Equivalent fractions represent the same portion of a whole, despite having different numerators and denominators. By increasing the number of equally divided parts of a whole and accordingly adjusting the number of shaded parts, you create equivalent fractions such as 1/2 and 3/6, which look different but represent the same amount.
Explanation:The question is addressing a concept in Mathematics, specifically the idea of equivalent fractions and how changing the number of parts in a whole affects those fractions. When you look at the model showing 1/2 = 3/6, you see that the whole is divided into different numbers of parts. The fraction 1/2 means that one out of two equal parts of the whole is shaded, whereas 3/6 indicates that three out of six equal parts of the whole are shaded.
To understand this, imagine dividing a shape into two equal parts. Shading one of these gives you 1/2. If you further divide each half into three parts, making six equal parts in total, and shade three, you still have the same amount shaded (which is half) but in terms of six parts now, hence 3/6. This shows that by increasing the number of parts into which the whole is divided, while maintaining the proportion of the shaded area, you increase both the numerator and denominator of the fraction proportionally, thus creating what is known as an equivalent fraction.
1. You and your friend are splitting a restaurant bill and leaving a tip. You pay half of the bill plus $5. Your friend pays half of the bill plus 25% of half the bill. You and your friend pay the same total amount. How much is half the bill?
(a) Write an equation. Let x be the cost of half the bill.
(b) Solve the equation. Show your work.
(c) Check your solution. Show your work.
(d) State the solution in complete sentences. Answer:
(2. The graph shows the number of laps Kailee ran around a track over a given number of minutes.
(a) What is the slope of the line? Use the slope formula and show your work.
(b) How many laps did Kailee run per minute?
(c) If she continued to run at the same rate, how many laps would she run in 24 min?
3. A family is tracking its spending habits. Over the past year, the grocery bill has ranged from $110 to $170. Suppose you were going to plot these points on a coordinate grid.
(a) What is a good scale to use for the y-axis? Explain your reasoning.
(b) What is a good interval to use for the y-axis? Explain your reasoning. Answer:
Order the numbers from least to greatest. −1.4,−85, 0.6,−0.9, 14
Answer:
Numbers from least to greatest is -85 , -1.4 , -0.9 , 0.6 , 14 .
Step-by-step explanation:
Given : Numbers −1.4,−85, 0.6,−0.9, 14.
To find : Order the numbers from least to greatest ?
Solution :
According to number system,
In left side there are negative numbers before zero and after on right side there are positive numbers.
In left side, number written from larger to smallest with negative sign.
In right side, number written from smallest to larger with positive sign.
Numbers from least to greatest is -85 , -1.4 , -0.9 , 0.6 , 14 .
3 packs of Soda cost $10 less than 5 packs of soda. Write an equation that models this.
I'll need help with case 5
What's the pattern in 30 21 12 3 -6
How many sentences are in 3 paragraph.
Distributive property 5x18
Todd has 2 frogs. This is 1/3 the number of frogs that heather has. How many frogs doEs heather have
the factory workers make 715 twice per day if they work 5 days per week how many toys will the workers make in 3 weeks
is the number 731934030 written in standard form
No, The number 731934030 is not written in standard form.
What is Number system?
A system of writing to express the number is called number system.
Given that;
The number is;
⇒ 7,319,34,030
Now,
Since, We know that;
A number that can be write as a decimal number, between 1.0 and 10, multiplied by a power of 10, is called a standard form.
So, The number 731934030 is not written in standard form.
Thus, The number 731934030 is not written in standard form.
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A construction company bought 9 tons of gravel and 0.8 tons of sand.hoq many tons of material did the comapany but in all
A florist has 8 roses and 24 daffodils.she wants to make as nany identical bouquets as possible, with the same combination of roses and daffodils.what is the largest amount of bouquets she can make?
The florist can make 8 identical bouquets with the same combination of roses and daffodils.
Explanation:To find the largest amount of identical bouquets that can be made with 8 roses and 24 daffodils, we need to determine the highest common factor (HCF) of both numbers. The HCF of 8 and 24 is 8. Therefore, the florist can make 8 identical bouquets with the same combination of 1 rose and 3 daffodils in each bouquet.
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If you multiply me by 7, subtract 2 and then divide by 6, you get 9. What number am I ?
The number in question is 8. Multiplying it by 7, subtracting 2, and dividing the result by 6 gives you 9.
To find the number that, when multiplied by 7, subtracted by 2, and then divided by 6, results in 9, we can set up the equation to solve for the unknown number (let's call it x):
7x - 2 = 54 (since 6 times 9 equals 54)
7x = 54 + 2
7x = 56
x = 56 / 7
x = 8
So the number you're looking for is 8 because when you multiply 8 by 7, subtract 2, and then divide by 6, you indeed get 9.
A collector has 180 movie posters and 100 band posters. She wants to sell 36 movie posters but still have her poster collection maintain the same ratio of 180:100. If she sells 36 movie posters, how many band posters should she sell? Explain?
How many gallons of gas are left after driving 200 miles
A baseball stadium sold some burgers 2,806 we're cheeseburgers 1,679 burgers didn't have cheese how many burgers did they sell in all
Simplify:
3(3t – 2) – 2(t + 1)
there are 1505 fruits for sale at a Farmers Market 39% of them are apples 28% are oranges 13% are honeydew melons and the rest are watermelons how many watermelons are there
Final answer:
As per the given case, there are 301 watermelons.
Explanation:
To calculate the number of watermelons at the farmer's market, we need to subtract the percentages of apples, oranges, and honeydew melons from the total percentage (100%) and then apply that percentage to the total number of fruits available. The calculations are as follows:
Percentage of apples: 39%Percentage of oranges: 28%Percentage of honeydew melons: 13%Total percentage of these three fruits: 39% + 28% + 13% = 80%
Percentage of watermelons = 100% - 80% = 20%
So, if 20% of the fruits are watermelons, and there are 1505 fruits in total, we calculate the number of watermelons as follows:
Number of watermelons = 20% of 1505 = 0.20 × 1505 = 301 watermelons
Therefore, there are 301 watermelons for sale at the farmer's market.
square root of 97 someone help plz
What is the unit rate 360 miles traveled on 12 gallons of gasoline
We are required to find the unit rate in miles per gallons of gasoline.
The unit rate 360 miles traveled on 12 gallons of gasoline is 30 miles per gallon
Units rate refers to the single unit of one quantity to another. for example; unit of miles to gasolineTotal miles travelled = 360 miles
Total gallons used = 12 gallons
Unit rate in miles per gasoline = Total miles travelled / Total gallons used
= 360 miles / 12 gallons
= 30 miles / 1 gallon
Unit rate in miles per gasoline = 30 miles per gallon
Therefore, the unit rate 360 miles traveled on 12 gallons of gasoline is 30 miles per gallon
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What is 5 1/9 - 2 5/9???
You water the plants in your classroom at a constant rate. After 5 seconds, your watering can contains 58 ounces of water. Fifteen seconds later, the can contains 28 ounces of water.
a. Write an equation in slope-intercept form that represents the amount yy (in ounces) of water in the can after xx seconds.
To write an equation in slope-intercept form, we can use the given points to find the slope and y-intercept of the line. The equation that represents the amount of water in the can after x seconds is y = -2x + 68.
Explanation:To write an equation in slope-intercept form, we need to find the equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.
Given that the watering can contains 58 ounces of water after 5 seconds and 28 ounces of water after 20 seconds, we can use these two points to find the slope (m).
m = (28 - 58) / (20 - 5) = -30 / 15 = -2
Next, we can substitute one of the points and the slope into the equation and solve for b:
58 = -2(5) + b
b = 68
Therefore, the equation that represents the amount of water in the can after x seconds is
y = -2x + 68
Therefore, the equation in slope-intercept form that represents the amount y (in ounces) of water in the can after x seconds is y = -2x + 68.
To write the equation in slope-intercept form that represents the amount y (in ounces) of water in the can after x seconds, we need to determine the rate at which the water level decreases over time.
Given data:
- After 5 seconds, the can contains 58 ounces of water.
- After 20 seconds (5 seconds + 15 seconds), the can contains 28 ounces of water.
Let's define our points based on this data:
- First point: (5, 58) (5 seconds, 58 ounces)
- Second point: (20, 28) (20 seconds, 28 ounces)
Now, let's find the slope m of the line passing through these two points. The slope m is calculated as:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
[tex]\[ m = \frac{28 - 58}{20 - 5} \][/tex]
[tex]\[ m = \frac{-30}{15} \][/tex]
[tex]\[ m = -2 \][/tex]
Now that we have the slope m, we can use the point-slope form of the equation of a line, [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( (x_1, y_1) \)[/tex] is one of our points. Let's use the point (5, 58):
[tex]\[ y - 58 = -2(x - 5) \][/tex]
Now, simplify and solve for y to get the equation in slope-intercept form (y-intercept form), y = mx + b:
[tex]\[ y - 58 = -2x + 10 \][/tex]
[tex]\[ y = -2x + 10 + 58 \][/tex]
[tex]\[ y = -2x + 68 \][/tex]
A bag contains 2 red crayons, 4 blue crayons, and 1 green crayon. A crayon is selected, kept out of the bag, and then another crayon is selected. What is P( blue
Jessie estimated the weight of his cat to be 12 pounds. The actual weight of the cat is 15 pounds.
What is the percent error?
Round your answer to the nearest whole percent.
Enter your answer in the box.
Answer:
The answer is 20%
Step-by-step explanation:
The percent error is 20%
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
We have been given that Jessie estimated the weight of his cat to be 12 pounds. The actual weight of the cat is 15 pounds.
We have to determine the percent error.
Here the percent error is the percentage of the difference between the estimated weight and actual weight of the cat.
So the percent error is
⇒ the percentage of (15 - 12)/15 = (3/15) = 20 %
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Manny makes dinner using 1 box of pasta and 1 jar of sauce. if pasta is sold in packages of 6 boxes and sauce is sold in packages of 3 jars, what is the least number of dinners that Manny can make without any supplies leftover?
-2/3 * x=-4
What is X?
LaShea would like to invest her $100 in birthday money. Which option should she choose so that she will have the most money? 1 year at 8 percent
C 2 years at 6.5 percent
Step-by-step explanation:
On my quiz it said c was correct.
A bakery uses 475 pounds of apples to make 1000 apple tart each tart contains the same amount of apples how many pounds of apples are used in each tart
Hurry!! Please help!!!
Expand the expression and combine like terms:
{-5(1-5k)-4(2k+5)}−5(1−5k)−4(2k+5)space, minus, 5, left parenthesis, 1, minus, 5, k, right parenthesis, minus, 4, left parenthesis, 2, k, plus, 5, right parenthesis
Please choose from one of the following options.
-17k-25−17k−25minus, 17, k, minus, 25
-17k+25−17k+25minus, 17, k, plus, 25
17k+2517k+2517, k, plus, 25
17k-2517k−25
what is 1962 divided by 13
Answer:
150.92
Step-by-step explanation: