[tex]|\Omega|=6\\|A|=2\\\\P(A)=\dfrac{2}{6}=\dfrac{1}{3}[/tex]
Answer:
1/3
Step-by-step explanation:
The list of sample space's elements: {1, 2, 3, 4, 5, 6}
The number of elements in sample space: 6
The list of elements belonged to the event "choosing the number larger than 4": {5, 6}
The number of elements in the event: 2
Hence, the probability of event "choosing a number larger than 4":
P = number of event's elements/number of sample space's elements
= 2/6
= 1/3
solve the equation: sin(2x)= sin x
Answer:
Below
Step-by-step explanation:
sin(2x) = 2 ×cos(x)× sin(x)
● sin(x) = 2 × cos(x) × sin(x)
● 2 × cos(x) = 1
● cos (x) = 1/2
So we can deduce that:
● x = Pi/3 + 2*k*Pi
● or x = -Pi/3 + 2*k*Pi
K is an integer
The Solution of x:
x = π/3 + 2πn, where n is an integer.
x = 2π/3 + 2πn, where n is an integer.
In degrees:
x = 60° + 360°n, where n is an integer.
x = 120° + 360°n, where n is an integer.
To solve the equation sin(2x) = sin(x), we can use the properties of trigonometric functions.
First, let's simplify the equation using the double angle identity for sine:
sin(2x) = 2sin(x)cos(x).
Now we can rewrite the equation as:
2sin(x)cos(x) = sin(x).
2cos(x) = 1.
Dividing both sides of the equation by cos(x), we get:
2 = 1/cos(x).
Now, we can find the value of cos(x) by taking the reciprocal of both sides:
cos(x) = 1/2.
From the unit circle or trigonometric values,
we know that cos(x) = 1/2 corresponds to angles of π/3 or 2π/3 (in radians) or 60° or 120° .
So, the solutions for x are:
x = π/3 + 2πn, where n is an integer.
or
x = 2π/3 + 2πn, where n is an integer.
In degrees:
x = 60° + 360°n, where n is an integer.
or
x = 120° + 360°n, where n is an integer.
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Roselyn is driving to visit her family, which live 150 150150 kilometers away. Her average speed is 60 6060 kilometers per hour. The car's tank has 20 2020 liters of fuel at the beginning of the drive, and its fuel efficiency is 6 66 kilometers per liter. Fuel costs 0.60 0.600, point, 60 dollars per liter. How long can Roselyn drive before she runs out of fuel?
Answer:
She can go 120 km before she runs out of fuel
It will take 2 hours.
Step-by-step explanation:
150 km is the distance
60 km/ h is the speed
The gas tank is 20 liters
We can go 6 km per liter
Fuel costs .60 dollars per liter
We need to determine how far she can go on a tank of gas
20 liters * 6 km / liter = 120 km
She can go 120 km before she runs out of fuel
120 km = 60 km/ h * x hours
Divide each side by 60
120/60 = x
2 hours
Answer:
Hopes this helps!
Step-by-step explanation:
This table represents a quadratic function.
y
x
0
14
1
10.5
2
8
3
6.5
4
5
6.5
What is the value of a in the function's equation?
A.2
B.1/2
C.-1/2
D.1
Answer:
B. 1/2
Step-by-step explanation:
y = ax^2 + bx + c
14 = a(0)^2 + b(0) + c
c = 14
10.5 = a(1)^2 + b(1) + 14
10.5 = a + b + 14 ____(i)
8 = a(2)^2 + b(2) + 14
8 = 4a + 2b + 14
4 = 2a + b + 7 ___ (ii)
i - ii
10.5 - 4 = -a + 7
6.5 = -a + 7
a = 7- 6.5
a = 0.5
Value of a in the quadratic function is 0.5
What is Quadratic function?In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree
Given,
Quadratic function
y = [tex]ax^{2}+bx+c[/tex]
Consider values in the table x= 0 and y =14
[tex]14=a(0)^{2}+b(0)+c\\ c=14[/tex]
Consider x=1 and y = 10.5
[tex]10.5=a(1^{2})+b(1)+c\\ a+b=10.5-14\\a+b=-3.5[/tex]
Consider x=2 and y =8
[tex]8=a(2^{2})+b(2)+c\\ a\\8=4a+2b+14\\4a+2b=-6\\2a+b=-3[/tex]
Subtract a + b= -3.5 from 2a + b= -3
a=-3--3.5=0.5
Hence, the Value of a in the quadratic function is 0.5
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Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be
written using function notation?
O FID = - Šv
O f(x) = - 3x + 4
Of(x) = -x +
O fly) = -34+4
Answer:
f(x) = - 3x + 4
Step-by-step explanation:
Note that y = f(x)
Rearrange making y the subject
9x + 3y = 12 ( subtract 9x from both sides )
3y = - 9x + 12 ( divide all terms by 3 )
y = - 3x + 4 , that is
f(x) = - 3x + 4
The distance of planet Mercury from the Sun is approximately 5.8. 107 kilometers, and the distance of planet Venus from the Sun is 1.1. 10 kilometers. About how many more kilometers is the
distance of Venus from the Sun than the distance of Mercury from the Sun?
Answer:
I would say about 5 times but I am not sure so if it is wrong am sorry.
Solve for x 3x - 4 = 2x - 10
Answer:
-6
Step-by-step explanation:
To solve this problem, you should move all of the variables onto one side, and all of the constants onto the other side as such:
3x-4=2x-10
+10 +10
3x+6=2x
-3x -3x
6=-x
/-1 /-1
x=-6
Hope this helps!
P.S. Please give me brainliest. Thanks :)
Answer:
[tex]x = -6[/tex]
Step-by-step explanation:
Looking at the expression [tex]3x - 4 = 2x - 10[/tex], our goal is to get rid of the x term on one side.
To do this, we can subtract 2x from both sides which gets us
[tex]x - 4 = -10[/tex]
Add 4 to both sides:
[tex]x = -6[/tex]
Hope this helped!
plz ans asap i havd limited time ill give brainliest
Answer:
C. $128
Step-by-step explanation:
320 x 0.5 = 160
320 - 160 = 160
160 x 0.20 = 32
160 - 32 = 128
Lori works as a cartoonist for a teen magazine. The time she spends sketching is given by the equation m = 12s, where m is the number of minutes and s is the number of sketches.
If Lori made of a sketch, she spent minutes sketching.
Answer:
A. 9
Step-by-step explanation:
Lori works as a cartoonist for a teen magazine. The time she spends sketching is given by the equation m=12s where m is the number of minutes and s is the number of sketches if Lori made 3/4 of a sketch she spent A.9 B.12 C.16 D.20 minutes sketching
Solution
m= number of minutes
s= number of sketches
Equation is
m=12s
If Lori made 3/4 of the sketch, then the time spent is ?
s=3/4
m=?
m=12s
m= 12 × 3/4
=36/4
=9
m=9
If Lori made 3/4 of the sketch, then she spent 9 minutes sketching.
Answer:
I hope this helps
Step-by-step explanation:
|-6+8| = simplify the expression
Answer:
2
Step-by-step explanation:
|-6+8|
Add/subtract the numbers: -6 + 8 = 2
= |2|
Apply the absolute value rule: |a| = a, a ≥ 0
= 2
Use linear regression to predict the length of a 40-month-old animal. The ages and lengths of several animals of the same species are recorded in the following table: (2 points)
Answer:
Aw what animal
Step-by-step explanation:
Srry I need pointse
Please answer this question now
Answer:
298.3 square centimeters
Step-by-step explanation:
We are given
Slant height (l)= 14cm
Radius (r)= 5cm
Since we are given the slant height ,
the formula for surface area of a cone =
πrl + πr²
πr(l + r)
π = 3.14
Hence,
3.14 × 5(14 + 5)
3.14 × 5(19)
= 298.3 square centimeters
if the first step of the equation -8 - 7x = -5x - 10 is " add 10" then what should be done next?
Answer:
Add 7x to each side
Step-by-step explanation:
-8 - 7x = -5x - 10
Add 10 to each side
-8 - 7x+10 = -5x - 10+10
2 -7x = -5x
Add 7x to each side
2-7x+7x = -5x+7x
2 = 2x
Answer: See below
Step-by-step explanation:
[tex]-8 - 7x = -5x - 10[/tex]
I believe it is adding 8 on both sides
The next step after adding 8 on both sides is adding 5x on both sides
[tex]-7x=-5x-2[/tex]
[tex]-7x+5x=-5x-2+5x[/tex]
[tex]-2x=-2[/tex]
x=1
What are the vertical asymptotes of the function above?
1) x= -1 and x = -2
2) x= -1 and x = 2
3) x= 1 and x = -2
4) x = 1 and x = 2
Answer:
third option
Step-by-step explanation:
Given
f(x) = [tex]\frac{5x+5}{x^2+x-2}[/tex]
The denominator cannot be zero as this would make f(x) undefined.
Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.
solve x² + x - 2 = 0 ← in standard form
(x + 2)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 2 = 0 ⇒ x = - 2
x - 1 = 0 ⇒ x = 1
The vertical asymptotes are x = 1 and x = - 2
Look at the picture and answer the question
Answer:
b
Step-by-step explanation:
Answer:
80 degrees
Step-by-step explanation:
m∠4 is the same as m∠2
I measured it with a protracter
( plz mark me as brainliest, that would be most appreciated! )
a number is multiplied by 5 and the results is twice the number added to 2 find the number
Answer:
5x=2x+2
3x=2
X=2/3
Hope this helps ФωФ
Can I name my Angle VTS as STV? And use it interchangeably in proving?
Answer:
both angles are the same, so you can use it interchangeably in proving.
But i suggest you to mantain only one, because it's easier to understand and it looks better.
Which theorem or postulate proves the two triangles are similar?
AA Postulate
SSS Theorem
AS Postulate
SAS Theorem
Answer:
AA Postulate
Step-by-step explanation:
The bottom lines are parallel. In this case they are also congruent. Combined with the top angle this makes in AA postulate
What is the factored form of 125x6 – 8?
Answer:
Step-by-step explanation:
125 = 5 *5 * 5 = 5³
8 = 2 * 2 *2 = 2³
125x⁶ - 8 = 5³(x²)³ - 2³
= (5x²)³ - 2³ { a³ - b³ = (a -b)(a² + ab + b²)
= (5x² - 2) ([5x²]² + 5x²*2 + 2²)
= (5x² - 2)(25x⁴ + 10x² + 4)
Hint: (5x²)² = 5² * (x²)² = 25* x²ˣ² = 25x⁴
SIMPLIFY.
6y^3(3 + 4y^2)
Answer:
18y^3 + 24y^5.
Step-by-step explanation:
6y^3(3 + 4y^2)
= 6*3 y^3 + 6*4 y^(3+2)
= 18y^3 + 24y^5.
Ella's pet snake is 42 inches long, and Roya's pet snake is 8 feet long. How many inches longer is Roya's snake?
Answer:
54 inches
Step-by-step explanation:
First, let's convert the measurements into a common measurement.
Since inch is the smallest measurement here, let's use that.
Ella's pet snake is 42 inches long.
Roya's pet snake is 8 feet long. There are 12 inches in one foot. Therefore, 8 feet would mean 12 times 8 or 96 inches.
Therefore, Roya's snake is 96 inches long.
To find out how many inches longer is Roya's snake, subtract:
96 - 42 = 54.
Therefore, Roya's snake is 54 inches longer than Ella's.
A machine fills 680 bottles in 5hours how many bottles will it fill in three hours?
Answer:
408 bottles
Step-by-step explanation:
the machine can fill 136 bottles in 1 hour, 136×3=408
Answer:
408
Step-by-step explanation:
680 bottles in 5 hours
in three hours:
1 hour =680/5=136
in three hours:it will be 136*3=408
Bryce is making a model building. He raises the walls of the building by 2centimeters five times. By how many centimeters does Bryce raise the walls all together?
Answer:
C. 10cm
Step-by-step explanation:
Bryce is making a model building.
He raises the walls of the building
by 2 centimeters five times. By how
many centimeters does Bryce raise
the walls all together?
(A) 2 cm
(C) 10 cm
(B) 5 cm
(D) 20 cm
Bryce raises the walls of the building 2centimeters five times
This means, he raises the walls 2centimeters five different times
By how many centimeters does Bryce raise the walls all together?
We can solve this by finding the product of 2centimeters five times
The total centimeters Bryce raises the walls altogether= 2 centimeters × 5 times
=2cm × 5
=10cm
Evaluate 5 - t/3 when t =12
Answer:
1
Step-by-step explanation:
Plug in t = 12 in the expression
[tex]5-\frac{t}{3}=5-\frac{12}{3}[/tex]
= 5 - 4/1
= 5 - 4
= 1
Answer:
[tex]\Huge \boxed{1}[/tex]
Step-by-step explanation:
[tex]\displaystyle 5-\frac{t}{3}[/tex]
The value of [tex]t[/tex] in the expression is 12.
Replace the [tex]t[/tex] variable with 12.
[tex]\displaystyle 5-\frac{12}{3}[/tex]
Evaluate the expression.
[tex]5-4[/tex]
[tex]1[/tex]
Which equation has a constant of proportionality equal to 3? A. y= 8/5 x B. y= 1/3 x C. y= 1/4 x D. y= 18/6 x PLEASE HELP ME :c
Answer:
(D) [tex]y=\frac{18}{6}x[/tex]
Step-by-step explanation:
We will be able to know if an equation has a constant of proportionality of 3 if the constant which is being multiplied by x is equal to 3.
[tex]\frac{8}{5} =1.6[/tex] so no for A.
[tex]\frac{1}{3} = 0.\overline{33}[/tex] so no for B too.
[tex]\frac{1}{4} = 0.25[/tex] so no for C as well.
[tex]\frac{18}{6} = 3[/tex], so D works.
Hope this helped!
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
x<10
Step-by-step explanation:
On the number line it shows that the dot is at 10. Since the dot is not colored in, we know it's not greater/less than or equal to. Greater/less than or equal to is where it shows the symbol, but it's underlined, like this: ≤. Only when the dot is colored in, is there a possibility it is greater/less than or equal to. So it can be greater than or less than something. Since it starts at 10 and is decreasing, it is going to be less than.
X will be less than something. And because the dot is at 10, it means 10 was the start. X is less than 10 since the arrow is pointing to where the numbers are decreasing. So, x<10.
Evaluate the expression 5^-2
Hi there! :)
Answer:
[tex]\huge\boxed{\frac{1}{25}}[/tex]
When evaluating an expression with a negative exponent, the reciprocal will need to be taken. Therefore:
[tex]5^{-2} = \frac{1}{5^{2} } = \frac{1}{25}[/tex]
What is the area of a circle with a radius of 40 cm?
cm2
(Use 3.14 for Pi.)
Duane is making a casserole for dinner. He has been cooking the casserole for 48 minutes. The casserole
needs to cook for 47 more minutes.
How many minutes does the casserole cook in total?
Answer:
95 minutes
Step-by-step explanation:
Add together how long it has been cooking plus how long it needs to cook
48+47 = 95
95 minutes
Answer:
155
Step-by-step explanation:
Add 60 and 48 to get 108 then add 108 and 47 to get 155
Find x
A. 33
B. 44√3
C. 33√2
D. 11√3
Answer:
d
Step-by-step explanation:answer is d on edg
Could someone please explain/help me to do this using Pythagoras theorem?
Answer:
[tex]\boxed{478.02}[/tex]
Step-by-step explanation:
→ First understand what Pythagoras theorem is
Pythagoras is a theorem used to find the hypotenuse (the side opposite to the right-angle) of a triangle. We would need the base lengths as well the height in order to use Pythagoras.
→ State the formula and identify the letters
a² + b² = c² ⇒ where 'a' is 380cm, 'b' is 290cm and 'c' is what we are trying to work out
→ Substitute in the values into the formula
380² + 290² = c²
⇒ Simplify
144400 + 84100 = c²
⇒ Collect the numbers together
228500 = c²
⇒ Square root both sides to find 'c'
478.0167361 = c
→ The length of the diagonal is 478.02
