Answer:
The Z score for $37,000 is 8.49.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean family income is $34,000, with a standard deviation (for the population) of $5,000.
This means that [tex]\mu = 34000, \sigma = 5000[/tex]
Subsample of 200 city residents.
This means that [tex]n = 200, s = \frac{5000}{\sqrt{200}} = 353.55[/tex]
What is the Z score for $37,000 ?
This is Z when X = 37000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{37000 - 34000}{353.55}[/tex]
[tex]Z = 8.49[/tex]
The Z score for $37,000 is 8.49.
HELP what's the distance for this question?
Answer:
[tex]Distance = 38.57ft[/tex]
Step-by-step explanation:
Given
[tex]Base = 60[/tex]
[tex]\theta = 50[/tex]
Required
The distance between the top and John
The distance is calculated using:
[tex]sin\alpha = \frac{Distance}{Base}[/tex]
Where
[tex]\alpha = 90 - \theta[/tex] --- the angle between the diagonal line and the vertical line
[tex]\alpha = 90 - 50[/tex]
[tex]\alpha = 40[/tex]
So, we have:
[tex]Sin(40) = \frac{Distance}{60}[/tex]
[tex]Distance = 60 * sin(40)[/tex]
[tex]Distance = 60 * 0.6428[/tex]
[tex]Distance = 38.57ft[/tex]
[tex]Distance = 986 * tan(38)[/tex]
[tex]Distance = 986 * 0.7812[/tex]
[tex]Distance = 770ft[/tex] --- approximated
Please help me answer this
9514 1404 393
Answer:
a) zeros: -2/3, 6
b) x < -2/3, signs: -, -; sign of product: +
-2/3 < x < 6, signs: +, -; sign of product: -
x > 6, signs: + +; sign of product: +
c) solution: x < -2/3 ∪ x > 6
Step-by-step explanation:
a) The zeros of the product are the values of x that make either factor zero. (A product is only zero if one of the factors is zero.)
3x +2 = 0 ⇒ x = -2/3
x -6 = 0 ⇒ x = 6
The zeros of the quadratic are x = -2/3 and x = 6.
__
b) For values of x left of the left-most zero, both factors are negative. For values of x between the zeros, the left factor is positive and the right factor is negative. For values of x greater than the right-most zero, both factors are positive. That is, for large negative values of x, all factors are negative. Working left-to-right, each time a zero is crossed, one factor changes sign.
__
c) The solution is where the signs of the factors match:
x < -2/3 or -6 < x
True or false. Explain.
The volumes of a rectangular-based pyramid and a triangular-based pyramid with congruent heights and equal base areas are equal
Answer:
true
Step-by-step explanation:
You would like to have $10,000 in an account after eight years time. If the account earns 2.5% compounded interest yearly, how much would you have to deposit today
Answer:
You have to deposit $8,207.5 today.
Step-by-step explanation:
Compound interest:
The amount of money in yearly compounded interest, after t years, is given by the following equation:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the initial deposit and r is the interest rate, as a decimal.
You would like to have $10,000 in an account after eight years time.
This means that when [tex]t = 8, A(t) = 10000[/tex]
2.5% compounded interest
This means that [tex]r = 0.025[/tex]
So
[tex]A(t) = A(0)(1+r)^t[/tex]
[tex]A(t) = A(0)(1+0.025)^t[/tex]
[tex]A(t) = A(0)(1.025)^t[/tex]
How much would you have to deposit today?
We have to find A(0), when [tex]t = 8, A(t) = 10000[/tex]. So
[tex]A(t) = A(0)(1.025)^t[/tex]
[tex]10000 = A(0)(1.025)^8[/tex]
[tex]A(0) = \frac{10000}{(1.025)^8}[/tex]
[tex]A(0) = 8207.5[/tex]
You have to deposit $8,207.5 today.
Flying against the wind, an alrplane travels 4700 kilometers in 5 hours. Flying with the wind, the same plane travels 9520 kilometers in 7 hours. What is the rate of the plane in still air and what is the rate of the wind?
Answer:
i think this
Step-by-step explanation:
Let Va = the velocity of the airplane
Let Vw = the velocity of the wind
When flying with the wind:
(Va+Vw)*(4 hours) = 4000
4Va + 4Vw = 4000
4Vw = 4000 - 4Va
Vw = 1000 - Va
When flying against the wind:
(Va-Vw)*(7 hours) = 4200 km
7Va - 7Vw = 4200
Substitute 1000-Va for Vw and solve for Va:
7Va - 7(1000-Va) = 4200
7Va -7000 + 7Va = 4200
14Va = 11200
Va = 800 km/hr
Rate of wind:
Vw = 1000 - Va = 1000 - 800 = 200 km/hour
H=17+x/6 solve for H step for step
Answer: h -18 =14
Step-by-step explanation:
You need to plug in -18 into the equation. So h(-18)=17+(-18)/6
h(-18)=17-3
h(-18)=14
PLS HELP
i said 45 but it was marked incorrect, im super confused
Answer:
60
Step-by-step explanation:
trangles always equal 180 degrees on the inside angles
180-75-45 = 60
Which property justifies the statement below?
a(2b+c)=a(c+2b)
a. commutative property of addition
b. commutative property of multiplication
c. associative property of addition
d. distributive property
Answer:
d. distributive property
Step-by-step explanation:
The political opinion organization hired 100 new employees, which increases its staff by 40%. What was the original number of employees?
Answer:
40(?)
I don't remember exactly if that's correct, but I hope it's right! Comment if you want the explanation
what is the product of the Trinomial and the Binomial below
(x2+5x-2)(x-3)
Answer:
x3+2x2-17x+6.
Step-by-step explanation:
(x2+5x-2)(x-3)
= x(x2+5x-2)-3(x2+5x-2)
= x3 +5x2-2x-3x2-15x+6
Simplifying like terms:
= x3+2x2-17x+6
What will be the total cost of treys on 2 truck when we the price of each trye is 35,00:00
Answer:
45$?
Step-by-step explanation:
help me on math pls plss I'm stuck agian:(((((
Answer:
the answer to a is 25, im unsure what B is.
Step-by-step explanation:
hope this helps!!!
Will mark Brainliest! What is the value of P. Thank you!
Answer:
question of number 10 is 3
Explain why the denominator does not change when you are counting by the
unit fraction 1
··4
to reach 3
··4 .
Answer: Your splitting 1 into 4 parts and I don't think anything here tells me you need to simplify bc then it would be, 1/2, which is not 3/4. It's like having one quarter that equals 25c, 50, 75, a 1.00, but it's 0.25 and 0.75?
Step-by-step explanation:
What is sinK?
A. 12/13
B.13/12
C.5/13
D.5/12
Answer:
A. 12/13
Step-by-step explanation:
Remember SOH, CAH, TOA.
In this situation, the function is sine so sine= opposite/hypotenuse.
The side opposite of K is 12.
The hypotenuse is the longest side so it will be 13.
Therefore, sineK= 12/13(a)
Answer:
12/13
Step-by-step explanation:
A sphere has a volume of 36(pi) in^3. What is the surface area in terms of Pi
Answer:
la verdad que depende de la situación
does anyone know the answer to this? 5x-(4+3x)
Answer:
2x-4
Step-by-step explanation:
5x-(4+3x)
5x-4-3x
5x-3x-4
2x-4
The farm raises some rabbits and native chickens. The number of native chickens is six times the number of rabbits, with a total of 560 feet. farm
Raised ? rabbit.
The farm raises some rabbits and native chickens. The number of native chickens is six times the number of rabbits, with a total of 560 feet. farm
Raised ? rabbit.
What is 12 1/2 - 7 6/7?
Answer:
4 9/14
Step-by-step explanation:
Answer:
The answer is 4 9/14
help please i’ll give extra points & brainlist:)!
please help me out ~ 20 points
Answer:
12.5 sq. units
Step-by-step explanation:
Area of a Trapezoid Formula: (see the image attached)
7.5 + 2.5 = 10
10/2 = 5
5(2.5) = 12.5
So, the area of the trapezoid is 12.5 sq. units.
Peggy took a timed 30
question test. She answered
60% of the questions and
skipped the rest. How many
did she answer?
Answer: 18 questions
Step-by-step explanation:
First we want to make 60% a decimal so we divide by 100.
This gives us 0.6
Then we multiply 30*0.6=18
18 questions
2X^2 - 9x + 10 . solve by factoring area model (show work)
Step-by-step explanation:
2x²_4x_5x+10
2x(x-2)-5(x-2)
(2x-5)(x-2)
Find the discriminant and the num
x2 + 2x + 7 = 0
A. 28; two real roots
Answer:
Discriminant = -24, no real roots.
Step-by-step explanation:
The discriminant is what's inside the square root in the quadratic formula.
The quadratic formula is:
[tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
a = 1
b = 2
c = 7
The question wants the discriminate, we can just focus on the square root part.
When we plug in the parts we got, it becomes:
[tex]\sqrt{4-4(1)(7)}\\\sqrt{4-28} \\\sqrt{-24}[/tex]
Since the inside of the square root is negative, there are no real roots.
I got 49 will someone double check me please?!
Answer:
m<YVX = 49°
Step-by-step explanation:
Given:
m<YVZ = 52°
m<ZVW = 36°
m<XVU = 43°
m<YVX + m<YVZ + m<ZVW + m<XVU = 180° (angles in a straight line)
m<YVX + 52 + 36 + 43 = 180 (substitution)
m<YVX + 131 = 180
m<YVX = 180 - 131
m<YVX = 49°
james has a recipe that calls for 6 cups of sugar he wants to use only 1/2 of the recipe today how much sugar will he need do you multiply or divide
answer:
he would use 3 cups of sugar and would need to multiply
step-by-step explanation:
since he only wants 1/2, we would multiply by the original amount6 X 1/2 = 3 cups of sugar
What is the input value for which g(x) = 3 khan academy
Answer:
x = 9
Step-by-step explanation:
If g(x) = 3, that means that the output is three.
Outputs are y values.
Look at the graph. When y=3, the x = 9.
So the input value for which g(x) = 3 (aka that gives the output y = 3) is x = 9
Question 60/62 (3.p.)
KAH
ht
w
2011
Solve and choose the correct answer.
A water tank is in the form of a cylinder whose radiusis 2 m and length is
3.5 m. The quantity of water in litres that can be stored in the tank is
..
Answer:
Capacity of tank = 44,000 l
Step-by-step explanation:
Given:
Height of tank = 3.5 m
Radius = 2 m
Find:
Capacity of tank
Computation:
Volume of cylinder = πr²h
Volume of cylinder = (22/7)(2)²(3.5)
Volume of cylinder = 44 m³
1m³ = 1000 l
So,
Capacity of tank = 44 x 1,000
Capacity of tank = 44,000 l
Triangle Theorems I need helpppp
1)Apply the distributive property to solve the following.
(2 +19) x4
Answer:
Answer:
4x19+4x2 or 4x21
Step-by-step explanation:
If you multiply 4x19, you get 76. And if you multiply 4x2 you get 8. 76+8= 84
If you multiply 4x21 you get 84 also. Both of these answers are distributive property. (all it is, is different ways of solving the problem.)
Hope this helps! :)