Answer:
20,200
Step-by-step explanation:
Let the number of lines in each cube be a term in the sequence:
4, 12, 24, 40, ...
Work out the differences between the terms until the differences are the same:
[tex]4 \underset{+8}{\longrightarrow} 12 \underset{+12}{\longrightarrow} 24 \underset{+16}{\longrightarrow} 40[/tex]
[tex]8 \underset{+4}{\longrightarrow} 12 \underset{+4}{\longrightarrow} 16[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term. The coefficient of n² is always half of the second difference. Therefore, the coefficient of n² is 2.
To work out the nth term of the sequence, write out the numbers in the sequence 2n² and compare this sequence with the given sequence.
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5}2n^2 & 2 & 8 & 18 & 32\\\cline{1-5}\sf operation & +2&+4&+6&+8 \\\cline{1-5}\sf sequence & 4 & 12 & 24 & 40\\\cline{1-5}\end{array}[/tex]
From inspection of the table, we can see that the "operation" is to add 2n to 2n².
Therefore, the nth term is:
[tex]a_n=2n^2+2n[/tex]
To find the number of lines in the 100th cube, substitute n = 100 into the equation for the nth term:
[tex]\begin{aligned}n=100 \implies a_{100} & = 2(100)^2+2(100)\\& = 2(10000)+200)\\& = 20000+200\\& = 20200\end{aligned}[/tex]
Therefore, the 100th cube has 20,200 lines.
If Line t || Line v and m∠5 =5x + 45 and m∠7 = 12x - 11, find m∠5
The Line t || Line v the value of angle m∠5 is 69.28° .
What is line?
A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.
Given:
Line t || Line v
m∠5 =5x + 45
m∠7 = 12x - 11,
According to given question we have
Line t || Line v
Using the property of interior angles on same sides we get
m∠5 =m∠7
5x + 45=12x - 11
compare like terms we get
45-11=12x-5x
34=7x
x=34/7°
By put the value of x
m∠5 =5x + 45
m∠5 =5*34/7+45
m∠5 =485/7=69.28°
m∠7 =12x - 11=12*34/7-11
m∠7 =331/7°
m∠7 =47.28°
Therefore, the Line t || Line v the value of angle m∠5 is 69.28° .
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Plot the following points in a coordinate plane. (-5, 2), (-4, 0), (-3, -2), (-2, -4) Connect the points with a line. Name another point on the line. Is that point (1, -2) on the line? How do you know? If (1, -2) is part of the relation, is it a function? Why or why not?
Answer:
Step-by-step explanation: Can u please help me with my questionnn
Ted has started an 401k. His current income tax bracket is 30%. He is saving $172 a month by putting it into his 401k. Find how much income tax will Ted delay in paying every month by putting his money into an 401k. How much will Ted's take home pay decrease each month?
Income tax will Ted delay in paying every month by putting his money into a 401k is $51.6.
Income taxes are levied against individuals or groups based on their earnings or profits. Income taxes are normally calculated by multiplying tax rates by taxable income. Depending on the characteristics of the taxpayer and their source of income, tax rates may vary.
Ted started a 401k account.
The income tax bracket is 30%.
Ted's saving $172 every month in a 401k account.
The income tax that Ted will delay in paying every month will be:
= 172 × 30%
= $51.6
Hence, Ted's take-home pay will decrease by $51.6 each month.
The tax Ted will delay in paying every month is $51.6.
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Which of the following is an irrational number? A ㅠ B 0.16 C 2.53 D -1/5
Answer:
[tex]\pi[/tex]
Step-by-step explanation:
If a number can be written as an integer/integer in a fraction form or in a decimal form as a terminating or repeating decimal, it is rational. An integer is a set up numbers that fall into this pattern:
...-3,-2,-1,0,1,2,3...
0.16 is a terminating decimal or 16/100 as a fraction.
2.53 is a terminating decimal or 253/100
-1/5 can be written as a decimal at -0.2 and it terminating.
Will give 20 points please help 1. Refer to Expression 1 and Expression 2.
Expression 1
42-6-8-3+2³
Expression 2
720+2+7.23
(a) What is the value of Expression 1?
(b)Insert parentheses in Expression 2 so that it has a value of 2936. Then
show why your expression has a value of 2936.
Answer:
The value of the expression 1 (42 - 6 - 8 - 3 + 2³) will be 33. Then the value in the parentheses will be 2206.77.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The expression 1 is given below.
⇒ 42 - 6 - 8 - 3 + 2³
Then the value of the expression 1 will be
⇒ 42 - 6 - 8 - 3 + 2³
⇒ 42 - 6 - 8 - 3 + 8
⇒ 33
The expression 2 is given below.
⇒ 720 + 2 + 7.23
Insert parentheses in Expression 2 so that it has a value of 2936. Then the value in the parentheses will be
720 + 2 + 7.23 + (x) = 2936
729.23 + x = 2936
x = 2206.77
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29 POINTS IF YOU CAN HELP ME!!!!!!!!!!!!!!!!!!!! A Striped bass is swimming at an elevation of −3 feet, while a flounder is swimming at an elevation of −11 feet. Write and interpret a statement of the order showing the elevation of the striped bass compared to the elevation of the flounder. (1 point)
Responses
A, −3 < −11; the flounder is at a higher elevation than the bass.
B, −3 > −11; the bass is at a higher elevation than the flounder.
.
C, −3 > −11; the flounder is at a higher elevation than the bass.
D, −3 < −11; the bass is at a higher elevation than the flounder.
The correct option is,
⇒ −3 > −11; the bass is at a higher elevation than the flounder.
Option B is true.
What is Elevation?
Elevation is distance above the sea.
Given that;
A stripes bass is swimming at an elevation of −3 feet.
And, A flounder is swimming at an elevation of −11 feet.
Clearly, The bass is at higher elevation than the flounder.
So, -3 > -11
Hence, The correct option is,
⇒ −3 > −11; the bass is at a higher elevation than the flounder.
Option B is true.
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Need help on this text pt.3
The value of x is 10.
Option C is true.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The expression is,
x/7 = 3x + 20/ 35
Now, We can solve as;
x/7 = 3x + 20/ 35
Multiply 35 in both side,
35 × x/7 = 35 × (3x + 20)/35
5x = 3x + 20
Subtract 3x both side,
5x - 3x = 3x + 20 - 3x
2x = 20
Divide 2 both side,
x = 10
Hence, The value of x is 10.
Option C is true.
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This is due tomorrow. +10 points
The fitness center requires its swimming pool to be within 2 degrees of 85 degrees Fahrenheit.
a.) Which inequality can be used to find the least and greatest temperatures that meet this requirement? Use the inequality to find these temperatures.
A x − 85 ≤ 2
C |x−85|≥2start absolute value x minus 85 end absolute value is greater than or equal to 2
B x − 2 ≤ 85
D |x − 85| ≤ 2
b.) The least allowable temperature is ____ degrees Fahrenheit.
The greatest allowable temperature is ____ degrees Fahrenheit.
The inequality that can be used to find the least and greatest temperatures that meet this requirement is D. x − 2 ≥ 85
The least allowable temperature is 83° degrees Fahrenheit.
The greatest allowable temperature is 87 degrees Fahrenheit.
How to illustrate the inequality?From the information, the fitness center requires its swimming pool to be within 2 degrees of 85 degrees Fahrenheit.
In this case, the inequality that can be used to find the least and greatest temperatures that meet this requirement is D. x − 2 ≥ 85.
The least allowable temperature is:
= 85 - 2
= 83° degrees Fahrenheit.
The greatest allowable temperature is:
= 85 + 2
= 87 degrees Fahrenheit.
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help please i need this for homework
Answer:
It costs 50
Step-by-step explanation:
I think this is right
Consider a cookie recipe in which 1½ cups of chocolate chips are needed to make 25 cookies. Lara wants to double the number of cookies. How many cups of chocolate chips should she use?
The number of cups of chocolate chips she should use is 3 cups.
How to find the cups of chocolate chips that should be used?Consider a cookie recipe in which 1½ cups of chocolate chips are needed to make 25 cookies.
She decided to double the number of cookies.
Therefore,
Remember she wants to double the size of cookies,
25 cookies = 1½ cups of chocolate chips
2(25 cookies) = ?
cross multiply
number of cups of chocolate chips required = 50 × 1.5 / 25
number of cups of chocolate chips required = 75 / 25
number of cups of chocolate chips required = 3 cups
Therefore, the number of cups of chocolate chips she should use is 3 cups.
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Which expression is equivalent to (4x−3y4)−2?
negative quantity 16 times x raised to the sixth power end quantity over y raised to the eighth power
−16x6y8
1 over quantity 16 times x raised to the sixth power times y raised to the eighth power end quantity
x raised to the sixth power over quantity 16 times y raised to the eighth power end quantity
The equivalent expression to (4x−3y⁴) × −2 will be = -8x + 6y⁴.
How to calculate the value?It should be noted that the information is to calculate the equivalent expression to (4x−3y⁴) × −2.
This will be:
= -2(4x−3y⁴)
= -8x + 6y⁴
It should be noted that the equivalent expression will be = -8x + 6y⁴.
It should be noted that the options aren't written properly but the question has been solved.
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what is -5/12 x 8/13 in its simplest form
Answer:
-10/39
Step-by-step explanation:
I Think that thats the anwser i hope this helps.
Explain the difference in meaning |-3| and -3
Answer: |-3| is actually just positive 3 because when its in those lines it means absolute value. and -3 is just -3, but if it was in those lines then that just means its the positive of that number.
Step-by-step explanation:
The perimeter of the rectangle below is 48 units. Find the length of side AB. Write your answer without variables.
The value of the variables are x is 5. and AB is 10
Given, the sides of the rectangle are:
length = 2x ₊ 2 and
breadth = 3x ₋ 2
perimeter of the rectangle = 48 units
2(l ₊ b) = 48
2(3x ₋ 2 ₊ 2x ₊ 1) = 48
2(5x ₋ 1) = 48
10x ₋ 2 = 48
10x = 48 ₊ 2
10x = 50
x = 50/10
x = 5
therefore, length = 2x ₊ 1 = 2(5) ₊ 1 = 11 and
breadth = 3x ₋ 2 = 3(5) ₋ 5 = 10
hence we get the value of x as 5
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One number is seven more than six times another number. If the sum of the numbers is 28, find the numbers
The value of the numbers x and y is a 3 and 25.
According to the statement
We have to find that the value of the numbers.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
One number is seven more than six times another number. If the sum of the numbers is 28.
Then
Let The first number = y
The second number = x
Hence, y = (7 + 6x)
Their sum is therefore;
x + 7 + 6x = 28
7x = 21
x = 3
Hence, the second number is a; 7 + 6x = 7 + 6(3);
y = 25.
So, The value of the numbers x and y is a 3 and 25.
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You buy 3.18 pounds of grapes, 1.45 pounds of peaches, and 2.76 pounds of oranges. Each pound of grapes cost 1.29, each pound of peaches cost 1.19, and each pound of oranges cost 0.99. What is my total bill?
A wireless carrier offers the following plans that a person is considering.
The Family Plan: $90 monthly fee, unlimited talk and text on up to 5 lines, and data charges of $30 for each device for up to 2 GB of data per device.
The Mobile Share Plan: $110 monthly fee for up to 10 devices, unlimited talk and text for all the lines, and data charges of $15 for each device up to a shared total of 10 GB of data.
Find the model of the total cost of the Family Plan in dollars. Use P for the number of devices that need data plans as part of their cost.
The model of the total cost of the Family Plan will be 90 + 30P.
How to illustrate the information?It should be noted that Family Plan has $90 monthly fee, unlimited talk and text on up to 5 lines, and data charges of $30 for each device for up to 2 GB of data per device.
Therefore, the model will be:
= 90 + 30P
where p = number of devices
In conclusion, the model of the total cost of the Family Plan will be 90 + 30P.
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a cat ’s heart beats approximately 45 times in 15 seconds. At this rate how many times does the cat ’ s heart beat per second ?
Answer:
3 heartbeats
Step-by-step explanation:
The cat's heartbeats are 45 per 15 seconds.
To find out how many heartbeats it does per second (instead of 15), we should divide this amount by 15.
[tex]\frac{45}{15} \to 3[/tex]
Answer:
Step-by-step explanation:
45beats/15sec = 3beats/sec
The Office Supplies account started the year with a $3,225 balance. During the year, the company purchased supplies for $13,319, which was added to the Office Supplies account. The inventory of supplies available at December 31 totaled $2,838.
Based on the beginning office supplies balance, the supplies purchased by the company, and the supplies available at December 31, the journal entry for supplies is:
Date Account title Debit Credit
XX-XX Office supplies expense $14,131
Office supplies $14,131
What is the supplies expense?The supplies expense can be found as:
= 3,225 + 13,319 - 2,838
= $13,706
This supplies expense will be debited to the office supplies expense and credited to the office supplies account.
Question:
Record the entry to the Office supplies account
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The depth of a local river averages 16 ft, which is represented as |−16|. In January, it measured 4 ft deep, or |−4|, and in July, it was 18 ft, or |−18|. What is the difference between depths in January and July?
22 feet
14 feet
10 feet
2 feet
The difference between depths in January and July is 14 feets
The depth of a local river averages 16 ft., which is represented as |−16|.
In January, The depth of a local river measured 4 ft. deep, or |−4|
in July, The depth of a local river 18 ft., or |−18|
The average depth of a local river is measured as -16 because it is below the ground level and hence measured or plotted on -y axis
the difference between depths in January and July can be measured as
|−18| - |−4|
This is absolute sign which means every number inside this sign should be treated as positive
18 - 4 = 14
Hence, the difference between depths in January and July is 14 feets
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(a) A cylindrical glass jar whose height is 7 inches and whose diameter is 4 inches. Find the
capacity of the jar.
The volume of the glass jar is 87.96 cubic inch.
What is volume?Volume is a unit used to express how much three-dimensional space is occupied. It is usually represented quantitatively in different imperial measures, such as the gallon, quart, and cubic inch, or in SI-derived units like the cubic meter and liter. The cubic concept of length and volume are connected.
Volume is a three-dimensional measurement that's used to gauge a solid shape's capacity. It implies that the volume of a closed form determines how much space it may occupy in three dimensions.
The capacity of the jar is calculated as
Volume of cylinder = [tex]\pi r^{2}h[/tex] = [tex]\pi (2^{2})7[/tex] = [tex]28\pi[/tex] = 87.96 cubic inch.
Hence the capacity of the glass jar is 87.96 cubic inches.
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inverse of g(x)=2x^3+3
One month Pablo rented 5 movies and 3 video games for a total of $39. The next month he rented 2 movies and 12 video games for a total of 75 . Find the rental cost for each movie and each video game.
we get that the rental cost for each movie is $ 4.5 and each video game is $ 5.5.
Let the cost of number of movies be x and the cost of number of video games be y.
So, the equations are:
5 x + 3 y = 39
2 x + 12 y = 75
2 x = 75 - 12 y
x = 75/2 - 6 y
Put it in the first one, we get that:
5 ( 75/2 - 6y) + 3y = 39
375/2 - 30 y + 3 y = 39
27 y = 187.5 - 39
27 y = 148.5
y = 148.5 / 27
y = $ 5.5
x = 75/2 - 6 y
x = 37.5 - 6 (5.5)
x = 37.5 - 33
x = $ 4.5
Therefore, we get that the rental cost for each movie is $ 4.5 and each video game is $ 5.5.
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(b) A shopkeeper gave a bill to a customer. The bill was in two digits but was mistakenly interchanged thereby undercharging the customer by $45.00. If the sum of the digits is 9, find the actual value of the bill.
The actual value of the bill can either be $90 or $81 or $18 or $54 or $27 or $72 or $36 or $63 bill.
A digit is a part of a set that, when taken as a whole, makes up a numeration system. A digit is a number in that particular circumstance. The members of the set 0 through 9 make up the digits of the decimal (base-10) Arabic numbering system.
The bill of the customer was mistakenly interchanged by $45.
The sum of the two digits of the bill is 9.
Now,
9 = 9 + 0 or,
9 = 8 + 1 or,
9 = 1 + 8 or,
9 = 5 + 4 or,
9 = 2 + 7 or,
9 = 7 + 2 or,
9 = 3 + 6 or,
9 = 6 + 3
Therefore, $45 bill can be mistakenly interchanged by $90 or $81 or $18 or $54 or $27 or $72 or $36 or $63 bills.
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1.) You need 13 flower arrangements for table decorations. Each arrangement sells for $12.25. How much will you spend on flowers?
Answer:
159.25
Step-by-step explanation:
you just have to multiply 13 by 12.25
Michael used a stopwatch to time the baseball pitches for three of his friends.Order from least to greatest.
Pete:0.537
Ivan:0.58
Kat:0.4996
Answer:
this is called as ascending order, it is when numbers are arranged from least to greatest
here is the answer:
ivan:0.58
pete:0.537
kat:0.4996
Step-by-step explanation:
so you have to look at the nmbers and how many digits they have for example,
ivan's number has 3 digits so its the least
kat has 5 digits so its the greatest
Evaluate 3 + 2(x + 5)² for x = -2.
OA. 18
OB. 45
OC. 21
OD. 11
Answer:
The answer is C
Step-by-step explanation:
If you substitute -2 for x, then you get
3+2(-2+5)^2
so first we have -2+5, which is 3.
Then we hae 3^2, which is 9.
Then we have 9*2, which is 18.
Then we have 18+3, which equals 21.
Answer:
21
Step-by-step explanation:
The answer is 21
Hope this help you..
3/4(6x + 2) = 15
Help me please
16=3(7y+14)-21y solve for y then solve for x
x=7y+14
Answer:
I got y= no solution
Step-by-step explanation:
Hope this helps and sorry if I'm wrong
Find sin 0 and tan 0 if cos 0= 5/13, assuming that
[tex]0 \leqslant 0 < \ \frac{\pi}{2} [/tex]
sin( θ) = 12/13 and tan( θ) = 12/5.
sin θ, cos θ, tan θ are the three important trigonometry functions.
If θ lies in the first quadrant that is 0 ≤ θ < π/2, then the value of all trigonometry functions is positive.
The three most significant trigonometry functions are sin θ, cos θ, and tan θ.
If θ is located in the first quadrant, which is equal to θ/2, then all trigonometric functions have positive values.
The three important trigonometry identities are:
sin²( θ ) + cos²( θ ) = 1
1 + tan²( θ ) = sec²( θ )
1 + cot²( θ ) = csc²( θ )
Now we have,
cos θ = 5/13
Then,
sin²( θ ) + cos²( θ ) = 1
sin²( θ ) + ( 5/13 )² = 1
sin²( θ ) + 25/169 = 1
sin²( θ ) = 1 - 25/169
sin²( θ ) = ( 169 - 25)/ 169
sin²( θ ) = 144/ 169
sin( θ ) = √( 144/ 169 )
sin( θ ) = ± 12/13
Since, 0 ≤ θ < π/2
sin( θ ) = 12/13
Now we know,
tan(θ) = sin(θ) / cos(θ)
tan(θ) = ( 12/13 ) / ( 5/13)
tan(θ) = 12/5
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