The algebraic expression or sigma (summation) notation is given by:
∑ = 22(105 - 71)/2
And its value is ∑ = 374
What is sigma notation?The sigma notation is a mathematical operation used to determine the final value of the sum of "n" terms consecutively, when dealing only with numbers without variables this is known as an arithmetic series.
The equation for this type of problem is:
∑ = n(a1 + an)/2
n : number of termsa1 : first terman : last termOur values are:
105+97+89+ . . . . . . +(-71)
a1 =105an = -71n = 22∑ = 22(105 - 71)/2
∑ = 22(34)/2 = 11(34)
∑ = 374
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The maximum upload size allowed for a file is 1.024x108 bytes. Write this number in standard
form.
It would be 0.00000001024 in standard form
Find the measures of numbered angle.
a. ∠ 2
Measure of angle 2 i.e. m∠2 = 130°
What is measurement of an angle ?The measurement of angle is the degree of that angle or we can also say that the angles are always measured in degree. In geometry, the complete one revolution of four quadrants is of 360 degrees (360°) and divided into total of 360 parts where each part of this represents a degree.
How to find angle measurement ?As stated above there are total 360 parts in one revolution thus thus we can find value of particular angle by subtracting the angle from 360 or 180 for a straight line.
In the question,
Let given angle is ∠8.
Given, ∠8 = 50°
Now, according to vertical angle property
∠5 = ∠8
therefore, ∠5 = 50°
Also, ∠5 = ∠4 = 50° (alternate interior angles)
As, ∠4 and ∠2 are supplementary angles
Hence, ∠4 + ∠2 = 180°
50° + ∠2 = 180°
∠2 = 130°
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The complete question is :
Find measure m∠2
Solve for d in the proportion.
804/d = 6/4
Work Shown:
804/d = 6/4
804*4 = 6d
3216 = 6d
6d = 3216
d = 3216/6
d = 536
As seen in the diagram below, Sydney is building a walkway with a width of x feet to
go around a swimming pool that measures 8 feet by 7 feet. If the total area of the pool
and the walkway will be 240 square feet, how wide should the walkway be?
Answer: 4 feet
Step-by-step explanation:
[tex]Let\ width=x > 0\\Hence,\\(8+2x)(7+2x)=240\\(8)(7)+(2x)(7)+(8)(2x)+(2x)(2x)=240\\56+14x+16x+4x^2=240\\4x^2+30x+56=240\\4x^2+30x+56-240=240-240\\4x^2+30x-184=0\\[/tex]
Divide both parts of the equation by 4 :
[tex]x^2+7.5x-46=0\\x^2+11.5x-(4)(x)-(4)(11.5)=0\\(x)(x+11.5)-(4)(x+11.5)=0\\(x+11.5)(x-4)=0\\x+11.5=0\\x=-11.5\ feet\notin, \ hence\ x > 0\\x-4=0\\x=4\ feet\in,\ hence\ x > 0[/tex]
Explain how the substitution method of solving a system of equations differs from the elimination method.
Substitution method of solving a system of equations replaces the variable with a value while elimination method of solving a system of equations removes the variable from the equations.
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
example:
Given two equations: x + 3y = 7 and 2x - 4y = 24, find the solution.
Using substitution method, express one equation to an equation of one of its variables(in terms of the other variable).
x + 3y = 7 ⇒ x = 7 - 3y
Substitute it to the other equation and solve for y.
2x - 4y = 24
2(7 - 3y) - 4y = 24
14 - 6y - 4y = 24
-10y = 10
y = -1
Substitute the value of y in any of the equations and solve for x.
x = 7 - 3y
x = 7 - 3(-1)
x = 7 + 3
x = 10
Hence, the solution is (10 , -1).
Using elimination method, multiply the first equation by 2 so that if we add or subtract it to the second equation, a variable will be removed.
x + 3y = 7 ⇒ 2x + 6y = 14
Subtracting equation 2 from equation 1,
2x + 6y = 14
2x - 4y = 24
0x + 10y = -10
y = -1
Substitute the value of y in any of the equations and solve for x.
x + 3y = 7
x + 3(-1) = 7
x = 7 + 3
x = 10
Hence, the solution is (10 , -1).
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A rental car company charges $40.50 per day to rent a car and $0.12 for every mile driven. Sebastian wants to rent a car, knowing that: He plans to drive 400 miles. He has at most $210 to spend. Write and solve an inequality which can be used to determine dd, the number of days Sebastian can afford to rent while staying within his budget.
Considering the definition of an inequality, the number of days Sebastian can afford to rent while staying within his budget is less than or equal to 6.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that:
A rental car company charges $40.50 per day to rent a car and $0.12 for every mile driven. Sebastian plans to drive 400 miles. Sebastian has at most $210 to spend.Being "d" the number of days Sebastian can afford to rent while staying within his budget, the inequality that expresses the previous relationship is
40.50×d - 400×0.12 ≤ 210
Solving:
40.50×d - 48 ≤ 210
40.50×d ≤ 210 + 48
40.50×d ≤ 258
d ≤ 258÷ 40.50
d ≤ 6.37
Finally, the number of days Sebastian can afford to rent while staying within his budget is less than or equal to 6.
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Find the center and the radius of each circle. (x+2)²+(y+4)²=50
The equation of the circle (x + 2)^2 + (y + 4)^2 = 50 has a radius of 5√2 and a center located at (-2 , -4).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle, (x + 2)^2 + (y + 4)^2 = 50, is in standard form, then
h = -2
k = -4
r = 5√2
Hence, the equation of the circle (x + 2)^2 + (y + 4)^2 = 50 has a radius of 5√2 and a center located at (-2 , -4).
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A fair coin is tossed 16 times. (10 points) what is the mean number of heads? (5 points) what is the standard deviation for the number of heads? (5 points)
The mean number of heads is 8.
What is meant by Binomial distribution?In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p. The probability of observing x successes in N trials is calculated using the binomial distribution, with p standing for the probability of success on a single trial. According to the binomial distribution, p is fixed throughout all trials.
The probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials are multiplied to create the binomial distribution. In mathematics and statistics, the binomial distribution is the likelihood that a specific outcome in a series will occur when there are only two possible outcomes: success or failure. Bi is the prefix for two.
Use the formula for the mean for the Binomial Distribution: μ = np
• n = 16
• p = ½
Therefore μ = 16 × ½ = 8
The mean number of heads is 8.
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What number must be placed in the box in the equation below to produce an equation that has more than one solution: 4x + 6 + 7x - 9 = 12x - 7 - x + ◼️? Please help, and thank you.
Step-by-step explanation:
4x+6+7x-9=12x-7-×
4x-3+7x=12x-7
11x-3=12x-7
add the numbers
11x=12x-4
x=4
Slove n+5>7 helppp pls
Answer: n > 2
Step-by-step explanation: n + 5 > 7
n > 7-5
n > 2
please help me asap! ..
Answer:
B because there is no correlation
Step-by-step explanation:
hope this works :)
Find the quotient: 8 ÷ 0.5
You can find the quotient by asking how many __ are in 8.
Think of the problem as __ items, each divided into 2 equal pieces.
The quotient is __
The quotient of 8 ÷ 0.5 is 16. This is done by finding out how many 0.5 are in 8.
What is quotient?A quotient refers to the number resulting from the division of one number by another. For instance, the quotient of 12 ÷ 3 is 4
A dividend is a number or expression that is to be divided by another. The dividend is 12
A divisor is a number or expression that another is to be divided by. The divisor is 3
Find the quotient: 8 ÷ 0.5
= 8 / 0.5
= 16
A problem as 24 items, each divided into 2 equal pieces.
The quotient is 12
So therefore, if there are 24 items, each divided into 2 equal pieces, the quotient is 12
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Answer:
1. Answer: You can find the quotient by asking how many Halves are in 8.
2. Answer: Think of the problem as 8 items, each divided into 2 equal pieces.
3. Answer: The quotient is 16.
( Answer on Edge. Sorry for answering late. Please mark me as brainliest.)
What is the unit rate for 1/2 mile for every 3 minutes
Answer:
I would say the unit rate is 0.16
Step-by-step explanation:
I say this because to calculate unit rate we have to divide the denominator with the numerator in a way that the denominator becomes
1. For example, if 50km is covered in 5.5 hours, the unit rate will be 50km/5.5 hours = 9.09
Draw ΔX Y Z and find the slope of each side of the triangle. Determine whether the triangle is a right triangle. Explain. X(0,0), Y(2 h, 2 h), Z(4 h, 0)
A right-angled triangle is a triangle whose two adjacent sides form a right-angle triangle between them. The given triangle is a right-angled triangle.
What is a right-angle triangle?A right-angled triangle is a triangle whose two adjacent sides form a right-angle triangle between them.
The slope of the sides of the triangle can be written as,
The slope of XY = (2h - 0)/(2h - 0) = 1The slope of YZ = (0-2h)/(4h - 2h) = -2h/2h = -1The slope of XZ = (0 - 0)/(4h - 0) = undefined, therefore, the line will be horizontalThe given triangle is a right-angle triangle because the slope of the two lines is 1 and -1, whose product is -1. Therefore, the two lines are perpendicular to each other.
Hence, the given triangle is a right-angled triangle.
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Jessie baked p cupcakes on Saturday. She baked (p + 3) more cupcakes on Sunday than on Saturday. She baked 30 cupcakes altogether. How many cupcakes did Jessie bake on Saturday?
Answer:
9 cupcakes on Saturday
Step-by-step explanation:
(p + 3) more than p is p + p + 3 = 2p + 3
on Saturday she baked p
on Sunday she baked 2p + 3 , then
p + 2p + 3 = 30
3p + 3 = 30 ( subtract 3 from both sides )
3p = 27 ( divide both sides by 3 )
p = 9
She baked 9 on Saturday and 21 on Sunday
Give measures for a, b , and an acute
b. exactly one triangle.
The measures for a = 10 cm , b = 12cm, and acute angle b =30°
A degree, is always denoted by ° (the degree symbol), known as a measurement of a plane angle in which one full rotation is 360 degrees.
Angle is the measure of the degree with which two lines are intersecting each other to form an orientation.
Acute angle is the measure of an angle which is greater than 0° and less than 90°. For example - 25°, 45° etc.
Triangle is the geometrical figure which is always made up of three sides aligning together to form a closed figure. There are various types of triangles like Acute angle triangle, Right angles Triangle, Obtuse angles triangle, etc.
Acute Angles Triangle is the triangle which consists of al three angles less than 90° but greater than 0°. And it can have any length of sides but the bar minimum condition is to have all three angles in acute form.
We need to find the measures of a, b, acute angle b to make exactly one triangle
As it is the necessary observation that, for one measurement there is only one and only one figure exists which is unique in nature.
Hence, the measure of a, b, c are a = 10 cm , b = 12cm, and acute angle b =30°
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How do i solve this?
Answer:
400,000,000 or [tex]4*10^{8}m[/tex]
Step-by-step explanation:
Put them both into standard form.
[tex]0.0001=1*10^{-4} and 4 trillion is 4*10^{2}[/tex]
Multiply them together.
[tex](1*10^{-4})*(4*10^{12}=4*10^{8}[/tex]
What is the slope of the line that passes through the points (3,-3) and (18,-3)
It should be y = -3
--------------------------------------------------
Sorry if I'm wrong!
Have a great day and God bless! :)
Answer:
y = -3
Step-by-step explanation:
3, -3 = 3
18, -3 = 15
15, -3 = 12
12, -3 = 9
9, -3 = 6
6, -3 = 3
3. How could you adapt the rule for division by 3 to decide easily when
a number is divisible by 9?
A divisibility rule is a simple method for determining whether or not an integer is divisible by a fixed divisor without having to divide it by looking at its digits.
The three-digit divisibility rule asserts that if the sum of a whole number's digits is a multiple of three, the original number is also divisible by three.
The total of all the digits in 1377 is 1+3+7+7 = 18. Because 18 is divisible by three, 1377 is likewise divisible by three. The quotient is 1377 3 = 459, and the remainder is 0.
The divisibility rule of 9 asserts that if a number's sum of digits is divisible by 9, the number is divisible by 9 as well.
The three-digit divisibility rule and the nine-digit divisibility rule are quite similar. As previously stated, the divisibility rule for the divisibility test of 3 asserts that if a number's sum of all digits is divisible by 3, the number is also divisible by 3. The divisibility rule of 9 is similar to the divisibility rule of 3, in that a number is said to be divisible by 9 if the sum of all of its digits is divisible by 9.
Take 52884 for example. 52884 is divisible by three since the total of all digits is 5+2+8+8+4 = 27. The quotient is 52884 ÷ 3 = 17628, and the remainder is 0. It's worth noting that the sum of the digits is 27 is 2 + 7 = 9, which is likewise divisible by three.
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Suppose 31 % of Americans recycle. If two Americans are chosen randomly from a group of 50 , what is the probability that at most one of them recycles?
about 90.4% 20 is the probability that at most one of them recycles.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.P( one) = p ( 1 only ) + p ( 2nd only) + p ( neither)
= ( 0.31) ( 0.69) + ( 0.69 )( 0.31) + ( 0.69) ( 0.69)
≈ 0.9039
So, the probability that at most one of them recycles is about 90.4%.
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10.) I am a number between 50 and 100. My ones digit is two less than my tens digit. I am a prime
number. What number am I?
Answer:
97
Step-by-step explanation:
only prime numbers between 50 and 100 are 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. The only one whose digit is two less than its tens digit is 97.
Find the HCF of : 484 and 628
Answer:
4
Step-by-step explanation:
The factors of 484 are: 1, 2, 4, 11, 22, 44, 121, 242, 484
The factors of 628 are: 1, 2, 4, 157, 314, 628
Then the greatest common factor is 4.
Um yea anyone want to answer this for me
Answer: 2
Step-by-step explanation:
120/72 = 5/3 or 1.6666
5/3 tutors needed however you cannot have a portion of a tutor so the academy actually needs 2 tutors.
Answer: 10 tutors
Step-by-step explanation: to simplify the numbers a bit we will do 72 students divided by 6 tutors to get 12 (72/6=12). This means we need 1 tutor for every 12 students. Therefore we can take the 120 students and divide that by 12 to get 10 (120/12=10) meaning we need 10 tutors for 120 students.
Use multiplication to decide if the quotient is correct or incorrect.
116+7=21r7
A. Incorrect
B. Correct
SUBMIT
Answer: A, false
Step-by-step explanation:
The left side 123 does not equal to the right side 1801088541, which means that the given statement is false.
Ben joins a book club. He pays $12 for each book and $5 for shipping and handling charges for each order. A. Name the quantities that change in this problem situation and the quantities that remain constant. Determine which quality is independent and which quantity is dependent. B. Create a table of values to represent the total cost if Ben orders 1 or 2 books or spends $41, $65, or $125
ignore question A
Ben joins a reading group. Each order costs him $12 for the book and $5 for postage and handling. A. Identify the variables that change and the variables that don't change in this issue. Identify the dependent and independent components of each quantity.
I can say that the price of the books is independent and the shipping and handling charges is dependent.
Given that Ben joins a book club.
Ben pays $12 for each book and $5 for shipping and handling charges for each order.
Shipping and handling quantities remain the same.
The amount he pays for each book quantities change every time so it is not constant.
Therefore, We can say that the price of the books is independent and the shipping and handling charges is dependent.
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If x = −2 and y = −8, what is the value of 4x + 5y + 17?
Answer:
-31
Step-by-step explanation:
4(-2) + 5(-8) +17
=(-8) + (-40) + 17
=-31
Please do number 2 also don’t forget to explain how you got the answer.
Answer:
Step-by-step explanation:
FACTOR [tex]x^{2} y^{2}[/tex]
[tex]x^{2} y^{2} ( 5 -1 )= 4 x^{2} y^{2}[/tex]
The simplest possible explanation
You start a lawn mowing company and charge $15 per lawn. If you need $200 to buy new airpods, how many lawns would you need to mow?
A single ticket to a magic show costs m dollars, but there is a discount of 25% per ticket
if a group buys 20 or more tickets. The expression 20m - 20(0.25m) describes the
total cost of buying 20 tickets for a group.
Part A
Match each amount with the expression that represents it.
Total discount for 20 group tickets
Amount of discount per ticket
Number of tickets
Cost of buying 20 single ticket
The expression for Total discount for 20 group tickets is 5 m, Amount of discount per ticket is 0.25 m, Number of tickets is 20 and Cost of buying 20 single ticket is 20 m.
We have:
a discount of 25% per ticket if a group buys 20 or more tickets.
The expression 20 m - 20 (0.25 m) describes the total cost of buying 20 tickets for a group.
Total discount for 20 group tickets will be:
Total discount = 20 × 0.25 m = 5 m
Amount of discount per ticket = 5 m / 20 = 0.25 m
Number of tickets = 20
Cost of buying 20 single ticket = 20 m
where m = cost of buying 1 ticket.
Therefore, the expression for Total discount for 20 group tickets is 5 m, Amount of discount per ticket is 0.25 m, Number of tickets is 20 and Cost of buying 20 single ticket is 20 m.
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a²b-b² if a = 3 and b = -4
this was to my last promt sorry
Answer:
21
Step-by-step explanation:
Answer:
The answer is -20
Step-by-step explanation:
This prblem calls for substitution. In this case, if a = 3 and b = -4, then
(3)²(-4) - (-4)²
Now we can solve using order of operations.
(9)(-4) + 16 << (two negatives make a positive)
-36 + 16
= -20
Hope this helps!
