The probability of selecting at random, without replacement, two blue marbles is 5/12 i.e. A.
What exactly is probability?
Probability is a measure of the possibility or chance of an event to be occurred. It is a mathematical concept that is used to describe the degree of uncertainty or randomness associated with an event.
The probability of an event is represented by a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. For example, the probability of rolling a 6 on a fair six-sided die is 1/6, because there is only one way to roll a 6 out of the six possible outcomes.
Now,
Using formula for probability:
P(A and B) = P(A) × P(B|A)
where P(A and B) is the probability of events A and B occurring together, P(A) is the probability of event A occurring, and P(B|A) is the probability of event B occurring given that event A has occurred.
In this case, we want to find the probability of selecting two blue marbles without replacement. Let's break this down into two events:
Event A: Selecting a blue marble on the first draw
Event B: Selecting a second blue marble on the second draw (without replacement)
For Event A, the probability of selecting a blue marble on the first draw is 6/9, since there are 6 blue marbles out of a total of 9 marbles.
For Event B, the probability of selecting a blue marble on the second draw given that a blue marble was selected on the first draw is 5/8, since there are 5 blue marbles remaining out of a total of 8 marbles.
So, using the formula for probability, we have:
P(Event A and Event B) = P(Event A) × P(Event B|Event A)
= (6/9) × (5/8)
= 30/72
= 5/12
Therefore, the probability of selecting at random, without replacement, two blue marbles is 5/12.
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A house blueprint has a scale of 1 in. : 4 ft. The length and width of each room in the actual house are shown in the table. Complete the table by finding the length and width of each room on the blueprint. Living room Kitchen Office Bedroom Bedroom Bathroom Actual l w (ft.) 12 8 16 16 8 16 16 8 20 20 10 20 Blueprint l w (in.)
To find the length and width of each room on the blueprint, we need to use the given scale of 1 in. : 4 ft. This means that every 1 inch on the blueprint represents 4 feet in the actual house.
To find the length and width of each room on the blueprint, we can multiply the actual length and width of each room by 1/4 (or divide by 4). This gives us:
Living room: Length = 12 ft. ÷ 4 = 3 in., Width = 8 ft. ÷ 4 = 2 in.
Kitchen: Length = 16 ft. ÷ 4 = 4 in., Width = 16 ft. ÷ 4 = 4 in.
Office: Length = 16 ft. ÷ 4 = 4 in., Width = 8 ft. ÷ 4 = 2 in.
Bedroom: Length = 20 ft. ÷ 4 = 5 in., Width = 20 ft. ÷ 4 = 5 in.
Bedroom: Length = 10 ft. ÷ 4 = 2.5 in., Width = 20 ft. ÷ 4 = 5 in.
Bathroom: Length = 16 ft. ÷ 4 = 4 in., Width = 8 ft. ÷ 4 = 2 in.
Therefore, the length and width of each room on the blueprint are:
Living room: 3 in. x 2 in.
Kitchen: 4 in. x 4 in.
Office: 4 in. x 2 in.
Bedroom: 5 in. x 5 in.
Bedroom: 2.5 in. x 5 in.
Bathroom: 4 in. x 2 in.
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Identify the segment bisector of XY
XM= 3x+1
MY= 8x-24
The length of XY is
Answer:
The length of XY is 32.
Step-by-step explanation:
3x + 1 = 8x - 24
1 = 5x - 24
5x = 25
x = 5
3(5)+1 = 16
16*2 = 32
The length of XY is 32.
If a sandwich is made by randomly choosing each of the options, what is the probability it will be a sandwich that Andre would be happy with?
Probability in sandwich choices analysis refers to the likelihood of a particular sandwich being chosen, based on factors such as taste, price, and availability.
1. To calculate the total number of possible sandwiches, we need to consider the number of options for each category: bread, protein, cheese, and vegetables.
Bread: There are 3 options - Italian, white, and wheat.
Protein: There are 4 options - tuna, ham, turkey, and beans.
Cheese: There are 4 options - provolone, Swiss, American, and none.
Vegetables: There are 5 options, and since we need to choose two, we use combinations. Therefore, there are (5 choose 2) = 10 possible combinations of vegetables: lettuce and tomatoes, lettuce and peppers, lettuce and onions, lettuce and pickles, tomatoes and peppers, tomatoes and onions, tomatoes and pickles, peppers and onions, peppers and pickles, and onions and pickles.
To calculate the total number of possible sandwiches, we multiply the number of options for each category:
3 x 4 x 4 x 10 = 480
Therefore, there are 480 different possible sandwiches.
2. Since Andre only cares about the ham, lettuce, and tomatoes, we only need to consider the number of options for vegetables. He needs to choose two vegetables, so we need to count the number of possible combinations of lettuce, tomatoes, and the remaining vegetables. Since we don't care about the bread or cheese, we can ignore those options.
There are (3 choose 2) = 3 possible combinations of vegetables that would make Andre happy: lettuce and tomatoes, lettuce and peppers, or tomatoes and peppers. Since we don't care about the bread or cheese, there are no restrictions on those categories, so there are 4 options for cheese and 3 options for bread, for a total of 12 possible sandwiches that would make Andre happy.
3. To calculate the probability of randomly choosing a sandwich that would make Andre happy, we divide the number of sandwiches that would make him happy by the total number of possible sandwiches:
3/480 = 1/160
Therefore, the probability is 1/160, or approximately 0.00625. This means that if we were to randomly choose a sandwich, there is a 0.625% chance that it would be a sandwich that would make Andre happy.
The complete question is:
1. A submarine sandwich shop makes sandwiches with one kind of bread, one protein, one choice of cheese, and two vegetables. How many different sandwiches are possible? Explain your reasoning. You do not need to write out the sample space.
Breads: Italian, white, wheat
Proteins: Tuna, ham, turkey, beans
Cheese: Provolone, Swiss, American, none
Vegetables: Lettuce, tomatoes, peppers, onions, pickles.
2. Andre knows he wants a sandwich that has ham, lettuce, and tomatoes on it. He doesn’t care about the type of bread or cheese. How many of the different sandwiches would make Andre happy?
3. If a sandwich is made by randomly choosing each of the options, what is the probability it will be a sandwich that Andre would be happy with?
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To show that circle P is similar to circle Q, circle P is translated t
units to the right. The image is then dilated about its center by a
scale factor of s.
What are the values of t and s?
058
S=3
t = 13
s=1.75
t=-5
S=8
Answer:the scale factor of dilation from circle P to Q is 2.5
for among us
Step-by-step explanation:
The similar circles P and Q can be made equal by dilation and translation
The horizontal distance between the center of circles P and Q is 11.70 units
The scale factor of dilation from circle P to Q is 2.5
The horizontal distance between their centers?
From the figure, we have the centers to be:
P = (-5,4)
Q = (6,8)
The distance is then calculated using:
d = √(x2 - x1)^2 + (y2 - y1)^2
So, we have:
d = √(6 + 5)^2 + (8 - 4)^2
Evaluate the sum
d = √137
Evaluate the root
d = 11.70
Hence, the horizontal distance between the center of circles P and Q is 11.70 units
The scale factor of dilation from circle P to Q
We have their radius to be:
P = 2
Q = 5
Divide the radius of Q by P to determine the scale factor (k)
k = Q/P
k = 5/2
k = 2.5
Hence, the scale factor of dilation from circle P to Q is 2.5
Only numbers 20 and 22
1. The transformation of f is a reflection across the y-axis, followed by a shift of 8 units along the y-axis.
2. stretching by a factor of 2 along the y-axis
3. reflection
4. shift
5. reflection
6. stretch
7. stretch
8. reflection
What is modifying function?The transformation of a function f represented by g is the process of modifying the function f to create a new function g. This can be done in a number of ways, such as shifting the graph, stretching it, or reflecting it in some way.
1. f(x) = √x, g(x) = √(x+1)+8, the transformation of f is a reflection across the y-axis, followed by a shift of 8 units along the y-axis.
2. f(x) = √x, g(x) = 2√(x - 1), the transformation of f is a stretching by a factor of 2 along the y-axis, followed by a shift by -1 along the x-axis.
3. f(x) = ³√x, g(x) = −³√x-1, the transformation of f is a reflection across the x-axis, followed by a shift of -1 along the x-axis.
4. f(x) = ³√x, g(x) = ³√(x +4)-5, the transformation of f is a shift of 4 units along the x-axis, followed by a shift of -5 units along the y-axis.
5. f(x) = x^½, g(x) =1/4(-x)^½, the transformation of f is a reflection across the y-axis, followed by a stretching by a factor of 1/4 along the y-axis.
6. f(x) = x^⅓, g(x) =1/3x^⅓+6, the transformation of f is a stretching by a factor of 1/3 along the y-axis, followed by a shift of 6 units along the y-axis.
7. f(x)= ⁴√x, g(x) =2 ⁴√(x+5)-4, the transformation of f is a stretching by a factor of 2 along the y-axis, followed by a shift of 5 units along the x-axis, followed by a shift of -4 units along the y-axis.
8. f(x)= ⁵√x, g(x) =⁵√(-32x)+3, the transformation of f is a reflection across the x-axis, followed by a stretching by a factor of 32 along the x-axis, followed by a shift of 3 units along the y-axis.
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19. The transformation of f is a reflection across the y-axis, followed by a shift of 8 units along the y-axis.
20. The transformation of f is a stretching by a factor of 2 along the y-axis
21. The transformation of f is a reflection across the x-axis.
22. The transformation of f is a shift of 4 units along the x-axis, followed by a shift of -5 units along the y-axis.
23. The transformation of f is a reflection across the y-axis.
24. The transformation of f is a stretching by a factor of 1/3 along the y-axis.
25. The transformation of f is a stretching by a factor of 2 along the y-axis.
26. The transformation of f is a reflection across the x-axis, followed by a stretching by a factor of 32 along the x-axis
Define function modification?The transformation of a function f represented by g is the process of modifying the function f to create a new function g. This can be done in a number of ways, such as shifting the graph, stretching it, or reflecting it in some way.
19. f(x) = √x, g(x) = √(x+1)+8, the transformation of f is a reflection across the y-axis, followed by a shift of 8 units along the y-axis.
20. f(x) = √x, g(x) = 2√(x - 1), the transformation of f is a stretching by a factor of 2 along the y-axis, followed by a shift by -1 along the x-axis.
21. f(x) = ³√x, g(x) = −³√x-1, the transformation of f is a reflection across the x-axis, followed by a shift of -1 along the x-axis.
22. f(x) = ³√x, g(x) = ³√(x +4)-5, the transformation of f is a shift of 4 units along the x-axis, followed by a shift of -5 units along the y-axis.
23. f(x) = x½, g(x) =1/4(-x½, the transformation of f is a reflection across the y-axis, followed by a stretching by a factor of 1/4 along the y-axis.
24. f(x) = x⅓, g(x) =1/3x⅓+6, the transformation of f is a stretching by a factor of 1/3 along the y-axis, followed by a shift of 6 units along the y-axis.
25. f(x)= ⁴√x, g(x) =2 ⁴√(x+5)-4, the transformation of f is a stretching by a factor of 2 along the y-axis, followed by a shift of 5 units along the x-axis, followed by a shift of -4 units along the y-axis.
26. f(x)= ⁵√x, g(x) =⁵√(-32x)+3, the transformation of f is a reflection across the x-axis, followed by a stretching by a factor of 32 along the x-axis, followed by a shift of 3 units along the y-axis.
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what is the domain of the function?
how long does it take for a population that is growing with a constant relative growth rate of 10% per year to triple
1. In a five card poker hand what is the probability of being dealt exactly one ace and no picture cards?
2. The digits, 3,4,5,6 and 7 are randomly arranged to form q three digit number. Find the probability that the number is even and greater than 700
3. If you are dealt 3 cards from a shuffled deck of 52 cards find the probability of getting one queen and two kings
Therefore, the probability of randomly arranging the digits 3, 4, 5, 6, and 7 to form a three-digit number that is even and greater than 700 is 0.1.
What is Probability?Probability refers to the likelihood or chance that a particular event or outcome will occur. It is a mathematical concept that quantifies the degree of uncertainty associated with an event or situation. Probability is typically expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that it is certain to occur.
by the question.
Therefore, the total number of five card hands that have exactly one ace and no picture cards been 4 * (36 choose 4) = 253,440.
The total number of five card hands is (52 choose 5) = 2,598,960.
Therefore, the probability of being dealt exactly one ace and no picture cards in a five-card poker hand is 253,440 / 2,598,960, which simplifies to 0.097%.
2.There are a total of 5! = 120 possible arrangements of the digits 3, 4, 5, 6, and 7. To form a three-digit number, we need to use three of these digits, so there are 5 x 4 x 3 = 60 possible three-digit numbers we can form.
To be greater than 700, the first digit must be either 6 or 7. If we choose 7 as the first digit, there are 4 x 3 = 12 ways to choose the remaining two digits. If we choose 6 as the first digit, there are 4 x 3 = 12 ways to choose the second and third digits, since we can't repeat digits. Therefore, there are 12 + 12 = 24 three-digit numbers greater than 700.
To be even, the last digit must be either 4 or 6. If we choose 6 as the first digit, there are 2 ways to choose the last digit (either 4 or 6), and 3 ways to choose the middle digit (since we can't repeat digits). This gives us a total of 2 x 3 = 6 even numbers starting with 6.
If we choose 7 as the first digit, there are no even numbers we can form, since the last digit can only be 4 or 6 and we've already used the 6 digit. Therefore, the total number of even three-digit numbers greater than 700 is 6.
So, the probability of randomly selecting an even three-digit number greater than 700 is 6/60 = 1/10 or 0.1.
3.There is a total of C (52, 3) = 22,100 possible ways to choose 3 cards from a deck of 52 cards.
To get one queen and two kings, we need to choose one of the four queens and two of the four kings. There are C(4, 1) ways to choose one queen, and C(4, 2) = 6 ways to choose two kings. Therefore, there are 4 x 6 = 24 ways to choose one queen and two kings.
So, the probability of getting one queen and two kings is 24/22,100 or approximately 0.0011 (rounded to four decimal places).
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Work out the value of 2^6
Answer:
2^6 = 64
Step-by-step explanation:
2^6 = 2⁶ = 2*2*2*2*2*2
= 64
The cookie-stacking competition is a tradition at Westhaven's annual summer festival, and Bert is helping to set it up this year. The first contestant who creates a single stack using all of their cookies wins a prize! After Bert split all the cookies he had evenly among 4 contestants, each contestant got 24 cookies.
Let c represent how many cookies Bert had to start. Which equation models the problem?
Solve this equation to find how many cookies Bert had to start.
cookies
The problem states that Bert split all his cookies evenly among 4 contestants, so the total number of cookies Bert had can be found by multiplying the number of cookies each contestant received by the number of contestants:
4 * 24 = 96
Therefore, Bert had a total of 96 cookies to start with.
We can also write an equation to represent the problem, where c represents the number of cookies Bert had to start with:
c / 4 = 24
This equation states that the number of cookies Bert had divided by the number of contestants (4) is equal to the number of cookies each contestant received (24).
To solve for c, we can multiply both sides of the equation by 4:
c = 4 * 24
c = 96
So the solution confirms that Bert had 96 cookies to start with.
Is there anyone who would know how to write this recursive relationship? Also anyone who could write the equation for the second question
The recursive relationship that describes how the number of Marco's followers is changing each day is Pt = Pt-1 + 32.
It should be noted that after 5 days, Marco will have 597 followers.
How to explain the relationshipThe relationship is Pt = Pt-1 + 32 where Pt is the number of followers on day t and Pt-1 is the number of followers on the previous day.
In this case, to calculate how many followers Marco will have after 5 days, we can use this recursive relationship starting with P0 = 437 (the initial number of followers):
P1 = P0 + 32 = 437 + 32 = 469
P2 = P1 + 32 = 469 + 32 = 501
P3 = P2 + 32 = 501 + 32 = 533
P4 = P3 + 32 = 533 + 32 = 565
P5 = P4 + 32 = 565 + 32 = 597
Therefore, after 5 days, Marco will have 597 followers.
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A BICYCLE WHEEL HAS AN INSIDE RADIUS OF 12 CM. WHAT IS THE WIDTH OF THE TYRE IF THE OUTSIDE CIRCUMFERENCE IS 32П СМ?
Answer:
Your answer is 4cm.
Step-by-step explanation:
simple calculation
x (12+x) π = 32 π
x = 4cm
Of the following , which measurement is in the base units 5mg, 10kL, 2.5g, 100mm
For the given measurements of 5mg, 10kL, 2.5g, 100mm, the base unit is 10kL as per the metric system.
Explain about the standard measurement units?The most widely used measurement unit is a standard unit. As the units used are standardised, everyone can understand an object's size, weight, and perhaps other characteristics.
The values of Standard Units of Measurement are constant and cannot be altered. To ensure that everyone uses the same measurements and has the same understanding of measurement, measurements must be consistent between users.The identity of a quantity is described using standard units of measurement. It is simpler to identify the type of data we are working with when there are units of measurement available.The Metric System is currently used in the majority of nations. The Imperial Units of Measuring, often known as the US Standard Measurement System, are used in the US.
Given units :
5mg, 10kL, 2.5g, 100mm
In this, standard measurement units or base units if 10 kilo litres or 10 KL.
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Choose the item that has measurable volume.
a dollar bill
newspaper page
a water bottle
a postage stamp
A water bottle
Step-by-step explanation:
It's a water bottle because you cannot measure volume with a dollr bill or postage stamp.
Corey wrote an equation in factored form , quadratic function . Kimberly wrote the equation y = (x + 8)(x - 2); y=x^ 2 +6x-16, to represent a and Joshua wrote the equation y = (x + 3) ^ 2 - 25 A. What information can Corey’s form help you find that is more difficult to find using the others form?
As a result, x = 2 and x = -5 are the roots of the quadratic function y = (x - 2)(x + 5). They also serve as the function's x-intercepts on the graph.
what is equation ?Typically, it includes one or more variables that stand in for unknowable values and may include exponents, roots, multiplication, division, and other mathematical operations. Finding the value(s) of the variable(s) necessary to make an equation true is the aim of equation solving. In algebra, calculus, and other areas of mathematics, equations are frequently employed to model and resolve issues.
given
This is because the values of x are provided by a quadratic function's factored form.
Let's use Corey's equation, y = (x - 2)(x + 5), as an illustration. We solve for x and put y equal to zero to obtain the roots of this function:
0 = (x - 2)(x + 5)
Only when one of the factors on the left side equals zero is this equation true. As a result, we may set each factor to 0 and find x:
In each equation, the result of solving for x is:
x = 2 or x = -5
This is because the values of x are provided by a quadratic function's factored form.
Let's use Corey's equation, y = (x - 2)(x + 5), as an illustration. We solve for x and put y equal to zero to obtain the roots of this function:
0 = (x - 2)(x + 5)
Only when one of the factors on the left side equals zero is this equation true. As a result, we may set each factor to 0 and find x:
x - 2 = 0 or x + 5 = 0
In each equation, the result of solving for x is:
x = 2 or x = -5
As a result, x = 2 and x = -5 are the roots of the quadratic function y = (x - 2)(x + 5). They also serve as the function's x-intercepts on the graph.
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3) Hannah is making muffins. The recipe calls for 2/3 cup of milk to make 12
muffins.
a) What is the unit rate for cups of milk per muffin?
b) What is the unit rate for muffins per cup of milk?
a) The unit rate for cups of milk per muffin is 1/18 cup of milk per muffin.
b) The unit rate for muffins per cup of milk is 18 muffins per cup of milk.
What are the muffins?
(a) To find the unit rate for cups of milk per muffin, we need to divide the total amount of milk by the number of muffins:
2/3 cup of milk / 12 muffins = (2/3) ÷ 12 cup of milk per muffin
We can simplify this fraction by multiplying the numerator and denominator by 3:
(2/3) ÷ 12 = 2 ÷ (3 x 12) = 2 ÷ 36 = 1/18
So the unit rate for cups of milk per muffin is 1/18 cup of milk per muffin.
b) To find the unit rate for muffins per cup of milk, we need to divide the number of muffins by the total amount of milk:
12 muffins / (2/3 cup of milk) = 12 ÷ (2/3) muffins per cup of milk
To divide by a fraction, we can multiply by its reciprocal:
12 ÷ (2/3) = 12 x (3/2) = 36/2 = 18
So the unit rate for muffins per cup of milk is 18 muffins per cup of milk.
A muffin is a type of small, individual-sized baked good that is usually round in shape and has a slightly sweet taste. Muffins can be made with a variety of ingredients, including flour, sugar, eggs, butter, milk, and baking powder. They can also be flavored with various fruits, nuts, spices, or chocolate chips.
Muffins can be eaten for breakfast, as a snack, or as a dessert. They are often served warm and can be eaten plain or with butter, jam, or honey. Muffins are a popular baked good and are commonly found in coffee shops, bakeries, and grocery stores.
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Complete question is: Hannah is making muffins. The recipe calls for 2/3 cup of milk to make 12 muffins.
a) The unit rate for cups of milk per muffin is 1/18 cup of milk per muffin.
b) The unit rate for muffins per cup of milk is 18 muffins per cup of milk.
Gold Nest Company of Guandong, China, is a family-owned enterprise that makes birdcages for the South China market. The company sells its birdcages through an extensive network of street vendors who receive commissions on their sales. The company uses a job-order costing system in which overhead is applied to jobs on the basis of direct labor cost. Its predetermined overhead rate is based on a cost formula that estimated $85,500 of manufacturing overhead for an estimated activity level of $45,000 direct labor dollars. At the beginning of the year, the inventory balances were as follows: Raw materials $ 10,400 Work in process $ 4,800 Finished goods $ 8,100 During the year, the following transactions were completed: Raw materials purchased on account, $162,000. Raw materials used in production, $141,000 (materials costing $128,000 were charged directly to jobs; the remaining materials were indirect). Costs for employee services were incurred as follows: Direct labor $ 159,000 Indirect labor $ 225,000 Sales commissions $ 28,000 Administrative salaries $ 50,000 Rent for the year was $18,600 ($13,100 of this amount related to factory operations, and the remainder related to selling and administrative activities). Utility costs incurred in the factory, $20,000. Advertising costs incurred, $15,000. Depreciation recorded on equipment, $21,000. ($17,000 of this amount related to equipment used in factory operations; the remaining $4,000 related to equipment used in selling and administrative activities.) Manufacturing overhead cost was applied to jobs, $ ? . Goods that had cost $229,000 to manufacture according to their job cost sheets were completed. Sales for the year (all paid in cash) totaled $512,000. The total cost to manufacture these goods according to their job cost sheets was $217,000. Required: 1. Prepare journal entries to record the transactions for the year. 2. Prepare T-accounts for each inventory account, Manufacturing Overhead, and Cost of Goods Sold. Post relevant data from your j
The journal entries to record the transactions for the year is showed below.
1. Journal Entries:
a. Raw materials purchased on account:
Raw Materials Inventory $162,000
Accounts Payable $162,000
b. Raw materials used in production (direct and indirect):
Work in Process Inventory $128,000
Manufacturing Overhead $13,000
Raw Materials Inventory $141,000
c. Costs for employee services (direct labor, indirect labor, sales commissions, administrative salaries):
Work in Process Inventory $159,000
Manufacturing Overhead $225,000
Sales Commissions Expense $28,000
Administrative Salaries Expense $50,000
d. Rent for the year (factory operations and selling/administrative activities):
Manufacturing Overhead $13,100
Selling and Administrative Expenses $5,500
Rent Payable $18,600
e. Utility costs incurred in the factory:
Manufacturing Overhead $20,000
Cash $20,000
f. Advertising costs incurred:
Selling and Administrative Expenses $15,000
Cash $15,000
g. Depreciation recorded on equipment (factory operations and selling/administrative activities):
Depreciation Expense (Factory) $13,100
Depreciation Expense (Selling and Administrative) $4,900
Accumulated Depreciation $18,000
2. T-Accounts:
a. Raw Materials Inventory:
Beginning balance: $10,400
Purchases: $162,000
Direct Materials Used: $128,000
Ending balance: ?
b. Work in Process Inventory:
Beginning balance: $4,800
Direct Labor: $159,000
Manufacturing Overhead: ?
Direct Materials Used: $128,000
Ending balance: ?
c. Finished Goods Inventory:
Beginning balance: $8,100
Cost of Goods Manufactured: $217,000
Ending balance: ?
d. Manufacturing Overhead:
Beginning balance: $0
Rent: $13,100
Utilities: $20,000
Depreciation (Factory): $13,100
Applied to Jobs: ?
Ending balance: ?
e. Cost of Goods Sold:
Beginning balance: $0
Cost of Goods Manufactured: $217,000
Ending balance: ?
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When her first baby was born, a mom started investing $200 each month into a college fund earning 6% compounded monthly, how much will be available when the child turns 18 years?
Use graphing technology to find the range of the function f ( x) = − ∣ x∣ + 7. f(x)=−∣x∣+7.
Using graphing technology, we have came to know that the range οf the given functiοn is f(x )≤ 7.
What is range οf a functiοn?The set οf all resulting values οf a functiοn is called the range οf a functiοn.
Fοr example if the functiοn is f(x)= 2x.
Fοr the given set οf values x={ 1,2,3 and sο οn} the range will be {2,4,6 and sο οn}
Given functiοn is f(x)= -|x|+7
The range οf an absοlute function οf the fοrm -c| [tex]ax+b[/tex]| is f(x) ≤ k
here k=7
sο the range will be f(x) ≤ 7
Hence range οf the given functiοn will be f(x) ≤ 7.
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A teacher assigns a score from 1 to 4 to each student project. The table below shows the probability distribution of the scores for a randomly selected student. Which score is most likely?Probability DistributionScore: XProbability: P(X)10.0620.2030.4840.261234
Based on the probability distribution, the score that is most likely is 3, since it has the highest probability of 0.48.
4. The value of (1+2+3+...+20) is 210. What is the value of (3+6+9+...+57)?
B) 630
A) 627
C) 570
D) 573
E) 580
By using sum of sequence the value of (3+6+9+...+57) is 570, which is option C).
What is sum of the sequence ?
The sum of a sequence is the total result of adding up all the numbers in the sequence. The method for finding the sum of a sequence depends on whether the sequence is arithmetic or geometric.
For an arithmetic sequence, in which each term is obtained by adding a fixed number (called the common difference) to the previous term, the sum of the first n terms can be found using the formula:
[tex]Sn = n/2(2a + (n-1)d)[/tex]
where a is the first term, d is the common difference, and n is the number of terms.
For a geometric sequence, in which each term is obtained by multiplying the previous term by a fixed number (called the common ratio), the sum of the first n terms can be found using the formula:
[tex]Sn = a(1-r^n) / (1-r)[/tex]
where a is the first term, r is the common ratio, and n is the number of terms.
According to the question:
We can notice that each number in the sequence 3, 6, 9, ..., 57 is 3 times the corresponding number in the sequence 1, 2, 3, ..., 19.
So, we can find the sum of the sequence 3, 6, 9, ..., 57 by finding the sum of the sequence 1, 2, 3, ..., 19 and then multiplying by 3.
The sum of the sequence 1, 2, 3, ..., 19 is:
1 + 2 + 3 + ... + 19 = (19/2)(1 + 19)/2 = 190
Multiplying by 3, we get:
3 + 6 + 9 + ... + 57 = 3(1 + 2 + 3 + ... + 19) = 3(190) = 570
Therefore, the value of (3+6+9+...+57) is 570, which is option C).
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If 2x2 + 8x – 14 = 0, find the sum and the product of its roots.
a. sum = 4; product = 7 c. sum = -4; product = -7
b. sum = -4; product = 7 d. sum = 4; product = -7
Answer:
c
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0
then
sum of roots = - [tex]\frac{b}{a}[/tex]
product of roots = [tex]\frac{c}{a}[/tex]
2x² + 8x - 14 = 0 ← is in standard form
with a = 2 , b = 8 , c = - 14
sum of roots = - [tex]\frac{b}{a}[/tex] = - [tex]\frac{8}{2}[/tex] = - 4
product of roots = [tex]\frac{c}{a}[/tex] = [tex]\frac{-14}{2}[/tex] = - 7
7. Reasoning Hilary walked 654 feet in 3
minutes. She says she walked 218 feet
per minute. Is Hilary's answer reasonable?
Explain.
E I D 27° A I C m DC = 40° F B What is the mZAFB? |
let's keep in mind that arc's get their angle value from the central angle they cover, so in this case whatever angle value the arcAFB has, will also be the same for the ∡AFB.
Check the picture below.
4.1 Exponential Functions
189
Work these problems. (See Example 5.)
37. Finance If money loses value, then as time passes, it takes
more dollars to buy the same item. Use the results of Exercise
36(a) to answer the following questions.
(a) Suppose a house costs $105,000 today. Estimate the cost of
the same house in 10 years. (Hint: Solve the equation
.74t =
$105,000.)
(b) Estimate the cost of a $50 textbook in 8 years.
we can estimate the cost of a $50 textbook in 8 years to be approximately $32.78.
What is logarithms?
Logarithms are mathematical functions that are used to solve equations involving exponents. Specifically, a logarithm is the inverse operation of exponentiation. Just as exponentiation involves raising a base to a power, logarithms involve finding the power to which a base must be raised to produce a given value.
The logarithm of a number y with respect to a base b is written as logb y, and it is defined as the exponent to which the base b must be raised to produce the number y. In other words, if [tex]b^x = y[/tex], then logb y = x.
According to the question:
In Exercise 36(a), we found that the value of a dollar decreases by 26% over 5 years. We can use this information to answer the following questions:
(a) To estimate the cost of the same house in 10 years, we need to solve the equation:
0.74t = 105,000
where t is the time in years. Solving for t, we get:
[tex]t = log(105,000) / log(0.74) = 17.9[/tex]
So it will take approximately 17.9 years for the value of the dollar to decrease by 26% enough to make the $105,000 house cost the same as it does today. Therefore, we can estimate the cost of the same house in 10 years to be:
[tex]$105,000 * (1 / 0.74)^(10/17.9) = $211,775.22[/tex]
(b) To estimate the cost of a $50 textbook in 8 years, we need to find the value of k in the exponential function:
[tex]V(t) = V(0) * e^kt[/tex]
where V(0) is the initial value (in this case, $50), t is the time in years, and V(t) is the value after t years. We know that the value of a dollar decreases by 26% over 5 years, so we can use this information to find k:
[tex]0.74 = e^(k*5)[/tex]
Taking the natural logarithm of both sides, we get:
ln(0.74) = 5k
Solving for k, we get:
k ≈ -0.064
So the exponential function for the value of a dollar over time is:
[tex]V(t) = $50 * e^{-0.064t}[/tex]
To estimate the cost of the textbook in 8 years, we can plug in t = 8 into this function and solve:
[tex]V(8) = $50 * e^{-0.064*8} = $32.78[/tex]
Therefore, we can estimate the cost of a $50 textbook in 8 years to be approximately $32.78.
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Help!! I guessed on this so I’m not sure if it’s right but if it isn’t please help me lol
Answer:
x + 4
Step-by-step explanation:
When factored x^2 -16 is (x + 4)(x - 4)
When factored x^2 + 2x - 8 is (x - 2)(x + 4)
The common expression is x + 4
two splices plants are cut from a piece of sheet steel that has an overall length of 15 3/8 in the plates are 8 1/4 in and 5 15/16 in long how much material remerial remains from the original piece if each saw cut removes 1/16 in
Using fractions, we can find that [tex]1\frac{1}{16}[/tex] length of material remains.
Define fractions?In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
A fraction is a non-integer that consists of a numerator and a denominator. A mixed fraction is made up of a whole number and a proper fraction. A proper fraction is a fraction where the numerator is less than the denominator.
Material left = initial length - length of the first plate - length of the second plate - (2 x 1/16)
= 123/8 - 33/4 - 95/16 - 2/16
= 17/16
= [tex]1\frac{1}{16}[/tex].
Therefore, [tex]1\frac{1}{16}[/tex] length of material remains.
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which expression is equivalent to g^2/3h
The given expression [tex]g^2/3h[/tex] is equivalent to the option (c) [tex]8g^2/24h[/tex]as we have multiplied 8 in both numerator and denominator.
The given expression is [tex]g^2/3h[/tex].
Now, to further simplify the expression, we can multiply both numerator and denominator by 8. This gives us:
[tex](g^2/3h) * (8/8)[/tex]
Simplifying further, we get:
[tex](8g^2)/(24h)[/tex]
Therefore, the expression equivalent to [tex]g^2/3h[/tex] is [tex](8g^2)/(24h)[/tex].
Thus, the given expression [tex]g^2/3h[/tex] is equivalent to the option (c) [tex]8g^2/24h[/tex] as we have multiplied 8 in both numerator and denominator.
The numerator is the top part of a fraction, which represents the number of equal parts being considered. It is the value that is above the fraction bar and represents the quantity being divided into equal parts.
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The complete question is :
Which expression is equivalent to [tex]g^2/3h[/tex]?
Click on the correct answer.
(A) [tex]g^2+5/3h+5[/tex]
(B) [tex]6g^2/15h[/tex]
(C) [tex]8g^2/24h[/tex]
PLEASE HELP
Part A: Given the function g(x) = |x − 7|, describe the graph of the function, including the vertex, domain, and range. (5 points)
Part B: If the parent function f(x) = |x| is transformed to h(x) = |x| + 2, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?
Part A:
The required graph of the function is described.
The vertex of the function is (7,0)
The domain is : (-∝ , ∝) and
The range is : [0,∝), {yIy ≥ 0}
Part B:
The transformation which occurs from f(x) to h(x) is a vertical shift up to 2 units.
Define functions?Expressions separated by an equal sign are functions. Both dependent and independent variables are present.
Given Part A:
given the function is g(x) = I x - 7 I
hence from the function, vertex = (h,k)
h = 7 and k = 0
(h,k) = (7,0)
Find the domain by finding where the function is defined.
therefore, domain = (-∝ , ∝) , where {xIx ∈ R}
The range is the set of values that corresponds with the domain.
therefore, range = [0,∝), {yIy ≥ 0}
Part B:
given the parent function is: f(x) = |x|
which is transformed to h(x) = |x| + 2
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x axis or y axis, and if there is a vertical stretch.
Parent function = f(x) = |x|
Horizontal shift = none
Vertical shift = up 2 units.
Reflection about the x axis = none
hence from the function we can determine the vertex (h,k)
= (0,2)
Find the domain by finding where the function is defined.
therefore, domain = (-∝ , ∝) , where {xIx ∈ R}
The range is the set of values that corresponds with the domain.
therefore, range = [2,∝) , {yIy ≥ 2}
Hence, we get the required answers.
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These figures are similar. The
area of one is given. Find the
area of the other.
9 in
area=32 in
12 in
[? ]in²
2
Answer:
18 in²--------------------------
Find the scale factor by dividing the corresponding sides of the given figures:
k = 9/12 = 3/4The area is the product of two dimensions therefore the ratio of areas of similar figures is the square of the scale factor. Let the area of the smaller figure be A, then we got the ratio:
A/32 = k²A/32 = (3/4)²A/32 = 9/16A = 32*9/16A = 18Answer: 18 in²
Step-by-step explanation: