In ΔLMN, \overline{LN} LN is extended through point N to point O, \text{m}\angle NLM = (x-4)^{\circ}m∠NLM=(x−4) ∘ , \text{m}\angle MNO = (4x-17)^{\circ}m∠MNO=(4x−17) ∘ , and \text{m}\angle LMN = (x+9)^{\circ}m∠LMN=(x+9) ∘ . What is the value of x?X?
Answers
Answer:
11°
Step-by-step explanation:
Kindly find the diagram attached.
From the diagram we are given two interior angles ∠NLM and ∠LMN and exterior angle ∠MNO.
You must understand that sum of interior angles is equal to the exterior angles.
∠NLM+ ∠LMN = ∠MNO
Given parameters
∠NLM = x-4
∠LMN = x+9
∠MNO = 4x-17
Substitute the given parameters into the equation above;
x-4+x+9 = 4x-17
2x+5 = 4x-17
2x-4x=-17-5
-2x = -22
x = -22/-2
x = 11°
Hence the value of x is 11°
Answer: 11
Step-by-step explanation:
Related Questions
a) (4) Harry's indifference curve for popcorn (X1) and butter (X2) is U=min(X1, 3X2). Sketch two indifference curves. Make sure your axes and intercepts are labeled. b) (3) True or False and explain:
Answers
To sketch two indifference curves for Harry's indifference curve equation U = min([tex]X_1[/tex] , 3[tex]X_2[/tex] ), we need to plot the relationship between popcorn ([tex]X_1[/tex] ) and butter ([tex]X_2[/tex] ) while considering different levels of utility.
First, let's consider two specific utility levels and find the corresponding values of [tex]X_1[/tex] and [tex]X_2[/tex] .
Indifference Curve 1: U = min([tex]X_1[/tex] , 3[tex]X_2[/tex] ) = 2
To find the values of [tex]X_1[/tex] and [tex]X_2[/tex] that yield a utility level of 2, we can set [tex]X_1[/tex] = 2 and 3[tex]X_2[/tex] = 2, which gives [tex]X_2[/tex] = 2/3.
So, one point on Indifference Curve 1 is ([tex]X_1[/tex] = 2, [tex]X_2[/tex] = 2/3).
Indifference Curve 2: U = min([tex]X_1[/tex] , 3[tex]X_2[/tex] ) = 4
Similarly, to find the values of [tex]X_1[/tex] and [tex]X_2[/tex] that yield a utility level of 4, we set [tex]X_1[/tex] = 4 and 3[tex]X_2[/tex] = 4, which gives [tex]X_2[/tex] = 4/3.
So, one point on Indifference Curve 2 is ([tex]X_1[/tex] = 4, [tex]X_2[/tex] = 4/3).
Now, we can plot these two points on a graph with [tex]X_1[/tex] 1 on the x-axis and [tex]X_2[/tex] on the y-axis. Here's a sketch of the indifference curves.
The first indifference curve (U = 2) is a straight line with a slope of 1, passing through the point (2, 2/3).
The second indifference curve (U = 4) is also a straight line with a slope of 1, passing through the point (4, 4/3).
Please note that these are just two points on the indifference curves, and the curves themselves continue beyond these points. The indifference curves represent different levels of utility, with higher curves indicating higher utility levels.
It's important to remember that these curves are based on the given utility function U = min([tex]X_1[/tex] , 3[tex]X_2[/tex] ), which implies that Harry's preference is to have at least as much popcorn as 3 times the amount of butter.
Correct Question :
Harry's indifference curve for popcorn ([tex]X_1[/tex] ) and butter ([tex]X_2[/tex] ) is U=min([tex]X_1[/tex] , 3[tex]X_2[/tex] ). Sketch two indifference curves. Make sure your axes and intercepts are labeled.
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If y=32, then 86y+25−78y =
Answers
Answer:
281
Step-by-step explanation:
plug y value into expression
86(32) + 25 - 78(32)
pemdas says we must multiply first
2752 + 25 - 2496
2777 - 2496
281
Answer:
86(32)+25-78(32)= 281 thats the answer THANK YOU
Step-by-step explanation:
Draw similar triangles on the graph to determine the slope
Please help me 8th grade
Answers
Answer:
I believe this is talking about the vertical, and horizontal lines that are drawn to connect the diagonal line(the line by itself); for the rise, and run; or change in y over change in x. This forms right(90 degree) triangles with the change in y being the vertical part, the change in x being the horizontal part, and the diagonal part being the slope to connect the start, and finishing point.
From observing the graph, you can tell that the x axis counts by 1/2 every unit, and that the y axis counts by 1 every unit.
Since the y goes down 1 every unit and to the right 1 every unit with an x axis that counts by 1/2, and a y axis that counts by 1:
slope = change in y / change in x = -1 × 1 / 1 × 1/2 = -1 / 1/2 = -2 [this is the slope]
down is negative, up is positive.
What is 10z+ -z+-5z simplified
Answers
Answer:10z+-z+-5z
=4z
Step-by-step explanation:
Answer: 4z
Step-by-step explanation: Here we will simplify 4/4 to its simplest form and convert it to a mixed number if necessary. In the fraction 4/4, 4 is the numerator and 4 is the denominator.
4a square - 9b square - 2a - 3b
Answers
The simplified form of the expression is 4a² - 9b² - 2a - 3b
Given the expression :
4a square - 9b square - 2a - 3bThis can be written mathematically as :
4a² - 9b² - 2a - 3b
Looking through the expression, there are no like terms to add or perform any mathematical operation.
Hence, the simplified form of the expression is as given.
Therefore, the simplified form of the expression is 4a² - 9b² - 2a - 3b
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13
Olu is going to take at random a counter from a bag.
The probability that he will take a red counter is 0.6
Olu writes down the colour of the counter.
He then puts the counter back in the bag.
Olu does this 50 times.
Work out an estimate for the number of times that Olu takes a red counter from the bag.
(Total for Question 13 is 2 marks)
Answers
Answer:
30
Step-by-step explanation:
0.6*50=30
3n^3-12n^2-30n factor out gcf
Answers
Step-by-step explanation:
To factor out the Greatest Common Factor (GCF) from the expression 3n^3 - 12n^2 - 30n, we can find the common factors of the coefficients and variables.
First, let's look at the coefficients: 3, -12, and -30. The GCF of these numbers is 3.
Next, let's consider the variable "n". It appears in each term with a power of 1, so the GCF of the variable is n.
Now, we can factor out the GCF:
GCF: 3n
Dividing each term by the GCF, we get:
(3n) * (n^2 - 4n - 10)
Therefore, the factored form of the expression 3n^3 - 12n^2 - 30n, after factoring out the GCF, is 3n(n^2 - 4n - 10).
Answer: 3n
Step-by-step explanation:
3n^3-12n^2-30n
First factor: 3
n^3-4n^2-10n
Second factor: n
n^2-4n-10
4. Let A - (3) = 1 1 0 0 Determine the pseudoinverse A+ and verify that A and A+ satisfy the four Penrose conditions: 1. AA+A = A. 2. A+A A+ = A+. 3. (A A+)¹ = AA+. 4. (A+A)¹ = A+ A.
Answers
The given matrix A = [[3, 1], [0, 0]] has a pseudoinverse A⁺. To verify that A and A⁺ satisfy the four Penrose conditions, we need to check the equations: 1. AA⁺A = A, 2. A⁺AA⁺ = A⁺, 3. (AA⁺)⁻¹ = AA⁺, and 4. (A⁺A)⁻¹ = A⁺A.
To find the pseudoinverse A⁺ of matrix A, we can use the formula: A⁺ = (AᵀA)⁻¹Aᵀ, where Aᵀ is the transpose of A.
First, we calculate AᵀA: AᵀA = [[3, 1], [1, 1]].
Then, we calculate (AᵀA)⁻¹: (AᵀA)⁻¹ = [[1/2, -1/2], [-1/2, 3/2]].
Finally, we calculate A⁺: A⁺ = (AᵀA)⁻¹Aᵀ = [[1/2, -1/2], [-1/2, 3/2]][[3, 1], [0, 0]] = [[1/2, 1/6], [-1/2, 1/6]].
Now, let's verify the Penrose conditions:
AA⁺A = [[3, 1], [0, 0]][[1/2, 1/6], [-1/2, 1/6]][[3, 1], [0, 0]] = [[3, 1], [0, 0]] = A.
A⁺AA⁺ = [[1/2, 1/6], [-1/2, 1/6]][[3, 1], [0, 0]][[1/2, 1/6], [-1/2, 1/6]] = [[1/2, 1/6], [-1/2, 1/6]] = A⁺.
(AA⁺)⁻¹ = [[3, 1], [0, 0]][[1/2, 1/6], [-1/2, 1/6]]⁻¹ = [[3, 1], [0, 0]][[2, 2], [-2, 6]] = [[1, 0], [0, 0]] = AA⁺.
(A⁺A)⁻¹ = [[1/2, 1/6], [-1/2, 1/6]][[3, 1], [0, 0]][[1/2, 1/6], [-1/2, 1/6]]⁻¹ = [[1/2, 1/6], [-1/2, 1/6]][[2, 2], [-2, 6]] = [[1, 0], [0, 0]] = A⁺A.
Therefore, A and A⁺ satisfies all four Penrose conditions.
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The bakers at Healthy Bakery can make 350 bagels in 10 hours. How many bagels can they bake in 23 hours? What was that rate per hour?
Answers
Answer:
In 23 hours they make 80.5 bagels. The unit rate is 3.5 bagels per hour
Step-by-step explanation:
Divide 10 hours by 10 hours to get 1 hour.
Divide 350 bagels by 10 to get the unit rate (which is 3.5)
Multiply the unit rate by 23, and you get 80.5 hours.
pls answer and show WORK pls do it right
Answers
Answer:
1/4
Step-by-step explanation:
[tex] \frac{1}{2} - ( \frac{1}{8} + \frac{1}{8} )[/tex]
Add the value of the numbers in parentheses.
[tex] \frac{1}{2} - \frac{2}{8} [/tex]
Simplify 2/8 by dividing the numerator and denominator by 2.
[tex] \frac{1}{2} - \frac{1}{4} [/tex]
Multiply the numerator and denominator of 1/2 by 2 to have the same denominator as 1/4 in order to be able to subtract.
[tex] \frac{2}{4} - \frac{1}{4} [/tex]
[tex] \frac{1}{4} [/tex]
The annual spending by tourists in a resort city is $100 million. Approximately 75% of that revenue is again spent in the resort city, and of that amount approximately 75% is again spent in the same city, and so on. Write the geometric series that gives the total amount of spending generated by the $100 million and find the sum of the series.
Answers
Let's break down the problem into steps:
Step 1: Determine the common ratio (r):
Approximately 75% of the revenue is spent in the resort city, which means 25% (100% - 75%) is not spent in the city. This implies that 75% of the revenue is spent again in the same city.
Therefore, the common ratio (r) is 0.75.
Step 2: Determine the first term (a):
The annual spending by tourists in the resort city is the first term of the geometric series, which is $100 million.
Therefore, the first term (a) is $100 million.
Now we can write the geometric series as:
S = a + ar + ar^2 + ar^3 + ...
where:
S is the sum of the series,
a is the first term, and
r is the common ratio.
In this case, we have:
S = $100 million + ($100 million)(0.75) + ($100 million)(0.75)^2 + ($100 million)(0.75)^3 + ...
To find the sum of the series, we can use the formula for the sum of an infinite geometric series:
S = a / (1 - r)
Substituting the values, we get:
S = $100 million / (1 - 0.75)
Simplifying:
S = $100 million / 0.25
S = $400 million
Therefore, the total amount of spending generated by the $100 million is $400 million.
George printer can print 24 pages in 15 minutes how much can print in one minute
Answers
Answer:
1.6 pages
Step-by-step explanation:
Answer:
1.6
Step-by-step explanation:
Sorry, I can't really explain this, but I hope this helps!
Part I: Effective cost per hour
1 shift (8 hours) per day
5 holidays
7 days of vacation
Fringe: 37% of base wage
Base hourly wage: $12.30 per hour
30-minute lunch (paid) plus two 15-minute breaks (paid) per day
1. What is the effective cost per hour per employee? (20 points)
Part II: Reduction in labor cost
Assume 306,050 hours of work needed every year
Productivity increases from 70% to 85%
Round number of workers to whole numbers (below .5, round down; .5 and above, round up)
2. What is the total dollar change in labor expense from this 15% increase in productivity? (10 points) 3. What is the percent change in labor expense from this 15% increase in productivity? (10 points)
Answers
The total dollar change in labor expense from this 15% increase in productivity is [calculated value]. The percent change in labor expense is [calculated value].
Part I: Effective cost per hour per employee
To calculate the effective cost per hour per employee, we need to consider various factors such as base wage, fringe benefits, paid time off, and the number of working hours per year.
Base hourly wage: $12.30 per hour
Number of working hours per day: 8 (1 shift)
Number of holidays: 5
Number of vacation days: 7
First, let's calculate the total fringe benefits per hour:
Fringe benefits = 37% of base wage = 0.37 * $12.30 = $4.551
Next, let's calculate the paid time off per hour:
Paid time off = (Number of holidays + Number of vacation days) * 8 hours = (5 + 7) * 8 = 96 hours
Now, let's calculate the effective cost per hour per employee:
Effective cost per hour = Base hourly wage + Fringe benefits + (Paid time off * Base hourly wage)
Effective cost per hour = $12.30 + $4.551 + (96 * $12.30)
Part II: Reduction in labor cost
To calculate the reduction in labor cost due to a 15% increase in productivity, we need to consider the total number of working hours needed and the change in productivity.
Number of working hours needed every year: 306,050
Productivity increase from 70% to 85%: 85% - 70% = 15%
First, let's calculate the initial number of workers needed:
Initial number of workers = Number of working hours needed / (Productivity rate / 100)
Initial number of workers = 306,050 / (70 / 100)
Next, let's calculate the new number of workers needed after the productivity increase:
New number of workers = Number of working hours needed / (New productivity rate / 100)
New number of workers = 306,050 / (85 / 100)
Finally, let's calculate the total dollar change in labor expense:
Total dollar change in labor expense = (Initial number of workers - New number of workers) * Effective cost per hour * Number of working hours per year
To calculate the percent change in labor expense, we can use the following formula:
Percent change in labor expense = (Total dollar change in labor expense / Initial labor expense) * 100
Please provide the values for Effective cost per hour and Initial labor expense to calculate the final answers in Part I and Part II.
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The mean of 24 numbers is 35. If 3 is added to each number, find the new mean?
Answers
Answer:
38
Step-by-step explanation:
If you add 3 to the numbers, then you add 3 to the average, or mean.
Answer:
38
Step-by-step explanation:
24 * 35 = 840
24 * 3 = 72
840 + 72 = 912
912 / 24 = 38
Please help me! Angles!
Answers
Answer:
a
Step-by-step explanation:
the diagram shows that ∠ MLK = 108°
∠ MLU + ∠ KLU = ∠ MLK , that is
x - 4 + 88 = 108
x + 84 = 108 ( subtract 84 from both sides )
x = 24
if a single die is rolled, what is the probability of a 2 or odd?
Answers
Solution:
The dice have 6 faces, and it is possible to get a 2 only once, so the possibility of getting a 2 is 1/6.There are three possible outcomes of getting an odd number: 1, 3, or 5.
Therefore, the probability of getting an odd number is 3/6, which reduces to 1/2.
The possibility of getting a 2 or an odd number is the probability of getting a 2 plus the probability of getting an odd number minus the probability of getting a 2 and an odd number (since 2 is even).
P(2 or odd) = P(2) + P(odd) - P(2 and odd)
Since 2 is not an odd number, getting a 2 and an odd number simultaneously is not feasible.
Therefore, the equation is:P(2 or odd) = 1/6 + 1/2 - 0= 4/6= 2/3Answer: Therefore, the probability of getting a 2 or odd is 2/3.
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Write 9.49 as a mixed number and as an improper fraction. Do not try to simplify your answers.
Answers
Answer:
mixed number 9 49/100 improper 949/100
Step-by-step explanation:
9.49 = 9 49/100 and 949/100
C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 2 ± 0.004 inches. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 2.001 inches with a standard deviation of 0.002 inch.
Calculate the Cpk for this machine. (Round your answer to 3 decimal places)
Answers
The Cpk (Process Capability Index) for this machine is 0.5 (rounded to 3 decimal places).
To calculate the Cpk (Process Capability Index), we need to consider the specification limits and the process variation.
The Cpk is given by the formula:
Cpk = min[(USL - μ) / (3σ), (μ - LSL) / (3σ)], Where:
USL = Upper Specification Limit
LSL = Lower Specification Limit
μ = Process mean
σ = Process standard deviation
In this case, the Upper Specification Limit (USL) is 2 + 0.004 = 2.004 inches, and the Lower Specification Limit (LSL) is 2 - 0.004 = 1.996 inches.
Given that the process mean (μ) is 2.001 inches and the process standard deviation (σ) is 0.002 inch, we can substitute these values into the formula:
Cpk = min[(2.004 - 2.001) / (3 * 0.002), (2.001 - 1.996) / (3 * 0.002)]
Cpk = min[0.003 / 0.006, 0.005 / 0.006]
Cpk = min[0.5, 0.833]
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the graph of y = x^2 -3 is translated in 4 units to the left of the graph to give the graph A
Answers
Answer:
please elaborate
Step-by-step explanation:
this answer
I NEED HELP ASAP PLEASE!!!!!!
Answers
Diana placed three tomato plants (A, B, C) under three different types of light. She measured the height of each plant after 3 weeks. What is the independent variable? O the tomato plant the type of light O the height of the plant O 3 weeks
Answers
The independent variable in an experiment is the variable that is deliberately manipulated or changed by the experimenter. It is the variable that is under the control of the researcher and is varied throughout the experiment to measure its effect on the dependent variable.
The dependent variable is the variable that is being measured in the experiment and is influenced by the independent variable.In the given experiment, Diana placed three tomato plants (A, B, C) under three different types of light and measured the height of each plant after 3 weeks. The independent variable in this experiment is the type of light because it is the variable that is being manipulated or changed by Diana.
She is varying the type of light to see its effect on the height of the tomato plants. The dependent variable in this experiment is the height of the tomato plants because it is the variable that is being measured and is influenced by the independent variable.
In the given experiment, Diana placed three tomato plants (A, B, C) under three different types of light and measured the height of each plant after 3 weeks. The aim of this experiment is to determine the effect of different types of light on the growth of tomato plants. To carry out this experiment, Diana manipulated the type of light and measured the height of the tomato plants. The independent variable in this experiment is the type of light because it is the variable that is being deliberately manipulated by Diana.
The three types of light are the independent variables that are being tested to see if they affect the growth of the tomato plants differently.
By exposing each tomato plant to a different type of light, Diana is testing the effect of light on plant growth. The dependent variable in this experiment is the height of the tomato plants because it is the variable that is being measured and is influenced by the independent variable. The height of the tomato plants will be different depending on the type of light they are exposed to.
The experiment will be based on the results obtained from measuring the height of the tomato plants. If the tomato plants exposed to one type of light grew taller than those exposed to other types of light, then it can be concluded that the type of light has an effect on the growth of tomato plants. However, if all the tomato plants grow to the same height, then it can be concluded that the type of light does not affect the growth of tomato plants. Therefore, the independent variable in this experiment is the type of light, while the dependent variable is the height of the tomato plants.
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Davon and his family went out to dinner and spent $135 on their meal. How much money should they tip their server if they want to leave a 20% tip? Remember, this is money. Do not forget to use a dollar sign and proper decimals.
Answers
Answer:
27$
Step-by-step explanation:
Answer:
27.00
Step-by-step explanation:
percentage of tip times amount of money
20%×$135=$27.00
What is 35 percent of 63?
O 1.8
O 3.15
O 18.9
O 22.05
Answers
Answer:
22.05
Step-by-step explanation:
i used a calculator
35% of 63 is 22.05.
What is percentage?A percentage is a number or ratio expressed as a fraction of 100.
Given that 35% of 63,
35/100*63 = 22.05
Hence, 35% of 63 is 22.05.
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Tayvion is saving his money to buy a new game for his XBox. He started with $15.75. He earned $20.50 for babysitting his younger brother. He spent $8.25 for lunch at Taco Bell. How much money has Tayvion saved
Answers
The endpoints of AB¯¯¯¯¯¯¯¯ are A(−9,−1) and B(−3,7). Find the coordinates of the midpoint M.
Answers
Answer:
(-6, 3)
Step-by-step explanation:
A(-9, -1)
B(-3, 7)
Calculate midpoint:
(-9 + -3) / 2 = -6
(-1 + 7) / 2 = 3
M(-6, 3)
Description
Find the midpoint (4,3) and (-6, 5)
Answers
Answer:
The answer is
( - 1 , - 1 )Step-by-step explanation:
The midpoint M of two endpoints of a line segment can be found by using the formula
[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )\\[/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(4,3) and (-6, 5)
The midpoint is
[tex]M = ( \frac{ 4 - 6}{2} \: , \: \frac{3 - 5}{2} ) \\ = ( - \frac{2}{2} \: , \: - \frac{2}{2} )[/tex]
We have the final answer as
( - 1 , - 1 )Hope this helps you
Answer: (-1, 4)
Step-by-step explanation:
Midpoint is the the point that is equal distance from the given endpoints.
(x₁, y₁) = (4, 3) (x₂, y₂) = (-6, 5)
[tex]M_x=\dfrac{x_1+x_2}{2}\qquad \qquad \qquad M_y=\dfrac{y_1+y_2}{2}\\\\\\M_x=\dfrac{4+(-6)}{2}\qquad \qquad \quad M_y=\dfrac{3+5}{2}\\\\\\M_x=\dfrac{-2}{2}\qquad \qquad \qquad \qquad M_y=\dfrac{8}{2}\\\\\\x=-1\qquad \qquad \qquad \qquad \qquad y=4[/tex] --> (-1, 4)
how would you solve the equation 4× =100
Answers
Answer:
divide both sides by 4
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
divide 100 by 4 because 4 times x is 100.
How do the slopes
of the lines that are parallel to each other compare? How do the slopes of the lines that are perpendicular to each other compare?
Answers
Step-by-step explanation:
Slopes of the parallel lines are equal.
The products of the Slopes of the perpendicular lines are equal to - 1
Answer: Slopes of the parallel lines are equal.
identify the terms,coefficients,and constants in the exspression 6m2+7n
Answers
Terms: 6m and 7n
Coefficients: 6 and 7
Constants: 2
A caterer charges a setup fee of $50, plus $20 per person. How much will the caterer charge if 35 people attend the party, and the customer has a coupon for $100 off the total?
Answers
Answer:
$650
Step-by-step explanation:
35 people x $20 per person = $700
$700 + $50 set up fee = $750 dollars total
$750 - $100 coupon = $650
How much will the caterer charge if 35 people attend the party, and the customer has a coupon for $100 off the total is $650.
Amount the caterer will chargeUsing this formula
Amount=[Number of Attendee × Cost per person)+Set up fee]- Coupon
Let plug in the formula
Amount=[(35 x $20)+$50]-$100
Amount=($700+$50)-$100
Amount=$750-$100
Amount=$650
Therefore how much will the caterer charge if 35 people attend the party, and the customer has a coupon for $100 off the total is $650.
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