Answer:
C
Step-by-step explanation:
The scores in a recent statistics test are given in the frequency distribution below.
[tex]\left|\begin{array}{c|cc}$Scores&$Frequency\\---&--\\0-60&4\\61-70&10\\71-80& 12\\81-90&4\\91-10&5\\----&--\\$Total&35\end{array}\right|[/tex]
The relative frequency is calculated in the table below.
[tex]\left|\begin{array}{c|c|c}$Scores&$Frequency&$Relative Frequency\\---&--&-----\\0-60&4&\dfrac{4}{35}\times 100=11.43\% \\\\61-70&10&\dfrac{10}{35}\times 100=28.57\%\\\\71-80& 12&\dfrac{12}{35}\times 100=34.29\%\\\\81-90&4&\dfrac{4}{35}\times 100=11.43\%\\\\91-10&5&\dfrac{5}{35}\times 100=14.29\%\\----&--&---\\$Total&35&100\end{array}\right|[/tex]
Therefore, the relative frequency table is that in Option C.
How many gallons of fuel costing $1.15 a gallon must be mixed with a fuel costing $0.85 per gallon to get 40
gallons of a fuel that costs $1 per gallon? Formulate an equation and then solve it in order to determine how
many gallons of fuel costing $1.15.
Answer:
multiply 0.85x40
Step-by-step explanation:
Create a unique equation using the graphic above with the solution (answer)36
6*6 = 36
36/6=6
6^2
please mark me brainliest!
The equation will be:
What is a Coordinate Plane?A coordinate plane is a graphing and description system for points and lines.
How to determine?Now create your equation using the values below: mm: If the answer is 12, there are
several possible equations: 2D+G=12 —r 2(3)+fi=12 4C+H—D —1 4(2)+T—3 DQC} —+ 3(2 1: 2) There are many
more options!
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The base of pyramid A is a rectangle with a length of 10 meters and a width of 20 meters. The base of pyramid B is a square with 10-meter sides.
The heights of the pyramids are the same.
The volume of pyramid Als
y the volume of pyramid B. If the helght of pyramid B increases to twice that of pyramid A, the
new volume of pyramid B is
the volume of pyramid A.
Answer:
a. The volume of Pyramid A is double that of Pyramid B.
b. The new volume of B is equal to the volume of A.
Step-by-step explanation:
The base of pyramid A is a rectangle with length 10 meters and width 20 meters.
The base of pyramid B is a square of side length 10 meter.
Both pyramids have the same height, h.
The volume of a pyramid is given as:
V = lwh / 3
where l = length
w = width
h = height
The volume of Pyramid A is:
V = (10 * 20 * h) / 3 = 66.7h cubic metres
The volume of Pyramid B is:
V = (10 * 10 * h) / 3 = 33.3h cubic metres
By comparing their values, the volume of Pyramid A is double that of Pyramid B.
If the height of B increases to 2h, its new volume is:
V = (10 * 10 * 2h) / 3 = 66.7h cubic metres
The new volume of B is equal to the volume of A.
O número inteiro positivo, cujo produto de seu antecessor com seu sucessor é igual a 8, é
A) 5
B) 4
C) -3
D) 3
El 2
Answer:
Olá!
`~~~~~~~~~~~~~~~~~~
3 (número inteiro positivo)
2 (antessor)
4 (sucessor)
Para provar isso, simplesmente multiplicamos entre 4 e 2:
4 x 2 = 8
Espero que isso tenha ajudado! Também seria bom se você me desse Brainliest!
The total number of students enrolled in MATH 123 this semester is 6,072. If it decreases by 0.76% for the next semester, what will be the enrollment next semester? Round to a whole person.
Answer:
6026
Step-by-step explanation:
6072 × (1 - 0.76%)
6072 × 0.9924
= 6025.8528
Round to the whole number.
The enrollment for next semester will be 6026.
Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with a mean of 49 days and a standard deviation of 10.2 days. Find the probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days.
Answer:
The probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days is P(M>54)=0.00004.
Step-by-step explanation:
In this case, we have a population lifetime normally distributed with mean 49 and standard deviation 10.2.
We take a sample of size n=64.
Then, we can calculate the z-score for a sample mean M=54, in order to calculate P(M>54):
[tex]z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{54-49}{10.2/\sqrt{64}}=\dfrac{5}{1.275}=3.922\\\\\\P(M>54)=P(z>3.922)=0.00004[/tex]
The probability that a simple random sample of 64 protozoa will have a mean life expectancy of 54 or more days is P(M>54)=0.00004.
I NEED HELP PLEASE, THANKS! :) A commercial passenger jet is flying with an airspeed of 185 miles per hour on a heading of 036°. If a 47-mile-per-hour wind is blowing from a true heading of 120°, determine the velocity and direction of the jet relative to the ground. 186.1 mph, 021° 188.5 mph, 021° 195.6 mph, 069° 186.1 mph, 069°
We are given that the passenger's jet is flying at a speed of 185 miles per hour, with a direction of 36 degrees, and the wind speed being 47 mph with a direction of 120 degrees. From this, you could create a diagram is shown in the attachment.
[ 185 cos 36, 185 sin 36 ]
+ [ 47 cos 120, 47 sin 120 ]
_______________________
[ 185 cos 36 + 47 cos 120, 185 sin 36 + 47 sin 120 ]
√( 4263 + 33988 )^2
= ( About ) √38251 = 195.57 mph
Solution = 195.6 mph, 069°
Skylar has 4 times as many books as Karen. If Skylar has 164 books, how many books does Karen have?
Answer:
41
Step-by-step explanation:
If Skylar has 4 times as many books as Karen, that means that you have to do a division problem to figure out how books Karen has. Because Skylar has 4 times as many books, and she has 164 books, the division problem is 164÷4=41 books.
The number of books Karen has will be 41.
What exactly is simplification?Simplifying means making something easier to do or comprehend, as well as making something less difficult.
Let,
Skylar has x number of books
Karen has y number of books = 164
Given condition;
y=4x
164=4x
x=41 books
Hence Karen has 41 books.
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Please answer this correctly
Answer:
1/4
Step-by-step explanation:
The probability of landing on an odd number is 2/4.
The probability of landing on a number greater than 5 is 2/4.
2/4 × 2/4
4/16 = 1/4
9. Look at triangle RST below.
Which side of the triangle is the longest?
Answer:
ST is longest
Step-by-step explanation:
Theorem: If one side of a triangle is longer than another side, then the angle opposite the longer side will be larger than the angle opposite the shorter sideThe values of the angles are:
∠S= 50°, ∠T= 60°,∠R= 180°- (50°+60°)= 180° - 110° = 70°Since ∠R is the largest angle, the side ST is longest
Determine whether the lines L1:x=25+7t,y=17+6t,z=t and L2:x=−12+8ty=−17+8tz=−11+4t intersect, are skew, or are parallel. If they intersect, determine
Answer: The lines are skew.
Step-by-step explanation: Two lines can only be parallel OR skew Or intersect each other. To determine that:
1) If the lines are parallel, divide the coefficient that precedes the variable of each equation and compare:
[tex]\frac{7}{8} \neq \frac{6}{8} \neq \frac{1}{4}[/tex]
Since they are not equal, L1 and L2 are not parallel.
2) If the lines intersect, when you equal the equations the variable is a valid statement:
25 + 7t = - 12 + 8t (1)
17 + 6t = - 17 + 8t (2)
t = - 11 + 4t (3)
Using (3) to solve the system:
t - 4t = - 11
3t = 11
t = [tex]\frac{11}{3}[/tex]
Substituing t in (1):
25 + 7(11/3) = -12 + 8(11/3)
25 + 77/3 = - 12 + 88/3
[tex]\frac{152}{3} = \frac{52}{3}[/tex]
Which is not true, so, the lines does NOT intersect.
As they are none of the other options, it can be concluded that the lines L1 and L2 are skew.
Can you explain these words Rate, Per, Divide, Unit and the connections you see between them. Thank you very kind!!!
Answer:
A rate is a little bit different than the ratio, it is a special ratio. It is a comparison of measurements that have different units, like cents and grams. A unit rate is a rate with a denominator of 1.
Per is defined as to, for, by or according to. An example of per used as a preposition is in the phrase, "as per standards," which means by the standards
Division is splitting into equal parts or groups. It is the result of "fair sharing
A tank contains 40 lb of salt dissolved in 500 gallons of water. A brine solution is pumped into the tank at a rate of 5 gal/min; it mixes with the solution there, and then the mixture is pumped out at a rate of 5 gal/min. Determine A(t), the amount of salt in the tank at time t, if the concentration of salt in the inflow is variable and given by cin(t)
Answer:
[tex]A(t)=500C_{in}(t)+[40-500C_{in}(t)]\cdot e^{-\frac{t}{100}}[/tex]
Step-by-step explanation:
Volume of water in the Tank =500 gallons
Let A(t) be the amount of salt in the tank at time t.
Initially, the tank contains 40 lbs of salt, therefore:
A(0)=40 lbs
Rate of change of the amount of Salt in the Tank
[tex]\dfrac{dA}{dt}=R_{in}-R_{out}[/tex]
Rate In=(concentration of salt in inflow)(input rate of brine)
[tex]=(C_{in}(t))( 5\frac{gal}{min})\\=5C_{in}(t)\frac{lbs}{min}[/tex]
Rate Out=(concentration of salt in outflow)(output rate of brine)
[tex]=(\frac{A(t)}{500})( 5\frac{gal}{min})=\frac{A}{100}[/tex]
Therefore:
[tex]\dfrac{dA}{dt}=5C_{in}(t)-\dfrac{A}{100}[/tex]
We then solve the resulting differential equation by separation of variables.
[tex]\dfrac{dA}{dt}+\dfrac{A}{100}=5C_{in}(t)\\$The integrating factor: e^{\int \frac{1}{100}}dt =e^{\frac{t}{100}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{100}}+\dfrac{A}{100}e^{\frac{t}{100}}=5C_{in}(t)e^{\frac{t}{100}}\\(Ae^{\frac{t}{100}})'=5C_{in}(t)e^{\frac{t}{100}}[/tex]
Taking the integral of both sides
[tex]\int(Ae^{\frac{t}{100}})'=\int [5C_{in}(t)e^{\frac{t}{100}}]dt\\Ae^{\frac{t}{100}}=5*100C_{in}(t)e^{\frac{t}{100}}+C, $(C a constant of integration)\\Ae^{\frac{t}{100}}=500C_{in}(t)e^{\frac{t}{100}}+C\\$Divide all through by e^{\frac{t}{100}}\\A(t)=500C_{in}(t)+Ce^{-\frac{t}{100}}[/tex]
Recall that when t=0, A(t)=40 lbs (our initial condition)
[tex]A(t)=500C_{in}(t)+Ce^{-\frac{t}{100}}\\40=500C_{in}(t)+Ce^{-\frac{0}{100}}\\C=40-500C_{in}(t)\\$Therefore, the amount of salt in the tank at any time t is:\\\\A(t)=500C_{in}(t)+[40-500C_{in}(t)]\cdot e^{-\frac{t}{100}}[/tex]
The height of a projectile launched upward at a speed of 32 feet/ second from a height of 128 feet is given by the function h(t)=-16t^2+32t+128. How long will it take the projectile to hit the ground?
Answer:
8.51 seconds
Step-by-step explanation:
Time to reach maximum height
=( Usin90)/2g
= 32/2*9.81
= 32/19.62
= 1.63 s
Max height = U²Sin²tita/g
= 32²/9.81
= 1024/9.81
= 104.38ft
Total height=104.38 + 128= 232.38
Time to fall back to the ground using the formula
h = ut+(1/2)gt²
U= 0
H= 232.38
g = 9.81
(232.38 *2 )/9.81= t²
47.376= t²
t = 6.88 s
Total time taken to hit ground
= 6.88 + 1.63
= 8.51 seconds
What is the quotient in polynomial form?
Answer:
The quotient in polynomial form= 2x + 6
Step-by-step explanation:
In order to calculate the quotient in polynomial form of the following synthetic division we would have to make the following:
According to the given data we have the following:
-1|2 8 6
Therefore, quotient in polynomial form would be calculated as follows:
-1 | 2 8 6
-2 -6
2 6 0
Therefore, quotient in polynomial form= 2x + 6
The quotient in polynomial form= 2x + 6
In a book the characters are trying to determine whether the Poisson probabilistic model can be used to describe the locations that rockets landed in a city. They divided the city into 0.25-kmsquared regions. They then counted the number of rockets that landed in each region, with the results shown in the table below. Complete parts (a) through (e). Number of rocket hits 0 1 2 3 4 5 6 7 Observed number of regions 228 214 94 32 7 0 0 1 (a) Estimate the mean number of rocket hits in a region by computing mu equals Summation from nothing to nothing xP left parenthesis x right parenthesis.
Answer:
The estimated mean number of rockets hits in the region is 533.
Step-by-step explanation:
We are given the following information,
Number of rocket hits | Observed number of regions
0 | 228
1 | 214
2 | 94
3 | 32
4 | 7
5 | 0
6 | 0
7 | 1
We are asked to estimate the mean number of rocket hits in the region.
The mean or expected value is given by
[tex]\mu = \sum (x \cdot P(x)) \\\\\mu = (0 \cdot 228) + (1 \cdot 214) + (2 \cdot 94) + (3 \cdot 32) + (4 \cdot 7) + (5 \cdot 0) + (6 \cdot 0) + (7 \cdot 1) \\\\\mu = 0 + 214 +188+ 96 +28 +0+ 0 + 7 \\\\\mu = 533[/tex]
Therefore, the mean number of rockets hits in the region is 533.
Functions f(x) and g(x) are shown below: f(x) = x2 g(x) = x2 + 8x + 16 In which direction and by how many units should f(x) be shifted to obtain g(x)? (1 point) Left by 4 units Right by 4 units Left by 8 units Right by 8 units
Answer: left 4 units
Step-by-step explanation: use the formula -b/2a to find the new x value. Or use a graphing calculator and compare the position of g(x) to f(x)
Answer:
Answer: left 4 units
Step-by-step explanation:
9(d − 93) = –36 d = _______
Steps to solve:
9(d - 93) = -36d
~Distribute
9d - 837 = -36d
~Subtract 9d to both sides
-837 = -45d
~Divide -45 to both sides
18.6 = d
Best of Luck!
The board of directors of a company decides to promote 3 of its 10 senior staff members to the position of first vice president, second vice president, and third vice president. In how many ways can this promotion be made?
Answer:
720 ways
The number of ways in which the promotion can be made is 720 ways
Step-by-step explanation:
Given that;
The board of directors of a company decides to promote 3 of its 10 senior staff members to the position of first vice president, second vice president, and third vice president.
This is a permutation problem because the order of selection is relevant. They will be promoted to various positions.
N = nPr = n!/(n-r)!
n = 10, r = 3
Substituting the values;
N = 10P3
N = 10!/(10-3)! = 10!/7!
N = 720 ways
The number of ways in which the promotion can be made is 720 ways
Parker wants to buy a car and has a choice between two different banks. One bank is offering a simple interest rate of 3 2% and the other bank is offering a rate of 3%
compounded annually. If Parker decides to deposit $7,000 for 25 years, which bank would be the better deal?
A.)a simple interest rate of 3.2%
B.)a compound interest rate of 3%
Answer:
The better deal would be simple interest rate of 3.2%
Step-by-step explanation:
In order to calculate which bank would be the better deal If Parker decides to deposit $7,000 for 25 years, we would have to make the following calculation:
A. simple interest rate of 3.2%.
Therefore, FV= P*r*t
=$7,000*3.2%*25
=$5,600.
B. compound interest rate of 3%
Therefore, FV=PV(1+r)∧n
FV=$7,000(1+0.03)∧25
FV=$14,656
The better deal would be simple interest rate of 3.2%
A random sample of vacationers were asked whether they were traveling to another country for their upcoming trip. The resulting confidence interval for the proportion of vacationers traveling abroad is (0.14,0.16). What is the margin of error?
Answer:
The Margin of error = 0.01
Step-by-step explanation:
Explanation:-
step(i):-
Given confidence interval for the proportion of vacationers traveling abroad
(0.14,0.16)
The 95% of confidence interval for Population proportion with margin of error is determined by
( p⁻ - M.E , p⁻ + M.E)
step(ii):-
The margin of error is determined by
[tex]M.E = Z_{\alpha } \sqrt{\frac{p(1-p)}{n} }[/tex]
Given Confidence interval is ( 0.14 , 0.16 )
Now
(( p⁻ - M.E , p⁻ + M.E) = (0.14,0.16)
Equating
p⁻ - M.E = 0.14 ...(i)
p⁻ + M.E = 0.16 ...(ii)
Solving (i) and (ii) equations , we get
p⁻ - M.E = 0.14
p⁻ + M.E = 0.16
- - -
- 2 M.E = -0.02
M.E = 0.01
The margin of error = 0.01
Conclusion:-
The margin of error = 0.01
what is (x – 3)(2x + 1)
Answer:
(x – 3)(2x + 1)
Expand the terms
We get
2x² + x - 6x - 3
Final answer
2x² - 5x - 3
Hope this helps you.
Finally, you meet a group of six natives, U, V, W, X, Y, and Z, who speak to you as follows. U says: None of us is a knight. V says: At least three of us are knights. W says: At most three of us are knights. X says: Exactly five of us are knights. Y says: Exactly two of us are knights. Z says: Exactly one of us is a knight. Which are knights
Answer:
w and y are knights
Step-by-step explanation:
Of the six natives, W and Y are the knights.
What is the reasoning?In mathematics, reasoning entails making logical deductions from data or presumptions. Making sense of something can be defined as gaining comprehension of a situation, setting, or idea by relating it to what is already known or has already happened.
Given that you meet a group of six natives, U, V, W, X, Y, and Z, who speak to you as follows. U says: None of us is a knight. V says: At least three of us are knights. W says: At most three of us are knights. X says: Exactly five of us are knights. Y says: Exactly two of us are knights. Z says: Exactly one of us is a knight.
From the given data it is concluded that W and Y are the knights because their statement is W says: At most three of us are knights and Y says: Exactly two of us are knights.
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PLEASE HELP ME WITH THESE QUESTIONS!! :((( #2 & 4a)
Answer:
2 a. 210 ways
b. 50 ways
c. 28 ways
d. 0.205
4 a. 1716 ways
Step-by-step explanation:
2. a. The number of ways, [tex]n_w[/tex] of selecting without restriction is given as follows;
[tex]\dbinom{10}{4}[/tex] = 10!/(4!(10 - 4)!) = 210
b. The number of ways of selecting 3 boys from 5 is 5!/(3!(5 - 3)!) = 10 ways
The number of ways of selecting the remaining 1 girl from 5 = 5!/(1!(5 - 1)!) = 5 ways
The number of ways of the selection where there must be three boys = 5×10 = 50 ways
c. Given that Maggie and Marley must be chosen, each of whom can be chosen only one way, we have;
Selection of 2 from 8 gives;
8!/(2!(8 - 2)!) = 28
Therefore, the number of ways of the selection where there must be Maggie and Marley is 28 × 1 × 1 = 28 ways
d. The probability of no boys is given by the relation;
P(k success from n trials) = [tex]_nC_r \cdot p^k \cdot (1 - p)^{n-k}[/tex]
Where n = number of persons = 10
k = Number of person in the group = 4
p = Probability of success of girls = 1/2
Therefore, we have for no boys;
[tex]\dbinom{10}{4} \times \left (\dfrac{1}{2} \right )^4\times \left (1-\dfrac{1}{2} \right )^{10-4} = \dfrac{210}{16 \times 64} = \dfrac{105}{512} = 0.205[/tex]
4a) The number of ways of selecting 9 softball players from 15 where Rylea and Emily must be included;
Given that Rylea and Emily are already selected, we have;
The number of ways of selecting 7 softball players from 13 given as follows;
13!/(7!(13 - 7)!) = 1716 ways
Given that Rylea and Emily can both be selected in only one way, the total number of ways = 1×1×1716 = 1716 ways
Which of the following lists of ordered pairs is a function?
Α. (Ο, 2), (2, 3), (ο, - 2), (4, 1)
Β. (1, 2), (1,2), 2), (3, 4)
C. 1, 5). 2, 1, 4, 9), το, 5)
D. (2, 4), (0, 2), (2, -4), (5, 3)
Answer:
the answer will be D
Step-by-step explanation:
Find the distance from point X to line p. An image of a point X, a line p, and three segments joining the point and the line. Question 12 options:
A. 2 √34 units
B. √85 units
C. 2 √17 units
D. √17 units
Answer:
Step-by-step explanation: Answer is 2√17 units
Distance =√ (−2−0) ^2−(5−(−3)) ^2
=√ (−2) ^2−(5+3) ^2
=√4+64
=√68
=2√17 units
On Wednesday and Thursday
a total of 32 records were sold.
The number of records sold on
Thursday was 3 times the number
of records sold on Wednesday.
c) How many records were (2)
sold on Wednesday?
d) How many records were (1)
sold on Thursday?
Total marks: 5
Answer:
8 records were sold on Wednesday, and 24 records were sold on Thursday
Step-by-step explanation:
Let's call the number of records sold on Wednesday w, and the number sold on Thursday t.
t+w=32
t=3w
Substituting:
(3w)+w=32
4w=32
w=8
t=3w=3(8)=24
Hope this helps!
Ujalakhan01! Please help me! ASAP ONLY UJALAKHAN01. What's (x-1)(x-1)?
Answer:
[tex]x^2-2x+1[/tex]
Step-by-step explanation:
=> (x-1)(x-1)
Using FOIL
=> [tex]x^2-x-x+1[/tex]
=> [tex]x^2-2x+1[/tex]
Answer:
[tex]\boxed{x^2-2x+1}[/tex]
Step-by-step explanation:
[tex](x-1)(x-1)[/tex]
Apply FOIL Method.
[tex]x(x-1)-1(x-1)[/tex]
[tex]x^2-x-x+1[/tex]
Combine like terms.
[tex]x^2-2x+1[/tex]
Suppose that a box contains 6 cameras and that 5 of them are defective. A sample of 2 cameras is selected at random. Define the random variable X as the number of defective cameras in the sample.
Answer:
[tex]\begin{array}{cc}X&P(X)\\0&0\\1&0.3333\\2&0.6667\end{array}[/tex]
E(X)= 1.667
Step-by-step explanation:
The question asks for the probability distribution and the expected value of X.
The possible values for the number of defective cameras (X) are 0, 1 or 2.
The probability distribution for X is:
[tex]P(X=0)=0[/tex]
Since there is only one camera in the box that is not defective, it is impossible for no camera to be defective when picking 2.
[tex]P(X=1)=\frac{1}{6}*\frac{5}{5}+\frac{5}{6}*\frac{1}{5}\\ P(X=1)=0.3333[/tex]
[tex]P(X=2)=\frac{5}{6}*\frac{4}{5}\\ P(X=2) =0.6667[/tex]
The probability distribution is:
[tex]\begin{array}{cc}X&P(X)\\0&0\\1&0.3333\\2&0.6667\end{array}[/tex]
The expected value of X is:
[tex]E(X) = 0.3333*1+0.6667*2\\E(X) = 1.667[/tex]
The expected value is 1.667 defective cameras.
Answer this question :)
Hey there! :)
Answer:
f(x) = x³ -6x² -16x. (Simplified)
Step-by-step explanation:
Given:
Zeros: -2, 0, 8; degree: 3
To begin, write the polynomial in factored form involving the zeros:
f(x) = x(x + 2)(x - 8).
If you were to convert this to standard form, you would FOIL the factors:
f(x) = x(x + 2)(x - 8)
f(x) = x(x² -6x -16)
f(x) = x³ -6x² -16x. This is your equation in standard form.