The measure of the missing angle in a given pentagon is 115°. Therefore, option A is the correct answer.
What is the formula for interior angle of a regular polygon?The formula for calculating the sum of interior angles is (n-2)×180° where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.
2) The sum of the interior angles of a nonagon
Here, n=9
(9-2)×180°
= 1,260°
3) Here, ∠3+∠4=180°
∠3=101°
101°+∠4=180°
∠4=79°
So, option A is the correct answer.
4) Given that, a regular polygon with 12 sides.
Now, sum of the interior angles = (12-2)×180°
= 1800°
Measure of each angle = 1800/12
= 150°
5) Four of the angles of a pentagon measure 85°, 110°, 135°, and 95°.
Let the measure of fifth angle be x°
85°+110°+135°+95°+x°=540°
425°+x°=540°
x°=115°
So, option A is the correct answer.
The measure of the missing angle in a given pentagon is 115°. Therefore, option A is the correct answer.
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On a typical day, brianne uses her computer for 3 hours and her hair dryer for 10 minutes. what is the total cost of using both appliances for 6 days?
The total cost of using both appliances for 6 days is about 3000-4000 watt.
According to the statement
Brianne uses her computer for 3 hours
Brianne uses hair dryer for 10 minutes
Now we use the formula
C = wtc/1000
substitute the values in it
then
C = 600*6/1000
C = 3.6
and same for hair dryer
So, The total cost of using both appliances for 6 days is about 3000-4000 watt.
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Using the defects method, which of these relationships represents the law of cosines if the measure of the included angle between the sides a and b of ∆abc is more than 90°? a. area of square c2 = -area of square a2 − area of squareb2 area of defect1 area of defect2 b. area of square c2 = area of square a2 area of squareb2 area of defect1 − area of defect2 c. area of square c2 = area of square a2 area of squareb2 − area of defect1 − area of defect2 d. area of square c2 = area of square a2 area of squareb2 area of defect1 area of defect2 e. area of square c2 = area of square a2 − area of squareb2 area of defect1 − area of defect2
The relationship that represents the law of cosines if the measure of the included angle between the sides a and b is D. area of square c² = area of square a² area of squareb² area of defect1 area of defect2
What is the law of cosine?It should be noted that the cosine law is simply used to solving triangles.
The law simply states that c² = a² + b² - 2abcosC.
The correct option that illustrates this is D.
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Answer:
c. area of square c2 = area of square a2 + area of square b2 – area of defect1 – area of defect2
Step-by-step explanation:
[tex]27a^3+189a^2b+441ab^2+343b^3[/tex]
27a³ + 189a²b + 441ab² + 343b³ = (3a + 7b)³
How to simplify an expression?27a³ + 189a²b + 441ab² + 343b³
Therefore,
27a³ = (3a)³
189a²b = 3(3a)²(7b)
441ab² = 3(3a)(7b)²
343b³ = (7b)³
(3a)³ + (7b)³ + 3(3a)²(7b) + 3(3a)(7b)²
a³ + b³ + 3a²b + 3ab² = (a + b)³
Therefore,
27a³ + 189a²b + 441ab² + 343b³ = (3a + 7b)³
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On a plat map are two adjacent rectangular lots. Lot A has a square footage of 46,060, and Lot B has a square footage of 43,005. The common boundary they share is 235 feet long. What is the width of Lot B
The Width of plot B is 183 ft.
According to the statement
we have given that the Plot A has a square footage of 46,060, and Plot B has a square footage of 43,005. The common boundary they share is 235 feet long.
And we have to find the width of the Plot B
We know that
Area of plot A = 46,060 square footage.
Area of plot B = 43005 square footage.
Common area share by both Plot = 235 feet long.
So, Now
The width of Plot B = Area of plot B / Common area
Substitute the values in it then
width of Plot B = Area of plot B / Common area
width of Plot B = 43005 / 235
width of Plot B = 183 feet.
So, The Width of plot B is 183 ft.
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d all the time and I like the time you
Answer:
Step-by-step explanation:
1a+1b(a+b-c)+1b+1c(b=c-a)+ 1a+1c(c+a-b)
1a+1b-c+1b +1c-a+1a+1c-b
1a+2b-c+a+1c-b
2a+1b+c this is the answer I think lol
hy some help me with this I'd appreciate it and also show the work
[tex] \sqrt{5612} = \frac{5612 + 5625}{2 \sqrt{5625} } = \frac{11237}{2 \times 75} = 74.913333[/tex]
Aubree's parents invested $500 into a mutual fund that paid 6.5% interest each year compounded annually when she was born. Find the value of the mutual fund in 18 years.
The value of the fund in 18 years as required by the task is; $1553.5.
What is the value of the fund in 18 years?Since, the interest rate is compounded annually as described, the value of the fund in 18 years can be calculated by means of the compound interest formula as;
Value = 500(1.065)^18.
Hence, we have; Value = $1553.5.
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Huan runs a business selling sweets. She is designing a container to hold the sweets. She uses rectangular pieces of cardboard measuring 20 cm by 30 cm. The mass of 1 square metre of the cardboard is 210 grams. She cuts a square from each corner of a piece of cardboard. She then folds the cardboard to make an open box. By changing the size of the square she cuts out, Huan can change the volume of the box.
(a) Work out the mass of the box made when she cuts a square of side 5cm from each corner.
(b) Huan cuts a square of side x from each corner of the cardboard.
(i) Explain why the volume of the box she makes is given by x(20-2x)(30-2x).
(ii) Explain why 0<x<10
(c) Huan wants to make a box with volume of at least 900cm3. She wants the mass of the box to be as small as possible.
By drawing a suitable graph, work out the mass of the box she will make
Answer:
d33z3 n0ts divided by ur m0m square root that x10 then divide by your d3pression.
Step-by-step explanation:
gotem
The distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. A sample size of 40 is drawn randomly. Find the probability that the sum of the 40 values is less than 7,100. (Round your answer to four decimal places.)
Using the normal distribution, there is a 0.2148 = 21.48% probability that the sum of the 40 values is less than 7,100.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For this problem, these parameters are given as follows:
[tex]\mu = 180, \sigma = 20, n = 40, s = \frac{20}{\sqrt{40}} = 3.1623[/tex]
A sum of 7100 is equivalent to a sample mean of 7100/40 = 177.5, which means that the probability is the p-value of Z when X = 177.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{177.5 - 180}{3.1623}[/tex]
Z = -0.79
Z = -0.79 has a p-value of 0.2148.
There is a 0.2148 = 21.48% probability that the sum of the 40 values is less than 7,100.
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SELECT ALL THAT APPLY. In a population of 250 students, 60% are Whites, 20% are Latinos, 15% are Blacks, and 5% others. In a proportionate stratified random sample of 120, ______.
In a proportionate stratified sample of 120, there are 72 Whites, 24 Latinos, 18 Blacks and 6 others.
Proportionate Stratified Sample
A proportionate stratified sample is one in which the size of the strata in the sample is proportional to the size of the strata in the population; in other words, the chance of selecting a unit from a stratum depends on the relative size of that stratum in the population.
Calculating the Proportionate Stratified Sample
The given percentage of -
Whites = 60%
Latinos = 20%
Blacks = 5%
Strength of the sample = 120
⇒ Number of Whites = 60% of 120
= 0.6 × 120
=72
Number of Latinos = 20% of 120
= 0.2 × 120
=24
Proportionate Stratified Sample of Blacks and Others
Count of Blacks = 15 % of 120
= 0.15 × 120
= 18
Count of others = 5% of 120
= 0.05 × 120
6
Thus, in a Proportionate Stratified Sample of 120, 72 are Whites, 24 are Latinos, 18 are Blacks, and 6 are others.
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i dont know how to do this
The dimensions of the rectangle are: length= 18 in and width =1 in.
QuadrilateralsThere are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
The area of a rectangle can be found for the formula : l*w, where b = length and w =width. The question gives that the area is 18 in².
For this question, the length exceeds its width by 17 inches - l=w+17. Thus, from the value of area given, you can find the values of the length and width of the rectangle.
A=l*w
18=(w+17)*w
18=w²+17w
w²+17w-18=0
Next step will be solve the previous equation ( W²+17W-18=0)
[tex]w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}\\ \\ w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}[/tex]
Therefore,
[tex]w_1=\frac{-17+19}{2\cdot \:1}=1\\ \\ \\ w_2=\frac{-17-19}{2\cdot \:1}=-18[/tex]
For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.
As, the area (l*w) is 18 in², you have.
18=l*w
18=l*1
l=18 in
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Chocolate costing $\$10$ per pound is mixed with nuts costing $\$4$ per pound to make a mixture costing $\$6$ per pound. What fraction of the mixture's weight is chocolate
1/3 portion of the mixture, costing $\$6$ contains chocolate.
Calculation of the weight of the chocolate in the mixture:Assume that, in a mixture:
chocolate = x pound
nuts = y pound
mixture= x+y
The desired value is found by dividing the weight of the chocolate by the overall weight, or x/(x+y).
From the given data,
cost of x pound chocolate at $\$10$per pound = 10x
cost of y pound nuts at $\$4$ per pound = 4y
cost of x+y pound mixture at $\$6$ = 6(x+y)
As per condition,
⇒10x + 4y = 6(x+y)
⇒10x + 4y = 6x+ 6y
⇒4x = 2y
⇒y = 2x
The fraction of the chocolate in the mixture is
[tex]x/(x+y)[/tex] = [tex]x/(x+2x)[/tex] = [tex]x/3x[/tex] = 1/3
Therefore, chocolate makes 1/3 of the mixture's weight.
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Answer:
1/3
Step-by-step explanation:
The angle measurements in the diagram are represented by the following expressions.
Answer:
since those 2 lines are parrelel that means the angles are the same so
8x+6=4x+38
minus 6
8x=4x+32
minus 4x
4x=32
divide by 4
x=8
Hope This Helps!!!
The value of the x is 11 and the measure of the angle B is 82 degrees.
What are vertically opposite angles?It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
We have:
The angle measurements in the diagram are represented by the following expressions:
Angle A = 8x - 6
Angle B = 4x + 38
By using the vertically opposite angle property in angle B
As we know the alternate exterior angle are equal
8x - 6 = 4x + 38
4x = 44
x =11
Measure of angle B = 4(11) + 38 = 82 degrees
Thus, the value of the x is 11 and the measure of the angle B is 82 degrees.
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The probability that a football game will go into overtime is 18%. What is the probability that two of three football games will go to into overtime
The probability that two of three football games will go to into overtime is 0.08
How to determine the probability that two of three football games will go to into overtime?From the question, we have the following parameters about the probability
Sample size, n = 3
Proportion that goes to overtime, p = 18%
Number that goes into overtime, x = 2
The probability that two of three football games will go to into overtime is calculated using the following binomial probability
P(x) = nCx * p^x * (1 - p)^(n -x)
Substitute the known values in the above equation
P(2) = 3C2 * (18%)^2 * (1 - 18%)^(3 -2)
Express 18% as decimal
P(2) = 3C2 * (0.18)^2 * (1 - 0.18)^(3 -2)
Evaluate the difference
P(2) = 3C2 * (0.18)^2 * (0.82)^1
Evaluate the combination expression
P(2) = 3 * (0.18)^2 * (0.82)^1
Evaluate the exponent
P(2) = 3 * 0.0324 * (0.82)
Evaluate the product
P(2) = 0.079704
Approximate
P(2) = 0.08
Hence, the probability that two of three football games will go to into overtime is 0.08
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Solve the logarithmic equation. write the answer in exact, simplified form. log(-c) + log8= log (7c-75)
The value of c is 5 when we simplify the logarithmic equation log(-c) + log8= log (7c-75). This can be obtained using the properties of the logarithm.
What is the value of c ?Given that,
log(-c) + log8 = log (7c-75)
log (-8c) = log (7c-75) (∵ log a + log b = log ab)
- 8c = 7c - 75
(8+7)c = 75
15c = 75
⇒ c = 5
Hence the value of c is 5 when we simplify the logarithmic equation log(-c) + log8= log (7c-75).
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How do i find the value of y?
Answer: 65
Step-by-step explanation:
We know that from the 65-degree angle, x=130.
So, by the inscribed angle theorem, y=65.
Charmaine's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Charmaine $4.25 per pound, and type B coffee costs $5.40 per pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $451.50. How many pounds of type A coffee were used
30 pounds of coffee A and 60 pounds of coffee B used.
According to statement
Type A coffee costs Charmaine $4.25 per pound
Type B coffee costs $5.40 per pound.
Total cost of month on coffee is $451.50
AND
B=2A -(1)
Let's form the equation
4.25A + 5.40B = 451.50
Put equation 1 in it then
4.25A + 5.40*2A = 451.50
15.05A = 451.50
A = 30 pounds then
B = 60 pounds.
So, 30 pounds of coffee A and 60 pounds of coffee B used.
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Ben has 3/4 pounds of cherries and ate 2/3 of the cherries. How many pounds of cherries does Ben eat?
Answer:
1/2 pounds
Step-by-step explanation:
3/4 * 2/3 = 1/2 pounds
I need to find the table of -csc theta
See below for the table of -csc theta
How to determine the table?The function is given as:
-csc theta
Rewrite properly as:
[tex]-\csc(\theta)[/tex]
This is calculated as:
[tex]-\csc(\theta) = -\frac{1}{\sin(\theta)}[/tex]
Set [tex]\theta[/tex] to 0, 30, 45, 60 and 90
[tex]-\csc(0) = unde fined[/tex]
[tex]-\csc(30) = -2[/tex]
[tex]-\csc(45) = -\sqrt 2[/tex]
[tex]-\csc(60) = -\frac{2\sqrt 3}{3}[/tex]
[tex]-\csc(90) = -1[/tex]
So, the table of -csc theta is
Angle -csc theta
0 undefined
30 -2
45 -√2
60 -2/3 √3
90 -1
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33. Companies will likely have autonomous robots delivering packages in the next few years. It has been determined that robots can meet their quotas if they have 4 robots for every 30 square miles of area they cover. If they want to offer service to a city of 75 square miles, how many robots must they have?
A)12 robots
B)10 robots
C)9 robots
D)15 robots
The number of robots have have for a city of 75 square miles would be 10 robots.
How many robots is needed for a 75 square miles?
The first step is to determine how many robots are needed for 1 square mile: 4/30.
The second step is to multiply this fraction by 75
4/30 x 75 = 10 robots
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If a school opens at 10 am and closes at 3.30pm. if the lunch interval is of 30 minutes, find the ratio of lunch interval to the total times of class periods.
The ratio of lunch interval to the total times of class periods is 1:10
Given that timing of school opens is 10am , the timing of school closes is 3:30pm and the lunch interval is 30 minutes
We need to find the ratio of lunch interval to the total times of class periods.
Now,
Timing of a school(10.a.mto3.30p.m)=5hours30minutes
Timing for lunch interval=30minutes
Total time of the class periods=5hours30minutes−30minutes
=5hours
=60×5=300 minutes.
Ratio of lunch interval to total time of the class period=30minutes:300 minutes=1:10
Hence the ratio of lunch interval to the total times of class periods is 1:10
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Do 7 ft, 9 ft, 11 ft form a right triangle
Answer:
no
Step-by-step explanation:
using the converse of Pythagoras' identity
if the square on the longest side is equal to the sum of the squares on the other 2 sides then the triangle is right.
longest side = 11 and 11² = 121
7² + 9² = 49 + 81 = 130
since 121 ≠ 130 then sides do not form a right triangle
A medication order states, normal saline (ns) iv to infuse at 125 ml/hr. How many ml will infuse in 8 hours? (record answer as a whole number. Do not use a trailing zero. )
The amount of medicine infused in 8 hours is 1000ml.
According to the statement
we have given that the medicine normal saline (ns) iv to infuse at 125 ml/hr.
and we have to find the total amount of medicine infuse in the 8 hours in the whole number value.
So,
An infusion is the creation of a new substance by steeping another substance in a liquid, usually water
we have given a rate of infusion of medicine per hour which is 125 ml/hr.
And
Amount of medicine infuse in 1 hour is 125 ml
And the Amount of medicine infuse in 8 hours = 125*8
Amount of medicine infuse in 8 hours = 1000 ml.
So, The amount of medicine infused in 8 hours is 1000ml.
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A bag contains 50 tokens: 20 pink ,13 blue and 17 purble.if a person selects one token, replaces it,and then selects a second token,what is the probability of selecting 2 of the same colour
Answer:
Step-by-step explanation:
this is independent
20/50= 2/5= 40% of getting pink, probability of getting 2= 20%
13/50=0.26= 26% of getting blue, probability of getting 2= 13%
17/50=0.34=34% of getting purple, probability of getting 2 = 17%
70%
A restaurant owner wants to determine the effectiveness of his servers. the owner places a survey regarding the servers' effectiveness with randomly selected customer bills. what is the sample?
The sample is the randomly selected customers.
Sampling:
Suppose I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents.
Sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a larger population. The methodology used to sample from a larger population depends on the type of analysis being performed, but it may include simple random sampling or systematic sampling.
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please help me i need to turn this in soon and i don't understand
Answer:
(a) C=88pi
A=1936pi
(b) Area
(c) Circumference
Step-by-step explanation:
Circumference formula = 2r(pi)
Area formula = pi(r^2)
Circumference = 2(44)(pi) = 88pi
Area = pi(44^2) = 1936pi
When something is paved it is the whole area not just the border so AREA
The chain will surround the place not fill it up so CIRCUMFERENCE
Using the image below, identify the type of angle relationship, construct the equation, and find x. Do not include any spaces in your answers.
If you are using a screen-reader, please consult your instructor for assistance.
Type of Angle Relationship:
Angles (You may use spaces in your answer here.)
Equation:
+
=
Solve: x=
A rectangular parking lot is 253.5 feet long and 176.5 feet wide. a 55-gallon drum of asphalt sealer covers
4,000 square feet and costs $99.50. find the cost to seal the parking lot. (sealer can only be purchased in full
drums.)
Answer:
$1,194
Step-by-step explanation:
The area of the parking lot is 253.5(176.5) which equals 44,472.75. You then divide 44,472.75 by 4000 to see how many gallons you need to cover the parking lot. The answer to that was about 11.2 and since you can only purchase full drums you have to round it up to 12 to have enough. Finally, you multiply 12 by 99.50 and get your answer.
a rectangle has a lengths and width of twelve and eight units, respectively. Using only multiplication show in a diagram which of the solutions below represent the perimeter of the entire rectangle
96 units
384 units
None of these
20 units
40 units
192 units
Answer:
40 units
Step-by-step explanation:
lengths:
12+12=24
width:
8+8=16
perimeter:
2l+2w
2(12)+2(8)
24+16=40
The income statement comparison for rush delivery company shows the income statement for the current and prior year. required: a) determine the operating income (loss) for each year. (2 marks) b) determine the operating income (% of sales) for each year. (2 marks) c) the company made a strategic decision to invest in additional assets in the current year. these amounts are provided. using the total assets amounts as the investment base, calculate the roi. was the decision to invest additional assets in the company successful? explain. (3.5 marks) d) assuming an 8% cost of capital, calculate the ri for each year. explain how this compares to your findings in (c). (3.5 marks)
Company's average operating assets for last year is $193000, company's margin is 15%, return on investment is 42%, company's residual income for last year is $521000.
Given the balance sheet and income statement of Joel de Paris and we have to calculate company's average operating assets for last year, company's margin,return on investment and company's residual income for last year.
1) Company's average operating assets=
(beginning operating assets+closing operating assets)/2
={(2562000-349000-253000)+(2634000-434000-25000)}/2
=(1910000+1950000)/2
=3860000/2
=$1930000
2)Company's margin= net operating income/ sales
=810000/540400
=15%
3)Turnover=sales/average inventory
=540400/1930000*100
=27.9%
=28%
4) Return on investment=margin* turnover
=15% of 28%
=42%.
Hence company's average operating assets for last year is $193000, company's margin is 15%, return on investment is 42%, company's residual income for last year is $521000.
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The question is incomplete and the information of question is in figure.