The simplification of 3 hours : 45 m is 4 minutes : 1 minutes.
How to simplify ratio?Ratio refers to a number representing a comparison between two named quantities.
3 hours : 45 m
Convert hours to minutes:
1 hour = 60 minutes
3 hours = 180 minutes
3 hours : 45 m = 180 minutes : 45 minutes
= 180/45
= 4 / 1
= 4 : 1
Ultimately, 3 hours : 45 m is 4 minutes ratio 1 minutes.
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Simplify: Simplify: StartRoot StartFraction 27 x Superscript 12 Baseline Over 300 x Superscript 8 Baseline EndFraction EndRoot
The solution of the given expression is 9*\(x^{4}\)/100.
GIven an expression equal to 27\(x^{12}\)/300\(x^{8}\).
We have to simplify the expression in which variable comes only once.
Expression is combination of numbers ,symbols, fraction, coefficients, indeterminants,determinants, etc. It is mostly not found in equal to form. It expresses a relationship between variables.
The given fraction is 27\(x^{12}\)/300\(x^{8}\).
When we observe we find that in numerator x has large power and denominator x has small power as compared to power in numerator. So we will deduct the powers so that they will give only one power to us.
=27\(x^{4}\)/300
Now divide numerator an denominator by 3.
=9\(x^{4}\)/300
Hence the expression 27\(x^{12} /300x^{8}\) will look like \(9x^{4} /100\) after simplifying.
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Answer:
\(Simplify:\sqrt\frac{27x^{12} }{300x^{8} }\)
\(O \frac{9}{100}x^{4}\)
✔ \(\frac{3}{10} x^{2}\)
\(O \frac{27}{300} x^{4}\)
\(O\frac{9}{10} x^{2}\)
David was asked to solve the problem below:
If a = 5x - 4 and b = 3x, what is the value of a - b?
David used the steps below to solve the problem
Step 1: a - b
Step 2: (5x-4) - 3x
Step 3: 5x-4-3x
Step 4: -2x
Determine whether David's solution is correct. If he is correct, show the work that proves he is
correct. If he made an error, explain what he should have done instead, and provide the correct
solution.
Answer:
not correctStep 4: 2x -4Step-by-step explanation:
You want to know if David's solution of -2x for (5x-4) -(3x) is correct, and what David should have done.
SolutionDavid's solution is correct up to Step 4.
At that point, it appears as though David treated -4 as if it were -4x. The constant cannot be combined with x terms. Step 4 should have been ...
Step 4: (5 -3)x -4 = 2x -4
David's incorrect solution should have been 2x -4.
How do I do number 1??
Help me it’s due tomorrow!!!
The values of x and y are 20 and 12.
The values of x and y are -3 and 2.
We have,
In a parallelogram,
- Opposite sides are congruent:
The opposite sides of a parallelogram have equal lengths.
- Opposite angles are congruent:
The opposite angles of a parallelogram have equal
Now,
a)
Opposite angles are congruent:
So,
5x + 29 = 7x - 11
29 + 11 = 7x - 5x
40 = 2x
2x = 40
x = 40/2
x = 20
And,
3y + 15 = 5y - 9
15 + 9 = 5y - 3y
24 = 2y
y = 24/2
y = 12
b)
Opposite sides are congruent:
So,
-6x = -4x + 6
-6x + 4x = 6
-2x = 6
x = -3
And,
7y + 3 = 12y - 7
12y - 7y = 3 + 7
5y = 10
y = 2
Thus,
The values of x and y are 20 and 12.
The values of x and y are -3 and 2.
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Find all pairs of positive integers (a,n) such that n greater than 2 and a + (a + 1) + (a + 2) + ... + (a + n - 1) = 100.
(49,5), (19,10), (9,20), (4,50), (1,100) are the only pairs of positive integers (a,n) such that n is greater than 2 and a + (a + 1) + (a + 2) + ... + (a + n - 1) = 100.
In mathematics, an integer is a number that can be written without a fractional or decimal component.
To start, we can use the formula for the sum of an arithmetic series to find the value of n.
The formula for the sum of n terms in an arithmetic series is given by
=> S = n/2 (a + a + n - 1),
where a is the first term and n is the number of terms. Substituting the values from the problem, we have:
=> 100 = n/2 (2a + n - 1)
Expanding the right side, we get:
100 = n/2 (2a + n - 1)
Multiplying both sides by 2 and rearranging, we get:
200 = n (a + n/2)
Dividing both sides by n, we get:
a + n/2 = 200/n
Since n is an integer greater than 2, we know that n must divide 200. To find all possible values of n, we can use the divisibility rule for 2, which states that an integer is divisible by 2 if and only if its last digit is 0, 2, 4, 6, or 8. Thus, we can list all possible values of n as follows:
=> n = 2, 4, 5, 8, 10, 20, 25, 40, 50, 100
For each value of n, we can use the formula for a to find all possible values of a that satisfy the conditions of the problem. Substituting n = 2 into the formula for a, we get:
=> a + n/2 = 200/n
=> a + 1 = 200/2
=> a = 199/2
Since a is a positive integer, we see that a = 199/2 is not an integer, so the pair (a,n) = (199/2,2) is not a solution. Continuing this process for each value of n, we find the following pairs of positive integers (a,n) that satisfy the conditions of the problem:
=> (a,n) = (49,5), (19,10), (9,20), (4,50), (1,100)
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A plastic page designed to hold trading cards will hold up to 8 cards. How many pages will be needed to store 583 cards? Give an appropriate counting number answer to the question. (Find the least counting number that will work.)
The number of pages that would be needed to store 583 cards is (blank).
Answer:
73 pages
Step-by-step explanation:
You want the number of pages required to hold 583 cards when each page will hold 8.
Least integerThe number of pages required is ...
(583 cards)/(8 cards/page) = 72 7/8 pages
The least integer greater than this number is 73
The number of pages needed to store 583 cards is 73.
You decide to make an investment in bonds. After much deliberation, you decide to purchase 10 State Farm bonds at a price of 99.40. These bonds have a 5% interest paid annually.
• How much did you pay for the 10 bonds (excluding commission)?
• How much interest will you receive each year from the bonds?
• What is your bond yield (to the nearest tenth percent)?
The bond yield is approximately 5.0% to the nearest tenth of a percent.
We have,
To find the total cost of the 10 State Farm bonds, we can multiply the price per bond by the number of bonds:
10 bonds x $99.40 per bond = $994.00
So, we paid $994.00 for the 10 State Farm bonds.
To calculate the amount of interest we will receive each year from the bonds, we can use the following formula:
Interest = Principal x Rate
where:
The principal is the amount invested in the bonds
Rate is the interest rate
In this case, our principal is $994.00 and our rate is 5%, or 0.05 as a decimal.
So, the annual interest we will receive from the bonds is:
Interest = $994.00 x 0.05 = $49.70
So,
We will receive $49.70 in interest each year from the bonds.
To calculate the bond yield, we need to use the following formula:
Bond yield = (Annual interest / Total cost) x 100%
In this case, the annual interest is $49.70 and the total cost is $994.00, so we can plug these values into the formula:
Bond yield = ($49.70 / $994.00) x 100% ≈ 5.0%
Therefore,
The bond yield is approximately 5.0% to the nearest tenth of a percent.
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Andrew wants to build a square garden and needs to determine how much area he has for planting the perimeter of the garden is between 12 and 14 feet what is the range if the possible areas
Answer:
9 ft^2 and 12.25 ft^2
Step-by-step explanation:
We need to figure out the area for a square with a perimeter of 12 feet and 14 feet.
A square has four sides that are all equal in length, therefore:
12/4 = 3
14/4 = 3.5
3 and 3.5 are the individual side lengths of the garden, so to find the area, we just multiply those numbers by themselves (since it is a square garden).
3*3 = 9
3.5*3.5 = 12.25
Therefore, the answer is 9 ft^2 and 12.25 ft^2
What is the answer to
2x squared?
Answer:
it’s just 2x^2
it’s not factorable
I need help or my grade is going to go to a f-
Answer:
1
Step-by-step explanation:
65.751 = 6 x 10 + 5 x 1 + 7 x 1/10 + 5 x 1/100 + 1 x 1/1,000
6 x 10 = 60
5 x 1 = 5
7 x 1/10 = 0.7
5 x 1/100 = 0.05
1 x 1/1000 = 0.001
60 + 5 + 0.7 + 0.05 + 0.001 = 65.751
10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
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Convert the measurement. 5 days = sec
Answer:
5days = ? sorry I don't understand sorry
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Every day has 24 hours .
Every hour has 60 minutes .
Every minute has 60 seconds.
Thus ;
\(5 \times 24 \times 60 \times 60 = 120 \times 60 \times 60 = \\ \)
\(2 \times 60 \times 60 \times 60 = \)
\(2 \times {6}^{3} \times {10}^{3} = \)
\(2 \times 216 \times 1000 = \)
\(432 \times 1000 = \)
\(432,000 \: \: \: seconds\)
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9) The 50 cars used by a firm were inspected. 10 had faulty brakes and 15 had faulty tyres. There were 2 cars with faulty brakes but good tyres. How many cars had good brakes and good tyres? The answer is 33
Based on the information, there are 25 cars with good brakes and good tires.
How to calculate the valueTotal cars = 50
Cars with faulty brakes = 10
Cars with faulty tires = 15
Cars with faulty brakes and good tires = 2
Let's calculate the number of cars with good brakes and good tires:
Cars with faulty brakes or faulty tires = Cars with faulty brakes + Cars with faulty tires - Cars with faulty brakes and good tires
= 10 + 15 - 2
= 25
Cars with good brakes and good tires = Total cars - Cars with faulty brakes or faulty tires
= 50 - 25
= 25
Therefore, there are 25 cars with good brakes and good tires.
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What is the x-coordinate of the image when M(4, -1) is reflected in y = 3.
Answer:
4
Step-by-step explanation:
y=3 is a horizontal line, so it will not affect the x coordinate.
The x-coordinate of the image when M(4,-1) is reflected in y = 3 is : 4
What is reflection?Reflection is the mirror image of a shape.
It is the process of flipping a shape around a certain axis to look like the original shape.
Analysis:
Since the reflection is at y = 3 which is along the x-axis, only the y coordinate changes. The x coordinate remains the same. So, the x- coordinate is still 4.
In conclusion, the x-coordinate is 4.
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please help measure
Answer:
x = 15
Step-by-step explanation:
The definition of alternate interior angles means that both of these labeled angles will be equal. Therefore, 60 = (3x + 15)
60 = 3x + 15
Divide this by 3 on both sides
20 = x + 5
Subtract 5 from both sides
15 = x or x = 15
1.25 +1.25+1.25+1.25
Answer:
5
Step-by-step explanation:
1.25+1.25+1.25+1.25=5
A vehicle is purchased for $19,800 and the lender requires a down payment of 20% of the purchase prize find the down payment
Answer:
the answer is 15840
Step-by-step explanation:
h(a) = -a^3 - 2ag(a) = 4a + 3Find h(a) - g(a)
ABCD ~ EFGH
С
B
140°
G
3
50°
4.5
2
110°
DE
х
A
2.4
H н.
x = [?]
Enter your answer in decimal form.
Enter
Answer:
x = 3.6
Step-by-step explanation:
Since ABCD ~ EFGH, therefore:
AB/EF = AD/EH
AB = 3
EF = 2
AD = x
EH = 2.4
Plug in the values into the equation:
3/2 = x/2.4
Cross multiply
3*2.4 = 2x
7.2 = 2x
Divide both sides by 2
7.2/2 = x
3.6 = x
x = 3.6
Freddie put an empty bucket underneath a leaking pipe. After 34 hours, Freddie collected 12 cups of water. What is the rate, in cups per hour, at which the water is leaking from the pipe?
Answer:
0.35 cups/hour
Step-by-step explanation:
To be able to determine the rate at which the water is leaking from the pipe with the information given, you have to divide the number of cups by the number of hours in which they were collected:
12 cups/34 hours= 0.35 cups/hour
According to this, the answer is that the rate at which the water is leaking from the pipe is 0.35 cups/hour.
Which is the better deal? [You must show your work in order to receive full credit (2 points).]
12 packs of fruit snacks for $9.12 or 9 packs of fruit snacks for $6.99
Answer:
i think it is 12 packs of fruit snacks for $9.12
Step-by-step explanation:
(1,−1)and(6,9) Write the slope-intercept form of the equation of the line through the given points.
Answer:
2
Step-by-step explanation:
So first you would do y2-y1/x2-x1
9-(-1)/6-1
10/5=
2
One of the legs of a right triangle measures 2 cm and the other leg measures 17 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
17.1
Step-by-step explanation
a^2+b^2=c^2
2^2 + 17^2 = c^2
4 + 289 = c^2
293 = c^2
square root of 293 or 17.1
someone please answer this its confusing me
Convert r=tanθ into rectangular form
Answer:
\(\sqrt{x^2+y^2} = \dfrac{y}{x}\)
Step-by-step explanation:
Convert the expression given equation in polar coordinates to rectangular coordinates.
\(r=\tan\theta\)
\(\text{Using the following conversions:}\\\boxed{\left\begin{array}{ccc}\text{\underline{Rect. to Polar:}}\\(x,y)\rightarrow(r, \theta)\\\\r=\sqrt{x^2+y^2}\\\\\theta=\tan^{-1}(\frac{y}{x})\end{array}\right}\)
\(r=\tan\theta\\\\\\\Longrightarrow \sqrt{x^2+y^2} = \tan\theta\\\\\\\Longrightarrow \sqrt{x^2+y^2} = \tan(\tan^{-1}\Big(\dfrac{y}{x} \Big))\\\\\\\Longrightarrow \boxed{\sqrt{x^2+y^2} = \dfrac{y}{x} }\)
Thus, the problem is solved.
Consider the following complex number.
12-9i
1) Plot the complex number.
2)Find its absolute value.
|12-9i|
1. The point on the plane where the lines intersect represents the complex number (CLICK IMAGE)
2. The absolute value of the complex number 12-9i is 15.
1. To plot the complex number 12-9i, we can visualize it on the complex plane. The real part (12) corresponds to the x-axis, and the imaginary part (-9) corresponds to the y-axis.
Plotting the complex number:
On the complex plane, we move 12 units to the right along the x-axis and 9 units downward along the y-axis to represent the complex number 12-9i.
2. Finding the absolute value:
The absolute value (or modulus) of a complex number is calculated using the formula:
|a + bi| = √(a^2 + b^2)
For the complex number 12-9i, the absolute value is:
|12-9i| = √(12^2 + (-9)^2)
= √(144 + 81)
= √225
= 15
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How many solutions does the equation sin(5x) = 1/ I have on the interval(0, 2π]?
Answer:
10
Explanation:
The graph of sin(x) = 1/2 has two solutions. Because the graph is
Then, the graph for sin(5x) is horizontal compression by a factor of 5, which means that sin(5x) = 1/2 will have 10 solutions, because
2(5) = 10
Therefore, the answer is 10.
Consider the equation and the following ordered pairs: (1,y) and (x,−3).
6x+3y=15
What number is equivalent to
32 + 6 – (14 – 5 × 2) ÷ 4
A
234
B
1012
C
14
D
15
Answer:
C you all welcome:)
Step-by-step explanation:
A was wrong sorry to tell you
write answers that are not integers rounded to the nearest tenth
The value of x is 12.82, the value of z is 40.25.
Using Pythagorean theorem
50²= 39² + y²
y²= 2500- 1521
y= 32.28
Again Using Pythagorean theorem
z²= y²+ x²
z²- x²= 979
and, (39 + x)² = 50² + z²
(39 + x)² = 50² + (x² + 979)
1521 + 78x + x² = 2500 + x² + 979
78x = 1000
x ≈ 12.82
Substituting this value of x back into the first equation, we get:
z² - x² = 979
z² - (12.82)² = 979
z² ≈ 1620.12
Taking the square root of both sides, we get:
z ≈ 40.25
Therefore, the value of x is 12.82, the value of z is 40.25.
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Find the area of a sector with an arc length of 60 in. and a radius of 15 in.
A. 117.75 in.2
B. 282.60 in 2
C. 450 in.2
D. 6,750 in.2
Answer:
C. 450 in.2
Step-by-step explanation: