The value of f(7) is 31
Now, According to the question:
First fundamental theorem of integral calculus states that “Let f be a continuous function on the closed interval [a, b] and let A (x) be the area function. Then A′(x) = f (x), for all x ∈ [a, b]”.
"Information available from the question"
If f(3) = 15, f ' is continuous, and 7 f '(x) dx 3 = 16,
Since ∀x, f'(x) = f(x) , f is a primitive function of f'.
Therefore,
[tex]=\int\limits^7_3f' {x} \, dx = f(x)|^7_3[/tex]
= f(7) - f(3)
= f(7) - 15 = 16
by the fundamental theorem of calculus (part 2) (because f' is continuous and thus integrable).
= f(7) = 16 + 15
=> f(7) = 31
Hence, The value of f(7) is 31
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Apply the distributive property to factor out the greatest common factor. 24+18t =24+18t=24, plus, 18, t, equals.
The distributive property to factor out the greatest factor 24+18t is 6(4+3t).
The distributive property to factor out the greatest common factor 24+18t.
The Distributive Property is an algebraic property that is used to multiply a single value and two or more values within a set of parenthesis. The distributive Property States that when a factor is multiplied by the sum/addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation. This property can be stated symbolically as:
A ( B+ C) = AB + ACWell, some of the common factors that 24 and 18 shares are 2, 3, and 6.
The greatest factor is 6.
⇒ [tex]\frac{24}{6}[/tex]=4
⇒ [tex]\frac{18t}{6}[/tex]=3
Because 6x4=24 and 6 x 3t= 18t
Therefore, the distributive property to factor out the greatest factor 24+18t is 6(4+3t).
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Mr. Cortez is building a brick boarder the bricks are 1 ft. How many bricks does he need to buy? Use 3.14 for pi
The number of bricks needed to border the circular pool is 6.28r.
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
Given, Mr. Cortez is putting a brick border around his circular pool.
So, He is boarding the circumference of the circular pool which has a distance of 2πr.
Now, The bricks are 1 foot in length.
Therefore, The number of bricks needed is,
= 2πr/1.
= 2πr.
= 6.28r.
According to the radius number of bricks can be determined.
Q. Mr. Cortez is putting a brick border around his circular pool. The bricks are 1 foot in length. How many bricks does Mr. Cortez need to buy to build the border? Use 3.14 for π.
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As the marketing designer for Burger King, you are given a 4 inch by 6 inch logo and have been told to create an advertisement with sides six times larger. What is the area of your advertisement (in square feet)?
The area of the logo is 6 square feet.
What is the area of your advertisement?We start wit a logo of 4 inches by 6 inches, and we want to make it 6 times larger, so the new dimensions are:
6*(4 inches) = 24 inches.
6*(6 inches) = 36 inches.
Remember that:
1ft = 12 in
Writting that in feet, we will get:
24 inches = (24/12) ft = 2ft
36 inches = (36/12) ft = 3ft
Then the area of the logo is:
A = 2ft*3ft = 6 ft²
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PLEASE HELP ME !! I WILL GIVE A LOT OF POINTS
The value of the integral expression is -1/2ln(9)
How to evaluate the integralFrom the question, we have the following parameters that can be used in our computation:
Integral of 4/(9 - 8x) from 2 to 9
Using a graphing calculator as a guide, we have the following:
Integrand = -ln(|8x - 9|)/2 from 2 to 9
Substitute the known values in the above equation, so, we have the following representation
Integrand = -ln(|8 * 9 - 9|)/2 + ln(|8 * 2 - 9|)/2
Evaluate
Integrand = -1/2(ln(63/7)
Evaluate the quotient
Integrand = -1/2ln(9)
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Solve each of the following inequalitie and illutrate the olution on number line a) -4x < 28
The inequality and number line that shows the solution is x>-7.
What is inequality?A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance. Less than symbol (), greater than symbol (>), more than or equal to symbol (), less than symbol (), and not equal to symbol () are the five inequality symbols used in mathematics.A connection in mathematics that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line.Simply put, a compound inequality is more than one inequality that we want to address simultaneously. If we want to refer to the answer to both of the inequalities, we can use the word "and," or if we want to refer to the solution to just one of the inequalities, we can use the word "or" (or).Given,
-4x <28
(-4x) (-1) > 28 (-1)
Simplify
4 x>-28
Divide both sides by 4
[tex]\frac{4 x}{4} > \frac{-28}{4}[/tex]
Simplify
x>-7
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Bernard borrows a sum of money from the bank which charges a compound interest of 4. 2% per annum, compounded quarterly. Given that Bernard had to pay $96. 60 in interest payments at the end of the first year, find the original sum of money borrowed, giving your answer correct to the nearest dollar.
(answer : $2264 )
The original sum of money borrowed would be $ 2246.51.
What is meant by Future Value?A financial concept called future value (FV) determines the worth of an asset by using projected factors like future interest rates or cashflows. An investor could find it interesting to know how much, given a projected rate of return, their investment might be in five years. Future value is the idea that an investment will be worth more in the future if its current value is multiplied by anticipated growth.
Interest = $ 96.60
Interest is compounded 6 times in a year; n = 6
time = 1 year ; Rate of interest (r) = 4.2 %
Interest = Future Value - Principal Value
Future Value = Principal [tex]$\cdot\left(1+\frac{r}{100 \times n}\right)^{n \cdot t}$[/tex]
Substituting this value in equation (1), We get
Interest = Principal [tex]$\cdot\left(1+\frac{r}{100 \times n}\right)^{n \cdot t}-$[/tex]Principal
96.60 = Principal [tex]$\left[\cdot\left(1+\frac{4.2}{100 \times 6}\right)^{6 \cdot 1}-1\right]$[/tex]
Principal = $ 2246.51
Therefore, the original sum of money borrowed would be $ 2246.51.
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I am a multiple of 7 le then 50. When my digit are revered,I am a multiple of 8. What number am I
The number which satisfies the given condition is 28.
According to the question
The number 28 is less than 50 and has a multiple of 7. It becomes 82, which is also a multiple of 8 when its digits are inverted. As a result, the criteria can only be satisfied by the number 28. This may be verified by quickly determining whether any other number less than 50 that is a multiple of 7 has its digits switched around to become a multiple of 8. However, it is clear that none of the other figures satisfy both requirements.
In light of this, the answer to this issue is 28.
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The number which satisfies the given condition is 28.
According to the question
The number 28 is less than 50 and has a multiple of 7. It becomes 82, which is also a multiple of 8 when its digits are inverted. As a result, the criteria can only be satisfied by the number 28. This may be verified by quickly determining whether any other number less than 50 that is a multiple of 7 has its digits switched around to become a multiple of 8. However, it is clear that none of the other figures satisfy both requirements.
In light of this, the answer to this issue is 28.
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Find the measure of each interior angle of the regular polygon. 7th
The measure of each interior angle of the regular polygon is equal to 150°.
What is a regular polygon?In Euclidean geometry, a regular polygon simply refers to a form of polygon which has all of its sides and interior angles being equal.
In Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:
Sum of interior angles = 180 × (n - 2)
Where:
n represents the number of sides of a regular polygon.
Similarly, the measure of each interior angle of a regular polygon can be calculated by using this mathematical expression:
Interior angles = [180 × (n - 2)]/n
Interior angles = [180 × (12 - 2)]/12
Interior angles = 180 × (10)/12
Interior angles = 1800/12
Interior angles = 150°
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You pick a card at random.
5
6
7
8
What is P(odd or less than 6)?
Write your answer as a percentage
The probability of odd or less than 6 is 0.75 which is 75%
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
From the question, there are 4 numbers
These include: 5,6,7,8
Pr(odd) 2/4
Pr(x<6) 1/4
Adding the fractions we have
1/2 + 1/4 = 3/4 = 0.75
Converted to percentage = 75%
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(x+y)²+8(x+y)+12 factorize
The expression is factorized to give x(x+ 12) + 8( y + 12)
How to factorize the expressionFrom the information given, we have that the expression as;
(x+y)²+8(x+y)+12
Now, expand the bracket, we get;
(x + 2) (x+2) + 8x + 8y + 12
expand the squared bracket, we get;
x² + 2x + 2x + 4 + 8x + 8y + 12
Now, collect like terms
x² 2x + 2x + 8x + 8y + 4 + 12
Add the collected like terms, we get;
x² + 12x + 8y + 16
Now, let's factorize in airs by grouping, we get;
(x² + 12x) + (8y + 16)
Factor the common terms
x(x+ 12) + 8( y + 12)
Hence, the expression is x(x+ 12) + 8( y + 12)
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Tell which equation you would choose to solve for one of the variables when solving the system by substitution. Then solve the system by substitution.
Equation 1: 2x − 3y = 11
Equation 2: x + 2y = −5
PLEASE I REALLY NEED HELP RIGHT NOW, IM IN A CRISIS! I WILL MARK THE BRANLIEST I SWEAR!!!!
The equation we will use is Equation 1: 2x − 3y = 11. The values of x and y are 1 and -3.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given;
Equation 1: 2x − 3y = 11
Equation 2: x + 2y = −5
Now,
Equation 2: x + 2y = −5
x=-5-2y
Substituting the value of x in equation 1
2(-5-2y)-3y=11
-10-4y-3y=11
-10-7y=11
-7y=11+10
-7y=21
y=-3
Substituting the value of y in equation 2
x+2*-3=-5
x=-5+6
x=1
Therefore, the solution of the system of equations will be x=1,y=-3
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compute the number of ways you can select n elements from n elements. n = 2, n = 10
The number of ways you can select n elements from N elements by using factorial (!) when n=2 and N=10 is 45.
Describe a factorial.Factorial is a crucial mathematical operation that is used to determine the number of possible arrangements or the ordered set of numbers. Daniel Bernoulli is credited with discovering the factorial function's well-known interpolating feature. Numerous mathematical ideas, including probability, permutations and combinations, sequences and series, etc., use the factorial concept. A factorial function, in essence, multiplies a number by each number below it until it equals 1. For instance, the factorial of 3 is equal to 6 and reflects the multiplication of the integers 3, 2, and 1.
Now,
The number of ways you can select n elements from N elements when n=2 and N=10 is [tex]\frac{N!}{n!(N-n)!}[/tex]
=[tex]\frac{10!}{2!(8)!}[/tex]
=[tex]\frac{10 \times 9 \times \times 8!}{8! \times 2 !}[/tex]
=45
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Joey earns $12 an hour. Blake earns $16 per hour. Joey receives a raise of $1. 50 every six months, and Blake receives a raise of $0. 50 every six months. Which equation can be used to find x, the number of six month intervals it will take Joey to earn hourly the same as Blake?
Therefore, in order for Joey to earn the same hourly wage as Blake, she will have to labor for 8 six-month periods or 4 years.
We'll refer to the quantity of six-month intervals as x. Blake's hourly wage can be represented as 16 + 0.50x, and Joey's hourly wage may be represented as 12 + 1.50x after x intervals. We may set the two expressions equal to one another and solve for x to determine when Joey's salary will match Blake's salary:
12 + 1.50x = 16 + 0.50x \s0.50x = 4 \sx = 8
Joey will therefore need to work for 8 six-month periods, or 4 years, in order to make the same hourly rate as Blake.
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Find the missing length. The triangles in each pair are similar.
Answer:
1) 117
2) 24
Step-by-step explanation:
Corresponding sides are in the same ratio for similar triangles
1)
For triangles MUL and WUV:
UW/UM = UV/UL
?/45 = 104/40
? = 45 x 104/40 = 117
2)
For triangles RST and RKH
RS/RK = RT/RJ
?/12 = 20/10 = 2
? = 2 x 12 = 24
the base of is the parabolic region {(,)|2≤≤1}. cross-sections perpendicular to the -axis are squares.
The volume of the solid is 0 cubic units.
What do you mean by integration?Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.
There are two main types of integration: definite and indefinite integration. Definite integration involves finding the exact area between a curve and the x-axis over a specified interval. Indefinite integration involves finding the general antiderivative of a function, which is a function that, when differentiated, will yield the original function.
The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.
The volume of the solid is given by the definite integral:
V = ∫_[tex]{y=2}^{1} A(y) dy[/tex]
Where A(y) is the area of the cross-section at y. Since the cross-sections are squares, we know that A(y) = [tex]y^{2}[/tex].
So, the volume is given by:
V = ∫_[tex]{y=2}^{1} y^{2} dy = [\frac{y^{3} }{3} ]_{y=2}^{y=1} = (\frac{8}{3} - (\frac{2^{3} }{3}= (\frac{8}{3}-\frac{8}{3} ) =0[/tex]
The volume of the solid is 0 cubic units.
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rewrite the quadratic equation in factored form
Answer:
(x - 7)(x + 8)
Step-by-step explanation:
x² + x - 56
Multiples of 56 whose difference is 1: 7, 8
So, splitting the equation:
x² + 8x - 7x - 56
(x - 7)(x + 8)
The factored form of a quadratic expression is a way to rewrite the expression which shows the sums of products.
general form: [tex]y= a(x-r)(x-s)[/tex]
in which the parenthesis, when solved for will give the roots/x-intercepts of the equationwhen the a value is equal to zero:
find two numbers that sum to the middle term and when multiplied give you the product of the third term[tex]y=x^2+x-56[/tex]
find two numbers that are the sum of 1 and are the multiply to give you -56+8 and -7 create a sum of +1 and the product of -56[tex]y=(x+8)(x-7)[/tex]
If tan x° = 3 divided by y and co x° = y divided by z ,what i the value of in x°?
The value of in x° is sin x = 3/z
The ratio of an angle's opposing side to its adjacent side, or its tan
tan x = 3/y
cos x = y/z
We choose 3 and y to represent the opposite and adjacent sides, respectively, because this ratio is 3:y.
Technically, we ought to write 3t and yt, but we'll take a chance since y appears in the second ratio as well!
Since y is already used to represent the adjacent side, z is used to represent the length of the hypotenuse.
The right triangle's sides are now finished.
Because tan x = sin(x)/cos(x), therefore
sin x = tan(x)*cos(x)
= (3/y)*(y/z)
= 3/z
Answer: a) sin x = 3/z
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You decide to invest in government bonds to save money for your eventual wedding. You have an
initial investment of $7,000 and when you choose to invest for 14 years you get a 10% rate
of return. What will be the value of your investment at maturity?
y = a(1+r)²
Round off to the nearest whole number
(don't forget to change your rate to a decimal percentage)
The value of your investment at maturity at a 10% rate of return will be,
$8470.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = P(1 + r/100)ⁿ.
Where, A = amount, P = principle, r = rate, and n = time in years.
Given, An initial investment of $7,000 and when you choose to invest for 14 years you get a 10% rate of return.
We know, 10% = 10/100 = 0.1.
Therefore, The value of your investment at maturity will be,
y = 7000(1 + 0.1)².
y = 7000(1.1)².
y = 7000×1.21.
y = 8470.
So, The value of the maturity will be $8470.
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A class used cars(x) and vans(y) to go on a field trip. They used 11 cars and vans. Each car holds 5 students and each van holds 8. If 73 students went on the trip then how many of each vehicle did the class use.
Answer:
X=5 Cars
Y=6 Vans
Step-by-step explanation:
Let's assume the number of cars used is x and the number of vans used is y.
We can set up two equations based on the information given:
x + y = 11 (the total number of vehicles used)
5x + 8y = 73 (the total number of students that went on the trip)
We can use substitution to solve for one of the variables in terms of the other:
y = 11 - x
5x + 8(11 - x) = 73
5x + 88 - 8x = 73
-3x = -15
x = 5
So the class used 5 cars and 11 - 5 = 6 vans.
1. (10 pts) use the definition of big o notation to find the constants c, no which show that t(n) is o(f(n)). a. ()= 32 4, ()= 52
use the definition of big o notation to find the constants c, no which show that t(n) is o(f(n)) then 5^n+25 is not = 5^n
The main purpose of the computational complexity is to categorize the algorithms about their show. And we can represent the T(n), which is the time function with the help of the big O notation, for showcasing an algorithm runtime complexity. As an example,
T(n) = O(n3)
proves that the algorithm has the cubic time complexity.
Now let's define Bio O, and from here we will get our answer. For any function which is monotonic in nature, f(n) and g(n) from the +ve integers to the +ve integers, we assume that f(n)= O(g(n)) when exist a c>0 which is the constant, and n0 greater than 0, such that
f(n) < c * g(n), for each n>=n0
i) if O (5^n)= 4^n + 25
O (f) should be = (20^n)/f + 25
Then constant
O(5^n)= (20^n)/(5^n) + 25 = (20/5)^n +25=4^n+25
ii) O (4^n)=(20^n)/(4^n) + 25 = (20/4)^n +25=5^n+25
And 5^n+25 is not = 5^n
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complete question is
Use the definition of O (f) to show that 4^n + 25 is O (5^n) (ii) show that 5^n is not O (4^n)
Line m and line n are parallel.
Which is the value of x?
Responses
x=15
x = 15
x=12.5
x = 12 . 5
x=7.5
x = 7 . 5
x=2
x = 2
If line m and n are parallel, the value of x is determined as 10.
What is the value of x?The value of x is determined by applying the following rules of parallel lines as shown below.
The corresponding angles of the parallel lines are equal,
the corresponding angles are given as;
8x + 50 = 130
now solve for x, by making x the subject of the formula.
8x = 130 - 50
8x = 80
divide through by 8
8x / 8 = 80 / 8
x = 10
Thus, the value of x is function of the corresponding angles.
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Both circles have the same center. What is the area of the shaded region?
d=22 yd
yd
Use 3. 14 for. Write your answer as a whole number or a decimal rounded to the nearest
hundredth
square yards
The area of the shaded portion is area of the outer circle - area of the inner circle = 1017.36 - 379.94 = 637.42 yards²
What is Circle ?All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
The following are some of the circle's crucial characteristics:
If the circles have equal radii, they are said to be congruent.The longest chord in a circle is its diameter.In the center of a circle, equal chords subtend equal angles.The chord is divided in half by the radius drawn perpendicular to the chord.Circles with various radii are comparable.A circle can encircle a kite, triangle, square, trapezium, rectangle, and more.You may encircle a square, triangle, or kite with a circle.Equal in length are the chords that are equally spaced from the center.The longest chord's (diameter) distance from the circle's center is equal to zero.As the chord length rises, the perpendicular distance from the circle's center decreases.The tangents are parallel to one another if they are drawn at the diameter's end.The radii connecting the ends of a chord to the center of a circle create an isosceles triangle.The radius of the inner circle = 22 /2 = 11 yard = r1
The distance between the inner cirle and outer circle = 7 yards
The radius of the outer circle = 18 yards = r2
The Area of the outer circle = π*r2² = 3.14 * 18² = 1017.36 yards²
The Area of the inner circle = π*r1² = 3.14 * 11² = 379.94 yards²
The area of the shaded portion is area of the outer circle - area of the inner circle = 1017.36 - 379.94 = 637.42 yards²
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2 c −3 d 6 tart fraction, c, divided by, 2, end fraction, minu, 3, plu, tart fraction, 6, divided by, d, end fraction when c=14c=14c, equal, 14 and d=3d=3
2/5th of a number is 40% of that number.
In order to calculate the percentage of a given number that is equal to 2/5 of that number, we must first convert the fraction to percentage form, which is as follows:
= 2/3 * 100
= 0.4 * 100
= 40%
We will use the following example to validate the aforementioned process:
Assume that it is 50.
First, 2/5 of 50 equals 2/5 * 50, or 20.
Second, 40% of 50 equals 40/100 * 50 = 0.4 * 50 = 20.
The equality of the two results is evident.
2/5 of a number is therefore 40% of that number.
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The question is incomplete;
\dfrac25 start fraction, 2, divided by, 5, end fraction of a number is what percentage of that number?
Which shape has only acute angles?
Answer: Acute Triangles
GRAPHING EXPONENTIAL FUNCTIONS
Please show work I don’t understand how to do this
Solving the provided question, we can say that the given exponent is
[tex]32 = 2^{ 3x - 1 }[/tex] => 64 = [tex]2^{3x}[/tex] => [tex]2^{3(2)} = 2^{3x}[/tex] on comparing both side, we have x = 2
what are exponents?Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where
the given exponent is
[tex]32 = 2^{ 3x - 1 }[/tex]
64 = [tex]2^{3x}[/tex]
[tex]2^{3(2)} = 2^{3x}[/tex]
on comparing both side, we have
x = 2
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A set of eight cards were labeled as M, U, L, T, I, P, L, Y. What is the sample space for choosing one card? S = {I, U, Y} S = {M, L, T, P} S = {I, L, M, P, T, U, Y} S = {I, L, L, M, P, T, U, Y}
The sample space for choosing one card is, S={I, L, L, M, P, T, U, Y}
What is a sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.
Given that,
A set of eight cards were labeled with M, U, L, T, I, P, L, Y.
Here, the sample space is;
{ S, U, B, T, R, A, C, T}
Now, Elements in order is,
⇒ S = {I, L, L, M, P, T, U, Y}
Therefore, the sample space for the given cards is,
S = {I, L, L, M, P, T, U, Y}
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Answer: I think the answer would be C
Circles equations and coordinates
Desperate help!!!!
The complete coordinates are (8, 0), (0, -8), (-8, 0) and (0, 8)
How to determine the corodinatesFrom the question, we have the following parameters that can be used in our computation:
x^2 + y^2 = 64
The above is the equation of a circle
Express 64 as 8^2
So, we have
x^2 + y^2 = 8^2
When y = 0, the possible values of x are
x = -8 and x = 8
When x = 0, the possible values of y are
y = -8 and y = 8
This means that the complete coordinates are (8, 0), (0, -8), (-8, 0) and (0, 8)
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earth is approximately a sphere of radius 6.37 x 10 6 m. what are (a) its circumference in kilometers, (b) its surface area in square kilometers, and (c) its volume in cubic kilometers?
(a) Circumference of Earth in kilometers: 40,075.017 km
(b) Surface area of Earth in square kilometers: 510.1 million km^2
(c) Volume of Earth in cubic kilometers: 1.08 trillion km^3
To calculate these values, we use mathematical formulas that relate to the sphere shape of the Earth.
For (a), we use the formula for the circumference of a circle, C = 2 * pi * r, where r is the radius of the Earth in meters (6.37 x 10^6 m). We then convert this result to kilometers by dividing by 1000.
For (b), we use the formula for the surface area of a sphere, A = 4 * pi * r^2, where r is the radius of the Earth. Again, we convert this result to square kilometers.
For (c), we use the formula for the volume of a sphere, V = (4/3) * pi * r^3, where r is the radius of the Earth. We then convert this result to cubic kilometers by dividing by 10^9.
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(1 point) solve the system using elimination ⎧⎩⎨⎪⎪6x5x−4x−5y−4y 3y 3z 6z 6z===−70−755 x= y= z=
The solution to the system of linear equations is: x = 5, y = (6x + 7 - 10/4)/(-5) = -4/5, z = -5/4.
To solve the system of linear equations using elimination, we can manipulate the coefficients of the variables to make one of the variables zero in one of the equations. Then, we can use this equation to eliminate that variable from the other equations.
Starting with the first two equations:
6x - 5y - 4z = -7
5x - 4y - 4z = -5
We can multiply the first equation by 5 and the second equation by 6 to get rid of the coefficients of x in both equations:
30x - 25y - 20z = -35
30x - 24y - 24z = -30
Now, we can subtract the first equation from the second equation to eliminate x:
0y - 4z = 5
So, z = -5/4
Next, we can use this value of z to solve for y in either of the first two equations:
6x - 5y - 4(-5/4) = -7
Expanding the right side:
6x - 5y + 10/4 = -7
And solving for y:
y = (6x + 7 - 10/4)/(-5)
Finally, we can use the value of y and z to solve for x in any of the first two equations:
6x - 5((6x + 7 - 10/4)/(-5)) - 4(-5/4) = -7
Expanding and solving for x:
6x - (6x + 7 - 10/4)/5 - 10/4 = -7
Multiplying both sides by 5:
30x - 6x - 7 + 2 = -35
And solving for x:
x = 5
Finally, we can use the values of x, y, and z to check the third equation:
3y + 6z = 6
Substituting the values we found:
3((6x + 7 - 10/4)/(-5)) + 6(-5/4) = 6
Expanding and solving:
The left side is equal to 6 and the right side is equal to 6, so the solution is consistent.
Therefore, the solution to the system of linear equations is:
x = 5, y = (6x + 7 - 10/4)/(-5) = -4/5, z = -5/4
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Calculate the length and width of the original figure with a scale factor of 50%.
Answer:To calculate the length and width of the original figure with a scale factor of 50%, you need to reverse the scaling by multiplying the new dimensions by 100% / 50% = 2.
So if the new length is L, the original length would be L * 2 = 2L. Similarly, if the new width is W, the original width would be W * 2 = 2W.
Step-by-step explanation:here's a step-by-step explanation:
Identify the new length (L) and new width (W) of the figure.
Multiply the new length by a factor of 2 to find the original length: 2L = L * 2
Multiply the new width by a factor of 2 to find the original width: 2W = W * 2
The original length is 2L and the original width is 2W.
Note: This process works for any scale factor, not just 50%. To find the original dimensions, simply multiply the new dimensions by 100% / the scale factor.