflection questions in complete sentences. What is the domain and range of the rainbow?
Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not? What are the x- and y-intercepts of the rainbow? Explain what each intercept represents.
The domain is all the real values of x between - 6 and 6: - 6 ≤ x ≤ 6
The range is all the values between 0 and 36: 0 ≤ y ≤ 36
The domain represents the horizontal distance between the extremes of the rainbow at the ground.
The range represents: the altitude of the rainbow from the ground (y = 0). The height is at x = 0, y = 36.
The x-intercepts are - 6 and 6, that is the opening of the rainbow at the ground level.
The y-intercept is when x = 0, it is y = 36, and is the height of the rainbow.
Is the linear function you created positive or negative? Explain. What are the solutions or solution to the system of equations created? Explain what it or they represent.
The linear function is positive and decreasing. It is positive because it goes above the x-axis, this is y ≥ 0.
The solutions were already signaled: (0,6) and (4, 20). They are the points at which the drone intercepts the rainbow.
Calculator
Pyramid ABCDE is a square pyramid.
What is the lateral area of pyramid ABCDE?
URGENT
The lateral area of the pyramid is 512√3 in.
What is area?Area is the region bounded by plane shape.
To calculate the area of the pyramid, we use the formula below
Formula:
A = 8aL.................................... Equation 1Where:
A = Area of the pyramida = Length of the square baseL = Slight height of the PyramidFrom the question,
Given:
a = 16 inL = 8sin60° = 4√3 inSubstitute these value into equation 1
A = (8×16×4√3)A = 512√3 inHence, the right option is D. 512√3 in.
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The circle below has a radius of 8 inches, find it's approximate area and circumference. Use the fact that π ≈ 3.14.
.
The approximate area and circumference of the circle is given as 201 inch² and 20 inch respectively
What is the area of a circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant
The area and perimeter of a circle can be calculated using the formula
πr = πd, where r is the radius and d is the diameter of the circle
Area = πr² and
the perimeter is 2πr
r= 8 inch, π = 3.14
Area = 3.14 * 8 * 8
Area = 200.96 square inches
Area = 201 inch²
the perimeter is = 2*3.14*8
The perimeter is = 50.24 square inches
Perimeter = 50 inch
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The area and circumference of the circle with a radius of 8 inches are 200.96 square inches and 50.24 inches respectively.
What is the area and circumference of the circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The area of a circle is expressed mathematically as;
A = πr²
The circumference of a circle is expressed as:
C = 2πr
Where r is radius and π is constant pi ( π = 3.14 )
Given that the radius of the circle is 8 inches.
Substituting this value into the formula, we get:
A = πr²
A = 3.14 × ( 8 in )²
A = 3.14 × 64 in²
A = 200.96 in²
Next, we calculate the circumference:
C = 2πr
C = 2 × 3.14 × 8 in
C = 50.24 in
Therefore, the value of the circumference is 50.24 in.
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Divide: 5m³n-25m²n²
5m²n
Om³n² - 5m²n³
Om-25m²n²
Om-20n
Om-5n
Answer:m-5n
Step-by-step explanation:
The following figure is made of 1 rectangle and 2 triangles find the area of each part of the figure and the whole figure
The area of the rectangle is 32 square units, the area of each triangle is 6 square units, and the Total area is 44 square units.
1. The rectangle, which has a length of 8 units and a width of 4 units.
2. The two triangles, which are identical and have a base of 4 units and a height of 3 units.
To find the area of the rectangle, we can use the formula:
Area = Length x Width
Area = 8 x 4 = 32 square units
To find the area of each triangle, we can use the formula:
Area = 1/2 x Base x Height
Area = 1/2 x 4 x 3 = 6 square units
So, the total area of both triangles is:
Total area = 6 + 6 = 12 square units
Now, to find the total area of the figure, we can add the areas of the rectangle and the two triangles:
Total area = Area of rectangle + Total area of triangles
Total area = 32 + 12 = 44 square units
Therefore, the area of the rectangle is 32 square units, the area of each triangle is 6 square units, and the total area is 44 square units.
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2 questions please answer both parts
A)Find the perimeter of the plot land
B) Find the area of the plot land without the building and parking lot.
The perimeter of the plot land is 78.49 units and the area of the plot land without the building and parking lot is 210 square units
Finding the perimeter of the plot landFrom the graph, the vertices of the land are
A = (0, 20), B = (25, 19), C = (20, 2) and D = (5, 0)
Calculate the distance between adjacent vertices
So, we have
AB = √[(0 - 25)² + (20 - 19)²] = 25.02
BC = √[(20 - 25)² + (2 - 19)²] = 17.72
DC = √[(20 - 5)² + (2 - 0)²] = 15.13
AD = √[(0 - 5)² + (20 - 0)²] = 20.62
The perimeter of the plot land is
P = 25.02 + 17.72 + 15.13 + 20.62
P = 78.49 units
Finding the area of the plot landThis is calculated as
Area = Plot land - Building - Parking lot
Using the vertices, we have
Area = 1/2 * |0 * 19 + 25 * 2 + 20 * 0 + 5 * 20 - (20 * 25 + 19 * 20 + 2 * 5 + 0 * 0)| - [1/2 *(15 - 7 + 17 - 7) * (15 - 10)] - [(18 - 10) * (10 - 5)]
This gives
Area = 295 - 45 - 40
So, we have
Area = 210
Hence, the area is 210 square units
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Practice A shuttle space suit, including the life support system, weighs about 310 pounds. The break in the y-axis represents the values from 0-300. What does each ordered pair on the line represent? 2. Write an equation to represent the relationship shown in the graph. 3. Is this a proportional relationship? Justify your answer. 4. In this problem situation, do all the points on the line make sense? Explain your reasoning. 5. Determine the weight of an astronaut without the shuttle suit given that the astronaut's weight while wearing the shuttle suit. a. 480 lb b. 467 lb c. 520 lb Weight of Astronaut With Suit (pounds)
Step-by-step explanation:
Each ordered pair on the line represents the weight of an astronaut with the shuttle space suit, given in pounds, and the total weight of the shuttle space suit and life support system, also given in pounds.
Let x represent the weight of the astronaut without the shuttle suit, and let y represent the weight of the astronaut with the shuttle suit and life support system. Then the equation for the relationship shown in the graph is: y = x + 310.
No, this is not a proportional relationship because the slope of the line is not constant. In a proportional relationship, the ratio of y to x would always be the same, but in this case, the ratio changes depending on the value of x.
No, not all the points on the line make sense in the context of the problem situation. For example, the point (0, 310) would represent an astronaut with no weight without the shuttle suit, which is not physically possible. Also, the point (480, 790) would represent an astronaut with a weight of 480 pounds without the suit, which is also not physically possible. Therefore, we need to restrict the domain of the equation to make sense in the context of the problem situation.
To determine the weight of an astronaut without the shuttle suit, we need to solve the equation y = x + 310 for x, given that y = 480. Substituting y = 480 into the equation, we get: 480 = x + 310. Solving for x, we get: x = 170. Therefore, the weight of the astronaut without the shuttle suit is 170 pounds.
The volume of a triangular pyramid is 120 units cubed. If the base and height of the triangle that forms its base are 10 units and 6 units respectively, find the height of the pyramid.
The height of the pyramid is 12 units
To find the height of the pyramid, we need to use the formula for the volume of a pyramid,
V = (1/3) * B * h,
where V is the volume, B is the area of the base, and h is the height of the pyramid.
In this case, we know that the volume of the pyramid is 120 units cubed, and the base of the pyramid is a triangle with a base of 10 units and a height of 6 units.
Therefore, the area of the base is,
(1/2) * 10 * 6 = 30 square units.
Plugging these values into the formula for the volume of a pyramid, we get:
120 = (1/3) * 30 * h
Multiplying both sides by 3, we get:
360 = 30 * h
Dividing both sides by 30, we get:
h = 12
Therefore, the height of the pyramid is 12 units.
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Help as soon as possible please!!
The coordinates of the triangle A'B'C' after rotating triangle ABC 90 degrees clockwise are A'(3, 6), B'(3, 2), and C'(7, 4).
To rotate the points of a triangle 90 degrees clockwise, we can use the following formula for a 2D rotation:
x' = x cos(θ) + y sin(θ)
y' = -x sin(θ) + y cos(θ)
Let's apply this formula to each point of the triangle ABC:
For point A(-6, 3):
x' = -6 cos(90°) + 3 sin(90°) = -6 (0) + 3(1) = 3
y' = -(-6) sin(90°) + 3 cos(90°) = 6 (1) + 3 (0) = 6
So, point A' is (3, 6).
For point B(-2, 3):
x' = -2 cos(90°) + 3 sin(90°) = -2 .0 + 3. 1 = 3
y' = -(-2) sin(90°) + 3 cos(90°) = 2 .1 + 3 .0 = 2
So, point B' is (3, 2).
For point C(-4, 7):
x' = -4 cos(90°) + 7 sin(90°) = -4 .0 + 7 . 1 = 7
y' = -(-4) sin(90°) + 7 cos(90°) = 4.1 + 7 .0 = 4
So, point C' is (7, 4).
Therefore, the coordinates of the triangle A'B'C' after rotating triangle ABC 90 degrees clockwise are A'(3, 6), B'(3, 2), and C'(7, 4).
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Two friends visited a taffy shop. Jon bought 4 kilograms of strawberry taffy and 1 kilogram of banana taffy for $23. Next, Charlotte bought 5 kilograms of strawberry taffy and 2 kilograms of banana taffy for $34. How much does the candy cost?
A kilogram of strawberry taffy costs $____, and a kilogram of banana taffy costs $____.
A kilogram of strawberry taffy costs $4, and a kilogram of banana taffy costs $7.
Let us assume
the price of 1 kg strawberry taffy = $x
And the price of 1kg banana taffy = $y
Then according to given information
the expression for Jon be,
4x + y = 23 ....(i)
the expression for Charlotte be,
5x + 2y = 34 ...(ii)
Now use elimination method
2x(i) - (ii) we get,
3x = 12
x = 4
Plug it into (i) we get
y = 7
Hence, costs are:
1 kg strawberry taffy = $4
1kg banana taffy = $7
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I WILL GIVE THE BRAINLIEST 69 POINTS
Step-by-step explanation:
the answer is 3
the answer is 3
Answer:
3
Step-by-step explanation:
explanation
f(x) =2x + 1 and g(x) = [tex]x^{2}[/tex]- 7
Thus, we have:
(g/f ) (x) = g(x) / f(x) = [tex]x^{2}[/tex]-7 ÷ 2x ÷ [tex]x^{2}[/tex] + 1
Find the volume of the sphere show ur work it’s
Answer:
904.78 [tex]in^{3}[/tex]
Step-by-step explanation:
The volume formula for a sphere is the following:
[tex]v=\frac{4}{3} \pi r^{3}[/tex]
[tex]d = 2r[/tex]
Replace with values and the answer is 904.78
what is the mean of this data set 3,5,15
Answer:
7.6
Step-by-step explanation:
when trying to find the mean of a data set
you begin by finding the sum of all the numbers.
3+5+15=23. Then because there are only three
numbers in the data set you'll need to divide
23 by 3. 23 / 3 = 7.6.
help me Find the base angles of the figure below.
A) 130°
B) 65°
C) 25°
D) 50°
Answer:
C) 25°
Step-by-step explanation:
You want the base angles in an isosceles triangle with vertex angle 130°.
Base anglesThe base angles of an isosceles triangle are congruent. If each is represented by 'b', then the sum of angles in the triangle is ...
2b +130° = 180°
2b = 50° . . . . . . . . subtract 130°
b = 25° . . . . . . . divide by 2
The base angles of the triangle are 25°, choice C.
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What conclusion can be determined from the dot plot below?
The number of observations is 10.
The median of the data set is 10.
The mean of the data set is 15.
The range of the data set is 12.
The conclusion can be determined from the dot plot is
The median of the data set is 10.
1. The number of observations is 10:
There are total 15 observations.
2. The median of the data set is 10.
From the dot plot the data is
9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12
Thus, the median is 10.
3. Mean = Sum of observation / Total Number of observation
Mean = (9+9+9+9+9+10+10+10+10+10+10+11+11+11+12) /15
Mean= 150/15=10
Thus, the Mean is 10.
4. Range = 12 - 9
Range = 3.
Learn more about dot plot here:
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 write a quadratic function that is three units write four units down and five times narrower then y=x squared
Answer:
y = 5(x - 3)^2 - 4 + c
Step-by-step explanation:
The standard form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants. To shift the graph three units to the right and four units down, we can modify the constant term c and the linear term bx:
y = a(x - 3)^2 - 4 + c
To make it five times narrower, we can modify the coefficient of the squared term a:
y = (1/5)a(x - 3)^2 - 4 + c
Since we want the shape to be the same as y = x^2, we can set a = 5:
y = 5(x - 3)^2 - 4 + c
The value of c will depend on the specific context of the problem or graph.
