There are (53)2 ⋅ 50 hens in a bird enclosure. What is the total number of hens in the enclosure? (1 point)


0

55

56

530

Answer:

The answer is letter D, credit risk.

Step-by-step explanation:

A bond is considered to be a contract between two occurring parties. It allows companies to borrow money from people (investors). These investors purchase the bond and are given a certain interest for a particular period of time. The rate varies according to the economic situation or the company's standing. This affects the supply and demand for the bond.

Remember that the price of the bond and the interest rate are indirectly proportional. This means that as the price of the bond increases, the interest rate decreases and vice-versa.

In the situation above, Rashid is facing a credit risk as an investor. He has been purchasing bonds from a company that has recently gotten a poor rating. This means that the company is not performing well. This can affect the amount of money (including the interest) that will be paid back to Rashid. There is a chance that some of the amount of money he invested will not be returned to him. It was also mentioned that the bond's interest rate has increased. This means that the bond prices will decrease and thus the number of bond investors will also decrease. The issuer of the bond in this situation can have a hard time paying the investor back.

Answer:

D

Step-by-step explanation:

Answer:

47cm

Step-by-step explanation:

if she already has 2cm and can knit 1 more very night after 45 nights that leaves you with 45cm in scarf then you add the 2cm you already had.

The width of the rectangle is 14 cm and the length is 23 cm.

Let's assume the width of the rectangle is x cm. According to the question, the length is 5 cm less than twice the width, so the length would be 2x - 5 cm. The perimeter of a rectangle is calculated by adding up the lengths of all its sides. In this case, the perimeter is given as 74 cm, so the equation becomes:

2(x + 2x - 5) = 74

Simplifying the equation, we get:

6x - 10 = 74

Adding 10 to both sides:

6x = 84

Dividing both sides by 6:

x = 14

So the width of the rectangle is 14 cm, and the length is 2(14) - 5 = 23 cm.

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Final answer:

The correct answer is C. outside 45 degrees. In this question, we are asked to identify which directions are NOT vector directions. Options A, B, and D all describe vector directions, but option C does not.

Explanation:

The correct answer is C. outside 45 degrees.

In this question, we are asked to identify which directions are NOT vector directions. A vector direction is a specific direction or angle that describes the orientation of a vector.

Options A, B, and D all describe vector directions:

A. 35 degrees north of east: This describes a vector direction that is 35 degrees north of the east direction.

B. north: This is a vector direction that points directly north.

D. 35 degrees inside: This describes a vector direction that is 35 degrees inside the reference angle.

Option C, outside 45 degrees, does not describe a specific vector direction. It is not clear whether the direction is outside 45 degrees to the left or right. Therefore, option C is NOT a vector direction.

Answer:

12.5 minutes

Step-by-step explanation:

87.5 m / 7 m/min = 12.5 min

The equation to represent the number  of umbrellas (u) and ponchos (p) he sold last  week is 5u + 3.5p = 190

Solution:

Given that Karachi earns $5 for each umbrella that he  sells and $3.50 for each rain poncho that he  sells

Thus we can say,

Amount earned from 1 umbrella  = $ 5

Amount earned from 1 rain poncho  = $ 3.50

To find: equation to represent the number  of umbrellas (u) and ponchos (p) he sold last  week.

Let "u" be the number of umbrellas sold

Let "p" be the number of ponchos sold

He earned $190 last week selling  ponchos and umbrellas

Thus we can frame a equation as,

number of umbrellas sold x Amount earned from 1 umbrella + number of ponchos sold x Amount earned from 1 rain poncho = $ 190

[tex]u \times 5 + p \times 3.50 = 190\\\\5u + 3.5p = 190[/tex]

Thus the equation to represent the number  of umbrellas (u) and ponchos (p) he sold last  week is found

To represent the number of umbrellas (u) and ponchos (p) sold by Karachi last week, the equation is 5u + 3.50p = 190.

To represent the number of umbrellas (u) and ponchos (p) sold by Karachi last week, we can set up an equation based on the given information:

5u + 3.50p = 190

This equation represents the earnings from selling umbrellas (at $5 each) and rain ponchos (at $3.50 each) totaling $190. We can use this equation to find the values of u and p.

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The distance between the y-intercept and the x-intercept of the line is 12.64911 units or [tex]\sqrt{160}[/tex] units

Solution:

Given equation is y = 3x + 12

We have to find the distance between y-intercept and the x-intercept of the line whose equation is y = 3x + 12

Let us first find the x - intercept and y - intercept

The x-intercept is the point at which the line crosses the x-axis. At this point, the y-coordinate is zero.

The y-intercept is the point at which the line crosses the y-axis. At this point, the x-coordinate is zero

Finding x - intercept:

To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'.

Substitute y = 0 in given equation

y = 3x + 12

0 = 3x + 12

3x = -12

x = -4

Thus the x - intercept is (-4, 0)

Finding y - intercept:

To find the y-intercept, plug 0 in for 'x' and solve for 'y'

Substitute x = 0 in given equation

y = 3x + 12

y = 3(0) + 12

y = 12

Thus the y - intercept is (0, 12)

Now let us find the distance between x intercept and y intercept

Distance between two points [tex]P(x_1, y_1) \text{ and } Q(x_2, y_2)[/tex] is given by:

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

Here the distance between (-4, 0) and (0, 12) is given as:

[tex]\begin{aligned}&d=\sqrt{(0-(-4))^{2}+(12-0)^{2}}\\\\&d=\sqrt{4^{2}+12^{2}}\\\\&d=\sqrt{16+144}=\sqrt{160}\\\\&d=12.64911\end{aligned}[/tex]

Thus the distance between the y-intercept and the x-intercept of the line is 12.64911 units or [tex]\sqrt{160}[/tex] units

The y-intercept of the line y=3x+12 is (0,12) and the x-intercept is (-4,0). The distance between these two points is approximately 12.65 units.

The equation given is y=3x+12. The x-intercept is the point where the line crosses the x-axis (where y=0), and the y-intercept is where the line crosses the y-axis (where x=0).

For the y-intercept, we simply replace x with 0, so y = 3(0) + 12 = 12. Thus, the y-intercept is (0,12).

For the x-intercept, we replace y with 0, so 0 = 3x + 12. Solving this equation for x gives x = -4. Thus, the x-intercept is (-4,0).

The distance between two points in the coordinate plane is given by the formula √[(x2-x1)² + (y2-y1)²]. Therefore, the distance between the x-intercept and the y-intercept is √[(-4-0)² + (0-12)²] = √(16 + 144) = √160 = 12.65.

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Answer: 213

Step-by-step explanation:

852/4 = 213

Answer:

213

Step-by-step explanation:

852/4 = 213

He is splitting 852 beads into 4 bracelets (groups)

the product of (10x - 17) and (6y + 29)(8x + 1) is:

[tex]\[ 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]

you want to multiply the expressions (10x - 17) and (6y + 29)(8x + 1). Let's proceed with the multiplication:

First, distribute (6y + 29) into (8x + 1):

[tex]\[ (6y + 29)(8x + 1) = 6y \cdot 8x + 6y \cdot 1 + 29 \cdot 8x + 29 \cdot 1 \]\[ = 48xy + 6y + 232x + 29 \][/tex]

Now, multiply the result by (10x - 17):

[tex]\[ (10x - 17)(48xy + 6y + 232x + 29) \]\[ = 10x \cdot (48xy + 6y + 232x + 29) - 17 \cdot (48xy + 6y + 232x + 29) \]\[ = 480xy^2 + 60xy + 2320x^2 + 290x - 816xy - 102y - 3944x - 493 \]\[ = 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]

So, the product of (10x - 17) and (6y + 29)(8x + 1) is:

[tex]\[ 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]

The probable question maybe:

multiply the expressions (10x - 17) and (6y + 29)(8x + 1).

The product of (10x - 17) and (6y + 29)(8x + 1) is: = [tex]\[ 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]

You have to multiply the expressions (10x - 17) and (6y + 29)(8x + 1). Let's proceed with the multiplication:

First, distribute (6y + 29) into (8x + 1):

[tex]\[ (6y + 29)(8x + 1) = 6y \cdot 8x + 6y \cdot 1 + 29 \cdot 8x + 29 \cdot 1 \]\[[/tex]

= 48xy + 6y + 232x + 29

Now, multiply the result by (10x - 17):

[tex]\[ (10x - 17)(48xy + 6y + 232x + 29) \]\\\\ = 10x \cdot (48xy + 6y + 232x + 29) - 17 \cdot (48xy + 6y + 232x + 29) \]\\\\ = 480xy^2 + 60xy + 2320x^2 + 290x - 816xy - 102y - 3944x - 493 \]\\\\ = 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]

So, the product of (10x - 17) and (6y + 29)(8x + 1) is:

[tex]\[ 480xy^2 - 756xy + 2320x^2 - 3654x - 102y - 493 \][/tex]

The complete question is:

Multiply the expressions (10x - 17) and (6y + 29)(8x + 1).

Answer:

y=24x

Step-by-step explanation:

(48-24)/(2-1)=24/1

24=24(1)+b

24=24+b

b=0

The linear equation with points (1, 24),  (2, 48), and (3, 72) is y = 24x.

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.

Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.

An example of a non-linear function is a quadratic function.

From the table,

At x = 1, y = 24 ⇒ (1, 24).

At x = 2, y = 48 ⇒ (2, 48).

At x = 3, y = 72 ⇒ (3, 72).

Therefore the linear equation representing the table is y = 24x.

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Answer:

C

Step-by-step explanation:

The red bordered area is the patio. We need to find its area.

We will consider

If this was a square, full red square. Then we find the area of the square.

After that, we will subtract the white part that is not there to create the patio shape.

Hence,

Area of Patio = Area of Square - Area of White Portion

So,

Area of Square is Side * Side

If we look at the coordinates, x goes from 5 to 15, so side is 15 - 5 = 10

also, y goes from 5 to 15, so same, that is 10

Area of Square = 10  * 10 = 100

Now, the small white portion is also a square with length 5 (looking at coordinates),

So,

Area of White Portion = 5 * 5 = 25

Hence,

Area of Patio = 100 - 25 = 75 sq. meters

Correct answer is C

Answer:

The correlation coefficient is 0.96

Step-by-step explanation:

The Given Table showing year and cost:

Year          Cost

1948           0.36

1963           0.86

1974           1.89

1978           2.34

1985           3.55

1991            4.21

1997           4.59

2005         6.41

2010          7.89

Regression table:

Regression table can be made if we rewrite the year column by associating

1948 with 0, and the years after 1948 to be associated with the number of years after 1948. For example, if 1948 is associated with 0, then 1963 would come after 15 years, hence 1963 would be represented by 15, and with the same way, we can associate other years as well. Have a look:

Year (X)          Cost  (Y)             X²                   XY  

0                         0.36                  0                    0

15                        0.86                225                 12.9

26                       1.89                 676                 49.14

30                       2.34                900                 70.2

37                        3.55               1369                 131.35

43                        4.21                1849                 181.03

49                        4.59               2401                 224.91

57                        6.41                3249                 365.37

62                        7.89               3844                  489.18

∑X= 319           ∑Y= 32.1           ∑X²= 14513        ∑XY= 1524.08            

As the correlation coefficient (r) can be determined as follows:

r = n (∑ XY) - (∑X) (∑Y)  ÷ √[n(∑X²)-(∑Y)²][n(∑Y²)-(∑Y)²]

But, we need an additional column Y²

So,

         Y²          

        0.1296            

         0.7396          

         3.5721        

         5.4756          

         12.6025          

         17.7241          

         21.0681            

         41.0881        

         62.2521  

   ∑Y² = 164.6518

As,

r = n (∑ XY) - (∑X) (∑Y)  ÷ √[n(∑X²)-(∑Y)²][n(∑Y²)-(∑Y)²]

So,

r = 9 (524.08) - (319)(32.1) ÷ √[9(14513 )-(319)²][9(164.6518)-(32.1)²]

[tex]r = \frac{3476.82}{\sqrt{(28856)(451.4562)}}[/tex]

[tex]r = \frac{3476.82}{\sqrt{(13027220.11)}}[/tex]

[tex]r = \frac{3476.82}{\sqrt{(3609.32)}} = 0.96[/tex]

So, the correlation coefficient is 0.96.

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Answer:

11

10

9

8

7

50

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

11

78

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

64.1

Hope this helps :) -Zach

Step-by-step explanation:

To determine the fraction of total interest owed on a loan after the fifth month of a 12-month loan, calculate the numerator by adding the interest paid in each of the first five months, and the denominator by summing the interest amounts for all twelve months. Divide the numerator by the denominator to get the fraction (to the nearest tenth).

To determine the fraction of total interest paid after the fifth month of a 12-month loan, we can use the Rule of 78. This rule states that the majority of the interest on a loan is paid in the early months of the term.

The formula for the Rule of 78 is:

(n + 5)(n + 4)(n + 3)(n + 2)(n + 1) / (n × (n + 1) × (n + 2) × (n + 3) × (n + 4))

where 'n' represents the number of payments remaining.

In this case, we have 7 payments remaining after the fifth month. Plugging this value into the formula, we get:

(7 + 5)(7 + 4)(7 + 3)(7 + 2)(7 + 1) / (7 × (7 + 1) × (7 + 2) × (7 + 3) × (7 + 4)) = 0.505

Therefore, after the fifth month of a 12-month loan, approximately 50.5% of the total interest has been paid.

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Answer:

y + 1 = -5(x - 4)

y + 1 = -5x + 20

y = -5x + 19

The correct answer is :

B) parallelism

The rails of a railway track demonstrate parallelism because they run alongside each other without intersecting, maintaining a constant distance apart. This allows trains to travel smoothly along the track without veering off course.

The complete question is here:

Which property is shown by the rails of a railway track?

A) perpendicularity

B) parallelism

C) intersecting lines

D) opposites​

1. Population: All adults with a mortgage provider.

2. Sample size: 1,627.

3. Margin error: Approximately 0.02.

4. Confidence interval (95%): 0.204 to 0.236

5. Proportion of adults fully engaged with their mortgage provider falls from 0.204 to 0.236.

Given that,

Gallup poll conducted in 2015

Sample size: 1,627 adults

Population: All adults with a mortgage provider

Percentage of adults who felt fully engaged with their mortgage provider: 22%

Confidence level: 95%

1. Population: All adults who have a mortgage provider.

2. Sample size: 1,627 adults.

3. Margin of error:

To calculate the margin error,

The sample size (n) and the confidence level.

Given that, the confidence level = 95%,

The margin error can be calculated using the formula:

The Margin of Error [tex]= Z \sqrt{(p (1-p) / n)}[/tex]

Assume a conservative estimation for p = 0.5 (since we don't have the sample proportion), and using a Z-value of 1.96 for a 95% confidence level,
The margin error would be:

The margin of error is,

[tex]1.96\sqrt{(0.5 (1-0.5) / 1627)} \approx 0.02[/tex]

Therefore, the 95% margin error is approximately 0.02.

4. 95% Confidence Interval:

Without the sample proportion, we cannot provide a specific confidence interval.

Assume a conservative estimate of p = 0.5,

Calculate the interval using the formula:

Confidence Interval = Sample Proportion ± Margin of Error

Given that,

The sample proportion is 0.22

The margin error is 0.016,

The 95%  of the confidence interval is,

0.22 ± 0.016 = 0.24 or 0.2

5. Expressing the answer in a meaningful sentence:

With a 95% confidence level,

It can be estimated that the proportion of adults who feel fully engaged with their mortgage provider falls between 0.2 to 0.24.

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The complete question is:

A 2015 Gallup poll of 1627 adults found that only 22% felt fully engaged with their mortgage provider. 1. What is the population? 2. What is the sample size? 3. What is the 95% margin of error? 4. What is the 95% confidence interval? 5. Express your answer to 4 in a meaningful sentence.

Answer:

The numbers are -14,-13 and -12

Step-by-step explanation:

The correct question is

Find three consecutive integers such that the sum of the first, twice the second and three times the third is -76. What is the number?

Let

x ----> the first consecutive integer

x+1 ---> the second consecutive integer

x+2 ---> the third consecutive integer

we have that

[tex]x+2(x+1)+3(x+2)=-76[/tex]

solve for x

apply distributive property

[tex]x+2x+2+3x+6=-76[/tex]

Combine like terms

[tex]6x+8=-76[/tex]

subtract 8 both sides

[tex]6x=-76-8[/tex]

[tex]6x=-84[/tex]

Divide by 6 both sides

[tex]x=-14[/tex]

so

[tex]x+1=-14+1=-13[/tex]

[tex]x+2=-14+2=-12[/tex]

therefore

The numbers are -14,-13 and -12

There is actually some tactics to this. I tried to find x and y first but they are very messy numbers but...

We know...

(x+y)²=x²+2xy+y²

In this case, (x+y)² = 11² = 121.

So, x²+2xy+y²=121

We also know that xy=15 and furthermore that 2xy=30.

x²+y² = 121-30 = 91

answer: 91

The value of x^2 + y^2 is 91.

To find the value of x^2 + y^2 given that x+y=11 and xy=15, we can use algebraic identities. We will use the fact that (x+y)^2 = x^2 + 2xy + y^2. We know that x+y=11, so (x+y)^2 = 11^2 = 121. Also given is xy=15, which we'll use in the identity mentioned.

Now, let's substitute the values into the identity:

(x+y)^2 = x^2 + 2xy + y^2

121 = x^2 + 2(15) + y^2

121 = x^2 + 30 + y^2

121 - 30 = x^2 + y^2

91 = x^2 + y^2

Answer:

f(6) = - 4 is incorrect.

Step-by-step explanation:

In the given table the values of x and corresponding values of f(x) are given.

The ordered pairs are (-4,6), (-2,3), (0,-1) and (2,-4).

Now, we have to determine the function y = f(x) from any two of the given ordered pair.

The equation of the function is

[tex]\frac{y - 6}{6 - 3} = \frac{x - (- 4)}{- 4 - (- 2)}[/tex]

⇒ -2(y - 6) = 3(x + 4)

⇒ 2y + 3x = 0 ........... (1)

Now, putting x = 6 in the above equation (1), we get y = - 9

Therefore, f(6) = - 9

Hence, f(6) = - 4 is incorrect. (Answer)

B. Continuous, D. Non Linear, And G. Both Increasing and Decreasing.

I think.

Answer:

Dr. Johnson treated about 18 patients a day.

Step-by-step explanation:

1134 ÷ 63 = 18

On average, Dr. Johnson treated 18 patients each day.

Why?

1134/63=18

I hope this helped! If so, please mark brainliest!

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}4x = -3y + 17&\text{add}\ 3y\ \text{to both sides}\\3x - 4y = -6\end{array}\right\\\\\left\{\begin{array}{ccc}4x+3y=17&\text{multiply both sides by 4}\\3x - 4y = -6&\text{multiply both sides by 3}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}16x+12y=68\\9x -12y = -18\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad25x=50\qquad\text{divide both sides by 25}\\.\qquad x=2\\\\\text{Put the values of }\ x\ \text{to the second equation}[/tex]

[tex]3(2)-4y=-6\\6-4y=-6\qquad\text{subtract 6 from both sides}\\-4y=-12\qquad\text{divide both sides by (-4)}\\y=3[/tex]

Answer:

x2-12x+3

Step-by-step explanation:

=x(x-3)-9(x-3)

=x2-3x-9x+3

=x2-12x+3

HOPE IT HELPS U.............

Jamal's age is 24

Mikes age is 7

so their ages together would equal 31

Answer:

The sum of the ages of Mike and Jamal is 31

Step-by-step explanation:

First we need to translate the questions into mathematical equation and then solve.

Let x be Jamal's age and y be Mike's age.

"Jamal's age is 3 more than 3 times Mike's age" can be written mathematically as;

x =3 + 3y ---------------------------------------------------------------(1)

"Mike's age is 17 years less than Jamal's age" can be written mathematically as ;

y = x - 17  -----------------------------------------------------------------(2)

Substitute equation (1) into equation (2)

y = 3 + 3y - 17

y = 3y - 14

subtract 3y from both-side of the equation

y - 3y = 3y - 3y - 14

-2y = -14

Divide both-side of the equation by -2

[tex]\frac{-2y}{-2}[/tex] = [tex]\frac{-14}{-2}[/tex]

y = 7

Mike is 7 years old

Substitute y = 7 into equation (1)

x = 3 + 3y

   = 3 + 3(7)

   = 3+21

    =24

Jamal is 24 years old

The sum of their ages is = x + y = 24 + 7 = 31

Therefore, The sum of the ages of Mike and Jamal is 31

Answer:

102

Step-by-step explanation:

X=5 so from A to E is  5. 5 squared is 25 plus 4 = 29 then add 29 to 5 you get 34. Then multiply 34 times 6  you get 204 then divide by 2 because area of triangle is base times height divided by 2 you get 102.

Answer:

If we already have two points of the line, we can find its slope ([tex]m[/tex]), its intersection with the y-axis ([tex]b[/tex]), hence its point-slope form equation in the following way:

Let's call Point 1: [tex](x_{1},y_{1})[/tex]  and Point 2: [tex](x_{2},y_{2})[/tex]

The Slope equation is:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Now, the equation of the line in its point-slope form is:

[tex]y=mx+b[/tex]

And we can find the intersection with the y-axis ([tex]b[/tex]) by evaluating the equation with any of the two given points and then isolating [tex]b[/tex].

Answer:

The net forces exerted on the horse and cart are not the same, so they are not balanced forces.

Step-by-step explanation:

Please see the Newton's 2nd Law which states  that an object accelerates if there is a net or unbalanced force on it. In this scenario there is just one force exerted on the wagon i.e: the force that the horse exerts on it. The wagon accelerates because the horse pulls on it. And the amount of acceleration equals the net force on the wagon divided by its mass.

As there are two forces the push and pull the horse; the wagon pulls the horse backwards, and the ground pushes the horse forward. The net force is determined by the relative sizes of these two forces.

If the ground pushes harder on the horse than the wagon pulls, there is a net force in the forward direction, and the horse accelerates forward, and if the wagon pulls harder on the horse than the ground pushes, there is a net force in the backward direction, and the horse accelerates backward.

If the force that the wagon exerts on the horse is the same size as the force that the ground exerts, the net force on the horse is zero, and the horse does not accelerate.

Answer:

The net forces exerted on the the horse and cart are not the same, so they are not balanced forces.

Step-by-step explanation:

According to Newton's 2nd Law, an object accelerates if there is a net or unbalanced force on it. For a body to accelerate, two factors are involved which are the mass of the object and the net force acting upon the body.  In this situation, there is just one force exerted on the cart i.e: the force that the horse exerts on it. The cart accelerates because the horse pulls on it. The amount of acceleration can be calculated by dividing the net force on the cart by its mass.

In this scenario, we can clearly see the actions of the pull and push forces. The pull force brings an object closer while the push moves an object away from something. The cart pulls the horse backwards, and the ground pushes the horse forward. They both work in opposite directions. The net force is determined by the relative sizes of these two forces.

If the push force is greater(i.e the ground pushes harder on the horse than the cart pulls), then there is a net force in the forward direction, and the horse accelerates forward. But if the pull force is greater( the cart pulls harder on the horse than the ground pushes), then there is a net force in the backward direction, and the horse accelerates backward.

If the force that the cart exerts on the horse is the same size as the force that the ground exerts, the net force on the horse is zero, and the horse does not accelerate.

Answer:

The ratio of boys to girls in a math class is not proportional to the ratio of boys to girls in a science class

154=288

Step-by-step explanation:

Let

x ----> the number of boys

y ----> the number of girls

we know that

The ratio of boys to girls is x/y

we have

Math class

[tex]\frac{x}{y}=\frac{18}{11}[/tex]

Science class

[tex]\frac{x}{y}=\frac{14}{16}[/tex]

equate both ratios

[tex]\frac{14}{16}=\frac{18}{11}[/tex]

Multiply in cross

[tex]14(11)=18(16)[/tex]

[tex]154=288[/tex] ----> is not true

therefore

The ratio of boys to girls in a math class is not proportional to the ratio of boys to girls in a science class

Answer:

The height of the astronaut from the center of the Earth is 85865 km.

Step-by-step explanation:

It is assumed that the astronaut will be going towards space, so we have to find out that at what height from the center of the earth would the value of g will be [tex]\frac{g}{180}[/tex].

The weight of astronaut on the surface of Earth 180 pounds.

g=9.81 [tex]m/s^{2}[/tex]

Required value of g'=[tex]\frac{g}{180}[/tex]

g'=[tex]\frac{gR^{2} }{h^{2} }[/tex]

where R=Radius of the Earth

h=Height of the point from the center of the earth

[tex]\frac{g}{180} = \frac{gR^{2} }{h^{2} } \\\\h^{2} =180R^{2} \\h=\sqrt{180}  R\\[/tex]

h=13.42

The value of R is approximately 6400 km.

So, h=85865 km.

The astronaut would need to be approximately 85,552 kilometers from the center of the Earth to weigh 1 pound.

Newton's law of universal gravitation is given by the formula:

[tex]F = G \frac{m_1 m_2}{r^2}[/tex]

Where:

On Earth's surface, the weight of the astronaut is the gravitational force exerted by the Earth. This can also be expressed as:

[tex]Weight = m_1 \cdot g[/tex]

Where [tex]g[/tex] is the acceleration due to gravity (approximately [tex]9.8 \text{m/s}^2[/tex]).

Given that the astronaut weighs 180 pounds on Earth, we use the following relation to find the new distance where the astronaut's weight would be 1 pound:

[tex]180 \text{ pounds} \div r^2 = 1 \text{ pound}[/tex]

[tex]r^2 = 180[/tex]

[tex]r = \sqrt{180}[/tex]

However, we need this distance in terms of the Earth's radius [tex]( R_E )[/tex]. The Earth's radius is approximately 6,371 km.

Let's form the ratio:

[tex]\left( \frac{d}{R_E} \right)^2 = 180[/tex]

[tex]\frac{d}{R_E} = \sqrt{180} \approx 13.42[/tex]

Thus, the astronaut would need to be approximately 13.42 times the Earth's radius away from the center of the Earth to weigh 1 pound.

To convert this to an actual distance:

[tex]d = 13.42 \cdot R_E[/tex]

[tex]d \approx 13.42 \cdot 6371 \text{ km} \approx 85,552 \text{ km}[/tex]