Please help me !!!!!!!!

Answer:

Step-by-step explanation:

Number of students in class= 64

Boys : Girls= 5:3

Total ratio=5+3

                =8

Number of boys= 5/8 * 64

                           =40

Number of girls = 3/8* 64

                          =24

Step-by-step explanation:

here's your solution

=> angle 3 and angle 8 are interior angles

we know that sum of both angle is 180°

=> angle 3 + angle 8 = 180°

=> angle 3 + 129° = 180°

=> angle 3 = 180° - 129°

=> angle 3 = 51°

now , angle 3 and angle 1 are vertical angle

hence both angle are equal

=> angle 1 = 51°

hope it helps 【€€】

The distance that she runs from one corner of the field to another is given as follows:

147.1 yards.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The distance in this problem is the diagonal of a rectangle, which is the hypotenuse of a right triangle in which the length and the width are the sides, hence:

d² = 85² + 120²

d = sqrt(85² + 120²)

d = 147.1 yards.

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The multiplier effect refers to the theory that government spending intended to stimulate the economy causes increases in private spending that additionally stimulates the economy.In essence,the theory is that government spending gives households additional income, which leads to increased consumer spending.

The answer is (C) 5/2 i.e. the time t guaranteed by the Mean Value Theorem is 5/2.

What is Mean Value Theorem ?

The Mean Value Theorem (MVT) for derivatives states that for a function f(x) that is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), there exists a number c in (a, b) such that:

f'(c) = \(\frac{f(b) - f(a)}{(b - a)}\)

In this problem, we want to find the time t guaranteed by the MVT when the instantaneous velocity of the rock equals the average velocity between t=0 and t=5/4 seconds.

The instantaneous velocity of the rock at time t is given by the derivative of s(t):

s'(t) = -32t

The average velocity between t=0 and t=5/4 seconds is given by the slope of the line connecting the points (0, s(0)) and (5/4, s(5/4)):

Savg(t) = \(\frac{s(5/4) - s(0)}{5/4 - 0}\) =\(\frac{100 - 16*(5/4)^2}{5}\)

We want to find the time t guaranteed by the MVT when s'(t) equals Savg(t), i.e., when:

\(-32t = \frac{100 - 16*(5/4)^2}{5}\)

Solving for t gives:

t = 5/2

Therefore, the answer is (C) 5/2.

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Answer:

7 months

Step-by-step explanation:

If the box holds 2 layers with 15 cubes in each layer, the volume of the box is 56.25 cubic inches.

To find the volume of the box, we need to multiply the length, width, and height of the box. Since the cubes are all the same size, we can use the dimensions of a single cube to determine the size of the box.

Each cube has a side length of 1/2 inch, so its volume is (1/2)^3 = 1/8 cubic inch. Since there are 30 cubes in the box, the total volume of all the cubes is:

30 cubes x 1/8 cubic inch per cube = 3 3/4 cubic inches

The box has two layers, each with 15 cubes, arranged in a rectangular shape. Therefore, the length and width of the box are each 1/2 inch x 15 cubes = 7 1/2 inches.

The height of the box is equal to the height of two layers of cubes, which is 2 x 1/2 inch = 1 inch.

Now, we can calculate the volume of the box by multiplying its length, width, and height:

Volume of box = length x width x height = 7 1/2 inches x 7 1/2 inches x 1 inch = 56.25 cubic inches.

In summary, by using the dimensions of a single cube and the number of cubes in the box, we can calculate the total volume of the cubes. Then, by using the dimensions of the arrangement of the cubes, we can calculate the dimensions of the box, which allows us to find its volume by multiplying its length, width, and height.

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Answer:

D and A

Step-by-step explanation:

1. 610:488 simplify

5:4

2.360:(488+551+610+360+391)

360:2400

3:20

-3(v+4) = 2v-37

-3v-12 = 2v-37

-3v-2v = -37+12

-5v = -25

v = -25/-5

v = +5

Answer:

One solution.

v = 5

Step-by-step explanation:

- 3(v + 4) = 2v - 37

- 3v - 12 = 2v - 37

- 3v - 12 + 12 = 2v - 37 + 12

- 3v = 2v - 25

- 3v - 2v = 2v - 2v - 25

- 5v = - 25

- 5v ÷ - 5 = - 25 ÷ - 5

v = 5

The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.

The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:

(a) Local non-satiation:

This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.

(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:

MU1 = α * xi^(α−1) * x2^(β)

The marginal utility of x2 can be obtained as:

MU2 = β * xi^(α) * x2^(β−1)

Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.

(c) Quasi-concavity:

The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.

(d) Homotheticity:

The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.

In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.

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Step-by-step explanation:

these are the answers of your questions

Answer #1:

x ( 3 x − 4 ) ²

Answer: b=-18

Step-by-step explanation:

1/3b+57=3

Subtract 57

1/3b=-54

Divide by 1/3 (basically you’re dividing by 3)

p=-18

Given :

We have to find value of m\(.\)

➠ 9(m + 5) - 3(m - 2) = 8m + 31

➠ 9m + 45 - 3m + 6 = 8m + 31

➠ 9m - 3m + 45 + 6 = 8m + 31

➠ 6m + 51 = 8m + 31

➠ 51 - 31 = 8m - 6m

➠ 20 = 2m

➠ m = 20/2

➠ m = 10

Answer:

the answer would be 2 and 2/5

Step-by-step explanation:

3/5 + 2/5 = 1

and, 4 + 2 = 6

6 + 1 = 7

hope this helps :)

Answer:

\(2 \frac{2}{5} \)

Step-by-step explanation:

To find the answer we subtract four and three fifths from 7

\(7 - 4\frac{3}{5} = \frac{7}{1} - \frac{23}{5} \)

when subtracted we get

\(2 \frac{2}{5} \)

The 95th percentile of the variance of a random sample of size 15 from a normal population with a variance of 3 is approximately 23.685.

The sampling distribution of the variance follows a chi-square distribution, with degrees of freedom equal to n-1, where n is the sample size.
When the population variance is known, we can use the chi-square distribution to find the probability of getting a certain sample variance. In this case, the population variance is given as 3.
Therefore, the sampling distribution of the variance will be a chi-square distribution with 14 degrees of freedom:

(n-1 = 15-1 = 14).

To find the 95th percentile of the chi-square distribution with 14 degrees of freedom, we can use a chi-square table or a calculator. Using a chi-square table or calculator, we find that the 95th percentile of the chi-square distribution with 14 degrees of freedom is approximately 23.685.

This means that there is a 95% chance that the sample variance will be less than or equal to 23.685.

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The 95th percentile of the variance of a random sample of size 15 from a normal population with a variance of 3 is approximately 23.685.

The sampling distribution of the variance follows a chi-square distribution, with degrees of freedom equal to n-1, where n is the sample size.

When the population variance is known, we can use the chi-square distribution to find the probability of getting a certain sample variance. In this case, the population variance is given as 3.

Therefore, the sampling distribution of the variance will be a chi-square distribution with 14 degrees of freedom:

(n-1 = 15-1 = 14).

To find the 95th percentile of the chi-square distribution with 14 degrees of freedom, we can use a chi-square table or a calculator. Using a chi-square table or calculator, we find that the 95th percentile of the chi-square distribution with 14 degrees of freedom is approximately 23.685.

This means that there is a 95% chance that the sample variance will be less than or equal to 23.685.

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The angular velocity of the ladybug is 2.61799 radians/second, the speed of the ladybug is 26.1799 cm/second and after 20 seconds, the ladybug has traveled 523.598 cm

Angular velocity or rotational velocity, also known as angular frequency vector, is a pseudovector representation of how fast the angular position or orientation of an object changes with time

The angular velocity of the ladybug can be calculated as follows:

Angular velocity = (2π × rotation per minute) / 60 seconds per minute

Angular velocity = (2π × 25) / 60

Angular velocity = 2.61799 radians/second

Therefore, the angular velocity of the ladybug is 2.61799 radians/second.

b) The speed of the ladybug can be calculated using the formula:

Speed = (radius × angular velocity)

Speed = 10 × 2.61799

Speed = 26.1799 cm/second

Therefore, the speed of the ladybug is 26.1799 cm/second.

c) After 20 seconds, the distance traveled by the ladybug can be calculated using the formula:

Distance = Speed × time

Distance = 26.1799 × 20

Distance = 523.598 cm

Therefore, after 20 seconds, the ladybug has traveled 523.598 cm.

d) After 20 seconds, the angle turned through by the ladybug can be calculated using the formula:

Angle = angular velocity × time

Angle = 2.61799 × 20

Angle = 52.3598 radians

Therefore, after 20 seconds, the ladybug has turned through an angle of 52.3598 radians.

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Answer:

Step-by-step explanation:

Volume of a pyramid can be found by using the formula

\(v = \frac{1}{3} \times a \times h \\ \)

a is the area of the base

h is the height

Since the base is a square we have

\(v = \frac{1}{3} \times {15.3}^{2} \times 19.6 \\ = 78.03 \times 19.6 \\ = 1529.388\)

We have the final answer as

Hope this helps you

Ans :

90 minutes, the sloth may move 600 units .

Given :

250*5/8 = 250 × (8/5) = 400

Hour :

a period of time equal to the twenty-fourth part of a day and night and divided into 60 minutes.

1 hour =  60 minute

Slot :

a long, narrow aperture or slit in a machine for something to be inserted.

sloth may move 400 units per hour.

a sloth may move in 400 units = 60 minutes.

A slot of 200 units = 30 minutes.

Therefore,

it will move (400 + 200) units =  (60 + 30) minutes.

Hence,

in 90 minutes, the sloth may move 600 units.

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A system of equations is the set of equations in which the finite set of the equation is present for which the common solution is sought.

System of equations that can be graphed to solve the given equation is,

\(\rm y_1= \dfrac{logx}{log0.5}\\\\ y_2=\dfrac{log2}{log3}\)

Thus the option D is the correct option.

A system of equations is the set of equations in which the finite set of the equation is present for which the common solution is sought.

Given information-

The given logarithmic equation is,

\(\rm log_{0.5}x=log_32+x\)

Logarithmic functions are given in the system of equations.

Solve the above equation using the properties of logarithmic function as;

\(\rm \dfrac{logx}{log0.5}=\dfrac{log2}{log3}+x\)

The system of equation with the above equitation can be given as,

\(\rm y_1= \dfrac{logx}{log0.5}\\\\ y_2=\dfrac{log2}{log3}\)

Hence, the system of equations that can be graphed to solve the given equation is;

\(\rm y_1= \dfrac{logx}{log0.5}\\\\ y_2=\dfrac{log2}{log3}\)

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Answer:

its b

Step-by-step explanation:

Answer:

600

Step-by-step explanation:

Answer:

D. y = { -x + 2 x ≥ 1}

          { x + 1  x < 1}

Step-by-step explanation:

First is to eliminate A and C, why?

This is because of the end points shown on the graph.

As shown, if you look at the point of (2,1) it is black, this means that not only is it closed but it is also means ≤ or ≥ symbol.

You are now left with B and D

The difference between these two is the symbols; they are facing the opposite directions.

While B says x ≤ 1, and x > 1

While D says x ≥ 1, and x < 1

The direction of the symbols depends on the direction of the lines and what is part of it (some what like a shaded area)

So you answer would be D

Answer:

x=66

Step-by-step explanation:

180-114=66

Interior angles on the same side of transversal are supplementary (180°).

So,

x + 114° = 180°

=> x = 180° - 114°

=> x = 66°

Answer:false

Step-by-step explanation:

The length and width of the rectangle are 20 cm and 5 cm respectively.

Let's assume the length of the rectangle is x cm.

According to the given information, the width of the rectangle is 55 cm less than three times its length. So, the width can be expressed as:

Width = 3x - 55

Area = Length x Width.

Thus: Area = x * (3x - 55) = 100

\(3x^2 - 55x - 100 = 0\)

Using the quadratic formula

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 3, b = -55, and c = -100.

x = (-(-55) ± √((-55)^2 - 4 * 3 * -100)) / (2 * 3)

= (55 ± √(3025 + 1200)) / 6

= (55 ± √4225) / 6

= (55 ± 65) / 6

x = (55 + 65) / 6 = 120 / 6 = 20 OR

x = (55 - 65) / 6 = -10 / 6 = -5/3

Therefore, the length of the rectangle is 20 cm.

Width = 3x - 55

= 3 x 20 - 55

= 60 - 55

= 5

Therefore, the dimensions of the rectangle are length = 20 cm and width = 5 cm.

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Step-by-step explanation:

c = 2,8    and   d = 6,5

Use the distance formula  ( kind of a modified Pythagorean theorem)

s^2 = (x1-x2)^2  + (y1-y2)^2             ( s = distance)

s^2 = ( 2-6)^2 + ( 8-5)^2

s^2 = 25

s = 5 units

Answer:

28467.5

Step-by-step explanation:

11 divides 2r+1 when r=2, 3, 4, or 5

prove the following: There exists an n ∈ N for which 11 | (2n −1).

To prove this statement, we need to show that there exists a natural number n such that 11 divides 2n-1.

Let's consider the remainders when we divide powers of 2 by 11:

2^1 ≡ 2 (mod 11)
2^2 ≡ 4 (mod 11)
2^3 ≡ 8 (mod 11)
2^4 ≡ 5 (mod 11)
2^5 ≡ 10 (mod 11)
2^6 ≡ 9 (mod 11)
2^7 ≡ 7 (mod 11)
2^8 ≡ 3 (mod 11)
2^9 ≡ 6 (mod 11)
2^10 ≡ 1 (mod 11)
2^11 ≡ 2 (mod 11)
...

We can see that the remainders repeat after every 10 powers of 2. Therefore, if we take any natural number n and divide it by 10, we can write n as:

n = 10q + r

where q and r are natural numbers and r is the remainder when n is divided by 10.

Now, let's consider 2n-1:

2n-1 = 2(10q+r) - 1
     = 20q + 2r - 1
     = 11q + 9q + 2r - 1

We can see that 11 divides 11q, and it remains to show that there exists a natural number r such that 11 divides 2r-1.

Since the remainders repeat after every 10 powers of 2, we can take r to be the remainder when n is divided by 5. This gives us two cases:

Case 1: r = 1

2r-1 = 1
11 divides 1, so 11 divides 2n-1 when r=1.

Case 2: r = 2, 3, 4, or 5

In this case, we can write r as:

r = 1 + (r-1)

This gives us:

2r-1 = 2(1 + (r-1)) - 1
     = 2r + 1

We can see that 11 divides 2r+1 when r=2, 3, 4, or 5.

Therefore, we have shown that there exists a natural number n such that 11 divides 2n-1, and the proof is complete.

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Answer:

(0, 3 )

Step-by-step explanation:

Given the 2 equations

16x - 2y = - 6 → (1)

8x - 8y = - 24 → (2)

Multiplying (2) by - 2 and adding to (1) will eliminate the x- term

- 16x + 16y = 48 → (3)

Add (1) and (3) term by term to eliminate x, that is

0 + 14y = 42

14y = 42 ( divide both sides by 14 )

y = 3

Substitute y = 3 into either of the 2 equations and solve for y

Substituting into (1)

16x - 2(3) = - 6

16x - 6 = - 6 ( add 6 to both sides )

16x = 0 , thus

x = 0

solution is (0, 3 )