give the length and width in whole inches of three different rectangles that each have an area of 48 in. squared

The first term of the geometric sequence is 3 and the common ratio is 2.

To identify the first term and the common ratio of a geometric sequence, we can use the formula:  an = a1 * r^(n-1), where an is the nth term, a1 is the first term, r is the common ratio, and n is the position of the term.

Given a5 = 48 and a11 = 3,072, we can substitute the values into the formula:

48 = a1 * r^(5-1)

3,072 = a1 * r^(11-1)

By dividing the second equation by the first equation, we can eliminate a1:

64 = r^6

Taking the sixth root of both sides gives:

r = 2

Substituting this value back into the first equation, we can solve for a1:

48 = a1 * 2^4

a1 = 3

So, the first term (a1) is 3 and the common ratio (r) is 2.

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Answer:

The line parallel to this one and through the given point would be y = -3.

Step-by-step explanation:

In order to find a parallel line, we first have to accept that this is a horizontal line. This is because there is no x value in the equation. That means in order to make it horizontal as well, we need it to have no x value again.

Given the ordered pair, this means our new equation is y = -3

The population growth function represented by an initial value A that increases 22% per year with x representing time in years is y=A(1.22)^x.

The function which represents an initial population that increases 22% per year, where A is the initial value and x is time in years, is given by y=A(1.22)^x. This formula calculates the future value (y) based on the premise of exponential growth, which embodies a continual increase year after year. The rate of growth is 22%, therefore we add this to 100% to get 122% (1.22). This entire value is raised to the power of x, representing the number of time periods (years).

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Answer:

The area of triangle DEF is 9 square units.

Step-by-step explanation:

It is given that triangle ABC and DEF are similar and the ratio of the side lengths in triangle ABC to triangle DEF is 1:3.

Let the length of their sides be x and x respectively.

If two triangles are similar then the ratio of their areas is equal to the square of the ratio of their sides.

Since triangle ABC and DEF are similar, therefore

[tex]\frac{Area(ABC)}{Area(DE F)}=\frac{(x)^2}{(3x)^2}[/tex]

[tex]\frac{1}{Area(DE F)}=\frac{(x)^2}{9(x)^2}[/tex]

Cancel out the common factors.

[tex]\frac{1}{Area(DE F)}=\frac{1}{9}[/tex]

On cross multiplication, we get

[tex]1\times 9=1\times Area(DE F)}[/tex]

[tex]9=Area(DE F)}[/tex]

Therefore the area of triangle DEF is 9 square units.

A - the sum of two dice is 7

B - the first die is 2

[tex] P(A|B)=\dfrac{P(A \cap B)}{P(B)}\\\\
|\Omega|=6^2=36\\
|A\cap B|=1\\
|B|=1\cdot6=6\\\\
P(A\cap B)=\dfrac{1}{36}\\
P(B)=\dfrac{6}{36}=\dfrac{1}{6}\\\\
P(A|B)=\dfrac{\dfrac{1}{36}}{\dfrac{1}{6}}=\dfrac{1}{36}\cdot6=\dfrac{1}{6} [/tex]

Answer:

The value of x is 12

Step-by-step explanation:

we have

[tex]f(x)=\sqrt{4x+9} +2[/tex]

we know that

The radicand must be greater than or equal to zero

so

[tex]4x+9 \geq0 \\ 4x\geq -9 \\x\geq -\frac{9}{4} \\ x\geq -2.25[/tex]

the domain is is the interval--------> [-2.25,∞)

therefore

the answer is

[tex]4x+9 \geq0[/tex]

Cesar purchased a total of 10 quarts of juice after converting [tex]1\frac{1}{2}[/tex] gallons to quarts and adding it to the quarts from the two bottles.

Cesar bought 2 bottles of juice that each hold 2 quarts and another bottle that holds [tex]1\frac{1}{2}[/tex] gallons of juice. To find out how many quarts of juice he bought in total, we need to convert gallons to quarts.

We know that there are 4 quarts in 1 gallon, so [tex]1\frac{1}{2}[/tex] gallons equal 6 quarts ( [tex]1\frac{1}{2}[/tex] × 4 quarts/gallon).

Adding the quarts from the two bottles, we have 2 × 2 quarts which equal 4 quarts. Now, add the quarts from the single bottle to the total:

4 quarts (from two bottles) + 6 quarts (from  [tex]1\frac{1}{2}[/tex] gallon bottle) = 10 quarts

So, Cesar bought a total of 10 quarts of juice.

Answer:

b

Step-by-step explanation:

Final answer:

Mark paid $3162.50 in interest on a $5500 loan at 11.5% over five years using the simple interest formula Interest = Principal × rate × time.

Explanation:

To calculate the total amount of interest Mark paid on a $5500 loan at 11.5% for five years, we can use the formula for simple interest, which is:

Interest = Principal × rate × time

In Mark's case, the principal is $5500, the rate is 11.5% or 0.115 when converted to a decimal, and the time is 5 years. Plugging these values into the formula yields:

Interest = $5500 × 0.115 × 5 = $3162.50

So Mark will have paid $3162.50 in interest over the five years of the loan.

If the length of a rectangle is a two-digit number with identical digits and the width is 1/10 the length and the perimeter is 2 times the area of the rectangle, what is the the length and the width

Solution:

Let the length of rectangle=x

Width of rectangle=x/10

Perimeter is 2(Length+Width)

= 2(x+x/10)

Area of Rectangle= Length* Width=x*x/10

As, Perimeter=2(Area)

So,2(x+x/10)=2(x*x/10)

Multiplying the equation with 10, we get,

2(10x+x)=2x²

Adding Like terms, 10x+x=11x

2(11x)=2x^2

22x=2x²

2x²-22x=0

2x(x-11)=0

By Zero Product property, either x=0

or, x-11=0

or, x=11

So, Width=x/10=11/10=1.1

Checking:

So, Perimeter=2(Length +Width)=2(11+1.1)=2*(12.1)=24.2

Area=Length*Width=11*1.1=12.1

Hence, Perimeter= 2 Area

As,24.2=2*12.1=24.2

So, Perimeter=2 Area

So, Answer:Length of Rectangle=11 units

Width of Rectangle=1.1 units

Final answer:

The probability that Talia will pull a red ball out of the bag is 2/7, given she has 2 red, 1 blue, and 4 green balls in the bag making a total of 7 balls.

Explanation:

The question you have asked is related to the subject of probability in mathematics. Specifically, it is about the probability of drawing a red ball from a bag containing red, blue, and green balls. To calculate this probability, you need to know the total number of balls and the number of red balls in the bag. Then, you use the formula for probability which is the number of favorable outcomes divided by the total number of possible outcomes.

In Talia's bag, there are 2 red, 1 blue, and 4 green balls, making a total of 2+1+4=7 balls. The probability of pulling a red ball out of the bag is the number of red balls divided by the total number of balls, which gives:

Probability of red ball = Number of red balls / Total number of balls = 2/7.

So, the correct answer to the probability that Talia will pull a red ball out of the bag is 2/7.

Final answer:

The correct statement is that the lengths AB and AC are equal.

Explanation:

The correct statement is that the lengths AB and AC are equal. When Amy walks from point A to point B along the segment AB, and Fraser walks from point A to point C along the segment AC, the statement is correct because both points are on the circumference of the same circle with B as the center.

Answer:

No picture so i cannot answer the question but i can guide you to support.

Step-by-step explanation:

The way you would do a rectangle is: The area of a rectangle is A = l × w and the way you would do the triangle is The area of a triangle is A = one half × b × h...

Hope this helps...

:)  

Final answer:

The equation to find the cost of 3.5 pounds of grapes, with one pound costing $1.55, is represented by the proportion 1 pound / 3.5 pounds = $1.55 / x. By solving this equation, we find that x, the total cost for 3.5 pounds of grapes, is $1.55 multiplied by 3.5 = $5.425

Explanation:

The student is asking about the cost of 3.5 pounds of grapes, given that one pound costs $1.55. To find the equivalent ratio that can be used to calculate the cost of 3.5 pounds, we can set up a proportion where the cost of 1 pound is to 3.5 pounds as $1.55 is to the unknown cost (let's call it x). The equation representing the pair of equivalent ratios is:

1 pound / 3.5 pounds = $1.55 / x.

To solve for x, we multiply both sides of the equation by 3.5 pounds, which gives us:

1 pound * ($1.55 / 1 pound) * 3.5 = x

And this simplifies to:

x = $1.55 * 3.5 = $5.425

Therefore, by calculating $1.55 * 3.5, we can find the cost of 3.5 pounds of grapes.

Step-by-step explanation:

                                                     MEAN

First, add all the values together and divide by the number of values in the set. Imagine 3 people donated money to red cross. Their names are Allisa, John, and Thomas. Allisa gave 20 dollars, John gave 35, and Thomas gave 20. Next, you add the amount of money they donated, which is 70. Then you divide 70, the amount of money, by 3, because thats the amount of people that donated. Then you get a mean of 23.

To put it simpler,

add the values.

then, add the amount of whatever carries that value, such as people.

after, you devide the value and the amount of people or etc.

when you finish, your mean will be what you have divided.

Another example would be this.

There are several whales out in the ocean. One is the Cuvier's beaked whales, which can swim as deep as 2,992 m. Another whale, named the sperm whale, can swim down to at least  1,000 m.

So, what is the mean?

Once again, first, we add the value, which in this case, is how deep the whales can dive. We then get 3992 m.

Next, we add the amount of whatever carries that value, which in this case are whales.

after, you devide the value by the amount of whales.

when you finish, you will get 1996

                                                     MEDIAN

Arrange your numbers in numerical order. If they were scrambled like this, 9, 7, 3, 9, 6, 1, 5, rearrange them like this. 1, 3, 5, 6, 7, 9, 9.  

When you do this, check how many numbers are in that row. In this case, the amount is 7, which is odd.

If you have an odd number like in the example above, select the number in the middle, which in our case, its 6. ( 1, 3, 5, 6, 7, 9, 9 )  So your median would be six, since median means "the middle number"

If you have an even number, add them together then divide by 2. Heres an example. 1, 3, 5, 6, 7, 9, 9. (1, 3, 5, 8, 12, 9, 9, 12) You would add 8 and 12. Your answer would be 20. So now, you divide 20 by 2. 20 divided by 2 is 10, so your median would be 10.

I did not plagerise this, I made these example up myself and solved them the way they are supposed to be and used these examples on another question similar to this.