Assuming the interest is compounded continuously what interest rate to the nearest hundredths of a percent would be required in order for Jamar to end up with $4200 is 4.62%.
How is the interest rate for continuous compounding determined?Using the formula r = ln(A/P) / t, the interest rate, r, can be determined using an online finance calculator as follows:
Total P+I (A) = $4,200.00
Principal (P) = $2,200.00
Compound (n) = Compounding Continuously
Time (t in years) = 14 years
R = 4.619% per year
The calculation steps are as follows:
Solving for rate r as a decimal
r = ln(A/P) / t
r = ln(4,200.00/2,200.00) / 14
r = 0.0461877
Then convert r to R as a percentage:
R = r * 100
R = 0.0461877 * 100
R = 4.62%/year
Thus, the interest rate required to get a total amount of $4,200.00 from compound interest on a principal of $2,200.00 compounded continuously over 14 years is 4.62% per year.
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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.
-7n + 5n^2 + 6 - 3n^2 - 11n + 30
Answer:
2 (n - 3) (n - 6)
Step-by-step explanation:
[tex]-7n+5n^2+6-3n^2-11n+30[/tex]
Group like terms and combine...
[tex]2n^2-18n+36[/tex]
Observe that all terms contain a factor of 2. Factor out a 2...
[tex]2(n^2-9n+18)[/tex]
The leading coefficient is 1. The shortcut applies. Find the factors of "c" (18)
18 = 1 * 1818 = 2 * 918 = 3 * 6Of these factor pairs, -3 & -6 will multiply to make 18, and add to make -9 (the "b").
Finish factoring the trinomial into two binomials:
[tex]2(n-3)(n-6)[/tex]
To verify that this is a valid factoring, distribute, and recombine terms:
[tex]2(n-3)(n-6)[/tex]
[tex]2(n^2-3n-6n+18)[/tex]
[tex]2(n^2-9n+18)[/tex]
find the least common multiple of x^2-25 and x-5
Answer: The least common multiple is (x−5) (x−5)
Step-by-step explanation:
The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.
Michael purchased stereo equipment for $2500. His wife claims that was not a smart investment because stereo equipment decreases in value at a rate of 9% per year. How much will his stereo equipment be be worth after 8 years?
Based on an exponential decay factor, Michael's stereo equipment will be worth $2,116 after 8 years, given the decreasing rate of 9% per year.
What is an exponential decay factor?The decay factor is represented by (1 - r), where r is the constant periodic decreasing rate.
The decay factor is used in exponential decay functions to determine the depreciated value of an asset.
Current price of stereo equipment = $2,500
Annual decreasing rate = 9%
Decrease factor = 0.91 (100% - 9%)
The number of years = 8 years
Value of the equipment after 8 years = ($2,500 x 0.91^8)
= $2,116.125 ($2,500 x 0.47025)
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9. Which statements contradict each other? I. triangle ABC is a right triangle. II. m angle A = 41° III. m angle B = 103° A. I and II B. I and III C. II and III D. None of the statements are contradictory. 1
The contradicting statement is
B. I and III
How to know the contradictory statementThe contradictory statement is that of I and III since the sum of angles in a triangle is always 180 degrees.
Given that
I. triangle ABC is a right triangle. say angle C = 90 degrees and
angle B = 103 degrees,
So the sum of the angles in the triangle would be:
= angle B + m angle C
= 103 + 91
= 194
This is against the law of angles of a triangle
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I have part (a) answered, I just need part (b) if anyone could help with that please?
(a) The two dots on the graph at 53 represent two different samples of size 40 that both had a range of 53.
(b) No, the simulation does not provide evidence that the sample range is a biased estimator of the population.
What is range?Range is a statistical measure that refers to the difference between the highest and lowest values in a set of data. In other words, it is the distance between the largest and smallest values in a dataset.
According to given information:(a) The two dots on the graph at 53 represent two different samples of size 40 that both had a range of 53.
(b) No, the simulation does not provide evidence that the sample range is a biased estimator of the population. A biased estimator systematically overestimates or underestimates the population parameter of interest. The fact that the distribution of sample ranges is approximately symmetric and centered around the true population range suggests that the sample range is an unbiased estimator of the population range. However, the variability of the sample range is quite large, which means that a single sample range may not be a very precise estimate of the population range.
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2. Graph x² + (y-2)² = 36
Answer:
The graph will be a circle with center (0, 2) and radius 6.
Natasha is cutting construction paper into rectangles for a project. She needs to cut one rectangle that is 20 inches × 15 1 4 inches. She needs to cut another rectangle that is 10 1 2 inches by 10 1 4 inches. How many total square inches of construction paper does Natasha need for her project? Mixed number
the following figure, assume that a and b = 3, c = 5, e = 12, and d = 13
Looking at the information provided, we can guess the triangle is similar to the one attached.
Therefore the area of the joint triangle is 40.825 unit²
How did we find the area of the joint triangle?a = b = 3 is the side lengths of the equilateral triangle c = 5 is the side length shared by both triangles = 12 which is the base of the right triangled = 13 which is the hypotenuse of the right triangle
The height of the equilateral triangle is 4.33 units.
Looking at this information, we solve for the area of the equilateral triangle;
Area = (base × height) / 2 (5 × 4.33) / 2= 10.825
Area = (base × height) / 2
Area of the right angle triangle = (12 × 5) / 2 = 30
The total area 10.825 + 30 = 40.825
The above answer is partly based on the figure provided in the image. The numbers used were the ones provided by you, except for the height of the equilateral triangle.
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Looking at the information provided, we can guess the triangle is similar to the one attached. Therefore the area of the joint triangle is 40.825 unit²
How did we find the area of the joint triangle?a = b = 3 is the side lengths of the equilateral triangle
c = 5 shared by both triangles
12 = the base of the right triangle
13 = the hypotenuse of the right triangle
4.33 = height of the equilateral triangle
To solve the total area, we say
Triangle 1
Area = (base × height) / 2
(5 × 4.33) / 2= 10.825
Triangle 2
Area = (base × height) / 2
Area of the right angle triangle = (12 × 5) / 2 = 30
The total area ∴ 10.825 + 30 = 40.825
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How can you describe its content and style in Words of the Devil, by Parau na te Varua ino, that was painted in 1892. ??
Answer:
Words of the Devil, by Parau na te Varua ino, is a painting that was created in 1892 in French Polynesia. The painting depicts a scene from Tahitian mythology, in which the goddess Hina is visited by the devil, who is represented as a horned figure with a large, forked tongue. The painting is rich in detail and vivid color, with the figures depicted in bright, bold colors that stand out against the darker background.
The style of the painting is characteristic of the Tahitian art of the time, which was heavily influenced by the traditional Polynesian art forms of carving, tattooing, and tapa cloth decoration. The figures in the painting are depicted in a stylized, almost abstract way, with exaggerated features and bold, sweeping lines. The use of bright colors and bold brushstrokes gives the painting a dynamic, almost chaotic energy that reflects the intense emotions of the scene.
Overall, Words of the Devil is a powerful and striking work of art that captures the mythology and cultural traditions of French Polynesia in the late 19th century.
During a sale, a store offered a 25% discount on a bed that originally sold for $800. After the sale, the discounted price of the bed was marked up by 25%. What was the price of the bed after the markup? Round to the nearest cent.
The price of the bed after mark up is $475.00
What is discount?Discount results in the reduction of the selling price of the product, which makes it more attractive for the customer.
The first discount given is 25% , therefore the price of the bed before mark up is
25/100 × 800
= 25×8
= 200
the price before mark up = 800-200 = $600
Another 25% is given after the first sale, there the price of the bed after mark up is
25/100 × 600
=$ 125
price after markup = 600-125
= $475.00
therefore the price of the bed after markup is $475.00
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Can someone please help me do this ?
Using multiplication operation, the amount of pension that Edith will receive after 4 years of service and using the vesting percentage and the pension multiplier is $49,725.
How the pension amount is computed:The pension amount is the product of the multiplication of the average salary, the vesting percentage and the pension multiplier factor.
Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.
Edith's average salary = $65,000
The number of years of service = 4 years
Pension Multiplier = 2%
Pension multiplier factor = 1.02 (100% + 2%)
Vesting percentage = 75%
Pension to be received = $49,725 ($65,000 x 75% x 1.02)
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Which expression is not equivalent to 2/3×4
The only expression that is not equivalent to the given fraction expression is: D (2 x 1/3) + (4 x 1/3)
How to multiply fractions?The correct procedure that we will use to multiply fractions is:
- find a common denominator
- multiply the numerators
- multiply the denominators
- Simplify if necessary.
- Add the numerators and add the denominators
Looking at the options and comparing with the given fraction multiplication problem 2/3 * 4, we see that only option D is not equivalent to it because:
(2 x 1/3) + (4 x 1/3) = 6/3 = 2
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Complete question is:
Which expression is NOT equivalent to 2/3 x 4
A (2x4) /3
B 1/3 x (2x4)
C (4 x 1/3) x 2
D (2 x 1/3) + (4 x 1/3)
a. Use the graph to approximate the value of the car after 4 years.
b. Use the graph to approximate the value of the car after 5 years.
c. Use the graph to approximate when the car will be worth half its original value. (Determine the number of years.)
The car will be worth half its original value after 4 years
How to solveA graph for straight-line depreciation for a car is given.
a
The number of years the car totally depreciates is 8 years as seen in the graph which is x -intercept.
Step 3/7
The model makes straight-line depreciation. In a straight line depreciation equation, the intercepts are
(0, maximum car value) and (maximum lifespan,0)
Let y represent the value of the car at any time during its lifetime. The minimum y -value is zero dollars and the maximum y -value is the purchase price of $25,600
The intercepts are (0, 25, 600) and (8,0)
Determine the slope of the equation.
Two points determine a line, so only two points are needed to determine the slope of a line.
Let the coordinates of the -intercept be the first point. That is, (xi,yi) = (0, 25, 600)
Let the coordinates of the -intercept be the second point. That is (x2, y2)= (8,0)
Use the slope ratio as shown below;
The slope of the depreciation equation is.
-3200
The general form for the equation of a straight line is:
y = mx + b
Where m represents the slope of the line and b represents the y-intercept.
The slope is -3,200 and the -intercept is 25,600 as obtained.
Therefore, the straight line depreciation equation is:
y = -3,200x + 25,600
Therefore, the value of the car after 4 years is $12,800
b.
Use the depreciation equation and substitute x=5 years to find the car worth after 5 years.
Therefore, the value of the car after 5 years is $9,600
c.
The half value of the car is half of $25,600 which is $12,800
The car will be worth half its original value after 4 years
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Can anybody help me ASAP
The volume of the rectangular prism is given as follows:
V = 0.9375 cubic inches.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:
Volume = length x width x height.
The dimensions for this problem are given as follows:
Height of 4 x 1/4 = 1 inch.Length of 5 x 1/4 = 1.25 inches.Width of 3 x 1/4 = 0.75 inches.Hence the volume is given as follows:
V = 1 x 1.25 x 0.75
V = 0.9375 cubic inches.
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Jeannie designs jewelry. The figure shows a
pendant on a necklace Jeannie is making. It is
composed of three individual beads.
The larger triangular bead cost $1.52. The
rectangular bead costs $0.42, and the smaller
triangular bead costs $0.92.
What is the cost per square millimeter of the
pendant? Round your answer to the nearest
hundredth.
Answer: ≅ $0.02
Step-by-step explanation:
First, lets find the area of the large triangle
0.5 x 14 x 11 = 77 mm^2
Next lets find the area of the middle rectangle:
4 x 14 = 56 mm^2
Last lets find the area of the small triange:
0.5 x 14 x 3 = 21 mm^2
So the total area is: 77 + 56 + 21 = 154 mm^2
the total cost is given to be: 1.52 + 0.42 + 0.92 = $2.86
dividing the cost by the area to find the cost/mm:
2.86/154 ≅ $0.02
A wrestler weighs in on the first day at 162 pounds. To make weight for the first match, the wrestler must lose 1.1 pounds per week. This can be modeled by the equation y=−1.1x+162. Use this model to predict the wrestler’s weight at the first match that is 9 weeks away.
The wrestler's weight at the first match will be 152.1 pounds. The solution has been obtained by using the substitution method.
What is the substitution method?
The substitution method is a strategy used in algebra to solve simultaneous linear equations. In this process, as the name suggests, the value of one variable from one equation is swapped in the second equation.
We are given that the given situation can be modeled by the equation
y = −1.1x + 162.
Now, we need to find weight at the first match which is 9 weeks away.
So, we get that x = 9.
By substituting this value in the equation, we get
⇒ y = -1.1 (9) + 162
⇒ y = -9.9 + 162
⇒ y = 152.1
Hence, the wrestler's weight at the first match will be 152.1 pounds.
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If someone wants to call Havana, Cuba from the United States, begins with US three digit exit code 011 followed by the two digit country code for Cuba which is 53, followed by the country code of Havana which is 7 and finally by seven-digit local telephone numbers. But this seven-digit local telephone number cannot begin with 0. How many different telephone numbers are possible?
There are possible 4,782,969 different telephone numbers.
We will multiply the number of options for each digit to calculate the total number of possible telephone numbers,.
How to calculate the total number of possible telephone numbers?Using the multiplication principle to estimate the number of possible telephone numbers for each digit:
n1 x n2 x n3 x ... x nk
Here:
the first three digits are fixed: 011
The 4th digit (the first digit of the local phone number) can be any digit from 1 - 9 (i.e. 9 options).
The remaining 6 digits (the second to seventh digit of the local phone number) can be any digit from 0 to 9, except 0 (9 options for each digit).
Therefore, the total number of possible telephone numbers:
9 x 9 x 9 x 9 x 9 x 9 x 9 = 4,782,969,
Therefore, 4,782,969 different telephone numbers are possible.
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is 2^7 equal to 2x 7
Answer: No, 2^7 is not equal to 2x7.
2^7 means 2 raised to the power of 7, which is 2 multiplied by itself 7 times:
2^7 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128
On the other hand, 2x7 means 2 multiplied by 7:
2x7 = 2 x 7 = 14
So 2^7 is not equal to 2x7.
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
See, 2 ^ 7 is 2 TO THE POWER OF 7, which is repeated multiplication.
2 x 7 is 2 MULTIPLIED BY 7
2 ^ 7 written out completely is:
2 * 2 * 2 * 2 * 2 * 2 * 2 = 128
See the repeated multiplication above?
2 x 7 is just 14.
See the difference!
14 is NOT equal to 128
May I please have brainliest?
Given the two concentric circles with center X below, find the area of the shaded region. Round your answer to the nearest tenth if necessary.
The area of the shaded region is given as follows:
298.3 units².
How to calculate the area of a circle?The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:
A = πr²
The larger circle has a radius of 7 + 5 = 12 units, hence it's area is given as follows:
A = 3.14 x 12²
A = 452.16 units².
The smaller circle has a radius of 7 units, hence it's area is given as follows:
A = 3.14 x 7²
A = 153.86 units².
Hence the area of the shaded region is given as follows:
452.16 - 153.86 = 298.3 units².
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what is the surface area of 11cn and 14cm
The surface area of the shape will be 46 yards².
What is the surface area?Surface area refers to the total area that the surface of a three-dimensional object covers. It is measured in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), etc.
The formula for the surface area of the 2 bases is just b*h
12*8=96 yd²
Finding the lateral area:
(10*10)+(10*10)+(12*10)=
100+100+120=
320 yd²
Add the lateral surface area and the surface area of the 2 bases for the total surface area:
320+96=416 yd²
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Wouldn't be 29 and 1/1.5? becaus ethen it would be 60 + 27 + 2
If John pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.
How to solve
In order to arrive at a solution, it is necessary to commence by reducing the fraction 1/1.5 into a more basic form.
Thus, we do this below:
1 ÷ 1.5 = 1 ÷ (3/2) = 1 × (2/3) = 2/3
So, John has 29 full buckets and another bucket that is 2/3 full.
If he pours the partially filled bucket into an empty one, he would still have 29 full buckets and a bucket with 2/3 of its capacity filled.
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John has 29 full buckets of water and another bucket that is 1/1.5 full. How many full buckets of water would he have if he pours the partially filled bucket into an empty one?
11. The angle of elevation to the top of a building is found to be 18 degrees from the ground at a distance of 510 feet from the base of the building. Using this information, find the height of the building to the nearest whole number.
Answer:
Set your calculator to degree mode.
Please sketch the figure to confirm my answer.
tan(18°) = h/510
h = 510tan(18°) = 165.7 feet
Answer:
Construction Model Stats
User
Consider the time taken to completion time (in months) for the construction of a particular model of homes: 4.1 3.2 2.8 2.6 3.7 3.1 9.4 2.5 3.5 3.8 Find the mean, median mode, first quartile and third quartile. Find the outlier?
ChatGPT
To find the mean, we add up all the values and divide by the number of values:
Mean = (4.1 + 3.2 + 2.8 + 2.6 + 3.7 + 3.1 + 9.4 + 2.5 + 3.5 + 3.8) / 10
Mean = 36.7 / 10
Mean = 3.67
To find the median, we need to put the values in order:
2.5, 2.6, 2.8, 3.1, 3.2, 3.5, 3.7, 3.8, 4.1, 9.4
The middle number is the median, which is 3.35 in this case.
To find the mode, we look for the value that appears most often. In this case, there is no mode as no value appears more than once.
To find the first quartile (Q1), we need to find the value that separates the bottom 25% of the data from the top 75%. We can do this by finding the median of the lower half of the data:
2.5, 2.6, 2.8, 3.1, 3.2
The median of this lower half is 2.8, so Q1 = 2.8.
To find the third quartile (Q3), we need to find the value that separates the bottom 75% of the data from the top 25%. We can do this by finding the median of the upper half of the data:
3.7, 3.8, 4.1, 9.4
The median of this upper half is 3.95, so Q3 = 3.95.
To find the outlier, we can use the rule that any value more than 1.5 times the interquartile range (IQR) away from the nearest quartile is considered an outlier. The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1
IQR = 3.95 - 2.8
IQR = 1.15
1.5 times the IQR is 1.5 * 1.15 = 1.725.
The only value that is more than 1.725 away from either Q1 or Q3 is 9.4. Therefore, 9.4 is the outlier in this data set.
We can use trigonometry to solve this problem. Let h be the height of the building, and let d be the distance from the base of the building to the point where the angle of elevation is measured. Then we have:
tan(18 degrees) = h / d
Solving for h, we get:
h = d * tan(18 degrees)
Substituting d = 510 feet and using a calculator to evaluate the tangent of 18 degrees, we get:
h = 510 feet * tan(18 degrees)
h ≈ 157.3 feet
Rounding this to the nearest whole number, we get that the height of the building is approximately 157 feet.
For the right triangle below, find the measure of the angle.
Figure is not to scale.
For the given right-angled triangle the measure of the angle is 11.30°.
Given adjacent base of the triangle = 10
given opposite side of the triangle = 2
To find out the angle we can use a little bit of trigonometry. By trigonometry, we know that tan ∠ = opposite side / adjacent side.
So, we can use the above tan ∠ relation to find the angle.
Tan ∠ = opposite side / adjacent side
Tan ∠ = 2/10
Tan ∠ = 1/5
∠ = Tan⁻¹(1/5)
∠ = 11.30°.
From the above explanation, we can conclude that the measure of the angle for the given right triangle is 11.30°.
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To the nearest ten dollars, what can Carlos expect the value of the computer to be 3 years after purchase
Carlos can expect the value of the computer to be $580 three years after purchase.
To model the value of the computer, we can use the formula:
y = abˣ
We know that the initial value of the computer is $1,350, so a = 1350.
We also know that one year after purchase, the value of the computer is $810, so we can use this to find the value of b:
810 = 1350b
b= 0.6
b = 0.6
So our exponential equation is:
y = 1350(0.6)ˣ
To find the value of the computer 3 years after purchase, we can substitute x = 3:
y = 1350(0.6)³
y = 583
Hence, Carlos can expect the value of the computer to be $580 three years after purchase.
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What type of conic section is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone?
The conic section that is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone is a circle
Determining type of conic section formedThe summary statement from the question is given as
A plane parallel to the base of a circular cone that intersects the cone.
By definition, a circle is the cross-section that is parallel to the base of a cone
This means that when a cone is cut through the base, the resulting shape is a circle
So, the conic section that is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone is a circle
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Find the length of the shortest path from vertex A to vertex L.
The shortest path from vertex A to vertex L in the given diagram is ABDGJLKFI, with a total length of 89.
We can find the length of the shortest path from vertex A to vertex L by calculating the sum of the shortest paths from A to C to F to I to L.
Using Dijkstra's algorithm, we can find the shortest path from A to C, then from C to F, then from F to I, and finally from I to L.
The shortest path from A to C is AB + BC = 3 + 16 = 19. The shortest path from C to F is CF = 25. The shortest path from F to I is FI = 21. The shortest path from I to L is IL = 24.
Therefore, the length of the shortest path from A to L is 19 + 25 + 21 + 24 = 89.
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Alejandro is learning how to play guitar. One day out of the week, he attends a 45-minute lesson. The remaining days of the week, he practices guitar for 25 minutes per day. What total number of minutes does Alejandro spend at his lesson and practicing in 3 weeks?
Answer:
3 x 195 = 585 minutes
Step-by-step explanation:
In one week, Alejandro attends a 45-minute lesson and practices for (6 x 25) = 150 minutes (assuming a 7-day week). So, the total number of minutes that Alejandro spends on his guitar in one week is:
45 + 150 = 195 minutes
In 3 weeks, the total number of minutes that Alejandro spends on his guitar is:
3 x 195 = 585 minutes
Therefore, Alejandro spends 585 minutes on his guitar in 3 weeks, including attending a 45-minute lesson once a week and practicing for 25 minutes on the remaining days of the week.
Answer: The mean absolute deviation is approximately is 11.43.
if 2 (m-2n)÷6m-2n=4÷15, find the ratio of m:n
Answer:
[tex]\frac{10n}{1-30n}:\frac{m}{10(1+3m)}[/tex]
Step-by-step explanation:
Solve for 'm' and 'n':
'm' = [tex]\frac{10n}{1-30n}[/tex]
'n' = [tex]\frac{m}{10(1+3m)}[/tex]
Ratio: [tex]\frac{10n}{1-30n}:\frac{m}{10(1+3m)}[/tex]
Please help me I really don’t get this. ILL GOVE BRAINLIEST TO ANYONE PLEASD I GIVE 18 points
Answer: C, yes
Step-by-step explanation:
Again you have do the same thing to both sides
They added 1 to both sides
Answer is C , yes they are same
what is the
quotient of 62.72+4.9
Answer:
12.8
Step-by-step explanation:
Quotient means the answer of two things divided.
62.72/4.9=12.8