Final answer:
To determine if a proportion is true, we must verify that the cross-products of the ratios are equal. Only two of the given proportions, 16/36 = 12/27 and 15/20 = 24/32, are true when applying this method.
Explanation:
To determine if a proportion is true, we check whether the cross-products are equal. In other words, for a proportion in the form a/b = c/d, if a * d equals b * c, the proportion is true.
Let's apply this to the provided proportions:
12/15 = 47/50 is not true because 12*50 does not equal 15*47.
16/36 = 12/27 is true because 16*27 equals 36*12.
15/20 = 24/32 is true because 15*32 equals 20*24.
4/16 = 2/14 is not true because 4*14 does not equal 16*2.
Proportions can be a useful tool in many areas of mathematics, such as solving for unknown variables and comparing relative frequencies. Remember, if you encounter large numbers or fractions, simplifying before checking the cross-product can often make the process easier.
The crime rate in New York City has been steadily dropping over the past decades. In 1970, the murder rate was 15.8 per 100,000 people. In 2012, it had dropped to 3.5 per 100,000 people. What was the rate of decline?
Out of 25 students in mrs. Green class 19 have a pet what percent of students in mrs. Green class don't have a pet
the sum of three consecutive even numbers is 42. The sum can be represented by the equation n+(n+2)+(n+4)=42. what does n represent
Is 0.5 equal to 9/18
Use distributive property and mental math to find the product
7x49
Lisa's coffee shop makes a blend that is a mixture of two types of coffee type A coffee cost Lisa $4.50 per pound and type B coffee cost $5.50 per pound. This month's blend uses three times as many pounds of type B coffee as type A, for a total cost of $634.50. How many pounds of type a coffee were used?
The number of pounds of coffee used is 30 pounds.
Given data:
Let x be the number of pounds of type A coffee used.
Since the blend uses three times as many pounds of type B coffee as type A, the number of pounds of type B coffee used is 3x.
The cost of type A coffee is $4.50 per pound, so the cost of x pounds of type A coffee is 4.50x dollars.
The cost of type B coffee is $5.50 per pound, so the cost of 3x pounds of type B coffee is 5.50 * 3x = 16.50x dollars.
The total cost of the blend is $634.50, so the equation is:
4.50x + 16.50x = 634.50
Combine like terms:
21x = 634.50
On solving for x:
x = 634.50 / 21
x = 30
Hence, 30 pounds of type A coffee were used in the blend.
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how do i find the range and domain? please leave detailed steps because i'm struggling with this :(
if half of a loaf of bread is cut into six equal slices, what fraction is each slice of the original loaf?
The sales tax for an item was $24.50 and it cost $350 before tax. Find the sales tax rate.
To determine the sales tax rate, divide the sales tax amount by the item's pre-tax cost and convert to a percentage, yielding a 7% sales tax rate for this scenario.
To find the sales tax rate, you need to divide the amount of sales tax by the cost before tax and then convert it to a percentage. For an item that cost $350 before tax and had a sales tax of $24.50:
Divide the sales tax ($24.50) by the cost before tax ($350): $24.50 \/ $350 = 0.07.
Convert the decimal to a percentage: 0.07 x 100 = 7%.
Therefore, the sales tax rate for the item is 7%.
The formula for the circumference of a circle is C=3.14 multiplied by the radius Determine the circumference when the radius r is 10 cm.
600 can be written as 2a x b x cd where a,b,c and d are all prime numbers find the values of a, b, c and d
600 can be written as [tex]\(2^3 \times 3^1 \times 5^2\)[/tex], where 2, 3, and 5 are prime numbers.
To express 600 as the product of prime numbers, we'll use prime factorization.
Prime factorization involves breaking down a number into its prime factors.
Here's how we can do it:
Step 1 :**Start with the smallest prime number, 2:**
[tex]\( 600 \div 2 = 300 \)[/tex]
[tex]\( 300 \div 2 = 150 \)[/tex]
[tex]\( 150 \div 2 = 75 \)[/tex]
Step 2 :**Next, continue with the next smallest prime number, 3:**
[tex]\( 75 \div 3 = 25 \)[/tex]
[tex]\( 25 \div 5 = 5 \)[/tex]
Step 3 :**Now, we can't divide further by smaller prime numbers, so we try dividing by the next smallest prime, 5:**
[tex]\( 5 \)[/tex] is already a prime number.
Step 4 :**There are no more prime factors to consider, so we stop.**
Now, let's write down the prime factors we obtained:
[tex]\[ 600 = 2 \times 2 \times 2 \times 3 \times 5 \times 5 \][/tex]
So, [tex]\( a = 2 \), \( b = 2 \), \( c = 3 \), and \( d = 5 \).[/tex]
Therefore, we can write:
[tex]\[ 600 = 2 \times 2 \times 2 \times 3 \times 5 \times 5 \][/tex]
Thus, [tex]\( 600 \)[/tex] can be written as [tex]\( 2^3 \times 3^1 \times 5^2 \)[/tex], where [tex]\( 2, 3, \) and \( 5 \)[/tex] are all prime numbers.
Train A and train B leave a central station at the same time. They travel the same speed, but in opposite directions, with train A heading towards station A, and train B heading towards station B. Train A reaches station A after 212 h. Train B reaches station B after 4 h. Station A and Station B are 585 mi apart. What is the rate of the trains?
I just had the same question on a test and the answer was 90 MPH. Hope this helps somebody!
A coffee pot holds 2 3/4 quarts of coffee. How much is this in cups?
Analyze each product in the table.
A. Why is the first product less than 3/4?
B. Why is the second product equal to 3/4?
C. Why is the third product greater than 3/4?
A because you are multiplying 3/4 by 1/2, you make the product smaller than 3/4
B beacue any number multiplied by one remains that number, since you are multiplying 3/4 by 1 it will remaim 3/4
C because the number multiplied by 3/4 is larger than 1 ( 3/2 = 1 1/2) the product will be larger than 3/4
How are the numbers 579 and 597 different
597 is a greater value than 579.
What is the number pattern?A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.
Rounding some number to a specific value is making its value simpler mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
We have to find How are the numbers 579 and 597 different to each other.
As we can see that the last two digit of the numbers 79 and 97 are flipped.
We know that 97 is greater than 79.
Therefore, 597 is a greater value than 579.
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Remove the parentheses from the following expression and combine like terms. 3(ax + b2 - c) + 2
Answer:
[tex]3ax+3b^2-3c+2[/tex]
Step-by-step explanation:
We have been given an expression [tex]3(ax+b^2-c)+2[/tex]. We are asked to remove the parenthesis and combine like terms for our given expression.
Using distributive property [tex]a(b+c)=ab+ac[/tex], we will get:
[tex]3*ax+3*b^2-3*c+2[/tex]
[tex]3ax+3b^2-3c+2[/tex]
We can see that our given expression don't have like terms, therefore, our expression would be [tex]3ax+3b^2-3c+2[/tex].
A population has a mean of 40 and a standard deviation of 15. a sample of size 100 is taken at random from this population. the standard deviation of the sampling distribution of sample mean equals:
Round to the nearest hundred thousand
89, 659
Answer:
The nearest hundred thousand of the provided number is 100,000.
Step-by-step explanation:
Consider the provided number 89, 659
According to place value.
Hundred Th. Ten Th. Thousands hundreds Tens Ones
100,000 10,000 1000 100 10 1
We need to round it to the nearest hundred thousand.
The provided number can be written as 089,659
The digit at the hundred thousand place is 0.
The rule of rounding a number is:
If 0, 1, 2, 3, or 4 follow the number, then no need to change the rounding digit.
If 5, 6, 7, 8, or 9 follow the number, then rounding digit rounds up by one number.
Here, the number at the ten thousands place is 8, so to round up the number increase the digit of hundred thousand place by 1.
The digit at the hundred thousand place is 0 so increase it by 1.
Thus, the number can be rounded to the nearest hundred thousand is shown as:
100,000
The nearest hundred thousand of the provided number is 100,000.
What number represents the most accurate estimation of 65+77
Add integer help just explain
Is the difference of two rational numbers always rational? Explain
IT TAKES YOU 15 MINUTES TO BIKE 5 MILES. HOW LONG DOES IT TAKE YOU TO BIKE 1 MILE
For what value(s) of x is g continuous? g(x) = 0 if x is rational 4x if x is irrational x is in the set of real numbers x = 4 x = −4 x = 0 none of these
Final answer:
The function g(x), being different for rational and irrational numbers, is nowhere continuous on the set of real numbers because it cannot satisfy the condition for continuity at any point.
Explanation:
We are asked to determine for what values of x the function g(x) is continuous. The function is defined to be 0 if x is rational, and 4x if x is irrational, over the set of real numbers. First, let's understand a key concept: for a function to be continuous at a point, the limit of the function as it approaches the point from either direction must be equal to the function's value at that point. In the case of g(x), the function takes the value of 0 for all rational numbers, but instantly changes to 4x for irrational numbers which are densely populated around every rational number.
Since the value of g(x) for rationals (0) is different from the nearby values for irrationals (which would be non-zero and depend on x), g(x) does not have a limit that equals its value at rational points and thus cannot be continuous at any rational number. Moreover, at irrational values of x, we cannot have continuity either, as any neighborhood around an irrational number contains rational numbers where g(x) would suddenly jump to 0, disrupting the limit process once again.
Therefore, the function g(x) is nowhere continuous on the set of real numbers since it cannot satisfy the condition for continuity at any point. Hence, the correct answer to the given question is 'none of these'.
How much greater is 98×50 than 97×50 with actual calculating it
Pre Calc question please help!
Liem is 6 feet 2 inches, Eli is 5 feet 9 inches, Faith is 6 feet, and Simon is 5 feet 4 inches. In yards, what is the total of their heights?
which values are equivalent to the fraction below 3^6/3^8
Ian is 10 years old, how many candles has Ian had on all of his birthday cakes. Remember he has had 10 cakes
The total area of this shape is 44 square inches. The area of the triangle is 20 square inches. Write and solve an equation to find the area of the rectangle
Answer:
The equation is: x + 20 = 44
The area of the rectangle is 24 inches.
Step-by-step explanation:
The total area of the shape is 44 square inches.
The area of the triangle is 20 square inches.
We need to find the area of the rectangle.
Total area = Area of the triangle + Area of the rectangle.
Let "x" be the area of the rectangle.
So the equation is
44 = 20 + x
This can be written as x + 20 = 44
Now let's find the value fo x.
Subtract 20 from both sides, we get
x + 20 - 20 = 44 - 20
x = 24 square inches.
Therefore, the area of the rectangle is 24 inches.
what is the y intercept of c=0.05m+4.95