Answer:
a. [tex]\mathbf{P(\overline x < 68) = 0.9998}[/tex]
b. [tex]\mathbf{P(68 < \overline x < 69 ) =0}[/tex]
c. [tex]\mathbf{P ( \overline x > 66 ) =0.02275}[/tex]
Step-by-step explanation:
Given that ;
Let Y be a random variable In a population, where:
mean [tex]\mu_y[/tex] = 65
[tex]\sigma^2_y[/tex] = 49
standard deviation σ = [tex]\sqrt{49}[/tex] = 7
The objective is to determine the following :
In a random sample of size n = 69, find Pr(Y <68) =
Using the Central limit theorem
[tex]P(\overline x < 68) = \begin {pmatrix} \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{68 - \mu }{\dfrac{\sigma}{\sqrt{n}}} } \end {pmatrix}[/tex]
[tex]P(\overline x < 68) = \begin {pmatrix}Z < \dfrac{68 - 65 }{\dfrac{7}{\sqrt{69}}} } \end {pmatrix}[/tex]
[tex]P(\overline x < 68) = \begin {pmatrix}Z < \dfrac{3 }{\dfrac{7}{8.3066}} } \end {pmatrix}[/tex]
[tex]P(\overline x < 68) = (Z < 3.5599 )[/tex]
From the z tables:
[tex]\mathbf{P(\overline x < 68) = 0.9998}[/tex]
In a random sample of size n = 124, find Pr (68< Y <69)=
[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{68- \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{ 69 - \mu}{\dfrac{\sigma}{\sqrt{n}}} \end {pmatrix}[/tex]
[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{68- 65}{\dfrac{7}{\sqrt{124}}} < Z < \dfrac{ 69 - 65}{\dfrac{7}{\sqrt{124}}} \end {pmatrix}[/tex]
[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} \dfrac{3}{\dfrac{7}{11.1355}} < Z < \dfrac{ 4}{\dfrac{7}{11.1355}} \end {pmatrix}[/tex]
[tex]P(68 < \overline x < 69 ) = P \begin {pmatrix} 4.7724 < Z < 6.3631 \end {pmatrix}[/tex]
[tex]P(68 < \overline x < 69 ) = P( Z < 6.3631 ) - P ( Z < 4.7724 )[/tex]
From z tables
[tex]P(68 < \overline x < 69 ) = 0.9999 - 0.9999[/tex]
[tex]\mathbf{P(68 < \overline x < 69 ) =0}[/tex]
In a random sample of size n = 196, find Pr (Y >66)=
[tex]P ( \overline x > 66 ) = P ( \dfrac{\overline x -\mu }{\dfrac{\sigma}{\sqrt{n}}} > \dfrac{66 -\mu }{\dfrac{\sigma}{\sqrt{n}}})[/tex]
[tex]P ( \overline x > 66 ) = P ( Z> \dfrac{66 - 65 }{\dfrac{7}{\sqrt{196}}})[/tex]
[tex]P ( \overline x > 66 ) = P ( Z> \dfrac{1 }{\dfrac{7}{14}})[/tex]
[tex]P ( \overline x > 66 ) = P ( Z> \dfrac{14 }{7})[/tex]
[tex]P ( \overline x > 66 ) = P ( Z>2)[/tex]
[tex]P ( \overline x > 66 ) = 1 - P ( Z<2)[/tex]
from z tables
[tex]P ( \overline x > 66 ) = 1 - 0.9773[/tex]
[tex]\mathbf{P ( \overline x > 66 ) =0.02275}[/tex]
u= ab/k, for a
Solve form A
a = uk/b
Step-by-step explanation:u = ab/k
uk = ab
a = uk/b
Determine the rate of change for 3/2x -5/4y = 15
Answer:
-6/5
Step-by-step explanation:
3/2x - 5/4y = 15
-5/4y = -3/2x + 15
multiply each side by (-4/5)
(-4/5)(-5/4y) = (-4/5)(-3/2x + 15)
y = -6/5x - 12
rate of change: -6/5
Find the midpoint of CD when
C (-2, -1) and D (4, 3).
Answer: (1, 1)
Step-by-step explanation:
Midpoint formula: [tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]
(x1, x2)=(-2, 4)
(y1, y2)=(-1, 3)
-----------------------------------------
[tex](\frac{x1+x2}{2} ,\frac{y1+y2}{2} )[/tex]
=[tex](\frac{-2+4}{2} ,\frac{-1+3}{2} )[/tex]
=[tex](\frac{2}{2} ,\frac{2}{2} )[/tex]
=[tex](1, 1)[/tex]
Hope this helps!! :)
Please let me know if you have any question or need further explanation
I’m a constant function. There are two possible ways to write me; one way being slope-intercept form and the other being constant form
(I don’t really understand what this question is asking)
Answer:
constant function has the same output no matter what are the inputs and it is written in the form : y=b where b is a constant that does not change. the slope of this function always equal to zero.
slope intercept form : y=mx+b ( where m=0)
constant form : y=b ( y equal a constant that does not change)
Principal: $1500.
Annual interest rate: 72%.
What is the interest after
6 months?
I NEED HELP Are the two functions inverses? f ( x ) = − 8 x + 5 g ( x ) = − 1 8 x + 5 8 Group of answer choices Yes No
Answer: No
Step-by-step explanation:
To know if the functions are inverses of each other, it is easiest to just find the inverse of one of the functions. To find the inverse, you want to replace y with x and x with y and solve for y.
y=-8x+5 [switch x with y and y with x]
x=-8y+5 [subtract both sides by 5]
x-5=-8y [divide both sides by -8]
y=(x-5)/-8
f⁻¹(x)=(x-5)/-8
Since we know that the inverse doesn't match g(x), we know that these functions are not inverses of each other.
49 divided by 7 get a decimal answer
Answer:
7.0?
Step-by-step explanation:
49/7 would be 7, If the question was 7/49 the answer would be 0.14285714285 (a decimal)
If you count 14 beats in 6 seconds, what is your approximate rate?
Answer:
About 2.3 beats per second
Step-by-step explanation:
14 / 6 is approximately 2.3.
Answer: About 2.33 beats per second
Step-by-step explanation:
Divide the number of beats by the seconds and find the approximation rate.
View Lab
Which of the following functions is most likely to have the smallest value for y if x is large? (Assume k is positive.)
a direct variation function with a small value fork
a direct variation function with a large value fork
an inverse variation function with a small value fork
an inverse variation function with a large value fork
Nexi
Subm
Save and Exit
Mark this and retum
Answer:
an inverse variation function with a small value for k
Step-by-step explanation:
The attached graph shows the cases described. The function with the smallest function value for large x is ...
an inverse variation function with a small value for k
___
On the graph, it is the green curve. The inverse variation functions both continue to decrease for large x, but the function with the smaller k value has a smaller function value.
Answer:an inverse variation function with a small value for k
Step-by-step explanation:Because i took the test
Please HELP ASAPPPP uts not -3!!!
Answer:
x= 11
Step-by-step explanation:
(7x -1)° + (9x +5)°= 180° (adj. ∠s on a str. line)
7x -1 +9x +5= 180
16x +4= 180 (simplify)
16x= 180 -4 (-4 on both sides)
16x= 176 (simplify)
x= 176 ÷16
x= 11
The sum of the angles on a straight line is 180°
Each school day, Aidon wolks 11 blocks to school after school, he wolks 4 blocks to the library
and 12 blocks home. How many blocks does Aidon wolk in a week? *
e
Answer:
189
Step-by-step explanation:
Aidon walked 11 blocks to begin with than he walks 4 blocks to the library and 12 blocks home. This mean we add 11+4+12=27 and a week has 7 days which means we need to multiply that by 7 which gives us the product of 189.
Also, i double checked
circle the digit is in the tens place
219,358,675
Answer:
219,358,675
the tens digit is the second digit before decimal point (from right to left)
219,358,675
Hope this helps!! :)
Answer:
Hey!
The 7 in *...675* is in the tens place!!
Step-by-step explanation:
Tens place??
AkA THE SECOND PLACE IN FROM RIGHT
▶hOPE IT HELPED!!◀
Write a ratio for the following description: Kaleel made three times as many baskets as John during basketball practice. Type your answer in the format: 3:4 with no spaces.
Answer:
3:1
Step-by-step explanation:
hey there,
< We know Kaleel made 3x as many baskets as John.
We're going to make our ratio Kaleel:John.
The answer would be 3:1 because every time John makes 1 basket, Kaleel makes 3 baskets. If John made 2, then Kaleel would make 6, etc...
Sorry, I can't explain this very well! >
Hope this helped. Feel free to ask anything else.
Please help me please
Answer:
y = 4 (Answer C)
Step-by-step explanation:
We want to find side y. The sine function relates the 30 degree angle, the hypotenuse 8 and the opposite side y:
y
sin 30 degrees = 1/2 = -----------
8
so y = 4 (Answer C)
How can i write all the names that apply √36 NEED IT ASAP
Answer:
square of 36 is 6
or maybe 6²
please quickly answer. i cant be waiting for 20 mins.
Answer:
C ( -2,4)
Step-by-step explanation:
In quadrant II, the x values are negative and the y values are positive
( -, +)
(-2,4) is the only point that meets this
Answer:
[tex]\huge \boxed{\mathrm{\bold{C.}} \ ( -2,4)}[/tex]
Step-by-step explanation:
The x values are negative and the y values are positive in quadrant II.
The point (-2, 4) is in quadrant II.
Helpp me out pls!!!!!!!!!
Answer:
a. Maurice walked farther.
b. 0.62 m
Step-by-step explanation:
Maurice
4.1 × 1.8 = 7.38 miles
Junnie
2.5 × 3.2 = 8 miles
This shows that Junnie walked more than Maurice.
8 - 7.38 = 0.62
Junnie walked 0.62 m more than Maurice
Write 6.93 repeating a mixed number in simplest form.
6.93 =?
Answer:
[tex]6\frac{93}{100} = \frac{693}{100}[/tex]
Step-by-step explanation:
Turn 6.93 into a fraction: [tex]6\frac{93}{100}[/tex] To turn into a mixed number, first multiply 6 and 100, then add 93. Put 693 over 100: [tex]\frac{693}{100}[/tex]I hope this helps!
Answer: [tex]6 \frac{31}{33}[/tex]
This is a mixed number where the whole part is 6, and the fractional part is 31/33.
=============================================
Explanation:
The 93 repeats forever, so we can say
x = 6.939393...
100x = 693.939393....
Subtracting the left hand sides leads to 100x-x = 99x
Subtracting the right hand sides leads to 693.939393.... - 6.939393... = 687
Notice how the decimal terms cancel out when we subtract.
We're left with 99x = 687 which solves to x = 687/99
This reduces to 229/33 when you divide both parts by 3.
The last step is to convert to a mixed number
The answer will be in the form [tex]6 \frac{x}{33}[/tex] where 6 is the whole part and x/33 is the fractional part. We know the whole part is 6 from the 6 in the original number given.
229/33 = 6.939393... helps confirm we're on the right track so far
this is another way of saying 229/33 = 6 remainder x, where x is the unknown remainder and the numerator we're after for the fraction x/33.
To get the remainder, we just compute 229-6*33 to get 31
This means 31/33 = 0.93939393...
and that [tex]6 \frac{31}{33} = 6.\overline{93} = 6.93939393...[/tex]
1/2(-2x - 12) > 7(3 - 4x)
The solution is____
Answer:
x > 1
interval (1,∞)
Step-by-step explanation:
1/2(-2x - 12) > 7(3 - 4x)
-x - 6 > 21 - 28x
-x + 28x > 21 + 6
27 x > 27
x > 27 / 27
x > 1
interval (1,∞)
-x - 6 > 21 - 28x if x = 2
-2 - 6 > 21 -28(2)
-8 > 21 - 56
- 8 > - 35
A 2000 kilogram sports car accelerates at a ratr of 30 meters per second squared. The velocity of the car is v=at where a is acceleration in meters per second squaref and t is tome in seconds. The kinetic energy of the car is KE = 1/2 mv^2
Answer:
KE = 900,000t²
Step-by-step explanation:
The formula for calculating the kinetic energy of a body is expressed as KE = 1/2mv² where;
m is the mass of the sport car = 2000kg
v is the velocity of the car
Since v = at
v = 30t
Substituting the given values into the KE formula;
KE 1/2 * 2000 * (30t)²
KE = 1000*900t²
KE = 900,000t² Joules where t is the time measured in seconds
Answer:
KE = 900,000t²
Step-by-step explanation:
Answer is D if you use edgenuity, answers do not mix
please help// geometry question.... “the distance from” is cut off from the picture
Answer:332
Step-by-step explanation:
A research company wants to test the claim that a new multi vitamin helps improve short term memory state the objective of the experiment suggest a population determine the experimental and control groups and describe a simple procedure
Answer:
To test the effects of the multi-vitamin, we must test it on people with short-term memory loss. So the population should be people with short-term memory loss. The independent variable is the multi-vitamin and the dependent variable is the short term memory state of the people being tested. A control group can consist of people with short-term memory loss NOT being treated by the multi-vitamin.
If you would like more help on math or other subjects for FREE, check out growthinyouth.org.
Please help me with the question below
Answer:
The answer is A.
Step-by-step explanation:
This is because Tia's amount of money minus Dana's amount of money should be at least 5
Solve the equation 6x + 2x - 5= 19 x=? Simplify your answer
Answer:
x = 3
Step-by-step explanation:
6x + 2x - 5= 19
8X -5 = 19
8x = 24
x = 3
17 POINTS!!!! List the elements in the set described. {x|x is a natural number between 9 and 17} (Use a comma to separate answers as needed. use ascending order.)
Answer:
10, 11, 12, 13, 14, 15, 16
Step-by-step explanation:
The natural numbers are 1, 2, 3, 4, ...
The natural numbers between 9 and 17 are 10, 11, 12, 13, 14, 15, 16.
Answer: 10, 11, 12, 13, 14, 15, 16
Lee spent $29 to purchase a combination of drinks, sandwiches, and chips for himself and his friends. A drink costs $1.50, a sandwich costs $5, and chips cost $1.25. Identify the linear equation that represents this situation.
Answer:
1.5d+5s+1.25c=29
Step-by-step explanation:
let d be the number of drinks, s be the number of sandwich, and c be the number of chips Lee purchased.
1.5×d and 5×s and 1.25×c must total 29, or
1.5d+5s+1.25c=29.
Simplify: (3n2 +9+5n4 – 3n)+(-9n* - 7 -5n?)
Answer:
3n^2+9+5n^4+55n
Step-by-step explanation:
Steps
$\left(3n^2+9+5n^4-3n\right)+\left(-9n\left(-7\right)-5n\right)$
$\mathrm{Remove\:parentheses}:\quad\left(a\right)=a,\:-\left(-a\right)=a$
$=3n^2+9+5n^4-3n+9n\cdot\:7-5n$
$\mathrm{Add\:similar\:elements:}\:-3n-5n=-8n$
$=3n^2+9+5n^4-8n+9\cdot\:7n$
$\mathrm{Multiply\:the\:numbers:}\:9\cdot\:7=63$
$=3n^2+9+5n^4-8n+63n$
$\mathrm{Add\:similar\:elements:}\:-8n+63n=55n$
$=3n^2+9+5n^4+55n$
on a piece of paper, graph y<-3/4x+2. Then determine which answer choice matches the graph you drew.
Answer:
D. Graph D
Step-by-step explanation:
The "y <" tells you two things: (1) shading will be below the line, where y-values are less than those on the line, and (2) the line will be dashed, because the "equal to" case is not included.
Only one graph has a dashed line with shading below: Graph D.
Simplify 3√-1000 and 3√g6h30
Answer:
[tex] \sqrt[ ]{1000} [/tex]
Step-by-step explanation:
[tex]3 \sqrt{ - 1000} = 3 \sqrt{1000i {}^{2} } \\ = 3 \times 10i \\ = 30i \\ (in \: complex \: form \: i {}^{2} = - 1)[/tex]
Answer:
1st one = -10
2nd one = g2h10
Step-by-step explanation:
Edge2020!!
3x-30 =1.5 plz help me
Answer:
x = 10.5
Step-by-step explanation:
3x - 30 = 1.5
3x = 31.5
x = 10.5