Two​ trains, Train A and Train​ B, weight a total of 301 tons. Train A is heavier than Train B. The difference of their weights is 217 tons. What is the weight of each​ train?

Answer: $18.49

Step-by-step explanation:

First, add both the tax rate, 4.315 + 4 = 8.315%

Then take 17.07 divided by 100%, then times 8.315% = $1.42

Then add 17.07 + 1.42 = $18.49

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 150\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 150 = (600)(0.05)(t) \implies \cfrac{150}{(600)(0.05)}=t\implies 5=t[/tex]

The solution to the linear equation 3(x + 5) = 1/9 is

x = -4 26/27.

The correct answer is option D; None of these choices are correct.

3(x + 5) = 1/9

open parenthesis

3x + 15 = 1/9

Substract 15 from both sides

3x = 1/9 - 15

3x = (1-135)/ 9

3x = -134/9

divide both sides by 3

x = -134/9 ÷ 3

Multiply by the reciprocal of 3

x = -134/9 × 1/3

= -134/27

x = -4 26/27

Therefore, -4 26/27 is the solution that satisfies the equation 3(x + 5) = 1/9

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Therefore the solution to this question of 2 pulleys is )16 rpm

b)360 rad/min  c)39.6 rad/min d) 7200cm/min

A pseudovector used in physics to express how quickly an object's angular position or orientation changes over time is called an angular velocity, rotational velocity, or angular frequency vector.

For the smaller pulley, it does 48 rpm (revolutions per minute) each revolution is 360 degrees. This indicates that the pulley completes one revolution every second .

radians / π = degrees / 180  

radians = πx 360 / 180 = 2 π radians per second

The distance covered by both pulleys is equivalent for the larger pulley.

then d1 = d2

every second, small pulley covers a distance of 40π (small pulley circumference) = d1

d2 = 40π = 120π (large pulley circumference) x factor (f)

f = 1/3

a) the revolutions per min by larger pulley=16 rpm

b) the speed of smaller pulley = 3*2π=6π=6rad/sec=360rad/min

c) then speed of the large pulley = 1/3 * 2π = 2/3 π = 0.66 rad/sec=39.6rad/min

d)the speed of smaller pulley=7200 cm/min

Therefore the solution to this question of 2 pulleys is )16 rpm

b)360 rad/min  c)39.6 rad/min d) 7200cm/min

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The probability of landing on a 5 and then landing on an even number is 8.3%.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

The number of 5 on the dice is one.

Probability is the ratio of the number of favorable outcome to the total number of outcome.

The number of faces of dice is 6.

The probability of getting 5 is 1/6.

The even faces on the dice are 2, 4, 6.

The number of even number faces is 3.

The probability of getting even number is 3/6 = 1/2.

The probability of two independent event is the product of the probability of the events.

Therefore, the probability is (1/6) × (1/2)

                                              = 1/12

                                               = 0.083

                                              = 8.3%

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Answer:

the percent being discounted is 25% and the flat booking fee is 15

Step-by-step explanation:

t is the cost of the ticket.  -.25t is the 25% coupon being taken off.  The 15 is the booking fee.

Answer:

the answer is 40q

Step-by-step explanation:

8x5 is 40 when using the distributive property

Answer:

Slope is 1, since we use rise over run which is expressed as 1/1

Answer:$26.6

Step-by-step explanation:

Answer:

= 26.6

Step-by-step explanation:

38 * 20/100 = 38 *1/5 = 7.6

38 - 7.6 = 30.4

38 * 10/100 = 38 *1/10 = 3.8

30.4 - 3.8 = 26.6

Answer: x= 6/5

Step-by-step explanation:

Let an unknown number be x

5x - 2 = 4

5x = 6

x= 6/5

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As per the concept of margin of error, the standard deviation increases as the margin of error increases.

The term margin of error is referred as the estimate of a small sample drawn from a relatively large population data.

Here the margin of error is usually governed by parameters such as standard deviation of population, sample size and desired confidence level.

Here we have given that for fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error ......... as the margin of error increases.

And we need to find the missing term in the statement.

Here let us consider that the following values are represented the given situation,

=> σ = Standard deviation for population

=> m = Margin of error

=> Z = Empirical value of Z-score at a given confidence level

Then the minimum sample size for a given confidence level is written as

=> (Z x σ)²/m²

Here from the above given formula it can be inferred that the minimum sample size is directly related to the population standard deviation. Therefore, the minimum sample size required would increase with the increase in population standard deviation.

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Answer:

16[tex]\pi[/tex]

Step-by-step explanation:

Area = [tex]\frac{\pi r^{2} }{4}[/tex]  It is only 1/4 of a circle so we have to divide by 4

a = [tex]\frac{8^{2}\pi }{4}[/tex]

a = 16[tex]\pi[/tex]

The solution to the equations using the substitution method is x = - 2 and y = 0

The two equations given are known as system of equations. The equations have to be solved simultaneously to determine the required values.

y = 6x + 12 equation 1

y = 4x + 8 equation 2

Equate equation 1 and equation 2 together

6x + 12 = 4x + 8

6x - 4x = 8 - 12

2x = -4

x = -4 / 2

x = -2

Substitute for x in equation 1:

y = 4(-2) + 8

y = -8 + 8

Y = 0

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The system of inequalities is:

x + y ≤ 10

x*$1.25 + y*$1.50 ≥ $24

And the graph can be seen below, on the graph, we can see that there are no solutions.

So we need to start by defining the variables we will be using, these are:

First, we know that Larissa wants to make at most 10 loaves of bread, then we can start with the inequality:

x + y ≤ 10

We also know that each banana bread sells for $1.25 and each but bread sells for $1.50, and she wants to make at least $24, then:

x*$1.25 + y*$1.50 ≥ $24

So the system of inequalities is:

x + y ≤ 10

x*$1.25 + y*$1.50 ≥ $24

So to graph these inequalities, we need to shade the region abovce the first line:

x + y = 10

and below the second line:

1.25*x + 1.50*x = 24

The graph of that system of inequalities can be seen below. The graph shows that the system has no real solutions (only has solutions for negative values of x).

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Angle ∠IKJ is 29.5 degrees for triangle IKJ.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The given triangle is IKJ.

The angles are given as follow.

∠JIK = 53°,

∠IKJ = (82-5x), and

∠KJI = (7x+24)°.

We need to find the angle ∠IKJ .

By angle sum property of triangle, the sum of three angles is 180 degrees.

∠JIK+∠IKJ+∠KJI = 180

Fifty three plus eighty two minus five times of x plus seven times of x plus twenty four equal to one hundred and eighty.

53+82-5x+7x+24=180

Add the like terms

159+2x=180

One hundred fifty nine plus two times of x equal to one hundred eighty.

subtract 159 on both sides

2x=21

Divide both sides by 2.

x=10.5

So ∠IKJ is 82-5(10.5)=29.5 degrees.

Hence, the value of angle ∠IKJ is 29.5 degrees.

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Using the percentage writing form, we know that Ivan ate 4 pizza slices.

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage.

The percentage calculation formula is (value/total value)100%.

Add all percentages as numbered values, divide by the total number of sets, and you get the average percentage.

The results by 100.

So, we know that:

Ivan ate 40% of the pizza.

And the pizza was cut into 10 slices.

Rewrite the percentage value as:

4/100 = 0.4

We can calculate how many slices Ivan consumed by multiplying the percentage value by the number of slices:

10 + 0.4 = 4

Hence, Ivan ate 4 slices of pizza.

Therefore, using the percentage writing form, we know that Ivan ate 4 pizza slices.

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Answer:

Unless these took place in different time periods, Laticia did first.

Step-by-step explanation:

28.7 < 42.7

Answer:

-2 = x 4-2 square units

Step-by-step explanation:

sum = as per as chart

The unknown angle in the triangle is as follows:

∠E = 100 degrees.

The sum of angles in a triangle is 180 degrees.

In the diagram, BCD is cut by transversal ACE , AB and perpendicular to BCD and CE ≅ ED.

Therefore,

∠ACB = 180 - 50 - 90 (sum of angles in a triangle)

∠ACB = 180 - 140

∠ACB = 40 degrees

Therefore,

∠ACB ≅ ∠DCE

Hence,

∠DCE = 40 degrees.

Triangle CDE is an isosceles triangle since CE ≅ DE.

Hence,

∠CDE = 40 degrees

∠E = 180 - 40 - 40

∠E = 180 - 80

∠E = 100 degrees.

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Answer:

104.5 min

Step-by-step explanation:

47.5:5=x:11

1. Simplify

9.5:1=x:11

2.Solve

x=104.5

Answer:

[tex]\huge\boxed{\sf k = 3}[/tex]

Step-by-step explanation:

[tex]5+6i+(-2+ki)=3+9i\\\\5 + 6i-2+ki=3+9i\\\\Combine \ like \ terms\\\\5-2+6i+ki=3+9i\\\\3+(6+k)i=3+9i\\\\Comparing \ both \ sides\\\\6 + k = 9\\\\Subtract \ 6 \ both \ sides\\\\k = 9-6\\\\k = 3\\\\\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

wait

There is ONLY ONE __ line parallel to the provided line that passes through a certain point that is not contained in the supplied line.

Parallel lines are any two or more lines that are in the same plane but never cross one another ( never intersect). Both have the same slope and are equally far from one another.

We have a line and a point outside the line;

from that point, we can generate many lines, but only one of those lines will be parallel to the line as it is. From a point, we can make many lines, but that point can only create one line that will be parallel to a given line.

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People in my family ordered 1 chicken dinner and 5 steak dinner.

There are total 6 peoples in a family.

Let's x number of people order chicken dinner

and y number of people order steak dinner.

Here we have to use concept of linear equation.

we have to make 2 linear equation and solve them to get the value.

sum of number of people is 6.

[tex]x + y = 6[/tex] --- i

total bill came to $99.

1 chicken dinner takes $14.

So x chicken dinners takes x*14

1 steak dinner takes $17.

So y steak dinners takes y*17.

Sum of both dinners price

[tex]x*14+y*17 = 99[/tex] -- ii

From equation i x = 6 - y.

put value of x in equation ii.

(6-y)*14+y*17 = 99

84-14*y+17*y = 99

3*y = 99-84

3*y = 15

y = 5

x = 6-5 = 1.

So 1 people ordered chicken dinner and 5 people ordered steak dinner.

Given Question is incomplete Complete Question here

Your family goes to a southern style restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14 and some order the steak dinner for $17. If the total bill was $99 l, how many people ordered each dinner?

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Answer: The number is 12

Step-by-step explanation:

Let x= the number that is unknown

The sum of three and a "number"= 3+"x"

Divided by three, means that x+3 is divided by 3

Is five, means that (x+3)/3=5

Algebra:

[tex]\frac{x+3}{3}=5[/tex]

Multiply by 3 to arrive at x+3=15

Subtract both sides by 3, then x=12

Answer:

10626 different recital programs possible

Step-by-step explanation:

Since  there is no repetition we can tackle this problem in the following manner.

Out of the 23 pieces, the pianist can choose the first one in 23 ways

Out of the remaining 22 pieces she can choose the second one in 22 different ways

Out of the remaining 21 pieces she can choose the third one in 21 different ways

So total number of ways in which 3 pieces can be played without repetition is 23 x 22 x 21 = 10,626 ways

There is a formula for this kind of situation
If there are a total of n items and you want to choose r items from this, the number of possible ways to do this without repetition is given by the formula

[tex]_{n}P_{r} = \dfrac{n!}{(n-r)!}[/tex]

In this case, n = 23, r = 3 so we get
[tex]_{23}P_{3} = \dfrac{23!}{(23-3)!} = \dfrac{23!}{20!} = 23 \times 22 \times 21 = 10626[/tex]

Same as the above

Answer:

Step-by-step explanation:

To prove this statement, we can use the contrapositive. The contrapositive of the statement "If a + b > 100, then a, b, or both must be greater than 50" is "If a and b are both less than or equal to 50, then a + b is less than or equal to 100."

To prove the contrapositive, we must show that if a and b are both less than or equal to 50, then a + b is indeed less than or equal to 100. This is easy to do, because if a and b are both less than or equal to 50, then the largest possible value for a is 50 and the largest possible value for b is 50. Therefore, the largest possible value for a + b is 50 + 50, which is equal to 100.

Since the contrapositive is true, it follows that the original statement must also be true. Therefore, we have proven that if a + b > 100, then a, b, or both must be greater than 50.

Answer:

108

324

12

and 54

Step-by-step explanation:

Answer: C≈28.27cm

Step-by-step explanation:

C=2πr=2·π·4.5≈28.27433cm

Answer:

  28.3 cm

Step-by-step explanation:

You want the circumference of a circle with radius 4.5 cm.

The circumference of a circle is given by ...

  C = 2πr

For the given circle, the circumference is ...

  C = 2π(4.5 cm) = 9π cm ≈ 28.3 cm

The circumference is about 28.3 cm.

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