Using the normal distribution and the central limit theorem, it is found that the probabilities are given as follows:
24. Single person has an IQ score above 105: 0.3694.
25. Sample mean (55 people) above 105: 0.0067.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation of IQ scores are given as follows:
[tex]\mu = 100, \sigma = 15[/tex]
The probability that a single person has an IQ score higher than 105 is one subtracted by the p-value of Z when X = 105, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (105 - 100)/15
Z = 0.33
Z = 0.33 has a p-value of 0.6306
1 - 0.6303 = 0.3694.
For the sample of 55, the standard error is:
[tex]s = \frac{15}{\sqrt{55}} = 2.02[/tex]
Hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (105 - 100)/2.02
Z = 2.48
Z = 2.48 has a p-value of 0.9933.
1 - 0.9933 = 0.0067.
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Find the volume of the cylinder. Either enter an exact answer in terms of or use 3.14 for 4 units 3 Stuck? Watch a video or use a hint.
the volume of a cilinder is:
[tex]V=\pi r^2h[/tex]So we can replace the radius and the high so:
[tex]\begin{gathered} V=\pi6^24 \\ V=36\cdot4\cdot\pi \\ V=144\pi \end{gathered}[/tex]Now we can replace pi by 3.14 so:
[tex]undefined[/tex]Which expression is equivalent to the quantity five raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power? three raised to the third power divided by five raised to the fourth power negative three raised to the third power divided by five raised to the fourth power five raised to the fourth power divided by three raised to the tenth power negative five raised to the fourth power divided by three raised to the tenth power
Answer:
(c) five raised to the fourth power divided by three raised to the tenth power
Step-by-step explanation:
You want the simplified version of the quantity five raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power.
Rules of exponentsThe relevant rules of exponents are ...
(ab)^c = (a^c)(b^c)
a^-b = 1/a^b
(a^b)^c = a^(bc)
ApplicationThe given expression can be simplified as follows:
[tex](5^{-2}3^5)^{-2}=5^{(-2)(-2)}3^{(5)(-2)}=5^43^{-10}=\boxed{\dfrac{5^4}{3^{10}}}[/tex]
__
Additional comment
We find math expressions easier to understand when they are written using math notation, instead of words.
1. **Graph y = 12x + 3 2. ** y = -3x + 4 y 9 T 구 8 16 5 다 2 1 19 18 454 - 6 3-2 1 6 a x 대 - 2 1 2 6 B 9 x 1 0 2 3 10 . -6. R bo 를
Answer:
Graphing the points we have;
Above is the graph of the given equation showing the derived points.
Explanation:
Given the equation;
[tex]y=|2x|+3[/tex]To plot the graph we need to calculate the corresponding values of x and y at each point.
Let us calculate the values of y for x = -4,-2,0,2, and 4;
[tex]\begin{gathered} y=|2x|+3 \\ at\text{ x=-4;} \\ y=|2\times-4|+3 \\ y=8+3 \\ y=11 \\ (-4,11) \end{gathered}[/tex][tex]\begin{gathered} at\text{ x=-2} \\ y=|2\times-2|+3 \\ y=4+3 \\ y=7 \\ (-2,7) \end{gathered}[/tex][tex]\begin{gathered} at\text{ x=0;} \\ y=|2\times0|+3 \\ y=3 \\ (0,3) \end{gathered}[/tex][tex]\begin{gathered} at\text{ x=2;} \\ y=|2\times2|+3 \\ y=4+3 \\ y=7 \\ (2,7) \end{gathered}[/tex][tex]\begin{gathered} at\text{ x=4;} \\ y=|2\times4|+3 \\ y=8+3 \\ y=11 \\ (4,11) \end{gathered}[/tex]Therefore, Graphing the points we have;
Above is the graph of the given equation showing the derived points.
10. Seth is analyzing his basketball statistics. The following table shows a probability model for the results of his next two free throws. Outcome Miss both free throws. Is this a valid probability model? True) Yes, this is a valid probability model.False) No, this is not a valid probability model.
Please, give me some minutes to take over your question
_________________________________
I'm working on it
__________________________
a probability model has some features
Events (This part is ok, the probabilities are between 0 - 1 )
1) p1 = 0.2
2) p2 = 0.5
3) p3 = 0.1
____________________
The sample space is not 1 because p1+p2+p3 = 0.8
______________________________________
Answer
FALSE. No, this is not a valid probability model
I don't remember what an isosceles triangle is
An isosceles triangle is a triangle which has two of its sides with the same length
What is the value of the number in the tenths place?6.748O A. 0.7B. 0.04C. 0.07D. 0.6
Answer:
Choice A. 0.7
Explanation:
The place value of the numbers is given below
T
i don't know how to setup the equation and neither getting the answer, please help, i only need question 4 btw
The sum of exterior angles of a regular polygon is 360 degree.
Determine the measure of last exterior angle of a regular pentagon.
[tex]\begin{gathered} 52+87+90+43+x=360 \\ x=360-272 \\ =88 \end{gathered}[/tex]So measure of last angle of a regular pentagon is 88 degree.
A circle in the xy-plane has a center at G 3 1 42 3 and a radius that is units long. Which of the 15 following is an equation of the circle?
We are asked to find the equation of a circle on the xy-plane, with center (3/4 , 1/2) and a radius of 3/5 units. For doing so, we remember the general equation of a circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h,k) represents the center of the circunference, and r its radius.
In our example, we obtain that,
[tex]\text{Center}=(\frac{3}{4},\frac{1}{2})[/tex]And so,
[tex]\begin{gathered} h=\frac{3}{4},k=\frac{1}{2} \\ r=\frac{3}{5} \end{gathered}[/tex]Applying the above formula, we get that the equation of the circle will be:
[tex](x-\frac{3}{4})^2+(y-\frac{1}{2})^2=(\frac{3}{5})^2[/tex]This is:
[tex]\mleft(x-\frac{3}{4}\mright)^2+\mleft(y-\frac{1}{2}\mright)^2=\frac{9}{25}[/tex]
Consider the function given by the graph. What are
these values?
f(-2)=
f(0) =
f(4) =
The values of the function given by the graph are:
f(-2 ) = 2
f(0) = 3
f(4) = -1
The graph depicts an inequality equation with discontinuities. Points of discontinuity are breaks in the graph caused by an undefined point when the f(x) function is substituted with an x point that is not part of the solution. Looking at the graph of the provided function f(x), we can clearly see that the function f(x) increases in the interval (-∞ ,0] and subsequently decreases in the interval (0,∞).Furthermore, the function terminates at x=0.
(Because there is a gap in the graph and the function's left and right-hand limits are not equal at x=0)
So from the graph, we can determine the values of the functions as,
f(-2 ) =2
f(0) = 3
f(4) = -1
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Answer:
f(–2 ) = 2
f(0) = 3
f(4) = -1
Step-by-step explanation: i hope this helps :)
A new computer cost $890 but is being discounted 15%. Find total cost (include 7% sales tax).
Answer:
$809.455
Step-by-step explanation:
How to find the new cost:
890/100*15
= 133.5
So: 890-133.5
= 756.5
next we find 7% of it (tax):
Which we will find the 7% of it and plus it in
so the new answer is: 809.455
Stella has 35 rocks in her rock collection. Each month she will add 15 rocks to the collection. Which equation can be used to find y, the total number of rocks in Stella's collection after x months? A) y = 35x + 15 B) y = 15x - 35 c) y = 35x - 15 D) y = 15x +35
Answer:
A
Step-by-step explanation:
y = 35 + 15x
A
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I need help with this question for my computer class
SOLUTION:
Case: Spreadsheet calculations
Method:
Some common signs
'+' does sum
'-' does difference
'*' does the product
'/' does division
Hence
C7-B6 does the difference for cells C7 and B6
Final answer: Option (D)
C7-B6
I'll give brainliest!
Answer:
The side length, s, of the square is 18
Step-by-step explanation:
The sides can be found by taking the square root of the area.
(Area)^1/2=s, where s = side.
(324)^1/2=18
Match each of the following expressions to its meaning in the context of this situation.Question is in picture
Step 1
Given;
[tex]\begin{gathered} Pizza\text{ store charges 6\% sales tax and \$5 on delivery} \\ Functions\text{ that represent the situation are;} \\ f(a)=1.06a \\ g(b)=b+5 \end{gathered}[/tex]Step 2
Match each of the following expressions to its meaning in the context of this situation.
[tex]undefined[/tex]For what value of t does t / 4 / 16 = 1/16?
Answer: t = 4
Isolating a variable: rearranging an equation so that the variable is on its own
A value of t that satisfies the equation must be foundA variable can be isolated by performing opposite operationsCalculations:
[tex]\frac{\frac{t}{4} }{16} = \frac{1}{16}[/tex]
[tex]\frac{t}{4}= 16/16[/tex] - calculated by multiplying 1/16 by 16
[tex]t= 16/16[/tex] × [tex]4[/tex]
[tex]t= \frac{64}{16}[/tex]
[tex]t=4[/tex] - simplified answer
Help what would be the answer to this question?
Based on the division of polynomials and logical inference, the missing factor is 10x².
What is the proof for the above answer?Note that the result of:
[15x³ - 22x² + (?)] / (5x-4) = 3x²
This means that
3x² * (5x-4) = [15x³ - 22x² + (?)] .............................1
But
3x² * (5x-4) = 15x³ - 12x²
By reverse calculation, therefore,
We state:
-22x² + (?) = - 12x² [Assume for a moment that x² is eliminated]
-22 + (?) = -12
(?) = -12 +22, Hence
(?) = 10x²
Thus,
[15x³ - 22x² + 10X²) ] / (5x-4) = 3x² .........................................2
Proof:
15x³ - 22x² + 10x² ...................................................................3
= 15x³ - 12x²
Taking common factors:
15x³ - 12x² ⇒ 3(5x³-4x²)
Find one factor
3x² (5x-4) .....................................................................................4
Recall that the problem states that equation 3 / (5x-4) = 3x²
If 15x³ - 22x² + 10x² when simplified =
3x² (5x-4)
Then
15x³ - 22x² + 10x²/ (5x-4) = 3x² (5x-4)/(5x-4)
= 3x²
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A U-Haul moving truck covered a total distance of 6223 kilometers averaging a speed of 47 km/h in slow moving traffic and 87 km/h in fast moving traffic. The journey took 89 hours. How many hours did the U-Haul moving truck spend in slow moving traffic?
Select all of the segments that must be 9 centimeters long.
Given:
KM=12 cm.
KO=1+KL
[tex]KL=\frac{1}{3}LM[/tex]Since KM=12 cm, we can write
[tex]\begin{gathered} KM=KL+LM \\ KM=\frac{1}{3}LM+LM \\ 12\text{ =}\frac{4}{3}LM \\ LM=\frac{12\times3}{4} \\ LM=9 \end{gathered}[/tex]Therefore, KL can be calculated as,
[tex]\begin{gathered} KL=\frac{1}{3}LM \\ =\frac{1}{3}\times9 \\ =3 \end{gathered}[/tex]Now, KO can be calculated as,
[tex]\begin{gathered} KO=1+KL \\ =1+3 \\ =4 \end{gathered}[/tex]Now, using geometric property,
[tex]KM\times KL=KN\times KO[/tex]Putting the values in the above equation, KN can be calculated as,
[tex]\begin{gathered} 12\times3=KN\times4 \\ KN=\frac{12\times3}{4} \\ KN=9 \end{gathered}[/tex]Now, ON can be calculated as,
[tex]\begin{gathered} ON=KN-KO \\ =9-4 \\ =5 \end{gathered}[/tex]Since LM=9 is a chord longer than MN in the given circle, the length of MN is less than 9.
Therefore, the segments with length 9 are LM and KN.
Felipe the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On
Using system of equations:
Length of each Plan A workout is: 0.5 hour
Length of each Plan B workout is: 1.25 hours
How to Solve a System of Linear Equations?The number of hours that each of the workout plans last can be represented as a system of linear equations. The explanation below shows how to solve this problem using the elimination method.
Let,
x = number of hours for each plan A workout.
y = number of hours for each plan B workout.
Create the system of equations below:
Equation for Friday would be:
3x + 2y = 4 --> equation 1
Equation for Saturday would be:
8x + 4y = 9 --> equation 2
Multiply equation 1 by 4 and equation 2 by 2:
12x + 8y = 16 --> eqn. 3
16x + 8y = 18 --> eqn. 4
Substract eqn. 4 from eqn. 3:
-4x = -2
x = 1/2 = 0.5 [0.5 hours or 1/2 an hour for Plan A]
Substitute x = 0.5 into eqn.1:
3(0.5) + 2y = 4
1.5 + 2y = 4
2y = 4 - 1.5
2y = 2.5
y = 2.5/2
y = 1.25 [1.25 hours for Plan B]
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5. Graph the function f (x) = 3sin (2x) + 1 Be sure to identify the midline, period, and amplitude.Period= pi Amplitude= 3 Midline = -1 Need help with graphing
Answer:
[tex]\begin{gathered} \text{Amplitude}=3 \\ \text{Midline is at: }y=1 \\ \text{Period}=\pi \end{gathered}[/tex]we can now graph the function as;
Explanation:
Given the equation;
[tex]f(x)=3\sin (2x)+1[/tex]Firstly, to derive the period, Amphitude and midline, let us compare to the general form;
[tex]\begin{gathered} f(x)=A\sin (Bx+C)+D \\ A=\text{Amplitude} \\ D=\text{midline} \\ \text{ since C=0 for the given equation;} \\ \text{Period=}\frac{2\pi}{B} \end{gathered}[/tex]From the given equation;
[tex]\begin{gathered} A=3 \\ D=1 \\ B=2 \\ \therefore \\ \text{Amplitude}=3 \\ \text{Midline is at: }y=1 \\ \text{Period}=\frac{2\pi}{2} \\ \text{Period}=\pi \end{gathered}[/tex]With the above characteristics we can now graph the function as;
R1.56P12TSIn the diagram, QT || RS, PQ = 6, QR = 1.5 and PT = 12. Find ST.STtype your answer...units
Answer:
[tex]ST=3\text{ units}[/tex]Explanation:
Let x represent the length of segment ST.
Given that the lines QT and RS are parallel, the, then the triangles QPT and RPS are similar.
So, the ratio of their sides will be equal;
[tex]\frac{QP}{PT}=\frac{RP}{PS}[/tex]Given;
[tex]\begin{gathered} QP=6 \\ PT=12 \\ RP=6+1.5=7.5 \\ PS=12+x \end{gathered}[/tex]substituting;
[tex]\begin{gathered} \frac{6}{12}=\frac{7.5}{12+x} \\ 12+x=\frac{7.5\times12}{6} \\ 12+x=15 \\ x=15-12 \\ x=3 \\ ST=3\text{ units} \end{gathered}[/tex]Therefore;
[tex]ST=3\text{ units}[/tex]a circle has a radius 6 in in a central age of 60 what is the measure of the arc length is associated with this angle a 2pie b pie c 6pie d 3 pie
Formula for arc length when the angle is in degrees:
[tex]\text{Arc length = }\frac{\theta}{360}\times2\pi r[/tex]r = radius = 6 in
θ= 60 degrees
[tex]\begin{gathered} \text{Arc length = }\frac{60}{360}\times2\times\pi\times6 \\ \text{arc length = }2\pi\text{ in ches (option A)} \end{gathered}[/tex]How do I solve this?
The functions and its domain are a representation of their dependance on one another.
Functionsfunction, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). In the given question, we have two functions and we are required to find the composite of which ever form of the functions as well as the domain of the said function.
[tex]f(x) = \frac{3}{x}, g(x) = 2x + 8;\\(f.g)(x) = \frac{3}{2x + 8}[/tex]
The domain of the function is given as
[tex]domain = (-\infty , -4) U (-4, \infty)\\[/tex]
In the second composition of the function,
[tex](g.f) = \frac{6}{x} + 8\\domain = (-\infty, 0) U (0, \infty)[/tex]
The third composition of function
[tex](f.f) = x\\domain = (-\infty, \infty)[/tex]
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What statement is true? 3/7 is greater than 0.516 3/7 is less than 0.516 3/7 equal 0.516
ANSWER
3/7 is less than 0.516
EXPLANATION
Wwe want to compare the two numbers 3/7 and 0.516.
Let us convert 3/7 to decimal so we can compare properly:
3/7 = 0.429
As we can see:
0.429 is less than 0.516
So, 3/7 is less than 0.516
Amber solved the equation −2=10−3(2+6).
Match the property with each of Amber's steps for solving the equation.
The property use to solve the equation is as follows:
Distributive propertyCombine like termsAdditive property of equalityDivision property of equalityHow to solve equations?The equation can be solved as follows:
−2a = 10 − 3(2a + 6)
Using distributive property,
−2a = 10 − 3(2a + 6)
- 2a = 10 - 6a - 18
According to distributive law, multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.
Combine like terms
- 2a = 10 - 6a - 18
- 2a = -6a - 8
Using additive property of equality, we will add 6a to both sides of the equation.
The additive property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.
- 2a = -6a - 8
- 2a + 6a = -6a + 6a - 8
4a = - 8
using division property of equality, we will divide both sides of the equation by 4.
The division property of equality states that if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal.
4a = - 8
4a / 4 = -8 / 4
a = - 2
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three dice are tossed. what is the probability of rolling 3 different numbers?
Given:Three dice are tossed.
To find: Probability of rolling 3 different numbers.
Let E be the event of getting same number on three dice.
So,the favorable cases for E will be
(1,1,1) , (2,2,2) , (3,3,3), (4,4,4), (5,5,5) , (6,6,6).
So, the number of favorable cases=6
Now,the total number of cases for E will be
[tex]6\times6\times6[/tex]Since each dice has 6 numbers so three dice will have these number of cases.
Now, the probability to have a same number on 3 dice will be
[tex]P(E)=\frac{\text{Number of favorable cases}}{\text{Number of cases}}\text{ }[/tex][tex]\begin{gathered} P(E)=\frac{6}{6\times6\times6} \\ =\frac{1}{36} \end{gathered}[/tex]Now, probability of rolling 3 different numbers is
[tex]P(nu\text{mbers are different on thr}ee\text{ dice)}=1-P(E)[/tex][tex]\begin{gathered} =1-\frac{1}{36} \\ =\frac{30}{36} \\ =\frac{15}{18} \end{gathered}[/tex]Hence, the probability of rolling three different numbers is
[tex]\frac{15}{18}[/tex]HELP ASPP PLEASE SHOW UR WORK
Answer: 7
Step-by-step explanation:
1) Set up an equation. Let x be the number of hours he works.
[tex]400\leq 64x[/tex]
2) Solve the equation
(<= mean less or equal to)
400/64 <= x
6.25 <= x
3) Solve the problem
We need to round up 6.25 as 6.25 is not on the list. Since the number has to be greater than 6.25, the next option is 7.
1. The number of identity theft cases from 2005 through 2010 can be represented by
the function f(x) = 0.058x + 2.175x + 340.2x² - 1,500x+20,000, where x
represents the number of years since 2005. Approximately when will the number of
identity theft cases reach 50,000
We need to know about quadratic equation to solve the problem. The year when the number of cases will be 50,000 is 2017.
Quadratic equation is an equation that has a maximum degree of two. Quadratic equations always have two roots, it can be solved by factorization method. In this question we have been given a function that we can simplify to get a quadratic equation. We need to find the year when the identity theft cases reach 50,000, we need to equate the equation to 50,000 and then solve the quadratic equation to get x.
f(x)=0.058x+2.175x+340.2[tex]x^{2}[/tex]-1500x+20000 =340.2[tex]x^{2}[/tex]-1497.767x+20000
50000=340.2[tex]x^{2}[/tex]-1497.767x+20000
340.2[tex]x^{2}[/tex]-1497.767-30000=0
Using Sridharacharya's method,
x=1497.767±[tex]\sqrt{2243305.99+40824000}[/tex]/680.4=1497.767±6562.56855/680.4
x=11.85 or x=-7.44
Here x cannot be negative, so the right value of x is approximately 12,
year when cases is 50000= 2005+12=2017
Therefore the year when identity theft cases reach 50000 is 2017.
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Look at the photo i placed below for further info
In order to find the value of x, we need to remember that the sum of the interior angles of a triangle is 180°
the equation to find x is
[tex]61+29+x=180[/tex]we need to isolate the x
[tex]\begin{gathered} x=180-61-29 \\ x=90 \end{gathered}[/tex]the answer is c x=90°
find value of p. help
If the two line segments are parallel to each other, we can establish the following proportion and reach the result.
[tex]\frac{3p}{3p+(2p-5)} =\frac{26}{26+14}[/tex][tex]120p=130p-130[/tex][tex]130=130p-120p[/tex][tex]130=10p[/tex][tex]13=p[/tex]Therefore, our answer is [tex]p=13[/tex].