Given that x is a normal variable with mean = 47 and standard deviation = 6.4, find the following probabilities.
(a) P(x ≤ 60) = 0.9356 (b) P(x ≥ 50) = 0.6744 (c) P(50 ≤ x ≤ 60) = 0.2612What are the probabilities?Generally, To solve these problems, we can use the standard normal distribution table or a computer program to find the desired probabilities.
First, we need to standardize the given values of x by subtracting the mean and dividing by the standard deviation. This gives us a standard normal random variable, denoted by Z, with a mean of 0 and a standard deviation of 1.
(a) P(x ≤ 60) = P(Z ≤ (60 - 47)/6.4) = P(Z ≤ 1.5625). From the standard normal distribution table or a computer program, we find that P(Z ≤ 1.5625) = 0.9356.
(b) P(x ≥ 50) = P(Z ≥ (50 - 47)/6.4) = P(Z ≥ 0.46875). From the standard normal distribution table or a computer program, we find that P(Z ≥ 0.46875) = 0.6744.
(c) P(50 ≤ x ≤ 60) = P(0.46875 ≤ Z ≤ 1.5625) = P(Z ≤ 1.5625) - P(Z ≤ 0.46875) = 0.9356 - 0.6744 = 0.2612.
Therefore, the probabilities are as follows:
(a) P(x ≤ 60) = 0.9356 (b) P(x ≥ 50) = 0.6744 (c) P(50 ≤ x ≤ 60) = 0.2612
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If the radio program plays 40 minutes of music, how many minutes will be used for commercials?
The number of minutes that will be used for commercials will be 20 minutes.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
If the radio program plays 40 minutes of music.
Suppose the radio program is of one hour which is 60 minutes. Then the number of minutes will be used for commercials will be given as,
⇒ 60 - 40
⇒ 20 minutes
The number of minutes that will be utilized for plugs will be 20 minutes.
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In triangle ABC, m∠B = (14x − 22)° and the measure of the exterior angle to ∠B is (6x − 18)°. Find m∠B.
After solving the equation, the value obtained for m ∠B will be equal to 132°.
What is an angle?An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol.
Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.
As per the given information in the question,
The inside angle plus the external angle add up to 180°.
So,
m ∠B = (14x − 22)°
14x - 22° + 6x - 18° = 180°
14x + 6x - 22° - 18° = 180°
20x - 40° = 180°
20x = 180° + 40°
20x = 220°
x = 220° / 20
x = 11°
Now, let's find m∠B.
m ∠B = (14x − 22)°
Put x = 11° in above equation,
m ∠B = (14(11) − 22)°
m ∠B = 154° - 22°
m ∠B = 132°.
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Suppose that a steel company views the production of its continuous caster as a continuous income stream with a monthly rate of flow at time t given by
f(t)=12,000e^0.04t (dollars per month).
Find the total income from this caster in the first year. (Round your answer to the nearest dollar.)
The Total Income from this caster in the first year = $184,822 approximately
What is Total Income?
Total income is the sum of all earnings, save those specifically mentioned in Section 12 of this Act, that a person receives during a certain accounting period, before any deductions are taken into account.
Given that : f(t)=12,000e^0.04t (dollars per month)
We could calculate our twelve calculations and evaluate this function once a month, but it would take some time. Instead, we should keep in mind that a continuous function can be represented by an integral. This indicates that we can simplify our calculation by simply taking the integral of this function between 0 and 12.
∫₀¹² 12000e⁰·⁰⁴t dt
Since we will transform this integrand into something for which we have the antiderivative, we may utilise u-substitution to simplify the calculation of this integral.
u=0.04t
du=0.04
dt0.04(0)=0
0.04(12)=0.48
To get the substitute for d u, we must slightly modify our integrand. This can be accomplished by adding 0.04 inside and canceling it outside by its reciprocal. The Fundamental Theorem of Calculus will then be used to calculate this definite integral.
12000 (1/0.04) ∫₀¹² 0.04e⁰·⁰⁴t dt = 30000 ∫₀⁰·⁴⁸ e⁴du
30000[tex]e^{u}[/tex] | ₀ ⁰·⁴⁸
30000(1.61607 -1)
184822.32
Therefore, the total income over the first year is approximately $184,822.
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The length and height of room & 6m and 3m and its volume is 90m cube then find the breadth and cost of carpenting the floor the rate of Rs. 12 per square meter.
The cost of the carpentering of the floor at the rate 12 rupees per square meter is 60 rupees.
What is cuboid?A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.
We have the room as a cuboid.
And its length is 6 meters and height is 3 meters.
The volume of the cuboid = length x height x width
90 = 6 x 3 x width
width = 90 / 18
width = 5 meter.
To find the cost of carpentering the floor, the rate of Rs. 12 per square meter.:
12 x width = 12 x 5 = 60 rupees.
Therefore, at the rate of 12 rupees per square meter, the cost of the carpentering of the floor is 60 rupees.
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Solve for X
HELPPPPPP
The value of [x] is equivalent to 9.72 units.
What is similarity of triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
The triangle similarity criteria are:
AA (Angle-Angle)SSS (Side-Side-Side)SAS (Side-Angle-Side)Given is a triangle as shown in the image.
The smaller triangle and the larger triangle are similar to each other. So, we can write -
3x - 4 = 10x - 72
- 4 + 72 = 10x - 3x
68 = 7x
x = 68/7
x = 9.72 units
Therefore, the value of [x] is equivalent to 9.72 units.
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Help please!!
Diana and Teri have a collection of books.
The number of books in Diana's collection can be represented with x.
Teri has four times as many books as DIana.
The total number of books is 200.
How many books does Diana have?
Answer:
Diana has 40 books in her collection.
Step-by-step explanation:
We can set up the equation 4x + x = 200 to represent the total number of books in the collection, where x is the number of books in Diana's collection and 4x is the number of books in Teri's collection. Solving for x, we get 5x = 200, so x = 40. This means that Diana has 40 books in her collection.
Answer:
Teri has 160 books
Step-by-step explanation:
Janelle works at Heedle's Computer
Outlet. She receives a weekly salary of
$200 plus 3% commission on her sales.
Last week, she sold $29,700 of
computer equipment. How much did
Janelle earn last week?
Using the concept of percentage, she earned a total of $1091 last week
PercentageA percentage is a number or ratio that can be expressed as a fraction of 100. Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
To determine the amount she earned last week, we need to calculate the amount in commission and add it with her weekly salary.
She received 3% commission on her sales and she made a sale of $29700.
Let's find 3% of 29700
3 / 100 = x / 29700
0.03 = x / 29700
x = 29700 * 0.03
x = 891
The amount she earns will be 891 + 200 = 1091
Janelle earned $1091 last week
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Select all the points that are on the graph of the line Y=2x+5
Answer:
Some points that are on this line are:
(-7,-9) (-6,-7) (-5,-5) (-4,-3) (-3,-1) (-2,1) (-1,3) (0,5) (1,7) (2,9)
Convert the hexadecimal expansion of each of these integers to a binary expansion.a) (80E)_{16} b) (135AB)_{16} c) (ABBA)_{16} d) (DEFACED)_{16}
The binary representation of each of these hexadecimal numbers is given as follows:
a) 80E = 100000001110
b) 135AB = 00010011010110101011
c) ABBA = 1010101110111010
d) DEFACED = 1101111011111010110011101101
How to convert from hexadecimal to binary?To convert a number from hexadecimal to binary, each hexadecimal character is converted to it's respective four bit binary code, given as follows:
0 = 00001 = 00012 = 00103 = 00114 = 00105 = 01016 = 01107 = 01118 = 10009 = 1001A = 1010B = 1011C = 1010D = 1101E = 1110F = F111Then, for example:
80E hexadecimal = 100000001110.
As:
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(10 points) Find the height y and length of a side of its base x of a square pyramid with congruent isosceles triangle sides whose volume is cubic meters and whose lateral surface area is as small as possible. (The lateral surface area includes the sides but excludes the base of the pyramid.) Justify that the dimensions you found give minimum lateral surface area.
The minimum lateral surface area of the prism is approximately 1.194 square units.
The given base and height of the prism is y and x respectively.
Hence volume of the prism
V = 1/3 x²y
again 1/3 x²y = 1/6
or, y = 1/2x²
The lateral surface area of the prism is given by :
F = √(4y²+x²)
By the equation 1 we get :
F = x √ (1/x⁴ + x²)
Now we will use differentiation:
[tex]\frac{df}{dx} = \frac{2x^6-1}{x^4(x^2+\frac{1}{x^2} )}[/tex]
Now for the critical points we have to take df/dx = 0
hence solving the equation for x we get :
[tex]x = (\frac{1}{2} )^{\frac{1}{6}}[/tex]
Hence the values of x is [tex](\frac{1}{2} )^{\frac{1}{6}}[/tex] and the value of y will be [tex]\frac{1}{2^\frac{2}{3}}[/tex] units,
And the lateral surface are will be :
F (min ) = √(4y²+x²)
= √ (0.795 + 0.633)
= 1.194 square units
The approximate values of x and y are
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The sum of three numbers is 96. The first number is 6 less than the second. The third number is 4 times the second. What are the numbers?
Step-by-step explanation:
x = second number
first number = x - 6
third number = 4x
x - 6 + x + 4x = 96
6x - 6 = 96
6x = 102
x = 102/6 = 17
first number = x - 6 = 17 - 6 = 11
second number = x = 17
third number = 4x = 4×17 = 68
Solve each of the quadratic equations.
0 = 5x2 - 2x + 6
the triangles are similar solve for x
Answer:
show the whole question
Step-by-step explanation:
DUE IN AN HOUR HELP!!!!
Answer:
D. x=4
Step-by-step explanation:
32. m<1=m<2 ==> angle bisectors divide an angle into two equal angles
m<2=m<RQP
m<1=m<SQP
m<RQP+m<SQP=m<SQR
m<2+m<1=m<SQR
m<2+m<2=m<SQR
(2+7x)+(2+7x)=16x-4
2+7x+2+7x=16x-4
2+2+7x+7x=16x-4
4+14x=16x-4
4-4+14x=16x-4+4
4+4+14x=16x-4+4
14x+8=16x
14x-14x+8=16x-14x
8=2x
x=8/2
x=4 ==> D
Erin has a balance of $1,123.72 in her check register. On her statement, the balance of her account is $879.87.
Not reported on the bank statement are deposits of $62.42, $21, and $61.14. There are outstanding checks in the
amount of $60.24 and $50.24 and an ATM withdrawal of $40. After Erin reconciles her check register with her
statement, what entry does she need to make in her register?
Answer: After reconciling her check register with her statement, Erin needs to make the following entry in her register: $1123.72 - $879.87 + $62.42 + $21 + $61.14 - $60.24 - $50.24 - $40 = $226.23. This is the updated balance in Erin's account after accounting for all the transactions that were not reflected on her bank statement.
Newsweek performed a poll in which 500 American parents were asked the question, “Would you prefer to have your child taught by a male or female for grades K-2?” Only 40% responded that they would prefer to have their child taught by a male in grades K-2. Construct a 95% confidence interval for the poll.
Newsweek performed a poll in which 500 American parents were asked the question, “Would you prefer to have your child taught by a male or female for grades K-2?” 95% confidence interval for the poll is
(38.88%, 41.12%)
What is a confidence interval?Generally, To construct a 95% confidence interval for the poll, we need to first calculate the margin of error. The margin of error for a poll is a measure of the precision of the estimate and is calculated based on the sample size, the level of confidence, and the standard deviation of the population.
In this case, the sample size is 500, the level of confidence is 95%, and the standard deviation of the population is unknown. We can approximate the standard deviation using the sample proportion of 40% as an estimate of the population proportion.
Using these values, the margin of error can be calculated as follows:
Margin of error = z * standard error
Where z is the critical value from the standard normal distribution for the desired level of confidence (in this case, 1.96 for a 95% confidence interval) and the standard error is calculated as:
Standard error = √(p * (1 - p) / n)
Where p is the sample proportion (40% in this case) and n is the sample size (500 in this case).
Substituting these values into the formula for the margin of error, we get:
Margin of error = 1.96 * √(0.4 * (1 - 0.4) / 500)
= 1.96 * sqrt(0.16 / 500)
= 1.96 * √(0.000032)
= 1.6 * 0.005656854
= 0.011168
So the margin of error for this poll is approximately 0.011168 or 1.12%.
To construct the 95% confidence interval, we need to add and subtract the margin of error from the sample proportion. The 95% confidence interval for the poll is, therefore:
40% ± 1.12%
= (38.88%, 41.12%)
This means that we can be 95% confident that the true population proportion of parents who would prefer to have their child taught by a male in grades K-2 lies within the interval between 38.88% and 41.12%.
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Decide which of the two given prices is the better deal. You can buy laundry product in a 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08 .
A) not enough information
B) 24-ounce bottle for $4.08
C) equal value
D) 30-ounce bottle for $6.00
30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.
The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of the logical grammar, such as the operation order.
We are given that there are two conditions for bottles. A 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08. The unit price for each bottle will be: The bottle having the lower price will be:-
30-ounce bottle = $6.00
One ounce bottle = 30 / 6.00 = $5.00
and
24-ounce bottle = $4.08
One ounce bottle = $24/ 4.08 = $5.88
30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.
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Type your answers into the boxes.
What are the next two numbers in this sequence?
45.7
46.2
46.7
47.2
Answer:
Step-by-step explanation:
Well, it seems like you're adding 5 each time so
45.7
46.2
46.7
47.7
48.2
48.7
Becca's dog-walking business started with 1 dog. By the end of the first month , she was walking 2 additional dogs per month . The graph represents the situation . How many dogs was Becca walking by the end of the third month?
The graph shows that Becca walks five dogs at the end of the third month.
How many dogs are there in the third month?
We know that we can be able to read off the graph of an function that has been shown such as the one that we have in the image that has been attached to this answer.
We can see that the graph of the function agrees that Becca's dog-walking business started with 1 dog. By the end of the first month , she was walking 2 additional dogs per month . We would now read off the graph to know the number of dogs that he walks after three months.
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Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students. You may use your calculator to solve.
Confidence interval for the mean score of all students is (91.679, 98.321)
Given:
Sample mean = 95
Standard deviation = 6.6
The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.
We have to construct a 99% confidence interval for the mean score of all the students.
Sample Standard Error =
[tex]\frac{Standard Deviation}{\sqrt{n} } \\= \frac{6.6}{\sqrt{30} }[/tex]
= 1.205
t-value for the 99% confidence interval = 2.756
(use the t-tables for this)
Margin of error = 2.756 x 1.205 = 3.321
If you are asked to report the confidence interval, you should include the upper and lower bounds of the confidence interval.
So, for the 99% confidence interval:
(95 - 3.321, 95 + 3.321) = (91.679, 98.321)
This is the final confidence interval.
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Use a proof by contraposition to prove that if m and n are integers and mn is even, then m is even or n is even.
In order for mn to be even, m must be even or n must be an even number.
What is Contraposition ?The relationship between two propositions when the subject and predicate of one are respectively the negation of the predicate and the negation of the subject of the other.
Suppose that the statement “m is even or n is even” is not true. Then both m and n are supposed to be odd. Let’s see if the product of two odd numbers is an even or an odd number:
Let n and m be equal to 2a +1 and 2b + 1 respectively, then their product is:
(2a +1) (2b + 1) = 4ab + 2a + 2b + 1
= 2(2ab +a + b) + 1
This shows that the expression 2(2ab +a + b) + 1 is of the form 2n +1, thus the product is odd. If the product of odd numbers is odd, then mn is not true to be even. Therefore, in order for mn to be even, m must be even or n must be an even number.
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A manufacturer cuts a piece of metal for a microscope. The resulting piece of metal can be
represented in a coordinate plane by a triangle with vertices A(0, 0), B(3, 8), and C(6,0).
One unit in the coordinate plane represents one millimeter.
Prove that AABC is isosceles.
The triangle ABC is an isosceles triangle because AB = BC = √73
How to prove that the triangle is an isosceles triangle?From the question, we have the following parameters that can be used in our computation:
A(0, 0), B(3, 8), and C(6,0).
An isosceles triangle is any triangle that has two of its sides to be equal
So, we start by calculating the lengths of the sides using the distance equation represented as follows
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substitute the known values in the above equation, so, we have the following representation
AB = √[(0 - 3)² + (0 - 8)²]
AB = √73
AC = √[(0 - 6)² + (0 - 0)²]
AC = 6
BC = √[(3 - 6)² + (8 - 0)²]
BC = √73
Because AB = BC = √73, then the triangle is an isosceles triangle
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Write an equivalent fraction to 5/8 with a denominator of 40
Step-by-step explanation:
So you have 5/8 and you want the equivalent fraction to have a denominator of 40. You put 5/8=X/40 and find for x.
First, multiply both sides by 40
5/8*40=x
Express 5/8 * 40 as a single fraction.
5*40/8=x
Multiply 5 40 to get 200.
200/8=x
Divide 200 by 8 to get 25.
25=x
Swap sides so that all variable terms are on the left-hand side.
x=25
What is the root of the polynomial equation x(x-2)(x+3)= 18? Use a graphing calculator and a system of equations.
-3
0
2
3
Answer:
3
Step-by-step explanation:
on edge
Answer:
x = 3
Step-by-step explanation:
You want the root of the polynomial equation x(x -2)(x +3) = 18.
GraphA graph of the equation in the form x(x -2)(x +3) -18 = 0 is attached. The solution is the x-intercept. It shows the only real root is x = 3.
System of equationsThere are many ways the polynomial can give rise to a system of equations. The basic idea is to write two expressions that are supposed to be equal to each other. The graphing calculator can show the value(s) of x that make them equal.
Dividing both sides of the given polynomial by (x -2)(x +3) gives the equation ...
x = 18/((x -2)(x +3))
This can be graphed as two equations:
y = x
y = 18/((x -2)(x +3))
This is shown in the second attachment. It tells us the root is x=3. (Both sides of the "x=" equation have the value 3 at x=3.)
__
Additional comment
Here, you are asked to use a system of equations. A graphing calculator can usually find the solution more easily when the equation is written in the form f(x) = 0. Often x-intercepts are easier to identify than points where graphs cross each other.
consider the value of t such that 0.05 of the area under the curve is to the right of t. step 2 of 2: assuming the degrees of freedom equals 18, select the t value from the t table.
Thus after assuming the degrees of freedom equals 18 so the t-critical value will be =2.306
Degree of freedom {df}=18
We have to calculate the t-value such that 0.05 of the area under the curve is to the right of t
It means that, [tex]$\mathrm{P}(\mathrm{T} > \mathrm{t})=0.05$[/tex]
As we know, t distribution provides the cumulative probability
As the value of the total area under the t distribution will 1
So, we can write it as:
[tex]$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-\mathrm{P}(\mathrm{T} > \mathrm{t})$$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-0.05$$=0.95$[/tex]
Now, using excel, we can easily calculate the t-critical value as follows
=T. INV ( Probability, DF)
Where Probability is the area and DF is the degree of freedom,
Now we will enter these values in excel:
=T. INV (0.95,18)
t-critical value can also be found using t table
Look up for df = 18, in very first column
Now look up for 0.05 in one tail row
Now intersect both of them to get the t-critical value
We will get it as: 2.306
So t-critical value will be =2.306
[tex]$\mathrm{P}(\mathrm{T} > 2.306)=0.05$[/tex]
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Haylee selects 10 small businesses at random from her state's directory. Let BBBB be the number of businesses she selects that have websites What type of variable is B? Binomial Geometric Neither
From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.
What is binomial variable ?The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probabilitq=1-pq=1-p).
This distribution is used in probability theory and statistics.
A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results. For a single trial, or n = 1, the binomial distribution is a Bernoulli distribution.
The popular binomial test of statistical significance is based on the binomial distribution.
A sample of size n drawn with replacement from is widely used to model the number of successes using the binomial distribution.
Hence, From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.
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Choose ALL solutions of the following system of linear inequalities listed below.
A (0, -1)
B (6, 2)
C (9, 9)
D (8, 2)
E (-2, 4)
F (2, 6)
All solutions of the following system of linear inequalities are given-
B (6, 2), C (9, 9), D (8, 2)
Explain the term linear inequalities?Mathematical expressions known as linear inequalities compare two expressions using the inequality sign. The expression may be either a numerical or an algebraic expression, or it may be both.The linear inequality x - 5 > 3x - 10 is an illustration. Due to the greater than symbol being utilized in this inequality, the LHS is clearly greater than the RHS.For the stated question,
The solution for the blue line given in graph will be the region under the line including the values on the line.Similarly, the solution for the red line given in graph will be the region above the line excluding the values on the line.Thus, the total solution becomes, the common shaded region of containing both lines.Therefore, the solutions of the following system of linear inequalities are-
B (6, 2), C (9, 9), D (8, 2).
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Lines DE and AB intersect at point C.
What is the value of x?
A.12
B.25
C.38
D.05
Answer:
B
Step-by-step explanation:
2x + 2 + 5x + 3 = 180
7x + 5 = 180
7x = 180 - 5
7x = 175
x = 175/7
x = 25°
k x 20 = 1.07 what is k
which of the following number lines shows the solution to the inequality given below? 4x + 7 _< -37 or 5x + 3 > -7
The graph of the compound inequality can be seen in the image at the end.
Which number line shows the solution set for the inequality?
Here we have a compound inequality which is:
4x + 7 ≤ -37
5x + 3 > -7
First we need to isolate x in both of these inequalities, on the first one we will get:
4x + 7 ≤ -37
4x ≤ -37 - 7
4x≤ -44
x ≤ -44/4
x ≤ -11
The other inequality gives:
5x + 3 > -7
5x > -7 - 3
5x > -10
x > -10/5
x > -2
So the compound inequality is:
x > -2
x ≤ -11
To graph this we need to have a open circle at x = -2, and we need to graph a line to the right. And a closed circle at x = -11 and a line that goes to the left.
The number line is below
Learn more about inequalities:
https://brainly.com/question/24372553
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