The twenty-six coins are all dollars and quarters, and they add up to seventeen dollars in value. How many dollars and how many quarters are there?

Answer:

The discount is 4584.375 p.

Step-by-step explanation:

Given :  The oil tank can take up to 1200 litre of oil. There are already 450 litres of oil in the tank.

The price of oil is 81.5p per litre . As a loyal customer, Mr Leonard gets a 7.5% discount on the price of the oil.

To find : How much discount does Mr Leonard get on this purchase?

Solution :

First we find out the number of litre required in the tank

Total capacity of tank = 1200 litre of oil

There are already 450 litres of oil in the tank.

The required oil is = 1200 L – 450 L = 750 L

The price of oil is 81.5 p per litre.

i.e, 1 liter oil price is = 81.5 p

For 750 liter oil price is = [tex]81.5\times 750=61125p[/tex]

There is 7.5% discount on the price of oil.

i.e, [tex]61125\times\frac{7.5}{100}=4584.375[/tex]

The discount is 4584.375 p.

The discount Mr Leonard receives on his purchase is  £45.84.

A discount is a reduction in the price of a good or service. After a discount, the price of an item becomes cheaper.

Quantity of oil that would be bought = capacity of the oil tank - oil already in the tank

1200 - 450 = 750 liters

Total cost of the 750 liters = total liters to be bought x cost per liter

750 x 81.5 = 61,125 p =£611.25

Value of the discount = 7.7% x £611.25 = £45.84

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Answer: Using the graph to find the solution of the given equation, the solutions are:

Option A.) -4 and 2

Solution:

The solutions in the graph are the values of "x" where the curves intercept. In this case the curves intercept at x=-4 and at x=2, then the solution of the equation are -4 and 2

Adding and subtracting decimals are easy to understand you are just adding a decimal point

For example, 2 plus 2 equals 4

2.0 plus 2.0 equals 4.0

To create the ideal blend, the merchant should combine 40 pounds of coffee worth $3.00 per pound and 160 pounds of coffee worth $3.25 per pound.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Let's call the amount of coffee worth $3.00 per pound "x" and the amount of coffee worth $3.25 per pound "y".

We know that the total amount of coffee is 200 pounds, so we can write the equation:

x + y = 200

We also know that the total cost of the coffee is $3.20 per pound times 200 pounds, or $640. So we can write another equation based on the cost:

3.00x + 3.25y = 640

Now we have two equations with two variables, so we can solve for x and y.

Let's start by solving for x in the first equation:

x + y = 200

x = 200 - y

Now we can substitute this expression for x into the second equation:

3.00x + 3.25y = 640

3.00(200 - y) + 3.25y = 640

600 - 3.00y + 3.25y = 640

0.25y = 40

y = 160

So we know that the merchant needs to use 160 pounds of coffee worth $3.25 per pound.

We can use the first equation to solve for x:

x + y = 200

x = 40

So the merchant needs to use 40 pounds of coffee worth $3.00 per pound.

Therefore, the merchant should use 40 pounds of coffee worth $3.00 per pound and 160 pounds of coffee worth $3.25 per pound to make the desired blend.

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Answer:

The answer is option A : 4 gallons.

Step-by-step explanation:

A recipe for 10 servings of raspberry sorbet calls for 2 cups of water, 1/1.2 cups of granulated sugar, and 4 cups of frozen raspberries.

Now 10 servings need = 2 cups of water.

And 320 servings will need = [tex]\frac{2}{10}\times320= 64[/tex] cups of water.

Now, 1 cup = 0.0625 gallons

So, 64 cups are = [tex]0.0625\times64=4[/tex] gallons

Therefore, answer is option A : 4 gallons.

The expression shows the difference in the lengths of the posters will be  0.85 - ( 1 - 0.55). The correct option is A.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Amanda's poster is 0.85 meters long. Orlando's poster is 0.55 meters less than 1 meter long.

Amanda's poster = 0.85 meters long

Orlando's poster = 0.55 meter less than 1 meter long: 1 meter - 0.55 meter = 0.45 meter

Orlando's poster = 0.85 - (1 - 0.55)

Therefore, the expression shows the difference in the lengths of the posters will be  0.85 - ( 1 - 0.55). The correct option is A.

The complete options are given below:-

A.0.85 - ( 1 - 0.55).

B. -0.85 + ( 1 - 0.55).

C. -0.85 - ( 1 - 0.55).

D. 0.85 + ( 1 - 0.55).

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The difference in lengths of the posters is 0.40 meters, calculated as [tex]\( |1 - 0.55 - 0.85| = 0.40 \)[/tex].

Step 1:

Find the length of Orlando's poster:

Orlando's poster is 0.55 meters less than 1 meter. Subtract 0.55 meters from 1 meter.

[tex]\[ \text{Length of Orlando's poster} = 1 - 0.55 \][/tex]

Step 2:

Calculate the difference in lengths:

Subtract the length of Amanda's poster (0.85 meters) from the length of Orlando's poster obtained in step 1.

[tex]\[ \text{Difference in lengths} = \text{Length of Orlando's poster} - \text{Length of Amanda's poster} \][/tex]

Step 3:

Perform the calculation:

[tex]\[ \text{Difference in lengths} = (1 - 0.55) - 0.85 \][/tex]

Step 4:

Simplify the expression:

[tex]\[ \text{Difference in lengths} = 0.45 - 0.85 \][/tex]

[tex]\[ \text{Difference in lengths} = -0.40 \][/tex]

Step 5:

Since negative length doesn't make sense, take the absolute value:

[tex]\[ \text{Difference in lengths} = |-0.40| = 0.40 \][/tex]

Step 6:

Conclusion:

The difference in lengths of the posters is 0.40 meters.

A vertical number line resembles a thermometer. It emphasizes that we count up in the number system.  Vertical number lines are just alternative way to look at the numbers.

This is commonly used in adding or subtracting

For example: 5 – 3

5 is the start, the sign determines whether you go down or go up, the minus sign denotes down then so the last number denotes how many steps you are going down where you land is the answer. The same goes with addition but instead of down, the plus sign denotes going up.

Answer:

The y-intercept means that Karma was given $60 for her birthday. Therefore, option C is the correct answer.

The given equation that models the given situation is y=75x+60.

The y-intercept of a graph is the point where the graph intersects the y-axis.

We know that the x-coordinate of any point on the y-axis is 0. So the x-coordinate of a y-intercept is 0.

Now, Graph the line using the slope and y-intercept, or two points.

Slope: 75

y-intercept: (0, 60)

The coordinates to plot the graph is (0, 60) and (1, 135).

Here, in the graph, if we then look at the y-intercept we can see that the function crosses the y-axis at a value of 60.

Therefore we can safely say that the y-intercept means that Karma was given $60 for her birthday.

The y-intercept means that Karma was given $60 for her birthday.

Therefore, option C is the correct answer.

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The pitcher shown has a height of 10 inches and a volume of 64 oz. The pitcher has a shape of cylinder and the volume formula of cylinder is:

V = π r^2 h

So given volume and height, we can find for the radius:

64  = π r^2 (10)

r = 1.427

So for a 47 oz volume is poured out, what remains is:

V remain = 64 oz – 47 oz = 17 oz

So the height at a volume of 17 oz is:

17 = π (1.472)^2 h

h = 2.66 inches

To determine a function rule between the height of the juice and the amount poured out, we need additional specifics such as initial height and pitcher capacity. Without this, we cannot define the exact function or determine the juice height after pouring out 47 ounces.

To write a function rule that represents the relationship between the height of juice h in the pitcher and the amount of juice j poured out, we need additional information about the initial height of the juice when the pitcher is full and its capacity. Without this information, we cannot construct an exact function. Generally, if 'H' is the initial height and 'C' is the capacity of the pitcher in ounces, then the function could look something like h = H - (k x j), where 'k' is a constant that converts ounces to inches based on the shape of the pitcher.

Regarding the second part of the question, without a specific function or more information about the pitcher, we cannot determine the height of the juice after 47 ounces have been poured out.

The product of 7⋅(−4)⋅(−6) from the information illustrated is D. 168.

It should be noted that the product of a number simply means the multiplication of the numbers that are given.

This is quite a straightforward question. The product will be:

= 7⋅(−4)⋅(−6)

It should be noted that (-) × (-) = +

Therefore, 7⋅(−4)⋅(−6)

= 7 × 4 × 6

= 168

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The Standard form of number is,

⇒ 0.1588

We have to give that,

Scientific notation is,

⇒ 1.588 × 10⁻¹

Since Scientific notation is a way of writing very large or very small numbers.

For example; 230,000,000 can be written in scientific notation as

2.3 x 10⁸.

Hence, the Standard form of number is,

⇒ 1.588 × 10⁻¹

⇒ 1.588 / 10

⇒ 0.1588

Therefore, The solution is, 0.1588

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