Use 3.14 for and round your final answer

let x = amount invested at 3%

so, (2600 - x) is invested at 7%

.07 *(2600 - x) + .03 *(x) = 138

182 - .07x + .03x = 138

-.07x + .03x = 138 - 182

-.04x = -44

-.04x / -.04 = -44 / -.04

x = 1,100

so amount invested at 7% is (2600 - 1100) or 1500

consequently amount invested at 3% is 1100

$1,100 invested at 3%

$1,500 invested at 7%

The money invested in both of the funds are $800 and $1800 respectively.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

Suppose the money invested in one of the funds be x.

Then, in the other fund the investment is (2600 - x).

Now, the equation for the total profit from both investments can be obtained as,

7% × x + 3% × (2600 - x) = 150

⇒ 7/100 × x + 3/100 × (2600 - x) = 150

⇒ 4x/100 = 150 - 78

⇒ x = 1800

Thus, the investment in the other fund is 2600 - 800 = $800.

Hence, the investment for both the funds are $800 and $1800 respectively.

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"4√7" means four times the square root of 7, approximately equal to 10.582, an irrational number with decimal expansion.

The expression "4√7" represents the square root of 7, multiplied by 4. Let's break it down step by step:

1. Square Root: The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 × 3 = 9. Similarly, the square root of 25 is 5 because 5 × 5 = 25.

2. √7: This symbol (√), called the radical symbol, represents the square root. So, √7 represents the square root of 7, which is an irrational number, meaning it cannot be expressed as a simple fraction and has decimal places that go on indefinitely without repeating.

3. 4√7: This means you're taking the square root of 7 and then multiplying it by 4. So, if you calculate it, it's like doing 4 times the square root of 7.

To give a numerical example, if we want to find the value of 4√7:

  4 × √7 ≈ 4 × 2.6457513110645905905016157536393... (approximately)

Thus, 4√7 is approximately equal to 10.582, depending on how many decimal places you round to.

In summary, "4√7" represents four times the square root of 7, which is an irrational number, approximately equal to 10.582.

Answer:

If two lines intersect, then their intersection is exactly one point.

Step-by-step explanation:

Yes, the equation provided can be used to calculate the original price of the phone case. After solving the equation, we found out that the original price of the phone case was approximately $80.

Yes, the equation you provided, 3/4(0.7c) = 42, can certainly be used to find the original price of the phone case (c). The equation is obtained by recognizing that you're receiving two discounts: a 30% or 0.3 discount off the original price (leaving 70% or 0.7 of the original price) and then a 25% or 0.25 discount (meaning you're paying 75% or 0.75 of the price after the first discount).

To find the original price, you want to solve this equation for 'c'. That would involve dividing both sides by 3/4(0.7) equaling to 0.525. So, it will look like: 42 ÷ 0.525 = c. Doing the calculation, c equals approximately $80.

Therefore, the original price of the phone case was $80.

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Answer:

  a. The cost of 10 tickets

Step-by-step explanation:

We don't know what the expression is supposed represent, but the answer choices suggest that ...

  c = 5t +3

represents the cost of t tickets. Then, when t=10, c = 53 will represent the cost of 10 tickets.

The statement that justifies how the area of a sector of a circle is derived is:

This refers to the quantity that expresses the extent of a region on the plane such as on a curved surface.

Furthermore, the area of sector of a circle is talking about the amount of space enclosed within the boundary of the sector.

Generally, it is explained in step that we first calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply ​the area of the circle​ by this fraction.

Therefore, the Option B is correct.

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[tex]\text{Consider the sum of the finite arithmatic series}\\ \\ 7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5)\\ \\ \text{We know that the sum of the finite arithmatic series }\\ \\ a_1,a_2, a_3, ..., a_n \text{ is given by the formula}\\ \\ S_n=\frac{n}{2}\left ( a_1+a_n \right )\\ \\ \text{here in the given series, we can see that }a_1=7.6, \ a_n=-1.5 \text{ and}\\ \text{the number of terms is, }n=8. \text{ so using above formula, we get}[/tex]

[tex]S_8=\frac{8}{2}\left ( 7.6+(-1.5) \right )\\ \\ =4\left ( 7.6-1.5 \right )\\ \\ =4\left ( 6.1 \right )\\ \\ =24.4[/tex]

Hence the sum of the finite Arithmetic series is: 24.4

Answer:

There are 8 band members in each row

Step-by-step explanation:

Given : A band performed at halftime during the football game.

There were 64 band members marching in 8 equal rows.

To Find : How many band members were in each row?

Solution :

Let there are x members in each row .

Since there are 8 rows

So, no. of members in 8 rows = 8x

We are also given that there are 64 band members .

⇒[tex]8x=64[/tex]

⇒[tex]x= \frac{64}{8}[/tex]

⇒[tex]x= 8[/tex]

Thus there are 8 band members in each row

Final answer:

The expression equivalent to 32 might refer to a mathematical manipulation or a unit conversion. In equations, 32 is what remains when you subtract 32 from one side of an equation like x + 32 = 64. Meanwhile, in conversions, multiplying the number of quarts by 32 gives you the equivalent volume in fluid ounces.

Explanation:

The expression is equivalent to 32 and could be interpreted in different contexts. Using mathematical manipulation, when you subtract 32 from both sides of an equation, the equality holds. For example, if you have an equation like x + 32 = 64, subtracting 32 from both sides gives us x = 64 - 32, which simplifies to x = 32. This demonstrates an application of the principle that you can add or subtract the same number from both sides of an equation without changing its solution.

In relation to conversion between different units of measurement, specifically volume, when you convert quarts to fluid ounces, the conversion factor is 32 because there are 32 fluid ounces in one quart. Consequently, to find how many fluid ounces are in a given number of quarts, you multiply the number of quarts by 32. For example, 4 quarts equal 4 × 32, which is 128 fluid ounces.

Furthermore, when dealing with electrical resistance, 'equivalent resistance' is another situation where the number 32 might be relevant. Depending on the context and the specific details of an electrical circuit, one of the listed equivalent resistances may be the correct answer to a problem involving calculating the total resistance.

The round off to nearest half is 1/2.

Although the term "rounding" is a general one, we typically use the terms "round up" or "round down" to indicate whether the number has gone up or down after being rounded. The supplied number is said to be rounded up when the rounded number is increased, and it is said to be rounded down when the rounded number is dropped.

Given:

The fraction = 5/9.

Now, rounded to the nearest half is 1/2

we know 9 halved value is 4.5 which is much closer to 5.

So, we can write it as 5/10 = 1/2.

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Answer:

C. (11 unit cubes and 2 smaller cubes of volume 1/8 cubic inch each.)

Step-by-step explanation:

90 cubes * 1/8 inch = 11 1/8 inch.

Final answer:

Solomon has 2/3 of the book left to read. To finish it over 5 nights, he needs to read 2/15 of the book each night.

Explanation:

Solomon has read 1/3 of his book already. To finish the remaining 2/3 of the book in 5 nights, we need to calculate the fraction of the book he should read each night. Since he has to evenly distribute the remaining portion over 5 nights, we will divide 2/3 by 5.

Here's the calculation step-by-step:

First, represent the remaining part of the book as a fraction, which is 2/3.

To divide this fraction by 5, we multiply the denominator by 5. This gives us (2/3) × (1/5).

Multiplying these fractions, we get (2 × 1) / (3 × 5), which simplifies to 2/15.

Thus, Solomon reads 2/15 of the book each night for the next 5 nights.

Answer:

9 or (5,4)

Step-by-step explanation:

Just subtract it on each side :)

Answer:

A) 2 13/15 x + 3

B) 2 7/12 x - 7 4/5 over 2 3/5

C) 5 16/21 x - 18 6/7

D) 16 4/7 x - 2 2/5

Step-by-step explanation:

area of triangle is = 1/2 * base * altitude

1- each side is made 8 times

so the net change in area is 64 times

The area of A'B'C' is 64 times the area of ABC

2- each side is made 4 times

so the net change in area is 16 times

The area of D'E'F' is 16 times the area of DEF

3- each side is made 3 times

so the net change in area is 9 times

The area of A'B'C' is 9 times the area of ABC