A cable that weighs 8 lb/ft is used to lift 900 lb of coal up a mine shaft 450 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter xi* as xi.)

To find the distance between Basti and Cian, we can use the law of sines in triangle ABC. The law of sines states that the ratio of the length of a side to the sine of the opposite angle is constant for all sides and their corresponding angles in a triangle.

Let's label the distance between Basti and Cian as "x". We know that the measure of angle ABC is 50 degrees and the measure of angle BAC is 60 degrees. We also know that Ali is exactly 150 ft away from Basti.

Using the law of sines, we can set up the following equation:

sin(50°) / 150 = sin(60°) / x

To solve for "x", we can rearrange the equation:

x = (150 * sin(60°)) / sin(50°)

Using a calculator, we can evaluate the expression:

x ≈ (150 * 0.866) / 0.766

x ≈ 168.4 ft

Therefore, the distance between Basti and Cian is approximately 168.4 ft.

The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.

To write the equation of a line in slope-intercept form, we use the formula:y = mx + b

where:

- y represents the dependent variable (the vertical axis)

- x represents the independent variable (the horizontal axis)

- m represents the slope of the line

- b represents the y-intercept, the point where the line intersects the y-axis.

In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:

y = (3/5)x + 2

This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).

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Answer:

  see attached

  H31 = -0.2

Step-by-step explanation:

The matrix sum H is the element-by-element sum of corresponding elements of F and G. For example, H31 = F31 +G31 = -4.7 +4.5 = -0.2.

__

For repetitive calculations using the same formula, it is convenient to do them using a spreadsheet.

Answer:

Step-by-step explanation:

1). Since, XM is the radius of the circle,

   Therefore, area of the circle = \(\pi r^{2}\)

                                                   = \(\pi (XM)^2\)

                                                   = \(\pi (12)^2\)

                                                   = 452.39 units²

2). Circumference of a circle = 2πr

                                                = 2π(XM)

                                                = 2π(12)

                                                = 24π

                                                = 75.40 units

3). By applying Pythagoras theorem in ΔYXM,

    YM² = XY² + XM²

    (43)²= (XY)² + (12)²

     1849 - 144 = (XY)²

     XY = 41.29 units

4). tan(∠M) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

                  = \(\frac{XY}{XM}\)

    m∠M = \(tan^{-1}(\frac{41.29}{12} )\)

              = 73.79°

5). Area of ΔXYM = \(\frac{1}{2}(\text{Base)}(\text{Height})\)

                             = \(\frac{1}{2}(41.29)(12)\)

                             = 247.74 square units

6). Area of the minor sector created by ΔXYM = \(\frac{\theta}{360}(\pi r^2)\)

                                                                             = \(\frac{73.79}{360}(452.39)\)

                                                                             = 92.73 units²

you need help

nice for you                                                                                                                                   / fyi this is payback

Answer:

30 square units

Step-by-step explanation:

10 (height) x 6 (base) / 2 =

60 / 2 =

30 square units

Hope that helps!

Answer:

Ounces :)

Step-by-step explanation:

Answer:

$5.19

Step-by-step explanation:

→ Write the ratio

3 : 15.57

→ Divide both sides by 3

1 : 5.19

Answer:

5

Step-by-step explanation:

Answer:

58

Step-by-step explanation:

case I added it and I m right

Answer:

200

Step-by-step explanation:

you subtract

Answer:

  (a)  y = x/8

  (b)  y = 7/8

Step-by-step explanation:

You want a direct variation equation that relates x and y, given y = 2 when x = 16.

The equation for direct variation is usually written in the form ...

  y = kx

where k is the constant of proportionality.

The value of k can be found from ...

  k = y/x . . . . divide by x

For the given values, k is ...

  k = 2/16 = 1/8

The direct variation equation is ...

  y = (1/8)x

The value of y for x=7 is found by substituting 7 for x in the equation above:

  y = (1/8)·7

  y = 7/8

<95141404393>

The 95 percent confidence interval is (0.20, 0.32).

a. We can construct a 95% confidence interval to estimate the percentage of yellow peas as follows:

Let p = proportion of yellow peas = 155/595 = 0.26

Sample size = n = 595

Standard error = SE = √(p × (1-p) / n) = √(0.26 × (1-0.26) / 595) = 0.03

95% confidence interval = p ± 1.96 × SE

= 0.26 ± 1.96 × 0.03

= 0.26 ± 0.06

So, the 95% confidence interval is (0.20, 0.32).

b. Yes, the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow, as the 95% confidence interval does not include the expected value of 0.25.

Therefore, the 95 percent confidence interval is (0.20, 0.32).

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Answer:

Step-by-step explanation:

Wow, pretty harsh. Report someone who makes a fair effort but makes a mistake. Better report yourself then, because you obviously cannot do it yourself or you wouldn't be asking.

Coordinates of the vertex seem to be (-2, 2)

It's the point where the slope of the curve is zero.

Cannot tell for certain unless we have the equation of the curve.

Answer: A

Step-by-step explanation:

Answer:

a.30

b.12

i cant figure out the rest i am so sry im

trying to figure it out tho

Answer:

D

Step-by-step explanation:

your welcome!!!!!!! :D :)

Answer:

Step-by-step explanation:

Ajit has 5 coins in total

1 quarter = 25 cents

1 nickel = 5 cents

2 dimes = 20 cents

1 penny = 1 cent

The required coins that Ajit has are 1 quarter, 1 nickel, 2 dimes, and 1 penny.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let,
Quarter = x
Nickle = y

Dimes = z
penny = a

So, accoding to the quesiton
0.25x + 0.5y + 0.10z + 0.01a = $0.51

Ajit has 5 coins in total

So that the sum of x + y + z + a = 5

Apply hit and trial,

1 quarter = 25 cents

1 nickel = 5 cents

2 dimes = 20 cents

1 penny = 1 cent
Total coins value = $0.51

Similarly, various cases can be determined.

Thus, the required coin that Ajit has is 1 quarter, 1 nickel, 2 dimes, and 1 penny.

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Answer:

c ≈ 11.8

Step-by-step explanation:

using the law of sines to find c

\(\frac{c}{sinC}\) = \(\frac{b}{sinB}\)

where c is the side opposite ∠ C and b is the side opposite ∠ B

\(\frac{c}{sin105}\) = \(\frac{7}{sin35}\) ( cross- multiply )

c × sin35° = 7 × sin105° ( divide both sides by sin35° )

c = \(\frac{7sin105}{sin35}\) ≈ 11.8 ( to 1 decimal place )

Answer:

60'' × 52'' or a 79.4'' TV

Step-by-step explanation:

Leaving a room of 2 inches on all sides means we subtract 4 inches from the height and length to find the maximum dimensions of the TV.

With this, we get 60'' × 52''. To find the diagonal length of the TV, use the Pythagorean Theorem which simply states the length of the diagonal is equal to the square root of the sum of the squared dimensions.

\(\sqrt{a^2+b^2} =c\)

\(\sqrt{60^2+52^2}=79.4\)

Therefore your TV can have a maximum size of 79.4 inches.

A count of the number of times a card is selected until an ace is drawn is best modeled by Poisson distribution. Then the correct option is B.

A finite frequency distribution that estimates the likelihood that many independent occurrences will take place at the same moment.

A variable that plots symmetrically in the figure of a globe is the distribution of numerous unknown parameters.

A card is drawn from a well-shuffled deck of cards and then returned to the deck, which is then shuffled again.

A count of the number of times a card is selected until an ace is drawn is best modeled by Poisson distribution.

Then the correct option is B.

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Answer:

Step-by-step explanation:

The description is too ambiguous to reconstruct the diagram. You need to post the actual diagram.

That diagram is just one way to view division by a fraction. An easier way: DIVIDING by a fraction is the same as MULTIPLYING by the upside-down fraction. For example,

(1/2) ÷ (1/4) = (1/2) × (4/1) = 2

That doesn’t help you answer this particular question, though.

Answer:

C

Step-by-step explanation:

Answer:

I think its C

Step-by-step explanation:

A fraction of the students who have brown hair is equal to 1/7.

You should shade only one (1) section on the pie chart to show the number of students with brown hair.

In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.

Based on the information provided in the table (see attachment), we can logically deduce the following parameters about the various hair color;

Number of brown hair = 1 brown hair.

Number of blonde hair = 4 blonde hair.

Number of black hair = 2 black hair.

Therefore, the total number of hairs is equal to 7 hairs.

For the fraction of students with brown hair, we have;

Fraction = 1/7.

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The nth term rule of linear sequence is aₙ = aₙ₋₁ + 3

Linear sequence is a sequence of number in order with same difference .or same ratio.

when fixed number is added to any term of a sequence to get next term . That Fixed number is known as common difference.

The sequence in the given question

-5 , -2 , 1 , 4 , 7, . . . .

The first term of sequence : a₁ = -5

The second term : a₂ = -2

Common difference : d = a₂ - a₁

=> d = -2 - (-5)

=> d = -2 + 5

=> d = 3

The nth rule of linear sequence is aₙ = aₙ₋₁ + d

replacing the value of d

aₙ = aₙ₋₁ + 3 is nth rule of the linear sequence.

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Answer:

2.221992

Step-by-step explanation:

can i have the crown pls ૮ ♡ﻌ♡ა

Answer:

2.221

Step-by-step explanation:

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Correct question with correct options has been attached

Answer:

37

Step-by-step explanation:

Let C represent those dressed as heroes and let B represent those wearing mask

Thus;

n(C) = 39

n(D) = 45

We are told that 21 entrants were dressed as heroes wearing a mask.

Thus; n(C n D) = 21

We are also told that there were a total of 100 entries.

Thus, n(T) = 100

Now, number of entrants neither dressed as heroes nor wearing a mask is given by;

n(T) - n(C u D)

n(C u D) = n(C) + n(D) - n(C n D)

n(C u D) = 39 + 45 - 21

n(C u D) = 63

Thus;number of entrants neither dressed as heroes nor wearing a mask is: 100 - 63 = 37

To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.

Answer: 36 problems

Step-by-step explanation:

40% is nothing but 40/100, which is just 4/10. To start, multiply 60 by the fraction 4/10. Cancel out the 10 from the denominator of the fraction to get 4 x 6 = 24. Now, we just found the number of problems that the student solved, but we need to find how many problems still need to be solved. To do that, do 60 - 24 = 36. The student needs to solve 36 more problems.

I hope this helps!

Answer:

B.

Step-by-step explanation:

First angle 1 and 2 add up to 180 and then angle 2 and 3 also add up to 180. So angle 2 is common hence both are congruent to each other.