0.25 is the probability a bean bag lands closer to the center of the circle than to the edge of the circle.
What is the probability in simple terms?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.Let the radius of the circle be r.
Now the distsnce of the edge of the circle from the center is r units.
Now for any point lying in the circle, the sum of the distance of that point
from the center and from the nearest edge of the circle is r.
Thus, the bag will land closer to the circle if it lies within r/2 distance from the center.
Now, the area of the inner circle with radius r/2 is = [tex]\pi (\frac{r}{2})^{2} = \pi \frac{r^{2} }{4}[/tex]
The area of the actual circle = πr²
Thus, the bean bag will land closer to the center if it lies within the inner circle of area = π r²/4
Hence, the required probability = [tex]\pi r^{2} /4/ \pi r^{2}[/tex] = 1/4 = 0.25
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Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified term number. 5000+1000+200+. . . . . . ; n=5
The given series is geometric series. The sum of its first 5 terms is 6248.
To determine whether the series is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.
If it is an arithmetic series, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric series, then:
a(n) = a(n-1) . r
where r is the common ratio.
The given series is:
5000 + 1000 + 200 +. . . .
and the number of terms is 5.
In the given series:
a(1) = 5000
a(2) = 1000
a(3) = 200
Notice that
a(2)/a(1) = 1000/5000 = 0.2
a(3)/a(2) = 200/1000 = 0.2
Since the ratio of consecutive terms are constant, then the given series is a geometric series. Furthermore, its ratio, r = 0.2
Sum formula for the first n term of a geometric series is:
S(n) = a(1) . (1 - rⁿ)/(1 -r)
Substitute n = 5, a(1) = 5000, and r = 0.2
S(5) = 5000 . (1 - (0.2)⁵)/(1 - 0.2)
S(5) = 5000. (0.99968) / 0.8
= 6248
Since the number of terms is not much we can also evaluate the sum directly. Write all the terms until n = 5.
a(4) = 200 . (0.2) = 40
a(5) = 40 . (0.2) = 8
Hence, the series is:
5000+1000+200+40+8 = 6248.
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Which of the following numbers is between -3/4 and 5/8
-1
-1/2
7/8
0.9
Answer:
7/8 if you divide you will get your answer
two non-zero real numbers, a and b, satisfy ab=a-b. Find a possible value of [tex]a/b +b/a -ab[/tex]
100 points
Answer:
2
Step-by-step explanation:
Given equations:
[tex]\begin{cases}ab=a-b\\\\\dfrac{a}{b}+\dfrac{b}{a}-ab\end{cases}[/tex]
Rewrite the second equation as a rational expression:
[tex]\begin{aligned}\implies \dfrac{a}{b}+\dfrac{b}{a}-ab & = \dfrac{a}{b} \cdot \dfrac{a}{a}+\dfrac{b}{a} \cdot \dfrac{b}{b}-ab\cdot \dfrac{ab}{ab} \\\\&=\dfrac{a^2}{ab}+\dfrac{b^2}{ab}-\dfrac{(ab)^2}{ab}\\\\&=\dfrac{a^2+b^2-(ab)^2}{ab}\\\\\end{aligned}[/tex]
Substitute the first equation [tex]ab=a-b[/tex] into the rational expression:
[tex]\begin{aligned}\implies \dfrac{a^2+b^2-(a-b)^2}{ab}&=\dfrac{a^2+b^2-(a^2-2ab+b^2)}{ab}\\\\&=\dfrac{a^2+b^2-a^2+2ab-b^2}{ab}\\\\&=\dfrac{2ab}{ab}\\\\&=2\end{aligned}[/tex]
Therefore, the possible value of the given expression is 2.
An equilateral triangle has
sides of 4x + 10. Write an
expression for the perimeter of
the triangle.
Determine the value of x when the perimeter is 42.
Answer:
x = 1 if the perimeter is 42
Step-by-step explanation:
Given
s = 4x + 10
when Perimeter = 42, what is x?
Solution
Perimeter = 3s
Perimeter = 3(4x +10) Remove the brackets
Perimeter = 12x + 30
Let the Perimeter = 42
42 = 12x + 30 Subtract 30 from both sides
42-30 = 12x + 30-30 Combine
12 = 12x Divide by 12
12/12 = 12x/12
x = 1
Expand and simplify (2x+5) (2x-5) (3x+7)
Answer:
yall i tried
Step-by-step explanation:
bring it to the formula first then gotta multiply
LCM of 21, 56
I really need help it’s due today
Answer: the answer is 168
Divide. State any restrictions on the variables.
3 y-12 / 2y+4 ÷ 6y-24 / 8+4 y
The restrictions on the variables x and y of the equation
(3y-12)/(2y+4) ÷ (6y-24)/(8+4y) be y ≠ 4 and y ≠ -2
What is meant by expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure exists as pursues: Expression: (Math Operator, Number/Variable, Math Operator)
Let the equation be (3y-12)/(2y+4) ÷ (6y-24)/(8+4y)
simplifying the equation, we get
(3y-12)/(2y+4) × (8+4y)/(6y-24)
⇒ (3y-12)/(2y+4) × 2(4+2y)/2(3y-12)
⇒ 2/2 = 1
What are the restrictions on the variables?If y = 4 ⇒ denominator (6 × 4 - 24) = 0 = ∞
Similarly, If y = -2 ⇒ denominator ((2 × -2) + 4) =0 = ∞
So, y ≠ 4, y ≠ -2
How to find restrictions on the variables?
The denominator determines the restrictions of a rational expression's domain.Find those limitations without regard to the numerator.Set the denominator to 0 and solve the provided expression to discover the domain restrictions.To learn more about restrictions on the variables, refer:
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If a student picked is 10 years old, what
are the chances that they skip breakfast?
Answer:
There are 29% chance that they will skip their breakfast
Step-by-step explanation:
40 / 14 x 10 = the percentage of the kid skipping his breakfast
40 / 14 x 10 = 28.5%
28.5 = (rounded off) = 29%
The kid has a 29% chance of skipping the breakfast
Write an equation of the line through the pair of points in slope-intercept form. (Lesson 3-4 )
(-1,8) and (5,-4)
y = -2x + 6 is the equation of the line in slope-intercept form passing through points (-1 , 8) and (5 , -4).
An equation of a line in slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept.
Given two points passed through by the line, you can use them to write the equation of the line in slope-intercept form.
1. Find the slope of the line using the two given points.
let Point 1(-1 , 8) and Point 2(5 , -4)
slope = m = (y2 - y1) / (x2 -x1)
m = (-4 - 8) / (5 - -1)
m = -12 / 6
m = -2
2. Use the value of the slope and one of the points to find the value of the y-intercept, b. Plug in these values in the formula for slope-intercept form.
y = mx+ b
y = -2x + b
Using Point 1,
8 = -2(-1) + b
8 = 2 + b
b = 6
3. Write the equation of the line in slope-intercept form.
y = mx+ b
where m = -2 and b = 6
y = -2x + 6
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Karen is planning a graduation party for the senior class. She plans to rent a meeting room at the convention center that costs 400 . There is an additional fee of 5.50 for each person who attends the party.
c. There are 285 people in Karen's class. If 2/3 of these people attend, how much will the party cost?
The party costs a total of 1445.
Given,
The rent of meeting room at the convention center = 400
Additional fee for each person attends the party = 5.50
Number of people in Karen’s class = 285
The number of people attended the graduation party:
2/3 of 285
= (2/3)285
= 95 x 2
= 190
Therefore the additional fee collected from 190 people,
190 x 5.50 = 1045
Now the total cost of the party = rent of room + total additional fees
= 400 + 1045
= 1445
That is, the party costs a total of 1445.
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891.8 ÷ 5.2 = pls with the work out to
The answer to your question would be, 171.5
Write the function rule for each function reflected in the given axis.
f(x)=4+x ; x -axis
Functions can be reflected on the x-axis, the y-axis, or both axes. For example, function reflection y= f(x) can be written as y= -f(x) or y= f(-x) even y= -f(-x). There are four types of function or graph transformations: reflection, rotation, translation, and dilation. In mathematics, especially geometry, mirror or mirroring means flipping, so basically, the mirroring of a function is the mirror image of a given function or graph. Hence the reflection function is commonly known as the reflection function.
The reflection of the given function should be similar in size and shape to the original function.
f(x)=4+x; x -axis
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5 more than one eighth of a number equals 13
Answer:
Step-by-step explanation:
Ten more than x x + 10
A number added to 5 5 + x
A number increased by 13 x + 13
5 less than 10 10 - 5
A number decreased by 7 x - 7
Difference between x and 3 x - 3
Difference between 3 and x 3 - x
Twice a number 2x
Ten percent of x 0.10x
Ten times x 10x
Quotient of x and 3 x/3
Quotient of 3 and x 3/x
Five is three more than a
number
5 = x + 3
The product of 2 times a
number is 10
2x = 10
One half a number is 10 x/2 = 10
Five times the sum of x and 2 5(x + 2)
Seven is greater than x 7 > x
Five times the difference of a
number and 4
5(x - 4)
Ten subtracted from 10 times a
number is
that number plus 5
10x - 10 = x
+ 5
The sum of 5x and 10 is equal
to the product of x and 15
5x + 10 =
15x
The sum of two consecutive
integers
(x) + (x + 1)
The sum of two consecutive
even integers
(x) + (x + 2)
The sum of two consecutive odd
integers
(x) + (x + 2)
Answer:
x=64
Step-by-step explanation:
5+(1/8)x=13
Subtract 5 to both sides to get (1/8)x=8
Multiply by the reciprocal of 1/8 (8) on both sides. The 1/8 and 8 cancel and the answer should be x=64
In this problem, you will investigate the relationships among three points of concurrency in a triangle.
c. Draw a right triangle and find the circumcenter, centroid, and orthocenter.
Construct the centroid (medians), circumcenter (perpendicular bisectors), and orthocenter of a right triangle (altitudes).
What points of concurrency are always inside the triangle?The three angle bisectors of a triangle are concurrent in a point equidistant from its sides. The incenter of a triangle is the point at which the triangle's angle bisectors intersect. The incenter is always inside the triangle.
The point where the three perpendicular bisectors meet is the circumcenter of a triangle. It is the circumcenter of the circle encircling the triangle, equidistant from the triangle's three vertices.
The incenter exists crucial for angle bisectors; the orthocenter is important for perpendicular bisectors; the circumcenter is important for altitudes; and the centroid is important for medians.
Construct a right triangle's centroid (medians), circumcenter (perpendicular bisectors), and orthocenter (altitudes).
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A scientist measures 4.62 ml of a chemical into a beaker. \with a pipette, he carefully takes out 0.67 of the chemical. finally, he adds 1.25 ml of water into the beaker. how much liquid is in the beaker now?
Using basic mathematical operations such as addition and subtraction, the beaker now has 5.2 ml of liquid.
Basic mathematical operations include addition, subtraction, multiplication, and division.
Addition is combining two or more values to come up with a total or sum. On the other hand, subtraction, the opposite of addition, is removing a value from another resulting to their difference.
If a scientist measures 4.62 ml of a chemical into a beaker, then takes out 0.67 ml of the chemical, and finally adds 1.25 ml of water into the beaker, subtracting the amount of chemical taken out from the initial amount of chemical and adding the amount of water, we can solve how much liquid is in the beaker.
4.62 ml - 0.67 ml + 1.25 ml = 5.2 ml
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Find the slope of the line passing through the points (-5, 2) and (3, -9).
Answer: -8/11
Step-by-step explanation:
apply the formula
x sub 2- x sub 1
over
y sub 2 - y sub 1
yw
What is 50+50 and explain how you got the anwer
Answer:
50+50=100
How I got answer there are two 50 so if I multiply 50×2 I will get 100
and answer will come
Answer:
100
Step-by-step explanation:
Columnar addition
50
+50
____
100
Write in simplest form.
x³ = 686
Due today
Answer:
[tex]x = 7 \sqrt[3]{2} [/tex]
Which graph shows a set of ordered pairs that represent a function?
3
2
1 .
5-4-3-2-11. 2.3
-2-
3+
Mark this and return
3-2.
3-
2-
4
+2+
-3-
O
123
5
34
2+
1+
4-3-2-1₁- 1 2 3 4 5
.
Save and Exit
+24
-3-
4
O
4
3-
2
44
54-3-2-11-
•
1 2 3 4 5 X
Next
Submit
The second graph shows a set of ordered pairs that represent a function.
What is function?Functions are an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
here, we have,
A relation is a function in which every x value will have different y values, this represents "every input will have unique output" part of the definition of the function,
When we observe the graphs (attached), we will notice in graph 1) there are two ordered pairs with same x value and different y values, (2, -1) and (2, -3), which is making them out of the list of being a function,
In graph 2) we have, (-2, 2), (1, 1), (5, 4), (-4, -4), (2, -5) and (4, -3), in this all the order pairs have different x-y values, therefore, this set of ordered pairs that represent a function.
Hence, the second graph shows a set of ordered pairs that represent a function.
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The question do not have graph, so, the question is solved for the graph attached.
9xy-22
Term(s):
Coefficient(s):
Variable(s):
Constant(s):
Answer:
Coefficient(s):9
Variable(s):x,y
Constant(s):-22
Step-by-step explanation:
Solve for x.
33 ÷ x = 3
Will mark brainlest
=================================
[tex]\\[/tex]
[tex]33\div x=3\\[/tex]
multiplying both sides by x
[tex]33=3x\\3x=33[/tex]
dividing by 3 both sides
[tex]x=11[/tex] {SOLUTION}===================================
#Carryonlearning
[tex]\textcopyright ELIZA[/tex]
Answer:
x = 11
Step-by-step explanation:
33/x = 3
33 = 3x
x = 33/3
x = 11
Hope it helps!!!
Squere root
Find the using division methos
15384
The square root of the 15384 by division method is a 124.032.
According to the statement
We have to find that the square root with the division method.
So, For this purpose, we know that the
The long division is the mathematical method for dividing large numbers into smaller groups or parts
And
A generalised version of this method called polynomial long division is also used for dividing polynomials
From the given information:
The number is a 15384.
And then
Firstly in this number by the squaring of the same number and by this method after going down until the remainder is zero.
And after solving the square root of 15384
The answer will become 124.032.
So, The square root of the 15384 by division method is a 124.032.
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Which of the following domain restrictions would allow the inverse of f(x) = (x + 4)^2 - 1 graphed below to also be a function? Select the THREE (3) that apply!
The domain restrictions that would allow the inverse of f(x) to also be a function are given as follows:
x ≤ -4.x ≥ 1.x > -3.When does a graph represents an one to one function?The function is one to one if there are no horizontally aligned points, that is, each value of y is also related to only one value of x. A function will have an inverse in the part of the domain of the function that is one to one.
For this problem, the relation is symmetric at x = -4, hence the domains x <= -4 and x >= -4 must not intersect for the inverse to be a function, and the restrictions are given by:
x ≤ -4. (no horizontally aligned points considering only x ≤ -4).x ≥ 1. (same).x > -3(same).More can be learned about one to one functions at brainly.com/question/10853542
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By first rounding each number to 1 significant figure, estimate the answer to 527 +389
Answer:
900
Step-by-step explanation:
527 to 1sf is 500
389 to 1sf is 400
400+500=900
Answer:
900
Step-by-step explanation:
527 to 500
389 to 400
500+400=900
Use the graphs of f and g to graph h(x)=(f+g)(x). I need help with #4.
Answer:
My teacher helped
Step-by-step explanation:
solve the equation for the indicated variable
A = 1/2(pi)(r)^2 solve for pi
Answer:
(2A)/(r^2)=pi
Step-by-step explanation:
The goal is to get pi by itself, so you have to move all the other elements over
2A=pir^2
(2A)/(r^2)=pi
Determine whether the quadrilateral can always, sometimes, or never be inscribed in a circle. Explain your reasoning.kite
A pair of opposite angles is supplementary, a quadrilateral ABCD can be inscribed in a circle.
What can be inscribed in a circle?
Every circle has an inscribed triangle with any three given angle measurements (summing to 180°, of course), and every triangle can be inscribed in any circle (which is called its circumscribed circle or circumcircle). Every triangle has an incircle, which is a circle that has been inscribed.
A cyclic quadrilateral is one that can be encircled by a circle. If and only if a pair of opposite angles is supplementary, a quadrilateral ABCD can be inscribed in a circle. Because the sum of all the angles is 360 degrees, it is true that one pair of supplementary angles is supplementary if and only if both pairs are supplementary.
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What can we use to represent repeated multiplication
Answer:
This expression can be written in a shorter way using something called exponents. An expression that represents repeated multiplication of the same factor is called a power.
Answer:
Step-by-step explanation:
This formula can be written shorter using so-called exponents. Expressions representing repeated multiplications of the same factor are called exponentiations. 5 is called the base and 2 is called the exponent.
An athlete preparing for a marathon runs 21.3miles .how many kilometers did they run?
An athlete preparing for a marathon runs 21.3 miles then the athlete will run 34.27903 kilometer.
What is kilometer?The kilometer (spelled kilometer in American English) is just a metric unit of length equivalent to one thousand meters.
Since there are 1.6 kilometers in a mile, multiply the number of miles by 1.6 to convert them to kilometers. Because 20 × 1.6 = 32 kilometers, 20 miles is equivalent to 32 kilometers. The more precise method would yield a conversion of 20 miles to kilometers of 32.1868.
Conversion of mile into kilometer.
It is known that, 1 mile = 1.60 kilometer.
Then, 21.3 mile = 1.60 × 21.3 = 34.08 kilometer.
An athlete training for a marathon will cover 34.27903 kilometers if they run 21.3 miles.
Therefore, the athlete will run 34.27903 kilometer.
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Use the table below to complete the following statements.
The value of m • n (8) is
The value of n • m (-4) is
Answer:
Step-by-step explanation:
