9514 1404 393
Answer:
900 grams
Step-by-step explanation:
The equation tells you the initial amount of A is 700 grams.
The table tells you B is being cut in half each hour, so the amount when h=0 is 2×800 = 1600 grams.
The difference in the initial amounts is ...
1600 -700 = 900 . . . grams
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
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 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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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.
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.
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?
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
please help me im in a rush
Answer:
Step-by-step explanation:
A = 4 ft
B = 10 ft
C = 8 ft
D = 6 ft
b) Area of rectangle = length * width
Area of 2 triangle = base * height
Area of right triangular prism = area of 2 triangles +area of left rectangle + area of middle rectangle + area of right rectangle
= 6 * 8 + 4* 6 + 4 * 10 + 4 * 8
= 48 + 24 + 40 + 32
= 144 ft²
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Formulas:}[/tex]
[tex]\huge\text{Area of rectangle is: }\huge\boxed{\rm{\bold{w}idth \times \bold{h}eight = \bold{a}rea}}[/tex]
[tex]\huge\text{Area of triangle is: }\huge\boxed{\rm{\dfrac{1}{2} \times \bold{b}ase \times \bold{h}eight = \bold{a}rea}}[/tex]
[tex]\huge\textbf{Now, that we have that out of the}\\\\\huge\textbf{way, we can label your given equation:}[/tex]
[tex]\rm{A \rightarrow 4\ \boxed{\rm{ft}}}\\\\\rm{B \rightarrow 10\ \boxed{\rm{ft}}}\\\\\rm{C \rightarrow 8 \ \boxed{\rm{ft}}}\\\\\rm{D \rightarrow 6\ \boxed{\rm{ft}}}[/tex]
[tex]\huge\textbf{What should your equation look like?}[/tex]
[tex]\rm{6\times 8 + 4\times 6 + 4 \times 10 + 4 \times 8}[/tex]
[tex]\huge\textbf{What should it look like when we're}\\\huge\textbf{solving for the answer?}[/tex]
[tex]\rm{6\times 8 + 4\times 6 + 4 \times 10 + 4 \times 8}[/tex]
[tex]\rm{= 48 + 4\times6 + 4\times10 + 4\times8}[/tex]
[tex]\rm{= 48 + 24 + 4 \times 10 + 4\times8}[/tex]
[tex]\rm{= 72 + 4\times 10 + 4\times8}[/tex]
[tex]\rm{= 72 + 40 + 4\times8}[/tex]
[tex]\rm{= 112 + 4\times8}[/tex]
[tex]\rm{= 112 + 32}[/tex]
[tex]\rm{= 144}[/tex]
[tex]\huge\textbf{What is the answer?}[/tex]
[tex]\huge\boxed{\textsf{Answer: }\boxed{\frak{144\ ft^2}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The points (1, 5) and (0, –2) fall on a particular line. What is its equation in slope-intercept form?
The equation of the line in slope intercept form is y = 7x - 2
How to find the equation of a line?The equation of the line can be solved with the following equation.
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = -2 - 5 / 0 - 1 = -7 / -1
m = 7
Hence, using (1, 5)
y = 7x + b
5 = 7(1) + b
5 - 7 = b
b = -2
Therefore,
y = 7x - 2
Hence, the equation of the line in slope intercept form is y = 7x - 2
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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
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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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
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]
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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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%
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=
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
thanks!!
1) Now is your chance to find examples of sinusoids. Come up with some examples of natural or man-made phenomena that repeat at predictable intervals.
Search the Internet to find descriptions, and post the link as well as your analysis of why the behavior is periodic. You do not have to find an equation or write one. Examples already given in the lessons for this unit are off limits, so look for something new.
As you ride a ferris wheel, your distance from the ground varies sinusoidally with time. When the last passenger boards the ferris wheel and the ride starts moving, let your position be modeled by the diagram provided.
2) Let t be the number of seconds that have elapsed since you began moving. It takes you 5 seconds to reach the top of the wheel (38 feet above the ground) and 20 seconds to make a complete revolution. The diameter of the wheel is 30 feet.
Work with your classmates to answer the following questions:
What is the lowest you go as the ferris wheel turns?
Why is this number always greater than zero?
Write the equation of a sinusoid that describes this motion.
Predict your height above the ground when t = 3, t = 8, t = 15, and t = 19.
The examples of sinusoids include sound and water waves.
How to illustrate the information?Simple harmonic motion such as that of a pendulum or a weight attached to a spring results in a sinusoidal relationship between position and time.
The angle will be formed after t time of the starting of the motion.
θ = wt = 2πt/20 = πt/10
Radius of the wheel = 30/2 = 15 feet
Distance from the ground = (15 - 15cosθ) + 8 = (15 - 15cosπt/10) + 8
= 23 - 15cos(πt/10)
As we know the minimum value of the cos is -1
-1 ≤ cos(πt/10) ≤ 1
8 ≤ 23 - 15cos(πt/10) ≤ 38
The lowest distance = 8 feet
It should be always greater than zero as the lowest point of what should be above the ground.
d = 23 - 15cos(πt/10)
Plug t = 3 in the above equation:
d(3) = 14.18 feet
For t = 8
d(8) = 35.13 feet
For t = 15
d(15) = 23 feet
For t = 19
d(19) = 8.73 feet
Thus, the lowest distance is 8 feet, and the lowest point of what should be above the ground and the equation is d = 23 - 15cos(πt/10).
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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.
[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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If the farmer isn't present, the fox cannot be left with either the dog or the goose, or both. if need be, the goose can be left with the grain provided the dog is present because the dog will guard the grain and won't eat the goose. help the farmer cross the river.
Answer:
See below
Step-by-step explanation:
Take fox across
go back to get goose
take goose across
take fox BACK
grab dog.....take dog across
go back get grain and take it across
go back get fox and take it across
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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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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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
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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help me please guys!!!
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation \#1.}[/tex]
[tex]\mathsf{|-8| + 9 = }[/tex]
[tex]\huge\textbf{Random note:}[/tex]
[tex]\textsf{The additive inverse of }\mathsf{|-8|}\textsf{ is positive 8.}[/tex]
[tex]\huge\textbf{Solving for the equation:}[/tex]
[tex]\mathsf{|-8| + 9}[/tex]
[tex]\mathsf{= \bold 8 + 9}[/tex]
[tex]\mathsf{= 17}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{17}}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation \#2.}[/tex]
[tex]\mathsf{|-8 + 9| =}[/tex]
[tex]\huge\textbf{Random note:}[/tex]
[tex]\textsf{We will convert your equation to }\mathsf{-8 + 9}\textsf{ because it can make the equation}\\\textsf{a lot easier to solve.}[/tex]
[tex]\huge\textbf{Solving for the equation:}[/tex]
[tex]\mathsf{|-8 + 9|}[/tex]
[tex]\mathsf{= -8 + 9}[/tex]
[tex]\text{Start at }\rm{-8}\text{ and go \boxed{up} 9 spaces to the right and you have your answer.}[/tex]
[tex]\mathsf{= 1}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
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:
Solve algebraically:
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation a.}[/tex]
[tex]\rm{2x^2 - 162 = 0}[/tex]
[tex]\huge\textbf{Solving for:}[/tex]
[tex]\rm{2x^2 - 162 = 0}[/tex]
[tex]\huge\textbf{Add \boxed{\bf 162} to both sides:}[/tex]
[tex]\rm{2x^2 - 162 + 162 = 0 + 162}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{2x^2 = 0 + 162}[/tex]
[tex]\rm{2x^2 = 162}[/tex]
[tex]\huge\textbf{Divide \boxed{\bf 2} to both sides:}[/tex]
[tex]\rm{\dfrac{2x^2}{2} = \dfrac{162}{2}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{x^2 = \dfrac{182}{2}}[/tex]
[tex]\rm{x^2 = 81}[/tex]
[tex]\huge\textbf{Take the square root of \boxed{\bf 81}}[/tex]
[tex]\rm{x = \pm \sqrt{81}}[/tex]
[tex]\rm{x = 9\ or\ x = -9}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\textsf{x = } \frak{9\ or } \ \textsf{x = }\frak{-9}}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation b.}[/tex]
[tex]\rm{-\dfrac{1}{2}(x - 3)^2 = -2}[/tex]
[tex]\huge\textbf{Solving for:}[/tex]
[tex]\rm{-\dfrac{1}{2}(x - 3)^2 = -2}[/tex]
[tex]\huge\textbf{Simplify both sides of your equation:}[/tex]
[tex]\rm{-\dfrac{1}{2}x^2 + 3x - \dfrac{9}{2} = -2}[/tex]
[tex]\huge\textbf{Subtract \boxed{\bf -2} to both sides:}[/tex]
[tex]\rm{-\dfrac{1}{2}x^2 + 3x - \dfrac{9}{2} - (-2) = -2 - (-2)}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{- \dfrac{1}{2}x^2 + 3x - \dfrac{5}{2} = 0}[/tex]
[tex]\huge\textbf{Now, we can convert the equation to:}[/tex]
[tex]\rm{-0.5x^2 + 3x - 2.5 = 0}[/tex]
[tex]\large\text{When we changed the equation entirely, we made it easier to solve}\uparrow[/tex]
[tex]\huge\textbf{Use the quadratic formula to solve.}[/tex]
[tex]\large\textsf{The quadratic formula:}[/tex]
[tex]\mathsf{x= \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]
[tex]\huge\textbf{Here are your labels:}[/tex]
[tex]\text{a = }\rm{-0.5}\\\\\text{b = }\rm{ 3}\\\\\rm{c = }\rm{\ -2.5}[/tex]
[tex]\huge\textbf{Your new equation:}[/tex]
[tex]\rm{x = \dfrac{-(3) \pm \sqrt{3^2 - 4(-0.5)(-2.5)}}{2(-0.5)}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{x = \dfrac{-3 \pm \sqrt{4}}{-1}}[/tex]
[tex]\rm{x = 1\ or \ x = 5}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\textsf{x = }\frak{1}\ \textsf{or x = }\frak{5}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex][tex]a)\ x_1=-9,\ x_2=9\\\\b)\ x_1=1,\ x_2=5[/tex]
Step-by-step explanation:Given equations:
[tex]a)\ 2x^2 - 162 = 0\\\\b) -\dfrac{1}{2}(x-3)^2=-2[/tex]
A) 2x² - 162 = 0
Step 1: Divide both sides by 2.
[tex]\\\implies \dfrac{2x^2 - 162}{2} = \dfrac{0}{2}\\\\\implies x^2-81=0\\\\\implies x^2=81[/tex]Step 2: Take the square root of both sides (using both the positive and negative roots).
[tex]\\\implies \sqrt{x^2}=\sqrt{81}\\\\\implies x=\pm\ 9[/tex]
Step 3: Separate into two cases.
[tex]\implies x_1 = -9,\ x_2 =-9[/tex]
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B) -1/2(x - 3)² = -2
Step 1: Multiply both sides by -2.
[tex]\\\implies -2\left(-\dfrac{1}{2}(x-3)^2\right)=-2(-2)\\\\\implies (x-3)^2=4[/tex]
Step 2: Take the square root of both sides (using both the positive and negative roots).
[tex]\\\implies\sqrt{(x-3)^2}=\sqrt{4}\\\\\implies x-3=\pm\ 2[/tex]
Step 3: Separate into two cases and solve each one.[tex]1)\ x-3=-2\implies x=-2+3\implies \boxed{x=1}\\\\2)\ x-3=2\implies x=2+3\implies \boxed{x=5}[/tex]
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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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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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?
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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