1) The value of given random variable having mean 20 and variance 25 is (a) 0.1587, (b) 0.0228 and (c) 0.5328.
2) The z-score corresponding to a probability of a) 0.95 is 1.645, b) 0.05 is -1.645 and c) 0.1515 is -1.04.
What about mean?The mean is a measure of central tendency, which represents the average value of a set of numbers. It is calculated by adding up all the values in the set and then dividing by the total number of values.
According to question:1) (a) We can standardize the random variable X using the formula z = (X - μ) / σ, where μ is the mean and σ is the standard deviation. Therefore,
z = (15 - 20) / 5 = -1
Using a standard normal distribution table or calculator, we can find P(Z < -1) = 0.1587.
(b) Similarly, we have
z = (30 - 20) / 5 = 2
Using the standard normal distribution table or calculator, we can find P(Z > 2) = 0.0228.
(c) To find P(18 ≤ X ≤ 25), we can again standardize the random variable:
z1 = (18 - 20) / 5 = -0.4
z2 = (25 - 20) / 5 = 1
Then we can use the standard normal distribution table or calculator to find P(-0.4 ≤ Z ≤ 1) = 0.5328.
2) (a) Since we are given that X is a standard normal random variable, we can use the standard normal distribution table or calculator to find the value of a such that P(X < a) = 0.95. From the table, we find that the z-score corresponding to a probability of 0.95 is 1.645. Therefore,
a = μ + σ * z = 0 + 1 * 1.645 = 1.645
(b) Similarly, we can find the value of b such that P(X ≤ b) = 0.05 using the standard normal distribution table or calculator. From the table, we find that the z-score corresponding to a probability of 0.05 is -1.645. Therefore,
b = μ + σ * z = 0 + 1 * (-1.645) = -1.645
(c) We want to find the value of c such that P(X > c) = 0.8485. Since the normal distribution is symmetric about the mean, we know that P(X > c) = 1 - P(X < c), so we can find the value of c such that P(X < c) = 1 - 0.8485 = 0.1515. From the standard normal distribution table, we find that the z-score corresponding to a probability of 0.1515 is -1.04. Therefore,
c = μ + σ * z = 0 + 1 * (-1.04) = -1.04.
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How many times smaller is 1.2 × 106 than 1.47 × 107?
Answer: It is 1.24x smaller.
Step-by-step explanation:
1.2(106)= 127.2
1.47(107)= 157.3
157.3/127.2 = 1.24x smaller
Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1. 18sin^2(x)cos^2(x)
An equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.
How did we get the value?The power-reducing formulas state that:
sin^2(x) = (1 - cos(2x))/2
cos^2(x) = (1 + cos(2x))/2
Using these formulas, we can rewrite the expression 18sin^2(x)cos^2(x) as:
18sin^2(x)cos^2(x) = 18[(1 - cos(2x))/2][(1 + cos(2x))/2]
Expanding the right-hand side of the equation, we get:
18[(1 - cos^2(2x))/4]
Using the identity cos^2(2x) = (1 + cos(4x))/2, we can simplify further:
18[(1 - (1 + cos(4x))/2)/4] = 9 - 9cos(4x)/8
Therefore, an equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.
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Sarah is borrowing money from a friend. She is paying 5% interest. after 18 months, she paid her friend the principal plus $45. what was the original amount she borrowed?
Consider the following.
f(x) = x^5 − x^3 + 4, −1 ≤ x ≤ 1
(a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.
The function has a local maximum at x = 1 and a local minimum at x = 1/5, as shown in the graph, and the absolute maximum and minimum occur at x = 0 and x = (3/5), respectively.
what is function?Numbers and their variants, equations and related structures, forms and their arrangements, and the places where they might be found are all topics covered in mathematics. The term "function" describes the relationship between a collection of inputs, each of which has a corresponding output.
A function is an association between inputs and outputs that yields one unique outcome for each input. Every function has a domain and a codomain, often known as a scope. Functions are commonly represented with the letter f. (x). As input, an x is used. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four fundamental types of functions available.
To obtain the absolute maximum and lowest values of the function over the interval −1 ≤ x ≤ 1, we must examine the critical points and the interval endpoints.
We first take the derivative of f(x) and set it to zero to determine the critical points:
The function is then assessed at these pivotal points and the interval's endpoints:
As we can see from the information above, f(x) has a maximum value of 4 and occurs at the values x = 0 and x = 1. The absolute minimum value of f(x) is approximately 2.65 for x = (3/5).
We can corroborate these findings by charting the graph of f(x) across the 1 x 1 interval: graph of f(x) = x5 x3 + 4
According to the graph, the function has a local maximum at x = 1 and a local minimum at x = 1/5, but the absolute maximum and lowest are, respectively, x = 0 and x = (3/5).
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Pls help with this homework pls
Answer: 480 in²
Step-by-step explanation:
To calculate the surface area, we will find the area of each side and add it together.
Area of the rectangular sides can be found with A = LW:
A = LW
A = (12 in)(10 in)
A = 120 in²
A = LW
A = (12 in)(10 in)
A = 120 in²
A = LW
A = (12 in)(12 in)
A = 144 in²
All the rectangular sides added together:
120 in² + 120 in² + 144 in² = 384 in²
Now, we will find the triangle sides. The formula for a triangle is [tex]A=\frac{BH}{2}[/tex], but since we have two congruent triangles I will not be dividing by 2.
A = BH
A = (12 in)(8 in)
A = 96 in²
Lastly, I will add them both together:
384 in² + 96 in² = 480 in²
Please help studying for next grade:
192-84÷(71+16)x3
Answer:
189.1034.
Step-by-step explanation:
The result of the expression is approximately 189.1035.
To calculate the expression 192 - 84 ÷ (71 + 16) x 3, follow the order of operations, which is commonly remembered by the acronym PEMDAS:
Parentheses: Perform the operation within the parentheses first.
71 + 16 = 87
Division: Perform the division.
84 ÷ 87 ≈ 0.9655 (rounded to four decimal places)
Multiplication: Perform the multiplication.
0.9655 * 3 ≈ 2.8965 (rounded to four decimal places)
Subtraction: Finally, perform the subtraction.
192 - 2.8965 ≈ 189.1035 (rounded to four decimal places)
The result of the expression is approximately 189.1035.
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Chanasia buys a plastic bucket. The bucket weighs 460 g. The label on the bucket says made with 20% recycled plastic. How many grams of recycled plastic are used to make Chanasia’s bucket?
please help and please show work
92 grams of recycled plastic were used to make Chanasia's bucket
How to calculate the amount of recycled plastic that was used to make Chanasia's bucket?Chanasia buys a plastic bucket
The bucket weighs 460 grams
The label on the bucket says it was made with 20% recycled plastic
The number of grams of recycled plastic that was used to make the bucket can be calculated as follows
= 460/100
= 4.6
= 4.6 × 20
= 92
Hence 92 grams of recycled plastic was used to make the bucket
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A dance instructor ears $75 for teaching 3 classes. The instructor receives a 10% raise. Enter how much the instructor earns, in dollars, per class after the raise.
What is the slope of the line
Answer:
- 2/1
Step-by-step explanation:
if u look at the graph/line it's going up by 2 then across 1
Consider the following random sample of diameter measurements (in inches) of 14 softballs.
4.75, 4.71, 4.78, 4.81, 4.69, 4.89, 4.68, 4.86, 4.84, 4.86, 4.75, 4.72, 4.71, 4.69
Send data to calculator Send data to Excel
If we assume that the diameter measurements are normally distributed, find a 99% confidence interval for
the mean diameter of a softball. Give the lower limit and upper limit of the 99% confidence interval.
Step-by-step explanation:
sadly, we have only 14 data points. that is a very small sample to find a more or less reliable standard deviation for the production of softballs.
because to create the desired answer we need to calculate the mean value and the standard deviation. and we need to mix that with the Z- value of the standard normal distribution table representing the 99% confidence (= coverage of 99% of the area under the normal distribution curve, meaning therefore from 99.5% to 0.5%).
the confidence interval limits are
mean ± Z×sd/sqrt(n)
mean = mean value of the sample.
sd = standard deviation (either of - preferred - the entire population or of the sample)
n = number of data points (here 14).
Z = Z value of the standard normal distributing table for 99% (2.576).
here a little table for different confidence intervals :
Confidence Interval Z
80% 1.282
85% 1.440
90% 1.645
95% 1.960
99% 2.576
99.5% 2.807
99.9% 3.291
mean value = sum of all data points divided by the number of data points :
mean = 66.74/14 = 4.767142857...
sd = sqrt(sum((data point difference to mean)²)/n)
let's use some calculation tool like Excel (after all, the mean value is not a simple number, and to write this all up here takes a lot of space).
sd = 0.069941667...
the confidence interval limits are then
4.767142857... ± 2.576×0.069941667.../sqrt(14) =
= 4.767142857... ± 0.048152387...
upper limit = 4.815295244 ... ≈ 4.82
lower limit = 4.71899047 ... ≈ 4.72
that means, we are 99% sure that the true mean value across all produced softballs is between these 2 limits.
in other words, for 99% of such samples we can pick, their mean values will be between these 2 limits. and 1 % of such samples we expect to have a mean value outside of these 2 limits.
Let uequals
Start 3 By 1 Table 1st Row 1st Column 4 2nd Row 1st Column 20 3rd Row 1st Column 8 EndTable
and Aequals
Start 3 By 2 Table 1st Row 1st Column 5 2nd Column negative 3 2nd Row 1st Column negative 2 2nd Column 6 3rd Row 1st Column 1 2nd Column 1 EndTable
.
Is u in the plane in set of real numbers R
cubed
spanned by the columns of A? Why or why not?
Question content area bottom
Part 1
Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or decimal for each matrix element.)
A.
Yes, multiplying A by the vector enter your response here
writes u as a linear combination of the columns of A.
B.
No, the reduced echelon form of the augmented matrix is enter your response here
,
which is an inconsistent system.
U is located in the plane or vector that A's columns span.
Describe vector?A mathematical concept with both magnitude and direction is a vector. It is frequently used to symbolise forces like the gravitational pull of an object or the electrical forces that exist between charged particles. It can be expressed mathematically as a line segment with two ends, a direction, and a magnitude.
Part 1
To calculate the resulting vector, vector operations including addition, subtraction, multiplication, and division can be used. The individual x, y, and z components of a vector—which stand for its magnitude and direction—can also be determined.
Part 2
Why the answer in Part 1 is correct?
Part 1's answer I gave was A. Yes, writing u as a linear combination of the columns of A after multiplying A by the vector [4, 20, 8]. This is so because the vector [4, 20, 8] may be expressed as a linear combination of the columns of A since it is a solution to the system of linear equations generated by the augmented matrix [A|u]. U is thus in the plane that is covered by the columns of A.
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ASAPPP PLEAse 25 pointss
Show work it's already solved but show work\
`its 2 questions
Volume First Cylinder: 50.24 in³
Volume Second Cylinder: 127.5625 inch³
Volume Third Cylinder: 904.32 inch³
Volume First Cylinder:
= πr²h
= 3.14(2)² (4)
= 3.14 x 16
= 50.24 in³
Volume Second Cylinder:
= πr²h
= 3.14(2.5)² (6.5)
=3.14 (6.25)(6.5)
= 127.5625 inch³
Volume Third Cylinder:
= πr²h
= 3.14(6)² (8)
=3.14 (36)(8)
= 904.32 inch³
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what is 5x-9 and 3x+9
Answer:
5x - 9 and 3x + 9 are two mathematical expressions. The first expression, 5x - 9, represents a value obtained by multiplying 5 by x and then subtracting 9. The second expression, 3x + 9, represents a value obtained by multiplying 3 by x and then adding 9. Both expressions can be simplified further or used in various mathematical operations depending on the context of the problem or equation in which they are being used.
Answer:-45 and -3
Step-by-step explanation:
cylinder radius2 cm height7 cm
13. What is the shape of the bases?
Answer:
88
Step-by-step explanation:
y=2cm h=7cm
CSA=22/7×4×7
the sevens get crossed out and then 22/1 ×4=88.
The probability that the friend is at least 22 minutes late is
The probability that the friend is at least 22 minutes late is 0.266
Uniform density function for a friend = x minutes late
The Friend is at least 21 minutes late
Based on the above information, the probability that the friend is at least 21 minutes late is
= (Total minutes - minimum minutes)/Total minutes
=30-22/30
=8/30
=0.266
Based on the above formula we can easily find out the probability for the friend who is at least 22 minutes late
Hence, the probability that the friend is at least 22 minutes late is 0.266
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help please quick i need these
ANSWER:
368
EXPLANATION:
youre given:
l=14
w=5
h=5
just plug those into the given formula,
2×(14×5)+2×(14×6)+2×(5×6)
(you should do it yourself to check my math...)
The committee spends $462 on costumes for 24 people. Each costume costs the same amount of money.
How much did each costume cost, in dollars?
Answer:
Step-by-step explanation: 462 Divided by 24 = 19.25$
Proof: 19.25 x 24 = 462
Answer: 19.25$
for your land line phone service monthly bill, you pay 3¢ for each minute you use plus a $10 monthly charge. you budget yourself to spend no more than $40 on your phone bill. what is the range of minutes you can use this month?
Answer:
100 Minutes
Step-by-step explanation:
Step 1: Break it down-
3¢ can be expressed as 0.3
Step 2: Add monthly charge-
Since there is a 10$ monthly charge: 40-10=30
Step 3: Subtract-
Now divide: 30 ÷ 0.3
Step 4: Final Answer-
Hence the amount of minutes per month= 100
On July 26, 2005, it rained a record
37 inches in Mumbai, India, in a 24-hour
period. Which equation of direct
variation relates the number of inches
of rain y to the number of hours x?
F. y=24/37x
G.y=37/24x
H.y=24x
J.y=37x
G. y = 37/24x
Direct variation means that the number of inches of rain (y) is directly proportional to the number of hours (x). In this case, 37 inches of rain fell in a 24-hour period. To find the constant of proportionality, divide the total inches of rain by the total hours:
k = 37 inches / 24 hours
Now, we can write the equation of direct variation:
y = kx
Substitute the value of k:
y = (37/24)x
Which step is missing?
OA.
ADCA
ADCA
OC. ADAC
OD. ADAC
B.
ABCA by ASA
ABCA by SAS
ABCA by SAS
ABCA by ASA
The missing step in the two column proof is
Statement Reason
Δ DAC ≅ ΔBCA ASA congruence theorem
What is ASA theorem?The ASA theorem, also known as the angle side angle theorem, is a rule used in geometry to determine whether two triangles are congruent (meaning they have the same shape and size).
The angle side angle theorem states uses the side two parameters which includes:
angle and included sideThe parameters are used for the theorem to say that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
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Select the correct answer. Which expression is equivalent to the given expression? (6n^-5)(3n^-3)^2
The equivalenet expression is 54[tex]n^{-11}[/tex]
What is expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.
What is exponent?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
To simplify the given expression, we need to apply the power of a power rule, which states that to raise a power to another power, we need to multiply the exponents.
Starting with:
([tex]6n^-5[/tex])([tex]3n^-3[/tex])²
We can simplify as follows:
([tex]6n^-5[/tex])([tex]9n^-6[/tex])
Now, we can use the product of powers rule, which states that when multiplying two powers with the same base, we add their exponents.
Therefore:
6 x 9 = 54
[tex]n^-5 * n^-6 = n^-11[/tex]
So the simplified expression is:
[tex]54n^-11[/tex]
Therefore, the expression [tex](6n^-5)(3n^-3)^2[/tex] is equivalent to [tex]54n^-11.[/tex]
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The expression that is equal to (6n-5)(3n-3) option D, 54n11.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
We can use the distributive property of multiplication to expand the expression (6n - 5)(3n - 3) as follows:
(6n - 5)(3n - 3) = 6n(3n) - 6n(3) - 5(3n) + 5(3)
= 18n² - 18n - 15n + 15
= 18n² - 33n + 15
Therefore, the expression that is equivalent to (6n - 5)(3n - 3) is 18n² - 33n + 15, which is option D.
So, the answer is option D, 54n11.
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. According to the National Highway Traffic Safety Administration, seat belt using among American
drivers and front-seat passengers passed 90% for the first time in 2016. At that time, 90.1% of
people used seat belts. If four people are selected at random, find the probability that all four
regularly use seat belts.
The probability that all four people regularly use seat belts is approximately 0.656 or 65.6%.
To find the probability that all four people regularly use seat belts, we need to use the multiplication rule of probability which states that the probability of two or more independent events occurring together is the product of their individual probabilities.
The probability that the first person uses a seat belt is 0.901, and assuming that the events of seat belt use by different people are independent, the probability that the second person also uses a seat belt is 0.901.
The probability that the third person uses a seat belt is also 0.901, and the probability that the fourth person uses a seat belt is also 0.901.
Therefore, the probability that all four people regularly use seat belts is:
P(all four use seat belts) = P(person 1 uses seat belt) x P(person 2 uses seat belt) x P(person 3 uses seat belt) x P(person 4 uses seat belt)
P(all four use seat belts) = 0.901 x 0.901 x 0.901 x 0.901
P(all four use seat belts) = 0.656
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Enter the value for x that makes the equation 3(2x+5)=x-10 true.
Answer:
Step-by-step explanation:
6x + 15 = x - 10
5x + 15 = -10
5x = -25
x = -5
89, 93, 54, 64, 91, 103, 46, 64, 82, 123, 112, 99
1188
median :
mean
mode
range
What should be added to
[tex] \frac{17}{24} [/tex]
get
[tex] \frac{ - 5}{12} [/tex]
Answer:
See the below process
Step-by-step explanation:
let the Unknown value be x.
Now
[tex] \frac{17}{24} + x = \frac{ - 5}{12} [/tex]
[tex]x = \frac{ - 5}{12} - \frac{17}{24}[/tex]
Taking LCM
[tex]x = \frac{ - 10 - 17}{24} [/tex]
[tex]x = \frac{ - 27}{24} \\ = \frac{8}{9} [/tex]
we should add 8/9 to 17/24 to get -5/12
I hope it helped you
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Q1: Use the image to determine the type of transformation shown.
Preimage of polygon ABCD. A second image, polygon A prime B prime C prime D prime to the right of the first image with all points in the same position.
Reflection across the x-axis
90° clockwise rotation
Horizontal translation
Vertical translation
the correct answer is a reflection across the x-axis.
How to solve questions?
Based on the given image, the type of transformation shown is a reflection across the x-axis.
A reflection is a transformation that flips a figure over a line of reflection, in this case, the x-axis. The resulting image is a mirror image of the original figure, with corresponding points on either side of the line of reflection equidistant from it.
In the given image, polygon ABCD is the preimage, and polygon A'B'C'D' is the resulting image. We can see that the two polygons are mirror images of each other across the x-axis. For example, point A in the preimage is reflected across the x-axis to point A' in the resulting image, which is directly below point A. Similarly, point B in the preimage is reflected to point B', point C to C', and point D to D'.
A 90° clockwise rotation would result in a different orientation of the polygon, where point A would move to the position of point B, point B to C, point C to D, and point D to A. A horizontal or vertical translation would result in a shift of the polygon in the respective direction, which is not the case here.
Therefore, the correct answer is a reflection across the x-axis.
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If 31.2 out of every 100 pregnant women in Indiana deliver their babies by C-section, how many pregnant women out of 85,733 would be expected to deliver by C-section?
If 31.2 out of every 100 pregnant women in India deliver their babies by C-section.
First, we need to find the fraction of pregnant women who deliver by C-section
31.2 out of 100 = 31.2/100 = 0.312
Then, we can use this fraction to find the number of pregnant women out of 85,733 who would be expected to deliver by C-section.
0.312 x 85,733 = 26,723.896
Rounding to the nearest whole number, we get
26,724 pregnant women.
26,724 pregnant women out of 85,733 would be expected to deliver by C-section.
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poppy seed muffins 1
cinnamon rolls 3
bran muffins 2
apple fritters 2
croissants 2
Considering this data, how many of the next 20 pastries served should you expect to be bran muffins?
We can expect 4 of the next 20 pastries served to be bran muffins based on the given data.
What is meant by the term data?
Data refers to a collection of facts, statistics, measurements, or observations that are gathered and analyzed to gain insights or information about a particular topic or subject. Data can be both quantitative (numerical) and qualitative (descriptive) in nature, and it can be obtained from various sources, such as surveys, experiments, sensors, or records. The processing and interpretation of data can lead to new discoveries, trends, or predictions in various fields, including science, business, and technology.
According to the given information
The proportion of bran muffins out of the total pastries served can be calculated by dividing the number of bran muffins by the total number of pastries:
The proportion of bran muffins = 2 / (1 + 3 + 2 + 2 + 2) = 2 / 10 = 0.2
This means that 20% of the pastries served are bran muffins. To find out how many of the next 20 pastries served should be expected to be bran muffins, we can multiply 20% by 20:
The number of expected bran muffins = 0.2 * 20 = 4
Therefore, we can expect 4 of the next 20 pastries served to be bran muffins based on the given data.
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Find the surface area of the following figure. Round your final answer to the nearest
tenth.
The surface area is approximately 41.7 square units.
The rectangle has dimensions 18 units by 6 units, so its area is:
A(rectangle) = l x h = 18 x 6 = 108 square units
The semicircle has a radius of 5 units, so its area is half that of a full circle:
A(semicircle)
= 1/2 x π x r²
= 1/2 x π x 5²
= 1/2 x 25π
= 12.5π
To find the total surface area, we need to add the areas of the rectangle and the semicircle. However, since the semicircle is attached to the top of the rectangle, we need to subtract the area of the portion of the circle that overlaps with the rectangle. This overlapping area is equal to the width of the rectangle (18 units) times half the circumference of the circle (1/2 x π x r), or:
A(overlap)
= w x 1/2 x π x r
= 18 x 1/2 x π x 5
= 45π
Therefore, the total surface area is:
Surface area = A(rectangle) + A(semicircle) - A(overlap) = 108 + 12.5π - 45π ≈ 41.7 square units
Rounding to the nearest tenth, the surface area is approximately 41.7 square units.
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Hallar la ecuación de la parábola cuya directriz es la recta x= - 6 y su foco es F(0,0).
The required equation of the parabola is y² = 24x for focus (6,0) and directrix x= -6 .
The focus and directrix of the required parabola are as,
Focus (6, 0)
and, Directrix x = - 6
Since the focus of the parabola lies on the x- axis, the x- axis is said to be the axis of the parabola.
Therefore, the equation of the parabola is either of the form,
y² = 4ax
or, y2 = - 4ax
depending on which axis the parabola is in, that is whether negative or positive axis.
It is also seen that the directrix, x = - 6 which implies it is to the left of the y- axis while the focus is (6, 0) which implies it is to the right of the y-axis.
Hence, the parabola is of the form y² = 4ax.
Since, a = 6
Thus, the equation of the parabola is y² = 4(6)x
⇒ y² = 24x
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