Answer:
The mean number of the students who develop hypertension over a life time is 7.8.
Step-by-step explanation:
For each person, there are only two possible outcomes, either they will develop hypertension, or they will not. The probability of a person developing hypertension is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
Suppose that the probability that a person will develop hypertension over a life time is 60%.
This means that [tex]p = 0.6[/tex]
13 graduating students from the same college are selected at random.
This means that [tex]n = 13[/tex]
Find the mean number of the students who develop hypertension over a life time
[tex]E(X) = np = 13*0.6 = 7.8[/tex]
The mean number of the students who develop hypertension over a life time is 7.8.
1. Ewa has 20 balls of four colors: yellow, green, blue, and black. 17 of them are not green, 5 are black, and 12 are not yellow. How many blue balls does Ewa have? (Use Gaussian elimination method).
Answer:
In a bag of balls, 1/4th are green, 1/8th are blue, 1/12th are yellow and the remaining 26 are white. How many balls are blue?
There are 4 colours of balls - green, blue, yellow and white.
Add (1/4)+(1/8)+(1/12) = (6/24)+(3/24)+(2/24) = 11/24 so the balance or (24–11)/24 = 13/24 = 26 white. Hence the total number of balls are 2*24 = 48.
Of the 48 balls, green are (1/4)*48 = 12, blue are (1/8)*48 = 6, yellow are (1/12)*48 = 4 and the rest, white are 26.
Check: Total number of balls = 12+6+4+26 = 48
Answer: 6 balls are blue....
Find the quotient of 90 over -10
90/-10
= 9/-1
= -9
So, -9 is the quotient.
y
Which point on the x-axis lies on the line that passes
through point C and is parallel to line AB?
5 4
C
NU
1
O (1,0)
O (1, 1)
0 (0, 2)
O (20)
А
54
214
2 3
4 5
х
h
B
3
4
ch
I think it's (2,0).
Because u use the slope of line AB to go down from point C until one of the answers are met.
The point on the x-axis that will make the line that passes through point C parallel to line AB is: D. (2, 0).
Slope of Parallel LinesTwo lines on a coordinate plane are parallel to each other if they have the same slope.Slope = change in y/change in x.Slope of AB = -(3/6)
Slope of AB = -1/2
Slope of from point (2, 0) to point C(-2, 2):
Slope = (2 - 0)/(-2 - 2) = 2/-4
Slope = -1/2
Therefore, the point on the x-axis that will make the line that passes through point C parallel to line AB is: D. (2, 0).
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Find the length of FT
Step-by-step explanation:
Hey there!
From the given figure;
Angle FVT = 43°
VT = 53
Taking Angle FVT as reference angle we get;
Perpendicular (p) = FT = ?
Base (b) = VT = 53
Taking the of tan;
[tex] \tan( \alpha ) = \frac{p}{b} [/tex]
Keep all values and simplify it;
[tex] \tan(43) = \frac{ft}{53} [/tex]
0.932515*53 = FT
Therefore, FT= 49.423.
Hope it helps!
Answer:
A. 49.42
Step-by-step explanation:
tan 43 = FT ÷ VT
0.932515086 = FT ÷ 53
49.42 = FT
if f(x)=x+7 and 9(x)=1/x-13 what is the domain of (f•g)(x)
Answer:
The only limitation is x≠0
The interval notation is (-∞,0)∪(0,∞)
Step-by-step explanation:
Set up the expression.
[tex](x+7)*(\frac{1}{x}-13)[/tex]
Multiply using FOIL.
[tex](x*\frac{1}{x})+(x*-13)+(7*\frac{1}{x})+(7*-13)[/tex]
[tex]1-13x+\frac{7}{x}-91[/tex]
[tex]-13x+\frac{7}{x}-91[/tex]
Find the Domain.
The only limitation is x≠0
The interval notation is (-∞,0)∪(0,∞)
Which point on the number line shows the graph of
Answer:
the correct answer is point b
A. The interquartile range is 55
B.Three fourths of the data is less than 65
C. The median of the upper half of the data is 65
D. The median if the data is 55.
Answer:
d the median if the data is 55
Five subtracted from seven times a number is 9. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
The equation is _____________
B) Solve your equation in part [A] for
Answer:
x=
Answer:
18
Step-by-step explanation:
7-5=2
2x9=18
4) Daily tickets to Six Flags cost $50 each.
Variable #1:
What is the variable
Answer:
Amount of tickets
Step-by-step explanation:
The variable is the amount of tickets purchased because that is the only thing that changes, according to the statement that says that daily tickets are $50.
Select the correct answer.plz answer fast due at 11:59
What is the solution for x in the equation?
-4 + 5x − 7 = 10 + 3x − 2x
A. x=4/13
B. x=13/4
C. x=4/21
D. x=21/4
Question: -4 + 5x -7 = 10 + 3x -2x
⇒ 5x -11 = 10 + x
⇒ 5x - x = 10+11
⇒ 4x = 21
⇒ x = 21/4
Answer is Option D
x = 21/4
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A normal distribution has a mean of 20 and a standard deviation of 4. Determine the z-score for the data value of 42.
Answer:
Z = (42-20)/4 = 5.5
Z = X-μ / σ
Step-by-step explanation:
The z-score for the data value of 42 is 5.5.
What is a z-score?A z-score is defined as the fractional representation of data point to the mean using standard deviations.
Formula of z-score = (X - μ) / σ
Given,
μ = 20
σ = 4
X = 42
z-score = (X - μ) / σ
Substitute the values,
z-score = (42-20)/4
z-score = 22/4
z-score = 5.5
Hence, the z-score for the data value of 42 is 5.5.
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If x = 1, y = 7, and z = 15, determine a number that when added to x, y, and z yields
consecutive terms of a geometric sequence. What are the first three terms in the
geometric sequence?
You're looking for a number w such that the numbers
{1 + w, 7 + w, 15 + w}
form a geometric sequence, which in turn means there is a constant r for which
7 + w = r (1 + w)
15 + w = r (7 + w)
Solving for r, we get
r = (7 + w) / (1 + w) = (15 + w) / (7 + w)
Solve this for w :
(7 + w)² = (15 + w) (1 + w)
49 + 14w + w ² = 15 + 16w + w ²
2w = 34
w = 17
Then the three terms in the sequence are
{18, 24, 32}
and indeed we have 24/18 = 4/3 and 32/24 = 4/3.
Payton took a friend for a birthday dinner. The total bill for dinner was $44.85 (including tax and a tip). If Payton paid a 19.5% tip, what was his bill before adding the tip?
(Round your answer to the nearest cent.)
$
Number
Answer:
The answer closest to 36.10425. So 36.10 or 36.1
Step-by-step explanation:
x = 44.85 ( 1 - 0.195) = 36.10425
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The amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
For this case, we can assume the amount of bill without tip being A.
Then, as given, Payton gave 19.5% tip (tip is given assumingly on A), then:
Total price of the bill = Bill amount before tip + Tip
44.85 = A + (19.5 % of A)
(we don't write symbols like of currency generally in equations, and understand it from context(which is dollars here))
44.85 = A + (19.5 % of A)
or
[tex]44.85 = A + \dfrac{A}{100} \times 19.5\\\\\text{Multiplying 100 on both the sides}\\\\4485 = 100A + 19.5A\\4485 = 119.5A\\\\\text{Dividing both the sides by 119.5}\\\\\dfrac{4485}{119.5} = A\\\\37.53 \approx A\\\\A \approx 37.53 \: \rm \text{(in dollars)}[/tex]
Thus, the amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.
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What is the probability of randomly picking a red marble from a bag of 10 green marbles, 10 yellow marbles, and 5 red marbles?
Answer
20%
Step-by-step explanation:
The probability distribution of a random variable X is given. x 1 2 3 4 P(X = x) 0.4 0.1 0.3 0.2 Compute the mean, variance, and standard deviation of X. (Round your answers to two decimal places.) mean variance standard deviation
Mean:
[tex]E(X) = \displaystyle \sum_{x\in\{1,2,3,4\}}x\,P(X=x) = 1\times0.4 + 2\times0.1 + 3\times0.3 + 4\times0.2 = \boxed{2.3}[/tex]
Variance:
[tex]\displaystyle V(X) = E\left((X-E(X))^2\right) = E(X^2) - E(X)^2 \\\\ E(X^2) = \sum_{x\in\{1,2,3,4\}}x^2\,P(X=x) = 1^2\times0.4 + 2^2\times0.1 + 3^2\times0.3 + 4^2\times0.2 = 6.7 \\\\ \implies V(X) = 6.7 - 2.3^2 = \boxed{1.41}[/tex]
Standard deviation:
[tex]\sigma_X = \sqrt{V(X)} = \sqrt{1.41} \approx \boxed{1.19}[/tex]
the difference between a number and 6
Step-by-step explanation:
=The difference between a number and 6
the term difference is used in mathmatics as subtraction
let x = a number
x - 6 = the difference between that unknown number and 6
Answer:
Step-by-step explanation:
difference means subtract. Difference is always worded the same way. What you have written means that you start with an algebraic letter and then comes the minus sign and then the number
Let the number = x
x - 6
If it was worded as difference between 6 and a number, you would write it this way
6 - x
answer no explantion pls i need asap
Answer:
Below.
Step-by-step explanation:
Area = 5(x + 3)
= 5x + 15
Perimeter = 2(x + 3) + 2(5)
= 2x + 6 + 10
= 2x + 16.
If a= 3 and b= 5; find
(a+b)
Answer: 3/8
Step-by-step explanation:
A=3
B=5
3/3+5=3/8
8 thousand+7tens=6thiusand+. tens
Answer:
207 tens
Step-by-step explanation:
If you mean
8,000 + 70 = 6000 + X tens
then it should be 207 tens
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis.
Using the shell method, the volume integral would be
[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx[/tex]
That is, each shell has a radius of x (the distance from a given x in the interval [0, 2] to the axis of revolution, x = 0) and a height equal to the difference between the boundary curves y = x ⁸ and y = 256. Each shell contributes an infinitesimal volume of 2π (radius) (height) (thickness), so the total volume of the overall solid would be obtained by integrating over [0, 2].
The volume itself would be
[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx = 2\pi \left(128x^2-\frac1{10}x^{10}\right)\bigg|_{x=0}^{x=2} = \boxed{\frac{4096\pi}5}[/tex]
Using the disk method, the integral for volume would be
[tex]\displaystyle \pi \int_0^{256} \left(\sqrt[8]{y}\right)^2\,\mathrm dy = \pi \int_0^{256} \sqrt[4]{y}\,\mathrm dy[/tex]
where each disk would have a radius of x = ⁸√y (which comes from solving y = x ⁸ for x) and an infinitesimal height, such that each disk contributes an infinitesimal volume of π (radius)² (height). You would end up with the same volume, 4096π/5.
The volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have a function:
[tex]\rm y = x^8[/tex] or
[tex]x = \sqrt[8]{y}[/tex]
And y = 256
By using the vertical axis of rotation method to evaluate the volume of the solid formed by revolving the region bounded by the curves.
[tex]\rm V = \pi \int\limits^a_b {x^2} \, dy[/tex]
Here a = 256, b = 0, and [tex]x = \sqrt[8]{y}[/tex]
[tex]\rm V = \pi \int\limits^{256}_0 {(\sqrt[8]{y}^2) } \, dy[/tex]
After solving definite integration, we will get:
[tex]\rm V = \pi(\frac{4096}{5} )[/tex] or
[tex]\rm V =\frac{4096}{5}\pi[/tex] cubic unit
Thus, the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.
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A right triangle has sides 20 and 48. Use the Pythagorean Theorem to find the length of the hypotenuse
Answer: Let the length of the hypotenuse be x
Applying the Pythagorean theorem we have :
x²=20²+48²
⇒x²=2704
⇒x=52( ∀ x >= 0 )
Step-by-step explanation:
Let assume the hypotenuse(longest side of right triangle) be x
By Pythagoras theorem
[tex] \bf \large \longrightarrow \: {c}^{2} \: = \: {a}^{2} \: + \: {b}^{2} [/tex]
c = xa = 20b = 48Applying Pythagoras theorem
[tex] \bf \large \implies \: {x}^{2} \: = \: {20}^{2} \: + \: {48}^{2} [/tex]
[tex]\bf \large \implies \: {x}^{2} \: = \:400 \: + \: 2304[/tex]
[tex]\bf \large \implies \: {x}^{2} \: = \:2704[/tex]
[tex]\bf \large \implies \: \sqrt{x} \: = \: \sqrt{2704} [/tex]
[tex]\bf \large \implies \: \: x \: = \: 52[/tex]
Hence , the length of hypotenuse is 52.
Jane and her two friends will rent an apartment for S550 a month, but Jane will pay double what each friend does because she will have her own bedroom.
How much will Jane pay a month?
Answer:
$275 a month
Step-by-step explanation:
Let x represent how much each friend is paying.
The amount Jane pays can be represented by 2x, since she is paying double than her friends.
Add together these terms and set them equal to 550. Then, solve for x:
x + x + 2x = 550
4x = 550
x = 137.5
So, each friend is paying $137.50. Double this to find how much Jane is paying:
137.5(2)
= 275
So, Jane is paying $275 a month
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Alan needs a total of $370 to buy a new bicycle. He has $40 saved. He earns $15 each week delivering newspapers. How many weeks will Alan have to deliver papers to have enough money to buy the bicycle?
CAN YOU DO IT??
Answer:
22 weeks
Step-by-step explanation:
Let Suppose if weeks is x
So if we count it:
$40 + $15x = $370
$15x = $330
x = 22 weeks
So, Alan needs 22 weeks to have enough money to buy the new bicycle
In a high school graduating class of 300, 200 students are going to college, 40 are planning to work full-time, and 80 are taking a gap year.
a. These are mutually exclusive events.
b. These are not mutually exclusive events.
c. You should add their individual probabilities.
d. None of the above are true.
–21:(–2 – 5) + ( –14) + 6.(8 – 4.3)
Pete receives a weekly allowance for doing chores around the
house. Pete saves his money for 17 weeks. After 17 weeks, he
saves $187. How much money does Pete get for his allowance
each week
9514 1404 393
Answer:
A. $11 per week
Step-by-step explanation:
$187 = (17)(weekly allowance) . . . . . Pete's savings after 17 weeks
weekly allowance = $187/17 = $11 . . . . . divide by 17
Pete gets $11 each week.
Answer:11 per week
Step-by-step explanation:I did the test
please help! thanks!
find y.
Answer:
y = 4
Step-by-step explanation:
The ratio of the lengths of the sides of a 30-60-90 triangle is
1 : √3 : 2
The sides in this triangle are in the order:
y : 4√3 : x
y/1 = 4√3/√3
y = 4
Which of the following is a monomial?
A. 8x^2 +7x+3
B. √x-1
C. 9/x
D. 7x
Answer:
7x is monomial according to question.
If the white rod is 1/3, what color is the whole??
Answer:
brown
Step-by-step explanation:
it might be brown because it compelled
3. Solve the system of equations using the elimination method.
5x + 2y = 9
-5x + 4y = 3
please give detailed steps!!
Answer:
x = 1
y = 2
Step-by-step explanation:
5x + 2y = 9
-5x + 4y = 3
==> 6y = 12 ==> y = 12/6 ==> y = 2.
we replace y by its value in the first or the second equation, so will have:
5x + 2×2 = 9
5x + 4 = 9
5x = 5
x = 1
