Answer:
The sample size needed is of 10,484.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The weekly earnings of students in one age group are normally distributed with a standard deviation of 88 dollars.
This means that [tex]\sigma = 88[/tex]
Find the sample size needed to assure with 98 percent confidence that the sample mean will not differ from the population mean by more than 2 dollars.
This is n for which M = 2. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 2.327\frac{88}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 2.327*88[/tex]
[tex]\sqrt{n} = \frac{2.327*88}{2}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327*88}{2})^2[/tex]
[tex]n = 10483.3[/tex]
Rounding up:
The sample size needed is of 10,484.
Translate into algebra,
the sum of twice the number x and 25 more than 3 times the number y
Answer: The expression would look like 2x+(25+3y).
Step-by-step explanation:
Let the number be x
2x+(25+3y)
The algebraic expression will be [tex]2x+(25+3y)[/tex] .
What is expression ?Expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
We have,
A number [tex]x[/tex]
Number [tex]y[/tex],
The sum of twice the number [tex]x[/tex] and [tex]25[/tex] more than [tex]3[/tex] times the number [tex]y[/tex] ,
So,
According to the question,
sum of twice the number [tex]x[/tex] [tex]=2x[/tex]
And,
ore than [tex]3[/tex] times the number [tex]y[/tex] [tex]=25+3y[/tex]
Now,
The whole algebraic expression,
[tex]2x+25+3y[/tex]
Hence, we can say that the algebraic expression will be [tex]2x+(25+3y)[/tex] .
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Help fast please in a test and don’t know the answer I have tried Googling and everything please help
Answer:
Surface Area = 3,543.7 cm²
Step-by-step explanation:
Surface area of the cylinder = 2πr(h + r)
Where,
radius (r) = 12 cm
height (h) = 35 cm
Plug in the values into the surface area formula
S.A = 2*π*12(35 + 12)
S.A = 24π(47)
S.A = 3,543.71651 cm²
≈ 3,543.7 cm² (approximated to the nearest tenth)
How would I answer this: How many minutes are in a 30-day month.... use vertical multiplication to get the right answer
Answer:
There are 43200 minutes in a 30-day month.
Step-by-step explanation:
We know that:
60 minutes = 1 hour
24 hours = 1 day
Thus to determine the minutes in a 30-day month, let us first determine the number of hours in the month.
30
x 24
_______
120
60
_______
720 hours
The 30-day month has a total of 720 hours.
So that the number of minutes that make up 720 hours can be determined by;
720
x 60
_______
000
4320
_______
43200
Therefore, there are 43200 minutes in a 30-day month.
The zeros of polynomial function g are -5, -1, and 7. Complete the factors to write an equation for function g. Assume that g has only three zeros and three factors.
Answer:
g(x) = (x + 5)(x + 1)(x - 7)
Step-by-step explanation:
i know for a fact im right
The complete equation of function whose zeros are given;
f(x) = (x+5)(x+1)(x-7)
What is Polynomial?
A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number.
Here, given zeros are;
-5, -1, 7
then we can write;
x = -5, x = -1; x = 7
x +5 = 0 ; x + 1 = 0 ; x - 7 = 0
On multiplying all the terms we get;
(x+5)(x+1)(x-7) = 0
Thus, The complete equation of function whose zeros are given;
f(x) = (x+5)(x+1)(x-7)
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solve: 5y +12 - 3y + 12 = 18
Answer:
5y-3y+12+12=18
2y = 18 - 24
y = -6/2
y = -3
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{5y + 12 - 3y + 12 = 18}\\\\\large\text{COMBINE the LIKE TERMS}\\\\\large\textsf{(5y - 3y) + (12 + 12) = 18}\\\\\large\text{NEW EQUATION: \textsf{2y + 24 = 18}}\\\\\large\text{SUBTRACT 24 to BOTH SIDES}\\\\\large\textsf{2y + 24 - 24 = 18 + 24}\\\\\large\text{Cancel out: \textsf{24 - 24} because it gives you 0}\\\\\large\text{Keep: \textsf{18 - 24} because it helps solve it helps solve for y}\\\\\large\textsf{18 - 24 = \bf -6}[/tex]
[tex]\large\text{NEW EQUATION: \textsf{2y = -6}}\\\\\large\text{DIVIDE 2 to BOTH SIDES}\\\\\mathsf{\dfrac{2y}{2y}=\dfrac{-6}{2}}\\\\\large\text{Cancel out: }\mathsf{\dfrac{2}{2}}\large\text{ because it gives you 1}\\\\\large\text{KEEP: }\mathsf{\dfrac{-6}{2}}\large\text{ because it gives you the y-value}\\\\\large\textsf{y = }\mathsf{\dfrac{-6}{2}}\\\\\mathsf{\dfrac{-6}{2}= \bf -3}\\\\\\\\\\\boxed{\boxed{\huge\textsf{Answer: y = \bf -3}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}\\\\\\\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]
3n+4 sequence
4n-5 sequence
Answer:
Step-by-step explanation:
3n +4 sequence
n = 1 , 3*1 + 4 = 3 + 4 = 7
n = 2 ; 3*2 + 4 = 6 + 4 = 10
n = 4 ; 3*3 + 4 = 9 + 4 = 13
n = 5 ; 3 *4 + 4 = 12 + 4 = 16
Sequence : 7, 10, 13 , 16, ........
4n - 5
n= 1 ; 4*1 - 5 = 4 - 5 = -1
n = 2; 4*2 - 5 = 8 - 5 = 3
n = 3 ; 4*3 - 5 = 12 - 5 = 7
n = 4 ; 4*4 - 5 = 16 - 5 = 11
Sequence: -1, 3 , 7 , 11 ,........
A side of the triangle below has been extended to form an exterior angle of 72°. find the value of x.
Answer:
108°
Step-by-step explanation:
The sum of angles on a straight line is 180°
Therefore:
x + 72° = 180°
x = 180° - 72°
x = 108°
Therefore, the value of x is 108°
Find the percentage of the following:
20/60
18/60
21/60
31/60
Answer:
20/60 = 33%
18/60 = 30%
21/60 = 35%
31/60 = 52%
Step-by-step explanation:
Just divide em'
Simple as that.
Answer:
20/60 = 33%18/60 = 30%21/60 = 35%31/60 = 51.67%I hope th is helps you I just divided the fractions by the way :)
2. A cylindrical candle has a volume of 785 cm. Determine the minimum amount of plastic which is needed to cover
the outside of the candle for packaging and find the dimensions of the candle which produce this surface area
3. A company which produces pizza ovens has had complaints about their ovens losing too much heat to be
efficient. They have decided to redesign their ovens. The ovens must have a volume of 0.512 m. Find the
optimal design for the oven so that the surface is as small as possible to minimize heat loss Calculate that
surface area.
Answer:
2. Candle dimensions: x = 6.3 cm h = 6.29 cm
A (min) = 373.49 cm²
3. Cylindrical oven dimensions: x = 0.54 m h = 0.55 m
A (min)= 1.4747 m²
Step-by-step explanation:
2.A The volume V of the cylindrical candle is 785 cm³
V = π*x²*h x is the radius of the base and h the heigh of the cylinder
The surface area A is area of the base π*x² . plus lateral area 2*π*r*h
then . A = π*x² + 2*π*x*h . h = V/π*x²
A as a function of x . is
A(x) = π*x² + 2*π*x*785/π*x²
A(x) = π*x² + 1570/x
Taking derivatives on both sides of the equation we get:
A' (x) = 2*π*x - 1570/x²
A'(x) = 0 . 2*π*x - 1570/x² = 0 . 2*π*x³ = 1570
x³ = 250
x = 6.3 cm . and . h = 785/π*x² . h = 785/124.63
h = 6.29 cm
Then dimensions of the cylindrical candle:
x = 6.3 cm h = 6.29 cm
A (min) = 3.14 * (6.3)² + 6.28*6.3*6.29
A (min) = 124.63 + 248.86
A (min) = 373.49 cm²
3. For a cylindrical oven V = 0.512 h = 0.512/ π*x²
Following the same procedure
A(x) = π*x² + 2*π*x*0.512/π*x² .A(x) = π*x² + 1024/x
A'(x) = 2* π*x - 1.024/x²
A'(x) =0 . 2* π*x - 1.024/x² =0 . 2* π*x³ . = 1.024
x³ = 0.512/π . x³ = 0.163
x = 0.54 m h = 0.512/π*x² . h = 0.55 m
A(min) = 3.14*(0.54)² + 1024/x
A(min)= 0.9156 + 0.5591
A (min)= 1.4747 m²
help asap no wrong answers----------------------
Answer:
[tex]y=-2(sin(2x))-7[/tex]
Step-by-step explanation:
1. Approach
Given information:
The graph intersects the midline at (0, -7)The graph has a minimum point at ([tex]\frac{\pi}{4}[/tex], 9).What conclusions can be made about this function:
The graph is a sine function, as its y-intercept intersects the midlineThis graph has a negative coefficient, this is because after intersecting the midlines at the y-intercept, the function has a minimum.This graph does not appear to have undergone any horizontal shift, as it intercepts the midlines with its y-interceptTherefore, one has the following information figured out:
[tex]y=-n(sin(ax))+b[/tex]
Now one has to find the following information:
amplitudemidlineperiod2. Midline
The midlines can simply be defined as a line that goes through a sinusoidal function, cutting the function in half. This is represented by the constant (b). One is given that point (0, -7) is where the graph intersects the midline. The (y-coordinate) of this point is the midline. Therefore, the midline is the following:
y = -7
2. Amplitude
The amplitude is represented by the coefficient (n). It can simply be defined by the distance from the midline to point of maximum (the highest part of a sinusoidal function) or point of minimum (lowest point on the function). Since the function reaches a point of minimum after intercepting the (y-axis) at its midlines, the amplitude is a negative coefficient. One can find the absolute value of the amplitude by finding the difference of the (y-coordinate) of the point of minimum (or maximum) and the absolute value of the midline.
point of minimum: [tex](\frac{\pi}{4},9)[/tex]
midline: [tex]y=-7[/tex]
Amplitude: 9 - |-7| = 9 - 7 = 2
3. Period
The period of a sinusoidal function is the amount of time it takes to reach the same point on the wave. In essence, if one were to select any point on the sinusoidal function, and draw a line going to the right, how long would it take for that line to reach a point on the function that is identical to the point at which it started. This can be found by taking the difference of the (x- coordinate) of the intersection point of the midline, and the (x-coordinate) of the point of minimum, and multiplying it by (4).
point of minimum: [tex](\frac{\pi}{4},9)[/tex]
midline intersection: [tex](0, -7)[/tex]
Period: [tex]4(\frac{\pi}{4}-0)=4(\frac{\pi}{4})=\pi[/tex]
However, in order to input this into the function in place of the variable (a), one has to divide this number by ([tex]2\pi[/tex]).
[tex]a=\frac{2\pi}{\pi}=2[/tex]
4. Assemble the function
One now has the following solutions to the variables:
[tex]n =-16\\a=2\\b=-7\\[/tex]
Substitute these values into the function:
[tex]y=-2(sin(2x))-7[/tex]
Jernel has to figure out the area of her square garage. She knows that one side of the garage is equal to the length of her rabbit pen. The dimensions of the rectangular rabbit pen are 13 by 10.
Answer:169
Step-by-step explanation:13 x 13 = 169
You would take the larger side of the pen (13) or else it wouldn’t fit if you chose 10.
which of these graphs represents a function
Answer:
W
Step-by-step explanation:
The vertical line test is a simple tool to determine if a graph is a function. Draw a vertical line through the graph. If at any point where you draw this line you hit the relation twice or more you know it to not be a function. What I mean is that if you have multiple Y's for a single X, then it cant be a function.
Side note: Vertical is up and down, like the line in X.
Strat with k add 2 multiply by 6 then subtract 8
Answer:
6(k+2) -8
Step-by-step explanation:
Start with k
k
Add 2
(k+2)
Multiply by 6
6(k+2)
Then subtract 8
6(k+2) -8
6(k+2)-8 is a required answer.
Answer:
Solution given:
Start with k.
Kadd 2
k+2multiply by six
(k+2)*6subtract by 8
6(k+2)-8WORD PROBLEM -
Sohanlal is a gardener He is paid 160 daily find how much money will he get in the month of September
GIVE ME UR ANSWERS SOON PLS
Suppose that a1, a2, a3, . . . is an arithmetic sequence, in which a3 = 19 and a14 = 96. Find a1.
In Australia, road distance is measured in kilometres.
In the USA, road distance is measured in miles.
5 miles is about the same distance as 8 kilometres.
About how many miles is 120 kilometres?
Answer:
75
Step-by-step explanation:
5 miles-8km
x miles-120 km
x=120×5÷8
x=75 (miles)
Answer:
s
Step-by-step explanation:
since 5 miles is the same as 8 kilometers,how many miles is 120 kilometers..use ratio and proportion
5miles:8kilometers
x. :120kilometers
8x/8=600/8
x=75miles
I hope this helps
Niko wants to put soil in his garden shown below. If soil comes in bags that fill 6 square yards each, how many bags of soil should Niko buy? Hint: you may have some leftover soil.
Answer:
444 pot soils
Step-by-step explanation:
What happens when f(x) becomes -f(x-4)
f(x) -> - f(x): Relflection across x-axis
-f(x) -> -f(x-4): Vertical Translation right 4 units
can anyone help me by explaining this? i would really appreciate it
Answer:
156
Step-by-step explanation:
the frost burg truth bus travels on a straight road from Frostburg mall to sojourner truth park. The mall is 3 miles west and 4 miles south of the city center. The park is 3 miles east and 5 miles north of the center. How far is it from the mall to the park to the nearest 10th of a mile?
9514 1404 393
Answer:
10.8 miles
Step-by-step explanation:
The distance between (-3, -4) and (3, 5) can be found using the distance formula.
d = √((x2 -x1)^2 +(y2 -y1)^2)
d = √((3 -(-3))^2 +(5 -(-4))^2) = √(6^2 +9^2) = √117
d ≈ 10.8
It is about 10.8 miles from the mall to the park.
Q5. Evaluate this expression when a=6
Q6. Which option shows this expression simplified correctly?
Q7. Which option shows this expression simplified correctly?
Q8. Find the following:
Q9. Which option shows this expression expanded correctly?
What are the coordinates of the image of L for a dilation with center (0, 0) and scale factor ?
Answer:
The vertices of ABCD:
A ( - 3, 1 )
B ( 4 , - 3 )
C ( 1, 3 )
D ( - 1 , 4 )
∴ ( 4 x, 4 y ):
A ` ( - 12, 4 )
B ` ( 16, - 12 )
C ` ( 4, 12 )
D ` ( - 4 , 16 )
Step-by-step explanation: I hope this helps! ™(*/ω＼*)
enlarge shape a by 1/3 with the centre enlargement (3,-3)
(-9,9) (-9,6) (-3,6)
Answer:
0033
Step-by-step explanation:
.033 of a whole number so its .033
10. There is a carnival at a local state park. It cost $5 to get in and $1.50 per ride.
Suppose Maya Mapleton has $25 to spend for the day. Which inequality would
model this situation?
5+1.50x 2 25
5x + 1.50 s 25
5 + 1.50x s 25
0 25x +1.50 s 5
Answer:
C. 5+ 1.50x is less than or equal to 25
Step-by-step explanation:
Maya has 25 dollars to spend, and it cost 5 to get in. Each ride will cost her 1.50, so she has to spend up to or less than 25 on the entry fee and each ride.
Find the measure of arc BC?
Answer:
129
Step-by-step explanation:
Since,
AD = BC
AD = 3x + 24
BC = 4x - 11
3x + 24 = 4x - 11
4x - 11 = 3x + 24
4x - 3x = 24 + 11
x = 35
BC = 4x - 11
= 4 ( 35 ) - 11
= 140 - 11
BC = 129
Answer:
[tex]AB=BC[/tex]
[tex]3x+24=4x-11[/tex]
[tex]3x-4x=-11-24[/tex]
[tex]x=35[/tex]
[tex]BC=4\times 35-1[/tex]
[tex]=140-11[/tex]
[tex]=129[/tex]
--------------------------
Hope it helps..
Have a great day!!
solve for x−4 + x ≤ 9
Answer:
x ≤ 6.5
Step-by-step explanation:
x−4 + x ≤ 9
Combine like terms
2x-4≤ 9
Add 4 to each side
2x-4+4≤ 9+4
2x≤ 13
Divide by 2
2x/2 ≤ 13/2
x ≤ 6.5
Evaluate (5.6 x 10^-4 ) - (9.3x10^-6)
Give your answer in standard form to 3SF
Answer:
I got 5.51x10^-4
Step-by-step explanation:
Answer:
.0005507
Step-by-step explanation:
5.6 x [tex]10^{-4}[/tex]
9.3 x [tex]10^{-6}[/tex]
560 x [tex]10^{-6}[/tex]
- 9.3 x [tex]10^{-6}[/tex]
550.7 x [tex]10^{-6}[/tex]
.0005507
15) The ratio of girls to boys is 1:2 and that there are 22 boys, what is the number of girls?
Answer:
11
Step-by-step explanation:
first you sum the ratios
1+2=3
[tex] \frac{2}{3} \times x = 22 \\ 2x = 66 \\ x = 33 \\ this \: mean \: that \: we \: have \: 33 \: \\ students[/tex]
since boys are 22 , all we have to do is to subtract 22 from 33 the answer would be 11
therefore we have 11 girls.
Answer:
its 11
Step-by-step explanation:
I need help.please with this math problem
Answer:
1372 cubic centimeters
Step-by-step explanation:
V = 4/3(π)(r^3)
Exchange π for 3
4/3(3)(r^3) = ?
Exchange r for the radius, 7
4/3(3)(7^3) = ?
4/3(3)(343) = ?
4(343) = 1372
1372 cubic centimeters
If the outliers are not included what is the mean of the data set 76,79,80,82,50,78,79,81,82
Answer:
The answer is 80
Step-by-step explanation:
we know that
the outlier is 50, as it is not around the other numbers in the data set.
therefore
mean=[76+ 79 + 80 + 82+ 78 + 83 + 79 + 81 + 82]/9
mean=[720]/9
mean=80
Answer:
80
Step-by-step explanation:
mean=[76+ 79 + 80 + 82+ 78 + 83 + 79 + 81 + 82]/9
mean=[720]/9
mean=80
