Answer:
[tex]12\frac{1}{6}[/tex] cups of punch
Step-by-step explanation:
Peter is making a punch. He mixes :
Orange juice = [tex]4\frac{1}{2}[/tex] cups
Ginger ale = [tex]1\frac{1}{3}[/tex]
Strawberry lemonade = [tex]6\frac{1}{3}[/tex]
Now we will add all the mixes
[tex]4\frac{1}{2}[/tex] + [tex]1\frac{1}{3}[/tex] + [tex]6\frac{1}{3}[/tex]
Now first we convert all the mixed fractions to improper.
[tex]\frac{9}{2}+ \frac{4}{3}+ \frac{19}{3}[/tex]
Now take LCM of 2,3,3 = 6
= [tex]\frac{27+8+38}{6}[/tex]
= [tex]\frac{73}{6}[/tex] = [tex]12\frac{1}{6}[/tex]
The total number of cups of puch that peter makes is [tex]12\frac{1}{6}[/tex]
Peter makes a total of 12 cups and 1/6 cup (or approximately 2/3 cup) of punch by mixing 4 1/2 cups of orange juice, 1 1/3 cups of ginger ale, and 6 1/3 cups of strawberry lemonade.
To find the total number of cups of punch that Peter makes,
need to add together the quantities of orange juice, ginger ale, and strawberry lemonade.
Here are the quantities given:
Orange juice = 4 1/2 cups
Ginger ale = 1 1/3 cups
Strawberry lemonade = 6 1/3 cups
Now, add these quantities together:
4 1/2 cups + 1 1/3 cups + 6 1/3 cups
To add these mixed numbers together, it's helpful to first find a common denominator, which in this case is 6.
Convert 4 1/2 to an improper fraction: 4 1/2
= (2 × 4 + 1)/2
= 9/2
Convert 1 1/3 to an improper fraction: 1 1/3
= (3 ×1 + 1)/3
= 4/3
Keep 6 1/3 as it is since it's already in mixed fraction form.
Now, add the fractions:
(9/2) cups + (4/3) cups + (6 1/3) cups
To add the fractions, first, find a common denominator of 6:
(9/2) cups + (8/6) cups + (19/3) cups
Now, all fractions have a common denominator of 6:
(27/6) cups + (8/6) cups + (38/6) cups
Now, add the fractions:
(27/6 + 8/6 + 38/6) cups
Combine the numerators:
(27 + 8 + 38)/6 cups
Now, add the numerators:
(27 + 8 + 38) = 73
So, Peter makes a total of 73/6 cups of punch. You can also simplify this fraction:
73/6 = 12 1/6
Therefore, Peter makes 12 cups and 1/6 cup (or approximately 2/3 cup) of punch in total.
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Starting at home, Ishaan traveled uphill to the gift store for 18 minutes at just 10 mph. He then traveled back home along the same path downhill at a speed of 30 mph.
What is his average speed for the entire trip from home to the gift store and back?
how many ways can you arange the letters in the word cube
during a festive season a shop offered a discount of 20 percent on the marked price of all items find the SP of 3 trousers mardep at rs 1800 each and two t shirts marked at rs 550 each
The Daily Focus newspaper has a circulation of 382 198. Round this number to the nearest 100 000.
Kyle and his brother have a marble set. Of the marbles, 12 are blue. This represents 50/100 of all the marbles. What decimal is equivalent to 50/100
The decimal equivalent to 50/100 is 0.50, which is found by dividing 50 by 100.
The decimal equivalent to 50/100 is 0.50. This is because 50/100 is the same as dividing 50 by 100, which gives you 0.50.
This conversion is a standard way of expressing fractions where the denominator is 100, and it's commonly used to convert fractions into percentages or decimals.
For example, to convert 1/4 to a percent, you multiply by 25 (since 4 times 25 equals 100) to get 25 percent, which is equivalent to the decimal 0.25.
So, 50/100 is equivalent to 0.5 as a decimal.
What is 4 1/3 times 18
Rewrite the following equation in slope-intercept form. 5x + 7y = 7 Write your answer using integers, proper fractions, and improper fractions in simplest form.
An artist is deciding between two different triangular shapes to use for a sculpture. The first triangle has a base of 20 feet and a height of 5 feet. The second triangle has a base of 25 feet. If the two triangles have the same area, what is the height of the second triangle?
The height of the second triangle is 4 feet, which is found by using the formula for the area of a triangle (A = bh/2) and equating the area of the first triangle to that of the second.
To find the height of the second triangle with the same area as the first, we use the formula for the area of a triangle, A = bh/2, where b is the base and h is the height. The area of the first triangle with a base of 20 feet and height of 5 feet is:
A1 = (20 feet * 5 feet) / 2 = 50 [tex]feet^2[/tex]Since the second triangle must have the same area, we can set up the equation:
50 feet2 = (25 feet * h2) / 2Solving for the height (h2) of the second triangle:
100 feet2 = 25 feet * h2h2 = 100 [tex]feet^2[/tex] / 25 feeth2 = 4 feetTherefore, the height of the second triangle is 4 feet.
Josie has /60 cubic centimeter of candle wax. She wants to make a hexagonal prism candle with a vase area of 21 square centimeters and height of 8 centimeters. She also wants to make a triangular prism candle with a height of 14 centimeters. Can the bass area of the triangular prism candle be 7 square centimeters
Use the formula A=bh , where A is the area, b is the base length, and h is the height of the parallelogram, to solve this problem.
Brittany is painting a mural on one of the walls in her room. The mural is in a parallelogram-shaped frame. The area of the mural is 1056 in² and the base is 32 inches.
What is the height of the mural?
Enter your answer in the box.
[___] in
The area of the mural is 1056 in² and the base is 32 inches. We have to determine the height of the mural.
Area of parallelogram = [tex] b \times h [/tex]
where 'b' is the base and 'h' is the height.
1056 [tex] in^{2} [/tex] = 32 [tex] \times h [/tex]
[tex] h=\frac{1056}{32} [/tex] in
Therefore, the height of the mural is 33 inch.
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Help me with them I just learned it and I don’t understand...plzz
find the values of x and y
The first step to solve this problem is to formulate equations. Since the triangle has two equal sides, you can conclude that the angles adjacent to the sides are equal which means:
3x – 11 = 2x + 11
We can now solve for the value of x:
3x – 2x = 11 + 11
x = 22
The sum of the angles of a triangle is 180 so we can formulate another equation:
3x – 11 + 2x + 11 + 2y = 180
5x + 2y = 180
Remember that the value of x is 22 so you should substitute the value of x:
5(22) + 2y = 180
110 + 2y = 180
2y = 180 – 110
2y =70
y = 35
Ken is a tour guide at an art museum. He earns $11 an hour regular pay and receives time-and-a-half for overtime. Last week he worked 40 hours plus overtime. If he made $66.00 in overtime, how many overtime time hours did he work?
Answer:
Ken worked 4 hours overtime.
Step-by-step explanation:
Ken earns $11 for an hour in his regular pay.
He receives time-and-a-half for overtime = $11 + (11/2) = 11 + 5.50 = $16.50
Ken worked 40 hours plus overtime and he made $66.00 in his overtime.
So he worked overtime = $66.00 ÷ 16.50 = 4 hours
Ken worked 4 hours overtime.
when the value of a dependant variable decreases at the independent variable increases the function is said to be.....
what makes this true
If the value of a dependant variable decreases as the independent variable increases the function is said to be an inverse function.
What are ratio and proportion?A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.
When the value of a dependant variable decreases as the independent variable increases the function will be
We know that in inverse relation if the value of the independent variable (x) increases then the value of the dependent variable (y) decreases.
Then the value of y is inversely proportional to the value of x.
More about the ratio and the proportion link is given below.
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what is the greatest common factor (GCF) OF 88 and 72?
The Greates Common Factor (GCF) is: 2 x 2 x 2 = 8
What is the Value of:
What is the area of the shape?
50 POINT QUESTION. ANSWER AND EXPLAIN HOW YOU GOT THE ANSWER. IF NOT, YOU GET REPORTED. THANK YOU VERY MUCH !
In the morning, a farm worker packed 3 pints of strawberries every 4 minutes. In the afternoon, she packed 2 pints of strawberries every 3 minutes. What was the difference between her morning and afternoon packing rates, in pints per hour?
A. 5
B. 10
C. 40
D. 45
at a local gas station, regular gasoline sells for $2.899 per gallon, while premium gasoline sells for $3.379 per gallon. how much does a person save on 15.25 gallons of gas by buying regular instead of premium?
What is the approximate volume of the cone that is 8 cm in height and 12 cm as a radius use 3.14 for pi
use the formula for the ares of a trapezoid A=h (b^2+b^2/2)= where A is area b1 and b2 are the length of the bases and h is the height to answer the question how many square fet of grass and there on a trapezoidal field with a height of 75 ft bases of 125 ft and 81 ft?
A. 725 ft^2
B. 1025 ft^2
C. 7725 ft^2
D. 15,450 ft^2
There are 254 212 610 registered cars in the United States.
What is this number rounded to nearest million?
Answer:
254,000,000
Step-by-step explanation:
As it's 212,610 you round it down
The value of number rounded to nearest million is,
⇒ 254,000,000
What is rounding off?Rounding numbers refers to changing a number's digits such that it approximates a value. The provided number is more simply represented by this value. For instance, 700,000 rather than 698,869 could be used to express a town's population.
Given that;
There are 254 212 610 registered cars in the United States.
Hence, The value of number rounded to nearest million is,
⇒ 254,000,000
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12+18n+7-14n write an equivalent expression using like terms
What is the measure of angle x?
Enter your answer in the box.
x = ( )°
Two supplementary angles have the same measurements of 2x - 8 and 8x - 12. What is the measurement of the largest angle?
What is the equation of a line that is parallel to x=−5 and that passes through the point (1,4)
Please help I’ll give brainiest answer
The Marriott family bought a new apartment three years ago for $65,000. The apartment is now worth $86,515. Assuming a steady rate of growth, what was the yearly rate of appreciation?
The annual appreciation rate for the Marriott family's apartment they bought three years ago for $65,000, now worth $86,515, is 10%.
Explanation:The subject matter of this question is the calculation of the appreciated rate of the Marriott family's apartment. They bought this apartment three years ago for $65,000, and now it is worth $86,515. We want to find a constant rate of growth over these three years.
To determine the annual rate of appreciation, we need to use the formula for exponential growth: final value = initial value × (1 + annual growth rate) ^ number of years.
Let's plug in the given values: $86,515 = $65,000 × (1 + growth rate)³.
First, we divide the final value by the initial value: $86,515/$65,000 = 1.33177.
Second, we must calculate the cubic root of 1.33177 (since we have three years), which is 1.1. Therefore, the annual growth rate is 1.1 - 1 = 0.1 or 10%.
Hence, the yearly rate of appreciation for the apartment is 10%.
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What is the GCF of 95,42 and 97?
The GCF of 95, 42, and 97 is 1 because the prime factorizations of these numbers do not share any common factors other than 1.
Explanation:To find the Greatest Common Factor (GCF) of the numbers 95, 42, and 97, we need to look for the highest number that can divide all three numbers without leaving any remainder. When considering 95, 42, and 97, we notice that:
95 is a product of the prime numbers 5 and 19,42 is a product of the prime numbers 2, 3, and 7,97 is a prime number itself, hence it only has 1 and 97 as its factors.Since the prime factorization of these numbers does not share any common factors other than 1, the GCF of 95, 42, and 97 is 1.
The area if a dog kennel is 20 square feet. If the kennel is 4 feet.what is the width of the kennel?
The width of the dog kennel is 5 feet, obtained by dividing the area (20 square feet) by one of the dimensions provided (4 feet).
Explanation:The student is asking for the width of a dog kennel, given that the area is 20 square feet, and one dimension (possibly the length) is given as 4 feet. To find the width, we can use the formula for the area of a rectangle, which is Area = Length × Width. Since the area is given as 20 square feet and the length is given as 4 feet, we can rearrange the formula to solve for the width:
Width = Area ÷ Length
Width = 20 square feet ÷ 4 feet = 5 feet
Therefore, the width of the dog kennel is 5 feet.
The width of a dog kennel with an area of 20 square feet and a length of 4 feet is found to be 5 feet using the area formula for rectangles, which is Area = Length × Width. The width of the kennel is 5 feet.
Explanation:To determine the width of a dog kennel with an area of 20 square feet and a length of 4 feet, we can use the formula for the area of a rectangle, which is:
Area = Length × Width
We have the area (20 square feet) and the length (4 feet), so we can solve for the width:
20 square feet = 4 feet × Width
To find the width, we divide both sides of the equation by the length (4 feet):
Width = 20 square feet / 4 feet
Width = 5 feet
Therefore, the width of the kennel is 5 feet.