In a running competition, a bronze, silver and gold medal must be given to the top
three girls and top three boys. If 15 boys and 11 girls are competing, how many
different ways could the six medals possibly be given out?

Answer:

--15 and --10 respectively

Step-by-step explanation:

Let the first no be a and second no be b

From the interpretation of the question

a + 20 (added) -- 5 (subtracted) = 0

a + 20 -- 5 = 0

a + 15 = 0

a = --15

Product = 150

a×b = 150

(--15) × b = 150

b = --150/15

b = --10

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Answer:

the answer is -17 8/9

Step-by-step explanation:

when "subtracting" negative numbers you actually add all of them together and attach the negative sign

The answer is (B) 18.

In order to calculate the area of a triangle we must use the equation 1/2·base·height.

In this case, the base of the triangle would be QR, which is 12. The height would be PH, which is 3.

Using the formula above, we can do 1/2·12·3 which equals 18. This is the area of triangle PQR and our final answer.

Hope this helps.

Answer: The answer should be 10^2  or C

Step-by-step explanation: 65.108 if you move the six to left 2 times you will get 6,510.8

Answer:

R=100%

Step-by-step explanation:

Here

Increased population (Pt) = 5.2-2.6 = 2.6

Time = 1987-1952

Rate of increase=?

By formula

Pt = P(1-R/100)^t

2.6=2.6(1-R/100)^35

1=(1-R/100)^35

0^35 = (1-R/100)^35

0=1-R/100

0= 100-R

R=100%

so the average annual population growth rate of the world between 1952and1987 is 100%

Answer/Step-by-step explanation:

Five more than a number = 5 + n

The sum of 3.6 and a number = n + 3.6

The difference of ten and a number = 10 - n

One-half less than a number = n - (1/2)

I hope this helps!

Answer:

The difference of 10 and a number: 10-n

Five more than a number: 5+n

The sum of 3.6 and a number: n+3.6

one-half less than a number: n-1/2

i.

it is an corresponding angles

ii.

the realtion we have is that the angles are equal

iii.

4+10x=11x-1

or 4+1=11x-10x

5=x

iv

4+10x=4+10×5

=54

11x-1=11×5-1=54

Answer:

A)Corresponding angles (When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles

B)They are congruent to each other

C) 4+10x=11x-1

4=x-1

5=x

( we put them equal to each other because they are the same)

D)4+10(5)=

4+50=54

D)11(5)-1=

55-1=54

Answer:

43

Step-by-step explanation:

→ Set up an equation

2x + 9 = 0.5 ( 8x - 50 )

→ Simplify

2x + 9 = 4x - 25

→ Minus 4x from both sides

-2x + 9 = -25

→ Minus 9 from both sides

-2x = - 34

→ Divide both sides by -2

x = 17

→ Substitute into AM

2 × 17 + 9 = 34 + 9 = 43

Answer:

c

Step-by-step explanation:

The set of integers as described in the task content which are greater than 9 and less than or equal to -6 can be represented using interval notation as all integer values in the set ; (9, infinity) U (-infinity, -6].

It follows from the task content that the set of integers greater than 9 and less than or equal to -6 is to be determined.

By considering each set of possible solutions for the integer in discuss; we have;

Therefore, the required set of Integers includes integers in union of the two sets above and hence, we have;

x = (9, infinity) U (-infinity, -6].

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An equation or inequality to model the situation: The distance d to school is 1 1/2 miles more than the distance p to the park is  d = p + 3/2

a statement that the values of two mathematical expressions are equal indicated by the sign =, is known as equation.

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions is known as inequality.

For this situation, we would assume that both the distances i.e 'd' and 'p' are in miles.

It is mentioned that the distance d is more than the distance p by 3/2 miles.

It means that if we add  3/2 miles to the distance 'p' the output will be distance 'd'

The equation for this is as follows :- d = p + 3/2

It also means that if we substract 3/2 miles from distance 'd', the output will be distance 'p'

The equation for this is as follows :- p = d - 3/2

But we are asked in the situation that distance d is more than than the distance 'p'.

Therefore , an equation or inequality to model the situation: The distance d to school is 1 1/2 miles more than the distance p to the park is d = p + 3/2.

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Answer: Use cross-product to determine if the two ratios form a proportion.

The graph shows a quadratic function.

The quadratic function has been shifted downwards by 2 units and to the left by 3 units.

The rules that show the translation above are given to be:

1) f (x) − b shifts the function b units downward.

2) f (x + b) shifts the function b units to the left.

Therefore, the transformation for h(x) is given to be:

A puzzle, defined as "anything which baffles or perplexes," refers to an enigma or a conundrum that requires creative thinking to solve.

The answer is A = 7.

A puzzle, defined as "anything which puzzles or perplexes," refers to a riddle or issue that defies creativity to be solved.

Retaining mental quickness and short-term memory while working on a puzzle strengthens connections between brain cells.

Dopamine, a neurotransmitter that controls mood, memory, and focus, is produced more readily as a result of solving puzzles.

Every time we complete the puzzle, dopamine is produced.

Given the puzzle condition,

The sum of any 3 consecutive digits must be 17.

Given numbers 8, 2

So the third number would be 8 + 2 + A = 17

10 + A = 17

Therefore A is 17-10 = 7

A = 7

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Let's write out the formula for the sum of geometric series,

Let's solve for the sum of seven geometric series,

Hence,

Therefore, option 5 is the correct answer.

Option 5 is none of these are correct.

By applying sine trigonometry, the angle θ in this right angled triangle is approximately equal to 50 degrees.

In Trigonometry, the law of sines is also referred to as sine law or sine rule and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.

In order to determine the value of H, we would apply basic trigonometry. From the information provided about this right angled triangle, we can logically deduce the following parameters:

Therefore, we would use the sine trigonometry to determine the value of H as follows:

Sinθ = Opp/Hyp

0.7071 = 5/H

H = 5/0.7071

H = 7.0711.

Now, we can determine the angle θ in this right angled triangle as follows:

Sinθ = Opp/Hyp

Angle, θ = sin⁻¹(Opp/Hyp)

Angle, θ = sin⁻¹(5/7.0711)

Angle, θ = sin⁻¹(0.7071)

Angle, θ = 44.999 ≈ 50°.

Angle, θ = 50 degrees.

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The ratio of the net force to the weight of the scallop (F net/Weight) for this motion exists 792.657 Newtons.

The net force exists the vector sum of all the forces that act upon an object. The total of all forces exerted on an object is known as the net force. A mass can accelerate due to net force. A body is subject to another force whether it is at rest or in motion. When there are a lot of forces acting on a system, the term "net force" is employed.

Given, mass = 29g, speed = 4.10 m/s , Time = 0.15 s

Acceleration (a ) = (final speed - initial speed)/time taken

                           = 4.10 - 0/ 0.15 = 27.333 m/s/s

F = m × a = 29 g × 27.33 m/s

            =  792.657 Newtons

Therefore, the ratio of the net force to the weight of the scallop (F net/Weight) for this motion exists 792.657 Newtons.

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For the given question,

Figure A and D are the cases of reflection over y and x axis respectively.

For the given question,

Figure B and C are the cases of translation 3 right and 4 down respectively.

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Memory of the phones = 32 gigabytes

Now,

Therefore ,

Also ,

Therefore,

Thus the memory of the phone in bits is ,

If two events are mutually exclusive this means they cannot occur at the same time and do not over lap

If two events are mutually inclusive this means they can occur at the same time and they over lap

Event A and Event B are mutually exclusive

Event A and event C are not mutually exclusive

To find the complement of event A (A'), which is the part of the universal set of events not in A

We use the formula

P(A) = 0.45

substituting this into the equation yields

P(A') = 0.55

So the initial equation is:

To writte the equation in the standard form we have to make it equal to 0, so we can add 2 in bout sides of the equation:

now, (a) is the number thas goes with the x^2, (b) is the number that goes with the x and (c) is the number that is alon, so:

Now we can substitute this numbers in the quadratic equation:

and finally we can simplify the equation:

Answer: 17

Step-by-step explanation:

Answer:

0.1538461583

Step-by-step explanation:

2 divided by 13

Using the t-distribution, the 98% confidence interval for the mean temperature is of:

(47.335, 65.624).

The confidence interval is given as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the parameters are:

Using a calculator, the parameters from this sample are given as follows:

[tex]\mu = 56.43, s = 10.198, n = 10[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 10 - 1 = 9 df, is t = 2.82.

The lower bound of the interval is:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 56.43 - 2.82\frac{10.198}{\sqrt{10}} = 47.335[/tex]

The upper bound of the interval is:

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 56.43 + 2.82\frac{10.198}{\sqrt{10}} = 65.524[/tex]

Hence the interval is:

(47.335, 65.624).

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7100 mL

to solve this we need to do a subtraction, note the unit must be the same, so

Step 1

convert 1.6 Liters into mL

to do this we need to use the equivalence:

so,

a) convert 1.6 Liters into mm

Step 2

b)now, we can do the subtraction:

so

soup she froze = total soup made - soup she packed

so, replace

therefore, the answer is

7100 mL

I hope this helps you

The equation for the graph sketched below is given as y = -3(3)^x

The standard form of an exponential equation is given as y = ab^x

Using the coordinate points on the graph (-1, 1) and (0, -3)

The equivalent equations are;

1 = ab^-1

-3 = ab^0

From equation2;

a= -3

Substitute into equation 1;

1 = ab^-1

1 = 3b^-1

1 =3/b

b =3

Determine the equation

y = ab^x

y = -3(3)^x

This gives the required exponential equation

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The transformation is non rigid

Transformations involve the rotation, reflection, or translation of forms on a coordinate plane. Transformational geometry is a fresh viewpoint on geometry that Felix Klein suggested in the 19th century. The majority of geometric proofs rely on the transformations of objects. Any image in a coordinate plane can be changed using transformations. Applying the transformational laws will help you better understand the graphics in video games. Learn to recognize transformations, comprehend function transformation principles, and investigate the various forms of transformations.

Non-Rigid Transformations actually alter the original object's structure. Scaling, for instance, allows us to make our object larger or smaller. Alternatively, shearing can be used to "push" it up or to the side. In essence, non-rigid transformations allow an object's size to change.

because the size became small as compare to pre image it is non rigid transformation

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if two lines are perpendicular it is true that:

For the line:

Let's check every line:

So, A is a correct choice

B is not a correct choice

C is a correct choice

D is a correct choice

E is not a correct choice

The experiment has a binomial distribution just because the product could be or not defective. In this case you have n=26 the number of product that the company will check and you also know that the probability to get a defective one is 3.6%. Now we will proceed as follows, to find the probability of getting 2 or fewer defective products is exactly the same that

We also should notice that

Now,

Then the probability that the company takes 2 or fewer defective products in this batch is

Now, to get the probability that the company find 4 or more defective products we proceed as follows. Since

then

Notice that we only need to find one of these probabilities to get the answer.

Then the probability to get more than 4 defective products is

So if the company finds 5 defective products in this batch the company should stop the production because the probability to get more than 4 defective products is around 1.3%. It means that if you get 5 defective products even with this small probability then we could say that is really probable to get more defective products that those who were expected.