The last term b of the expression is 99
What is Arithmetic Progression?
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP : Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
Sum of first n terms of an AP : Sₙ = ( n/2) ( a+b )
where a = first term
b = last term
Given data ,
First term a = 3
Number of terms n = 12
Sum of n terms Sₙ = 612
Let the last term of the AP be = b
Sum of first n terms of an AP : Sₙ = ( n/2) ( a+b )
Substitute the values of a , Sₙ and n in the equation
612 = ( 12/2 ) ( 3 + b)
612 = 6 ( 3 + b )
Divide by 6 on both sides , we get
102 = 3 + b
Subtract 3 on both sides , we get
b = 99
Hence , the last term of the Arithmetic Progression is 99
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Write the equation in standard form for the circle with center (2,–
9) and radius 2
Required standard form for given circle is [tex](x-2)^{2}+(y+9)^{2}=4[/tex]
What is the standard form of equation of circle?Standard form of circle is expressed as[tex](x-h)^{2}+(y-k)^2=r^{2}[/tex] ,where h,k are the coordinate of the center of circle and r is radius.
According to the given data:Center (h, k) = (2, -9)
radius = 2 units
Using standard form of equation,
[tex](x-h)^{2}+(y-k)^2=r^{2}[/tex]
Putting the given values,we get
[tex](x-2)^{2}+(y-(-9))^{2}=2^{2}[/tex]
⇒ [tex](x-2)^{2}+(y+9)^{2}=4[/tex]
Hence, the standard form of equation of circle is [tex](x-2)^{2}+(y+9)^{2}=4[/tex] .
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What number should fill in the blank? 36 x 8 =_________+6)x 8
The number to be filled in the blank is 30
How to calculate the missing number?Let us consider the number in the blank = x
Rewriting it as a linear equation,
36 * 8 =( x + 6 )8
288 = ( x + 6) 8
288 /8 = x + 6
36 = x + 6
x = 36- 6
x = 30
The number to be filled in the blank is 30
What is a linear equation?A linear equation is one that has a degree of 1 as its maximum value. Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. Both linear equations with one variable and those with two variables exist. Ax+ B = 0, where A and B are both real integers, and x is the only variable, is the standard form or general form of a linear equation in one variable. A vertical line that is parallel to the y-axis is formed on the graph of a linear equation with one variable, x, and vice versa.To learn more about linear equation, refer:
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PLEASE HELPP!!!! Bob has $12.75 and plans to purchase snow cones for his friends at $1.25 each. If he needs to save at least $8.75 to pay for lunch, how many snow cones can he buy. Use the inequality below to help answer.
Answer:
Bob can buy no more than 3 snow cones.
Step-by-step explanation:
[tex]12.75 - 1.25c \geqslant 8.75[/tex]
[tex] - 1.25c \geqslant - 4[/tex]
[tex]1.25c \leqslant 4[/tex]
[tex]c \leqslant 3.2[/tex]
So Bob can buy up to 3 snow cones.
What is the solution of 2|7x – 4| + 3 = 51?
The midpoint of AB is M(-6, 1). If the coordinates of A are (-7,-3), what are
the coordinates of B?
Answer:
(-5,5)
Step-by-step explanation:
Find the length of an arc for a circle whose central angle is 220 degrees and radius is 32
inches.
Answer:
below
Step-by-step explanation:
The arc length is 220 / 360 ths of the total circumference
find the total circumference = pi *2r = 64 pi inches
now multiply by the fraction of the total circumference
220 / 360 * 64 pi = 122.9 in
if you choose two cards out of a deck of cards, what are the chances one is a red face card and the other is a black non-face card?
Using the probability, if you choose two cards out of a deck of cards, then the chances one is a red face card and the other is a black non-face card is 1/2.
In the given question,
If you choose two cards out of a deck of cards, then we have to find the chances one is a red face card and the other is a black non-face card.
As we know that in a deck having 52 cards. In which 26 are red and 26 are black.
We have to choose a red face card.
As we know that in a deck have 12 face cards. In which 6 red face cards and 6 black face cards.
So the chance of getting red face card is
P(R)=Total number of red face cards/Total number of cards
P(R)=6/52
We have to choose a black non-face card.
We know that in a deck have 6 black face cards and total black cards are 26. So the non face cards are 20.
So the chance of getting black non-face card is
P(B)=Total number of black non-face cards/Total number of cards
P(B)=20/52
Now the chances of getting one is a red face card and the other is a black non-face card is
P(R or B)=P(R)+P(B)
P(R or B)=6/52+20/52
P(R or B)=(6+20)/52
P(R or B)=26/52
P(R or B)=1/2
Hence, if you choose two cards out of a deck of cards, then the chances one is a red face card and the other is a black non-face card is 1/2.
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There are a total of 58 schools and 23,581 students attend those schools. Sarah only works in 23 of those schools, how many students has Sarah worked with?
If Sarah only works in 23 of those schools then Sarah worked with 9,351 students.
Given, There are a total of 58 schools and 23,581 students attend those schools. Sarah only works in 23 of those schools
now, as 58 schools = 23581 students
1 school = 23581/58 students
now,
23 schools = 23× 23581/58 students
23 schools = 9,351 students
So, Sarah worked with 9,351 students.
Hence, Sarah worked with 9,351 students.
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Please solve this asap.
Answer:
Step-by-step explanation:
hopes this helps please mark brainliest
Follow up answer is 90/500
9/50
Find the amount if
8.4% of it is 17.22kg
Answer:
205 because 8.4% of 17.22 is 205
Factorise this : 6xy-18y
6xy - 18y
common factor is 6y:
6y(x - 3)
Gavin drove 88 mile in 12 minute. If he drove at a contant rate, how far did he travel in one hour?
Answer:
440 miles
Step-by-step explanation:
5 pairs of 12 mintues make 1 hour
5 *88 = 440
Multiply 6.75 x 10 to the 6th power and 1.2 × 10 to the 6th power
Value for multiplication of 6.75 x 10⁶ and 1.2 × 10⁶ : 8.1 x 10¹²
What is Multiplication?
The process of finding the sum of two or more numbers is known as multiplication. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of the same size, we employ multiplication.
The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
We have the given values to multiply:
6.75 x 10⁶ and 1.2 × 10⁶
Now,
= 6.75 x 10⁶ x 1.2 × 10⁶
= (6.75 x 1.2) x (10⁶ x 10⁶)
= (8.1) x 10⁽⁶⁺⁶⁾
= 8.1 x 10¹²
Hence, the value of multiplication of 6.75 x 10⁶ and 1.2 × 10⁶ is 8.1 x 10¹²
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the bureau of alcohol, tobacco, and firearms (batf) has been concerned about lead levels in california wines. in a previous testing of wine specimens, lead levels ranging from 45 to 750 parts per billion were recorded. how many wine specimens should be tested if the batf wishes to estimate the true mean lead level for california wines to within 10 parts per billion with 95% confidence? (round your answer up to the nearest whole number.)
Using the Uniform Distribution and the Z- distribution, it is found that 1591 specimens should be tested.
Uniform Distribution: It refers to a type of probability distribution in which all outcomes are equally likely.
Z- Distribution: The standard normal distribution, also known as z distribution, is a special normal distribution where the mean is 0 and standard deviation is 01.
For an uniform distribution of bounds a & b the standard deviation is given by: α = √ (b-a)²÷12
here, α= standard deviation.
in this problem, a = 45 and b = 750, thus the estimate is:
α = √(750-45)² ÷ 12
= √497025 ÷ 12
= 203.5
the margin of error of a Z confidence interval is given by:
M = z (α ÷√n)
where, z is the critical value
α is the population Standard deviation
n is the sample size.
Now, finding the critical value which is z with a p - value of (1+∝ )÷2, where ∝ is confidence level.
here, ∝ = 0.95, thus z with a p-value of (1+0.95)÷ 2 = 0.96
∴ z= 0.96
standard deviation estimates is 203.5.
now, we want sample for a margin of error of 10, then,
M= z( α ÷ √n)
⇒ 10 = 1.96 ( 203.5 ÷ √n)
⇒ 10√n = 1.96 (203.5)
⇒ √n = 0.196 (203.5)
⇒ (√n)² = [0.196(203.5)]²
⇒ n = 1590.89
Round up the value 1590.89 by:
1591 specimen should be tested
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-5
Graph y=-3x + 5
10
5
Check it
10
Answer:
See the attached graph.
Step-by-step explanation:
Pick any two values of x that are on the x axis and compute the values of y using the equation. I'll pick x values of -1 and 2 for illustration.
x=-3x + 5
X Y
-1 2
2 -1
Plot those poins and then connect them with a ruler to form the line for y = -3x + 5
Se the attached graph.
Select all the expressions that are equivalent to 434( – 9).
The equivalent expression for the exponential expression 4³ . 4⁻⁹ is either 4⁻⁶ or 1/4⁶
Exponential expression:
Exponential expression means a mathematical expression consisting of a constant raised to some power.
Given,
Here we have the expression 4³ . 4⁻⁹.
Now, we have to simplify this expression to find the equivalent expression.
According to the following exponent rule,
xᵃ . xᵇ = x⁽ᵃ⁺ᵇ⁾
Based on this rule, we have rewritten the expression as,
=> 4⁽³ ⁺ ⁽⁻⁹⁾⁾
Thus the resulting value of the expression is,
=> 4 ⁽³⁻⁹⁾
=> 4⁻⁶
By using the another exponent rule, we get the value as,
=> 1/4⁶
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PLEASE HELP ASAP
The result of 6 subtracted from a number n is at least 2. what numbers are solutions?
A.n-2>6;n>8
B.n-6>2;n>8
C.n+6>2;n<4
D.n+6>2;n>4
Answer:
B) n - 6 ≥ 2; n ≥ 8------------------------
Translate
6 subtracted from a number n ⇒ n - 6at least 2 ⇒ n - 6 ≥ 2Solution
n - 6 ≥ 2n ≥ 2 + 6n ≥ 8Option B is the closest one.
Answer:
b) n - 6 > 2 ; n > 8
Step-by-step explanation:
Given statement,
→ The result of 6 subtracted from a number n is at least 2.
Forming the inequation,
→ n - 6 > 2
Now the value of n will be,
→ n - 6 > 2
→ n > 2 + 6
→ [ n > 8 ]
Hence, the value of n is 8.
PLEASE HELP
I dont understand this
Answer: I EXPLAINED IT TELL ME IF YOU NEED THE ANSWER!
Step-by-step explanation: You can find the final equation for the segment of a circle area: A segment = A sector - A isosceles triangle = (0.5 × r² × α) - (0.5 × r² × sin(α)) = 0.5 × r² × (α – sin(α)) Formula given radius and height. A segment = r² × Arcos((r-h)/r) - (r-h) × √ (2 × r × h - h²) where h is the height of a segment, also known as sagitta.
Students at a sports college choose activities for games.
In Year 7 they chose between rounders and athletics in the ratio 1 : 4.
There are 60 students in Year 7.
Work out how many chose athletics.
Answer: 48 students
Step-by-step explanation: 1+4=5
60÷5=12
12x4=48
At the tart of the day, a decorator reted a 3 m ladder | againt a vertical wall o that the foot of the ladder wa | 60 cm away from the bae of the wall. | During the day, the ladder lipped down the wall, cauing | the foot of the ladder to move 80 cm further away from the bae of the wall. | How far down the wall, in centimetre, did the ladder lip? | Give your anwer to the nearet 1 cm. |
The distance at which the ladder slips down the wall is equal to 5cm.
As given in the question,
figure of the given situation attached.
Length of the ladder AD or BE = 3m
= 300cm
Distance between base of wall and ladder before slipping 'DC'= 60cm
Distance after slipping 'EC' = 80 cm
In ΔADC,
AC =√AD² -CD²
= √ 300² - 60²
= √86400
= 293.9
= 294 cm ( nearest cm)
BC = √ BE² - EC²
= √300² -80²
= √ 83600
= 289.1
= 289 cm ( nearest cm)
Distance AB = AC - BC
= 294 - 289
= 5cm
Therefore, distance between the ladder before and after slipping on the wall is 5cm.
The complete question is :
At the start of the day , a decorator rested a 3m ladder against a vertical wall so that the foot of the ladder was 60cm away from the base of the wall. During the day, the ladder slipped down the wall, causing the foot of the ladder to move 80cm further away from the base of the wall. How far down the wall, in centimeters, did the ladder slip? Give your answer to the nearest 1cm.
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Last week, Colton sold 14 magazine subscriptions and 36 raffle tickets for a fundraiser. This week, he sold 18 magazine subscriptions and 26 raffle tickets. If Colton charged $10.25 for each magazine subscription and $0.50 for each raffle ticket, how much money did he earn for the fundraiser over these two weeks?
If in Last week, Colton sold 14 magazine subscriptions and 36 raffle tickets for a fundraiser. This week, he sold 18 magazine subscriptions and 26 raffle tickets. If Colton charged $10.25 for each magazine subscription and $0.50 for each raffle ticket, Then $359 money he earned for the fundraiser over these two weeks
What is Equation?Two or more expressions with an Equal sign is called as Equation
Given,
10.25 for each magazine subscription and $0.50 for each raffle ticket,
M=10.25 and T=0.50
Last week:
14 magazine subscriptions and 36 raffle tickets for a fundraiser.
14M+36T
Now substitute M and T values
14(10.25)+36(0.50)
143.5+18
161.5
Current week:
18 magazine subscriptions and 26 raffle tickets.
18M+26T
Now substitute M and T values
18(10.25)+26(0.50)
184.5+13
197.5
So total money he earned for two weeks is 161.5+197.5
$359
Hence $359 money did he earn for the fundraiser over these two weeks
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Please help guys<333
Answer:
2
Step-by-step explanation:
because u need to multiply
if each flash is .1 lumens and we want 40 lumens at least 70% of the time, how many fireflies do we need?
4373 are many fireflies do we need linear equation.
What is an explanation of a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.If each flash is 0.1 lumens, 40*10 flashes OR 400 flashes equal 40 lumens
P(X>400) = 0.7 (given information)
P(X < 400) = 0.3
P(Z < z0) = 0.3 when z0 = -1.88 (from the z-table)
z0 = -1.88 = (400 - E(X))/V(X)
= -1.88V = 400 - E
= -1.88 √(n*0.1*0.9) = 400 - n*0.1
= -1.88*0.3√n = 400 - 0.1n
= 0.1n - 0.564√n - 400 = 0
n = 4373
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What is an equation of the line that passes through the points (5,3) and (5,5) (please help)
Answer:
The x value does not change between the two points, meaning that our line includes all possible points in which x=5.
x=5 is the slope.
Answer:
x = 5
Step-by-step explanation:
slope: undefined
So, x = 5
Can you guys help me with my work, please?
The image point of (-9, -5) after applying this translation rule (T₋₅, ₀) and dilation (D₂) is (-28, -10).
What is a translation?In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.
Mathematically, a horizontal translation to the left is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent a function.By applying the transformation rule T₋₅, ₀ to the pre-image point (-9, -5), we have:
(x, y) → (x − 5, y + 0)
(-9, -5) → (-9 − 5, -5 + 0) = (-14, -5)
Next, we would apply a dilation (D₂) by using a scale factor of 2:
(x, y) → (kx, ky) = (2x, 2y)
(-14, -5) → (2(-14), 2(-5)) = (-28, -10).
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Write a function rule of a line in slope intercept form that is parallel to line 5x - 3y = 7 and has the same y intercept of the line 4x-y=9
Answer:
y = [tex]\frac{5}{3}[/tex] x -9
Step-by-step explanation:
Put both equations in the slope intercept form
y =mx + b
5x - 3y = 7 Subtract 5x from both sides
-3y = -5x + 7 Divide both sides by -3
y = [tex]\frac{-5}{-3}[/tex] x + [tex]\frac{7}{-3}[/tex] Cleaned up
y = [tex]\frac{5}{3}[/tex] x - [tex]\frac{7}{3}[/tex]
4x -y = 9 Subtract 4x from both sides
-y = -4x + 9 Divide all the way through by -1
y = 4x - 9
To make a line parallel to the first equation, we need the same slope. The slope of the first equation is [tex]\frac{5}{3}[/tex]. We are also told to have the same y intercept as the second equation which is -9
y = [tex]\frac{5}{3}[/tex] x - 9
which expression represents the product if 3 and 7
Answer:
3X7
Step-by-step explanation:
product means to multiply
Which expression is equivalent to the sum 25 + 60? *
Answer:
85
Step-by-step explanation:
solo lo sumas para que le entiendas consulta a una maestro jajja
For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
20
12
X
The side length [tex]x = \sqrt{444}[/tex] => x = 21
What are the properties of right triangle?The right angle, or 90°, is always one angle.
The hypotenuse is the side that will be 90° away from the other angle.
The longest side is always the hypotenuse.
The other two inside angles will add up to 90 degrees.
Also known as base and perpendicular are the other two sides that are close to the right angle.
The first two sides of the triangle are :
1st angle = 20°
2nd angle = 12°
Thus by using the Pythagoras theorem ;
20² + 12² = x²
400 + 144 = x²
this implies , 444 = x²
Taking square roots on both sides we get
[tex]x = \sqrt{444}[/tex]
x = 21
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How many quarts are there in 21 pints?
Answer:
10.5
Step-by-step explanation:
each quart is half a pint so 21 divided by 2 is this 10.5
