The train stops to pick passengers every 500 yards. The same train also stops to pick up supplies every 600 yards. What is the shortest distance in yards the train will travel to pick up both passengers and supplies at the same stop?

Hey there,

Please check the picture attached as my answer.

Convey me if you have any doubts.

~ Benjemin360

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

\(\cfrac{a}{18}=\cfrac{32}{a}\implies a^2=(32)(18)\implies a=\sqrt{(32)(18)}\implies a=24 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{b}{50}=\cfrac{32}{b}\implies b^2=(32)(50)\implies b=\sqrt{(32)(50)}\implies b=40\)

Answer: 11/4

or 2.75

Step-by-step explanation:

The minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.

We are given that a water pumping station is to be built on a river at point P in order to deliver water to points A and B. The design requires that LAPD = /BPC so that the total length of piping that will be needed is a minimum. We need to find this minimum length of pipe.

The given figure is shown below: \(AB = 10 \ miles\)\(BC = 6 \ miles\)\(CP = 12 \ miles\). We are given that \(LAPD = LCPB\).

Now, we need to find the minimum length of pipe required for delivering the water to points A and B.The total length of the pipe, \(L_{total} = LA + AB + BP\)Since \(LAPD = LCPB\), we can say that\(AP^2 + PD^2 = BP^2 + PC^2\).

From the triangle ACP, we can say that\(AC^2 = AP^2 + PC^2\). So, we can substitute AP^2 + PC^2 with AC^2 to get\(AP^2 + PD^2 = BP^2 + AC^2\)Now, we can substitute AP = AC - PC and BP = BC + PC in the above equation to get\((AC - PC)^2 + PD^2 = (BC + PC)^2 + AC^2\).

After solving this equation, we get\(AC = \frac {37}{8}\) and \(PC = \frac {27}{8}\)Now, we can calculate the length of pipe required as follows: \(L_{total} = LA + AB + BP = 10 + 6 + \frac {27}{8} = \boxed{20.375 \ miles}\). Therefore, the minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.

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Answer:

Step-by-step explanation:

We can use the formula for a confidence interval for the population mean:

CI = x¯¯¯ ± z*(σ/sqrt(n))

where:

x¯¯¯ is the sample mean, which is 81.

σ is the population standard deviation, which is 11.8 (assuming the sample is drawn from a normally distributed population).

n is the sample size, which is 175.

z is the z-score corresponding to the desired level of confidence, which is 2.33 for a 98% confidence level.

Substituting the known values, we get:

CI = 81 ± 2.33*(11.8/sqrt(175))

Calculating this expression, we get:

CI ≈ (79, 83)

Therefore, a 98% confidence interval for the population mean is approximately (79, 83).

Therefore, the answer is (B) (79, 83).

Answer:

About 583,160 books.

Step-by-step explanation:

1912 times 305 equals 583160.

Hello!

For this you would just need to multiple straight across. Here's how you would set it up:

3/4 ·1/8

Then you would multiple 3 x 1 = 3

And 4 x 8 =32

Your answer should be 3/32, it cannot be simplified so that is the final answer :).

The equation of the hyperbola on the graph is (y - k)²/a² - (x - h)²/b² = 1

The graph represents the given parameter

On the graph, we can see that the the coordinates are not labelled

This means that the equation that can be derived from the graph is the general form of the hyperbola which is represented as

(y - k)²/a² - (x - h)²/b² = 1

The above equation is true because the graph of the hyperbola has a vertical transversal

Next, the label of the variables are

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Answer:

Step-by-step explanation:

Well it doesn't help you very much, but the answer is A. What this does is separates 7/8 x so that (x/8) sits by itself. After you subtract 3/4 from both sides, you can divide both sides by 7. When you do that, you get x/8 = something, but the fractions are going to be awkward at best. I'll just do a very quick run through

7(x/8) = -6 - 3/4

7(x/8) = - 6.75                     Divide by 7

x/8 = 0.9642                      Multiply by 8

x = 8 * 0.9642

x = 7.7143

The measure for the exterior angle to the angle X of the triangle XYZ is 112.55°

In any triangle, an exterior angle is equal the sum of its two opposite interior angles is equals.

For the triangle XYZ, the exterior angle to the angle X is equal to the sum of the two opposite interior angles Y and Z

angle Y = 38.25° and angle Z = 74.3°

exterior angle to X = 38.25° + 74.3°

exterior angle to X = 112.55°

This implies that the angle X = 180° - 112.55° = 67.45°

and 67.45° + 38.25° + 74.3° = 180° which is true for the sum of interior angles of a triangle.

Thus, exterior angle to the angle X that is derived to be 112.55° is true for the triangle XYZ.

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Answer:

112.55

Step-by-step explanation:

i got it right

Answer:

s = \(\frac{149}{10} - \frac{7t}{10}\)

t = \(\frac{149}{10} -\frac{10s}{7}\)

Step-by-step explanation:

(Hope this helps can I pls have brainlist (crown)☺️)

\(10s + 7t = 149 \\ 10s + 7t + - 7t = 149 + - 7t \\ 10s = - 7t + 149 \\ \frac{10s}{10} = \frac{ - 7t + 149}{10} \\ \boxed{s = \frac{ - 7}{10} t + \frac{149}{10} }\)

____________________

\(5s+7t=99 \\ 5s+7t+−7t=99+−7t \\ 5s=−7t+99 \\ \frac{5s}{5} = \frac{ - 7 + 99}{5} \\ \boxed{s = \frac{ - 7}{5} t + \frac{99}{5} }\)

correct me if I'm wrong.

Using compound interest formula, her balance after retirement is $430797.77

To calculate the balance of Marissa's retirement account after 30 years, we need to determine how much her savings account and index fund will be worth after 30 years, taking into account the interest earned and her monthly contributions.

First, we'll calculate the balance of her savings account:

Initial deposit: $2000

Interest rate: 1.5%

Monthly contribution: $150

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her savings account after 30 years will be:

2000*(1+0.015/12)^360 + 150*(((1+0.015/12)^360-1)/(0.015/12))

A = $71280.33

Next, we'll calculate the balance of her index fund:

Initial deposit: $1000

Interest rate: 6.8%

Monthly contribution: $300

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her index fund after 30 years will be:

A = 1000*(1+0.068/12)^360 + 300*(((1+0.068/12)^360-1)/(0.068/12))

A = $359517.44

Then we can add the balance of both the savings account and the stock market to get the total balance of Marissa's retirement account.

Her balance = $71280.33 + $359517.44 = $430797.77

Please note that the above answer is an estimation, in reality there are other factors such as taxes, inflation, fees, and market conditions that should be considered in a real-world scenario.

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Answer:

Step-by-step explanation:

Area = \(Area = \pi r^2 = \pi(3)^2 = 9\pi = 28.27\\Circumference = 2\pi r = 2\pi 3 = 6\pi = 18.85\)

Answer:

\(area = 28.27 {m}^{2} \\ c = 18.84m\)

Explanation is attached to the picture

Hope this helps you.

Answer:

500

Step-by-step explanation:

54%=0.54

0.54x=270

x=270/0.54

x=500

Answer : 500

Whole : ?

Part : 270

Percentage : 54

100 : 100

How to find the Whole of a Part . . . Part x 100 / Percent

270 x 100 = 27,000 / 54 = 500

270 is 54% of 500

The three true statements are as follows:

In the list, there are several true statements and some of them include the facts that all triangles are polygons, they are closed figures and they have three straight sides.

A polygon is a shape with two or more sides. Triangles ahve three sides, so we can easily address them as polygons. Also, all triangles are closed figures and they also have three straight sides.

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A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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Answer:  3×22+c≤85

Step-by-step explanation: i think the answer is 3×22+c≤85 because 3x 22 represent the total cost of azaleas + c the cost of salvia is less than or equal to 85 because the buget is 85 and it cannot be greater

Hope this helped

The inequality for the given situation is 66+c ≤ 85.

Given that, Frank plans to spend no more than $85 on plants for his front garden. He purchases a salvia and 3 azaleas. The azaleas cost $22 each.

In mathematics, inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Let c be the cost for a salvia.

Three azaleas + A salvia ≤ 85

3×22+c ≤ 85

⇒ 66+c ≤ 85

Therefore, the inequality for the given situation is 66+c ≤ 85.

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Answer:

(0,-2)

Step-by-step explanation:

Plug in each value for the equation

-3(0) - (-2) = 2

0 - (-2) = 2

2=2

Answer:

Step-by-step explanation:

The volume of this pyramid in cubic inches is 16.

Given that,

The base and height is 8 and 6.

Based on the above information, the calculation is as follows:

The volume is

= 16

You should write down and track only the 20lbs weight during your weighted exercise while ignoring your body weight.

Actual weight is also referred to as gross weight and it can be defined as the exact (original) weight of an object, as measured using an appropriate weighing scale.

This ultimately implies that, you would write down and track only the 20lbs weight during your weighted exercise such as a single rep of weighted overhand chin ups.

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Answer:

$2,500 or 25%

Step-by-step explanation:

Let's use the same example:

Cost of Equipment = $10,000

Useful Life = 4 years

Depreciation Rate = (Annual Depreciation / Cost of Equipment) * 100

Annual Depreciation = Cost of Equipment / Useful Life

Annual Depreciation = $10,000 / 4 years

Annual Depreciation = $2,500

Depreciation Rate = ($2,500 / $10,000) * 100

Depreciation Rate = 0.25 * 100

Depreciation Rate = 25%

Answer:

Step-by-step explanation:

17.308

this is the decimaal

The original volume of the gas would be 4.00 liters

Boyle's law is a gas law that states that the pressure of a gas is inversely proportional to it's volume with temperature kept constant.

It is represented thus;

P1V1 = P2V2

Where P1 = Original pressure = 6 atmospheres

V1 = Original volume =?

P2 = Final pressure =4 atmospheres

V2 = Final volume= 6 liters

Make the original volume V1, subject of formula

V1 = P2× V2 ÷ P1

V1 = 4× 6 ÷ 6 = 24 ÷ 6 = 4. 00 liters

Hence, the original volume of the gas is 4.00 liters

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For Pizza 1, Adam multiplies 6 by 6 slices

For Pizza 2, he multiplies 6 by 7 slices

For Pizza 3, he multiplies 4 by 7 slices, while

for Pizza 4, he multiplies 4 by 8 slices.

A product is the outcome of multiplication or an expression that indicates factors to be multiplied in mathematics.

To put it another way, we may deduce that in math, multiplying implies adding equal groups.

The number of items in the group grows as we multiply. A multiplication issue includes the two elements and the product. The factors in the multiplication problem, 4 7 = 28, are the numbers 4 and 7, while the result (product) is the number 28.

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Answer:

The number can have no more than 5 digits

Step-by-step explanation:

Answer:

You just have to put the numbers in order hopefully this helps.

Step-by-step explanation:

Answer: Hello There!...................

The given data is expressed as 1204, 1206, 1345, 1306, 1207, 1078, 1357, 1232, 1228, 1302, 1189, 1177, 1083, 1094, 1326, 1071, 1427, 1348, 1420, 1253, 1270 The number of items in the data, n is 21. The lowest value is 1071 while the highest value is 1427. The convenient starting point would be 1070.5 and the convenient ending point would be 1427.5 The number of class intervals is √n = √21 = 4.5 Approximately 5 The width of each class interval is (1427.5 - 1070.5)/5 = 72 The end of each class interval would be 1070.5 + 72 = 1142.5 1142.5 + 72 = 1214.5 1214.5 + 72 = 1286.5 1286.5 + 72 = 1358.5 1358.5 + 72 = 1430.5 The frequency for the fifth class, that is between 1358.5 to 1430.5 would be 2

Step-by-step explanation:

Mark me brainest please. Hope this helps. Anna ♥

Answer:

With the metric system, the formula for BMI is weight in kilograms divided by height in meters squared. Since height is commonly measured in centimeters, an alternate calculation formula, dividing the weight in kilograms by the height in centimeters squared, and then multiplying the result by 10,000, can be used.

Hope this helped

Step-by-step explanation:

The machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

0.1587*850 = 134.857..

A vending machine automatically pours soft drinks into cups.

The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6oz and a standard deviation of 0.4oz.

Examine figure 7.- and answer the following questions.

a) estimate the probability that the machine will overflow an 8oz cup.

Procedure:

Determine the z-score for 8

z(8) = (8-7.6)/0.4 = 0.4/0.4 = 1

P(x>8) = P(z>1) = 0.1587..

-----------------------

b) Estimate the probability that the machine will not overflow an 8oz cup.

P(z<1) = 1 - 0.1587 = 0.8413..

-----------------

c) the machine has just been loaded with 850 cups. How many of these do you expect will overflow when served?

0.1587*850 = 134.857..; Rounded down you get 134 cups

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Answer:

f(x) =  -2 log3x - 3.

Step-by-step explanation:

f(x) = log3x

Reflecting over x axis makes it  f(x) = f(x) = -log3x

Vertical stretch gives -2 log3x

Finally moving the graph down 3 units gives  -2 log3x - 3.