A population has a mean of 200 and a standard deviation of 50. Suppose a simple random sample of size 100 is selected and x is used to estimate . a. What is the probability that the sample mean will be within 65 of the population mean
Answer:
z(195) = (195-200)/50 = -0.1
z(205) = (205-200)/50 = +0.1
P(195 < x < 205) = p(-0.1 < z < 0.1) = 0.0797
Step-by-step explanation:
step by step is in they're
Using the normal distribution and the central limit theorem, it is found that there is a 1 = 100% probability that the sample mean will be within 65 of the population mean.
In 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].In this problem:
The mean is of 200, hence [tex]\mu = 200[/tex].The standard deviation is of 50, hence [tex]\sigma = 50[/tex].The sample size is of 100, hence [tex]n = 100, s = \frac{50}{\sqrt{100}} = 5[/tex].We want the probability that the sample mean will be within 65 of the population mean, hence:
[tex]Z = \frac{65}{s}[/tex]
[tex]Z = \frac{65}{5}[/tex]
[tex]Z = 13[/tex]
The probability is P(|Z| < 13), which is the p-value of Z = 13 subtracted by the p-value of Z = -13.
Looking at the z-table:
Z = 13 has a p-value of 1.Z = -13 has a p-value of 0.1 - 0 = 1
1 = 100% probability that the sample mean will be within 65 of the population mean.
To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213
QUICK! I NEED HELP ASAP
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w−(−1/3)=2.05
Enter your answer as a mixed number in simplest form in the box.
w =
Answer:
w=6
Step-by-step explanation: you should just look it up on line
Answer:
The correct answer is 1 43/60
Step-by-step explanation:
you convert 2.05 to a fraction and get 2 23/60 - (-1/3) = 1 43/60
i also took the test
Answer: 3x10^2 mi
example:
Answer:
3000
Step-by-step explanation:
Answer:
300
Step-by-3step explanation:
Does anyone know this?
Answer: 8.6?
Step-by-step explanation:
Sierra is getting a loan to purchase a car, but she has a few options for loan terms. She is comparing the cost of each loan to determine which loan will cost the least in terms of interest paid. (Interest is the fee paid for the use of borrowed money, and it is expressed as a percentage of the amount borrowed multiplied by the amount of time the borrower takes to repay the loan.) All of the loan offers are for $10,000, and include an upfront fee of $200. They are all simple interest loans (as opposed to compound interest loans). Loan A is to be paid back over five years with an annual interest rate of 6 percent. Loan B is to be paid back over four years with an annual interest rate of 4 percent. Loan C is to be paid back over three years with an interest rate of 5 percent. How does Sierra figure out which loan will require the lowest interest payments?
Answer:
B
Step-by-step explanation:
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=59(0.59)^x
what is the % increase
Answer:
Step-by-step explanation:
y=59(0.59)ˣ
As the number under the exponent is less than 1, this is a decay function.
Value of y will be decreased by (1.00 - 0.59)100 = 41% for each unit increase in x.
Elliot ran 4 laps in 209.2 seconds. If he ran at the same
speed for each lap, what was his time for each lap?
Answer: 52.3 seconds
Step-by-step explanation:
209.2 divided by 4
which is 52.3 seconds
A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 feet deep at its deepest point. If the pool is being filled at a rate of 0.8ft3/min, how fast is the water level rising when the depth at the deepest point is 5 ft
Using implicit differentiation, it is found that the water level is rising a rate of 0.001 ft/sec.
The volume of a pool of length l, width w and height h is given by:
[tex]V = lwh[/tex]
Applying implicit differentiation, the rate of change of the volume is given by:
[tex]\frac{dV}{dt} = wh\frac{dl}{dt} + lh\frac{dw}{dt} + lw\frac{dh}{dt}[/tex]
Neither the width nor the length changes, hence [tex]\frac{dl}{dt} = \frac{dw}{dt} = 0[/tex], and:
[tex]\frac{dV}{dt} = lw\frac{dh}{dt}[/tex]
We are given that:
[tex]\frac{dV}{dt} = 0.3, l = 20, w = 40[/tex], hence:
[tex]\frac{dV}{dt} = lw\frac{dh}{dt}[/tex]
[tex]0.8 = 20(40)\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{0.8}{800}[/tex]
[tex]\frac{dh}{dt} = 0.001 [/tex]
Water level is rising at rate of 0.001 ft/sec.
A similar problem is given at https://brainly.com/question/9543179
4.
Faiza had 1/2 litres of juice in a jug. She drank of it in the 1/4
morning. Her sister added 3/8 ſlitres more in the jug. How much juice
is in the jug now?
Step-by-step explanation:
1/4*0.5lit=0.125lit
0.125+(3/8*1000)=0.125+0.375=0.5lit
a fingernail grows about 0.1 millimeter eachday how much does a fingernail grow in 90 days
Answer:
9 mm
Step-by-step explanation:
90*0.1=9
Dan bought a truck for $29,800. The value of the truck depreciated at a constant rate per year. The table shows the value of the truck after the first and second years: Year 1 2 Value (in dollars) 26,522 23,604.58 Which function best represents the value of the truck after t years? f(t) = 29,800(0.89)t f(t) = 26,522(0.89)t f(t) = 29,800(0.11)t f(t) = 26,522(0.11)t
Answer:
A) f(t) = 29,800(0.89)^t
Step-by-step explanation:The truck value decreases by 11% each year.
The present value of the truck was $29,800.
29,800 x 0.11 = 3,728 dollars lost from value.
29,800 - 3,728 = 26,522, the value of the truck after one year.
26,522 x 0.11 = 2,917.42 cash lost from value.
26,522 - 3,728 = 23,604.58, the value of the truck after two years.
Therefore, the answer is A) f(t) = 29,800(0.89)^t.
You read 9.75 pages in your science book and 24.5 pages of a play for English class. It takes you 1.2 minutes to read each page of science and 0.8 of a minute to read each page of the play. How much time do you spend reading?
Answer:
9.75*1.2= 11.7min (time spent reading in science)
24.5*0.8=19.6min (time spent reading play)
19.6+11.7= 31.3min (total time spent reading)
what is the value of x?
(3x-1)º
(3x-1)))))]))))))))])))))))))))))])))))))))))))))))))))))
Please help quick!!!
Answeer two questions
Answer:
x = 4[tex]2^2*3*7[/tex]Step-by-step explanation:
First, we add 16 and 28 [tex]16+28=44[/tex]
Now we have to solve for x
We know we have to do parenthesis first so [tex](4+7)=11[/tex]
[tex]44=x(11)[/tex]
Then we divided both sides by 11
[tex]\frac{44}{11} =\frac{11x}{11}[/tex]
[tex]x=4[/tex]
To find the Prime Factorisation of 84 we have to divide 84 by the smallest prime number which is 2
So [tex]\frac{84}{2} = 42[/tex]
Since 42 is an even number we can still divide it by 2
So [tex]\frac{42}{2} = 21[/tex]
Now we can divide 21 by the 2nd smallest prime number which is 3
So [tex]\frac{21}{3} = 7[/tex]
So the prime factors of 84 would be [tex]2*2*3*7[/tex] or [tex]2^2*3*7[/tex]
1.
Write the equation of the parabola in vertex form.
A. y = –(x – 1)2 + 3
B. y = –x2 – 4
C. y = –x2 + 3
D. y = –x2 + 4
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{o pens~\cap}\qquad \stackrel{"a"~is~positive}{o pens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\begin{cases} h= 0\\ k = 4 \end{cases}\implies y=a(x-0)^2+4~\hfill \textit{we also know that} \begin{cases} x = 1\\ y = 3 \end{cases} \\\\\\ 3=a(1-0)^2+4\implies 3=1a+4\implies \boxed{-1=a} \\\\\\ y=-1(x-0)^2+4\implies \blacktriangleright y = -x^2+4\blacktriangleleft[/tex]
Answer:
A. y = –(x – 1)2 + 3 = Rewrite in vertex form and use this form to find the vertex (h,k). (1,3)= Already in vertex form. y=−(x−1)2+3
OR
D. y = –x^2 + 4 = Rewrite in vertex form and use this form to find the vertex (h,k). (0,4)= Find the vertex form. y=−(x+0)2+4
Step-by-step explanation:
A. y = –(x – 1)2 + 3 = Rewrite in vertex form and use this form to find the vertex (h,k). (1,3)= Already in vertex form. y=−(x−1)2+3
B. y = –x^2 – 4 = Rewrite in vertex form and use this form to find the vertex (h,k). (0,−4)= Find the vertex form. y=−(x+0)2−4
C. y = –x^2 + 3 = Rewrite in vertex form and use this form to find the vertex (h,k). (0,3)= Find the vertex form. y=−(x+0)2+3
D. y = –x^2 + 4 = Rewrite in vertex form and use this form to find the vertex (h,k). (0,4)= Find the vertex form. y=−(x+0)2+4
Answer the following:
a) 3-8=
b) -6 -4 =
c) -2 + 6 =
Answer:
a) =5
b) = -10
c) = 4
Step-by-step explanation:
Which table represents y as a function of x?
X
1
2
0
0
1
2
3
3
X
-1
-1
o
2
1
0
2
3
X
V
1
10
2
3
0
1
2
3
x
V
-1
-1
0
-1
Answer:
reduce
Step-by-step explanation:
become it is un solvef
What is the equation of this line in slope-intercept form? (-1,5) (1,-1)
y = 3x - 2
y = -1/3x + 2
y = -3x + 2
y = 3x + 2
Answer:
C
Step-by-step explanation:
y=-3x+2
Simplify the expression 2.1(3.7 +5.7u) using the Distributive Property.
PLEASE HELP! :(
Answer:
7.77+11.97u
Step-by-step explanation:
2.1(3.7+5.7u)=7.77+11.97u
Adrienne biked 24 miles in 5 1/2 hours. If she biked at a constant speed, how many miles did she ride in one hour?
1. How can you solve this?
Answer:
4.36
Step-by-step explanation:
dividing the amount of hours by how many miles Adrienne went will give you how many miles she went per hour.
Equation:
a÷b
a=24
b=5.5 (5 1/2)
24÷5.5=4.36
If a deck of cards is 7/10 of an inch tall, how tall is the package of 6 decks of cards?
2. Twenty machines can embroider 1000 sweaters in 5 days.
a. In how many days can 10 machines embroider the same 2000 sweaters?
b. How many machines would needed to embroider 5000 sweaters in 10 days?
Answer:
a) 20 days
b) 50 machines
61 = 7 - 6x
this is 8th grade math
Answer:
x = -9
Step-by-step explanation:
Solve:
61 = 7 - 6x54 = -6xx = -9-Chetan K
Answer:
[tex]\large\boxed{\boxed{\underline{\underline{\maltese{\pink{\pmb{\sf{\: Solution :- \: x = -9 }}}}}}}}[/tex]
Step-by-step explanation:
[tex]61 = 7 - 6x\\61 - 7 = - 6x\\54 = -6x\\-\frac{54}{6} = x\\\boxed{- 9 = x}[/tex]
______
Hope it helps!
[tex]\mathfrak{Lucazz}[/tex]
1/4 of students in a class play a musical instrument of those students 2/5 also speak a second language. What fraction of the whole class plays a musical instrument and speak a second language
Answer:
Step-by-step explanation:
Say the class has 20 students
20(1/4) = 5 play instruments
5(2/5) = 2 speak a second language
2 / 20 = 1/10
5
which ratio is greater than 5/8
12/24
3/4
15/24
4/12
Answer:(B)
Explanation: 3/4. Hope this helped :)
simplify fully
2√3 x 3√8
Answer: 12√6
Step-by-step explanation:
Given the expression;
2√3 * 3√√8
= (2*3) * (√3*√8)
= 6 * (√24)
= 6 * √4*6
= 6 * (2√6)
= (6*2)√6
= 12√6
Therefore, the simplified form of the expression is 12√6.
Please help me quickly thank you!
Answer:
i think it is a if its wrong sorry
Step-by-step explanation:
Answer:
its 115
Step-by-step explanation:
if you take the angle and look at the end if the triangle it shows the end of the angle as 50. if 50 is the top and right angle and you see another angle that looks like that spliting it in half it is 115. its 115 tho because the right side of the missing angle is bigger than the left. hopefully this helps
Do Babies Understand Probability? Can babies reason probabilistically? A study1 investigates this by showing ten- to twelve-month-old infants two jars of lollipop shaped objects colored pink or black. Each infant first crawled or walked to whichever color they wanted, determining their "preferred" color. They were then given the choice between two jars that had the same number of preferred objects, but that differed in their p
Answer:
Step-by-step explanation:
Wow, that’s interesting!
Is this a question?
6% of a value is 510
Answer:
The value is 8500
Step-by-step explanation:
Of means multiply and is means equals
6% * V = 510
Change percent to decimal form
.06V = 510
Divide each side by .06
V = 510/.06
V =8500
Answer:
9
(6 ÷ 100) 150
6÷2×3
9
ans 9
Work out the circumference and area of glass needed for the top of a display cabinet which has a diameter of 1.8m
Answer:The area of a circle with radius 0.2865 is 0.2579
Step-by-step explanation: Area of a circle in terms of radius:
Area = π·r2 = 3.14·0.292 = 0.26 square meters(*)
Area of a circle in terms of diameter:
Area = π·(d
2
)2 = 3.14·(0.57
2
)2 = 3.14·(0.29)2 = 0.26 square meters(*)
Area of a circle in terms of circumference:
Area = C2
4π
= 1.82
4π
= 3.24
(4·3.14)
= 3.24
12.56
= 0.26 square meters(*)
The circumference of circle is 5.652m.
What is Circumference of circle?The circumference of a circle is its boundary or the length of the complete arc of a circle.
The formula for the circumference of a circle is expressed using the radius 'r' of the circle and the value of 'pi'. It is expressed as, Circumference of a circle formula = 2πr. While using this circumference formula, if we do not have the value of the radius, we can find it using the diameter.
For example:
If the radius of the circle is 25 units, find the circumference of the circle. (Take π = 3.14)
Solution: Given, radius = 25 units
Let us write the circumference formula and then we will substitute the value of r (radius) in it.
Circumference of circle formula = 2πr
C = 2 × π × 25
C = 2 × 3.14 × 25 = 157 units
Therefore, the circumference of a circle is 157 units.
Given:
diameter= 1.8 m
radius= 0.9m
Now, Circumference of circle
=2πr
= 2* 3.14 * 0.9
= 5.652 m
Hence, the circumference of circle is 5.652m.
Learn more about circumference of circle here:
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