1/7 is the probability that the product is an odd number.
What is the simple definition of probability?
A probability is a number that expresses the possibility or likelihood that a specific event will take place.
Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Total Cards are 7
2 cards out of 7 cards can be selected in ⁷C₂ = 21 ways
Product would be odd if both cards are odd
3 , 5 , 7 are odd cards
2 cards out of 3 Can be selected in ³C₂ = 3 ways
( 3 , 5) , ( 3 , 7) , ( 5 , 7)
Hence probability the product of the numbers on the 2 cards is odd number
= 3/21
= 1/7
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Can you plz help me solve these plss i begg
Answer:
a): A line has a total degree of 180. So just subtract it. 180-92 is
y=88
b): Similar to the previous, a right angle has a total angle of 90. 90-45=45.
y=45.
These are all the ones I can figure out. I hope someone else can get c) and d).
Find the EXACT values of ALL SIX trigonometric functions of θ(sin, cos, tan, cot, sec, csc) from the information given. (a) cosθ=7/12, sinθ<0 (b) tanθ=4/3, θ in Quadrant III
(a) Since cosθ = 7/12 and sinθ < 0, we can find the other four trigonometric functions as follows:
sinθ = √(1 - cos²θ) = √(1 - (7/12)²) = √(1 - 49/144) = -√(95/144)
tanθ = sinθ / cosθ = (-√(95/144)) / (7/12) = -4√(5/18)
cotθ = 1 / tanθ = -1 / (-4√(5/18)) = 1/(4√(5/18))
secθ = 1 / cosθ = 1 / (7/12) = 12/7
cscθ = 1 / sinθ = -1 / (-√(95/144)) = √(95/144)
(b) Since tanθ = 4/3 and θ is in Quadrant III, we can find the other five trigonometric functions as follows:
cosθ = √(1 / (tan²θ + 1)) = √(1 / (16/9 + 1)) = √(9 / 25) = 3/5
sinθ = cosθ * tanθ = (3/5) * (4/3) = 4/5
cotθ = 1 / tanθ = 1 / (4/3) = 3/4
secθ = 1 / cosθ = 1 / (3/5) = 5/3
cscθ = 1 / sinθ = 1 / (4/5) = 5/4
What is trigonometric functions?Trigonometric functions are a set of functions that relate the angles of a right triangle to the ratios of the sides of the triangle. The six most commonly used trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
The sine function, represented by sin, gives the ratio of the side opposite the angle to the hypotenuse. The cosine function, represented by cos, gives the ratio of the adjacent side to the hypotenuse. The tangent function, represented by tan, gives the ratio of the opposite side to the adjacent side.
The cotangent function, represented by cot, gives the ratio of the adjacent side to the opposite side. The secant function, represented by sec, gives the ratio of the hypotenuse to the adjacent side, and the cosecant function, represented by csc, gives the ratio of the hypotenuse to the opposite side.
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x^5 multiplied by x^3 /x^4
Answer:
x^4
Step-by-step explanation:
[tex]x {}^{5} \times \frac{x {}^{3} }{x {}^{4 \\ } } \\ \\ \frac{ {x}^{8} }{x {}^{4} } \\ \\ x {}^{8 \: - \: 4} \\ {x}^{4} [/tex]
1.5x = 3 someone help plz
Answer:
1.5x=3
x=3/1.5
x=2
.....
Answer:
Hello! answer: x = 2
Step-by-step explanation:
1.5 × 2 = 3
therefore x = 2 Hope that helps!
Which quadratic function is represented by the graph?
f(x) = 0.5(x + 3)(x − 1)
f(x) = 0.5(x − 3)(x + 1)
f(x) = 2(x + 3)(x − 1)
f(x) = 2 (x − 3)(x + 1)
Answer:
f(x) = 0.5(x + 3)(x − 1)----------------------------------
hope it helps..
have a great day!!
Answer:
[tex]f(x) = 0.5(x+3)(x-1)[/tex]
Step-by-step explanation:
GIVEN :-
A quadratic function is represented by the graph in which :-
Vertex of the parabola = (-1 , -2)The function intersects x-axis at (-3 , 0) and (1 , 0)Y-intercept of the function = -1.5TO FIND :-
The quadratic functionGENERAL CONCEPT USED IN THIS QUESTION :-
A quadratic function has 2 forms :-
General form → f(x) = ax² + bx + cStandard form → f(x) = a(x - h)² + k [∵ where h = x-coordinate of the vertex of the function & k = y-coordinate of the vertex of the function.]SOLUTION :-
The quadratic function in the graph intersects x-axis at two points (-3 , 0) & (1 , 0). But there are infinite parabolas which also intersect the same two points. And those parabolas have their unique quadratic function.
Method 1 (System of equations method) -To find the unique quadratic function , you need to use three points on the
curve so that you can form 3 equations & solve them.
Using the General form of quadratic function , substitute the known values for x & y.
Let the three points be -
(-3 , 0)(1 , 0)(0 , -1.5)Substitute (-3 , 0) in general form of function -
[tex]0 = a(-3)^2 + b(-3) + c[/tex]
[tex]=> 9a-3b+c = 0[/tex] (eqn.1)
Substitute (1 , 0) in general form of function -
[tex]0 = a(1)^2 + b(1) + c[/tex]
[tex]=> a + b +c =0[/tex] (eqn.2)
Substitute (0 , -1.5) in general form of function -
[tex]-1.5 = a(0)^2 + b(0) + c[/tex]
[tex]=> c = -1.5[/tex]
Substitute c = -1.5 in -
1) eqn.1 → [tex]9a - 3b - 1.5 = 0[/tex]
[tex]=> 9a - 3b = 1.5[/tex]
[tex]=> 3(3a-b) = 1.5[/tex]
[tex]=> 3a-b = 0.5[/tex] (eqn.4)
2) eqn.2 → [tex]a+b-1.5=0[/tex]
[tex]=> a+b=1.5[/tex] (eqn.5)
Add eqn.4 & eqn.5 to get the value of 'a'.
[tex](3a-b)+(a+b) = 0.5+1.5[/tex]
[tex]=> 4a = 2[/tex]
[tex]=> a = \frac{2}{4} = \frac{1}{2} = 0.5[/tex]
Substitute a = 0.5 in eqn.5 -
[tex]0.5 + b = 1.5[/tex]
[tex]=> b = 1.5 - 0.5 = 1[/tex]
Now, rewrite the function in general form by putting the values of 'a' , 'b' & 'c'.
[tex]f(x) = (0.5)x^2 + (1)x - 1.5[/tex]
[tex]=> f(x) = 0.5(x^2 + 2x - 3)[/tex]
Factorise the quadratic polynomial.
[tex]=> f(x) = 0.5(x^2 + 3x - x - 3)[/tex]
[tex]=> f(x) = 0.5[x(x+3)-1(x+3)][/tex]
∴ [tex]f(x) = 0.5(x+3)(x-1)[/tex]
Method 2 (Vertex method) -Another way to find the function is by taking any point on the curve & using the vertex of the parabola ; substitute the known values for x , y , h & k in the Standard form of the function.
Let that point on the curve be (-3 , 0)
Vertex = (-1 , -2)
Substitute the values of x , y , h & k in Standard form of function.
[tex]0 = a[-3 - (-1)]^2 + (-2)[/tex]
[tex]=> 0 = 4a-2[/tex]
[tex]=> 4a = 2[/tex]
[tex]=> a = \frac{2}{4} = 0.5[/tex]
Now rewrite the Standard form of the function by putting the values of h , k & a.
[tex]f(x) = 0.5(x+1)^2-2[/tex]
Expand it.
[tex]=> f(x) = 0.5(x^2+2x+1)-2[/tex]
[tex]=> f(x) = 0.5x^2+x+0.5-2[/tex]
[tex]=>f(x) = 0.5x^2 + x- 1.5[/tex]
[tex]=>f(x) = 0.5(x^2 + 2x - 3)[/tex]
Factorising it will give the final answer.
∴ [tex]f(x) = 0.5(x+3)(x-1)[/tex]
List the elements C={7n|n belongs to N, n<5}
Answer:
[tex]C = \{0,7,14,21,28\}[/tex]
Step-by-step explanation:
Given
[tex]C \{7n: n < 5\}[/tex]
Required
List the elements
Assume that n is not negative, the values of n are:
[tex]n = \{0,1,2,3,4\}[/tex]
So, the values of C is:
[tex]C = 7 * n[/tex]
[tex]C = 7 * \{0,1,2,3,4\}[/tex]
Multiply each set element by 7
[tex]C = \{7 *0,7 *1,7 *2,7 *3,7 *4\}[/tex]
[tex]C = \{0,7,14,21,28\}[/tex]
helppppppppppppppppp
Answer:
The common difference is 6
Step-by-step explanation:
14 - 6 = 8
8 - 6 = 2
In the adjoining figure, the area of the rectangular surfaces of the prism is 720 sq. Cm, XX' 20 cm and XY : XZ: YZ = 5:3 : 4, find the length of XY
The length of XY, with the area of the rectangular surface of the prism 720 sq.cm, XX' 20 cm and XY : XZ: YZ = 5:3:4, is 12 cm.
Area of the rectangular surface of the prism = 720 sq. cm
XX' = 20 cm
XY : XZ: YZ = 5:3:4
As we know, area of prism = 3 × area of rectangle
⇒720 = 3 × area of rectangle
⇒area of rectangle = 720/3
⇒XY × XX' = 240
⇒XY × 20 = 240
⇒XY = 240/20
⇒XY = 12 cm
Thus, the length of the XY is 12 cm.
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A triangle has side lengths 4.9 cm, 7.3 cm, and 8 cm. The angle measures are 36°, 64°, and 80°. What type of triangle is this triangle? please help for 15 points
Answer:
scalene acute triangle
Step-by-step explanation:
By looking at the side lengths, we can see that all of them are different, meaning the triangle is scalene. Next, we can notice that all of the angles are less than 90 degrees, meaning the triangle is acute. Putting this together, we get the triangle is a scalene acute triangle.
James purchased a gaming computer for $2,499. He anticipates each year it will decrease in value by 7.9% from the previous year. Write an exponential function that models the value in dollars of the computer x years after James's purchase.
Answer:
f(x)=2499(0.079)
Step-by-step explanation:
I WILL GIVE YOU BRAINLY PLS
Each time a student scores an 80% or higher on a quiz, a teacher puts a raffle ticket
in a jar. At the end of the quarter the teacher draws three tickets. Does EVERY
student in the class have a fair chance of having their name drawn when the teacher
draws the names for the raffle? Why or why not?
To be honest I don't know❤️
Please help! This is due soon
Answer:
slope is 1/2
Step-by-step explanation:
which algebraic expression represents the following phrase "2.5 less than a number d and 4"
The algebraic expression is represented as 4d - 2.5
What is an algebraic expression?An algebraic expression is simply defined as an expression that is composed of coefficients, factors, constants, terms, and variables.
They are also composed of mathematical operations, such as;
AdditionSubtractionDivisionBracketMuitiplicationParentheses, etcFrom the information given, we have that;
The variable = d
The constant = 2.5
The coefficient = 4
This is represented as;
4d - 2.5
Hence, the expression is 4d - 2.5
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If a supermarket sells 5 bags of grapes for Rs. 16.60, what is the unit price of a bag of grapes?
A. 3.32
B. 4.32
C. 5.32
D. 2.32
Answer:
It's A
Step-by-step explanation:
choose vertical or adjacent to tell how each pair of angles is related
Answer:
1 and 2 is adjacent. 1 and 3 are vertical. 3 and 4 are adjacent. 2 and 4 are vertical angles.
Angles ∠1 and ∠2 as well as angles ∠3 and ∠4 are linear and supplementary angles. And angles ∠2 and ∠4 as well as ∠1 and ∠3 are vertically opposite angles.
What is an angle?Angle is the space between the line or the surface that meets. And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.
Angles ∠1 and ∠2 are linear and supplementary angles.
Angles ∠1 and ∠3 are vertically opposite angles.
Angles ∠3 and ∠4 are linear and supplementary angles.
Angles ∠2 and ∠4 are vertically opposite angles.
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What is the log value of log2?
The log value of log2 is 1Log2 is defined as the logarithm base 2. This means that the logarithm of any number x is equal to the power to which the base 2 must be raised to produce x.
In other words, log2(x) = y, where 2^y = x.
Therefore, when x = 2, 2^y = 2. This means that the logarithm of 2 is equal to 1, since 2^1 = 2.
Therefore, the log value of log2 is 1.
Log2 is an important mathematical concept that is used to calculate the logarithm of a number. Logarithms are used in a variety of fields, including mathematics, physics, engineering, and computer science. Log2 is the logarithm with a base of 2, which means that the logarithm of any number x is equal to the power to which the base 2 must be raised to produce x. To calculate log2 of a number, the formula is log2(x) = y, where 2^y = x. This means that the logarithm of 2 is equal to 1, since 2^1 = 2. Therefore, the log value of log2 is 1. Log2 is often used to calculate logarithms of numbers that are not powers of 2, such as log2(3) = 1.5849. Log2 can also be used to calculate logarithms of numbers with decimals, such as log2(1.5) = 0.5849. Log2 can also be used to calculate exponents, such as 2^3 = 8.
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Points D, B, and E are collinear. Find the value of a so that points A, B, and C
are collinear.
Answer: x = 14
Step-by-step explanation:
For points A, B, and C to be collinear, angle ABD and EBC must be vertical angles. Vertical angles are congruent so we will set them equal to each other and solve for x.
Given:
126 = 9x
Divide both sides of the equation by 9:
14 = x
Reflexive property:
x = 14
Solve x^2+2x>15 algebraically and graphically, brainliest to the best detailed answer, including the steps.
The algebraic solutions are x < -5 and x > 3.
The graph is given below.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x² + 2x > 15
x² + 2x - 15 > 0
x² + (5 - 3)x - 15 > 0
x² + 5x - 3x - 15 > 0
x(x + 5) - 3(x + 5) > 0
(x - 3)(x + 5) > 0
x + 5 > 0 and x - 3 > 0
x < -5 and x > 3
The graph is given below.
Thus,
x < -5 and x > 3 is the solution.
The graph is given below.
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How do you solve 3 to the power of 3?
As per the power rule of exponents, the solution of 3 to the power of 3 is 27.
The term exponent in math is defined as a number shows how many times the number is multiplied by itself.
Here we have to solve 3 to the power of 3.
Here according to the Power Rule of Exponents then we have the rule as
=> aⁿ = a × a × a... (n times)
Therefore, the given expression is written as
=> 3³
Now, based on the power of exponent rule it can be rewritten as,
=> 3 × 3 × 3
Then we have to multiply the values then we get
=> 27
Therefore, the value of 3 raised to 3rd power is 27.
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Complete the square to write each equation in vertex form. Then, state whether the vertex is a minimum or a maximum and give its coordinates.
Answer:
vertex form: y = (x + 3)² + 1 the vertex is minimum coordinates of the vertex: (-3, 1)Step-by-step explanation:
[tex]y=x^2+6x+10\\\\y=x^2+6x+9-9+10\\\\\bold{y=(x+3)^2+1}[/tex]
a = 1 > 0 ← it means the parabla opens up, so, the vertex is minimum
The vertex form is y = a(x - h)² + k, where (h, k) is the vertex
So, from y = (x + 3)² + 1 the vertex is: (-3, 1)
THIS IS KINDA HARD I NEED HELP
Answer:
4
Step-by-step explanation:
Looking at the stem and leaf plot, we have 4 zoos that have less than 18 sloths, with one zoo having 3, one having 16, and two having 17.
Look down below for the question
Answer:
1.centre
2.chord
3.chord
4.radius
5.diameter
BRAINLY ME PLEASE IF HELPFUL!!!
The first equation in the system is graphed below. Graph the linear equation on the coordinate plane and use the Mark Feature tool to place a point at the solution(s) of the system.
Answer:
(0,-7) and (-7,0)
Step-by-step explanation:
Answer:
(4,6) and (-2,6) Then you draw a line between these two points.
Step-by-step explanation:
Just wanna thank everyone on this app for helping me pass my sophomore year bc without y’all i would be in deep sh*t everyone have a great summer and live it up
Answer:
this app is good
Step-by-step explanation:
yah
Can some one help me with this question its hard :( down below ill give brainliest
Answer:
B
Step-by-step explanation:
It's B
First we multiply the coefficients. 6*3= 18, so we can immediately cross out A and D. Now, c^2 * c is c^3. So, its B.
Hope this helps !!
-Ketifa
Step-by-step explanation:
=>6c²*3c=>18c²+¹=>18c³Find the volume of the sphere with 1 inch radius. Round your answer to the nearest tenth. Use 3.14 for Pi.
The volume of the sphere is about______in³.
Answer:
4.16 in^3
Step-by-step explanation:
Given data
Volume of sphere= 4/3πr^3
Radius= 1 inch radius
Substitute
Volume of sphere= 4/3*3.14*1^3
Volume of sphere= 4/3*3.14*1
Volume of sphere= 4*1.04
Volume of sphere= 4.16 in^3
26 °
100°
X=
help anyone ?
Answer:
Step-by-step explanation:
26° + 100°
= 126°
360° - 126°
234°
Kanene wants to know how much wrapping paper she needs to cover this cube. How much wrapping paper does she need?
Find the surface area
Answer:
Step-by-step explanation:
the side length of the cube is not given so i cant answer this
A number increased by 1 2/3 is equal to 8
Answer:
19/3
Step-by-step explanation:
x+1 2/3=8
1 2/3=5/3
x+5/3=8
x=8-5/3
x=24/3-5/3
x=19/3
What is the inverse of the logarithmic function f x log9x?
The inverse of the logarithmic function f x log9x is f-1(x)=9^x.
The inverse of a logarithmic function is the exponential function. To find the inverse of the logarithmic function f x log9x, we can use the following equation: f-1(x)=9^x. This equation states that the inverse of the logarithmic function f x log9x is the exponential function f-1(x)=9^x.
The inverse of the logarithmic function f x log9x is f-1(x)=9^x, which is the exponential function.This means that for any value of x, the inverse of the logarithmic function f x log9x is equal to 9 raised to the power of x. For example, if x=2, then the inverse of the logarithmic function f x log9x is 9^2, or 81. Similarly, if x=3, then the inverse of the logarithmic function f x log9x is 9^3, or 729. In general, the inverse of the logarithmic function f x log9x is 9 raised to the power of x, for any value of x.
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Answer: f –1(x) = 9x
Step-by-step explanation: