Answer:
Volume = 105 cm³
Step-by-step explanation:
Volume of a cuboid = l × b × h (l = length. b = breadth. h = height)
Volume = 7 × 5 × 3
Volume = 35 × 3
Volume = 105 cm³
Find the value of y.
y= ?
Answer:
2
Step-by-step explanation:
Answer:
y=x-1
Step-by-step explanation:
Work out the base of a square with area, A = 169cm2
Answer:
a=p/4
Step-by-step explanation:
Match the graph of the system of equations with the appropriate description of the solution.
No solution.
The solution is (0, 0).
The solution is (-1, -2).
There are infinitely many solutions.
The requried solution of the system of equations is (-1, -2). Option C is correct.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Two intersecting lines will have exactly one solution (i.e., a unique point of intersection) if and only if they are not parallel.
In other words, if the slopes of the two lines are different, they will intersect at a single point. This is because the slopes of the lines determine how steep they are, and if they are not the same, they will eventually cross at a single point. So from the graph, both lines intersect at (-1, -2) implying that The solution is (-1, -2).
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A bag contains 8 green candies and 4 red candies. You randomly select one candy at a time to eat. If you eat five candies, there are relatively prime positive integers m and n so that m n is the probability that you do not eat a
green candy after you eat a red candy. Find m + n.
If m/n is the probability that you do not eat green candy after you eat a red candy, then m + n is 6.
A bag contains 8 green candies and 4 red candies. If you eat five candies, there are relatively prime positive integers m and n so that m/n is the probability that you do not eat green candy after you eat a red candy. Below list the ways to accomplish this ordering along with their respective probabilities:
GRRRR : \(\frac{8}{12}\times\frac{4}{11} \times\frac{3}{10} \times\frac{2}{9} \times\frac{1}{8}\)
GGRRR : \(\frac{8}{12}\times\frac{7}{11} \times\frac{4}{10} \times\frac{3}{9} \times\frac{2}{8}\)
GGGRR : \(\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{4}{9} \times\frac{3}{8}\)
GGGGR : \(\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}\)
GGGGG : \(\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}\)
The sum is \(\frac{8\times3\times4(2+14+42+70+70)}{12.11.10.9.8}\)
Probability that you do not eat green candy after you eat a red candy =\(\frac{1}{5}\)
so m = 1 and n = 5
m + n =6
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HELPP!!!
The area of the figure is ____ square units.
Answer:
The answer is 132 square units
Step-by-step explanation:
Cutting the shape
we have two trapeziums
A=(area of small +Area of big)Trapezium
A=1/2(3+9)8 + 1/2(9+12)8
A=1/2×12×8 + 1/2×21×8
A=12×4 + 4×21
A=48+84
A=132 square units
If the least value of n is 4, which inequality best shows all the possible values of n?
n ≤ 4
n ≥ 4
n < 4
n > 4
If the least value of n is 4, then the inequality best shows all the possible values of n is, n ≥ 4. So Option B is correct
What are inequalities?Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.
We use these symbols to represent inequalities, '>' , '<', '≥', '≤'
Given that,
The least value of n is 4,
Inequality representation = ?
It is known that,
Least value of n is 4
So, Minimum possible value of n is 4
Maximum value of n should be more than 4,
In order to satisfy the condition,
So,
n > 4
By combining both the things,
It can be written as,
n ≥ 4
Hence, the best inequality representation is n ≥ 4
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Austin deposited $3000 into an account with a 4.6% annual interest rate, compounded quarterly. Assuming that no withdrawals are made, how long will it take
for the investment to grow to $4179?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
The number of years for the compound interest to reach an amount of value $ 4179 is given by n = 7.25 years
Given data ,
Let the compound interest amount be represented as A
Now , the interest rate r = 4.6 %
The number of times the interest is applied = quarterly
The principal amount P = $ 3000
Let the number of years be represented as n
And , t = ln(A/P) / n[ln(1 + r/n)]
t = ln(4,179.00/3,000.00) / ( 4 × [ln(1 + 0.046/4)] )
t = ln(4,179.00/3,000.00) / ( 4 × [ln(1 + 0.0115)] )
t = 7.247 years
On simplifying , we get n = 7.25 years
Hence , time required to get a total amount of $4,179.00 with compounded interest on a principal of $3,000.00 at an interest rate of 4.6% per year and compounded 4 times per year is 7.25 years
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a container of water has 1/4 water and 1/3 oil. how much is the fraction of the empty space
The Fraction of empty space in the container is 5/12. This means that 5/12 of the container is not filled with water or oil, and is instead empty.
The container is made up of two substances: water and oil. We know that the container has 1/4 water and 1/3 oil. This means that the remaining space in the container is made up of neither water nor oil, i.e., empty space.
To find the fraction of empty space, we need to add the fractions of water and oil together and subtract them from 1. This is because the sum of the fractions of water, oil, and empty space must equal 1, which represents the total volume of the container.
The fraction of water in the container is 1/4, and the fraction of oil is 1/3. Therefore, the fraction of the container that is not empty is:
1/4 + 1/3 = 3/12 + 4/12 = 7/12
To find the fraction of empty space, we subtract this fraction from 1:1 - 7/12 = 5/12
Therefore, the fraction of empty space in the container is 5/12. This means that 5/12 of the container is not filled with water or oil, and is instead empty.
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it takes 126 cubes that have edge lengths of 1/3feet to completely fill this plastic bin what is the area of the base of bin
Answer: 1) Each of the 126 cubes has a volume = (1/3)3 = 1/3 × 1/3 × 1/3 = 1/27 cubic feet.
2) It takes 126 cubes to fill the bin, so the bin has a volume of 126 × 1/27 = 126/27 cubic feet. (Don't do this division yet - leave it as an improper fraction)
3) The volume of the bin is also given by the formula Volume = Area of Base × Height. Plus we know the volume is 126/27 cubic feet and the height is 2 1/3 = 7/3 of a foot, so:
Step-by-step explanation: Volume = Area of Base × Height
126/27 = Area of Base × 7/3
126/27 × 3/7 = Area of Base
The area of the base of bin is 2 feet².
What is Volume of Cube?The formula of volume of the cube is given by: Volume = a³, where a is the length of its sides or edges.
Given:
Edge = 1/3 feet
Volume of 1 cube= l³= (1/3)³ = 1/27
Totals cubes= 126
So, Volume of 126 cube= 126 x 1/27 = 126/ 27
Then, Volume of Plastic Bin= Area of base x height
126 / 27 = Area of base x 7/3
Area of base = 126 /27 x 3 /7
Area of base = 2 ft²
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Her bill was $140 after receiving a 15% discount. What was the original amount of the sale
The original amount of the sale is $165
What was the original amount of the sale?The given parameters are:
Bill after discount = $140
Discount = 15%
The original amount of the sale is calculated as:
Bill after discount = original amount * (1 - Discount)
So, we have:
140 = original amount * (1 - 15%)
This gives:
140 = original amount * 0.85
Divide by 0.85
Original amount = 165
Hence, the original amount of the sale is $165
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Solve for x. Using that value, find the measurement of
Given: Four corners of a perpendicular intersection
\(\begin{gathered} m\angle ABE=(6x+2)^0 \\ m\angle DBE=40^0 \end{gathered}\)To Determine: The value of x and the measure of angle m∠ABE
From the given diagram, it can be seen that m∠ABE and m∠DBE are in one of the four corners of the perpendicular intersection.
Also note that all four corners of a perpendicular intersection is a right angle. Therefore:
\(\begin{gathered} m\angle ABE+m\angle DBE=90^0 \\ 6x+2^0+40^0=90^0_{} \\ 6x+42^0=90^0 \\ 6x=90^0-42^0 \\ 6x=48^0 \\ x=\frac{48^0}{6} \\ x=8^0 \end{gathered}\)\(\begin{gathered} m\angle ABE=6x+2 \\ m\angle ABE=6(8)+2 \\ m\angle ABE=48+2 \\ m\angle ABE=50^0 \end{gathered}\)Hence:
x = 8⁰
m∠ABE = 50⁰
Use the average daily balance method to compute the finance charge on the credit card account
for the month of August (31 days). The starting balance from the previous month is $270. The
transactions on the account for the month are given in the table to the right. Assume an annual
interest rate of 19% on the account and that the billing date is August 1st.
aug 7th. payment of $70
aug. 10 purchase of $135
aug. 15 purchase of $20
aug. 29 purchase of $25
what is the finance charge for the month of August?
The finance charge for the month of August is $4.93.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. Moreover, it is indicated by the symbol "%."
Given:
The starting balance from the previous month is $270.
The transactions on the account for the month are given in the table to the right.
Assume an annual interest rate of 19% on the account and that the billing date is August 1st.
After finding the balance outstanding each day, we sum it up.
And get the average as $305.4839
Now we find the average balance by dividing it by 31 days of the August month.
Average balance = $305.4839
Finance charge = $305.4839 x19 x 31/365 days
Finance charge = $4.929589
Finance charge = $4.93
Therefore, the Finance charge = $4.93.
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Please help I’ll mark you as brainliest if correct!
The proportionality from the given given similar triangles is OQ/PQ = RQ/QS.
From the given figure, ∠Q=∠R and ∠RQS=∠PQO.
Since ∠Q=∠R, SR is parallel to OP.
By AA similarity criterion, ΔRQS is similar to ΔPQO.
Now, OQ/RQ = PQ/QS
OQ/PQ = RQ/QS
Therefore, the proportionality from the given given similar triangles is OQ/PQ = RQ/QS.
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What is Four divided by 1 8. It’s a faction the one and eight
Answer: 32
Step-by-step explanation:
4 ÷ 1/8
You can reduce the expression by cancelling out common factors;
4/1 ÷ 1/8
Cross cancel the ones, and then multiply 4 and 8
4 x 8 = 32
1.3.1 1.3.2 1.3.3 1.3.4 Government receives income from various sources, like tax and loans. This income is then distributed to the different sectors. TABLE 3 below shows the source of the income and the expenditure for the 2019/20 tax year. SOURCE Tax INCOME Loans ASC QP Other income Non-tax income AMOUNT (in billion rand) 1370 242.7 180.3 31.5 EXPENDITURE SECTOR Social Development Basic Education Health Peace and safety Economic development Community Development Debt service cost AMOUNT (in billion rand) Further Education and Training Other 278.4 262.4 222.6 211.0 209.2 208.5 202.2 APRIL 2021 112.7 B 1823.72 TOTAL A Write the amount received from loans as a number in millions (1) (3) (3) Calculate the missing value A Calculate the missing value B. Show ALL calculations. Determine the amount allocated for Community Development as a percentage of the total expenditure. (4)
The amount received from loans as a number in millions is 242,700 million rand.
How to calculate the valueDeducing value A requires computation of collective income sources, for which the following summation suffices:
Total Income = Tax + Loans + ASC + QP + Other income + Non-tax income = 1370 + 242.7 + 180.3 + 31.5 + A + 0 = 1825.5 + A
In this context, it follows that A amounts to (1825.5 - 1370 - 242.7 - 180.3 - 31.5) = 0 million rand.
Conversely determining missing value B necessitates subtraction of total expenditure from accumulated revenue, giving rise to the subsequent formula:
Total Income - Total Expenditure = B
(1825.5 - 112.7 - 278.4 - 262.4 - 222.6 - 211.0 - 209.2 - 208.5 - 202.2 - 0) = B
Following calculation, B equates to -77.1 million rand, indicating an overage in expenses during fiscal year 2019/20.
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Question 1 of 20
What is the solution to the following inequality?
Increase 2400 by 25%
Answer:
3,000
Step-by-step explanation:
New value =
2,400 + Percentage increase =
2,400 + (25% × 2,400) =
2,400 + 25% × 2,400 =
(1 + 25%) × 2,400 =
(100% + 25%) × 2,400 =
125% × 2,400 =
125 ÷ 100 × 2,400 =
125 × 2,400 ÷ 100 =
300,000 ÷ 100 =
3,000
The graph of g is a translation 1 unit down of the graph of f(x) = 3|x| – 4. The rate of change of g over the interval 2 ≤ x ≤ 5 is
The solution is: the rate of change is 3.
Here, we have,
Since the graph of f(x) is translated 1 unit down, we need to decrease the value of f(x) by 1 to find g(x):
g(x) = f(x) - 1
f(x) = 3|x| – 4
so, we get,
g(x) = 3|x| – 4 - 1
= 3|x| – 5
Now, to calculate the rate of change over the interval 2 <= x <= 5, we can use the formula below:
rate = g(5) - g(2)/ 5-2
so, we get,
rate = 9/3 = 3
Therefore the rate of change is 3.
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What is the value of x in this equation? 3x + 8 - 2(1 - x) = 1 Show how you got your
answer.
Answer:
3x+8-2(1-x)=1
First, multiply 2x1 and 2x-x
3x+8-2+2x=1
Then rearrange the terms
3x+2x+8-2=1
Then combine like terms
5x+6=1
Then subtract 6 on both sides
5x=-5
Then divide 5 on both sides
x=-1
Step-by-step explanation:
Value of x = -1
What is Equation?when any mathematical values are made equal with help of some variables and constant.
Given equation 3x + 8 - 2(1-x) = 1
simplify equation 3x + 8 - 2 +2x = 1
5x + 6 = 1
5x = 1 - 6
5x = -5
x = -1
Hence x = -1
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Jasmine was expected to get $150 for her bonus, but she only got $100. What was the percent error?
Answer:
Jasmine expected to get $150 for her bonus, but she only got $100. What was the percent error?
-----
Amt of error:: $50
----------
% error:: 50/150 = 1/3 = 33 1/3%
let be the amount of coffee (in ounces) that an undergraduate student at uiuc drinks per day. suppose we know that has a mean of 10 oz and a standard deviation of 5.2 oz. suppose there are 120 students in stat 107. assuming stat 107 students are a random sample, calculate the standard error of the average amount of coffee a stat 107 student drinks per day . is greater than 12.7 oz.
0.137606 the standard error of the average amount of coffee a stat 107 student drinks per day is greater than 12.7 oz.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Statisticians can assess if the data fits into a normal distribution or another mathematical connection using the standard deviation. The average, or mean, data point will be within one standard deviation of 68% of the data points if the data follow a normal curve.
Given that,
Standard deviation (σ) = 5.2 oz
mean (μ) = 10 oz
Number of students (n) = 120
As we know,
P ( z > 12.7 oz.) = P (z > [{x(avg.) - μ\(\sqrt{n}\)}/σ])
= P (z > [{12.7 - 10\(\sqrt{120}\)}/5.2])
= P (z > 1.86)
= 1 - P ( z < 1.86)
= 1 - 0.862394
= 0.137606
Thus, P( z > 12.7 oz.) = 0.137606
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lve for m.
-3 + m
9 = 10
A.
-30
B.
63
C.
87
D.
93
The value of m that satisfies the equation -3 + m = 9 is m = 12.
To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.
-3 + m = 9
To move -3 to the other side, we can add 3 to both sides of the equation:
-3 + 3 + m = 9 + 3
Simplifying, we have:
m = 12
Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.
None of the provided answer options (A, B, C, D) match the correct solution.
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James took a math quiz in which he earned 1 point for every correct answer and lost 0.5
point for every incorrect answer. James answered 12 out of 18 questions correctly. What
was James quiz score?
A. 6
B.9
C 15
D. 18
Answer:
is the b
Step-by-step explanation:
i did the correct operation oki?
The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 26.50 mpg and a standard deviation of σ = 3.25 mpg.
(a) What is the standard error of X¯¯¯
, the mean from a random sample of 25 fill-ups by one driver? (Round your answer to 4 decimal places.)
The standard error represents the average deviation of the sample means from the true population mean. Rounding this value to four decimal places, the standard error of X¯¯¯ is approximtely 0.6500 mpg.
A smaller standard error indicates that the sample means are more likely to be close to the population mean.To calculate the standard error of X¯¯¯, the mean from a random sample of 25 fill-ups by one driver, we can use the formula:
Standard Error (SE) = σ / sqrt(n),
where σ is the standard deviation and n is the sample size.
In this case, the standard deviation (σ) is given as 3.25 mpg, and the sample size (n) is 25.
Plugging in these values into the formula, we have:
SE = 3.25 / sqrt(25).
Calculating the square root of 25, we get:
SE = 3.25 / 5.
Performing the division, we find:
SE ≈ 0.65.
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3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
4x^2 + 10 + x - 50 - x^2 + 4 + 11x
The factorization of the polynomial is determined as (x + 6)(x - 2).
What is the factorization of the polynomial?The factorization of the polynomial is calculated as follows;
4x² + 10 + x - 50 - x² + 4 + 11x
collecting similar terms, we will have;
3x² + 12x - 36
divide through by 3;
x² + 4x - 12
Factorize the expression as follows;
x² + 6x - 2x - 12
x (x + 6) - 2(x + 6)
(x + 6)(x - 2)
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How do you complete the square for this problem ? (if you just explain to me how to complete the square of a trinomial it would be gladly appreciated)
a^2 + 2a - 3
a^2 - 2a - 8
p^2 + 16p - 22
The complete square of the a² + 2a - 3 = 0,a² - 2a - 8 = 0 and p² + 16p - 22 = 0 are (a + 1)² - 4 = 0,(a - 1)² - 9 = 0 and (p + 8)² - 86 = 0 respectively.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
As per the given trinomial,
a² + 2a - 3 = 0
a² + 2a = 3
Add 1 on both sides,
a² + 2a + 1 = 3 + 1
(a + 1)² = 4
(a + 1)² - 4 = 0
As per the given trinomial,
a² - 2a - 8 = 0
a² - 2a = 8
Add 1 on both sides,
a² - 2a + 1 = 8 + 1
(a - 1)² = 9
(a - 1)² - 9 = 0
As per the given trinomial,
p² + 16p - 22 = 0
p² + 16p = 22
Add 64 on both sides,
p² + 16p + 64 = 22 + 64
(p + 8)² = 86
(p + 8)² - 86 = 0
Hence "The complete square of the a² + 2a - 3 = 0,a² - 2a - 8 = 0 and p² + 16p - 22 = 0 are (a + 1)² - 4 = 0,(a - 1)² - 9 = 0 and (p + 8)² - 86 = 0 respectively".
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3 and (5 + 1 + 3)
What is the answer
Answer:
27
Step-by-step explanation:
3(5+1+3) distribute
15+ 3+ 9 add
27
Four students are competing in a race. In how many different combinations could the four students place in the race?
"Combinations" isn't really the right word, because a combination doesn't take order of elements into account, and the outcome of a race certainly does depend on order. "Permutations" would be the correct term.
If 4 students are competing, then the race has
4! = 4 • 3 • 2 • 1 = 24
possible outcomes.
After adding up all your expenses for the month you spent $465.36. your total budget for the month is$529.What percentage are under budget?(Round to the nearest whole percentage).Do not include symbol
Answer:
.12
Step-by-step explanation
529-465.36=63.64
63.64/529= .12
Answer:12%
Step-by-step explanation
Step 1:
Subtract 465.36 from 529
529-465.36= 63.64
Step 2:
Check what percent that is of the total value
63.64 / 529 = .12
Final Answer:
The answer is 12%
A marble is selected from a bag containing eight marbles numbered 1 to 8. The number of the marble selected will be recorded as the outcome. Consider the following events. Event A: The marble selected has an even number.
Event B: The marble selected has a number from 3 to 6.
a) Event "A or B":
b) Event "A and B":
c) The complement of the event A.
A) - Event "A or B" Consists of the Outcomes:
{2, 3, 4, 5, 6, 8}
B) - Event "A or "B" Consists of the Outcomes:
{4, 6}
C) - The "COMPLEMENT of EVENT "A" Consists of the Outcomes:
{1, 3, 5, 7}
Step-by-step explanation:MAKE A PLAN:
List The OUTCOMES for EACH EVENT and their COMBINATIONS:
SOLVE THE PROBLEM:a) - EVENT "A": {2, 4, 6, 8}
EVENT "B": {3, 4, 5, 6}
EVENT "A" or "B": {2, 3, 4, 5, 6, 8}
b) - EVENT "A" or "B": {4, 6}
c) - The COMPLEMENT of the EVENT "A": {1, 3, 5, 7}
Draw the conclusion:A) - Event "A or B" Consists of the Outcomes:
{2, 3, 4, 5, 6, 8}
B) - Event "A or "B" Consists of the Outcomes:
{4, 6}
C) - The "COMPLEMENT of EVENT "A" Consists of the Outcomes:
{1, 3, 5, 7}
I hope this helps!