The probability that the sample mean will be less than 318 is 0.0011.
Mean is defined as the average of given numbers i.e. sum of all numbers divided by the total number of numbers. The Mean is denoted as m or μ. Standard deviation is the measure which it shows the variation from the mean exists or not. The standard deviation is denoted as σ.
We know that,
P ( x < n ) = P ( z < x - μ / ( σ / √n ) ) → 1
where, z = x - μ / ( σ / √n )
As per the given question,
The average life of the electric bulbs i.e. mean ( μ ) = 330 hoursThe standard deviation of the bulbs ( σ ) = 35A random of 80 bulbs are tested i.e. n = 80The probability of the sample mean is less than 318 i.e.P ( x < 318 ) = ?
Substitute the values in 1,
P ( x < 318 ) = P ( z < x - μ / ( σ / √n ) )
= P ( z < 318 - 330 / ( 35 / √80 )
= P ( z < -12 / ( 35 / 8.94 )
= P ( z < -12 / 3.91 )
= P ( z < -3.069 )
= P ( z < -3.07 )
P ( x < 318 ) = 0.0011
Therefore, 0.0011 is the probability that the sample mean will be less than 318. Hence Option a is correct.
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The complete question is
A certain brand of electric bulbs has an average life of 330 hours with a standard deviation of 35. A random sample of 80 bulbs is tested. What is the probability that the sample mean will be less than 318?
a.) 0.0011
b.) 0.9989
c.) 0.0006
d.) 0.0127
hi :)
1. Define term
2. Define binomial
3. Define variable
A term denotes a mathematical object while a formula denotes a mathematical fact
A binomial is a polynomial that is the sum of two terms, each of which is a monomial.
A variable is a symbol and placeholder for any mathematical object.
How to define the terms?A single mathematical expression is referred to as a term. It could be a single number (positive or negative), a single variable (a letter), or a combination of variables multiplied but never added or subtracted. Variables with a number in front of them are used in some terms. A coefficient is the number that appears in front of a term.
A variable in mathematics is a symbol and placeholder for any mathematical object. A variable could also specifically represent a number, a vector, a matrix, a function, a function's argument, a set, or an element of a set.
A binomial is a polynomial in algebra that is the sum of two terms, each of which is a monomial. After monomials, it is the most basic type of sparse polynomial.
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What is the slope of a line perpendicular to the line whose equation is
3x+18y=-486
The required slope of a line perpendicular to the line is -1/6.
What is the slope?The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.
The slope of a line can be used to gauge how steep it is.
The slope is theoretically determined as "rise over run" (change in y divided by change in x).
So, we have the equation:
3x+18y=-486
Now, get the slope as follows:
3x+18y=-486
18y = -3x - 486
Tale 18 common:
y = -1/6x - 60.75
Therefore, the required slope of a line perpendicular to the line is -1/6.
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in regression analysis, the response variable is the . a. dependent variable b. intercept c. slope of the regression function d. independent variable
By using regression, it can be calculated that-
The response variable is a dependent variable
Option a is correct
What is regression?
The process which is used to find a relationship between a dependent variable and one or more independent variables is called regression
In regression analysis, the variable which is to be predicted is called response variable.
Since response variable is the variable to be predicted, response variable is dependent on other variables
So response variable is a dependent variable
Option a is correct
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in addition to measuring the group of participants who joined a fraternity/sorority, dr. ba decides to give the same measure to another group of 55 participants who decided to not join a fraternity/sorority. this type of design is known as a(n)
This type of design is termed as Non-Equivalent Control Group Design
What is Experimental Mathematics?
The study of mathematical objects through computation in order to discover their properties and patterns is known as experimental mathematics. According to one definition, it is "that branch of mathematics that ultimately deals with the codification as well as transmission of insights inside the mathematical community by means of experimental (in the Galilean, Baconian, Aristotelian, as well as Kantian feeling) exploration of conjectures and much more informal beliefs as well as a careful analysis of the information acquired in this pursuit." "Mathematics is not really a deductive science—a that's cliché," said Paul Halmos. You wouldn't just list this same hypotheses and begin to reason when attempting to prove a theorem. You work through error, trial and error, experimenting, and conjecture.
Solution:
This type of design is termed as Non-Equivalent Control Group Design
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Five times a number, x, is not less than 15. Write and solve the inequality.
Answer:
[tex]5x \geq 15\\x\geq 3[/tex]
Step-by-step explanation:
5 times x must be greater than or equal to 15, thus the inequality is
[tex]5x \geq 15[/tex]
To solve, pretend the [tex]\geq \\[/tex] is an = and solve, putting back the [tex]\geq[/tex] for the final answer
[tex]5x \geq 15\\5x = 15\\5x/5 = 15/5\\x = 3 \\x \geq 3[/tex]
20 points yahhhhhhhh
Determine the area of the figure below
The area of the figure above is
blank + 25pi/4
The area of the figure is 75 + 25π/4 squared unit. The value of the blank is 75
How to find the area of the figure?(Consider the image I attached)
The area of the figure = Area of rectangle A + Area of square B + Area of sector C
The area of the figure = (L×W) + (L²) + (θ/360 × πr²)
Note: Area of sector = θ/360 × πr². The sector has an angle of 90° and a radius of 5
The area of the figure = (10×5) + (5²) + (90/360 × π×5²)
The area of the figure = 50 + 25 + 25π/4 = 75 + 25π/4 squared unit
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The solution of which of the following equations is neither a fraction nor an integer?
A.2x+6=0
B.3x-5=0
C.5x-8=x-4
D.4x+7=x+2
The solution of which of the following equations is neither a fraction nor an integer
C. 5x-8=x-4
An assignment of values to the unknown variables that establishes the equality in the equation is a solution. In other terms, a solution is a value or set of values (one for each unknown) that, when used in place of the unknowns, transform the equation into an equality.
5x-8=x-4
4x=-12
x=-3
hence the integer is -3.
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Three friends go grocery shopping together and buy apples.Login buys 4 pounds (lb) and pays $7:00.Lin buys 6 lb and pays $10.50. Chita buys 2 lb and pays 3:50
Identify the graph and unit price that represent the cost of apples
The unit cost of all kinds of apples is $1.75 per apple thus it will be a linear function and the slope will be the same.
What is a linear function?A linear function can be used to depict a straight line on the coordinate plane.
A linear function has the formula f(x) = ax + b, where a and b are real numbers.
As per the given,
Login buys 4 pounds (lb) and pays $7:00.Lin buys 6 lb and pays $10.50. Chita buys 2 lb and pays 3:50.
Unit cost = $7/4 = $1.75 per apple
Unit cost = $10.5/6 = $1.75 per apple
Unit cost = $3.50/2 = $1.75 per apple
Since the unit cost is the same and the unit cost represents the slope thus the graph will be a linear line as given below.
Hence "Since all varieties of apples cost $1.75 each, the function will be linear and have the same slope.".
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Sarah has $12000 to invest and decides to invest it in a
mutual fund that has averaged a compound rate of return of
15.2% for each of the last 6 years. How many years will
it take for her money to grow to $600 000 if this fund
continues to average 15.2% during the time invest? Round
off your answer to the nearest year.
O 15
0 28
0 45
0 43
Answer:
Step-by-step explanation:
Evaluate 1/4 + 1/24 when n= 1/6
Answer: it equals 7/24 for 1/4 + 1/24 but where is n in the equation? if u tell me i can give the answer again
Step-by-step explanation:
i need your help guys
Answer:
i got 6.6, 2.9, and 50 but i don't think it's right
Step-by-step explanation:
D
Statement
E
C is the midpoint of
AD and
overline EB
EC BC
DC AC
ZECDLBCA
ΔΕCD`Δ BCA
BD BA
Reason
U
Given
A
B
If E is between D and F, then DE = DF - EF.
If BD divides ABC into two angles, ABD and DBC, then mABC = mABC mDBC.
1. Given: E is between D and F
Prove: DE = DF - EF.
Since ,E is between D and F Given
D, E, and F are collinear points, and E is on ¯DF Definition of between
Statements Reasons
DE + EF = DF Segment Addition Postulate DE = DF EF Subtraction property of equality2.If BD divides ABC into two angles, ABD and DBC, then mABC = mABC - mDBC.
Given: BD divides ABC into two angles, ABD and DBC
Prove: mABD = mABC - mDBC.
Statements Reasons
mABD + mDBC = mABC Angle Addition Postulate mABD = mABC - mDBC Subtraction property of equalityLearn more about Geometry at:
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a group of scientists discovered a small creature at the bottom of the ocean that they called a "piknit". when this interesting creature dies, it explodes itself into a number of baby piknits called gogles. the scientists randomly selected 20 piknits from the sea-floor and measured their respective weights in grams. after the piknits died they counted the number of gogles that each piknit produced. they wanted to know if the weight of the piknits can be used to predict the number of gogles.
The required explanation of null hypothesis and alternate hypothesis for given question is below.
What is hypothesis test?Hypothesis testing is a type of measurable derivation that utilizes information from an example to make inferences about a populace boundary or a populace likelihood circulation. Initial, a speculative supposition that is made about the boundary or dissemination.
According to question:Connection is a factual measure that communicates the degree to which two factors are directly related (meaning they change together at a consistent rate).
It's a typical device for portraying basic connections without saying something about circumstances and logical results.
As indicated by the inquiry,
A gathering of researcher haphazardly chose 20 Piknits from the ocean bottom and estimated their particular loads in grams.
Likewise, They were curious as to whether the weight of the Piknits can be utilized to foresee the quantity of Gogles.
From the given data,
Null hypothesis : H0 : There is no direct connection between the heaviness of piknits and the quantity of gogles
Alternative hypothesis : Ha: There is a direct connection between the heaviness of piknits and the quantity of gogles
Choice 4 is right about Null hypothesis and Alternative hypothesis.
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what shape is the cross section of a triangular pyramid sliced by a plane that is perpendicular to its base?
The shape of the cross section of a triangular pyramid sliced by a plane that is perpendicular to its base is triangle.
What is meant by cross section?The non-empty intersection of a solid body in three dimensions with a plane, or its equivalent in higher dimensions, is referred to as a cross section in geometry and science. Many parallel cross-sections are produced when an object is sliced. The boundary of a cross-section in three dimensions that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line.
A triangle-shaped pyramid essentially has a triangle-shaped base. The cross section formed when an imaginary line is produced to cut through perpendicular to the base will still have a triangular orientation, but it will be smaller than it was when the pyramid's original triangular orientation or sides were there.
Therefore, the shape of the cross section of a triangular pyramid sliced by a plane that is perpendicular to its base is triangle.
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What are the 4 types of slope lines?
The four types of slope lines are positive, negative, zero and undefined.
Slope is the term that measure the extent of steepness of any figure or any curve. If we want to find the equation of the line, then the slope is the most useful term. The general formula for determining the slope between two points (x₁, y₁) and (x₂, y₂) is expressed as
m = (y₂ - y₁)/(x₂ - x₁) where m is the slope .
There are generally four types of slope.
If the value of both the numerator and denominator are positive or negative, then the slope is said to be positive means line goes upward.If the value of either the numerator or denominator is negative, then the slope is said to be negative means line goes downward.If the value of the numerator is zero, then slope is said to be zero means line is parallel to x-axis.If the value of the denominator is zero, then the slope is said to be undefined means line is parallel to y-axis.Learn more about Slope at:
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What is the vertex of â XYZ â XYZ?
The measure of the vertex X in the given triangle XYZ is 90° .
In the question ,
it is given that ,
that there is a triangle XYZ ,
and the measure of vertex Y is 45° and vertex Z is 45° ,
By Applying the Angle Sum Property of triangle ,
measure of angle X + angle Y + angle Z = 180°
So , X + 45° + 45° = 180
Adding the terms ,
X + 90° = 180°
Subtracting 90° from both sides of the equation ,
we get,
X = 180° - 90°
X = 90°
Therefore , the measure of the vertex X is 90° , so the triangle XYZ is a right triangle .
The given question is incomplete , the complete question is
What is the measure of the vertex X of the triangle XYZ which have ∠Y = 45° and ∠Z = 45° ?
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The tangent of O in this triangle is Which equation must be true?
The correct answer is option D, which states tan∝ = 1/2
What is Trigonometry
The field of mathematics concerned with the relationships between triangle sides and angles, as well as the pertinent functions of any angles is Trigonometry.
Solution:
we are given that tanθ = 1/2
this implies θ = 45°
We know that the sum of all interior angle of triangle is 180°
so, it can be calculated that the value of
angle ∝ = 45°
Therefore, tan∝ = 1/2
The correct answer is option D, which states tan∝ = 1/2
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What is the curve which passes through the point 1 1 and whose slope is?
The curve that passes through the point (1,1) with a given slope is a line.
1. The equation of a line can be determined using the point-slope form of the equation, which is y - y1 = m(x - x1).
2. For the given point (1,1) and slope, the equation of the line is y - 1 = m(x - 1).
3. Substituting the given slope m for the equation, we get y - 1 = m(x - 1).
4. Simplifying the equation, we get y = mx - m + 1.
5. The equation of the line can also be written in the general form of the equation of a line, which is y = mx + b.
6. Substituting the given slope m and the y-intercept b = -m + 1, the equation of the line can be written as y = mx - m + 1.
7. The slope of the line can be determined by calculating the rise (change in y-coordinate) over the run (change in x-coordinate).
8. For the given point (1,1) and another point (x2, y2), the slope can be calculated using the formula m = (y2 - y1)/(x2 - x1).
9. For example, if the second point has coordinates (3, 4), the slope of the line can be calculated as m = (4 - 1)/(3 - 1) = 3/2.
10. The equation of the line can then be determined using the point-slope form of the equation, which is y - y1 = m(x
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6840 precent of 38000
Answer:
x=2599200
Step-by-step explanation:
38000/x=100/6840
(38000/x)*x=(100/6840)*x - we multiply both sides of the equation by x
38000=0.014619883040936*x - we divide both sides of the equation by (0.014619883040936) to get x
38000/0.014619883040936=x
Formula: A = P (1 + ht
Solve the problem by answering the following questions:
An initial investment of $5575 is appreciated for 12 years in an account that earns 3.25%
interest, compounded semiannually. Find the amount of money in the account at the end
of the period.
i. What does each of these variables represent:
A:
P:
r:
n:
t: 12
ii. List all the known and the unknown for the problem.
iii. Use the given formula and show your work in finding the unknown.
iv. Briefly, explain what your finding means.
The amount of investment after compound interest will be $8183.24.
What is compound interest?Compound interest is the addition of interest to the principal sum of a loan or deposit or interest on interest plus interest.
In finance and economics, interest is the payment of an amount above the repayment of the principal sum by a borrower or deposit-taking financial institution to a lender or depositor at a specific rate by a borrower or depositor. It differs from a fee that the borrower may pay to the lender or a third party.
The formula calculates compound interest is calculated by the formula,
[tex]A=P(1+\dfrac{r}{100})^{nt}[/tex]
Here,
A = Amount
P = Principle amount
r = rate of interest
n= Number of times amount compounded
t = time
The compounded amount will be calculated as,
A = 5575 ( 1 + 0.0325 )¹²
A = 5575 x 1.4678
A = $8183.24
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suppose that in a random sample of size 100, the standard deviation of the sampling distribution of the sample proportion is 0.08. if a researcher wanted to reduce the standard deviation to 0.04, what sample size would be required?
The sample size would be required is 400.
What is standard deviation?
A measure of a group of values' variance or dispersion in statistics is called the standard deviation. When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.
The lowercase Greek letter sigma, which stands for the population standard deviation, or the Latin letter s, which stands for the sample standard deviation, are most frequently used in mathematical equations and texts to represent standard deviation. Standard deviation is also sometimes referred to as SD.
suppose that in a random sample of size 100, the standard deviation of the sampling distribution of the sample proportion is 0.08.
Since we know the weights from the population, we can find the population mean.
μ = 0.08
if a researcher wanted to reduce the standard deviation to 0.04.
Hence, The sample size would be required is 400.
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productivity is defined by the formula of outputs divided by ______ for a specified period of time.
Productivity is referred as the formula for the outputs divided by inputs in a given specified period of time.
All created products and services are considered as outputs. Along with labor, inputs also include capital, supplies, and energy. A common definition of productivity is the ratio of input volume to output volume. In other words, it assesses how effectively an economy uses labor and capital as production inputs to create a particular amount of output.
The simplest productivity calculation yields a straightforward ratio: Total output divided by total input is productivity. By dividing total output by total input, the labor productivity equation can be used to calculate employee productivity. Let's say your business spent 1,500 labor hours to produce $80,000 worth of goods or services (input). To determine the labor productivity of your business, divide 80,000 by 1,500, which results in the number 53.
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What is AAS ASA SSS SAS?
The rules AAS, ASA, SSS and SAS are congruence rule of triangle and the each rules has been explained
The rules AAS, ASA, SSS and SAS are congruence rule of triangle
SSS rule is side-side-side rule, it states that if three sides of the one triangle and three sides of the other triangles are equal, then both triangles are congruent
SAS rule is side-angle-side rule, it states that if two sides and one included angles between the sides of the one triangle is equal to the two sides and one included angles between the sides of the other triangle, then both triangles are congruent
ASA rule is angle-side-angle rule, it states that if two angles and one included side between the angle of the one triangle is equal to the two angles and one included sides between the angles of the other triangle, then both triangles are congruent
AAS rules is angle-angle-side rule, it states that if two angles and one non included sides of the one triangle is equal to the two angles and one non included sides of the another triangle, then both triangles are congruent
Therefore, the AAS, ASA, SSS and SAS are the rules of congruence of the triangle
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identify the statistical test in which the mean difference between two groups are compared to a distribution of differences between means.
The statistical test in which the mean difference between two groups is compared to a distribution of differences between means is known as the t-test.
What statistical test to use when comparing more than two groups?The one-way analysis of variance (ANOVA) is the suitable procedure in place of the t-test for a comparison of more than two group means. The ANOVA is interested in the locations of the distributions indicated by means as well since it has the same underlying assumptions as the t-test.
What is the difference between ANOVA and a t-test?ANOVA is used to compare the means among three or more groups, while the Student's t-test is used to compare the means between two groups. First receives a shared P value in an ANOVA. The ANOVA test results with a significant P value for at least one pair where the mean difference was statistically significant.
From the above theory, the test specified above is termed as the t-test.
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Between sing-sing and tarrytown i met my worthy friend, John Brown, and seven daughters , riding nags, and everyone had seven bags. In every bag there were thirty cats, and every cat had forty rats. besides a brood of fifty kittens, all but the nags ad bags wore mittens. mitten, kittens-cats, rats-bags, nags-Browns. How many were met between the towns
The number met between the town are
mitten = 67,137
kittens = 50
cats = 1680
rats = 67,200
bags = 56
nags = 7
Browns = 8
How to find the numbersFrom the given information it can be deduced that
John Brown, and seven daughters
Browns = 1 + 7 = 8
everyone had seven bags
number of bags = 8 * 7 = 56 bags
In every bag there were thirty cats
number of cats = 56 * 30 = 1680 cats
the number of kittens = 50
every cat had forty rats
number of rats = 1680 * 40 = 67,200 rats
all but the nags and bags wore mittens.
number of mittens = 67 200 - the nags (Brown's daughters) - the bags
number of mittens = 67 200 - 7 - 56 = 67 137
The number of mittens is 67,137
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How do I simplify the expression
The value of the equation A = n³ ( 2n )⁻² is given by A = ( n / 4 )
What are the laws of exponents?
When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the equation be represented as A
Now , the value of A is
A = n³ ( 2n )⁻²
On simplifying the equation using the laws of exponents , we get
The value of A = n³ / ( 2n )²
Taking the powers to the value of 2n , we get
The value of A = n³ / 4n²
On dividing the numerator and denominator by n² , we get
The value of A = n / 4
Therefore , the value of A = n / 4
Hence , The value of the equation A = n³ ( 2n )⁻² is given by A = ( n / 4 )
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Deepa needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4. 25 hours and charged her $167 for parts. The total was $655. 75. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.
The cost of the labor per hour is 115 hours.
The equation is going to be:
4.25x + 167 = 655.75
your x is going to be:115
The duration was 4.25 hours.
The parts cost 167.
Cost in full: 655.75
so the price per hour is x.
As a result, when you write your equation, the total number of hours (multiplied by the cost per hour) will be added to the cost of the parts, and the sum of these two amounts will be your total cost.
In order to solve the problem, you must deduct the cost of each component from the total cost. This should give you the following result: 4.25x = 488.75
After that, divide 4.25 by each side as you normally would.
The cost of labor per hour follows. 115
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Which of the following options have the same value as 40\%40%40, percent of 848484?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
40\cdot 8440⋅8440, dot, 84
(Choice B)
B
0.4\div 840.4÷840, point, 4, divided by, 84
(Choice C)
C
\dfrac{40}{100}\cdot 84
100
40
⋅84start fraction, 40, divided by, 100, end fraction, dot, 84
(Choice D)
D
84 \div 4084÷4084, divided by, 40
(Choice E)
E
0.4\cdot 840.4⋅840, point, 4, dot, 84
On calculating, the 40% of 84 is found to be 33.6.
What is an expression? What is a expression? What is a mathematical equation? A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.Given is that to find the 40% of 84.
Assume that the 40% of 84 is equivalent to [x]. Then, we can write -
x = (40/100) x 84
x = 4/10 x 84
x = 8.4 x 4
x = 33.6
Therefore, on calculation, the 40% of 84 is equivalent to 33.6.
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as he walked along the beach, johnny counted seashells and starfish that washed up in the sand. johnny counted 9 seashells. that is 3 more than the number of starfish he counted. which equation can you use to find how many starfish johnny counted?
Answer:
There’s 3 starfish and 9 seashells.
Step-by-step explanation:
3 x _ = 9
9 / 3 = 3
3 starfish