A train takes 16 hours to travel a distance of 35,376 km. Find the distance travelled in one hour if it covers the same distance every hour

Answer:

Option 3 ) 18x - 9 = 72

Step-by-step explanation:

Algebraic equations:

  \(\sf \dfrac{3}{5}(30x - 15) = 72\\\\\\\)

Multiply each term of (30x - 15) by 3/5,

    \(\sf \dfrac{3}{5}*30x - \dfrac{3}{5}*15=72\\\\\\3*6x - 3*3 = 72\\\\18x - 9 = 72\)

The given equation is same as 18x - 9 = 72

Answer:

This is a die used to play games. Well we generally use more than one, so we use dice. The addition of each pair of opposite sides always yields 7:

Dice games are very popular and they can also help understand how math and probability work. As with all games, probability always favors the house, but the risk of loss is part of the entertainment.

Is this question complete, or is it missing some requirements?

Answer:

80

Step-by-step explanation:

edge 2023

Answer:

21x^2 + 33x + 16

Step-by-step explanation:

(14x^2 + 13x + 12) + (7x^2 + 20x + 4)

Combine like terms:

14x^2 + 7x^2 = 21x^2

13x + 20x = 33x

12 + 4 = 16

Thus:

21x^2 + 33x + 16

Answer:

21x^2 + 33x + 16.

Step-by-step explanation:

(14x2 + 13x + 12) + (7x2 + 20x + 4)   Remove the parentheses:

= 14x2 + 13x + 12 + 7x2 + 20x + 4    Bring like terms togethher:

= 14x^2 + 7x^2 + 13x + 20x + 12 + 4

= 21x^2 + 33x + 16.

Given data:

The first side of the triangle is a=3 ft.

The second side of the triangle is b=54 ft.

For a triangle the sum of any two sides mus be greater than third side.

(3 ft+54 ft)>c

c<57 ft.

and

(3 ft+c)>54 ft

c>51 ft

Thus, the side of the triangle lie between 51

Answer:

5: A

6: B

Step-by-step explanation:

Answer:

20.84

Step-by-step explanation:

$25.36 - $4.52 = $20.84

Hope this helps

Y in represents the following in this linear regression Y = α₀+α₁X+α₂X₂+ε: C. dependent variable.

In Mathematics and Geometry, a regression line is a statistical line that best describes the behavior of a data set. This ultimately implies that, a regression line simply refers to a line which best fits a set of data.

In Mathematics and Geometry, the general functional form of a linear regression can be modeled by this mathematical equation;

Y = α₀+α₁X+α₂X₂+ε

Where:

In conclusion, Y represent the dependent variable or response variable in a linear regression.

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Answer:

7/16

Step-by-step explanation:

5/8-3/16=7/16

Subtract how much more angle 1 is from the total. :

112 - 48 = 64

Divide by 2:

64/2 = 32

Angle 2 = 32 degrees

Answer:

measure of angle 2 is 32 degrees.

Step-by-step explanation:

I will refer to the measure of the angles as m1 and m2 (I don't have the angle symbol on my keyboard).

we are looking for measure of angle 2, so let's call m2 "x".

so,

m2 = (x)

m1 = (48 + m2) or m1 = (48 + x)

and we know that:

m1 + m2 = 112

so we substitute the values above into the equation.

m1 + m2 = 112

(48 + x) + (x) =  112

combine like terms:

42 + x + x = 112

42 + 2x = 112

subtract 42 from both sides, leaving us with

2x = 64

divide by 2, giving us

x = 32

remember that we are looking for m2, which is x, so m2 is 32 degrees. hope this helped! (:

If ~A and ~B are true, then either ~C or ~D is also true. This means that if any two of the three propositions, ~A, ~B, and ~(C & D), are true, then the third proposition must be true.

GivenC: ~(C & D)1: ~A2: (A V B) <-> C3: ~B

Thus, to get the solution for this problem, we will consider the following proposition P for C.    

P: C & D

We will apply De Morgan's Law to P to get its negation.    

~(C & D) = ~C V ~D

Also, we can apply bi-conditional equivalence to proposition 2.    

(A V B) <-> C = (A V B) -> C & C -> (A V B)

By applying the logical operator implication to the first part of the bi-conditional equivalence, we get    

(A V B) -> C is equivalent to ~C -> ~(A V B)

Using De Morgan's law, we get    

~(A V B) = ~A & ~B

Thus, the contrapositive of the implication can be written as    

~C -> ~A & ~B

So, the premises can be rewritten as    

~C V ~D     ~A     ~B

We can now apply the resolution rule of inference to the premises to get the

We have given three propositions. Propositions 1, 2, and 3 state that ~A, (A V B) <-> C, and ~B, respectively. We have also been given another proposition, C: ~(C & D), which is negated.Using the bi-conditional equivalence of proposition 2 and applying the logical operator implication, we can rewrite it in the form ~C -> ~A & ~B. Also, we have P: C & D, which we have negated to ~C V ~D. Applying the resolution rule of inference to these four propositions, we get the Main Answer as ~A V ~D.

Thus, the conclusion can be drawn as follows:

If ~A and ~B are true, then either ~C or ~D is also true. This means that if any two of the three propositions, ~A, ~B, and ~(C & D), are true, then the third proposition must be true.

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Answer:

x^4 - 16x^3 + 96x^2 -256x + 256

Step-by-step explanation:

The coefficients of this using the pascal triangle is ;

1 4 6 4 1

Thus, we have that;

1(x^4•(-4)^0) + 4(x^3)(-4)^1 + 6(x^2)(-4^2) + 4(x^1)(-4)^3 + 1(x^0)(-4)^4

= x^4 - 16x^3 + 96x^2 -256x + 256

Answer:

Step-by-step explanation:

Q1

AT = 8.5 ft

AT is radius, the diameter is:

Q2

AH = 6 yd, AH is radius

Q3

Q4

∠MAT = 115°

Arc MT is:

Q5

C = 6π, A = ?

A = πr² = π*3² = 9π

Answer:

-9x^2 + 12x + 5

Step-by-step explanation:

I'm assuming you meant (3x – 2)^2.  The " ^ " indicates exponentiation and is required.  We then have:

9 - (3x – 2)^2, which, when expanded, is

9 - (9x^2 -12x + 4), or:

-9x^2 + 12x + 5

The relation R defined on the positive integers is not a partial order, as it does not satisfy the antisymmetric property.

The relation R is an equivalence relation, as it satisfies the three defining properties: reflexivity, symmetry, and transitivity.

The relation R defined on the positive integers is not a partial order. This can be explained as follows :

The relation R does not satisfy the antisymmetric property. Specifically, there exist positive integers a and b such that a R b and b R a, but a ≠ b. For example, consider a = 4 and b = 6. Both 4 and 6 have a common divisor greater than 1 (namely, 2), so 4 R 6 and 6 R 4. However, 4 ≠ 6, so the relation R is not antisymmetric and therefore cannot be a partial order.

The relation R is an equivalence relation. This is because it satisfies the three defining properties: reflexivity, symmetry, and transitivity.

Reflexivity follows immediately from the definition of a common divisor, since any positive integer has itself as a common divisor.

Symmetry also follows from the definition, since if a and b have a common divisor greater than 1, then so do b and a.

Finally, transitivity follows from the fact that if a and b have a common divisor greater than 1, and b and c have a common divisor greater than 1, then a and c must also have a common divisor greater than 1 (namely, any common divisor of b and a, and any common divisor of b and c, must also be a common divisor of a and c). Therefore, the relation R is an equivalence relation on the positive integers.

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The growth of the population after .t. years would be \(y_t = 16000^{(1.06t)}\).

The formula for exponential growth is \(y = y_0e^{(kt)}.\)

The formula for exponential decay is \(y = y_0e^{(-kt)}.\).

Given, The number of students enrolled at a college is 16,000 and grows ​6% each year.

Now, 6% in terms of decimals is 0.06 hence k = 1 + 0.06 = 1.06.

The initial amount is 16000.

So, After t number of years, the population would be, \(y_t = 16000^{(1.06t)}\).

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Answer:

28 Pi

Step-by-step explanation:

circumference = 24(2)(π) = 48π

arc ABC = 360° - 150° = 210°

(210/360)(48π) = 28 Pi

Answer:

there equal

I think but I'm not sure

Answer:

1508cm²

Step-by-step explanation:

Assuming that the label doesnt cover the top and bottom of the can, the area of the cyllinders side is

\(2\pi \: r \: h\)

Plugging in given values of r=12 and h=20, we get that the area is 480pi cm², or 1508cm²

Answer:

Step-by-step explanation:

you got this i believe in you!

The values of {x} would be 38.1 units.

According to the Pythagoras theorem, we can write -

(hypotenuse)² = (base)² + (perpendicular)²

Given is a right angled triangle JKL.

We can solve for {x} using the cosine function as -

cos(27) = 34/x

x = 34/cos(27)

x = 38.1 units

Therefore, the values of {x} would be 38.1 units.

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the linear approximation for 3√126 is approximately 5.06667, rounded to five decimal places.

To estimate the given number 3√126 using a linear approximation (or differentials), follow these steps:

Choose a nearby value that is easy to work with: For 3√126, we can choose 3√125 since 125 is a perfect cube (5^3). So, let our base point be x=125, and we want to estimate at x=126.

Compute the actual value at the chosen point: We know that 3√125 = 5, since 5^3 = 125.

Find the derivative of the function: Our function is f(x) = 3√x, so its derivative f'(x) = (1/3)x^(-2/3).

Compute the derivative at the chosen point: Plug x=125 into f'(x) to get f'(125) = (1/3)(125^(-2/3)) = (1/3)(5^(-2)) = 1/15.

Calculate the linear approximation: Use the formula L(x) = f(a) + f'(a)(x-a), where a is our chosen point (125) and x is the point we want to estimate (126). In this case, L(126) = 5 + (1/15)(126-125) = 5 + (1/15)(1) = 5 + 1/15.

Simplify the linear approximation: L(126) = 5 + 1/15 ≈ 5.06667.

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Although part of your question is missing, you might be referring to this full question: What are the vertex and range of y = |2x + 6| + 2?

(0, 2); 2 < y < ∞

(0, 2); −∞ ≤ y < ∞

(−3, 2); 2 < y < ∞

(−3, 2); −∞ ≤ y < ∞

The vertex of the function is (–3, 2) and the range of the function is 2 < y < ∞.

The given modulus function:

y = |2x + 6| + 2

Now, we get two equations out of the absolute value function:

y = 2x + 6 + 2

y = 2x + 8

and

y = –2x – 6 + 2

y = –2x – 4

The vertex of the function will be at a point where these two equations are equal. So, we can calculate the vertex as follows:

2x + 8 = –2x – 4

2x + 2x = –4 – 8

4x = –12

x = –3

If x = –3, then y = 2(–3) + 8 = –6 + 8 = 2

Thus, the vertex of the function is (–3, 2).

Now, the values that y can take will range from 2 to infinity as y cannot take values below the vertex.

Thus, the range of the function is 2 < y < ∞.

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The equation that represents the total number of apples that Sally has will be the equations x + y = 8 and 8x + 14y = 58

System of equations are equations that consists of two or more equations.

Let the number of small fruits basket be y

Large fruit basket be y

If Sally buys a total of 5 fruit baskets, then;

x + y = 8

If there are 8 apples in a small fruit basket and 14 apples in a large fruit basket with a combined total of 58 apples, then;

8x + 14y = 58

The equation that represents the total number of apples that Sally has will be the equations x + y = 8 and 8x + 14y = 58

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a) The probability that he will make both free throws is 81 %

b) The probability that he will make at least one free throw is 18 %

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the particular NBA player makes 90 % of his free throws

Now , the equation will be

The probability that the first shot going in = 90 %

And , the probability that the first shot does not go in = 10 %

So , there are 4 scenarios when he is awarded 2 free throws

Both the shots going in = 90 % x 90 %

Both the shots not going in = 10 % x 1- %

Missing one shot and and one shot going in = 10 % x 90 %

And , One shot going in and missing one shot = 90 % x 10 %

a)

Now , the probability that he will make both free throws = Both the shots going in

Substituting the values in the equation , we get

The probability that he will make both free throws = 0.9 x 0.9 = 0.81

The probability that he will make both free throws = 81 %

b)

The probability that he will make at least one free throw = Missing one shot and and one shot going in = 10 % x 90 %   +   One shot going in and missing one shot = 90 % x 10 %

Substituting the values in the equation , we get

The probability that he will make at least one free throw = 0.1 x 0.9 + 0.9 x 0.1

The probability that he will make at least one free throw = 0.09 + 0.09

The probability that he will make at least one free throw = 0.18

The probability that he will make at least one free throw = 18 %

Hence , the probabilities are solved

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The total cost price of the basket is $22.

What is Discount ?

 The discount is determined by dividing the purchase price by the item's par value. The discount is a type of cost price reduction or deduction for a product. It is primarily employed in consumer interactions when discounts on various goods are offered to customers. A percentage represents the discount rate.

Here ,

Original cost price of the basket = $40

After 50% offer the cost price of the bag is,

=> 40- 50% of 40

=> 40 - 20

=> $20.

Now the sales tax is 10% then,

=> 20+ 10% of 20

=> 20+ 2

=>$22

Therefore the total cost is $22 after discount.

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12.566

Hope this helped :T