Answer:
[tex]84n-27[/tex]
Step-by-step explanation:
[tex]-9(1-10n) -2(3n+9)[/tex]
[tex]-9+90n-6n-18[/tex]
[tex]{84n-27}[/tex]
The spinner is divided into 8 equal sections.
a. If the arrow lands on a number, what is the probability that it will land on 3 ?
The probability for the arrow that land in the number 3 is 1/8.
Probability:
Basically, the word probability means the possibility of occurring the required event.
Given,
The spinner is divided into 8 equal sections.
Here we need to find if the arrow lands on a number, what is the probability that it will land on 3.
Let us consider that the spinner has 8 equal-sized sections numbered 1 to 8.
Since the sections have equal size, each section is equally probable.
The probability of falling on each section is therefore 1/8.
We know that, in the 8 sections,
There is only one 3 in this list.
So, the possibility of the event = 1
Hence, probability is
=> 1/8
Therefore, the probability for the arrow that land in the number 3 is 1/8.
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What is the common ratio of the geometric sequence below?
18, −6, 2, - —–—‚ ...
OA.
113
OB. -3
OC.--1/3
OD. 3
Determine whether the events are mutually exclusive or not mutually exclusive. Then find the probability. Round to the nearest tenth of a percent, if necessary.
tossing a coin and getting heads or tails
According to the question, to calculate the probability of the event which states that tossing a coin to get either head or tail
The total number of a coin is [tex]1[/tex]
And total number of possibilities are {H,T}
Therefore, the total number of favorable outcomes in which either head or tail can come: [tex]1[/tex]
As per question, the probability can be written as:
P(h or t) = P(h) + P(t)
[tex]= \frac{1}{2} +\frac{1}{2} =1 = 100%[/tex]
Hence, the probability of getting either head or tail is [tex]1[/tex].
The given event is mutually exclusive because it has [tex]100[/tex] percent which is close to tenth of a percent. And these two events cannot happen at the same time also, so they are mutually exclusive.
What are mutually exclusive events?
Mutually exclusive events are those events which cannot happen at the same time. For instance, in any event nobody can run forward or backward together at the same time.
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a. What is an equation of the circle for a circular irrigation field that has radius 12 and center (7,-10) ?
The equation of the circle for a circular irrigation field with radius 12 and center at (7 , -10) is (x - 7)^2 + (y + 10)^2 = 144.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circular irrigation field, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (7 , -10)
r = 12
(x - 7)^2 + (y - -10)^2 = 12^2
(x - 7)^2 + (y + 10)^2 = 144
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If h = 7, what is ✓-27 + 4h?
suppose that Angle Hik and Angle LIJ are verticle angles. find their measures if the following conditions apply. Question 2...
=========================================================
Explanation:
Vertical angles are always congruent.
Set the two expressions equal to one another and solve for x.
6x - 6 = 3(x+6)
6x - 6 = 3x + 18
6x - 3x = 18 + 6
3x = 24
x = 24/3
x = 8
Then use this x value to find each angle
angle HIK = 6x - 6 = 6*8 - 6 = 42angle LIJ = 3(x+6) = 3*(8+6) = 42Both angles are 42 degrees each to confirm the answer.
Determine whether the given conclusion is based on inductive or deductive reasoning.
Andrew's mom makes spaghetti for dinner on Mondays. Today is Monday. He concludes that his mom will make spaghetti for dinner.
Inductive reasoning is a bottom-up technique, whereas deductive reasoning is a top-down approach. The given conclusion is deductive reasoning.
What are Inductive reasoning and Deductive Reasoning?Inductive reasoning is a bottom-up technique, whereas deductive reasoning is a top-down approach. Inductive thinking proceeds from the particular to the universal, whereas deductive reasoning proceeds from general premises to specific conclusions.
Given the statements,
Andrew's mom makes spaghetti for dinner on Mondays. Today is Monday. He concludes that his mom will make spaghetti for dinner.From the given sentences, the first sentence is a general statement, the second statement is a specific statement. And, at the last, the third statement is a conclusion statement.
Hence, the given conclusion is deductive reasoning.
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Alex and ben share £520 in the ratio 1: 3 what fraction of the £520 does ben receive
Ben will receive £390
How to calculate the fraction that will be received ?
Alex and Ben share £520
They share this money in the ratio 1:3
The fraction of this amount that Ben will receive can be calculated as follows
1 + 3
= 4x
4x= 520
x= 520/4
x= 130
Ben Fraction= 130 × 3
= 390
Hence Ben's fraction of the money is £390
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HELP ASP SHOW UR WORK YOULL GET BRAINILEST IF UR CORRECT
Answer:
x = 5
Step-by-step explanation:
[tex]12x = 70 - 2x[/tex]
[tex]14x = 70[/tex]
[tex]x = 5[/tex]
Answer:
Here :))
Step-by-step explanation:
add.
5 3/4 + (-1/4) =
-2/3 + 1/6 =
-8/5 + (-3/4) =
will give brainliest !
Exercise 1
5 3/4 + (-1/4)
Multiply 5 and 4 to get 20.
20 + 3/4 - 1/4
Add 20 and 3 to get 23.
23/4 - 1/4
Since the fractions 23/4 and 1/4 have the same denominator, subtract their numerators to subtract them.
23 - 1/4
Subtract 1 from 23 to get 22.
22/4
Reduce the fraction 22/4 to its lowest expression by extracting and canceling 3.
11/4
Exercise 2
-2/3 + 1/6
Convert -2/3 and 1/6 to fractions with like denominators.
- 2×2/3 × 2 + 1/6
Simplify
-4/6 + 1/6
Since -4/6 and 1/6 have the same denominator, add their numerators to add them together.
-4 + 1/6
Add −4 and 1 to get −3.
-3/6
Reduce the fraction -3/6 to its lowest expression by extracting and canceling 3.
-1/2
Exercise 3
-8/5 + (-3/4)
Convert -8/5 and 3/4 to fractions with like denominators.
-32/20 - 15/20
Since -32/20 and 15/20 have the same denominator, subtract their numerators to subtract them.
-32 - 15/20
Subtract 15 from −32 to get −47.
-47/20
Michael Spymore
A room is (……) feet wide and 16 feet long.
Find the area of the room
A storage tank will have a circular base of radius r and a height of r . The tank can be either cylindrical or hemispherical (half a sphere).
a. Write and simplify an expression for the ratio of the volume of the hemispherical tank to its surface area (including the base). For a sphere, V=4/3πr³ and SA=4πr²
The ratio of the volume of the hemispherical tank to its surface area is, V/A = 2r/9.
What is meant by TSA?A three-dimensional object's total surface area exists the whole area of all of its external surfaces.
Let r be the radius of the circle and h be the height
To find volume of the hemispherical tank and its surface area.
Here,
TSA = Total Surface Area
CSA = Curved Surface Area
Volume of a hemisphere (V) = (2/3) πr³
TSA of the hemispherical tank(A) = CSA of the tank + CSA of the base.
TSA(A) = 2πr² + πr² = 3πr²
The ratio of the volume of the hemispherical tank to its surface area is,
V/A = (2/3)πr³ / 3πr²
V/A = 2r/9
Therefore, the ratio of the volume of the hemispherical tank to its surface area is, V/A = 2r/9.
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Solve 1/2 + 5/8 and simplify as mixed numbers
Answer:
9/8 = 1 1/8
Step-by-step explanation:
داند
14) The weight of Callie's backpack is 2 ½ times the weight of Carl's backpack. If
Carl's backpack weighs 3 pounds, how much does Callie's backpack weigh?
The weight of Callie's backpack is 7½ pounds which is calculated by multiplication of the number of times the bag is heavier with the weight of the bag.
Multiplication or product of two constants is defined as the number of times a particular constant is added . If we want to multiply a and b then their product is equal to b times a added.
a+a+a+a....... b times=ab
The multiplication is one of the four basic arithmetic operations that are used in mathematics and everyday lives.
Given the weight of Callie's bag is 2 ½ times the weight of Carl's backpack.
Therefore to calculate the the weight of Callie's backpack we multiply the weight of Carl's backpack with 2 ½.
Weight of Carl's backpack=3 pounds
Therefore weight of Callie's backpack= 2 ½×3 pounds= 7½ pounds
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f(x)=x² + 3
Which answer pairs a possible domain restriction that if placed upon f(x) would impact f¹(x) as shown?
f(x) domain: x ≥ 3
f-¹(x) domain: x ≥ 3
f(x) domain: x≥3
f-¹(x) range: y ≥ 3
f(x) domain: x ≥ 0
f-¹(x) domain: x ≥0
f(x) domain: x ≥ 0
f-¹(x) range: y ≥ 0
The restriction will be f-¹(x) range: y ≥ 0
Domain of a function:
The domain of a function refers to the set of all possible inputs for the function. For example, we get that the domain of f(x) = x² is all real numbers, and the domain of g (x) = 1 / x is all real numbers except for x = 0( as it will make the function indefinite.) Some special functions can also be defined whose domain are limited.
Range of a function:
The range of a function refers to the complete set of all possible resulting values of the dependent variable, after we have substituted the domain.
So, the restriction will be f-¹(x) range: y ≥ 0 as x² will always be positive.
Therefore, the restriction will be f-¹(x) range: y ≥ 0.
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If x2+y2 = 12 and x2-y2=18, what is the value of x4-y4?
Answer:
Step-by-step explanation: add the equations
2x² = 30
x² = 15
y² = 12 - 15
= -3
x4 -y4 = 15² - (-3)²
= 216
Determine the next 2 terms if it is a geometric sequence, then write a recursive definition that matches the sequence in the form f(1)=120,f(n)=_*f(n-1) for n>2
The next 2 terms if it is a geometric sequence is 360 and 480.
What's a geometric sequence ?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant. where r is the common ratio between successive terms.
Given:
The sequence in the form
[tex]f_{1} =120,[/tex]
[tex]f_{n} =f_{n-1}[/tex] for n>2
According to given question we have
[tex]f_{1} =120,[/tex]
The formula would be:
[tex]f_{n} =f_{n-1}+f_{1}[/tex] for n>2
[tex]f_{2} =f_{2-1}+f_{1} =f_{1}+f_{1} =240\\\\f_{3} =f_{3-1}+f_{1} =f_{2}+f_{1} =240+120=360\\\\f_{4} =f_{4-1}+f_{1} =f_{3}+f_{1} =360+120=480\\[/tex]
Therefore, the next 2 terms if it is a geometric sequence is 360 and 480.
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Solve each equation. Check each solution. 2x / 3 - 1/2 = 2x + 5/6
The solution to given equation 2x / 3 - 1/2 = 2x + 5/6 is x = -1
In this question, we have been given an equation.
2x / 3 - 1/2 = 2x + 5/6
We need to find the solution of given equation.
⇒ 2x / 3 - 1/2 = 2x + 5/6
⇒ (4x - 3)/6 = (12x + 5)/6
⇒ 4x - 3 = 12x + 5
⇒ 4x - 12x = 5 + 3
⇒ -8x = 8
⇒ x = -1
We need to check above solution.
so, substitute x = -1 in LHS of given equation.
LHS
= 2(-1) / 3 - 1/2
= -2/3 - 1/2
= -(2/3 + 1/2)
= -[(4 + 3)/6]
= -7/6
Now, substitute x = -1 in RHS of given equation.
RHS
= 2(-1) + 5/6
= -2 + 5/6
= (-12 + 5)/6
= -7/6
For x = -1, LHS = RHS
Therefore, the solution to given equation 2x / 3 - 1/2 = 2x + 5/6 is x = -1
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Which one of the following is testable?
A) science
B) pseudoscience
Answer: science
Step-by-step explanation:
Stella is going to a carnival that has games and rides. Each game costs $2.50 and each ride costs $4. Stella spent $52.50 altogether at the carnival and the number of rides she went on is twice the number of games she played. Write a system of equations that could be used to determine the number of games Stella played and the number of rides Stella went on. Define the variables that you use to write the system.
Answer:
Let r be the number of rides and g be the number of games.
2.50g + 4.00r = 52.50
r = 2g
The equations are 2.5g +4r = 52.5 and g=2r.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Cost of game = $2.50
Cost of ride = $4
let g be the number of games
and, let r be the number of rides taken
total they played = $52.50
So, the equation can be
2.5g +4r = 52.5
and, number of rides she went on is twice the number of games she played.
So, g = 2r
Hence, The equations are 2.5g +4r = 52.5 and g=2r.
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Find the zeros of the function. Enter the solutions from least to greatest.
f(x) = (x + 2)^2 - 16
Answer:
x = 2, x = -6
Step-by-step explanation:
Given quadratic function in vertex form:
[tex]f(x)=(x+2)^2-16[/tex]
The zeros of a function occur when f(x) = 0:
[tex]\implies (x + 2)^2 - 16 = 0[/tex]
Add 16 to both sides:
[tex]\implies (x + 2)^2 - 16+16 = 0+16[/tex]
[tex]\implies (x + 2)^2 =16[/tex]
Square root both sides:
[tex]\implies \sqrt{ (x + 2)^2} =\sqrt{16}[/tex]
[tex]\implies x+2= \pm 4[/tex]
Subtract 2 from both sides:
[tex]\implies x+2-2= -2 \pm 4[/tex]
[tex]\implies x= -2 \pm 4[/tex]
Therefore:
[tex]\implies x=-2+4=2[/tex]
[tex]\implies x=-2-4=-6[/tex]
The zeros of the given quadratic function are x = 2, x = -6.
10-2 (2x+1) = 4 (x-2)
x=2
10-2(2x+1)=4(x-2)
10-4x-2=4x-8
10-2=8x-8
8=8x-8
16=8x
2=x
Answer:
X = 2
Step-by-step explanation:
[tex] \sf \: First, solve \: the \: brackets. [/tex]
[tex] \sf \: 10 - 2(2x + 1) = 4(x - 2) \\ \sf10 - 4x - 2 = 4x - 8 \: \: \: \: \: \: \: [/tex]
[tex] \sf \: Combine \: like \: terms .[/tex]
[tex] \sf8 - 4x = 4x - 8[/tex]
[tex] \sf \: Subtract \: 4x \: from \: both \: sides \: to \: remove \: 4x.[/tex]
[tex] \sf \: 8 - 4x - 4x = 4x - 8 - 4x \\ \sf8 - 8x = - 8[/tex]
[tex] \sf \: Subtract \: 8 \: from \: both \: sides \: to \: remove \: 8.[/tex]
[tex] \sf8 - 8 - 8x = - 8 - 8 \\ \sf - 8x = - 16[/tex]
[tex] \sf \: Divide \: both \: sides \: by \: -8.[/tex]
[tex] \sf \: x = 2[/tex]
Tamika has a points card for a movie theater.
She receives 20 rewards points just for signing up.
She earns 10.5 points for each visit to the movie theater.
She needs 167 points for a free movie ticket.
Write and solve an equation which can be used to determine xx, the number of visits Tamika must make to earn a free movie ticket.
Tamika's number of visits required to earn a free movie ticket is 14 visits.
What is meant by a linear equation with only one variable?A linear equation for one variable has only one solution and therefore is expressed as ax+b = 0, where a and b are two integers and x is a variable.For example, 2x+23=18 is a linear equation with the a single variable.According to the question, the given data is;
Tamika has a points card for a movie theatre which are as follow;
Signup rewards = 20 points
Each visit reward = 10.5
Total points needed = 167
Let 'x' be the number of visits.
Total points earned for x number of visits: 10.5x.
Thus, the equation according to statement;
20 + (10.5 × x) = 167
10.5x = 167 - 20
10.5x = 147
x = 147/10.5
x = 14 visits.
Therefore, Tamika's number of visits required to earn a free movie ticket are 14 visits.
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which picture has an area equivalent to 8/12 shaded?
Answer:
B)1/3 + 1/3 = 2/3 or 8/12Step-by-step explanation:
semplify
8/12 = 2/3
B)
1/3 + 1/3 = 2/3
How many times will the graph of y=x^2+3 interest the x-axis?
Evaluate |2x+y-3z| for x=-2, y=10, and z=3.
Answer:
|2x + y - 3z|
Plug in the values
|-4 + 10 - 9|
= |-3|
= 3
Step-by-step explanation:
the answer is (3) because when all the letters are turned into numbers then solved it becomes [-4+10+(-9)] then you have to turn it into a positive because of the lines.
PLEASE PLEASE HELP QUICK
Which relation is displayed in the graph?
Answer:
First option A
Step-by-step explanation:
Solved this by looking at the points of the graph from left to right. (-3,-2) is the first being the furthest left then so on.
Points that are on the same line are collinear. Use the definition of slope to determine whether the given points are collinear.
(3,-5),(-3,3),(0,2)
Using the definition of slope, the points (3 , -5), (-3 , 3), and (0 , 2) are not collinear.
Three or more points are said to be collinear if they lie on a single straight line.
To determine whether the given points are collinear, use the definition of slope. The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.
m = (y2 - y1)/(x2 - x1)
Getting the slope of each pair of points:
(3 , -5) and (-3 , 3)
m = (y2 - y1)/(x2 - x1)
m = (3 - -5)/(-3 - 3)
m = 8/-6
m = -4/3
(-3 , 3) and (0 , 2)
m = (y2 - y1)/(x2 - x1)
m = (2 - 3)/(0 - -3)
m = -1/3
(3 , -5) and (0 , 2)
m = (y2 - y1)/(x2 - x1)
m = (2 - -5)/(0 - 3)
m = 7/-3
m = -7/3
Since collinear points lies on the same line, the slope of any pair of points should be the same. Since the slopes of each pair of points is not equal with each other, then they are not collinear.
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Given mn, find the value of x. Xº 154°
Answer: 154º
Step-by-step explanation: vertically opposite angles => xº = 154º
Divide the quantity 1.365 times ten raised to the eighteenth power end quantity divided by the quantity 9.1 times ten raised to the eighth power end quantity.. write the final answer in scientific notation. 0.15 x 1010 1.5 x 109 0.15 x 1026 1.5 x 1010
The division will give a value of 0.15 × 10^10.
How to calculate the value?The information is to divide the quantity 1.365 times ten raised to the eighteenth power end quantity divided by the quantity 9.1 times ten raised to the eighth power end quantity.
This will be:
(1.365 × 10^18) / (9.1 × 10^8)
= 1.365/9.1 × 10^10
= 0.15 × 10^10
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