Answers
The missing angles in the diagram are: Angle ABD = 60 degrees, Angle BDC = 120 degrees, Angle ACD = 60 degrees, and Angle ADC = 120 degrees.
To find the measure of the missing angles, we can use the fact that the sum of the angles in a triangle is 180 degrees, and the sum of the angles around a point is 360 degrees.
Let x be the measure of angle ABD.
Therefore, angle BDC has measure 180 - x degrees.
Similarly, angle ACD and angle ADC form a straight line, so their measures sum to 180 degrees. Therefore, angle ADC has measure 180 - 60 = 120 degrees.
Finally, since angle BCD and angle ADC form a straight line, their measures sum to 180 degrees. Therefore, angle BCD has measure 180 - 120 = 60 degrees.
Let y be the measure of angle CFE.
Similarly, angle DEF and angle CDF form a straight line, so their measures sum to 180 degrees. Therefore, angle DEF has measure 180 - 75 = 105 degrees.
Finally, since angle CDE and angle DEF form a straight line, their measures sum to 180 degrees. Therefore, angle CDE has measure 180 - 105 = 75 degrees.
Therefore, the missing angles have measures of 60 degrees and 75 degrees for the left and right triangles.
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find the measure of missing angles?
Related Questions
A box contains four apples, six oranges, and a pear. Preston reaches into the box and selects two of the 11 fruits uniformly at random without replacement. Let m/n be the probability that he selects an apple and an orange, where m and n are relatively prime positive integers. Find m+n.
Answers
the answer is m + n = 24 + 55 = 79.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
There are two ways this can happen: either he selects an apple first and then an orange, or he selects an orange first and then an apple. We can compute the probability of each of these events separately and then add them together.
First, let's consider the probability that Preston selects an apple first and then an orange. The probability of selecting an apple first is 4/11, and then the probability of selecting an orange from the remaining 10 fruits (which includes 3 apples and 6 oranges) is 6/10. So the probability of this event is (4/11) * (6/10) = 24/110.
This can be simplified by dividing the numerator and denominator by 2:
48/110 = 24/55
So the probability that Preston selects an apple and an orange is 24/55. Therefore, the answer is m + n = 24 + 55 = 79.
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The following data indicate the scores of some students in a competition. Which a box plot represents the data?
100 points!!!!!
Answers
The correct answer to the given question is graph D
How to solveGiven a set of data points, we are tasked with identifying the correct box plot representation.
We begin by arranging the data in ascending order, which gives us 12, 17, 21, 23, 24, 28, and 29 points.
Next, we use the properties of a box plot to eliminate incorrect representations.
The left end of the whisker should correspond to the smallest data point, and the right end to the largest.
Among the given graphs, only one satisfies this condition.
The middle point is identified as the fourth data point, which is 23.
Finally, we determine the lower and upper lines of the box to be 17 and 28, respectively.
The only graph that satisfies all conditions is graph D.
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A company is focus testing a new type of fruit drink. The focus group is 47% male. Of the responses, 40% of the males and 54% of the females said they would buy the fruit drink. Find the ratio of males who would buy the drink to females who would buy the drink. Round to the nearest ten thousandth if necessary.
Answers
Answer: the ratio of males who would buy the drink to females who would buy the drink is approximately 0.6560.
Step-by-step explanation:
Let's assume that there are 100 people in the focus group. Then, the number of males in the focus group is 47 and the number of females is 53.
Out of 47 males, 40% said they would buy the fruit drink, which is 0.4 x 47 = 18.8 males (rounded to the nearest whole number). Out of 53 females, 54% said they would buy the fruit drink, which is 0.54 x 53 = 28.62 females (rounded to the nearest whole number).
The ratio of males who would buy the drink to females who would buy the drink is:
18.8/28.62 = 0.6560 (rounded to the nearest ten-thousandth)
Therefore, the ratio of males who would buy the drink to females who would buy the drink is approximately 0.6560.
What is the lowest common multiple of 8 and 12?
Answers
Answer:
2 hope that helps
Step-by-step explanation:
Solution:
24
Use mental math to assess reasonableness. Explain your thinking
Cameron spends $130 on a gaming system and $80 on video games. He
says he spends about $215. Is his statement reasonable? Explain your
thinking.
Answers
To assess the reasonableness of Cameron's statement that he spent about $215 on a gaming system and video games, we can use mental math to estimate the total cost.
We know that he spent $130 on a gaming system and $80 on video games. If we round $80 up to $100 and add it to $130, we get:
$130 + $100 = $230
So based on this estimate, it seems like Cameron's statement of spending about $215 is not entirely accurate. However, it is close to the actual total cost, which is within 10% of the estimated total.
Therefore, we can say that while Cameron's statement may not be entirely precise, it is reasonably close to the actual total cost and can be considered reasonable.
Please Help! A picture is 60cm wide and 1.8 meter long.The ratio of its width to its perimeter in the lowest term is?
Answers
Answer:
60:61.8 OR 10:10.3
Step-by-step explanation:
Cant be simplified - unless your in advanced classes. If so
10:10.3
Answer:
Step-by-step explanation:
1/3 or 0.3 or 33.333333% or 3^-1 or 3.333333 x 10^-1
Smith, from Los Angeles, and Jones, from New York City, are both traveling to Kansas City, beginning their trips at the same time. The graph shows the distance in miles from Kansas City for each of them after they have both traveled for the same number of hours. After how many hours from the start of their journeys were they the same distance from Kansas City?
Answers
Answer: The answer should be 20 hours
Step-by-step explanation:
That is when the 2 lines meet up so that is when they are the same difference from Kansas City.
The entry fee to East Egg Hunt Event is $7.00. Each ride requires a ticket that cost $2.00. Cassie spent a total of $45.00. How many tickets Cassie Purchase?
Answers
Answer: 19 tickets
Step-by-step explanation: $45 - $7 = 38 38 divided by $2 = 19 tickets
Help asap will give brainiest
Use the image to determine the line of reflection.
4
3
2
1
0
?
Ty
5
-6
-7
-8
-9
-10
1
2
B
A
A
3₂
Α',
В'
4
E
5
E
6
с
Reflection across x = 6
D'
Reflection across the x-axis
Reflection across y = -3
C₁
Reflection across the y-axis
Answers
Answer: D
Step-by-step explanation: so if we look at the picture, youll notice 2 things right off the bat, firstly, the top shape goes over the y axis, so that wont work, secondly, the shapes are on the same side of the x axis (the positive side) so that wouldnt work, the last thing we now have to look at is making the shapes even, essentially if you were to flip one shape over a certain distance, the mirrored shape needs to be the same distance you flipped the first shape. In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.
side note: reflecting over the x axis or y axis, means the line of reflection is equal to 0 on either the y axis or x axis
To try to make this less confusing, another way to find the reflection is by evenly counting the shapes to the middle, how-ever many squares/spaces it takes for both shapes to reach the center of the two in this case, is how many spaces they are reflected.
The image undergoes a reflection at y=-3, Option D is correct.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.
Reflections are congruence transformations that generate a mirror image of an object, without changing its size or shape.
In the given figure the above image is original and it is flipped to form the image which is below the x axis.
In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.
Hence, the image undergoes a reflection over y axis which is at y=-3.
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[tex]8x ^{2} y + 12xy - 16xz[/tex]
Factorize the expression
Answers
The factοrs οf the expressiοn is 4x(2xy+3y-4z).
What is factοrizatiοn?Tο factοrise an algebraic statement, we first identify the terms' highest cοmmοn factοrs and then arrange the terms intο grοups in accοrdance with thοse grοups. In plain English, factοrizatiοn is the prοcess thrοugh which an algebraic expressiοn gets expanded in the οppοsite directiοn.
Here the given expressiοn is ,
=> [tex]8x^2y+12xy-16xz[/tex]
Nοw factοrizing the given expressiοn then,
=> 4×2×x×x×y+4×3×x×y-4×4×x×z
=> 4x(2xy+3y-4z)
Hence the factοrs οf the expressiοn is 4x(2xy+3y-4z).
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IT A MULTI-STEP PROBLEM HELP! 6 PARTS TO IT!!! IM GOING TO FAIL!! CAN PLEASE DO IT STEP BY STEP
Answers
a. The cost of one large pizza with one topping is $13.50. To purchase one large and five medium pizzas, we would need to buy one large pizza at regular price and five medium pizzas at the discounted price. The cost of the large pizza is $13.50, and the cost of each medium pizza is $6.25. Therefore, the total cost would be:
Total cost = Cost of large pizza + Cost of 5 medium pizzas
Total cost = $13.50 + ($6.25 x 5)
Total cost = $13.50 + $31.25
Total cost = $44.75
Therefore, it would cost $44.75 to purchase one large pizza and five medium pizzas.
b.Number of medium pizzas Total cost
0 | $13.50
1 | $19.75
2 | $26.00
3 | $32.25
4 | $38.50
c. Let "m" be the number of medium pizzas. Then the total cost of purchasing one large pizza with one topping and m medium pizzas can be represented as:
Total cost = 13.50 + 6.25m
d. If you have a total of $100 and purchase one large pizza, you would have $100 - $13.50 = $86.50 left to spend on medium pizzas. The cost of each medium pizza is $6.25. Therefore, you can buy:
Number of medium pizzas = $86.50 ÷ $6.25 = 13.84
Since you cannot buy a fraction of a pizza, you can only buy 13 medium pizzas with $86.50.
e. The area of a pizza is given by the formula A = πr^2, where A is the area and r is the radius. The area of a large pizza is:
A = πr^2
A = 3.14 x 8^2
A = 3.14 x 64
A = 200.96
The area of a medium pizza is:
A = πr^2
A = 3.14 x 5^2
A = 3.14 x 25
A = 78.5
Therefore, the total area of one large pizza and five medium pizzas is:
Total area = Area of large pizza + (Area of medium pizza x 5)
Total area = 200.96 + (78.5 x 5)
Total area = 200.96 + 392.5
Total area = 593.46
Rounding to the nearest inch, the total area of pizza is 593 square inches.
f. To calculate the cost per square inch of pizza, we need to divide the total cost of the pizzas by the total area of the pizzas. The total cost of one large pizza and five medium pizzas is $44.75, and the total area is 593 square inches. Therefore, the cost per square inch of pizza is:
Cost per square inch = Total cost / Total area
Cost per square inch = $44.75 / 593
Cost per square inch = $0.08 (rounded to the nearest cent)
Therefore, the cost per square inch of pizza is 8 cents.
Solve the following linear programming problem. Maximize: z = 7x + 2y subject to: 7x-y≤ 16 2x+y≥ 10 X≥2 y≤9 The maximum value is
Answers
Answer:
To solve the linear programming problem, we need to first graph the feasible region determined by the constraints, and then evaluate the objective function at each corner point of the feasible region to find the maximum value of z.
Plotting the lines corresponding to the inequalities, we get:
Graph of the feasible region:
The feasible region is the shaded polygon in the graph. We can see that the vertices of the feasible region are (2, 9), (2, 12), (4, 7), and (8, 2).
Next, we evaluate the objective function at each of these vertices to find the maximum value of z.
At (2, 9): z = 7x + 2y = 7(2) + 2(9) = 23
At (2, 12): z = 7x + 2y = 7(2) + 2(12) = 31
At (4, 7): z = 7x + 2y = 7(4) + 2(7) = 35
At (8, 2): z = 7x + 2y = 7(8) + 2(2) = 58
Therefore, the maximum value of z is 58, which occurs at the point (8, 2).
Hence, the answer is: the maximum value of z is 58.
Natasha worked for part of the year before receiving a raise in her hourly rate of pay. The graph below shows the amount of money she has made this year and the hours she has worked since she received the raise. What was the initial amount of money Natasha made?
Answers
Answer:
Unfortunately, I cannot see the graph you are referring to since we are communicating through text. However, based on the information given, we can make some general observations.
We know that Natasha received a raise in her hourly rate of pay at some point during the year. Before the raise, she earned some initial hourly rate of pay. Let's call this initial rate of pay "x". Let's also assume that she worked for "h" hours before receiving the raise, and "k" hours after receiving the raise.
We can write an equation to represent the total amount of money she made this year:
Total amount of money = (initial hourly rate of pay x number of hours worked at the initial rate) + (new hourly rate of pay x number of hours worked at the new rate)
Using the variables we defined earlier, we can write:
Total amount of money = (x × h) + ((x + y) × k)
where y is the increase in her hourly rate of pay after the raise.
We also know that she earned a certain amount of money before the raise. Let's call this amount "M". This means that:
M = x × h
Solving for x, we get:
x = M/h
Substituting this expression for x into the first equation, we get:
Total amount of money = (M + yh) + ((M/h + y) × k)
We don't know the values of M, y, h, or k, so we cannot determine the initial hourly rate of pay x or the total amount of money Natasha made this year. However, we have set up an equation that can be used to solve for these values if we have more information.
Solve the right triangle (tan,sin,cos)
Answers
The value of the trigonometric functions for the right triangle is tan(29) = 0.518. cos(29) = 0.838. sin (29) = 0.435.
What are basic trigonometric functions?The sine, cosine, and tangent trigonometric ratios are the three most important ones. These are their definitions:
Sine (sin) is the proportion of a right triangle's hypotenuse to the length of the side that faces an angle.
The length of the side next to an angle in a right triangle divided by the length of the hypotenuse is known as the cosine (cos).
In a right triangle, the tangent (tan) is the ratio between the lengths of the sides that face each other and the angle.
These ratios are used in trigonometry to connect the angles and sides of right triangles, and they may be used to a number of triangle- and other geometric shape-related problems.
In the given triangle using the sum of interior angle of triangle we have:
180 - 90 - 29 = 61
The measure of the third angle is 61 degrees.
Now, tan(61) = XZ/XY
XZ = XY * tan(61)
XZ = 18 * 1.927 = 34.686
Now, using the Pythagoras theorem we have:
ZY² = XZ² + XY²
ZY² = 34.686² + 18²
ZY² = 1712.3996
ZY = 41.38
Now, the value of:
sin(29) = opposite/hypotenuse = XY/ZY = 18/41.388 = 0.435
cos(29) = adjacent/hypotenuse = XZ/ZY = 34.686/41.388 = 0.838
tan(29) = opposite/adjacent = XY/XZ = 18/34.686 = 0.518
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How many solutions does it have ?
Y =4
Y =4x-1
Answers
4 = 4x - 1
Adding 1 to both sides, we get:
5 = 4x
Dividing both sides by 4, we get:
x = 5/4
Therefore, the system has a unique solution, which is (x, y) = (5/4, 4).
Answer:
1 solution
Step-by-step explanation:
Y = 4
Y = 4x - 1
Substitute value of Y here,
4 = 4x - 1
4 + 1 = 4x
5 = 4x
5/4 = x
1.25 = x
•°• The given equation can have only 1 solution, i.e, a linear equation with 1 variable gives only 1 solution.
______
hope this helps!
Which of the following equations will reduce the graph shown below
Answers
The equation y = -1/2(x-3)² + 5 reduces the graph, which means that the graph decreases as we move away from the vertex (3, 5) in both directions along the x-axis.
What is graph?In mathematics, a graph is a visual representation of a set of objects (called vertices or nodes) and the connections (called edges) between them.
The equation y = -1/2(x-3)² + 5 is a quadratic function in vertex form. The vertex of this parabola is at the point (3, 5), and the coefficient of the x² term is negative (-1/2), which tells us that the parabola opens downwards. This means that the graph of this equation reduces.
To see why this is the case, consider the behavior of the y-values as x moves away from the vertex. Since the leading coefficient is negative, the y-values will decrease as x moves to the left or right from the vertex. Additionally, the squared term inside the parentheses means that the graph will be symmetric around the x-coordinate of the vertex, which is 3 in this case.
Thus, as x moves away from the vertex to the left or right, the y-values decrease in a symmetric manner, resulting in a graph that reduces. This can be seen in the shape of the parabola as it curves downwards from the vertex.
Therefore, the equation y = -1/2(x-3)² + 5 reduces the graph, which means that the graph decreases as we move away from the vertex (3, 5) in both directions along the x-axis.
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the unit rate for this relationship is 1 gallon per 18.25 minutes
Answers
The amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is calculated to be approximately 6.58 gallons.
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
Assuming the unit rate of 1 gallon per 18.25 minutes, we can convert 2 hours to minutes by multiplying it by 60, which gives us 120 minutes.
So, in 120 minutes, the amount of liquid that can be processed at a unit rate of 1 gallon per 18.25 minutes would be:
(120 minutes) / (18.25 minutes/gallon) = 6.58 gallons
Therefore, the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is found out to be approximately 6.58 gallons.
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The complete question is :
What is the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes?
the sum of two numbers is 30. The difference between the two numbers is 15. what are the two numbers?
Answers
15 + y + y = 30
15 + 2y = 30
2y = 15
y = 7.5
x + y = 30
x + 7.5 = 30
X = 22.5
Cyndi is making a mixture of cashews and peanuts the cashews are $7 per pound and $3 a pound for peanuts. Cyndi wants 20 pounds of the mixture which will cost $5.40 per pound .. what's the system and how much would she need to equal $108
Answers
The amounts of each substance needed to obtain a mixture of 20 pounds at a price of $5.4 per pound is given as follows:
Cashews: 12 pounds.Peanuts: 8 pounds.How to obtain the amounts?The amounts are obtained by a system of equations, for which the variables are given as follows:
Variable x: amount of cashews.Variable y: amount of peanuts.The mixture has a total of 20 pounds, hence:
x + y = 20.
y = 20 - x.
The total cost of the mixture is of $108, as 108/20 = 5.4, hence:
7x + 3y = 108
Replacing the second equation into the first, the value of x is given as follows:
7x + 3(20 - x) = 108
4x = 48
x = 12.
Then the value of y is given as follows:
y = 20 - 12
y = 8.
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Simplificacion de 18/25
Answers
Answer:
Step-by-step explanation:
Ici, nous allons réduire la fraction 18/25 aux termes les plus bas et la convertir en un nombre fractionnaire, si nécessaire.
Dans la fraction 18/25, 18 est le numérateur et 25 est le dénominateur.
On commence par trouver le plus grand diviseur commun de 18 et 25, qui est 1. Ensuite, on divise 18 et 25 par le plus grand diviseur commun pour obtenir la plus petite expression, écrite comme suit :
(18 ÷ 1) / (25 ÷ 1)
= 18/25
what is the value of 6(2b-4) when b =3
Answers
Answer: 12
Step-by-step explanation:
Use BODMAS, so first solve the inside of the bracket:
2*3= 6
6-4= 2
Now we can multiply that by the number outside the bracket. Why?
Because a number outside a bracket means to multiply that number by everything in the bracket. So:
6 * 2 = 12
Answer: 12
Step-by-step explanation:
2 x 3 = 6
6 - 4 = 2
6 x 2 = 12
Find the value of angle ZOX
using the image below
Answers
Answer: 64°
Step-by-step explanation:
Had this problem and got it right
Match each metric measurement on the left with an equivalent unit of measurement on the right.
Answers
According to the information, the values that coincide are: 2.2 meters with 2200 millimeters, 14 decimeters with 0.014 hectometers, 0.14 meters with 0.014 decameters, 0.022 decameters with 22 centimeters.
How to find the numbers that match?To find the numbers that match we must take into account the relationship between the values:
Decameter: Unit of length equal to 10 meters.Centimeter: Unit of length equal to one hundredth of a meter.Decimeter: Unit of length equal to one tenth of a meter.Millimeter: Unit of length equal to one thousandth of a meter.Hectometer: Unit of length equal to 100 meters.According to the above, we can infer that the values that match are:
2.2 meters with 2200 millimeters.14 decimeters with 0.014 hectometers.0.14 meters with 0.014 decameters,0.022 decameters with 22 centimeters.Learn more about measurements at: https://brainly.com/question/4725561
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Your firm is considering adding a product line. The accounting department has determined that the cost
function for this new product will be C(x) = 55x + 3500 and the revenue function will be R(x) = 80x,
where x is the number of units sold. Additionally, the sales department has determined that you reasonably
can expect to sell around 164 units. You must decide whether to go ahead with the new product line.
Find the break-even quantity:
Find the profit function: P(x) =
Make your decision:
O Proceed with the product line: the products are profitable and we can reasonably expect to meet
our break-even quantity.
Cancel the product line: the quantity needed to break even is more than our firm can reasonably
expect to sell.
O Cancel the product line: producing these products is not profitable.
Submit Question
Answers
the profit function is positive, producing 164 units of the new product line would yield a profit of $600.
We should proceed with the product line since it is profitable and we can reasonably expect to meet our break-even quantity.
To find the break-even quantity, we need to set the cost function equal to the revenue function and solve for x:
C(x) = R(x)
55x + 3500 = 80x
25x = 3500
x = 140
Therefore, the break-even quantity is 140 units.
To find the profit function, we subtract the cost function from the revenue function:
P(x) = R(x) - C(x)
P(x) = 80x - (55x + 3500)
P(x) = 25x - 3500
Now we can evaluate the profit function at different values of x to see if producing these products is profitable or not.
If we plug in x = 164, the expected sales quantity, we get:
P(164) = 25(164) - 3500
P(164) = 4100 - 3500
P(164) = 600
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Determine which expression is equivalent to
3
4
−
x
(
1
2
−
5
8
)
+
(
−
3
8
x
)
4
3
−x(
2
1
−
8
5
)+(−
8
3
x).
A
−34x−
4
3
x
B
12x
2
1
x
C
18−78x
8
1
−
8
7
x
D
34−14x
4
3
−
4
1
x
Answers
Answer: We can simplify the expression step by step:
3/4 − x(1/2 − 5/8) + (−3/8)x
3/4 − x(-1/8) + (−3/8)x
3/4 + x/8 − 3/8x
Multiplying everything by 8 to get rid of the fractions:
6 − x + (−3x)
6 − 4x
Therefore, the equivalent expression is D) 34 - 14x / (4/3).
Step-by-step explanation:
work out the product of 1 and 3/3 and 1 and 2/6 give your answer in its simplest form
Answers
Answer:
To multiply 1 3/3 by 1 2/6, we can first convert these mixed numbers to improper fractions, then multiply them together, and finally simplify the result to its simplest form.
1 3/3 can be written as 4/3 (since 1 whole and 3/3 is equivalent to 4/3)
1 2/6 can be written as 8/6 (since 1 whole and 2/6 is equivalent to 8/6)
Now, we can multiply these two fractions together:
4/3 x 8/6 = (4 x 8) / (3 x 6) = 32/18
To simplify this fraction, we can divide the numerator and denominator by their greatest common factor, which is 2:
32/18 = (2 x 16) / (2 x 9) = 16/9
Therefore, the product of 1 3/3 and 1 2/6 is 16/9, or 1 and 7/9 in mixed number form, in its simplest form.
Find the value of each variable.
Answers
Answer:
x = 63 , y = 90
Step-by-step explanation:
assuming DF is the diameter of the semicircle , then
∠ DEF = y = 90° ( angle inh a semicircle )
then
x + y + 27° = 180° ( angle sum of a triangle )
x + 90 + 27 = 180
x + 117 = 180 ( subtract 117 from both sides )
x = 63
ALGEBRA HW!! I WILL GIVE BRAINLYEST
please answer both questions parts.
Answers
The table of original value and rounded values are
x y
0.2 0
0.5 1
0.9 1
1.08 1
1.49 1
1.72 2
2.3 2
2.94 3
The graph is attached
How to make the graphThe graph is made in a cartesian coordinate by tracing the point of intersection of the two points
The table is represented as ordered pair as (original value, rounded value) for the given x and y values:
(0.2, 0), (0.5, 1), (0.9, 1), (1.08, 1), (1.49, 1), (1.72, 2), (2.3, 2), (2.94, 3)
The graph is a scattered plot and its attached
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the great zlatan ibrahimović always scores a goal if he manages to take no less than six shots in a game (and sometimes he scores even without shooting). the following is a probability distribution of the number of shots zlatan ibrahimović must make to score a goal:
No. of shots Probability of scoring
0 0.02
1 0.13
2 0.34
3 0.32
4 0.16
5 0.02
6 0.01
(A). Calculate the expected ( mean) number of shots he takes to score a goal ?
(B). Calculate the standard deviation of the distribution.
Answers
a) The expected (mean) number of shots that Zlatan Ibrahimović must make to score a goal is 3.11.
b) The standard deviation of the distribution is 2.46.
How are the expected number and standard deviation computed?The expected number or mean (μ) of a distribution is computed as sum resulting from the multiplication of each value of the random variable by its probability and adding the products.
The formula for the mean is given as E(x) = ∑x P(x).
On the other hand, to compute the standard deviation (σ) of a probability distribution, we find each deviation from its expected value, square it, multiply it by its probability, add the products, and take the square root.
No. of shots Probability Expected Squared Squared Deviation
of scoring No. of shots Deviation x Probability
0 0.02 0 9.6721 0.193442
1 0.13 0.13 8.8804 1.154452
2 0.34 0.68 5.9049 2.007666
3 0.32 0.96 4.6225 1.4792
4 0.16 0.64 6.1009 0.976144
5 0.02 0.1 9.0601 0.181202
6 0.01 0.6 6.3001 0.063001
The expected (mean)
number of shots = 3.11 6.055107
Standard Deviation = Square root of 6.055107 = 2.46
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Roselli's Machine Manufacturing Co reported its sales as R120 000, a gross profit of R50 000, and current liabilities of R25 000. If the current ratio is 2,5 and the quick ratio is 1,75, what is the inventory turnover for the company?
Answers
Answer:
Step-by-step explanation:
To find the inventory turnover for Roselli's Machine Manufacturing Co, we need to use the formula:
Inventory turnover = Cost of goods sold / Average inventory
First, we need to find the cost of goods sold (COGS):
COGS = Sales - Gross profit
COGS = R120 000 - R50 000
COGS = R70 000
Next, we need to find the average inventory. We can use the quick ratio formula to find the current assets:
Quick ratio = (Current assets - Inventory) / Current liabilities
Rearranging the formula to solve for inventory, we get:
Inventory = Current assets - (Quick ratio x Current liabilities)
Plugging in the values we know, we get:
1.75 = (Current assets - Inventory) / R25 000
Current assets - Inventory = 1.75 x R25 000
Current assets - Inventory = R43 750
Inventory = Current assets - R43 750
Since the current ratio is 2.5, we know that:
Current assets / Current liabilities = 2.5
Solving for current assets, we get:
Current assets = 2.5 x R25 000
Current assets = R62 500
Substituting the values we found for inventory and COGS into the inventory turnover formula, we get:
Inventory turnover = COGS / Average inventory
Inventory turnover = R70 000 / [(R62 500 - R43 750) / 2]
Inventory turnover = R70 000 / (R18 750 / 2)
Inventory turnover = R70 000 / R9 375
Inventory turnover = 7.47
Therefore, the inventory turnover for Roselli's Machine Manufacturing Co is 7.47.