A ratio is used to describe how two or more quantities are related. For example, we might say that a fruit drink calls for sugar crystals to be mixed with water in a ratio of 2:8. This means that for every 2 scoops sugar crystals, there will need to be 8 ounces of water. If there were 200 scoops of sugar crystals, there would need to be 800 ounces of water.
Sure, we'll start off by simplifying the ratio 2:8. Simplifying it gives us 1:4.
Our aim is to find a number, let's denote it by x, such that the ratio 2:x will be the same as 1:4.
To find such an x, we need to set up an equation using the principle of equivalence of ratios. This gives us 2/x = 1/4.
Now we proceed to solve this equation for x. We do this by cross-multiplying the fractions in the equation.
Cross-multiplication gives us 2*4 = x*1. Simplifying this yields 8 = x.
Hence, we can conclude that the number x that makes the ratio 2:x equivalent to 2:8 is 8.
To estimate the product 3.48 times 7.33,Marisa multiplied 4 times 8 to get 32.Exsplain how she can make a closer estimate
Marisa had rounded 3.48 to 4 and times it to 7.33 which she rounded to 8
In fact 3.48 is closer to 3 we know this since the .48 of 3.48 s below .50 if it was .50 or above it would round to 4 but it doesn't the same applies to 7.33 so
it should be 3 x 7 = 21
If Marisa is going to estimate, then she needs to round each number. If she rounds to the nearest ones place, then she should have rounded 3.48 to 3 and rounded 7.33 to 7.
3 x 7 = 21
Each of 25 students in Group A read for 45 minutes. Each of 21 students in Group B read for 48 minutes. Which group read for more minutes? Explain.
Please help!! Worth 20 points!
Please help me with this
What is the greatest common factor between 10 and 24?
The greatest common factor between 10 and 24 is 2.
What is Greatest common factors?
The highest number that divides exactly into two more numbers, is called Greatest common factors.
Given that;
The numbers are;
10 and 24
Now,
The factors of 10 = 1, 2, 5, 10
The factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.
Clearly, The greatest common factor of the number 10 and 24 is highest number which is common in both factors.
Thus, The greatest common factor between 10 and 24 is 2.
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compare the ratios 2 to 7 and 5:7 using the circles to model
To compare the ratios 2 to 7 and 5:7 using the circles to model we need to make two circles first.
Then we need to make 7 parts of each circle.
For 2:7 ratio, we need to shade 2 parts of the total 7 parts of the circle.
For 5:7 ratio, we need to shade 5 parts of the total 7 parts of the circle.
So, the first circle represents 2:7 ratio and second circle represents 5:7 ratio.
Answer:
To compare the ratios 2 to 7 and 5:7 using the circles to model we need to make two circles first.
Then we need to make 7 parts of each circle.
For 2:7 ratio, we need to shade 2 parts of the total 7 parts of the circle.
For 5:7 ratio, we need to shade 5 parts of the total 7 parts of the circle.
So, the first circle represents 2:7 ratio and second circle represents 5:7 ratio.
Step-by-step explanation:
PLEASE HELP ME WITH B AND C.
B)The numbers are being divided by 10 repeatedly.
The numbers are:
7000
700
70
.7
.07
.007
(See it now?)
The number that is missing is 7
My conjecture is that 7 can’t be written in scientific notation.
Hope I helped!
Good Luck!
⛈
Ben solved an equation as shown below, Equation 2 (-3×+1)=9×-8. what did he do wrong. step1. -6×+2=9×- 8. step2. -6×+9×=-8+2. step3. 3x=-6. step4. x=-2
failed to evaluate 9 × - 8
2( - 3x + 1) = 9 × - 8
- 6x + 2 = - 72 ( subtract 2 from both sides )
- 6x = - 74 ( divide both sides by - 6 )
x = [tex]\frac{-74}{-6}[/tex] = [tex]\frac{37}{3}[/tex]
simplify (2x^2+6x+5) - (6x^2+3x+5)
Your answer will turn out to be −4x^2+3x.
Simplify. Distribute -1 to all terms within the second parenthesis
-(6x² + 3x + 5) = -6x² - 3x - 5
Combine like terms
2x² - 6x² = -4x²
6x - 3x = 3x
5 - 5 = 0
-4x² + 3x is your answer
~Rise Above the Ordinary
Why is it good to have holes in your t-shirts
Answer:
They make it easier to get your arms through
The plates at the local restaurant have a diameter of 6.3 inches. What is the circumference of the plates?
Use 3.14 for π.
A.
12.6 inches
B.
18.9 inches
C.
19.732 inches
D.
19.782 inches
Answer:
B: 18.9
Step-by-step explanation:
Name the property of equality that justifies this statement if RS=ST and ST=TU then RS=TU
Thanks
Answer:
This is called Transitive property of equality.
Step-by-step explanation:
If a quantity a=b and b=c, then we can say a=c, this property is called transitive property of equality.
help me out please!
Solve for z.
[tex]\dfrac{8(4-z)}{7}=-z\\\\8(4-z)=-7z\\\\32-8z=-7z\\\\-7z+8z=32\\\\z=32[/tex]
8(4 - z)/ 7 = -z
8(4 - z) = -7z
32 - 8z = -7z
-8z + 7z = -32
-z = -32
z = 32
What is the product of 3 × 50 × 18 × 2?
A. 2,700 B. 540 C. 1,800 D. 5,400
The answer is D because when you insert it into a calculator it gives you D. Yet, if you do it manually you still get the same number .
Answer:
The answer is D
Step-by-step explanation:
Hope I helped!! :)
at 1:30 in the afternoon an old freight train and a new dart express train pull out of the new garland station going in opposite directions the dart express train goes three times faster than the hold freight train. fifteen minutes later the two trains are already 30 miles apart find the speed of each train?
Answer:
[tex]V_{E} = -22.5 / 15 = 1.5 miles/minute\\V_{F} = 7.5 / 15 = 0.5 miles/minute[/tex]
Step-by-step explanation:
To answer this problem, we must bear in mind that the express train travels 3 times faster than the freight train.
If we call F the distance that the freight train travels and we call E at the distance that the express train travels, we must have the distance between them after 15 minutes it must be 30 miles.
So
[tex]F + E = 30\\[/tex]
We also know that:
[tex]E = 3F[/tex]
Since the express train travels 3 times faster than the freight train.
So, like both equations, we have to:
[tex]F + 3F = 30\\F = 30/4\\F = 7.5 miles\\[/tex]
Then [tex]E = 7.5*3 = 22.5[/tex] miles in the opposite direction.
This is the distance you traveled in 15 minutes.
Therefore, the speed of the express train ([tex]V_{E}[/tex]) is the distance traveled between the time it did
[tex]V_{E} = -22.5 / 15 = 1.5 miles/minute\\V_{F} = 7.5 / 15 = 0.5 miles/minute[/tex]
the diameter of a circle is 12yd. find the exact area and circumference of the circle. write your answers in terms of pie
The exact circumference of the Circle Measurements is 12π yards and the exact area is 36π square yards.
To find the exact area and circumference of the circle, we can use the formulas given:
Circumference of a circle = 2πr
Area of a circle = πr^2
Given that the diameter of the circle is 12 yards, we can find the radius by dividing the diameter by 2: r = 12 / 2 = 6 yards.
Now we can substitute the value of r into the formulas:
Circumference = 2πr = 2π(6) = 12π yards
Area = πr^2 = π(6^2) = 36π square yards
So, the exact circumference of the circle is 12π yards and the exact area is 36π square yards.
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marcela's dog gained 4.1 kilograms in two months. Two months ago, the dog's mass was 5.6 kilograms. What is the dog's current mass?
A boy jogs 250 meters in 110 seconds. What is his average speed in m/s?
Answer:
2.72 m/s
Step-by-step explanation:
We are given that
Boy jogs=250 meters
Time taken by boy=110 seconds
We have to find the average speed in m/s
In order to find the average speed then we will divide distance by time
[tex]Average\;Speed=\frac{distance}{time}[/tex]
Using the formula then we get
Average speed=[tex]\frac{250}{110}=2.72 m/s[/tex]
Hence, the average speed=2.72 m/s
Final answer:
To calculate the average speed, the boy's distance jogged (250 meters) is divided by the time taken (110 seconds), yielding an average speed of 2.27 m/s.
Explanation:
The student's question asks how to calculate the average speed of a boy who jogs a certain distance in a given amount of time. To find the average speed, you divide the total distance traveled by the total time taken. In this case, the boy jogs 250 meters in 110 seconds.
The calculation for the average speed (v) would be:
Distance (d) = 250 meters
Time (t) = 110 seconds
Average Speed (v) = d / t
Plugging the values into the equation yields:
Average Speed (v) = 250 m / 110 s = 2.27 m/s
Hence, the boy's average speed is 2.27 meters per second.
Anyone ??
I’m confused
Which graph shows a slope of m = −1 / 2 and a y intercept of b = -4?
Letter D, because the y intercept is on -4 and if you look at the slope and use the method "Rise over Run" you can see that the rise is one and negative a half.
if the sum of two numbers is 21 and their quotient is 2 what are they?
Set up the equations:
two numbers: a and b
sum: a+b=21
quotient: a/b=2
(the last one means b=a/2)
combine them:
a+a/2=3a/2=21
a=14
and so
b=7
the two numbers are 14 and 7
Final answer:
To find two numbers given their sum and quotient, set up and solve a system of equations. In this case, the numbers are 14 and 7.
Explanation:
The sum of two numbers is 21 and their quotient is 2. To find the two numbers, we can set up a system of equations:
Let the two numbers be x and y. We have the equations x + y = 21 and x/y = 2.
Solve the system by substituting y = 21 - x into the second equation to get x = 14 and y = 7.
Therefore, the two numbers are 14 and 7.
Calculate the number of ways in which four paintings can be awarded first, second, third, and fourth prizes at an art competition in which a total of 30 paintings are displayed
Answer:
657720 ways
Step-by-step explanation:
This is the number pf permutations of 4 from 30:-
= 30! / (30 - 4)!
= 30! / 26!
= 30*29*28*27
Ally made a net to find the surface area of a box she was designing. The box measure 12 centimeters long by 9 centimeters high by 9 centimeters deep. What is the surface area, in square centimeters, of the box?
Final answer:
Ally's box has a total surface area of 594 square centimeters, calculated using the surface area formula for a rectangular prism: Surface Area = 2lw + 2lh + 2wh.
Explanation:
The surface area of a box can be calculated by finding the area of all six faces and adding them together. Since the box Ally is designing has dimensions of 12 cm long, 9 cm high, and 9 cm deep, we will have two faces for each dimension. To calculate the surface area of Ally's box, we use the formula:
Surface Area = 2lw + 2lh + 2wh
Where l is the length, w is the width, and h is the height of the box. Now, plugging in Ally's box dimensions:
Surface Area = 2(12 cm)(9 cm) + 2(12 cm)(9 cm) + 2(9 cm)(9 cm)
Surface Area = 2(108 cm2) + 2(108 cm2) + 2(81 cm2)
Surface Area = 216 cm2 + 216 cm2 + 162 cm2
Surface Area = 594 cm2
Therefore, the total surface area of Ally's box is 594 square centimeters.
Jane is X years old today. her brother Kenny is four years older l. after seven years of their total combined age will be 24 years. Write a linear equation for their total combination age after seven years
Answer:
The linear equation for the total combination age is [tex]X+7+(X+4)+7=24[/tex]
Step-by-step explanation:
If Jane is X years old today. And her brother is 4 years older then her brothers age is,
X+4.
Jane's age after 7 years = X+7
Jane's Brothers age after 7 years = (X+4)+7
So after seven years their combined age will be 24, Lets write this in an equation form,
[tex]X+7+(X+4)+7=24[/tex]
So the linear equation for the total combination age is,
[tex]X+7+(X+4)+7=24[/tex]
Find three consecutive odd integers such that the sum of the smaller two is three times the largest increased by seven
three consecutive odd integers are : -17,-15,-13
Solve the following proportion (solve p) p/6=7/8
Answer is: p = [tex]\frac{21}{4}[/tex]
x^2-4y^2=0
A.(x+4y)(x-y)
B. (x-4y)(x+y)
C. (x+2y)(x-2y)
D. (x-2y)(x-2y)
[tex]x^{2}[/tex]-4[tex]y^{2}[/tex] = 0
Solution
Here we have to find the factors.
[tex]x^{2} - 4y^{2} = 0[/tex]
Here we can write 4y^2 as (2y)^2
[tex]x^{2} - (2y)^{2} = 0[/tex]
Now we have to use the formula, a^2 - b^2 = (a + b)(a - b)
Here a = x and b = 2y
Therefore, we get
(x + 2y)(x -2y)
Hence, the answer isC. (x + 2y)(x -2y)
Which relation is a function?
{(5, 0), (0, –8), (5, –5)}
{(5, 0), (0, 5), (–5, –5)}
{5, 0, –8, –5}
{(5, 0), (–8, –5), (–8, 5), (–5, –8)}
Based on the analysis, the only relation that is a function is {(5, 0), (0, 5), (–5, –5)}.
How to determine Which relation is a function?A relation is considered a function if each input value (x-value) in the relation corresponds to exactly one output value (y-value).
1. {(5, 0), (0, –8), (5, –5)}
In this relation, the input value 5 corresponds to both 0 and -5. Therefore, this relation is not a function.
2. {(5, 0), (0, 5), (–5, –5)}
In this relation, each input value has a unique output value. For example, 5 corresponds to 0, 0 corresponds to 5, and -5 corresponds to -5. This relation satisfies the definition of a function since each input value has only one corresponding output value.
3. {5, 0, –8, –5}
This is not a relation since it consists only of individual numbers and does not show any pairings between input and output values. Therefore, it is not a function.
4. {(5, 0), (–8, –5), (–8, 5), (–5, –8)}
In this relation, the input value -8 corresponds to both -5 and 5. Therefore, this relation is not a function.
Based on the analysis, the only relation that is a function is {(5, 0), (0, 5), (–5, –5)}.
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Final answer:
The relation {(5, 0), (0, 5), (–5, –5)} is a function because each domain value maps to exactly one range value, which meets the definition of a function.
Explanation:
To determine which relation is a function, we must ensure that each input (or domain value) maps to exactly one output (or range value). A function cannot have one domain value paired with multiple range values.
Relation 1: {(5, 0), (0, –8), (5, –5)} is not a function because the domain value 5 is associated with two different range values (0 and –5).Relation 2: {(5, 0), (0, 5), (–5, –5)} is a function because each domain value is unique and maps to exactly one range value.Relation 3: {5, 0, –8, –5} is not a relation in the form of ordered pairs, so it cannot be considered a function.Relation 4: {(5, 0), (–8, –5), (–8, 5), (–5, –8)} is not a function because the domain value –8 has two different range values (–5 and 5).Therefore, the relation that is a function is the second one: {(5, 0), (0, 5), (–5, –5)}.
paula has 6 video games. myles has 1 more video game than paula. what could you use to find how many video games in all?
13, paula has 6, myles has 1 more than her that mean he has 7
6+7= 13
Answer:
13
Step-by-step explanation:
We know that Paula has 6 video games and Myles has one more video game than Paula.
So the number of video games Myles has will be equal to 6 + 1 = 7.
Now that we know the number of games that Paula and Myles have, we can find the number of video games in all by simply adding the two numbers:
Total number of video games = 6 + 7 = 13
Therefore, Paula and Myles together have 13 video games.
Sally consumed 2.5 gallons of water in one day. How many milliliters are equal to 2.5 gallons, if 1 liter = 1,000 milliliters and 1 gallon = 3.785 liters?
there are 9463.53 milliliters in 2.5 gallons of water.
Answer:
9,462,5 milimiters.
Step-by-step explanation:
In order to be able to calculate how many milimeters there are in 2.5 gallons of water we just have to convert the units, so we first have to convert from gallons to liters, there are 3.785 liters in each gallon, so we just do the convertion:
[tex]\frac{1 gallon}{3.785 liters}=\frac{2.5 gallons}{x}[/tex]
If we clear the x we get:
[tex]x=\frac{(3.785 liters)(2.5gallons)}{1 gallon}[/tex]
[tex]x=\frac{(9.4625 liters*gallons)}{1 gallon}[/tex]
[tex]x=9.4625 liters[/tex]
Now we just ocnvert to mililiters, since there are 1000 mililiters in a liter we just multiply:
[tex]\frac{1 liter}{1000mililiter}=\frac{9.462liters}{x}[/tex]
[tex]x=\frac{(9.4625 liters)(1000mililiter)}{1 liter}[/tex]
[tex]x=9462.5 mililiters}[/tex]