Final answer:
By setting up an equation based on the given ratio 2:5 and the additional information that Julie receives £45 more than Pat, we find that Pat received £30.
Explanation:
The question deals with understanding ratios and how they can be used to solve problems involving sharing amounts in specified proportions. Pat and Julie share some money in the ratio 2:5, and it's given that Julie gets £45 more than Pat. To approach this problem, let's designate the amount Pat receives as 2x and the amount Julie receives as 5x, where x is a common multiplier.
It is stated that Julie gets £45 more than Pat, which can be represented as 5x = 2x + 45.
Solving the equation for x gives us 3x = 45, hence x = 15.
To find out how much Pat received, we substitute x = 15 into 2x, giving us 2(15) = 30.
Therefore, Pat got £30.
A shopping company charges $3.50 plus $0.85 per pound to ship a package. Janet shipped a package and the total charge was $8.60. Write and solve an equation to find the weight of the package.
Based on the information, the weight of the package is approximately 6 pounds.
How to calculate the weightAccording to the given information, the shopping company charges $3.50 as a base fee and an additional $0.85 per pound to ship the package.
The total charge for shipping the package, which is $8.60, can be expressed as:
$3.50 + ($0.85 * w) = $8.60
To find the weight of the package, we need to solve this equation for "w". Let's solve it step by step:
$0.85 * w = $8.60 - $3.50
$0.85 * w = $5.10
Now, we can isolate "w" by dividing both sides of the equation by $0.85:
w = ($5.10) / ($0.85)
w ≈ 6
Therefore, the weight of the package is approximately 6 pounds.
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A road map has a scale of 1:20000 on the map a road has a length of 4cm work out the actual distance five your answer in metre
To determine the actual distance of a 4 cm road on a map with a 1:20000 scale, multiply the map measurement by the scale factor to get 80000 cm, then convert it to meters to obtain an actual distance of 800 meters.
Explanation:To work out the actual distance of a road on a map that has a scale of 1:20000, you need to convert the map length to the actual length. If the road measures 4 cm on the map, you would use the following steps:
Determine the scale ratio, which is 1 cm on the map represents 20000 cm in reality.Multiply the map distance by the scale factor. In this case:Therefore, the actual distance of the road is 800 meters.
Felicia bought 4 buckets of popcorn at the movies if she paid a total of $15 how much is one bucket of popcorn?
The Georgia sales tax is 4%. However, some places in Georgia charge a higher rate of sales tax. This is MOST LIKELY because Question 3 options: shipping goods to some localities in Georgia can be extremely expensive. the sales tax in Georgia is determined by how much money the buyer makes per year. localities in Georgia can add a certain percentage to sales tax for their own needs. sellers can charge whatever they want as long as the minimum state rate is collected.
Final answer:
The most likely reason some localities in Georgia charge higher sales taxes is that they can add to the state's 4% tax to cater to their own financial needs, funding local services and needs.
Explanation:
The question relates to why some places in Georgia might charge a higher rate of sales tax than the state's baseline of 4%. The most likely reason is that localities in Georgia have the authority to add additional percentages to the state sales tax to address their individual financial requirements. This is commonly seen in states where local governments utilize the sales tax mechanism to fund specific local public services and projects. For instance, a city may add a percentage to fund improvements in education, transportation, or healthcare facilities.
The amount of sales tax is determined by multiplying the price of the goods or services by the sales tax rate. When a locality opts to add to the state sales tax, the total sales tax a consumer pays is the sum of the state rate plus any local rates. This system allows for local governments to cater to their unique budgetary needs while still adhering to the broader state tax structure. This is different from other variables, like shipping costs, buyer's income, or seller preferences, which do not generally affect the sales tax rate.
Mr. Jacobs is going to make a histogram of the test scores from the last math test he gave. He plans to first organize the data into a stem-and-leaf plot and then make the histogram from the stem-and-leaf plot. The test scores are listed below. 79, 82, 65, 61, 94, 97, 84, 77, 89, 91, 90, 83, 99, 71, 68, 77, 87, 85 Which of the following expressions could be used to find how many students scored less than a 90 on the test?
3 + 44 + 63 + 4 + 63 + 4 + 6 + 1
Answer:
The answer is 3 + 4 + 6
There are 13 numbers that are lower than 90, and 3 + 4 + 6 is the correct expression because 3 + 4 + 6 = 13.
I did this on my lesson and I got it right.
Why is #1-3 still wrong?
NEED HELP FAST PLEASE!! Draw the base plan for the set of stacked cubes, assume the no cubes are hidden from view.
Explain the advantage of creating a linear function from a set of data; why bother to do this?
The distance around a circle is 56.55 meters long. What is the diameter of the circle?
Answer: Diameter of circle = 18m
Explanation:
Given that distance around a circle is = 56.55 meter
The distance around a circle on the other hand is called the circumference .
That means Circumference = 56.55 m
We know the formula of circle's circumference= 2πr
where r is the radius and 2r is diameter of the circle
So,
2πr = 56.55
divide by π both the side
2r = [tex] \frac{56.55*7}{22} [/tex]
Value of π = [tex] \frac{22}{7} [/tex]
2r = 17.993 ≈ 18 m
Diameter of circle = 18m
A rope that is 2 feet and 6 inches long is cut into 3 strips in a ratio of 2: 3: 5 How long is the longest piece How much longer is the longest piece than the shortest one?
Over several months, a meteorologist recorded a total snowfall of 8.6 centimeters. During this period, the average monthly snowfall was 4.3 centimeters. For how many months did the meteorologist collect measurements of the snowfalls?
you have to find the volume of this figure
A triangular prism and two nets are shown:
Which is the correct net of the prism and what is the surface area of the prism?
The correct net of the prism is net A and the surface area of the prism is 510 square inches
How to determine the surface areaTo calculate the area of the triangular prism, we make use of the net A
Start by calculating the area of the rectangle.
The dimension of the rectangle is (5 + 12 + 13) by 15
So, the area of the rectangle is:
[tex]Area = (5 + 12 + 13) * 15[/tex]
[tex]Area = 450[/tex]
Next, calculate the area of the two congruent triangles of base 5 and height 12
[tex]Area = 2 * 0.5 * (5 * 12)[/tex]
[tex]Area = 60[/tex]
Sum both areas
[tex]Total = 450 + 60[/tex]
[tex]Total = 510[/tex]
Hence, the surface area of the prism is 510 square inches
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rename each mixed number as an equivalent mixed number with the same denominator. 4 6/9= 7 5/3= 3 7/8= 5 19/14=
To rename mixed numbers with the same denominator, we simplify the fractions where the numerator is larger than the denominator by dividing the numerator by the denominator and expressing the remainder as a fraction. The simplified mixed numbers for the examples are 4 6/9, 8 2/3, 3 7/8, 6 5/14.
Explanation:Renaming Mixed Numbers To Have The Same DenominatorTo rename each mixed number as an equivalent mixed number with the same denominator, you first must understand that the denominator is the bottom number in a fraction. To make two fractions have the same denominator, you need to find the least common denominator (LCD). The LCD is the least common multiple of the two denominators.
Let's walk through on how this works for the provided numbers:
4 6/9: The fraction here is already simplified. So, it remains the same, i.e., 4 6/97 5/3: Here, the numerator is larger than the denominator. So, we simplify the fraction 5/3 by dividing 5 by 3 which gives 1 remainder 2. So, it becomes 7 1/3 + 2/3 and further simplifies to 8 2/3.3 7/8: The fraction here is already simplified. So, it remains the same, i.e., 3 7/85 19/14: Here, the numerator is larger than the denominator. So, we simplify the fraction 19/14 by dividing 19 by 14 which gives 1 remainder 5. So, it becomes 5 1/14 + 5/14 and further simplifies to 6 5/14.So, the mixed numbers with the same denominator are 4 6/9, 8 2/3, 3 7/8, 6 5/14.
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Rectangle???ABCD has vertices A(8, 5) , B(8, 10) , C(14, 10) , and D(14, 5) . A dilation with a scale factor of 1.2 and centered at the origin is applied to the rectangle. Which vertex in the dilated image has coordinates of (9.6, 6) ?
A???
B???
C???
D???
A (8, 5)
hope this helps!
Show 39c in two ways
which names the opposite and absolute value of 12
-1/5 of a number is n is at least 17
The image on a movie poster was shrunk to make the DVD cover art for the movie, so that the cover art is a scale image of the poster. The poster is 36 inches wide, and the DVD cover art is 6 inches wide. If the diagonal of the poster is 4 feet, what is the diagonal of the DVD cover art?
Gabe filled 5 glasses of the same size with ice tea from a full 64-ounce pitcher. There were 3 ounces left in the pitcher. Which equation and solution give the number of ounces, s, in each glass?
Answer:
The number of ounces in each glass is [tex]12.2\ ounces[/tex]
Step-by-step explanation:
Let
s-------> the number of ounces in each glass
we know that
To get the number of ounces in each glass, subtract the amount of tea left in the pitcher from the total amount of tea and divide the result by the number of glasses.
so
The equation that represent the situation is
[tex]s=(64-3)/5[/tex]
[tex]s=(61)/5=12.2\ ounces[/tex]
Answer:
Step-by-step explanation:
Approximate the length of the diagonal of the square to the nearest tenth. the square sides are 6
Semi annually means how many times a year?
Elmo buckets made 54 out of 80 free throw .What percent did he miss
Answer:
67.50%
Step-by-step explanation:
We can prove that the answer is correct by taking 67.50 percent of 80 to get 54:
(80 x 67.50)/100 = 54
Note that our calculator rounds the answers up to two decimals if necessary. Once again, the answer is as follows:
67.50%
{(6,-6), (7, -6), (8, -6), (9,-6)}
EXPLAIN whether or not the following relations is a function.
a bottle of hand lotion is on sale for $2.25 . If this price represents a 50% discount from the original price , what is the original price to the nearest cent ?
Answer:
$4.50
Step-by-step explanation:
Since there is a 50 % discount on the price, the new price is 100 % − 50 % = 50 % of the original price.
Let the original price be x . Then we have:
x ⋅ 50 % = $ 2.25
x ⋅ 1 2 = $ 2.25
x = $ 2.25 ⋅ 2 =
$ 4.50
So, the bottle of hand lotion's original price was $ 4.50 .
1.2 decreased by 40%
An economy package of cups has 200 green cups. If the green cups are 10% of the total package, how many cups are in the package?
Final answer:
Set up a proportion where 10% of the total number of cups equals 200 green cups, then calculate to find that there are 2000 cups in the entire package.
Explanation:
To find the total number of cups in the package when 200 green cups represent 10% of the total, we can set up a simple proportion. Here, 10% corresponds to the number of green cups we know about. We need to find 100% to discover the total number of cups in the package.
The proportion we'll set up is:
10% / 200 cups = 100% / x cups
To solve for x (the total number of cups), we will divide 200 cups by 10% to find the value of 1% and then multiply by 100%:
1% of total = 200 cups / 10
x (total cups) = (200 cups / 10) × 100
Perform the calculation:
x = 20 cups × 100
x = 2000 cups
So, there are 2000 cups in the total package.
What’s the answer? Thank You
Ravi is driving 440 miles to visit his grandma. He drives at a rate of 55 miles per hour. How many hours will it take him to get 34 of the way there?
Answer:
The answer is 6 hours
Step-by-step explanation:
;)
Explain how the scale factor is calculated and how the numerical value of the scale factor differs for enlargements and reductions.
Answer: The scale factor is the ratio of the scale figure dimensions to the original dimensions. The scale factor for an enlargement is a number greater than 1. The scale factor for a reduction is a decimal or fraction between 0 and 1.
HOPE THIS HELPS!!!!
Answer:
According to the scale factor, the original dimensions are smaller than the scaled figures. An enlargement's scale factor is a number greater than one. A reduction's scale factor is a decimal or fraction between 0 and 1.
Step-by-step explanation: changed up the sample answer ^^