Answer:
b
Step-by-step explanation:
How large a sample should be selected to provide a 95% confidence interval with a margin of error of 6? Assume that the population standard deviation is 40 . Round your answer to next whole number.
Using the z-distribution, it is found that a sample of 171 should be selected.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.For this problem, the parameters are:
[tex]z = 1.96, \sigma = 40, M = 6[/tex]
Hence we solve for n to find the needed sample size.
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]6 = 1.96\frac{40}{\sqrt{n}}[/tex]
[tex]6\sqrt{n} = 40 \times 1.96[/tex]
[tex]\sqrt{n} = \frac{40 \times 1.96}{6}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{40 \times 1.96}{6}\right)^2[/tex]
n = 170.7.
Rounding up, a sample of 171 should be selected.
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solve for x by completing the square: x2 − 8x + 13 = 0. show all work
There are two real roots for the quadratic equation x² - 8 · x + 13 = 0, contained in the number x = 4 ± √2.
How to find the roots of a polynomial by completing the square
In this question we must apply algebraic handling to simplify a quadratic equation and find the roots that satisfy the expression. Completing the square consists in transforming part of the equation into a perfect square trinomial, and then we clear for x:
x² - 8 · x + 13 = 0
x² - 8 · x + 16 = 3
(x - 4)² = 3
x - 4 = ± √2
x = 4 ± √2
There are two real roots for the quadratic equation x² - 8 · x + 13 = 0, contained in the number x = 4 ± √2.
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for this graph, mark the statements that are true.
Answer:
C,D
Step-by-step explanation:
C: Range refers to the y axis and all values shown on this graph (and even beyond the graph) are greater than 0
D: The domain refers to the x-axis. The line goes on forever both to the right and the left therefore meaning all x values are used.
Please help me put them in correct place
The inequalities that match the given expressions are
x ≤ 95
x > 100
5x ≤ 100
20 ≤ x ≤100
respectively
Writing linear inequalitiesFrom the question, we are to match the statements with the corresponding inequalities
Nora's height(x) is at least 5 cm less than Stacy who is 100 cm tallx ≤ 100 -5
x ≤ 95
Temperature(x) is greater than the boiling point of water (100 °C)x > 100
John buys x chocolates worth $5 each but he has only $100 in his pocket5x ≤ 100
Ronny decided not to exceed 100L of water usage and ends up using at least 1/5th of this limit every dayx ≤ 100
and
x ≥ 1/5 × 100
x ≥ 20 ≡ 20 ≤ x
∴ 20 ≤ x ≤100
Hence, the inequalities that match the given expressions are
x ≤ 95
x > 100
5x ≤ 100
20 ≤ x ≤100
respectively
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I'm have some issues with the problem shown in the screenshot and would love some help.
The dimensions and volume of the largest box formed by the 18 in. by 35 in. cardboard are;
Width ≈ 8.89 in., length ≈ 24.89 in., height ≈ 4.55 in.Maximum volume of the box is approximately 1048.6 in.³How can the dimensions and volume of the box be calculated?The given dimensions of the cardboard are;
Width = 18 inches
Length = 35 inches
Let x represent the side lengths of the cut squares, we have;
Width of the box formed = 18 - 2•x
Length of the box = 35 - 2•x
Height of the box = x
Volume, V, of the box is therefore;
V = (18 - 2•x) × (35 - 2•x) × x = 4•x³ - 106•x² + 630•x
By differentiation, at the extreme locations, we have;
[tex] \frac{d V }{dx} = \frac{d( 4 \cdot \: {x}^{3} - 106 \cdot \: {x}^{2} + 630\cdot \: {x} ) }{dx} = 0[/tex]
Which gives;
[tex] \frac{d V }{dx} =12\cdot \: {x}^{2} - 212\cdot \: {x} + 630 = 0[/tex]
6•x² - 106•x + 315 = 0
[tex]x = \frac{ - 6 \pm \sqrt{106 ^2 - 4 \times 6 \times 315} }{2 \times 6} [/tex]
Therefore;
x ≈ 4.55, or x ≈ -5.55
When x ≈ 4.55, we have;
V = 4•x³ - 106•x² + 630•x
Which gives;
V ≈ 1048.6
When x ≈ -5.55, we have;
V ≈ -7450.8
The dimensions of the box that gives the maximum volume are therefore;
Width ≈ 18 - 2×4.55 in. = 8.89 in. Length of the box ≈ 35 - 2×4.55 in. = 24.89 in. Height = x ≈ 4.55 in.The maximum volume of the box, V ≈ 1048.6 in.³Learn more about differentiation and integration here:
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A customer's stock value seems to be rising exponentially. The equation for
the linearized regression line that models this situation is log(y) = 0.30x +0.296,
where × represents number of weeks. Which of the following is the best
approximation of the number of weeks that will pass before the value of the
stock reaches $600?
Answer:
B: 8.3
Step-by-step explanation:
We will substitute 600 to the y, since our final answer will be a number that makes the value of the stock reach $600.
log (y) = 0.30x + 0.296
Replacing y with 600, the equation becomes:
log (600) = 0.30x + 0.296
2.78 = 0.30x + 0.296
To move all the x and real numbers to different sides, we take 0.296 away from both sides to form:
2.78 - 0.296 = 0.30x
2.484 = 0.30x
x = 8.28
The approximation of 8.28 will be rounded to 8.3.
Then our final answer will be B: 8.3
answer this please only the ones that are blank
Answer:
#3 5(2a+4)
#4 5(a+2+4)
#5 5a+5(2+4)
Step-by-step explanation:
I think so, I am probably wrong
Help Me Please with this Math Money Question It Wont Me Screenshot But
Question: CD's are 5 for $30.00.
What is the price of 3 CD's?
Answers:
A) $18.00
B) $15.00
C) $6.00
D) $3.00
Answer:
A
Step-by-step explanation:
$30.00 ÷ 5 = $6.00
$6.00 × 3 = $18.00
– 42 – 54 + 96 =
what is the answer
Answer:
Answer:the answer is zero
Answer:the answer is zero Step-by-step explanation:
Answer:the answer is zero Step-by-step explanation:when we add -42 and -54 the answer we get is -96. -96and +96 cut each other and then the answer is zero
[tex] - 42 - 54 + 96 = 0[/tex]
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=-14x^2+1035x-10266
The price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit is 62.13
Quadratic equationy = -14x² + 1035x - 10266
solve the quadratic equation-14x² + 1035x - 10266 = 0
x = -b ± √b² - 4ac / 2a
= -1035 ± √1035² -4(-14)(-10266) / 2(-14)
= -1035 ± √1071225 - 574896 / -28
= -1035 ± √496329 / -28
x = 1035 / 28 ± √496329 / 28
x = 11.80 or 62.13
The maximum value of x is 62.13
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Please Help! Brainliest Avaliable! Literally Multiple Choice!
It's very simple. Subract 554.26 from 866.32
then, we got the difference is
312.06
thank you
Brainlist please.
The plot below shows the volume of paint left in 444 cans.
All measurements are rounded to the nearest \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction pint.
A line plot labeled Volume in pints shows, moving left to right, labeled tick marks at two, two and one-half, three, three and one-half, four, four and one-half, five, five and one half, and six. Dots are plotted as follows: 1 dot above two and one-half; 2 dots above four; and 1 dot above five and one-half.
A line plot labeled Volume in pints shows, moving left to right, labeled tick marks at two, two and one-half, three, three and one-half, four, four and one-half, five, five and one half, and six. Dots are plotted as follows: 1 dot above two and one-half; 2 dots above four; and 1 dot above five and one-half.
If we split the total amount of paint so that each can had the same amount, how much paint would be in each can?
The amount of paint that would be contained in each of the can would be 8.
How to solve for the amount of paint.
Using the information in the question we have the following
We have to solve the equation as
(2 1/2) + 2(4) + 1(5 1/2) =
2.5 + 8 + 5.5
= 16
Each of these would have to hold 16/2 = 8 pints.
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Answer:
4 pints
Step-by-step explanation:
the expert is wrong
find x and y pls help
30 + 110 + 30 + 110 = 280
360-280 = 80
2y = 80
y = 40 degrees
If y is 40. Then the angle next to 30 is also y due to vertically opposite angles.
30 + 40 = 70
The line with 2 arrows is parallel to the line with x degrees. So, I use co-interior angles adds to 180.
In that c shaped, we got the bottom angle to be 70 & the top to be 110 because co-interior angles =180
Forget the c shape exists, and move onto the triangle that's visible. The top angle is 110 as found.
Angles in triangle add to 180.
180 - 110 - 30 = 40.
Thus, x = 40 degrees
There's a short cut I realise now because we can have alternate angles are equal; creating a z shape to find what x is equal to & that turns out to be the same value as y. ( due to vertically opposite angles)
Hope this helps!
Which is the graph of the inequality?
5y+x>−10
Number graph ranging from negative twenty to twenty in increments of two on the x and y axes. A dotted line with a positive slope is drawn in the fourth quadrant of the graph. The area above the line is shaded gray.
Number graph ranging from negative ten to ten on the x and y axes. A solid line passes through (negative one, zero) and (zero, three). The area to the left of the line is shaded gray.
Number graph ranging from negative twenty to twenty in increments of two on the x and y axes. A solid line passes through (zero, negative fourteen) and (two, zero). The area to the right of the line is shaded gray.
Number graph ranging from negative ten to ten on the x and y axes. A dotted line passes through (zero, negative two) and (five, negative three). The area above the line is shaded gray.
We can simplify the inequality to:
y > (-1/5)*x - 2
From that, we conclude that the correct option is the last one.
Which is the graph of the given inequality?
Here we have the inequality:
5y + x > -10
If we isolate y, we get:
y > (-10 - x)/5
y > (-1/5)*x - 2
Then the inequality will be a dashed/dotted line with a negative slope, that passes through the point (0, -2), such that the region above and to the right of the line is shaded.
From that we conclude that the correct option is the last one:
"Number graph ranging from negative ten to ten on the x and y axes. A dotted line passes through (zero, negative two) and (five, negative three). The area above the line is shaded gray."
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The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 140 pints of a mixture that is 70% pure fruit juice?
We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.
How to use weighted averages to find the correct juice concentration
In this problem we have to use two kinds of juice with different concentrations. To get a certain concentration, we must adjust quantities of each kind and weighted averages offers a method that is easy to apply:
70 · 140 = 55 · x + 80 · (140 - x)
70 · 140 = 80 · 140 - 25 · x
25 · x = 10 · 140
x = 56
We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.
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Calculate the geometric center of the grapg under the function
The geometric center of the graph under the function is 5/3
How to determine the geometric center of the graph under the function?The equation of the function is given as:
f(x) = 3 - |x - 2|
The interval is given as:
x ∈ [0, 3]
The geometric center (gc) of the graph under the function is calculated using
gc = ∫x f(x) dx/∫f(x) dx
Substitute the known values in the above equation
gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx
Integrate the numerator and the denominator of the above equation
gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]
Recall that the interval is given as x ∈ [0, 3]
Substitute the interval values in the above equation.
The equation is then simplified using a graphing calculator.
So, we have
gc = (65/6)/(13/2)
Express the quotient expression as a product
gc = (65/6) * (2/13)
Divide 65 by 13
gc = 5/6 * 2
Divide 2 by 6
gc = 5/3
Hence, the geometric center of the graph under the function is 5/3
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Complete the frequency table:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
What percentage of students age 15 and above travel to school by bus? Round to the nearest whole percent.
The percentage of students age 15 and above travel to school by bus is 47%
How to complete the table?The table of values is given as:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
Using the column total of column 1, we have:
Under age 15 + 65 = 152
This gives
Under age 15 = 87
Using the column total of column 2, we have:
Age 15 and above + 18 = 110
This gives
Age 15 and above = 92
Using the row total of row 1, we have:
Car + 87 + 18 = 165
This gives
Car = 60
Using the row total of row 2, we have:
Car + 65 + 92 = 195
This gives
Car = 38
So, the complete frequency table is
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 87 18 60 165
Age 15 and above 65 92 38 195
Column totals 152 110 98 360
The percentage of students age 15 and above travel to school by bus is:
Percentage = 92/195 * 100%
This gives
Percentage = 47%
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One-fifth of a number x is less than 8. Find the greatest possible prime number x.
Complete the table. Each column should contain equivalent values. One column has been completed for you. Make sure the fractions are stated in simplest form.
Fraction Decimal Percent
0.39 39%
0.82
22%
0.8
The complete table will be:
Fraction Decimal Percent
39/100 0.39 39%
82/100 0.82 82%
22/100 0.22 22%
3/4 0.75 75%
80/100 0.8 80%
Percentage
The percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the following example:
[tex]\frac{25}{100} =0.25*100=25%[/tex]
The percentage is considered a math tool with several applications and areas, for example: medicine, engineering, investments, supermarkets, drugstores,banks etc.
Line 1Fraction Decimal Percent
39/100 0.39 0.39*100=39%
Line 2Fraction Decimal Percent
82/100 0.82 0.82*100=82%
Line 3
Fraction Decimal Percent
22/100 0.22 22%
Line 4
Fraction Decimal Percent
3/4 0.75 0.75*100=75%
Line 5
Fraction Decimal Percent
80/100 0.8 0.80*100=80%
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How many full cases and additional items are needed to fulfill the order? 50 8
The computation illustrate that there'll be 13 cases and 2 additional units.
How to illustrate the information?From the information given, it was stated that 80 units are needed, 6. units per case.
Therefore, the number of cases will be:
= 80/6
= 13 remainder 2.
Therefore, there'll be 13 cases and 2 additional units
Complete information
80 units are needed, 6. units per case. What is the number of cases and the number of additional units?
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a = 2bh+6
make b subject algebraic expression
Answer:
b = (a - 6)/2h
Step-by-step explanation:
a = 2bh + 6 (subtract 6 from both sides)
a - 6 = 2bh (divide both sides by 2)
(a - 6)/2 = bh (divide both sides by h)
(a - 6)/2h = b
Brainliest, please :)
Theodore invests $20,000 at 6% simple interest for 1 year. How much is in the account at the end of the 1
year period?
Answer:
Answer:
$21200
Step-by-step explanation:
6% × 20000 = 1200.
20000 + 1200 = 21200
basically yout find 6% of 20000 then add it the original 20000
Question 2: Xiulin and Meifang had an equal number of postcards. Meifang gave some of her postcards to Xiulin. After that, Meifang had 76 fewer postcards than Xiulin. Given that Meifang had 72 postcards left, find the number of postcards Xiulin had at first.
110 postcards Xiulin had at first.
What is algebric equation?Algebric equation is a mathematical statement in which two equation set equal to each other.
Let the number of postcards belonging to Xiulin and Meifang be x.
Let the number of postcard Meifang gave to Xuilin be 'a'
Number of postcard left with meifang
=> x-a = 72
=> x = 72+a
Meifang had 76 fewer postcards than Xiulin.
so, (x+a)-72=76
72+a+a-72=76
2a = 76
a = 38
meifang give 38 cards to xuilin
x = 72+38
= 110
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help me pls: what is
four and two eighths minus two and five eighths equals
Answer:
13/8
Step-by-step explanation:
4 2/8 - 2 5/8
34/8 - 21/8 = 13/8
1 5/8 as a mixed fraction
solve the following portion for x/11=8/3. round to nearest tenth
The profit function for a certain commodity is given by () = 110 − 2 − 1000. Find the level of production that yields maximum profit and hence find the maximum profit.
Based on the profit function given, the level of production that yields the maximum profit is 55 units. The maximum profit is $2,025.
What is the maximum profits unit?With a profit function:
=-x² + 110x - 1,000
Using a parabola function, we know:
= -b / 2a
The maximum units is:
= -110 / (-2 x 1)
= 55 units
The maximum profit is:
= -(55)² + (110 x 55) - 1,000
= $2,025
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Officially, variable names in Python can be any length and can consist of uppercase and lowercase letters ( A-Z, a-z ), digits ( 0-9 ), and the underscore character ( _ ). An additional restriction is that, although a variable name can contain digits, the first character of a variable name cannot be a digit. Python’s most-followed style guide, PEP8 also suggests we limit each line to 79 characters, so, to be extra careful, we will assume variables can be of at most 7 characters in length.How many variable names can there be in Python if we abide by these two rules?
Abiding by the two rules, the number of variable names we can have in Python are; 63
How to name variables in Python Programming?The rules for python are given as;
1) Variable names in Python can be any length and can consist of uppercase and lowercase letters ( A-Z, a-z ), digits ( 0-9 ), and the underscore character ( _ ).
1b) An additional restriction is that, although a variable name can contain digits, the first character of a variable name cannot be a digit.
2) We limit each line to 79 characters, so, to be extra careful, we will assume variables can be of at most 7 characters in length.
Now, abiding by the two rules above, the number of variable names we can have in Python are;
26( A-Z) + 26(a-z) + 10(0-9) + 1 ( _ ) = 63 variable names
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Sets A,B , and C are subsets of the universal set U.
These sets are defined as follows.
U= {f,g,h,p.q.r.x.y.z}
A={f,h,p.q.r}
B={q,r,y,z}
C={g,h,p,q,y}
Find (B' U A) ∩ C.
Write your answer in roster form or as Ø.
[tex]B'=\{f,g,h,p,x\}\\B'\cup A=\{f,g,h,p,q,r,x\}\\(B'\cup A)\cap C=\{g,h,p,q\}[/tex]
I NEED ANSWER ASAP please and thank you
Answer:
hexagon and pentagon structure. also known as a truncated icosahedron
Step-by-step explanation:
hope that gives you a good enough description.
Complete the frequency table:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
What percentage of students age 15 and above travel to school by bus? Round to the nearest whole percent.
The percentage of students age 15 and above travel to school by bus is 47%
How to complete the table?The table of values is given as:
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 18 165
Age 15 and above 65 195
Column totals 152 110 98 360
Using the column total of column 1, we have:
Under age 15 + 65 = 152
This gives
Under age 15 = 87
Using the column total of column 2, we have:
Age 15 and above + 18 = 110
This gives
Age 15 and above = 92
Using the row total of row 1, we have:
Car + 87 + 18 = 165
This gives
Car = 60
Using the row total of row 2, we have:
Car + 65 + 92 = 195
This gives
Car = 38
So, the complete frequency table is
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 87 18 60 165
Age 15 and above 65 92 38 195
Column totals 152 110 98 360
The percentage of students age 15 and above travel to school by bus is:
Percentage = 92/195 * 100%
This gives
Percentage = 47%
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