if a tank holds 2000 gallons of water, andthe water can drain from the tank in 40 min-utes, then torricelli’s law gives the volumevof water remaining in the tank aftertminutesasv

The angle of BDC is 60 degrees.

The angle sum property of a triangle states that the sum of a triangle's three internal angles is 180 degrees. A triangle is a closed figure made up of three line segments that have both internal and external angles. When the values of the other two angles are known, the measure of an unknown interior angle can be determined using the angle sum property.

The data listed above can be inserted into our diagram. ADB and BDC complement one another, therefore their combined degree measurement is 180. Thus, m∠ADB is equal to 180 – 60, or 120 degrees.

Given,

∠ADC = 59

∠BDC = ?

∠ADB = ∠BCD

∠BCD = 90

∠ADB = 90

∠ADC = 59

∠ADB + ∠BDC = 59

90 + ∠BDC = 59

∠BDC = -31

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The reflection of a coordinate about the y = x  will interchange the coordinate thus the reflection of points A(0, -3), B(2, 2), C(5,0) will be A'(-3,0)B'(2,2)C',(0,5).

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

It is known that,

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

Therefore,

A(0, -3) → A'(-3,0)

B(2, 2) → B'(2,2)

C(5,0) →C'(0,5)

Hence "The reflection of a coordinate about the y = x  will interchange the coordinate thus the reflection of points A(0, -3), B(2, 2), C(5,0) will be A'(-3,0)B'(2,2)C',(0,5)".

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Answer:

Step-by-step explanation:

1 to the 10th power is 1.

Answer: 16x^2+144x+18

Step-by-step explanation:

The sum of two given expressions is 16x²-6x+14.

Addition of Algebraic Expressions is the process of collecting like terms and adding them. Identify and add the coefficients of like terms and sum them to find the final expression of given problems.

The given expressions are 8x²-x+9 and 8x²-5x+5.

Now, sum =8x²-x+9+8x²-5x+5

Group like terms and simplify, we get

(8x²+8x²)+(-x-5x)+(9+5)

= 16x²+(-6x)+14

= 16x²-6x+14

Therefore, the sum of two given expressions is 16x²-6x+14.

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Answer:

Step-by-step explanation:

art I 5.00% per annum ------------- Amount invested =x

Part II 9.00% per annum ------------ Amount invested = y

8000

Interest----- 520.00

Part I 5.00% per annum ---x

Part II 9.00% per annum ---y

Total investment

x + 1 y= 8000 -------------1

Interest on both investments

5.00% x + 9.00% y= 520

Multiply by 100

5 x + 9 y= 52000.00 --------2

Multiply (1) by -5

we get

-5 x -5 y= -40000.00

Add this to (2)

0 x 4 y= 12000

divide by 4

y = 3000

Part I 5.00% $ 5000

Part II 9.00% $ 3000

CHECK

5000 --------- 5.00% ------- 250.00

3000 ------------- 9.00% ------- 270.00

Total -------------------- 520.00

Triangle RST is rotated 180° about the origin, and then translated up 3 units.  Then , ΔRST ≅ ΔBAC

We know that  To rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y).

Thus, The coordinates of triangle RST becomes

R (1,1) → R'(-1,-1)

S (3,4) → S'(-3,-4)

T(-5,0) → T'(5,0)

Also ΔRST after rotation is translated up 3 units. , so we apply the rule (x,y)→(x,y+3)

R'(-1,-1)→R"(-1,-1+3)=R"(-1,2)→ B

S'(-3,-4) → S"(-3,-4+3) = R"(-3,-1) → A

C'(-5,0) → C"(-5,0+3) → C"(-5,3) → C

As rotation and translation both are rigid transformation that maps only congruent figures.

Therefore, ΔRST ≅ Δ BAC

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Answer:

16

Step-by-step explanation:

→ Add the fractions

[tex]2\frac{1}{4} +\frac{1}{2} =\frac{9}{4} +\frac{1}{2} =\frac{9}{4} +\frac{2}{4} =\frac{11}{4}[/tex]

→ Equate to 44

[tex]\frac{11}{4} x=44\\[/tex]

→ Multiply both sides by 4

11x = 176

→ Divide both sides by 11

x = 16

Answer: Summary: The equation which represents the inverse of the function f(x) = 4x is h(x) = 1/4 x.

Step-by-step explanation: THERE IS NO EXPLANATION

(hope this helps) :)

a.  4 million registered voters in the state where  the 5,000 registered voters is drawn from the pool of registered voters.

Options: a. 4 million registered voters in the state

b. 5,000 registered voters interviewed

c. 54 %,  voters interviewed who plan to vote for him

d. 46 %,  voters interviewed who plan not to vote for him

The population of interest is the group from which a sample set is collected. Here, the 5,000 registered voters is drawn from the pool of registered voters. The people surveyed are representative of the total number of voters. The population of interest here is the 4 million registered voters.

For example, if a survey is carried out to figure out the age that kids start walking, the population of interest is kids in general and not just the children who are surveyed.

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The answer is : 7/18
Step by step:
(0.38 x 10) - 0.3/9
3.5     =      35
----              ----
9                 90

= 7/18

The experimental probability of the roll is greater than the theoretical probability

Probability is the likelihood of a desired event happening.

Experimental probability is a probability that relies mainly on a series of experiments.

Theoretical probability is the theory behind probability. To find the probability of an event, an experiment is not required. Instead, we should know about the situation to find the probability of an event occurring.

Given that:

Jeffrey rolled a 12-sided dice 15 times and it landed on a number greater than 10 three times

Experimental probability = 3/15 = 1/5

But theoretically,  a number greater than 10 in 12-sided dice have the probability of 2 out of 12 as illustrated with the numbers below:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Theoretical probability = 2/12 =1/6

Therefore, the experimental probability (1/5) of rolling a number greater than 10 is greater than the theoretical probability (1/6)

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Answer:

23cm

Step-by-step explanation:

in this problem the 4cm actually doesnt matter. so what you can dois 7cm+6cm+10cm=answer

7cm+6cm+10cm=23cm

The distance from the midpoint to the origin is [tex]\sqrt{5}[/tex].

What is midpoint?

Midpoint is the point that is in the middle pf the line, and to calculate midpoint the formula is

[(x)1 + (x)2]/2, [(y)1 + (y)2]/2

given coodinates are (-2, -4) and (0, 8)

midpoint = (-2+0/2, 8-4/2)

=(-1, 2)

to find the distance from the midpoint to origin.

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

the points are (-1,2) and (0,0)

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

d = [tex]\sqrt{5}[/tex]

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Answer: no entiendo la estructura de la operacion

Step-by-step explanation:

The value of square root of √28 will be;

⇒ 4√7 = 5.28

What is square root of a number?

A square root of a number is a value that multiplied by itself gives the same number.

Given that;

The number is,

⇒ √28

Now,

Let the value of square root of √28 is find as;

Since,

28 = 2 x 2 x 7

Hence,

⇒ √28 = √2 x 2 x 7

⇒ √28 =  2√7

⇒ √28 = 2 x 2.64

⇒ √28 = 5.28

Therefore,

The value of square root of √28 will be;

⇒ 4√7 = 5.28

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Answer:

y=40 z= 5h+15

5 hours to make the same amount of money

Step-by-step explanation:

40-15=25

25/5=5

hope this helped

The value of KM is 20

A line, ray, line segment, or point that cuts a line segment at its center and divides it into two equal portions is known as a segment bisector. A segment is a section of a line with definite ends, which is also how the word segment is sometimes used. Any object or line is divided into two equal halves when it is bisected. Consequently, when two line segments cut or bisect each other at a location that divides the lines into equal halves, this is known as a segment bisector.

Given that : The line q bisects KM at point V, KV = 2.5z and VM = 5z - 10

the line q bisects KM at point V so KV = VM

KV = 2.5z

VM = 5z - 10

2.5z= 5z - 10

10 = 2.5z

4 = z

Now put the value of 4 in KV and VM

KV = 2.5(4)

VM = 5(4) - 10

KV + 10

VM = 10

KM = KV + VM
KM = 10 + 10

= 20

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The inequality for the statement: the difference between a number and seven eighths exceeds negative two thirds is g - 7/8 > -2/3.

The correct answer option is option c

Let

difference between a number and seven eighths

g - 7/8

difference between a number and seven eighths exceeds negative two thirds

g - 7/8 > -2/3

The options;

A. g plus 7 over 8 is greater than 2 over 3

g + 7/8 > 2/3

B. g minus 7 over 8 is less than or equal to negative 2 over 3

g - 7/8 ≤ -2/3

C. g minus 7 over 8 is greater than negative 2 over 3

g - 7/8 > -2/3

D. g minus 7 over 8 is less than negative 2 over 3

g - 7/8 < -2/3

So therefore, the inequality statement can be written as g - 7/8 > -2/3.

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Cluster Sample is the sampling method used in this type of data collection.

Cluster sampling is a sampling technique used in statistics that divides the total population under consideration into externally homogeneous but internally heterogeneous groupings known as clusters. Each cluster essentially serves as a miniature representation of the overall population.

Using simple random sampling, some clusters are picked after the clusters have been identified, while the remaining clusters are left out of the study. A researcher must determine the right sampling strategy for each cluster after identifying the clusters.

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The polynomial identity can be used to prove that 61 = 125 − 64 is the difference between cubes therefore, option (a) is correct.

The number system is a way to represent or express numbers.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

As per the given polynomial,

61 = 125 - 64

It is known that a³ = a × a × a

Therefore, 5³ = 5 × 5 × 5 = 125

And, 4³ = 4 × 4 × 4 = 64

Therefore, 61 = 5³ - 4³

Hence "The polynomial identity can be used to prove that 61 = 125 − 64 is the difference between cubes".

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The volume of the cube is 27[tex]z^{15}[/tex]

A cube is a three dimensional shape having 6 square faces , all the faces are of equal length , breadth and height.

Here we have to find the volume of a cube

The length of the side is 3[tex]z^{5}[/tex].

The formula for the volume of the cube = a³

where a is the length of the side.

Substituting the value of a we get,

The volume of the cube = (3[tex]z^{5}[/tex])³

                                        = 27[tex]z^{15}[/tex]

Therefore the volume of a cube is 27[tex]z^{15}[/tex].

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The key feature of the function H(X) = 0.6X + 38 at H(0) is 3.8

Function:

A function is defined as the an expression, rule, or law that defines a relationship between one independent variable and another dependent variable.

Given,

Here we have the function H(X) = 0.6X + 3.8 models the height in inches of a stack of X cups.

And we need to find the key features is at H(0).

To find the key feature at H(0), then we have to simple apply the value of X as 0,

Like the following, we have to replace the X value in the function with 0, then we get the expression like the following,

=> H(0) = 0.6(0) + 3.8

=> H(0) = 0 + 3.8

H(0) = 3.8

Therefore, the key feature at H(0) is 3.8.

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Step-by-step explanation:

I hope this helps you with your answer

Answer:

Main can buy 8 tickets.

Step-by-step explanation:

Use the equation total amount ÷ cost of each ticket

Input your information: $36 ÷ $4.50

The equation adds up to 8.

So therefore, Main can buy 8 tickets.

Considering that R and S are points on the number line If RS= 10 and R lies at 13 then s will lie at

A number line is a sequence of numbers arranged at a particular pattern in a straight line

Information gotten form the question have it that"

RS= 10

R lies at 13

In a number line if R lies in point 13 and RS = 10 then we solve as follows

R + | 10 |

13 + 10 = 23

13 - 10 = 3

Hence R lies at point 3 or 13

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Answer:

Yes, you have to distribute.

Step-by-step explanation:

2+5(x+3)-3(x-4)=x+2(2x+4)

2+5x+15-3x+12=2(2x+4)

Add the Numbers

2+5x-3x=2(2x+4)

Combine Like Terms, Then you can rearrange the terms for simplification. You should end up with an exation looking like this:

2x+29=5x+8

Subtract 29 from both sides. Simplify, then subtract 5x from both sides.
2x-5x=5x-21-5x
Simplify, then Divide both sides by the same factor. Simplify once more then you should have
x=7

Hope this helps ;)

The number with the unit digit equal to x and the tens digit three more than the one's digit is; 30 + 11 X  

The place values on the left of the decimal point start as ones, tens, hundreds, and so on. The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths so on...

Given the statement as“the number with the units digit equal to x and the tens digit three more than the ones digit”

We need to convert the statement into the algebraic expression.

We know that unit digit number = X × 1

Then Tens digit number = (3 + X ) 10

Thus, the number = 30 + 10X + X

Hence, the Number = 30 + 11 X  

The number with the unit digit equal to x and the tens digit three more than the one's digit is; 30 + 11 X  

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Answer:

0.724

Step-by-step explanation:

percent means ' out of 100 ' , then

72.4% = [tex]\frac{72.4}{100}[/tex] = 0.724

The height of the part of the post that is above the ground is 10 - 3(1/3)

= 6(2/3) feet.

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