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A rectangular swimming pool is 6 It deep. One side of the pool is 4.5 times longer than the other. The amount of water needed to fill the swimming pool is 3898 cubic feet. Find the
dimensions of the pool.
The smaller dimension of the pool ist and the larger dimension is blank ft

The value of x when f(x) of 8 according to the graph is; 4.

In order to determine a point's coordinates in a coordinate system, you must do the opposite. Start at the point and move in a vertical line in either an upwards or downwards direction to the x-axis. Here is the x-coordinate for you. Next, repeat the process while following a horizontal line to determine the y-coordinate.

According to the graph;

To determine the value of x when f(x) = 8.

We must plot a line of the equation; y = 8.

This y = 8 line produces a horizontal line.

The point at which the horizontal line, y = 8 intersects the given graph has an x coordinate.

Ultimately, this point has x coordinates of 4, making 4 the value of x when f(x) = 8.

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Step-by-step explanation:

in the slope- intercept form

y = mx + b

m is the slope, b is the y-intercept (the y-value when x = 0).

a parallel line must have the same slope, but a different y- intercept.

as you can see, the slope is always the factor of x, when we have a "y = ..." form.

so, coming from

3x + 4y = 15

4y = -3x + 15

y = (-3/4)x + 15/4

the slope is therefore -3/4.

b we get by using the given point coordinates in the equation :

-2 = (-3/4)×8 + b = -24/4 + b

b = -2 + 24/4 = -2 + 6 = 4

so, the full equation is

y = (-3/4)x + 4

Answer:

x^-3

Step-by-step explanation:

The reciprocal of x^3 is x to the power of negative 3 (aka [tex]\frac{1}{x^3}[/tex]).

The probabilities for the given problem is calculated as 0.081 and 0.06 respectively.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.

Given that,

There are 3 blue marbles, 5 red marbles and 4 green marbles.

Then, the total number of marbles is 12.

The given problem can be solved as follows,

Part A:

The probability of getting 1 blue and 2 green marbles is,

P( 1 blue and 2 green) = (³C₁ × ⁴C₂)/¹²C₃

                                     = ( 3 × 6)/ 220

                                     = 9/110

                                     = 0.081

Part B:

The probability of selecting one blue marble = 3/12 = 1/4

After one blue marble is selected, the remaining number of marbles is 11.

Thus, probability of selecting 3 red marbles is,

⁵C₃/¹¹C₃

= 10/165

= 0.06

Part C:

In the Part A the probability is calculated by taking the ratio of total number of ways of selecting 3 marbles and the number of ways of selecting 1 blue and 2 green marbles.

And, in Part B the number of ways is calculated from the remaining number of marbles after one blue marble is chosen.

Hence, the probabilities for the given parts in the question are 0.081 and 0.06 respectively.

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Answer:

3

Step-by-step explanation:

5x = 6x - 3

6x - 5x = 3

x = 3

What is speed?

Velocity is defined as the speed of movement of an object along its direction. Velocity tells you how fast an object is moving and the direction it's moving. Similar to velocity, but also adds direction. Therefore, velocity is directed velocity, although velocity has no direction.

how to calculate speed

Find the initial velocity of an object by dividing the time it took the object to travel the specified distance by the total distance. In the formula V = d/t, V is velocity, d is distance, and t is time.

According to the question given data,

Distance=3000miles

Time=4.5hours

Put the value of formula

V=3000/4.5

V=666.66m/s

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Answer: Rose got the better deal!

Step-by-step explanation:

Rose got the better deal, she only spent .10 cents for every piece, while joe spent .15 cents and only got 10 pieces.

A single survivorship life insurance policy can provide coverage for up to two persons.

A contract between an insurance policy holder and an insurer or assurer in which the insurer agrees to pay a specified beneficiary a certain amount of money upon the death of an insured person is known as life insurance (or life assurance, particularly in the Commonwealth of Nations) (often the policyholder). Other occurrences, such critical illness or terminal disease, may also result in payment, depending on the contract. Usually, a premium is paid by the policyholder, either on a regular basis or all at once. Other costs, such burial costs, can be covered by the benefits.

Consequently, a single survivorship life insurance policy might provide coverage for two persons. These policies, which are also known as second-to-die joint life insurance, only provide a death benefit following the passing of both policyholders.

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Answer:

63.2%

Step-by-step explanation:

percentage increase= (Increase \ old number) * 100

= {(19 -7)/ 19} * 100

= (12\19) * 100

=63.16 %

Answer: 1 Student

Step-by-step explanation:

Hope this helps!

Answer: A

Step-by-step explanation:

We see that the x is a right angle, so it must be a 90-degree angle!

For y, we know that a triangle has 180 degrees, we already know the other two angles are 90 and 64, add both together, equal 154.

180 - 154 = 26, so y is 26 degrees!

So the answer is A

Answer:

427 miles

Step-by-step explanation:

725-298=427 miles

Answer: Kate drove 427 miles.

Explanation: 725 - 298 = 427.

Answer:

[tex]\frac{t^6u^4w^{10}}{v}[/tex]

Step-by-step explanation:

1.) Simplify. Anything to the power of 0 is equal to 1, meaning that you don't have to pay attention to those variables. This brings us with [tex]t^5u^7v^{-1}wtu^{-3}w^9[/tex].

2.) Combine common powers. When you multiply, you add the exponents. This brings us with [tex]t^6u^4w^{10}v^{-1}[/tex].

3.) Finally, negative exponents can be brought to the denominator, so we get [tex]\frac{t^6u^4w^{10}}{v}[/tex].

speed of plane's ground = 155.769 Km/h

Speed is the rate at which an object travels along a path over time, whereas velocity is the speed and direction of an item's motion. In other words, speed is a scalar value, but velocity is a vector.

Units of speed = meter per second

So ln [tex]$\triangle A O B$[/tex], we have

[tex]$$[/tex]A=65[tex]^{\circ}+45^{\circ}=110^{\circ} \\[/tex]

O A=[tex]150 \mathrm{~km} / \mathrm{h} \\[/tex]

A B=15 [tex]\mathrm{~km} / \mathrm{h}[/tex]

[tex]\end{aligned}[/tex]using cosine Rule

[tex]\cos A=\frac{O A^2+A B^2-O B^2}{2(O A)(A B)} \\[/tex]

[tex]\cos 110^{\circ}=\frac{(150)^2+(15)^2-O B^2}{2(150)(15)} \\[/tex]

[tex]4500 \cos 110^{\circ}=22500+225-0 B^2 \\[/tex]

[tex]-1539.09064=22725-0 B^2 \\[/tex]

[tex]O B^2=22725+1539.09064 \\[/tex]

[tex]O B^2=24,264.0906 \\[/tex]

[tex]O B=155.769351 \approx 155.769 \mathrm{~km} / \mathrm{hr} \\[/tex]

[tex]O B \approx 17 \mathrm{k}[/tex]

using sine rule

[tex]\frac{\sin (A O B)}{15}=\frac{\sin A}{O B} \\[/tex]

[tex]\frac{\sin (A O B)}{15}=\frac{\sin 110^{\circ}}{155.769351} \\[/tex]

[tex]\sin (A O B)=\frac{15 \sin 110^{\circ}}{155.769351}=\frac{14.0953893}{155.769351}[/tex]

[tex]\sin (A \cap B)=0.0904888491 \\[/tex]

[tex]A O B=\sin ^{-1}(0.0904888491) \\[/tex]

[tex]A D B=5.19173084^{\circ} \\[/tex]

[tex]A O B=5.2^{\circ}[/tex]

Direction of plane [tex]=65^{\circ}+5.2^{\circ} \\[/tex] = [tex]=70.2^{\circ}[/tex]

Direction N = 70.2° E

speed of plane's ground [tex]$=155.769 \mathrm{~km} / \mathrm{h}$[/tex]

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Answer:

Step-by-step explanation:

x<60

13.2 square ft  area of  carpet will you need .

What is a right-angle triangle, exactly?

A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The sum of the other two angles is 90 degrees.

                                       The triangle's base and perpendicular sides both include the right angle. The hypotenuse, or third side, is the longest of the three. It is also known as the hypotenuse.

the area of rigth triangle

      20² = 15² + x

      400 = 225 + x²

        x² = 400 - 225

        x = 13.2

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The image point of (9,3) after the transformation r x-axis is (-9, -3 ).

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

Since we know that Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Therefore, Under a counterclockwise

a point (x, y ) → (- x, - y ) , thus

(9, 3 )→ (-9, -3 )

Therefore, the image point of (9,3) after the transformation r x-axis is (-9, -3 ).

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Answer:

x = 71

Step-by-step explanation:

Since the legs of the triangle are congruent, both 21 , then the triangle is isosceles with base angles congruent.

Then

x = (180 - 38) ÷ 2 = 142 ÷ 2 = 71

Answer: -6 and 5

Step-by-step explanation:

-6 and 5

x+y = -1

xy = -30

x=-1-y

y(-1-y)=-30

-y^2-y=-30

-y^2-y+30=0

(y-5)(5+6)

y=5,-6

Answer:

28

Step-by-step explanation:

[tex]80 \times \frac{35}{100 } \\ = 28[/tex]

Answer:

28

Step-by-step explanation:

From the given pie chart:

If a total of 80 people were surveyed, to find the number of people in the sample that chose blue, simply find 35% of 80:

[tex]\begin{aligned}\implies \sf 35\%\;of\;80 & = \sf \dfrac{35}{100} \times 80\\\\&= \sf \dfrac{35 \times 80}{100} \\\\&= \sf \dfrac{2800}{100} \\\\&=\sf 28\end{aligned}[/tex]

Therefore, 28 people from a total of 80 surveyed chose blue as their favorite color.

The 4th term and the 6th term in the sequence are 1 and 5/6

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

Tn= (4 + n)/2n

The 4th term and the 6th term in the sequence means that

n = 4 and n = 6

Substitute the known values in the above equation, so, we have the following representation

n = 4:

T(4) = (4 + 4)/2(4)

Evaluate

T(4) = 1

n = 6:

T(6) = (4 + 6)/2(6)

Evaluate

T(6) = 5/6

Hence, the terms are 1 and 5/6

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Using Mathematical operations we can conclude that Jill gave 11 brownies to her friend.

A mathematical function known as an "operation" in mathematics is one that converts zero or more input values into a precisely specified output value.

The quantity of operands has an impact on the operation's complexity.

Most people concur that the four basic mathematical operations are addition, subtraction, multiplication, and division.

So, we know that Jill has 3 full pans of brownies.

Each pan contains 110 brownies.

So total brownies Jill has:
10*3 = 30 brownies

Now, she gave 3/8 brownies to her friend.

So, the number of brownies Jill gave away are:

30 * 3/8

15 * 3/4

45/4

11.25

Rounding off: 11

Therefore, using Mathematical operations we can conclude that Jill gave 11 brownies to her friend.

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After solving the given expression, the value obtained will be equal to 7/12.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the given fraction in the question,

4/6 - 1/12

Take LCM as 12 and then solve,

= (8 - 1)/12

= 7/12

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Answer:

93.331 ft

Step-by-step explanation:

Use the trigonometric function sine (opposite/hypotenuse)

sin(59) = 80

   1           x

You can switch x and sin(59)

x =     80  

     sin(59)

Plug into calculator

x = 93.331 ft

The number of containers that he can fill is 3108.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The formula for the division of fractions is:

= a/b ÷ c/d

= a x d / b x c

Amount of rice in a container = 1/4 kg

The total amount of rice = 777 kg.

The number of containers.

= 777 ÷ (1/4)

= 777/(1/4)

= 777 x 4

= 3108

Thus,

The number of containers is 3108.

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The percent of the total calories in each brownie comes from fat will be;

⇒ 35.84%

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The wrapper said each brownie was 451 calories, and had 252 calories of fat.

Now,

Since, The wrapper said each brownie was 451 calories, and had 252

calories of fat.

Hence, Total calories = 451 + 252

                                 = 703 calories

And, The calories of fat = 252 calories

Thus, The percent of the total calories in each brownie comes from fat is find as;

⇒ Percent = 252/703 × 100

                = 35.84%

Therefore, The percent = 35.84%

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Jaylen and Ryan will have same amount of money after 12 weeks .

Let the no of weeks after which both of them will have equal amount be x

therefore, after x weeks the amount of money in

Jaylen's account = 340 + 15x

Ryan's account = 220+ 25x

Now, since these amount is equal

therefore,

340 + 15x = 220+ 25x

on solving this equation we get ,

=>340 - 220 = 25 x - 15x

=> 120 =10x

=> x = 12

First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable).

Multiple variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, and 3x - y + z = 3.

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Answer: = 7 i believe

Step-by-step explanation:

2^3 (2 power by 3) x - 1 for 1 which is 7

Answer:

B. 49

Step-by-step explanation:

21/3 = 7 new houses

7*7 = 49 old houses

Answer:

Answer to the question is B: 49