Answer:
Sophia is not correct
Step-by-step explanation:
The given situation represent the problem of a ratio and it is predicted to do the simplify the ratio by determining the smallest possible values
Here it can be presented 60:36 as a fraction i.e. [tex]\frac{60}{36}[/tex]
Now the fraction should be fall by dividing both the numerator and denominator by a common factor i.e. 6
Now after dividing it, the fraction would be [tex]\frac{10}{6}[/tex]
Now it can be further reduced by a common factor i.e. 2
So now the fraction is [tex]\frac{5}{2}[/tex]
Thus, the ratio is 5:2
Hence, she is not correct
Please help with this easy fraction problem <3
18 + 7/9
14 + 7/8
First, rewrite each fraction in terms of a common denominator. 8 and 9 don't share a common multiple until 8 * 9 = 72, so we have
7/9 = (7/9) • (8/8) = (7 • 8)/(9 • 8) = 56/72
7/8 = (7/8) • (9/9) = (7 • 9)/(8 • 9) = 63/72
Next, write each whole number in terms of fractions with the same denominator. We have
18 • 72 = 1296 ==> 18 = 1296/72
14 • 72 = 1008 ==> 14 = 1008/72
Write each mixed number as an improper fraction:
18 + 7/9 = 1296/72 + 56/72 = (1296 + 56)/72 = 1352/72
14 + 7/8 = 1008/72 + 63/72 = (1008 + 63)/72 = 1071/72
If the backpack and book together weigh 18 + 7/9 pounds, and the backpack without the book weighs 14 + 7/8 pounds, then the book alone weighs the difference, call it b :
b = (18 + 7/9) - (14 + 7/8)
b = 1352/72 - 1071/72
b = (1352 - 1071)/72
b = 281/72
Convert this to a mixed number. 72 • 4 = 288, so 72 • 4 - 7 = 281:
b = (72 • 4 - 7)/72
b = (72 • 4)/72 - 7/72
b = 4 - 7/72
b = (3 + 1) - 7/72
b = 3 + (1 - 7/72)
b = 3 + 65/72
A pumpkin grows with a constant of proportionally of 4 cm in diameter per week. If Susan begins growing her pumpkin 10 weeks before Halloween will her pumpkin be larger that 50 cm in diameter?
How can you use the order of operation to explain why you cannot combine the variable terms before using the distributive property when solving the equation 7(x+5)-x=42
Answer:
Step-by-step explanation:
The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.
This standard is critical to simplifying and solving different algebra problems. Without it, two different people may interpret an equation or expression in different ways and come up with different answers. The Order of Operations is shown below.
Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.
Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.
Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.
Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.
Before we begin simplifying problems using the Order of Operations, let's examine how failure to use the Order of Operations can result in a wrong answer to a problem.
Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways
We cannot combine the variable terms before using the distributive property when solving the equation as it will results in wrong answer.
What is distributive property of multiplication over addition ?
If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.
Here the expression given is :
7(x+5)-x=42
The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.
Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.
Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.
Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.
Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.
Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways.
Read more about property of multiplication here :
https://brainly.com/question/14391436
#SPJ2
Which is true 0.45>0.5
0.45<0.5
4.05=0.45
4.05 <0.45
Answer:
4.05 is greater than 0.45
question 10 I mark as brainliest
Answer:
134 is the answer
Answer: 134
Step-by-step explanation:
54+ (48+72) x 2/3
54+120x2/3=134
Is this a function or not a function? (Picture)
Answer:
Not a Function
Step-by-step explanation:
Use rounding to estimate the product of 5,555 and 4,444 round both numbers to the nearest thousand to find answer
Step-by-step explanation:
Given that the first number is
5,555 and
the second number is 4,444
the product of 5,555 and4,444= 24686420
to the nearest thousand 5,555= 6000
to the nearest thousand 4,444= 5000
Therefore the product of 6000 and 5000 is
=6000x5000
=30000000
Which of the following is a true statement about the triangles shown on the graph?
The slope of the smaller triangle is smaller than the slope of the larger triangle
The slope of the larger triangle is larger than the slope of the smaller triangle.
The triangles are congruent triangles.
The slopes of the two triangles are the same.
The correct statement about the triangles shown in the graph is given as follows:
The slopes of the two triangles are the same.
How to obtain the slope?Considering a graph, a slope is calculated as the division of the vertical change by the horizontal change.
For the smaller triangle, we have that:
The vertical change is of 2.The horizontal change is of 2.Hence the slope is of:
m = 2/2
m = 1.
For the larger triangle, we have that:
The vertical change is of 3.The horizontal change is of 3.Hence the slope is of:
m = 3/3.
m = 1.
Meaning that they have the same slope.
More can be learned about slope at https://brainly.com/question/24808124
#SPJ1
What value of a will make the following equation true?
Answer:
a=16
Step-by-step explanation:
Answer:
A=4
Step-by-step explanation:
4(3x + 1)
What is the answer to 4(3x + 1)
Answer:
Answer is 12x+4. Hope that helped.
The set A = {1, 3, 5}. What is a larger set this might be a subset of?
Answer:
Step-by-step explanation:
A larger set that a particular set can be a subset of is a Universal set. A universal set is parent where all other sets are derived from.
For example, given a universal set U = {1,2,3,4,5}, a set A = {1, 3, 5} is said to be a subset of the set U because the elements of set B are contained in the Universal set U.
Also, sets like {1, 4,5} and {3,4,5} can also be regarded as the subset of U since all the elements of the sets can be found in the Universal set U. Hence the correct name of the set is a UNIVERSAL SET
So, the number of maximum subsets we can create from the given set is 8.
Subsets:The subsets of any set consists of all possible sets including its elements and the null set. Let us understand with the help of an example.
Example: Find all the subsets of set A = {1,2,3,4}
Solution: Given, A = {1,2,3,4}
Subsets =
The subsets of any set consisting of all possible sets including its elements and the null set. Let us understand with the help of an example.
Example: Find all the subsets of set A = {1,2,3,4}
{}
{1}, {2}, {3}, {4},
{1,2}, {1,3}, {1,4}, {2,3},{2,4}, {3,4},
{1,2,3}, {2,3,4}, {1,3,4}, {1,2,4}
{1,2,3,4}
So, the formula is [tex]2^n[/tex].
The given set is,
[tex]A = \{1, 3, 5\}[/tex]
Here the number of an element is 3.
So, the maximum number of subsets we can create is,
[tex]2^n=2^3=8[/tex]
Learn more about the topic Subsets:
https://brainly.com/question/17514113
You are buying fruit to make fruit baskets. Apples come in bags of 20. Oranges come in bags of 16, and bananas come in bags of 32. You have one bag of each fruit. Each fruit basket must be identical. What is the greatest number of fruit baskets that you can make using all of the fruit? *
Answer:
4 fruit baskets.
Step-by-step explanation:
Use GCF to find the answer. 20 divided by 4 is 5, 16 divided by 4 is 4, and 32 divided by 4 is 8.
3x - 5 = 2x + 10
What’s the value of x
Answer:
x = 3
Step-by-step explanation:
braniest pls
Answer:
x=3
Step-by-step explanation:
-5 +10
+5=15
+5=0
3x, 2x
+2 -2
5x=15
_ _
x=3
how do I write an equation in standard form with the points (3,3) (0,-3) (2,-3)
what is /4 of 3/4 =
What is 1/4 of 3/4
Answer:
3/16
Step-by-step explanation:
1/4 of 3/4 is just another way of saying (1/4)*(3/4). When multiplying fractions, you must multiply the numerators and denominators to get the product so the numerator of the products is 1*3 and the denominator is 4*4 to get:
3/16
Answer:
3/16
Step-by-step explanation:
1/4 of 3/4
= 1/4 × 3/4
you multipy the numerators together and then multiply both denominators
ie. 1×3 divided by 4×4
= 3/16
Which of the following equations has exactly one solution?
O A. 4x - 4 + 2x = 6x - 4
O B. 2(4x + 5) = 8x + 10
C. 4x - 8 = 4(x - 4)
O D. 3x + 5 = 2x - 6
Why do we study?give me reason
Answer:
Simple to help us improve our lives
Answer:
To do good in school
Step-by-step explanation:
the thing is teachers want us to study so we remember whatever is on the test for an example and that is good but not alt of people always study.
I need help with Number 7 please!!!
Answer:
8.06 ft or [tex]\sqrt{65}[/tex] ft
Step-by-step explanation:
Since Rebecca bought a square table and squares have equal sides, you can take the square root of the area of the table, which gives you [tex]\sqrt{65}[/tex] ft per side. This can be approximated to 8.06 ft.
At a school, there are 120 athletes. The ratio of boy athletes to giri athletes is 3:5. How many of the athletes are girls?
А
75
B
45
с
24
D 5
Answer:
a
Step-by-step explanation:
because there are over half girls and half of 120 is 60 and 75 is over half
Help with this one please
Answer:
(3x - 14) (2x - 7)
I hope this helps!
Playing golf, Mike got a + 2on the first hole and - 2 on the second hole. What is his combined score for the first two holes?
Answer:
0
Step-by-step explanation:
he had a score of 2 on the first hole and then he go a birdie i think and it subtracted 2 from that leaving 0
In which number is the digit 7 ten times larger than it is in the number 175?
A) 379
B) 607
C) 730
D) 7,513
Answer:
c 730
Step-by-step explanation:
because the 7 in 730 is one digit to the left
Answer:
C. 730
Step-by-step explanation:
The 7 in the original number is in the tens place. So if you multiply that by 10, the seven moves into the hundreds place.
5d+1/2=d-4 section 2.04
Answer: d = -9/8
Steps: 5d + ½ = d - 4
Subtract ½ from both sides: 5d + ½ - ½ = d - 4 - ½
Simplify: 5d = d - 9/2
Subtract d from both sides: 5d - d = d - 9/2 - d
Simplify: 4d = -9/2 ÷ 4
Simplify: d = -9/8
PLz mark brainliest:)
The mean and standard deviation of a random sample of n measurements are equal to and , respectively. a. Find a % confidence interval for if n. b. Find a % confidence interval for if n. c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]33.55 < \mu < 35.5[/tex]
b
[tex]34.03 < \mu < 34.969 [/tex]
c
Generally the width at n = 49 is mathematically represented as
[tex]w = 2 * E[/tex]
[tex]w = 2 * 0.952 [/tex]
[tex]w = 1.904 [/tex]
Generally the width at n = 196 is mathematically represented as
[tex]w = 2 * E[/tex]
[tex]w = 2 * 0.4687 [/tex]
[tex]w = 0.9374 [/tex]
d
The correct option is E
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 34.5[/tex]
The standard deviation is [tex]s = 3.4[/tex]
Generally given that the confidence level is 95% then the level of significance is
[tex]\alpha = (100 - 95)\%[/tex]
=> [tex]\alpha = 0.05 [/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Considering question a
From the question n = 49
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{s }{\sqrt{n} }[/tex]
=> [tex]E = 1.96* \frac{ 3.4 }{\sqrt{49} }[/tex]
=> [tex]E = 0.952 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < p < \=x +E[/tex]
[tex]34.5 -0.952 < p < 34.5 + 0.952[/tex]
=> [tex]33.55 < \mu < 35.5[/tex]
Considering question b
From the question n = 196
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{s }{\sqrt{n} }[/tex]
=> [tex]E = 1.96* \frac{ 3.4 }{\sqrt{196} }[/tex]
=> [tex]E = 0.4687 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < p < \=x +E[/tex]
[tex]34.5 -0.4687 < p < 34.5 +0.4687[/tex]
=> [tex]34.03 < \mu < 34.969 [/tex]
Considering question c
Generally the width at n = 49 is mathematically represented as
[tex]w = 2 * E[/tex]
[tex]w = 2 * 0.952 [/tex]
[tex]w = 1.904 [/tex]
Generally the width at n = 196 is mathematically represented as
[tex]w = 2 * E[/tex]
[tex]w = 2 * 0.4687 [/tex]
[tex]w = 0.9374 [/tex]
Now when the sample size is quadrupled i.e from n = 49 to n = 196
The width of the confidence interval decrease by 2 from 1.904 to 0.9374
Point V is on line segment UW. Given VW = 5x - 4, UV = 2x, and
UW = 52, determine the numerical length of VW.
Answer:
VW = 36
Step-by-step explanation:
From the question, we are given:
VW = 5x - 4, UV = 2x,
UW = 52
Hence,
UV + VW= UW
2x + 5x - 4 = 52
7x = 52 + 4
7x = 56
x = 56/7
x = 8
VW = 5x - 4,
VW = 5(8) - 4
VW = 40 - 4
VW = 36
ANSWER PLEASE NEED HELP ASAP
Answer: 43 should be divided into 0.37 to find “x”.
Step-by-step explanation:
the first 5 multiples of 18 after 0 are?
Answer:
18,36,54,72,90 are first five multiples of 18
Step-by-step explanation:
Answer:
18,36,54,72,90
Step-by-step explanation:
9. What is the likelihood that a randomly selected couple's relationship survived between 90 and 150 days
Answer:
0.5818
Step-by-step explanation:
Suppose the average teenage romantic relationship is normally distributed with a mean number of 100 days with a standard deviation of 30 days.
Answer:
The z score is used to determine how many standard deviations that the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and if it is negative then it is below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}\\ \\where\ \mu=mean,\sigma=standard\ deviation, x=raw\ score[/tex]
Given that:
[tex]\mu=100\ days,\sigma=30\ days\\\\For\ x=90\\\\z=\frac{90-100}{30} =-0.33\\\\For\ x=150\\\\z=\frac{150-100}{30} =1.67[/tex]
Therefore, from the normal distribution table, P(90 < x < 150) = P(-0.33 < z < 1.67) = P(z < 1.67) - P(z < -0.33) = 0.9525 - 0.3707 = 0.5818
I need to do this assignment but I need help on how to draw it and answer the questions because I am confused on how to do these things. Thank you
1) The domain is [0,300]. The range is [0,250]
2) The slope for the initial climb is 3.57. The equation of the line is
3) The rate of change of the second hill is -1.4
4) The rate of change of the third hill is -2.1
5) The blue hill is steeper
6) It is not a function
Step-by-step explanation:
1)
The domain of a function is the set of values of x (the input) for which the function itself is defined.
Instead, the range of a function is the set of values of y (the output) that the function can take.
To find the domain, we have to look at the x-axis and see for which values of x the function is defined. By looking at the graph, we see that the function is defined between
x = 0 and x = 300
So, the domain is [0,300].
To find the range, we have to look at the y-axis and see for which values of y the function has an output. By looking at the graph, we see that the function has values of y between
y = 0 and x = 250
So, the range is [0,250].
2)
The slope of a function in a certain range is given by
where
is the change in the y-coordinate
is the change in the x-coordinate
For the initial climb (pink line), we have:
Therefore, the slope in this part is
We can now write the equation of the line in the form
y = mx + b
where b is the y-intercept: since it is zero, the line has simply the form
3)
Again, to calculate the slope of the hill, we use:
where
is the change in the y-coordinate
is the change in the x-coordinate
For the green hill, we have:
So the rate of change is
4)
As before, the rate of change of the hill is
For the blue hill, we have:
So the rate of change is
5)
To know which hill is steeper, we need to compare the magnitude of their rate of change.
In fact, both hills have rate of change negative - because we are going down along the slope. Therefore, we have to consider the magnitude of their slope.
For the green hill:
For the blue hill:
We see that the blue hill has a greater slope (in magnitude): therefore, the blue hill is steeper.
6)
A function is defined as a mapping (operation between two sets of variables) in which to one value of x (the input) corresponds one and only one value of y (the output).
This means that a function cannot have multiple values of y for the same x (the input).
By looking at the graph, we see that this function does not respect this criterium: in fact, we see that certain values of x give multiple values of the output, y (for instance, at x=300 the function has two values). So, this is not a function.
Kai is making a chessboard using pieces of wood that measure 1 square inch.
When he finishes, the chessboard will have an area of 64 square inches.
How many pieces of wood should he put along each side?
A cube has a volume of 125 cubic inches. What is the length of each edge?
Answer:
The correct option will be: c. 8 pieces of wood.Step-by-step