The manufacturer needs to adjust the equipment to meet the standard with the margin of error of 2.34.
Define the term margin of error?The calculated number known as the margin of error is added to and removed from the mean value to get the resulting confidence interval. The confidence interval expands as the margin of error does.
Alpha value = 0.05Standard deviation = 5Sample size = 20Sample average = 246Calculate the 95% confidence interval's margin of error based on the aforementioned data.
α = 0.05
n = 20
s = 5
The following is the formula to determine the margin of error:
E = T(n-1) ×s/√n
The t-distribution table is used to determine the value of tn-1 at 19 degrees of freedom.
Replace the values in the formula above.
E = 2.093 ×5/√20
Thus, its margin of error is 2.34 as a result.
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What is the equation of the line that passes through the points (-4, -6) and (2, 8)
The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
A linear equation or function is given as ;
y = mx + c
Here, m is the slope and is given as (y₂ - y₁)/(x₂ - x₁).
The slope of the line passing through (-4, -6) and (2, 8) will be,
m = (8 + 6)/(2 + 4)
m = 14/6
So, y = (14/6)x + c
Substitute, (2, 8)
8 = (14/6)2 + c
c = 8 - 14/3 = 10/3
Therefore, y = (14/6)x + 10/3
Hence "The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3".
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What is the remainder of the following division problem?
x StartLongDivisionSymbol x + 1 EndLongDivisionSymbol. minus x to get a remainder of 0 + 1 and a quotient of 1.
x
1
0
–1
The remainder of the long division problem (x + 1)/x is given as follows:
1.
What is a long division?The representation of a long division problem is given as follows:
di(x)/d(x) = q(x) + (r(x)/b(x))
In which the meaning of each symbol is listed as follows:
di(x) is the dividend of the division operation.d(x) is the divisor of the division operation.q(x) is the quotient of the division operation.r(x) is the remainder of the division operation.In the context of this problem, the operation is presented as follows:
(x + 1)/x.
This division can be separated into two divisions that are added, hence:
(x + 1)/x = x/x + 1/x = 1 + 1/x.
Comparing to the standard symbols, we have that:
The quotient of the division operation is of 1.The remainder of the division operation is of 1.Missing informationThe expression is:
(x + 1)/x.
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Answer:
B 1
Step-by-step explanation:
a toy manufacturer inspects boxes of toys before shipment. each box contains 17 toys. the inspection procedure consists of randomly selecting three toys from the box. if one or more of the toys are defective, the box is not shipped. suppose that a given box has two defective toys. what is the probability that it will be shipped? a) 0.1765 b) 0.6691 c) 0.3309 d) 0.0221 e) 0.4341 f) none of the above.
The probability that it toys will be shipped is option b ) 0.6691 .
Hypergeometric Distribution will be used
P ( X = x ) = h ( x , N , n , k ) = [tex]C_{k,x}[/tex][tex]C_{N-k,n-x}[/tex] / [tex]C_{N,n}[/tex]
[tex]C_{n,x}[/tex] = n! / [ x! ( n - x ) !
According to question,
N = 17
k = 2
n = 3
To find : P ( X = 0 ) ,
P ( X = 0 ) = h ( 0 , 17 , 3 , 2 )
= [tex]C_{2,0} C_{15,3} / C_{17,3}[/tex]
= 455 / 680
= 0.6691
So there is 66.91 % probability that toys will be shipped .
Hence , option b ) 0.6691 is the correct answer .
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79 ala decena mas cercana
Answer:
80
Step-by-step explanation:
When you answer, could you just put the letter of the number you have? Thank you.
In the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.
As given in the question,
In the given triangle KLM,
Coordinates of the triangle KLM are given by :
K(0,2) ,L(2 ,9) ,M(4,2)
Dilation from the origin is represented by:
a. K'(0,2) , L'(8,9) , M'(16, 2)
Dilation scale factor does not effect on all the coordinates .
Not a correct option.
b. K'(0,2) , L'(2,36) , M'(16, 2)
Dilation scale factor does not effect on all the coordinates .
Not a correct option.
c. K'(0,8) , L'(8,36) , M'(16, 8)
Multiply by scale factor 4.
Dilation exist.
d. K'(4,6) , L'(6,13) , M'(8, 6)
Scale factor of addition of 4.
Dilation does not exist.
Therefore, in the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.
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the prices of used car tires is a normally distributed variable with a mean of $50 and variance of $100. what is the probability that the price of a used car tire will be less than $65?
The probability that the price of the used car is less than $65 is 0.55962.
Here it is given that the price of the used car has a mean of $50 and a variance of $100.
Since it follows normal distribution X~N(μ, σ²)
where,
μ = 50
σ = 100
Here we need to find the probability P(X < 65)
To find this we need to convert the distribution to the standard normal form, N~(0, 1)
We know,
P(X < (x - μ)/ σ) = Φ(Z)
Therefore we get
P(X < (65 - 50)/ 100)
Solving this we get the Z value
= Φ(0.15)
From the Z table, we can get our p-value.
= 0.55962
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(b) Write down the value of 12⁰
(c) Write down the value of 3-²
Answer:
b) 1 c) 0.1Step-by-step explanation:
b) The value of 12⁰ will be?
→ 12⁰ = ?
→ 12⁰ = 1
Hence, the solution is 1.
c) The value of (3)^(-2) will be?
→ (3)^(-2) = ?
→ (3)^(-2) = 0.1
Hence, the solution is 0.1.
3. Another bank offers 1.9% annual simple interest for deposits of $10,000 or more. Carter opened an account at this bank with an initial deposit of $12,000. Ruth opened a Deluxe Savings account that same day. If they have both earned the same amount in interest after one year, what was the amount of Ruth's initial deposit?
Ruth must have an initial deposit of $12000 in order to have the same simple interest at the same rate within the same time as Carter
Simple InterestSimple Interest (S.I) is the method of calculating the interest amount for some principal amount of money. Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.
The formula of simple interest is given as
S.I = PRT
p = principal amountr = ratet = timeWe can set up equivalent equations since both interest are equal.
S.I = P(1 + RT)
S.I = 12000(1 + 0.019 * 1)
S.I = 12228
But since they earned the same interest at the same rate within the same period, their principal or initial amount invested must be equal
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coppinger corp. is considering the use of a computer to assign probability distributions to the input variables used in the analysis. the computer would then randomly select input variables from their distributions and calculate npvs based on those selections. what kind of analysis is this? sensitivity analysis simulation analysis scenario analysis
Coppinger Corp is using Scenario Analysis.
Given, that Coppinger Corp is considering the use of a computer to assign probability distributions to the input variables used in the analysis.
The computer would then randomly select input variables from their distributions and calculate npvs based on those selections
Now, A scenario analysis consists of multiple inputs. For eg. a Company may consider how an increase in available fuel can impact their number of goods sold etc.
Here, also Coppinger Corp is assigning multiple values to the computer and getting outputs.
So, this can be the Scenario Analysis.
Hence, Coppinger Corp is using Scenario Analysis.
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The sum of twice a number "x" and sixteen is
negative fifty six. Translate and find the number.
Answer:
The number is -36 or x = -36
Step-by-step explanation:
2x + 16 = -56
2x = -72
x = -36
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
The equation of the parabola
f(x) = [tex]7x^2[/tex]
The standard vertex form of a parabola is
y = [tex]a(x-h)^2[/tex] + k
The coordinates of the vertex of a parabola = (3, 5)
Where (h, k) is the coordinates
From the given function of the parabola f(x) = [tex]7x^2[/tex]
The value of a = 7
Substitute the values in the vertex form of a parabola
y = [tex]7(x-3)^2[/tex] + 5
Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
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the simple interest formula is i = prt where i = the interest p=the principal r is the annual interest rate in the decimal form and t is the time in years. find the simple interest earned for a principal of 2,000 at an 8% interest the ate for 5 years.
The simple interest earned on a 2,000 principal at 8% interest for 5 years is I = $1,937.50.
What is meant by simple interest formula?Simple interest is calculated by multiplying the daily interest rate by the principal and the number of days between payments. Customers who pay their loans on time or early each month save money on interest.Interest-only loans are prevalent for short-term personal loans and car loans. Simply multiply the principal amount by the interest rate and the time to determine simple interest.The written formula is "Simple Interest = Principal x Interest Rate x Time." Simple interest is calculated on the loan principal or the first deposit into a savings account.Due to the fact that simple interest does not compound, a creditor will only pay interest on the principal amount, and a borrower will never be required to pay interest on previously accumulated interest.Therefore,
I = Prt
First, converting R percent to r a decimal
r = R/100 = 3.875%/100 = 0.03875 per year,
then, solving our equation
I = 10000 × 0.03875 × 5 = 1937.5
I = $ 1,937.50
The simple interest accumulated
on a principal of $ 10,000.00
at a rate of 3.875% per year
for 5 years is $ 1,937.50.
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how to find 3 to the power of x equals 2187?
i need a step by step detail on how to solve it.
Answer: [tex]x=7[/tex]
Step-by-step explanation:
[tex]3^x=2187\\\\x=\log_{3} (2187)\\\\x=7[/tex]
What are the solutions of the quadratic equation?
`2x^{2}+12x+18=0`
show work
The solutions for the quadratic equation:
2x^2 + 12x + 18 = 0
are:
x₋ = -5.55
x₊ = -0.4
How to solve the quadratic equation?
Remember that for a general quadratic equation:
a*x^2 +b*x + c = 0
The solutions are of the form:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
Here we have the quadratic:
2x^2 + 12x + 18 = 0
Then using the formula for the solutions we will get:
[tex]x = \frac{-12 \pm \sqrt{12^2 - 4*2*18} }{2*2} \\\\x = \frac{-12 \pm 10.2}{4}[/tex]
The two solutions of the quadratic equation are:
x₋ = (-12 - 10.2)/4 = -5.55
x₊ = (-12 + 10.2)/4 = -0.4
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Given:-16=m-18;Prove:m=10
Answer:
m=2
Step-by-step explanation:
-16=m-18
-16+18=m
2=m
daysha loves the caramel macchiato at the coffee shop. the 16 oz. medium size has 260 calories. how many calories will she get if she drinks the larger 20 oz. size?
After using proportion method 325 calories will she get if she drinks the larger 20 oz. size.
What is proportion?
Ratio and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion. In this case, a and b can be any two integers. The ratio and proportion are important building blocks for understanding the numerous ideas in science and mathematics. Numerous challenges in daily life can be solved with proportion, including those in business when handling transactions or in the kitchen, among other situations. It creates a relationship between two or more quantities and aids in comparing them.
Here 16 oz medium size has 260 calories.
Then
=> [tex]\frac{size of coffee}{ calories}[/tex]
=>[tex]\frac{16}{260}=\frac{20}{x}[/tex]
=>x=[tex]\frac{20*260}{16}[/tex]
=> x = 325
Hence 325 calories will she get if she drinks the larger 20 oz. size.
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What is the simplest positive form of
-35(mod 6)?
Select all equations that are equivalent to
(6x + 2)
3
-=2(3x +14)
(Select all that apply.)
(6x + 2)
3
(6x + 2) = 2 (3x+14)
2x+3=2-(3x +14)
=-3x-12
6x + 2 = -9x-36
(6x + 2)
3
= -3x+16
Using simplification, the equations that are equivalent to [tex]\frac{(6x+2)}{3} =2-(3x+14)[/tex] are [tex]\frac{(6x+2)}{3 } = -3x-12[/tex] and 6x + 2 = -9x - 36
What are equivalent equation?Two systems of equations are equivalent if they have the same solution(s)
In a simpler term, two equations are equivalent if they have the same solution.
Therefore, let's simplify the equation to find the equivalent solutions.
[tex]\frac{(6x+2)}{3} =2-(3x+14)[/tex]
let's open the brackets of the right side of the equation.
[tex]\frac{(6x+2)}{3}=2-(3x+14)[/tex]
[tex]\frac{(6x+2)}{3} = 2-3x-14[/tex]
[tex]\frac{(6x+2)}{3 } = -3x-12[/tex]
Therefore, let's cross multiply
6x + 2 = 3(-3x - 12)
6x + 2 = -9x - 36
Therefore, the equivalent equation are as follows:
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a flagpole has a height of 15 yards it will be supported by 3 cables edach of which is attached to the flagpole at a point 3 yards below the top of the pole and attached to the ground at a point that is 9 yards from the base of the pole find the total number of yards of cable that will be required
There are 45 yards of cable that will be required.
Let us find the total number of yards of cable that will be required.Since we have given that
Height of cable = 15 yards - 3 yards = 12 yards
Distance from pole = 9 yards
cable is the hypotenuse of the right-angled triangle.
So, it becomes,
[tex]c^{2} = b^{2}+p^{2}[/tex]
[tex]c^{2} = 12^{2}+9^{2}[/tex]
[tex]c^{2} = 144+81[/tex]
[tex]c^{2} = 225[/tex]
[tex]c = \sqrt{225}[/tex]
c=15 yards
Since the number of cables supported = 3
So, the number of yards of cable that will be required would be
= 3 x 15 = 45
Hence, there are 45 yards of cable will be required.
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20 4/0 - 3 1/10
Give answer as mixed number
The solution to the difference 20 4/10 - 3 1/10 is 17 3/10
We have been given two fractions.
20 4/10 and 3 1/10
We need to find the difference 20 4/10 - 3 1/10
First we write improper fraction as a proper fraction.
20 4/10 = 204/10
3 1/10 = 31/10
So, the difference would be,
20 4/10 - 3 1/10
= 204/10 - 31/10
= 173/10
= 17 3/10
Therefore, the solution to the difference 20 4/10 - 3 1/10 is 17 3/10
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guys i seriously need help with this one
The option(1) that is g(1) is 3 is True and remaining are false.
Explain the function by its graph?Function of a variable is when a change in one is accompanied by a change in the other. The graph's x-axis denotes the function's domain, and the y-axis its range.
What kinds of functions can you find on a graph?Eight distinct types of regularly used functions correspond to eight distinct types of function graphs. They include linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal function graphs.
According to given data in the question:we have,
g(x) = f(x - 3)
The value of g(1) is 3As graph in question,
g(1) = f(1-3) = f(-2) = 3
This option is true.
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Which histogram shows a left-skewed distribution? A. A bar chart plots data points (1, 1), (2, 4), (3, 1), (4, 2), (5, 3), (6, 4) and (7, 3). B. A bar chart plots data points (1, 1), (2, 2), (3, 3), (4, 4), (5, 3), (6, 2) and (7, 1 point 5). C. A bar chart plots data points (1, 3), (2, 4), (3, 2), (4, 2), (5, 1), (6, 1) and (7, 1). D. A bar chart plots data points (1, 4), (2, 2), (3, 4), (4, 3), (5, 1), (6, 1) and (7, 2).
The histogram that shows a left-skewed distribution is given by:
A. A bar chart plots data points (1, 1), (2, 4), (3, 1), (4, 2), (5, 3), (6, 4) and (7, 3).
What is an histogram?An histogram is a graph that shows the number of times each element x was observed on the data-set.
Hence, the meaning of a point (x,y) on the histogram is given as follows:
Observation x was observed y times on the data-set.
The skewness of a distribution can be explained as follows:
Left-skewed: The higher values are the ones that are observed the most in the data-set.Symmetric: The middle values are the ones that are observed the most in the data-set.Right-skewed: The lower values are the ones that are observed the most in the data-set.Hence in this problem, for the left-skewed histogram, we want an "increasing" histogram, hence option A is correct.
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The equation for line j can be written as y=1/2x-4. Parallel to line j is line k which passes through the point (-8, -5). What is the equation of line k?
The equation of line k is y = 1/2x - 1.
What is the equation of a line?The equation y = mx + c is the general equation of any straight line, where m is the gradient of the line and c is the y -intercept.
Given that, the equation for line j can be written as y=1/2x-4. Parallel to line j is line k which passes through the point (-8, -5)
When two lines are parallel their slope are equal, so solving for c,
-5 = 1/2*-8 + c
c = -1
The equation will be,
y = 1/2x - 1
Hence, The equation of line k is y = 1/2x - 1.
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Four different linear functions are shown below. Drag the representation of each function in order from greatest y intercept ti least y intercept
Order of greatest y intercept to least y intercept,
1). A linear function has been given as,
y = [tex]\frac{1}{2}[/tex]x + 4
Y intercept = 4
2). The graph,
Y intercept = (2)
3). Graph represented by table
Y intercept = 1
4). A line passes through two points (-2, -3) and (4, 0)
Y intercept = -2
What is Y- intercept?
It is the total distance from the origin and the intersection of y axis and the formed line. It may be positive, negative or zero.
From the graph,
y-intercept = (2)
A line passes through two points (-2, -3) and (4, 0),
Slope of the line = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
= [tex]\frac{0-(-3)}{4-(-2)}[/tex]
= 1/2
Equation of a line passing through a point (x', y') and slope = m
y - y' = m(x - x')
If the point is (4, 0) and slope = 1/2
y - 0 = 1/2 ( x - 4 )
y = 1/2x - 2
y-intercept of this line = (-2)
A linear function has been given as,
y = [tex]\frac{1}{2}[/tex]x + 4
Comparing it with the slope intercept equation,
y = mx + b
b = y-intercept = 4
From the given table,
For x = 0, f(x) = 1
Therefore, y-intercept = 1
Order of greatest y intercept to least y intercept,
1). A linear function has been given as,
y = [tex]\frac{1}{2}[/tex]x + 4
Y intercept = 4
2). The graph,
Y intercept = (2)
3). Graph represented by table
Y intercept = 1
4). A line passes through two points (-2, -3) and (4, 0)
Y intercept = -2
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The half-life of a radioactive kind of americium is 7,380 years. How much will be left after
22,140 years, if you start with 188,320 grams of it?
grams
Heeelllllllllllp Simplify the expression completely.
√144 +18 √12-5√64
Answer:
A
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{12}[/tex]
= [tex]\sqrt{4(3)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]
= 2[tex]\sqrt{3}[/tex]
Then
[tex]\sqrt{144}[/tex] + 18[tex]\sqrt{12}[/tex] - 5[tex]\sqrt{64}[/tex]
= 12 + 18(2[tex]\sqrt{3}[/tex] ) - 5(8)
= 12 + 36[tex]\sqrt{3}[/tex] - 40
= - 28 + 36[tex]\sqrt{3}[/tex]
Find a description this equation represents. Of the numbers 1, 2, 3, 4, and 5, which are solutions to the equation?
4x+6=18
A. If you add four to six times a number, you get 18.
B. Four more than six times a number is 18.
C. If you add six to four times a number, you get 18.
D. Six more than four times a number is 18.
E. Six less than four times a number is 18.
F. Four less than six times a number is 18.
G. If you add six times a number to four, you get 18.
H. If you subtract six from four times a number, you get 18.
A line includes the points (1, 10) and (0, 8). What is its equation in slope-intercept form?
Answer:
Y = 2x+8
Step-by-step explanation:
Y=mx=b equations
Nigel is selling candy bars for his outdoor club. He is averaging 4 bars every 3 days. If he continues at this rate, how many days will it take to sell his box of 35? Answer in whole number form and round up to the next whole number.
The number of days that it will take to sell his box of 35 is 21 days.
What is a ratio?Ratio simply demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this case, Nigel is selling candy bars for his outdoor club and he is averaging 4 bars every 3 days.
Let the number of days be x.
This will be:
3/x = 4/35
Cross multiply
4x = 3 × 35
x = (3 × 35)/4
x = 105 / 4
x = 21
It will take 21 days
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help meeeeeeeeeeeeeeeeee please
Answer: 81
Step-by-step explanation:
[tex]v=\sqrt{2gh}\\\\g=32, v=72\\\\\implies 72=\sqrt{2(32)h}\\\\5184=64h\\\\h=81[/tex]
