find 1/2 and 2/3 on the number line​

The point after 30, 000 km will they first have to change the oil, rotate the tires and replace the wiper blades all at once.

Arithmetic Progression (AP) is a numerical series in which the difference between any two consecutive numbers is a constant value. Arithmetic Sequence is another name for it.

The First term is an "oil change" with a step d = 3000 km;

and, the second term is tire rotation = 10, 000 Km

and, the third term is replacement of wiper blades = 15, 000 Km

Now, we know from the formula of Arithmetic Progression is

[tex]a_n[/tex] = [tex]a_1[/tex]+ d(n-1)

So, 15,000 = 10,000 + 10,000 (n-1)

15, 000 = 10,000 + 10, 000n- 10,000

150000 = 10000n

n = 1.5

This means that at the point 15 000 km and all three progressions will not intersect.

Now, We take the second term of the progression as [tex]a_n[/tex] = 30,000 km

So, 30,000 = 10,000 + 10,000 (n-1)

20,000 = 10,000n - 10,000

30, 000 = 10,000n

n= 3

Similarly, check this intersection point for the first progression with a step of d = 3 000 km we get n =9.

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Answer:

6 chairs per table

Step-by-step explanation:

We know

36 chairs at 6 tables. Find the unit rate.

36 / 6 = 6 chairs per table

So, the answer is 6 chairs per table.

Given:-

To find:-

Solution:-

Since 1 pound has 16ounches we need to find the number of calories for 16 ounches.

Here we can use the Unitary Method to find the number of calories as ,

In 9ounces there are 576 calories.

In 1 ounce there will be 576/9 calories

In 16 ounce there will be 576/9 * 16 = 1024 calories .

Hence there are 1024 calories in 1 pound of icecream.

and we are done!

The dimensions of triangle are 1m 60cm, 1m 80cm and 2m. Therefore, the perimeter of Triangle is 540 cm.

Perimeter of Triangle:

The perimeter of a triangle is the sum of the three sides. The word circumference is a combination of two Greek words - "peri" meaning around and "matron" meaning measure. The total distance around any two-dimensional shape is defined as its perimeter. Since the perimeter gives the length of the boundary of the shape, it is expressed in linear units.

According to the Question:

We know:

1 m = 100 cm

1 m 60 cm = 100 + 60 = 160 cm

1 m 80 cm = 100 + 80 = 180 cm

2m = 200 cm

Therefore,

Perimeter = (a + b + c) cm

Perimeter of triangle = 160 + 180 + 200

                                   = 540 cm

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Answer: 9:20:5

Step-by-step explanation:

Answer:

45:100:25

9:25:5

9:5:1

Answer:

A. S(n) = $25,000 + $6,000n

B. S(8) = $73,000

Step-by-step explanation:

A. The equation for S(n), the amount of sales, in years, of the sports injury products in n years is:

S(n) = $25,000 + $6,000n

Where n is the number of years after the first year.

B. To find S(8), we substitute n = 8 into the equation above:

S(8) = $25,000 + $6,000(8)

S(8) = $73,000

Therefore, the amount of sales of sports injury products in 8 years is $73,000.

Answer:

The function g(x)=x^2+x-20 can be expanded as follows:

g(x) = x^2 + x - 20

= x^2 + 5x - 4x - 20

= x(x + 5) - 4(x + 5)

= (x - 4)(x + 5)

Therefore, the equivalent function to g(x)=x^2+x-20 after expansion is f(x) = (x - 4)(x + 5).

Step-by-step explanation:

Answer:

g(x) = (x - 4) (x + 5)

Step-by-step explanation:

Consider the form x² + bx +c. Find a pair of integers whose product is c

and whose sum is b. In this case, whose product is −20 and whose sum is 1.

-4, 5 matches this requirement of the AC method.

Write the factored form using these integers.

(x - 4) (x + 5)

So, the answer is g(x) = (x - 4) (x + 5)

Answer:

56 degrees

Step-by-step explanation:

The foul lines intersect at a 90 degree angle, and we want to find the angle between 34 degrees from the left foul line and the right foul line

90 - 34 = 56

The errors mentioned in the question can affect the calculated values of the molar mass from the boiling-point elevation method in the following ways:

a. If a small amount of unknown adheres to the inside of the test tube and did not get dissolved in the cyclohexane, it would result in a lower calculated value of the molar mass. This is because the amount of unknown dissolved in the cyclohexane would be less than the actual amount, leading to a lower boiling-point elevation and therefore a lower calculated value of the molar mass.

b. If some solvent is lost by volatilization, it would result in a higher calculated value of the molar mass. This is because the loss of solvent would lead to a higher concentration of the unknown in the cyclohexane, leading to a higher boiling-point elevation and therefore a higher calculated value of the molar mass.

c. If the thermometer used in the experiment was miscalibrated to read 0.5°C lower than the actual temperature over its entire scale, it would result in a lower calculated value of the molar mass. This is because the boiling-point elevation would be underestimated due to the lower temperature reading, leading to a lower calculated value of the molar mass.

In conclusion, the errors mentioned in the question can affect the calculated values of the molar mass from the boiling-point elevation method, leading to either higher or lower values depending on the specific error. It is important to be aware of these errors and take steps to minimize them in order to obtain accurate results in the experiment.

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Therefore , the solution of the given problem of area comes out to be  15 square units.

How much space it occupies on the surface is a reliable indication of its overall dimensions. The nearby surroundings are considered when calculating a triangular shape's surface. Something's total dimensions are determined by its surface area. The total of the capacities for each of a cuboid's six rectangular sides makes up its internal water capacity. To calculate the size of the box, use the following method.

Here,

We must measure the lengths of the sides of the polygon and sum them up to determine its perimeter.

The length of each edge can be determined using the distance formula:

=> CD = √((2 - 2)² + (1 - 4)²) = √(9) = 3

=>  DE = √(7 - 2)² + (4 - 4)²) = 5

=>  EF = √((7 - 7)² + (1 - 4)²) = 3

=>  FC = √(7 - 2)² + (1 - 1)²) = 5

As a result, the boundary is:

CD = DE + EF + EF + FC = 3 + 5 + 3 + 5 = 16

Area of CDE = 1/2*base*height*1/2*DE*CD =1/2*5*3*area of CDE, which equals 7.5.

Area of CEF = 1/2*3*5=7.5

Consequently, the polygon's size is:

Size = CDE + CEF combined, which equals 7.5 + 7.5 = 15 square units.

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Answer: In mathematics, a function is a rule that assigns each element of a set (called the domain) to a unique element in another set (called the range). The range of a function is the set of all possible output values of the function.

The range of a function can be determined by analyzing the behavior of the function as its input values change. For example, a linear function like f(x) = -3x + 4 has a slope of -3, which means that as x increases, the value of -3x decreases. This in turn means that the value of f(x) decreases as x increases.

Another important consideration in determining the range of a function is the domain of the function. The domain is the set of all possible input values of the function. If the domain is limited in some way (for example, if the function is only defined for non-negative values of x), then the range will also be limited.

In the case of f(x) = -3x + 4, the domain is all real numbers, so the range is also all real numbers. In other words, the function can take on any value on the real number line. This can be written in interval notation as (-∞, +∞) or (-∞, ∞).

I hope this explanation helps you understand the concept of the range of a function more deeply.

Step-by-step explanation:

The current ratio is 2.6:1 and the quick ratio is 1.8:1.

To calculate the current ratio, we add up the current assets (cash, cash at bank, accounts receivable, prepayments, and inventory) and divide by the current liabilities (accounts payable, wages payable, and taxes payable).

Current Assets = $2,000 + $20,000 + $5,500 + $1,500 + $10,000 = $39,000

Current Liabilities = $12,000 + $1,500 + $1,500 = $15,000

Current Ratio = Current Assets / Current Liabilities = $39,000 / $15,000 = 2.6:1

To calculate the quick ratio, we use the same formula but only consider the quick assets, which are the current assets minus inventory and prepayments.

Quick Assets = $2,000 + $20,000 + $5,500 = $27,500

Quick Liabilities = $12,000 + $1,500 + $1,500 = $15,000

Quick Ratio = Quick Assets / Quick Liabilities = $27,500 / $15,000 = 1.8:1

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Therefore, it will take the car 25 minutes to travel a distance of 5 miles at a speed of 1/5 mile per minute.

Knowing how far something moves in a certain length of time allows you to calculate an object's speed. If a car travels 70 miles in an hour, for instance, it is going at a speed of 70 miles per hour (miles per hour).

One possible word problem for 5 ÷ 1/5 is:

If a car travels at a speed of 1/5 mile per minute, how many minutes will it take to travel a distance of 5 miles?

To solve this problem, we can use the formula:

time = distance ÷ speed

Plugging in the given values:

time = 5 miles ÷ (1/5 mile per minute)

Simplifying:

time = 5 miles ÷ 1/5 mile per minute = 5 miles × 5 minutes/mile = 25 minutes

Therefore, it will take the car 25 minutes to travel a distance of 5 miles at a speed of 1/5 mile per minute.

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Answer:

Since the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, we can find the range of values for the third side by subtracting the known side lengths from their sum and taking the absolute value of the difference.

For the given triangle with side lengths 35 and 33, the range of values for the third side would be:

|35 - 33| < X < 35 + 33

2 < X < 68

Therefore, the range of values for the third side is 2 to 68.

The expression (6-3i)(3-3i)​ when simplified is 9 - 27i

From the question, we have the following parameters that can be used in our computation:

(6-3i)(3-3i)​

Open the brackets, so we have

(6-3i)(3-3i)​ = 18 - 9i - 18i - 9

Evaluate the like terms

(6-3i)(3-3i)​ = 9 - 27i

Hence, the simplified expression is 9 - 27i

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Step-by-step explanation:

3 root 3 + 6 root 3 + 7/ root 3

= (27 +7)/ root 3

= 34 root 3 / 3

Yes, the given equation AB+ BC= AC is correct for the given condition that three points A, B and C, and B lies between A and C.

The segment addition postulate states that if there are three points A, B, and C, and B is between A and C, then the length of segment AB plus the length of segment BC is equal to the length of segment AC. In other words, which can be written as,

AB + BC = AC

This can be easily visualized by drawing a line segment AC and marking a point B on it such that B is between A and C. Then, we can see that segment AB and segment BC together exactly cover the length of segment AC. The mentioned postulate is a fundamental concept in geometry and is used in many geometric proofs and constructions.

Therefore, the equation AB+ BC= AC is satisfied for the three points A, B, and C , where B lies between A and C.

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The question is :

If there are three points A, B and C, and B is between A and C, then AB+ BC= AC. (the segment addition postulate)

Analyn and John ate a total of 1/8 + 3/8 = 4/8 = 1/2 of the bibingka. So they ate half of the bibingka, or in other words, they ate 50% of the bibingka.

Analyn sliced the bibingka into 8 equal pieces. She ate 1/8 of the bibingka, which means that there are 7/8 left. John ate 3/8 of the remaining bibingka, which means that there are 4/8 or 1/2 of the bibingka left after they both ate. Therefore, the total amount of bibingka that they ate is 1/2 of the whole bibingka.

In terms of percentage, 1/2 can be written as 50%, so they ate 50% of the bibingka.

In this scenario, Analyn sliced the bibingka into 8 equal pieces. She ate 1/8 of the bibingka, which means she ate one of the eight equal pieces. John ate 3/8 of the bibingka, which means he ate three of the eight equal pieces.

To find the total part of the bibingka they ate together, we can add the fractions 1/8 and 3/8. After adding these fractions, we get:

1/8 + 3/8 = 4/8

Simplifying the fraction 4/8, we get:

4/8 = 1/2

Therefore, Analyn and John ate 1/2 of the bibingka together, which means they ate 4 of the 8 equal pieces.

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Answer:

Undefined.

Step-by-step explanation:

slope is the change in y over the change in x.

(-5,8) and (-5,4)

The y values are 4 and 8. You find the change by subtracting.

The x values are -5 and -5.  You find the change by subtracting

[tex]\frac{4-8}{-5--5}[/tex] = [tex]\frac{-4}{-5+ 5}[/tex] = [tex]\frac{-4}{0}[/tex]  we cannot have zero as our denominator, so we say thatthe slope is undefined.  The would be a vertical line, if we graphed it.

An animal shelter has 9 puppies. If the puppies are 36% of the total dog and cat population. There are 27 dogs and cats are in the animal shelter

Now,

Let total number of dog and cat population in animal shelter be x.

As per the statement:

An animal shelter has 27 puppies.

⇒ Total number of puppies = 27

It is also given that if the puppies are 36% of the total dog and cat population.

⇒ 27 = 36/100  × X

By cross multiply we get;

2700 = 36x

Divide both sides by 36 we get;

   x = 2700/36

⇒ x = 75

Therefore, total number of dogs and cat population in animal shelter are 75.

Complete Question:

An animal shelter has 27 puppies. If the puppies are 36% of the total dog and cat population, how many dogs and cats are in the animal shelter?

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Answer:

51

Step-by-step explanation:

ABC is a inscribed angle.

This means ABC is 1/2 of the arc of AC.

[tex] \frac{1}{2} (16x - 26) = 5x + 11[/tex]

[tex]8x - 13 = 5x + 11[/tex]

[tex]3x = 24[/tex]

[tex]x = 8[/tex]

Plug in 8 for 5x+11,

[tex]5(8) + 11 = 51[/tex]

Answer: 1800 degrees

Step-by-step explanation: A Dodecagon consists of 12 sides. The formula for the sum of the interior angles is (n-2)*180. In this case, 12 (number of sides in Dodecagon) is n. (12-2)*180 = 10*180 = 1800.

Answer:

It should be B. The mean of the sampling distribution is 140, but there isn't enough information to determine the standard deviation.

Answer:

9 units

Step-by-step explanation:

6/8 = Enlargement Scale Factor

ESF = 0.75

12*0.75 = AE

AE = 9 units

A cake recipe calls for 4/5 cups of chocolate if a baker has 7/3 cups of chocolate the baker can make a maximum of 2 cakes.

If a cake recipe calls for 4/5 cup of chocolate and the baker has 7/3 cups of chocolate, we can find the maximum number of cakes the baker can make by dividing the total amount of chocolate by the amount of chocolate per cake:

Maximum number of cakes = Total amount of chocolate ÷ Amount of chocolate per cake

Amount of chocolate per cake = 4/5 cup

The total amount of chocolate = 7/3 cups

Therefore, the maximum number of cakes the baker can make is:

Maximum number of cakes = (7/3) ÷ (4/5) = (7/3) × (5/4) = 35/12 ≈ 2.92

Since we can't make a fraction of a cake, the baker can make a maximum of 2 cakes with the available chocolate.

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Answer:

There are 90 3 digit palindromic numbers

There are 90 3-digit numbers that are palindromes.

A 3-digit number is a palindrome if the first and third digits are the same. The middle digit can be any number from 0 to 9.

Therefore, there are 9 choices for the first and third digits (1 to 9) and 10 choices for the middle digit (0 to 9).

So, the total number of 3-digit palindromes is:

9 × 10 = 90

Therefore, there are 90 3-digit numbers that are palindromes.

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The basic divergence test states that if the limit of a series does not equal zero, then the series must diverge.

The sequence of real numbers , where n goes from 1 to infinity has a limit L, the the sequence is convergent to L. If the sequence doesn't have limit then it is divergent.

In the case of the series Cnz1 COS (1/n), we can apply the basic divergence test by taking the limit of the series as n approaches infinity:

lim(n→∞) Cnz1 COS (1/n)

Since the cosine function oscillates between -1 and 1, the limit of the series does not exist. Therefore, by the basic divergence test, we can conclude that the series Cnz1 COS (1/n) diverges.

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If a park is built at the coordinates (12,10) and jim hoping that a park will be built within 5 miles of his house, then the park does not meet his criteria.

To determine whether the park at the given coordinates (12,10) meets Jim's criteria, we need to find the distance between Jim's house and the park. We are told that Jim's house is located at the origin, which is (0,0) on a Cartesian plane.

To calculate the distance between Jim's house and the park, we can use the distance formula, which is:

distance = √((x₂ - x₁)^2 + (y₂ - y₁)^2)

where (x₁,y₁) is the coordinate of Jim's house, and (x₂,y₂) is the coordinate of the park.

Substituting the given coordinates into the formula, we get:

distance = √((12 - 0)^2 + (10 - 0)^2) = √(144 + 100) = √(244) ≈ 15.62

This means that the park is approximately 15.62 miles away from Jim's house. Since this distance is greater than 5 miles, the park does not meet Jim's criteria of being within 5 miles of his house.

In conclusion, the distance formula was used to calculate the distance between Jim's house and the given coordinates of the park. The calculated distance was found to be greater than 5 miles, indicating that the park at the given coordinates does not meet Jim's criteria.

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Complete question is:

Jim is hoping that a park will be built within 5 miles of his house if a park is built at he coordinates (12,10) does that meet jim's criteria. Assume Jim house it at (0,0).

Richard's expenses will decrease by 77.5% in July

A percentage decrease refers to the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.

The total expenses in June is:

= 1311.60+207.63+356.95+75.80+101.88+596.64

= $2,650.50.

When the credit cards is be paid in full after June, the total expenses in July is:

= 2650.5 - 596.64

= $2053.86

The Percentage decrease that is observed on the expenses will be:

= $2053.86/$2650.5 * 100

= 0.77489530277

= 77.50%

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Answer:

The correct answer is 10 units.

To solve this problem, you can use the tangent function, which relates the ratio of the opposite side and the adjacent side of a right triangle.

In this case, the opposite side is 9 units, and the tangent of angle A is 0.45.

Thus, the adjacent side (AB) is equal to 9/0.45, which is equal to 10 units.

Step-by-step explanation:

Identify the given values of the right triangle: the opposite side is 9 units and the tangent of angle A is 0.45.

Use the tangent function to calculate the adjacent side length: adjacent side = opposite side ÷ tangent(angle A)

Substitute the given values into the equation: adjacent side = 9 ÷ 0.45

Solve for the adjacent side length: adjacent side = 10 units Therefore, the approximate length of AB is 10 units.

Answer:

22

Step-by-step explanation: