Answer:
The percentage of people that could be expected to score the same as Matthew or higher on this scale is:
= 93.3%.
Step-by-step explanation:
a) Data and Calculations:
Mean score on the scale, μ = 50
Distribution's standard deviation, σ = 10
Matthew scores, x = 65
Calculating the Z-score:
Z-score = (x – μ) / σ
= (65-50)/10
= 1.5
The probability based on a Z-score of 1.5 is 0.93319
Therefore, the percentage of people that could be expected to score the same as Matthew or higher on this scale is 93.3%.
You may recall that the area of a rectangle is A=L⋅W, where W is the width and L is the length.
Suppose that the length of a rectangle is 3 times the width. If the area is 300 square feet, then what is the width of the rectangle, in feet?
Do not type the units in your answer.
Answer:
The width is 10 feet.
Step-by-step explanation:
We know that the area of a rectangle is given by the formula:
[tex]\displaystyle A=L\cdot W[/tex]
Where L is the length and W is the width.
We are given that the length of the rectangle is three times the width. In other words:
[tex]L=3W[/tex]
The total area is 300 square feet. And we want to determine the width of the rectangle.
So, substitute 300 for A and 3W for L:
[tex](300)=(3W)\cdot W[/tex]
Multiply:
[tex]300=3W^2[/tex]
Divide both sides by three:
[tex]W^2=100[/tex]
And take the principal square root of both sides. So:
[tex]W=10[/tex]
Thus, the width of the rectangle is 10 feet.
In the figure, ∆ABD ≅ ∆CBD by Angle-Side-Angle (ASA). Which segments are congruent by CPCTC?
Answer:
[tex]\angle ADB \cong \angle CDB[/tex]
[tex]\angle DBA \cong \angle DBC[/tex]
[tex]BD = BD[/tex]
Step-by-step explanation:
Given
[tex]\triangle ABD \cong \triangle CBD[/tex]
Required
The congruent segments by CPCTC
From the question, we have:
[tex]\angle ADB \cong \angle CDB[/tex] --- given
[tex]\angle DBA \cong \angle DBC[/tex] --- given
Both triangles share a common side (length BD);
So, we have:
[tex]BD = BD[/tex]
Hence, the congruent segments are:
[tex]\angle ADB \cong \angle CDB[/tex]
[tex]\angle DBA \cong \angle DBC[/tex]
[tex]BD = BD[/tex]
Suppose the age that children learn to walk is normally distributed with mean 12 months and standard deviation 2.5 month. 34 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.
Answer:
Step-by-step explanation:
a.) it's just mean, variance
so here it's just 12,6.25
b.) For the x bar thing just divide the variance by the number of people (mean stay the same)
the variance is then (2.5²/34)= .1838
which makes it (12,.1838)
c.) here we don't use x bar (and so it's normal (12,2.5²))
p(11.6) = (11.6-12)/(2.5)= -.16 = .4364
p(12.4)= (12.4-12)/2.5 = .16= .5636
.5636-.4364= .1272
d.) here we use x bar because it's asking for an average so it's normal (12, .1838)
same deal
p(11.6)=(11.6-12)/√.1838= -.93295= .1762
p(12.4)= (12.4-12)/√.1838= .93295= .8238
.8238-.1762= .6476
d.) no because they're probably IID
f.) It's average so here we use x bar
q1 is just the 25th percentile
the 25th percentile is -.6745
-.6745=(x-12)/(√.1838)= 11.711
q3 is the 75th percentile
.6745=(x-12)/√.1838
x=12.289
The interquartile range is just the difference between the two
12.289-11.711= .5784
Can someone help me with this problem
9514 1404 393
Answer:
x = 30°
Step-by-step explanation:
The lines will be parallel if and only if the sum of the marked angles is 180°:
4x +2x = 180°
6x = 180° . . . . . collect terms
x = 30° . . . . . . . divide by 6
PLEASE HELP! ILL MARK !!
Answer:
c) tan
Step-by-step explanation:
tan = Opposite side / close side
When close side = v and Opposite side = 2,8m
Which choice correctly shows the line y =
2x+3?
А
B
HN
N
1-3 -2 -1 1 2 3 4
-1
NH
-4 -3 -2 -1
1 2 3 4
D
c
2
1
1-3-2-1
1
2 3 4
-4 -3 -2
1 2 3
-1
-2
Suppose that E and F are points on the number line. If EF=20 and E lies at 4, where could F be located?
Answer:
F lies at 24Step-by-step explanation:
Since EF = 20 and E is at 4
F is at:
4 + 20 = 24A case of 6 cost 7.5 what it the price per item
Which number is located to the right of on the horizontal number line?
A. -1 1/3
B. -2 1/3
C. -2 2/3
D. -3 1/3
Please help me
Answer:
A
Step-by-step explanation:
since it's negative so it will get smaller
Medallia calculates and publishes various statistics concerning car quality. The dependability score measures problems experienced during the past 12 months by the owners of vehicles. Toyota had 1.02 problems per car. If you had purchased a Toyota model, what is the probability that in the past 12 months the car had. in excel
Answer:
Hence the answers are,
a) Probability that in the past 12 months the car had more than one problem = P(X > 1) is 0.2716.
b) The Probability that in the past 12 months the car had almost two problems = P( X < 2) is 0.9160.
c) The Probability that in the past 12 months the car had zero problems = P(X= 0 ) is 0.3606.
Step-by-step explanation:
Let's take X to be the number of problems per car.
By considering the given statement, X follows a Poisson Distribution with Mean (X) = 1.02.
The Poisson probability formula is :
e Pr( X = k) = e- k! k= 0,1,2...
a)
The Probability that in the past 12 months the car had more than one problem = P(X > 1)
[tex]P(X > 1) =1- P(X < 1) \\\\=1- (P(X = 0) + P(X = 1)-1.021.02 e + 1.021.02 =1-6 0!\\= 1-0.3606 + 0.3678\\= 1-0.7284\\= 0.2716[/tex]
b)
The Probability that in the past 12 months the car had almost two problems = PX < 2)
[tex]Pr(X < 2) = Pr(X = i) = Pr(X = 0) + Pr(X = 1) + Pr(X = 2)\\-1.021.020 -1.021.02 -1.021.02 e e + e + 0! 1! 2!\\= 0.3606 + 0.3678 + 0.1876\\= 0.9160[/tex]
c)
The Probability that in the past 12 months the car had zero problems = P(X= 0 )
[tex]- 1.021.02 e 0!\\= 0.3606[/tex]
FastForward has net income of $19,090 and assets at the beginning of the year of $209,000. Its assets at the end of the year total $264,000. Compute its return on assets.
Given:
Net income = $19,090
Assets at the beginning of the year = $209,000.
Assets at the end of the year total = $264,000.
To find:
The return on assets.
Solution:
Formula used:
[tex]\text{Return of assets}=\dfrac{\text{Net income}}{\text{Average of assets at the beginning and at the end}}[/tex]
Using the above formula, we get
[tex]\text{Return of assets}=\dfrac{19090}{\dfrac{20900+264000}{2}}[/tex]
[tex]\text{Return of assets}=\dfrac{19090}{\dfrac{473000}{2}}[/tex]
[tex]\text{Return of assets}=\dfrac{19090}{236500}[/tex]
[tex]\text{Return of assets}\approx 0.0807[/tex]
The percentage form of 0.0807 is 8.07%.
Therefore, the return on assets is 8.07%.
A 17 feet ladder is placed against a building. The bottom of the ladder is 15 feet away from the building. How many feet high is the top of the ladder?
7 feet
12 feet
8 feet
15 feet
Answer:
[tex]8 \ feet[/tex]
Step-by-step explanation:
In this situation, one is given the following information. A ladder is leaning against a wall and has a measure of (17) feet. The bottom of the ladder is (15) feet away from the wall. One can infer that the wall forms a right angle with the ground. Thus, the triangle formed between the ground, ladder, and wall is a right triangle. Therefore, one can use the Pythagorean theorem. The Pythagorean theorem states the following,
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs or the sides adjacent to the right angle of the right triangle. The parameter (c) represents the hypotenuse or the side opposite the right angle. In this case, the legs are the ground and wall, and the hypotenuse is the ladder. Substitute this into the formula a solve for the height of the wall.
[tex]a^2+b^2=c^2[/tex]
Substitute,
[tex](ground)^2+(wall)^2=(ladder)^2\\\\(15)^2+(wall)^2=(17)^2\\[/tex]
Simplify,
[tex](15)^2+(wall)^2=(17)^2\\\\225+(wall)^2=289[/tex]
Inverse operations,
[tex]225+(wall)^2=289\\\\(wall)^2=64\\\\wall=8[/tex]
In a shipment of toys from a manufacturer, the probability that a toy is defective is
1
50
. If Marie selects 2 toys from a shipment, what is the probability that both toys are defective?
Answer:
The probability is 1/2500. (1/50)*(1/50)
Step-by-step explanation:
Feedback:Correct answer
Question 2 of 10
10.0 Points
3
Find the interquartile range for a data set having the five-number
summary: 4.6, 14.3, 19.7, 26.1, 31.2
A. 26.6
B. 11.8
C. 11.5
D. 15.1
what is a value between 1/4 and 1/3 is
9514 1404 393
Answer:
2/7
Step-by-step explanation:
Any unit fraction with a denominator between 3 and 4 will be between 1/3 and 1/4. For example, ...
1/3.5 = 2/7 . . . . is between 1/3 and 1/4
__
You can also go at this considering decimal equivalents.
1/4 = 0.25
1/3 = 0.333... (repeating)
So, decimal numbers like 0.26, 0.295, 0.3330 are all values that are between 1/4 and 1/3.
Need help please....
Answer:
-14 x²
Step-by-step explanation:
10 x² - 24 x² = -14 x²
The answer is 14
if you multiply both P(x) and Q(x), the third part becomes 14x², so the coefficient of x² becomes 14.
Answered by GAUTHMATH
please help to solve this in written format
Answer:
50 dozen total
Step-by-step explanation:
8/12 & 10/12.... average 9/12
11/12 - 9/12 =
2/12x = 100
2x = 1200
x = 600/12
50 dozen total
Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible are possible
Answer:
10
Step-by-step explanation:
5C2 =5!
2! (3)!
=1 x 2 x 3 x 4 x 5
(1 x 2) (1 x 2 x 3)
=4 x 5
2
=20
2
5C2 = 10
8. Calculate the Perimeter AND Area of
the RIGHT Triangle below.
17 m
10 m
21 m
Answer:
[tex]\text{Perimeter: }48\:\mathrm{m},\\\text{Area: }84\:\mathrm{m^2}[/tex]
Step-by-step explanation:
The area of a triangle with side lengths [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] is given by:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]s=\frac{a+b+c}{2}[/tex]
Substituting [tex]a=21, b=17, c=10[/tex], we have:
[tex]A=\sqrt{24(24-21)(24-17)(24-10)},\\A=\sqrt{24(3)(7)(14)},\\A=\sqrt{7,084},\\A=\boxed{84\:\mathrm{m^2}}[/tex]
The perimeter of a polygon is given by the sum of its sides. Since the triangle has sides 10, 17, and 21, its perimeter is [tex]10+17+21=\boxed{48\:\mathrm{m}}[/tex].
Suppose a basketball player has made 231 out of 361 free throws. If the player makes the next 2 free throws, I will pay you $31. Otherwise you pay me $21.
Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.
Answer:
The expected value of the proposition is of -0.29.
Step-by-step explanation:
For each free throw, there are only two possible outcomes. Either the player will make it, or he will miss it. The probability of a player making a free throw is independent of any other free throw, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Suppose a basketball player has made 231 out of 361 free throws.
This means that [tex]p = \frac{231}{361} = 0.6399[/tex]
Probability of the player making the next 2 free throws:
This is P(X = 2) when n = 2. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.6399)^{2}.(0.3601)^{0} = 0.4095[/tex]
Find the expected value of the proposition:
0.4095 probability of you paying $31(losing $31), which is when the player makes the next 2 free throws.
1 - 0.4059 = 0.5905 probability of you being paid $21(earning $21), which is when the player does not make the next 2 free throws. So
[tex]E = -31*0.4095 + 21*0.5905 = -0.29[/tex]
The expected value of the proposition is of -0.29.
A surveyor is using indirect measurement to find the height of a cliff. He is 4 feet tall and is standing 32 feet away. How tall is the cliff?
Is it possible to have a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive
Answer:
Yes, it is possible to have a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive
Step-by-step explanation:
Let
Set A={a,b,c}
Now, define a relation R on set A is given by
R={(a,a),(a,b),(b,a),(b,b)}
For reflexive
A relation is called reflexive if (a,a)[tex]\in R[/tex] for every element a[tex]\in A[/tex]
[tex](c,c)\notin R[/tex]
Therefore, the relation R is not reflexive.
For symmetric
If [tex](a,b)\in R[/tex] then [tex](b,a)\in R[/tex]
We have
[tex](a,b)\in R[/tex] and [tex](b,a)\in R[/tex]
Hence, R is symmetric.
For transitive
If (a,b)[tex]\in R[/tex] and (b,c)[tex]\in R[/tex] then (a,c)[tex]\in R[/tex]
Here,
[tex](a,a)\in R[/tex] and [tex](a,b)\in R[/tex]
[tex]\implies (a,b)\in R[/tex]
[tex](a,b)\in R[/tex] and [tex](b,a)\in R[/tex]
[tex]\implies (a,a)\in R[/tex]
Therefore, R is transitive.
Yes, it is possible to have a relation on the set {a, b, c} that is both symmetric and transitive but not reflexive.
SCC U of 1 pt 3 of 1 1.2.11 Assigned Media A rectangle has a width of 49 centimeters and a perimeter of 216 centimeters. V The length is cm.
Answer:
The length is of 59 cm.
Step-by-step explanation:
Perimeter of a rectangle:
The perimeter of a rectangle with width w and length l is given by:
[tex]P = 2(w + l)[/tex]
Width of 49 centimeters and a perimeter of 216 centimeters:
This means that [tex]w = 49, P = 216[/tex]
The length is cm.
We have to solve the equation for l. So
[tex]P = 2(w + l)[/tex]
[tex]216 = 2(49 + l)[/tex]
[tex]216 = 98 + 2l[/tex]
[tex]2l = 118[/tex]
[tex]l = \frac{118}{2}[/tex]
[tex]l = 59[/tex]
The length is of 59 cm.
15. Mark Twain one observed that the lower Mississippi River is very crooked and that over the years, as the bends and turns straighten out, the river gets shorter and shorter. Using numerical data about the length of the lower part of the river, he noticed that in the year 1700 the river was more than 1200 miles long, yet by the year 1875 it was only 973 miles long. Twain concluded that any person “can see that 742 years from now the lower Mississippi will be only a mile and three-quarters lone.” What is wrong with his inductive reasoning?
Answer:
Step-by-step explanation:
I'm sure he was making a joke at the expense of people who rely on mathematics rather than common sense. It is funny, but then Twain was a remarkably funny author..
The problem is that the comparison is apt using some sort of proportion, but it is absurd to think that the land holding the river would also shrink a proportional amount.
The river reached a minimum (presumably) in 1875 by cutting out all the loops that were there in 1700. The Mississippi was then a straight line from it's beginning to its delta on the gulf of Mexico. It could not get any shorter. Still, Twain managed to get laughs with his whimsical humor.
Thanks for posting. This made my evening.
Suppose you just received a shipment of 14 televisions. Three of the televisions are defective. If two televisions are randomly selected , compute the probability that both televisions work. What is the probability at least one of the two televisions does not work?
Answer:
Probability of defective televisions : Now, If two televisions are randomly selected, then the probability that both televisions work. Hence, the probability that both televisions work is 0.5289 . Hence, the probability at least one of the two televisions does not work is 0.4711.
Which of the following proportions is true?
10/40 = 8/36
8/18 = 6/16
9/15 = 44/50
12/18 = 16/24
Answer:
D. 12/18 = 16/24
Step-by-step explanation:
The method we must go about to solve this is finding the constant. For A, we can solve it by doing 10 divided by 8 (which is 1.25) and then 40 divided by 1.25 to see if it is 36. Alternatively, we can do 10 divided by 8 and then 40 divided by 36 to see if the constant is the same. It's up to you!
My answers:
A. No (constant varies)
B. No (constant varies)
C. No (constant varies)
D. Yes! Constant is 0.75
How to solve for D:
12/16 = 0.75
18/0.75 = 24 OR 18/24 = 0.75
I hope this helps! Please don't hesitate to reach out with more questions!
Hello!
10/40 = 8/36 ?
10 × 36 = 40 × 8
360 = 40 × 8
360 ≠ 320 => 10/40 ≠ 8/36
8/18 = 6/16 ?
8 × 16 = 18 × 6
128 = 18 × 6
128 ≠ 108 => 8/18 ≠ 6/16
9/15 = 44/50 ?
9 × 50 = 15 × 44
450 = 15 × 44
450 ≠ 660 => 9/15 ≠ 44/50
12/18 = 16/24 ?
12 × 24 = 18 × 16
288 = 18 × 16
288 = 288 => 12/18 = 16/24
Good luck! :)
Help please and thanks !!
Answer:
4th option
Step-by-step explanation:
tanZ = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{XY}{ZY}[/tex]
What is the value of x if 2/ 3 - 2 = -4 ?
Answer:
x= -3
Step-by-step explanation:
(2x/3)-2=-4
Add 2 to both sides
2x/3=-2
multiply both sides by 3
2x=-6
divide both sides by 2
x= -3
Answer:
x = -3
Step-by-step explanation:
2x/3 - 2 = -4
Add 2 to both sides.
2x/3 = -2
Multiply both sides by 3/2.
x = -2 * 3/2
x = -3
In the given figure, find m_RST, if m RSU = 43° and m_UST = 23°.
Answer:
66
Step-by-step explanation:
Add both of the angles given together
43 + 23
This one is tricky! Imagine that you meet a new friend who is also a beginner, and she can run the 5k in 23.5 minutes. You wonder what percentage of the beginner running population could run the 5k faster than your new friend (that is, what percentage of the population has a time that is less than your new friend
Answer:
38.74%
Step-by-step explanation:
Given the data:
21 21 22 22 23 23 23 24 24 24 24 24 25 25 25 26 26 27 27
We obtain the beginner running population and standard deviation
Population mean, μ = Σx/n = 456/19 = 24
Standard deviation, σ = 1.747 (using calculator)
Friend's Runtime, x = 23.5 minutes
Obtaining the friend's Zscore :
Z = (x - μ) / σ
Z = (23.5 - 24) / 1.747
Z = - 0.286
Obtaining the Pvalue :
Using a standard normal distribution table :
P(Z < - 0.286) = 0.38744
Hence. Percentage of population that has lesser time :
0.38744 * 100% = 38.74%