The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.
Mutually exclusive events are events that cannot occur at the same time, or that do not have any overlap. In the case of flipping a coin, the possibility of getting a head and the possibility of getting tails are independent of each other, and both can occur simultaneously. Therefore, the chance that you will get heads or tails when you flip a coin once is not mutually exclusive.
On the other hand, the other events listed (B, C, and D) are mutually exclusive. The chance that you will only study for the test alone or with a friend cannot occur simultaneously, as you can either study alone or with a friend, but not both. Similarly, the chance that you will meet your friends for pizza or at a Chinese restaurant for dinner today at 6 cannot occur at the same time, as you can either go to the pizza place or the Chinese restaurant, but not both. And the chance that you will answer the ringing phone or take a walk cannot occur simultaneously, as you can either answer the phone or take a walk, but not both.
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The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.
this question is related to probability.
mutually exclusive
Mutually exclusive events are those events that do not occur at the same time.
For example, when a coin is tossed then the result will be either head or tail, but we cannot get both the results. Such events are also called disjoint events since they do not happen simultaneously.
probability
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
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17/12 × 2/4 × 9/3 50 points full explanation
Step-by-step explanation:
First you simplify the fractions
17/12 × 1/2 × 3
17×1×3=51 and 12×2=24
51/24
Further simplifying after dividing the two numbers by 3 you get
17/8
Answer:
Step-by-step explanation:
If you are looking for an exact form, it will be 17/8
If you are looking for a decimal form, it will be 2.125.
If you are looking for a mixed number form, it will be 2 1/8
I hope this helps.
100 POINT QUESTION
Solve using substitution.
6x − 5y = 10
x − 3y = –20
( _,_ ) (It has to be an ordered pair
Answer:
To solve this system of equations using substitution, we first need to solve one of the equations for one of the variables in terms of the other.
Let's solve the first equation for x:
6x - 5y = 10
x = (10 + 5y)/6
Now let's substitute this expression for x into the second equation:
x - 3y = -20
(10 + 5y)/6 - 3y = -20
10/6 + 5y/6 - 3y = -20
(10/6 - 3y) + (5y/6) = -20
(10 - 3y)/6 + 5y/6 = -20
10/6 - 3y/6 + 5y/6 = -20
(-3y + 5y)/6 = -20
2y/6 = -20
y = -10
Now that we have found the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:
6x - 5y = 10
6x - 5(-10) = 10
6x + 50 = 10
6x = -40
x = -40/6
x = -40/6
x = -6.666666666666667
So the solution to the system of equations is (x, y) = (-6.666666666666667, -10).
The ratio of the lengths of the sides of â–³ABC is 3:4:6. The perimeter of the triangle whose vertices are the midpoints of the sides of â–³ABC is 13 cm. What are the lengths of the sides of â–³ABC?
The length of the sides of triangle ABC are: 6, 8, and 12.
One of the conditions that two triangles are similar is their Three pairs of corresponding sides are proportional.
In the given problem, the ratio of the sides of triangle ABC is 3 : 4 : 6
Another triangle, let's say triangle DEF, is made with its vertices at midpoints of the sides of triangle ABC.
Hence, all three pairs of corresponding sides have the same proportion.
AB/DE = BC/EF = AC/DF = 1/2
Due to similarity, the ratio of the sides of triangle DEF is also 3 : 4 : 6.
ratio f sides : perimeter = 3 : 4 : 6 : 13
Since its perimeter is 13, it means that the length of sides of triangle DEF are: 3, 4, and 6
Length of the sides of triangle ABC = 2 x length of the sides of Δ DEF
Length of the sides of triangle ABC are: 6, 8, and 12.
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The graphs of f and g are given. Use them to evaluate each limit, if it exists. (If an answer does not exist, enter DNE.)
The limits of the functions (a) 1, (b) does not exist (c) 2, (d) does not exist, (e) -4 and (f) 3.
What is Limits?Limit of a function is defined as a value that the function tends to the output for the given input values.
(a) [tex]\lim_{x \to 2} [f(x)+g(x)][/tex] = [tex]\lim_{x \to 2} f(x)[/tex] + [tex]\lim_{x \to 2} g(x)[/tex]
[tex]\lim_{x \to 2} f(x)[/tex] is the value of y when x is approaching 2 from left and right.
[tex]\lim_{x \to 2} f(x)[/tex] = -1
Similarly, [tex]\lim_{x \to 2} g(x)[/tex] = 2
[tex]\lim_{x \to 2} [f(x)+g(x)][/tex] = -1 + 2 = 1
(b) [tex]\lim_{x \to 0} [f(x)-g(x)][/tex] = [tex]\lim_{x \to 0} f(x)[/tex] - [tex]\lim_{x \to 0} g(x)[/tex]
[tex]\lim_{x \to 0} f(x)[/tex] = 2
But [tex]\lim_{x \to 0} g(x)[/tex] does not exist as the function g(x) has different limits 3 and 1 from left and right respectively as x approaches 0.
So [tex]\lim_{x \to 0} [f(x)-g(x)][/tex] does not exist.
(c) [tex]\lim_{x \to -1} [f(x)g(x)][/tex] = [tex]\lim_{x \to -1} f(x)[/tex] × [tex]\lim_{x \to -1} g(x)[/tex]
[tex]\lim_{x \to -1} f(x)[/tex] = 1
[tex]\lim_{x \to -1} g(x)[/tex] = 2
[tex]\lim_{x \to -1} [f(x)g(x)][/tex] = 1 × 2 = 2
(d) [tex]\lim_{x \to 3} [f(x)/g(x)][/tex] = [tex]\lim_{x \to 3} f(x)[/tex] / [tex]\lim_{x \to 3} g(x)[/tex]
[tex]\lim_{x \to 3} f(x)[/tex] = 1
[tex]\lim_{x \to 3} g(x)[/tex] = 0
[tex]\lim_{x \to 3} [f(x)/g(x)][/tex] = 1 / 0, not defined. So does not exist.
(e) [tex]\lim_{x \to 2}[x^{2} f(x)][/tex] = [tex]x^{2} \lim_{x \to 2} f(x)[/tex]
[tex]\lim_{x \to 2} f(x)[/tex] = -1
[tex]\lim_{x \to 2}[x^{2} f(x)][/tex] = (2)² × -1 = -4
(f) f(-1) = 1
[tex]\lim_{x \to -1} g(x)[/tex] = 2
f(-1) + [tex]\lim_{x \to -1} g(x)[/tex] = 1 + 2 = 3
Hence the values of the limits are given.
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Y equals X minus 2X plus Y equals 10
The solution to the given system of equations as given in the task content.is; x = 6 and y = 4.
What is the solution for the given system of equations?It follows that the given system of equations is;
Y equals X minus 2X plus Y equals 10
y = x - 2
x + y = 10
By substituting y into the second equation; we have;
x + x - 2 = 10
2x = 10 + 2
2x = 12
x = 6
Since, y = x - 2;
y = 6 - 2
y = 4.
On this note, it follows that the solution to the system of equations is such that; x = 6 and y = 4.
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Last year Nancy’s annual salary was x dollars. This year she received a raise of y dollars per year. She is paid semimonthly. a. Express her semimonthly salary last year algebraically. b. Express her semimonthly salary this year algebraically. c. On a monthly basis, how much more does Nancy earn as a result of her raise?
Answer:
a. x/24
b. (x+y)/24
c. y/12
Step-by-step explanation:
semimonthly = twice a month or 24 times a year (because 12 months * twice a month = 24 times)
a. as she was paid 24 times a year for x dollars last year,
24 semimonthly payments of d dollars = x
divide both sides by 24 to get d
x / 24 = d dollars per semimonthly payment
b. she is paid x + y dollars this year, so she is paid (x+y)/24 dollars for her semimonthly salary
c. she earns y additional dollars per year. divide by 12 (because 12 months = 1 year) to get one month's worth of additional dollars = y/12 dollars extra per month
A model rocket is launched. The height, in feet, of the rocket h(t) at t (t≥ 0) seconds after
determined by the equation h(t)=-1/2t^2+ 15t. The maximum height of the rocket is 112.5 feet. For how many seconds will the rocket be at a height of more than 100 feet?
The rocket will be at a height more than 100 feet for 10 seconds.
What is Quadratic Equation?Quadratic equations are second degree equations involving a variable of the form [tex]ax^{2} + bx+c = 0[/tex].
We have the equation relating height and time as,
h(t) = -[tex]\frac{1}{2}[/tex] t² + 15 t
When height is 100 feet, equation becomes,
100 = -[tex]\frac{1}{2}[/tex] t² + 15 t
-[tex]\frac{1}{2}[/tex] t² + 15 t - 100 = 0
Multiplying throughout with -2, we get,
t² - 30t + 200 = 0
(t - 10) (t - 20) = 0
t - 10 = 0 or t - 20 = 0
t = 10 or t = 20
When rocket is at maximum height of 112.5 feet,
-[tex]\frac{1}{2}[/tex] t² + 15 t - 112.5 = 0
Multiplying throughout with -2, we get,
t² - 30t + 225 = 0
(t - 15) (t - 15) = 0
t - 15 = 0
t = 15
Hence the rocket reached at a height of 100 feet at t = 10 seconds and after 5 seconds it reached it's maximum height at t = 15 seconds and then the rocket goes down and again reached at a height of 100 m at t = 20 seconds. So the rocket is at height more than 100 m for 10 seconds.
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Molly spent 40% of her savings to pay for a bicycle that cost her $85.
a. How much money was in her savings to begin with?
b. How much money does she have left in her savings after buying
the bicycle?
a. She had in her savings to begin with $212.5
b. She has $127.5 left in her savings after buying the bicycle.
Answer:
a) Molly had $212.50 in her account to begin with.
b) She has $127.50 in her account after buying the bicycle.
Step-by-step explanation:
40% of what number is 85.
.4x = 85 Divide both sides by .4
x = 212.50
212.50 - 85 = 127.50
Another way to look at it is if she spent 40%, she still have 60% left in her account.
.6 x 212.50 = 127.50
two real numbers a and b are chosen independently and uniformly at random in the interval (0,75). let o and Let $O$ and $P$ be two points on the plane with $OP = 200$. Let $Q$ and $R$ be on the same side of line $OP$ such that the degree measures of $\angle POQ$ and $\angle POR$ are $a$ and $b$ respectively, and $\angle OQP$ and $\angle ORP$ are both right angles. The probability that $QR \leq 100$ is equal to $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
The probability that[tex]$QR \leq 100$[/tex] is equal to the ratio of the area of the region in which[tex]$QR \leq 100$[/tex] to the area of the region in which [tex]$0 \leq a \leq 75$ and $0 \leq b \leq 75$[/tex]. Therefore,[tex]$m + n$[/tex] is equal to the area of the region in which [tex]$0 \leq a \leq 75$ and $0 \leq b \leq 75$.[/tex]
The probability that
[tex]$QR \leq 100$[/tex]
is equal to the ratio of the area of the region in which
[tex]$QR \leq 100$[/tex]
to the area of the region in which
[tex]$0 \leq a \leq 75$[/tex]
[tex]$0 \leq b \leq 75$[/tex]
. To find this probability, we first need to find the area of the region in which
[tex]$0 \leq a \leq 75$ and $0 \leq b \leq 75$[/tex]
This region is a rectangle with sides of length[tex]$75$,[/tex] so its area is
[tex]$75^2$[/tex]. To find the area of the region in which
[tex]$QR \leq 100$[/tex],
we need to calculate the area of the triangle in which[tex]$QR$[/tex] is the hypotenuse.
This triangle has base [tex]$75$[/tex]and height [tex]$200$[/tex], so its area is [tex]$3750$[/tex]. Therefore, the desired probability is
[tex]$\frac{3750}{75^2}$, and $m + n[/tex]
[tex]= 75^2$.[/tex]
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If the Q and R are on the same side of the line OP and angle OQP and angle ORP are right triangles then the probability that QR ≤ 100 is 16/25 and the value of m+n is 41 .
The angles OQP and angle ORP are given as right angles that means
∠OQP = ∠ORP = 90° ,
In order to find the required probability we draw a semicircle having the diameter OP and points Q and R on the same side of the semicircle .
given that diameter OP = 200 ,
So , the radius of the circle will be = 100 ,
Let QR = x ≤ 100 , From the figure ,
we can write ,
[tex]OQ = 200 \times Cos(a)[/tex] and [tex]PQ = 200 \times Sin(a)[/tex]
[tex]OR = 200 \times Cos(b)[/tex] and [tex]PR = 200 \times Sin(b)[/tex]
From the figure given below , we can conclude that the quadrilateral OQRP is a cyclic quadrilateral .
So , [tex]200x + (200 Cosa)\times(200 Sinb) = (200 Sina)\times(200 Cosb)[/tex]
we get , [tex]x = |200 Sin(a-b)| \leq 100[/tex] ,
| Sin(a-b)| ≤ 1/2 ;
which implies that |a-b| ≤ 30 ,
that means , -30 ≤ (a-b) ≤ 30 ,
it is given that a and b are chosen independently and uniformly at random in interval (0,75).
which means , 0<a, b <75 .
The Probability that x ≤ 100 is = [tex]\frac{Favorable Area}{Total Area}[/tex]
= [tex]\frac{75\times75-45\times45}{75 \times75}[/tex] = 1 - [tex]\frac{9}{25}[/tex] ,
On simplifying ,
we get
= 16/25 ,
and it is given that the probability is = m/n ,
So on comparing , we get that , m = 16 and n = 25 ,
and the value of m+n = 16+25 = 41 .
Therefore , the probability is 16/25 and the value of m+n is 41 .
The given question is incomplete , the complete question is
Two real numbers a and b are chosen independently and uniformly at random in the interval (0,75). Let O and P be two points on the plane with OP = 200. Let Q and R be on the same side of line OP such that the degree measures of angle POQ and angle POR are a and b respectively, and angle OQP and angle ORP are both right angles. The probability that QR ≤ 100 is equal to m/n , where m and n are relatively prime positive integers. Find m + n.
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Solve both for brainliest and 20 pts!
Answer:
1. c.) x + x + 22. d.) 3x + 3 = 96; (31, 32, 33)Step-by-step explanation:
if it help pls like or CommentsAnswer: C and D respectively
Step-by-step explanation:
To find the sum "n" consecutive even/odd integers you need to do x + (x+2) + (x + 4) ... for n times. You can just add them and solve.
To find the sum of "n" consecutive integers you need to do x + (x + 1) + (x + 2) ... for n times. In this problem we do x + (x + 1) + (x + 2) = 96; 3x +3 = 96; x = 31. Then we can find the other numbers by plugging in 31 for x. 31, 32, 33.
A wrench weighs three times as much as two screwdrivers. What is the weight of each screwdriver, if the wrench weighs 600 grams?
Answer: The weight of each screwdrivers is 100 grams.
Step-by-step explanation: Solution:
Given,
wrench weight= 600 grams
weight of 1 screwdrivers =?
By the question
wrench weighs 3 times as much as 2 screwdrivers
So,
2 screw drivers= 600g÷3
= 200g
1screw drivers = 200g÷2
= 100grams
Therefore, one screwdriver weight is 100 grams.
Đ) Write 28 + 24 as a product of two factors using the GCF and the distributive property. 28 + 24 = ? (?+?)
What is the value of x? Round to the nearest hundredth.
The value of x using trigonometric functions will be 5.66.
What are trigonometric functions?
Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trigonometric functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.
The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant and cosecant can be derived from the primary functions
Now,
In given triangle, 3rd angle will be 54 degree.
(Sum of all angle in triangle=180degree)
Therefore
sin 54=P/H (P=Perpendicular, H=Hypotenuse)
0.809=x/7
x=7*0.809
x=5.66
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a ABCD is a parallelogram and [DB] is one of its diagonals.
Use properties of parallel lines to show that Δs ABD and CDB are congruent.
b What are the consequences of this congruence?
The consequences of this congruence are AB is parallel to CD( property of parallelogram)
∠ABD is congruent to ∠CDB( Angles opposite of equal sides are congruent)
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
We are given that ABCD is a parallelogram and [DB] is one of its diagonals.
In Δs ABD and CDB
The Lines AB and CD are parallel
Therefore Angle B and Angle D are equal ; both angles are equal as they are alternate interior angles.
So An angle is always congruent to itself (Reflexive property of congruence)
Hence, the proved that Δs ABD and CDB are congruent.
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Proportional Tables - Determine if the values in the table are proportional yes or no and explain (show work)
x -12 y -32
x -9 y -24
x -6 y -16
x -3 y -8
Yes, the values in the table form a proportional relationship, with a constant of 8/3.
How to determine if the table represents a proportional relationship?A proportional relationship is a linear function with an intercept of zero modeled as follows:
y = kx.
In which k is the constant of proportionality.
The constant then can be written as follows:
k = y/x.
This means that a data-set will only represent a proportional relationship if the division of y by x is constant for all coordinate pairs in the data-set.
The constant for each pair in the data-set given in the table is calculated as follows:
k = -32/-12 = 2.67.k = -24/-9 = 2.67k = -16/-6 = 2.67.k = -8/-3 = 2.67.As the constant is equal for all coordinate pairs of the data-set, the table in fact represents a proportional relationship.
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Question 4
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Determine where discontinuous.
{
f(x)=
Select one:
O
a. 0; 3
b. 3
C.-3
d. 0; -3
e. 0
O
√=x if x<0
3-x if 0
(3-x)² if x>3
Discontinuous points of the function f(x) occur at x = 0, x = 3, and x = -3.
What is discontinuous?Discontinuous is a term used to describe something that is not continuous. It can refer to physical objects, such as a line that is broken into two or more parts, or to abstract concepts, such as a set of data points that are not evenly spaced or connected. In mathematics, discontinuous functions have jumps or breakpoints where the graph of the function changes abruptly. For example, the graph of a discontinuous function might jump from one value to another, rather than smoothly transitioning between the two values. Discontinuous functions are often used to describe the behavior of certain physical systems, such as electrical circuits and mechanical systems.
At these points, the value of the function f(x) changes abruptly and does not follow the same pattern as other points.
For example, at x = 0, the value changes from 0 to (3-x)², and at x = 3, the value changes from 3 to 0. Similarly, at x = -3,
the value changes from -3 to 0. Thus, the discontinuous points of the function f(x) are 0, 3, and -3.
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PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
Answer:
Part A: From the table, it is clear that as the number of workers increases, the number of units produced also increases. This indicates a positive correlation between the number of workers and the number of units produced. As the number of workers increases by 10, the number of units produced also increases by 50. This pattern is consistent throughout the data, which supports the conclusion that there is a positive correlation between the number of workers and the number of units produced.
Part B: A function that best fits the data is y = 5x + 2, where y is the number of units produced and x is the number of workers. This function can be determined by using the slope-intercept form of a linear equation (y = mx + b) and substituting the values for the slope and y-intercept from the data. The slope (m) of the function is 5 and the y-intercept (b) is 2.
Part C: The slope of the plot (5) represents the rate of change in the number of units produced for every 1 unit change in the number of workers. In this case, for every 1 additional worker, the number of units produced increases by 5. The y-intercept (2) represents the point at which the line intercepts the y-axis when x = 0. In this case, when there are no workers, 2 units are produced.
2
Drag each expression to the correct location on the table.
Simplify each exponential expression using the properties of exponents and match it to the correct answer.
(2-3-2)(5-32)2
(3-2)(5-2)2
2
(3³) (40)² (3-2)-³(2²)
Reset
1
(37-47)(2-5) (52)
127-5-1-2-4
Next
(2-3) ¹.20
(2-3) ¹
1|2
The completed table that indicates the values of the specified exponential expressions is presented as follows;
[tex]\begin{array}{|c|c|cc|}\\2&1&\dfrac{1}{2} &\\&&&\\\dfrac{\left(3^7\cdot 4^7\right)\cdot \left(2\cdot 5\right)^{-3}\cdot \left(5^2\right)}{12^7\cdot 5^{-1}\cdot 2^{-4}} &\dfrac{\left(2\cdot 3\right)^{-1}\cdot 2^0}{\left(2\cdot 3\right)^{-1}} &\left(3^3\right)\cdot \left(4^0\right)^2\cdot \left(3\cdot 2\right)^{-3}\cdot \left(2^2\right) &\\ &&& \\&\dfrac{\left(2\cdot 3^{-2}\right)^3\cdot \left(5\cdot 3^2\right)^2}{\left(3^{-2}\right)\cdot \left(5\cdot 2\right)^2} & & \\\end{vmatrix}[/tex]
What is an exponential expression?An exponential expression is a mathematical expression that consists of numbers and or variables that have index of numbers and or variables, validly combined together using mathematical operators.
The exponential expressions are;
First expression;
[tex]\dfrac{\left(2\cdot 3^{-2}\right)^3 \times \left(5\cdot 3^2\right)^2}{\left(3^{-2}\right)\cdot \left(5\cdot 2\right)^2}[/tex] = (2³ × 3⁻⁶) × (5² × 3⁴) ÷ ((3⁻²) × (5 × 2)²)
(2² × 3⁻⁶) × (5² × 3⁴) ÷ ((3⁻²) × (5² × 2²)) = 2⁽²⁻²⁾ × 3⁽⁻⁶⁺²⁺⁴⁾ × 5⁽²⁻²⁾
2⁽²⁻²⁾ × 3⁽⁻⁶⁺²⁺⁴⁾ × 5⁽²⁻²⁾ = 2⁰ × 3⁰ × 5⁰ = 1
Second expression;
(3³)×(4⁰)²×(3×2)⁻³(2²) = 3⁽³⁻³⁾ × (4⁰)² × 2⁽² ⁻ ³⁾ = 3⁰ × 4⁰ × 2⁻¹ = 1/2
(3³)×(4⁰)²×(3×2)⁻³(2²) = 1/2
Third expression;
(3⁷·4⁷) × (2·5)⁻³ × (5²) ÷ (12⁷ × 5⁻¹ × 2⁻⁴)
(3⁷·4⁷) × (2·5)⁻³ × (5²) ÷ (12⁷ × 5⁻¹ × 2⁻⁴) = (3×4)⁷ × (2⁽⁻³ ⁺ ⁴⁾) × 5⁽⁻³⁺¹⁺²⁾ ÷ 12⁷
12⁽⁷⁻⁷⁾ × (2⁽⁻³ ⁺ ⁴⁾) × 5⁽⁻³⁺¹⁺²⁾ = 12⁰ × 2 × 5⁰ = 2
Therefore;
(3⁷·4⁷) × (2·5)⁻³ × (5²) ÷ (12⁷ × 5⁻¹ × 2⁻⁴) = 2
Fourth expression;
(2·3)⁻¹ × 2⁰ ÷ (2 × 3)⁻¹
2⁽⁻¹⁺¹⁾ × 3⁽⁻¹⁺¹⁾ × 2⁰ = 2⁰ × 3⁰ × 2⁰ = 1 × 1 × 1 = 1
(2·3)⁻¹ × 2⁰ ÷ (2 × 3)⁻¹ = 1
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What is the period of the sinusoidal function?
The period of the sinusoidal function is 4 s
What is period of a sinusoidal function?The period of a sinusoidal function is the time it takes for the sinusoidal function to complete one cycle of revolution.
How to find the period of the given sinusoidal function?To find the period of the given sinusoidal function, we observe the graph. The period is the time at which the graph completes one cycle. Now, since the graph passes through the origin at x = 0 and completes one cycle at x = 4. So, the complete cycle is from x = 0 to x = 4.
Thus the period of the function is 4 s
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The air pressure reading from a barometer is 742mm Hg. Express this reading in kilopascals, KPa. (use 760mm Hg=1.013 X 10^5 Pa)
Answer:
Below
Step-by-step explanation:
742 mm / ( 760 mm / 1.013 x 10^5 Pa) = 9.89 x 10^4 Pa
The measure of central angle XYZ is 1.25m radians.
8
N
What is the area of the shaded sector?
O 10# units²
O20m units²
40 units²
80 units²
The measure of the given angle is given as 1.25 π radian the measure of the shaded portion is 40 π radian
How to find the shaded portion in the figureThe given figure is a circle to find the shaded portion we use the formula for area of sector in radian
Area of sector = (1/2) × r²θ
1.25 π radian = θ
8 = radius, r
Area of sector = (1 / 2) × 8² * 1.25 π radian
Area of sector = (1 / 2) × 64 * 1.25 π radian
Area of sector = (1 / 2) × 80 π radian
Area of sector = 40 π radian
The area of the sector the shaded portion is 40 π radian
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Sara Averett's previous savings account balance was $74,561.49 with $1,017.98 in interest, deposits of
$918.37 and $944.56, and withdrawals of $959.40 and $14,391.47. What is her new balance?
Answer:
$62091.53
Step-by-step explanation:
Their starting money was 74561.49, so we add that with the interest she gained and her deposits. That comes out to 77442.40. Then we subtract her two withdrawals, and we get to $62,091.53.
I’ll give BRAINLIEST if correct
Answer:
y < 4
Step-by-step explanation:
the broken horizontal line y = 4 means that y cannot equal 4
The shaded area below the line represents the solution, which is
y < 4
The correct answer is y<4.
Recall that the horizontal line has an equation of the type y=b, where b is the perpendicular distance from the x-axis. As the shaded region is below the line y=4, the inequality representing the region is y<4.
Due to the earth's rotatDue to the earth's rotation, a person would be traveling faster at the equator than they would at a position halfway from the equator to the North Pole.ion, a person would be traveling faster at the equator than they would at a position halfway from the equator to the North Pole.
Due to the earth's rotation, a person would be traveling faster at the equator than they would at a position halfway from the equator to the North Pole. This is true.
What is rotation of the Earth?The rotation of the planet Earth around its own axis and variations in the orientation of the rotation axis in space are referred to as Earth's rotation or Earth's spin. Earth rotates progradely in an easterly direction. The Earth rotates counter-clockwise when viewed from the northern polar star Polaris.
We cross the line separating day from night every day because the Earth is perpetually rotating. The length of our shadows is yet another pattern brought on by the Earth's rotation.
The circumference of the Earth is largest at the equator because of how the rotation of the Earth causes it to bulge there. In comparison to a location closer to the poles, the equator requires a person to travel a greater distance in a given amount of time. A person at the equator would therefore move more quickly than someone farther from the poles.
In conclusion, it is true.
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Due to the earth's rotation, a person would be traveling faster at the equator than they would at a position halfway from the equator to the North Pole.
True or false?
Please Help! 100 Points!
Answer:
Step-by-step explanation:
A cat runs a mile every two minutes squirrel runs a mile every five minutes a cat and a squirrel start together running around a 1 mile track how long will it take before they meet at the starting point
The cat and the squirrel will meet again at the finish line after 10 minutes.
How to calculate how long it takes for both animals to meet again at the goal?To calculate how long it takes for both animals to meet again at the goal, we must identify the useful information to solve this problem, the information is presented below.
The cat runs 1 mile/2 minutesThe squirrel runs 1 mile/5 minutesAccording to the above, we must find a number that when divided by 5 and 2 gives us an integer. For example, 10 divided by 2 would give 5, that is, the cat would turn 2 times in this time. If we divide 10 into 2, they would give us 5, which means that the squirrel would go around 5 times in this time. So the answer would be 10 minutes.
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A phone is on sale: 30% off! The phone now costs £128. How much did the phone cost before the sale?
Answer:
If the phone is on sale for 30% off, this means the phone has had 30% of its original price taken off to arrive at the new price of £128. To find the original price of the phone, we can use the equation:
Original price = Sale price / (1 - Discount percentage)
In this case:
Original price = 128 / (1 - 0.30)
When we calculate this we get:
Original price = 128 / 0.7
Original price = £183.33
So the phone cost £183.33 before the sale.
What is the Factored Form of 7d^6 + 8g^12
Using factorization, the algebraic expression 27d⁶ + 8g¹² is equal to (3d² + 2g⁴)(9d⁴ - 6d²g⁴ + 4g⁸)
What is FactorizationFactorization, also known as factoring, is the process of breaking down a number or an algebraic expression into its prime factors. It is a mathematical process that helps to simplify complex algebraic equations and it is used in a variety of mathematical applications, including algebra, calculus, and number theory.
In this problem, we have an expression in which can be factored to produce two smaller expressions.
27d⁶ + 8g¹² = (3d² + 2g⁴)(9d⁴ - 6d²g⁴ + 4g⁸)
The expression 27d⁶ + 8g¹² is equal to (3d² + 2g⁴)(9d⁴ - 6d²g⁴ + 4g⁸)
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please help meeeeeeee!!!!!
The mathematical result applied to prove sin²Ф + cos² = 1 , is the Pythagorean theorem.
Define the term Pythagorean theorem?Any right triangle has an area equal to the sum of a sides of the squares which sides are the two legs (remember, the hypotenuse is the side opposite the right angle).
Consider the given triangle ABC, right angled at C.
Then,
AC² + BC² = AB²
Divide the equation by AB².
AC²/ AB² + BC²/ AB² = AB²/ AB²
(opposite/ hypotenuse)² + (adjacent/ hypotenuse)² = 1
Thus,
sin²Ф = (opposite/ hypotenuse)²
cos² = (adjacent/ hypotenuse)²
Then,
sin²Ф + cos² = 1
Thus, the mathematical result applied to prove sin²Ф + cos² = 1 , is the Pythagorean theorem.
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C-14 = 33 what is c
Answer:
[tex]c=47[/tex]
Step-by-step explanation:
[tex]c-14=33[/tex]
Step 1: Add 14 to both sides.
[tex]c-14+14=33+14[/tex]
[tex]c=47[/tex]
