Your friend Pat bought a fish tank that has a volume of 175 liters. The brochure for Pat's tank lists a "fun fact that it would take 7.43 x 1018 tanks of that sizeto fill all the oceans in the world. Pat thinks the both of you can quickly calculate the volume of all the oceans in the world using the fun fact and the size ofher tankPart a.) Given that 1 liter = 1.0 x 10-12 cubic kilometers, rewrite the size of the tank in cubic kilometers using scientific notation.b) Determine the volume of all the oceans in the world in cubic kilometers using the "fun fact"

Two sides are in same proportion and the included angle is common as per SAS. Therefore, both the triangles are similar.

Triangle:

A triangle is the three-sided polygon, which has three vertices. The three sides are interconnected with each other end to end at a point, which forms the angles of the triangle.

Here there are two triangles KLP and KMN. And the sum of all three angles of the two triangle is equal to 180 degrees.

Given,

Here we have the two triangle and we need to find that they are similar or not.

For that we have to calculate the total length of the sides of the triangle,

That,

KM = KL + LM

KM = 8 + 2 = 10

Similarly,

KN =  KP + PN

KN = 12 + 3 = 15

In triangles KLP & KMN,

KL/KP = 8/12 = 2/3

Similarly, for the triangle KMN,

KM/KN = 2/3

Here the angles have the same values so they are parallel. Which states that, Angle O is common in both the triangles.

Therefore, the two sides are in same proportion and the included angle is common (SAS) . Hence both the triangles are similar.

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a) Given:

The length of the side of a square is,

To find:

The area of the square.

Explanation:

Using the formula of the area of the square,

Final answer:

The area of the square is,

To find the time it takes the object to reach the maximum height we need to remember that this happens in the axis of symmetry of the parabola described by the function:

The axis of symmetry is given as:

in this case we have that a=-16 and b=64, then we have:

Therefore it takes 2 seconds to the object to reach its maximum height.

Now, to find the maximum height we plug this value of t in the equation, then we have:

therefore the maximum height is 144 ft.

this is a combination, so

answer: 2024 ways

Given the expression

SOLUTION

We want to know which of the options would give us

y = 34,

Let's try A. 8y = 9

This becomes

We didn't get y = 34, hence A is incorrect.

Let's try B. y − 1= − 14

This becomes

B too is incorrect.

Let's try C. 4y = 6

C too is incorrect

Let's check D. 7 − y = 614

D too is incorrect

we have

7 3/4 + 1 5/6​

step 1

Convert mixed number to an improper fraction

7 3/4=7+3/4=31/4

Remember taht

If you multiply 31/4 by (1.5/1.5) you obtain an equivalent fraction

so

(31/4)(1.5/1.5)=46.5/6

multiply by 10/10

465/60

1 5/6=1+5/6=11/6

multiply by 10/10

(11/6)(10/10)=110/60

step 2

Adds the fractions

465/60+110/60=575/60

simplify

Convert to mixed number

575/60=540/60+35/60=9+35/60

simplify the fraction 35/60

35/60=7/12

so

we have

9+7/12=9 7/12

we need to find the value of h when D is 9, so we need to replace D by 9 and find h:

Given:

A bee produce 0.05 ml of honey per day

We will find how many liters of honey can the bee produce in its lifetime if they live for 28 days

Let it produces x ml

So, using the ratio and proportions

Solve for x:

Convert ml to liters

1 liter = 1000 ml

So, 1.4 ml = 0.0014 liters

So, the answer will be

The bee can produce honey in its lifetime = 0.0014 liters

Given the system of equations:

The two equations appear to be just the same, thus, we are only given one system of equations.

Therefore, the answer is letter B. It has infinite solutions because the two equations are just the same line.

REQUIRED:

Round to 3 decimal placed the value of the irrational number e.

Step-by-step solution/explanation;

The letter e in mathematics is also known as the Eular's number and is a mathematical constant used in many calculations especially natural logarithms of numbers.

The value of the Eular's number is approximately;

It can continue till infinity, however approximations of this number is always used to avoid unnecessary complications.

Therefore, rounded to 3 decimal places, the value of e is now;

ANSWER:

Note that we take 3 digits aftre the decimal and then if the fourth digit after the decimal is 5 or greater than 5, we make it 1 and add that 1 to the third digit after the decimal. Otherwise we simply make it zero and cancel it along with all other digits after it.

The digit that follows 8 (third digit) is less than 5, therefore, we write it off along with all other digits after it, and we are left with the decimal point and then ...718.

Option C is the correct answer.

The given system of equation is:

Multiply through the first equation by 2:

Subtract the second equation from the first equation to get:

Therefore, the steps that will eliminate the variable x are:

Multiply the first equation by 2. Then subtract the second equation from the first.

Choice C

Answer:

Option C,  [tex]f(x)=-3x^2-6xh-3h^2+2x+2h+1[/tex]

Step-by-step explanation:

Oooo the ol canvas quiz yeesh.

Anyway, for this sort of problem, anywhere in your second equation that you see an x, sub for (x+h).

[tex]f(x)=-3x^{2} +2x+1[/tex]

[tex]f(x)=-3(x+h)^{2} +2(x+h)+1\\[/tex]

You must foil the first part

[tex]f(x)=-3(x^2+h^2+2xh)+2(x+h)+1\\[/tex]

Now distribute to eliminate the parentheses

[tex]f(x)=-3x^2-3h^2-6xh+2x+2h+1[/tex]

As your answer choice has it:

[tex]f(x)=-3x^2-6xh-3h^2+2x+2h+1[/tex]

Measures of center:

The mean is usually the better measure of center, however, this measure is greatly affected by extreme values (very low or very high values). If the data set is strongly skewed or has extreme values, the mean will be affected and won't reflect the true center of the said data set.

The median separates the data set in halves and is not affected by extreme values.

Given that this data set is strongly skewed to the left, the best measure of center will be the median.

Measures of dispersion:

The standard deviation is usually the most preferable measure of dispersion. But, one of

to solve this, question, we would have to convert the percentage to fractions or decimals.

Let x represent the numbers of employees the had a year ago

a year ago, the company had 1224 empolyees

EXPLANATION

The measure that represent the most typical driving time is the mean.

We have to calculate the volume of the pyramid with the following dimensions:

We can express and calculate the volume as:

Answer: the volume is 128 dm³

If the fraction whose denominator are equal then they will add up

In the given fraction 1/2 +1/9, the denominator of both the fraction 1/2 & 1/9 is not same

so, to make the base same we take the LCM of the 2 & 9

Answer : 11/18

Given:

A diver starts at 342 feet below the surface, which means -342 feet.

Now, she swims 237 feet upward.

It shows that she is moving in a positive direction.

So, the current depth of diver is,

The depth is -105 feet, which shows that the diver is still 105 feet below the surface.

[tex]\angle J = 90^{\circ}\\\\\cos (\angle K)=\frac{5}{23} \implies \angle K=\arccos(5/23)\\\\\sin (\angle I)=\frac{5}{23} \implies \angle I=\arcsin(5/23)[/tex]

Given: A water tower has a volume of 874 m³

To Determine: How many liters of water it would take to completely fill the

water tower

Solution

Please note that 1 cubic meter (m³) = 1 kiloliter (KL)

Therefore

Also note that Kilo means 1000

Therefore

Hence, the water tower will be completely fill with 874000 liters(L)

Answer:

The length of the base is:

The resulting quadratic is

Step-by-step explanation:

Base = x

Height = 4x

Area, A = 1/2* base * Height

           A = (1/2) * (x) * (4x)

          A = 2x²           (1)

But,    A = 6              (2)

Since (1) = (2);

2x²= 6

x²= 3

Resulting quadratic:

x² - 3= 0

For the difference between 2 squares:

a² - b² = (a-b)(a+b)

Using that identity, we can factorize our quadratic:

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

So, we have 2 roots:

x = 3 and x = -3

Now, noting that length must take a positive value, we go for the first:

x = 3

The length of the base is:

The resulting quadratic is

Answer:

Explanation:

Given the sequence with the recursive formula:

First, we determine the first three terms in the sequence.

Therefore, the first three terms of the sequence are: 7, 14 and 28.

This is a geometric sequence where:

• The first term, a=7

• The common ratio, r =14/7 = 2

We use the formula for the nth term of a GP.

The explicit formula for the sequence is:

a.

∠A is the right angle of the triangle ABC, so the corresponding angle is ∠P, which is the right angle of the triangle PQR.

b.

BC is the hypotenuse of the triangle ABC, so the corresponding side is QR, which is the hypotenuse of the triangle PQR.

c.

∠C is the smaller angle of the triangle ABC, so the corresponding angle is ∠R.

d.

∠Q is the bigger angle of the triangle PQR, so the corresponding angle is ∠B.

e.

PQ is the smaller leg of the triangle PQR, so the corresponding side is AB.

If the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.

It is given that, the first number is 2 and the last number is 18,

a = 2

L=18

n=5

a₅=5

a₅=a+(5-1)d

18=2+4d
4d = 18-2

4d = 16

d= 16 / 4

d=4

The terms of the sequence are,

a₁=2

a₂=2+4=6

a₃=6+4=10

a₄=10+4=14

a₅=14+4=18

Thus, if the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.

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the graph of a line passing through point

with gradient m

is given by

In order to find how many pages can be typed, first let's convert 1.5 hours to minutes:

Then, to find the number of pages, let's do the following rule of three:

Therefore Chuck can type and spell check 52.5 pages in 1.5 hours.

Answer:

2x^2 + 12x

Step-by-step explanation:

The perimeter is the sum of all the sides of a geometric figure.

So x^2 + 6x - 3 + 5x + 3 + x^2 - x

Add like terms:

2x^2 + 12x

The reason I said 2x^2 + 12x here is that this is likely a misprint, and you'll have to ask your teacher about this. Since the 3s (3 and -3) cancel each other out, but there are only 10 x's, your true answer is 2x^2 + 10x.

However, it is more likely that the misprint concerns the x^2 - x, meaning it was meant to be x^2 + x, which would give you answer A. The idea that the problem is just missing a random 9 somewhere is much more farfetched.

I would select answer A.

This is a complicated and incorrectly formatted question. Hope this helps!

Answer:

D

Step-by-step explanation:

Solution:

Given the function:

whose graph is shown below:

Suppose that the parent function is expressed as

This implies that the parent function is transformed by a horizontal shift to the left by four spaces.

The correct option is

Okay, here we have this:

Considering the provided data set, we are going to calculate the requested data, so we obtain the following:

Mean:

It corresponds to the result of adding all the data and dividing it by the amount of data, then we have:

Mean=(89+81+96+85+93+70+66+64+68+70)/10

Mean=782/10

Mean=78.2

Median:

First we will order the data from smallest to largest and the value that is in the center will be the median:

Sorted Data Set: 64, 66, 68, 70, 70, 81, 85, 89, 93, 96

Since 70 and 81 are in the middle, the median will be their average.

Median=(70+81)/2=151/2=75.5

Mode:

It is the data that is repeated the most, in this case it is 70 because it is twice

Range:

It is the difference between the smallest and largest value, then:

Range=96-64=32