x ≤ 12
Solution:
Let us take the number be x.
A number : x
A number divided by three : [tex]$\frac{x}{3}[/tex]
A number divided by three less two : [tex]$\frac{x}{3}-2[/tex]
A number divided by three less two is at most two : [tex]$\frac{x}{3}-2\leq 2[/tex]
Now, simplify the inequality,
[tex]$\Rightarrow\frac{x}{3}-2\leq 2[/tex]
Add 2 on both sides of the inequality,
[tex]$\Rightarrow\frac{x}{3}-2+2\leq 2+2[/tex]
[tex]$\Rightarrow\frac{x}{3}\leq 4[/tex]
Multiply by 3 on both sides of the equation,
[tex]$\Rightarrow\frac{x}{3}\times3\leq 4\times3[/tex]
[tex]$\Rightarrow x\leq 12[/tex]
Hence x ≤ 12.
Final answer:
The question requires setting up an inequality to express the condition 'a number divided by three less two is at most two.' The solution of the inequality reveals that the number in question is any number less than or equal to 12.
Explanation:
The student's question involves a number theoretical concept that requires setting up and solving an inequality. To understand the requirement of 'at most two' when a number is divided by three and reduced by two, we would establish an inequality as X / (3-2) ≤ 2, where X is the unknown number. This inequality represents the condition mentioned in the question, which restricts the value of X to a certain range after the operations are performed.
When working through the inequality, we aim to isolate X to determine the possible values it can hold. Here, we would start by adding two to both sides of the inequality to remove the subtraction, leading to X / 3 ≤ 4. Multiplying both sides by 3 gives us X ≤ 12. This tells us that the number in question is any number that is less than or equal to 12.
Understanding mathematical operations and the interpretation of numerals in context is necessary to solve such problems. Specifically, discerning the difference between an 'at least' and 'exactly' reading of numerals impacts the formation and solution of such inequalities.
Rob cuts a 15-foot wire into 8 equal pieces.About how long is each piece in fractions
Answer:
1 7/8
Step-by-step explanation:
15/8= 15/1 * 1/8
15/8
Simplify that and you get 1 7/8.
Hope it helps!
Answer:
1 7/8
Step-by-step explanation:
Length of wire= 15foot
Cut into 8 equal pieces
Length of each piece = 15/8
1 7/8 foot each
How much 5/16 are in 1 7/8
Answer:
convert 1 7/8 to an improper fraction.
1 times 8 is 8 plus 7 is 15.
1 7/8 = 15/8
15/8=30/16
30/16 divided by 5/16 is 6.
six 5/16 are in 1 7/8
Can anyone explain how to solve this?
Answer:
18.75
Step-by-step explanation:
since you are scaling up you do
125/80 which is 1.5625 and multiply that by 12.
The number 42524 is a palindrome, because it reads the same backwards as forward. How many integer palindromes are between 10,000 and 70,000, and are even?
Answer:
300
Step-by-step explanation:
The first (and last) digit can be any of {2, 4, 6}. The 2nd and 3rd digits can be any from 00 to 99. The 4th digit is the same as the 2nd, and the 5th digit is the same as the first.
There are 3·10·10 = 300 possible even palindromes in the given range.
Answer:
300
Step-by-step explanation:
:):
What is 3 2/3 divided by 2 1/6
Answer:
Exact form:
22/13
Decimal form:
1.692307
hcf and lcm 112 and 46 using prime factorisation
Answer:
HCF of 112 and 46 = 2
Step-by-step explanation:
HCF/GCD/GCF all mean the same. They are the highest common factor of two or more numbers.
Step 1: First you extract all the 'Prime' factors of each number.
The ladders on the image show that you are dividing each number with the smallest prime number. You keep doing it till you reach 1 .
Step 2: Then you write the factors of each.
Step 3: You choose the common factors.
Step 4: Multiply the common factors (if any) and then you have your answer.
Answer:
HCF: 2
LCM: 2576
Step-by-step explanation:
Prime factorizations:
112 = 2×2×2×2×7
46 = 2×23
HCF: 2 (only common factor)
LCM: 2×2×2×2×7×23 = 2576
(UPLOADED AGAIN) Please give the answer and how you got it
Answer:
B.
Step-by-step explanation:
B. <b and <A are complementary - remember that complementary angles means that the 2 angles will add up to 90 degrees, and in this case, they add up to 180 degrees.
Is -38,-68,-98,-128,... arithmetic
Answer:
yes
Step-by-step explanation
the common difference is -30
Final answer:
The sequence -38, -68, -98, -128,... is an arithmetic sequence because the common difference between consecutive terms is consistent, which is -30.
Explanation:
The student has asked whether the sequence -38, -68, -98, -128,... is arithmetic. To determine if a sequence is arithmetic, we need to check if the difference between any two consecutive terms (also known as the common difference) is the same.
Let's calculate the difference between the first two terms:
-68 - (-38) = -68 + 38 = -30
Now, let's calculate the difference between the second and the third terms:
-98 - (-68) = -98 + 68 = -30
Similarly, the difference between the third and the fourth terms is:
-128 - (-98) = -128 + 98 = -30
Since the common difference is the same (-30) for all consecutive terms mentioned, the sequence is indeed an arithmetic sequence.
James, Priya, and Siobhan work in a grocery store. James makes $7.00 per hour. Priya makes 40% more than James, and Siobhan makes 5% less than Priya. How much does Siobhan make per hour?
Siobhan makes $
per hour.
Answer:
The per hour income of Siobhan is $9.31 per hour.
Step-by-step explanation:
Working in a grocery store James makes $7.00 per hour. Priya's hourly income is 40% more than James, and Siobhan's hourly income is 5% less than Priya.
Therefore, using formula of percentage, the per hour income of Priya will be
[tex]7.00(1 + \frac{40}{100}) = 7 \times 1.4 = 9.8[/tex] dollars per hour.
Again, the per hour income of Siobhan is [tex]9.8(1 - \frac{5}{100}) = 9.8 \times 0.95 = 9.31[/tex] dollars per hour. (Answer)
Please help! Give the answer and how you got it
Answer:
MN = 10
Step-by-step explanation:
To find the length of a line segment or the straight distance between two points, use the formula [tex]L = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex] , where you can substitute two points, which would be (x₁ , y₁) and (x₂ , y₂). "L" stands for length.
Choose point 1 and point 2:
Point 1: M (2, -3) x₁ = 2 y₁ = -3
Point 2: N (8, 5) x₂ = 8 y₂ = 5
Substitute the values for the variables:
[tex]L = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]L = \sqrt{(8-2)^{2}+(5-(-3))^{2}}[/tex] Solve inside each bracket first by adding
[tex]MN = \sqrt{(6)^{2}+(8)^{2}}[/tex] Square each number
[tex]MN = \sqrt{36+64}[/tex] Add the numbers
[tex]MN = \sqrt{100}[/tex] Find the square root
[tex]MN = 10[/tex] Length of the line segment
Therefore the length of the line segment MN is 10.
David is making a wall out of bricks. Each brick is 2/3 foot long. There are 20 bricks lined up end to end to make the wall. What is the total length of the wall in inches?
The total length of wall is 160 inches
Solution:
Given that,
[tex]Length\ of\ each\ brick = \frac{2}{3}\ foot[/tex]
1 feet = 12 inches
Therefore,
[tex]Length\ of\ each\ brick = \frac{2}{3} \times 12\ inches = 8\ inches[/tex]
There are 20 bricks lined up end to end to make the wall
To find: Total length of wall in inches
[tex]Total\ length\ of\ wall = \text{length of each brick } \times \text{ total number of bricks}[/tex]
Thus we get,
[tex]Total\ length\ of\ wall = 8 \times 20\\\\Total\ length\ of\ wall = 160\ inches[/tex]
Thus total length of wall is 160 inches
For which problem do you need to regroup 1 ten as 10 ones subtract 16 from 38 or subtract 27 from 85 or subtract 51 from 72
the total yearly cost to rent a trumpet is $114. The montly cost is constant with no initial fee
Answer:
$9.5 is the cost of 1 month.
Step-by-step explanation:
the total yearly cost = 12 months = $114
Cost of per month = 1 month = $114 / 12 = $9.5
(3+4) + (4x+56) - (5x+3) = 45
Will Mark Brainliest
Answer:
X=21
Step-by-step explanation:
(7)+ (4x+56) - (5x+3)=45
7+4x+56-5x+3=45 add similar numbers
56+7+3=66
4x-5x= -x
-x+66=45
-66 -66
-x=-21
divide by - and x=21
The average yearly rainfall in Lakeview is 21.55 inches. What is the total amount of rainfall in inches in Lakeview in 5.75 years? A 1,239.125 B 12.39125 C 123.9125 D 27.3
Answer:
123.9125
Step-by-step explanation:
The total amount of rainfall in Lakeview in 5.75 years is approximately 123.9125 inches. The correct answer is option C.
Lakeview gets 21.55 inches of rain per year on average.
To find the total amount of rainfall in Lakeview in 5.75 years, we can multiply the average yearly rainfall by the number of years.
Average yearly rainfall: 21.55 inches
Total rainfall in 5.75 years: 21.55 inches/year * 5.75 years
Calculating the result:
= 21.55 x 5.75
≈ 123.9125
Therefore, the total amount of rainfall in Lakeview in 5.75 years is approximately 123.9125 inches.
The correct answer is option C.
Learn more about averages here:
brainly.com/question/13000783
#SPJ6
QUESTION 4 of 10: Real estate taxes for commercial property in your town are $11 per $1,000 assessed value. You plan on buying a
rundown property for $200,000 and putting in $300,000 in improvements. Which of the following is the best estimate of your yearly real
estate taxes?
a) $2,000
b) $3,000
c) $5,500
d) $11,000
Answer:
c. 5,500
Step-by-step explanation:
The best estimate of your yearly real estate taxes is $5,500.
Option C is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The total assessed value of the property.
= 200,000 + 300,000
= 500,000
Taxes.
$11 for $1000 assessed value.
This means,
$1000 value = $11
Multiply 500 on both sides.
500 x $1000 = 500 x $11
$500,000 = $5,500
Thus,
The best estimate of the taxes is $5500.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
what is the slope of (-1,0) (0,-1)
Answer:
-1
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-0)/(0-(-1))
m=-1/(0+1)
m=-1/1
m=-1
Math question. Photo attached
Answer:
2x+7
Step-by-step explanation:
John measures the angle of elevation to the top of a cliff to be 23 degrees. He walks 720 metres horizontally towards the cliff and finds the angle of elevation has doubled. What is the height of the cliff to the nearest metre ?
Answer:
The answer to this question is 1,495 ft
Step-by-step explanation:
Hope this helps
Is 2,509 less than 2,590
Answer:
Yes
Step-by-step explanation:
Answer:
Yes, 2,509 is less than 2,590
Step-by-step explanation:
When comparing 2509 to 2590, you first look at the first number on the left. In our case it is 2, then you look at the second number, which is 5, then you look at the third number which is 0 and 9, since the 9 is bigger that makes 2590 bigger than 2509, or 2509 less than 2590
Hope this helps ;)
(5x2 - 13x + 3) +(x-3)
Answer:
5x^2 - 13x + 3 + x - 3
5x^2 - 12x
What is the place value of the underlined number 4,382
Answer: Unit =2
tens=8
hundred= 3
thousand= 4
Step-by-step explanation:
Which of the statements are true for a linear function
Answer:
Attach image plz
Step-by-step explanation:
Answer:
The slope is constant
Step-by-step explanation:
2 Points
Kendra took out a loan for $750 at an 8.4% APR, compounded monthly, to buy
a stereo. If she will make monthly payments of $46.50 to pay off the loan,
which of these groups of values plugged into the TVM Solver of a graphing
calculator could be used to calculate the number of payments she will have
to make?
O
O
A. N=;1% = 0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12;
PMT:END
B. N=;1% = 0.7; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12;
PMT:END
C. N=;1% = 8.4; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12;
PMT:END
D. N=;1% = 8.4; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12;
To calculate the number of payments for Kendra's loan using a TVM Solver, the correct setup includes an APR of 8.4% converted to a monthly rate of 0.7%, with matching payment and compounding frequencies, making Option A the accurate choice.
Explanation:When Kendra takes out a loan to buy a stereo, calculating the number of payments she will have to make involves understanding the terms used in Time Value of Money (TVM) calculations. The correct set of values must account for the annual percentage rate (APR) being compounded monthly, which requires converting the APR to a monthly rate, and ensuring the payment and compounding periods match.
For Kendra's loan:
APR is 8.4%, implying a monthly interest rate (I%) of 0.7% (8.4% divided by 12).The present value (PV) of the loan is -$750, indicating an outflow of cash.Her monthly payment (PMT) is $46.50, aimed at reducing the loan balance.The future value (FV) she aims for is $0, meaning she intends to fully repay the loan.P/Y (Payments per year) and C/Y (Compounding periods per year) both should match the monthly nature of the loan, hence should be 12.Given these conditions, the only option that correctly configures all elements for a TVM Solver is Option A:
N=; I% = 0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
This configuration accurately reflects the loan's terms, allowing the calculation of the number of payments (N) Kendra will need to make.
The correct answer is: D. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END. Option A uses annual percentage rate (APR), while option D uses the periodic interest rate (monthly rate). Given that the interest rate is compounded monthly, it's more appropriate to use the periodic interest rate (option D).
To calculate the number of payments Kendra will have to make to pay off the loan, we can use the Time Value of Money (TVM) Solver feature of a graphing calculator. We need to set up the values correctly to solve for the number of payments (N).
Let's go through the options:
A. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12; PMT:END
B. N=; I% =0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
C. N=; 1% =0.7; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12; PMT:END
D. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
Let's analyze each option:
A. This option has the correct annual interest rate (8.4%), correct present value (loan amount), correct payment amount, and correct compounding periods per year. Hence, it's a potential correct option.
B. This option has the interest rate incorrectly set as 0.7%. It should be 8.4%, not 0.7%. Hence, it's incorrect.
C. Similar to option B, this option has the interest rate incorrectly set as 0.7%. Hence, it's incorrect.
D. This option has the correct interest rate (8.4%), correct present value, correct payment amount, and correct compounding periods per year. Hence, it's a potential correct option.
So, options A and D are potential correct options. Both have the correct interest rate and payment amount. The difference lies in how the interest rate is represented: option A uses annual percentage rate (APR), while option D uses the periodic interest rate (monthly rate).
Given that the interest rate is compounded monthly, it's more appropriate to use the periodic interest rate (option D). Therefore, option D is the most suitable choice.
Complete Question:
Kendra took out a loan for $750 at an 8.4% APR, compounded monthly, to buy a stereo. If she will make monthly payments of $46.50 to pay off the loan, which of these groups of values plugged into the TVM Solver of a graphing to make?
A. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12; PMT:END
B. N=; I% =0.7; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
C. N=; 1% =0.7; PV=-750; PMT=46.5; FV=0; P/Y=1; C/Y=12; PMT:END
D. N=; 1% =8.4; PV=-750; PMT=46.5; FV=0; P/Y=12; C/Y=12; PMT:END
if the ratio of the two numbers is7:8and theri sum 135 find the numbers
Answer:
63 and 72
Step-by-step explanation:
Sum the parts of the ratio, 7 + 8 = 15 parts
Divide the sum by 15 to find the value of one part of the ratio
135 ÷ 15 = 9 ← value of 1 part of the ratio, thus
7 parts = 7 × 9 = 63
8 parts = 8 × 9 = 72
The numbers are 63 and 72
describe the error in using the percent equation to answer the equation.
30 is 60% of what number is?
5.5*10^-1/
5.3 x 10^2
Answer:
10.3773584906
Step-by-step explanation:
A single sheet of 20-pound bond paper is about a tenth of a millimeter thick. Each time you fold an ordinary sheet of paper in half, you double the thickness. What would be the thickness in kilometers if you were physically able to fold it 50 times? Note: For comparison, the distance from Earth to the Sun is about 149,600,000 kilometers. (Round your answer to the nearest kilometer.)
The paper would be 112589991 km thick if folded 50 times.
Step-by-step explanation:
Step 1; The sheet is [tex]\frac{1}{10}[/tex]mm thick which equals 0.1 mm. Every time it is folded it doubles in thickness. So if folded once it becomes 0.2 mm thick, if folded thrice it becomes 0.4mm thick.
Thickness if folded once = [tex]2^{1}[/tex] × 0.1 mm
thickness if folded twice = [tex]2^{2}[/tex]× 0.1 mm
Thickness if folded thrice = [tex]2^{3}[/tex] × 0.1 mm.
So if the paper is folded nth fold it would be [tex]2^{n}[/tex] × 0.1 mm thick.
Step 2; Using the above formula, if the paper is folded 50 times the thickness would be equal to [tex]2^{50}[/tex] × 0.1 mm = 112,589,990,684,262.4 mm.
1 km is equivalent to [tex]10^{6}[/tex]mm so 112,589,990,684,262.4 mm = 112,589,990.6842624 km which is rounded off to 112589991 km.
find the mean of 37.5, 25.5, 30.5, 41.5, 52.5, 28.25, 30.5
Answer:
35.1785714286
Step-by-step explanation:
To find the mean you have to add all numbers. After you have added all numbers, you must divide the sum by the number of how many points you have.
Answer:
35.18
Step-by-step explanation:
Given the above scores .
Mean
= sum of scores/ number of scores
37.5 + 25.5 + 30.5 +41.5 +52.5 + 28.25 + 30.5 /7
246.25/7
35.18
what is the third quartile of this data set?
20, 21, 24, 25, 28, 29, 35, 37, 39, 42, 44
Answer:
39
Step-by-step explanation:
Answer:
39
Step-by-step explanation: