The parent function for the graph to the right is of the form y = ab*. Write the parent function. Then write a function for the
translation indicated.
translation: left 6 units, down 7 units
The parent function is [tex]y = ab^x[/tex]
A function for the translation indicated is [tex]y = ab^{x+6} - 7[/tex].
What is a translation?In Mathematics and Geometry, the vertical translation a geometric figure or graph downward simply means adding a digit to the value on the y-coordinate of the pre-image or function.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent functions.In this scenario, we can logically deduce that the graph of the parent function was translated or shifted to the left (horizontally) by 6 units and downward (vertically) by 7 units;
[tex]y = ab^x[/tex]
[tex]y = ab^{x+6} - 7[/tex]
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The table shows the results of rolling a die several times. Outcome 1 2 3 4 5 6 Number of times outcome occurred 7 4 4 5 6 4 To the nearest percent, what is the experimental probability of rolling a 6? Question 1 options: 17% 20% 13% 67%
The experimental probability of the rolling a 6 is 13%.
How to find the experimental probability of rolling a 6?Probability is the likelihood of a desired event happening. Experimental probability is a probability that relies mainly on a series of experiments.
From the table:
The total number of times all the numbers appear is:
total number of times = 7 + 4 + 4 + 5 + 6 + 4 = 30
The number six (6) occurred 4 times.
Experimental probability = (occurrence of 6 / total number of times)
Experimental probability = 4/30 * 100
Experimental probability = 13%
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4,12,44,176,890
which is odd one ?
Answer:
If we are looking at 100th it is 176 if it's tens look at 7 and 9
help
A grocery store clerk is placing cans of soup on an 8-ft long shelf. If the cans are lined up in a row, how many more of the smaller cans will fit on the shelf than the larger cans? Round to the nearest whole number.
There is 1 smaller can that will be put on the shelve.
Given that, a clerk is placing cans of soup on an 8-ft long shelf, we need to find how many more of the smaller cans will fit on the shelf than the larger cans,
Volume of small cans = 127.2 in³
Therefore,
127.2 = 3.14 × 4.5 × r²
r² = 127.2 / 14.13
r² = 9
r = 3
Similarly, the volume of the large can = 301.6 in³
301.6 = 3.14 × 6 × r²
r² = 16
r = 4
The number of small cans that can be out on the shelve = 8/3 ≈ 9
The number of larger cans that can be out on the shelve = 8/4 = 2
Hence, there is 1 smaller can that will be put on the shelve.
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Find the missing angle
The measure of the missing angle is 20 degrees.
What is the measure of the missing angle?The figure in the image is a right triangle.
Missing angle θ = ?Opposite to angle θ = 8Adjacent to angle θ = 20To solve for the missing angle. we use trigonometric ratio.
Note: Tangent = Opposite / Adjacent
Plug in the values and solve for the angles:
tanθ = 8/20
Take the tan inverse
θ = tan⁻¹( 8/20 )
θ = 21.8°
θ ≈ 20°
Therefore, the angle is 20 degrees.
Option B)20° is the correct answer.
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There are 35 boys in the sixth grade. The number of girls in the sixth grade is 42. Lonnie says that means the ratio of the number of boys in the sixth grade to the number of girls in the sixth grade is 5: 7. Is Lonnie correct? Show why or why not.
Answer:
Step-by-step explanation:No, Lonnie is not correct. Step-by-step explanation: Because if we put 35 and 42 in rational form we can write it to its simple form by dividing it and after dividing we get the answer as 5 : 6. so that means Lonnie in incorrect.D
The area of a square table top can be represented by (9x^2-30x+25) square feet. The perimeter of the table top is 34 feet. What is the value of x? Explain ow you solved this problem.
The requried value of x that satisfies the problem is 4.5,
Let's start by finding the side length of the square tabletop, which is equal to the square root of its area. We have:
Area = 9x² - 30x + 25
Side length = √(Area) = √(9x² - 30x + 25)
To find x, we need to use the fact that the perimeter of the table top is 34 feet. The perimeter of a square is given by 4 times the length of one of its sides, so we can write:
Perimeter = 4 * Side length
34 = 4 * √(9x² - 30x + 25)
8.5 = √(9x² - 30x + 25)
9x² - 30x - 47.25 = 0
We can solve this quadratic equation by using the quadratic formula gives,
x = 4.5 and -1.16
Therefore, the value of x that satisfies the problem is approximately 4.5, since the other solution is negative and not meaningful in this context.
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Classify the function type of f(x) = x+2−−−−−√3
x
+
2
3
A. square root
B. cube root
C. quadratic
D. exponential
The function type of f(x) = √3x + 2 is A. square root
Classifying the function type of f(x)From the question, we have the following parameters that can be used in our computation:
f(x) = √3x + 2
In the above function, we have the notation √
The notation √ is a square root notation
This means that the function type of f(x) is A. square root
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Triangle ABC and triangle DEF are similar. What is the measure
of side DF?
B
E
9 cm
15 cm
D
с
? cm
25 cm
F
The measure of side DF is 15cm
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. For two traingles to be similar, the corresponding angles of the triangles must be equal.
And also, the ratio of corresponding sides of Similar triangles are equal
This means;
15 /25 = 9/DF
representing DF by x
15/25 = 9/x
15x = 25×9
15x = 225
divide both sides by 15
x = 225/15
x = 15cm
Therefore the measure of DF is 15cm
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PLEASE HELP 50 POINTS
To check if a solution is correct for a system of equations, we substitute the values of the solution into both equations and see if they are true.
Let's assume that the solution for the system of equations is (x,y) = (1,-1).
To check if this solution is correct for the first equation y = 2x - 3, we substitute x = 1 and y = -1:
-1 = 2(1) - 3
-1 = -1
Since -1 = -1, the solution (1,-1) satisfies the first equation.
To check if this solution is correct for the second equation y = -1/2x + 2, we substitute x = 1 and y = -1:
-1 = -1/2(1) + 2
-1 = 1
Since -1 is not equal to 1, the solution (1,-1) does not satisfy the second equation.
Therefore, the solution (1,-1) is not a solution for the system of equations y = 2x - 3 and y = -1/2x + 2.
Analyze a CSR capital investment proposal for Ganon Inc.
Ganon Inc. is evaluating a proposal to replace its HID (high intensity discharge) lighting with LED (light emitting diode) lighting throughout its warehouse. LED lighting consumes less power and lasts longer than HID lighting for similar performance. The following information was developed:
Line Item Description Value
HID watt hour consumption per fixture 500 watts per hr.
LED watt hour consumption per fixture 300 watts per hr.
Number of fixtures 800
Lifetime investment cost (in present value terms)
to replace each HID fixture with LED $300
Operating hours per day 10
Operating days per year 300
Metered utility rate per kilowatt-hour (kwh)* $0.12
*Note: A kilowatt-hour is equal to 1,000 watts per hour.
a. Determine the investment cost for replacing the 800 fixtures.
$240,000
b. Determine the annual utility cost savings from employing the new energy solution.
c. Should the proposal be accepted?
Yes
Evaluate the proposal using net present value, assuming a 15-year life and 8% minimum rate of return. (Click here to view Present Value of Ordinary Annuity.)
a)
The investment cost for replacing the 800 fixtures is $240,000.
b)
Annual utility cost savings is $57,600/year.
c)
Since the NPV is positive, the proposal should be accepted as it generates a positive return and is expected to be profitable.
We have,
a.
The investment cost for replacing the 800 fixtures is given as $300 per fixture, so the total investment cost would be:
Total Investment Cost = Number of fixtures x Investment cost per fixture
Total Investment Cost = 800 x $300
Total Investment Cost = $240,000
b.
To calculate the annual utility cost savings, we need to find the difference in the watt-hour consumption per fixture between HID and LED lighting, and multiply it by the number of fixtures, operating hours per day, operating days per year, and the metered utility rate per kilowatt-hour:
Energy consumption savings per fixture per hour = HID watt hour consumption - LED watt hour consumption
Energy consumption savings per fixture per hour = 500 watts/hr - 300 watts/hr
Energy consumption savings per fixture per hour = 200 watts/hr
Total energy consumption savings per hour for 800 fixtures:
= Energy consumption savings per fixture per hour x Number of fixtures
Total energy consumption savings per hour for 800 fixtures.
= 200 watts/hr x 800
Total energy consumption savings per hour for 800 fixtures.
= 160,000 watts/hr
Total energy consumption savings per year = Total energy consumption savings per hour x Operating hours per day x Operating days per year
Total energy consumption savings per year = 160,000 watts/hr x 10 hrs/day x 300 days/year
Total energy consumption savings per year = 480,000,000 watt-hours/year
Total energy consumption savings per year in kilowatt-hours (kWh):
= Total energy consumption savings per year / 1,000
Total energy consumption savings per year in kWh = 480,000,000 / 1,000
Total energy consumption savings per year in kWh = 480,000 kWh/year
Annual utility cost savings:
= Total energy consumption savings per year in kWh x Metered utility rate per kWh
Annual utility cost savings = 480,000 kWh/year x $0.12/kWh
Annual utility cost savings = $57,600/year
c.
To evaluate the proposal using net present value (NPV), we need to calculate the present value of the investment cost and the present value of the annual utility cost savings over a 15-year period.
Using the Present Value of the Ordinary Annuity formula with a 15-year life and 8% minimum rate of return, we get:
PV of Investment Cost = -$240,000 (negative because it's a cash outflow)
PV of Annual Utility Cost Savings = $514,883.81
NPV = PV of Annual Utility Cost Savings - PV of Investment Cost
NPV = $514,883.81 - (-$240,000)
NPV = $754,883.81
Therefore,
The investment cost for replacing the 800 fixtures is $240,000.
Annual utility cost savings is $57,600/year.
Since the NPV is positive, the proposal should be accepted as it generates a positive return and is expected to be profitable.
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(c) log12-(1/2log 9+1/3 log8) write a single form equation
The log expression in single equation is log 12 - log 3 + log 2.
What is the solution of the log equation?
The solution of the log equation is calculated by applying the following method.
log 12 - ¹/₂log 9 + ¹/₃log 8
we can simplify the equation as follows;
log 12 - log 3 ⁽² ˣ ¹/₂⁾ + log 2 ⁽³ ˣ ¹/₃⁾
= log 12 - log 3¹ + log 2¹
= log 12 - log 3 + log 2
Thus, the log equation or expression has been simplified in the form of single equation.
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HELP FASTER WILL GIVE BRAINLIEST!!!!!!!!! NOTICE ITS + AND THEN - IN EQUATION NOT TWO +, SO D ISNT CORRECT!!!!!!
Identify the correct graph of the system of equations.
3x + y = 12
x − 4y = 4
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12.
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma 12.
The graph shows a line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 1. There is a second line with an x-intercept at 4 comma 0 and a y-intercept at 0 comma negative 12.
The correct graph of the system of equations 3x + y = 12 and x - 4y = 4 is:
The graph shows a line with an x-intercept at (4, 0) and a y-intercept at
(0, -1). There is a second line with an x-intercept at (4, 0) and a y-intercept at (0, 12).
We have,
To graph the system of equations 3x + y = 12 and x − 4y = 4, we first need to rearrange them in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept:
3x + y = 12 => y = -3x + 12
x - 4y = 4 => y = (1/4)x - 1
Now we can see that the first equation has a slope of -3 and a y-intercept of 12, while the second equation has a slope of 1/4 and a y-intercept of -1.
Now,
The x-intercept is when y = 0.
So,
3x + y = 12
3x = 12
x = 4
And,
x - 4y = 4
x = 4
Thus,
The correct graph of the system of equations 3x + y = 12 and x - 4y = 4 is:
The graph shows a line with an x-intercept at (4, 0) and a y-intercept at
(0, -1). There is a second line with an x-intercept at (4, 0) and a y-intercept at (0, 12).
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The distance between (2,2) and (8,2) is 6 units on a coordinate plane. Select all of the pairs of points that are 6 units apart.
The points are not at a distance of 6 units from each other.
Given that the distance between point (2, 2) and point (8, 2) is 6 units a coordinate plane.
We need to find which other pairs of points are also 6 units apart.
The distance between two points (x₁, y₁), (x₂, y₂) are 6 if and only if either
( x₂ - x₁ = 6 and y₂ = y₁ )or ( x₂ = x₁ and y₂ - y₁ = 6 ).
If either of the conditions is satisfied, then only we can say that the two points has distance of 6 units between them.
Now, As given
Let (x₁, y₁) = ( 2, 2) , (x₂, y₂) = (8, 2)
Check whether the conditions are satisfied or not .
Here x₁ = 2 , x₂ = 8, y₁ = 2, y₂ = 2
Now,
x₂ - x₁ = 8 - 2 = 6 , y₂ - y₁ = 2 - 2 = 0
∴ we get
1st condition is satisfied, So the points have a distance of 6 units between them.
Now,
Let us suppose another point (x₁, y₁) = ( 4, 3) , (x₂, y₂) = (3, 3)
Here x₁ = 4 , x₂ = 3, y₁ = 3, y₂ = 3
Now,
x₂ - x₁ = 4 - 3 = 1 , y₂ - y₁ = 3 - 3 = 0
Here neither of the conditions are satisfied.
So, the points are not at a distance of 6 units from each other.
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If the rate of inflation is 2.6% per year, the future price p (1) (in dollars) of a certain item can be modeled by the following exponential function, where t is the
number of years from today.
p(t)=1200 (1.026)
Find the current price of the item and the price 8 years from today.
Round your answers to the nearest dollar as necessary.
Current price ?$
Price 8 years from today?$
a) Based on the exponential function, p(t)=1200 (1.026)^t, the item's current price with a rate of inflation of 2.6% per year is $1,200.
b) In 8 years, the future price of the item would be $1,473.53.
What is an exponential function?An exponential function is a mathematical equation depicting the relationship between one variable and another with a periodic constant rate of growth or decline.
Exponential functions are classified into two:
Exponential growth functionExponential decay function.Let the number of years from today = t
Annual inflation rate = 2.6%
Current price = $1,200
Time in years = 8 years
Exponential function:p(t)=1200 (1.026)^t
p(8) = 1,200(1.026)^8
= $1,473.53
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clara is running a bakery she has made a street sign to direct people to her bakery . She painted one of the post and sign. What is the painted area?8in,8in,5in, 60in, 4in
The painted area of the sign is approximately 324 square inches. This was calculated by finding the area of the pole, square signboard, and triangle portion of the signboard and adding them together.
To find the painted area, we need to find the area of the pole, the area of the square signboard, and the area of the triangular portion of the signboard.
Area of pole
The pole is a rectangular prism with height 60in and width 4in. Therefore, the area of the pole is:
60in x 4in = 240 sq. in.
Area of square signboard
The square signboard has a side length of 8in. Therefore, the area of the square signboard is:
8in x 8in = 64 sq. in.
Area of triangular portion of the signboard
The triangular portion of the signboard has a base of 8in and a height of 5in. Therefore, the area of the triangular portion of the signboard is:
(1/2) x 8in x 5in = 20 sq. in.
Total painted area
The total painted area is the sum of the area of the pole, the area of the square signboard, and the area of the triangular portion of the signboard. Therefore, the painted area is:
240 sq. in. + 64 sq. in. + 20 sq. in. = 324 sq. in.
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--The given question is incomplete, the complete question is given
" clara is running a bakery she has made a street sign to direct people to her bakery . She painted one of the post and sign. What is the painted area?8in,8in,5in, 60in, 4in "--
Solve the following for θ, in radians, where 0≤θ<2π.
6sin2(θ)−3sin(θ)−8=0
Select all that apply:
0.6
0.16
2.68
5.08
4.34
0.27
Answer:5.08
4.34 are correct
Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):
6u^2 - 3u - 8 = 0
We can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 6, b = -3, and c = -8. Substituting these values, we get:
u = (3 ± sqrt(9 + 192)) / 12
u = (3 ± sqrt(201)) / 12
Therefore, either:
A. Roel organized his students' scores on the following line plot.
Students' Scores
00000
60
65
70
75
80
85
90
95
100
Based on this information, which of the following BEST describes the median student
score?
A 35
B. 80
C. 85
D. 90
Answer: - None of the above.
Step-by-step explanation:
The median is the middle value of the data set when arranged in order. In this case, we have an even number of values, so we need to take the average of the middle two values to find the median. The middle two values are 80 and 85. Therefore, the median student score is: (80 + 85) / 2 = 82.5
The closest answer choice to this value is C. 85, but it is not the correct answer. Therefore, the correct answer is none of the above.
Help me please and thank you very much! :)
Answer:
2700
Step-by-step explanation:
20 inches x 15 inches x 9 inches! <3
also get some sleep lol
I am confused on this question. "George is building flower boxes to sell as gifts. Draw and label a net to represent a flower box. Then find the amount of material George needs for each box. Explain why you drew the net the way you did." There is also a picture that goes with it down below.
Answer:
To answer the question, you first need to understand what a net is. A net is a two-dimensional diagram that can be folded to form a three-dimensional object. In the context of this question, a net represents the unfolded and flattened-out shape of a flower box before it is assembled.
To draw a net that represents a flower box, you need to imagine what the box would look like if it were flattened out and unfolded. You can start by drawing a rectangle for the bottom of the box. Then draw four rectangles that represent the sides of the box. Each of the side rectangles should be the same length as the length of the bottom rectangle, and the width of each side rectangle should be the same as the height of the box.
Next, you need to label the net to indicate which sides will be connected to form the box. Label the edges of the rectangles with the corresponding letter to show how the box will be assembled. For example, label the top edge of the bottom rectangle as "A" and the bottom edge of one of the side rectangles as "B". Then, label the side edges of the side rectangle as "C" and "D".
To find the amount of material George needs for each box, you need to calculate the total surface area of the net. The surface area represents the amount of material needed to cover the entire box. You can find the surface area by calculating the area of each rectangle and adding them together.
In this case, the bottom rectangle has an area of 16 square inches, and each of the four side rectangles has an area of 8 square inches. Therefore, the total surface area of the net is:
16 + 4(8) = 48 square inches
This means that George needs 48 square inches of material to make one flower box.
You drew the net the way you did because it represents the flattened-out and unfolded shape of the flower box before it is assembled. Labeling the edges and rectangles helps to visualize how the box will be assembled and allows you to calculate the surface area needed to cover the entire box.
have a good day and stay safe
A swimming pool is shaped like the figure below. Each end is a semicircle, and the length and width of the rectangle are 60 feet and 30 feet, respectively.
The area of the border is 105.53 feet².
We have,
The swimming pool is a combination of two shapes.
Rectangle:
Length = 60 feet
Width = 30 feet
Area = 60 x 30 = 1800 feet²
Semicircle:
Diameter = 30 feet
Radius = 15 feet
Area = π/2 r² = 1/2 x 3.14 x 15 x 15 = 353.25 feet².
Now,
The area of the swimming pool.
= 1800 + 353.25
= 2153.25 feet²
Now,
Without the border.
Area of the swimming pool.
= rectangle area + semicircle area
= 60 x (30 - 1) + 1/2 x π x (15 - 1)²
= 60 x 29 + 1/2 x 3.14 x 14 x 14
= 1740 + 307.72
= 2047.72 feet²
Now,
The area of the border.
= 2153.25 - 2047.72
= 105.53 feet²
Thus,
The area of the border is 105.53 feet².
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PLEASE HELP (WILL GIVE BRAINLIEST
Answer: C. V ≈ 635.2 cm^3.
Explanation: The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height (or slant height in this case).
Using the given values, we have:
V = (1/3)π(4.25 cm)^2(12 cm)
V ≈ 635.2 cm^3 (rounded to the nearest tenth)
Therefore, the answer is C. V ≈ 635.2 cm^3.
johnathannes brahms destoryed or left many because of his work unplublished because
A. He didnt want to be sucessful
B. He thought they were too good to publish
C. He was a perfectionist and was never satisfied with them.
Answer asap for brainlist
Mary has the qualities of being a team leader.
Here, we have,
Team leaders upload any other stage of control. They’re employed to persuade and construct relationships, to make matters happen. Team chief’s to-do lists may be vast, however through categorizing them, it’ll come up with readability approximately the reason of your job.
A group chief has an outline of a set of humans, motivates, offers guidance and video display units performance. It is probably an professional identify alternate or a delegation exercising out of your management, however both way, being a group chief separates you out of your friends as a depended on individual to manipulate a assignment or institution of humans.
Team leaders and executives have exceptional responsibilities. Unlike managers, group leaders won’t have the authority to direct, alternate plans, put in force or construct their groups via hiring and firing. Their position is mostly a motivational and inspirational one inside an organization. They’re professional dating developers and mediators, liaising among the humans and management.
Thus this are the qualities of team leader.
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complete question;
Mary is a perfectionist . She loves participating on teams and often takes on too many tasks because she wants to ensure that they are done on time and on budget.
math hw for tonight
help solve this problem! Thank you!
ap cal bc
The magnitude of the speed of the particle is determined as √ (17), m/s.
option A.
What is the particle's speed?The speed of a particle is defined as the rate of change of the particle's displacement with time.
Mathematically, the formula for the speed of the a particle is given as;
v = dx/dt
where;
dx is the change in the particle's displacementdt is the change in the time of motion of the particleThe speed of the particle is calculated as;
v = u + at
where;
u is the initial speeda is the accelerationat time, t = 0, the equation for the speed of the particle becomes;
v = u
v = i + 4j
The magnitude of the speed is calculated as follows;
v = √ (1² + 4²)
v = √ (17), m/s
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An urn contains 6 red and 8 black balls. Five balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 5 balls drawn from the urn are black? Round your answer to three decimal places.
3cm
7 cm
2 cm
Surface area of the prism
The surface area of the rectangular prism is 82 square cm.
Given that:
Length, L = 3 cm
Width, W = 7 cm
Height, H = 2 cm
Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as,
SA = 2(LW + WH + HL)
The surface area of the rectangular prism is calculated as,
SA = 2 x (3 x 7 + 7 x 2 + 2 x 3)
SA = 2 x (21 + 14 + 6)
SA = 2 x 41
SA = 82 square cm
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A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment and find the probability of the given event. (Enter your answer as a fraction.)
The sum of the numbers is an even number.
The probability that the sum of the numbers is even is,
⇒ P = 0.47
Since, We know that;
To have this kind of event you can have the following events, where
(d₁ ,d₂), d1 is the number that appears uppermost on die 1 and d2 is the number that appears uppermost on dice 2:
(1, 1), (1, 3) , (1, 5), (2, 2), (2, 4) (2, 6) (3, 1) (3, 3) (4, 2) (4, 4) (4, 6), (5, 1) (5, 3), (5, 5) (6, 2) (6, 4) (6, 6)
And, the total number of events is 36 since every dice have 6 numbers.
The probability is:
P(Event)=P(sum is even)/Total number of events
P = 17/36
P = 0.47
Thus, The probability that the sum of the numbers is even is,
⇒ P = 0.47
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I need help with solving and graph each of the following inequalities
The solution and graph of each of the inequalities is shown below:
k ≥ 4v < 17x ≤ 6y > 8g > 3.9w > -7What is an inequality?In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Next, we would determine the solution for each of the inequalities as follows;
k + 7 ≥ 11
k ≥ 11 - 7
k ≥ 4
5 > v - 12
5 + 12 > v
17 > v
v < 17 (flip).
-5x ≤ -30
x ≤ 6
y/4 > 2
y > 2(4)
y > 8
10g + 19 > 49
10g > 49 - 19
10g > 39
g > 3.9
-w - 7 > 0
-w > 7
w > -7
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Calculus please help
Answer:
[tex]f(x)=\dfrac{1}{20}x^5+\sinh(x)-\dfrac{1}{2}\sinh(2)x+6[/tex]
Step-by-step explanation:
Given:
[tex]\phantom{ww} \bullet\;\;\;f''(x)=x^3+\sinh(x)[/tex]
[tex]\phantom{ww} \bullet\;\;\;f(0)=6[/tex]
[tex]\phantom{ww} \bullet\;\;\;f(2)=7.6[/tex]
To find f'(x), integrate f''(x):
[tex]\begin{aligned}\displaystyle f'(x)=\int f''(x)\; \text{d}x&=\int \left(x^3+\sinh(x)\right)\; \text{d}x\\\\&=\int x^3\;\text{d}x+\int \sinh(x)\; \text{d}x\\\\&=\dfrac{1}{4}x^4+\cosh(x)+\text{K}\end{aligned}[/tex]
To find f(x), integrate f'(x):
[tex]\begin{aligned}\displaystyle f(x)=\int f'(x)\; \text{d}x&=\int \left(\dfrac{1}{4}x^4+\cosh(x)+\text{K}\right)\;\text{d}x\\\\&=\int \dfrac{1}{4}x^4\; \text{d}x+\int \cosh(x) \; \text{d}x + \int \text{K}\; \text{d}x\\\\&=\dfrac{1}{20}x^5+\sinh(x)+Kx+\text{C}\end{aligned}[/tex]
Substitute f(0) = 6 to determine the value of the constant C:
[tex]\begin{aligned}f(0)=\dfrac{1}{20}(0)^5+\sinh(0)+K(0)+\text{C}&=6\\\\0+0+0+\text{C}&=6\\\\\text{C}&=6\end{aligned}[/tex]
Substitute f(2) = 7.6 and C = 6 to determine the value of the constant K:
[tex]\begin{aligned}f(2)=\dfrac{1}{20}(2)^5+\sinh(2)+K(2)+6&=7.6\\\\1.6+\sinh(2)+2K+6&=7.6\\\\\sinh(2)+2K&=0\\\\2K&=-\sinh(2)\\\\K&=-\dfrac{1}{2}\sinh(2)\end{aligned}[/tex]
Therefore, function f(x) is:
[tex]\boxed{f(x)=\dfrac{1}{20}x^5+\sinh(x)-\dfrac{1}{2}\sinh(2)x+6}[/tex]
[tex]\textsf{As}\;\;\sinh(2)=\dfrac{e^4-1}{2e^2},\;\textsf{we can also write the equation as:}[/tex]
[tex]f(x)=\dfrac{1}{20}x^5+\sinh(x)-\dfrac{1}{2}\left(\dfrac{e^4-1}{2e^2}\right)x+6[/tex]
[tex]f(x)=\dfrac{1}{20}x^5+\sinh(x)-\left(\dfrac{e^4-1}{4e^2}\right)x+6[/tex]
graphing transformations
Each of the graphs should be matched with the appropriate function as follows;
Graph 1: D. f(x) = (x - 2)² + 3
Graph 2: C. f(x) = -(x - 2)² - 3
Graph 3: B. f(x) = -(x - 3)² - 2
Graph 4: C. f(x) = (x - 3)² + 2
What is the general form of a quadratic function?In Mathematics and Geometry, the standard or general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Mathematically, the vertex form of a quadratic function is modeled by this equation:
f(x) = a(x - h)² + k
Where:
h and k represents vertex of the graph.a represents leading coefficient.In conclusion, we can logically deduce that each of the given quadratic function were either vertically translated or horizontally translated.
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