Suppose that X is normally distributed with a mean of 20 and a standard deviation of 18. What is P(X 2 62.48)? a) 0.991 b) 0,012 c) 0.491 d) 0.009 e) 0.014 f) None of the above
Answers
The value of P(X 2 62.48) is (d) 0.009.
How we get the value of P(X 2 62.48)?To solve this problem, we need to standardize the random variable X by subtracting the mean and dividing by the standard deviation to obtain a standard normal variable Z.
Calculate Z-score
\(Z = (62.48 - 20) / 18 = 2.9167\)Look up the probability in the standard normal table or use a calculator to find the area under the standard normal curve to the right of Z.
Using a standard normal table, we can find that the area to the right of 2.9167 is approximately 0.002.
The probability of X being greater than 62.48 is equivalent to the probability of Z being greater than 2.9167, which is the standardized version of X.
We use a standard normal table or calculator to find the area under the standard normal curve to the right of Z. The answer is the probability that Z is greater than 2.9167.
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Related Questions
Verify each identity.Express cosθ cscθ cotθ in terms of sin θ .
Answers
The identity cosθ cscθ cotθ = sinθ can be verified by expressing each term in terms of sinθ. After expressing cosθ, cscθ, and cotθ in terms of sinθ, we find that cosθ cscθ cotθ simplifies to sinθ, confirming the given identity.
We start by expressing each trigonometric function in terms of sinθ:
cosθ = 1/sinθ (reciprocal identity)
cscθ = 1/sinθ (reciprocal identity)
cotθ = cosθ/cscθ = (1/sinθ)/(1/sinθ) = 1 (simplification)
Substituting these expressions back into cosθ cscθ cotθ:
cosθ cscθ cotθ = (1/sinθ) * (1/sinθ) * 1 = 1/sin²θ.
Using the reciprocal identity sin²θ = 1/csc²θ, we simplify further:
1/sin²θ = 1/(1/csc²θ) = csc²θ.
Therefore, cosθ cscθ cotθ simplifies to csc²θ, which is equal to sinθ. Thus, the identity is verified.
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Holly says 4.131131113... is a rational number. Which of the following best describes whether Holly is correct and why??
Holly is correct. Repeating decimals are always rational numbers.
Holly is correct. The number is positive and all positive numbers are rational.
Holly is incorrect. The decimal does not terminate, so it cannot be a rational number.
Holly is incorrect. The decimal part follows a pattern but does not actually repeat.
Answers
Answer:
D. Holly is incorrect. The decimal part follows a pattern but does not actually repeat.
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
Which expression is equivalent to5(h+9)
Answers
Answer:
The answer would be 5h+45
Step-by-step explanation
5 (h+9)
You need to convert this equation into the equation
you multiply 5 by h and get 5h
Then multiply the same number outside the parenthesis, 5, by 9 which will give you the answer 45
Once you have 5h and 45 just put it together with the addition symbol which will will equal:
5 (h+9) = 5h + 45
Your Welcome! (hopefully this answers your question)
A recipe for 24 cookies calls for 4 tablespoons of sugar. If you make 40 cookies and use 5 tablespoons, will the cookies taste the same? Explain
Answers
Answer:
Step-by-step explanation:
No, because they wouldn't contain the same amount of sugar per cookie
for the first recipe - 24 cookies with 6 tablespoons
thats 6/24 so 0.25 tablespoons of sugar per cookie
for the second recipe - 36 cookies with 10 tablespoons
thats 10/36 so 0.276 tablespoons per cookie
the cookies in the second recipe would be slightly sweeter than the cookies in the first
The 24cookies per 4 sugar tbsps calls for 1 tbsp for every 6 cookies. This makes the ratio 6:1.
If u divide 40/5, you will get a ratio of 8:1. This means 1 tbsp of sugar in every 8 cookies. Making the cookies less sugary
What is the measure of n
Answers
Answer:
Step-by-step explanation:
This is a geometric means problem. Namely, n is the geometric mean between the 2 smaller triangles within that larger one. Set up the problem accordingly:
\(\frac{28}{n}=\frac{n}{7}\) and cross multiply:
\(n^2=196\) so
n = 14
Which of the following is like terms with -4yz²?
A. -4yz
B. 4y²z
C. 12xyz²
D. 18yz²
Answers
Answer:
D. 18yz²
Step-by-step explanation:
Like terms have the same variables and exponents.
-4yz² has as variables y and z².
Only one choice has the same variables and exponents:
D. 18yz²
Solve for X. Round your answer to the nearest tenth.
Answers
The side ratio theorem states that the value of x is 9.6 when BD/DA = BE/EC when DA = 12 and BE = 8 and EC = 10.
what is triangle ?Given it has triangles and three vertices, each triangle qualify as a polygon. It belongs to the primitive geometric. Triangle ABC is the term utilized to refer to a triangle with the points A, B, and C. Once the three components are not collinear, a unique rectangle and square in Geometric forms are discovered. Triangles are polygons because they have three sections and three corners. The points where the main parts of the triangle merge are called to as the triangle's corners. Three triangle ratios are multiplied to yield 180 degrees.
given
by Side ratio theorem
BD/DA = BE/EC
= x/12 = 8/10
x = 8*12/10
x = 9.6
The side ratio theorem states that the value of x is 9.6 when BD/DA = BE/EC when DA = 12 and BE = 8 and EC = 10.
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After my salary was increased by 12%, it was $62,720. What was my salary before the increase?
I'll mark brainliest!
Answers
Answer
56,000
Step-by-step explanation:
Change the word phrase to an algebraic expression. Use x to represent the number. The product of 9 and two more than a number
Answers
The algebraic expression for "The product of 9 and two more than a number" is 9(x + 2).
In the given word phrase, "a number" is represented by the variable x. The phrase "two more than a number" can be translated as x + 2 since we add 2 to the number x. The phrase "the product of 9 and two more than a number" indicates that we need to multiply 9 by the value obtained from x + 2. Therefore, the algebraic expression for this word phrase is 9(x + 2).
"A number": This is represented by the variable x, which can take any value.
"Two more than a number": This means adding 2 to the number represented by x. So, we have x + 2.
"The product of 9 and two more than a number": This indicates that we need to multiply 9 by the value obtained from step 2, which is x + 2. Therefore, the algebraic expression becomes 9(x + 2).
In summary, the phrase "The product of 9 and two more than a number" can be algebraically expressed as 9(x + 2), where x represents the number.
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The area of a square is 300 feet. What is the side length of the square? Round to the nearest tenths place.
Answers
Answer:
17.3
Step-by-step explanation:
square root of 300 is 17.32050808
17.32050808 rounded is 17.3
You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to flip a fair coin. She will give you $15 for heads and $25 for tails. Your mother says she wants you to spin a spinner with six outcomes, numbered 1 through 6, on it. She will give you $6 times the number that the spinner lands on. Determine the expected value of each game and decide which offer you should take.
Answers
Given that:
- Your sister will give you $15 for heads and $25 for tails.
- Your mother will give you $6 times the number that the spinner lands on.
you must calculate the Expected Value of each game:
- Game 1:
When you through the coin, the probability of getting a head is 50% and the probability of getting a tail is 50%.
You need to use the following formula for calculating the Expected Value:
\(E=\sum_^x\cdot p(x)\)Where "x" is the random variable, and p(x) is the probability obtained.
Therefore, for Game is:
\(E_1=(15)(0.5)+(25)(0.5)\)\(E_1=20\)- Game 2:
When you spin the spinner with six different outcomes. Therefore:
\(p(x)=\frac{1}{6}\)Then:
\(\begin{gathered} E_2=\frac{1}{6}\cdot6(1+2+3+4+5+6) \\ \\ E_2=1+2+3+4+5+6 \\ \\ E_2=21 \end{gathered}\)Hence, the answer is:
- Expected Value of your sister's game:
\(\text{ \$}20\)- Expected Value of your mother's game:
\(\text{ \$}21\)- You should take your mother's offer, because it has the greatest Expected Value.
Please solve on same Kind of coordinate plane. Thank you!
Answers
Answer:
(0,8)
Step-by-step explanation:
Evaluate 3x – 4 when x=7. The value of the expression is
Answers
Answer:
3(7) - 4 = 17
Step-by-step explanation:
Substitute 7 for x and solve.
the cost of different tickets (in rupees ) bought by different passengers travelling in a train is given below. find the median cost 54 51 55 45 40 45 38 50 35 42
Answers
Hope this helps :)
The weight of an object on the moon is
5 of its weight on Earth. If a moon rock
weighs 202 lb on Earth, how much did
the moon rock weigh on the moon?
Give your answer as a simplified mixed number.
Enter the number that belongs in the green box.
Answers
Answer:
40 2/5Ibs or \(40\frac{2}{5}\) lbs
Step-by-step explanation:
Let weight of object on the moon be represented = Wm
weight of object on the Earth = We
In the above question, we are told:
The weight of an object on the moon is
5 of its weight on Earth.
Hence, mathematically, this is represented as:
5Wm = We
If a moon rock weighs 202 lbs on Earth
5Wm = 202lbs
Wm = 202lbs/5
Wm = \(40\frac{2}{5}\)Ibs
Therefore, the moon rock weighs \(40\frac{2}{5}\)Ibs on the moon.
To increase usability in a spreadsheet, use comments, descriptive labels and?
Answers
To increase usability in a spreadsheet, you can use comments, descriptive labels, and data validation.
To increase usability in a spreadsheet, you can utilize the following techniques:
1. Comments: Comments allow you to add explanatory notes or instructions within cells. They can provide additional context or clarify the purpose of certain data or formulas. Users can view comments by hovering over the respective cell, making it helpful for collaboration and documentation.
2. Descriptive Labels: Instead of relying solely on cell references or generic labels, use descriptive labels that clearly indicate the purpose of each column, row, or range of cells. This approach enhances readability and makes it easier for users to understand the data and navigate through the spreadsheet.
3. Data Validation: Implement data validation rules to ensure the accuracy and integrity of the data entered into the spreadsheet. Data validation allows you to define constraints or conditions for input, such as numeric ranges, predefined lists, or specific text formats. It helps prevent errors and assists users in entering valid data.
4. Formatting: Properly formatting the cells, columns, and rows can greatly enhance usability. Use consistent formatting for similar types of data, apply color schemes or conditional formatting to highlight important information or trends, and adjust the column widths and row heights to optimize readability.
5. Sheet Organization: Organize the spreadsheet by using multiple sheets if needed. Group related information on separate sheets, and provide clear sheet names that reflect the content or purpose of each sheet. This helps users locate and navigate to specific sections or data within the spreadsheet.
6. Clear Instructions or Documentation: Provide clear instructions or documentation either within the spreadsheet or as separate documentation. Explain the purpose of the spreadsheet, any specific procedures or workflows, and how to interpret the data or use any embedded formulas or macros. This helps users understand the spreadsheet's functionality and ensures consistent usage.
7. Error Handling: Implement error handling mechanisms to provide informative error messages or alerts when users input incorrect or incompatible data. Clear error messages guide users in correcting their input and reduce frustration when dealing with potential errors.
By incorporating comments, descriptive labels, data validation, formatting, sheet organization, clear instructions/documentation, and error handling, you can significantly enhance the usability of your spreadsheet and make it more user-friendly for both yourself and others who interact with it.
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Triangle ABC has vertices at A(−3, 3), B(0, 4), and C(−3 , 0). Determine the coordinates of the vertices for the image if the preimage is translated 4 units down. A′(−3, −1), B′(0, 0), C′(−3, −4) A′(−3, 7), B′(0, 8), C′(−3, 4) A′(−7, 3), B′(−4, 4), C′(−7, 0) A′(1, 3), B′(4, 4), C′(1, 0)
Answers
The answer is correct, we can plot both triangles on a Coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.
To determine the coordinates of the vertices of the image of triangle ABC after being translated 4 units down, we need to subtract 4 from the y-coordinates of each vertex. This is because a translation is a type of transformation that moves each point of a figure a certain distance in a certain direction.
So, starting with the preimage of triangle ABC with vertices at A(-3, 3), B(0, 4), and C(-3, 0), we can find the image by subtracting 4 from the y-coordinates:
A'(-3, 3 - 4) = A'(-3, -1)
B'(0, 4 - 4) = B'(0, 0)
C'(-3, 0 - 4) = C'(-3, -4)
Therefore, the coordinates of the vertices for the image after the translation are A'(-3, -1), B'(0, 0), and C'(-3, -4).
So, the correct option is A) A′(−3, −1), B′(0, 0), C′(−3, −4).
To check if the answer is correct, we can plot both triangles on a coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.
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What is the vertex of the equation f(x) = x^2-12x+9
Answers
Answer:
the vertex is (6,-27)
Step-by-step explanation:
Ray QS bisects PQR and mPQR =57°
Find mPQS
Answers
Answer:
The measure of angle ∠PQS is 28.5°
Step-by-step explanation:
If a ray bisects an angle, then it divides it into two equal angles in measures and the measure of each one is half of the measure of this angle.
In our question
∵ Ray QS bisects ∠PQR
→ That means it divides it into two angles PQS and SQR
∴ m∠PQS = m∠SQR = \(\frac{1}{2}\) m∠PQR
∵ m∠PQR = 57°
→ Multiply its measure by \(\frac{1}{2}\) to find the measures its parts
∴ m∠PQS = \(\frac{1}{2}\) × 57°
∴ m∠PQS = 28.5°
∴ The measure of angle ∠PQS = 28.5°
An oil company conducts a geological study that indicates that an exploratory oil well should have a 35% chance of striking oil. What is the probability that the second strike comes on the fourth well drilled? Give answer to four decimal places.
Answers
0.0329
The question is asking about the probability that the second strike comes on the fourth well drilled. Here, the probability of striking oil is 35%. The probability of not striking oil is 65%. The question is asking about a specific combination of strikes, that is, the second strike comes on the fourth well drilled.Here, we can use the binomial distribution, with the following values, n = 4, p = 0.35, q = 0.65, k = 2Probability of exactly 2 successful attempts out of 4 attempts:The formula for binomial probability is:P(k)= (nck)(p^k)(q^(n−k))where n is the number of trials, k is the number of successful outcomes, p is the probability of success, and q is the probability of failure.The formula for finding the binomial coefficient (nCk) is:nCk = (n!)/(k!(n−k)!)where n is the total number of items, and k is the number of items being chosen.Explanation:Here, n = 4, k = 2, p = 0.35 and q = 0.65So, P(k=2) = (nCk)(p^k)(q^(n−k))= (4C2)(0.35^2)(0.65^(4−2))= (6)(0.1225)(0.4225)= 0.0329So, the probability that the second strike comes on the fourth well drilled is 0.0329 (rounded to four decimal places).
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Leah can skate around the park in 8 minutes. How many laps can she skate in 72 minutes?
Answers
Answer:
9 times 8x9=72
Step-by-step explanation:
hope this helps
if you have anymore questions ask me
Answer: 9 laps
Step-by-step explanation:
1. Divide: 72/8 = ?
2. Solve: 72/8=9
what is 654,984 × 548,784,844 × 99,999 ?
Answers
Answer:
3.594417e+19
Step-by-step explanation:
Maria builds a triangle using one stick 8 cm long and another stick 11 cm long. What could be the length of the third stick?
2cm
3cm
7cm
19cm
Answers
Answer:
7 cm
Step-by-step explanation:
I think its 7cm, because it would be very un-even if you we used a smaller or bigger number. I hope I am correct have a good day
Construct validity ensures that the measure includes an adequate and representative set of items. A) True B) False
Answers
Answer:
false
Step-by-step explanation:
The statement "Construct validity ensures that the measure includes an adequate and representative set of items." is true because researchers can determine the extent to which a measure has construct validity and whether it includes an adequate and representative set of items.
Construct validity is established by accumulating evidence through various means. One way to establish construct validity is by examining the content of the measurement tool. This involves carefully selecting items that represent the construct of interest.
In mathematical terms, we can think of construct validity as a process of creating a mathematical model that accurately reflects the construct being measured. This model should include a comprehensive set of items that adequately represent the construct.
In practice, researchers employ statistical techniques such as factor analysis to examine the relationships between the items and the construct.
Construct validity also involves assessing the convergent and discriminant validity of the measure. Convergent validity refers to the degree to which different items measuring the same construct are positively related to each other.
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Lightning storms trigger wildfires that burn up a lot of the plants and grasses in the ecosystem. Trees are mostly spared. what is the cause of this?
GIVING BRAINLIEST
Answers
Answer:
B
Step-by-step explanation:
:)
Tamar's house is greater than 472 and less than 500 which number can be on Tamar's house?
Answers
490
472 <490<500
it fits the criteria
which of the following are always perpendicular to a side of a triangle?
a. altitude
b. perpendicular bisector of a side
c. midsegment
d. angle bisector
e. median
f. an inscribed circle
Answers
Altitude and perpendicular bisector of a side are always perpendicular to a side of a triangle.
How do triangles work?
A triangle is a three-sided polygon with three vertices. The angles of the triangle are formed by the three sides' end-to-end connections at a point.
The triangle's three angles add up to a total of 180 degrees.
In a triangle, what is the altitude?
The perpendicular line drawn from a triangle's vertex to its opposite side is the definition of a triangle's altitude.
The altitude forms a right-angle triangle with the base and is also referred to as the triangle's height.
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what is equivalent to 4d-4?
Answers
Answer:
4 (d-1)
Step-by-step explanation:
hope this helped <3
Graph add and brainliest
Answers
Answer:
i think the answer is d.
Step-by-step explanation:
tell me if this is wrong.
Classify the polynomial by degree and number of terms.
2+3x^3-7x^3+10
Answers
Answer:
−4x^3+12
Step-by-step explanation:
2+3x^3-7x^3+10
simplify this
−4x3+12