The total number of stacks that were supposed to be delivered is 125.
In order to determine how many stacks of lumber were supposed to be delivered, we need to use a bit of algebra.
Let's start by assigning a variable to the total number of stacks. We can call this variable "x".
Now, we know that 40% of the lumber shipment will be late.
That means that only 60% of the shipment will arrive on time.
We can express this as an equation:0.60x = number of stacks that arrive on time
We also know that when the shipment arrives, there are 50 stacks of lumber missing.
This means that the total number of stacks delivered is 50 less than the number of stacks that were supposed to be delivered.
We can express this as another equation:x - 50 = number of stacks that were actually delivered
Now, we can set these two equations equal to each other, since they both represent the same thing:0.60x = x - 50
Solving for x, we can first subtract "0.60x" from both sides:x - 0.60x = 50
Simplifying the left side, we get:0.40x = 50
Finally, we can divide both sides by 0.40 to solve for x:x = 125
So, the total number of stacks that were supposed to be delivered is 125.
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Geometry
Solve both and show work
Answer:
y = - 5x - 1 and y = [tex]\frac{1}{3}[/tex] x + 8
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
14
y = - 5x + 4 ← is in slope- intercept form
with slope m = - 5
• Parallel lines have equal slopes , then
y = - 5x + c ← is the partial equation
to find c substitute P (- 1, 4 ) into the partial equation
4 = - 5(- 1) + c = 5 + c ( subtract 5 from both sides )
- 1 = c
y = - 5x - 1 ← equation of parallel line
15
y + 3x = 13 ( subtract 3x from both sides )
y = - 3x + 13 ← in slope- intercept form
with slope m = - 3
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , then
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute P (6, 10 ) into the partial equation
10 = [tex]\frac{1}{3}[/tex] (6) + c = 2 + c ( subtract 2 from both sides )
8 = c
y = [tex]\frac{1}{3}[/tex] x + 8 ← equation of perpendicular line
Answer:
To find the equation of a line perpendicular to another line, we need to determine the slope of the original line and then take the negative reciprocal of that slope.The given line is y + 3x = 13. We can rearrange it to the slope-intercept form (y = mx + b) by isolating y:y = -3x + 13The slope of this line is -3. The negative reciprocal of -3 is 1/3, which will be the slope of the perpendicular line.Now, we have the slope (1/3) and a point (6, 10) that the perpendicular line passes through. We can use the point-slope form (y - y1 = m(x - x1)) to find the equation of the line.Substituting the values into the point-slope form:y - 10 = (1/3)(x - 6)Distributing 1/3 to (x - 6):y - 10 = (1/3)x - 2Adding 10 to both sides to isolate y:y = (1/3)x - 2 + 10Simplifying:y = (1/3)x + 8Therefore, the equation of the line perpendicular to y + 3x = 13 and passing through the point (6, 10) is y = (1/3)x + 8.find the area of an equilateral triangle ABC, whose sides are 7cm each and the height 4.2cm
Step-by-step explanation:
Area of equalaterial triangle is 1/2bh
Here the base is 7.
The height is 4.2
[tex] \frac{1}{2} (7)(4.2) = 14.7[/tex]
(8m + 4) + (8m + 4) combine the like terms to simplify
The expression simplified can be written as:
16m + 8
How to combine the terms and simplify?Here we want to simplify the following expression:
(8m + 4) + (8m + 4)
To simplify, we start by removing the parenthesis:
8m + 4 + 8m + 4
Now we can change the order of the terms so we get:
8m + 8m + 4 + 4
Now we can group the like terms to get:
(8m + 8m) + (4 + 4)
And simplify this to get:
16m + 8
That is the simplified expression.
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Which sentence contains correct punctuation? A. Tammy is a good worker; she gets everything done on time. B. We had the following choices of colors; red, white, or blue. C. I am going home; and I intend to stay there. D. I have packed everything; including a bathing suit, a pair of sunglasses, and a book.
The sentence that contains correct punctuation is "Tammy is a good worker; she gets everything done on time."
Option A contains correct punctuation. It has a semicolon which separates two independent clauses and also makes a connection between them. This is the correct use of punctuation. It is also known as a semicolon conjunction.
Option B is incorrect as there is no semicolon between "colors" and "red." There should be a semicolon instead of a comma to create a connection between the two clauses.
Option C is incorrect as there is no need for a semicolon after "going home" because there is no second independent clause following it.
Option D is incorrect as there should be a semicolon between "everything" and "including" since there are two distinct groups of items being listed.
In conclusion, option A is the correct answer because it follows the rules of proper punctuation by using a semicolon correctly to join two independent clauses.
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My friend eats 5 apples I eat 7 apples. How many apples eat together?
Answer:
12 apples
Step-by-step explanation:
Apples eaten by friend = 5
Apples eaten by me = 7
Toral number of apples eaten together
= 5 + 7
= 12
________
hope this helps!
Answer:
12 apples
Step-by-step explanation:
If 1 person eats 5 apples, and another person eats 7, we should add the amount of apples together to get the total.
5+7
=12
So, 12 apples were ate altogether.
Hope this helps! :)
Compute the probabilites given the following probability distribution:
Your answers should be exact decimal values.
The probability of x being equal to 2 is
The probability of x being more than 2 is
Compute P(x ≤ 2).
x P(x)
1 0.52
2 0.13
3 0.24
4 0.11
The probability of x being equal to 2 is 0.13
The probability of x being more than 2 is 0.35
The probability of x ≤ 2 is 0.65
How to find the probability of x being equal to 2?To compute the probabilities using the given probability distribution, we can refer to the provided values for each value of x.
From the table, the probability of x being equal to 2 is 0.13.
The probability of x being more than 2 can be computed by adding the probabilities of x = 3 and x = 4:
P(x > 2) = P(x = 3) + P(x = 4)
P(x > 2) = 0.24 + 0.11
P(x > 2) = 0.35
To compute P(x ≤ 2), add the probabilities of x = 1 and x = 2:
P(x ≤ 2) = P(x = 1) + P(x = 2)
P(x ≤ 2) = 0.52 + 0.13
P(x ≤ 2) = 0.65
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Please Help!! - Find constants a and b so that (8, −7) is the solution of the system. Please answer in exact numbers.
Step-by-step explanation:
Plug in 8 for x, and -7 for y in both systems.
[tex]8a- 7b = 10[/tex]
[tex]8b - 7a = - 5[/tex]
Now, we use the elimination method to isolate a or b.
Let multiply the top equation by 8 and the bottom one by 7.
[tex]64a - 56b= 80[/tex]
[tex]56b - 49a = - 35[/tex]
Eliminate the b variable by adding the two systems.
[tex]15 a= 45[/tex]
[tex]a = 3[/tex]
Now, plug 3 for a into either the systems to find b.
[tex]24 - 7b = 10[/tex]
[tex] - 7b = - 14[/tex]
[tex]b = 2[/tex]
b) The following information was got from an international market in relation to United states and Britain.
Amount available to invest $ 1 000000
Spot exchange rate: $ 1.618 per sterling pound
180 days forward rate: $ 1.6052 per sterling pound
Annual interest rate in U.S 8%
Annual interest rate in Britain 15%
Required:
i. Compute arbitrage profit (if any) (5 marks)
ii. What are the possible moves which can eliminate the arbitrage profit in short run?
(3 marks)
iii. Which name do we give to the situation such that the arbitrage profit is nil.
(2 marks)
The arbitrage profit is $1,750,801.62.Borrow $1,000,000 in the U.S. at an annual interest rate of 8%.
Convert the borrowed amount to sterling pounds at the spot exchange rate.
Invest the borrowed sterling pounds in Britain at an annual interest rate of 15%.
Enter into a forward contract to exchange the future value of the investment back to U.S. dollars at the forward exchange rate.
To determine the arbitrage profit, we need to compare the potential gains from two different investment strategies: investing in the U.S. and investing in Britain.
i. Compute arbitrage profit:
1. Investing in the U.S.:
If we invest $1,000,000 in the U.S. at an annual interest rate of 8%, after 180 days (half a year), the investment will grow to:
$1,000,000 * (1 + 0.08/2) = $1,040,000
2. Investing in Britain:
To invest in Britain, we convert the $1,000,000 to sterling pounds using the spot exchange rate:
$1,000,000 * 1.618 = £1,618,000
Then, we invest the £1,618,000 in Britain at an annual interest rate of 15%:
£1,618,000 * (1 + 0.15/2) = £1,737,850
Now, we need to convert the future value of the investment back to U.S. dollars using the forward exchange rate:
£1,737,850 * 1.6052 = $2,790,801.62
Arbitrage profit = Future value of investment in Britain - Future value of investment in the U.S.
= $2,790,801.62 - $1,040,000
= $1,750,801.62
Therefore, the arbitrage profit is $1,750,801.62.
ii. Possible moves to eliminate arbitrage profit in the short run:
To eliminate the arbitrage profit, investors could take advantage of the discrepancy in interest rates and exchange rates by performing the following actions:
- Borrow $1,000,000 in the U.S. at an annual interest rate of 8%.
- Convert the borrowed amount to sterling pounds at the spot exchange rate.
- Invest the borrowed sterling pounds in Britain at an annual interest rate of 15%.
- Enter into a forward contract to exchange the future value of the investment back to U.S. dollars at the forward exchange rate.
By executing these actions, the arbitrage profit would be eliminated as the gains from the investment in Britain would be offset by the interest payments on the borrowed amount.
iii. The situation where the arbitrage profit is nil is referred to as "Arbitrage equilibrium" or "Arbitrage-free market." In this state, there are no opportunities for risk-free profits through exploiting discrepancies in prices, interest rates, or exchange rates. The market prices and rates are in balance, reflecting all available information and preventing arbitrage opportunities.
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What is the domain of y=√x+7 +5?
x20
O x27
x2-7
Oall real numbers
DONE
The domain of the function y = √(x + 7) + 5 is all real numbers (all real numbers). Option D.
To determine the domain of the function y = √(x + 7) + 5, we need to identify the values of x for which the function is defined.
In this case, the function includes two operations: addition and square root. To ensure the function is defined, we need to consider the restrictions imposed by each operation.
The square root function (√) is defined only for non-negative real numbers. In other words, the expression inside the square root (√(x + 7)) must be greater than or equal to zero for the function to be defined.
Setting x + 7 ≥ 0, we can solve for x:
x ≥ -7
Therefore, the expression inside the square root (√(x + 7)) is defined for x values greater than or equal to -7.
Additionally, there are no restrictions on the addition operation (+5). It can be applied to all real numbers.
Combining both restrictions, we find that the function y = √(x + 7) + 5 is defined for all real numbers x, since there are no limitations or exclusions. Option D is correct.
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How is the product of 2 and -5 shown on a number line
The product of 2 and -5 can be shown on a number line as a movement in the negative direction. To represent this on a number line, we start at zero and move 2 units to the right (in the positive direction) to the point labeled +2. Then, since the product is negative, we move 5 units to the left (in the negative direction) from the point +2. This brings us to the point labeled -3.
Start at zero on the number line.
Move 2 units to the right (in the positive direction) to the point labeled +2.
Since the product is negative, we need to move in the opposite direction (left) from the point +2.
Move 5 units to the left (in the negative direction) from the point +2.
The point we reach after moving 5 units to the left from the point +2 is labeled -3.
Therefore, on the number line, the product of 2 and -5 is represented by the point labeled -3. This indicates that starting from zero and moving 2 units to the right and then 5 units to the left results in a position of -3.
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The probable question could be:
How is the product of 2 and -5 shown on a number line?
Spanning trees assignments
Spanning trees assignments are a type of network problem that requires finding the minimum path or tree that spans all nodes or vertices in the network.
This is useful for optimizing the design and efficiency of networks, such as computer networks, transportation systems, and power grids.
A spanning tree is a subset of a graph that connects all vertices without any cycles, making it a tree.
Finding the minimum spanning tree involves selecting the minimum weight edge to add to the tree, while ensuring that there are no cycles.
This can be done using algorithms such as Kruskal's algorithm or Prim's algorithm.
Spanning trees assignments are important in network design and optimization and have applications in various fields such as computer science, electrical engineering, and transportation planning.
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Given: m ∥ n Prove: ∠4 and ∠6 are supplementary Two parallel lines m and n intersect another line. The first line forms 4 angles numbered 1, 2, 4, and 3 in clockwise direction and the second line forms 4 angles numbered from 5, 6, 8, and 7 in clockwise direction. Proof: Statements Reasons 1. m ∥ n Given 2. m∠6 = m∠7 Vertical angles theorem 3. ? Same-side interior angles theorem 4. m∠4 + m∠7 = 180° Definition of supplementary angles 5. m∠4 + m∠6 = 180° Substitution property of equality 6. ∠4 and ∠6 are supplementary Definition of supplementary angles Select the statement that completes the proof. A. ∠2 and ∠4 are supplementary B. ∠2 and ∠7 are supplementary C. ∠4 and ∠7 are supplementary D. ∠4 and ∠5 are supplementary
This statement follows from the fact that m∠4 + m∠6 = 180°. The statement that completes the proof is C. ∠4 and ∠7 are supplementary.
To complete the proof, let's analyze the given statements and reasons:
m ∥ n (Given) - This statement establishes that lines m and n are parallel.
m∠6 = m∠7 (Vertical angles theorem) - When two lines intersect, the vertical angles formed are congruent.
? (Same-side interior angles theorem) - This step is missing in the given proof. To prove that ∠4 and ∠6 are supplementary, we need to use the same-side interior angles theorem.
The same-side interior angles theorem states that when two parallel lines are intersected by a transversal, the interior angles on the same side of the transversal are supplementary. In this case, lines m and n are parallel, and the transversal is the line that intersects them.
To complete the proof, we can include the missing statement:
∠4 and ∠6 are interior angles on the same side of the transversal (Same-side interior angles theorem).
Now, we can continue with the remaining steps of the proof:
m∠4 + m∠7 = 180° (Definition of supplementary angles) - Supplementary angles add up to 180 degrees.
m∠4 + m∠6 = 180° (Substitution property of equality) - We substitute ∠7 with ∠6 since they are congruent.
∠4 and ∠6 are supplementary (Definition of supplementary angles) - This statement follows from the fact that m∠4 + m∠6 = 180°.
Therefore, the statement that completes the proof is:
C. ∠4 and ∠7 are supplementary.
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Pls help it’s for my homework
Answer: 150cm1 I think
What is the first step in sketching the graph of a rational function
Answer:
Answer is A. Find the functioning zeros and vertical asymptotes
Consider the two triangles shown below. Two triangles. The first triangle has a side length of seven units and a side length of five units. The second triangle has a side length of seven units and a side length of five units. Two triangles. The first triangle has a side length of seven units and a side length of five units. The second triangle has a side length of seven units and a side length of five units. Note: The triangles are not drawn to scale. Are the two triangles congruent?
The two triangles are congruent because they have identical side lengths, implying that all corresponding angles and side lengths are equal.
What are Congruent Triangles?Congruent triangles are triangles that have the same shape and size, with corresponding angles and side lengths being equal.
The image shows two triangles with given side lengths where the corresponding side lengths are each equal to each other.
Therefore, we can conclude that the two triangles are congruent since they have the exact same side lengths, which indicates that all corresponding angles and side lengths are equal.
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How many 7-digit numbers are there such that the digits 1, 2, and 3 each appear at least once?
Using the principle of inclusion-exclusion, we can see that the total number of numbers with the given restrictions is:
586,071
How many 7-digit numbers are there such that the digits 1, 2, and 3 each appear at least once?o find the number of 7-digit numbers where the digits 1, 2, and 3 each appear at least once, we can use the principle of inclusion-exclusion.
Step 1: Find the total number of 7-digit numbers without any restrictions.
Since each digit can be chosen independently from 0 to 9 (excluding leading zeros), there are 9 options for the first digit (1-9) and 10 options for each subsequent digit (0-9). Therefore, the total number of 7-digit numbers without any restrictions is 9 * 10⁶.
Step 2: Subtract the number of 7-digit numbers that do not contain 1, 2, or 3.
The number of 7-digit numbers that do not contain 1, 2, or 3 is equal to the total number of 7-digit numbers with digits from 0 to 9 (excluding 1, 2, and 3). So for each digit position, there are 7 options (0, 4, 5, 6, 7, 8, 9). Thus, the total number of 7-digit numbers without 1, 2, or 3 is 7⁷.
Step 3: Add back the number of 7-digit numbers that do not contain two of the digits 1, 2, or 3.
The number of 7-digit numbers that do not contain two of the digits 1, 2, or 3 is equal to the total number of 7-digit numbers with digits from 0 to 9 (excluding two of 1, 2, and 3). For each digit position, there are 6 options (0, 4, 5, 6, 7, 8, 9). Thus, the total number of 7-digit numbers without two of 1, 2, or 3 is 6⁷.
Step 4: Subtract the number of 7-digit numbers that do not contain all three digits 1, 2, and 3.
The number of 7-digit numbers that do not contain all three digits 1, 2, and 3 is equal to the total number of 7-digit numbers with digits from 0 to 9 (excluding all three of 1, 2, and 3). For each digit position, there are 4 options (0, 4, 5, 6, 7, 8, 9). Thus, the total number of 7-digit numbers without all three of 1, 2, and 3 is 4⁷.
Now we can apply the principle of inclusion-exclusion to find the desired count:
Total number of 7-digit numbers = 9 * 10⁶ - 7⁷ + 6⁷ - 4⁷
Calculating this expression, we find:
Total number of 7-digit numbers = 586,071
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PLSSS HELP!! Ty whoever helped me! :) Question: Select the statement that is true about the two-dimensional figure.
A quadrilateral with the vertices labeled L, M, N and O. Angles M L O and L M N are greater than 90 degrees, and angles L O N and M N O are less than 90 degrees.
∠LMN is an acute angle.
∠LMN is an obtuse angle.
∠MNO is an obtuse angle.
∠MNO is a right angle.
∠LMN is an obtuse angle.
==========================================
Explanation
Let's go through the answer choices to see which are true, and which are false.
A. This is false. It is stated that "LMN is greater than 90 degrees", so this angle is obtuse. Acute angles are less than 90 degrees.B. This is true. See choice A above.C. This is false. We're told that "angle MNO is less than 90 degrees". That makes the angle acute. D. This is false. See choice C above. Right angles are 90 degrees exactly. Often a small square marker is used to denote a 90 degree angle.washington plastic products pays kim 2420 monthly salary plus 11% commission each month.assume her sales were 74000 last month what's commission and gross
Kim's commission was $8140, and her gross pay was $10560 for last month.
Washington Plastic Products pays Kim $2420 monthly salary plus 11% commission each month.
If her sales were $74000 last month, her commission and gross pay can be calculated as follows:
Kim's commission = 11% of $74000
= $8140Kim's gross pay
= $2420 + $8140 = $10560
Therefore, Kim's commission was $8140 and her gross pay was $10560 last month.
In the given problem, Kim's monthly salary is $2420, and she earns an 11% commission on her sales.
Assuming her sales last month were $74000, her commission and gross pay for the month can be found by multiplying her sales by the commission rate and adding her monthly salary.
Commission = 11% of $74000 = $8140Gross Pay = $2420 + $8140 = $10560
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which expression is equivalent to
2x-11x-6
Answer:
Step-by-step explanation:
The expression 2x - 11x - 6 can be simplified as follows:
2x - 11x - 6 = -9x - 6
So, the equivalent expression is -9x - 6.
The answer is:
-9x - 6
Work/explanation:
To simplify this expression, we combine the like terms :
[tex]\huge\text{2x - 11x - 6} \\ \\ \\ \text{-9x - 6}[/tex]
There's nothing that we can do for this expression. It's been simplified as much as possible.
Hence, the answer is -9x - 6.Chris conducted a experiment in his 1st period class which has 30 total students Chris had everyone flip a coin and record the result the result was 18 of them came up heads based on this situation what is the experimental probability of members of his class ending up with heads
The experimental probability of members of Chris's class ending up with heads is about 3/5 or 0.6 (60%).
What is the experimentThe experimental probability is one that can be calculated by:
dividing the number of favorable outcomes (the number of heads) by the total number of outcomes (the total number of students).
So, the number of heads recorded was 18, and the total number of students was 30.
Experimental probability = Number of heads / Total number of students
= 18 / 30
So one can simplify the fraction by:
Experimental probability = 3 / 5
Therefore, the experimental probability of members of Chris's class ending up with heads is 3/5 .
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3.2.4 Practice: modeling: slope-intercept equation of a line b) The y-intercept (1 point)
The y-intercept of the line with a slope of 2 and passing through the point (3, 5) is -1.
The y-intercept of a line is the point where the line intersects the y-axis. In the slope-intercept form of a linear equation, y = mx + b, the y-intercept is represented by the value of b.
To determine the y-intercept, we need to have information about the line, such as its slope and at least one point it passes through.
If we are given the slope, m, and a point (x₁, y₁) on the line, we can use the point-slope form of the equation, y - y₁ = m(x - x₁), to find the equation of the line and determine the y-intercept.
For example, let's say we are given the slope m = 2 and a point (3, 5) on the line. We can substitute these values into the point-slope form:
y - 5 = 2(x - 3)
Expanding the equation:
y - 5 = 2x - 6
Next, we can rearrange the equation to isolate y:
y = 2x - 6 + 5
y = 2x - 1
From this equation, we can see that the y-intercept is -1. The point where the line crosses the y-axis is (0, -1), and the value of b in the slope-intercept form is -1.
Therefore, the y-intercept of the line with a slope of 2 and passing through the point (3, 5) is -1.
In general, to determine the y-intercept of a line, we need to know the slope and at least one point it passes through. With this information, we can use the point-slope form of the equation and solve for the y-intercept.
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● Blondies are squares with 3 inch sides. ● Brownies are squares with 6 inch sides. ● The tray that displays the blondies and brownies has an area of 648 square inches and is completely full. If she has 4 rows of blondies and 4 rows of brownies, what fraction of the area of the tray, in square inches, is blondies? Show your work.
The fraction of the area of the tray occupied by the blondies is 1/9.
To find the fraction of the area of the tray occupied by blondies, we need to determine the area occupied by the blondies and compare it to the total area of the tray.
Let's calculate the area of each individual blondie:
The blondies are squares with 3-inch sides, so the area of each blondie is 3 inches × 3 inches = 9 square inches.
Now, let's calculate the area occupied by the blondies in each row:
Since there are 4 rows of blondies and each row contains 4 blondies, the total number of blondies is 4 rows × 4 blondies per row = 16 blondies.
So, the total area occupied by the blondies is 16 blondies × 9 square inches per blondie = 144 square inches.
Next, let's determine the area occupied by the brownies:
The brownies are squares with 6-inch sides, so the area of each brownie is 6 inches × 6 inches = 36 square inches.
Since there are also 4 rows of brownies and each row contains 4 brownies, the total number of brownies is 4 rows × 4 brownies per row = 16 brownies.
Therefore, the total area occupied by the brownies is 16 brownies × 36 square inches per brownie = 576 square inches.
Now, let's calculate the total area of the tray:
Given that the tray is completely full and has an area of 648 square inches, we can subtract the area occupied by the brownies from the total area to find the remaining area occupied by the blondies:
Total area of the tray - Area occupied by the brownies = Area occupied by the blondies
648 square inches - 576 square inches = 72 square inches.
So, the fraction of the area of the tray occupied by the blondies is:
Area occupied by the blondies / Total area of the tray = 72 square inches / 648 square inches.
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 72 in this case:
72 square inches / 648 square inches = 1/9.
Therefore, the blondies' percentage of the tray's surface area is 1/9.
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please awnser ASAP i will brainlist
a) The graph of the function represents an exponential decay.
b) The numeric values are given as follows:
f(0) = 1.f(1) = 0.3.How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function for this problem is given as follows:
[tex]f(x) = 0.3^x[/tex]
The parameters for this problem are given as follows:
a = 1, b = 0.3.
The numeric values are given as follows:
[tex]f(0) = (0.3)^0 = 1[/tex][tex]f(1) = (0.3)^1 = 0.3[/tex]More can be learned about exponential functions at brainly.com/question/2456547
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in the poisson probability calculation, why does the 3! of the 3yr become 6?
The 3! is used to calculate the number of permutations of three objects, and is included in the Poisson probability formula to account for the number of ways in which three events can occur in a specific order over a given period.
In Poisson probability calculation, 3! (3 factorial) is used to find the number of ways in which three independent events can occur in a specific order over a given period. In other words, 3! refers to the number of permutations of 3 objects.
The formula used in Poisson distribution is as follows: [tex]P (X = x) = (e^{-\lambda } \lambda^x)/x![/tex], where λ is the mean rate of the event occurring over a specific time interval, and x is the number of events that occur within that time interval.
The x! term is included in the formula because it represents the number of ways in which x events can occur in a specific order over the given time period. The exponents of λ are used to represent the probability of an event occurring in the interval.
In the case of 3! we are calculating the number of ways that three independent events can occur in a specific order over a given period. This can be expressed as 3 x 2 x 1 = 6, which is why 3! becomes 6 in the Poisson probability calculation.
The term 3! (6) is included in the formula to account for the number of ways in which three events can occur in a specific order over a given period.
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9x - 16y =54
5x + 17y =30
Resuelto en 4 metodos con procedimiento porfa
The solution to the system of equations 9x - 16y =54 and 5x + 17y =30 is x = 6 and y = 0.
What is the solution to the system of equations?Given the system of equations in the question:
9x - 16y = 54 -------equ1
5x + 17y = 30 -------equ2
Using the elimination method:
First, multiply equation (1) by 17 and equation (2) by 16 to make the coefficients of y in both equations equal:
17 × (9x - 16y) = 17 × 54
16 × (5x + 17y) = 16 × 30
We have:
153x - 272y = 918 ....... equ3
80x + 272y = 480 .......equ4
Add Equation 3 and Equation 4:
(153x - 272y) + (80x + 272y) = 918 + 480
153x - 272y + 80x + 272y = 918 + 480
233x = 1398
x = 1398/233
x = 6
Now, pug x = 6 into equation 2 and solve for y:
5x + 17y = 30
5(6) + 17y = 30
30 + 17y = 30
17y = 30 - 30
17y = 0
y = 0
Therefore, the value of x is 6 and y is 0.
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Brad wants to buy flowers for his friend with $39. The daisies are S1 each and the roses are $3 each. He buys 3 more daisies than roses.
¿Cuál es el cociente de la división 1,24:0,08?
The Ratio of 1.24 to 0.08 can be expressed as 15.5, 31:2, or 31/2.
To find the ratio of 1.24 to 0.08, we divide 1.24 by 0.08.
1.24 ÷ 0.08 = 15.5
Therefore, the ratio of 1.24 to 0.08 is 15.5.
We can also express this ratio as a fraction. To do this, we write 15.5 as a fraction over 1:
15.5/1
To simplify the fraction, we can multiply both the numerator and the denominator by 10 to get rid of the decimal:
(15.5 × 10)/(1 × 10) = 155/10
Further simplifying the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 5:
(155 ÷ 5)/(10 ÷ 5) = 31/2
So, another way to express the ratio 1.24:0.08 is 31:2.
In conclusion, the ratio of 1.24 to 0.08 can be expressed as 15.5, 31:2, or 31/2.
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Travel Expenses, Meals And Entertainment, Educational Expenses (LO 3.4, 3.5, 3.6) Bob is a self-employed lawyer and is required to take a week of continuing legal education every year to maintain his license. This year he paid $1,400 in course fees for his continuing legal education in a different city. He also paid $500 for airfare and a hotel room and paid $300 for meals, all of which were provided by the hotel’s restaurant. Bob also purchased a $10 bag of snacks from a newsstand while waiting for his plane in the airport because he missed lunch. What is the total amount he can deduct on his Schedule C related to these expenses? fill in the blank 1 of 1$
Bob can deduct a total of $2,210 on his Schedule C related to these expenses.
How to calculate deductible amount?To determine the total amount Bob can deduct on his Schedule C related to these expenses, consider the specific categories that can be deducted. Based on the information provided, categorize the expenses as follows:
Course fees for continuing legal education: $1,400
Airfare and hotel room: $500
Meals provided by the hotel's restaurant: $300
Snacks from the newsstand: $10
To calculate the total amount that Bob can deduct, add up these expenses:
$1,400 + $500 + $300 + $10 = $2,210
Therefore, Bob can deduct a total of $2,210 on his Schedule C related to these expenses.
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ANSWER THIS QUICK 50 POINTS
The solution of the compound inequality is as follows:
x < -4 or x ≥ 3.
How to solve compound inequality?Compound inequality is an inequality that combines two simple inequalities. In other words, a compound inequality contains at least two inequalities that are separated by either "and" or "or".
Therefore, let's find the compound inequality graphed on the number line as follows:
Hence,
if the symbol is (≥ or ≤) then you fill in the dot, like the top two examples in the graph below.
if the symbol is (> or <) then you do not fill in the dot .
Therefore, the compound inequality is as follows:
x < -4 or x ≥ 3.
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In a survey conducted for students studying in class 10 of Shree Sharada Secondary School, which of Pokhara, Lumbini and Ilam would be suitable for an educational trip, 40 people said that Pokhara, 30 people would go to Lumbini and 45 people would go to Ilam. While 15 students of that class said that all three places are suitable, 5 students did not express any opinion.
(a) Let P, L and I denote the number of students for whom Pokhara, Lumbini and Ilam respectively are suitable, and write the group of students for whom all places are suitable in numerability notation.
(b) Present the above information in a venn diagram.
(c) How many students are studying in Class 10 in Sharda Secondary School? Calculate.
(d) If 5 students who did not express an opinion in the survey said that Lumbini is a suitable place, what would be the ratio of students who said Pokhara was the only suitable place and Lumbini was the only suitable place?
a) The group of student for whom all places are suitable is 15.
b) The presentation of the information in a Venn Diagram about the choices of locations for an educational trip by students of Class 10 studying at Shree Sharada Secondary School is attached.
c) The total number of students studying in Class 10 in Sharada Secondary School is 90.
d) The ratio of students who said that Pokhara was the only suitable place and Lumbini was the only suitable place is 4:5.
What is a Venn Diagram?A Venn Diagram is a graphical representation of groups of data to show their contrasts or differences and their similarities.
Students of Class 10
Shree Sharada Secondary Schoo
Educational Trip Locations
Pokhara, P = 40
Lumbini, L = 30
Ilam, I = 45
All three places (P, L, and I) = 15
No Opinion = 5
The number of P only = 25 (40 - 15)
The number of L only = 15 (30 - 15)
The number of I only = 30 (45 - 15)
The number of P, L, and I = 15
The number expressing no opinion = 5
b) The Venn Diagram is attached.
c) The total number of students in Class 10 = 90 (25 + 15 + 30 + 15 + 5)
Ratios of Lumbibi as a suitable place to Pokhara only:
The number of P only = 25
The number of L only = 15
Initial ratio = 15:25 = 3:5
Addition of 5 to Lumbini:
The number of P only = 25
The number of L only = 15
d) Final ratio = 20:25 = 4:5
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Answer:
Step-by-step explanation:
