You collected 27 gallons of rain water in a drum. How many liters of water did you collect?

The value of the angles in the triangle are:

∠A = 60°, ∠B = 80° and ∠C = 40°

We  are given that BD = DC

Thus, ∠DBC = ∠BCD ---- 1  (angle in isosceles triangle)

We also have ∠BDC = 100°

In ΔBDC

∠BDC + ∠DBC + ∠BCD = 180°  (sum of angles of triangle is 180°)

Using 1:

∠BDC + 2∠DBC = 180°  

100° + 2∠DBC = 180°  

2∠DBC = 180 - 100

2∠DBC = 80

∠DBC = 80/2

∠DBC = 40°

∠DBC = ∠BCD = ∠2 = 40°

Thus, ∠C = 40°

We are given that  m∠1 = m∠2

Thus, ∠1 = ∠2 = 40°

Now,  ∠BDC +  ∠BDA = 180° (Linear pair)

100° + ∠BDA = 180°

∠BDA = 180 - 100

∠BDA = 80°

In ΔABD

∠ABD + ∠BDA +  ∠BAD = 180° (sum of angles of triangle is 180°)

∠1 + ∠BDA +  ∠BAD = 180°

40° +  80° +  ∠BAD = 180°

120° +  ∠BAD = 180°

∠BAD = 60°

So,  ∠A = 60°

∠B =  ∠1  + ∠2 = 40° + 40° = 80°

Therefore,  ∠A = 60°, ∠B = 80° and ∠C = 40°

Learn more about triangle on:

brainly.com/question/9132922

#SPJ1

Complete Question

m∠1=m∠2

D∈

AC

, BD = DC

m∠BDC = 100°

Find: m∠A, m∠B, m∠C

There are 540 men living in the mini city.

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

Therefore, there are 540 men living in the mini city.

To check our answer, we can substitute x = 540 into our original equation:

540 + (540 + 150) = 1230

690 = 1230

This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.

We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

For such more questions on mini

https://brainly.com/question/29266607

#SPJ8

Answer:

59 degrees

Step-by-step explanation:

180 - 126 = 54

6x-1 + 5x + 17 +54 =180

11x + 70 = 180

11x = 180 -70

11x = 110

x =10

Therefore

6(10) - 1 = 59 degrees

Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.

Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.

How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.

Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.

The weight per carton is 55 pounds.

For more such questions on pounds

https://brainly.com/question/30400939

#SPJ8

Answer:

0.125

Step-by-step explanation:

I calculated 2 divided by 16, and got 0.125.

Answer:

12

Step-by-step explanation:

I got it right on edg

The statistical method used to predict the values of one numerical variable based on the values of another is regression analysis.

Regression analysis:

Regression analysis is a statistical method that shows the relationship between two or more variables. Usually expressed in a graph, the method tests the relationship between a dependent variable against independent variables.

Regression analysis is used to estimate the relationship between a dependent variable and one or more independent variables.

The common form of regression analysis is linear regression. Regression analysis allows us to infer that there is a relationship between two or more variables.

Therefore regression method is used to predict values of one numerical on another.

To know more about the regression analysis refer to the link given below:

https://brainly.com/question/7781679

#SPJ4

Flint is starting a business. Before starting to sell anything, he bought fixtures for £1,200, a van for £6,000 and an inventory of goods for £2,800. Although he has paid in full for the fixtures and the van, he still owes £1,600 for some of the inventory. B. Rub lent him £2,500. After the above, Flint has £200 in the business bank account and £175 cash in hand. Total capital is £10,375

What do you mean by capital?

Any employed financial asset might be considered capital. A company's capital is represented on its balance sheet as the earnings from its ongoing operations. The money in a bank account, the proceeds from the sale of stock shares, and the proceeds from the sale of bonds are a few examples.

A factory and its equipment, intellectual property like patents, or the financial assets of a company or a person are all examples of things that provide value or benefit to their owners and fall within the broad definition of capital.

Fixtures= £1,200, van= £6,000, inventory of goods= £2,800, cash =£375

So, Total assets= £10,375

Payable=  £1,600, loan from Rub= £2,500, Balancing figure= £6,275

Total liabilities= £10,375

To learn more about capital from the given link

https://brainly.com/question/29548445

#SPJ1

Answer:

The sum of the interior angle measures of a regular hexagon is 720°.

Step-by-step explanation:

To find the sum of the interior angle measures of a regular hexagon, we can use the fact that any polygon can be divided into triangles. The formula to find the sum of the interior angles of any polygon with n sides is:

Sum of interior angles = (n - 2) × 180°

In the case of a hexagon, n = 6. So, we can plug this value into the formula:

Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

To explain this using triangles, let's divide the hexagon into triangles. A hexagon can be divided into four triangles by drawing three diagonals from one vertex to the three non-adjacent vertices. Since the sum of the interior angles of each triangle is 180°, and we have four triangles:

Sum of interior angles of hexagon = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

The question is an illustration of a system of linear equations.

Let the number of miles be x.

Getting trained and licensed

So, the equation is:

\(y=450 + 2x\)

Delivery

So, the equation is:

\(y = 350 + 6x\)

Hence, the system of linear equations is:

\(y=450 + 2x\) and \(y = 350 + 6x\)

To solve the equation, we equate both, as follows:

\(450 + 2x = 350 + 6x\)

Collect like terms

\(6x - 2x = 450 - 350\)

\(4x = 100\)

Divide both sides by 4

\(x = 25\)

Substitute 25 for x in \(y=450 + 2x\)

\(y = 450 + 2 \times 25\)

\(y = 450 + 50\)

\(y = 500\)

Hence, the solution to the equation is (25,500)

Read more about linear equations at:

https://brainly.com/question/14323743

We transformed 630 square yards to square inches, resulting in a value of 816,480 square inches.

To convert 630 square yards to square inches, we can utilize the following unit multipliers:

1 yard = 3 feet (since there are 3 feet in a yard)

1 foot = 12 inches (since there are 12 inches in a foot)

1 square yard = 1 yard × 1 yard = 3 feet × 3 feet = 9 square feet

1 square foot = 12 inches × 12 inches = 144 square inches

Now, we can set up the conversion using the unit multipliers:

630 square yards × (9 square feet / 1 square yard) × (144 square inches / 1 square foot) = 630 × 9 × 144 square inches

Simplifying the calculation:

630 × 9 × 144 square inches = 816,480 square inches

Therefore, 630 square yards is equal to 816,480 square inches.

By using the four unit multipliers and converting yards to feet and then to inches, we successfully transformed 630 square yards to square inches, resulting in a final value of 816,480 square inches.

For more questions on square inches

https://brainly.com/question/29198438

#SPJ8

Answer:

You are correct it is A. cos B

Step-by-step explanation:

Answer:

a) f(1) = 3

b) f(-1) = -0.25

c) x = 0, 3

d) x = -0.75

e) domain   [-2, 4]

    range   [-1, 3]

Step-by-step explanation:

In this graph, f(x) is represented by the y-axis.

a) We can see that f(1) (the y-value when x = 1) is 3.

b) Looking at the graph, we can estimate f(-1) as about -0.25.

c) We need to find the x-values when the y-axis is at 1. We can see that there are two points at x = 0, 3.

d) Looking at the graph, we can estimate that f(x) = 0 around when x = -0.75.

e) The domain of a function is its set of x-values. We can see that f(x) spans from x = -2 to x = 4. That range in interval notation is: [-2, 4]

The range of a function is its set of y-values. We can see that f(x) spans from y = -1 to y = 3. That range in interval notation is: [-1, 3].

Answer:

-4

Step-by-step explanation:

I use this equation to solve it^^

Matching of the functions domain and range are as follows:

f(x)   = 4-4x ;

Domain:{0,1,3,5,6}

Range;{-20,-16,-8,0,4}

f(x) = 5x - 3

Domain:{-2,-1,0,3,4}

Range:{-13,-8,-3,12,4}

f(x) = -10x

Domain:{-4,-2,0,2,4}

Range:{-40,-20,0,20,40}

f(x) = (3/x) + 1.5

Domain:{-3,-2,-1,2,6}

Range:{0.5,0,-1.5,3,2}.

1) The function f(x) = 4 - 4x

Take Domain:{0,1,3,5,6}

If, we take x=0 and put in the function then we get

f(x)=4-0

f(x)=4

put x=1

f(x) = 4 - 4 =0

put x=3 then we get

f(x)=4-12=--8

put x=5 them we get

f(x)=4-20=-16

put x=6 then we get

f(x)=4-24=-20

Therefore ,range:[-20,-16,-8,0,4}

2) The function f(x)=5x-3

Take domain{-2,-1,0,3,4}

Now, put x=-2 in the function then we get

f(x) = -13

now put x=-1 then we get

f(x)=-5-3=-8

Put x=0 then we get

f(x)=0-3=-3

Put x=3 then we get

f(x)=15-3=12

Put x=4 then we get

f(x)=20-3=17

Therefore , range:{-13,-8,-3,12,17}

3) The function f(x)=-10x

Take domain:{-4,-2,0,2,4}

Put x=-4 in the function then we get

f(x)=40

Put x= -2 then we get

f(x)=20

Put x=0 then we get

f(x)=0

Put x=2 then we get

f(x)=-20

Put x=4 then we get

f(x)=-40

Therefore , range :{-40,-20,0,20,40}

4) The function f(x)= (3/x) + 1.5

Take domain:{-3,-2,-1,2,6}

Put x= -3 in the taken function then we get

f(x)=-1+1.5=0.5

put x=-2 then  we get

f(x)= -1.5+1.5=0

Put x=-1 then we get

f(x)=-3+1.5=-1.5

Put x= 2 then we get

f(x)=1.5+1.5=3

Put x= 6 then we get

f(x)=0.5+1.5=2

Therefore, range : {0.5,0,-1.5,3,2}.

Read more about Domain and Range at: https://brainly.com/question/10197594

#SPJ1

Answer:

the answer is 4

Step-by-step explanation:

A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.

Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.

Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.

Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of

To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).

First, let's convert the fractions 1/5 and 2/3 to fifteenths:

\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)

\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)

Now we can rewrite the expression using the common denominator:

\(3 + \frac{3}{15}+\frac{10}{15}\)

Answer:

V =3.14 ( 2)^2 2.5  ft^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

Using 3.14 for pi

The diameter is 48 so the radius is 1/2 d = 1/2(48) =24inches and the height is 2.5 ft

We need to have the same units on the radius as the height

24 inches = 2 ft

V =3.14 ( 2)^2 2.5  ft^3

Answer:

There are 3 lie detectors each of which accurate 70% of time what is the

Step-by-step explanation:

There are 3 lie detectors each of which accurate 70% of time what is the combined accuracy of the three lie detectors put together? (In the case where two lie detector predict one result and the third predicts an opposite result the result of the two detector giving same result will be considered )

Answer:

6 97/100 bags

Step-by-step explanation:

4 1/10 ⋅ 1 7/10 = ?

41/10 ⋅ 17/10 = 697/100

697/100 = 6 97/100

6 97/100 bags

Answer:

697/100 bags

or

6 97/100 bags

Step-by-step explanation:

it is fractions. just plain and simple.

when you eat a pizza slice, it is usually one of 8 slices that make the whole pizza. 1/8 or one 8th. meaning that the whole thing is 8/8 or eight 8ths.

the same for 10ths or any other fractions.

4 1/10 bags = 41/10 bags

1 7/10 times = 17/10 times

and now we multiply fractions, as 17/10 times is similar to 2 times or 3 times something - we multiply by this factor.

41/10 × 17/10

as we learned in early elementary school : numerators (top part of the fraction) are multiplied with each other, and denominators (bottom part) are multiplied with each other. and then we simplify the result as much as possible.

41/10 × 17/10 = (41×17) / (10×10) = 697/100

no simplification is possible, sadly.

but that means he used almost 7 bags of hot dog buns.

exactly 6 full bags and 97/100 of the 7th bag.

so, either

697/100 bags

or

6 97/100 bags

or as alternative (not wanted here in this example but just FYI)

6.97 bags

Answer:

AAA

Stp-by-step explanation:

naw

g4jtnbjtrnjbnrtibnrijnbngtrjnb jtkgnbrbgbn

Answer:

The closet is 108 inches wide.

Step-by-step explanation:

Because 1 yard is 36 inches, and 36 times 3 is 108.

Step-by-step explanation:

The expression you provided involves taking the square root of a negative number, which results in an imaginary number. In standard real number arithmetic, the square root of a negative number is undefined. However, in the realm of complex numbers, we can define a square root of negative numbers using the imaginary unit "i," where i is defined as the square root of -1.

Let's break down the expression step by step:

√(-25) / √9

The square root of -25 can be written as √(-1 * 25), which can further be simplified as √(-1) * √25.

√(-1) is equal to "i," and the square root of 25 is 5.

So, the expression becomes:

i * 5 / √9

The square root of 9 is 3.

Now, we can simplify further:

i * 5 / 3

Thus, the simplified expression is (5i) / 3, where "i" represents the imaginary unit.

Answer:

C) \(g(x)=\sqrt[3]{\frac{x+2}{4}}\)

Step-by-step explanation:

\(f(x)=4x^3-2\)

\(y=4x^3-2\)

\(x=4y^3-2\)

\(x+2=4y^3\)

\(\frac{x+2}{4}=y^3 \)

\(\sqrt[3]{\frac{x+2}{4}}=y \)

\(f^{-1}(x)=\sqrt[3]{\frac{x+2}{4}}\)

\(g(x)=\sqrt[3]{\frac{x+2}{4}}\)

Answer:

1 and 7/24

Step-by-step explanation:

hope this helps!

Answer:

1 7/24

Step-by-step explanation:

1 5/8 - 1/3 = 1 7/24

The value of the fraction expression -2 1/2 - (-4 3/5) is 2 1/10

From the question, we have the following parameters that can be used in our computation:

−2 /2/1 −(−4 3/5)

Express properly

So, we have the following representation

-2 1/2 - (-4 3/5)

Remove the brackets

This gives

-2 1/2 - (-4 3/5) = -2 1/2 + 4 3/5

Express the denominator as 10

So, we have

-2 1/2 - (-4 3/5) = -2 5/10 + 4 6/10

Evaluate the difference

-2 1/2 - (-4 3/5) = 2 1/10

Hence, the solution is 2 1/10

Read more about fraction at

https://brainly.com/question/1622425

#SPJ1