31/6 or 5.167 feet of lumber was left.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Peter cut a piece of lumber 9 5/6 feet long from a piece that was 15 feet long.
Since the total length of wood is 15 feet
Thus,
The remaining wood = 15 - (9 5/6)
The remaining wood = 6 - 5/6
The remaining wood = 31/6
therefore, 31/6 or 5.167 feet of the lumber was left.
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Each student at state college has a student I.D number consisting of seven digits (the first digits may be repeated) Followed by three of the letters A,B,C,D and E (letter may not be repeated). how many different student numbers are possible
The different student number possible if a student I.D number consisting of seven digits (the first digits may be repeated) Followed by three of the letters A,B,C,D and E is 32659200.
What is permutation?A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.
The college ID consists of a total of 10 elements in which the first 7 can be a number and the last three are letters A, B, C, D, E.
Since, the number cannot start with a 0, we have the following combination of numbers:
9 * 9 * 8 * 7 * 6 * 5 * 4 * 5 * 4 * 3 = 32659200
where the first seven places represent digits, and the last three represent letters.
Hence, the different student number possible if a student I.D number consisting of seven digits (the first digits may be repeated) Followed by three of the letters A,B,C,D and E is 32659200.
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Complete the equation for the piecewise function graphed below.
The piecewise function will be f(x) = - 0.5x - 1.5 if -6 ≤ x ≤ - 1, f(x) = -2 if - 1 < x ≤ 3, and f(x) = (5/3)x + 7 if 3 < x ≤ 6.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The equation of the line in the interval [-6, -1] whose points are (-3, 0) and (-1, -1) is given as,
(y - 0) = [(0 + 1) / (- 3 + 1)](x + 3)
y = - 0.5x - 1.5
The equation of the line in the interval (1, 3] whose points are (0, -2) and (3, -2) is given as,
(y + 2) = [(-2 + 2) / (3 - 0)](x + 0)
y = - 2
The equation of the line in the interval (3, 6] whose points are (3, -2) and (6, 3) is given as,
(y + 2) = [(3 + 2) / (6 - 3)](x + 3)
y + 2 = (5/3)(x + 3)
y = (5/3)x + 7
The function is given as,
f(x) = - 0.5x - 1.5 if -6 ≤ x ≤ - 1
f(x) = -2 if - 1 < x ≤ 3
f(x) = (5/3)x + 7 if 3 < x ≤ 6
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Which expressions are completely factored?
Select each correct answer.
Responses
16a5−20a3=4a3(4a2−5)
16 a begin power 5 end power minus 20 a cubed equals 4 a cubed left parenthesis 4 a squared minus 5 right parenthesis
12a3+8a=4(3a3+2a)
12 a cubed plus 8 a equals 4 left parenthesis 3 a cubed plus 2 a right parenthesis
30a6−24a2=3a2(10a4−8)
30 a begin power 6 end power minus 24 a squared equals 3 a squared left parenthesis 10 a begin power 4 end power minus 8 right parenthesis
24a4+18=6(4a4+3)
24 a begin power 4 end power plus 18 equals 6 left parenthesis 4 a begin power 4 end power plus 3 right parenthesis
The expressions that are completely factored are:
16a5−20a3=4a3(4a2−5) is correct.12a3+8a=4(3a3+2a) is correct.24a4+18=6(4a4+3) is correct.Why are they considered to be correct?The expressions are considered correct because they have been completely factored, meaning they have been written in the form of "a common factor times another expression". This means that the expression on the right side of the equal sign can be simplified into its simplest form.
For example, in the expression 16a5−20a3=4a3(4a2−5), the 4a3 factor is common to both 16a5 and 20a3, so it can be factored out. The expression then becomes 4a3 times (4a2−5), which is the completely factored form.
Similarly, in the expression 12a3+8a=4(3a3+2a), the factor of 4 is common to both the expressions on the right side, so it can be factored out. This results in the completely factored form of 4 times (3a3+2a).
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Answer:
16a^5−20a^3=4a^3(4a^2−5)
and
24a^4+18=6(4a^4+3)
Step-by-step explanation:
PLEASE HELP!! DUE IN TEN MINUTES!!
Answer:
Step-by-step explanation:
During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time t
, in hours. At time t=0
hours, the population is 300. At time t=24
hours, the population is 1000. At what time t
is the population 500 ?
Step-by-step explanation:
The rate of change of the population is proportional to the population, so we can use the exponential growth formula:
P(t) = P0 * e^(kt)
Where P0 is the initial population (300), k is the constant of proportionality, and t is the time in hours. We can use the data from t=24 hours to solve for k:
1000 = 300 * e^(24k)
Dividing both sides by 300 and taking the natural logarithm of both sides:
ln(1000/300) = 24k
ln(3.33) = 24k
k = ln(3.33) / 24
Now that we have k, we can plug it into the formula and solve for t when P(t) = 500:
P(t) = 300 * e^(kt)
500 = 300 * e^(kt)
e^(kt) = 500/300
e^(kt) = 5/3
kt = ln(5/3)
t = ln(5/3) / k
Substituting k = ln(3.33) / 24:
t = ln(5/3) / (ln(3.33) / 24)
t ≈ 11.7 hours.
2. Find the simple interest for the following. Round to the nearest cent.
$7800 at 9.25% for 4 months
3. What is the difference between exact and ordinary interest? Don't forget about leap years.
Answer:
2. $240.50
3. See below
Step-by-step explanation:
2.
I = Prt
where I = interest
P = principal amount (amount of investment)
r = annual interest rate
t = time in years
t = 4 months = 4/12 year = 1/3 year
r = 9.25% = 0.0925
I = Prt
I = $7800 × 0.0925 × 1/3
I = $240.50
3. Exact interest takes into account every day of the year. In a regular year, there are 365 days. in a leap year, there are 366 days. Exact interest uses the exact number of days of the specific year for interest calculations of less than a year.
Ordinary interest rounds off a year to 360 days, and calculations are based on a year having 360 days, not 365 of 366 days.
Need help with solution please
Answer: The definition of a solution is a value or values which, when substituted for a variable in an equation, make the equation true. For example, the solutions to the equation x2 = 4 are 2 and -2. I hope this helped!
Corresponding points that lie
on the graph of
f(x) = (x-4)^3-6
(Type ordered pairs. Simplify
your answer.)
The missing coordinates of the cubic equations are filled out as ordered pairs as follows
function coordinates
y = x³ (-1, -1), (0, 0)
f(x) = (x - 4)³ - 6 (-1, -131), (0, -70)
How to find the missing coordinatesThe coordinates of the cubic equation is sought by substituting the values of x in the function and solve for y.
for x = -1
y = x³ = (-1)³ = -1
f(x) = (x - 4)³ - 6 = (-1 - 4)³ - 6 = -131
for x = 0
y = x³ = (0)³ = 0
f(x) = (x - 4)³ - 6 = (0 - 4)³ - 6 = -70
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determine the solution to the inequality
1/4|x+1|>4
a. x > -1 or > 17
b. x < -17 or x > 15
c. x < -9 or x > 7
d. x < -2 or x > 0
The solution to the inequality in this problem is given as follows:
b. x < -17 or x > 15.
How to solve the inequality?The inequality for this problem is defined as follows:
0.25|x + 1| > 4.
Isolating the absolute value, we have that:
|x + 1| > 4/0.25
|x + 1| > 16.
The absolute value of a number represents it's distance from the origin, meaning that the inequality can be written as follows:
x + 1 < -16 or x + 1 > 16.
Then the first interval in the solution of the inequality is given as follows:
x + 1 < -16
x < -17.
The second interval in the solution of the inequality is given as follows:
x + 1 > 16
x > 15.
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based on the data what is the difference between the median of the data including the outlier and excluding the outlier
The difference between the median is 0.5. option D
What is the difference?Getting the sets of values that we have in order, we can see that we have;
12, 15, 33, 45, 46, 51, 52, 93
We can find the median between 4th and 5th numbers this is now going to give us that; (45+46)/2 = 45.5
Median value = 45.5
We can see that 93 is the outlier in the data set so if we remove it we would have;
12, 15, 33, 45, 46, 51, 52
The median of the data set in this case is 45.
The difference is;
45.5 - 45 = 0.5
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Missing parts;
The number of lattes sold daily for two coffee shops is shown in the table:
Lattes
12
52
93
33
51
15
46
45
Based on the data, what is the difference between the median of the data, including the outlier and excluding the outlier?
A.46
B.45.5
C.45
D.0.5
9. Which of the following graphs represents the solution set for 5x + 38 ≤ 4(2 – 5x)?
We are given the following inequality.
[tex]5x+38 \leq 4(2-5x)[/tex]
Apply the distributive property on the right side:
[tex]5x+38\leq 8-20x[/tex]
Add both sides by 20x:
[tex]5x+38+20x\leq 8-20x+20x[/tex]
[tex]25x+38\leq 8[/tex]
Subtract both sides by 38:
[tex]25x+38-38\leq 8-38[/tex]
[tex]25x\leq -30[/tex]
Divide both sides by 25:
[tex]25x/25\leq -30/25[/tex]
[tex]x\leq -6/5[/tex]
Out of all the options, only option A accurately depicts this inequality. Thus, the answer is option A.
Let me know if you have any questions, thanks!
5
55 markers cost
$
6.55
$6.55dollar sign, 6, point, 55.
Which equation would help determine the cost of
4
44 markers?
Choose 1 answer:
Choose 1 answer:
The equation that can be used to represent the cost of 4 markers is y = k × 4
How to write equation?5 markers = $6.5
Unit cost of each marker = $6.5 / 5
= $1.3 per marker.
If
y = kx
Where,
y = total cost of markers
k = unit cost of marker
x = number of markers
The equation for the cost of 4 markers:
y = kx
y = 1.3 × 4
y = $5.2
Ultimately, y = k × 4 represents the equation for total cost of 4 markers.
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The ratio of saturated fat to total fat in a caramel frappucino is 2 to 3. There are 4 more grams of total fat than saturated
fat. How much total fat is there in a caramel frappucino?
On solving the provided question, we cans ay that ratio is 2:3=> 2x + 4x = 4 => x = total fat is 6.6666666667
what is ratio?Ratios show how often one number is contained in another in mathematics. For instance, the ratio of oranges to lemons in a fruit dish is 8 to 6 if there are 8 oranges and 6 lemons present. In a similar vein, the proportion of oranges to whole fruit is 8, while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b that is expressed as a / b, with b not equal to zero. An equation equating two ratios is known as a ratio. The ratio can be expressed as 1:3, for instance, if there is 1 boy and 3 girls (for every boy she has 3 girls) 3/4 are girls, while 1/4 are boys.
The ratio of saturated fat to total fat in a caramel frappucino is 2 to 3
There are 4 more grams of total fat than saturated fat
ratio is 2:3
2x + 4x = 4
x = 4/6*10
x = 6.6666666667
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You deposit $400 each month into an account earning 8% interest compounded monthly_ a) How much will you have in the account in 30 years? b) How much total money will you put into the account? c) How much total interest will you earn?
Answer:
400×30= 12000 in 30yrs
12000
Step-by-step explanation:
12000÷.08= 150000
Construct a dilated version of quadrilateral HIJK, shown below, with a scale factor of 2 and the center of dilation at (-1,-1).
K(-1,3)
H(-1, 2)
J(2,3)
I (1, 1)
Step-by-step explanation:
the new cocrfinations are
K' (-1, 7)
H' (-1, 5)
J' (5, 7
I' (2, 2)
answer to winterwonderland breakout edu
Answer:its a cool song
Step-by-step explanation:
listening, listened to it, its good
Fwam is going to use a computer at an internet cafe. The cafe charges an initial fee to use the computer and then an additional price per minute of usage. Let C represent the total cost of using a computer for t minutes at the internet cafe. The table below has select values showing the linear relationship between t and C. Determine the additional charge per minute.
t
3
6
9.5
C
10.30
13.60
17.45
The additional charge per minute is given as follows:
$1.1.
How to obtain the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change, which in the context of this problem is the charge per minute.The intercept b represents the initial value, which in the context of this problem is the flat initial fee.From the table, when the time in minutes increases by 3, from 3 to 6, the cost increases by $3.3, from $10.30 to $13.60, hence the slope m is obtained as follows:
m = 3.3/3
m = $1.1.
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Which is the equation of a line perpendicular to the line with the equation:
y = 1/4x + 2
The equation of a line perpendicular to the line y = 1/4x + 2 and passing through a point (x1, y1) is given by:
y - y1 = -4(x - x1)
This is because the slope of the original line is 1/4, so the slope of the perpendicular line must be -4 (the negative reciprocal).
What is a perpendicular line?A perpendicular line is a line that forms a 90-degree angle with another line. In other words, it is a line that is perpendicular to another line at their point of intersection. The slope of two perpendicular lines are negative reciprocals of each other, meaning that if one line has a slope of m, the slope of the perpendicular line is -1/m.
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Find the length of JM
The length of JM is 24 units.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
<H= <K= <N= 90
and, GH || JK || MN
then, Using proportion
GL/ GM = HK/ HN
18/ (18+ x) = 15/ (15+20)
18(15+20) = 15(18+x )
18 . 20= 15 x
x= (18)(20)/ 15
x= 24
Hence, the length is 24 units.
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54) If a spring stretches 6 meters when a 8-kilogram weight is attached to it, how much will it stretch when a 56-kilogram weight is attached to it?
The length of the spring stretched is given by the proportion A = 42 meters
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the length of the spring stretched when 56 kg weight is attached be A
Now , the equation will be
The length of the spring when 8 kg is attached to it = 6 meters
So , the proportion is
A / 56 = 6 / 8
On simplifying the equation , we get
Multiply by 56 on both sides of the equation , we get
A = ( 6 x 56 ) / 8
On further simplification , we get
A = 6 x 7
A = 42 meters
Therefore , the value of A is 42 meters
Hence , the equation is A = 42 meters
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Find an equation in point-slope form for the line having the slope m=-6 and containing the point (7,8)
[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ - 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{- 6}(x-\stackrel{x_1}{7})[/tex]
write 3 23/25 as rational numbers
what made the time ater sugauli treaty politically instable and complicated
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Equation line L is y=5x+1
The equation of line, L^2 is 2y-10x+3=0
Shows that these two lines are parallel
Answer:
Step-by-step explanation:
Yes, the two lines are parallel.
Lines are parallel if they have the same slope. The slope of a line can be found by rearranging the equation into the slope-intercept form: y = mx + b, where m is the slope.
For line L: y = 5x + 1, so the slope is 5.
For line L^2: 2y - 10x + 3 = 0, rearrange to get y = -5x + (3/2). The slope of the line is -5.
Since the two lines have the same slope (both 5), they are parallel.
What is the place value of the 5 in the number 2.35 x 10^4? Justify your answer.
The place value of 5 in 2.35 x 10⁴ is 500.
What is scientific notation?In scientific notations numbers are written in the form of a base that is
0 ≤ b < 10 and multiplied by 10ⁿ where n represents integers.
We write large standard numbers in scientific form in a compact manner.
Given, A number 2.35 x 10⁴ in scientific form.
Now, The decimal form of the number is 2.35 x 10000.
= 23500.
Now, In 23500 5 is in the hundredths place,
Therefore, The place value of 5 is 500.
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Melissa wants to check the accuracy of the finance charge on her promissory note. She has a $6,000, 4-year loan at an APR of 3.11%. Round to the nearest cent.
a. What is her monthly payment?
b. What is the total of all her monthly payments?
c. What is the finance charge?
The solution is,
a) Melissa's monthly payment on the promissory note is $133.10.
b) The total of Melissa's monthly payments is $6,388.80.
c) The total finance charge is $388.80.
How are the monthly payments and finance charges determined?Using an online finance calculator, we can compute the promissory note's monthly payments and finance charges (cost of credit).
The sum of the monthly payments is the total payments made by Melissa, consisting of the amount of the promissory note and the finance charges.
here, we have,
N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 3.11%
PV (Present Value) = $6,000
FV (Future Value) = $0
Results:
PMT = $133.10
Sum of all periodic payments = $6,388.80
Total Interest = $388.80
Thus, Melissa's finance charge on the promissory note is $388.80, with a monthly payment of $133.10 for 4 years.
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the actual cost per pound of potatoes for the 5- pound bag is $ blank per pound
The actual cost per pound of potatoes for the 5-pound bag is $0.76 per pound.
What is Rate?A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.
When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.
A 5-pound bag of potatoes costs $.3.80.
So the rate of the potato per pound is: 3.80/5 = 0.76
Therefore, the cost of potatoes per pound will be $0.76.
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Complete question:
A 5 pound bag of potatoes costs $.3.80. How much do the potatoes cost per pound?
The actual cost per pound of potatoes for the 5-pound bag is per pound.
Identify the constants B and M in the expression b+mt for the linear function r(t)= √3 - 0.4t√13
b=
m=
The value of the 'm' and 'b' will be negative 1.44 and 3.61, respectively.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + b
Where m is the slope of the line and b is the y-intercept of the line.
The linear equation is given below.
r(t)= √3 - 0.4t√13
r(t)= √3 - (0.4√13) t
Compare the equation with the standard equation. Then we have
m = - (0.4√13)
m = - 1.44
b = √13
b = 3.61
The value of the 'm' and 'b' will be negative 1.44 and 3.61, respectively.
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Even salaried employees can be paid by the hours they clocked in/out.
A) True
B) False
Answer:
B
Step-by-step explanation:
There are two types in this good ol' world, Salary and Hourly.
Hourly gets paid by, well, the hour
Salary has a set amount. Let's say there around is $1000 a week. If they work 70 hours, they get paid $1000, if they work 30 hours, they get paid $1000
O Math on the Spot Cara's muffin recipe calls
for 1½ cups of flour for the muffins 1/4 and cup
of flour for the topping. If she makes 1/2 of the
original recipe, how much flour will she use?
Answer:
For the muffins, she will use 3/4 cup of flour and for the topping, she will use 1/8 cup of flour.
Sophie needs to restock the paper and ink for the printer is in her office she wants to make sure that she has enough money before going to the office supply store if she needs to buy 6 reams of paper at $5.89 per ream and 9 ink cartridges at $29.30 per cartridge estimate the amount of money so he will need to purchase the paper and ink needed
The amount of money he will need to purchase the paper and ink is $299.04.
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,
Cost of 1 ream = $5.89
Cost of 1 ink cartridge = $29.30
Now,
Number of reams to buy = 6
Number of ink cartridges to buy = 9
The amount needed to buy.
= 6 x 5.89 + 9 x 29.30
= 35.34 + 263.7
= $299.04
Thus,
The amount of money needed is $299.04.
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