Find a(33) if the first term in the sequence is 3 and the common difference is -1.

Answer:

In 1981 was the building worth double it’s value.

Step-by-step explanation:

Given : A townhouse in San Francisco was purchased for $80,000 in 1975. The appreciation of the building is modeled by the equation : [tex]A=80000(1.12)^t[/tex], where t represents time in years.

To find : In what year was the building worth double it’s value in 1975?

Solution :

The amount is $80,000.

The building worth double it’s value in 1975.

i.e. amount became A=2(80000).

Substitute in the model,

[tex]2(80000)=80000(1.12)^t[/tex]

[tex](1.12)^t=\frac{2(80000)}{80000}[/tex]

[tex](1.12)^t=2[/tex]

Taking log both side,

[tex]t\log (1.12)=\log 2[/tex]

[tex]t=\frac{\log 2}{\log (1.12)}[/tex]

[tex]t=6.11[/tex]

i.e. Approx in 6 years.

So, 1975+6=1981

Therefore, in 1981 was the building worth double it’s value.

The building was worth double its value in [tex]1975[/tex] around the year [tex]1981[/tex]

To determine in what year the building was worth double its value in [tex]1975[/tex], we need to set up the equation based on the appreciation model given:

[tex]\[ A = 80000 \times (1.12)^t \][/tex]

Here, [tex]\( A \)[/tex] represents the current value of the townhouse in dollars, and [tex]\( t \)[/tex] represents the time in years since [tex]1975.[/tex]

We want to find the year [tex]\( t \)[/tex] when the value [tex]\( A \)[/tex] is double the initial value of [tex]\$80,000[/tex]

[tex]\[ A = 2 \times 80000 = 160000 \][/tex]

Now, substitute [tex]\( A = 160000 \)[/tex] into the equation:

[tex]\[ 160000 = 80000 \times (1.12)^t \][/tex]

Divide both sides by [tex]80000[/tex] to solve for [tex]\( (1.12)^t \)[/tex]

[tex]\[ 2 = (1.12)^t \][/tex]

To solve for [tex]\( t \)[/tex], take the natural logarithm ([tex]ln[/tex]) of both sides:

[tex]\[ \ln(2) = \ln((1.12)^t) \][/tex]

[tex]\[ \ln(2) = t \times \ln(1.12) \][/tex]

Now, divide both sides by [tex]\( \ln(1.12) \)[/tex] to solve for [tex]\( t \)[/tex]:

[tex]\[ t = \frac{\ln(2)}{\ln(1.12)} \][/tex]

Using a calculator to find the approximate value:

[tex]\[ t = \frac{0.6931}{0.1178} = 5.88 \][/tex]

Since [tex]\( t \)[/tex] represents years after [tex]1975[/tex], we add this to [tex]1975[/tex] to find the year when the building was worth double its value in [tex]1975[/tex]:

[tex]\[ \text{Year} = 1975 + 5.88 = 1980.88 \][/tex]

In [tex]1981[/tex], the building was worth double its value in [tex]1975.[/tex]

No. It is not true for all similar triangles.

Step-by-step explanation:

Answer:x^2-6x+9

Step-by-step explanation:

Answer: 5kg

Step-by-step explanation:

If 72 books weigh 9kg

Then, 1 book weighs 9/72 = 1/8 kg

Therefore, 40 books will weigh

40 times 1/8 = 5kg

Answer:

For any right triangle, the longest side is called the hypotenuse. Therefore, by Pythagorean theorem it is true that:

[tex]x^2=a^2+b^2[/tex]

Where:

x: Hypotenuse

a, b: The other two sides.

For instance, if we have a right triangle whose sides measure:

[tex]a=3 \\ \\ b=4[/tex]

Then, the hypotenuse can be found as:

[tex]x=\sqrt{3^2+4^2} \\ \\ c=\sqrt{25} \\ \\ c=5[/tex]

Answer:

(4 , 2)

Step-by-step explanation:

The solution of the graph is located where the two lines intersect. Remember, the x (horizontal line), is always first, and then followed by the y (vertical line).

The two lines intersect at (4, 2), making B) your answer.

~

The measure of arcWUX in circle V of the given diagram with the circle geometry is; C: 120°

From the complete image as seen online, we can say that;

The measure of ∠WUX is similar to the measure of vertex ∠V.

To get the measure of angle V (∠V), we will use the sum of angles in a triangle theorem to get;

30 + ∠V + ∠X = 180

60 + ∠V = 180

∠V = 180 - 60

∠V = 120°

Since ∠V = arcWUX

Then, measure of arcWUX is 120°

Read more about circle geometry at; brainly.com/question/24375372

Answer: C. 120

Step-by-step explanation: First guy wrote out the math cause he's smart like that.

Answer:

144

Step-by-step explanation:

12X12 is also 12+12+12+12+12+12+12+12+12+12+12+12

Lets simplify that though.

12(10)+12(2) (since 10 plus 2 is 12)

120+24

144

The value of the expression 12 * 12 = 144

The meaning of the expression 12 * 12 could also be interpreted as adding 12 in 12 places.

We could rewrite as thus :

Adding the above would give a value of 144.

Hence, 12 * 12 = 144

Learn more on Multiplication :https://brainly.com/question/2972832

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Option C: [tex]a=3, b=4[/tex] is the value of a and b

Explanation:

Given that the expression [tex]\sqrt{648}=\sqrt{2^a\times3^b}[/tex]

We need to determine the value of a and b

Let us consider the term [tex]\sqrt{648}[/tex] and take the prime factorization of the term 648

Thus, we have,

648 divides by 2,

[tex]648=2 \cdot 324[/tex]

324 divides by 2,

[tex]648=2 \cdot 2 \cdot 162[/tex]

162 divides by 2,

[tex]648=2 \cdot 2 \cdot 2 \cdot 81[/tex]

81 divides by 3,

[tex]648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 27[/tex]

27 divides by 3,

[tex]648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 9[/tex]

9 divides by 3,

[tex]648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3[/tex]

Thus, we have,

[tex]\sqrt{648}=\sqrt{2^{3} \cdot 3^{4}}[/tex]

Therefore, equating the powers of 2 and 3, we get,

[tex]a=3, b=4[/tex]

Hence, the value of a and b is 3 and 4

Thus, Option C is the correct answer.

The values of a and b which make the equation true are; a = 3 and b = 4 respectively.

From the question; the expression given is;

[tex] \sqrt{648} = \sqrt{ {2}^{a} \times {3}^{b} } [/tex]

In essence; we have;

By expression of of 648 as the product of its lowest factors; we have;

In which case; we have;

Ultimately, the values of a and b which make the equation true are 3 and 4 respectively.

Read more on indices:

https://brainly.com/question/1592472

Answer:

3^2X5

Step-by-step explanation:

Students learn that the prime factorization of a number is the given number written as the product of its prime factors. For example, to find the prime factorization of 45, use a factor tree to find that 45 is 5 x 9, and 9 is 3 x 3. So the prime factorization of 45 is 5 x 3 x 3, or 5 x 3^2.

Answer:

Option B, 3^2 * 5

Step-by-step explanation:

Step 1:  Find the prime factorization of 45

45 = 9 * 5

9 can be simplified as 3^2

5 cannot be simplified because it is a prime number

9 * 5

3^2 * 5

So, 45 = 3^2 * 5

Answer:  Option B, 3^2 * 5

Answer:

5

Step-by-step explanation:

Answer: 20

Step-by-step explanation:

C = 5/9 (f - 32)

since f = 68 and substitute it into the equation above

C = 5/9 ( 68 - 32)

C = 5/9 (36)

opening the bracket

C = 5/9 x 36

C = 180/9

C = 20

Answer:

Part 1) Vertical line : [tex]x=1[/tex]

Part 2) Horizontal line :  [tex]y=-4[/tex]

Step-by-step explanation:

Part 1) Write the equation for the vertical line passing through the point (1,-4)

we know that

The equation of a vertical line (parallel to the y-axis) is equal to the x-coordinate of the point that passes through it

so

The x-coordinate is 1

therefore

The equation of the line is

[tex]x=1[/tex]

Part 2) Write the equation for the horizontal line passing through the point (1,-4)

we know that

The equation of a horizontal line (parallel to the x-axis) is equal to the y-coordinate of the point that passes through it

so

The y-coordinate is -4

therefore

The equation of the line is

[tex]y=-4[/tex]

Answer:

B. 3 g/mL

Step-by-step explanation:

The first thing is to know the density formula:

Density is given as follows:

d = m / V

let m: mass and V: volume.

We have that the mass of the metal is 1800 grams and the volume of 600 milliliters.

Therefore, replacing:

d = 1800/600 = 3 g / mL

That is, the density is 3 grams per milliliter.

Answer: B. 3

Step-by-step explanation: I Just Took the Test

Answer:

a) rational

b) irrational

Step-by-step explanation:

a) 36 = 6²

So sqrt(36) = 6

b) 72 = 2 × 36

sqrt(72) = sqrt(2) × sqrt(36)

Since 2 is not a perfect square, sqrt(72) is irrational

Final answer:

√36 is a rational number because 36 is a perfect square, which results in a whole number when square rooted. However, √78 is an irrational number as it is not a perfect square and cannot be simplified to a fraction of two integers.

Explanation:

We are tasked with determining whether each given root, √36 and √78, is a rational or irrational number. First, we observe that √36 is the square root of 36. Since 36 is a perfect square (6 x 6), √36 equals 6, which is a rational number because it can be expressed as the quotient of two integers (6/1).

On the other hand, √78 is not a perfect square; its square root cannot be simplified to a whole number or a simple fraction of two integers. Therefore, √78 is an irrational number because it cannot be written exactly as a simple fraction or repeating or terminating decimal.

Answer:

r = 9ft

h = 4ft

Step-by-step explanation:

Answer:

y= −9.16x²+73.04x+183.3

Values increase till x = 4 and then decrease which means thus curve has a maximum turning point around 4.

Coefficient of x² should be negative

because max to (concave down)

x = -b/2a should be around 4

x = -73.04/(2×-9.16) = 3.987

Answer:

Part 1) [tex]30\ coupons[/tex]

Part 2) [tex]12\ sandwiches[/tex]

Part 3) [tex]60\ push-ups[/tex]

Part 4) [tex]96\ minutes[/tex]

Part 5) [tex]\$95[/tex]

Part 6) [tex]1\frac{7}{8}\ cups\ of\ pretzel[/tex]

Step-by-step explanation:

Part 1) we know that

At the Green House of Salad , you get a $1 coupon for every 3 salads you buy

so

Using proportion

Find out the number of salads you could buy to get $10 in coupons

[tex]\frac{1}{3}=\frac{10}{x} \\\\x=3(10)\\\\x=30\ coupons[/tex]

Part 2) we know that

Kim orders catering for $35

She spend $5 on a large order of potato salad and the rest on turkey sandwiches

Each sandwich is $2.50

How many sandwiches does Kim buy?

step 1

Find out how many Kim spent on turkey sandwiches

Subtract $5 from $35

35-5=$30

step 2

Using proportion, find out the number of sandwiches

so

[tex]\frac{1}{2.50}=\frac{x}{30}\\\\x=30/2.50\\\\x= 12\ sandwiches[/tex]

Part 3) we know that

Molly does 10 push-ups at the same time as Liza does  15 push-ups

so

Using proportion

Find out how many push-ups Liza does when Molly does 40 push-ups

[tex]\frac{10}{15}=\frac{40}{x}\\\\x=15(40)/10\\\\x=60\ push-ups[/tex]

Part 4) we know that

A shark swim at a speed of 25 miles per hour

The shark rest after 40 miles

How long in minutes, does the shark swim before resting?

Using proportion

Find out how long in minutes the shark swim 40 miles

Remember that

[tex]1\ h=60\ min[/tex]

[tex]\frac{25}{60}\ \frac{miles}{minutes}=\frac{40}{x}\ \frac{miles}{minutes}\\\\x=60(40)/25\\\\x=96\ minutes[/tex]

Part 5) we know that

For every bar of soap that Aly sells, she earns $5

For every mug that Janet sells, she earns twice as much as Aly

Aly sells 5 bars of soap and Janet sells 7 mugs

How much money did they make altogether?

step 1

Find out the amount earned by Aly

using proportion

[tex]\frac{1}{5}=\frac{5}{x}\\\\x=5(5)\\\\x=\$25[/tex]

step 2

Find out the amount earned by Janet

Remember that

For every mug that Janet sells, she earns twice as much as Aly

so

For every mug that Janet sells, she earns 2($5)=$10

using proportion

[tex]\frac{1}{10}=\frac{7}{x}\\\\x=10(7)\\\\x=\$70[/tex]

step 3

Adds the amount earned by Aly plus the amount earned by Janet

[tex]25+70=\$95[/tex]

Part 6) we know that

Ted is making trail mix for a party

He mixes 1 1/2 cups of nuts, 1/4 cup of rising and 1/4 cup of pretzel

How many cups of pretzel does Ted need to make 15 cups of trail mix?

Adds the quantities

[tex]1\frac{1}{2}+\frac{1}{4} +\frac{1}{4}=2\ cups\ of \ trail\ mix[/tex]

That means

For every 2 cups of trail mix we need 1/4 cup of pretzel

using proportion

Find out how many cups of pretzel does Ted need to make 15 cups of trail mix

[tex]\frac{2}{(1/4)}=\frac{15}{x}\\\\x=15(1/4)/2\\\\x=\frac{15}{8}\ cups\ of\ pretzel[/tex]

Convert to mixed number

[tex]\frac{15}{8}=\frac{8}{8}+\frac{7}{8}=1\frac{7}{8}\ cups\ of\ pretzel[/tex]

Answer:

Each result is equally likely

The sample space has 36 different outcomes

Step-by-step explanation:

A number cube has 6 sides, and there are 2 number cubes so there are 36 possible outcomes because 6²=36

Remind me if im wrong

The statements which are true are each result is equally likely , the sample space has 36 different outcomes and the total roll of 7 is very likely.

When a green number cube and a red number cube are rolled, the outcomes indeed have specific characteristics. Here's a breakdown based on the selections provided in the question:

Each result is equally likely is true, because when rolling two fair six-sided dice (or in this case, cubes), each side of each cube has an equal chance of landing face up, making each combination of the two cubes equally likely

The sample space has 36 different outcomes is  true, as each cube has 6 faces, and when two are rolled together, the total number of possible outcomes (or the sample space) is 6 times 6, equating to 36

The sample space has 11 different outcomes is false, because as previously stated, there are 36 possible outcomes based on the combination of two six-sided dice.

A total roll of 7 is very likely is true, not because it will happen every time, but because there are more combinations (6 in total) that sum to 7 than any other number. These are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).

Answer:

dot plots are best used to show a distribution of data

Answer:

Dot plots are best used for a.Dot plots are best used to show a distribution of data.

Step-by-step explanation:

Option C:

[tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)=21 x^{7} y^{11}[/tex]

Solution:

Given expression is [tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)[/tex].

To find the product of the above expression.

[tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)[/tex]

First multiply the numerical coefficients.

[tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)=21 x^{2} y^{3} x^{5} y^{8}[/tex]

Arrange the terms with same base.

                         [tex]=21 x^{2} x^{5} y^{3} y^{8}[/tex]      

Using exponent rule: [tex]a^m \cdot a^n = a^{m+n}[/tex]

                        [tex]=21 x^{2+5} y^{3+8}[/tex]

                        [tex]=21 x^{7} y^{11}[/tex]

[tex]\left(7 x^{2} y^{3}\right)\left(3 x^{5} y^{8}\right)=21 x^{7} y^{11}[/tex]

Hence option C is the correct answer.

Answer:

Answer below, let me know if it didn't make sense.  

Step-by-step explanation:

I attached a picture of the scatterplot with a line connecting the points.  There is a definite upside down u type shape, and it doesn't look close to a line at all, so linear is not a good choice.  

an upside down u shape (or right side up u shape for that matter) is exactly what a quadratic is, or any polynomial if you do it right, but quadratic is the simplest, so let's go with that.

A linear representation is not the best way to represent the data from the equation gotten from the regression calculator.

Regression simply means a statistical measurement that is used to determine the strength of the relationship that exists between the dependent and independent variables.

In this case, a linear representation is not the best way to represent the data from the equation. A quadratic equation will have been more appropriate in this case.

Learn more about regression on:

https://brainly.com/question/7781679

Answer:

8

Step-by-step explanation:

XY = X times Y

If you substitute them its 2 X 4

Answer:

The first thing we need to do is find the area of the rectangle...

l x w = A

7 x 8 = 56

So the area of the first rectangle is 56m.

Now we multiply each dimension by 5...

8 x 5 = 40

7 x 5 = 35

So, now the width is 40m and the length is 35m,

Then, find the area of the new rectangle...

35 x 40 = 1400

The area of this rectangle is 1,400m!

1,400 / 56 = 25

So, by multiplying each dimension by 5, the area is now multiplied by 25!

Answer:

32

Step-by-step explanation:

When you multiply 40 by 20% or 0.20, the product will be the amount of games he lost. When you subtract 40-8 you get how many games he won.

Answer:15.808

Step-by-step explanation:

you just multiply no need to line up the decimal points tho

Answer :

Toby: 4 of the $1.64, 1 of the $0.77, and 1 of the $3.59

Elisa: 3 of the $3.59

Heidi: 3 of the $3.59, and 1 of the $0.77

The question is a math problem about calculating the total cost of purchased fruits within a given budget. It requires us to determine the fruit combinations that match the total spending amount and the number of items bought for each individual.

The problem is a typical mathematics question focusing on money and budgeting. Toby, Elisa, and Heidi each have a budget between $10 and $12 to spend on fruit. Each fruit item's cost is given, and we need to assign a combination of fruits to each person that matches their total spending amount. Toby bought 6 items, Elisa bought 3, and Heidi bought 4.

For example, if Toby bought 6 bananas at 20 cents each, his total would be $1.20. As he needs to spend between $10 and $12, you would continue to mix and match the rest of the fruits until his purchase meets the criteria of total amount spent and number of items bought.

Answer:

4x-11(simplified)

x=2.75(solved, if needed)

Step-by-step explanation:

Simplify like terms

4x(-8-3)

4x-11

If you wanted it solved,

4x=11 (adding 11 to both sides)

x=2.75 (divide by 4)

Answer: x=2.75 or without simplifying 4x-11

hope it helps please give brainliest!

Step-by-step explanation:

[tex]4x-8-3\\4x-11\\[/tex]

This is the farthest you can go but you can simplify to...

[tex]4x-11\\x-\frac{11}{4}\\ x-2.75\\-x=-2.75\\/-1 /-1\\x=2.75[/tex]

For this case we must add the terms of the following expression:

[tex]6y \sqrt {a} + 7y \sqrt {a}[/tex]

It is noted that the terms are similar, so we can add:

We take common factor [tex]\sqrt {a}:[/tex]

[tex]\sqrt {a} (6y + 7y) =[/tex]

We add the terms within the parenthesis:

[tex]\sqrt {a} (13y) =[/tex]

finally we have:

[tex]13y \sqrt {a}[/tex]

Answer:

[tex]13y \sqrt {a}[/tex]

Answer:

D.) 13y sqrt a

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

36= 3 equal parts

so: 36/3 =12

One part=12

so 2 parts is 12*2

12*2=24mm is the answer

The measure of the matching side of the smaller triangle is 24 millimeters.

When dealing with similar triangles, the lengths of corresponding sides are proportional. This means that if one triangle has sides that are a constant multiple of the sides of another triangle, we can find the length of a matching side by using that constant multiple. In this case, the sides of the smaller triangle are said to be 2/3 the lengths of the sides of the larger triangle.

To find the matching side of the smaller triangle when a side of the larger triangle is 36 mm, we use the proportionality factor, which is 2/3. Therefore, the length of the corresponding side in the smaller triangle is 2/3 of 36 mm, which can be calculated as:

(2/3) * 36 mm = 24 mm

So, the measure of the matching side of the smaller triangle is 24 millimeters.