The probability of selecting none of the correct six integers, when the order in which they are selected doesnot matter is 0.43.
According to thr question.
We have to find the probability of selecting none of the correct six integers from the positive integers not exceeding 48.
Let E be the event of selecting 6 numbers from 40 and S be the sample space of all integers not exceeding 48.
Now,
The total number of ways of selecting 6 numbers from 48
[tex]= ^{48} C_{6}[/tex]
[tex]= \frac{48!}{6!\times 42!}[/tex]
[tex]= \frac{48\times 47\times46\times45\times44\times43\times42!}{6!\times\ 42!}[/tex]
= 8835488640/6!
And, the total number of ways of selecting 6 incorrect numbers from 42
= [tex]^{42} C_{6}[/tex]
[tex]= \frac{42\times41\times40\times39\times38\times37\times36!}{6!\times36!}[/tex]
= 3776965920/6!
Therefore, the probability of selecting none of the correct six integers, when the order in which they are selected does not matter is given by
[tex]= \frac{^{42C_{6} } }{^{48} C_{6} }[/tex]
[tex]= \frac{\frac{3776965920}{6!} }{\frac{8835488640}{6!} }[/tex]
= 3776965920/8835488640
= 0.427
≈ 0.43
Hence, the probability of selecting none of the correct six integers, when the order in which they are selected doesnot matter is 0.43.
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PLS HELP IM SO STUCK
3x-2y= 7
Slope intercept form y= mx+b
3x- 2y= 7
- 3x -3x
-2y/-2= 3x/-2 - 7/2
y= 3x/-2 -7/2
Answer:
3x/2 and the second 7/-2y
Step-by-step explanation:
thats how is what i got
Complete the steps in order to write the inverse of f(x)=x+5
=x45
1.
Writing the Inverse of a Function
2.
3,
1-x-5
The equation of the inverse function of the function f(x) = x + 5 is f'1(x) = x - 5
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function
How to determine the inverse functions?The function f(x) is given as
f(x) = x + 5
As a general rule, we start by writing f(x) as a variable (say f(x) = y).
So, the equation of the function becomes
y = x + 5
The next step is to switch/swap the positions of x and y in the above equation y = x + 5
The equation becomes
x = y + 5
The next step is to make y the subject of the formula in the above equation x = y + 5
The equation becomes
y = x - 5
This is done by subtracting 5 from both sides of the equation.
So, we have:
y = x - 5
Express as an inverse function
f'1(x) = x - 5
Hence, the inverse function of the function f(x) = x + 5 is f'1(x) = x - 5
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On saturday evening 5450 people visited india gate. out of these 1265 were men 1150 were woman and rest were children. how many children visited the india gate?
3435 were children visited the India gate.
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.Given,
men = 1265
women = 1150
Total women and men -
men + women = 2415
= 5450-2415 ⇒ 3435
Therefore, 3435 were children visited the India gate.
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Which number best represents the slope of the graphed line?
A graph is a line that extends from second quadrant to fourth quadrant through left parenthesis 0, 2 right parenthesis, and left parenthesis 0.5, 0 right parenthesis.
The number that best represents the slope of the graphed line that is given is: -4.
What is the Slope of a Line?The slope of a line is the ratio of the vertical distance to the horizontal distance across the line. It is calculated using the formula:
Slope (m) = rise/run = change in y / change in x = (y2 - y1)/(x2 - x1)
Given the two points on a coordinate plane as shown in the mage below, let:
(x1, y1) represent (0, 2)
(x2, y2) represent (0.5, 0)
Plug in the values
Slope (m) = change in y / change in x = (0 - 2) / (0.5 - 0)
Slope (m) = -2/0.5
Slope (m) = -4
Therefore, we can state that, the number that best represents the slope of the graphed line that is given is: -4.
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The actual answer is C.1/2
chust mee am a doktor
A sheet of glass has a density of 2.5 8 What is the density of the glass in k8 ? mi.
Based on the density and the given parameters, the density of the sheet of glass in kg per m cubed is 2500 kg/m cubed
How to determine the density of the sheet of glass in kg per m cubed?The density of the sheet of glass is given as
Density = 2.5g/cm cubed
Start by converting grams (g) to kilogram (kg)
This is done by dividing 2.5 by 1000
So, we have:
Density = 2.5/1000 kg/cm cubed
Evaluate the quotient
Density = 0.0025 kg/cm cubed
Next, we then convert cm cubed (cm^3) to meter cubed (m^3)
This is done by dividing the volume by 1000000
So, we have:
Density = 0.0025 kg/(1/1000000) m cubed
Express as product
Density = 1000000 * 0.0025 kg/m cubed
Evaluate the product
Density = 2500 kg/m cubed
Based on the density and the given parameters, the density of the sheet of glass in kg per m cubed is 2500 kg/m cubed
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Answer:
See below
Step-by-step explanation:
Are you wanting to convert density of gm/ cm^3 to kg/m^3 ??
there are 100 x 100 x 100 cm^3 = 1,000,000 cm^3/ m^3
2.5 gm / cm^3 * 1 000 000 cm^3 / m^3 = 2, 500 000 gm / m^3
now 1 kg is 1000 gm
2, 500 000 gm / m^3 * 1 kg / 1000 gm = 2500 kg / m^3
Simplify 0.4(5a-3.2b+7)
Step-by-step explanation:
2a -1.28b +2.8 for simplification.
Which of the following is a function?
A. {(2,9), (2,8), (-3,7), (-3,6))
B. ((-4,3), (1,0), (1,2), (2,3)}
C. {(2,1), (4,2), (6,3), (8,4))
D. {(1,2), (-2,3), (1,3), (-2,2))
Answer: C
Step-by-step explanation:
A function only exists if each x-value has only one possible y-value.
C is the only function because each x-value has only one y-value.
The other answer choices have x-values that have multiple y-values. In answer choice A, it has (2,9) and (2,8). In answer choice B, the set has (1, 0) and (1,2). And in answer D, it has (1,3) and (1,2)
Answer + Step-by-step explanation:
let f be the relation that we are studying.
f is a function if it associates a unique output (number) to each input (number) .
A. {(2,9), (2,8), (-3,7), (-3,6))
Since f(-3) = 7 and f(-3) = 6
Then
f associates -3 to two different outputs 7 and 6.
Then
f cannot be a function.
B. ((-4,3), (1,0), (1,2), (2,3)}
Since f(1) = 0 and f(1) = 2
Then
f cannot be a function.
C. {(2,1), (4,2), (6,3), (8,4))
f is a function.
D. {(1,2), (-2,3), (1,3), (-2,2)
Since f(-2) = 3 and f(-2) = 2
Then
f cannot be a function.
I need help here’s a picture can somone explain what I need to do??
Answer:
176 square feet
Step-by-step explanation:
add the areas of the rectangle and triangle
rectangle area is
16 times 8 which is
128
rectangle area is
1/2 times 12 times 8 which is
48
then add them
128 plus 48 is
176 square feet
a basketball player signs a cantract that pays him $16 million over 4 year. What is his average pay per year?
the average pay per year is $4 million
Answer:
The average is 4millon
Step-by-step explanation:
because 16 millon divide by 4 =4
ez
An apartment building contains 12 units consisting of one- and two-bedroom apartments that rent for $360 and $450 per month, respectively. When all units are rented, the total monthly rental is $4,950. What is the number of two-bedroom apartments?
Answer:
There are 7 two bed bedroom apartments.
Step-by-step explanation:
Solution Given:
let the one bedroom apartment be x and two bedroom apartment be y.
By the question we can make an equation as
x+y=12
or y=12-x............................[1]
Again:
$360x+$450y=$4,950
Now substituting value of y, we get
$360x+$450(12-x)=$4,950
Opening Bracket
$360x+$5400-$450x=$,4,950
solving equation
-90x=-450
dividing both side by -90,we get
x=5
again,
substituting value of x in equation 1,we get
y=12-5=7 two bed bedroom apartments.
Let, x represents the number of one bedrooms and 12 - x represents the number of two bedrooms.
According to the question,
[tex]360x + 450(12 - x) = 4950[/tex]
[tex]360x + 5400 - 450x = 4950[/tex]
[tex]5400 - 4950 = 450x - 360x[/tex]
[tex]450 = 90x[/tex]
[tex] \frac{450}{90} = x[/tex]
[tex]5 = x[/tex]
Therefore, one bedrooms = x = 5
For number of two bedrooms which is equal to 12 - x
= 12 - 5
= 7
So your required answer is 7
What is the margin of error for 95% confidence for a sample of size 700 where p = 0.65?
A. 0.0455
B. 0.0303
OC. 0.0651
D. 0.0353
Answer:
D 0.0353
Step-by-step explanation:
a= 0.05. p= 0.65. n=700
S N P = 700 × 065 = 45575
1 n ( 1 - p ) = 700× ( 1 - 0.65 ) = 24575
get the sample is big ,. p~ N ( π. √ π ( 1-π ) p - π
-----------. ------- ~ ( o. 1
n Ñ 1 ~ñ
the margin of error ∆ = Z a
-----. =. √ π ( 1 - π )
2 --------
n
according to the standard normal distribution,
Z d
---. = zo.o25 = 1.96
2
∆=1.96×√p ( 1 - p ). =. 1.96 × √ 0.65× ( 1 - 65)
---------. ---------
π. 700
= 0.0353
jean loads a ream of paper 500 sheets into the tray of her photocopier she has 23 sheets and need 20 copies each sheet how many sheets of paper remain unused
The answer is 40
you just times 23 by the number of photocopies you need with is 20
so 23x20 which is 460
500-460 is 40
The number of sheets of papers remain unused are 40.
Given that, Jean loads a ream of paper 500 sheets into the tray of her photocopier she has 23 sheets and need 20 copies each sheet.
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Number of sheets used = 23×20
= 460
Remaining sheets = 500-460
= 40
Therefore, the number of sheets of papers remain unused are 40.
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Given any two events, e1 and e2, what does the probability p(e1 ∪ e2) represent?
The equation of P(e₁ ∪ e₂) describes the condition that the mutually exclusive event stands one of the events occurs, or both occur.
What are Mutually Exclusive events?Mutually Exclusive events are described as in probability the particular addition rule exists practical when two occurrences exist incompatible with one another. It claims that the probability of either event exists equivalent to the probability of each possibility separately.
If e₁ and e₂ stand said to be mutually exclusive events then the probability of an event e₁ happening or the probability of event e₂ occurring exists given as P(e₁) + P(e₂) :
P(e₁ ∪ e₂) = P(e₁) + P(e₂)
Therefore, the equation of P(e₁ ∪ e₂) describes the condition that the mutually exclusive event stands for one of the events that happens, or both happen.
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Given the following information, calculate the perimeter of triangle RST. Assume triangle RZX is similar to triangle RST.
RZ = 21, RY = 24, RX = 42, ZY = 9, and SW = 15.
Check the picture below.
Suppose your parents decide to give you $10,000 to be put in a college trust fund that will be paid in equally quarterly installments over a 5 year period. If you deposit the money into an account paying 1.5% per quarter, how much are the quarterly payments (Assume the account will have a zero balance at the end of period.)
The quarterly annuity payment is $582.46.
What is an ordinary annuity?
An ordinary annuity in case of investment is the one that pays its end-of-the period cash flows rather than at the beginning as it is case of annuity due.
The applicable formula in this case is the present value formula of an ordinary annuity as shown below:
PV=quarterly payment*(1-(1+r)^-N/r
PV=initial investment=$10,000
quarterly payment=unknown(assume it is X)
r=quarterly interest rate=1.5%
N=number of quarterly payments in 5 years=5*4=20(there are 4 quarterly payments in a year)
$10,000=X*(1-(1+1.5%)^-20/1.5%
$10,000=X*(1-(1.015)^-20/0.015
$10,000=X*(1-0.742470418223773)/0.015
$10,000=X*0.257529581776227/0.015
X=$10,000/(0.257529581776227/0.015)
X=quarterly payment=$582.46
Note that the unknown in this case is the annuity payment, the present value can also be the unknown as well.
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if b=7, what is the value of the expression2(10-b)?
Answer: 6
Step-by-step explanation: Since we substitute the b with 7, 10-7= 3. Since the 2 is next to the parentheses, we multiply 3 by 2, getting 6.
Hey there!
2(10 - b)
= 2(10 - 7)
= 2(10) + 2(-7)
= 20 - 14
= 6
OR
2(10 - b)
= 2(10 - 7)
= 2(3)
= 6
Therefore, your answer should be: 6
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Find the value of x
(4x+10)
108° 67° 3x
Angles in quadrilateral add to 360
108 +67 +10 =185
4x + 3x = 7x
185 + 7x = 360
- 185
7x. = 175
÷ 7
x = 25
Check:
4x25 = 100
100 + 67 + 108 = 275
275 + (3x25) = 350 + extra 10 is 360
Hope this helps!
If f (x) = startroot 4 x 9 endroot 2, which inequality can be used to find the domain of f(x)? startroot 4 x endroot greater-than-or-equal-to 0 4 x 9 greater-than-or-equal-to 0 4 x greater-than-or-equal-to 0 startroot 4 x 9 endroot 2 greater-than-or-equal-to 0
Inequality can be used to find the domain of f(x) is (B) 4x+9 greater-than-or-equal-to 0.
What is inequality?The term inequality refers to a mathematical expression in which the sides are not equal. An inequality compares any two values and reveals that one is smaller, greater, or equal to the value on the opposite side of the equation.To find the domain:
“f(x) = StartRoot 4 x + 9 EndRoot + 2” should be written as, note that√(4x + 9) is a variation of the basic function y = √x, whose domain is [0, ∞ ). The domain of f(x) = √(4x + 9) + 2 is found by taking the “argument” 4x + 9 of √(4x + 9) and setting it equal to zero: 4x + 9 ≥ 0, or 4x ≥ -9, or x ≥ -9/4 This is the domain of the given function f(x) = √(4x + 9) + 2. So long as x is ≥ -9/4, the function f(x) will be defined.Therefore, inequality can be used to find the domain of f(x) is (B) 4x+9 greater-than-or-equal-to 0.
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The correct question is given below:
If f (x) = start root 4 x 9 enroot 2, which inequality can be used to find the domain of f(x)?
(A) startroot 4 x endroot greater-than-or-equal-to 0
(B) 4x+9 greater-than-or-equal-to 0
(C) 4 x greater-than-or-equal-to 0
(D) startroot 4 x 9 endroot 2 greater-than-or-equal-to 0
Answer:
(B)- 4X+9 greater than or equal to 0
Step-by-step explanation:
Sloane kicked a soccer ball off the ground at a speed of 56 feet per second. the height of the ball can be represented by the function h(t) = −16t2 56t, where t is the time in seconds. how many seconds did the ball travel before returning the ground? t = 56 seconds t = 16 seconds t = 3.5 seconds t = 0.29 seconds
The time in seconds that it took the ball to travel would be = 0.25 seconds.
Calculation of speed timeSpeed can be defined as the distance covered by an object per unit time.
The speed used to kick the soccer off the ground = 56 feet per second.
The height equation= −16t² + 56t
The time= ?
The formula for speed = distance/time
56= −16t² + 56t/t
56t = −16t² + 56t/t
−16t² = -56t + 56t
−16t² = 0
Make t the subject formula,
t = √1/16
t = 0.25 seconds.
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What is the approximate total volume of the silo? use 3.14 for π and round the answer to the nearest tenth of a cubic meter. 37.1 m3 71.9 m3 116.5 m3 130.8 m3
The total volume of silo is = 116.5[tex]{~m}^{3}[/tex]
The correct option is C
What are the geometric figures?Any arrangement of points, lines, or planes constitutes a geometric figure. Depending on their dimensions, geometric figures can be categorized as either a space figure, a plane figure, a line, a line segment, a ray, or a point.
Any object's surface area is the space that the object's surface takes up on a specific area or region. Volume, however, refers to how much room a thing has.
Given data:
Radius =4.4/2
=2.2
height of cylinder = 6.2
to find :
total volume of silo = volume of cylinder + volume of hemisphere
[tex]\begin{aligned}&=\pi r^{2} h+\frac{2}{3} \pi r^{3} \\&=\pi r^{2}\left(h+\frac{2}{3} r\right) \\&=\frac{22}{7} \times(2.2)^{2}\left[6.2+\frac{2 \times 2.2}{3}\right]\end{aligned}[/tex]
= 116.5[tex]m^2[/tex]
The total volume of silo is = 116.5[tex]m^2[/tex]
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I understand that the question you are looking for is:
A grain silo is composed of a cylinder and a What is the approximate total volume of the silo? Use hemisphere. The diameter is 4.4 meters. The height of 3.41 for [tex]\pi[/tex] and round the answer to the nearest tenth of its cylindrical portion is 6.2 meters. a cubic meter.
a. 37.1[tex]m^2[/tex]
b. 71.9 [tex]m^2[/tex]
c.116.5 [tex]m^2[/tex]
d. 130.8[tex]m^2[/tex]
25) Every month the cafeteria orders 120 gallons of milk and 220 gallons of chocolate milk. What is the ratio of milk to chocolate milk as a fraction in simplest form?
Answer:
Step-by-step explanation:
120:220
2 will go into 120 60 times and go into 220 110 times. So your answer comes down to;
60:110
10 will go into 60 6 times and go into 110 11 times So your answer comes down to;
6:11
That is your final answer 6:11
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:
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
Consider the points (1,7),(-5,-4) what are the domain and range of this function
Answer:
Domain is 1 and 7 and range is -5and -4
Step-by-step explanation:
because domain is a first group element and range is a second element of a set
What steps may be necessary to predict data not included in a data set using a scatter plot and line of best fit? Select all that apply.
Answer:
Step-by-step explanation:
3. A line of best fit can be roughly determined using an eyeball method by drawing a straight line on a scatter plot so that the number of points above the line and below the line is about equal (and the line passes through as many points as possible). This will help me to see weather or not it is positive or negative.3
If zeba were younger by 5 years than what she really is then the square of her age would have been 11 more than five times her actually age. What is her age now?
Answer:
I am not 100% confident, but I think that she is 11.
Step-by-step explanation:
Answer:
14 years old
Step-by-step explanation:
Define the variable
Let x be the actual age of Zeba (in years).
Create an equation using the give information and the variable x:
[tex](x - 5)^2=5x+11[/tex]
To find Zeba's age now, solve the equation for x.
Expand the brackets:
[tex]\implies x^2-10x+25=5x+11[/tex]
Subtract 5x from both sides:
[tex]\implies x^2-10x+25-5x=5x+11-5x[/tex]
[tex]\implies x^2-15x+25=11[/tex]
Subtract 11 from both sides:
[tex]\implies x^2-15x+25-11=11-11[/tex]
[tex]\implies x^2-15x+14=0[/tex]
Factor the found quadratic
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], then rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies x^2-14x-x+14=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-14)-1(x-14)=0[/tex]
Factor out the common term (x - 14):
[tex]\implies (x-1)(x-14)=0[/tex]
Apply the zero product property:
[tex]\implies (x-1)=0 \implies x=1[/tex]
[tex]\implies (x-14)=0 \implies x=14[/tex]
Therefore, Zeba's age now is either 1 or 14 years.
As the question states "If Zeba were younger by 5 years" then 1 must be an extraneous solution since 1 - 5 = -4 and Zeba cannot be -4 years old.
Therefore, Zeba's age now is 14 years old.
Check
Given the actual age of Zeba is 14 years old.
Therefore, If Zeba were younger by 5 years, she would be 9 years old as: 14 - 5 = 9
The square of 9 is: 9² = 81.
5 times her actual age: 5 × 14 = 70
81 is 11 more than 70, hence verifying that her actual age is 14 years old.
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Csn u please help me o have no idea
Answer:
D.= √29
Step-by-step explanation:
Greetings!The distance between the two complex numbers,
Z₁=a+bi and Z₂=c+di in the complex plane is
[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]
In the Cartesian plane, the distance between, one point and other is (x₁,y₁) and (x₂,y₂) is the distance formula is
[tex]d = \sqrt{(X₂-X₁)² + (Y₂-Y₁)²} [/tex]
To find the distance between the two complex numbers using the formula
[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]
where,
a=4b=3c=6d=-2[tex]d = \sqrt{(a - b) {}^{2} + (d - b) {}^{2} } \\ d = \sqrt{(6 - 4) {}^{2} + ( - 2 - 3) {}^{2} } \\ d = \sqrt{(2) {}^{2} + ( - 5) {}^{2} } \\ d = \sqrt{4 + 25} = \sqrt{29 \\ } [/tex]
1. Convert the numeral to a numeral in base ten.
3205 six
43
125
4325
725
Expanding the digits, we have
[tex]3205_6 \equiv 3\cdot6^3 + 2\cdot6^2 + 0\cdot6^1 + 5\cdot6^0 = \boxed{725}[/tex]
If the two lines below are perpendicular and the slope of the red line is -
what is the slope of the green line?
O A.
A.
OB. -3
314
O D.
D. -
-10
10
15
Answer:
-(10/7)
Step-by-step explanation:
See attached graphic. The slope of the Green Line is cut off in the problem photo, but can be calculated from the graph to find the slope of the Red Line. The answer options are on drugs; pick the one that looks closest.
Answer:
-4/3
Step-by-step explanation:
What is the area of this figure?
14 km
8 km
9 km
8 km
5 km
4 km
4 km
4 km
The Area of the composite figure as shown in the image below is: 105.57 km².
What is the Area of a Composite Figure?Referring to the diagram given below, the shape can be decomposed into one rectangle, one square, and one quarter circle.
The area of the composite figure = area of rectangle + area of square + area of quarter circle.
Area of the Rectangle = length × width
Length = 12 km
Width = 7 km
Area of the Rectangle = 12 × 7
Area of the Rectangle = 84 km²
Area of the square = (s)²
s = 3 km
Area of the square = 3²
Area of the Rectangle = 9 km²
Area of the quarter circle = 1/4(πr²)
r = 4 km
Area of the quarter circle = 1/4(π × 4²)
Area of the quarter circle = 12.57 km²
Area of the composite figure = 84 + 9 + 12.57
Area of the composite figure = 105.57 km².
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