Complete Question
The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 100 hours. A random sample of 64 light bulbs indicated a sample mean life of 350 hours
A. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment.
B. Do you think that the manufacturer has the right to state that the light bulbs have a mean life of 400
a. No.
b. Yes.
c. Maybe.
d. Do not know
Answer:
A
[tex]325.5 < \mu < 374.5[/tex]
B
correct option is a
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 100[/tex]
The sample mean is [tex]\= x = 350 \ hours[/tex]
The sample size is [tex]n = 64[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100- 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2 } } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{100 }{\sqrt{64} }[/tex]
=> [tex]E = 24 .5[/tex]
Generally the 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
[tex]350 - 24.5 < \mu < 350 + 24.5[/tex]
[tex]325.5 < \mu < 374.5[/tex]
This 95% confidence interval can be interpreted as follows
There is 95 confidence that the true population mean lies in this interval
Now looking at the interval we see that it dose not contain 400 hence
the correct answer is No the manufacturer do not have the right to state that the light bulbs last on average 400 hours
1.
Harriet has deposited $693 in a savings account that earns interest at a rate of 4.6% compounded monthly. What will the account balance be in thirteen years? (2 points)
$1,258.77
$1,243.50
$724.88
$3,187.80
Answer:
Future amount (A) = $1,258.77 (Approx)
Step-by-step explanation:
Given:
Amount deposit (p) = $693
Rate of interest monthly (r) = 4.9% / 12 = 0.003833
Number of month (n) = 13 × 12 = 156
Find:
Future amount (A)
Computation:
[tex]A = p [1+r]^n \\\\ A = 693 [1+0.003833]^{156}\\\\ A= 693[1.8163]\\\\ A = 1258.77[/tex]
Future amount (A) = $1,258.77 (Approx)
Using this figure, A' is the ____ of A
Image
Step-by-step explanation:
It's actually called Translation but image is the same thing as translation
Help me please thank you
Answer:
135°
Step-by-step explanation:
Because the lines are parallel, <1 and <3 are the same.
Land in downtown Columbia is valued at $10 a square foot. What is the value of a triangular lot with sides of lengths 119, 147, and 190 ft?
Answer:
$87,461
Step-by-step explanation:
Given that the dimensions or sides of lengths of the triangle are 119, 147, and 190 ft
where S is the semi perimeter of the triangle, that is, s = (a + b + c)/2.
S = (119 + 147 + 190) / 2 = 456/ 2 = 228
Using Heron's formula which gives the area in terms of the three sides of the triangle
= √s(s – a)(s – b)(s – c)
Therefore we have = √228 (228 - 119)(228 - 147)(228 - 190)
=> √228 (109)(81)(38)
= √228(335502)
=√76494456
= 8746.1109071 * $10
= 87461.109071
≈$87,461
Hence, the value of a triangular lot with sides of lengths 119, 147, and 190 ft is $87,461.
I don’t understand this?
Answer:
11.5 cm²
Step-by-step explanation:
We know that the triangle has a base of 3 + 4 = 7 and a height of 3 + 2 = 5. Therefore, the area of the triangle is 7 * 5 / 2 = 17.5. The area of the 3 by 2 rectangle is 3 * 2 = 6 so the shaded area is 17.5 - 6 = 11.5 square cm.
Find the greatest number of 5 digits which
when divided by 25, 30 and 40 leaves a
remainder 20,25, and 35 respectively.
Answer:
99,595
Step-by-step explanation:
We are looking at division and remainders. What do you do when a remainder is present? You usually add it when multiplying to get the final number, but since we are doing this backwards, we have to subtract the numbers divided by the remainder.
25 - 20 = 5
30 - 25 = 5
40 - 35 = 5
Look for the LCM (Least Common Multiple) for 20, 30, and 40 :
600
Now for the equation :
n + 5 = Multiple of all numbers and LCM =
n + 5 = 166 * 600 = 99,600
n = 99,600 - 5 = 99,595
The greatest 5 digit number which when divided by 25, 30 and 40 has a remainder of 20, 25, and 35 is 99,595
The reason why the above value arrived at is correct is as follows:
The required parameter;
To find a 5 digit number that with remainder of 20, remainder of 25 and a remainder of 35, when divided by 25, 30, and 40 respectively
Strategy;
Find the LCM of the divisor, then find the highest common multiple of the
LCM that is a 5 digit number, equate the expression for the required 5 digit
number to the highest common multiple of LCM of the divisors by adding
a value that will give a factor of the divisor as follows;
Let x represent the 5 digit number, from the question, we get;
x = 25·a + 20
x = 30·b + 25
x = 40·c + 35
x < 99,999
The 5 digit number is not a multiple of 25, 30, and 40, therefore, the number is not a multiple of the LCM of 25, 30, and 40 which is 600
The highest multiple of 600 which is a 5 digit number = 99,600
Therefore, we can write;
25·a + 20 + 5 = 30·b + 25 + 5 = 40·c + 35 + 5 = 99,600
However;
25·a + 20 + 5 = x + 5
By transitive property, we get
x + 5 = 99,600
∴ x = 99,600 - 5 = 99,595
The 5 digit number, x = 99,595
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Define the following sequence recursively: 4, 4/3, 4/9, ....
Answer:
Step-by-step explanation:
[tex]a_n=\frac{1}{3} a_{n-1}[/tex]
A brick layer can lay 320 bricks per day. Let y represent the total number of bricks he can lay in x days
Determine whether a graph created with each calculator display window defined in the table will show all points representing the total number of bricks that the brick layer can lay in 0 to 10 days
Select Yes or No for each display window.
The calculator display window shows:
Yes
No
O
о
400 < x < 3,400 and -1 < y < 11
-1
о
o
o
O
-1
-400 < x < 3,400 and - 400 < y < 321
о
O
Answer:
I may be incorrect but these are my answers
A) −400≤x≤3,400 and −1≤y≤11 NO
B) −1≤x≤11 and −400≤y≤3,400 YES
C) −1≤x≤11 and −1≤y≤321 YES
D) −400≤x≤3,400 and −400≤y≤321 YES
Step-by-step explanation:
The last three equations, B, C ,D all include the points needed to graph the total number of bricks he can lay in 0 to 10 days.
Answer:
Don't delete my answers!
No
Yes
Yes
Yes
I was doing the QUIZ!
Step-by-step explanation:
a companys product development division has 60 employees. Of these, 1/3 are engineers. If 40% of engineers are moved to another division. How many engineers will remain in the product development department?
Answer: There will be 12 engineers remaining in the product development department.
Step-by-step explanation:
So the givens are:
60 employees and 1/3 are engineers and if 40% of engineers are moved to another division and how many engineers will remain in the product development department?
So what we need to do:
60 * 1/3 = 60 / 3 = 20
There are 20 engineers.
20 * 40% = 8
There are 8 engineers that are going to be moved to another division.
20 - 8 = 12
12 engineers will remain in the development department.
Hence, your answer.
By calculations, 12 engineers will remain in the development department.
A companys product development division has 60 employees. Of these, [tex]\frac{1}{3}[/tex] are engineers.
The third part of a number is obtained by dividing a number by three, or what is the same, multiplying by a third ([tex]\frac{1}{3}[/tex]), thus dividing the number into a total of three equal parts.
In this case:
[tex]\frac{1}{3}[/tex]×60= 20
So, a companys product development division has 20 engineers.
40% of engineers are moved to another division.
The percentage is a way of referring to a proportion taking the number 100 as a reference. To calculate the percentage of a quantity, the quantity is multiplied by the percentage and divided by 100.
In this case:
40% of engineers= 40%×20=[tex]\frac{40x20}{100}[/tex]= 8
8 engineers are moved to another division.
The number of engineers who remain in the department is calculated by subtracting the total number of engineers in the department and the number of engineers who move to another division:
20 - 8= 12
12 engineers will remain in the development department.
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c) Chairs are placed in equal rows and column of a squared room. If there are 144 chairs in the room, how many chairs are there in the first row?
Answer:
12
Step-by-step explanation:
144 chairs in total.
the room is square, this means that the number must be multiplied by the same number
12x12= 144
there are 12 chairs on the first row.
Which of the following is not an undefined term?
point
ray
line
plane
Answer:
ray
Step-by-step explanation:
ray is the answer because it starts with a startline but has no endpoint so it goes on for infinity.
Manori’s bag has 10cent and 20cent coins. She has 202 coins with a total value of $31.90. How many 20cent coins does manori have?
a = 85 10cent coins
b = 117 20cent coins
Step-by-step explanation:a = 10c coins
b = 20c coins
$31.90 = c3190
a + b = 202 => a = 202 - b
10a + 20b = 3190
10(202 - b) + 20b = 3190
2020 - 10b + 20b = 3190
10b = 3190 - 2020
10b = 1170
b = 117 (20cent coins)
a = 202 - 117
= 85 (10cent coins)
I need help on this question, please stop by.
Answer:
last option from the left
Step-by-step explanation:
To find the price of one water bottle, we can calculate 6 / 24 because 24 bottles cost $6. Now, to find the price of 10 bottles, we can multiply the price of 1 bottle by 10 so the answer is 6 / 24 * 10.
Find the following quotient and express the answer in standard form of a complex number.
Hello, please consider the following.
When you have a complex number in the denominator you need to multiply by its conjugate to eliminate the imaginary component.
The conjugate of 4 - 3i is 4 + 3i, right?
So, let's do it!
[tex]\dfrac{5-7i}{4-3i}=\dfrac{(5-7i)(4+3i)}{(4-3i)(4+3i)}\\\\=\dfrac{5(4+3i)-7i(4+3i)}{4^2-(3i)^2}\\\\=\dfrac{20+15i-28i-21i^2}{16+9}\\\\=\dfrac{20+21-13i}{25}\\\\\large \boxed{=\dfrac{41}{25}-\dfrac{13}{25}i\\}[/tex]
Thank you.
Complex numbers are numbers with real and imaginary parts.
The expression in standard form of a complex number is: [tex]\mathbf{\frac{41}{25}-\frac{13}{25}i}[/tex]
The expression is given as:
[tex]\mathbf{\frac{5 - 7i}{4 - 3i}}[/tex]
Rationalize
[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{5 - 7i}{4 - 3i} \times \frac{4 + 3i}{4 + 3i}}[/tex]
[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{20 +15i -28i - 21i.i}{(4)^2 - (3i)^2}}[/tex]
[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{20 +15i -28i - 21(-1)}{16 - 9(-1)}}[/tex]
[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{20 +15i -28i + 21}{16 + 9}}[/tex]
Collect like terms
[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{20 + 21+15i -28i }{16 + 9}}[/tex]
[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{41-13i }{25}}[/tex]
Split
[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{41}{25}-\frac{13i }{25}}[/tex]
[tex]\mathbf{\frac{5 - 7i}{4 - 3i} = \frac{41}{25}-\frac{13}{25}i}[/tex]
Hence, the expression in standard form of a complex number is: [tex]\mathbf{\frac{41}{25}-\frac{13}{25}i}[/tex]
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Use Stokes' Theorem to calculate . F = 5yi + 7xj + z3k; C: the counterclockwise path around the perimeter of the triangle in the x-y plane formed from the x-axis, y-axis , and the line y = 5 - 2x (Hint: n = k)
Answer:
hello your question is incomplete attached is the complete question
answer : 25/2 ( A )
Step-by-step explanation:
using Stokes' Theorem to calculate
F = 5yi + 7xj + [tex]z^3 k[/tex]
line y = 5 - 2x
attached below is the remaining part of the solution to the question
hypothesis that there is a relationship between parents’ and children’s party identification. Would we be correct in inferring that such a relationship also exists in the population? Explain your answer. What is the probability that any relationship we found is due to pure chance?
Answer:
No
It could be purely due to chance.
Step-by-step explanation:
A population is defined as the whole group which has the same characteristics. For example a population of the college belongs to the same college . But a sample may be an element of a population.
So it is not necessary for a population to have the same characteristics as the sample.
But it is essential for the sample to have at least one same characteristics as the population.
So we would not be correct in inferring that such a relationship also exists in the population.
It is a hypothesis which can be true or false due to certain conditions or limitations as the case maybe.
For example in a population of smokers some may be in the habit of taking cocaine. But a sample of cocaine users does not mean the whole population uses it.
It could be purely due to chance if we find out that there is a relationship between parents’ and children’s party identification in the population.
please help! Please explain as well!!!!
Answer:
value of the variable: 3/2
perimeter: 84 feet
Step-by-step explanation:
Let's find the value of the variable first:
It is a square, so all 4 sides are the same (have the same length)
This means, 3(2f + 4) = 12f + 3
Simplify it,
6f + 12 = 12f + 3
6f = 9
f = 3/2
So, the variable f = 3/2!
Let's find the perimeter:
First, we find the value of one side of the square
12f + 3 is a side
because f = 3/2, we know that the one side of a square is 18 + 3 ft, which is 21 ft
Like I said, all 4 sides are the same in a square, so we can just calculate the length of 1 side, and multiply it by 4!
so 21 * 4 = 84!
The perimeter of this square is 84 feet!
I hope this helps! Please tell me if I did anything wrong, thank you and have a great day =D
Given paralleogram ACDB-parallelogram FGHE, what
is the value of x?
O x= 40°
O x= 50°
O x= 65°
O x = 130°
The value of x will be 50 degrees. The correct option is B.
What is a parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The opposite angles of the parallelogram are equal and the sum of the adjacent angles of the parallelogram is 180 degrees.
Angle A is 130 degrees then angle F will also be 130 degrees. The angle E will be calculated as below:-
∠F + ∠ E = 180
130 + ∠E = 180
∠E = 180 - 130
∠E = 50
Therefore, the value of x will be 50 degrees. The correct option is B.
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(04.07A)
Two quantities are related, as shown in the table below:
x y
2 3
4 4
6 5
8 6
Which equation best represents the relationship?
Answer:
The equation that best represents the relationship is [tex]y=\frac{1}{2}x+2[/tex].
Step-by-step explanation:
We are given the following table representing the two quantities below;
x y
2 3
4 4
6 5
8 6
Firstly, we will find the two-point slope here, that is;
Consider two points; ([tex]x_1,y_1[/tex]) = (2, 3) and ([tex]x_2,y_2[/tex]) = (4,4)
Now, the formula for finding slope is;
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{4-3}{4-2}[/tex] = [tex]\frac{1}{2}[/tex]
Similarly, finding the slope for the points (6,5) and (8,6);
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{6-5}{8-6}[/tex] = [tex]\frac{1}{2}[/tex]
Now, the linear equation of the line having slope is given by;
[tex]y-y_1=m\times (x-x_1)[/tex] ; where m = slope and consider ([tex]x_1,y_1[/tex]) = (2, 3)
So, the equation of the line is;
[tex]y-3=\frac{1}{2} \times (x-2)[/tex]
[tex]y-3=\frac{1}{2}x-1[/tex]
[tex]y=\frac{1}{2}x+2[/tex]
Hence, the equation that best represents the relationship is [tex]y=\frac{1}{2}x+2[/tex].
Answer:
y = -1/2x + 11
write another name for AE ? need asap
Answer:
EA, or s
Step-by-step explanation:
The line AE could also be named any of the following:
AC, EC, CE, CA, EA
If you’re only looking at the line segment AE, the only option is:
EA
Since I don’t know whether you need the line or line segment, you might want go with EA since it’s on both lists. It could also be line s.
if there are two numbers on one side, do i have to add them together?
Answer:
YES
Step-by-step explanation:
For example, in the figure displayed in the attachment, the length of [tex] YM = MS + SY [/tex]
[tex] MS = 3 [/tex]
[tex] SY = 10 [/tex]
Therefore, [tex] YM = 3 + 10 = 13 [/tex].
The lengths of segments MS and SY sums up to give you the length of YM.
Which of the following presents can also be expressed as a mixed number 310% or 49% or 7.4% or 0.001%
Answer:
310%
Step-by-step explanation:
310% can be expressed as a mixed number because 150% would be 1 1/2.
310% would be 3 1/10.
solve:
[tex]\underset{x\rightarrow~3}{\lim}~\dfrac{2x^2-18}{x^2-3x}[/tex]
Hello, please consider the following.
[tex]\displaystyle \lim_{x\rightarrow3}~\dfrac{2x^2-18}{x^2-3x} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x^2-3^2)}{x(x-3)} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x-3)(x+3)}{x(x-3)} \\ \\ \\ =\lim_{x\rightarrow3}~\dfrac{2(x+3)}{x} \\ \\ \\=\dfrac{2(3+3)}{3}\\ \\ \\=\dfrac{2*3*2}{3} =\Large \boxed{\sf \bf \ 4 \ }[/tex]
Thank you
[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2x^2-18}{x^2-3x}[/tex]
[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2(x^2-9)}{x^2-3x}[/tex]
[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2(x^2-3^2)}{x^2-3x}[/tex]
(a+b)(a-b)=a^2-b^2[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2(x+3)\cancel{(x-3)}}{x\cancel{(x-3)}}[/tex]
[tex]\\ \tt\longmapsto {\displaystyle{\lim_{x\to 3}}}\dfrac{2x+6}{x}[/tex]
[tex]\\ \tt\longmapsto \dfrac{2(3)+6}{3}[/tex]
[tex]\\ \tt\longmapsto \dfrac{6+6}{3}[/tex]
[tex]\\ \tt\longmapsto \dfrac{12}{3}=4[/tex]
pt 3 7/7 lasttt one helpppp
Answer:
2n+2
Step-by-step explanation:
-n + (-3) +3n + 5 -3
(-3+5) =2
-n +2+n+3n
3n-n = 2n
2n+2
1) write the equation of the
line in slope intercept form
that passes through (0,-2)
and (2,1).
Answer:
y=3/2x-2
Step-by-step explanation:
Find the slope first:
[tex]m=\frac{y_{2-y_{1} } }{x_{2}-x_{1} } =\frac{1-(-2)}{2-0}=\frac{3}{2}[/tex]
Then solve for y-intercept:
[tex]y=\frac{3}{2}x+b\\-2=\frac{3}{2}(0)+b\\-2=b[/tex]
Now, write out your complete equation:
y=3/2x-2
Find the standard form (ax + by + c = 0) of the line using the following information. Please show your work! Point: (6, -1) Slope: m is undefined I'll give brainliest!!!
Answer:
x - 6 = 0
Step-by-step explanation:
The only lines that have undefined slopes are vertical lines. Vertical lines are found in the form x = c where c is a constant. With vertical lines, it doesn't matter what the y value is because x will always be c. In this case, c = 6 because the x-coordinate of (6, -1) is 6. Therefore, our equation is x = 6. In standard form, that would be x - 6 = 0.
Answer:
[tex]\huge \boxed{x-6=0}[/tex]
Step-by-step explanation:
Vertical lines have undefined slopes.
The line crosses (6, -1), x = 6.
The equation of the vertical line is x = 6.
The equation of the line in standard form would be x - 6 = 0.
The sum of two numbers is 167. The second number is 29 less than three times the first number. Fine the numbers. The two required numbers are:
Answer:
49 and 118
Step-by-step explanation:
Let the two numbers be x and y
x+y = 167
y = 3x-29
Substitute into the first equation
x+ 3x-29 = 167
Combine like terms
4x - 29 = 167
add 29 to each side
4x = 167+29
4x = 196
Divide by 4
4x/4 = 196/4
x = 49
x+y = 167
49+y = 167
y = 167-49
y =118
Answer:
[tex]\Huge \boxed{\mathrm{49 \ and \ 118}}[/tex]
Step-by-step explanation:
Let the first number be [tex]x[/tex]
Let the second number be [tex]y[/tex]
[tex]x+y=167[/tex]
[tex]y=3x-29[/tex]
Applying substitution method.
[tex]x+3x-29=167[/tex]
Combining like terms.
[tex]4x-29=167[/tex]
Adding 29 to both sides.
[tex]4x=196[/tex]
Dividing both sides by 4.
[tex]x=49[/tex]
Substituting x = 49 for the second equation.
[tex]y=3(49)-29[/tex]
Multiplying the numbers.
[tex]y=147-29[/tex]
Subtracting.
[tex]y=118[/tex]
The two required numbers are 49 and 118.
how do you Evaluate. 58−(14)2= ________
Answer:
58-(14)2
58-28
30
Step-by-step explanation:
can someone please help me
Problem 6, part c)
The tickmarks indicate the sides are the same length. This triangle is isosceles.
The two base angles are always opposite the congruent sides. One base angle is 25, so the other base angle must be 25 as well (base angles are congruent for isosceles triangles).
The three angles of this triangle are
25, 25 and 4x+2
Add those three angles up, set the result equal to 180, and solve for x
4x+2+25+25 = 180
4x+52 = 180
4x = 180-52
4x = 128
x = 128/4
x = 32 is the answer====================================================
Problem 7, part a)
We use the same idea as with the last problem above. This works because this triangle is also isosceles (due to the tickmarks).
The three angles of this triangle are
(4x+1), (4x+1) and (5x-4)
note how (4x+1) shows up twice because it is a base angle
Add up those angles and set it equal to 180 to solve for x
(4x+1) + (4x+1) + (5x-4) = 180
13x - 2 = 180
13x = 180+2
13x = 182
x = 182/13
x = 14
Using this x value, we can find angle F
angle F = 5x-4
angle F = 5*14-4
angle F = 70-4
angle F = 66 degrees is the answer====================================================
Problem 7, part b)
We'll use the x value found back in part a) above.
angle D = 4x+1
angle D = 4*14+1
angle D = 56+1
angle D = 57 degrees is the answerAngle E is also 57, since D and E are congruent base angles
note how D+E+F = 57+57+66 = 180 to help confirm our answers
Use inductive reasoning to determine the next term in the sequence -2, 5, -4, 3, -6, ... *
Answer:1,-8
Step-by-step explanation: -2,5( add 7) 5,-4(sub 9),-4,3(add 7), 3,-6(sub 9)
Pattern of +7,-9,+7,-9
-6+7=1 and 1-9=-8