Answers
The vertex form of the quadratic equations in standard form are, respectively:
Case 9: y = 2 · (x + 2)² - 12
Case 10: y = - (1 / 2) · (x + 3 / 4)² + 33 / 32
Case 11: y = 3 · (x - 4 / 3)² - 16 / 3
Case 12: y = - 3 · (x - 3)²
Case 13: y = (x - 4)² + 3
Case 14: y = (x - 1)² - 7
Case 15: y = (x + 3 / 2)² - 9 / 4
Case 16: 2 · (x + 1 / 4)² - 1 / 8
Case 17: y = 2 · (x - 3)² - 7
Case 18: y = - 2 · (x + 1)² + 10
How to derive the vertex form of a quadratic equationIn this problem we find ten cases of quadratic equation in standard form, whose vertex form can be found by a combination of algebra properties known as completing the square. Completing the square consists in simplifying a part of the quadratic equation into a power of a binomial.
The two forms are introduced below:
Standard form
y = a · x² + b · x + c
Where a, b, c are real coefficients.
Vertex form
y - k = C · (x - h)²
Where:
C - Vertex constant(h, k) - Vertex coordinates.Now we proceed to determine the vertex form of each quadratic equation:
Case 9
y = 2 · x² + 4 · x - 4
y = 2 · (x² + 2 · x - 2)
y = 2 · (x² + 2 · x + 4) - 12
y = 2 · (x + 2)² - 12
Case 10
y = - (1 / 2) · x² - 3 · x + 3
y = - (1 / 2) · [x² + (3 / 2) · x - 3 / 2]
y = - (1 / 2) · [x² + (3 / 2) · x + 9 / 16] + (1 / 2) · (33 / 16)
y = - (1 / 2) · (x + 3 / 4)² + 33 / 32
Case 11
y = 3 · x² - 8 · x
y = 3 · [x² - (8 / 3) · x]
y = 3 · [x² - (8 / 3) · x + 16 / 9] - 3 · (16 / 9)
y = 3 · (x - 4 / 3)² - 16 / 3
Case 12
y = - 3 · x² + 18 · x - 27
y = - 3 · (x² - 6 · x + 9)
y = - 3 · (x - 3)²
Case 13
y = x² - 8 · x + 19
y = (x² - 8 · x + 16) + 3
y = (x - 4)² + 3
Case 14
y = x² - 2 · x - 6
y = (x² - 2 · x + 1) - 7
y = (x - 1)² - 7
Case 15
y = x² + 3 · x
y = (x² + 3 · x + 9 / 4) - 9 / 4
y = (x + 3 / 2)² - 9 / 4
Case 16
y = 2 · x² + x
y = 2 · [x² + (1 / 2) · x]
y = 2 · [x² + (1 / 2) · x + 1 / 16] - 2 · (1 / 16)
y = 2 · (x + 1 / 4)² - 1 / 8
Case 17
y = 2 · x² - 12 · x + 11
y = 2 · (x² - 6 · x + 9) - 2 · (7 / 2)
y = 2 · (x - 3)² - 7
Case 18
y = - 2 · x² - 4 · x + 8
y = - 2 · (x² + 2 · x - 4)
y = - 2 · (x² + 2 · x + 1) + 2 · 5
y = - 2 · (x + 1)² + 10
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Related Questions
is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 26 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answers
Answer:
x is first angle
y is second angle
and z is third angle
Step-by-step explanation:
This question is solved by a system of equations. We have that:x is the first angle.y is the second angle.z is the third angle.Doing this, we get that:The first angle measures 30º.The second angle measures 67º.The third angle measures 83º.The sum of the measures of the angles of a triangle is 180. This means that The sum of the measures of the second and third angles is five times the measure of the first angle.This means that:From this, the first angle can be found:The measure of the first angle is of 30º.The third angle is 16 more than the second.This means that:Since We get that the second angle is:The second angle measures 67º.For the third angle:The third angle measures 83º.
I want 3 halves of a cupcake for myself, 8 halves for my friend, and 7 halves for our other friend. Royalty would be great.
Answers
By adding fractions that represent each of the amounts of cupcakes, we can see that you need 9 cupcakes for you and your friends.
How many halves they need in total?Her we know that you want 3 halves of a cupcake for yourself, 8 halves for your friend, and 7 halves for your other friend.
So we just need to add all of these fractions, to do so, we need to solve the follwing opeartion:
3*(1/2) + 8*(1/2) + 7*(1/2)
3/2 + 8/2 + 7/2
All of these have the same denominator so we can directly add them up:
3/2 + 8/2 + 7/2 = (3 + 8 + 7)/2
(3 + 8 + 7)/2 = 18/2
18/2 = 9
You need 9 cupcakes for you and your friends.
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Complete question:
"I want 3 halves of a cupcake for myself, 8 halves for my friend, and 7 halves for our other friend. How many halves we need in total?"
A line has the equation y - 6 = 5x + 9 . work out the gradient and the y intercept of the line.
Answers
The gradient of the line is 5, and the y-intercept of the line is 15.
EquationsThe given equation is in the form of y = mx + c, where m is the gradient (slope) of the line and c is the y-intercept of a straight line represented in 2D plane.
Rearranging the given equation, we get:
y - 6 = 5x + 9
Adding 6 to both sides, we get:
y = 5x + 15
Now we can see that the equation is in the required form of y = mx + c. The gradient (slope) of the line is 5, which is the coefficient of x in the equation. The y-intercept is 15, which is the constant term in the equation.
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rewrite the following without an exponet. 3^-4
Answers
Answer:i think -81
Step-by-step explanation:3x (-3) = -9. -9x(-3)=27. 27x(-3)= -81
A truck is traveling due north at 60km/hr approaching a crossroad. On a perpendicular road a police car is traveling west toward the intersection at 75km/hr. Both vehicles will reach the crossroad exactly one hour. Find the vector currently representing the displacement of the truck with respect to the police car.
Displacement d=
Answers
In the given problem, the displacement vector of the truck with respect to the police car is (-75, 60). This means that the truck is 75 km to the west and 60 km to the north of the police car.
How to Solve the Problem?To solve this problem, we can use vector addition. Let's assume that the police car is at the origin, and let the positive x-axis point west and the positive y-axis point north. Then, the initial position of the truck can be represented by the vector (-d, 0), where d is the distance between the police car and the crossroad.
Since the truck is traveling due north, its velocity vector is (0, 60). Similarly, the velocity vector of the police car is (-75, 0). We know that both vehicles will reach the crossroad at the same time, which means that their displacement vectors will have the same magnitude and direction.
Let's call the displacement vector we're looking for "D". Using the formula for displacement, we can write:
D = vt
where v is the average velocity of both vehicles, and t is the time it takes for them to reach the crossroad (which is one hour). The average velocity is given by the vector sum of the velocities of the truck and the police car:
v = (0, 60) + (-75, 0) = (-75, 60)
Substituting in the values for v and t, we get:
D = (-75, 60) * 1 = (-75, 60)
Therefore, the displacement vector of the truck with respect to the police car is (-75, 60). This means that the truck is 75 km to the west and 60 km to the north of the police car.
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Jen is studying how years of drought conditions have caused the water level of Richland Reservoir to drop. At the start of the study, the water in the reservoir was 65 meters deep. Jen observed that the depth of the water dropped by about 0.8 meters the first month of the study. She wants to know what the depth of the water will be if it continues dropping at the same rate. You can use a function to approximate the depth of the water in the reservoir x months after the start of the study. Write an equation for the function.
Answers
The equation for the function is D(x) = 65 - 0.8x. Where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.
What is a linear function?
A linear function is a mathematical function that has a constant rate of change or slope between the independent variable (x) and the dependent variable (y). It is a function that can be graphically represented as a straight line.
We can use a linear function to approximate the depth of the water in the reservoir x months after the start of the study, since the depth is dropping at a constant rate of 0.8 meters per month. Let D(x) be the depth of the water in meters x months after the start of the study. Then we have:
D(x) = 65 - 0.8x
where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.
Therefore, the equation for the function is D(x) = 65 - 0.8x.
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100 Points!!! Algebra question, only looking for answer to last two. Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. Photo attached. Thank you!
Answers
1) y = -3x and y = -3x + 2: inconsistent system of equations.
2) y = x - 5 and -2x + 2y = - 10: consistent and independent.
3) 2x - 5y = 10 and 3x + y = 15 : consistent and independent.
Explain about the consistent and inconsistent system of equations?If there is at least one solution, an equation system is considered consistent. If there is no solution, a system is inconsistent.If one equation is a multiple of the other in a pair of equations that have two variables, both equations are dependant. Every point in dependent systems is a potential solution, giving them an endless number of solutions.The given equation are:
The graph for each system of equations is plotted.
1) y = -3x and y = -3x + 2
From the graph 1 it is shown that the lines for the each equation form the parallel lines.
Thus, system of equations are inconsistent.
2) y = x - 5 and -2x + 2y = - 10
From the graph 2 it is shown that the lines for the each equation form the coincident lines.
Thus, system of equations are consistent and independent.
3) 2x - 5y = 10 and 3x + y = 15
From the graph 2 it is shown that the lines for the each equation form the coincident lines.
Thus, system of equations are consistent and independent.
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Your tank has a volume of 10 L at the surface (1 atm pressure). You reach a depth of 66 ft. What is the
pressure? What is the volume?
Answers
the pressure at a depth of 66 ft is 197,580 Pa, and the volume of the tank at this depth is 0.000505 L.
EquationsTo find the pressure at a depth of 66 ft in a liquid, we can use the formula:
pressure = density x gravity x depth
Assuming the liquid in the tank is water, the density is 1000 kg/m³, and gravity is 9.81 m/s².
First, we need to convert 66 ft to meters:
66 ft x 0.3048 m/ft = 20.1168 m
Then, we can find the pressure at this depth:
pressure = 1000 kg/m³ x 9.81 m/s² x 20.1168 m = 197,580 Pa
To find the volume of the tank at this depth, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at a constant temperature:
P₁V₁ = P₂V₂
where P₁ and V₁ are the initial pressure and volume (1 atm and 10 L, respectively), and P₂ and V₂ are the final pressure and volume.
We can rearrange this equation to solve for V₂:
V₂ = (P₁ x V₁) / P₂
Substituting the values, we get:
V₂ = (1 atm x 10 L) / (197,580 Pa / 1 atm) = 0.000505 L
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13. The profit, in thousands of dollars, from the sale of x kilogram of coffee bean can be modelled by the function () = 5−400 +600 . a) State the asymptotes and the intercepts. Then, sketch a graph of this function using its key features. (5 pts) b) State the domain and range in this context. (2 points) c) Explain the significance of the horizontal asymptote. (1 point) d) Algebraically, find how much amount of tuna fish, in kg, should be sold to have a profit of exactly $4000? (4 points) SOLUTION
Answers
Answer: a) The profit function can be written as:
P(x) = 5x - 400x + 600
To find the asymptotes, we can look at the denominator of the second term, which is (x - 3). This means that there is a vertical asymptote at x = 3. To find the intercepts, we can set P(x) = 0:
5x - 400x + 600 = 0
Solving for x, we get:
x = 1.5 and x = 2.5
Therefore, there are x-intercepts at (1.5, 0) and (2.5, 0). To sketch the graph, we can also note that the coefficient of x^2 is negative, which means that the graph is a downward-facing parabola.
b) The domain of the function is the set of all possible values of x, which in this context represents the amount of coffee sold. Since we cannot sell a negative amount of coffee, the domain is x ≥ 0.
The range of the function is the set of all possible values of P(x), which represents the profit. Since the coefficient of x^2 is negative, the maximum profit occurs at the vertex of the parabola. The vertex has x-coordinate:
x = -b/(2a) = -(-400)/(2(-200)) = 1
Therefore, the maximum profit occurs when x = 1. The vertex has y-coordinate:
P(1) = 5(1) - 400(1) + 600 = 205
Since the coefficient of x^2 is negative, the range is (-∞, 205].
c) The horizontal asymptote of the function is y = -400, which represents the long-term average profit per kilogram of coffee sold. This means that as x gets very large, the profit per kilogram approaches -400. This could happen, for example, if the cost of producing the coffee increased significantly while the price remained the same.
d) To find the amount of coffee that must be sold to make a profit of $4000, we can set P(x) = 4000 and solve for x:
5x - 400x + 600 = 4000
Simplifying, we get:
-395x = -3400
Dividing both sides by -395, we get:
x ≈ 8.61
Therefore, approximately 8.61 kg of coffee must be sold to make a profit of $4000.
Step-by-step explanation:
1. Identify and clearly label the slope and y-intercept for each equation in slope intercept form. Choose the correct answer from the choices below.
Y=-5
A. Slope is-5 and the y-intercept is (0,0)
B.Slope is zero and the y-intercept is (0,-5)
C. Slope is zero and the y-intercept is (0,0)
D. Slope is -5 and the y-intercept is (0,-5)
Answers
Slope is zero and the y-intercept is (0,-5)
What is slope ?
In mathematics, slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between the same two points.
In other words, the slope of a line is the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line. It can also be thought of as the rate at which the line rises or falls as it moves horizontally.
The formula for calculating slope is:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
According to the question:
The equation Y = -5 is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Comparing the equation Y = -5 to y = mx + b, we can see that:
The slope, m, is 0, since there is no x-term in the equation.
The y-intercept, b, is -5, since that is the constant value in the equation.
Therefore, the correct answer is:
B. Slope is zero and the y-intercept is (0,-5)
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A company manufactures aluminum mailboxes in the shape of a box with a half-cylinder top. The company will make 1728 mailboxes this week. If each mailbox has dimensions as shown in the figure below, how many square meters of aluminum will be needed to make these mailboxes? In your calculations, use the value 3.14 for X, and round up your answer to the next square meter.?
Answers
Answer:
1759 square meters
Step-by-step explanation:
You want the surface area of a cuboid with a half-cylinder top.
Lateral areaThe lateral area of the figure is the product of the length of the mailbox (0.45 m) and the perimeter of the end. The perimeter of the end is the sum of the lengths of the straight sides and half the circumference of a circle with diameter 0.3 m.
P = 0.3 + 2·0.4 + π/2(0.3) = 1.571 . . . . . meters
LA = Ph = (1.571 m)(0.45 m) = 0.70695 m²
End areaThe end area is twice the area of the rectangular portion of the end, plus the area of a circle 0.3 m in diameter.
EA = (0.3 m)(0.4 m) + 3.14(0.3/2 m)² = 0.31065 m²
Total areaThe total area of 1 mailbox is ...
LA +EA = 0.70695 m² +0.31065 m² = 1.0176 m²
Then the area of 1728 mailboxes is ...
1728 × 1.0176 m² ≈ 1758.4 m² ≈ 1759 m²
About 1759 square meters of aluminum will be needed for the 1728 mailboxes.
__
Additional comment
This presumes there is no waste in cutting the semicircular shape from the supplied aluminum.
Find the product……..
Answers
The product of the expressions are;
Step 1: (x + 2)(x + 3) and 3(x + 3)/4(x + 5)
Step 3: 4(x + 3) × 3(x + 3)/4(x + 5)
Step 4: 3/x + 5
How to determine the productIt is important to note that algebraic expressions are described as expressions that are composed of variables, terms, coefficients, constants and factors.
From the information given, we have the fraction;
4x + 8/x² + 5x + 6 × 3x + 9/4x + 20
To determine the product, let us reduce the expressions to their lowest forms, we have;
4x + 8 = 4(x + 2)
x² + 5x + 6 = (x + 2)(x + 3)
3x + 9 = 3(x +3)
4x + 20 = 4(x + 5)
Substitute the expressions
4(x + 2)/(x + 2)(x + 3) × 3(x +3)/4(x + 5)
divide the common terms
4(x + 3) × 3(x + 3)/4(x + 5)
Divide further, we have.
3/x + 5
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video
Let the region R be the area enclosed by the function f(x) = ln (x) + 1 and
g(x)=x-1. If the region R is the base of a solid such that each cross section
perpendicular to the a-axis is a semi-circle with diameters extending through the
region R, find the volume of the solid. You may use a calculator and round to the
nearest thousandth.
Answers
The volume of the solid is approximately 0.558 cubic units.
To find the volume of the solid, we need to integrate the area of the semi-circles along the a-axis.
We know that the diameter of each semi-circle is the distance between the functions f(x) and g(x), which is:
d(a) = f(a) - g(a) = ln(a) + 1 - (a-1) = ln(a) - a + 2
The radius of each semi-circle is half of the diameter, which is:
r(a) = (ln(a) - a + 2) / 2
The area of each semi-circle is π times the square of its radius, which is:
[tex]A(a) = πr(a)^2 = π/4 (ln(a) - a + 2)^2[/tex]
To find the volume of the solid, we integrate the area of each semi-circle along the a-axis, from a = e to a = 2:
V = ∫[e,2] A(a) da
V = ∫[e,2] π/4 [tex](ln(a) - a + 2)^2 da[/tex]
V ≈ 0.558 (rounded to the nearest thousandth)
Therefore, the volume of the solid is approximately 0.558 cubic units.
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PLEASE HELP! Find missing side lengths of B and C. Explain
Answers
Answer:
b=7 & c=7√2
Step-by-step explanation:
b=7 as it is an isosceles triangle
now using Pythagoras theorem,
(c)^2= (7)^2+(7)^2
⇒(c)^2= 49+49
⇒(c)^2= 98
⇒c= √98
⇒c=7√2
Answer:
b = 7c = 7√2Step-by-step explanation:
You want the missing side lengths in an isosceles right triangle with one side given as 7.
Isosceles right triangleThe two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:
b = 7
The hypotenuse of an isosceles right triangle is √2 times the side length:
c = 7√2
__
Additional comment
You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.
c² = 7² + b²
c² = 7² +7² = 2·7²
c = √(2·7²) = 7√2
The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.
The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.
what is the answer of 10.9% of $8.85
Answers
Answer:
To find 10.9% of $8.85 we can convert the percentage into a decimal:
10.9% = 0.109
0.109x8.85 = $0.964
=$0.96 (Rounded to 2 decimal places)
If the graph of a polynomial function P(x) has -intercepts at x = - 4, x = 0, x * 1 point
= 5, which of the following must be true for P(x)?
• (x + 5) is a factor of the polynomial.
• (x-4) is a factor of the polynomial.
•' The degree of the polynomial is 3.
• The degree of the polynomial is greater than or equal to 3.
Answers
(x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.
What is a functiοn ?Functiοn can be define in which it relates an input tο οutput.
If the graph οf a pοlynοmial functiοn P(x) has x-intercepts at x = -4, x = 0, and x = 5, then we knοw that the factοrs οf P(x) are (x + 4), x, and (x - 5). This is because a pοlynοmial has x-intercepts where the value οf P(x) is equal tο zerο, and this οccurs when each factοr is equal tο zerο.
Therefοre, we can cοnclude that (x + 4) and (x - 5) are factοrs οf the pοlynοmial P(x), but x is nοt necessarily a factοr. This is because x is a linear factοr with a zerο intercept, but it cοuld be cancelled οut by anοther factοr in the pοlynοmial.
Thus, the cοrrect statement is:
(x + 5) is nοt necessarily a factοr οf the pοlynοmial.
(x-4) is a factοr οf the pοlynοmial.
The degree οf the pοlynοmial is 3 οr greater since the pοlynοmial has three x-intercepts. Hοwever, we cannοt determine the exact degree οf the pοlynοmial withοut additiοnal infοrmatiοn.
Therefοre, (x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.
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Solve the problems. Show your work.
7
1. Mr. Nguyen had 7/8
pint of water in his water bottle. Then, he drank 2/3
pint. How much water is left in the bottle?
Answers
Answer:
7/8 - 2/3 = 5/8 pint of water left in the bottle.
Note: For questions 13–21, remember to show all of the steps that you use to solve the problem. You can use the comments field to explain our work. Your teacher will review each step of your responses to ensure your receive proper credit for your answers.
Note: Your teacher will grade your response to this question to ensure you receive proper credit for your answer.
Sarah is making a scale drawing of a painting that is 48 in. wide by 120 in. high. Her paper is 12 in. wide and 24 in. tall. She decides to use the scale 1 in. = 4 in. Is this a reasonable scale?
SOMEONE, PLEASE HELP! I WILL MAKE BRAINLIST!!!
Answers
Answer:
This isn't a reasonable scale
Step-by-step explanation:
Using the scale 1 in. = 4 in., the width of the scaled down painting will be:
48 in. ÷ 4 = 12 in.
And the height of the scaled down painting will be:
120 in. ÷ 4 = 30 in.
So the scaled down painting will be 12 in. wide and 30 in. tall. Since Sarah's paper is 12 in. wide and 24 in. tall, the scaled down painting will fit within the paper's width but will be taller than the paper.
Therefore, the scale is not reasonable because the scaled down painting will not fit within the dimensions of Sarah's paper.
please help immediately
please go to my profile and answer the other I need them asap.
Answers
10³•10⁵•10³
Step-by-step explanation:
10³means 10×3,10⁵means 10×5and 10³means 10×3 30+50+30=110
7 x 10 the the power of -5
Answers
Answer:
0.00005
Step-by-step explanation:
you move 5 decimal places left starting from 7 and right it as a decimal.
Ans=0.00007
what is required for a current to flow?
A. Electrons, protons, and an energy source
B. An insulator, battery, and recipient
C. A recipient, a connection, and something made out of rubber
D. An Energy source, a recipient, and a connection
Answers
Therefore , the solution of the given problem of unitary method comes out to be enable the current to travel, a connection, such as a wire or conductor, is required.
What is a unitary method?Utilizing previously well-known variables, this uniform convenience, or all crucial elements from a prior flexible study that followed a particular methodology event can all be used to achieve the goal. It will be possible to contact the entity again if the anticipated assertion outcome actually happens; if it doesn't, both important systems will surely miss the statement.
Here,
D. In order for a current to move, there must be an energy source, a recipient, and a connection.
Current is the movement of charged ions through a conductor, most frequently electrons.
The energy required to transport the charged particles is provided by an energy source, such as a battery or generator.
The current has a route through a recipient, which can be a machine or a circuit.
In order to finish the circuit and enable the current to travel, a connection, such as a wire or conductor, is required.
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Suppose 50 rabbits are on Groff Farm… DOUBLING every SIX MONTHS…
How many rabbits after 5 years?
How many rabbits after 10 years?
Answers
Using geometric progression Rabbits after 5 years will be 5120. Rabbits after 10 years will be 52,428,800.
What is geometric progression?When each term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the series. It should be mentioned that the common ratio is obtained by dividing any succeeding term by its preceding term.
What is ratio?Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate organizations or groups.
In this question,
The number of rabbits initially=50=a
rabbits after 6 months=100
common ratio=r= 100/50=2
Since it is a geometric progression, the 11th term will give us the number of rabbits after 5 years.
a₁₁=a₁(r)¹¹⁻¹
=50(2)¹⁰=5120
the 21th term will give us the number of rabbits after 10 years.
a₂₁=a₁(r)²¹⁻¹
=50(2)²⁰=52,428,800
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Can some one help with this problem
Answers
Step-by-step explanation:
Area of the trapezoid = height x average of bases
area = 4 x (8+13)/2) = 42 in^2
Area of triangle = 1/2 base * height = 1/2 (13-8) * 4 = 10 in^2
Interpret the data in the circle graph. If 560 books were sold at the book fair, find the number of the books that were mystery books.
If 560 books were sold at the book fair,
(Type a whole number.)
of the books were mystery books.
Circle graph
Fantasy 8%
Science
Fiction
12%
Comic 15%
Other 5%
Mystery 20%
-Fictic
Answers
Answer:
112
Step-by-step explanation:
According to the circle graph, the mystery books make up 20% of all books sold. So, we can calculate the number of mystery books sold as follows:
Number of mystery books = 20% of 560
= (20/100) x 560
= 112
Therefore, the number of mystery books sold at the book fair was 112.
In one town 44% of voters are democrats if two voters are randomly selected for a survey find the probability that they are both Democrats assume events are independent round to the nearest thousand if necessary
Answers
the probability that they are both Democrats. round to the nearest thousandth if necessary is 0.194
The probability that BOTH is democrats means the probability of "one being democrat" AND "another also being democrat".
The AND means we need to MULTIPLY the individual probability of a person being a democrat.
The probability that a voter is democrat is 44% (0.44) -- stated in the problem
Now, the Probability of BOTH being Democrats is simply MULTIPLYING 0.44 with 0.44
Rounded to the nearest thousandth, 0.194
The last answer choice is correct.
the complete question is-
In one town 44% of all voters are Democrats if two voters are randomly selected for a survey find the probability that they are both Democrats. round to the nearest thousandth if necessary.
0.189
0.880
0.440
0.194
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Find the area of the shaded sector of the circle
Answers
Answer:
32.67 square meters
Step-by-step explanation:
finding the area of the shaded region.
area of sector = (θ/360°) x πr²
where "θ" is the central angle of the sector in degrees, "r" is the radius of the sector, and π is a mathematical constant approximately equal to 3.14.
Substituting the given values into the formula, we get:
area of sector = (60°/360°) x π(14m)²
area of sector = (1/6) x 3.14 x 196m²
area of sector = 32.67m² (rounded to two decimal places)
Therefore, the area of the section is 32.67 square meters
Lyla invests $2,500 into a savings account
which earns 5% per year. In 15 years, how
much will Lyla's investment be worth if interest
is compounded semiannually (twice a year)?
Round to the nearest dollar.
Answers
Answer:
The formula for compound interest is given by:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $2,500, r = 0.05 (since 5% = 0.05), n = 2 (since interest is compounded semiannually), and t = 15. Substituting these values into the formula, we get:
A = 2500(1 + 0.05/2)^(2*15)
A ≈ $5,551.33
Therefore, Lyla's investment will be worth approximately $5,551.33 after 15 years if interest is compounded semiannually.
The two top concert tours in 2016 were concert A and concert B. Based on average ticket prices, it cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B. Three tickets for concert B cost a total of $687. How much did an average ticket cost for each tour?
Answers
The average ticket cost for each concert is given as follows:
Concert A: $188.83.Concert B: $95.67.How to obtain the ticket costs?The ticket costs are obtained by a system of equations, for which the variables are given as follows:
Variable a: cost for Concert A.Variable b: cost for Concert B.It cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B, hence:
6a + 6b = 1707
a + b = 284.5.
Three tickets for concert B cost a total of $687, hence the cost for concert B is of:
3b = 687
b = 287/3
b = $95.67.
Replacing into the first equation, the cost for concert A is given as follows;
a = 284.5 - 95.67
a = $188.83.
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One of outstanding journal recently published an article indicating differences in perception of gender equality on the job between men and women. The article claimed that women perceived the gender equality problem to be much more compared to men. One question asked of both men and women was: "Do you think gender equality is a major problem in the workplace?" 60% of the women responded "Yes", compared to men about 25%. Assuming W designates women's responses and M designates men's, what hypothesis should journal test in order to show that its claim is TRUE?
Answers
The journal could use a one-tailed hypothesis test with a significance level (α) of 0.05 to determine whether there is a significant difference between the proportion of women and men.
What is p value?In statistics, the p-value is a measure of the evidence against the null hypothesis. It is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming that the null hypothesis is true. In other words, the p-value is the probability of obtaining the observed results, or more extreme results, if the null hypothesis were true.
Given by the question.
To test the claim that women perceive the gender equality problem to be much more compared to men, the journal could test the following hypothesis:
Hypothesis: The proportion of women who perceive gender equality to be a major problem in the workplace (W) is significantly greater than the proportion of men who perceive gender equality to be a major problem in the workplace (M).
H0: W = M (there is no significant difference in perception of gender equality between men and women)
Ha: W > M (women perceive gender equality to be a major problem more than men do)
who perceive gender equality to be a major problem in the workplace. They could calculate the p-value and compare it to α. If the p-value is less than α, they would reject the null hypothesis and conclude that the proportion of women who perceive gender equality to be a major problem in the workplace is significantly greater than the proportion of men who perceive it to be a major problem.
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COMM 291C Applications of Statistics in Business
Winter 2023
Assignment 07
1. A fish tank is filled with the fish of three different species, and each fish comes in three sizes. The
counts of all the fish are summarized in the following contingency table:
Small Medium Large Total
Goldfish 48 45 19 112
Guppy 70 42 19 131
Gourami 40 9 10 59
Total 158 96 48 302
a. If I randomly catch any one fish from this tank, what is the probability that the caught
fish is medium-sized? Show your calculations. (1)
b. If I randomly catch one fish from this tank, what is the probability that the caught fish is a
medium-sized guppy? Show your calculations. (1)
c. If I randomly catch one medium-sized fish from this tank, what is the probability that the
caught fish is a guppy? Show your calculations. (1)
d. If I randomly catch one guppy from this tank, what is the probability that the caught fish
is medium-sized? Show your calculations. (1)
e. If I randomly catch one fish from this tank, what is the probability that the caught fish is a
not a goldfish? Show your calculations. (1)
f. Are two events, randomly catching a guppy and randomly catching a medium-sized fish,
independent? Explain how you know. (2)
Answers
a) If I randomly catch any one fish from this tank, the probability of catching a medium-sized fish from the tank is 0.3182.
b) the probability of catching a medium-sized guppy from the tank is 0.1391.
c) the probability of catching a guppy if we randomly select a medium-sized fish from the tank is 0.4375.
d) the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is 0.3206.
e) the probability of catching a fish that is not a goldfish if we randomly select a fish from the tank is 0.6291.
f) 0.1384 is not equal to 0.1391, which indicates that the two events are not independent
Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.
The explanation to the above probability answer are given below:
a)
From the contingency table, we can see that the total number of medium-sized fish is 96. The total number of fish in the tank is 302. Therefore, the probability of catching a medium-sized fish is:
Probability of catching a medium-sized fish = Total number of medium-sized fish / Total number of fish
Probability of catching a medium-sized fish = 96 / 302
Probability of catching a medium-sized fish = 0.3182
Therefore, the probability of catching a medium-sized fish from the tank is 0.3182
b)
From the contingency table, we can see that the total number of medium-sized guppies is 42. The total number of fish in the tank is 302. Therefore, the probability of catching a medium-sized guppy is:
Probability of catching a medium-sized guppy = Total number of medium-sized guppies / Total number of fish
Probability of catching a medium-sized guppy = 42 / 302
Probability of catching a medium-sized guppy = 0.1391
Therefore, the probability of catching a medium-sized guppy from the tank is 0.1391.
c)
From the contingency table, we can see that the number of medium-sized guppies is 42, and the number of medium-sized fish is 96. Therefore, the probability of catching a guppy if we randomly select a medium-sized fish is:
Probability of catching a guppy given a medium-sized fish = Number of medium-sized guppies / Total number of medium-sized fish
Probability of catching a guppy given a medium-sized fish = 42 / 96
Probability of catching a guppy given a medium-sized fish = 0.4375
Therefore, the probability of catching a guppy if we randomly select a medium-sized fish from the tank is 0.4375.
d)
To calculate the probability of catching a medium-sized guppy if we randomly select a guppy from the tank, we need to find the number of medium-sized guppies in the tank and divide it by the total number of guppies in the tank.
From the contingency table, we can see that the number of medium-sized guppies is 42, and the total number of guppies is 131. Therefore, the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is:
Probability of catching a medium-sized guppy given a guppy = Number of medium-sized guppies / Total number of guppies
Probability of catching a medium-sized guppy given a guppy = 42 / 131
Probability of catching a medium-sized guppy given a guppy = 0.3206
Therefore, the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is 0.3206.
e)
From the contingency table, we can see that the total number of non-goldfish is 190 (45 medium goldfish + 70 small guppy + 42 medium guppy + 9 medium gourami + 10 large gourami + 14 small gourami). The total number of fish in the tank is 302. Therefore, the probability of catching a fish that is not a goldfish is:
Probability of catching a fish that is not a goldfish = Total number of non-goldfish / Total number of fish
Probability of catching a fish that is not a goldfish = 190 / 302
Probability of catching a fish that is not a goldfish = 0.6291
Therefore, the probability of catching a fish that is not a goldfish if we randomly select a fish from the tank is 0.6291.
f)
From the contingency table, we can see that the probability of randomly catching a guppy is 131/302, which is approximately 0.4344. Similarly, the probability of randomly catching a medium-sized fish is 96/302, which is approximately 0.3182.
Now, let's consider the joint probability of randomly catching a medium-sized guppy, which we calculated earlier to be 42/302, or approximately 0.1391. To determine if the events are independent, we need to compare the product of the probabilities of the individual events (catching a guppy and catching a medium-sized fish) to the joint probability of the events occurring together.
If the events are independent, then the product of their individual probabilities should be equal to the joint probability:
P(catching a guppy) x P(catching a medium-sized fish)
= P(catching a medium-sized guppy)
0.4344 x 0.3182 = 0.1391
0.1384 is not equal to 0.1391, which indicates that the two events are not independent.
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