Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did she earn? Use the formula I=Prt to find your answer, where I is interest, P is principal, r is rate and t is time. Enter your solution in decimal form rounded to the nearest hundredth. For example, if your solution is 12%, you would enter 0.12.

Final answer:

The winner, Person A, ate 52 hot dogs, the runner-up, Person B, ate 44 hot dogs, and Person C finished third with 34 hot dogs.

Explanation:

The question involves solving a system of linear equations to find out how many hot dogs each participant in a hot dog eating contest ate. Let's assign variables to each person: A for the winner, B for the runner-up, and C for the third-place finisher. According to the problem, A ate 8 more hot dogs than B, and C ate 10 fewer hot dogs than B.

Here are the equations based on the information provided:

Now we substitute the expressions for A and C in terms of B into the third equation:

Therefore, Person A ate 52 hot dogs, Person B ate 44 hot dogs, and Person C ate 34 hot dogs.

A) There are 3 terms in the simplified expression. B) There are 2 terms in the simplified expression that are negative.

First, let's combine the terms that are alike. We can combine the [tex]x^2[/tex] terms and the [tex]y^2[/tex] terms:

(-3 [tex]x^2[/tex]  + 5 [tex]x^2[/tex] ) + (2 [tex]y^2[/tex]- 3 [tex]y^2[/tex]) + 5xy - 2y

This gives us:

2 [tex]x^2[/tex]  -  [tex]y^2[/tex]+ 5xy - 2y

We can then combine the xy and y terms:

2 [tex]x^2[/tex]  - ( [tex]y^2[/tex]+ 2y)

This gives us:

2 [tex]x^2[/tex]  - [tex]y^2[/tex]- 2y

So, the simplified expression is 2 [tex]x^2[/tex]  - [tex]y^2[/tex]- 2y.

There are 3 terms in the simplified expression.

There are 2 terms in the simplified expression that are negative.

Here is a breakdown of the steps involved in simplifying the expression:

Combine the  [tex]x^2[/tex]  terms and the [tex]y^2[/tex] terms.

Combine the xy and y terms.

Check to make sure that there are no common factors that can be canceled.

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Answer:

The Eighth Figure would be an 8 by 8 square with 64 small squares

Step-by-step explanation:

The Figures shown in the picture are following a fairly simple pattern. Each variation is adding 1 row and 1 column of squares. Variation 4 has a 4 by 4 square with 16 small square (4*4 = 16). If we continue with pattern then variation 8 will be an 8 by 8 square with 64 smaller squares inside it (8*8 = 64)

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

B) 72 sq in

Step-by-step explanation:

The maximum size of the picture that can fit into the frame must be equivalent to the area of the shape. Given that the frame is 9 in x 8 in, it may be safe to conclude that the frame is a 4 sides plane shape, a rectangle.

The area of a rectangle is given as the product of it's length and breadth, which are 9 in and 8 in respectively. Hence, maximum area the picture can have to fit in the frame

= 9 in * 8 in

= 72 sq in

Answer:

-12 and 2

Step-by-step explanation:

[tex]x^2+10x=24\\[/tex]

[tex]x^2+2*5*x=24[/tex]

[tex]x^2+2*5*x+5^2-5^2=24[/tex]

[tex](x^2+2*5*x+5^2)-5^2=24[/tex]

Using the identity

[tex]a^2+2*a*b+b^2 = (a+b)^2[/tex]

we get

[tex](x+5)^2-5^2=24[/tex]

[tex](x+5)^2-25=24\\[/tex]

[tex](x+5)^2=24+25\\(x+5)^2=49\\(x+5)=+7 \\or (x+5)=-7\\[/tex]

Solving both of them we get

x=-12 or x=2

Answer:

A

Step-by-step explanation:

The volume of prism B is [tex]\rm 260 \; cm^3[/tex] and this can be determined by taking the ratio of the volume of both the prism.

Given :

To determine the volume of prism B, first determine the ratio of the volume of prism A to the volume of prism B that is:

[tex]\rm \dfrac{V_A}{V_B}=\dfrac{8^3}{4^3}[/tex]

[tex]\rm \dfrac{V_A}{V_B}=8[/tex]

Now, put the value of the volume of prism A in the above expression.

[tex]\rm \dfrac{2080}{V_B} = 8[/tex]

Divide 2080 by 8 in the above equation.

[tex]\rm V_B = \dfrac{2080}{8}[/tex]

[tex]\rm V_B = 260\;cm^3[/tex]

So, the volume of prism B is [tex]\rm 260 \; cm^3[/tex].

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Final answer:

To find AR in quadrilateral JPRA similar to quadrilateral KDEW, use the concept of similar triangles to determine AR = 45 mm.

Explanation:

To find AR in quadrilateral JPRA that is similar to quadrilateral KDEW, we can use the concept of similar triangles.

Calculate the scale factor between the two quadrilaterals: PR/DE = AR/WE

Substitute the known values: 27/15 = AR/25 and solve for AR which gives AR = 45 mm.

Answer:

Step-by-step explanation:

Alright, lets get started.

Please refer the diagram I have attached.

The width of the room is 30 meters.

If two beams will be making an angle, they will half the width.

There will be a right triangle made, so using SOH CAH TOA,

[tex]cos x=\frac{adjacent}{hypotenuse}[/tex]

[tex]cos x=\frac{15}{17}[/tex]

taking cos inverse

x = [tex]cos^{-1} (\frac{15}{17} )[/tex]

x = 28.07°   :   Answer

Hope it will help :)

Answer:

28.07

Step-by-step explanation:

Credit to first said it

The solution is Option A.

The value of the equation is 2( y - 4 ) - 5y = 3

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the value of x = y - 4   be equation (1)

Let the value of the equation 2x - 5y = 3   be equation (2)

Now ,

We know the value of the equation x = y -4

Substituting the value of equation (1) in equation (2) , we get

2 ( y - 4 ) - 5y = 3

So , the equation has now become ,

2 ( y - 4 ) - 5y = 3

Hence , the value of the equation is 2 ( y - 4 ) - 5y = 3

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Alright to solve it

Part A)

C = 1.5  

F =1

You will need to solve it for volume= length times width and times height

3.14 x 1^2 x 1.5

The answer you will get is 5 in^3

Part B)  Just do the same proccess as i did on the first one

CV= 192 in^3

Part C)

C=36x5in^3

So this is going to be 180 in^3 because is the less volume.

Hope this helps

Tobey

30 degrees / 360 degrees = 0.0833

0.0833 * 96 = 8

 answer is 8π m²

The area of a [tex]30^{\circ}[/tex] sector of this circle is [tex]8\pi \ m^2[/tex]. The correct option is B. [tex]8\pi \ m^2[/tex].

The area of circle is [tex]96 \pi \ m^2[/tex].

We have to calculate the area of [tex]30^{\circ}[/tex] sector of this circle.

We know that, Area of circle is,

[tex]A=\pi r^{2}[/tex]

Here, [tex]96\pi =\pi r^{2}[/tex]

Or,

[tex]r^{2} =96[/tex]

[tex]r=\sqrt{96}[/tex]

[tex]r=4\sqrt{6}[/tex]

So, radius of the circle,  

[tex]r=4\sqrt{6}[/tex] [tex]m[/tex].

Now we know that Area of a Sector of Circle

Say [tex]A_{1}[/tex],

[tex]A_{1} = \frac{\Theta}{360} \pi r^{2}[/tex]  

where [tex]\Theta[/tex]  is the angle subtended at the center, given in degrees, and '[tex]r[/tex]' is the radius of the circle.

So,

[tex]A_{1} =\frac{30}{360} \pi (4\sqrt{6} )^{2}[/tex]

[tex]A_{1} =\frac{1}{12} \pi \times96[/tex]

[tex]A_{1} =8\pi \ m^2[/tex].

Hence the area of a [tex]30^{\circ}[/tex] sector of this circle is [tex]8\pi \ m^2[/tex]. the correct option is B [tex]8\pi \ m^2[/tex].

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