Answers
Cos45= s/6
s= 4.24264068712
s= 3 sqrt 2
Therefore the answer is A.
Hello,
an other method
Pythagorean theorem :
x² + x² = 6²
2x² = 36
x² = 36/2
x² = 18
x = √18 (and not -√18 because x ≥ 0)
x = √(9 × 2)
x = √(3² × 2)
x = 3√2
Answer A
Related Questions
I need to find the table of -csc theta
Answers
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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Do 7 ft, 9 ft, 11 ft form a right triangle
Answers
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
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
Answers
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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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=
Answers
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
Answers
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
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.
Answers
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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Solve the logarithmic equation. write the answer in exact, simplified form. log(-c) + log8= log (7c-75)
Answers
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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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
Answers
Answer:
d33z3 n0ts divided by ur m0m square root that x10 then divide by your d3pression.
Step-by-step explanation:
gotem
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?
Answers
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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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. )
Answers
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
Answers
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%
The angle measurements in the diagram are represented by the following expressions.
Answers
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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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
Answers
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:
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
Answers
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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hy some help me with this I'd appreciate it and also show the work
Answers
[tex] \sqrt{5612} = \frac{5612 + 5625}{2 \sqrt{5625} } = \frac{11237}{2 \times 75} = 74.913333[/tex]
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.)
Answers
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.
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)
Answers
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.
How do i find the value of y?
Answers
Answer: 65
Step-by-step explanation:
We know that from the 65-degree angle, x=130.
So, by the inscribed angle theorem, y=65.
14. Ashley is holding a fair six-sided die and a fair
coin. If Ashley rolls the die once and then flips
the coin, what is the probability that the die will
show a 5 and the coin will come up tails?
Answers
Answer:
1/12
Step-by-step explanation:
Landing on the 5 is a 1/6 chance, landing on tails is a 1/2 chance, multiply, and you get 1/12
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
Answers
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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please help me i need to turn this in soon and i don't understand
Answers
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
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, ______.
Answers
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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Ben has 3/4 pounds of cherries and ate 2/3 of the cherries. How many pounds of cherries does Ben eat?
Answers
Answer:
1/2 pounds
Step-by-step explanation:
3/4 * 2/3 = 1/2 pounds
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.
Answers
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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[tex]27a^3+189a^2b+441ab^2+343b^3[/tex]
Answers
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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The write right company manufactures ballpoint pens and has been experiencing a 5% rate of defective pens. modifications are made to the manufacturing process in an attempt to improve quality, and the manager claims that the modified procedure is better, because a test of 50 pens shows that only one is defective. a. assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, exactly one is defective. b. assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, none are defective. c. what probability value should be used for determining whether the modified process results in a defect rate that is less than 5%? d. what do you conclude about the effectiveness of the modified production process?
Answers
a. The probability that exactly one is defective is 0.2025
b. The probability that none will be defective is 0.0769
c. The probability rate that should be used is 2%
d. The modified production process is better.
The question has to do with binomial probability.
What is binomial probability?Binomial probability is probability in which the event can only have two values or is binary.
Given the binomial probability formula,
P(X = x) = ⁿCₓpˣ(1 - p)ⁿ ⁻ ˣ
where
p = probability of defective = 5% = 0.05 and n = 50a. Assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, exactly one is defective.For the probability that exactly one is defective, x = 1
So, P(x = 1) = ⁵⁰C₁p¹(1 - p)⁵⁰ ⁻ ¹
= ⁵⁰C₁p(1 - p)⁴⁹
= ⁵⁰C₁(0.05)(1 - 0.05)⁴⁹
= ⁵⁰C₁(0.05)(0.95)⁴⁹
= 50(0.05)(0.95)⁴⁹
= 50(0.05)(0.081)
= 0.2025
So, the probability that exactly one is defective is 0.2025
b. Assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, none are defective.For the probability that exactly one is defective, x = 0
So, P(x = 0) = ⁵⁰C₀p⁰(1 - p)⁵⁰ ⁻ ⁰
= ⁵⁰C₀(1 - p)⁵⁰
= ⁵⁰C₀(1 - 0.05)⁵⁰
= ⁵⁰C₀(0.95)⁵⁰
= 1 × (0.95)⁵⁰
= 0.0769
So, the probability that none will be defective is 0.0769
c. What probability value should be used for determining whether the modified process results in a defect rate that is less than 5%?
Since the modified result results in a defective rate of one out of 50 pens.
The probability rate that should be used is p = number of defective pens/total number of pens = 1/50
= 1/50 × 100 %
= 2%
The probability rate that should be used is 2%
d. What do you conclude about the effectiveness of the modified production?Since the defective rate of the modified production process is 2% which is less than that of the previous production process which is 5%, the modified production process is better.
So, the modified production process is better.
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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
Answers
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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ales volume last weekend for four samples, each consisting of five car dealerships, were as follows: Data Point 1 2 3 4 5 Sample 1 37 15 43 25 21 Sample 2 38 31 12 19 28 Sample 3 16 21 45 32 25 Sample 4 19 10 45 37 22 What is the standard deviation of the distribution of sample means
Answers
The sample standard deviation of sample 1 is 11.54, of sample 2 is 10.21, of sample 3 is 11.25, of sample 4 is 14.15.
Given
Data point sample 1 sample 2 sample 3 sample 4
1 37 38 16 19
2 15 31 21 10
3 43 12 45 45
4 25 19 32 37
5 21 28 25 22
We have to find the sample standard deviation of each sample.
We have to first mean of each sample.
Sample mean of 1=141/5=28.2
Sample mean of 2=128/5=25.6
Sample mean of 3=139/5=27.8
Sample mean of 4=133/5=26.6
Sample standard deviation=[tex]\sqrt{}[/tex]∑[tex](x-x bar)^{2}/n-1[/tex]
∑[tex](x-x bar)^{2}[/tex] is calculated in the figure.
Sample standard deviation of sample 1=[tex]\sqrt{532.8/4}[/tex]
=[tex]\sqrt{133.2}[/tex]
=11.54
Sample standard deviation of sample 2=[tex]\sqrt{417.2/4}[/tex]
=[tex]\sqrt{104.3}[/tex]
=10.21
Sample standard deviation of sample 3=[tex]\sqrt{506.8/4}[/tex]
=[tex]\sqrt{126.7}[/tex]
=11.25
Sample standard deviation of sample 4=[tex]\sqrt{801.2/4}[/tex]
=[tex]\sqrt{200.3}[/tex]
=14.15.
Hence the sample standard deviation of sample 1 is 11.54, sample standard deviation of sample 2 is 10.21, sample standard deviation of sample 3 is 11.25, sample standard deviation of sample 4 is 14.15.
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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
Answers
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 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.)
Answers
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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