The answer in fraction form is c = 1/2
The answer in decimal form is c = 0.5
=============================
Explanation:
Saying "A is 1 less than B" means A = B-1. So whatever B is, subtract 1 from it and you get the value of A.
Replace A with the expression 2(3-5c). Replace B with 4(1-c)
We go from this
A = B - 1
to this
2(3-5c) = 4(1-c) - 1
----------
Let's isolate c
2(3-5c) = 4(1-c) - 1
2(3)+2(-5c) = 4(1)+4(-c) - 1
6-10c = 4 - 4c - 1
6-10c = 3 - 4c
6-3 = -4c+10c
3 = 6c
6c = 3
c = 3/6
c = 1/2
c = 0.5
The value of c in the given expressions is 1.
The value of c when the expression 2(3–5c) is 1 less than the expression 4(1–c) is 1.
First, we set up the equation: 2(3-5c) = 4(1-c) - 1.
Solving this equation step by step will lead us to the value of c.
In this case, the solution is c = 1.
Jane deposited $10,000 into her bank account in December, 2010. Her account earns interest at a rate of 5% compounded monthly. How much money will she have in December of this year (2018)?
Round your answer to the nearest whole number.
Compound Interest: A = P ( 1 + r/n )^nt
Answer:
14905.85
Step-by-step explanation:
P(1+r/n)^nt
10000 (1 + (.05/12))^ (12*8)
Answer:
she will have $14,906 in December of year 2018
Step-by-step explanation:
To find the amount of money she will have in December of the year 2018, we will simply use the formula;
Compound Interest: A = P ( 1 + r/n )^nt
where p = principal
R = rate
n = the number of times the interest is compounded per unit time
T = time
A= Accrued amount
From the question
Principal (p) = $10,000
Rate (r) = 5% = 0.05
Time(t) = 2018-2010 = 8 years
n = 12
We can now proceed to insert the values into our formula;
Compound Interest: A = P ( 1 + r/n )^nt
= $10 000 ( 1 + 0.05/12) ^12×8
=$10,000(1 + 0.00416667)^96
= $10 000(1.00416667)^96
=$10 000(1.4905859)
=$14,905.895
≈$14,906 to the nearest whole number.
Therefore she will have $14,906 in December of year 2018
What does x <-20 mean
X is greater than negative 20 (-20)
use the following table to find the value of h'(3) if h(x)=g[f(x)]
A differential equation is an equation that contains one or more functions with its derivatives. The value of h'(3) iss 14.
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
Given
h(x) = g(f(x))
Let us differentiate with respect to x by using chain rule we get
h'(x) = g'(f(x))f'(x)
plug the value x =3 in the above equation
h'(3) = g'(f(3))f'(3)
The value of f(3)=4, f'(3)=7 by table given
Plugging in values we get
h'(3) = g'(4)×7
We have g'(4)=2
so h'(3) = 2×7
h'(3) = 14
Hence the value of h'(3) is 14.
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Quadrilateral ABCD is a parallelogram if its diagonals bisect each other. Prove that Quadrilateral ABCD is a parallelogram by finding the value of x.
A) x = 2
B) x = 3
C) x =- 9|2
D) x = -3|4
Information that goes with the picture:
AO = 5x + 2
BO = x − 1
CO = 3x − 7
DO = 3x + 8
Because this is a parallelogram, we know that the diagonals bisect. This means that AO = DO, and CO = BO
It doesn't matter which two segments we use, but I'm going to use CO = BO for this one.
3x - 7 = x - 1
2x = 6
x = 3
Option B. is the answer.
Answer: d
Step-by-step explanation:
A large beetle can be 2x2x2x2x2x2x2 millimeters long. One of the smallest beetles can be 2(-2 (power)) millimeter long. How many times as great is the length of the large beetle than the length of the small beetle?
Answer:
I think the answer is 2^8 millimeters longer than the small beetle
Step-by-step explanation:
Andy has 9 math books and 6 reading books. If he wants to distribute them evenly among some bookshelves so that each has the same combination of books, with none left over, what is the greatest number of bookshelves Andy can use?
Answer:
3 is the greatest number of book shelves Andy can use.
Step-by-step explanation:
You can solve this by finding the greatest common factor of 9 and 6, which turned out to be 3.
6/3 = 2 (reading books per shelf)
9/3 =3 (math books per shelf)
Every shelf there are 2 reading books and 3 math books.
1.) (7.RP.3) Tracy started a savings account that is set up so that the simple interest earned on the investment is moved into a separate account at the end of each year. Tracy invests $5,000 at 4.5%, what is the total simple interest accumulated in the checking account after 2 years? (1 pt) *
a) $4.50
b) $45
c) $450
d) $4,500
e) $45,000
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2. 2. (7.RP.3) Sylvia bought a 6-month $1900 certificate of deposit. At the end of 6 months, she received a $209 simple interest. What rate of interest did the certificate pay? Show all of your work.
Answer:
1. c. $450.
2. 22%
Step-by-step explanation:
1. We will use simple interest formula to find the amount of interest after 2 years on $5,000. As interest is not compounded, so it will not matter if she moves the simple interest earned in separate account or not.
[tex]I=P*r*t[/tex], where,
I= Amount of interest.
P= Principal amount.
r= Interest rate in decimal form.
t= Time in years.
[tex]4.5\text{ percent}=\frac{4.5}{100}=0.045[/tex]
Upon substituting our given values in above formula we will get,
[tex]I=5000*0.045*2[/tex]
[tex]I=5000*0.09[/tex]
[tex]I=450[/tex]
Therefore, Tracy will get an amount of $450 as simple interest after 2 years and option c is the correct choice.
2. Sylvia bought a 6-month $1900 certificate of deposit. At the end of 6 months, she received a $209 simple interest.
6 months is same as 1/2 year.
[tex]I=P*r*t[/tex]
Upon substituting our given values in above formula we will get,
[tex]209=1900*r*\frac{1}{2}[/tex]
[tex]209=950*r[/tex]
[tex]r=\frac{209}{950}[/tex]
[tex]r=0.22[/tex]
Since interest rate is in decimal form, let us convert it in percent.
[tex]\text{Interest rate}=0.22\times 100=22\text{ percent}[/tex]
Therefore, interest rate of certificate of deposit was 22%.
Help with trig homework
A 6 m ladder is leaning against a wall. The base of the ladder is 1.5 m from the wall. Calculate how high up the wall the ladder reaches.
Answer:
height = 5.809
Step-by-step explanation:
l=6m
b=1.5m
l^2=b^2+h^2
36=2.25 +h^2
h^2 = 36 - 2.25
h=[tex]\sqrt{33.75}[/tex]
h = 5.809
Perform the specified operations on the polynomials: Subtract 5a−6b+7c from 13a−4b+8c
Answer:
8a + 2b + c
Step-by-step explanation:
For subtracting polynomials we just need to operate subtracting the terms with same unknown. In our case we sum/subtract the terms that include a between them, the terms that have b between them and the therms with c between them. So we have:
(13a−4b+8c) - (5a−6b+7c) =?
13a−4b+8c - 5a+6b-7c = ?
Lets operate putting together terms with same unknown:
(13a - 5a) + (-4b +6b) + (8c-7c) =
8a + 2b + c
So, if we subtract 5a−6b+7c from 13a−4b+8c we get 8a + 2b + c
I hope it is clear!
What is the value of (4x^2-10)/y when x=5 and y=6
using the order of operations. select true or false for 81 ÷ 9 + 2 = 11
Answer: true
Step-by-step explanation: Using the order of operations, 81 / 9 would be first, which is equal to 9. Then, add 2. 2+9 = 11, so the answer is true.
Since division goes before addition we first divide 81:9 and get 9 and to that we add 2 addition goes after division. 9+2 is equal to 11 so the answer is True.
A good way to remember it is:
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Hope this helps! <3
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
Answer:
see explanation
Step-by-step explanation:
to find the first, fourth and tenth terms, substitute n = 1, 4, 10 into the rule
A(1) = - 3 + (1 - 1)(- 2.2) = - 3 + (0 × - 2.2) = - 3 + 0 = - 3
A(4) = - 3 + (4 - 1)(- 2.2) = - 3 + (3 × - 2.2) = - 3 - 6.6 = - 9.6
A(10) = - 3 + (10 - 1)(- 2.2) = - 3 + (9 × - 2.2) = - 3 - 19.8 = - 22.8
the required terms are - 3, - 9.6, - 22.8
(3x+7x-20) ÷ (x+4) can someone solve this?
Answer:
Alright well solve by dividing using polynomial division
10 - 60/x + 4 Hope this helps have a nice day :)
Step-by-step explanation:
Solve for k:
k + 6 > -20
Answer:
k > -26
Step-by-step explanation:
To isolate the k, you subtract 6 from both sides to get k < -26.
The correct answer is k > -26
Explanation:
To solve our equation first we need to set out our equation, k + 6 > -20. Next, we have to subtract 6 from both sides of the equation, k + 6 - 6 > -20 - 6 = k > -26. Finally, we have our answer of k > -26.
Hope This Helps!!!
-AnimeDabGirl
What number is 30% of 20?
Answer:
6
Step-by-step explanation:
20 times .3 equals 6
the answer is 6 because (30 ÷ 100) × 20
The pattern of the spread of the virus will be 1,2,4,8 identify the next three numbers in this pattern
Answer:
16 32 64
Step-by-step explanation:
Remark
Though it is easy just to add the next three numbers, it would be a good idea to develop some sort of formula. It is what you always want to do if you are representing a sequence. Then you don't have to struggle to find the 100 term of the given sequence. The only way to explain this is to say it is a geometric sequence.
Givens
t1 = 1t2 = 2t3 = 4t4 = 8Solution
r = t4/t3 = 8/4
r = 2
a = 1
Formula
tn= a*r^(n - 1)t5 = 1*2^(5 - 1)t5 = 2^4t5 = 16Answer
By similar methods the next 2 items will be 32 and 64.
Note
t_100 = 1 * r^(100 - 1)t_100 = 2 ^99 = 633825300114114700748351602688A formula is the only way to go when the numbers are this big.The next three numbers in the given pattern (1,2,4,8) are 16, 32, and 64, obtained by doubling the last known number in the series for each subsequent term.
Explanation:This question is related to a mathematical pattern in which each number is being doubled to get the next one. The series given is 1, 2, 4, 8. Here, you can notice that each successive number is two times the prior number. So, to find the next three numbers, you'd multiply the last given number by 2.
When you multiply 8 (the last number in the given series) by 2, you get 16. That's your first number. Continuing this pattern:
Multiply 16 by 2 to get 32. This is your second number.Then, multiply 32 by 2 to get 64, which is your third number.So, the next three numbers in this pattern would be 16, 32, and 64.
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Identify the explicit function for the sequence in the table.
(PLEASE HELP NEED ANSWERS ASAP)
Answer: B(APEX)
Step-by-step explanation:
What is the area of a parallelogram ABCD
Answer:
Area of a parallelogram would be 13.46
Step-by-step explanation:
Since area of a parallelogram is represented by the formula
Area = [tex]\frac{1}{2}[/tex] ([tex](D_{1}*D_{2})[/tex]
Where [tex]D_{1}[/tex] and [tex]D_{2}[/tex] are two diagonals of the given parallelograms.
In the given figure [tex]D_{1}=AC[/tex] and [tex]D_{2}[/tex] = BD
We will find the length of [tex]D_{1}[/tex] and [tex]D_{2}[/tex] first
Since points A and C are (3,6) and (5,1)
So distance AC = [tex]\sqrt{(6-1)^{2}+(3-5)^{2} }[/tex]
= [tex]\sqrt{5^{2}+(-2)^{2}}[/tex]
= [tex]\sqrt{25+4}=\sqrt{29}[/tex]
Since B and D are the points (6, 5) and (2, 2)
So length of BD = [tex]\sqrt{(6-2)^{2}+(5-2)^{2}}[/tex]
BD = [tex]\sqrt{4^{2}+3^{2}}=\sqrt{25}=5[/tex]
Now we will put these values in the formula
Area of parallelogram = [tex]\frac{1}{2}(\sqrt{29})(5)[/tex]
= [tex]\frac{5}{2}[/tex] × [tex]\sqrt{29}[/tex]
= (2.5) (5.385)
= 13.46
Total blood cholesterol level was measured for each of
8 adults. Here are the 8
measurements (in mg/dL):
264, 191, 160, 148, 262, 212, 268, 246
Step-by-step explanation:
Given blood cholesterol level was measured for each of 8 adults (in mg/dL) are:
264, 191, 160, 148, 262, 212, 268, 246
In order to find the mean, we need to add all those 8 numbers and divide by 8.
Therefore, mean = [tex]\frac{264+191+160+148+262+212+268+246}{8} =\frac{1751}{8} =218.9.[/tex]
Mean = 218.9.In order to find the median, we need to arrange them in ascending order:
148, 160, 191, 212, 246, 262, 264, 268.
The middle most two values are 212 and 246.
Therefore, median = [tex]\frac{212+246}{2} =\frac{458}{2} = 229.[/tex]
Median = 229.[tex]\mathrm{The\:mode\:is\:the\:term\:in\:the\:data\:set\:that\:appears\:the\:most.}[/tex]
[tex]\mathrm{If\:there\:is\:more\:than\:one\:term\:that\:appears\:the\:most,\:then\:there\:is\:no\:mode.}[/tex]
[tex]\mathrm{Count\:the\:number\:of\:times\:each\:element\:appears\:in\:the\:list}[/tex]
[tex]\begin{pmatrix}148&160&191&212&246&262&264&268\\ 1&1&1&1&1&1&1&1\end{pmatrix}[/tex]
[tex]\mathrm{The\:most\:common\:element\:is\:not\:unique,\:so\:there\:is\:no\:mode}[/tex]
Therefore, Mode = Zero mode.Irene bought six pounds of fish for $12.90. Based on that cost, how much would 3.4 pounds of the same fish cost?
A) $2.15
B. $6.45
C) $7.31
D. $22.76
Please help.
Answer:
B. 6.45
Step-by-step explanation:
So we know that you bought six pounds for $12.90, and you need to know how much it would cost for three pounds. You need to find out what one pound would cost, then multiply that by three.
You would do:
12.90 ÷ 6
Which equals : 2.15
Then take that and multiply it by 3:
2.15 × 3
Giving you 6.45.
Thus leading to, this fish would cost $6.45 for three pounds.
Lina bought 22 boxes of crayons for $28.16 how much did she pay for each box of crayons
Cost per box = $1.28
The cost of each box of crayons can be calculated by dividing the total cost by the number of boxes purchased.
Total cost: $28.16
Number of boxes: 22
Cost per box = Total cost / Number of boxes
Cost per box = $28.16 / 22
=$1.28
Adam's car traveled 465.3 miles on 18.5 gallons of gas. Which equation can be used to determine the average number of miles that the car traveied on each gallon of gas?
Answer:
25.15 miles per gallon
Step-by-step explanation: The equation to find the number of miles traveld per galon would be to divide the number of miles traveled by the number of gallons used.
What is the value of y ?
Answer:the value of y is 44
Step-by-step explanation:
factor each expression 45x + 63y
Answer:
9(5x+7y)
Step-by-step explanation:
Select all trips that would take 2 hours. Show your work for each situation. Walk 5 miles per hour to school, which is 2.5 mikes away. Drive 50 miles per hour between Buffalo and Seneca Falls, which are 150 miles apart. Take a train going 90 miles per hour from Albany to NYC, which are 180 miles apart.
Walk 5 mph for 2.5 miles : Would take 30 minutes. X
Drive 50mph : Would take 3 hours X
90mph for 180 miles : Would take 2 hours
Alissa would like to make a deposit into her savings account. She filled out a deposit ticket and handed it to the teller at her bank. The teller apologizes to Alissa and explains that she cannot accept the deposit ticket in its current form. Determine what, if anything, Alissa will have to change in order for her deposit ticket to be accepted. a. The sub total is calculated incorrectly b. Alissa forgot to sign the deposit ticket for less cash back c. The total is calculated incorrectly d. Alissa forgot to date the deposit ticket
The correct option is c. The total is calculated incorrectly.
When making a deposit, it is crucial that the total amount being deposited is calculated correctly on the deposit ticket. This total amount should match the sum of the cash and checks being deposited. If there is a discrepancy between the subtotal of the individual amounts and the total, the deposit ticket will not be accepted because it does not accurately reflect the amount of money being handled.
Here's the logic behind why the other options are not the primary issue:
a. The sub total is calculated incorrectly: While this is a potential error, the primary concern for the teller would be the total amount being deposited. The subtotal informs the depositor and the bank of the breakdown of the deposit, but the total is what ultimately needs to be correct for the deposit to be processed accurately.
b. Alissa forgot to sign the deposit ticket for less cash back: While a signature is important for verification purposes, especially if cash back is requested, the absence of a signature would typically result in the teller asking for a signature rather than outright rejection of the deposit ticket. The calculation of the total deposit amount is a more fundamental error that must be corrected before the deposit can be accepted.
d. Alissa forgot to date the deposit ticket: The date on a deposit ticket is important for record-keeping purposes. However, forgetting to date the deposit ticket is usually a minor issue that can be resolved quickly at the teller's window. It would not typically prevent the deposit from being accepted, assuming the total deposit amount is correct.
In summary, the teller's refusal to accept the deposit ticket in its current form most likely stems from an incorrect total calculation, as this directly affects the accuracy of the deposit transaction. Alissa will need to ensure that the total on the deposit ticket correctly reflects the sum of the cash and checks she is depositing. Once the total is corrected, the deposit ticket should be accepted by the teller.
Calculate a5 for the geometric sequence in which a1=1600 and the common ratio is 3/4.
Answer:
a₅ = 506.25 option a
Step-by-step explanation:
Given that,
first term a₁ = 1600
common ratio (r) = [tex]\frac{3}{4}[/tex]
We need to find the fifth term of the geometric progression
We know that the nth term formula
aₙ = a₁rⁿ-¹
where a₁ is first term and r is the common ratio
n is the number of terms
So, n = 5
a₅ = 1600 [tex](\frac{3}{4})^{5-1}[/tex]
a₅ = 1600*[tex](\frac{3}{4}) ^{4}[/tex]
a₅ = 1600*81/256
a₅ = [tex]\frac{2025}{4}[/tex]
a₅ = 506.25 option a
That's the final answer
Answer:
A. 506.25
Step-by-step explanation:
Answer the following questions showing all your work. You are trying to save up money by working in the summer. You have been able to secure two part time jobs. a. Your first job is to babysit a couple of times a week. You charge a flat fee of $10 for transportation back and forth to the house plus $5.50 per hour. Let t be the time in hours that you babysit. Write an algebraic expression to define the amount of money you will make for t hours of work. b. You also work at a local coffee shop in the mornings. You are paid $10 per hour. Write an algebraic expression to define the amount of money you will make for t hours of work. c. Write an algebraic expression for how much money will you will make for both jobs together.
Jim drove 605 miles in 11 hours. At the same rate, how many miles would he drive in 13 hours?
Answer: 715 Miles
Step-by-step explanation:
Divide 605 miles by 11 hours, which would give you how far he travels in 1 hour. (605/11=55) Since they give you 13 hours, multiply 13 hours by 55 miles which gets you 715 miles :)
Trent earned a total of $18 by selling 6 cups of lemonade. After selling a total of 12 cups of lemonade, how much money will Trent have made in all?
Answer:$36
Step-by-step explanation:
He has sold 6 and made $18 6x2=12 2x18=36