Answer:
1. a > 6
2. a = 6
3. 0 < a < 6
4. a is divisible by 6
Answer:
1. a>6 the answer could be, 7, 8, 9, 10 and it keeps going on.
2. the answer is 6
3. a<6 the answer is anything below 6 so 5, 4, 3, 2, 1, and more.
4. anything that is a multiple of 6 is true. like 6, 12, 18, 24, 30, 36, and it keeps going.
the twenty-third term in an arithmetic sequence is $\frac23$ and the fifty-third term in the sequence is $\frac32$. what is the thirty-fifth term?
The thirty-fifth term in an arithmetic sequence is 1.
The formula for the nth term of an arithmetic sequence is:
[tex]t_{n}[/tex] = a + (n - 1)d
The twenty-third term in an arithmetic sequence is [tex]$\frac{2}{3}[/tex].
a + 22d = [tex]$\frac{2}{3}[/tex] ...... (1)
The fifty-third term in an arithmetic sequence is [tex]$\frac{3}{2}[/tex].
a + 52d = [tex]$\frac{3}{2}[/tex]........(2)
Subtracting both the equations.
Subtract equation (1) from equation (2):
a + 52d - (a + 22d) = [tex]$\frac{3}{2} - \frac{2}{3}[/tex]
a + 52d - a - 22d = [tex]$\frac{9-4}{6}[/tex]
30d = [tex]$\frac{5}{6}[/tex]
d = [tex]$\frac{1}{36}[/tex]
Substitute the value of d in equation (1).
We get:
a + 22[tex]$(\frac{1}{36})[/tex] = [tex]$\frac{2}{3}[/tex]
a + [tex]$\frac{11}{18}[/tex] = [tex]$\frac{2}{3}[/tex]
a = [tex]$\frac{2}{3}[/tex] - [tex]$\frac{11}{18}[/tex]
a = [tex]$\frac{12}{18} - \frac{11}{18}[/tex]
a = [tex]$\frac{1}{18}[/tex]
To find the 35th term substitute the values of a and d in the nth term equation.
The thirty-fifth term in an arithmetic sequence is:
= [tex]$\frac{1}{18}[/tex] + (35 - 1) [tex]$\frac{1}{36}[/tex]
= [tex]$\frac{1}{18}[/tex] + [tex]$\frac{34}{36}[/tex]
= [tex]$\frac{1}{18}[/tex] + [tex]$\frac{17}{18}[/tex]
= [tex]$\frac{18}{18}[/tex]
= 1
Therefore the thirty-fifth term is 1.
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At the end of an advertising campaign, weekly sales amounted to $25,000 and then decreased by 10% each week after the end of the campaign. A. Write the equation of the exponential function that models the weekly sales. B. Find the sales 6 weeks after the end of the advertising campaign
The final amount after a certain rate of decrease over a period of time can be calculated by Xₙ = X₀ (1-r)ⁿ. From calculations the sales after 6 weeks are 13286.025.
If the percent increase or decrease, period of time and initial amount are given, the final amount can be calculated using the equation Xₙ = X₀ (1±r)ⁿ. Here the percentage decrease is given. So the equation is
Xₙ = X₀ (1-r)ⁿ
Xₙ is the final amount
X₀ is the initial amount
r is the rate
n is the period of time
Here percent is given as 10%. So the rate, r = 10/100 = 0.10
Xₙ = X₀ (1-r)ⁿ
= 25000× (1-0.10)⁶
= 13286.025
So the sales after 6 weeks are 13286.025
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Joseph has 93332 apples. she gets 1849032 more how many does he have?
Answer:
1,942,364
Step-by-step explanation:
1 8 4 9 0 3 2
+ 9 3 3 3 2
------------------------
1 9 4 2 3 6 4
Joseph now has 1,942,364 apples.
No. of apples Joseph had in the beginning = 93332
No. of apples he gets more = 1849032
Total no. of apples he has now = 93332 + 1849032
= 1,942,364
How many ounces are in ten and half pounds?
Answer:
10 1/2 lbs = 168 oz
Answer:
168
Step-by-step explanation:
i think
The sum of $4 500 is divided among Anesha. Sian and Joanne. Sian received half, Anesha received $1050 and Joanne received the remainder. Calculate:
(a) Sian's share
(b) Joanne's share
(c) the ratio in which the $4500 was divided among the three persons
(d) the percentage of the total amount that Anesha received.
Answer:
a: 2250. b: 1200. c: 5:2.3:2.7 d: 23.3%
Step-by-step explanation:
Sian gets 1/2 so 4500/2 = 2250
Anesha = 1050
Joanna = 2250-1050 = 1200
gasoline is sold by the liter in many countries. how many liters are required to fill a 12.0-gal gas tank?
The Volume or liters required to fill a 12.0 - gal gas tank is 45.42 liters.
Gallon to liter conversion factors are:
[tex]1 \ Gallon = 3.785 \ Liter[/tex]
Assuming that the gallon measurement for the gas tank is 12.0 gal.
We now need to calculate the gas tank's liter capacity.
As, 1 gallon = 3.785 liter
[tex]So \ 12\ gallon = 12*3.785[/tex]
[tex]=45.42\ gallons.[/tex]
Therefore, 45.42 liters of liquid are needed to fill the gas tank.
Meaning of gasoline:
Petroleum is the source of gasoline, which is a mixture of flammable, volatile liquid hydrocarbons used as a fuel for internal combustion engines and as a solvent for oils and fats.
It is a by-product of the petroleum industry and is used as fuel for cars because it burns with a high degree of energy and mixes easily with air in a carburetor.
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Given that mLKN=145°, find the mLKM and mMKn
Answer: ∠LKM=56° and ∠MKN=89°
Step-by-step explanation:
Notice that ∠LKM and ∠MKN make up ∠LKN. That means ∠LKM and ∠MKN combines equals 145°.
2x+10+4x-3=145 [combing like terms]
6x+7=145 [subtract both sides by 7]
6x=138 [divide both sides by 6]
x=23
We are almost done. We still need to plug it in to find the angle values.
∠LKM
2x+10 [plug in x=23]
2(23)+10 [multiply]
46+10 [add]
56
∠LKM=56°
------------------------------------------------------------------------------------------------------------
∠MKN
4x-3 [plug in x=23]
4(23)-3 [multiply]
92-3 [subtract]
89
∠MKN=89°
Therefore, ∠LKM=56° and ∠MKN=89°.
Use point-slope form to write the equation
of a line that passes through the point
(11, 18) with slope 3.
By using the point-slope form, the equation of a line that passes through the point (11, 18) with slope 3 is equal to y - 18 = 3(x - 11).
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represents the data points.From the information provided above, we have the following slope and data points on the line:
Points = (11, 18).Slope, m = 3At data point (11, 18), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - 18 = 3(x - 11)
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Use mental math to find a solution for 2/8 = 3/x+2
Answer:
answer - x = − 12/7
determine if the three side lengths form a right triangle. 15, 8, 7
yup
Step-by-step explanation: the triplets of 15,8,7 make a right triangle
u can also add 8 squared and 7 squared and if it equals to 15 squared then it’s right
Question 1 (2 points) ✓ Saved
Emilio has a bank account that pays 4% interest each year. He has $200 in his
account. How much interest will he earn after 1 year?
$10
$6
$4
$8
2.10
speedy boat rental charge 15$ deposit fee plus 2$ for each hour of use to rent a paddle boat Write an equation to find how many hours,h,
The number of hours that the rented the boat, if the total cost was $33 would be represented by the equation: 33 = 2h + 15
How to write the equation ?To write the equation on the number of hours that the boat would have been rented for to get a total cost of $ 33, use the formula :
Total cost = Deposit fee + ( Cost per hour x Number of hours boat was used)
Total cost = $ 33
Cost per hour = $ 2
Number of hours boat was in use = h
The equation therefore is:
33 = 2 h + 15
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The full question is:
Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddleboat. Write an equation to find out for how many hours, h, they rented the Boat if the total cost was $33.
(ii) Hence, given that 6log 3+7-3 log, a = 0, find the possible values of a.
Answer: Given that 6log3 + 7 - 3loga = 0, we can start by isolating the variable a. To do this, we'll add 3loga to both sides:
6log3 + 7 = 3loga
Next, we'll divide both sides by 3:
2log3 + (7/3) = loga
Now we have loga on one side of the equation and a constant on the other. To find the possible values of a, we'll need to use the properties of logarithms.
We know that logb(x) = y is equivalent to b^y = x, so we can rewrite the equation as:
a = 3^(2log3 + (7/3))
To find the possible values of a, we'll need to evaluate the exponent on the right side of the equation. Since we don't know the value of log3, we can't find the exact value of a. However, we can say that the possible values of a are all the values that can be expressed as 3 raised to the power of (2log3 + (7/3))
Step-by-step explanation:
Maria orders 8 pizzas for 24 people coming to her party.
a) How many people can be fed
b) How many pizzas would she need if 33 people come to the party.
Using the arithmetic operation of division -
a) 3 people can be fed by 1 pizza.
b) Maria would need 11 pizzas for 33 people.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The number of pizzas ordered = 8
The number of people are = 24.
Number of people that can be fed if 1 pizza was there =
Number of people = Number of people that came/ Number of pizza
Use the arithmetic operation of division -
Number of people = 24/8
Number of people = 3
Therefore, 3 people can be fed.
Now, the number of people = 33
Number of pizzas required for 33 people can be obtained as -
Use the arithmetic operation of division -
Number of pizzas = Number of people/ Number of people fed by 1 pizza
Number of pizzas = 33/3
Number of pizzas = 11
Therefore, Maria will require 11 pizzas.
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Pick one of the two companies and sketch a normal curve for a be sure to label it and use vertical lines to locate the mean and one standard deviation on either side of the mean
The sketch a normal curve is attached below and in Normal Curve with mean of 50 and a Standard Deviation of 2.
The term normally curve in math is defined as a normal distribution is proper term for a Probability bell curve.
While we looking into the question we know that here from the Right of Normal standard curve we have to draw 3 vertical lines. And these lines would count up by 2 for each standard deviation 52, 54,56.
And then we have to plot from the Left of Normal standard curve, and then draw 3 vertical lines. And those lines would count up by 2 for each standard deviation 48,46,44.
Thus Normal standard curve extends indefinitely in both directions, and by approaching on the other hand it never touching the horizontal axis as it does so.
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GEOMETRY 9.3.5 POINT ON A CIRCLE JOURNAL ASSIGNMENT
FULL DOCUMENT PLS
Suppose that this grid represents the customer’s yard. The bottom left corner is the origin point, (0, 0), and the x- and y- axes represent the two fences. The rose bush is at point (16, 18).
the solution of the given problem of coordinates comes out to be the coordinate P = (7, 0.4).
How do coordinates work?A coordinate system is a technique used in geometry to precisely locate points or other topological objects on a continuum, such as Euclidean space, using one or more numbers or coordinates. A point or item on an a double plane is located using a pair of integers known as coordinates. The x and y positions are two integers that describe a point's location on a 2D plane.
David want to find the coordinate are a useful tool for segmenting lines into smaller units.
P's coordinate is P = (7, -0.4)
The criteria are as follows:
A = (8,0)
=> B = (3,-2) (3,-2)
m: n=1:4
Using P = mx2+nx1 my2+ny
m+n
m+n, line ratio is computed.
The result is:
P 1x3+4x8 /1x-2+4x0 = 1+4 / 7
=> P = 35, 2
=>P = (7, -0.4) (7, -0.4)
1+4
P therefore has the coordinate P = (7, 0.4).
Therefore , the solution of the given problem of coordinates comes out to be the coordinate P = (7, 0.4).
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Round each mixed number to the nearest whole number and then estimate the sum. 12 +2 11/14 5/7
16
13
14
15
(HELP FAST<3)
The rounding up of each of the 12 +2 11/14 5/7 mixed number to the nearest whole number then the estimatation of the sum can be expressed as A.16.
How can the sum be calculated?The concept here is addition of the fractions and the digits, In mathematics, summation is the process of adding a series of different types of numbers, known as addends or summands, to produce their sum or total.
The rounding up to whole number can be done as :
12 = 12.0
2 11/14 = 39/14 = 2.786= 3.0
5/7 = 0.71=1.0
Then the sum = 12+3+1=16
Therefore, option A is correct.
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A university class has had 18 adult education students enroll so far, as well as 18 other students. Considering this data, how many of the next 14 students to enroll should you expect to be adult education students?
The number of next 14 students that will be expected to be adults education students would be = 7 adult education students.
Who is an adult education student?An adult education student is the student that is undertaken by individuals that are mature men and women who take course for continuing education.
The first enrollment consist of the following;
Adult education student = 18
other = 18
Total for first enrollment = 18+18 = 36
If first 36 enrolled students = 18 adult students
second 14 enrolled students = X adults
Make X the subject of formula;
X adults = 14× 18/36
= 252/36
= 7
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The highschool student council has decided to have a dance-a-thon and needs to hire a disk jockey for the event. Council members have investigated 3 companies. Gabe's Mobile Music charges $60 per hour. Derek's DJ Service charges $100 plus $40 per hour. Solid Sounds charges $175 plus $30 per hour. Which company should they choose? Why?
Answer:
Solid Sounds
Step-by-step explanation:
As a test, let's say the dance-a-thon lasted 10 hours. Plug in 10 hours to each:
Gabe's: $60/hr x 10 hr = $600
Derek's: $100 + ($40/hr x 10 hr) = $500
Solid Sounds: $175 + ($30/hr x 10 hr) = $475
This shows that Solid Sounds is the cheapest (no matter how many hours the dance lasts)
A three-column table is given. Part 10 B D Part 12 30 60 Whole A C 102 What is the value of C in the table?
According to the information in the table, the value of C is 51.
How to find the value of C?To find the value of C we must calculate the constant, for that we have to perform the following operation:
constant = whole / partconstant = 102 / 60In this case, we use the values of another column to identify the constant that applies to all the values in the table and the result is the following:
constant = 1.7Additionally, to find the value of C we must perform the following operation:
whole = part * constantwhole = 30 * 1.7whole = 51According to the above, the value of C is 51.
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The graphs of lines k1 and k2 are shown on the grid. Which system of equations is best represented by this graph?
F. 3x-y=2
4x+9y=36
G. 3x-y=6
4x+9y=4
H. x-3y=-18
9x+4y=9
J. x+y=10
9x+4y=13
The equations which represents the given graph is 3x-y=2 and
4x+9y=36 .
What is Linear equation ?
Linear equation can be defined as the equation in which the highest degree is one
Given ,
The graphs of lines k1 and k2 are shown on the grid.
From the given graph ,
The Two lines are intersecting at a point x = 49/31 and y=85/31
So, lets put the values of and y in the given linear equations
so we get,
3x-y=2
4x+9y=36
put values x = 49/31 and y=85/31
so ,
3*(49/31) - 85/31 = 2
= 62/31
= RHS
which is equals to RHS
4*(49/31)+9*(85/31) = 36
=36* 31 / 31
= RHS
Which equals to RHS
Hence, The equations which represents the given graph is 3x-y=2
4x+9y=36 .
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Solve the inequality and write the solution in set-builder notation.
b+2≥4
The set builder notation for the given inequality is [tex]\left \{ {{b | b \geq 2\right \}[/tex].
What is set builder notation?The answer set of an inequality is expressed in mathematics using a set builder notation. For instance, the set builder notation is understood to mean the collection of all y, where y is bigger than 0.
What is inequality equation?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than, larger than, or not equal to signs are used in place of the equal sign.
The given inequality is:
b + 2 ≥ 4
Subtract 2 on both sides of the equation:
b + 2 - 2 ≥ 4 -2
b ≥ 2
Hence, the set builder notation for the given equality is [tex]\left \{ {{b | b \geq 2\right \}[/tex].
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DE is a midsegment of the triangle
If BC=6x-2 and DE=2x+2 find the length of BC
If BC=6x-2 and DE=2x+2, then the length of BC is 16.
DE is a midsegment of the triangle.
As we know that;
A midsegment is a line segment that joins two of the midpoints of a triangle's sides.
The midsegment linking the midpoints of two sides of a triangle is parallel to the third side of the triangle, and its length is half that of the third side, according to the midsegment theorem.
So according to Midpoint Theorem
DE = BC/2
Now putting the value
2x+2 = (6x-2)/2
Multiply by 2 on both side, we get
4x + 4 = 6x-2
Add 2 on both side, we get
6x = 4x + 6
Subtract 4x on both side, we get
2x = 6
Divide by 2 on both side, we get
x = 3
Now putting the value of x in BC=6x-2
BC = 6(3) - 2
BC = 18 - 2
BC = 16
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Both circles have the same center. The circumference of the inner circle is 100.48 kilometers.
What is the area of the shaded region?
13 km
O
C=100.48 km
Vic
The area of the shaded region of the circle is 1836.9 km².
How to find the area of the shaded region?Both circles have the same centre. The circumference of the inner circle is 100.48 kilometres. The circumference of a circle is the perimeter of the circle.
Therefore, the area of the shaded portion can be calculated as follows:
Hence,
circumference of the inner circle = 2πr
100.48 = 2 × 3.14 × r
100.48 = 6.28 r
r = 100.48 / 6.28
r = 16 km
Therefore,
area of the inner circle = πr²
area of the inner circle = 3.14 × 16²
area of the inner circle = 803.84 km²
area of the outside circle = πr²
area of the outside circle = 3.14 × (16 + 13)²
area of the outside circle = 3.14 × 29²
area of the outside circle = 2640.74 km²
Therefore,
area of the shaded region = 2640.74 - 803.84
area of the shaded region = 1836.9 km²
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Nick and Lauren hiked 3. 75 kilometers to a lake 45° east of south from their campsite. Then they hiked 30° west of north to the nature center 6. 5 kilometers from the lake. How many kilometers are they away from their campsite? Round to the nearest tenth
Answer:
Step-by-step explanation: 23.4
question 1 a number increases by 10%, and then decreases by 10%. will the result be greater than, less than, or equal to the original number
The number is decreased by 1%.
Now, According to the question:
Let the number be 100
Number is increased by 10% = 100+10% of 100
=100+10
=110
Now, the resultant number is reduced by 10% =110-10% of 110
=110-11
=99
The number obtained is 99
Decrease in value = 100 – 99 = 1
Percentage decrease = 1100 × 100=1%
Hence, the number is decreased by 1%.
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Question 1 of 10
Which algebraic expression represents this word description?
The quotient of nine and the sum of a number and one
O A. 2+1
B. z1
C. +1
OD. +1
An algebraic expression which represents this word description "The quotient of nine and the sum of a number and one" is: D. 9 over x+1.
What is a quotient?In Mathematics, a quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.
In order to translate this word problem into algebraic equation, we would assign a variable to the unknown number and then translate the word problem into algebraic equation as follows:
Let the variable n represent the unknown number.
Translating the word problem into an algebraic equation, we have the following;
Quotient = 9/(x + 1)
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Complete Question:
Which algebraic expression represents this word description?
The quotient of nine and the sum of a number and one
A. x+1 over 9 B. 9/x +1 C. x/9 +1 D. 9 over x+1
Brynn has $1,200 in her savings account and plans to save an additional $350 each month in order to purchase a car. Write an equation to represent the total amount she has saved each month
An equation to represent the total amount she has saved each month is 350x + 1200.
We have to write an equation to represent the total amount she has saved each month.
Brynn has $1,200 in her savings account and plans to save an additional $350 each month in order to purchase a car.
To write an expression we have to read the statement very carefully and also write the expression after reading the statement.
Let she save the money in x months.
If she save $350 each month, then the total saving in x months = 350x
She has $1200 in saving account. Now the expression is
= 350x + 1200
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4x+40=y
HELPPP PLEASE
Here we are given a right angled triangle in which there are two unknown angles x and y . we need to find out the values of x and y. Firstly, as we know that the angle sum property of a triangle is 180° . So that,
[tex]\longrightarrow x + y +90^o = 180^o\\[/tex]
[tex]\longrightarrow x + y = 180^o -90^o = 90^o \dots \\[/tex]
[tex]\longrightarrow y = 90^o - x \dots (i) \\[/tex]
And we also have,
[tex]\longrightarrow 4x + 40 = y \\[/tex]
from equation (i) , we have ,
[tex]\longrightarrow 4x + 40 = 90 - x \\[/tex]
[tex]\longrightarrow 4x + x = 90 +40 \\[/tex]
[tex]\longrightarrow 5x = 130\\[/tex]
[tex]\longrightarrow x =\dfrac{130}{5}\\[/tex]
[tex]\longrightarrow \underline{\underline{x = 26^o}} \\[/tex]
substitute this value in equation (i) ,
[tex]\longrightarrow y = 90 - 26 \\[/tex]
[tex]\longrightarrow \underline{\underline{y = 64^o}} \\[/tex]
And we are done!
Where do you stash your allowance, birthday cash or paycheck? There are lots of ways to keep your money safe, but knowing which option is best for you means researching your choices. After the videos watched in class, write down four facts that you learn about each type of institution below. Watch the videos twice if needed to fill in the chart. Then, decide which one you would choose to put your money in and why.
I stash my allowance, birthday cash or paycheck in a bank.
The facts about Banks include the following:
They are profit oriented.They accepts deposits with a lower interest rate.They give loan at a higher rate.They provide a larger range of services.The facts about Credit union include the following:
They are not profit oriented.They accepts deposits with a higher interest rate.They give loan at a lower rate.They provide a smaller range of services.What is a Credit union?These are non profit organizations that exist to serve their members and offer some banking services.
They accepts deposits with a higher interest rate and give loan at a lower rate which is why my decision in where to put my money will be in a credit union due to the high interest rate.
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