Using the normal distribution, we have that the desired information is given as follows:
a) X ~ N(3,1.8).
b) 3 days.
c) Z = 0.5556.
d) 0.33 = 33%.
e) 0.2048 = 20.48%.
f) 5.3 days.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 3, \sigma = 1.8[/tex]
Hence the distribution is X ~ N(3,1.8), and, as is standard in the normal distribution, the median is the same as the mean, which is of 3 days.
The Z-score for a patient that took 4 days to recover is Z when X = 4, hence:
Z = (4 - 3)/1.8 = 0.5556.
The probability of spending more than 3.8 days in recovery is one subtracted by the p-value of Z when X = 3.8, hence:
Z = (3.8 - 3)/1.8 = 0.44.
Z = 0.44 has a p-value of 0.67.
1 - 0.67 = 0.33.
The probability is of 0.33 = 33%.
The probability of spending between 3.2 and 4.2 days in recovery is the p-value of Z when X = 4.2 subtracted by the p-value of Z when X = 3.2, hence:
X = 4.2:
Z = (4.2 - 3)/1.8
Z = 0.67.
Z = 0.67 has a p-value of 0.7486.
X = 3.2:
Z = (3.2 - 3)/1.8
Z = 0.11.
Z = 0.11 has a p-value of 0.5438.
0.7486 - 0.5438 = 0.2048 = 20.48%.
The 90th percentile is X when Z = 1.28, hence:
1.28 = (X - 3)/1.8
X - 3 = 1.8 x 1.28
X = 5.3 days.
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Solve the inequality 6 > x² - 5x.
Answer:
Step-by-step explanation:
6 > x² - 5x.
The answer for the inequality is -1 the greater than sign x greater than 6
The interval notation is ( -1,6)
Answer:
[tex]-1 < x < 6[/tex]
Step-by-step explanation:
Moving all terms to one side, we get [tex]x^2-5x-6 < 0[/tex]. Notice that we can factor the left side. Doing so, we get [tex](x-6)(x+1) < 0[/tex]. The zeroes in this equation are [tex]x-6=0 \Rightarrow x=6[/tex] and [tex]x+1=0\Rightarrow x=-1[/tex]. Now, we must create test points in the intervals: [tex]x < -1, -1 < x < 6, x > 6[/tex]. For example, we can choose [tex]x=-2,x=0,x=7[/tex]. For [tex]x=-2[/tex], we get that [tex](-2-6)(-2+1) = 8 < 0[/tex] is false, since the expression is positive. Doing the same thing for [tex]x=0[/tex] and [tex]x=7[/tex], we get that only [tex]x=0[/tex] creates a negative value. This means that the values in the interval [tex]\boxed{-1 < x < 6}[/tex] all work.
Factor the greatest common factor: −5k2 20k − 30. −1(5k2 − 20k 30) −5(k2 − 4k 6) −5k(k2 − 4k 6) −5(k2 4k − 6)
The greatest common factor−5k2 20k − 30 is [tex]-5(k^{2} -4k-6).[/tex]
What is meant by the greatest common factor?The most common factor in mathematics is the highest number that may divide evenly into two other numbers.The largest factor that splits both numbers is the greatest common factor. List the prime factors of each integer before calculating the greatest common factor. One 2 and one 3 are shared by those aged 18 and 24. We multiply them to obtain the GCF. Therefore the GCF for 18 and 24 is 2 * 3 = 6.The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a collection of whole numbers.To find the greatest common factor:
−5k2 20k − 30.
Factor the expression: [tex]5(-k^{2} +4k-6)[/tex]
Factor the expression: [tex]5(-k^{2} -4k+6)[/tex]
Multiply the monomials: [tex]5(k^{2} +4k+6)[/tex]
The greatest common factor: [tex]-5(k^{2} -4k-6).[/tex]
The greatest common factor−5k2 20k − 30 is [tex]-5(k^{2} -4k-6).[/tex]
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The complete question is:
Factor the greatest common factor: [tex]-5k^2+ 20k - 30.[/tex]
a) [tex]-1(5k^2- 20k+ 30)[/tex]
b) [tex]-5(k^2 -4k+ 6)[/tex]
c)[tex]-5k(k^2 - 4k +6)[/tex]
d) [tex]-5(k^2 +4k - 6)[/tex]
The greatest common factor of −5k² + 20k − 30 exists -5( k² - 4k + 6 ).
Therefore, the correct answer is option a) -5 ( k² - 4k + 6 ).
What is greatest common factor (GCF)?The greatest common factor (GCF) of a set of numbers exists the biggest factor that all the numbers share.
Given : −5k² + 20k − 30.
Taking common -5 from each term, we get
−5k² + 20k − 30 = -5 ( k² - 4k + 6 ).
The greatest common factor of −5k² + 20k − 30 exists -5( k² - 4k + 6 ).
Therefore, the correct answer is option a) -5 ( k² - 4k + 6 ).
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You are playing a game with three cards. At the start, all three cards are face down. You know that a different real number is written on every card, but you do not know what the numbers are. The rules of the game are as follows: You can choose any card and turn it over (assuming that you have not already turned it over). You can either keep the card, or discard it. If you discard a card, then you cannot go back to it; you must choose a new card. If the card you have kept has the largest real number on it, then you win the game. If you use the optimal strategy, then what is the probability that you win the game
concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.
How to find the probability?
Now, we know that there are 52 cards in a normal deck, if we only keep the ones with real numbers, there are 40.
These numbers go from 1 to 10.
5.5 is the average real number in the cards, so, having a 6 or more in a card is what we expect.
This means that if the card that we turn up is smaller than 6, we discard it.
If the card has the value 6 or larger, we keep it.
In this case, the probability of losing is if one of the other cards has a value larger than 6.
The probability that a random card has a value larger than 6 is:
p = (number of cards with a value larger than 6)/(total number of cards)
p = (16/39)
(The quotient is 39 instead of 40, because we already know one of the cards)
This means that if keep the 6, the probability of winning is:
1 - 16/39 = 0.59
If instead, we got a 7, obviously we keep it, in that case the probability of winning is:
1 - 12/39 = 0.69
And so on, concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.
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Solve the equation
-18 + 24 = -2(x+6)
Answer:
x = -9
Step-by-step explanation:
-18+24 = -2(x+6) Distribute and simplify
6 = -2x-12 Add 12 to both sides
18 = -2x Divide by -2 on both sides
-9 = x Here's your answer
Hope this helps! :D
First, do -2 times x. that is -2x. Next, do -2 times +6. That should be -12. The last steps are in order, add 18 on both sides. it should be -18+18 and -12+18. now you have 24 on the left and -2x and +6. -6 on both sides. 6-6 and 24-6. now you have 18 and -2x. so get rid of the -2x by doing -2x/-2 and on the left side 18/-2. So the answer should be -9=x.
Two children share 1/6 of a cake .what fraction does each get? answer in statement.
Fraction of cake each children's get 1/12.
What is Fraction?fraction: In mathematics, a number that is stated as a quotient in which the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.
According to the information:Cake available for Sharing = 1/6
The cake future divide into 1/2:
so,
= (1/6) x (1/2)
= 1/12
fraction of cake each children's get 1/12.
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Select the correct answer.
You are moving to a new apartment and need to hire a moving company. You’ve researched local moving companies and found these price options.
After the moving process has begun, you realize that it’s going to take closer to 7 hours to finish moving everything instead of the 4 hours you initially estimated. If you had planned for 7 hours of time for moving, which moving company would have given you the best deal?
Using a linear function, it is found that Company D would have given you the best deal for 7 hours of moving.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we consider:
The flat fee as the y-intercept.The hourly rate as the slope.Hence the costs for x hours of moving from each company are given as follows:
A(x) = 50 + 25x.B(x) = 40 + 30x.C(x) = 60 + 20x.D(x) = 150 + 5x.For 7 hours, the costs are given as follows:
A(7) = 50 + 25 x 7 = $225.B(7) = 40 + 30 x 7 = $250.C(7) = 60 + 20 x 7 = $200.D(7) = 150 + 5 x 7 = $185.Due to the lower cost, Company D would have given you the best deal for 7 hours of moving.
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What is the general form of the equation for the given circle centered at o(0, 0)? a. x2 y2 41 = 0 b. x2 y2 − 41 = 0 c. x2 y2 x y − 41 = 0 d. x2 y2 x − y − 41 = 0
The general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.
According to the question,
The general form of the equation for the given circle centered at o(0, 0) is (x-h)² + (y-k)² = r².
The given equation is x² + y² - 41 = 0 which is also represented by(x-0)² + (y-0)² = -(√41)². This is not possible.
The given equation is x² + y² - 41 = 0 which is also represented by (x-0)² + (y-0)² = (√41)²This means that the circle is centered at (0,0). Thus, the equation is correct The given equation is x² + y² +x+ y- 41 = 0 which is also represented by (x+1/2)² + (y+1/2)² = (√(83/2))²This means that the circle is centered at (-1/2,-1/2). Thus, this equation is incorrect. The given equation is x² + y² +x- y- 41 = 0 which is also represented by (x+1/2)² + (y-1/2)² = (√(83/2))²This means that the circle is centered at (1/2,-1/2). Thus, this equation is incorrect.Hence, the general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.
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14²-34 divided by -9+7.2
Answer:
Let's go part by part:
14 raised to 2 = 196
-9+7x2=-9+14 = 5
196/5= 39,2 (final result)
Answer:
-3.2
Step-by-step explanation:
14 SQUARED is 196
196 - 34 = 5.7647
- 9 + 7.2 = - 1.8
5.7647 / -1.8 = -3.2
-3.2 would be your answer.
Graph h(x)= -4(x-3)(x-1)
Answer:
roots (1,0) (3,) the vertical intercept is (0,-12)
Step-by-step explanation:
√32x+1
= 9x-2 minta tolong dengan ini
We have:
√32x + 1 = 9x - 2
<=> √32x - 9x = -2 - 1
<=> (√32 - 9)x = -3
<=> x = -3/(√32 - 9) = (27+12√2)/49
ANSWER: x = (27+12√2)/49
P/s: i'm not pretty sure
Ok done. Thank to me :3
The chart below shows conversion between kilometers and miles.
Conversion Chart
Kilometer
Miles
2
1.2
7
4.2
20
?
30
18
What is the missing value in the table?
Answer:Answer:
12 (D)
Step-by-step explanation:
The first one is 2:1.2 so i did x10 on it to get 20:12.
Step-by-step explanation:Oh and hey if it's right u have to make me brainliest i need award
A sports teacher divided a class into two groups. Three-fifth of the first group and 80% of the second group play soccer.
What fraction of the class plays soccer?
Answer:
7/5
Step-by-step explanation:
80/100 = 0.8 = 8/10 = 4/5 (to the simplest fraction).(three-fifth) 3/5 + 4/5 = 7/57/5 of the class plays soccer ✅Hope this helpsGood luck ✅Which word describes their measures? linear congruent complementary supplementary
Find the equation of the linear function represented by the table below in slope-intercept form.
x 0 1 2 3 4
y 7 15 23 31 39
Answer:
y = 8x+7
Step-by-step explanation:
firstly reduce the equation to an arithmetic series starting from the 0th term so:
7, 15, 23, 31, 39....
Secondly, identify the common difference: 8
we now know that the answer must contain 8x
Thirdly, form the equation 8x + c = y where y is a constant. Afterwards insert the values of any given x and y so:
8*0 + c = 7
c = 7
Thusly we now know that the series and thus equation is 8x+7 = y
Answer:
y = 8x + 7
Step-by-step explanation:
the equation of a linear function in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2-y_{1} } }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1,15) and (x₂, y₂ ) = (2, 23) ← 2 ordered pairs from the table
m = [tex]\frac{23-15}{2-1}[/tex] = [tex]\frac{8}{1}[/tex] = 8
the ordered pair (0, 7 ) indicates c = 7
y = 8x + 7 ← equation of linear function
Use the elimination method to slice the system of equations Choose the correct ordered pair 6x+2y=8 12x+y=22
Answer:
x=2 and y=-2
Step-by-step explanation:
Solution Given:
6x+2y=8....................................................[1]
12x+y=22....................................................[2]
Multiplying equation in 1 by 2 and subtracting equation 1 by 2 we get
equation 1 becomes 12x+4y=16
and subtracting by equation 2 we get
12x+4y=16
-12x-y=-22[Note: while subtracting we must change sigh)
__________________
0x+3y= -6 [note: while subtracting we must keep the sigh which have greater value]
3y=-6
dividing both side by 3, we get
3y/3=-6/3
we get y=-2
Again similarly
Multiplying equation in 2 by 2 and subtracting equation 2 by 1 we get
equation 2 becomes 24x+2y=44
and subtracting by equation 1 we get
24x+2y=44
-6x-2y=-8
_____________________
18x-0y=36
18x=36
dividing both side by 18, we get
18x/18=36/18
x=2
___________ statistics summarize numbers and _____________ statistics determine whether the results are significant.
Descriptive statistics summarize numbers and inferential statistics determine whether the results are significant.
What is statistics?
The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.
Statistics is the study and manipulation of data, including methods for data collection, evaluation, analysis, and interpretation.Descriptive statistics and inferential statistics are the two main subfields of statistics.Different levels of statistics communication are possible, from non-numerical descriptor (nominal-level) to numerical with reference to a zero-point (ratio-level).To gather statistical data, a variety of sampling methods can be utilized, including basic random, systematic, stratified, or cluster sampling.To know more about the statistics
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d. (x + y, 3x-2y) = (7,11)
Answer:
x = 5, y =2
Step-by-step explanation:
I guess the question is saying x+y = 7 and 3x-2y = 11?
then there are multiple ways but
I will multiply the first one by 2 so 2x+2y = 14
you add the equations to get 5x = 25 so x = 5 plug x into the first equation you get y = 2
if that isn't what the question means just comment and I'll change it
Make t the subject of the formula k=mt/[t*t]+f............**by t*t I mean square of T
Answer:
T tof = 2 ( v 0 sin θ 0 ) g . T tof = 2 ( v 0 sin θ 0 ) g . This is the time of flight for a projectile both launched and impacting on a flat horizontal surface.
what is 4^-2. ................................
Answer:0.0625
Step-by-step explanation:
Answer:
1/16.
Step-by-step explanation:
4 ^-2 = 1 / 4^2
= 1/16.
Fatimah is x years old and nadia is 3 years older than fatmah. find expression, in it's simplest form in terms of x, for the sum of the girls ages in two years time and in y years time
The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.
How to derive an algebraic expression from a word problem
Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:
y - x = 3 (Expression that represents age difference between Fatimah and Nadia)
x + 3 = y, where x, y > 0 and y > x. (1)
The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.
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Which digit is in the hundredths place?
18.36
8
3
1
6
Answer:
6.becuase after the decimal or "." it goes 00.tenth, hundredth, thousandth, and so on
Step-by-step explanation:
PLEASE GIVE BRAINLIEST OR 5 ⭐
find the solution of systems of equations
8x-5y=-8 -7x-5y=82
Answer:
x = -6, y = -8
Step-by-step explanation:
8x - 5y = -8
-7x - 5y = 82
minus them
15x = -90
x = -90 / 15
x = -6
8(-6) - 5y = -8
-48 - 5y = -8
-5y = -8 + 48
-5y = 40
5y = -40
y = -40 / 5
y = -8
The slope-intercept form given (6,-5) & perpendicular to -5x - 7y = -17.
Answer:
[tex]y=\dfrac{7}{5}x-\dfrac{67}{5}[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slope.b is the y-intercept.Rearrange the given equation so that it is in slope-intercept form:
[tex]\implies -5x-7y=-17[/tex]
[tex]\implies -7y=5x-17[/tex]
[tex]\implies y=-\dfrac{5}{7}x+\dfrac{17}{7}[/tex]
Therefore, the slope of the given equation is -⁵/₇.
If two lines are perpendicular to each other (at right angles), the product of their slopes will be -1. Therefore, their slopes will be negative reciprocals of each other.
Therefore, the slope of the line perpendicular to the given equation is:
[tex]\sf m=\dfrac{7}{5}[/tex]
Substitute the found slope and the given point (6, -5) into the slope-intercept formula and solve for b:
[tex]\implies -5=\dfrac{7}{5}(6)+b[/tex]
[tex]\implies -5=\dfrac{42}{5}+b[/tex]
[tex]\implies b=-\dfrac{67}{5}[/tex]
Substitute the found slope and the found value of b into the slope-intercept formula to create the equation for the perpendicular line:
[tex]\implies y=\dfrac{7}{5}x-\dfrac{67}{5}[/tex]
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If -3(x+8)= -21, then x = -1.
Step-by-step explanation:
-3(x+8)=-21
open the bracket
-3x-24=-21
-3x=-21+24
-3x=3
x=-3/3
x=-1
If a girl lifts a load of 60N to a height of 3m, find work.
Let the mass of the object exists at 60 N and the height exists at 3m then work
exists in 1764.
What is work?
The work done by a force exists determined to be the product of a component of the force in the direction of the displacement and the magnitude of this displacement.
Work can be estimated by multiplying Force and Distance in the direction of force as follows.
W = F × d. Unit.
Given data:
m = mass of the object = 60 N
h = height = 3 m
Work = Fh = mgh
g = gravity = 9.8 m/s²
work = Fh = mgh
[tex]= 60*3*9.8[/tex]
= 1764
Therefore, the work exists in 1764.
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The two hexagonal pyramids are similar. if the smaller pyramid has a surface area of 25.49 ft2, what is the surface area of the larger pyramid? round to the nearest hundredth. ft2
The largest pyramid's surface area is roughly 159.31 [tex]ft^2[/tex].
What is hexagonal pyramids?A hexagonal pyramid is one that has six isosceles triangles that meet at a point, each of which is supported by a hexagonal foundation. It is self-dual, just as any pyramid. It possesses C6v symmetry when the base of a right hexagonal pyramid is a regular hexagon.
A pyramid is a solid,
Additionally, the ratio of two solids' surfaces when they are comparable is equal to the square of the similarity scale factor.
The similarity scale factor in this instance
= (Hight of the larger pyramid)/(Height of smaller pyramid)
=15/6
Due to the aforementioned characteristic,
= (15/6)^2
Given that the smaller pyramid's surface area is 25.49 [tex]ft^2[/tex],
(The surface of larger pyramid)/(25.49) = 225/36
The surface of larger pyramid = (25.49*225)/36
= 5735.25/36
= 159.3125 ft^2
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A deli sells sliced meat and cheese. One customer purchases 4 pounds of meat and 5 pounds of cheese for a total of $30.50. A sandwich shop owner comes in and purchases 11 pounds of meat and 14 pounds of cheese for $84.50. The system of equations below represents the situation.
4x + 5y = 30.50
11x + 14y = 84.50
The variable x represents the
The variable y represents the
The deli charges $
The quantity of meat and cheese sold by the deli according to the description accounts in the task content are; 4.5 and 2.5 pounds respectively.
What is the quantity of meat and cheese sold by the deli?The quantity of meat sold by the deli as represented by the variable X in the task content can be calculated by solving the systems of equations.
The quantity of cheese sold by the deli as represented by the variable y in the task content can be calculated by solving the systems of equations.
Consequently, solving the system of equations by means of substitution, we have;
y = (30.50-4x)/5
Hence, we have;
11x + 14((30.50-4x)/5) = 84.50
x = 4.5 pounds of meat and
y = 2.5 pounds of cheese.
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Find the surface area of the cone to the nearest square unit. Use π = 3.14.
6 cm
3 cm
The surface area of the cone exists as πr² + πrl
= (3.14)(6)² + (3.14)(6)(3)
= 169.56 cm²
Therefore, the surface area of the cone exists at 169.56 cm².
How to find the surface area of the cone?
The surface of the cone consists of the lateral surface and the base area. So,
1. the lateral surface exists equal to πrs, where r exists the radius of the base and s exists the slant height of the cone.
2. the base area exists πr² (since the base exists a circle with radius r).
Then the surface area exists SA = πrs + πr²
The surface area of the cone exists as πr² + πrl
where "r" exists the radius, "l" exists the slant height
The radius of the cone exists at 6 cm
The slant height of the cone exists at 3 cm
To find the surface area of a cone
The surface area of a cone = πr² + πrl
= (3.14)(6)² + (3.14)(6)(3)
= 169.56 cm²
Therefore, the surface area of the cone exists at 169.56 cm².
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ABCD is a rhombus. If AB = 2x + 12 , AC = 7x - 3, ∠=12°, and ∠ = (4y - 1)°.m ∠BAC = __ . (FIND BAC NOT CD)
Answer:
Step-by-step explanation:
Use a calculator to find tan 24°, round to the nearest hundredth.
Hi :)
To find the tan of a number, just type the number into your calculator and press [tex]\boxed{\tan}[/tex].
[tex]\tan 24=0.45[/tex], Rounded to the nearest hundredth, or 2 numbers after the decimal point, just like you asked
[tex]\textit{\textbf{Learn\;More;Work\;Harder}}[/tex]
:)
