Ali is y years old.
Bhavara is twice as old as Ali.
Ceris is 3 years younger than Ali.
The total of their ages is 125
years.
Work out the age of each person.
(4 marks)
Ali years=
Bhavara years=
Ceris years​=

Answer:

2 1/6

Step-by-step explanation:

3 1/2- 1 1/3

Answer:

2 1/6 ft. long

Step-by-step explanation:

You have to find a common denominator for the fractions which in this case is 6. You have to do whatever you do to the bottom to the top so since 3 x 2 is 6 and 2 x 3 is 6 the fractions change. They become 3 3/6 and 1 2/6. You subtract the fractions and get 1/6, then subtract the whole numbers that will be 3-1 and that equals 2 so your final equation is 3 1/2 - 1 1/3= 2 1/6. So the other piece of rope is 2 1/6 feet long.

Answer:

$10 + x = $25

Hope this helps!

(X = 15)

The Volume of Alcohol when Mass is 1000 Kg and Density is 790kg/m³

is 1.265 m³

The relationship between a substance's mass and the amount of space it occupies is known as its density (volume). The density of a substance is determined by the mass, size, and arrangement of its atoms. Density (D) is defined as the product of a substance's mass and volume.

Given:

Mass of Alcohol = 1000 Kg

Density of alcohol = 790kg/m³

Using The formula

Density= Mass / Volume

790 = 1000/ Volume

Volume = 1000/ 790

Volume = 1.265 m³

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The Translation of given Question:

What volume in cubic meters does 1000kg of alcohol occupy with a density of 790kg/m3

The largest interval on which the solution is defined is (-∞, -1) ∪ (-1, ∞). The interval notation for the largest interval is (-∞, -1) U (-1, ∞).

An initial-value problem is a type of boundary-value problem in mathematics, particularly in the field of differential equations.

The given initial-value problem is a separable differential equation, which can be written as:

dy/dt = -2(t + 1)y²

Integrating both sides, we get:

(1/y) = t² + 2t  + C

where C is the constant of integration.

Since we have an initial condition, we can use it to find the value of C:

y(0) = -1/15
C = -1/15

Solving for C, we get:

C = -1/15

So, the solution to the differential equation is:

(1/y) = t² + 2t -1/15

y = 1 / (t² + 2t -1/15)

The solution is defined for all t ≠ -1, since y = 0 is not defined. So, the largest interval on which the solution is defined is (-∞, -1) ∪ (-1, ∞). The interval notation for the largest interval is (-∞, -1) U (-1, ∞).

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The probability of ending up with an orange hat is 1/12. It is because here are twelve possible outcomes.

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

It is represented mathematically as;

Probability = Number of Expected outcomes / Total number of outcomes

From the question, we can have the following outcomes;

Clothing = 4

Colors = 3

Pr (pick a clothing) = 1/4

Pr (pick a color) = 1/3

Pr (picking an orange hat) = 1/4 x 1/3

Pr (picking an orange hat) = 1/12.

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Comparison of Enrollments in Vocational and Theoretical Courses in India

States: Uttar Pradesh and Maharashtra

In Uttar Pradesh, there were more male enrollments in vocational courses than female enrollments in all years. The difference was more pronounced in the early years, but it has narrowed over time. In 2010, there were 2.5 times more male enrollments in vocational courses than female enrollments. By 2020, the ratio had decreased to 1.75.

In Maharashtra, the difference between male and female enrollments in vocational courses was smaller than in Uttar Pradesh. In 2010, there were 1.5 times more male enrollments in vocational courses than female enrollments. By 2020, the ratio had decreased to 1.25.

Age

In Uttar Pradesh, the majority of enrollments in vocational courses were from the 15-29 age group. In Maharashtra, the majority of enrollments in vocational courses were also from the 15-29 age group.

The data also shows that there are some differences in the enrollment patterns between the two states. In Uttar Pradesh, the majority of enrollments are from the 15-29 age group, and the most popular vocational courses are in the areas of IT, engineering, and healthcare. In Maharashtra, the majority of enrollments are also from the 15-29 age group, but the most popular vocational courses are in the areas of IT, hospitality, and manufacturing.

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Answer: Therefore the ration 5 : 9 is equal to 10 : 18 

Step-by-step explanation:

Answer:

10:18

Step-by-step explanation:

There is infinitely many ratios which are equivalent to 5:9. As we know always we can write divide as fraction, so \(\frac{5}{9}\) . We can multiply nominator and denominator by the any number (by the same) and get another numbers but ratio will be the same, so equivalent.

ex: 10:18, 15:27.. and etc..

But We find the closest ratio = 10:18

[RevyBreeze]

The total amount spent is given as follows:

B. $14.28.

The total amount spent is obtained applying the proportions in the context of the problem.

The purchases are given as follows:

Considering the sales tax of 6.5%, the sum of these prices is multiplied by 1.065, hence the total price is given as follows:

1.065(5.69 + 1.39 + 1.45 + 2.38 + 2.5) = $14.28.

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The most reasonable metric measurement for the height of a kitchen counter is in cm (centimeters), i.e., 9.20×10 −4 cm.

The metric system consists of standard units of measurement for length, weight, and volume. The metric system is based on the decimal system and is used in most countries in the world, except for the United States.

The height of a kitchen counter is a measurement of length. One reasonable metric measurement for the height of a kitchen counter is centimeters (cm). Centimeters are a commonly used unit of measurement in the metric system and are appropriate for measuring smaller lengths such as the height of a kitchen counter.

Therefore, the option C,  9.20×10 −4 cm. is correct.

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Answer:

Please read below

Step-by-step explanation:

We are told that 1/2 of the orange juice is concentrate

So 50% is concentrate

100 - 50 = 50

This leaves another 50% to be water
50:50 is the same as 1:1

Infinitely many solutions exist for a system with fewer equations than unknowns, yet there may be none. An underdetermined system is one that operates in this manner.

What in mathematics is a linear system?

A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.

                          Equations with unknowns or variables that have powers of one are known as linear equations. Because the variables x, y, and z are linear, for instance, 3x - 4y + 5z = 3 is a linear equation, however xy + 3z = 7 is not because the phrase xy is a product of two variables.

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Answer: You switch the direction of the given symbol when multiplying or dividing by a negative number. As well as this, you must flip the sign of the original equation, after solving, to make it the opposite.

When you do either process to both sides by a negative value you make the side that is greater have a bigger negative number. This means it is now less than the other side.

Hope this helps!

The friend has to save for 5 and 2/3 of a month to in order to make up the remaining 85 to get the 125 headphone.

An inequality that consists of two or more parts is called a compound inequality. Either "or" or "and" may be used in these components. A number between 5 and 10 could be used as x in an inequality, for instance, if it states that "x is larger than 5 and less than 10". Any time one of the two inequalities is true when the two inequalities are united by the word or, the compound inequality is solved. The two separate solutions have been combined to form the final answer. Inequalities that are separated by "and" or "or" form a compound inequality. The intersection of the inequality graphs is shown by the graph of a compound inequality with a "and."

Cost of the headphone 125.

What the friend have: 40.

What need to save: 125-40 = 85

Let x = amount to be saved per month

Months to save up the 85 is 15

The equation would be 15 x = 85

Therefore x = 85/15

Which is 5 2/3 months.

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Answer:

no

Step-by-step explanation:

The square root of 169 is indeed 13.When simplifying the square root of a perfect square (a number that has an exact integer square root), we find the square root by identifying the largest perfect square factor of the given number. In this case, 169 is a perfect square because it can be expressed as 13^2.

To simplify the expression √169, we need to find the square root of 169. The square root of a number is a value that, when multiplied by itself, equals the original number.

In this case, we can calculate the square root of 169 as follows:

√169 = 13

So, the simplified form of the expression √169 is 13.

To verify this result, we can square 13 to check if it equals 169:

13^2 = 169

Therefore, the square root of 169 is indeed 13.

In general, when simplifying the square root of a perfect square (a number that has an exact integer square root), we find the square root by identifying the largest perfect square factor of the given number. In this case, 169 is a perfect square because it can be expressed as 13^2.

Taking the square root of a perfect square yields the positive and negative square roots of that number. However, when referring to the principal square root (which is typically denoted by the radical symbol), we consider only the positive square root.Hence, the simplified form of √169 is 13.

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Step-by-step explanation:

this is the answer

25+10y+y^2

Answer:

x=128

Step-by-step explanation:

step-by-step.

1

4

x−8=

1

8

x+8

Step 1: Subtract 1/8x from both sides.

1

4

x−8−

1

8

x=

1

8

x+8−

1

8

x

1

8

x−8=8

Step 2: Add 8 to both sides.

1

8

x−8+8=8+8

1

8

x=16

Step 3: Multiply both sides by 8.

8*(

1

8

x)=(8)*(16)

x=128

Brooks finished the race in 3.982 minutes.

To find Brooks's finish time, we can subtract the time difference between Parker and Brooks from Parker's finish time. Parker finished the race in 4.29 minutes, and Brooks beat Parker's time by 0.308 minutes.

To calculate Brooks's finish time, we subtract the time difference from Parker's finish time:

4.29 - 0.308 = 3.982

Therefore, Brooks's finish time is 3.982 minutes.

Let's break down the calculation further for better understanding. Parker finished the race in 4.29 minutes, which we can represent as 4 minutes and 0.29 minutes (or 4 minutes and 29 seconds). Brooks beat Parker's time by 0.308 minutes, which is equivalent to 0 minutes and 0.308 minutes (or 0 minutes and 18.48 seconds).

To find Brooks's finish time, we subtract the time difference from Parker's finish time. Let's calculate the minutes and seconds separately:

Minutes:

4 minutes - 0 minutes = 4 minutes

Seconds:

0.29 minutes (or 29 seconds) - 0.308 minutes (or 18.48 seconds) = -0.018 minutes (or -1.08 seconds)

Since we have a negative value for seconds, we need to subtract it from the total minutes. Converting -0.018 minutes to seconds, we get -1.08 seconds.

Final Calculation:

4 minutes - 1.08 seconds = 3 minutes and 59.92 seconds

Converting the seconds back to minutes, we have 59.92 seconds ÷ 60 = 0.9987 minutes (or approximately 0.999 minutes).

Adding the minutes and seconds together, we get:

3 minutes + 0.999 minutes = 3.999 minutes

Rounding to the nearest thousandth, Brooks's finish time is approximately 3.982 minutes.

Therefore, Brooks finished the race in 3.982 minutes.

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The probability of getting injured by falling off a ladder is approximately 0.0001113.

The odds against getting injured by falling off a ladder are 8,988 to 1. This means that for every 8,988 people who do not get injured by falling off a ladder, only one person does get injured by falling off a ladder.

To determine the probability of the underlined event, we can use the formula:

Probability = 1 / (odds + 1)

Plugging in the given odds, we get:

Probability = 1 / (8,988 + 1)

Probability = 1 / 8,989

Probability ≈ 0.0001113

Therefore, the probability of getting injured by falling off a ladder is approximately 0.0001113, or about 0.01113%. This is a very low probability, which highlights the importance of taking safety precautions when using a ladder.

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Answer:

cashier

Step-by-step explanation:

the discount is $7.50

Therefore, the car's average velocity between t = 1 and t = 4 is approximately 20.17 m/s.

To find the car's average velocity between t = 1 and t = 4, we need to calculate the total displacement of the car during that time interval and divide it by the total time.

Given that the velocity function of the car is v(t) = 3t + 12, we can integrate it to find the displacement function.

The displacement function, s(t), is the integral of the velocity function v(t):

s(t) = ∫(3t + 12) dt = (3/2)t² + 12t + C

To find the constant of integration (C), we can use the initial condition s(0) = 0. Since the car's initial position is not provided, we assume it starts at the origin.

s(0) = (3/2)(0)² + 12(0) + C

0 = 0 + 0 + C

C = 0

Therefore, the displacement function becomes:

s(t) = (3/2)t² + 12t

To find the total displacement between t = 1 and t = 4, we can evaluate s(t) at those points and subtract:

Δs = s(4) - s(1)

Δs = [(3/2)(4)² + 12(4)] - [(3/2)(1)² + 12(1)]

Δs = (3/2)(16) + 48 - (3/2) - 12

Δs = 24 + 48 - 3/2 - 12

Δs = 72 - 3/2 - 12

Δs = 60.5 meters

The total displacement of the car between t = 1 and t = 4 is 60.5 meters.

To find the average velocity, we divide the total displacement by the total time:

Average velocity = Δs / Δt = 60.5 / (4 - 1) = 60.5 / 3 ≈ 20.17 m/s

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The best linear approximation to the function f(x) = e^x near x = 0 is L(x) = x + 1.

The given function is f(x) = e^x near x = 0.

To find the best linear approximation, L(x), we use the formula:

L(x) = f(a) + f'(a)(x-a),

where a is the point near which we are approximating.

Let a = 0, so that a is near the point x = 0.

f(a) = f(0) = e^0 = 1

f'(x) = d/dx (e^x) = e^x;

so f'(a) = f'(0) = e^0 = 1

Substituting these values into the formula: L(x) = 1 + 1(x-0) = x + 1

Therefore, the best linear approximation to f(x) = e^x near x = 0 is L(x) = x + 1.

For instance, linear approximation is used to approximate the change in a physical quantity due to a small change in another quantity that affects it.

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The volume of the region in the first octant enclosed by the cylinder x² + y² = 1 is 1/15 cubic units.

The region in the first octant enclosed by the cylinder x² + y² = 1 can be expressed as:

0 ≤ x ≤ 1

0 ≤ y ≤ √(1-x²)

0 ≤ z ≤ x²y²

To find the volume of this region, we need to evaluate the iterated triple integral of the function f(x,y,z) = 1 over this region in the order dz dy dx. This integral can be expressed as:

V = ∫∫∫ f(x,y,z) dz dy dx

V = ∫₀¹ ∫₀√(1-x²) ∫₀^(x²y²) 1 dz dy dx

V = ∫₀¹ ∫₀√(1-x²) x²y² dy dx

V = ∫₀¹ x² (∫₀√(1-x²) y² dy) dx

To evaluate the inner integral with respect to y, we can use the power rule:

∫₀√(1-x²) y² dy = [y³/3]₀√(1-x²) = (1/3)(1-x²)^(3/2)

Substituting this into the previous equation, we get:

V = ∫₀¹ x² (1/3)(1-x²)^(3/2) dx

To evaluate this integral with respect to x, we can use the substitution u = 1-x²:

du/dx = -2x, dx = -1/2√(1-u) du

Using this substitution, the integral becomes:

V = ∫₁⁰ (1-u)(-1/2√u)(1/3) du

V = (1/6) ∫₁⁰ (u^(1/2) - u^(3/2)) du

V = (1/6) [(2/3)u^(3/2) - (2/5)u^(5/2)]₁⁰

V = (1/6) [(2/3) - (2/5)]

V = 1/15

Therefore, the volume of the region in the first octant enclosed by the cylinder x² + y² = 1 is 1/15 cubic units.

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(a) The probability that both Anderson and Box will be selected is 0.1

(b) The probability that at least one of the two members whose name begins with C is selected is 0.7

(c) The probability that the two chosen representatives have a total of at least 17 years teaching experience there is 0.6

(a) You will have to consider the 10 different outcomes. Each combination of "A−B","B−Cox", "B−Cramer",... is equally likely to be drawn.

There are \(\left \{ {{5} \atop {2}} \right. =10\)

10 ways to choose 2 people from a group of 5. Since we are only considering 1 possibility, the answer will be 1/10=0.1

(b), there are a few possibilities where at least 1 "C" member gets selected. Consider

"Cox−A", "Cox−B", "Cox−Cramer", "Cox−F"

and

"Cramer−A", "Cramer−B", "Cramer−Cox", "Cramer−F"

Notice that "Cox−Cramer" appears twice, so one needs to be eliminated. Turns out there are 7 different possibilities out of 10...so we have 0.7

(c), I'd personally recommend taking the "compliment" of events. ie, how many combinations have LESS than 17 years? Turns out there are 4 combinations - (3,6),(3,7),(3,10),(6,7).

You can use the answer from (a) and evaluate this to become

1−4/10=0.6.

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Answer:

a) 55°

b) 125°

c) 55°

d) 55°

Step-by-step explanation:

a) 180-(90+35) = 55

b) this angle forms a straight angle with ∡a

c) this angle is vertical, and congruent, with ∡a

d) 180-(70+55) = 55

Answer:

depending on how you need the answer it's 13/7, 1 6/7 or 1.8571428571429

Let's simplify the expression step by step: Expand the squared term:

(x - 3y)² = (x - 3y)(x - 3y) = x² - 6xy + 9y²

Expand the second term:

3(x + y)(x − 4y) = 3(x² - 4xy + xy - 4y²) = 3(x² - 3xy - 4y²)

Expand the third term:

x(3x + 4y + 3) = 3x² + 4xy + 3x

Now, let's combine all the expanded terms:

(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)

= x² - 6xy + 9y² + 3(x² - 3xy - 4y²) + 3x² + 4xy + 3x

Combining like terms:

= x² + 3x² + 3x² - 6xy - 3xy + 4xy + 9y² - 4y² + 3x

= 7x² - 5xy + 5y² + 3x

The simplified form of the expression is 7x² - 5xy + 5y² + 3x.

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Answer: A positive shape.

Step-by-step explanation:

I mean, that's just what it's called.