Final answer:
An equation that sets two fractions equal to each other is known as a proportion, where equivalent ratios or fractions indicate the same value. This maintains the equality governed by the rules of algebra, important when performing operations on both sides of an equation.
Explanation:
An equation that sets two fractions equal to each other is called a proportion. This type of equation indicates that two ratios or fractions are equivalent. For example, if we have ½ on one side of the equation and 2/4 on the other, we have a proportion because both fractions represent the same amount.
When we have fractions with the same value in the numerator and the denominator, such as ¹¹/₁₀⁰ for micrometers to meters, we can simplify this to 1 because the quantities cancel each other out. This is true by the rules of algebra, specifically the property that if we perform the same operation on both sides of an equality, the equation remains balanced. This concept is crucial when working with proportions and equations involving fractions.
It's also important to remember that when adding fractions, they must have a common denominator. Ratios and percentages are other forms of expressing relative sizes or amounts which can also be related back to fraction and proportion concepts.
20% of what number is 47?
Need help
20% of 235 is the number 47.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Percentage is usually denoted by the symbol '%'.
Let x be the unknown number.
Given that 20% of the number x is 47.
Mathematically, this can be written as,
20% × x = 47
(20/100) x = 47
0.2x = 47
x = 47 / 0.2
x = 235
Hence the unknown number is 235.
Learn more about Percentage here :
https://brainly.com/question/1166793
#SPJ2
make x the subject 6x+a=5(x+t)
To make x the subject of the equation, you can rearrange the equation x = 5t - a.
Explanation:To make x the subject of the equation, we need to isolate the variable on one side of the equation. Here's how:
Distribute 5 to both x and t: 6x + a = 5x + 5tSubtract 5x from both sides: 6x - 5x + a = 5tCombine like terms: x + a = 5tSubtract a from both sides: x + a - a = 5t - aCancel out a: x = 5t - aTherefore, to make x the subject, the equation is x = 5t - a.
Learn more about Rearranging equations here:https://brainly.com/question/10945620
#SPJ2
Ms. Wilson draws a model of the factorization of a polynomial with integer factors. Her model is partially complete.
Answer:
b
Step-by-step explanation:
A baseball bat manufacturing company needs to meet a daily target of producing 600 bats to 3,000 bats.
A single worker can complete 15 bats per day. The time taken to meet the daily target is inversely proportional to the number of workers. If t is the total time and n is the number of workers, then the function is represented by t(n)=k/n . Determine an appropriate domain to represent this function.
A. n<=15
B. n>=15
C. 600<=n<=3000
D. 40<=n<=200
Which of the following is not the correct name for the line segment?
MH
MH with aline above it
line segmant MH
or HM with a line above it
Answer:
MH is not the correct name for the line segment.
Step-by-step explanation:
Consider the provided information.
A line segment is a line having a starting and end point or we can say portion of a line between two points.
We can represents a line segment by single over bar over the letters.
For example: Consider the figure 1.
The line segment shown in figure 1 is represented by either:
[tex]\overline {GH}\ or\ \overline {HG}[/tex]
The above notation can be read as line segment GH or line segment HG.
Now consider the provided statement. We need to identify the correct name for the line segment.
Option A) MH is wrong notation for the line segment.
Option B) [tex]\overline {MH}[/tex] is the correct notation for the line segment.
Option C) Line segment MH is correct name for the line segment.
Option D) [tex]\overline {HM}[/tex] is the correct notation for the line segment.
Hence, MH is not the correct name for the line segment.
Find the minimum, maximum, range, mean, and median for the data set.
2.4, 2.6, 7.2, 5.5, 4.1, 5.5, 6.1, 6.1
A.
minimum: 2.4
maximum: 7.2
range: 4.8
mean: 5.5
median: 4.9
B.
minimum: 2.4
maximum: 7.2
range: 9.6
mean: 4.9
median: 5.5
C.
minimum: 7.2
maximum: 2.4
range: 4.8
mean: 4.9
median: 5.5
D.
minimum: 2.4
maximum: 7.2
range: 4.8
mean: 4.9
median: 5.5
what two numbers add to 7 and multiply to 10
3/8(m−2/9)=4 3/4
What does M equal
Find the discriminant of the following equation.
4x2 + 16x + 16 = 0 ...?
Answer:
The discriminant is 0.
Step-by-step explanation:
Since, the discriminant of a quadratic equation [tex]ax^2+bx+c=0[/tex] is,
[tex]D=b^2-4ac[/tex]
Here, the given equation is,
[tex]4x^2+16x+16=0[/tex]
By comparing,
a = 4, b = 16 and c = 16,
Hence, the discriminant of the given equation is,
[tex]16^2-4\times 4\times 16[/tex]
[tex]=256 - 256[/tex]
[tex]=0[/tex]
You realize that more than 8000 gallons per year was a lot of water to waste with a leaky faucet. You fixed your faucet so that it now takes 11 minutes longer to fill a cup of water than it did when it leaked 1 fluid ounce 30 seconds. How many gallons will the faucet waste in 1 year?
When solving negative one over eight (x + 35) = −7, what is the correct sequence of operations?
Multiply each side by negative one over eight , add 35 to each side
Multiply each side by negative one over eight , subtract 35 from each side
Multiply each side by −8, subtract 35 from each side
Multiply each side by −8, add 35 to each side
Answer:
3
Step-by-step explanation:
i have done this test before
write 3 different improper fractions that equal 4 2/3
What is 1 1/2 plus 2/3?
What is the sum of the first 18 terms of the arithmetic series 11+15+19+23+...?
4. Which of the following sets of numbers is a Pythagorean triple?
A. 4, 5, 6
B. 8, 15, 17
C. 5, 12, 14
D. 8, 24, 25
Suppose a triangle has side lengths 6, 7, and 10. Which of the following best describes this triangle?
A. obtuse
B. acute
C. right
D. Cannot be determined.
The set 8, 15, 17 is a Pythagorean triple because 8^2 + 15^2 = 17^2. A triangle with sides of 6, 7, and 10 is an obtuse triangle, because 10^2 > 6^2 + 7^2.
Explanation:The set of numbers, 8, 15, 17, represents a Pythagorean triple. A Pythagorean triple consists of three positive integers a, b, and c, such that a^2 + b^2 = c^2. In this case, 8^2 + 15^2 = 64 + 225 = 289, and 17^2 = 289, so the equation is satisfied.
Furthermore, a triangle with sides 6, 7, and 10 would be described as obtuse. In any triangle, if the square of the length of the longest side is greater than the sum of the squares of the other two sides, then the triangle is obtuse. Thus, if 10^2 > 6^2 + 7^2, or 100 > 36 + 49, then the triangle is obtuse. Since this statement holds true, the triangle is indeed obtuse.
Learn more about Pythagorean triple and types of triangles here:https://brainly.com/question/29081563
#SPJ3
The correct options are: B. 8, 15, 17 and A. obtuse
We can use the Pythagorean theorem to determine which set of numbers is a Pythagorean triple. The theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides (a and b): a2 + b2 = c2.
Option A: 4, 5, 6: [tex]4^2 + 5^2 = 16 + 25 = 41[/tex], and [tex]6^2=36[/tex], which is not equal to 41.Option B: 8, 15, 17: [tex]8^2 + 15^2 = 64 + 225 = 289[/tex], and [tex]17^2=289[/tex], equal.Option C: 5, 12, 14: [tex]5^2 + 12^2 = 25 + 144 = 169[/tex], and [tex]14^2=196[/tex], which is not equal to 169.Option D: 8, 24, 25: [tex]8^2 + 24^2 = 64 + 576 = 640[/tex], and [tex]25^2=625[/tex], which is not equal to 640.The correct Pythagorean triple is 8, 15, 17.
To determine the type of triangle with side lengths 6, 7, and 10, we use the idea that for a triangle with sides a, b, and c (where c is the longest side):
If [tex]c^2 = a^2 + b^2[/tex], the triangle is right.If [tex]c^2 < a^2+b^2[/tex], the triangle is acute.If [tex]c^2 > a^2+b^2[/tex], the triangle is obtuse.For the triangle with sides 6, 7, and 10:
[tex]6^2+7^2=36+49=85[/tex] and [tex]10^2=100[/tex].
Since 100 > 85, the triangle is obtuse.
Bob has some 10 lb weights and some 3 lb weights. Together, all his weights add up to 50 lbs. If x represents the number of 3 lb weights and y represents the number of 10 lb weights, which equation can be used to find the number of each type of weight Bob has?
A)3x – 10y = 50
B)3x = 50 – 10y
C)50 + 10y = 3y
D)50 + 3y = 10y
Data set 1: 0, 25, 50, 75, 100
Data set 2: 30, 40, 50, 60, 70
Data set 3: 40, 45, 50, 55, 60
Note that all three data sets have a median of 50. Notice how spread out the points are in each data set and compare this to the standard deviations for the data sets. Describe the relationship you see between the amount of spread and the size of the standard deviation and explain why this connection exists.
am going to assume you know how to calculate standard deviation, as it is long and tedious to type up. If you really don't understand how to calculate them, I will explain it. The standard deviation is larger in data set 1 than 2, because the spread is larger. The larger the spread, the larger the deviation of the numbers in the set are from the mean (average) number. The standard deviation in 1 is greatest. 2 is in the middle, and 3 is the lowest standard deviation. Hope this helps, good luck.
Answer:
Larger the standard deviation larger the spread present in data.
Step-by-step explanation:
Standard Deviation is the square root of sum of square of the distance of observation from the mean.
[tex]Standard deviation(\sigma) = \sqrt{\frac{1}{n}\sum_{i=1}^{n}{(x_{i}-\bar{x})^{2}}}[/tex]
where, [tex]\bar{x}[/tex] is mean of the distribution.
It is used to measure dispersion (spread) of the data. Larger the standard deviation larger the dispersion (spread) present in data.
The Standard deviation of 1st data set is 39.53
The Standard deviation of 2nd data set is 15.81
The Standard deviation of 3rd data set is 7.91
Hence,
(Spread of 1st data set) > (Spread of 2nd data set) > (Spread of 3rd data set)
According to Professor Robinson, which of the following aspects of A Streetcar Named Desire can be said to reflect elements of Tennessee Williams's life?
a. hunger for love
b. feelings of unworthiness
c. feelings of guilt
d. using alcohol for its mood-altering affects
e. all of the above
The time of year at the beginning (May) and ending (October) of A Streetcar Named Desire symbolize:
a. rebirth and the coming death
b. life c. death
d. joy and laughter
e. good luck and bad luck
A box has dimensions of 17 inches long, 1.3 feet wide, and 8 inches high. What is the volume of the box? The formula for the volume is V = l w h. (1 point)
2121.6 cubic inches (in3)
176.8 cubic inches (in3)
14.7 cubic inches (in3)
1.2 cubic inches (in3)
To find the volume of the box, convert all units to inches, then apply the formula for the volume of a rectangular prism, resulting in 2,121.6 cubic inches.
Explanation:To calculate the volume of the box with dimensions given in inches and feet, we first need to convert all units to the same system. Since the width is given in feet (1.3 feet), we convert it to inches knowing that 1 foot equals 12 inches. Thus, 1.3 feet is equal to 1.3 × 12 = 15.6 inches.
To find the volume of the box, you need to multiply the length, width, and height together:
Convert the dimensions to a consistent unit, such as inches.
Calculate: 17 inches x 1.3 feet x 8 inches = 176.8 cubic inches.
Therefore, the volume of the box is 176.8 cubic inches (in3).
Now, with all dimensions in inches: the length is 17 inches, the width is 15.6 inches, and the height is 8 inches. Applying the formula for the volume of a rectangular prism, V = l × w × h, we get:
V = 17 inches × 15.6 inches × 8 inches = 2,121.6 cubic inches.
Therefore, the correct option is 2121.6 cubic inches (in3).
A set of cards contains cards numbered 1 – 8. Mrs. Jacob’s class is conducting an experiment in which a card is drawn from the pile, the number is recorded, and then the card is returned to the set. The class will conduct 1,000 trials. Based on the theoretical probability, which is the best prediction for the number of times a 4 will be drawn from the pile?
Answer:
125
Step-by-step explanation:
Answer:
The best prediction for the number of times a 4 will be drawn from the pile is:
125
Step-by-step explanation:
It is given that:
A set of cards contains cards numbered 1 – 8.
So, the theoretical probability that 4 comes up is:
Ratio of Number of favorable outcome( outcome of 4) to the total umber outcome(i.e. 8 )
Hence, Theoretical Probability that 4 is drawn=1/8
Now, out of 1000 trials the best prediction of number of times 4 is drawn is:
(The probability of drawing 4)×(Number of experiments or trials)
=(1/8)×1000
=125
Using the completing-the-square method, find the vertex of the function f(x) = 5x2 + 10x + 8 and indicate whether it is a minimum or a maximum and at what point.
Maximum at (1, 8)
Minimum at (1, 8)
Maximum at (−1, 3)
Minimum at (−1, 3)
The vertex of the function f(x) = 5x²+ 10x + 8 and indicate Minimum at (-1, 3)
To find the vertex of the function f(x) = 5x² + 10x + 8 using the completing-the-square method, follow these steps:
Step 1: Write the function in the form (ax² + bx + c).
f(x) = 5x² + 10x + 8
Step 2: Identify the coefficient of x² and divide it by 2. This gives us (b/2a).
In this case, a = 5, b = 10, so (b/2a) = 10 / (2 * 5) = 1.
Step 3: Square the result from Step 2 [(b/2a)²].
(1)² = 1.
Step 4: Add and subtract the result from Step 3 to the function inside the parentheses.
f(x) = 5x² + 10x + 1 - 1 + 8
Step 5: Group the terms.
f(x) = (5x² + 10x + 1 - 1) + 8
Step 6: Factor the quadratic expression inside the parentheses and simplify.
f(x) = 5(x² + 2x + 1) + -5 + 8
f(x) = 5(x + 1)² + 3
Now the function is in the form f(x) = a(x - h)² + k, where (h, k) represents the vertex of the parabola.
Comparing the function with this standard form, we can see that the vertex is at (-1, 3). The value of 'h' represents the x-coordinate of the vertex, and 'k' represents the y-coordinate of the vertex.
Therefore, the correct answer is:
Minimum at (−1, 3)
To know more about vertex click here:
https://brainly.com/question/16027045
#SPJ2
How many solutions are in 6x-9y=-9 and 2x-3y=-6?
Simplify. (–8x) ÷ (–4)
Senator Snortsalot is campaigning for reelection. During his visit to Patheticville, he plans to have 17,500 brochures distributed. His schedule is very tight, and he will only be in Patheticville for 4 hours. How many volunteers will he need if each volunteer can distribute 225 brochures in one hour?
A new savings account is opened with $300 and gains 3.1% yearly for 5 years
At the end of 5 years, with the 3.1% interest rate, your savings account will grow to $349.47.
Use the concept of percentage defined as:
A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.
Given that,
A new savings account is opened with $300.
The account earns a 3.1% interest rate per year.
The interest is calculated yearly.
The duration of the investment is 5 years.
After the first year,
Savings will increase by 3.1% of $300, which is $9.30.
So, your balance at the end of the first year will be $309.30.
For the following years,
you will continue to earn 3.1% interest on the new balance each year. Here's a breakdown of your balance at the end of each year:
Year 1: $309.30
Year 2: $309.30 + 3.1% of 309.30 = $318.88
Similarly
Year 3: $328.77
Year 4: $338.96
Year 5: $349.47
Hence,
At the end of 5 years, with the 3.1% interest rate, your savings account will grow to $349.47.
Learn more about the percent visit:
https://brainly.com/question/24877689
#SPJ5
Which two super powers engaged in the cold war?
The Cold War was a prolonged period of geopolitical tension between the United States and the Soviet Union, involving an arms race, proxy wars, and a race for technological superiority, but avoiding direct military conflict due to the threat of nuclear annihilation.
Explanation:The two superpowers that engaged in the Cold War were the United States and the Soviet Union. The Cold War was a period of geopolitical tension between these two countries that began shortly after the end of World War II and lasted until the collapse of the USSR in 1991. This era was characterized by political and ideological conflicts that were expressed through proxy wars, the arms race, propaganda, and competition in technological advancements such as the space race.
While it was called a 'war', the Cold War did not result in direct military conflict between the two nations. Instead, the struggle for global supremacy was played out through indirect means, including support for opposing sides in regional conflicts such as the Korean War, the Vietnam War, and the Soviet-Afghan War. The fear of Mutually Assured Destruction (M.A.D.) due to both nations possessing extensive nuclear arsenals was a deterrent against a 'hot' war.
The Cold War impacted almost every aspect of international relations and domestic policies within the superpower nations and their allies, with each side attempting to limit the influence and spread of the other's ideology. The United States followed a policy of containment to prevent the spread of communism, and the Soviet Union tried to expand its socialist model and create a buffer zone against the West.
Factor completely 5x2 + 30x + 50
Answer: Complete factorization would be
[tex]5(x^2+6x+10)[/tex]
Step-by-step explanation:
Since we have given that
[tex]5x^2+30x+50[/tex]
We need to find the factors:
Since the terms of above expression is a factor of 5.
So, it becomes,
[tex]5x^2+30x+50\\\\=5(x^2+6x+10)[/tex]
Hence, complete factorization would be
[tex]5(x^2+6x+10)[/tex]
You and three friends earn money by painting houses. You agree to split the profits equally. You buy brushes, tape, and paint for $750. If your total income is $2,600, how much is your share of the profit?
y = 2 x^2 + 4 linear or non i think its linear
The top of a square box has an area of 121 cm2. What is the length of one side of the box? A) 9.0 cm B) 11.0 cm C) 15.125 cm D) 30.25 cm