Answer:
17 / 4
Step-by-step explanation:
To find the right sum, you need to....
Step #1: Find Δx
Step #2: Find [tex]x_k[/tex]
Step #3 Make the right-hand sum equation: ∑[tex]^n_{k=1}f(x_k)[/tex]Δx
Step #4: Solve the right-hand sum equation
Consider the interval [2, 3) = {x € r : 2 <= x < 3}. Find the complement of this interval where the universal set is taken to be r, the set of real numbers.
The complement of the interval [2, 3) is ( -∞, 2) ∪ (3, ∞).
According to the given question.
We have an interval [2, 3).
Let A = [2, 3)
Which is defined as
[2, 3) = {x ∈ r : 2 ≤ x < 3}
This means that the interval [2, 3) contains all the real numbers which are greater and equal to 2 and less than 3.
And, here it is also given that the universal set is r ( set of real numbers).
As we know that " the complement of an interval is a set A of real numbers that conatins all the elements of universal set U except the number that lying between the given two numbers in the inerval" i.e.
[tex]A^{c} = U - A[/tex]
Where,
[tex]A^{c}[/tex] is the complement of interval A
Thereofre, the complement of the given interval [2, 3) will be all the elements of universal set i.e real numbers except 2 and the real numbers which lies in between 2 and 3.
So, we can say that
[tex]A^{c} = (-\infty, 2) \cup(3, \infty)[/tex]
Where, [tex]A^{c}[/tex] is the complement of the interval A.
Hence, the complement of the interval [2, 3) is ( -∞, 2) ∪ (3, ∞).
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Three interior angles of a quadrilateral measure 55°, 117°, and 120°. What is the measure of the fourth interior angle?
68°
78°
88°
98°
Answer:
68
Step-by-step explanation:
We know the sum of interior angles for a quadrilateral must equal 360, so we can create the following equation
[tex]55+117+120+x=360[/tex]
Simplify
[tex]292+x=360[/tex]
Subtract 292 from both sides
[tex]x=68[/tex]
Answer:
68
Step-by-step explanation:
The sum of the interior angles of a quadrilateral is 360. The sum of the interior angles or a triangle is 180. If you think about a rectangle, you can cut that up into two triangles, so 180 + 180 = 360.
Now subtract out the 3 angles that you know
360-55-117-120 = 68
Select the correct answer. which exponential equation is equivalent to this logarithmic equation?
logarithmic equation log x = 4 is given by- [tex]10^{4}[/tex] = x
What is logarithmic equation?
A logarithmic equation is an equation that involves the logarithm of an expression containing a variable. To solve exponential equations, first see whether you can write both sides of the equation as powers of the same number.The given logarithmic equation is;
[tex]log x = 4[/tex]
Since, log with base 10 is written as [tex]log x[/tex] simply, therefore, we have:
[tex]log_{10} x[/tex] = 4
Using the definition of logarithm, we get;
[tex]x = 10^{4}[/tex]
Equivalently, [tex]10^{4} = x[/tex]
Thus, the exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by- [tex]10^{4}[/tex] = x
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The complete question is -
Which exponential equation is equivalent to this logarithmic equation?
log x = 4
Find the measure of two complementary angles of the measure of one angle is 3 more than the measure of its complement
ANSWER: 22.5 and 67.5
let, one angle be x then the another one is 3×(90-x)
x = 270 - 3x
x + 3x = 270
4x = 270
x = 270/4
x = 67.5 (first angle)
then, another angle = 90- 67.5 = 22.5
would really appreciate help thank you!
Answer:
(2, 2) ⇒ (-2, 2)
(-5, 6) ⇒ (-6, -5)
(2, 6) ⇒ (-6, 2)
(-5, 2) ⇒ (-2, -5)
Step-by-step explanation:
The new coordinates can be found using the transformation function for figures rotated 90° about the origin.
TransformationRotation 90° (counterclockwise) about the origin can be described by ...
(x, y) ⇒ (-y, x)
ApplicationThe end points of the diagonal that comes closest to the origin will be transformed to ...
(2, 2) ⇒ (-2, 2)
(-5, 6) ⇒ (-6, -5)
The other diagonal end points will be on the same horizontal and vertical lines as these.
(2, 6) ⇒ (-6, 2)
(-5, 2) ⇒ (-2, -5)
Help please!
A collection of numbers M consists of all positive integers less than 20. If a collection of numbers N is a collection created by randomly choosing five numbers from M. Which of the following must be true about M?
i. The range must be at least 4
ii. The median must be at least 3
iii. The mean can be above 17
a. i only
b. ii only
c. i and ii only
d. i and iii only
The answer choice which represents statements which are correct regarding the datasets described in the task content is; Choice C; i and ii only.
Which of the answer choices represents statements which are true about the dataset described?It follows from the task content that the universal set M is described to contain all positive integers less than 20 while the collection of numbers N is created randomly by choosing five numbers from it.
Consequently, it follows that since 5 number are to be chosen, the range must be at least 4 as this follows from the extreme case scenario of selecting consecutive numbers. Hence, statement i is correct.
Also, the median must be at least three as the extreme case scenario in which numbers 1,2,3,4 and 5 are chosen still renders the median to be 3.
The mean of the five numbers cannot be above 17 because, when when numbers, 15,16,17,18 and 19 are chosen, the mean is 17 and does not exceed 17. Hence, statement iii is incorrect.
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Suppose that a, b, c, d are positive real numbers such that a/b < c/d . What can you say about the fraction (a+c)/(b+d) ? Is it always, sometimes, or never between the fractions a/b and c/d ? Provide evidence of your claim. (If always or never, give an algebraic proof, otherwise, give two quadruples values of a, b, c, d in which one quadruple has (a+c)/(b+d) between a/b and c/d and the other does not.)
Answer: (a−c)(b−c)>0
Step-by-step explanation:
ab>1 and ac<01. a>0 if c<0 and also b>02. a<0 if c>0 and also b<0
how i did it:
At the vert first, write the inequality as an equation.
Solve the provided equation for one or more values.
Now, display all the values obtained in the number line.
Use open circles to show the excluded values on the number line.
Find the interim.
At the moment, take any random value from the interval and substitute it in the inequality equation to check whether the values reassure the inequality equation.
Intervals that reassure the inequality equation are the solutions of the given inequality equation.
Solve the compound inequality. 5x – 11 < –11 or 4x + 2 > 14
Answer:
5x-11<-11
group like terms
5x<11+11
5x<22
divide both sides by 5
In one afternoon's shopping Seedevi spent half as much money as Georgia, but $6 more than Amy. If the three of them spent a total of $258, how much did Seedevi spend?
The amount spent by Seedevi is $66
How to determine the amount spent by Seedevi?From the question, the given parameters are:
Seedevi = half as much money as Georgia,
Seedevi = $6 more than Amy
The three of them = $258
To solve this question, we use the following representations
x = Seedevi
y = Georgia
z = Amy
So, we have the following equations
x = 0.5y
x = 6 + z
x + y + z = 258
Make y and z the subjects
y = 2x
z = x - 6
Substitute y = 2x and z = x - 6 in x + y + z = 258
x + 2x + x - 6 = 258
Evaluate the like terms
4x = 264
Divide by 4
x = 66
Hence, the amount spent by Seedevi is $66
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We can fill a certain barrel with water if we use water from 6 small pitchers, 3 medium pitchers, and one large pitcher, or from 2 small pitchers, 1 medium pitcher, and 3 large pitchers. If we use only large pitchers of water, how many of them do we need to fill the barrel?
Answer:
Solution Given:
let pitcher which is small be S medium be M and large be L and barrel be B.
By question
6S+3M+1L= 1B...... eq. 1
2S+1M+3L=1B.......eq. 2
The difference in 2L from the first to the second is 4S and 2M
Therefore, each L=2S+M
In equation 2
2S+1M+3L=1B
replacing 2S +1M by L,we get
L+3L=1B
4L=1B
Therefore, 4 large pitcher is required
Answer:
4 large pitchers
Step-by-step explanation:
Define the variables:
Let x = volume of a small pitcherLet y = volume of a medium pitcherLet z = volume of a large pitcherLet b = volume of a barrelCreate two equations with the given information and the defined variables.
Equation 1
If the barrel can be filled with 6 small pitchers, 3 medium pitchers and 1 large pitchers:
⇒ 6x + 3y + z = b
Equation 2
If the barrel can be filled with 2 small pitchers, 1 medium pitcher and 3 large pitchers:
⇒ 2x + y + 3z = b
Substitute Equation 2 into Equation 1
⇒ 6x + 3y + z = 2x + y + 3z
Subtract 6x from both sides:
⇒ 3y + z = -4x + y + 3z
Subtract y from both sides:
⇒ 2y + z = -4x + 3z
Subtract z from both sides:
⇒ 2y = -4x + 2z
Divide both sides by 2:
⇒ y = -2x + z
Substitute the found expression for y into Equation 1:
⇒ 6x + 3(-2x + z) + z = b
⇒ 6x - 6x + 3z + z = b
⇒ 4z = b
Therefore, 4 large pitchers are needed to fill the barrel.
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find the domain and range
Answer:
domain should be x=1
range is all real numbers
Step-by-step explanation:
Answer:domain should be x=1
range is all real numbers
Step-by-step explanation:
Solve using the quadratic formula.
n2 + 2n + 1 = 0
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
n = ____
or n = ____
i wasnt ever smart lol please help quick
Answer:
-1
Step-by-step explanation:
n^2+2n = -1
n(n+2) = -1
What type of polynomial is: 3x^4 - 2x^3 - 2
This polynomial has only 3 terms, so it is a trinomial. Hope it helps!
The Williard family was saving up for their summer vacation. Mrs. Williard had $475.88 in their savings account for the trip. Mr. Williard received a bonus at work for $609.00 that he is saving for the trip. If the trip will cost the Warren's a total of $1675.98, how much more money do they need for their vacation
Answer:
$591.10
Step-by-step explanation:
First, add up $475.88 and $609.00 together. Then, subtract it from $1675.88. They need $591.10 more for their vacation.
Geometry: complete this proof (ASAP!!!! It’s urgent)
Answer:
1. Given.
2. Reflexive Property of Congruence.
3. Alternate Interior Angles Theorem.
4. SAS
5. <4 ~= <2
6. Converse of Alternate Interior Angles Theorem.
Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted: rectangle with a length of x plus 25 and width of x plus 15 with a rectangle in the bottom right corner labeled bench that has a length of 10 and width of 3 write an equation to determine the area, a, of the patio that will be painted. a = (x 18)(x 35) a = (x 15)(x 25) 30 a = (x 5)(x 22) a = (x 25)(x 15) − 30
The correct option is D.
An equation to determine the area, a, of the patio that will be painted :
a = (x + 25)(x + 15) - 30
What is Geometrical figure?Geometric shapes are the mathematical figures that show how ordinary objects in our world are shaped. Shapes in geometry are the configurations of things with boundary lines, angles, and surfaces.
According to the given Information:Length of the rectangular patio is (x+25).
Width of the rectangular patio is (x+15).
Length of bench is 5.
Width of the bench is 1.
Area of rectangle:Area of a rectangle is:
A = Length x Width
Area of rectangular patio is:
A[tex]_1[/tex] = (x + 25)(x + 15)
Area of bench is:
A[tex]_2[/tex] = 10 x 3
= 30
The painting area is:
A = A[tex]_1[/tex] - A[tex]_2[/tex]
A = (x + 25)(x + 15) - 30
Therefore, the correct option is D.
An equation to determine the area, a, of the patio that will be painted :
a = (x + 25)(x + 15) - 30
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A rhombus with horizontal diagonal length 25 millimeters and vertical diagonal length 8 millimeters. what is the area of the rhombus? 25 mm2 33 mm2 50 mm2 100 mm2
The area of the rhombus is 100 mm². The correct answer is D.
What is a rhombus?A rhombus is one type of parallelogram and has 4 sides and 4 vertices.
Every side is equal in length and opposite angles are equal.
Given:
A rhombus with horizontal diagonal length 25 millimeters,
and vertical diagonal length 8 millimeters.
Let d₁ = 25 mm and, d₂ = 8 mm.
Let A be the area of rhombus.
To find the area of rhomus:
Using diagonals,
A = (1/2) × d₁× d₂.
Substituting the values of diagonals,
A = 1/2 x 25 x 8
A = 200/2
A = 100 mm².
Therefore, 100 mm² is the area of the rhombus.
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In the power function f(x) = -2x, what is the end behavior of f(x) =-2x^3 as x goes to [infinity]?
The end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.
In this question,
The power function is f(x) =-2x^3
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
The graph below shows the behavior of the function f(x).
The above equation has the degree of 3, which is odd and the leading coefficient has the negative coefficient.
Then the end behavior is
As x -> ∞,
[tex]\lim_{x \to \infty} f(x)[/tex]
⇒ [tex]\lim_{x \to \infty} -2x^{3}[/tex]
⇒ [tex]-2(\infty)^3[/tex]
⇒ - ∞
Hence we can conclude that the end behavior of a polynomial function is as x tends to infinity, f(x) tends to negative infinity.
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Enduro solved -4x > 120 by adding 4 to each side of the inequality. What mistake did he make?
The mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides
What are inequalities?Inequalities are expressions that have unequal values, when compared
How to determine Enduro's mistake?The inequality is given as
-4x > 120
When 4 is added to both sides, the inequality becomes
4 - 4x > 120 + 4
The above is not the solution to the inequality.
The solution is as follows:
We have:
-4x > 120
Divide both sides inequality by -4
x < -30
Hence, the mistake made by Enduro is that he is supposed to divide both sides by -4 instead of adding 4 to each sides
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help
4/10 as a decimal
Answer:
0.4
Step-by-step explanation:
4/10 is 4÷10 = 0.4
I need help to complete this question
The complete fractional question given in the above picture is 55/3 = 1 + 52/3 = 2 + 49/3 = 5 + 40/3 = 8 + 31/3 = 10 + 25/3
FractionLet
Each empty box = x55/3 = 1 + x/3
55/3 = (3+x) / 3
55/3 × 3 = 3 + x
55 = 3 + x
55 - 3 = x
52 = x
55/3 = 2 + x/3
55/3 =(6+x) / 3
55/3 × 3 = 6+x
55 = 6 + x
55 - 6 = x
49 = x
55/3 = x + 40/3
55/3 = (3x+40) / 3
55/3 × 3 = 3x + 40
55 = 3x + 40
55 - 40 = 3x
15 = 3x
x = 15/3
x = 5
55/3 = x + 31/3
55/3 = (3x+31) / 3
55/3 × 3 = 3x + 31
55 = 3x + 31
55 - 31 = 3x
24 = 3x
x = 24/3
x = 8
55/3 = 10 + x/3
55/3 = (30+x) / 3
55/3 × 3 = 30 + x
55 = 30 + x
55 - 30 = x
25 = x
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20. A trader took a loan of 1,800.00 at an interest of 12 percent per annum. It was agreed that the loan and the interest must be paid in one year equal monthly instalments.
a) Calculate
i) the interest on the loan.
ii) the amount to be paid at the end of the year.
iii) the monthly instalment.
b) Another trader took a loan at the same rate interest and conditions. If she had to pay $200.00 monthly instalment, find to the nearest cedi, how much she took.
Step-by-step explanation:
i)I=PRT/100
I=1800*12*1/100
I=$216
ii) amount to be paid =1800+216
=$2016
iii) monthly installments=2016/12
=$168
b)I=PRT/100
I=
If a trader took a loan of 1,800.00 at an interest of 12 percent per annum
a. Interest on the loan is $216.
Amount to be paid at the end of the year is $2016
Monthly Installment is $168
b. She took $2184 to the nearest dollar.
What is the Interest?a) i) Interest on the loan:
Interest = Principal × Rate × Time
Interest = $1800 × 0.12 × 1
Interest = $216
ii) Amount to be paid at the end of the year:
Amount = Principal + Interest
Amount = $1800 + $216
Amount = $2016
iii) Monthly installment:
Number of monthly installments = 12
Monthly Installment = Total Amount / Number of Installments
Monthly Installment = $2016 / 12
Monthly Installment ≈ $168
b) Let's X represent the amount she took
Total Payment = Monthly Installment × Number of Months
Total Payment = $200 × 12
Total Payment = $2400
So
Total Payment = X + $216
$2400 = X + $216
Subtract $216 from both sides:
$2400 - $216 = X
$2184 = X
Therefore she took approximately $2184 to the nearest dollar.
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Orlando is 12 years older than Omar. Carl is three times older than Orlando. The sum of their ages is 68.Find the ratio of Omar’s age to Carl’s age to Orlando’s age.
Step-by-step explanation:
let's name the variables for the age of the people as the people themselves :
orlando = omar + 12
carl = 3×orlando
carl + orlando + omar = 68
using the first equation in the second equation, and then that result and the first equation in the third equation :
carl = 3×(omar + 12)
3×(omar + 12) + (omar + 12) + omar = 68
3×omar + 36 + omar + 12 + omar = 68
5×omar + 48 = 68
5×omar = 20
omar = 4
orlando = omar + 12 = 4 + 12 = 16
carl = 3×orlando = 3×16 = 48
the ratio omar : carl : orlando
4 : 48 : 16 = 1 : 12 : 4
If a right circular cone has a circular base with a diameter of length 16 cm and a volume of 320???? cm3, find its lateral area in square centimeters.
The lateral surface area of a right circular cone is 234.09 [tex]cm^2[/tex]
Given that volume = [tex]320cm^3[/tex]
Radius = 8cm
we know that
The volume of the right circular cone = [tex]V = \frac{\pi r^2h}{3}[/tex]
[tex]320 = \frac{22 \times 8^2h}{3 \times 7}[/tex]
after solving the equation we get
h = 4.77cm
now, the lateral surface area of the cone = [tex]A = \pi \times r \times \sqrt{h^2 + r^2}[/tex]
now putting the values in the above equation
[tex]A = \pi \times 8 \times \sqrt{4.77^2 + 8^2}[/tex]
A = 234.09 [tex]cm^2[/tex]
What is lateral surface area?All sides of an object, excluding its base and top, are considered its lateral surface (when they exist). The size of the lateral surface is referred to as its area.This must be distinguished from the total surface area, which consists of the base and top areas as well as the lateral surface area. In a broader sense, the total area of the sides of a prism makes up its lateral surface area.Calculating this lateral surface area requires multiplying the prism's height by the base's perimeter.To learn more about lateral surface area with the given link
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Annel sells a phone which costs $180 and earns $9 commission. If he sells $640
worth of phones the following day, how much will he earn on commission?
Answer:
he will earn 32$ worth of commision
Step-by-step explanation:
so if the commission is 9$ and 9 is 5% of 180$ then commission percentage is 5% so to find how much commission he got selling 640$ worth of phones we just have to find 5% of 640$ which is 32$
The motion of an object was recorded by measuring the velocity of the object in meters per second at various times, as shown in the table.
The scatterplot below was graphed from the data in the table, where t represents the time, and v represents the velocity. Based on the scatterplot, which equation BEST represents the relationship between velocity and time?
The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.
According to the statement
we have given some data in the form of graph according to the velocity per time and we have to find the relationship between the velocity and time.
So, for this purpose,
we know that the best method show the relationship is a slope intercept form.
So,
The slope intercept form is a the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
And
Using the coordinate points on the plane (0, 6) and (10, 28)
now we Determine the slope
Slope = 28-6/10-0
Slope = 22/10
Slope = 2.2
And then Determine the y-intercept
6 = 2.2(0) + b
b = 6
And now we have to put in the general form of the slope intercept form which is y = mx + b
Then the equation become
y = 2.2x + 6
So, The equation BEST represents the relationship between velocity and time is y = 2.2x + 6.
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Enter the correct answer in the box. jackson needs to determine the value of x in this equation. rewrite the expression as a logarithmic quotient that he could enter in his calculator.
A logarithmic equation exists as an equation that uses the logarithm of an expression containing a variable. The value of the logarithmic equation x = log 2.97/log 1.13.
What is a logarithmic equation?A logarithmic equation exists as an equation that applies the logarithm of an expression having a variable. To estimate exponential equations, first, see whether you can note both sides of the equation as powers of the same number.
Given: [tex]$1.13^x = 2.97[/tex]
Taking log on both sides, we get
log [tex]$1.13^x[/tex] = log 2.97
x log 1.13 = log 2.97
x = log 2.97/log 1.13
Therefore, the value of logarithmic equation x = log 2.97/log 1.13.
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Using the digits below form the smallest number which is a multiple of 3
9,4,5
This would be the least common multiple of 3, 4, 5, and 9. We can start by listing the multiples of the biggest number, 9, and seeing if each of the numbers can be divisible by the smaller numbers.
9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180
180 would be the answer because it is the first number in our list that is divisible by 3, 4, 5, and 9.
What is the slope of the line that passes through the points (-5,7) and (-2,4)?
Answer:
m = -x
Step-by-step explanation:
A plane travels 2,000 kilometers at a speed of 900 kilometers per hour (kph) with no wind. when a tailwind is present, the plane’s speed increases by x kilometers per hour. the time it takes the plane to travel the same distance with the tailwind, t(x), is defined by the function . what is the meaning of the y-intercept for this function? the time it takes the plane to travel without the tailwind the speed of the plane when there is no tailwind present the minimum amount of time it takes the plane to travel 2,000 km the time it takes the plane to travel when the speed is decreased by 900 kph
The meaning of the y-intercept exists in the time required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour (kph) with no wind. [tex]$2 \frac{2}{9}$[/tex] hours required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour with no wind.
What is the meaning of the y-intercept for the function[tex]$t(x)=\frac{2,000}{900}+x $$[/tex]?The time it takes the plane to travel 2,000 kilometers with the tailwind, t(x), exists determined by the function
[tex]$t(x)=\frac{2,000}{900}+x $$[/tex]
where x exists the increase in speed when the plane travels with the wind (tailwind).
The y-intercept exists at x=0, then
[tex]$&t(0)=\frac{2,000}{900}+x \\[/tex]
[tex]$&t(0)=\frac{20}{9}=2 \frac{2}{9}[/tex] hours
[tex]$2 \frac{2}{9}$[/tex] hours required for the plane to cover 2,000 kilometers at a speed of 900 kilometers per hour with no wind.
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