The area of the triangle below is 25/18 square meters. What is the length of the base? Express your answer as a fraction in simplest form

The profit should be shared in proportion to Mr Jones, Mr Thomas and Mr forson capitals in the ratio 21 : 32 : 27 respectively.

Total capital = $12600 + $19200 + $16200

= $48,000

Mr Jones proportion = $12600 / $48,000

= 21/80

Mr Thomas proportion = $19200 / $48,000

= 32/80

Mr forson proportion = $16200 / $48000

= 27/80

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Answer: 2a < 2b

Step-by-step explanation:

We are given a statement:

a < b and b < c, then 2a ____ 2b

We can use simple numbers that make the statement true.

Where,

a = 2

b = 3

c = 4

Now lets plug it in.

2 < 3 and 3 < 4, then 2(2) ____ 2(3)

and lets simplify:

2 < 3 and 3 < 4, then 4 ____ 6

We can see that 4 is less than 6,

so as a is less than b, 2a is less than 2b.

The only thing changing is the coefficient being multiplied by the variables a and b.

Answer:

the 40th number in the pattern is 9

Answer:

17.32 meters

Step-by-step explanation:

Let’s call the height of the tower H. The distance from the point to the base of the tower is 10 m. The angle of elevation from the point to the top of the tower is 60 degrees.

Using trigonometry, we can calculate that:

tan (60) = H / 10

H = 10 * tan (60)

H = 10 * √3

H = 17.32 m

Therefore, the height of the tower is 17.32 meters.

Let me know if I helped :)

Answer:

  B)  15/17

Step-by-step explanation:

You want the sine of acute angle A in the right triangle shown.

The sine of the angle is the ratio ...

  Sin = Opposite/Hypotenuse

We can go to the trouble to figure the hypotenuse, or we can choose the only suitable answer from the list provided. (It is the one marked already.)

The leg lengths of the triangle shown are 8 and 15, with leg 15 being opposite angle A. This is the first clue that the ratio will have 15 in the numerator. Only answer choice B matches.

The value of the sine function is never greater than 1, eliminating answer choices A, C, and E, leaving choices B and D.

Since the side opposite angle A is the longest of the two legs, we know that angle A is more than 45°, and its sine is more than √2/2. That means choice D can be eliminated, since it is less than 1/2.

The sine of angle A is 15/17.

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Answer:

12 : 22

Step-by-step explanation:

Step-by-step explanation:

3:00 hours and 26 second

The distance between the two points is approximately 5.66 units

Using the formula for the distance between two points on a coordinate plane:

Distance = √[(y2 - y1)^2 + (x2 - x1)^2]

We can plug in the given values into the distance formula:

given that

y2 = 9, y1 = 13, x2 = 4, and x1 = 0

= √[(9 - 13)^2 + (4 - 0)^2]

= √[(-4)^2 + (4)^2]

= √(16 + 16)

= √32

= 4√2

= 5.6569

= 5.66

Therefore, the distance between the two points is approximately 5.66 units, which corresponds to option A.

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Answer:

its the one you have selected

Step-by-step explanation:

you have to ask something about your assignment

and its the one you have selected

have a nice day!

Answer:

There were 45 students in each bus

Step-by-step explanation:

Arithmetic

One can be in situations where different mathematic operations must be performed in order to find a result. Four operations are known as basics in arithmetic: addition, subtraction, multiplication, and division.  Some basic logic is also needed on certain problems to decide what operations are adequate.

We know 411 students went on a trip to the zoo. There were 9 buses filled but 6 students didn't fit, so they had to travel in cars. This information tells us that 411 - 6 = 405 students went on the buses.

Since there were 9 buses, it means that each bus had 405 / 9 = 45 students.

There were 45 students in each bus

Answer:

Step-by-step explanation:

The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."

When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.

Therefore, option 1 is the correct definitation of perpendicular lines.

Answer: 1. Two lines that intersect in a way that forms right angles.

Step-by-step explanation:

Hope this helped! :)

Because the angles add up to 180°, we conclude that the shelves are parallel.

Two adjacent angles always should add up to 180°. The top shelve and middle shelve will be parallel only if:

∠1 = ∠5

∠2 = ∠6

And we know that:

∠1 + ∠2 = 180°

Then we could rewrite this as:

∠5 + ∠2 = 180°

Replacing the measures we will get:

60° + 120° = 180°

180° = 180°

That equation is true, this, the shelves are parallel.

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Answer:

6.75 miles per 0.5 hours.

Step-by-step explanation:

The ratio 27/2 is equal to the ratio of 6.75/0.5. This can be shown by dividing the 2 in the denominator by 4, getting you 0.5, and dividing the numerator, 27, by 4 also, which gets you 6.75. Hope this helps!

There are 4 hundred billions in the number 432,845,979,484.

To determine how many hundred billions are in the number 432,845,979,484, we need to consider the place value of the hundred billions digit.

The number 432,845,979,484 has 12 digits, and we count the digits from right to left, starting with the units place. The digit in the hundred billions place is the seventh digit from the right.

Let's break down the number:

4 hundred billions (4 x 100,000,000,000)

3 ten billions (3 x 10,000,000,000)

2 billions (2 x 1,000,000,000)

8 hundred millions (8 x 100,000,000)

4 ten millions (4 x 10,000,000)

5 millions (5 x 1,000,000)

9 hundred thousands (9 x 100,000)

7 ten thousands (7 x 10,000)

9 thousands (9 x 1,000)

4 hundreds (4 x 100)

8 tens (8 x 10)

4 units (4 x 1)

As we can see, there are 4 hundred billions in the number 432,845,979,484.

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Answer:15.7 or 16

Step-by-step explanation:

The institution from the industrial revolution is the national institute of space and technology. Hence, option B is correct.

Agrarian and handcraft economies were replaced by industrialized and machine production during the Industrial Revolution in modern history. New modes of living and working were made possible by these technical advancements, which profoundly altered society.

In the 18th century, this practice started in Britain and then extended to other regions of the world. The English economics professor Arnold Toynbee (1852–83), who originally used the word to characterize Britain's economic growth from 1760 to 1840, although it had been used by French writers earlier.

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Answer:

9 litres

Step-by-step explanation:

the volume (V) of the tank is calculated as

V = lbh ( l is length, b is breadth , h is height )

here l = 60 cm, b = 15 cm, h = 10 cm , then

V = 60 × 15 × 10 = 9000 cm³

using the conversion 1 litre = 1000 cm³ , then

V = 9000 ÷ 1000 = 9 litres

Answer:

  9 liters

Step-by-step explanation:

It is often convenient to make use of the fact that 1 liter is 1000 cm³, or 1 dm³, where 1 dm = 10 cm. Expressing the tank dimensions in decimeters, we see they are ...

  L = 6 dm, W = 1.5 dm, H = 1.0 dm

Then the volume is ...

  V = LWH

  V = (6 dm)(1.5 dm)(1.0 dm) = 9.0 dm³ = 9 L

9 liters of water are needed to fill the empty tank.

Answer:

A) Both events are not independent.

B) Both events are not mutually exclusive

C) 8.33%

D) 80%

Step-by-step explanation:

A) Both events are not independent. This is because, If B occurs it means that it is very likely that J will occur as well.

B) Both events are not mutually exclusive. This is because it is possible for both events J and B to occur at the same time.

C) we want to find the probability that Joe who is not a business student will receive the job offer.

This is;

P(J|Not B) = P(J & Not B)/P(Not B)

Now,

P(J & Not B) = P(J) – (P(B) × P(J | B))

25% of the students who attended received job offers. Thus; P(J) = 0.25

40% were from the College of Business. Thus;

P(B) = 0.4

Among the business students, 50% received job offers. Thus;

P(J|B) = 0.5

Thus;

P(J & Not B) = 0.25 - (0.4 × 0.5)

P(J & Not B) = 0.25 - 0.2

P(J & Not B) = 0.05

Since P(B) = 0.4

Then, P(Not B) = 1 - 0.4 = 0.6

Thus;

P(J|Not B) = 0.05/0.6

P(J|Not B) = 0.0833 = 8.33%

D) This probability is represented by;

P(B | J) = P(B & J)/P(J)

P(B & J) = (P(B) × P(J | B)) = (0.4 × 0.5) = 0.2

P(B | J) = 0.2/0.25

P(B | J) = 0.8 = 80%

Answer:

the last one

Step-by-step explanation:

there is no rhythm

An examination, a candidate has to score a minimum of 24 marks in order to clear the exam. the maximum that he can score is 40 marks. The valid equivalence values of the student clears the exam is 29, 30, 31.

An examination, a candidate has to score a minimum of 24 marks in order to clear the exam. the maximum that he can score is 40 marks.

The class will be as follows:

Class i: values<24 => invalid class

Class ii: 24 to 40  => valid class

Class iii: values> 40 => invalid class

We need to identify valid equivalence values. Valid equivalence values will be there in a valid equivalence class. All the values should be in class ii.

Therefore, the answer is 29, 30, 31.

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To construct a frequency histogram based on the given temperature data, we will use the temperature ranges as the x-axis and the number of days as the y-axis.

The temperature ranges and their corresponding frequencies are as follows:

30-39: 2 days

40-49: 26 days

50-59: 28 days

60-69: 8 days

70-79: 2 days

To create the histogram, we will represent each temperature range as a bar and the height of each bar will correspond to the frequency of days.

Using an appropriate scale, we can label the x-axis with the temperature ranges (30-39, 40-49, 50-59, 60-69, 70-79) and the y-axis with the frequency values.

Now, we can draw rectangles (bars) on the graph, with the base of each rectangle corresponding to the temperature range and the height representing the frequency of days. The height of each bar will be determined by the corresponding frequency value.

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There will be 25 sample outcomes that are possible when two five sided dices are rolled.

Teo five sided dice rolled in this experiment, The sample space can be defined as:

n = (1,1) (1,2) (1,3) (1,4) (1,5)

(2,1) (2,2) (2,3) (2,4) (2,5)

(3,1) (3,2) (3,3) (3,4) (3,5)

(4,1) (4,2) (4,3) (4,4) (4,5)

(5,1) (5,2) (5,3) (5,4) (5,5)

n = 25

The sample space is defined as the event A is the sum of two dices is six :

n(A) = (1,5) (2,4) (3,3) (4,2) (5,1) = 5

The first die can land face-up in any one of n1 = 5 ways. For each of these 5 ways, the second die can also land face-up in n2 = 5 ways. Therefore, the pair of dice can land in n1n2 = (5)(5) = 25 possible ways.

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Answer:

-10 or -$10

Step-by-step explanation:

The 10 would be negative, due to taking away 10 instead of adding it.

Answer:

the coefficient are 9 and -8

the constant is 6........

\(x^2-12x+36=0\\(x-6)^2=0\\x-6=0\\x=6\)

The actual problem will be  9000 % 700, with the remainder 600 and quotient 12.

Since we are with the actual problem, which is 8,950 % 695, here the dividend is 8950  and the divisor is 695, the actual division we come up with the 12 as quotient and remainder 620. Now making the expression simple  using the round-off rule, here  in  the dividend  8950, the last two digits are 50, so we can round off it to 9000 and in the  divisor  695,  the last digit is 5, so we add 1 in the preceding  number converting it to 700, after the actual division of the estimated expression, the quotient we come up with is 12, and the remainder is 600.

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Answer:

the answer is 12.8

Step-by-step explanation:

Answer:

14 \(\frac{2}{5}\)

Step-by-step explanation:

3*4 \(\frac{4}{5}\)

4 \(\frac{4}{5}\) = \(\frac{24}{5}\)

\(\frac{3}{1} * \frac{24}{5}\)= \(\frac{72}{5}\)

\(\frac{72}{5}\) to a mixed number

\(\frac{72}{5}\)= 14.4 =14

72-(5*14)=2

14 \(\frac{2}{5}\)

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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