Sum of APs 2+5+8+........ as far as the 18th term is 495.
Sum of n terms of A.P.
[tex]S_{n} = \frac{n}{2}[2a+(n-1)d][/tex]
where,
[tex]S_{n}[/tex] = sum of n terms of A.P.
a = first term of A.P.
d = Common difference.
Given,
d=5−2=3
a=2
[tex]S_{11}[/tex]=[tex]\frac{18}{2}[/tex][4+(18-1)×3]
=[tex]\frac{18}{2}\\[/tex][4+51]
=[tex]\frac{18}{2}[/tex]×55
=495
An arithmetic progression, or arithmetic sequence, is a sequence of numbers in which the difference between successive members is constant. Here is the AP formula for AP a, a + d, a + 2d, a + 3d, . . . a + (n - 1) d. The formula for finding the nth term is [tex]a_{n}[/tex] = a + (n – 1) × d.
Then the formula for finding the sum of the arithmetic progressions is:[tex]S_{n} = \frac{n}{2}[2a+(n-1)d][/tex] where a = first term in arithmetic progression, n = number of terms in arithmetic progression, and d = total difference.
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A(-2, 2), B(6, 2), C(6, 3), and D(-2, 3).
What is the area of rectangle ABCD?
Answer: 80un^2
Step-by-step explanation:
The length of AB is 10
The length of BC is 8
The length of CD is 10
The length of DA is 8
10 x 8 = 80 and there are two pairs of 8 and ten which makes it 80un^2
A local pizza shop has a membership program for frequent buyers. The membership costs $25 per month and members get a discounted price of $1.25 per slice of pizza. Justin purchased a membership to this pizza shop. How much would Justin have to pay the pizza shop if he bought 12 slices of pizza this month? What would be the monthly cost for x slices of pizza?
PLEASE HURRY!
The amount that Justin would have to pay the pizza shop if he bought 12 slices of pizza this month is $15.
The monthly cost for x slices of pizza is $25 + $1.5x
What is the total cost?In order to determine the amount that Justin would have to pay the pizza shop if he bought 12 slices of pizza can be determined by multiplying the cost per pizza by the number of pizzas sold.
Multiplication is the operation used in mathematics that is used to calculate the product of two or more numbers. The sign that is used to represent multiplication is x.
Cost of 12 slices of pizza = discounted price x number of slices bought
$1.25 x 12 = $15
The monthly cost is the sum of the membership fee and the total cost of the pizzas bought
Monthly cost = monthly membership fee + cost of the slices
Monthly cost = monthly membership fee + (discounted price x number of slices bought)
$25 + (1.25 x x)
$25 + $1.25x
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What are the solutions to the equation? 4x³ = 36x Enter your answers in the boxes.
[tex]4 {x}^{3} - 36x = 0 \\ 4x( {x}^{2} - 9) = 0 \\ 4x = 0 \\ \\ or \\ {x}^{2} - 9 = 0 \\ \\ \frac{4x}{4} = \frac{0}{4} =0 \\ \\ \\ (x - 3)(x + 3) = 0 \\ \\ x + 3 = 0 \\ \\ or \\ x - 3 = 0 \\ \\ \\ x = 0 \\ or \\ x = - 3 \\ \\ or \\ \\ x = 3[/tex]
ATTACHED IS THE SOLUTION
Divide negative 2 and 3 over 4 ÷ negative 5 and 1 over 7.
negative 77 over 144
negative 221 over 28
221 over 28
77 over 144
The fractions are divided to give 77/144. Option A
What is a fraction?A fraction can simply be defined as the part of a whole set or element.
The types of fractions includes;
Improper fractionsProper fractionsMixed fractionsComplex fractionsSimple fractionsExamples of simple fractions are: 1/2 , 1/4
Examples of proper fractions are; 2/3, 5/6
Examples of improper fractions are; 5/3, 9/7
Examples of mixed fractions are; 2 1/2, 3 1/4
Given the expression as;
2 3/4 ÷ 5 1/7
Turn into improper fractions
11/4 ÷ 36/7
Take the inverse of the divisor
11/4 × 7/36
Multiply the numerators and denominators
77/144
Thus, the value is 77/144
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Answer: #1 / A
Step-by-step explanation:
A group of friends wants to go to the amusement park. They have no more than $710
to spend on parking and admission. Parking is $9, and tickets cost $10.75 per person,
including tax. Which inequality can be used to determine p, the maximum number of
people who can go to the amusement park?
The inequality for maximum number of people is 710 ≥ 9 + 10.75p
The correct option is (d)
Given,
Total money spend on amusement park is $710
Parking charge is $9.
and, tickets cost $10.75 per person
To find the inequality for maximum number of people (p) who can go to the amusement park?
Now, According to the question:
Costs of people tickets = 10.75 p
Total Cost will be = 9 + 10.75p
The inequality will be
9 + 10.75p ≤ 710
=> 710 ≥ 9 + 10.75p
Hence, The inequality for maximum number of people is 710 ≥ 9 + 10.75p .The correct option is (d).
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HELP ME PLEASE I GOT A 67 IN MATH
Answer:
0.5
Step-by-step explanation:
(-6,-5) ( 6,1) The slope is the change in y over the change in x.
([tex]x_{1}[/tex],[tex]y_{1}[/tex]) ([tex]x_{2}[/tex], [tex]y_{2}[/tex]) Will will use this for the points above and then put in the numbers
[tex]\frac{y_{2 - y_{1} } }{x_{2 - x_{1} } }[/tex]
[tex]\frac{1 - -5}{6 - -6}[/tex]
[tex]\frac{1+ 5}{6+6}[/tex]
[tex]\frac{6}{12}[/tex]
[tex]\frac{1}{2}[/tex] = 0.5 as a decimal
If you start at any point on the line and go up one unit and 2 units of the right, you will end up on the line again. This pattern repeats over and over and over.
Write an equation of a line perpendicular to 4x + 3y = 6 that passes through the point (-8, -5)
Answer:
Step-by-step explanation:
Hope it helps :D
If a segment has one endpoint at (0,0) and a midpoint at (4,-6) where is the other endpoint?
The coordinates of the second end point of the line is (8, -12).
What is defined as the mid point of coordinate?For the points on the coordinate axes, the midpoint formula is defined. Let the endpoints of the a line segment be (x)1, (y)1, and (x)2, (y)2. The midpoint is equal to one-half of the sum of the two points' x-coordinates and half of a sum of the two points' y-coordinates.For the given question;
The end point of the line segment is (0,0).
The mid-point of the line segment is at (4,-6).
Thus,
(x₁, y₁) = (0,0)
(x₂, y₂) = ?
(xₐ, yₐ) = (4,-6)
Thus, the formula for finding the mid point is;
xₐ = (x₁ + x₂)/2
Put the values;
4 = (0 + x₂)/2
On simplification;
x₂ = 8.
For y coordinate;
Thus, the formula for finding the mid point is;
yₐ = (y₁ + y₂)/2
Put the values;
-6 = (0 + y₂)/2
On simplification;
x₂ = -12
Thus, the coordinates of the second end point of the line is (8, -12).
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I need help. Answer first and get brainest.
Answer:
1,312.5
Step-by-step explanation:
6.25x10=62.5
3500x62.5%=2,187.5
3500-2,187.5=1,312.5
I hope this is correct :-|
we have
3500 = Pe^(0.0625) x(10)
3500= Pe^(0.625)
P = 3500 / e^(0.625) = 1873
thus 1873 Macaws remaining in 10 years
A bag contains four green balls three blue gumballs and two red gumballs all the same size and shape what is the probability of choosing a red gumball choosing a blue gumball and choosing a green gumball
Probability of choosing a red gumball choosing a blue gumball and choosing a green gumball are 2/9, 3/9, 4/9 RESPECTIVELY.
four green balls three blue gumballs and two red gumballs all the same size and shape.
total number of balls =9;
red ball =2
green ball=4
blue ball =3
as we know, the probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes.
so, according to the question;
probability of choosing a red gumball choosing= no. of red balls/total number of balls
=>2/9=0.22
probability of choosing a blue gumball choosing= no. of blue balls/total number of balls
=>3/9=0.33
probability of choosing a green gumball choosing= no. of green balls/total number of balls
=>4/9=0.44;
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Compare 0.79 and 0.789.
Answer:
0.79 greater than 0.789 by 0.001
Step-by-step explanation:
[tex]{ \tt{ \delta x + 0.79 = 0.789}} \\ { \tt{ \delta x = 0.001}}[/tex]
What percentage of the area lost to deforestation will have been replanted by the preservation consortium after 1 year, 5 years, and 10 years?
What is the equation of the line that passes through (7,4) and (4, -2)?
Oy=2x-10
Oy=-2x-10
Oy=2x+18
Oy=-2x+18
[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{7}}} \implies \cfrac{ -6 }{ -3 }\implies 2[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{2}(x-\stackrel{x_1}{7}) \\\\\\ y-4=2x-14\implies {\Large \begin{array}{llll} y=2x-10 \end{array}}[/tex]
Simplify the expression .
A.
B.
C.
D.
Using properties of exponents, the simplified expression for 5³ x 5^(-5) is given by:
A. 1/(5²).
How do we multiply two terms with the same base and different exponents?The exponent property applied to multiply the terms with the same base but different exponents is that we keep the bases and then add the exponents.
For this problem, the expression is given as follows:
5³ x 5^(-5)
Hence:
The base is of 5.The exponents are of 3 and -5.Adding the exponents, we have that:
3 + (- 5) = 3 - 5 = -2.
Hence the simplified expression is:
5³ x 5^(-5) = 5^(-2).
When a number has a negative exponent, we can move it to the denominator, then the exponent becomes positive, hence:
5^(-2) = (1/5)² = 1/5² = 1/25.
Meaning that option A is correct.
What is the missing information?The expression in this problem is 5³ x 5^(-5), and the correct options are given by the image at the end of the answer.
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A pizza shop offers a choice of 3 sizes (small, medium, and large) and 7 different toppings. Different pizzas can be created by changing the size and/or the choice of toppings. If Cody wants to order a pizza with exactly 2 different toppings, how many different pizzas can he create?
1. 6
2. 21
3. 63
4. 121
Using permutation and combination we can calculate that she can get 63 different types of pizza.
Permutations and combinations are the various ways in which elements from a set may be chosen, typically without replacement, to create subsets. This choice of subsets is known as a permutation when the order of the selection is taken into account, and as a combination when it is not.
The total of the decisions we make given an initial set of n items is known as a combination. Permutation, on the other hand, counts the number of possible arrangements of n separate items. This will help us recall that combinations place more emphasis on choice than on placement, order, or arrangement.
Now Cody can get any two toppings out of the 7.
Number of ways in which Cody can pick 2 toppings out of 7 is given by the use of combination,
7C2 = 21 different ways.
Again the number of ways in which 3 different pizza s can be selected is given by 21 × 3 = 63 ways.
Hence Cody can create 63 different pizzas.
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The sizes of four cell phone displays are 5.625 inches, 5 1/2 inches, 6 1/4 inches, and 5.125 inches. How much longer is the longest display than the shortest display? a) 3/4 in, b) 1 in, c) 1.125 in, d) 1 1/4 in
Longest display is 1.125 inches longer than the shortest display.
What is fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
Given Data
Size of cell phones
5.625 inches
5[tex]\frac{1}{2}[/tex] inches = [tex]\frac{11}{2}[/tex] inches
5.5 inches
6[tex]\frac{1}{4}[/tex] inches = [tex]\frac{25}{4}[/tex] inches
6.25 inches
5.125 inches
Longest display = 6.25 inches
Shortest display = 5.125 inches
Difference = longest display - shortest display
Difference = 6.25 - 5.125
Difference = 1.125
Longest display is 1.125 inches longer than the shortest display.
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There are 15 year 12 pupils in a football club, out of a total of 46 pupils. write this proportion as a percentage. give your answer correct to 1 decimal place when appropriate.
In the football club, the percentage of 15-year 12 pupils out of 46 pupils is equal to 30%.
The proportion can be found by dividing the number of 15-year pupils by the total number of pupils. Therefore;
number of 15-year pupils / total number of pupils = 12 / 46 = 0.260
Rounding it to one decimal;
0.260 = 0.3
Percentage in mathematics can be defined as a number or a rate in each hundred. A decimal value can be converted into a percentage by multiplying the decimal value by 100.
0.3 × 100 = 30%
Therefore, the proportion of the 15-year pupils in the football club is 12/46 and this proportion can be written in percentage as 30%.
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use properties of special parallelograms to complete the proof given: EFGH is a rectangle. J si the midpoint of EH. prove: triangle FJG is isosceles
Using the special parallelograms the proof with regard to the EFGH rectangle that triangle FJG is an isosceles is completed and attached. See further explanations below.
What is proof inMath?Proofs are examples of exhaustive deductive reasoning that establishes logical certainty, as opposed to empirical arguments or non-exhaustive inductive reasoning that establishes "reasonable expectation."
The following are various kinds of proof:
Direct proofs.Indirect proofs.Vacuous proofs.Trivial proofs.Proof by contradiction.Proof by cases.Proofs of equivalence.Existence proofs.Learn more about parallelograms:
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in a recent year, 389 of the 281,421,906 people in the united states were struck by lightning. estimate the probability that a randomly selected person in the united states will be struck by lightning this year.
Answer:
0.000001382 if you divide
Omar has been training for the Candlewood Footrace. The first week he trained, he ran 7 days and took the same two routes each day: 3 miles around the track before work and a longer route through his neighborhood after work. By the end of the week, Omar had run a total of 63 miles.
Which equation can you use to find how many miles, x, Omar ran each day after work?
The equation that can be use to find the how many miles, x, Omar ran each day after work is x = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7, he ran 6 miles each days after work
The total number of days he run = 7 days
Total distance he ran in one week = 63 miles
The distance he run before the work = 3 miles
The total distance he run before the work in one week= 7×3
= 21 miles
The total distance he run after the work = 63 - 21
= 42 miles
The equation that can use to find how many mile x, Omar ran each day after work = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7
Substitute the values in the equation
= 42/7
= 6 miles
Hence, the equation that can be use to find the how many miles, x, Omar ran each day after work is x = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7, he ran 6 miles each days after work
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Can someone pls explain how to solve this
Answer:
No solution
Step-by-step explanation:
A number squared cannot be negative. It is a trick question.
Solve for the value of q.
Answer:
q = 20
Step-by-step explanation:
The two angles shown in the image are supplementary angles which means their sum is equal to 180°
We can find the value of q using the following equation:
78 + 5q + 2 = 180 add like terms
80 + 5q =180 subtract 80 from both sides
5q = 100 divide both sides by 5
q = 20
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Guide to follow:}[/tex]
[tex]\bullet\large\textsf{ A supplementary angles (}\angle\large\textsf{) is equal to 180}^\circ\\\bullet\large\textsf{ A complementary angles (}\angle\large\textsf{) is equal to 90}^\circ[/tex]
[tex]\star \large\textsf{ The current angel that you are working with is a \boxed{\mathsf{supplementary \ angle \ (\angle)}}}}\\\large\textsf{so that means means \large\textsf{that your angle is equal to \boxed{\mathsf{180 ^\circ}}}}[/tex]
[tex]\huge\textsf{What does your equation look like?}[/tex]
[tex]\mathsf{(78) + (5q + 2) = 180}[/tex]
[tex]\huge\textsf{How we solve for your equation?}[/tex]
[tex]\mathsf{(78) + (5q + 2) = 180}[/tex]
[tex]\mathsf{78 + 5q + 2 = 180}[/tex]
[tex]\large\textsf{COMBINE the LIKE TERMS}[/tex]
[tex]\mathsf{(78 + 2) + (5q) = 180}[/tex]
[tex]\mathsf{78 + 2 + 5q = 180}[/tex]
[tex]\mathsf{80 + 5q = 180}[/tex]
[tex]\large\textsf{Simplifying}[/tex]
[tex]\mathsf{5q + 80 = 180}[/tex]
[tex]\large\textsf{SUBTRACT 80 to BOTH SIDES}[/tex]
[tex]\mathsf{5q + 80 - 80 = 180 - 80}[/tex]
[tex]\large\textsf{Simplify it:}[/tex]
[tex]\mathsf{5q = 180 - 80}[/tex]
[tex]\mathsf{5q = 100}[/tex]
[tex]\large\textsf{DIVIDE 5 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{5q}{5} = \dfrac{100}{5}}[/tex]
[tex]\large\textsf{Simplify it:}[/tex]
[tex]\mathsf{q = \dfrac{100}{5}}[/tex]
[tex]\mathsf{q = 20}[/tex]
[tex]\huge\textsf{So, what does mean your answer should be?}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{q = 20}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Help fast. I need help with this one as fast as you can. I mark brainliest
The true statement about the values x = - 2 and y = -0.5 is that: D. they are the only values that make both equations true.
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect, meet, or cross each other, which is typically represented as an ordered pair containing the point, x-axis and y-axis.
This ultimately implies that, a point of intersection simply represents the ordered pairs (values) that make a system of equations true.
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Complete Question:
Lan graphs these equations and finds that the lines intersect at a single point,
(-2,-0.5).
Equation A: 4y - 3x = 4
Equation B: -2x + 8y = 8
Which statement is true about the values x = -2 and y = -0.5?
A. They satisfy equation A but not equation B.
B. They satisfy equation B but not equation A.
C. They show that the equations represent the same line.
D. They are the only values that make both equations true.
You pay no federal taxes up to $9,525, 12% for income from $9,526 up to $38,700, 22% for income from $38,701 up to $82,500. If your income is $57,890, how much in taxes do you need to pay?
With an income of $57,890, you need to pay $12,735.8 in taxes.
What is mean by proportion?
A proportion is a fraction of a total amount, in which two ratios are set equal to each other.
Given that;
For incomes from $38,701 up to $82,500, you need to pay 22% in taxes.
And, No federal taxes up to $9,525, 12% for income from $9,526 up to $38,700, 22% for income from $38,701 up to $82,500.
Now,
An income of $57,890 is in this range, hence the amount paid is given by;
Amount paid = 57890 x 22%
= 57890 x 0.22
= $12,735.8.
So, Paid amount for the tax = $12,735.8
Thus, With an income of $57,890, you need to pay $12,735.8 in taxes.
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there are 6 quarters in a jar. jill adds 2 quarters to the jar every day. which linear equation represents the total amount of quarters in the jar after x days? responses 6y
– 0.3+ – 0.8×0.5–0.1 using PEMDAS
Answer:
-0.8
Step-by-step explanation:
=0.3-0.8*0.5-0.1
= -0.3-0.4-0.1
= -0.7-0.1
= -0.8
D
519
to
A
70°
E
70°
m/ABC= m/BAD because they are alternate interior angles.
m/BCA = m/CAE because they are alternate interior angles.
m/BAD + xº + m/CAE = 180° because the three angles form a straight
line.
So the value of x must be
Answer: 59
Step-by-step explanation:
[tex]51+x+70=180\\\\121+x=180\\\\x=59[/tex]
Agent Hunt is transferring classified files from the CIA mainframe into his flash drive.
SSS represents the size of the files on the drive (in megabytes) after ttt seconds.
S=5t+45S=5t+45S, equals, 5, t, plus, 45
How many megabytes are transferred every 101010 seconds?
Using the slope of the linear function, it is found that 50 megabytes are transferred every 10 seconds.
What is a linear function?A linear function is modeled according to the following rule, in slope-intercept form:
y = mx + b
In which:
m is the slope of the function, which is the rate of change of the function for every unit of the input.b is the y-intercept of the function, which is the initial value of the function, when the lower bound of the domain is of 0.For this problem, the function is given as follows:
S(t) = 5t + 45.
The slope of m = 5 means that every one second, 5 megabytes are transferred, hence the amount transferred every 10 seconds is given by:
Amount = 5 x 10 = 50 MB.
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PLS HELP WILL GIVE 20 POINTS AND BRAINLIEST!! ASAP!!!!
Answer:
7/49
Step-by-step explanation:
there is a sequence so you just need to follow it
so 11, 10, 9, 8 then the next one will be 7
49x + 56xy^2
———————-
7x + 7xy
Answer:
Step-by-step explanation:
31/2x-7