X is a normally distributed random variable with a mean of 5 and a standard deviation of 2. the probability that x is greater than 10.52 is
Answers
A suitable calculator can help with this.
Final answer:
The probability that X is greater than 10.52 for a normal distribution with a mean of 5 and a standard deviation of 2 is found by calculating the z-score of 10.52. The z-score is 2.76, and the area to the right under the normal curve represents a very small probability, typically less than 0.003.
Explanation:
To find the probability that X is greater than 10.52, when X is a normally distributed random variable with a mean of 5 and a standard deviation of 2, we first need to calculate the z-score for 10.52. Using the formula:
Z = (X - mean) / standard deviation
Substitute the given values into the formula:
Z = (10.52 - 5) / 2 = 5.52 / 2 = 2.76
This z-score tells us how many standard deviations above the mean our value lies. In this case, X = 10.52 is 2.76 standard deviations above the mean.
The probability of X being greater than 10.52 corresponds to the area under the standard normal distribution curve to the right of the z-score 2.76. Using standard normal distribution tables or software, we can find this probability to be very small, typically less than 0.003.
Related Questions
Which ordered pair is the best estimate for the solution of the system of equations? y=−12x+4y=12x−3 (7, 1) (7, 0) (7, 0.5) (7.5, 0.5)
Answers
[tex](7,0.5)[/tex]
EXPLANATION
We want to solve the system;
[tex]y = - \frac{1}{2} x + 4...(1)[/tex]
and
[tex]y = \frac{1}{2} x - 3...(2)[/tex]
Add equations (1) and (2) to get,
[tex]y + y = 4 + - 3[/tex]
This implies that,
[tex]2y = 1[/tex]
[tex]y = \frac{1}{2} [/tex]
or
[tex]y = 0.5[/tex]
We put y=½ into equation (2) to get,
[tex] \frac{1}{2} = \frac{1}{2} x - 3[/tex]
Multiply through by 2 to get,
[tex]1 = x - 6[/tex]
This implies that,
[tex]x = 1 + 6 = 7[/tex]
Therefore the best estimate for the system of equations is
[tex]
(7,0.5)[/tex]
The correct answer is C
Diana uses 30 grams of coffee beans to make 48 fluid ounces of coffee. How many grams of coffee beans foes Diana uses when company comes?
Answers
The question uses proportional reasoning to determine the quantity of coffee beans Diana would need to make a different volume of coffee. By setting up a ratio based on the original 30 grams for 48 fluid ounces, we can calculate the necessary amount of coffee beans for any new volume of coffee required which is 60 grams.
The question relates to proportion and unit conversion, both key concepts in mathematics, specifically in dealing with ratios and measurements. Diana uses 30 grams of coffee beans to make 48 fluid ounces of coffee. If 'company comes' and she needs to make more or less coffee, the same ratio of coffee beans to water would apply. To determine the amount of coffee beans Diana would need for a different volume of coffee, you would set up a proportion based on the given ratio and solve for the unknown quantity.
To calculate the amount of coffee beans for a new volume, you can use the following steps:
Determine the new volume of coffee in fluid ounces.
Set up a ratio comparing 30 grams of coffee beans to 48 fluid ounces.
Use the new volume in the ratio to solve for the amount of coffee beans required.
For example, if Diana wants to make 96 fluid ounces of coffee for her company, the proportion would be:
30 grams / 48 fluid ounces = X grams / 96 fluid ounces
Solving this gives us X = (30 grams * 96 fluid ounces) / 48 fluid ounces = 60 grams. Hence, Diana would need 60 grams of coffee beans for 96 fluid ounces of coffee.
Evaluate log416 -2 1/2 2
Answers
16 = 4²
So, by the definition of logarithms
[tex]\log_4{16}=2[/tex]
The exponential function represented by the table can be written in the form y=ab^x. Find the values for a and b.
Answers
4 = ab^0
a = 4
The value of a is 4.
We see that when x = 1, y = 2 thus
y = 4b^x
2 = 4(b^1)
b = 1/2
The answers are a = 4 and b = 1/2
The exponential function gotten from the table is given by y = 4(1/2)ˣ
Exponential function
An exponential function is in the form:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multipliers.
From the table, at point (0, 4):
4 = ab⁰a = 4At point (3, 1/2):
y = abˣ1/2 = 4b³b = 1/2The exponential function gotten from the table is given by y = 4(1/2)ˣ
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Q # 8 please solve the question
Answers
Their sum is 20, so we can write
x + y = 20
Their difference is 14, so we can write:
x- y = 14
Adding the two equations, we get:
2x = 34
x = 17
Using the value of x, in first equation, we get:
17 + y = 20
so,
y = 3
Thus the two numbers are 17 and 3.
So, option a is the correct answer
x + y = 20
x-y = 14
Where,
x: real number
y: real number
Solving the system we have:
x = 17
y = 3
Therefore, the numbers are:
17 and 3
Answer:
17 and 3
option 1
2(3y-1)3(y-4)=13 please show step by step
Answers
this is not a question i just need someone to make sure i did #16 right. Thanks;)
Answers
Also, the scale factor would be 144/16 = 9.
so length of pool = 12 inches x 12 feet = 144 inches
144 /16 = 9
so the scale factor would be 1:9
which means the blueprint is 9 times smaller than the real pool
At a college, 4/5 of the students take an English class. Of these students, 5/6 Composition. Which fraction of the students at the college take Composition?
Answers
The fraction of students who take Composition at the college is 2/3.
Explanation:To find the fraction of students who take the Composition class, we need to multiply the fraction of students who take an English class (4/5) by the fraction of English students who take the Composition class (5/6).
Multiplying these fractions, we get (4/5) * (5/6) = 20/30 = 2/3.
Therefore, 2/3 of the students at the college take Composition.
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What is the slope of the line y = 3?
Answers
This is because the equation y = a number represents a straight horizontal line on a graph.
Which of the following sets shows all the numbers from the set {0, 0.5, 1, 2.5, 3} that make the inequality 2a + 3 ≥ 8 true?
{2.5, 3}
{1, 2.5, 3}
{0, 0.5, 1}
{0.5, 1}
Explain how you got your answer
PLEASE AND THANK YOU
Answers
Answer: A
Step-by-step explanation:
A snow storm left 1.25 feet of snow on the ground overnight. At noon today, the temperature will be above freezing and the snow will melt. If the melting snow is modeled by the equation y = -1 3 x + 1.25, how long will it take for the snow to melt away?
Answers
0 = -13x + 1.25
-1.25 = -13x
3.75 = x
then,
3.75 hours to 3 hours 45 minutes
A series contains 18 numbers and has a sum of 4,185. The last number of the series is 275. What is the first number?
Answers
Sn=n/2(a1+an)
where:
n=number of terms
a1=first term
an=nth term
but
n=18, an=275, Sn=4185
plugging the values in the formula we get:
4185=18/2(a1+275)
simplifying this we get:
4185=9(a1+275)
dividing through by 9 we get:
465=a1+275
thus
a1=465-275
a1=190
Answer: first number is 190
Answer:
B on edge 190
Step-by-step explanation:
change -115 degrees to radian measure in terms of pi
Answers
In order to find this, you need to take the degrees [ in this case -115 ] and multiply that by \pi/180. Then simplify that result if possible.
Hope this helps!
Answer:
-23/36 pi
Step-by-step explanation:
(-115 x pi) / 180
If 75 capsules of a drug cost $60, what would 40 capsules of the same drug cost?
Answers
1 capsule = 60 ÷ 75 = $0.80
40 capsules = $0.80 x 40 = $32
Answer: $32
hey can you please help me posted picture of question
Answers
Discriminant = b² - 4ac
b = coefficient of x term = -9
a = coefficient of squared term = 4
c = constant term = 9
So, Discriminant = 81 - 4(4)(9) = -63
Since, the discriminant is negative, the equation will have complex zeros.This means its graph will not cross x-axis at any point.
So, the answer to this question is zero, option B
To test upper h 0 : mu equals 72 versus upper h 1 : mu less than 72, a simple random sample of size nequals20 is obtained from a population that is known to be normally distributed, and the sample standard deviation is found to be 6. complete parts (a) and (b) below.
Answers
what is the best estimate for the total weight of these cold meat 1 7/8 lb of Bologna 1 and 1/2 pounds of ham and 7/8 lb of roast beef
Answers
[tex]\bf \stackrel{mixed}{1\frac{7}{8}}\implies \cfrac{1\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{15}{8}} \\\\\\ \stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}}\\\\ -------------------------------\\\\ \cfrac{15}{8}+\cfrac{3}{2}+\cfrac{7}{8}\quad \stackrel{LCD~8}{\implies }\quad \cfrac{15+12+7}{8}\implies \cfrac{34}{8}\implies \stackrel{simplified}{\cfrac{17}{4}}\implies 4\frac{1}{4}[/tex]
Find (tan A+B) if A and B are in quadrant 2 with tan A=(1/3) and sin B=(20/29)
Answers
The value of [tex]\( \tan(A + B) \)[/tex] in quadrant 2, where [tex]\( \tan A = \frac{1}{3} \)[/tex] and [tex]\( \sin B = \frac{20}{29} \)[/tex], is [tex]\( \frac{11}{57} \)[/tex].
Explanation:To find [tex]\( \tan(A + B) \)[/tex], we can use the formula [tex]\( \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \)[/tex]. Given that \[tex]( \tan A = \frac{1}{3} \)[/tex] and [tex]\( \sin B = \frac{20}{29} \)[/tex], we can determine [tex]\( \cos B \)[/tex] using the fact that [tex]\( \sin^2 B + \cos^2 B = 1 \)[/tex]. Therefore, [tex]\( \cos B = \sqrt{1 - \sin^2 B} = \frac{21}{29} \)[/tex].
Now, substitute the values into the formula for [tex]\( \tan(A + B) \)[/tex]:
[tex]\[ \tan(A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \][/tex]
[tex]\[ = \frac{\frac{1}{3} + \frac{20}{29}}{1 - \frac{1}{3} \cdot \frac{20}{29}} \][/tex]
[tex]\[ = \frac{\frac{29 + 60}{87}}{\frac{87 - 20}{87}} \][/tex]
[tex]\[ = \frac{\frac{89}{87}}{\frac{67}{87}} \][/tex]
[tex]\[ = \frac{89}{67} \][/tex]
Therefore, [tex]\( \tan(A + B) = \frac{11}{57} \)[/tex] in quadrant 2.
To find (tan A+B) when A and B are in quadrant 2, find the components of A and B along the x- and y-axes using A = 34.0 m, θA = 63.0°. Calculate Ax = A cos θA and Ay = A sin θA. Then use the formula tan(A + B) = (tan A + tan B) / (1 - tan A tan B) to find the sum of the tangents.
Explanation:First, we find the components of A and B along the x- and y-axes. From the problem, we know that A = B = 34.0 m, and θB = 63.0°. We find the x-components by using Ax = A cos θ, which gives Ax = 34.0 cos 63.0° = -15.23 m.
Similarly, we find the y-components by using Ay = A sin θ, which gives Ay = 34.0 sin 63.0° = 29.88 m.
Now, we can find the sum of the tangents of A and B using the formula tan(A + B) = (tan A + tan B) / (1 - tan A tan B). Substituting the given values, we have tan(A + B) = (1/3 + Ay/Ax) / (1 - (1/3)(Ay/Ax)).
Regina's mom bought her some bracelets. There were a total of 85 bracelets in 5 packages.
Which of the following equations would describe n, the number of bracelets that were in one package?
A. n + 5 = 85
B. n ÷ 5 = 85
C. n - 5 = 85
D. n × 5 = 85
Answers
It costs $0.05 to send a text message and $0.10 to send a picture on your cell phone. You spend $4 and send five more text messages than pictures. How many text messages, x, and pictures, y, did you send?
Answers
x: text messages
Y: pictures
We write the system of equations:
0.05x + 0.10y = 4
x = y + 5
Solving the system we have:
x = 30
y = 25
Answer:
you send:
30 text messages
25 pictures
This is a problem of system of linear equations. We form two equations from the conditions given in the problem, and solve the system of equations to find the number of text messages and pictures sent.
Explanation:This is a problem of system of linear equations. Here are two conditions mentioned: The total cost and difference of number of text messages and pictures.
Let's denote the number of text messages as x and pictures as y as per your question.
From the cost, we have the equation: $0.05x + $0.10y = $4.
From the difference of the number of sent messages and pictures, we have: x = y + 5.
Now we can substitute x from the second equation into the first one, get the value for y, and calculate the value for x after. Here you have step-by-step solution for your problem.
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Given: triangle ABC, AB = BC Perimeter of ΔABC = 50 Perimeter of ΔABD = 40 Find: BD
Answers
The measure of angle ABC and BDC is 80° and 90° respectively.
What is the triangle?In geometry, a triangle is a closed, two-dimensional shape with three straight sides. A triangle is also a polygon.
Given the ΔABC in which AB ≅ BC, m∠ABD = 40° and BD is the median of ΔABC.
We have to find the measure of angle ∠ABC and ∠BDC.
As the median of the isosceles triangle split the angle at the vertex into two equal parts i.e ∠ABC is twice the angle ∠ABD.
[tex]\rm \angle ABC=2\angle ABD\\\\\angle ABC=2 \times 40\\\\\angle ABC=80[/tex]
Also, the median of an isosceles triangle is perpendicular to the opposite side i.e to the base. Here, BD is perpendicular to AC.
∠BDC=90°
Therefore, the measure of angle ABC and BDC is 80° and 90° respectively.
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What are the zeros of the function?
F (X) = x^3 - x^2 - 6x
A) -1, 0, and 3
B) -3, 0, and 1
C) -3, 0, and 2
D) -2, 0, and 3
Answers
if to re-write the function f(x)=x(x²-x-6), then to make up the equation x(x²-x-6)=0, it is possible to find the zeros requred:
x(x-3)(x+2)=0, x=0;x=-2;x=3.
answer: D -2;0;3
A certain country's postal service currently uses 6-digit zip codes in most areas. how many zip codes are possible if there are no restrictions on the digits used? how many would be possible if the first number could not be 0?
Answers
10×10×10×10×10×10 = 10⁶ = 1,000,000.
For a 6-digit zip code with no restrictions, there would be 1,000,000 possible zip codes. If the first digit could not be a '0', the number of possible zip codes would decrease to 900,000.
Explanation:We're dealing with a counting problem here. This problem involves basic principles of combinatorics.
Firstly, if there are no restrictions on the digits used, each of the six positions in the zip code can hold any digit from 0 to 9. There are 10 choices (from 0 to 9) for each of the 6 digits in the zip code which leads to 10^6 = 1,000,000 possible zip codes.
However, if the first number could not be 0, there are 9 possible choices for the first digit and 10 choices for each of the remaining 5 digits. Therefore, the number of possible zip codes would be 9 * 10^5 = 900,000.
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A display that shows how the values in a data set are distributed
Answers
Answer: Line Plot
Step-by-step explanation: A line plot is a display that shows how the values in a data set are distributed.
Answer: histogram
Step-by-step explanation:
What is 3km 9hm 9dm +7km 7dam
Answers
Good night hope thid helps
let km be the base unit
9 hm = 0.9km
9 dm = 0.0009 km
7 dam = 0.07km
adding all of the values
3 + 0.9 + 0.00009 + 7 + 0.07 = 10.97009
function is a line points (3,2), (5,8), and (8,y) what is y
Answers
[tex](3;\ 2)\to x_1=3;\ y_1=2\\\\(5;\ 8)\to x_2=5;\ y_2=8\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\to m=\dfrac{8-2}{5-3}=\dfrac{6}{2}=3[/tex]
Therefore we have: y = 3x + b.
Put the coordinates of the point (3; 2) to the equation of the line:
[tex]2 = 3\cdot3+b\\2=9+b\ \ \ |-9\\b=-7[/tex]
Therefore we have: y = 3x - 7
Substitute the coordinates of the point (8; y) to the equation of the line:
[tex]y = 3\cdot8-7=24-7=17[/tex]
Answer: y = 17.
Help me please!! I wanna make my mother proud>3
Find the product.
4(−12)(−3)
A) −144
B) −96
C) 144
D) 72
Answers
Hope this helps!
b) recognize that the even number of minus signs will mean the product is positive, and that 4*3 = 12, so this becomes 12² = 144 (math facts you have memorized).
The appropriate choice is ...
C) 144
Coco's garden has 888 tomato plants, 444 pepper plants, 333 squash plants, and 666 pumpkin plants.
For every 777 plants in Coco's garden, there are 2_____ plants.
Answers
Mr. Sanchez bought 2 magazine for 9.95 each and 1 book for 14.95 if the sales tax is 6% what is the total cost of Mr. Sanchez purchases
Answers
2 magazines for 9.95 each and a book for 14.95
9.95 + 9.95 + 14.95 = 34.85
Next you convert the percent to a decimal
6% = 0.06
Now you put a one in the ones place
1.06
Multiply this by the cost of everything
34.85 * 1.06 = 36.94
The answer is $36.94
Hope this helps!
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Find a unit vector that is perpendicular to the vector 5, −4
Answers
[tex]( \frac{4}{ \sqrt{41} } , \frac{5}{ \sqrt{41} } )[/tex]