[tex]\displaystyle\\|\Omega|=\binom{15}{3}=\dfrac{15!}{3!12!}=\dfrac{13\cdot14\cdot15}{2\cdot3}=455[/tex]
a)
[tex]\displaystyle\\|A|=\binom{10}{3}=\dfrac{10!}{3!7!}=\dfrac{8\cdot9\cdot10}{2\cdot3}=120\\\\P(A)=\dfrac{120}{455}=\dfrac{24}{91}\approx26.4\%[/tex]
b)
[tex]\displaystyle\\|A|=\binom{5}{3}=\dfrac{5!}{3!2!}=\dfrac{4\cdot5}{2}=10\\\\P(A)=\dfrac{10}{455}=\dfrac{2}{91}\approx2.2\%[/tex]
c)
[tex]\displaystyle\\|A|=\binom{10}{2}\cdot5=\dfrac{10!}{2!8!}\cdot5=\dfrac{9\cdot10}{2}\cdot5=225\\\\P(A)=\dfrac{225}{455}=\dfrac{45}{91}\approx49.5\%[/tex]
d)
[tex]A[/tex] - at least one is spoilt
[tex]A'[/tex] - none is spoilt
[tex]P(A)=1-P(A')[/tex]
We calculated [tex]P(A')[/tex] in a).
Therefore
[tex]P(A)=1-\dfrac{24}{91}=\dfrac{67}{91}\approx73.6\%[/tex]
Describe the graph of a function g by observing the graph of the base function ƒ.
A. g(x) = 2ƒ(–x) g(x)
B. g(x)= -1/2f(x)
C. g(x)= 1/2f(-x)
D. g(x)= f(-1/2x)
The correct answer is option B which is g(x)= 1/2f(-x).
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
As we can see in the graph that the value of the function g(x) will be calculated by the distance formula:-
[tex]g(x) = \dfrac{ 0 + 2}{2 - 0 }=\frac{2}{2}=1[/tex]
The value of the function f(x) will be:-
[tex]f(x) =\dfrac{2-0}{-4+0}=\dfrac{-1}{2}[/tex]
So g(x) = ( -1/2) f(x)
Therefore the correct answer is option B which is g(x)= 1/2f(-x).
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What is the value of x in the equation 1/5x - 2/3y=30 when y= 15
Substituting in y=15,
[tex]\frac{1}{5}x-\frac{2}[3}(15)=30\\\\\frac{1}{5}x-10=30\\\\\frac{1}{5}x=40\\\\x=\boxed{200}[/tex]
A house’s was valued at 269,00. After several years, the value increased by 18%. By how much did it increase in dollars? What is the current house value
Answer:
31742
Step-by-step explanation:
[tex]26900 \times \frac{100 + 18}{100 } = 31742 [/tex]
Write an equation of the line that passes through a pair of points: On a coordinate plane, a line goes through (4, 1) and (5, 2). a. y = x + 3 c. y = -x + 2 b. y = x - 3 d. y = -x - 2 Please select the best answer from the choices provided A B C D
Answer:
b. y = x - 3
Step-by-step explanation:
The general form of the equation of the line is y = mx + c.
1) Find for m (gradient) using the following formula:
m = y2 - y1 / x2 - x1
Substitute the values into it and solve for m.
m = 2 - 1 / 5 - 4
m = 1 / 1
m = 1
2) Substitute into m of the y = mx + c.
y = 1x + c
3) Choose one the coordinates that the line goes through ((4, 1) or (5, 2)) to find c (y-intercept). I will choose (4, 1). Then, substitute your chosen coordinates into your newfound equation (y = 1x + c)
1 = 1(4) + c
1 = 4 + c
1 - 4 = c
-3 = c
Substitute -3 in place of c.
y = 1x - 3, which can be simplified to y = x - 3. Therefore, the correct choice is b.
The interior angle of a regular polvgon is 9 times the size of its exterior angle
Work out how many sides the polygon has
==================================================
Work Shown:
x = exterior angle
9x = interior angle
interior + exterior = 180
9x+x = 180
10x = 180
x = 180/10
x = 18
n = number of sides
n = 360/x
n = 360/18
n = 20
There are 20 sides to the regular polygon.
Side notes:
The formula to determine n only works for regular polygons.A polygon with 20 sides is known as an icosagon.Any pair of adjacent interior and exterior angles are supplementary. They add to 180 degrees.What is the value of 6¹?
6° = 1
6 = 6
6 = 36
6 = 216
Answer:
6=6
Step-by-step explanation:
This is because the exponent is multiplying it by one so technically you don't have to do anything but multiply 6*1
Hope this helps
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Fun fact: ANY number powered to the}\\\huge\textbf{1 it automatically that number(just }\\\huge\textbf{regular multiplication).}[/tex]
[tex]\mathsf{6^1}\\\\\\\mathsf{\approx 6\times1}\\\\\\\large\text{So, you're making it 6 ONE TIME}\\\\\mathsf{= \bf 6}\\\\\\\\\\\\\huge\text{Thus, your answer should be: \boxed{\mathsf{Option\ B.\ 6^1 = 6}}}\huge\checkmark[/tex]
[tex]\large\text{Random\ note\ for\ rest\ of\ equations:}\\\\\mathsf{6^0\rightarrow \bf 1}\\\\\mathsf{6^2\rightarrow 6\times 6 \rightarrow \bf 36}\\\\\mathsf{6^3\rightarrow 6\times6\times6\rightarrow 36\times6\rightarrow \bf 216}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Determin d/dx (x²+1) (7x-3) and d/dt(3t-2/5t+1)
Answer:
2x(7x-3) + (x²+1)(7)
Step-by-step explanation: use product rule
can someone please help me solve this question step by step not just give me the answer I want to learn lol
find f(x)•g(x)
if f(x)=8x+1 and g(x)=-5+9.
Answer: 32x+4
Step-by-step explanation:
[tex]f(x) \cdot g(x)=(8x+1)(-5+9)=4(8x+1)=\boxed{32x+4}[/tex]
Sid makes a graph for estimating the y-value.He wants to compare it to the table before he turns it in. Do the table and the graph represent the same function?
Answer:
No
Step-by-step explanation:
The graph and the table do not show the same function as none of the y values on the graph correspond to the y values on the table.
3x² - 2x + 1 = [?]
x=4
Answer:
3x²-2x+1=?
3(4²)-2(4)+1=?
3(16)-8+1=?
48-8+1=?
40+1=41
If a=(-1 -3 2 2 5 -1 -4 -5 -4) and b=(3 3 5 2 -5 2 -4 -1 1) find AB?
Answer:
what is the control ofprice floir or price celling then scplain one advantage an one dissvantage
Someone do this please, ty.
5 is the missing value.
Step-by-step explanation:
12x = 60
x = 60/12
x = 5
Answer:
[tex]\boxed{\rm x = 5}[/tex]
Step-by-step explanation:
[tex] \rm \cfrac{12}{20} = \cfrac{3}{x} [/tex]
Find the missing value.
Solution with work shown:
Use criss-cross multiplication:
[tex]12 \times x = 3 \times 20[/tex][tex]12x = 60[/tex]Divide both sides by 12:
[tex] \cfrac{12x}{12} = \cfrac{60}{12} [/tex][tex]x = 5[/tex]Hence,the missing value is 5.
Need help anyone please!!!
On a unit circle, Ø = 60°. Identify the terminal point and Tan Ø
The terminal points when the value of r is 1 will be 0.5 and 0.86 and the value of tan 60 will be 1.732.
What is angle measurement?An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).
Given;
Ø = 60°
Let's assume the value of r = 1 units
The terminal points are;
x= rcosΘ
x=1 × cos 60°
x=0.5
y=rsinΘ
y=rsin60°
y = 0.86
The terminal points when the value of r is 1 will be 0.5 and 0.86.
The value of the tan for the given value of the angle;
Tan 60° = 1.732
Hence, the terminal points when the value of r is 1 will be 0.5 and 0.86 and the value of tan 60 will be 1.732.
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What is the slope of a line that is perpendicular to the line shown on the graph?
Answer:
4
Step-by-step explanation:
The slope of the line in the image is -1/4. I found that by starting at the point (0,2) and moving down 1, and right 4. This is because slope is rise over run, meaning that you move up/down and then right/left. You can see that the line is sloping downwards, so it is negative.
Perpendicular lines have a slope that is the opposite reciprocal, meaning the sign is opposite and the numerator and denominator are flipped (reciprocal). The current slope is -1/4, so the reciprocal is -4/1 (or just -4). Then just make the negative positive and you get 4.
1/4 ÷9=????????????????????????????????????????????????????????????????????????????????????????????????????????????
Answer:
1/36
Step-by-step explanation:
¼ / 9
9 as a fraction is 9/1
use KFC (keep flip change)
¼ x ⅑ = 1/36
[tex] \frac{1}{4} \div 9 \\ \\ first \: way \\ 0.25 \div 9 \\ 0.027 \\ \\ second \: way \: \\ \frac{1}{4} \times \frac{1}{9} \\ \frac{1}{36} \\ 0.027[/tex]
PLEASE GIVE BRAINLIEST
Which expression can be used to convert 80 US to Australian dollars?
Answer:
0.9668 USD
Step-by-step explanation:
1 USD=1.0343 AUD 1AUD=0.9668 USD.
Which graph shows y=1/2⌈x⌉?
The correct answer is option B which is the graph that represents the equation y = (1/2)x will be the second option in the figure. At every value of y, the value of x is double.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The graph of the equation y =1/2x is represented in the answer below we can see in the graph that at every value of y the value of x is double for example if we put y = 1 then the value of x will be 2.
y = 1/2 x
at x = 2
y = 1/2 x 2
x = 1
Therefore the correct answer is option B which is the graph that represents the equation y = (1/2)x will be the second option in the figure. At every value of y, the value of x is double.
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: a = -1[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
For a function f(x) = y,
x represents the value ( x - coordinate ) at which the function has a value y.
[tex]\qquad \tt \rightarrow \: f(x) = a {x}^{2} + 2[/tex]
for point (-1 , 1) to satisfy the equation, we have to calculate the value of a
[tex]\qquad \tt \rightarrow \: f( - 1) = a( - 1) {}^{2} + 2[/tex]
[tex]\qquad \tt \rightarrow \: 1 = a + 2[/tex]
[tex]\qquad \tt \rightarrow \: a = 1 - 2[/tex]
[tex]\qquad \tt \rightarrow \: a = - 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Substitute -1 into x
Substitute 1 into y
f(x)= a (-1) ^2+2=1
a=-1
James has available a 10% alcohol solution and a 60% alcohol solution find how many liters of each solution he shouldn’t mix to make 50 L of a 40% alcohol solution
Answer:
20 L
Step-by-step explanation:
I am guessing that you meant should instead of shouldn't.
To solve this we can set the amount of 10% solution needed equal to x. This means that the 60% solution will be the remaining amount needed, so 50 L - x.
We can do 10%*x+60%*(50-x)=50*40%. Solving for x we get:
0.1*x+0.6*50-0.6*x=50*0.4
0.1*x+30-0.6*x=20
-0.5*x=-10
x=20
A city has a population of 1300. If the city’s population grows 30%, what is its new population?
Answer:
1699
Step-by-step explanation:
30/100*13000
Then add answer with 1300
eg 1300+399
I hope this explanation helps you.Also You can follow me.
OLLEGE
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For the given functions, find (fog)(x) and (gof)(x) and the domain of each.
f(x) = 4x + 1, g(x)=√x
(fog)(x) =
(gof)(x) =
The domain of fog is ☐.
(Type your answer in interval notation.)
The domain of g of is.
(Type your answer in interval notation. Use integers or fractions for any numbe
Part 1
[tex](f\circ g)(x)=f(\sqrt{x})=4\sqrt{x}+1[/tex]
We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus, the domain is [tex]\boxed{[0, \infty)}[/tex]
Part 2
[tex](g \circ f)(x)=g(4x+1)=\sqrt{4x+1}[/tex]
We need to make sure the radical is defined, meaning the radicand has to be non-negative. Thus,
[tex]4x+1 \geq 0\\\\4x \geq -1\\\\x \geq -\frac{1}{4}[/tex]
Thus, the domain in interval notation is [tex]\boxed{\left[-\frac{1}{4}, \infty)}[/tex]
I need the answer for number 4 please!!
Answer:
-3 - false
0 - true
1 - true
2 - false
4 - true
Step-by-step explanation:
the "zeros" of a function are its x-intercepts
(because that is when the function = zero [0])
So, we can look at the x-intercepts of the graph to find the zeros:
at 0, 1, and 4 the function = 0, meaning that those are zeros of the function
hope this helps!! have a lovely day :)
What is the equation of the line that is parallel to the given line and passes through the point (−3, 2)?
3x − 4y = −17
3x − 4y = −20
4x + 3y = −2
4x + 3y = −6
Answer:
4x + 3y = - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
• Parallel lines have equal slopes
calculate the slope of the line using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (3, - 1) ← 2 points on the line
m = [tex]\frac{-1-3}{3-0}[/tex] = [tex]\frac{-4}{3}[/tex] = - [tex]\frac{4}{3}[/tex] , then
y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
to find c substitute (- 3, 2 ) into the partial equation
2 = 4 + c ⇒ c = 2 - 4 = - 2
y = - [tex]\frac{4}{3}[/tex] x - 2 ← equation in slope- intercept form
multiply through by 3 to clear the fraction
3y = - 4x - 6 ( add 4x to both sides )
4x + 3y = - 6 ← in standard form
Need help with this geometric question
Answer: A
Step-by-step explanation:
[tex]V=\frac{1}{3}Bh\\\\V=\frac{1}[3}(6.3)(2.4)(3.6)=\boxed{18.144}[/tex]
find SP when profit loss is given
Answer:
the formulas for profit and loss percentage are given below profit percentage p profit cost price into 100 loss percentage l is equal to loss cost price is into 100 SP
P is a polynomial of degree 4 with three zeros: -1 and 2 are zeros of multiplicity one, and 3 is a zero with multiplicity two. If P(0) = 90, what is the lead coefficient of P ?
Answer:
[tex]P(x) = (x+1)(x-2)(x-3)^2 + 108[/tex]
Step-by-step explanation:
let me know if you want an explanation
please help ive been stuck on this question.
The value of the expression 8 / m - 11 / 3m is 13 / 3m
How to simplify an expression?8 / m - 11 / 3m
Therefore,
8 / m - 11 / 3m
The factor of the denominator is 3m
Therefore,
8 / m - 11 / 3m = 3(8) - 11/ 3m
3(8) - 11/ 3m = 24 - 11 / 3m
24 - 11 / 3m = 13 / 3m
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An asset has a cost of $50,000, with a residual value of $10,000. It has a life of 5 years and was purchased on January 1. Under double-declining-balance, what’s the asset’s fourth full year of depreciation expense?
The asset’s fourth full year of depreciation expense will be $6,666.67.
What is double-declining-balance?An enhanced technique for recording loss over the lifetime of a product by adjusting the item's starting sales price by a discount factor.
An asset has a cost of $50,000, with a residual value of $10,000.
It has a life of 5 years and was purchased on January 1.
Then the asset’s fourth full year of depreciation expense will be
Annual depreciation = (cost – salvage value)/ useful life
Annual depreciation = (50000 – 10000) / 5 = $8,000
Year 1 Depreciation (for 10 months, from March to December) = $8,000 × 10/12 = $6,666.67.
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Determine if an exponential would be an appropriate model for the data shown in each scatter plot. Select
one that applies.
Answer:
Yes, No, No
Step-by-step explanation:
The function of an exponential graph is attached below. The first graph fits the look of an exponential graph. The rest do not.
Answer:
Yes, No, No
Step-by-step explanation:
1st graph represents exponential2nd graph represents quadratic3rd graph represents linear