Una Sección, compuesta por 18 soldados y 2 suboficiales, entra en combate y gasta la quinta parte del total de la munición de dicha Sección. Si la cantidad de cartuchos gastados por los soldados excede en 424 cartuchos al número de cartuchos gastados por los suboficiales. ¿Cuántos cartuchos gastaron los soldados y cuántos los suboficiales sabiendo que la dotación completa por cada hombre es de 175 cartuchos?

Answer:

12y=$3

114 cans

Step-by-step explanation:

Let the cost of every can be represented by y. Therefore, for 12 cans, the cost will be the product of y cans and 12 hence cost is 12y

Since the cost incurred is $3 then we can represent these as

12y=$3

To solve for y, we divide both sides by 12 hence

Y=$3/12=$0.25

To find the number of cans that one will get with a buget of $28.5, we divide the budget by the cost of a can. This will be $28.5/$0.25=114 cans

Answer:

iihiuhihiuiu

Step-by-step explanation:

ioiiuouioiiouuioooooooooooooooooooooiuuguygy

Answer:92.5%

Step-by-step explanation:

Divide 100 by 80 to find the percentage each student counts for

Then multiply the product(1.25) by 74 (the present students) to get the answer

Answer: 74/80 = 92.5% of the students are present.

Answer:

y=mx+b

Step-by-step explanation:

The formula to find the slope is y=mx+b

hope this helps

Answer:

you need to know what the pairs of numbers match to get a possible answer

Step-by-step explanation:

once u know that you can do the rest of the math and it depends how to multiply

Answer:(t-4)(4mn-1)

Step-by-step explanation:

Answer:

Blank 1: 40

Blank 2: 10

Step-by-step explanation:

You can start by representing the speed of the water as x and the speed of the dolphin as y, and writing an equation.

y+x=50

y-x=30

Adding these two equations together, you get:

2y=80

y=40 for the speed of the dolphin in still water. Now, you an use one of the previous equations to find the speed of the current.

40-x=30

x=10

Hope this helps!

Answer:

75

Step-by-step explanation:

9x5=45

15x5=75

Answer:

75

Step-by-step explanation:

9:15=45: _

very similar to cross multiplying

9/15  =  (45/ something)

something =  45 / (9/15)  =   45 * (15/9) = 5*15 = 75

Answer:

3

Step-by-step explanation:

to convert the centimeters to inches, divide 137. 16 by 2.54

you should get 54

then divide by 18

you get three

You can make 3 necklaces from 137.16 centimeters of silver chain, given that each necklace is 18 inches long. We first converted the necklace length to centimeters, and then divided the total length of silver chain by the length of each necklace.

To find out how many necklaces can be made from 137.16 centimeters of silver chain, we first need to convert the units because the length of the necklace chain is given in inches, while the total amount of silver chain is given in centimeters.

We know that 1 inch is equal to 2.54 centimeters. Therefore, if each necklace is 18 inches long, the length of each necklace in centimeters is 18 inches * 2.54 cm/inch = 45.72 cm.

Now, to find the number of necklaces that can be made, we divide the total length of silver chain by the length of each necklace. That is 137.16 cm / 45.72 cm/necklace = 3 necklaces (rounded down to the nearest whole necklace, because we cannot make a fraction of a necklace).

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Answer:

105 sqrt(2) =x

Step-by-step explanation:

Since this is a right triangle we can use trig functions

so  sin theta = opposite side/hypotenuse

    sin 45 = x/210

Multiply each side by 210

210 sin 45 = x

We know sin 45 = sqrt(2)/2

210 * sqrt(2)/2 = x

105 sqrt(2) =x

Answer:

B

Step-by-step explanation:

Using trig ratios

sin(45) = opposite/hypotenuse

sin(45) = x/210

sqrt(2)/2 = x/210

x = 210sqrt(2)/2

x = 105sqrt(2)

Answer:

y=5/2x + 8

Step-by-step explanation: Y=mx+b is the equation for slope intercept form. Basically you just have to plug in the numbers.

Given:

It is given that the value of the graph when the input 7 is [tex]g(x)=4[/tex]

We need to determine the value of x when [tex]g(x)=4[/tex]

Value of x when [tex]g(x)=4[/tex]:

The value of x can be determined by using the graph.

From the graph, we need to determine the value of x when [tex]g(x)=4[/tex] other than the value x = 7.

This can be determined by finding the point at which the line meets the point y = 4, we can find the corresponding x - value.

Thus, from the graph, it is obvious that the graph also meets the point y = 4 when x = -8.

Therefore, the input value is x = -8 which makes [tex]g(x)=4[/tex]

Hence, the input value other than 7 for which [tex]g(x)=4[/tex] is x = -8.

The input value other than 7 for which g(x) = 4 is x = -8.

It is given that the value of the graph when the input 7 is g(x)=4

We need to determine the value of x when g(x)=4

Value of x when g(x)=4:

The value of x can be determined by using the graph.

This can be determined by finding the point at which the line meets the point y = 4, we can find the corresponding x - value.

From the graph, we get that the graph of g(x) passes through the point (x = -8, y = 4),

Thus, from the graph, it is obvious that the graph also meets the point y = 4 when x = -8.

Then indeed, the input value (x) other than 7 for which g(x) = 4 is x = -8.

As, the function g(x) takes the value of 4 at x = -8, according to the graph.

Therefore, the input value is x = -8 which makes g(x) = 4.

Hence, the input value other than 7 for which g(x) = 4 is x = -8.

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Answer:

Step-by-step explanation:

If two quantities are inversely proportional, it means that an increase in the value of one variable would cause a corresponding decrease in the other variable and vice versa.

Given that M varies inversely as the square of P, if we introduce a constant of proportionality, k, the expression becomes

M = k/P²

If M = 9 when P = 2, then

9 = k/2² = k/4

k = 9 × 4 = 36

Therefore, the inverse variation equation is

M = 36/P²

When P = 3,

M = 36/3² = 36/9

M = 4

Answer:

3^9

Step-by-step explanation:

when multiplying and the bases are the same number simply add the exponents ex: a^b x a^c = a^b+c

Answer: The wheels turn about 3771 times in 5 miles.

Step-by-step explanation:

Given, Kelly rides on her bicycle such that the number of times wheels turn for every 140 feet = 20

Turns for every feet = [tex]\dfrac{20}{140}=\dfrac{1}{7}[/tex] ...(i)

To find : Number of times wheels turn in 5 miles.

Since , 1 mile = 5,280 feet

Then, 5 miles = 5 x (5,280 feet) = 26,400 feet

Now , Number of times the wheels turn in 26,400 feet = 26400 x (Turns for every feet)

[tex]26400\times\dfrac{1}{7}=3771.42857143\approx3771[/tex]   [From (i)

Hence, the wheels turn about 3771 times in 5 miles.

Answer:

Part to part ratios are comparing two different things that sum up to its whole, and part to whole ratios are a part of something compared to the whole thing.

Step-by-step explanation:

It's kinda hard to explain..

Answer:

sin ( θ ) = 3√21 / 17

Step-by-step explanation:

Given:-

- The angle (θ) lies in the first quadrant. Where theta is defined as:

                               cos ( θ ) = 10 / 17

Find:-

- Find sin ( θ ) :

Solution:-

- We will draw a right angle triangle in the first quadrant. With base, B = 10 and hypotenuse H = 17. Since,

                               cos ( θ ) = B / H = 10 / 17

- Using pythagorean theorem determine the perpendicular side length:

                               H^2 - B^2 = P^2

                               17^2 - 10^2 = P^2

                               √189 = P

                              P = 3√21

- Now evaluate sin ( θ ):

                               sin ( θ ) = P / H

                               sin ( θ ) = 3√21 / 17

Answer:

√111 / 20

Step-by-step explanation:

Hope This Helps! :)

Explanation:

The measure of the two sides of the triangle are 5√3 & 5 units respectively.

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given here: A triangle ABC with angle as C as a right angle and the hypotenuse is equal to 10

Let the perpendicular and the base of the triangle is p and b respectively.

Thus

Sin 60=p/10

p=10×√3/2

p=5√3

Also, Cos 60=b/10

             b=10×1/2

             b=5

Hence, The measure of the two sides of the triangle are 5√3 & 5 units respectively.

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The factored expression is 15(p - 2) . The discount per pair of shoe is $2

Using the expression given:

Factorize :

The greatest common factor of 15 and 30 is 15

Hence, the factored expression Using GCF is 15(p - 2)

b.)

The discount on the purchase is the constant value:

Number of shoes = 15

Discount per pair = Total discount/ Number of shoe pairs

Discount per pair of shoes = 30/15 = $2

Therefore, the discount on each pair of shoes is $2

Complete Question:

An online shoe store is having a sale. The original price of each pair of shoes is p dollars. The store sells 15 pairs of shoes and earns a total of (15p−30) dollars. a. Factor the expression using the GCF.

15p−30=

b. The discount per pair of shoes is $

Answer:

.5299192646

Step-by-step explanation:

Just plug it in a calculator

Jerry will spend $355.7988 on molding.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

we have,

Scale: 1 foot = 14 inches

As, the measurement of walls is 2372 inches.

The, using Scale the wall measured

= 2372/14

= 169.428 foot

Now, the molding costs $2.10 per foot then the cost of 169.428 foot is

= 169.428 x 2.10

= $355.7988

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Answer:

x = 51.1 degrees

Step-by-step explanation:

We notice that we can use the sine formula.

Why?

Well because Sin x =  (opposite side) /  hypotenuse

sin x = 7/9

x = arcsin 7/9 = 51.05755 degrees

rounded to the nearest tenth.

x = 51.1 degrees

Answer:

in scientific notation​ the answer is 5.75x10^8

Answer: [tex]5.75[/tex] [tex]x[/tex] [tex]10^{8}[/tex]

Step-by-step explanation: To write a number in scientific notation, first write a decimal point in the number so that there is only one digit to the left of the decimal point.

So here, we have 5.75000000 and notice that there

is only one digit to the left of the decimal point.

Next, we count the number of places the decimal point would

need to move to get back to the original number, 575,000,000.

Since we would need to move the decimal point 8 places to the right,

we have an exponent of positive 8.

Now, scientific notation is always expressed as a number between 1 and 10 including 1 but not 10 and it is multiplied by 10 to a certain power that must be an integer.

So we have [tex]5.75000000[/tex] [tex]x[/tex] [tex]10^{8}[/tex].

Notice that the exponent is positive.

This is because we would need to move the decimal point to the right in order to get back to the original number.

So 575,000,000 can be written in scientific notation

as [tex]5.75000000[/tex] [tex]x[/tex] [tex]10^{8}[/tex] or just [tex]5.75[/tex] [tex]x[/tex] [tex]10^{8}[/tex].

Remember that we can drop zeroes at the end of a decimal.

So we have [tex]5.75[/tex] [tex]x[/tex] [tex]10^{8}[/tex].

Answer:

The answer to your question is 365040000 lb or 3.65 x 10⁸ lb

Step-by-step explanation:

Data

Rectangular pyramid

base = 100 yd x 78 yd

height = 100 yd

weight of a stone = 468 lb/yd³

Process

1.- Calculate the volume of the pyramid

Volume = area of the base x height

-Substitution

Volume = 100 x 78 x 100

-Simplification

Volume = 780000 yd³

2.- Calculate the weight of the pyramid

                     468 lb ------------------------ 1 yd³

                         x      ------------------------780000 yd³

                         x = (780000 x 468) / 1

                         x = 365040000 lb or 3.65 x 10⁸ lb

Answer:

1438.52544

Step-by-step explanation:

Answer:

Proved down

Step-by-step explanation:

To prove that a triangle is isosceles use the distance formula to find the length of its side and check if there are two sides equal.

To prove that a triangle is right find the square of the longest side and then find the sum of the squares of the other two sides, if the two answers are equal, then the triangle is right (converse of Pythagoras Theorem).

The formula of the distance between two points is:

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

∵ x = (-1 , 5) and y = (4 , 4)

∴ [tex]x_{1}[/tex] = -1 and [tex]x_{2}[/tex] = 4

∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = 4

- Substitute them in the formula of the distance to find xy

∵ [tex]xy=\sqrt{(4--1)^{2}+(4-5)^{2}}=\sqrt{25+1}[/tex]

∴ [tex]xy=\sqrt{26}[/tex]



∵ x = (-1 , 5) and z = (-2 , 0)

∴ [tex]x_{1}[/tex] = -1 and [tex]x_{2}[/tex] = -2

∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = 0

- Substitute them in the formula of the distance to find xz

∵ [tex]xz=\sqrt{(-2--1)^{2}+(0-5)^{2}}=\sqrt{1+25}[/tex]

∴ [tex]xz=\sqrt{26}[/tex]

∵ xy = xz

- The isosceles triangle has two equal sides

∴ Δ xyz is an isosceles triangle

∵ y = (4 , 4) and z = (-2 , 0)

∴ [tex]x_{1}[/tex] = 4 and [tex]x_{2}[/tex] = -2

∴ [tex]y_{1}[/tex] = 4 and [tex]y_{2}[/tex] = 0

- Substitute them in the formula of the distance to find yz

∵ [tex]yz=\sqrt{(-2-4)^{2}+(0-4)^{2}}=\sqrt{36+16}[/tex]

∴ [tex]yz=\sqrt{52}[/tex]

yz is the longest side lets find its square

∵ (yz)² = ([tex]\sqrt{52}[/tex] )²

∴ (yz)² = 52

- Lets find the sum of the squares of the other two sides

∵ (xy)² + (xz)² =  ([tex]\sqrt{26}[/tex] )² +  ([tex]\sqrt{26}[/tex] )²

∴ (xy)² + (xz)² = 26 + 26 = 52

∴ (yz)² = (xy)² + (xz)²

- That means the angle opposite to yz is a right angle

∴ Δ xyz is a right isosceles triangle

Answer:

The area of the octagon is 505.76 [tex]inches^{2}[/tex]

Step-by-step explanation:

In this question, we are tasked with calculating the area of an octagon given the values of the apothem and the perimeter

Mathematically, the area can be calculated using the formula below;

Area = 1/2 × apothem × perimeter

where according to the question, the apothem = 11.6 inches and the perimeter = 87.2 inches

Plugging these value into the equation given above, we have

Area = 1/2 × 11.6 × 87.2 = 505.76 [tex]inches^{2}[/tex]

List the numbers from least to greatest:

1, 3, 3, 4, 5, 6, 8, 9, 10

Mode: ( most number repeated in the list)

Mode: 3

The mode of the numbers 6, 4, 1, 9, 3, 8, 3, 5, 10 is 3, as it is the number that appears most frequently in the set.

The question asks to find the mode of the following numbers: 6, 4, 1, 9, 3, 8, 3, 5, 10. The mode is a measure of central tendency that represents the most frequently occurring number in a set of values. To find the mode, we need to count how many times each number occurs in our set.

Since the number 3 appears more frequently than any other number in the set, occurring twice, the mode of this set of numbers is 3.