Answer:$0.25
Step-by-step explanation:
To find the expected value of playing the game, we need to multiply the payoff for each possible outcome by its probability and then add up all the values.
Let's first find the probabilities of each outcome:
- Probability of spinning1:1/6
- Probability of spinning2:1/6
- Probability of spinning3:1/6
- Probability of spinning4:1/6
- Probability of spinning5 or6:2/6( or1/3)
Now let's calculate the expected value:
Expected value=(1/6*$1)+(1/6*$3)+(1/6*$5)+(1/6*$7)+(1/3*-$1.25)
Expected value=$0.25
So the expected value of playing the game is$0.25 per spin.
In the long run, Scott can expect to gain money since the expected value is positive. However, this doesn't guarantee that he will actually win money every time he plays the game, as there is still a certain degree of randomness involved in each spin.
using the centriod explain the relationship between point z and the triangle. justify with applicable theorem.
4. if the length of gu is 18 units, what is the length of gz?
5. if the length of zt is 4.8 units, what is the length of ot?
show all work
Length of gz = 12 units
Length of ot = 14.4 units
Given,
Triangle EGD with centroid at Z .
Now,
As we know that centroid divides the line segment in the ratio 2:1 .
Firstly calculate the length of gz,
gu = 18 unit
gz:zu = 2:1
gz = 2/3 * 18
gz = 12 units .
Secondly calculate the length of ot,
zt = 4.8 units
oz:zt = 2:1
oz = 4.8 * 2
oz = 9.6 units
ot = 9.6+ 4.8
ot = 14.4 units
Hence with the centroid length of ot and gz can be found out .
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Match each system on the left with all words that describe the system on the right. Choices on the right can be used more than once. y = 3x - 1 2y - 6x = 4 2y = -x + 6 4y + 2x = 12 y = 2x + 3 x+y = -9 inconsistent consistent independent dependent
y = 3x - 1: consistent, independent
2y - 6x = 4: consistent, independent
2y = -x + 6: consistent, independent
4y + 2x = 12: consistent, independent
y = 2x + 3: consistent, independent
x + y = -9: consistent, dependent
y = 3x - 1 and 2y = -x + 6: inconsistent
Let's match each system on the left with the appropriate words that describe the system on the right:
y = 3x - 1: consistent, independent
This system represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.
2y - 6x = 4: consistent, independent
Similar to the first system, this represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.
2y = -x + 6: consistent, independent
This system also represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.
4y + 2x = 12: consistent, independent
Like the previous systems, this represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.
y = 2x + 3: consistent, independent
This system represents a linear equation with a unique solution. The equations are not multiples of each other, and they intersect at a single point.
x + y = -9: consistent, dependent
This system represents a linear equation with infinitely many solutions. The equations are multiples of each other, meaning they represent the same line. Therefore, any point on the line satisfies both equations.
y = 3x - 1 and 2y = -x + 6: inconsistent
This system represents inconsistent equations that do not have a common solution. The lines represented by the equations are parallel and do not intersect.
To summarize the matches:
y = 3x - 1: consistent, independent
2y - 6x = 4: consistent, independent
2y = -x + 6: consistent, independent
4y + 2x = 12: consistent, independent
y = 2x + 3: consistent, independent
x + y = -9: consistent, dependent
y = 3x - 1 and 2y = -x + 6: inconsistent
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ACTIVITY 1 1.1 Resources required: ruler, protractor, compass and coloured pencils Step 1: Draw a horizontal line segment, OM, of any length, the longer the better. Step 1 Solution
The solution to the problem at hand i.e. to draw a horizontal line segment, OM, of any length, the longer the better using ruler, protractor, compass and coloured pencils
are as follows:
Step 1: Take a ruler and align it with a sheet of paper and draw a line. This line can be of any length, although longer lines are preferred.
Step 2: The line is now OM; we must now label its endpoints. Label the leftmost point O, and the rightmost point M.
Step 3: The coloured pencils are used to add decorations to the line. To add decorations, use coloured pencils to make patterns and stripes along the length of the line. This is entirely optional and based on personal preference.
Step 4: To ensure that the line is perfectly horizontal, the protractor should be used. Place the protractor on the line and make sure the zero-degree angle is at O. The line will be horizontal if it is parallel to the baseline of the paper.
Step 5: Using a compass, measure the length of OM to ensure that it is of the desired length.
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Find the radius and height of this cylinder. Calculate the area (A] of the base of the cylinder.
Then, use the area of the base to calculate the volume (VI of the cylinder.
r=
10 cm
h = 30 cm
- 20 gm
ABase
= 3.14 - (30 cm)?
- 9,420 cm?
V = ABase
• h
cm
cm?
Given statement solution is :- The area (A) of the base of the cylinder, you need to use the formula for the area of a circle, which is A = [tex]πr^2[/tex], where π is approximately 3.14 and r is the radius of the base.
To calculate the area (A) of the base of the cylinder, you need to use the formula for the area of a circle, which is A = [tex]πr^2[/tex], where π is approximately 3.14 and r is the radius of the base.
Given that the radius (r) is 10 cm, the area of the base (ABase) can be calculated as follows:
ABase =[tex]πr^2[/tex]
ABase = 3.14 * [tex](10 cm)^2[/tex]
ABase = 3.14 * [tex]100 cm^2[/tex]
ABase = 314 [tex]cm^2[/tex]
The area of the base is [tex]314 cm^2.[/tex]
To calculate the volume (V) of the cylinder, you need to multiply the area of the base (ABase) by the height (h):
V = ABase * h
V = 314 [tex]cm^2[/tex] * 30 cm
V = 9420 [tex]cm^3[/tex]
The volume of the cylinder is 9420 [tex]cm^3.[/tex]
However, there seems to be some confusion in the provided information. The given values for the area of the base (ABase) and the volume (V) are not clear. The values "- 20 gm" and "cm cm?" are not meaningful units for area or volume.
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(PLEASE ANSWER ASAP)
Answer:
alternate interior angles are congruent
What is the instantaneous rate of change y=sqrtx of at x = 2? Responses negative 1 over 2 negative 1 over 4 negative 1 none of these none of these
The instantaneous rate of change of y = √x at x = 2 is √2 / 2.
To find the instantaneous rate of change of y = √x at x = 2, we need to calculate the derivative of the function with respect to x and evaluate it at x = 2.
Taking the derivative of y = √x using the power rule for differentiation, we have:
dy/dx = (1/2) × x^(-1/2)
Now, substituting x = 2 into the derivative expression:
dy/dx = (1/2) × 2^(-1/2)
= (1/2) × √2
= √2 / 2
Therefore, the instantaneous rate of change of y = √x at x = 2 is √2 / 2.
None of the provided options (-1/2, -1/4, -1) are the correct instantaneous rate of change at x = 2.
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How many of which types of roots does f(x) = 7x5 - 3x³ + 5x + 2 have?
Answer:
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x = 5/7,−3,3
Step-by-step explanation:
Translate this sentence into an equation. 42 is the sum of 23 and Janelle's age. Use the variable j to represent Janelle's age.
Answer:
42 = 23 + j
Step-by-step explanation:
The equation representing the given sentence would be:
42 = 23 + j
Here, the variable "j" represents Janelle's age.
what three costs contribute to the total cost of a mortage?
Answer:
The three costs that contribute to the total cost of a mortgage are the down payment, mortgage tax and monthly interest.
Step-by-step explanation:
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-4 over 5 + 1 over 10
Answer: -0.7
Step-by-step explanation:
Help this is pretty concussing and how am I supposed to know how many more balloons were filled?
Answer:
b) graph pass through origin for both.
c) mario would take 5minutes to have more balloons filled than tanesha
1) Complete one drawing of each regular polygon: equilateral triangle, square, and regular hexagon, following the animations.
2) Create a design based on one of the 3 polygons.
3) Write a description of your design. Include the following information:
How many lines of symmetry does the design have?
How many degrees does the design need to be rotated to match itself? (Hint: See the polygons at the start of the lesson.)
How did you decide to color your design?
What patterns do you see in your design?
The description of the image is one that has a four-horned star. The description is as follows:
It comprises of four equilateral triangles and One Square.
Next,
The image or shape has twelve (12) symmetrical lines.
Next,
It must be rotated 90° (clockwise or anticlockwise) in order for the image to match itself.
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a sine function has an amplitude of 6, a period of pi, and a phase shift of pi/4 . what is the y intercept of the function?
y intercept will be 0,-6 .
Given,
Amplitude = 6
Time period = pi
Phase shift = pi/4
In trigonometry, the sine function can be defined as the ratio of the length of the opposite side(perpendicular) to that of the hypotenuse in a right-angled triangle.
The sine function is used to find the unknown angle or sides of a right angled triangle.
Mathematically,
sinФ = p/h
Now ,
Let us assume the phase shift to be on right side.
So the graph will be at negative y axis.
Thus the points will be 0 , -6 .
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What is the value of the expression
226 28
●
(25)6
-? Show your work.
The value of the expression 226²⁸ ● (25)⁶ is approximately [tex]4.1406562 \times 10^{119.[/tex]
To evaluate the expression 226²⁸ ● (25)⁶, we can follow the order of operations (also known as PEMDAS/BODMAS) which states that we should perform any calculations inside parentheses, then evaluate any exponents, and finally perform any multiplications or divisions from left to right.
Let's break down the expression :
Evaluate the exponent (25)⁶
[tex](25)^{6} = 25^{(6\times 1)} = 25^6 = 244,140,625[/tex]
Substitute the value into the expression:
226²⁸ ● 244,140,25.
Evaluate the exponent 226²⁸
[tex]226^{28} = 226^{(2\times28) = 226^{56 \\[/tex]
Now, calculating [tex]226^{56}[/tex] might not be feasible manually due to the large exponent.
However, we can use a calculator or a computer program to obtain the result.
[tex]226^{56} \approx 1.6951718 \times 10^{112[/tex]
Substitute the value back into the expression:
[tex]1.6951718 \times 10^{112[/tex] ● 244,140,625
Perform the multiplication:
[tex]1.6951718 \times 10^{112}\times 244,140,625 \approx 4.1406562 \times 10^{119[/tex] .
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Fill in the table using this function rule y= - 2x + 3
Step-by-step explanation:
you just have to put that value in place of x in the function.
don't be so lazy you a hole do it yourself
A company was hired to build a tunnel through a mountain. The company started at the south end of the mountain and completed only five hundred eighty five feet of the required seven thousand, six hundred five feet before going bankrupt. A different company was hired to complete the job, but th
ey decided to use two crews. Crew A would start where the other company left off at the southern end, while Crew B would start at the northern end and dig towards the other crew. Crew A was able to dig fifty eight feet of the tunnel per week. Crew B, which was larger, was able to dig fifty nine feet of the tunnel per week.
Let's denote crew A's work per week as A and crew B's work per week as B.
We are given that A = 58 ft per week and B = 59 ft per week.
We have to calculate how many weeks it will take both crews to complete the tunnel.
585 feet have already been dug from the south end. So, the total tunnel length that needs to be dug is 7605 - 585 = 7020.
Now, let's assume that both the crews continue to work at their respective rate of A = 58 ft/week and B = 59 ft/week.
Therefore, total tunnel length that needs to be dug in weeks = (7020 ft) / (A + B)
= (7020 ft) / (58 ft/week + 59 ft/week)
= 120.20 weeks
Hence, it will take a total of 120.20 weeks for both crews to complete the tunnel.
pls help and show work
Hence the surface area of the given figure 168 km².
In the given prism contains
3 rectangular surface,
For rectangular surface 1:
Length = 6 km
Width = 7 km
Surface area = 6x7
= 42 km²
For rectangular surface 2:
Length = 8 km
Width = 7 km
Surface area = 8x7
= 56 km²
For rectangular surface 3:
Length = 10 km
Width = 7 km
Surface area = 10x7
= 70 km²
Hence total surface area of the given figure is,
⇒ 42 + 56 + 70
⇒ 168 km²
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4x Which reason is NOT typically used in a proof?
A
4x B
D
definition of supplementary angles
substitution property
C two angles being congruent
parallel fines
The reason that is NOT typically used in a proof is two angles being congruent. Option C.
Among the options A, B, C, and D, the reason that is NOT typically used in a proof is option C: two angles being congruent.
Congruence is a fundamental concept in geometry that refers to the equality of shape and size. When two angles are congruent, it means they have the same measure. While congruence is an important concept used in geometric proofs, it is typically not used as a standalone reason in a proof.
In geometric proofs, various properties, theorems, and postulates are used to establish relationships and make deductions. Let's briefly discuss the other options:
A. Definition of supplementary angles: This is a valid reason that is commonly used in proofs involving supplementary angles. The definition states that if the sum of two angles is 180 degrees, they are considered supplementary.
B. Substitution property: The substitution property is a logical property used in algebraic proofs. It allows us to replace one expression with another expression that is equal to it. This property is often employed when simplifying equations or substituting known values.
D. Parallel lines: The concept of parallel lines is frequently utilized in geometric proofs, particularly in proving angles and angle relationships. Properties such as alternate interior angles, corresponding angles, and vertical angles are established based on the parallel lines. Option C is correct.
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If A={o,b,s,e,r,v,a,n,t,l,y} and U={a,b,c,d,e,f,g,h,I,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z} find [A’]
Answer:
[A'] = {c,d,f,g,h,i,j,k,m,n,p,q,u,w,x,z}
Step-by-step explanation:
[A'] is read as the set of A complement, which is all the elements from the universal set that are not contained in set A.
Therefore, [A'] = {c,d,f,g,h,i,j,k,m,n,p,q,u,w,x,z}
Given f(x) = log2 (x+2), complete the table of values for the function -f(x) - 3. Show your work.
Answer:
Step-by-step explanation:
what is the distance form the sateltite to earth
The distance of Satellite B from the Earth is approximately 4915.71 kilometers.
To determine the distance of Satellite B from the Earth, we can use the concept of similar triangles.
Let's break down the problem step by step:
We have a triangle formed by Satellite A, Satellite B, and the center of the Earth.
Let's call the center of the Earth point O, Satellite A point A, and Satellite B point B.
Since Satellite A orbits closer to the Earth, its distance from the center of the Earth is equal to the radius of the Earth plus the distance from Satellite A to Satellite B.
Let's call this distance OA.
OA = Radius of the Earth + Distance from Satellite A to Satellite B
OA = 6371 km + 21185.5 km
OA = 27556.5 km
Now, we need to find the distance of Satellite B from the Earth. Let's call this distance OB.
We know that OA and OB form a triangle, and they are parallel to the side AB.
Since the triangle formed by OA, OB, and AB is similar to the triangle formed by OA, AB, and the radius of the Earth, we can set up a proportion to find OB.
OA / AB = Radius of the Earth / OB
OB = (Radius of the Earth x AB) / OA
OB = (6371 km x 21185.5 km) / 27556.5 km
OB ≈ 4915.71 km
Therefore, the distance of Satellite B from the Earth is approximately 4915.71 kilometers.
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Please please help me with this i have 40 missing assignments, if you help YOUR AMAZING
The volume of the prisms are:
1. 432 yd³
2. 36in³
3. 252 m³
4. 240 ft³
5. 576 mm³
6. 144 cm³
7. 343 m³
8. 120 yd³
9. 150 in³
How to determine the volumeThe formula for calculating the volume of a rectangular prism is expressed as;
V = lwh
such that;
l is the lengthw is the widthh is the heightNow, substitute the value for each of the prisms, we have;
1. Volume = 6 × 6 ×12
Multiply
Volume = 432 yd³
2. Volume = 2 ×9 × 2
Multiply
Volume = 36in³
3. Volume = 9 × 4 × 7
Multiply
Volume = 252 m³
4. Volume = 10 × 8 × 3
Multiply
Volume = 240 ft³
5. Volume = 4 × 12 × 12
Multiply the values
Volume = 576 mm³
6. Volume = 6 × 8 × 3
Volume = 144 cm³
7. Volume = 7 × 7 ×7
Volume = 343 m³
8. Volume = 8 × 3 × 5
Volume = 120 yd³
9. Volume = 5 × 6 × 5
Volume = 150 in³
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Please Help!! Solve For X
The value of x in the given figure is 8.
In the given figure there are two lines which are parallel.
We have to find the value of x.
In the straight line the sum of angles is 180 degrees.
8x+1+115=180
8x+116=180
Subtract 116 from both sides:
8x=180-116
8x=64
Divide both sides by 8:
x=64/8
x=8
Hence, the value of x in the given figure is 8.
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A cheetah's speed was timed over a 50-yard distance. The cheetah was clocked running 60 miles per hour. Write an equation to represent this situation. (If your answering please show how you solved this)
An equation to represent this situation is y = 60x
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m represent the slope or rate of change.x and y are the points.b represent the y-intercept or initial value.Based on the information provided above, we can logically deduce that the cheetah was clocked running 60 miles per hour over a 50-yard distance. This ultimately implies that, an equation that models this situation is given by:
y = 60x
Where:
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25% (iv) MP=Rs. 26600, Discount-10%
For an item with a marked price of Rs. 26,600 and a 10% discount, the discount price is Rs. 2,660. Therefore, the customer will pay Rs. 23,940 after applying the discount.
To calculate the amount of discount on an item with a marked price of Rs. 26,600 and a discount percentage of 10%, we can follow a simple formula.
First, let's calculate the discount amount. The discount percentage is 10%, which means we can find the discount amount by multiplying the marked price by the discount percentage:
Discount amount = Marked price × Discount percentage
= Rs. 26,600 × 10/100
= Rs. 2,660
So, the discount amount for the item is Rs. 2,660.
Now, let's understand what this means. A discount is a reduction in the original price of an item. In this case, the discount amount of Rs. 2,660 is the amount by which the price of the item is reduced. Therefore, after applying the discount, the customer would only need to pay Rs. 26,600 - Rs. 2,660 = Rs. 23,940.
It's important to note that the discount amount is not the final price the customer pays. The final price is the marked price minus the discount amount. So, in this scenario, the customer will receive a discount of Rs. 2,660, and they will pay Rs. 23,940 for the item.
Understanding how discounts work can be helpful when making purchasing decisions or comparing prices. It allows customers to evaluate the value they are receiving and make informed choices based on their budget and preferences.
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Probable question:
What is the amount of the discount if the marked price of an item is Rs. 26,600 and the discount percentage is 10%?
5. If a triangular figure is in the shape of an
isosceles right triangle, what is the measure
of each base angle?
Answer: each base angle in an isosceles right triangle measures 45 degrees.
Step-by-step explanation:
In an isosceles right triangle, two sides have equal lengths, and one angle is a right angle (90 degrees).
Since it is an isosceles triangle, the two base angles (the angles opposite the equal sides) must be congruent, meaning they have the same measure.
To find the measure of each base angle, we can use the fact that the sum of the angles in a triangle is 180 degrees.
Let's denote the measure of each base angle as "x". Then, the sum of the three angles in the triangle can be expressed as:
x + x + 90 = 180
Simplifying the equation:
2x + 90 = 180
Subtracting 90 from both sides:
2x = 90
Dividing both sides by 2:
x = 45
At Bud's company, bowling balls are shaped as a sphere with a diameter of 12 inches. If a store receives a shipment of 21 bowling balls, what is the total volume of the balls? (Use 3.14 for pi)
The total volume of the 21 bowling balls is 6048π cubic inches.
We have,
To find the total volume of the 21 bowling balls, we first need to calculate the volume of a single ball and then multiply it by the number of balls.
The volume of a sphere can be calculated using the formula:
V = (4/3) x π x r³
where V is the volume and r is the radius of the sphere.
Given that the diameter of the bowling ball is 12 inches, the radius can be calculated as half of the diameter:
r = 12/2 = 6 inches
Now we can calculate the volume of a single ball:
V_ball = (4/3) x π x (6³) = (4/3) x π x 216 = 288π cubic inches
Since there are 21 balls, we can calculate the total volume by multiplying the volume of a single ball by the number of balls:
Total volume = 21 x 288π = 6048π cubic inches
Thus,
The total volume of the 21 bowling balls is 6048π cubic inches.
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Collect like terms
5z - 7 - 13z + 35
Collecting the like terms in the expression 5z - 7 - 13z + 35 gives -8z + 28
How to collect like terms on the expressionFrom the question, we have the following parameters that can be used in our computation:
5z - 7 - 13z + 35
Consider an expression given as
Ax + Bx
Where A and B are constants and x is a variable
The terms Ax and Bx are like terms
using the above as a guide, we have the following:
5z - 7 - 13z + 35 = 5z - 13z - 7 + 35
Evaluate the like terms
5z - 7 - 13z + 35 = -8z + 28
Hence, collecting the like terms gives -8z + 28
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what is an example of "The restriction of a function f"?
The restriction of a function f is when the domain of f is limited to a subset of its original domain.
What is an example of "The restriction of a function f"?The restriction of a function f can be demonstrated by considering a function f: R -> R, where R represents the set of real numbers.
Let u say f(x) = x^2. Now, if we restrict the domain of f to the interval [0, 5], the new function becomes f restricted: [0, 5] -> R and its expression would be f restricted(x) = x^2 for x in the interval [0, 5].
This means that the function f restricted only takes inputs from the interval [0, 5] and behaves the same way as the original function within that interval.
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What cumulative frequency should be used in solving the 28th percentile
The cumulative frequency to be used in solving the 28th percentile is 16.
What is cumulative frequency?Cumulative frequency is described as the total of a frequency and all frequencies in a frequency distribution until a certain defined class interval.
we add up the frequencies until we reach or exceed 28% of the total data set in order to find the cumulative frequency for the 28th percentile.
Total frequency = 4 + 9 + 16 + 10 + 9 + 2 = 50
28th percentile = (28/100) * Total frequency
28th percentile = (28/100) * 50 = 14
We start from the beginning of the distribution and add up the frequencies until we reach or exceed 14 so as to find the cumulative frequency.
In conclusion, and with reference to the given data set we notice that the cumulative frequency exceeds 14 at the 91-120 minute interval = 16.
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