Using the normal distribution and the central limit theorem, it is found that there is a 0.5934 = 59.34% probability that there is an error of at most $1000.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Researching the problem on the internet, it is found that the population has mean and standard deviation given, respectively, by [tex]\mu = 57300, \sigma = 9600[/tex].
For samples of 64, the standard error is given by:
[tex]s = \frac{9600}{\sqrt{64}} = 1200[/tex]
The probability of an error of at most $1000 is the probability of a sample mean between $56,300 and $58,300, which is the p-value of Z when X = 58300 subtracted by the p-value of Z when X = 56300, hence:
X = 58300:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{58300 - 57300}{1200}[/tex]
Z = 0.83
Z = 0.83 has a p-value of 0.7967.
X = 56300:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56300 - 57300}{1200}[/tex]
Z = -0.83
Z = -0.83 has a p-value of 0.2033.
0.7967 - 0.2033 = 0.5934.
0.5934 = 59.34% probability that there is an error of at most $1000.
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The point (7,7) is a point on the terminal side of theta. What is the exact value of csc theta in simplest form?
[tex](\stackrel{a}{7}~~,~~\stackrel{b}{7})\qquad \impliedby \textit{let's find its \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{7^2+7^2}\implies c=\sqrt{7^2(1+1)}\implies c=\sqrt{7^2(2)}\implies c=7\sqrt{2} \\\\[-0.35em] ~\dotfill\\\\ csc(\theta )=\cfrac{\stackrel{hypotenuse}{7\sqrt{2}}}{\underset{opposite}{7}}\implies csc(\theta )=\sqrt{2}[/tex]
Hi guys can you please do this only question 6 and 8 ty
Question 6
End ÷ Initial = Growth + 1 (percent increase problems)
6,500/5,000 = 1.30
1.30 - 1 = 0.30
30% increase
Question 8
End ÷ Initial = 1 - Growth (percent decrease problems)
10.75/15.50 = 0.69
1 - 0.69 = 0.31
31% decrease
I hope this helps!
When solving this equation for x, what would you do next?
Answer: A. Distribute the 3 outside of the parathesis to everything inside the parenthesis
We use the order of operations, also known as PEMDAS.
Since there is a variable inside the parenthesis, we cannot add/subtract 4. This means the next step is to distribute.
After distributing, the equation looks like this and we can solve it from there:
4x + 12 = 30
Suppose a line, with a slope of -3 and a y-intercept of 4, is translated -4 units along the x-axis and 6 units along the y-axis. What is the equation of this new line?
pls hurry
Find equation of old line first
m=-3b=4Equation in slope intercept form
y=-3x+4Translated 4units left(x+4)
Translated 6 units up(y intercept +6)
Put it.
y=-3(x+4)+6+4y=-3x-12+10y=-3x-2Answer:
y = -3x -2
Step-by-step explanation:
The equation of the given line, with slope -3 and y-intercept 4, can be written in slope-intercept form as ...
y = -3x +4
When the line is translated by (h, k), it can be written as ...
(y -k) = -3(x -h) +4
__
Here, we want to translate the line -4 in the x-direction and 6 in the y-direction. That is, (h, k) = (-4, 6). Using these values in the above equation, we have ...
y -6 = -3(x -(-4)) +4
y = -3x -12 +4 +6 . . . . simplify, add 6
y = -3x -2
__
The attached graph shows the original line (red) with its y-intercept, and the translated line (green) with that y-intercept moved 4 units left and 6 units up.
convert 17/4 to a mixed
Answer:
17/4 is 4 ¼ as a mixed fraction
Step-by-step explanation:
hope this helps
When rounded to the hundreds place, which of the numbers below round to 23,400? Select all that apply.
A) 23,445
B) 23,345
C) 23,395
D) 23,410
E) 23,451
Answer:
I think the answer is B 23,345
pls help me with this i have a 0 in math
Answer:
(3−5)(+1)
Step-by-step explanation:
I hope this helps you and please mark me as brainliest
Answer:
The answer is ( p + 1 ) ( 3p - 5 )
Step-by-step explanation:
An awning that covers a sliding glass door that is 88 inches tall forms an angle of 50° with the wall. The purpose of the awning is to prevent sunlight from entering the house when the angle of elevation of the sun is more than X = 60°
The length of awning which covers a sliding glass door that is 88 inches tall forms an angle of 50° with the wall, is 44.7 inches.
What is the law of sine?The law of sine is nothing but the relationship between the sides of the triangle to the angle of the triangle (oblique triangle).
It can be given as,
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
Here (A,B,C) are the angle of the triangle and (a,b,c) are the sides of that triangle.
An awning that covers a sliding glass door that is 88 inches tall forms an angle of 50° with the wall.
The figure of the problem is attached below. The length of AB which is L has to be find out.
The purpose of the awning is to prevent sunlight from entering the house when the angle of elevation of the sun is more than X = 60°. Thus, the angle ABC is 30 degrees.
[tex]AB=90-60\\AB=30^o[/tex]
The sum of all the interior angle is 180 degree. Thus, the angle ACB is,
[tex]\angle ACB=180-50-30\\\angle ACB=100^o\\[/tex]
Let suppose, the length of AB is a. Thus, by the sine law,
[tex]\dfrac{\sin 30}{a}=\dfrac{\sin 100}{88}\\a=\dfrac{88\times\sin 300}{\sin 100}\\a=447\rm\; in[/tex]
Thus, the length of awning which covers a sliding glass door that is 88 inches tall forms an angle of 50° with the wall, is 44.7 inches.
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Which list shows the fractions in order from greatest to least? *
pls help i give brainliest
3/6, 2/5, 1/4, 2/5
2/3, 3/6, 1/4, 2/5
1/4, 3/6, 2/5, 2/3
2/3, 3/6, 2/5, 1/4
Answer:
1/4, 3/6, 2/5, 2/3.........
Each face of a cube has an area of 4 square units. What is the volume of the cube?
Each face of a cube has an area of 4 square units, then the volume of the cube is 8 cubic units.
The given information states that each face of the cube has an area of 4 square units.
Since a cube has 6 faces, this means that the total surface area of the cube is:
Total Surface Area = 6 * 4 square units = 24 square units
Now, let's relate the surface area of the cube to its volume:
For a cube, the surface area (S) and the volume (V) are related by the formula:
S = 6s²
Where "s" is the length of each side of the cube. In this case, we have:
S = 24 square units
Substitute this into the formula:
24 = 6s²
Now, solve for "s":
s² = 24 / 6
s² = 4
Take the square root of both sides:
s = √4
s = 2
So, each side of the cube is 2 units long.
Now, to find the volume of the cube, you can use the formula for the volume of a cube:
V = s³
Substitute the value of "s":
V = 2³
V = 8 cubic units
Therefore, the volume of the cube is 8 cubic units.
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Am I correct?!? Please tell me!
Answer:
B
Step-by-step explanation:
Standard form of a polynomial is when the terms are order from highest exponential power to lowest exponential power. The choice you chose has the highest exponential power of 1, and a leading coefficient of 1. You are incorrect. The correct answer would be the second choice of:
[tex]5 {x}^{2} + 6x - 7[/tex]
This polynomial is in standard form, and has a leading coefficient of positive 5.
Find the perimeter of each figure. 6 cm 2 cm 2 cm 6 cm
Answer:
That's not full question
Angle of _____ symmetry is the smallest angle through which a preimage can be rotated to coincide with its image.
Please answer the question correctly and with a good explanation. Please and thank you
Answer:
48
Step-by-step explanation:
To calculate the area of a composite shape you must divide the shape into rectangles, triangles, or other shapes you can find the area of and then add the areas back together. You may have to calculate missing lengths before finding the area of some of the shapes.
I split it into a square and a trapezoid
The area of the square is 6x5 = 30
The area of the trapezoid is
A=a+b
2h=3+6
2·4=18
So add the area together
30+18= 48
which answer is right and please explain
How many times greater is 7,000,000( 7 million ) than 700,000(700 thousand)?
Answer:
6300000
Step-by-step explanation:
7,000,000-700,000=6300000
Answer:
10 times greater
Step-by-step explanation:
When you do something for the benefit of another, it's a benefit to you as well.
Agree
Disagree
Explain why you voted the way you did.
Answer:
Yes, It is a benifit for both.
Step-by-step explanation:
Doing something for someone else that makes both of the people feel good so it is a benifit for both.
Answer:
Agree
Step-by-step explanation:
Agree, helping others to benefit them makes you feel good. In return, you get a sense of happiness for benefiting them. There is evidence that shows that helping people/letting them benefit ends up improving our mental health. Not only do you help someone but you're also helping yourself.
Kinda like volunteering. You're not required to volunteer at all. However, in doing so you're benefiting whatever you're volunteering for AND you end up feeling really good for helping out.
How do you recognize a geometric sequence? Can you find terms within a geometric sequence using a formula?
Answer:
See step by step explanation
Step-by-step explanation:
To reconize a geometric sequence, the factor at which one number is greater than the previous number should always be the same
For example,
2,4,8,16,32,64,128,256,512,1024 is a geometric sequence since the next number is always greater than the previous number by a factor of 2
to find the n-th term in a sequence, we can use a formula.
Going back to the example, let's label each number with a term
to find the nth term of this specific sequence, we need to find two things
the first number of the sequence, and the factor at which this sequence increases at
the first number is 2, so n1 = 2
each term increases by a factor of 2 (2*2=4, 4*2=8, 8*2=16, 16*2=32, 32*2=64), so the factor is 2
the equation is:
(the initial term)*(the factor)^(the term number - 1)
so,
[tex]2*2^{n-1}[/tex] is our equation
We can check our equation by plugging in a number
looking back at our list, we see that the 7th term is 128
plug in 7 into out equation
[tex]2*2^{7-1}=2*2^6=2^1*2^6=2^7=128[/tex], so our equation works
Here's a practice problem
for the sequence 3,9,27,81,243,729, what is the factor which the sequence increases at? what's the initial number? what's the equation for this sequence?
a harder practice problem:
for the sequence 2,6,18,54,162,486, what is the factor at which the sequence increases at? what's the intitial number? what's the equation for this sequence? what's the 8th term of this sequence if it were to be continued?
Yes we can
the formula given to find the terms is
a_n=ar^n-1Where
a_n is n the terma is first termr is common ration is an positive integerplease someone help.
4³/(-12+2²) / (2×3)²+(-5×2×3)+2
= 64/ (-12+4) / (4×9)+(-5×2×3)+2
= 64/ (-12+4) / 36+(-30)+2
= 64/8 / 8
= 8 /8
=1
In the equation y=2(3)^x what does the 2 represent? What does the 3 represent?
Answer:
This is an exponential function equation.
Therefore,
The 2 represents: Original amount (Y-intercept)
The 3 represents: Growth factor or (1+r)
A sequence can be generated by using a,n = a,n (-1) + 2, where a,1 = 6 and n is a whole number greater than 1.
What are the first 5 terms in the sequence?
A.) 6, 12, 24, 48, 96
B.) 2, 8, 14, 20, 26
C.) 2, 12, 72, 432, 2592
D.) 6, 8, 10, 12, 14
For her mother's birthday, Eva spends $6.78 on a photo. She also buys 4 balloons for $1.49 each and a box of blueberries for $4.50. How much money does she spend all together?
Hope the picture will help you!!
Answer: $17.24
Step-by-step explanation:
6.78 + (1.49 x 4) + 4.50= 17.24
A person sold a desk for rs. 400 and incurred a loss of 5%
approximately at what price would it be sold so as to earn
a profit of 6%?
a) 420
b)478
c)446
d)432
Answer: C
Step-by-step explanation:
1% of Rs. 400 = 4
10% of Rs.400 = 40
5%= 20
400+20= Rs. 420 was the price the person may have bought it for
To get a 6% profit, we need to add 6% on top of the price the chair was bought for by the owner
so...
420+ 5% +1%
so..
420+20+4= 444
The answer has come to 444 whereas it is not an option as a possible answer and I am unable to see a miscalculation in my working so if anyone spots a mistake it would be much appreciated. I have gotten a value close to one of the possible answers therefore I think the answer most probably should be "C" according to my working, however it may be that the person typing in the question may have written the incorrect options. Either way I have come to a conclusion and if it happens to be a typing error my maths was correct, if no, someone please reach out to me and help me identify where I have gone wrong, Thank you.
Which is the BEST definition of dilation?
A. a transformation that either reduces or enlarges an object in the coordinate plane
B. a transformation that flips an object in the coordinate plane
C. a transformation that spins an object in the coordinate plane
D. a transformation that either slides or shifts an object in the coordinate plane
Answer:
A. a transformation that either reduces or enlarges an object in the coordinate plane
Step-by-step explanation:
The definition of dilation is the size of an object/shape by increasing/ decreasing its dimensions by scaling factors.
Dialtions do not flip and object, spin it, or slide it. It's dimensions are either enlarged, or reduced. Therefore, option A makes the most sense.
i need help can someone help
Answer:
Step-by-step explanation:
The distributive property is for example 3(2*4) the outside number multiplies everything inside the parenthesis. For the communitive, its like opposites, but they give the same answer, for example 4*5, 5*4. And for associative is like the distributive property, but not at the same time, for example, (a*b)*c = a*(b*c) it has the numbers, but pluged in in another type of way
Hope this helps!
An airplane flies with a constant speed
of 820 miles per hour. How far can it
travel in 3 1/2 hours?
2870 miles
D= s x t
= 820 x 3.5
=2870
Hope this helps!
What is the surface area of the cylinder with height 4 in and radius 5 in? Round your answer to the nearest thousandth.
Answer:
282.74
Step-by-step explanation:
Answer:
[tex]\fbox{Surface area of cylinder = 282.6 sq. in.}[/tex]
Step-by-step explanation:
Given:
Shape of object = cylinder
height of cylinder= 4 inches
radius of cylinder= 5 inches
To find:
surface area of cylinder = ?
Solution:
we know that,
[tex]surface \: area \: of \: cylinder =2\pi{rh} + 2\pi {r}^{2}\\Substituting \:the \:constant\: (π =3.14)\\and \:given\: data,\\2\pi{rh} + 2\pi {r}^{2} \: =\\ 2×3.14×5×4+2×3.14× {5}^{2} \\2\pi{rh} + 2\pi {r}^{2} = 125.6 + 157 \\ 2\pi{rh} + 2\pi {r}^{2} = 282.6\\ \fbox{Surface area of cylinder = 282.6 sq. in.}[/tex][/tex]
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Please help I will give brainliest!
Explain how you would find the perimeter of this triangle.
Answer:
Step-by-step explanation:
51+90=141.3
180-141.3=38.7
90+38.7+51.3
So 4 and a number equal 90 degrees.
51.3 degrees are the number of 4 and c^2
We can use the Pythagorean theorem to find out that a^2 is 16
16 and b^2 will equal c^2 or the missing angle for 51.3 degrees.
a=51.3
b=90 meaning it has a 38.7 more of an angle than the 4 on the bottom.
Meaning it will be 7.02
7.02+4=11.02
9. The growth of mold in Specimen A can be modeled by A(t) = The growth
of mold in Specimen B can be modeled by B(t)
a. Find (A - B)(t).
b. Explain what the function (A - B)(t) represents
The value of the difference of the functions is 3t^2/3
The difference in the growth of the specimen is 3t^2/3
Exponential functionsExpoenential functions are written in the form y= ab^x
Given the following expoenential functions
A(t) = 5/6t^2/3
B(t) = 1/3t^2/3
a) Determine the function (A-B(t)
(A-B)(t) = A(t) - B(t)
Substitute
(A-B)(t) = 5/6t^2/3 - 1/3t^2/3
(A-B)(t) = (5/6-1/3)t^2/3
(A-B)(t) = 9/3t^2/3
(A-B)(t) = = 3t^2/3
b) This means that the difference in the growth of the specimen is 3t^2/3
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What is the value of x
x = 20°
The total sum of interior angles in a triangle is 180°
x + 5 + 7(x) - 5 + x = 180°x + 7(x) + x + 5 - 5 = 180°9(x) = 180°x = 20°Answer:
D) x = 20
Step-by-step explanation:
Theorem
The sum of the interior angles of a triangle is 180°
Solution
Add the angles and equate to 180:
⇒ (x + 5) + (7x - 5) + x = 180
Collect like terms:
⇒ x + 7x + x + 5 - 5 = 180
Combine like terms:
⇒ 9x = 180
Divide both sides by 9:
⇒ x = 20
