A water tank that initially contained 200 gallons of water is leaking water at a constant rate of 4 gallons per minute. For the amount of time the tank has water, which of the following function models gives the number of gallons, G. in the tank t minutes after the leak started?

a. g(t) = 196 - t
b. g(t) = 200 - 4t
c. g(t) = 200t - 4
d. g(t) = 200t - 4r^2
e. g(t) = 200(3/4)^t

The trigonometric function requires a domain restriction of [0, π/2) ∪ (π/2, pi] is tan x, sec x.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

tan x = (sin x)/(cos x)    

sec x = 1/(cos x)

cos x becomes zero at {-π/2,π/2}

Therefore, the both of the function are undefined at {-π/2,π/2}

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Answer:

n

6

Mean

11

Average Absolute Deviation (MAD)

4.6667

Step-by-step explanation:

Answer:

[tex]\sf D. \quad P(A|B)=\dfrac{24}{25}[/tex]

Step-by-step explanation:

General equation for conditional probability

[tex]\sf P(A \cap B)=P(A)\:P(B|A)[/tex]

As we need to find P(A|B) we can rewrite the equation:

[tex]\implies \sf P(B \cap A)=P(B)\:P(A|B)[/tex]

Given:

     [tex]\sf P(A \cap B)=\dfrac{4}{5}[/tex]

     [tex]\sf P(B)=\dfrac{5}{6}[/tex]

Remember that [tex]\sf P(A \cap B)=P(B \cap A)[/tex]

Substitute the given values into the formula:

[tex]\implies \sf P(B \cap A)=P(B)\:P(A|B)[/tex]

[tex]\implies \sf \dfrac{4}{5}=\dfrac{5}{6}\:P(A|B)[/tex]

[tex]\implies \sf P(A|B)=\dfrac{4}{5} \div \dfrac{5}{6}[/tex]

[tex]\implies \sf P(A|B)=\dfrac{4}{5} \times \dfrac{6}{5}[/tex]

[tex]\implies \sf P(A|B)=\dfrac{24}{25}[/tex]

Answer:

12

Step-by-step explanation:

you divide 120 by 10 since dimes are equal to ten cents

To determine how many dimes are in dollars:

  ⇒ must know the rate of conversion

     ⇒ for every dollar, there are 10 dimes

         ⇒  [tex]\frac{1_. dollar}{10_. dimes}[/tex]

Let's solve:

   [tex]120_. dimes * \frac{1_.dollar}{10_.dimes} = \frac{120}{10} *\frac{dimes}{dimes} *dollar=12_.dollars[/tex]

Thus you would get 12 dollars

Answer: 12 dollars

Hope that helps!

Answer:

18 inches

Step-by-step explanation:

The most frequent chain length for women's necklaces is 18 inches. This size is appropriate for a lady of medium height and weight.

Answer:

Sorry

Step-by-step explanation:

I not know this one

Answer:

v = 164.64

Step-by-step explanation:

Your friend forgot to divide 6.8 by two as 6.8 is the diameter not the radius.  The volume equation needs the radius so you divide 6.8 by 2 which equals 3.4 thats what inputed into the volume equation

The similarities/differences observed in the graph is (c) both f and g open upward; low point of f is 3 units below the x-axis; the low point of g is 3 units above the x-axis

The equations are given as:

f(x) = 5x² - 3

g(x) = 5x² + 3

Next, we plot the above equations on the same plane (see attachment)

From the attached graph, we can see that:

Hence, the similarities/differences observed in the graph is (c)

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Answer:

=1

Step-by-step explanation:

The range of name lengths is equal to 8.

In Mathematics and Statistics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.

In Mathematics and Statistics, the range of a data set can be calculated by using this mathematical expression;

Range = Highest number - Lowest number

From the given data set, we have:

Highest number = 10.

Lowest number = 2.

By substituting, we have:

Range = 10 - 2

Range = 8.

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The correct answer is option B which is when solving a radical equation with square roots, you should first.isolate the radical and then square both sides.

To solve radical equations, one common technique is to isolate the radical term first, then take both sides of the equation to a power to remove the radical.

Therefore the correct answer is option B which is when solving a radical equation with square roots, you should first.isolate the radical and then square both sides.

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Answer:

by o of u 999987ui87 u ko9h u kgnnh b mjuokkwuij

The combination that denotes the empty set{∅} is motor ∩ bicycle.

Set theory is the mathematical study of well-defined groups of things called elements of the set.

In the given Venn diagram, the elements in the set of Motor, Manual, and Bicycle are as follows:

The combination that represents an empty set {∅} is the intersection that occurred between motor and bicycle and can be expressed as:

= motor ∩ bicycle

This is because there are no set elements overlapping between motor and bicycle, this makes it an empty set{∅}.

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Answer: motor U bicycle

Step-by-step explanation:

Answer: 81

Step-by-step explanation:

Since x is given, just substitute the value.

5(10) + 31

50 + 31 = 81

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's evaluate ~

The given expression is :

[tex]\qquad \sf  \dashrightarrow \:5x + 1[/tex]

now, plug in the values of x as 10

[tex]\qquad \sf  \dashrightarrow \:5(10) + 31[/tex]

[tex]\qquad \sf  \dashrightarrow \:50 + 31[/tex]

[tex]\qquad \sf  \dashrightarrow \:81[/tex]

So, required value is 81

Answer:

7

Step-by-step explanation:

First put all the numbers in order. Like this,

1,2,3,4,5,7,7,7,8,8

Then subtract (take away) the lowest number from the highest. Like this,

8-1=7

Simplifying and expressing each term in standard and polar form are respectively; 49/2 and  -512 - 512i√3

1) We are given the expression;

[7 cos (45)]²

We know that cos (45) in standard form is 1/√2. Thus;

[7 cos (45)]² = (7 * 1/√2)² = 49/2

2) We are given the expression;

(-2 + 2i√3)⁵

Using binomial theorem, we have;

(−2)⁵ + 5(−2)⁴ (2i√3) + 10(−2)³(2i√3)² + 10(−2)²(2i√3)³ + 5 * −2(2i√3)⁴ + (2i√3)⁵

Simplifying each term gives;

−32 + 160i√3 + 960 − 960i√3 −1440 + 288i√3

⇒ -512 - 512i√3

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Answer:

The highest is 1 but i cannot work out the rest

Step-by-step explanation:

Bidmas

Answer:

B) 50%

Step-by-step explanation:

300% is the same as 3. So to find 300% of 7 you do 3 times 7 and get 21.

Now you need to find _% times 42 = 21. Divide 21/42 to get 0.5. This is the same thing as 50%.

Hope it helps and have a nice day! :)

The answer to the questions are given below.

The triangles which do not have same side length or angles but are similar in appearance are called similar Triangles .

It is given in the question that

If triangle abc and triangle def are similar, then their corresponding sides are proportional.

The hypothesis is

if the triangle abc and def are similar

The conclusion is

that the triangle abc and def are similar and the sides corresponding are proportional.

The converse is

If the sides of two triangles are proportional then two triangles are similar

Yes it is true

Inverse is if the two triangles are not similar then the sides corresponding are not proportional.

Contrapositive statement is if the sides are not proportional then the two triangles are not similar.

Yes , it is true.

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Answer:

see explanation

Step-by-step explanation:

f(x) = - (x + 1)(x - 3)(x + 2)

to find the zeros let f(x) = 0 , that is

- (x + 1)(x - 3)(x + 2) = 0

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 3 = 0 ⇒ x = 3

x + 2 = 0 ⇒ x = - 2

the zeros are x = -1, 3 and x = - 2

to find the y- intercept let x = 0

f(0) = - (0 + 1)(0 - 3)(0 + 2) = - (1)(- 3)(2) = - (- 6) = 6

y- intercept is located at (0, 6 )

The surface area of the cone rounded to the nearest whole number is; 289 cm².

We are given the parameters:

Radius; r = 4 cm

Slant height; l = 19 cm

Let us first calculate the base area;

The base is a circle and the area formula for a circle is;

A = πr²

Thus;

A = π(4 cm)²

A = 50.24 cm²

Lateral area;

The circumference of a circle is given by the formula;

C = 2πr

C = 2(π)(4 cm)

C = 25.12 cm

This circumference is the arc length of the sector

The area of the sector is;

 A = 1/2hs

where;

h is the radius of the sector.

s is its arc length

Thus;

A = ¹/₂(19 cm)(25.12 cm)

A = 238.64 cm²

The total surface area is;

SA = 50.24 cm² +238.64 cm²

S.A = 288.88 cm² ≈ 289 cm²

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Answer:

  289 cm²

Step-by-step explanation:

The net for the surface area of a cone is a circular sector representing the lateral area, together with a circle representing the area of the base. The arc length of the sector is equal to the circumference of the base.

__

The area of the circular base is given by the area formula for a circle:

  A = πr²

For the given radius, the area is ...

  A = (3.14)(4 cm)² = 50.24 cm²

The circumference of the circular base is ...

  C = 2πr = 2(3.14)(4 cm) = 25.12 cm . . . . also the arc length of the sector

The area of the sector is ...

  A = 1/2hs . . . . where h is the radius of the sector, and s is its arc length

  A = (1/2)(19 cm)(25.12 cm) = 238.64 cm²

The total surface area is the sum of the base area and the lateral area:

  SA = 50.24 cm² +238.64 cm² = 288.88 cm² ≈ 289 cm²

The surface area of the cone is about 289 cm².

1/5×1/5×1/5=1/125

$ give me a dollar $

Answer:

60%

Step-by-step explanation:

Step-by-step explanation:

100% = 3

1% = 100%/100 = 3/100 = 0.03

how many % are 1.8 ? well, as many % as 1% fits into 1.8 :

1.8 / 0.03 = 60%

The statement that is true about the given dot plot is: A. Exactly 2 goals was never scored by the team in a single game.

A dot plot is a graphical representation of data using dots to denote the frequency of one data point in a distribution.

In the dot plot given, for number of goals scored per game, the data point 2 has no dot. Therefore, the statement that is true about the dot plot is: A. Exactly 2 goals was never scored by the team in a single game.

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The statement that is true about whether A and B are independent events is D. A and B are not independent events because P(A∣B) = 0.375 and P(A) = 0.25.

Let A be the event that the person rides the bus to school, then:

P(A) = 75/300

P(A) = 0.25

Let B be the event that the person has 3 or more siblings, then:

P(B) = 24/300 = 0.25

P(A/B)=9/24

P(A/B)=0.375

Since P(A/B)=0.375 is different from P(A)=0.25 the events are not independent.

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Answer:

4 pt = 8 cups

28 qt = 7 gallons

Step-by-step explanation:

We know, from your chart, that 1 p = 2 c

4 p is four times 1 p

so, to scale up 1 pint to 4 pints, we multiply by 4

to figure out what the corresponding number of cups would be, we also have to multiply that value by 4

if                1 p    =    2 c

then          4 p    =    8 c

               (1 x 4)      (2 x 4)

8 cups

--------

If we have 28 quarts, and we know that 4 quarts is 1 gallon, we can divide 28 / 4 to find how many gallons are in 28 quarts (or, how many gallons can be made of 28 quarts)

28 / 4 = 7

7 gallons

Answer:

36.

Step-by-step explanation:

There were 10 elephants that were marked.  Only 4 of those were counted.  The other 26 were new elephants.  Because of this, we know that there were 6 other elephants that were not counted.  There were the 30 counted, and the other 6.  Add those and you get 36.

Answer:

  75 elephants

Step-by-step explanation:

This sort of population study assumes that the probability of catching any particular elephant is the same as for any other.

__

We are given that there is a population of 10 painted elephants, of which 4 of them are caught in a sample of 30 elephants. We know the total population of painted elephants is 10/4 = 2.5 times the number caught in the sample. This suggests the total population of elephants is 2.5 times the sample size.

  estimated population = 2.5 × 30 = 75 . . . elephants