Diego has $100 and spends ¼ of it. How much does he have left?

We have been given that Sandra bought a boat for $28,800. According to her insurance company the value of the boat depreciates 7% each year. We are asked to find the value of the boat x years after Sandra purchased it.

We will use exponential decay formula to solve our given problem.

An exponential decay function is in form [tex]y=a(1-r)^x[/tex], where,

y = Final amount,

a = Initial amount,

r = Decay rate in decimal form,

x = Time.

Let us convert 7% into decimal form.

[tex]7\%=\frac{7}{100}=0.07[/tex]

Initial value of car is $28,800, so our function will be:

[tex]y=$28,800(1-0.07)^x[/tex]

[tex]y=$28,800(0.93)^x[/tex]

Therefore, the value of boat after x years would be [tex]y=$28,800(0.93)^x[/tex].

Answer: -5

Step-by-step explanation:

Answer:

-5 is right

Step-by-step explanation:

Answer: X=7

Step-by-step explanation: Use the formula (b/2)^2 in order to create a new term. Solver for X by using this term to complete the square.

X=7

Answer:

c

Step-by-step explanation:

The function that has a vertex at (2, -9) is;

C: f(x) = (x - 5)(x + 1)

The formula for x-coordinate of a vertex is;

x = -b/2a

The correct function is Option C with f(x) = (x - 5)(x + 1).

We will expand to get;

f(x) = x² -5x + x - 5

f(x) = x² - 4x - 5

Putting 2 for x gives;

f(2) = 2² - 4(2) - 5

f(2) = -9

Also, x = -b/2a = -(-4)/(2*1) = 2

Thus, it is proved that option C has it's vertex at 2, -9

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Answer:

There are many different types of equations we can use to allow x to equal 19! Below are some examples :) See if you can come up with some on your own based off of these examples:

        x = 19.......................................There's one for you :)

        x - 4 = 15..................................Add 4 to both sides

         x = 19

Answer:

20

Step-by-step explanation:

The volume of a cone is given as:

[tex]V = \frac{1}{3} \pi r^2 h[/tex]

where r = radius

h = height

The volume of the cone is 540π and its radius is 9.

This implies that:

[tex]540 \pi = \frac{1}{3} \pi * 9^2 * h\\\\h = \frac{540 * 3}{81} \\\\h = 20[/tex]

The height of the cone is 20.

Answer:

The answer is 20 bro

Step-by-step explanation:

Joy's approach to sampling art at the gallery, by examining 2 pieces per artist, can be representative if the selections span the artists' exhibited range. However, the representativeness might be limited if artists have a wide variety of styles or themes not captured by just two pieces.

Joy, by examining 2 pieces of art by each artist at the art show, attempts a representative sampling of the gallery's overall offerings. Whether this approach yields a representative sample depends on a few key factors. Primarily, the diversity and range of the artists' works on display must be considered. If each artist displays a wide variety of work and Joy's selections span this variety, her sample could offer a fair representation of the gallery's exhibition. However, if the artists have a vast body of work with significant variations in style, theme, or period not captured by just two pieces per artist, Joy's sample may not accurately represent the entire collection.

Furthermore, the extent to which the selected works reflect the artists’ core themes or periods plays a critical role in determining representativeness. Assuming each artist's work on display has an equal chance of being selected and Joy chooses pieces that span the artists' exhibited range, the sample can be somewhat representative. Nonetheless, a truly comprehensive view would likely require examining a greater number or a more strategically chosen set of artworks.

Joy’s examination provides valuable insights, but for a truly representative view of the gallery, additional observations or data would be beneficial.

Let’s explore the concept of representative samples in the context of Joy’s art gallery experience.

1. Understanding Representative Samples:

o A representative sample is a subset of a larger population that accurately reflects the characteristics of the entire population. In this case, the population consists of all the art pieces displayed in the gallery.

o When we say a sample is “representative,” it means that the selected pieces adequately capture the diversity and essence of the entire collection.

2. Joy’s Situation:

o Joy closely examined 2 pieces of art by each artist. Since each artist had an equal number of pieces on display, Joy effectively observed a balanced representation of the artists’ work.

o By examining multiple pieces from each artist, Joy has a better chance of encountering a variety of styles, themes, and techniques.

3. Likelihood of Representativeness:

o Given that Joy looked at 2 pieces from each artist, we can consider this sample as potentially representative.

o However, there are a few factors to consider:

 Artistic Diversity: If the artists’ styles are vastly different, the sample may not fully represent the entire gallery’s range.

 Number of Artists: If there are only a few artists in total, the sample might be less representative.

 Gallery Size: The larger the gallery, the more challenging it is to capture full representativeness with a limited sample.

4. Conclusion:

o While Joy’s sample is a good start, it’s essential to recognize its limitations.

o To determine true representativeness, we’d need more information about the total number of artists, the overall collection size, and the diversity of artistic approaches.

In summary, Joy’s examination provides valuable insights, but for a truly representative view of the gallery, additional observations or data would be beneficial.

To find the surface area of a prism (or any other geometric solid) we open the solid like a carton box and flatten it out to find all included geometric forms. To find the volume of a prism (it doesn't matter if it is rectangular or triangular) we multiply the area of the base, called the base area B, by the height h.

This info should help you.

Answer:

94

Step-by-step explanation:

the area of the 3 x 5 face is used 4 times rather than twice

y = 5 * (1/2)^x

Step-by-step explanation:

This is an exponential function

y =ab^x

where a is the initial value ( where x = 0)

a = 5

y = 5 * b^x

Pick a point to determine b

(1,2.5)

2.5 = 5 * b^1

2.5 = 5 *b

Divide each side by 5

2.5/5 = b

b = 1/2

y = 5 * (1/2)^x

Answer:

∠ f = 37°

Step-by-step explanation:

f and 37 are vertical angles and congruent, so

∠ f = 37°

Answer:

200

Step-by-step explanation:

A=b×L

A=20×10

A=200

Answer:

45

Step-by-step explanation:

Answer:

382.5

Step-by-step explanation:

9x10=90

9x9=81

13.5x9=121.5

9x10=90

180+81+121.5= 382.5

There are two triangles.

Area of a triangle = 1/2 x 10 x 9 = 45 square in.

45 x 2 = 90 square inches

One side is 9 x 9 = 81 square inches.

One side ix 10 x 9  = 90 square inches.

One side = 9 x 13.5 = 121.5 square inches.

Total surface area = 90 + 81 + 90 + 121.5 = 382.5 square inches.

Answer:

B.supplementary

Step-by-step explanation:

Angle ABC and Angle CBD are supplementary angles, which means they add up to 180 degrees

Step-by-step explanation:

Step 1:  Convert miles to feet

1 mile = 5280 feet

1.5 * 5280

7920 feet

Answer:  7920 feet

Answer:

x=3  y=2

Step-by-step explanation:

2x-y=4

7x+3y=27

Multiply the first equation by 3

3(2x-y)=4*3

6x - 3y+12

Add this to the second equation to eliminate y

6x -3y = 12

7x+3y=27

---------------------

13x +0y = 39

Divide each side by 13

13x/13 = 39/13

x = 3

Now find y

2x-y =4

2(3) -y = 4

6-y=4

Subtract 6 from each side

6-y-6 = 4-6

-y = -2

y=2

Answer:

38.47 square units

Step-by-step explanation:

All we have to do is first find the perimeter of the square (which is equal to the circumference of the circle), then find the radius of the circle and finally the area of the circle.

The square has a side that measures 5.5 units.

The perimeter of a square is given as:

P = 4L

where L = length of side of the square

Therefore, the perimeter of the square is:

P = 4 * 5.5 = 22 units.

This means that the circumference of the circle is 22 units.

The circumference of a circle is given as:

C = 2πR

and the area of a circle is given as:

[tex]A = \pi R^2[/tex]

where R = radius

Therefore:

22 = 2πR

=> R = 22 / (2 * 3.14)

R = 22 / (6.28)

R = 3.50 units

The area is therefore:

[tex]A = \pi * 3.50^2[/tex]

A = 38.47  square units

The area of the circle is 38.47 square units.

The area of the circle is approximately 15.64 square units, calculated using the perimeter of the square and circle formulas.

To find the area of the circle with a circumference equal to the perimeter of the square, we'll first calculate the perimeter of the square using its side length. Then, we'll use the circumference formula to find the radius of the circle. Finally, we'll use the area formula for a circle to find the area.

Step 1:

Calculate the perimeter of the square.

Perimeter of square = 4 * side length = [tex]\(4 \times 5.5 = 22\)[/tex] units.

Step 2:

Set up the equation for the circumference of the circle.

Circumference of circle =[tex]\(2\pi \times\)[/tex] radius = Perimeter of square.

Step 3:

Solve for the radius.

[tex]\[2\pi \times \text{radius} = 22\][/tex]

[tex]\[\text{radius} = \frac{22}{2\pi}\][/tex]

Step 4:

Use the radius to find the area of the circle.

Area of circle = [tex]\(\pi \times \text{radius}^2\)[/tex]

Step 5:

Substitute the value of the radius and calculate.

[tex]\[Area = 3.14 \times \left(\frac{22}{2\pi}\right)^2\][/tex]

[tex]\[Area \approx 15.64\][/tex]

The area of the circle with a circumference equal to the perimeter of the square is approximately [tex]\(15.64\)[/tex] square units.

Answer:

133.97 cubic yard

Step-by-step explanation:

For Cone

radius (r) = 4yd

height (h) = 8yd

Volume of the Cone

= π r^2 * h/3

= 3.14 * 4*4 *8/3 yd

= 133.97 cubic yard

I believe you are looking for, intersecting.

Answer:

V=Bh so Volume = π4.0 2 16.0 = 804.25

Step-by-step explanation:

Answer:

D. 80

Step-by-step explanation:

edge 2021

The perimeter of the parallelogram LMNO is 80 cm

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Given that, in a parallelogram LMNO, the length of L M is 22 cm and the length of M N is 18 cm.

Perimeter of a parallelogram = 2(sum of two adjacent sides)

= 2(18+22)

= 2×40

= 80

Hence, the perimeter of the parallelogram LMNO is 80 cm

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Final answer:

When two number cubes are rolled, the events of rolling the same number and getting an odd sum are mutually exclusive, as one excludes the possibility of the other occurring.

Explanation:

Two events are considered mutually exclusive if the occurrence of one event excludes the possibility of the other event occurring simultaneously. When examining whether the events of rolling two number cubes are mutually exclusive, we look at two particular events:

   The numbers rolled are the same.

   The sum of the numbers rolled is odd.

Two number cubes can simultaneously show the same number, which would be an even number (since the pairs would be (2,2), (4,4), or (6,6)) and not lead to an odd sum. Therefore, if we roll the dice and get two numbers that are the same, we cannot get an odd sum. This means that these two events cannot happen at the same time, so the correct answer is:

A. Yes because if one event occurs, the other can't occur.

Answer:

100

Step-by-step explanation:

100+90+85+95+80= 450,

450/5=90

She has to earn on her next assignment to attain an average of 90 for grade 100.

The average is the middle value of the given data set and is calculated by adding up all the numbers and dividing the result by the total quantity of figures added.

Amy’s current grades for her assignments in math class are 85, 90, 95, and 80.

Let x be the grade she has to earn on her next assignment to attain an average of 90.

The grade does she have to earn on her next assignment to attain an average of 90 is;

[tex]\rm Average =\dfrac{Sum \ of \ all \ grades}{Number \ of \ grades}\\\\ 90 =\dfrac{x+90+85+95+80}{5}\\\\ 90 \times 5 = x+350\\\\450=x+350\\\\x =450-350\\\\x=100[/tex]

Hence, she has to earn on her next assignment to attain an average of 90 for grade 100.

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Answer:

Kayla can put 9 stickers in each bag.

she can distribute it into bags of 9 stickers each of the same colour.

Step-by-step explanation:

Given;

yellow stickers = 36

red stickers = 27

blue stickers = 18

For her to distribute the stickers into bags so that each bag contains only one color of stickers and every bag has the same number of stickers without remainder.

We need to find the highest common factor of the number of the three colours.

36 = 4×9

27 = 3×9

18 = 2×9

We can see that they are all divisible by 9

Therefore, she can distribute it into bags of 9 stickers each

Final answer:

The greatest common divisor of 36, 27, and 18 is 9, so Kayla can put 9 stickers of the same color in each bag.

Explanation:

Kayla wants to distribute her stickers into bags, with each bag containing the same number of stickers of only one color. To find out how many stickers she can put in each bag, we need to find the greatest common divisor (GCD) of the numbers of stickers she has for each color. Kayla has 36 yellow stickers, 27 red stickers, and 18 blue stickers. The GCD of 36, 27, and 18 is 9. Therefore, Kayla can put 9 stickers in each bag.

Step-by-Step Solution

Identify the quantity of each color of stickers: yellow (36), red (27), blue (18).

Calculate the GCD of the three quantities: GCD(36, 27, 18) = 9.

Distribute the stickers into bags with 9 stickers of the same color per bag.

Answer:

150 degrees

Step-by-step explanation:

HOPE THIS HELPED!

The measure of an angle between 0° and 360° coterminal with 510° is 150°. The difference between coterminal angles yields 360°.

The angles that share a common terminal side are said to be coterminal angles. So, the difference between those angles is 360°.

The given coterminal angle is 510°.

So, the reference angle = 510° - 360° = 150°

Thus, the angle is required as a measure of 150°.

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The rent of the apartment during the 7th year of living in the apartment is $2414.

Given that, principal = $1200, rate of interest =10.5% and time period = 7 years.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]

[tex]A=1200(1+\frac{10.5}{100} )^7[/tex]

[tex]A=1200(1+0.105)^7[/tex]

[tex]A=1200(1.105)^7[/tex]

[tex]A=1200\times2.0116[/tex]

[tex]A=2413.88[/tex]

A ≈ $2414

Therefore, the rent of the apartment during the 7th year of living in the apartment is $2414.

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Final answer:

To calculate the 7th year rent after a 10.5% annual increase starting from an initial rent of $1200, use the formula for compound interest. The rent amounts to approximately $2277.60 for the 7th year.

Explanation:

Calculating Future Rent Increase

To calculate the rent of the apartment during the 7th year after a consistent annual increase, we need to apply the percentage increase formula within a compound interest framework:

Rentₙ = Rent₀ × (1 + rate)ⁿ

Where Rentₙ is the rent after n years, Rent₀ is the initial rent, rate is the annual increase rate in decimal form, and n is the number of years.

For an initial rent of $1200 with a 10.5% increase per year:

Rent for the 7th year will be calculated as follows:

Rent₀ = $1200

rate = 10.5% or 0.105 in decimal form

n = 6 (since we are starting from year 1 to year 7)

Using the formula:

Rent₇ = $1200 × (1 + 0.105)⁶

Upon calculation, the rent for the 7th year is approximately:

Rent₇ = $1200 × (1.105)⁶ ≈ $1200 × 1.898 = $2277.60

Thus, the rent of the apartment during the 7th year of living there would be approximately $2277.60

Answer:

Like a square, a rectangle has lines that are perpendicular to two other lines. This means it also has four right angles.

Step-by-step explanation:

Answer:

a right triangle

Step-by-step explanation:

Final answer:

The value of 3a+4b is 87 when a=17 and b=9. Using the kinematics equation v=u+at, the final velocity is calculated as 13.5 m/s given the initial conditions provided.

Explanation:

To find the value of 3a+4b when a=17 and b=9, we substitute the given values into the expression:

3(17) + 4(9) = 51 + 36 = 87.

Thus, the value of 3a+4b is 87.

The next part of the question involves using the kinematics equation v = u + at to find the final velocity v. We are given an initial velocity u = 3 m/s, an acceleration a = 1.5 m/s2, and a time t = 7 seconds. Plugging the values into the formula gives us:

v = 3 m/s + (1.5 m/s2)(7 s) = 3 m/s + 10.5 m/s = 13.5 m/s.

The final velocity after 7 seconds is therefore 13.5 m/s.

Answer: The height of the monitor is 12 inches.

Step-by-step explanation:

First, you need to acknowledge the Pythagorean Theorum,

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

You already have the c and the b , so you just have to plug them in to find a!

This is what it looks like when you substitute:

a² + 16² = 20²

Then, simplify.

a² + 256 = 400

Now, to isolate the variable, you have to move 256 to the other side. This, of course, means it changes from a positive to a negative number.

a² = 400 - 256

a² = 144

Now, you have to remove the square root from a. But, don’t forget, what you do to one side, you have to do to the other side. So, your equation will now look like this:

√a²  = √144

The square root of a squared is obviously just a! And the square root of 144 is 12. Therefore, we now know that:

a = 12

So, the height of the monitor was 12 inches.