Solve the triangle:

Answer: Let x be the number of days it takes for y workers to weed the field. Then, we know that x and y are inversely proportional, meaning that x * y = k, where k is a constant.

Since it takes 6 days for 10 workers to weed the field, we have:

6 * 10 = k

So, k = 60.

Now, to find the number of days it would take if there were 12 workers, we can plug in y = 12 and solve for x:

x * 12 = 60

x = 60/12

x = 5

Therefore, it would take 5 days for 12 workers to weed the field.

Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answer:

10

Step-by-step explanation:

The coordinate of the y-intercept of the line y = 4x + 1 is (7.5, 10). And the value of 'k' is 7.5.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

a) The equation is given as,

y - 4x = 1

y = 4x + 1

Then coordinate of the y-intercept is (0, 1).

b) The equation is given as,

y = 2x + c

From the graph, the y-interept is -3. Then the equation is given as,

y = 2x - 3

At y = 10, the value of 'k' is given as,

10 = 2k - 3

2k = 13

k = 7.5

The coordinate of the y-intercept of the line y = 4x + 1 is (7.5, 10). And the value of 'k' is 7.5.

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The velocity of the bean is 0.63 feet/second

Angular velocity is the time rate at which an object rotates or revolves about an axis. Angular velocity is represented by the Greek letter omega (ω) It is measured in angle per unit time; hence, the SI unit of angular velocity is radians per second.

w = tetha/t

1 revolution = 360° = 2π

1 minutes = 60s

w = 12× 2π/60

w = 24×3.14/60

w = 1.26 radian/second

r = d/2

r = 1/2 = 0.5miles

v = wr

v = 1.26 × 0.5

v = 0.63feet/second

therefore the velocity of the bean is 0.63 feet/second.

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The surface area of the entire figure is 1764 ft².

A rectangular prism is a three-dimensional shape that has six faces, where each face is a rectangle. It is also sometimes referred to as a rectangular cuboid.

A rectangular prism has eight vertices (corners), 12 edges, and six faces. The opposite faces of a rectangular prism are parallel and congruent, and the angles formed between adjacent faces are all right angles (90 degrees).

The volume of a rectangular prism can be calculated by multiplying the length, width, and height of the prism. The formula for the volume of a rectangular prism is given by V = l x w x h, where V is the volume, l is the length, w is the width, and h is the height of the prism.

We can begin by finding the dimensions of the rectangular prism and the cuboid. Since the side of the rectangular prism is 9 ft, it must be the height of the entire figure. We can find the dimensions of the cuboid by subtracting the height of the rectangular prism from the height of the entire figure:

height of cuboid = 19.8 ft - 9 ft = 10.8 ft

width of cuboid = 15 ft

length of cuboid = 12 ft

Now we can find the surface area of the entire figure by adding the surface areas of the rectangular prism and the cuboid. The surface area of a rectangular prism is given by:

2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism, respectively. Substituting in the values we have:

surface area of rectangular prism = 2(9)(9) + 2(9)(19.8 - 9) + 2(9)(15) = 486 + 162 + 270 = 918 ft²

The surface area of a cuboid is given by:

2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the cuboid, respectively. Substituting in the values we have:

surface area of cuboid = 2(15)(9) + 2(12)(9) + 2(15)(12) = 270 + 216 + 360 = 846 ft²

Therefore, the surface area of the entire figure is:

surface area = surface area of rectangular prism + surface area of cuboid = 918 + 846 = 1764 ft²

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The area of shaded region would be 15.7 in² which is a difference between the area of the circle and area of the triangle.

The entire space filled by a triangle's three sides in a two-dimensional plane is defined as its area. The fundamental formula for calculating the area of a triangle is A = 1/2 b h.

We know that;

The area of an equilateral triangle = (√3/4) a²

Here, a = 3

Hence, The area of the given triangle = (√3/4) × 3²

The area of the given triangle = 0.43 × 9 = 3.9 in²

And, The area of the circle = π (d/2)²

Here d = 5

The area of the circle = π (5/2)² = 19.63 in²

Thus, The area of shaded region = area of the circle - area of the triangle

The area of shaded region = 19.63 - 3.9 = 15.7 in²

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The complete question is shown in figure.

Answer: -37j-2/24

Step-by-step explanation:

The amount of the down payment that is required to be paid is = $17025

The down payment is the initial amount that the buyer has to offer for the merchandise before they would later have to make the full payment. The down payment is a sign of seriousness on the part of a buyer

The amount that the house is selling for is $113,500.

The percentage that is to be considered for the down payment is 15 percent of the total amount.

This is given as 15 percent of $113,500.

down payment is 0.15 * $113,500

= $17025

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The number of gallons of paint nearest to tenth will be 0.0358 gallon.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The area of the wall is given as,

A = 6 inches x 172 inches

A = (6 / 12) feet x (172 / 12) feet

A = 0.50 x 14.33

A = 7.167

A ≈ 7.2 gallons

Then the number of gallons of paint is given as,

⇒ 7.167 / 200

⇒ 0.0358 gallon

The number of gallons of paint nearest to tenth will be 0.0358 gallon.

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The contents of r0 will be 0x20000851, which is the first byte of the word stored at address 0x20000850.

The TI TM4C123 is a little-endian processor, meaning that it stores data in the memory in reverse order. This means that the first byte of a word will be stored at the lower address, and the last byte at the higher address.

In this example, register r1 contains the address 0x20000850. When we execute the ldr r0, [r1] instruction, the processor will read the value stored in memory at address 0x20000850 and store it in register r0.

Since this is a little-endian processor, the value stored in memory at address 0x20000850 will be the last byte of the word, and the value stored in memory at address 0x20000851 will be the first byte of the word.

This means that the contents of r0 will be 0x20000851, which is the first byte of the word stored at address 0x20000850.

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Answer:

Step-by-step explanation:

To calculate the simple interest earned on an investment of $9710 at a semiannual rate of 3.6% for 4 years, we need to use the formula:

I = Prt

where I is the interest, P is the principal (initial investment), r is the interest rate (as a decimal), and t is the time (in years).

In this case, the principal is $9710, the interest rate is 3.6% per year, or 0.036/2 = 0.018 per 6-month period (since the interest is compounded semiannually), and the time is 4 years, or 8 periods of 6 months each.

Plugging in these values, we get:

I = $9710 x 0.018 x 8 = $1392.24

Therefore, the simple interest earned on the investment is $1392.24. Rounding to the nearest cent, the answer is $1392.24.

Answer:

I think the answer is B. Sorry if I'm wrong I really tried :(

Step-by-step explanation:

Mathematics is a computational system developed by the Babylonians.

Mathematics has its roots in ancient civilizations, such as the Babylonians and Egyptians, who used mathematical concepts for practical purposes such as measuring land, calculating taxes and predicting astronomical events. The ancient Greeks made major contributions to mathematics with the development of geometry by Euclid and the formulation of mathematical proofs by Pythagoras and his followers.

The 17th and 18th centuries saw a major development in calculus by mathematicians like Isaac Newton and Gottfried Wilhelm Leibniz, which revolutionized the field and opened up new avenues of scientific investigation. In the 19th and 20th centuries, mathematicians such as Georg Cantor, Kurt Gödel, and Alan Turing made major contributions to the foundations of mathematics and the development of computer science.

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The solution for the equation is [tex]x=\frac{\pi }{2} +2\pi n[/tex] ,for any integer n.

An equation is the statement that asserts th equality of the two expressions with 'equal to' (=) sign.

cot [tex]\frac{x}{2} =1[/tex],

Taking inverse on both sides we get,

[tex]\frac{x}{2}[/tex] = [tex]cot^{-1} (1)[/tex]⇒[tex]\frac{x}{2}=\frac{\pi}{4}[/tex]

                ⇒[tex]x=\frac{\pi }{2}[/tex].

cot is positive in first and third quadrant. To find the second solution add π to it.

[tex]\frac{x}{2} =\pi +\frac{\pi }{2}[/tex]

[tex]x=\frac{5\pi }{2}[/tex]

to find period for cot([tex]\frac{x}{2}[/tex])  

The periodic function can be calculated by [tex]\frac{\pi }{|b|}[/tex], replace b with [tex]\frac{1}{2}[/tex]  

we get [tex]2\pi[/tex]. we get period for  cot([tex]\frac{x}{2}[/tex])  is [tex]2\pi[/tex] so values will repeat every

radians in both directions.

[tex]x=\frac{\pi }{2} +2\pi n, \frac{5\pi }{2} +2\pi n,[/tex] for any integer n.

consolidating we get,

[tex]x=\frac{\pi }{2} +2\pi n[/tex], for any integer.

Hence, the solution for the equation cot [tex]\frac{x}{2}[/tex]= 1 is [tex]x=\frac{\pi }{2} +2\pi n[/tex]

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Answer:

40 ft²

Step-by-step explanation:

First way:

A = 1/2bh = 1/2(16)(5) = 40

2nd way:

Length of dotted line at top = x

16² - 8² = x²

x² = 192

x = √192 = 13.86

Area rectangle = 8 x 13.86 = 110.85

Find the shaded area:

110.85 - 1/2(8)(13.86) - 1/2(8)(13.86 - 10) = 40

Answer:

  40 ft²

Step-by-step explanation:

You want the area of a triangle two different ways. The height from the 10 ft base is given as 8 ft; the height from the 16 ft base is given as 5 ft.

The area formula for a triangle is ...

  A = 1/2bh . . . . . . where b is the base, and h is the height from that base

The base (side) dimensioned in red is 10 ft. The perpendicular distance to the opposite vertex is shown in red as 8 ft. Then the area is ...

  A = 1/2(10 ft)(8 ft) = 40 ft²

The base dimensioned in green is 16 ft. The perpendicular distance to the opposite vertex is shown in green as 5 ft. Then the area is ...

  A = 1/2(16 ft)(5 ft) = 40 ft²

The area of the triangle is 40 ft².

Of the given four estimators, the one that shows the most bias is Mean = 20, SE = 1. Hence, Mean = 20, SE = 1 is the accurate choice.

The estimator with the highest value (Mean = 20) compared to the population parameter (15) is the most biased. The lower the standard error (SE = 1), the more confident the estimate, but if the estimate is far from the population parameter, it is considered biased.

In this case, the Mean = 20 estimator is the most biased because it has the greatest difference from the population parameter and the lowest standard error, indicating a high level of confidence in the estimate despite it being significantly different from the actual population parameter.

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Using the distance formula, we can find the lengths of the sides of the triangle:

Side 1: From (1, −8) to (−3, 0)

d = √[(−3 − 1)² + (0 − (−8))²]

d = √[16 + 64]

d = √80

Side 2: From (−3, 0) to (−2, −7)

d = √[(−2 − (−3))² + ((−7) − 0)²]

d = √[1 + 49]

d = √50

Side 3: From (−2, −7) to (1, −8)

d = √[(1 − (−2))² + ((−8) − (−7))²]

d = √[9 + 1]

d = √10

To find the perimeter, we add the lengths of the three sides:

Perimeter = √80 + √50 + √10

Therefore, the exact perimeter of the triangle is:

Perimeter = √80 + √50 + √10

Answer:

33 miles per hour

Step-by-step explanation:

To find the speed of the car in miles per hour, we need to divide the number of miles traveled by the time in hours. We can convert minutes to hours by dividing by 60. So, the time in hours is 45 minutes / 60 minutes/hour = 0.75 hours. Then, we can divide the distance traveled by the time to find the speed:

25 miles / 0.75 hours = 33.33 miles per hour

Rounding to the nearest whole number, the speed of the car was 33 miles per hour.

Step-by-step explanation:

The probability of pulling out each type of coin at random can be found by dividing the number of coins of that type by the total number of coins in the bag. Let's assume the bag contains n quarters, m dimes, k nickels, and p pennies. The total number of coins in the bag would be n + m + k + p.

The probability of pulling out a quarter would be:

P(quarter) = n / (n + m + k + p)

The probability of pulling out a dime would be:

P(dime) = m / (n + m + k + p)

The probability of pulling out a nickel would be:

P(nickel) = k / (n + m + k + p)

And the probability of pulling out a penny would be:

P(penny) = p / (n + m + k + p)

It's important to note that the sum of the probabilities of all the possible outcomes must equal 1:

P(quarter) + P(dime) + P(nickel) + P(penny) = 1

Answer:

140

Step-by-step explanation:

simple interest=principle which is the money, multiply by 7%which is the rate multiply by 1yr which is the time divided by 100

SI=(2000x7x1)

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

100

Hence, the cylinder's content determines the apparent volume of the glassware, and also the difference between the cylinder as well as spherical volumes determines the glass's true capacity.

Capacity can be defined as the amount which can be held by any kind of vessel. This can depend upon their depth as well as their size.

Actual capacity is the volume of liquid that a glass vessel can contain while it is only partially filled, as opposed to capacity, which refers to the volume of liquid when the glass vessel is fully filled to the brim.

The distinction between both apparent capacity versus Actual capacity in parameters of surface area, as well as volume, is that the former refers to the entire surface area proportional volume of the vessel, whilst the latter refers to the surface area but instead the volume of the liquid that could also fit.

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The area of the rectangle is given by the equation A = 500 inches²

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P of rectangle = 2 ( Length + Width )

Given data ,

Let the area of the rectangle be represented as A

Now , the equation will be

The perimeter of the rectangle P = 120 inches

The length of the rectangle L = 5 ( width of rectangle )

Now , Perimeter P of rectangle = 2 ( Length + Width )

Substituting the values in the equation , we get

2 ( 5W + W ) = 120

Divide by 2 on both sides of the equation , we get

6W = 60

Divide by 6 on both sides of the equation , we get

W = 10 inches

So , the width of the rectangle = 10 inches

Now , L = 5W

So , the length of the rectangle = 50 inches

And , the area of the rectangle = L x W

Substituting the values in the equation , we get

The area of the rectangle A = 50 x 10

The area of the rectangle A = 500 inches²

Hence , the area of the rectangle is 500 inches²

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Answer:

A, There were about 204 principals in attendance

Step-by-step explanation:

In one exhibit room, there are 14 principals out of 60 people so the ratio is 14 to 60

If the ratio stays the same then, x is the number of principals in attendance at the conference, then

x/875 = 14/60

60x = 14(875)

60x = 12250

x = 12250/60 = 204

hope this helps.

Answer:

880 feet; 0.166666666 miles or ⅙ of a mile

Step-by-step explanation:

First convert miles to feet so 1 mile is 5280 feet.

Now divide it by 2 because we're working with half a mile per 3 minutes.

Now we know that Kelly can run 2640 feet every 3 minutes. Divide that by three to get her pace for every minute and we know that she runs 880feet per minute. In miles that would be 0.166 or ⅙ of a mile

Step-by-step explanation:

the ratio is

1/2 mile per 3 minutes

= 1/2 / 3

now, we need to keep the value of that ratio unchanged but still transform the ratio (= a fraction) so that we get as ultimate denominator 1 instead of 3 (how far did he run in 1 minute).

what do we need to do to transform 3 to 1 ?

we need to divide by 3.

and because we have to keep the ratio value, we have to devide also the numerator by 3 :

1/2 / 3 × 1/3 / 1/3 = (1/2 × 1/3) / (3 × 1/3) = 1/6 / 1

so, we can read from the result directly :

when running with the same pace (ratio) for 1 minute, he will run 1/6 mile.

Option A and B : This statements is generally false in probability theory.

A. P(A ∪ B) = P(A) + P(B) - This statement is generally false in probability theory. This is known as the inclusion-exclusion principle, which states that the probability of the union of two events is equal to the sum of their individual probabilities minus the probability of their intersection.

B. P(A | B) = P(A) - This statement is generally false in probability theory. In general, P(A | B) is not equal to P(A) because the occurrence of event B affects the probability of event A.

C. P(A ∩ B) = P(A)P(B) - This statement is generally true in probability theory. This is known as the independent events rule, which states that the probability of the intersection of two independent events is equal to the product of their individual probabilities.

D. P(A | B) + P(A' | B) = 1 - This statement is generally true in probability theory.

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Let A and B be any two events. Which of the following statements, in general, are false? P(A∣B)+P(A∣B)=1                                                                                                                                    

A. P(A ∪ B) = P(A) + P(B)

B. P(A | B) = P(A)

C. P(A ∩ B) = P(A)P(B)

D. P(A | B) + P(A' | B) = 1

Answer: A polynomial is an algebraic expression with 1, 2 or 3 variables, whereas, a multinomial is a type of polynomial with 4 or more variables.

Step-by-step explanation:

Answer:

There are many expressions equivalent to this.

Step-by-step explanation:

Let's solve the equation.

In the parentheses, you cannot do ×+, so I will assume that × is meant to be a variable, x.

You can use distributive property to solve this.

3(2x + 5)

3 × 2x + 6x

3 × 5 = 15

6x + 15 cannot be done.

So, the answer to the equation is 6x + 15.

An Equivalent Expression

An equivalent expression can be 2(3x + 7.5)

Let's solve it.

2 × 3x = 6x

2 + 7.5 = 15

So, the answer to this equation is 6x + 15.

6x + 15 = 6x + 15.

2(3x + 7.5) = 3(2x + 5)

Graph A and graph D represents quadratic function and linear function respectively.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

In the given figure,

In option A graph parabola represents the quadratic function.

In option B graph doe's not represents the function.

In option C graph doe's not represents the function.

In option D graph straight line represents the linear function.

Therefore, option A and option D are the correct answers.

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