The straight line shown below passes through the points (3, 1) and (8, 36).
What is the gradient of this line?
Give your answer as an integer or as a fraction in its simplest form.

A farmer reserves a portion of land to raise sheep. The portion of land contains 6 sections each containing 8 acres. If there are 96 sheep within the portion of land, There are A. 2 sheep per acre.

Number of acres of land = 6 x 8 = 48 acres

Number of sheep per acre = Total number of sheep / Total number of acres

Number of sheep per acre = 96 / 48 = 2 sheep per acre

To determine the number of sheep per acre, we need to divide the total number of sheep by the total number of acres. In this case, the farmer reserved a portion of land that contained 6 sections, each of which contained 8 acres.

Therefore, the total number of acres was 6 x 8 = 48 acres.

The total number of sheep within the portion of land was 96.

Therefore, the number of sheep per acre was 96 / 48 = 2 sheep per acre.

Therefore, the correct option is A.

The question was incomplete, Find the full content below:

A farmer reserves a portion of land to raise sheep. The portion of land contains 6 sections each containing 8 acres.

If there are 96 sheep within the portion of land, how many sheep are there per acre?

A. 2 sheep per acre

B. 12 sheep per acre

C. 16 sheep per acre

D. 48 sheep per acre

Know more about Number of sheep here:

https://brainly.com/question/14722521

#SPJ11

The reasons behind GDP is an imperfect measure of economic well being are value of goods and services , economic activity, distributional issues, and depletion of natural resources .

GDP (Gross Domestic Product) is an imperfect measure of economic well-being for several reasons.

First,

GDP only measures the monetary value of goods and services produced within a country's borders.

It does not take into account non-market activities such as household work or volunteer work,

This can be significant contributors to well-being but are not included in GDP calculations.

Second,

GDP does not distinguish between desirable and undesirable economic activity.

For example, expenditures on environmental cleanup or healthcare are counted in GDP

Just as much as expenditures on cigarettes or military weapons.

Even though the former are beneficial for society, while the latter are not.

Third,

GDP does not measure distributional issues such as inequality, poverty, or social welfare.

Even if GDP were to increase,

It does not necessarily mean that all citizens have benefited equally from the economic growth.

Fourth,

GDP does not account for the depletion of natural resources or damage to the environment.

While economic growth may be achieved through unsustainable or environmentally destructive practices.

These costs are not reflected in GDP calculations.

Finally,

GDP does not capture the value of intangible factors such as social cohesion, quality of life, or happiness.

If GDP were to include non-market activities such as household work.

It would provide a more accurate measure of overall economic activity.

However, GDP would still be an imperfect measure of economic well-being.

Because it would not account for the distributional issues or environmental factors mentioned earlier.

Additionally, including non-market activities could potentially create new problems.

Learn more about GDP here

brainly.com/question/13843833

#SPJ4

Annie made mistake in her trigonometric ratios. The opposite side of the right triangle should be 6 cm not 8 cm.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Annie tries to solve the angle ABC of the right triangle. The angle ABC can be found using trigonometric ratios as follows:

where

∅ = angle ABC

Therefore,

sin ∅ = opposite / hypotenuse

sin ∅ = 6 / 10

sin ∅ = 3 / 5

∅ = sin⁻¹ 0.6

∅ = 36.8698976458

∅ = 36.87 degrees

Therefore, she made mistake in her trigonometric ratios.

learn more on right angle triangle here: brainly.com/question/28322629

#SPJ1

Therefore , the solution of the given problem of expressions comes out to be the expression's value at x = -4 and y = 64 is 0.

Instead of using approximations produced at random, it is better to use shifting integers that may prove increasing, reducing, or blocking. They could only help one another by sharing materials, information, or solutions to issues. The justifications, components, or mathematical remarks for techniques like additional disapproval, production, and mixture may be included in a statement of truth equation.

Here,

The phrase is entrusted to us:

=> -4∛y + x²

Additionally, we are told that x = -4 and y = 64. When these numbers are inserted into the expression, we obtain:

=> -4∛y + x² = -4∛(64) + (-4)²

=> -4∛4³ + 16

=> -4(4) + 16

=> 0

Consequently, the expression's value at x = -4 and y = 64 is 0.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

The number of calories from protein if the client eats 3/4 cup is 54 calories. So, the correct option is 54 calories.

Calories are a unit of energy. The energy needed to raise the temperature of 1 gram of water through 1 °C is equal to one calorie. Calories are the energy that food supplies to the body.

Calories from protein: Protein supplies 4 calories per gram. To calculate the total number of calories from protein, you must first know the amount of protein that the food item contains.

To calculate the calories from protein in Greek vanilla yogurt: Greek vanilla yogurt contains about 10 grams of protein per cup.

Therefore, Calories from protein = Protein x 4 = 10 x 4 = 40 Calories per 1 cup Greek vanilla yogurt

If the client eats 3/4 of a cup of Greek vanilla yogurt, the number of calories from protein would be:

Calories from protein = 40 Calories x 3/4 cup = 30 Calories

Hence, the correct answer is 54 calories.

Know more about calories here:

https://brainly.com/question/1178789

#SPJ11

The distance across the lake, given the distance of the tree and Cade would be 14.36 ft.

We can use the concept of similar triangles to solve this problem:

(Length of the tree's shadow) / (Distance from the tree to the edge of the lake) = (Length of Cade's shadow) / (Cade's height)

36.2 / 15 = 2.5 / 6.2

Now we can set up another proportion using the length of the tree's shadow and the length of the lake:

(Length of the tree's shadow) / (Length of the lake) = (Distance from the tree to Cade) / (Length of Cade's shadow)

Plugging in the values we know, we get:

36.2 / 15.6 = 15 / 2.5

6.2 * 2.32051282 = 14.36 ft

Find out more on distance at https://brainly.com/question/29079393

#SPJ1

The full question is:

The trees shadow is 36.2 feet long. The tree is 15 feet away from the edge of the lake. Cade is 6.2 feet tall and his shadow is 2.5 feet long, his shadow is measured at the exact time the trees shadow reaches the other side of the lake which is 15.6 feet long. What is the distance across the lake (water's edge to opposite side)​

Answer:

it is option no d at least

cuz it is what it is

The coordinates of the resulting point, P' as required to be determined in the task content is; (1, -6).

It follows from the task content that the coordinates of the image point P' formed when point P(-1, 6) is rotated 180° counterclockwise around the origin is to be determined.

On this note, since a rotation of 180° is such that we have;

(x , y) ======> (-x, -y).

Hence, when point P(-1, 6) is rotated 180° counterclockwise around the origin, the resulting image point, P' has coordinates; (1, -6).

Read more on counterclockwise rotation;

https://brainly.com/question/29315058

#SPJ1

No, she have not enough time to fill the pool before he gets home. The garden hose with flow rate 24 gal/min will take 40 minutes to complete fill up the tank that is t ~ 40 minutes. So, she cannot complete fill up the pool before he come.

We have, the time in which Ines's younger brother will be home = an half hour = 1/2 hour

water flow rate of garden's hose = 24 gal/min

She want to fill up the pool. From the figure, depth of pool = 3 ft

Width of pool = 10 in.

1 inch = 0.0833 feet

So, 10 inches = 0.833 feet

outer diameter of pool = 9 ft

so, outer radius of pool = 4.5 ft

Now, inner diameter of pool/tank = outer diameter - 2(width)

= 9 - 2×0.833

= 9 - 1.666 = 7.334

Inner radius of pool = 7.334/2 = 3.667 ft

Water flow rate, Q = 24 gal/min

= 24/7.48 gal ( since 1 ft³ = 7.48 gal)

= 3.20 ft³

Using formula, Q = volume/ time

where t --> time to fill up the pool through hose

Volume of tank/pool = surface area × height (depth)

= π r² × h , where r is inner radius

= π (3.667)² × 3 ft³

= 126.71 ft³

So, Q = 126.71 ft³/t

=> t = 126.71 ft³/3.20 ft³

=> t = 39.59 min

Hence, required time is 39.59 ~ 40 minutes and she cannot complete before he come.

For more information about volume, visit :

https://brainly.com/question/463363

#SPJ4

Complete question:

Ines's younger brother will be home in a half hour. If her garden hose flows at a rate 24 gal/min, does she have enough time to fill the pool before he gets home? See the above figure

Explain. (Hint: 1 ft³ = 7.48 gal)

To identify which lines intersect the line y = 3, you would need to provide a list of lines to choose from. In general, any line that is not parallel to y = 3 will intersect it. Lines parallel to y = 3 will have equations of the form y = c, where c is a constant value different from 3.

The equation of line perpendicular to y = -4x and passing through the point (12, 6) is y = 1/4 x + 3.

Using the slope method, determine the slope.

To find the y-intercept (b), use the slope and one of the locations.

You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).

The given equation is y = -4x and we need to find the equation of the line which is passing through the point (12,6).

As y=-4x, therefore compared to the standard equation y = mx, hence the slope of the line is m = -4.

Therefore any line which is perpendicular and has a slope that is the negative reciprocal of the -4 is 1/4.

The modified equation becomes for the line that passes through (12, 6).

y-6 = 1/4 (x-12)

solving this equation we get,

y-6 = 1/4 x - 1/4 * 12

y-6 = 1/4 x - 3

y = 1/4 x -3 + 6

y = 1/4 x + 3

Therefore option 4 is correct, y = 1/4 x + 3

Learn more about the equation of line here:

https://brainly.com/question/21511618

#SPJ1

Answer:

x is the number of successes

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

There is a 17.18% probability that a randomly selected region had exactly two hits.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X=x)=\dfrac{e^{-\mu}\times\mu^x}{(x)!}[/tex]

In which

x is the number of successes

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

In this problem we have that:

A total of 525 bombs hit the combined area of 561 regions. So the mean hits per region is:

[tex]P=\dfrac{525}{561}=0.9358[/tex]

Assume that we want to find the probability that a randomly selected region had exactly two hits.

This is P(X = 2).

[tex]P(X=x)=\dfrac{e^{-\mu}\times\mu^x}{(x)!}[/tex]

[tex]P(X=2)=\dfrac{e^{-0.9358}\times(0.9358)^2}{(2)!}=0.1718[/tex]

There is a 17.18% probability that a randomly selected region had exactly two hits.

Answer:

I am 20.

Step-by-step explanation:

The GCF is 2 so the mystery number x must be even.

And as I am between 18 and 30 I could be

20, 22, 24, 26 or 28

But I am a multiple of 5 so i must be 20.

The Saints had the best overall record for the season because they had a larger mean value of about 200 points, whereas the Saints had a larger median value of 12 points.

To determine which team had the best overall record for the season, we need to consider the total number of points earned by each team across all games. We can calculate the total points for each team by adding up the points earned in each game.

For the Saints:

Total points = 21+12+3+3+10+10+14+3+12+28+40+10+17+20+7 = 200

For the Cowboys:

Total points = 10+3+8+6+24+12+21+3+10+28+28+7+7+13+3 = 183

Therefore, the Saints earned a total of 200 points, while the Cowboys earned a total of 183 points. Therefore, the Saints had the better overall record for the season.

To compare the central tendency of the points earned by each team, we can use either the mean or the median. However, in this case, the median is a better measure of center because it is less sensitive to extreme values than the mean.

Calculating the median for each team:

For the Saints:

Arrange the points earned in ascending order: 3 3 7 10 10 12 12 14 17 20 21 28 40

The median value is the middle value, which is 12.

For the Cowboys:

Arrange the points earned in ascending order: 3 3 6 7 8 10 10 12 13 21 24 28

The median value is the middle value, which is 10.

Therefore, the Cowboys have a median value of 10 points, while the Saints have a median value of 12 points. However, as we already determined, the Saints had a better overall record for the season based on the total points earned.

To know more about median value:

https://brainly.com/question/14693117

#SPJ4

She should multiply the prices on the tags by 0.9 to find the price she would have to pay, before tax, after the 10% discount.

To find the price Naomi would have to pay for her new sneakers after the 10% discount, she needs to multiply the original price on the tag by a factor that reflects the discount.

Since the discount is 10%, the factor by which she should multiply the original price is 1 minus 10% or 0.9. This is because the final price is equal to the original price minus the discount, which is 10% of the original price, or 0.1 times the original price.

So, if the price on the tag is $100, the price Naomi would have to pay, before tax, after the 10% discount would be:

$100 * 0.9 = $90

This means that she would save $10, which is 10% of the original price.

In general, if the original price on the tag is P, the price Naomi would have to pay, before tax, after the 10% discount would be:

P * 0.9 = 0.9P

Therefore, she should multiply the prices on the tags by 0.9 to find the price she would have to pay, before tax, after the 10% discount.

Learn more about original price :

https://brainly.com/question/731526

#SPJ4

28.26 is the volume of the fig.

Each thing in three dimensions takes up some space.

The volume of this area is what is being measured.

The space occupied within an object's borders in three dimensions is referred to as its volume.

It is sometimes referred to as the object's capacity.

Knowing an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.

Hence, 28.26 is the volume of the fig.

learn more about volume click here:

https://brainly.com/question/463363

#SPJ1

According to the given tangent of the circle and angle, the value of x is approximately 38.67.

In geometry, a tangent of a circle is a straight line that intersects the circle at exactly one point, which is known as the point of tangency. The tangent line is perpendicular to the radius of the circle at the point of tangency.

An angle is a geometric figure formed by two rays that share a common endpoint, known as the vertex. Angles are usually measured in degrees or radians and are commonly used to describe the direction or orientation of lines, shapes, or objects in space.

we do know that the angle between the tangent and the radius drawn to the point of tangency is 90 degrees. We can use this fact to set up an equation and solve for x:

(3x - 26) + 90 = 180

3x + 64 = 180

3x = 116

x = 38.67

Learn more about the tangent of the circle here:

brainly.com/question/23265136

#SPJ1

Below are few steps given to check what answer you got correct on edmentum.

What is edmentum?

Edmentum is an online learning platform that offers educational software and digital curriculum for K-12 students.

What is use of edmentum?

Edmentum is designed to support student learning and achievement, provide teachers with the tools and resources they need to be successful, and help schools and districts meet their academic goals.

To check your answers on Edmentum, you can navigate to the assignment or quiz that you completed and click on the "View Results" button. This will show you a breakdown of your score and which questions you answered correctly or incorrectly.

If you want to review specific questions and their answers, you can click on the individual question numbers to see the question prompt and your response. Depending on how your instructor has set up the assignment or quiz, you may also be able to see the correct answer and an explanation for why it is correct.

If you have trouble finding your results or accessing specific information, you can reach out to your instructor or the Edmentum support team for assistance.

To learn more about edmentum visit:

https://brainly.com/question/29183993

#SPJ9

Answer:

10,
7777777777777777777777777777777777

Step-by-step explanation:

The probability that a card drawn at random from an ordinary deck of 52 playing cards is: (a) An ace is 1/13. (b) A jack of hearts is 1/52. (c) A three of clubs or a six of diamonds is 1/26. (d) A heart is 1/4. (e) Any suit except hearts is 3/4. (f) A ten or a spade is 4/13. (g) Neither a four nor a club is 10/13.

We will find the probability of the given situations.

a) An aceThere are 4 aces in the deck.

Therefore, the probability of drawing an ace is given by

P(Ace) = 4/52 = 1/13

b) A jack of hearts

There is only one jack of hearts in the deck.

Therefore, the probability of drawing a jack of hearts is given by

P(Jack of hearts) = 1/52

c) A three of clubs or a six of diamonds

There is one three of clubs and one six of diamonds in the deck.

Therefore, the probability of drawing a three of clubs or a six of diamonds is given by

P(Three of clubs or six of diamonds) = 2/52 = 1/26

d) A heart

There are 13 hearts in the deck.

Therefore, the probability of drawing a heart is given by

P(Heart) = 13/52 = 1/4

e) Any suit except hearts

There are 39 cards that are not hearts in the deck.

Therefore, the probability of drawing any suit except hearts is given by

P(Any suit except hearts) = 39/52 = 3/4

f) A ten or a spade

There are 16 cards that are either tens or spades.

Therefore, the probability of drawing a ten or a spade is given by

P(Ten or spade) = 16/52 = 4/13

g) Neither a four nor a club

There are 12 cards that are either fours or clubs.

Therefore, the probability of drawing neither a four nor a club is given by

P(Neither four nor club) = 40/52 = 10/13

For similar question on probability

https://brainly.com/question/7965468

#SPJ11

bonjour,

a) on pourrait faire un produit en croix

8,3 m ----> 1s

combien de m en ----> 120s

120*8,3= 996m en 120s

soit 0,996 km (on décale de 3 rangs vers la gauche)

il parcoure donc 996m en 120secondes

b) pour parcourir 3km, de même faisons un produit en croix

(3 km = 3000m)

8,3 m ---> 1s

3000m ----> combien de secondes ?

3000*1/8,3= environ 361,45 secondes

transformons les en heures, minutes

361,45/60 = 6,02 minutes

0,02*60= 1,2

donc pour parcourir 3km, à cette vitesse, il mettra environ 6 minutes et 1 seconde.

c) posons un produit en croix :

vitesse en km/h

15km ----> 25 min

? -----> 60 min (1h)

60*15/25= 36

donc il a une vitesse de 36km/h

vitesse en km/mn

15km ----> 25 min

?km ------> 1 min

1*15/25 =0,6 km/mn

voilà j'espère t'avoir aidé

si t'as des questions n'hésite pas

Step-by-step explanation:

All three angels of a triangle have to sum to 180 degrees ....so there is only 90 degrees left for the other two  equal-sized angles (isosceles).....they must be 45° each

According to the question we can conclude that the total mass of the jars is 2.561 g.

The mass is the amount of matter in an object. It is measured in grams, kg, ect. According to the law of conservation, mass in such an isolated system may only be changed through one form to another and cannot be created or destroyed.

To find the total mass of the jars, we simply need to add up the masses of jar one, jar two, and jar three:

Total mass of jars = mass of jar one + mass of jar two + mass of jar three

Total mass of jars = 0.62 g + 1.431 g + 0.5 g

Total mass of jars = 2.561 g

So the total mass of the jars is 2.561 g.

To know more about law of mass conversion visit:

https://brainly.com/question/27891057

#SPJ9

If your friend went to bed at 1:00am on Friday and woke up at 1:00pm on Friday, she slept for 12 hours.

To see why, you can count the number of hours between 1:00am and 1:00pm:

1:00am to 2:00am = 1 hour

2:00am to 3:00am = 1 hour

...

11:00am to 12:00pm = 1 hour

12:00pm to 1:00pm = 1 hour

The total number of hours between 1:00am and 1:00pm is 12 hours.

Answer:

  8.5 years

Step-by-step explanation:

You want to know the number of years until 18500 depreciates to 9100 at the rate of 8% per year.

The depreciation rate given as a percentage of current value tells you the depreciation is exponential. The formula will be ...

  value = (initial value) × (1 - (depreciation rate))^t

where the rate is "per year" and t is in years.

  value = 18500·(1 -0.08)^t

  9100 = 18500·0.92^t . . . . fill in the value of interest

  9100/18500 = 0.92^t . . . . divide by 18500

  log(91/185) = t·log(0.92) . . . . take logarithms

  t = log(91/185)/log(0.92) ≈ -0.3081/-0.03621 ≈ 8.509

It will be about 8.5 years until the value is $9100.

__

Additional comment

The graph shows the solution to ...

  18500·0.92^t -9100 = 0

We find it fairly easy to locate an x-intercept, so we wrote the equation in the forms that makes the x-intercept the solution.

The dimensions of the can that use the least amount of material are a radius of approximately 4.38 cm and a height of approximately 3.11 cm.

To design a can that uses the least amount of material, we want to minimize its surface area. Since the can is shaped like a right circular cylinder, its surface area is given by:

A = 2πr² + 2πrh

where r is the radius of the base of the cylinder and h is its height.

We also know that the volume of the can is given by:

V = πr²h

We can use these equations to express h in terms of r, and then substitute this expression for h into the equation for surface area. Then we can differentiate the resulting equation with respect to r, set it equal to zero, and solve for r to find the value of r that minimizes surface area.

First, we solve for h in terms of r by rearranging the equation for volume:

h = V/(πr²)

Substituting this expression for h into the equation for surface area, we get:

A = 2πr² + 2πr(V/(πr²))

A = 2πr² + 2V/r

To minimize A, we differentiate with respect to r:

dA/dr = 4πr - 2V/r²

Setting this expression equal to zero and solving for r, we get:

4πr = 2V/r²

r³ = V/(2π)

Substituting the given value for V, we get:

r³ = 432/2π

r ≈ 4.38 cm

Now we can use the expression for h in terms of r to find the corresponding height:

h = V/(πr²) ≈ 3.11 cm

Therefore, the dimensions of the can that use the least amount of material are a radius of approximately 4.38 cm and a height of approximately 3.11 cm.

To learn more about dimensions  visit:https://brainly.com/question/28688567

#SPJ11

Answer:

[tex]a = \frac{1296}{5\pi} [/tex]

Step-by-step explanation:

Given:

C = 14,4 (circumference)

Find: A - ? (area)

Let's start by writing down both circumference and area formulas:

[tex]c = 2\pi \times r[/tex]

[tex]a = \pi \times {r}^{2} [/tex]

We can find the radius (r) from the 1st formula:

[tex]r = \frac{c}{2\pi} = \frac{14.4}{2\pi} =14 \frac{4}{10} \times \frac{1}{2\pi} = \frac{144}{10} \times \frac{1}{2\pi} = \frac{144}{20\pi} = \frac{36}{5\pi} [/tex]

Now, that we know the length of the radius, we can find the area:

[tex]a = \pi \times( { \frac{36}{5\pi} })^{2} = \frac{1296}{25 {\pi}^{2} } \times \frac{\pi}{1} = \frac{1296}{25\pi} [/tex]

Answer:

1

Step-by-step explanation:

Answer: 1 pair

Step-by-step explanation: Trapezoids only have one pair of parallel sides.