Two​ trains, Train A and Train​ B, weigh a total of 147 tons. Train A is heavier than Train B. The difference of their weights is 65 tons. What is the weight of each​ train?

The perimeter of the rectangular floor is the sum of its dimensions

The perimeter function is \(\mathbf{P(x) = \frac{2x^2 + 3000}x}\)

The area of the rectangular floor is given as: 1500

The area of a rectangle is calculated as:

\(\mathbf{Area = xy}\)

Where: x and y represents the width and the length of the floor, respectively.

So, we have:

\(\mathbf{xy = 1500}\)

Make y the subject

\(\mathbf{y = \frac{1500}x}\)

The perimeter of the rectangular floor is:

\(\mathbf{P = 2(x + y)}\)

Substitute \(\mathbf{y = \frac{1500}x}\)

\(\mathbf{P = 2(x + \frac{1500}x)}\)

Take LCM

\(\mathbf{P = 2(\frac{x^2 + 1500}x)}\)

Open bracket

\(\mathbf{P = \frac{2x^2 + 3000}x}\)

Express as a function

\(\mathbf{P(x) = \frac{2x^2 + 3000}x}\)

Hence, the perimeter function is \(\mathbf{P(x) = \frac{2x^2 + 3000}x}\)

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There are 56 milligrams in 8 milliliters of the drug if the drug's label says each milliliter contains 7 milligrams of the substance.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Let x milligrams would in 8 ​milliliters.

We can write this as a ratio as

As per the given information,

1 milliliter  : 7 milligrams  = 8 milliliter   : x milligrams

⇒ 1 / 7 = 8 / x

⇒ x = 8 × 7

⇒ x = 56 milligrams

Hence, there are 56 milligrams in 8 ​milliliters of the drug.

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Answer:

84.375%

Step-by-step explanation:

Total no. of computation problem=32-5=27

Total no. problems in the assignment=32

=) per%= 27/32×100%=84.375%

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The domain and range of the function  f(x) = 3/x + 2 are  (-∞, 0) ∪ (0, ∞) and  (-∞, 2) ∪ (2, ∞). The vertical and horizontal asymptotes are x = 0 and y = 2 respectively

In mathematics, the domain of a function is the set of all possible input values (also known as the independent variable) for which the function is defined. The range of a function is the set of all possible output values (also known as the dependent variable) that the function can produce.

To determine the domain and range of a function, it's important to consider the nature of the function, its graph or formula, and any restrictions that may apply.

The function f(x) = 3/x + 2

The domain of the function is (-∞, 0) ∪ (0, ∞)

The range of the function is (-∞, 2) ∪ (2, ∞)

The x - intercept is (-3/2, 0)

The y - intercept does not exist

The vertical asymptotes is x = 0

The horizontal asymptotes is y = 2

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Answer:

Jelly beans are $2.50 per pound

Almonds are $1.75 per pound

Step-by-step explanation:

3j + 2a = $11

5j + 6a = $23

Multiply equation 1 by 3

9j + 6a = $33

Subtract

9j + 6a = $33

-(5j + 6a = $23)

=(4j + 0a = $10)

4j = $10

j = $2.50

Plug j into any equation.

3(2.5) + 2a = $11

7.5 + 2a = $11

2a = 3.5

a = $1.75

Jelly beans are $2.50 per pound

Almonds are $1.75 per pound

Answer:The probability as a decimal to the nearest hundredth is 0.89

Step-by-step explanation:

i just did it and got it right

The probability that the next customer will pay with cash as a decimal to the nearest hundredth is 0.89

"Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are."

"A decimal is a fraction written in a special form. Instead of writing \(\frac{1}{2}\), for example, you can express the fraction as the decimal 0.5, where the zero is in the ones place and the five is in the tenths place."

We have

Customers paid cash = 93

Customers used debit card = 7

Customers used credit card = 5

Number of favorable outcomes n(S)

= 93

Total number of outcomes n(E)

= 93+7+5

= 105

The probability that the next customer will pay with cash

= \(\frac{n(S)}{n(E)}\)

= \(\frac{93}{105}\)

= \(0.885\)

= 0.89 (nearest hundredth)

Hence, the probability that the next customer will pay with cash as a decimal to the nearest hundredth is 0.89.

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Answer:

The correct answer is: (just took the test)

if a square is a rectangle and if a rectangle is a parallelogram, then a square is a parallelogram

if there is a children’s movie playing at the cinema, Maria’s mother will buy popcorn for Maria

Step-by-step explanation:

For the given answers the answers that follow the law of syllogism is options A and  B.

Given that,
4 statement is given, and we have to pick the statement that follows the low of syllogism.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here
There are only two statements that are following the law of syllogism. ie.

A. If there is a children's movie playing at the cinema, Maria's mother will take her to see it. When Maria's mother takes her to the movie, she buys Maria popcorn. Therefore, if there is a children's movie playing at the cinema, Maria's mother will buy popcorn for Maria.

B. If a square is a rectangle and if a rectangle is a parallelogram, then a square is a parallelogram.

C. and D. are invalid statement because it does not follow the Law of Syllogism.

Thus, for the given answers the answers that follow the law of syllogism is options A and  B.

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Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70

Answer:

Answer is 12

Step-by-step explanation:

I hope it's helpful!

Answer:

1,861.1 cubic centimeters

Step-by-step explanation:

Volume of a cylinder is

\(v = \pi {r}^{2}h\)

so you would plug it in and solve

\(v = \pi ({6.6})^{2}13.6\)

Answer:

Solution

\(x = - 3,\: y = -3\)

Step-by-step explanation:

If the objective is to solve for the system of equations
- 7x - 5y = 36    [1]

x = 2y + 3    [2]

Then the process is as follows

Answer:

8.25

Step-by-step explanation:

Divide 13.20 by 1.6 to get 8.25 because if the total is 13.20 and there is 1.6 pounds of almonds then you can find the price per pound

Based on the quantity of almonds bought and the price paid, the cost per pound of almond is $8.25.

Haley bought 1.6 pounds of almonds for $13.20.

The amount she effectively paid for each pound of almonds is therefore:

= Total cost / Quantity of almonds

Solving would give:

= 13.20 / 1.6

= $8.25

In conclusion, a pound of almonds cost $8.25.

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Answer:

A

Step-by-step explanation:

is moving by 2 but there negative numbers which makes it -2

Answer:

C)  I, III, IV, II

Step-by-step explanation:

Convert each number into a decimal:

\(\textsf{I.} \quad \dfrac{58}{67}=0.86567...\)

\(\textsf{II.} \quad 0.58\%=\dfrac{0.58}{100}=0.0058\)

\(\textsf{III.} \quad 58\%=\dfrac{58}{100}=0.58\)

\(\textsf{IV.} \quad 5.8\%=\dfrac{5.8}{100}=0.058\)

Comparing the tenths of all the numbers, 8 is the biggest tenth, so 58/67 is the largest number.

The next biggest tenth is 5, so 58% is the next largest number.

The two remaining numbers have zero tenths, so compare their hundredths. 5 is the largest hundredth, so 5.8% is the next largest number.  Therefore, 0.58% is the smallest number.

Therefore, the given set of numbers in order from greatest to least is:

Answer:

c) I, III, IV, II

Step-by-step explanation:

Values of l, ll, lll & lV respectively,

→ 58/67, 0.58%, 58%, 5.8%

→ 0.87, 0.0058, 0.58, 0.058

Arranging them in descending order,

→ 0.87 > 0.58 > 0.058 > 0.0058

→ 0.87, 0.58, 0.058, 0.0058

→ l, lll, lV, ll

Hence, the option (c) is correct.

El número "Novecientos mil cuatrocientos ochenta y nueve" se representa como 900,489 en notación numérica.

Por otro lado, el número "cuarenta mil dos" se representa como 40,002.

Si estamos buscando determinar cuál de estos dos números es mayor, podemos comparar las cifras en cada posición.

Comenzando desde la izquierda, el primer dígito de 900,489 es 9, mientras que el primer dígito de 40,002 es 4.

Dado que 9 es mayor que 4, podemos concluir que 900,489 es mayor que 40,002.

En general, al comparar números, se debe observar cada posición en orden de mayor a menor importancia.

Esto significa que el primer dígito a la izquierda es el más significativo y tiene más peso en el valor total del número.

Si los dígitos en la posición más significativa son iguales, se debe pasar a la siguiente posición hasta que se encuentre una diferencia.

En este caso, dado que el primer dígito de 900,489 es mayor que el primer dígito de 40,002, no es necesario comparar los dígitos en posiciones posteriores.

Por lo tanto, podemos concluir que el número "Novecientos mil cuatrocientos ochenta y nueve" (900,489) es mayor que "cuarenta mil dos" (40,002).

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Answer:

B 7x+1

Step-by-step explanation:

(5x+2)+(4x-3)

(5x+4x) = 7x

(2-3) = 1

7x+1

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer: 625 steps per hour

Step-by-step explanation:

10,000/16=625

The complete expression is (2 × x) + (2 × 6). This is an equivalent expression to the given expression.

What is an expression?

A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

Given expression is

2 (x+6)

Distributive property: The same outcome is obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend by the number separately and combining the resulting products.

The mathematical representation is a(b+c) = ab + ac.

Apply the Distributive property in the given expression:

(2×x) + (2×6)

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Answer:

Step-by-step explanation:

x^2 - 5x + 6 = 0

(x - 2)(x - 3)

So the critical point are x = 2 and x = 3.

The graph of the function opens upwards and pass through the x axis at (2, 0) and (3, 0).

So the required range is the values of f(x) between  when x = 2 and x = 3

that is  2 < x < 3.

Answer:

Step-by-step explanation:

1 Factor {x}^{2}-5x+6x

2

−5x+6.

(x-3)(x-2)<0

(x−3)(x−2)<0

2 Solve for xx.

x=3,2

x=3,2

3 From the values of xx above, we have these 3 intervals to test.

\begin{aligned}&x<2\\&2<x<3\\&x>3\end{aligned}

​

x<2

2<x<3

x>3

​

4 Pick a test point for each interval.

For the interval x<2x<2:

Let's pick x=0x=0. Then, {0}^{2}-5\times 0+6<00

2

−5×0+6<0.

After simplifying, we get 6<06<0, which is false.

Drop this interval..

For the interval 2<x<32<x<3:

Let's pick x=\frac{5}{2}x=

25

​

. Then, {(\frac{5}{2})}^{2}-5\times \frac{5}{2}+6<0( 25) 2−5× 25+6<0.

After simplifying, we get -0.25<0−0.25<0, which is true.

Keep this interval..

For the interval x>3x>3:

Let's pick x=4x=4. Then, {4}^{2}-5\times 4+6<04 2 −5×4+6<0.

After simplifying, we get 2<02<0, which is false.

Drop this interval..

5 Therefore,

2<x<3

2<x<3

37.5w + 155.95 = 455.95; where w = 8; signifies the number of weeks required to babysit the business in order to purchase the gaming chair.

A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality.

Equations can be categorized as identities or conditional equations.

w = (455.95-155.95)/(37.50)

=300/37.50

=8

So, number of weeks = 8

As a result, w = 8 and 37.5w + 155.95 = 455.95 is the solution.

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The  expression represents the total surface area of the prism is

2 (5 * 7) + 2 (4 * 7) +  2  (4 * 5)

The term "TSA" stands for "Total Surface Area" of a prism. The Total Surface Area represents the  sum of the areas of all the faces (including the bases) of the prism.

for the rectangular prism, the Total Surface Area can be calculated using the formula:

TSA = 2lw + 2lh + 2wh

where

l = 5

w = 4

h = 7

plugging in the values gives

TSA = 2 (5 * 7) + 2 (4 * 7) +  2  (4 * 5)

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Step-by-step explanation:

To graph them, sub 2 random x/y numbers and find the corresponding coordinates then plot these 2 points on the axes then connect to form a straight line :)

Topic: coordinate geometry

If you like to venture further, feel free to check out my insta (learntionary). It would be best if you could give it a follow. I'll be constantly posting math tips and notes! Thanks!

Answer:

the answer is 13 for this problem

Answer:

13

Step-by-step explanation:

\({a}^{2} + {b}^{2} = {c}^{2} \)

\( {5}^{2} + {12}^{2} = {c}^{2} \)

\( {c}^{2} = 169\)

\(c = \sqrt{169} \)

\(c = 13\)