Using integrals, it is found that the cumulative distribution function(cdf) at x = 2.27 is given by:
P(X ≤ 2.27) = 0.897.
How to find the cumulative distribution function of a distribution?The cumulative distribution function of a distribution given by f(x) at a value of x = x* is given by the following integral:
\(\int_{-\infty}^{x^{\ast}} f(x) dx\)
For this problem, the distribution is given by:
\(f(x) = e^{-x}, x > 0\)
Hence, at x = 2.27, the cdf is given by:
\(\int_{0}^{2.27} e^{-x} dx\)
The infinity was replaced by 0 because the lower bound of the definition of the distribution is of 0. Hence:
\(\int_{0}^{2.27} e^{-x} dx = -e^{-x}|_{x = 0}^{x = 2.27}\)
Applying the Fundamental Theorem of Calculus:
P(X ≤ 2.27) = -e^(-2.27) + e^0 = -e^(-2.27) + 1 = 0.897.
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pleasssssseeeeeeeeeeeeeeeeeeee
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▹ Answer
0.5 = 1/2 and the rectangle with 3 cubes shaded in
0.6 = 60/100 and circle with three parts shaded in
0.8 = Rectangle with 8 cubes shaded and 4/5
▹ Step-by-Step Explanation
You can convert the fractions into decimals, and count the shaded parts for the shaded images.
Hope this helps!
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Brainliest is greatly appreciated!
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Emily simplified this expression.
Expression: (5−2)2+23×4
Step 1: (3)2+23×4
Step 2: 9+23×4
Step 3: 9+9×4
Step 4: 9+36
Step 5: 45
Emily made a mistake. Which step shows her first mistake?
Step 1
Step 2
Step 3
Step 4
0.45 divided by 18 please help it is due today
Answer:
answer is 0.025
Step-by-step explanation:
answer is 0.025
please help me solve
Answer:
130 degrees
Step-by-step explanation:
DE+DA=130
The teachers at Eastside High School were asked the number of years they have been teaching. The results are as follows.
3, 4, 9, 12, 7, 5, 4, 12, 3, 9, 11, 4, 14, 9, 2, 10, 3, 10, 9, 7
Use the data to fill in the box-and-whisker plot below.
Answer:
I'm not your Slave
Step-by-step explanation:
do it yourself
1/4 minus 3/8 in fraction form
Answer: -1/8 is the answer
A 6 inch by 10 inch rectangle is dilated by a factor of 3. What is the area of the dilated
rectangle?
Answer:
Step-by-step explanation:
Dilated by a factor of three means that the two dimensions needed for the are are multiplied by 3.
width = 6*3 = 18
Length = 10 * 3 = 30
Area of dilated rectangle = 18*30 = 540 inches ^2
If a fair coin is tossed 8 times, what is the probability, rounded to the nearest
thousandth,of getting at least 6 heads?
The probability of getting at least 6 heads is3/256 or 0.0117
What is probability ?Probability shows possibility to happen an event, it defines that an event will occur or not. The probability varies from 0 to 1.
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.
Probability is a measure of how likely something is to occur. Calculating probability involves dividing the total number of outcomes by the number of possible ways an event may occur.
Given that,
A fair coin is tossed = 8 time.
We have to find the probability of getting at least 6 heads.
Since, the probability of getting head, when one coin is tossed = 1/2
And the probability of getting tale = 1/2
The probability of getting head at least 6 times when coin is tossed 8 times can be given as,
The head can come 6 times, then probability = \((1/2)\x^{6} (1/2)\x^{2}\) = (1/2)⁸
The head can come 7 times, then probability = (1/2)⁷(1/2) = (1/2)⁸
The head can come 8 times, then probability = (1/2)⁸
The probability of getting head at least 6 times
= (1/2)⁸ + (1/2)⁸ + (1/2)⁸ = 3(1/2)⁸ = 3/256 = 0.0117
The probability of getting at least 6 heads is3/256 or 0.0117
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A manufacturer has 576 square inches of material available to construct the 6 faces of a carton, which will be in the shape of a rectangular prism. To maximize the volume, the carton will have dimensions such that the length and width are each twice the height.
To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).
What is the dimension required to maximize the volume of the box?Assuming the height of the rectangular prism is h inches.
According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.
The total surface area of the rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Substituting the values, we have:
576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)
576 = 8h² + 4h² + 4h²
576 = 16h² + 4h²
576 = 20²
h² = 576/20
h² = 28.8
h = √28.8
h = 5.37
The height of the prism is approximately 5.37 inches.
The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.
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-5 a root of the Quadratic
equation n² - 8n-65 = o.
What is the other root of the
equation
Answer:
13
Step-by-step explanation:
It is a quadratic equation meaning it has 2 factors and since one of it has root -5, the first factor is (n + 5),
So, we have (n + 5)(n + a) = n^2 + an + 5n + 5a
Thus, by comparison,
n^2 + (5 + a)n + 5a = n^2 - 8n - 65 = 0
5 + a = -8
5a = -65
a = -13
Thus, the other factor is (n -13) and root is 13
Which of the following applications of undefined terms made use of the concept of point as a location in space?
A RADAR. C laser beam
b tip of needle. D mole o a face
What is the slope of the line?
Answer:
7/4 = 1.75
Step-by-step explanation:
step 1: pick two points on the line that have nice integer coordinates.
--> (3,4) and (-1,-3)
step 2: calculate the y difference and the x difference
--> y difference: 4 - -3 = 7
x difference: 3 - -1 = 4
step 3: the slope is y difference / x difference
--> slope = 7/4
Please help. I need a good step by step explanation
Answer:
the perimeter of a square is 4a.. where (a) is one side
therefore the equation formed is
3.5x(4)=2x+54
14=2x+54
2x= -40
x= -20
please solve to the nearest 10th
The value of the sides are;
c = 35. 5, y = 32. 2, <H = 65 degrees
Option D
How to determine the valueWe have that the ratios of the trigonometric identities are;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the information given, we have that;
Using sine identity
sin 25 = 15/c
cross multiply the values, we get;
c = 35. 5
Then, using tan identity;
tan 25 = 15/y
cross multiply
y = 32. 2
Sum of angles in a triangle is equal to 180 degrees.
Then, we have that;
90 + 25 + <H = 180
collect the terms
<H = 65 degrees
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Questions 9-10, deal with the ambiguous SSA case. For each, find all possible solutions and sketch the
triangle(s) in each case. (3 points each)
9: A=50, a=10, b=15
10: A=47, a=1.6, b=2
The possible solutions for (10) are B = 66, C = 67 and c = 2.01
How to determine the possible solutionsTriangle 9
Here, we have
A = 50, a=10, b = 15
The angle B can be calculated using the following laws of sines
sin(B)/b = sin(A)/a
So, we have
sin(B)/15 = sin(50)/10
sin(B) = 15 * sin(50)/10
So, we have
sin(B) = 1.1490
The sine of angles are always between 0 and 1
Hence, the triangle does not exist
Triangle 10
Here, we have
A=47, a=1.6, b=2
The angle B can be calculated using the following laws of sines
sin(B)/b = sin(A)/a
So, we have
sin(B)/2 = sin(47)/1.6
sin(B) = 2 * sin(47)/1.6
So, we have
sin(B) = 0.9142
B = 66
This means that
C = 180 - 66 - 47
C = 67
The length c is
c² = a² + b² - 2ab * cos(C)
So, we have
c² = 1.6² + 2² - 2 * 1.6 * 2 * cos(67 degrees)
c² = 4.06
Take the square roots
c = 2.01
See attachment for the triangles
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2023 1-100 math challenge answers
Answer:
Step-by-step explanation: 1*23= 23 because anything times one is equal to itself
6% pay increases 62,900 thanks i look forward to the additional _ per month
Answer:
Step-by-step explanation:
$314.50
Please help fast pls
Need if
Answer:
Dustin Earns $14,000 in a year but in the question, we are given the salary of a month
Monthly salary of dustin:
14000 / 12 = $1,166 (approx)
Hence,
The actual monthly salary of Dustin is $1166, excluding the commissions
For a specific month, the salary of Dustin including the commissions is $2,400
Money earned in commissions:
Salary earned - Actual monthly salary
2400 - 1166 = $1,234
We are given the sales of Dustin for that specific month = $ 18,000
Hence, Dustin Earned a commission of $1,234 for sales of $18,000
Commission rate of Dustin:
Commission Earned * 100 / Sales made
1234 * 100 / 18000
6.856 %
Therefore, the commission rate of Dustin is 6.856%
PLEASE HELP ME I AM STUCK
Answer:
About half of the fish in the pond are trout
Step-by-step explanation:
109 is about half of 215
What is the cost of a pair of shoes if they retail for $18.50, have a tax of 6%, and you have a coupon for 20% off after taxes
Answer:
$15.69
Step-by-step explanation:
multiply the retail price by 1.06 to get the price after taxes.
find the discounted price by multiplying the price after taxes(19.61) by 0.8 since it is 20% off to get the answer
A trucking company buys 25,275 gallons of gasoline. The federal excise tax is $0.195 per gallon. Find the amount of excise tax due. (Round your answer to the nearest cent if necessary)
Answer: 5,055
Step-by-step explanation
multiply the amount of gallons purchased by tax and round up
$4928.625 is the answer.
An Excise tax is an indirect tax, usually paid by the manufacturer or retailer of the product. then passes along in the price of the product to the consumer.
Amount of gasoline = 25,375 gallons.
The Excise tax = $0-195/gallon.
The amount of Excise tax dece = 25.875 X $0.195
= $4928.625
Se the amount of Excise tax due for 25975 gallons of gasoline is $ 4928.625
what is Excise tax?Excise tax is generally a tax levied on the sale of a particular good or service or for a particular purpose. State excise taxes are usually levied on the sale of gasoline, air tickets, heavy trucks, road tractors, tanning beds, tires, cigarettes, and other goods and services.
Excise can be used to charge prices for externalities or to discourage the consumption of goods by others. They can also be used as royalties to generate income from people who use certain government services. Income should be used to maintain those government services.
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Milena walked 25.086 kilometers on Monday, 19.8 kilometers on Tuesday, and 7 kilometers on Wednesday. What was the total distance that Milena walked
Find the area of the figure pictured below.
15 yd
10 yd
17 yd
5 yd
A
First find the area of the square, then the triangle.
15 times 17 = 255 sq. yd
Triangle:
(5 times 5)/2 = 12.5 sq. yd
Your answer is 267.5 sq. yd
Hope this helps.
what is sin 23º?
5/13
12/13
5/12
12/5
By using trigonometry, it can be calculated that- sin 23º = \(\frac{5}{13}\)
What is Trigonometry?
Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles. It is used to calculate the lengths of sides, the measures of angles, and the relationships between the two. Trigonometry is important for understanding many areas in mathematics, such as calculus and engineering. Trigonometric functions are used to model and analyze phenomena in many areas, such as sound waves, light waves, and ocean tides. Trigonometric identities allow us to simplify equations and solve problems. Trigonometry is a fundamental tool in many scientific and engineering disciplines.
There are six trigonometrical functions. They are
\(sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta\)
\(sin\theta = \frac{perpendicular}{hypotenuse}\\cos\theta = \frac{baser}{hypotenuse}\\tan\theta = \frac{perpendicular}{base}\\cot\theta = \frac{base}{perpendicular}\\sec\theta = \frac{hypotenuse}{base}\\cosec\theta = \frac{hypotenuse}{perpendicular}\\\)
Trigonometry is a very important tool in mathematics.
For an angle of 23º,
Perpendicular is 5, base is 12 and hypotenuse is 13
sin 23º = \(\frac{5}{13}\)
First option is correct.
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Thomas obtained a bank loan of k10 000 from BSP bank.He repays the money with 36% interest in one year.Calculate his installment payment he pays in one fortnight?
Thomas' installment payment that he pays in one fortnight is approximately k523.08.
To calculate Thomas' installment payment, we need to consider the principal amount (k10,000) and the interest rate (36%).
First, let's calculate the total amount to be repaid at the end of the year, including the interest. The interest is calculated as a percentage of the principal amount:
Interest = Principal × Interest Rate
= k10,000 × 0.36
= k3,600
The total amount to be repaid is the sum of the principal and the interest:
Total Amount = Principal + Interest
= k10,000 + k3,600
= k13,600
Now, we need to calculate the number of fortnights in a year. There are 52 weeks in a year, and since each fortnight consists of two weeks, we have:
Number of Fortnights = 52 weeks / 2
= 26 fortnights
To find the installment payment for each fortnight, we divide the total amount by the number of fortnights:
Installment Payment = Total Amount / Number of Fortnights
= k13,600 / 26
≈ k523.08
Therefore, Thomas' installment payment that he pays in one fortnight is approximately k523.08.
It's important to note that this calculation assumes equal installment payments over the course of the year. Different repayment terms or additional fees may affect the actual installment amount. It's always advisable to consult with the bank or financial institution for accurate information regarding loan repayment.
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6) Order the fractions and decimals from least to greatest 0.75, 1/2, 04, 1/5
Answer:
Order from least to greatest: 1/5, 0.75, 1/2, 04.
Explanation:
1/5 is the least because 0.75 is equivalent to 1/4 and 1/2 is greater than both of those. 04 is a whole number because the 0 doesn't matter if there's no decimal point, which there isn't. So take away the 0 and you get the whole number 4! Hope this helped :)
You and a group of art students have successfully drawn a panther logo that will be framed within a quadrilateral. The vertices of the quadrilateral are as follows: A (-4.5, 3.5), B (1.5, 10.5), C (5.5, -1.5) and D (-0.5, -8.5). The panther’s right eye pupil rests at (1.5, 3). Classify the quadrilateral formed by the points A, B, C, D that frame the panther logo. Justify your claim algebraically.
Solution
To determine that,
The quadrilateral formed by the points A, B, C, D is a parallelgram,
since
A - D = (-4.5, 3.5) - (-0.5, -8.5) = (-4, 12)
B - C = (1.5, 10.5) - (5.5, -1.5) = (-4, 12)
Hey! can you help me with question number 2? I am really confused about it
Solve for x
Pls help
Answer:
Hey mate....
Step-by-step explanation:
This is ur answer.....
first we need to find the angle that is above 63 degrees, it will be much easier to know the next one....
= (Supplementary angle) 180 - 63
= 117
Expression = 23x + 2
= 23 x ? + 2
= (Multiplication of 23)
= 23 x 5 + 2
= 117
SIMPLE!
Have a look on the pic given below....
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Use the laws of Sines and law of cosines to find missing dimensions
9514 1404 393
Answer:
11. inconsistent information
12. 26°
Step-by-step explanation:
11. The given numbers are inconsistent. (The first attachment shows one of the 4 possible solutions.)
__
12. In order to find angle C, we need to know side AC. We can find that using the Law of Cosines.
b = √(a² +c² -2ac·cos(B)) = √(19² +15² -2(19)(15)cos(120°)) = √871
b ≈ 29.513
Then angle C is found from the Law of Sines.
C = arcsin(c/b·sin(B)) = arcsin(15/29.513·sin(120°)) ≈ 26.11°
Angle C is about 26°.
The second attachment shows the output of a triangle solver.