The price of a liter of milk increased 10% compared with last year . If the new price is $1.21 per liter , what was last years price?

Answer:

i) 24 - x

ii) 5x + 120

Step-by-step explanation:

i) There are a total of 24 coins. We see that x of these 24 are 10 cent coins. The rest must be 5 cent coins, so they must be all the 24 coins that are NOT included in the x: 24 - x

ii) We know that there are x 10 cent coins, which are each 10 cents. There are also (24 - x) 5 cent coins, which are each 5 cents. In order to find their total value, we need to multiply the value of the denomination by how many there are of each denomination. So:

10x + 5(24 - x) = 10x + 120 - 5x = 5x + 120

Hope this helps!

Answer:

true

Step-by-step explanation:

Answer:

True is the answer

Step-by-step explanation:

got it correct on my quiz

Answer:

Step-by-step explanation:

x4 + 4x² – 45 = x^4 + 4x^2 - 45.  Use " ^ " to indicate exponentiation.

Temporarily substitute p for x^2.  Then we have:

p^2 + 4p - 45, or

(p + 9)(p - 5)

But p = x^2.

Therefore, our expression becomes

(x^2 + 9)(x^2 - 5)

We could stop here or we could factor further.  

Hint:  x^2 - 5 = (x - √5)(x + √5); (x^2 + 9) factors into imaginary roots.

Answer:

(4x + 5)(4x - 3)

Step-by-step explanation:

Given

16x² + 8x - 15

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 16 × - 15 = - 240 and sum = + 8

The factors are + 20 and - 12

Use these factors to split the x- term

16x² + 20x - 12x - 15 ( factor the first/second and third/fourth terms )

= 4x(4x + 5) - 3(4x + 5) ← factor out (4x + 5) from each term

= (4x + 5)(4x - 3) ← in factored form

Answer:

Step-by-step explanation:

In an arithmetic sequence, the consecutive terms differ by a common difference, d. Therefore,

d = Term 2 - Term 1 = Term 3 - Term 2

In an geometric sequence, the consecutive terms differ by a common difference, r. Therefore,

r = Term 2 /Term 1 = Term 3 / Term 2

1) 128, 32, 8, 2, .. Is a geometric sequence

r = 32/128 = 1/4

2) 1, 3, 9, 27, .. Is a geometric sequence

r = 3/1 = 3

3) 5, 10, 15, 20, ...is an arithmetic sequence

d = 10 - 5 = 5

4) 20, 17, 14, 11, … is an arithmetic sequence

d = 17 - 20 = - 3

Answer:

Sacing 490 spending 420

Step-by-step explanation:

If a is a fraction

Saving 7a Spending 6a

7a + 6a = 910

13a = 910

a = 910/13

a = 70

Saving 7×70 = 490

Spending 6×70 = 420

The sum is 490 + 420 is equal to 910

Answer:

the answer is 5b^3+8

Step-by-step explanation:

To subtract (5b^3 +9b+4)−(9b−4) in standard form, distribute the negative sign, combine like terms, and simplify the expression.

To subtract (5b^3 +9b+4)−(9b−4) in standard form, we need to remove the parentheses and combine like terms. Distribute the negative sign to both terms in the second parentheses, which changes the sign of each term inside.

This gives us 5b^3 + 9b + 4 - 9b + 4.

Combining like terms, we have 5b^3 + 4b + 8.

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The median of this data set is 133.5, the first quartile (Q₁) is 128, the third quartile (Q₃) is 139, and the interquartile range (IQR) is 11.

First, arrange the data in ascending order: 106, 127, 129, 132, 135, 138, 140, 158.

Median: The median is the middle value of a data set. Since there are 8 numbers, the median is the average of the 4th and 5th values: (132+135) ÷ 2 = 133.5.

First Quartile (Q₁): This is the median of the lower half of the data. Here, it is the average of the 2nd and 3rd values: (127+129) ÷ 2 = 128.

Third Quartile (Q₃): This is the median of the upper half of the data, which is the average of the 6th and 7th values: (138+140) ÷ 2 = 139.

Interquartile Range (IQR): You find the IQR by subtracting Q₁ from Q₃, hence IQR = 139 - 128 = 11. The IQR represents the middle 50% of the values when ordered from lowest to highest.

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Answer: $193.98

Step-by-step explanation:

$168 + $10 + $5 = $183

$183 x 6% = $10.98

$183 + $10.98 = $193.98

To find the sales tax and total price for purchasing these items, calculate the sales tax by multiplying the total cost of the items by the sales tax rate, and then add the sales tax to the total cost of the items.

To find the sales tax and total price for purchasing these items, we need to calculate the amount of sales tax and then add it to the total cost of the items.

Therefore, the sales tax is $11 and the total price for purchasing these items is $194.

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Answer:

y = 9x-3

Step-by-step explanation:

since the slope intercept form is in the y=mx+b form, you just have to plug in the slope for m and the y-intercept for b.

Answer:

[tex]60.2 + 124.6 = 184.8 \: calories[/tex]

The total number of calories in this breakfast is 184.8 calories if there are 86 calories in 100g of banana and there are 89 calories in 100g of yogurt.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

There are 86 calories in 100g of banana.

In 1 g = 0.86 calories

In 70 g

= 0.86×70 = 60.2 calories

There are 89 calories in 100g of yogurt.

1g = 0.89 calories

In 140g yogurt:

= 140×0.89

= 124.6 calories

Total calories = 60.2 + 124.6 = 184.8 calories

Thus, the total number of calories in this breakfast is 184.8 calories if there are 86 calories in 100g of banana and there are 89 calories in 100g of yogurt.

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Answer:

60 km/hour

Step-by-step explanation:

To find the speed, divide the number of kilometers by the number of hours

kilometers/hours

120 km/ 2 hours

120/2=60

60 km/hour

The speed of the bus is 60 kilometers per hour

Answer:

60km/hr

Step-by-step explanation:

120 divided by 2 equals 60

Answer:

See below.

Step-by-step explanation:

1. a and b are supplementary ( they add up to 180 degrees as they are on a straight line).

2,3 and 4 are complementary as in each case a + b = 90 degrees.

Answer:

Complementary angles are the angles which add up to 90°. example - 60° + 30° = 90° . Supplementary angles are those angles which add up to 180° . example - 110° + 70° = 180°.

Step-by-step explanation:

Without additional details about the triangle's angles or side lengths, it cannot be determined whether △KLM is a right triangle.

Based on the information given in your question, it is impossible to definitively state whether Seraphina is correct in her assertion that △KLM is a right triangle. Checking if a triangle is a right triangle typically involves measuring its angles or applying the Pythagorean theorem to its sides. However, there is insufficient information in your question to do either. For instance, you mentioned a '16 cm' measurement but did not specify to which side it corresponds. Similarly, no angles are provided. Thus, without additional information, the claim that △KLM is a right triangle cannot be confirmed or refuted.

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Answer:

Ratio of perimeters = 5:2

Ratio of areas: 25:4

Step-by-step explanation:

20/8 = 5/2 (ratio of lengths is equal to ratio of perimeters)

[tex](5/4) ^{2}[/tex] = 25/4 (ratio of areas is the square of ratio of lengths)

Answer:

106°

Step-by-step explanation:

(152 + 60)/2

212/2

106°

Answer: [tex]720[/tex]

Multiply

60%×1200=720

Note: When finding the percent of a number always multiply the percent times the number.

Answer:

[tex]720[/tex]

Step-by-step explanation:

[tex]1200 \times \frac{60}{100} \\ = \frac{72000}{100} \\ = 720[/tex]

hope this helps you...

Answer:

32901 gallons

Step-by-step explanation:

First, we find the volume of the cylindrical water tank when it is full.

The volume of a cylinder is given as:

V = [tex]\pi r^2h[/tex]

where r = radius and h = height of the cylinder

The diameter of the tank is 20 feet, hence, its radius is 10 feet.

Volume, V, is therefore:

V = [tex]\pi * 10^2*20 = 6283.19 ft^3[/tex]

This is the volume of the tank, when it is full.

When it is 70% full, the volume will be:

[tex]\frac{70}{100} * 6283.19 = 4398.23 ft^3[/tex]

1 cubic foot ([tex]ft^3[/tex]) is 7.48 gallons.

Therefore, the volume of the 70% full tank in gallons will be:

4398.23 * 7.48 = 32901.05 gallons ≅ 32901 gallons

The tank contains 32901 gallons of water.

Answer:

32886.476 gal

Step-by-step explanation:

Given:

Diameter of tank 'd'= 20 ft

∴radius 'r'= d/2=> 20/2=> 10ft

Height 'h' = 20 ft

Volume of cylinder can be determined by

V= π r² h

Substituting the values in above equation

V= π (10)² (20) =>π(100)(20)

V=2000π ft³

When the tank is 70% full.

70% of 2000π =>0.7 x 2000π

1400π ft³

As we know that, 1ft³ = 7.481 gal

1400π ft³= 1400π x 7.481 gal

1400π ft³= 32886.476 gal

Therefore, if the tank is 70% full then 32886.476 gallons of water are in the tank

Answer:

3 metres

Step-by-step explanation:

Work done = Force × displacement

60= 20×d

d= 60/20

d= 3 metres

Uisng the relationship between force, work and distance, the distance moved by the object would be 3 meters

Given the Parameters :

Recall :

Substituting the values into the formula :

60 = 20 × Distance

Distance = 60 / 20

Distance = 3

Therefore, the object moves a distance of 3 meters

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The correct matches are as follows:

Formula | Text

I. A equals the product of B or H, divided by 2. | Incorrect

II. A equals the product of B times H, divided by 2. | Correct

III. D equals P sub T plus the quantity 2 times T, divided by 3. | Correct

IV. D equals P sub T times the quantity 2 times T, divided by 3. | Incorrect

V. R sub T equals R sub 1 plus R sub 2. | Correct

VI. R sub T equals R sub 1 plus the sum R sub 2. | Incorrect

Here is a more detailed explanation of each match:

II. A equals the product of B times H, divided by 2.

This formula is correct for the area of a triangle, where A is the area, B is the base, and H is the height.

III. D equals P sub T plus the quantity 2 times T, divided by 3.

This formula is correct for the average distance traveled, where D is the total distance traveled, P sub T is the starting point, and T is the time taken.

V. R sub T equals R sub 1 plus R sub 2.

This formula is correct for the total resistance in a parallel circuit, where R sub T is the total resistance, and R sub 1 and R sub 2 are the resistances of the two parallel resistors.

The other formulas are incorrect. For example, formula I states that A is equal to the product of B or H, divided by 2. This is not correct, because A cannot be equal to two different things at the same time. Formula IV is incorrect because it states that D is equal to P sub T times the quantity 2 times T, divided by 3.

This is not correct, because the average distance traveled cannot be equal to the starting point multiplied by the time taken. Formula VI is incorrect because it states that R sub T is equal to R sub 1 plus the sum R sub 2.

This is not correct, because the total resistance in a parallel circuit cannot be equal to the sum of the resistances of the two parallel resistors.

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Answer:

its D 100%

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

photomath said 375m³n³

Step-by-step explanation:

-use exponent rules  3×(5mn)³

- calculate the product  3×125m³n³

-Solution 375m³n³

Answer:

Yes, the Pie Graph is the right choice.

Step-by-step explanation:

A Pie Graph, or Sector Graph is one of the good options to display, usually relative frequencies, proportionally.

In a Pie Graph the focus is to show the importance of each observation, or category in comparison with the whole.

You need to be careful with the angles, since 180º is equal to 50%, 90º to 25% and 360º is equal to 100% so each "slice" each portion must directly proportional to the angles of one circle.

Since the goal is to show the importance of each work to the whole team, definitely a Pie Graph is one the appropriate one to pick.

Answer:

The correct option is option C.

The width of the rectangular playground is  [tex]-8+8\sqrt5[/tex] ft.

Step-by-step explanation:

Area of rectangular plot is = length × wide.

Given that,

The ratio of longer length to the width of the rectangular playground is

(1+√5): 2

Let the length and width of the rectangular playground be (1+√5)x and 2x.

But the length of the longer side of the rectangular playground is = 16 feet.

According to the problem,

(1+√5)x= 16

[tex]\Rightarrow x= \frac{16}{1+\sqrt5}[/tex]

[tex]\Rightarrow x= \frac{16(1-\sqrt 5)}{(1+\sqrt5)(1-\sqrt 5)}[/tex]             [ rationalize]

[tex]\Rightarrow x= \frac{16(1-\sqrt 5)}{(1)^2-(\sqrt5)^2}[/tex]                 [ (a+b)(a-b)=a²-b²]

[tex]\Rightarrow x= \frac{16(1-\sqrt 5)}{1-5}[/tex]

[tex]\Rightarrow x= \frac{16(1-\sqrt 5)}{-4}[/tex]

[tex]\Rightarrow x=-4(1-\sqrt 5)}[/tex]

[tex]\Rightarrow x=-4+4\sqrt 5[/tex]

Then the width of the playground is = 2x

                                                            [tex]=2(-4+4\sqrt5)[/tex] ft

                                                            [tex]=-8+8\sqrt5[/tex] ft

Answer:

-11/72

Step-by-step explanation:

5/12+-5/18-7/24​

We need to get a common denominator of 72

5/12 *6/6 =30/72

5/18 * 4/4 = 20/72

7/24 *3/3 = 21/72

30/72 -20/72 - 21/72

10/72 -21/72

-11/72

Answer:  

Similarities: All the trigonometric functions are periodic functions. All these trigonometric function values can be found by using special right triangles from the unit circle.   Diffferences: The tangent has different domain and range values from sine and cosine. The tangent function is not a continuous function, unlike sine and cosine.

Step-by-step explanation:

The similarities and differences between the sine, cosine, and tangent ratios are given.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The sine, cosine, and tangent are three trigonometric ratios used in geometry to relate the angles of a right triangle to the lengths of its sides.

Similarities:

All three ratios involve comparing two sides of a right triangle to each other.

They are all functions of an angle and are dependent on the measure of the angle and not the size of the triangle.

They are all defined as ratios of two sides of a right triangle, and the values of these ratios depend on the angle in question.

Differences:

The sine and cosine ratios are periodic functions with a period of 2π, while the tangent ratio is not periodic, and its graph has vertical asymptotes.

The sine and cosine ratios are always between -1 and 1, while the tangent ratio can take any value, positive or negative.

The cosine of an angle is equal to the sine of its complement, while the tangent of an angle is equal to the sine of the angle divided by the cosine of the angle.

Hence, the similarities and differences between the sine, cosine, and tangent ratios are given.

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The probability that a randomly selected day of the year is in December or January is [tex]\( \frac{62}{365} \)[/tex].

To find the probability that a randomly selected day of the year is in December or January, we need to consider the total number of days in December and January and divide it by the total number of days in a year.

December has 31 days.

January also has 31 days.

A non-leap year has 365 days, and a leap year has 366 days.

Assuming we're considering a non-leap year for simplicity, the total number of days in a year is 365.

Now, let's calculate the probability:

Probability = [tex]\frac{\text{Number of days in December} \ + \ \text{Number of days in January}}{\text{Total number of days in a year}}[/tex]

Probability = [tex]\frac{31 + 31}{365}[/tex]

Probability = [tex]\frac{62}{365}[/tex]

Now, we can simplify this fraction if needed, but to keep it in the most accurate form, we can leave it as [tex]\( \frac{62}{365}[/tex].

Answer:

gradient = 4

Step-by-step explanation:

Calculate the gradient m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, 3) and (x₂, y₂ ) = (5, 7)

m = [tex]\frac{7-3}{5-4}[/tex] = 4

The gradient of the line segment between the points (4,3) and (5,7) is 4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The gradient of the line is also called as slope of line

Gradient of the line segment between the points (4,3) and (5,7)

Gradient = 7-3/5-4

=4/1

Hence,  the gradient of the line segment between the points (4,3) and (5,7) is 4

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