Least common multiple of 5y^2-45 and y+3

Answer: 27 students

Step-by-step explanation:

First take 45 + 90 = 135 students total

20% = 0.2

Then take 135 times 0.2 = 27 students

Answer:

10a-3b is your answer

Step-by-step explanation:

7a - 3(b - a)

7a-3b+3a

10a-3b

Solving this integral gives: ∫₀¹-ᵧ [(5/2)y² - 4y + (5/2)] dy = 1/6 Therefore, the final answer is: ∫ f(x,y,z) dV = 1/6

To solve this problem, we need to first find the limits of integration for each variable. Since R is bounded by the coordinate planes (x=0, y=0, z=0) and the plane x+y+z=1, we can write:

0 ≤ x ≤ 1-y-z
0 ≤ y ≤ 1-x-z
0 ≤ z ≤ 1-x-y

Next, we need to set up the integral:

∫∫∫ f(x,y,z) dV

Using the limits of integration we found above, we get:

∫∫∫ f(x,y,z) dV = ∫₀¹-ᵧ⁻_z ∫₀¹-ₓ⁻_z (5x - 3y) dz dxdy

Here, we have used the fact that z can be integrated from 0 to 1-x-y for each (x,y) pair.

Now, we can solve the inner integral with respect to z:

∫₀¹-ᵧ⁻_z ∫₀¹-ₓ⁻_z (5x - 3y) dz dx dy
= ∫₀¹-ᵧ⁻_z [(5x - 3y)z] from z=0 to z=1-x-y dx dy
= ∫₀¹-ᵧ⁻_z [(5x - 3y)(1-x-y)] dx dy

Finally, we can solve the outer integral with respect to x and y:

∫₀¹-ᵧ ∫₀¹-ₓ (5x - 3y)(1-x-y) dx dy
= ∫₀¹-ᵧ [(5/2)x² - (5/2)xy - (3/2)y² + (3/2)xy - (5/2)x + (3/2)y] from x=0 to x=1-y dy
= ∫₀¹-ᵧ [(5/2)(1-y)² - (5/2)(1-y)y - (3/2)y² - (5/2)(1-y) + (3/2)y] dy
= ∫₀¹-ᵧ [(5/2)y² - 4y + (5/2)] dy

Solving this integral gives:

∫₀¹-ᵧ [(5/2)y² - 4y + (5/2)] dy = 1/6

Therefore, the final answer is:

∫ f(x,y,z) dV = 1/6

Learn more about integral here:

brainly.com/question/14617716

#SPJ4

Answer: 2.95x+39.95(12)

Step-by-step explanation:

Hi, to answer this question we have t write an expression with the information given:

The yearly cost for x movie rentals is equal to : the product of the cost of each movie (2.95) and the number of movies (x) ;plus the product of the monthly fee (39.95) and the number of months in a year (12)

Mathematically speaking:

2.95x+39.95(12)

Answer:

D-295x+39.95(12)​

Step-by-step explanation:

EDG2021

Answer:

D)44 degrees

Step-by-step explanation:

2y+y+48=180

3y=132

Y=44

A scientific hypothesis is a proposed explanation or prediction based on limited evidence or prior knowledge, which is subject to further investigation and testing.

A guess is a speculative, unsupported statement without any logical basis, whereas a hypothesis is an educated assumption derived from existing knowledge, observations, or theories. Unlike a guess, a hypothesis is testable and can be supported or refuted by evidence gathered through scientific methods.

Scientists need a hypothesis to provide a framework for their research and guide their investigations. It helps them define the specific question they want to answer and provides a starting point for designing experiments or making observations. By formulating a hypothesis, scientists can systematically evaluate and analyze data, ultimately leading to a deeper understanding of the phenomenon under investigation.

There are indeed scientific hypotheses that cannot be directly tested or proven due to practical or ethical constraints. For example, hypotheses related to historical events that occurred in the distant past may not have accessible evidence for direct testing. Additionally, some questions related to consciousness, subjective experiences, or philosophical concepts may lie beyond the scope of scientific inquiry, as they may not be objectively measurable or observable.

While science has its limitations, it is a powerful tool for investigating and understanding the natural world. However, there are questions that fall outside the realm of scientific inquiry and require other methods of investigation, such as philosophical or ethical considerations.

Learn more about data here: brainly.com/question/29117029

#SPJ11

To solve this problem, we need to find a number that satisfies the given conditions of leaving a remainder of 2 when divided by 3, a remainder of 1 when divided by 5, and a remainder of 6 when divided by 7.

Let's denote the unknown number of horses as "x". According to condition (a), we have the equation x ≡ 2 (mod 3), meaning x leaves a remainder of 2 when divided by 3. Similarly, according to condition (b), we have x ≡ 1 (mod 5), and according to condition (c), we have x ≡ 6 (mod 7). To find a solution that satisfies all three conditions, we can use the Chinese Remainder Theorem. By solving the system of congruences, we can find the smallest positive integer value for x that satisfies all the conditions.

Using the Chinese Remainder Theorem, we can find x ≡ 92 (mod 105). This means that if there were a total of 92 horses, they could be divided equally among 3, 5, and 7 generals with the respective remainders of 2, 1, and 6. Therefore, 92 is the smallest possible number of horses that satisfies all the given conditions.

In summary, the Chinese emperor would need a total of 92 horses in order to divide them equally among his generals according to the given conditions.

To learn more about Chinese Remainder Theorem click here:

brainly.com/question/30811240

#SPJ11

Answer:

C. 16 cm

Step-by-step explanation:

Top side: 2 + 4 = 6

Right side: 1 + 1 = 2

Bottom: 2 + 4 = 6

Left side:  1 + 1 = 2

6+6+2+2 = 16 cm.

4.67

Have a luvely day!

Answer:

4.67

Step-by-step explanation:

Answer:

D, 9^4 * 8^4

Step-by-step explanation:

The rule is whenever you have multiplication inside arentheses and it is raised to a power, you distribute the power to both the number s and solve.

I confirmed D is right on a calculator also.

Answer:

D

Step-by-step explanation:

Answer:

y=-3x-4

Step-by-step explanation:

To put this in slope-intercept first put it in slope-point then simplify. So in slope-point, this would be y - 5 = -3 (x + 3), then solve

First, distribute the -3

y-5 = -3x-9

Then, move the five to the right side by adding it to both sides

y=-3x-4, therefore the slope is -3 and the intercept is -4.

Answer:

B. 6.47

Step-by-step explanation:

To determine the area of a polygon with given vertices, we can use the Shoelace Formula, also known as Gauss's Area Formula. This formula calculates the area by summing the products of the coordinates of consecutive vertices. By applying the formula, we can find the area of the polygon with vertices b(3,2), c(7,−2), d(2,−4), and e(1,−2).

The Shoelace Formula states that the area of a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) can be calculated as 1/2 times the absolute value of the sum [(x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1)]. Using the given vertices b(3,2), c(7,−2), d(2,−4), and e(1,−2), we can apply the Shoelace Formula as follows:

Area = 1/2 * |(3*(-2) + 7*(-4) + 2*(-2) + 1*2) - (2*7 + (-2)*2 + (-4)*1 + (-2)*3)|.

Simplifying the expression, we have:

Area = 1/2 * |-6 - 28 - 4 + 2 - 14 - 4 - 4 - 6|.

Area = 1/2 * |-64|.

Area = 1/2 * 64.

Area = 32.

Therefore, the area of the polygon with vertices b(3,2), c(7,−2), d(2,−4), and e(1,−2) is 32 square units.

Learn more about polygon here:

https://brainly.com/question/25907039

#SPJ11

Answer:

c 31b4

Step-by-step explanation:

Answer:

\557

Step-by-step explanation:

The linear equation to represent the situation is given by

The inequality that represents the graph of 3x−5 ≥ 1 ≥ x−4 is D.

let the fixed cost be a and the cost per day is b.

Let us form some linear equations and solve them

115 = 5b + a

151 = 7b + a

Now we will substitute the values to solve the equations by substitution method.

115-5b=151-7b

or, -36 = -2b

or, b = 18

115 =5b + a

a = 25

Therefore the linear equation is y = 18x + 25

In mathematics, an inequality is a connection that allows for a non-equal comparison of two integers or other mathematical expressions. It is most typically used to compare two numbers' sizes on a number line. There are several terms used to describe distinct types of inequalities.

3x−5≥1≥x−4

3x−5 ≥ 1

or, 3x ≥ 6

or, x ≥ 2

1 ≥ x−4

or, 5 ≥ x

Hence option D is the graph required.

to learn more about inequality visit:

https://brainly.com/question/20383699

#SPJ1

The probability that exactly 2 of the elks captured are tagged is approximately 0.218, or 21.8%.

The probability that exactly 2 of the captured elks are tagged can be calculated using the hypergeometric distribution.

The total number of elks in the forest is 20, of which 5 are tagged and 15 are untagged. We are randomly capturing 4 elks for analysis.

The probability of selecting exactly 2 tagged elks can be calculated as follows:

P(2 tagged elks) = (C(5, 2) * C(15, 2)) / C(20, 4)

Here, C(n, r) represents the number of combinations of choosing r items from a set of n items. In this case, we are selecting 2 tagged elks from the 5 available and 2 untagged elks from the remaining 15.

Evaluating this expression:

P(2 tagged elks) = (10 * 105) / 4845

P(2 tagged elks) ≈ 0.218

Therefore, the probability that exactly 2 of the elks captured are tagged is approximately 0.218, or 21.8%.

The hypergeometric distribution is used in situations where we are sampling without replacement from a finite population. In this case, we have a total of 20 elks in the forest, 5 of which are tagged and 15 are untagged. We are capturing 4 elks randomly, without replacement, for analysis. The probability of selecting exactly 2 tagged elks can be calculated by considering the number of ways to choose 2 tagged elks from the 5 available and 2 untagged elks from the remaining 15. Dividing this by the total number of possible combinations of selecting 4 elks from the 20 elks in the forest gives us the probability

Learn more about  hypergeometric distribution. here:

brainly.com/question/30911049

#SPJ11

Answer:

The graph below shows the graph of 3x - y = 1.

Hope this helps! :)

The radius of the largest circular tabletop that can be cut from the given rectangular wood is 0.60 meters.

To determine the radius of the largest circular tabletop that can be cut from a rectangular piece of wood measuring 1.20 m by 1.80 m, we need to find the maximum possible diameter that fits within the dimensions of the wood.

The largest circle will have a diameter equal to the shorter side of the rectangle, which is 1.20 m. This is because the circle must be entirely contained within the rectangular wood, and placing the circle's diameter along the shorter side ensures it fits perfectly without exceeding the wood's dimensions.

Now that we know the diameter of the largest circle is 1.20 m, we can easily find the radius by dividing the diameter by 2:

Radius = Diameter / 2

Radius = 1.20 m / 2

Radius = 0.60 m

So, the radius of the largest circular tabletop that can be cut from the given rectangular wood is 0.60 meters.

Know more about Radius here:

https://brainly.com/question/9221485

#SPJ11

Answer:

An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero

The volume of a sphere is given by the following formula

Where r represents the radius of the sphere.

To find the volume of a sphere with a radius equals to 2, we just need to evaluate r = 2 on the given formula.

The volume of this sphere is 32ft³.

Answer:

Picture Please

Answer:

In order to find area, multiply length x height

Step-by-step explanation:

Or in some cases, you can multiply length x height x width.

The stopping distance for a car traveling at 55 mph is 60,500 feet.

The equation to solve this problem would look like the following

s = v²/k

The stopping distance s will increase (varies directly) as the velocity increases.

Putting in the values we know

45 = 30²/k

⇒ k = 45/900

⇒ k = 0.05

Now,

at 55 mph we would have

    s = 55²/0.05

⇒ s = 3025/0.05

⇒ s = 60,500

s = 60,500 feet to stop

Complete Question:

The stopping distance s of a car varies directly as the square of its speed v. If a car traveling at 30 mph requires 45ft to stop, find the stopping distance for a car traveling at 55 mph.

Learn more about Distance:

https://brainly.com/question/15172156

#SPJ4

The average rate of speed of the wind is 18 mph and the average rate of speed of the plane is 36 mph.

To find the average rate of speed of the wind and the plane, we can set up a system of equations.

Let x be the average airspeed of the plane and y be the average wind speed.

From the initial trip, we have the equation: (x + y) * (1/3) = 18.
This is because the total distance traveled is the sum of the plane's speed and the wind's speed, multiplied by the time taken.

From the return trip, we have the equation: (x - y) * (3/5) = 18.
This is because the total distance traveled is the difference between the plane's speed and the wind's speed, multiplied by the time taken.

Now, we can solve these two equations to find the values of x and y.

Simplifying the equations, we get:
1/3 * (x + y) = 18
3/5 * (x - y) = 18

Cross-multiplying and simplifying further, we get:
x + y = 54
3x - 3y = 90

Next, we can solve this system of equations using any method (substitution, elimination, etc.).

Adding the two equations, we get:
4x = 144
x = 36

Substituting the value of x into one of the equations, we get:
36 + y = 54
y = 18

Therefore, the average rate of speed of the wind is 18 mph and the average rate of speed of the plane is 36 mph.

To know more about average rate visit:

https://brainly.com/question/28739131

#SPJ11

Dalia had an average airspeed of

42

miles per hour.

The average wind speed was

12

miles per hour.

The slope of the line perpendicular to the given line is equal to -4/1.

The equation is in the form y=mx+b

so, y=(1/4)x -10

First, find the slope of the line which is the value being multiplied by x. Therefore m=1/4

To find the slope perpendicular to the line you must find the negative reciprocal of 1/4. (Which just means change the sign then flip the fraction)

Multiplying 1/4 by -1 which is -1/4

Then flip the fraction and keep the sign with the numerator to find the reciprocal. So now it’s -4/1

Thus, the slope of the line perpendicular to the given line is equal to -4/1.

To know more about slopes visit: brainly.com/question/3605446

#SPJ4

The equation is in the form y=mx+b

so, y=(1/4)x -10

First, find the slope of the line which is the value being multiplied by x. Therefore m=1/4

Multiplying 1/4 by -1 which is -1/4

Then flip the fraction and keep the sign with the numerator to find the reciprocal. So now it’s -4/1

Answer:

R = 5.73 cm

Step-by-step explanation:

which equals the circumstance 36

hope it helps

Answer:

10.38 = 0.60b + 1.74p

Step-by-step explanation:

\({\Huge{\boxed{\mathbb{QUESTION}}}\)

Write three ratios equal to \(\frac{4}{36}\)

\({\huge{\boxed{\mathbb{EXPLANATION\:WITH\:REASONING\;}}}\)

This ratio can be represented as \(4:36\)

_______________________________

\({\Huge{\boxed{\mathbb{THE\:RATIOS}}}\)

_______________________________

_______________________________

\({\huge{\boxed{\mathbb{TERMS}}}\)

Equivalent/Equal ratios - Definition of Equivalent Ratio A ratio can be represented as a fraction. The concept of an equivalent ratio is similar to the concept of equivalent fractions. A ratio that we get either by multiplying or dividing by the same number, other than zero, to the antecedent and the consequent of a ratio is called an equivalent ratio.