Answer:
Step-by-step explanation:
A worldwide organization of academics claims that the mean IQ score of its members is 118, with a standard deviation of 17. A randomly selected group of 35 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 116.8. If the organization's claim is correct, what is the probability of having a sample mean of 116.8 or less for a random sample of this size
Answer:
0.3372 = 33.72% probability of having a sample mean of 116.8 or less for a random sample of this size
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.
The mean IQ score of its members is 118, with a standard deviation of 17.
This means that [tex]\mu = 118, \sigma = 17[/tex]
Sample of 35:
This means that [tex]n = 35, s = \frac{17}{\sqrt{35}}[/tex]
What is the probability of having a sample mean of 116.8 or less for a random sample of this size?
This is the pvalue of Z when X = 116.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{116.8 - 118}{\frac{17}{\sqrt{35}}}[/tex]
[tex]Z = -0.42[/tex]
[tex]Z = -0.42[/tex] has a pvalue of 0.3372
0.3372 = 33.72% probability of having a sample mean of 116.8 or less for a random sample of this size
Choose the item that has measurable volume.
newspaper page
a water bottle
a dollar bill
a postage stamp
Answer:
A water bottle
Step-by-step explanation:
It's a water bottle because you cannot measure volume with a dollr bill or postage stamp.
At a middle school, 24 of the 144 students speak Vietnamese. What is the ratio of students that do not speak Vietnamese to students who speak Vietnamese?
Answer:
1:6
Step-by-step explanation:
24 and 144 are divisible by 6. Do the math, it comes out as 1:6.
24:144 = 1:6
A spinner has 6 equal sections marked 1 through 6. You spin and land on a number less than 6?
If Sin C= 9/20, then which of the following is closest to the measure of angle C?
Show work
A) 31 degrees
B) 36 degrees
C) 27 degrees
D) 41 degrees
Answer:
Step-by-step explanation:
Pls help
If a varies jointly as b and c, find a when b = 4 and c = -3.
a = -96 when b = 3 and c = -8
a=
Answer:
a=4bc
a=4(4)(-3)=-48
a= - 48 when b equals to 3 is equals to - 8
The required answer by direct variation a is equal to 96. In other words, when b = 4 and c = -3, the value of a is 96.
When a variable varies jointly as two other variables, it means that the relationship between the variables can be expressed using direct variation. In this case, we have that "a varies jointly as b and c."
To find the value of a when b = 4 and c = -3, we can set up the proportion based on the direct variation relationship:
a/bc = k
where k is the constant of variation.
Substituting the given values:
a/(4)(-3) = k
Simplifying, we have:
a/-12 = k
Now, we can find the value of a when b = 4 and c = -3 by substituting these values into the equation and solving for a:
a/(-12) = k
a/(-12) = -96/-12 (since k = -96 when b = 3 and c = -8)
a = 96
Therefore, the required answer by direct variation a is equal to 96. In other words, when b = 4 and c = -3, the value of a is 96.
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How many ways can three people be selected from a group of seven people if order DOES matter?
Answer:
no it doesnt matter unless you do this The fundemetal principle of counting.
7 ways 3 people = 21 ways
Step-by-step explanation:
a
Henry runs business
preparing peoples taxes.
He has monthly expenses
off $25.30 for printer ink
and $52 for advertising.
So far his revenue for the
month has been $3,456,
what is the profit that he
had made?
Answer:
3,378.70
Step-by-step explanation:
First, find the total amount Henry spends a month. 25.30 for printer ink and 52 for advertising. 25.30+52=$77.30.
Subtract what he has spent from what he has made.
3,456-77.30=3,378.70
That is his profit.
CAN YALL HELP ME PLEASE Deanna's times, seconds, for running the 100 meter dash this week were: 10.80 0,10.99,11.02,10.80,11. and 10.96 . 10.78 1.10, 10.88, 10.72, 10.15 Which measure of center would most accurately describe Deanna's typical time, and what is the value of that measure of center? Move a word and a value to complete the sentence . The best center of measure for this data is the which is equal toseconds mean median 10.88 10.9010,8 11.1
Answer:
MEDIAN11.1Step-by-step explanation:
[tex]{hope it helps}}[/tex]
MEAN and 10.90
this is the answer i got u guys PLZ LIKE THIS so i can get my level up
Tyler sold a total of $115,000 of exercise equipment last month. If his commission is 6.5% of sales, how much commission did he earn?
A.
$2,342
B.
$7,475
C.
$12,719
D.
$115,065
Answer:
B
Step-by-step explanation:
Do 115000/100x6.5 You get 7.475k
Michael made a scale model of the Empire State Building. The building has an actual height of 381m. Michael's models used a scale in which 1 cm = 50 m. what is the height of of the model in cm
Answer:
7.62 cm
Step-by-step explanation:
set up a proportion then cross-multiply:
1 / 50 = x / 381
50x = 381
x = 381/50
The measure of
the arc is for all and each no rush!
Answer:
Step-by-step explanation:
1)
The given angle is 57° at least I think it is . so we need to look at the triangle being formed inside the circle. the legs from the center to the edge are both the radius. so they are the same lengths. so that triangle is an isosceles. and the two angle at the circles perimeter are going to be both the same, b/c that's a rule of an isosceles triangle. so now we not both angles on the perimeter of the circle of that inner triangle are both 57° :) that's great, b/c now we can find the angle of the inner point of that triangle. it's going to be 180 = 57 + 57 + inner angle x
180 - 57 -57 = inner angle x
66 = x , so that inside angle on the isosceles is 66°
that's great to know, that angle is also part of the bigger triangle that goes outside the circle and I'm pretty sure the angle that is at the top of the triangle , at least in the picture, is a right angle or 90° sooo we now know two angle of the triangle and can figure our the "?" one. :)
180 = 66 + 90 + ?
180-66-90 = ?
24 = ?
so that angle at the point with the "?" is 24 ° :)
2)
The given angle is 24° :0 look above.. that last we we solved was also 24°
everything is the same in drawing 2, as in drawing 1. We can simply use all the things we know about drawing 1.. The inside angle at the center of the circle will be 66 ° and the two angle out by the perimeter of the circle will be 57° just like in drawing 1. They made that a little too easy :D Le'ts hope we get a few more like that :)
3)
I'm just sure why the drew the circle in this drawing. we don't need it to solve this triangle. Maybe you're not supposed to use this very common way to solve the triangle yet? but maybe it's good to introduce it anyway? since we are given the hypotenuse (long side) and the adjacent side (next to) the angle we can just use SOH CAH TOA to find any angle or side of this triangle. I'll put the useful remind of how trig functions ( sin, cos, ect.) fit on triangles and then we'll use them to find the parts we want. :)
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
copy the above down. and put in in a handy place on your computer , for quick reference any time you have to solve a triangle. it's really super helpful :)
okay now look at the triangle in question 3) what do we know, and what do we want to find? we know the Hyp and Adj and one angle and want to find the Opposite (Opp) side from the known angle. sooo we have a choice of SOH or TOA.. let's use SOH,
SOH ⇒ Sin(Ф) = Opp / Hyp
Sin(53) = Opp/ 10
algebra skill engage :P
10* Sin(53) = Opp
7.9863551 = Opp
so that side with the question mark is 8.0 long. ( rounded to nearest 10th)
4)
On this triangle we are given the Opp and the Adj sides and an angle and are asked to find the Hyp
which trig function would you like to use?
Let's use CAH this time. We could also use SOH , but we just used that one. let's try out the "tools" of the trade :)
CAH ⇒ Cos(Ф) = Adj / Hyp
Cos(37) = 8/Hyp
use algebra skillz
Hyp = 8 / Cos(37)
use calculator to find Cos(37) :/
Hyp = 10.01708
? = 10.0 ( rounded to nearest 10th )
5)
oh for this one we do need the circle, and I don't know why they want people to know this , nobody uses this math :? Anyway,
there is a confusing formula for this type of problem
∠ = (bigger arc - smaller arc ) / 2
since we're given the 65° , we know that 2*65= 130 which is the angle of the bigger arc - smaller arc = 130 °
now we have to use our really keen algebra skillz to see that
if the total all the way around a circle is 360 and we have 130 of those left so
eq. 1) 360 = big arc + small arc
then
360-smal arc = big arc
and
eq. 2) 130 = big arc - small arc
plug in for "big arc" what we know from above :P
130 = 360-small arc - small arc
130 = 360 - 2small arc
130 + 2 small arc = 360
2 small arc = 230
small arc = 115
:0 wow.. we solved it.. that was a lot of fancy algebra huh :P
? = 115° ( the small arc)
6)
same as 5
given 72°
72*2=144°
eq. 1) 360 = big arc + small arc
eq. 2 ) 144 = big arc - small arc
solve for big arc this time
360-bigl arc = small arc
now plug into eq. 2
144 = big arc - (360-big arc)
144 = big arc - 360 + big arc
144 = 2big arc - 360
144+ 360 = 2 big arc
504 = 2 big arc
252° = big arc
yay solved !! phew.. that was a lot of algebra.. :P
5 and 6 are tough, ask the teacher how many others got it :)
What is the probability of choosing a numbered card from a deck of cards? Type your answer as a fraction.
Answer:
36/52 or 9/13
Step-by-step explanation:
Ace-9 for all suits; Diamond, Hearts, Spades and Clubs
Each evening, Billy jogs around the high school track at a constant rate. The following equation describes the relationship between t, the time he jogs in hours, and d, the distance he jogs in kilometers. d = 7t Which graph represents the relationship between the amount of time Billy jogs and the distance he jogs?
The slope of the given line d = 7t is 7 kilometers per hour. Then the correct option is A.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
Each evening, Billy jogs around the high school track at a constant rate.
The following equation describes the relationship between t, the time he jogs in hours, and d, the distance he jogs in kilometers.
d = 7t
The slope of the line will be 7,
Then graph A is correct.
More about the linear system link is given below.
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A square has an area of 64 square ft. What would be the measureme of its side? *
8ft
hope this helps, have an amazing day <3
Answer:8
Step-by-step explanation:
8x8=64
Brad has a garden with dimensions 12 feet long x 7 feet wide. He wants to enlarge the garden to an area of 119 square feet. How much farther will he need to extend the length of the garden to attain his desired area?
Answer:
he needs to increase the length to 17 feet
Step-by-step explanation:
[tex]12 \times 7 \\ = 84 \\ to \: get \: {119}^{2} feet \: he \: must \: say \: \\ 119 \div 7 \\ = 17 \\ = 17 \times 7 = 119 \\ [/tex]
Answer:
28
Step-by-step explanation:
f58t85h85y8578
What is 12% of 36 plz help
Answer:
12% of 36 is 4.32
A recipe for 12 cookies calls for 1 1/3 cups milk, 2 1/2 cups flour, and 1 3/4 cups other ingredients. How many cups of milk, flour, and other ingredients are needed to make 24 cookies?
Please help \^.^/
What is the solution to the inequality below?
x² =< 49
the answer would be B. I used m a th way to find out what the answer was, you could use that app if you ever come across a similar question!
8. A box is filled with candies in different colors. We have 40 white candies, 24 green ones, 12
red ones, 24 yellow ones and 20 blue ones. If we have selected one candy from the box
without peeking into it, find the probability of getting a green or red candy.
Answer:
[tex]P(Green\ or\ Red) = 0.30[/tex]
Step-by-step explanation:
Given
[tex]White = 40[/tex]
[tex]Green = 24[/tex]
[tex]Red = 12[/tex]
[tex]Yellow = 24[/tex]
[tex]Blue = 20[/tex]
Required
[tex]P(Green\ or\ Red)[/tex]
The total numbe of candy is:
[tex]Total = 40 + 24 + 12 + 24 + 20[/tex]
[tex]Total = 120[/tex]
This probability is calculated as:
[tex]P(Green\ or\ Red) = P(Green) + P(Red)[/tex]
For each, we have:
[tex]P(Green\ or\ Red) = \frac{Green}{Total} + \frac{Red}{Total}[/tex]
Take LCM
[tex]P(Green\ or\ Red) = \frac{Green+Red}{Total}[/tex]
[tex]P(Green\ or\ Red) = \frac{24+12}{120}[/tex]
[tex]P(Green\ or\ Red) = \frac{36}{120}[/tex]
[tex]P(Green\ or\ Red) = 0.30[/tex]
Which describes the cross section of a cube that passes through the vertices A, B, C, and D shown below?
a rectangle that is not a square
a square
a paralelogram that is not a rectangle or a square
a trapezoid
Answer:
B. A square
Step-by-step explanation:
Find the product. Simplify.
(8 – 6b)(5 – 36) =
Someone help me pls!!
Answer:
-62
Step-by-step explanation:
(8 – 6b)(5 – 36)
(8 – 6b)(-31)
-248 + 186
-62
How to write 4 508 300
in words?
HEEEEEEEEEEEEEELLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPP
Answer:
The volume of the tissue is 42 cubic inches
Step-by-step explanation:
Given
[tex]Base\ Area = 8.4in^2[/tex]
[tex]Height = 5in[/tex]
Required
The volume of the tissue
This is calculated as:
[tex]Volume = Base\ Area * Height[/tex]
So, we have:
[tex]Volume = 8.4in^2 * 5in[/tex]
[tex]Volume = 42in^3[/tex]
Find the surface area of each figure. Round answers to two decimal places. Use 3.14 for pi
Answer:
the top wpuld be 73.14 and i cant see the numbers at the bottom
Step-by-step explanation:
The total surface area of the given figure which has cone and hemisphere is 944.08 square inches
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Let us find the height of the cone by using pythagoras theorem
7²+h²=15²
49+h²=225
Subtract 49 from both sides
h²=225-49
h²=176
h=13.2
Now let us find surface area of cone
A=πr(r+√(h²+r²))
A = 482.5
The surface area of hemisphere is 3πr²
A=3×3.14×(7)²
=3×3.14×49
=461.58
The total surface area = 482.5+461.58
=944.08 square inches
Hence, the total surface area of the given figure which has cone and hemisphere is 944.08 square inches
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Computer software generated 500 random numbers that should look like they are from the uniform distribution on the interval 0 to 1. They are categorized into five groups:
1. less than or equal to 0.2
2. greater than 0.2 and less than or equal to 0.4
3. greater than 0.4 and less than or equal to 0.6
4. greater than 0.6 and less than or equal to 0.8
5. greater than 0.8.
The counts in the five groups are 113, 95, 108, 99, and 85, respectively. The probabilities for these five intervals are all the same. What is this probability? Compute the expected number for each interval for a sample of 500. Finally, perform the goodness of fit test and summarize your results.
Answer:
0.2 ; 100 ; 4.84
Step-by-step explanation:
Given that the probability of each of the 5 groups is the same :
Sum of probability = 1
Hence, Probability of each group = 1 / number of groups = 1 / 5 = 0.2
Expected number for each interval for a sample of 500 : ; X = 500
E(X) = X * P(x) = 500 * 0.2 = 100
Goodness of fit (X²) :
X² = Σ(X - E)² ÷ E
Groups :
113, 95, 108, 99, and 85
X : 113 ____ 95 ____ 108 ____ 99 _____ 85
(113 - 100)^2 / 100 = 1.69
(95 - 100)^2 / 100 = 0.25
(108 - 100)^2 / 100 = 0.64
(99 - 100)^2 / 100 = 0.01
(85 - 100)^2 / 100 = 2.25
(1.69 + 0.25 + 0.64 + 0.01 + 2.25) = 4.84
Rosalind made 969 donuts and put 8 donuts into each box. How many boxes of donuts were made
Answer:
121 donuts in each box
Step-by-step explanation:
969 divided by 8 = 121.125
(Ignore the remainder)
Step by step solution:
We know that there are 969 doughnuts, and there are 8 doughnuts per box. What we need to find out is how many boxes of doughnuts were made.
Step 1:
Set up an equation for Number of doughnuts (969) / Number of doughnuts per box (8) = Number of boxes made (x), which would look like this:
969/8 = x
Step 2:
Doing this, we can get 121.125, which leaves us with
121.125 = x
121.125 = 121.125
Which gives us the answer of 121.125, which we can shorten to 121, as the decimal is not necessary.
Checking our answer:
We can check our answer simply be rewording our 1st equation to solve for the number of doughnuts made. This would give us the equation Number of doughnuts per box (8) * Number of boxes made (121.125) = x. Solving this equation would look like
8 * 121.125 = x
969 = x
969 = 969
Answer: By completing the steps above we get 121, and we can check our work by rewording the problem to solve for the number of Doughnuts. Good Luck!
Plz plz plz plz help
Answer:
we can substract the power 4 by taking up with 15 because using indices rule
Please help me out!! :)
Answer:
3/4
Step-by-step explanation:
Tangent is opposite/adjacent
Therefore, 6/8 would be the answer which simplifies to 3/4.
How would I solve this?
If you help me with my last question I will help you with this one