Braces are used in interval or roster notation?

Answer:

Part 1) [tex]LA=(80+16\sqrt{13})\ in^{2}[/tex]

Part 2) [tex]TA=(104+16\sqrt{13})\ in^{2}[/tex]

Step-by-step explanation:

Part 1) Find the lateral area of the prism

we know that

The lateral area of the prism is equal to

[tex]LA=Ph[/tex]

where

P is the perimeter of the base

h is the height of the prism

Applying the Pythagoras Theorem

Find the hypotenuse of the triangle

[tex]c^{2}=4^{2}+6^{2}\\ \\c^{2}=52\\ \\c=2\sqrt{13}\ in[/tex]

Find the perimeter of triangle

[tex]P=4+6+2\sqrt{13}=(10+2\sqrt{13})\ in[/tex]

Find the lateral area

[tex]LA=Ph[/tex]

we have

[tex]P=(10+2\sqrt{13})\ in[/tex]

[tex]h=8\ in[/tex]

substitutes

[tex]LA=(10+2\sqrt{13})*8=(80+16\sqrt{13})\ in^{2}[/tex]

Part 2) Find the total area of the prism

we know that

The total area of the prism is equal to

[tex]TA=LA+2B[/tex]

where

LA is the lateral area of the prism

B is the area of the base of the prism

Find the area of the base B

The area of the base is equal to the area of the triangle

[tex]B=\frac{1}{2}bh[/tex]

substitute

[tex]B=\frac{1}{2}(6)(4)=12\ in^{2}[/tex]

Find the total area of the prism

[tex]TA=LA+2B[/tex]

we have

[tex]B=12\ in^{2}[/tex]

[tex]LA=(80+16\sqrt{13})\ in^{2}[/tex]

substitute

[tex]TA=(80+16\sqrt{13})+2(12)=(104+16\sqrt{13})\ in^{2}[/tex]

Let us say that the total amount paid in the first dealer is P1 and the total amount paid to the second dealer is P2. So that:

P1 = 2500 + 150 t

P2 = 3000 + 125 t

Where t is the total number of months

Now we are asked when the total amount paid would be equal for the two dealers, this means P1 = P2, therefore equating the two:

2500 + 150 t = 3000 + 125 t

25 t = 500

t = 20 months

Therefore the total amount paid for both dealers would be equal after 20 months.

The simple interest paid for 8 years on a $850 loan at a 7.5% annual interest rate is $510.

To calculate simple interest, you can use the formula:

Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

Where:

- Principal (P) is the initial amount of the loan.

- Rate (R) is the annual interest rate (in decimal form).

- Time (T) is the number of years.

In this case:

- Principal (P) = $850

- Rate (R) = 7.5% = 0.075 (decimal form)

- Time (T) = 8 years

Now, plug these values into the formula:

SI = $850 × 0.075 × 8

SI = $510

The simple interest paid for 8 years on a $850 loan at a 7.5% annual interest rate is $510.

For more such questions on Simple Interest :

https://brainly.com/question/30978175

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Answer:  The required fourth term in the given geometric sequence is [tex]\dfrac{5}{9}.[/tex]  

Step-by-step explanation:  We are given to find the fourth term of a geometric sequence with the following first term and common ratio :

[tex]a=15,~~r=\dfrac{1}{3}.[/tex]

We know that

the nth term of a geometric sequence with first term a and common ratio r is given by

[tex]a_n=ar^{n-1}.[/tex]

Therefore, the forth term of the given geometric sequence is

[tex]a_4=ar^{4-1}=ar^3=15\times\left(\dfrac{1}{3}\right)^3=15\times\dfrac{1}{27}=\dfrac{5}{9}.[/tex]

Thus, the required fourth term in the given geometric sequence is [tex]\dfrac{5}{9}.[/tex]  

Answer:

128 lawn mowers

Step-by-step explanation:

Given,

The overhead cost = $ 34,816,

The cost for one lawn mower = $ 388,

Let x be the number of lawn mowers manufactured,

So, the total cost of x lawn mowers = 34816 + 388x,

Now, if the average cost of x mowers = $ 660,

So, the total cost = 660x

[tex]\implies 660x = 34816 + 388x[/tex]

[tex]660x - 388x = 34816[/tex]

[tex]272x= 34816[/tex]

[tex]\implies x = \frac{34816}{272}=128[/tex]

Hence, 128 lawn mowers were manufactured.

Answer:

-20/29

Step-by-step explanation:

52 cards in a deck

 4 kings

 4 queens

 King = 4/52 reduces to 1/13

Queen = 4/52 reduces to 1/13

1/13 *1/13 = 1/169

 so none of the above

The question concerns a basic algebraic expression 'eight times the sum of a and b' which is represented as 8(a + b). The expression emphasizes the operation order: sum first, then multiply, which results in a value eight times greater than the original sum.

The question 'eight times the sum of a and b' is a mathematical expression that can be represented as 8(a + b). This expression means you first add the numbers 'a' and 'b' and then multiply their sum by eight. The result you get after the multiplication will be eight times greater than the original sum of 'a' and 'b'. For instance, if 'a' is 2 and 'b' is 3, their sum is 5, and when this is multiplied by eight, it becomes 40, which is the desired expression's value.

To understand this concept further, we can refer to the exponentiation rule mentioned, which states that (xa)b = xa.b. Although this is a different type of operation—exponentiation—it demonstrates a similar principle of first performing the operation inside the parentheses and then applying the outside operation.

Finally, when performing algebraic operations, it's essential to remember that whatever you do to one side of the equation, you should do to the other side to maintain balance. This is a fundamental principle in algebra that helps to solve equations, such as the example provided showing how to isolate 'a' by subtracting 'x' from both sides of the equation a b.

to calculate the vertical height multiply the hypotenuse ( 5280) by the sin of the angle (5)

5280 x sin(5) = 460.1823

round off to 460 feet

Answer:

I think Table C - Corralle

Answer:

c

Step-by-step explanation:

2

2x2 = 4

2+2 =4

0

0x0=0

0+0=0

Answer:

Option b. width = 16.5 inches and length = 24 inches

Step-by-step explanation:

Tim enlarged a picture wit a width of 5.5 inches and a length of 8 inches.

He enlarged the picture by a scale factor of 3.

We have to find the new dimensions of the picture.

Since, New dimension of the picture = Scale factor × dimensions before enlargement

So new width = 3×5.5 = 16.5 inches

new length = 3×8 = 24 inches

Therefore, option b. is the answer.