Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8.



Simplify R - S + T.

-3m - 4n + 14
-m + 2n - 2
m - 2n - 2
3m - 4n + 14

Because of this, we need to choose 15 integers in such a way that we can ensure that when they are divided by 14, at least two of them will provide the same residual.

In order to be sure that at least two of them have the same remainder when divided by 14.

Generally,  If you divide a number by 14, the result is a fraction. There are 14 remainders that might occur, and they are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and, 13.

So if we pick a number and divide it by 14, the remainder can be one of 14 (0 memory 13). So if we select 14 numbers, we have the option to select 14 unique memories ranging from 0 to 13.

Finally, if we choose another integer, we will have the same reminders according to the drawer principle, because there are only 14 reminders and 15 > 14.

Therefore, we should choose the number of 15 so that at least two numbers have the same remainder when divided by 14.

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Myra will paint approximately 213.52 square

centimeters

on the cylindrical pillar.

To determine how many square centimeters will be painted on the cylindrical pillar, we need to calculate the

surface area

of the cylinder. The formula for the surface area of a cylinder is given by:

S = 2πrh + 2πr^2

where S is the surface area, r is the

radius

, and h is the

height

.

In this case, the radius of the pillar is 2 cm and the height is 15 cm. We can substitute these values into the formula to find the surface area:

S = 2 * 3.14 * 2 * 15 + 2 * 3.14 * 2^2

Simplifying the expression:

S = 6.28 * 2 * 15 + 12.56 * 4

S = 188.4 + 50.24

S = 238.64 square centimeters

It's important to note that the

formula

for the surface area of a cylinder includes the areas of both the curved surface (2πrh) and the top and bottom circles (2πr^2). Since Myra is painting the entire pillar, including the top and bottom, we need to consider both of these areas in our calculation.

Using the value of π as 3.14, we have found that the surface area of the cylindrical pillar to be painted is approximately 238.64 square centimeters.

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Answer: 40 1/10

Step-by-step explanation:

40.100/1= 40.100 x 1000/ 1 x 1000= 40100/ 1000= 40100/100/ 1000/100= 401/10: = 40 1/10

Answer:

30%

Step-by-step explanation:

First subtract: 1 - .70 = .30

Then move decimal over to the right 2 times and add percentage sign instead of the decimal: 30%

The coordinates of the vertices of the image triangle are J'(-4, 0), K'(-2, 2), and L'(-1, 0).

To find the coordinates of the vertices of the image after dilation by a scale factor of 0.5 centered at the origin, we multiply each coordinate by the scale factor.

Let's apply the dilation to each vertex:

J' = (-8 * 0.5, 0 * 0.5) = (-4, 0)

K' = (-4 * 0.5, 4 * 0.5) = (-2, 2)

L' = (-2 * 0.5, 0 * 0.5) = (-1, 0)

Therefore, the coordinates of the vertices of the image triangle are J'(-4, 0), K'(-2, 2), and L'(-1, 0).

To graph the preimage and image, you can plot the points J(-8, 0), K(-4, 4), and L(-2, 0) on one sheet of paper to represent the preimage triangle. Then, on a separate sheet of paper, plot the points J'(-4, 0), K'(-2, 2), and L'(-1, 0) to represent the image triangle. Make sure to label each vertex accordingly.

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Calculate liquid weight by multiplying density by volume, resulting in 456.03 grams for a 465 milliliter container.

To find the weight of the liquid, we can use the formula: weight = density x volume. In this case, the density is given as 0.982 grams per milliliter and the volume is 465 milliliters.

So, weight = 0.982 grams/ml x 465 ml

To find the weight, multiply the density by the volume:

weight = 0.982 grams/ml x 465 ml = 456.03 grams

Therefore, the weight of the liquid that exactly fills a 465 milliliter container is 456.03 grams, rounded to the nearest hundredth.

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The simplified form of the expression -6w + (–8.3) + 1.5+ (–7w) is -13w - 6.8.

Given the expression in the question;

-6w + (–8.3) + 1.5+ (–7w)

To simplify, first remove the parenthesis

Note that;

-6w + × - 8.3 + 1.5 + × - 7w

-6w - 8.3 + 1.5 - 7w

Next collect and add like terms

-6w - 7w - 8.3 + 1.5

Add -6w and -7w

-13w - 8.3 + 1.5

Add -8.3 and 1.5

-13w - 6.8

Therefore, -13w - 6.8 is the simplified form.

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Answer: 2 feet

Step-by-step explanation:

It's 2 gal/min

8 liters is 2.1134 gallons, so its the closest to the the first option than the others.

Answer:6.80

Step-by-step explanation:

Answer:

the number of boxes that would take fill

the storage completely is 60 boxes.

Step-by-step explanation:

given:

A storage unit has the dimensions 6 ft. x 7 1/2 ft. x 4 1/2 ft.

find:

What number of

1 1/2 ft. x 1 1/2 ft. x 1 1/2 ft. cardboard boxes would it take to completely

fill this storage unit?

Volume of a storage unit = 6 x 7.5 x 4.5

Volume of a storage unit = 202.5  ft³

Volume of a cardboard box = 1.5 x 1.5 x 1.5

Volume of a cardboard box = 3.38 ft³

to get the number of cardboard boxes to fill in the storage unit,

Number of boxes =     202.5 ft³    

                                     3.38 ft³

Number of boxes = 60

therefore,

the number of boxes that would take fill the storage completely is 60 boxes.

Find the surface area of a Cuboid of length, breadth, and height equal to 12 cm, 8 cm and 5 cm respectively.

\( \bullet \) Length (l) of a Cuboid is 12 cm.

\( \bullet \) Breadth (b) of a Cuboid is 8 cm.

\( \bullet \) Height (h) of a Cuboid is 5 cm.

The surface area of a Cuboid.

We know,

Formula of surface area of a Cuboid is 2(lb + bh + lh) sq units.

So, Surface area of a Cuboid = 2(12×8 + 8×5 + 12×5) sq cm.

= 2(96 + 40 + 60) sq cm.

= 2 × 196

= 392 sq cm

We assume that the outcomes of successive trials in a binomial experiment are c) identical from trial to trial.

The correct answer is:

c. identical from trial to trial

In a binomial experiment, the outcomes of successive trials are assumed to be identical from trial to trial. This means that each trial has the same probability of success or failure, and the outcome of one trial does not affect the outcome of the subsequent trials. Each trial is considered independent and does not depend on the previous or future trials.

Option a is incorrect because the outcomes in a binomial experiment are not random numbers between 0 and 1. They are discrete outcomes, usually represented as success or failure, or yes or no.

Option b is incorrect because the outcomes in a binomial experiment are assumed to be independent, not dependent. The probability of success or failure in one trial does not affect the probability in subsequent trials.

Option d is incorrect because it mistakenly states that the outcomes are probabilistically independent. The correct term is "independent," without the term "probabilistically."

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Answer:

4.91

Step-by-step explanation:

4¹/6*2¹/5

25/6*11/5

275/30

4.91

5

Answer:

44

Step-by-step explanation:

Let the number of eggs be N, and the weight be M

M is directly proportional to N.

.: M= kN

264 = 6k

.; k(the constant of proportionality is) = 264/6

k = 44.

28 minutes later, when the car arrived at the second office, it had been traveling at speed of 60 miles per hour. The driver of the car received a ticket for going above the 60 mph limit; the office went over the limit.

Given ,

Distance = 30 miles

Time = 28mins

Determine the speed exceeds the limit:

speed = distance /time

speed = 30 miles / 28 minute

speed = 30 miles /28 minute x 60 minutes/1 hour

speed = 64 mph

The speed actually exceed the limit.

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Answer:

hope this helps:)

Step-by-step explanation:

Answer: 45$. The proportion to set up could be 30/100%=x/150%.

Step-by-step explanation: Let's set up a proportion. 30/100% = x/150%.

The 30/100% shows that this month you paid 100% of 30 dollars, which is 30. The x/150% shows that you paid 150% of 30 dollars. We can find x using cross-multiplying. We get 150 x 30 = 100 times X. Simplyfing the equation, we get 4500 = 100 times x. To make X by itself, we divide both sides of the equation by 100, leaving us with 45=x, showing the answer is 45$.

Therefore, Caleb paid approximately $14,067.90 for the shares.

Let's assume the amount Caleb paid for the shares is represented by the variable "x". According to the given information, his selling price was 130% of the amount he paid.

Selling price = 130% of the amount paid

$18,189.27 = 1.3 * x

To find the amount he paid for the shares, we can solve the equation for "x" by dividing both sides by 1.3:

x = $18,189.27 / 1.3

Calculating this, we find:

x ≈ $14,067.90

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The height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.

Given,

In the question:

Its angle of elevation (to the peak) is 3.5 degrees.

After you drove 13 miles closer, the angle of elevation is 9 degrees.

To find the approximate height of the mountain.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.

Now, According to the question:

It is given that:

In traveling across flat land you notice a mountain directly in front of you.

Applying tan ratio:

tan3.5 = h/(15+x)

Here h is the height of the mountain and x is the distance between the base of the mountain and to the second position of the car.

h = (15 + x) tan3.5

h = x tan9

(15 + x) tan3.5 = x tan9

x = 9.44

h = 9.44 tan9

h = 1.49 miles

Hence, the height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.

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Answer:

HCF = 1

Step-by-step explanation:

By factorising the terms, we get:

x² - 1 = (x + 1)(x - 1)

x³ + 1 = (x + 1)(x² - x + 1)

x³ - 1 = (x - 1)(x² + x + 1)

The common factor in the three terms is 1

HCF = 1

Answer:isosceles triangle

Step-by-step explanation:

A compound event is any event combining two or more simple events.

From the question, we have the following parameters that can be used in our computation:

combining two or more simple events.

As a general rule

When two or more simple events are combined, the result is a compound event

An example is selecting 1 in a die and head in a coin

This means that the statement that completes the blank is compound event

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Answer:

\(HD=5.5\)

Step-by-step explanation:

\(4(HD)=22 \implies HD=5.5\)

The probability of dying between ages 37 and 39 is 1 - e˙37:2.

We can use the formula:
10,000c = 10,000 * μ39 * (1 - e˙37:2)

By substituting the given values into the formula, we can find the value of 10,000c.To determine 10,000c, we need to use the given information about the 2-year select-and-ultimate mortality table.

Let's break down the steps:

Recall that the symbol μ[37]+t represents the select-and-ultimate mortality rate for a person aged 37 plus t years. We are given that μ[37]+t = μ37+t - c, where 0 ≤ t ≤ 2.

We also have the value of e˙37:2, which represents the probability of surviving from age 37 to age 39. The given value is e˙37:2 = 1.7.
Additionally, we know the value of e˙37, which represents the probability of surviving from age 37 to age 38. The given value is e˙37 = 57.5.

Now let's calculate 10,000c:

Step 1:

Find the value of μ39 using the given information.
Since we know that μ[37]+t = μ37+t - c,

we can substitute t = 2:
μ[37]+2 = μ37+2 - c

Step 2:

Calculate μ39.
μ[37]+2 = μ37+2 - c
μ39 = μ37+2 - c

Step 3:

Use the relationship between mortality rates and survival probabilities.
We know that the probability of surviving from age 37 to age 39 is given by e˙37:2 = 1.7.
This means that the probability of dying between ages 37 and 39 is 1 - e˙37:2.

Step 4:

Calculate the value of 10,000c.
We can use the formula:
10,000c = 10,000 * μ39 * (1 - e˙37:2)

By substituting the given values into the formula, we can find the value of 10,000c.

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The approximate thickness of the package of aluminum foil with given density and weight is equal to  0.002 millimeters.

1 ft = 30.48 cm

Area of aluminum foil = 50 ft²

                                    = 50 × ( 30.48 )² cm²

                                    = 46451.52 cm²

1 oz = 28.3495 grams

Weight of the aluminum = 9.0 oz

                                        = 255.1455 grams

Density = 2.70 g/cm³

Density = weight / ( area × thickness )

⇒ Thickness = weight / ( area × density )

⇒Thickness = 255.1455 grams / ( 46451.52 cm² × 2.70 g/cm³ )

⇒Thickness = 0.00203

⇒Thickness = 0.002 millimeters

Therefore, approximate thickness of the aluminum foil is equal to 0.002 millimeters.

The above question is incomplete, the complete question is:

A package of aluminum foil contains 50. ft2 of foil, which weighs approximately 9.0 oz . Aluminum has a density of 2.70 g/cm3.What is the approximate thickness of the foil in millimeters?

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Answer:

Center: (-4,1)

Radius: √2

Step-by-step explanation:

Complete the square for both variables

\(x^2+y^2+8x-2y+15=0\\x^2+8x+y^2-2y+15=0\\x^2+8x(+16)+y^2-2y+15(-14)=0+16-14\\x^2+8x+16+y^2-2y+1=2\\(x+4)^2+(y-1)^2=2\)

Comparing our result with \((x-h)^2+(y-k)^2=r^2\), then the center of the circle is \((h,k)=(-4,1)\) and our radius is \(r=\sqrt{2}\)

Answer:

A horizontal line with a slope of 0.

Step-by-step explanation:

Y=43,000 is a horizontal line on the Y-Axis at 43,000. Horizontal lines have 0 as their slope.

Answer:

yes by SAS

Step-by-step explanation:

EN = RP

EM = PQ

Angle N = Angle R