Answer:
518,400ways
Step-by-step explanation:
nPr=n/n-r
10P3=10/(10-3)
=10/7
=10x9x8x7x6x5x4x3x2x1/7
=3,628,800/7
=518,400 ways
There is a total of 120 ways by which a teacher can ask 3 students from 10 students to complete the task.
What is Binomial distribution?Statistics frequently employs the binomial distribution as a discrete distribution. When compared to a binomial distribution, the normal distribution is continuous.
The chance for 'x' success of an investigation in 'n' trials is represented by the binomial distribution.
As per the given data in the question,
Total number of students in the class = 10
So, the ways the teacher can ask 3 students to complete the task will be,
= ¹⁰C₃ = 10!/[3! (10 - 3)!]
= (10 × 9 × 8 × 7!)/[3! × 7!]
= 720 / 6
= 120 ways.
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A salesman who uses his car extensively finds that his gasoline bills average $125.32 per month with a standard deviation of $49.51. Assume monthly gasoline bill amounts are normally distributed. The probability that his bill will be less than $50 a month or more than $150 for a single month is:
Answer:
The probability that his bill will be less than $50 a month or more than $150 for a single month is 0.3728 = 37.28%.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
A salesman who uses his car extensively finds that his gasoline bills average $125.32 per month with a standard deviation of $49.51.
This means that [tex]\mu = 125.32, \sigma = 49.51[/tex]
Less than 50:
p-value of Z when X = 50. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{50 - 125.32}{49.51}[/tex]
[tex]Z = -1.52[/tex]
[tex]Z = -1.52[/tex] has a p-value of 0.0643
More than 150
1 subtracted by the p-value of Z when X = 150. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{150 - 125.32}{49.51}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a p-value of 0.6915
1 - 0.6915 = 0.3085
The probability that his bill will be less than $50 a month or more than $150 for a single month is:
0.0643 + 0.3085 = 0.3728
The probability that his bill will be less than $50 a month or more than $150 for a single month is 0.3728 = 37.28%.
Which binomial is a factor of 3x^2 + 2x − 5 ?
3x-1
3x-5
x-1
x-5
Answer:
3x-1
Step-by-step explanation:
3x^2+2x-5=3x-1 x1-25
f : x → ½x - 3, what is the value of 'x' when f(x) = 11?
Answer:
x=28
Step-by-step explanation:
1/2x - 3 = 11
Add 3 on both sides
1/2x = 14
Multiply 2 on both sides x=28
Answer:
For example, if f (x) and g (x) are inverses of each other, then we can ... Consider another case where a function f is given by f = {(7, 3), (8, –5), (–2, 11), (–6, 4)}. This function is one-to-one because none of its y - values appear more than once.
Step-by-step explanation:
1. A student enlarged this rectangle to fill as
much as possible of an 8.5 cm x 11 cm
piece of paper. What scale was used?
6.3 cm
4.7 cm
A 1.75
B 1 : 2.34
C 1 4.43
D 1 : 5.94
[tex]8 {}^{x + 2} = 4 {}^{2x + 3} [/tex]
Which of the following are true statements about a 30-60-90 triangle?
Lan
Answer:
C and F
Step-by-step explanation:
Answer:
A, F
Step-by-step explanation:
ratio of sides in a 30-60-90 triangle is 1 : [tex]\sqrt{3}[/tex] : 2
The length of a rectangle is 5 centimeters less than 3 times its width. The perimeter of the rectangle is 6 times the rectangle's width. What is the width of the rectangle in centimeters?
Answer:
width=6cm, lenth is 7cm
Step-by-step explanation:
In survey of 300 randomly selected adults at Target, 62% stated that Tide was their favorite laundry detergent. Based on this survey, predict the number of bottles of Tide the store will sell if they have 800 bottles on the shelf for sale.
Answer:
they would sell 496 bottles
Step-by-step explanation:
if %1 of 800 is 8, then pultiply that by 62, since 62% said they liked tide
NEED HELP DUE IN 6 MINUTES!!!!
Answer:
120
Step-by-step explanation:
volume of triangular prism = area of base times length
the base is a triangle and the area of a triangle can be calculated by using this formula
[tex]a=\frac{bh}{2}[/tex]
where b = base length and h = height
Dimensions of base
base length = 8cm and height = 3cm
Thus,
[tex]A=\frac{3*8}{2} \\3*8=24\\\frac{24}{2} =12\\[/tex]
The length of the triangular prism is 10cm
Thus volume = 10 * 12 = 120
What is the solution to this inequality?
Answer:
x>-4
:)
Step-by-step explanation:
Answer:
C. x > -4
Step-by-step explanation:
2x - 8 < 5x + 4
=> -3x < 12
=> x > -4 (have to change the inequality sign because it's divided by a negative number, -3)
which of these is incorrect
Answer:
b
Step-by-step explanation:
< less than
> greater than
= equal to
1,372 is less than 3,496 true
1,372 is greater than 3,496 false
2,583 is less than 4,194 true
3,496 is greater than 1,372 true
Help! Find the measure of the arc or angle indicated.
Answer:
m<QDC = 77
Step-by-step explanation:
First we need to generate an equation in order to find the value of x.
Thus:
m<QDC = ½(Arc QBC) => Inscribed Angles Theorem)
5x + 17 = ½(4x - 6 + 9x + 4)
5x + 17 = ½(13x - 2)
Multiply both sides by 2
2(5x + 17) = 13x - 2
10x + 34 = 13x - 2
Collect like terms
10x - 13x = -34 - 2
-3x = -36
Divide both sides by -3
-3x/-3 = -36/-3
x = 12
Find m<QDC:
m<QDC = 5x + 17
Plug in the value of x
m<QDC = 5(12) + 17 = 70 + 17
m<QDC = 77
What is the length of a 50-inch TV that has a width of 27 inches?
Answer:
42.08inches
Step-by-step explanation:
Given data
SIze of TV= 50 inch
Width= 27inches
Length= ??
Applying Pythagoras theorem
z^2= x^2+y^2
50^2= x^2+27^2
square root both sides
50^2= x^2+27^2
2500= x^2+ 729
2500-729=x^2
1771=x^2
x= √1771
x= 42.08
Hence the lenght is 42.08inches
The sum of two numbers is -47 and their difference is one. Find the numbers. Separate with a comma.
Answer:
-23, -24
Step-by-step explanation:
Adding negative numbers gets you another negative number. Therefore the numbers must be -23 and -24.
Factor the following expression.
10.25 + 513 – 14.12 – 7
A. (5.33-7)(2x2 + 1)
B. (5.04 + 7)(2.5 - 1)
C. (5.3 + 7)(2x2 - 1)
D. (5x4 - 7)(2x + 1)
Answer:
Step-by-step explanation:
ask cymath it will help you with any mathmatical problem
The length of a rectangle is shown below: On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis two points A and B are shown. The point A is on ordered pair 2, 1, and the point B is on ordered pair negative 1, 1. A straight line joins the points A and B. If the area of the rectangle to be drawn is 18 square units, where should points C and D be located, if they lie vertically below the line that connects B and A, to make this rectangle? (1 point) C(−1, −2), D(2, −2) C(−1, −8), D(2, −8) C(−1, −5), D(2, −5) C(−1, −6), D(2, −6)
9514 1404 393
Answer:
3. C(−1, −5), D(2, −5)
Step-by-step explanation:
The given points are 2 -(-1) = 3 units apart horizontally, so the remaining points will need to be 18/3 = 6 units below, vertically. Translating the given points down 6 gives ...
D = A -(0, 6) = (2, 1) -(0, 6) = (2, -5)
C = B -(0, 6) = (-1, 1) -(0, 6) = (-1, -5)
The two points required to make a rectangle with an area of 18 square units are ...
C(-1, -5), D(2, -5)
_____
The area of a rectangle is the product of length and width. If the area is 18 square units, and the width is 3 units, then the length must be 6 units. 3×6=18.
Graph the equation y=-4/3x + 2
Answer:
plz if you knew if you new it plz tell me
What is the magnitude of -3 +4i?
Answer:
we have
-3+4i
let magnitude be |z|
|z|=[tex] \sqrt{( - 3) {}^{2} + 4 {}^{2} } [/tex]
|z|=5 unit
Answer:
The magnitude of -3 +4i is 5
Step-by-step explanation:
Which fraction has the greatest value?
+
-1
0
Jh
1
O
Um
d
HELPPPPP!!!!
Tell whether the triangles are similar.
Answer:
No.
Step-by-step explanation:
In similar triangles, all the angles are congruent.
b = 180 - 90 - 43 = 47
c = 180 - 90 - 48 = 42
1 set of angles is 90, 43, and 47
And the other is 90, 48, and 42.
Meaning the triangles are not similar.
Question 5 of 10
How many solutions over the complex number system does this polynomial
have?
2x4 – 3x3 – 24.x2 + 13x +12=0
Enter your answer as an integer.
Answer:
4 solutions
Step-by-step explanation:
if the equation is 2x^4 -3x^3 -24x^2 +13x +12 = 0 you look at the highest degree to find how many solutions. the degree being the highest exponent. so in this case it would be the exponent that is 4 so there should be 4 solutions.
find the requivalent ratios of the following 7:12
Answer:
Step-by-step explanation:
So in the example you gave, a ratio of 7:12 means that for every 7 of the first item, there are 12 of the second. The order becomes very important, as changing the ratio to 12:7 would mean that for every 12 of the first item, there are 7 of the second, which is not the same thing at all
7:12
14:24
21:36
28:48
keep smiling always
pls help math brainers
Answer:
m
Step-by-step explanation:
b
Given the vector \mathbf{u}u equal to 3\left<\cos 255^{\circ},\,\sin 255^{\circ}\right>3⟨cos255
∘
,sin255
∘
⟩ and vector \mathbf{v}v equal to 2\left<\cos 215^{\circ},\,\sin 215^{\circ}\right>,2⟨cos215
∘
,sin215
∘
⟩, find the sum \mathbf{u}+\mathbf{v}u+v and write your answer in magnitude and direction form with the magnitude rounded to the nearest tenth and the direction rounded to the nearest degree, 0^{\circ}\le \theta < 360^{\circ}.0
∘
≤θ<360
Answer:
Is this the full question?
The sum of vector is (-2.4148, -4.0499), magnitude is 4.7 and [tex]\theta[/tex] = 239 degree.
What is Vector?A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.
Given:
Vector u = 3( cos 255, sin 255)
v = 2 (sin 215, cos 215)
So, u+ v
= (3 cos 255 + 2 cos 215, 3 sin 255 + 2 sin 215)
= (-2.4148, -4.0499)
and, Magnitude
| u +v | = √(-2.4148)² + (-4.0499)²
= 4.7
Then, tan [tex]\theta[/tex] = 4.0499/ 2.4148
So, [tex]\theta[/tex] = 239 degree
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HELP
Which Trig ratio should be used to find the missing side?
A.Sin
B.Cos
C.Tan
Answer:
tan
Step-by-step explanation:
take 19 degree as reference angle
using tan rule
tan 19=opposite/adjacent
0.34=14/x
x=14/0.34
x=41.17
x=41.2
Your neighbor's are building a dog pen in the shape of a right triangle. The legs of the triangular pen measures 9 meters and 12 meters. Find the perimeter of the enclosed space
Which polynomial function has a leading coefficient of 2, root-5 with multiplicity 3, and root 12 with multiplicity 1?
Of(x) = 2(x - 5)(x - 5)(x - 5)(x + 12)
Of(x) = 2(x + 5)(x + 5)(x + 5)(x - 12)
O f(x) = 3(x - 5)(x - 5)(x + 12)
Of(x) = 3(x + 5)(x + 5)(x - 12)
Answer:
Of(x) = 2(x + 5)(x + 5)(x + 5)(x - 12) or Choice 2
Step-by-step explanation:
The last two answers get eliminated because their leading coefficients aren't 2. The first option is wrong because if you plug in -5 and +12 into x the function won't equal 0. So the correct answer is the Second answer: Of(x) = 2(x + 5)(x + 5)(x + 5)(x - 12)
Answer:
The polynomial function that has a leading coefficient of 2, a root of 5 with a multiplicity of 3, and a root of 12 with a multiplicity of 1 is choice 2.
Step-by-step explanation:
A leading coefficient of 2 means that the number multiplying all the binomial would be 2, so you know it is not choices 3 and 4. A root of -5 with a multiplicity of 3 means that when you replace x with -5, three binomials will result in 0, which helps eliminate the first choice. A root of 12 with a multiplicity of 1 means that when you replace x with 12, you will have a binomial that results in 0. Using all of this information, you'll get that the polynomial that has a leading coefficient of 2, a root of -5 with a multiplicity of 3, and a root of 12 with a multiplicity of 1 is [tex]f(x)=2(x+5)(x+5)(x+5)(x-12)[/tex].
The table below shows the number of students in four schools with grade
point averages in various ranges. The grade point averages of the students in
which school represent a U-shaped distribution?
School A School B School C School D
Greater than 1.5 but less than 2.0 22 15 82 19
Greater than 2.0 but less than 2.5 39 43 46 57
Greater than 2.5 but less than 3.0 67 98 26
81
Greater than 3.0 but less than 3.5 41 45 59 50
Greater than 3.5 but less than 4.0 27 12 78 17
A. School B
O
B. School C
C. School D
Ο Ο
D. School A
Answer:
b
Step-by-step explanation:
Step-by-step explanation:
school c so B would be correct
7k-6,2k+14 solve for K
Answer:
0.8k +14
Step-by-step explanation:
See the steps below:)
Let me show you an exam
Michael works and gets paid $8.50 per hour. Show
equation is proportional and write an equation that describes this relationship
Answer:
[tex]y = 8,50x[/tex]
Step-by-step explanation:
Given
Let
[tex]y\to[/tex]earnings
[tex]x \to[/tex] hours
Solving (a): The proportion
x and y can be expressed as:
[tex]y\ \alpha\ x[/tex] --- direct variation
Write as an equation
[tex]y = kx[/tex]
Where
[tex]k = 8.50[/tex] --- the hourly rate
So, we have:
[tex]y = 8,50x[/tex]