How long will it take for $2100 to grow to $47200 at an interest rate of 4.5% if the interest is compounded continuously? Round the number of years to the nearest
hundredth

Answer:

The factors are..

1,3

Step-by-step explanation:

Hence we see that:

x2+4x+3= (x+3)(x+1)

Therefore the factors are

x= 3 or 1

Answer:

(x-1)(x-3)

Step-by-step explanation:

-3 times -1 equals 3 which is the number at the end

and -3-1=-4 which is the number in the middle

the put -3 and -1 into 2 different parentheses

(x-3)(x-1)

Answer:

100,000x5=500,000

500,000+250,000=750,000/100,000=7.5

5.0x14= $70

7.5x14= $105

They got $35

Answer:

For everyone in the future who uses this answer site. The person at the bottom with the answer 125,000 is correct. Even though I could not thank you commenter I thank you through this!

Step-by-step explanation:

To determine the number of ways to form a committee of 6 students from 30 council members, we use the combination formula C(30, 6), which yields 593,775 different combinations.

The question asks how many possible committees of 6 students can be formed from a group of 30 students on the student council. This is a combinatorial problem and can be solved using the combination formula which is given by C(n, k) = n! / (k! * (n - k)!), where C(n, k) is the number of combinations, n is the total number of items, and k is the number of items to choose. So to answer the question, we must calculate C(30, 6).

Calculating C(30, 6), we have:

C(30, 6) = 30! / (6! * (30 - 6)!)

C(30, 6) = 30! / (6! * 24!)

C(30, 6) = (30 × 29 × 28 × 27 × 26 × 25) / (6 × 5 × 4 × 3 × 2 × 1)

C(30, 6) = 593,775

There are 593,775 different ways to form a committee of 6 students from a student council of 30 members.

Answer:

-4

Step-by-step explanation:

y= -2x - 3

First, plug in 5 for y

5= -2x - 3

+3        +3

8= -2x

Divide by -2

-4= x

Final answer:

To find x when y = 5 in the equation y = -2x - 3, the solution is x = -4.

Explanation:

In the given equation y = -2x - 3, to find x when y = 5, substitute y with 5 in the equation:

5 = -2x - 3

Solve for x:

Add 3 to both sides: 5 + 3 = -2x

8 = -2x

Divide by -2: x = -4

Answer:

V = 330.513 cm^3

Step-by-step explanation:

Area = l x w and with a square the length and width are the same, additionally the volume of a pyramid can be found by using the formula (L)(w)(h)/3 so

8.7 x 8.7 = 75.69cm^2

75.69 x 13.1 = 991.539

991.539 ÷ 3 = 330.513 cm^3

Mark as brainliest please :)

Final answer:

The volume of a pyramid with a square base of side 8.7 cm and height 13.1 cm is calculated using the formula for volume, resulting in 330.35 cm³.

Explanation:

To find the volume of a pyramid with a square base, you can use the formula V = (1/3) × base area × height, where the base area for a square is given by side length × side length.

In this case, the side length of the base is 8.7 cm, and the height of the pyramid is 13.1 cm.

First, calculate the area of the base:

Base Area = 8.7 cm × 8.7 cm = 75.69 cm²

Then, calculate the volume of the pyramid:

Volume = (1/3) × 75.69 cm² × 13.1 cm = 330.35 cm³

Therefore, the volume of the pyramid is 330.35 cm³.

We have been given that Mrs. Culland is finding the center of a circle whose equation is [tex]x^2+y^2+6x+4y-3 = 0[/tex] by completing the square. We are asked to find the final step of her work.

Let us complete the square.

We know that to complete square, we need to add the half the square of coefficient of x and y term.

[tex]x^2+y^2+6x+4y-3+3 = 0+3[/tex]

[tex]x^2+6x+y^2+4y=3[/tex]

We can see that coefficient of x is 6 and coefficient of y is 4.

[tex](\frac{6}{2})^2=3^2=9[/tex]

[tex](\frac{4}{2})^2=2^2=4[/tex]

Now we will add 9 and 4 on both sides as:

[tex]x^2+6x+9+y^2+4y+4=3+9+4[/tex]

[tex](x^2+6x+9)+(y^2+4y+4)=16[/tex]

Now we will complete the square as:

[tex](x+3)^2+(y+2)^2=4^2[/tex]

We know that standard form of equation of a circle is in form [tex](x-h)^2+(y-k)^2=r^2[/tex], where point (h,k) represents center of circle and r represents radius of circle.

We can rewrite our equation as:

[tex](x-(-3))^2+(y-(-2))^2=4^2[/tex]

Now we can see that center is at point [tex](-3,-2)[/tex].

Therefore, the equation of the circle would be [tex](x+3)^2+(y+2)^2=4^2[/tex] with a center at point [tex](-3,-2)[/tex].

Answer:

d

Step-by-step explanation:

egd 2021

Answer:

y=1/8(-x^2+4x+44

Step-by-step explanation:

In this question the given focus is (2,4) and a directrix of y = 8 and we have to derive the equation of the parabola.

Let (x,y) is a point on the given parabola.Then the distance between the point (x,y) to (2,4) and the distance from (x,y) to diractrix will be same.

Distance between (x,y) and (2,4)

= √(x-2)²+(y-4)²

And the distance between (x,y) and directrix y=8

= (y-8)

Now √(x-2)²+(y-4)² = (y-8)

(x-2)²+(y-4)² = (y-8)²

x²+4-4x+y²+16-8y = y²+64-16y

x²+20+y²-4x-8y = y²-16y+64

x²+20-4x-8y+16y-64=0

x²+8y-4x-44 = 0

8y = -x²+4x+44

Answer:

3

Step-by-step explanation:

Answer:

314

Step-by-step explanation:

volume of cone = 1/3 * pi * r^2 * h = 1/3 * pi * 5^2 * 12

Answer:

the answer is 1/3

Step-by-step explanation:

If you dilate (3,2) by 3 it will come out a (9,6). Therefore, the scale factor is 1/3

Answer:

12 / 6 = 2

Step-by-step explanation:

If there are a total of 12 cookies, and these cookies will be divided evenly among 12 children, to find how many cookies each children will have, we just need to divide the total number of cookies by the total number of children:

Number of cookies per children = number of cookies / number of children

Number of cookies per children = 12 / 6 = 2

So each children will get 2 cookies.

Answer:

A.) 7x x 5=$50.00

Step-by-step explanation:

You can eliminate B and C as they don't include the 5 different stores.

D is incorrect because it doesn't include the 7 items.

Therefore, A is correct because 7x is the 7 items multiplied by the average cost per item and you multiply by 5 because she does that at each of the 5 stores. It = to 50 because she started with $65 but ends up with $15 so you subtract $65 with $15 to get $50 as that's how much she spent.

Answer:

A

Why:

$65.00-$15.00=$50.00

She visited 5 stores, and she bought 7 items.

So therefore it would be A.

Sorry that my answer was short.

Answer:

To the nearest hundredth : 628.32 [tex]cm^2[/tex]

To the nearest whole number : 628 [tex]cm^2[/tex]

Step-by-step explanation:

The formula for the area of a circle is : [tex]\pi*radius^2[/tex]

To work out the area you would first need to work out the radius. You can do this by dividing the diameter of 40 cm by 2, this gives you 20 cm. This is because the radius is half of the diameter.

Now that we have worked out the radius, the next step would be to work out the area. You can do this by multiplying pi by the radius of 20 squared, this gives you 1256.64.

The final step is to work out the area of this semi-circle. You can do this by dividing the area of 1256.64 by 2, this gives you 628.32 [tex]cm^2[/tex]. This is because a semi-circle is half of a circle.

1) Divide 40 by 2.

[tex]40/2=20 cm[/tex]

2) Multiply pi by 20 squared.

[tex]\pi*20^2=1256.64 cm^2[/tex]

3) Divide 1256.64 by 2.

[tex]1256.64/2=628.32 cm^2[/tex]

The area of the semicircle is approximately 628 square centimeters.

To find the area of a semicircle with a given diameter, we need to use the formula for the area of a circle and then divide it by 2, since a semicircle is half of a circle.

The formula for the area of a circle is:

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

where [tex]\( r \)[/tex] is the radius of the circle. Given the diameter is 40 cm, we can find the radius by dividing the diameter by 2:

[tex]\[ r = \frac{40 \, \text{cm}}{2} = 20 \, \text{cm} \][/tex]

Now, we can calculate the area of the full circle:

[tex]\[ A_{\text{circle}} = \pi (20 \, \text{cm})^2 = 400\pi \, \text{cm}^2 \][/tex]

Since the semicircle is half of the full circle, the area of the semicircle is:

[tex]\[ A_{\text{semicircle}} = \frac{1}{2} A_{\text{circle}} = \frac{1}{2} \times 400\pi \, \text{cm}^2 = 200\pi \, \text{cm}^2 \][/tex]

Using [tex]\(\pi \approx 3.14159\)[/tex]

[tex]\[ A_{\text{semicircle}} \approx 200 \times 3.14159 \, \text{cm}^2 \approx 628.32 \, \text{cm}^2 \][/tex]

Rounding to the nearest whole number:

[tex]\[ A_{\text{semicircle}} \approx 628 \, \text{cm}^2 \][/tex]

Answer:

B D E

Step-by-step explanation:

i did the quiz

Answer:

2,4,5 choices

Step-by-step explanation:

I did the quiz

The answer is 9 times. This is because if the radius of A is r, and the radius of B is 3r, the radii will be squared while finding the formula. So, r will become r squared, while 3r will become 9r squared.

The area of triangle ABC, with sides of 8 km and 5 km and an internal angle of 150 degrees, is calculated using the formula for the area of a non-right triangle. The result is 10 km².

The subject of this question is Mathematics, specifically Geometry dealing with calculation of area of a triangle using the properties of a non-right triangle.

The area of the triangle ABC can be calculated using the formula 0.5 * a * b * sin(C), where C is the angle between sides a and b.

Here, a is the length from A to B, which is 8 km; b is the length from B to C, which is 5 km; and the angle C (angle ABC) is 150°.

Plug these values into the formula: 0.5*8km*5km*sin(150°) which equals to 10 km².

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Answer:

R=7[tex]\pi[/tex]/Ф

7Pi/Theta

Answer:

13/20

Step-by-step explanation:

To find this, divide 13 by 20 to get .65

Hope this helped!

Answer:

13/20

Step-by-step explanation:

Answer:

-The answer for the radius:

[tex]\sqrt{61} = r[/tex]

Step-by-step explanation:

-The equation of a circle is:

[tex](x-h)^2+(y-k)^2=r^2[/tex] (where the center is known as [tex](h,k)[/tex], the point is [tex](x,y)[/tex] and the radius known as [tex]r[/tex]).

-Use both the center (-2,-1) and the point (-7,-7) for the equation:

[tex](-7+2)^2+(-7+1)^2=r^2[/tex]

-Then, solve the equation to get the radius:

[tex](-7+2)^2+(-7+1)^2=r^2[/tex]

[tex](-5)^2+(-6)^2=r^2[/tex]

[tex]25+36=r^2[/tex]

[tex]61 = r^2[/tex]

[tex]\sqrt{61} = \sqrt{r^2}[/tex]

[tex]\sqrt{61} =r[/tex]

So, therefore the radius is [tex]\sqrt{61}[/tex] .

Answer:

201.06 (2 decimal places)

Step-by-step explanation:

new radius 28 + 4 = 32

diameter = 64

circumference of the fence

= pi x d

= pi x 64

= 201.0619

Answer:

Radius AB = 9.3 units

Step-by-step explanation:

Given:

BC (tangent) make right angle with radius AB.

AC = 16 units

BC = 13 units

Find:

Radius AB = ?

Computation:

Using Pythagoras theorem:

[tex]Hypotenuse^2 = Perpendicular^2 +Base^2\\\\AB =\sqrt{AC^2 -BC^2}\\\\ AB =\sqrt{16^2 -13^2}\\\\AB =\sqrt{256 -169}\\\\AB =\sqrt{87}\\\\AB =9.327[/tex]

Radius AB = 9.3 units

The question lacks clear context for the radius calculation, but assuming AC and BC are sides of a right triangle with the hypotenuse as the diameter of a circle, the radius can be found using the Pythagorean theorem. The calculated radius would be approximately 10.307764.

The question seems to be asking for the radius of a circle given certain measurements from a triangle. However, the information provided is ambiguous as it lacks context and specifics such as which geometric scenario we are dealing with. Nonetheless, assuming that AC and BC are legs of a right triangle, and if the hypotenuse is the diameter of a circle, we can calculate the radius using the Pythagorean theorem.

To find the radius (R), we would expect to have a right triangle with sides AC and BC, and a hypotenuse that is twice the radius. However, the lengths given in the question (AC=16 and BC=13) do not correspond to one of the formulae provided which suggests using the lengths in a Pythagorean relationship. Instead, if these lengths are for a right-angled triangle, we would calculate the hypotenuse as follows:

√(AC² + BC²) = √(16² + 13²) = √(256 + 169) = √425 ≈ 20.615528

Therefore, if the hypotenuse is the diameter of the circle, the radius R would be approximately half of this value, or 10.307764.

Answer:

7. A- 5√2

9. C- 6√2

Step-by-step explanation:

Let's begin with question 7 asking to simplify √50.

We need to ask ourselves the question if 50 has a factor that is a square. It does!

We can break √50 into √25·2. Since 25 is a square, we can take it out of the radical by taking out its square root like this:

5√2.

For question 9, we can simply do the same exact process. √72 can be broken into a factor that is a perfect square as well!

√72 --> √36·2

Now, take the square root of 36 out of the radical to become:

6√2

Here are your answers!

Answer:

7 is A

Step-by-step explanation:

50 can be turned into 2 and 25 and you can simplify 25 into 5 giving you 5 to the square root of 2

Answer:

3.4

Step-by-step explanation:

Answer: The surface area for this cylinder is 252*pi square inches.

Step-by-step explanation:

The surface area of a cylinder can be calculated by using the following formula:

surface area = 2*pi*r² + 2*pi*r*h

Applying the data from the problem, we have:

surface area = 2*pi*(6)² + 2*pi*(6)*15

surface area = 2*pi*36 + 180*pi

surface area = 72*pi + 180*pi

surface area = 252*pi

The surface area for this cylinder is 252*pi square inches.

Step-by-step explanation: edge 2021

The surface area of the cylinder, given h = 15 inches and r = 6 inches, is 252π square inches.

To find the surface area (SA) of a cylinder, we use the formula [tex]\(SA = 2\pi r^2 + 2\pi rh\)[/tex], where r is the radius and h is the height. Given h = 15 inches and r = 6 inches, we substitute these values into the formula:

[tex]\[SA = 2\pi(6)^2 + 2\pi(6)(15)\][/tex]

[tex]\[SA = 2\pi(36) + 2\pi(90)\][/tex]

[tex]\[SA = 72\pi + 180\pi\][/tex]

[tex]\[SA = 252\pi\][/tex]

Thus, the surface area of the cylinder is 252π square inches. This includes the areas of the two circular bases and the lateral surface area formed by the curved surface.

Answer:

1/10

Step-by-step explanation:

In the question above we are given two data sets

a) A number cube labelled and it rolled, 1 to 6

b) A word called Music

We are asked to find the probability of

obtaining a 6 from the rolled dice and picking a consonant.

Step 1

Probability = Number of Possible Outcomes/ Number of events

Probability of obtaining a 6 from the rolled cube = P(6) = 1/6

Step 2

Probability = Number of Possible Outcomes/ Number of events

In the Letter MUSIC, we have 5 letters,

2 Vowels and 3 consonants

The Probability of Obtaining an Consonant = Number of possible outcomes ( Number of consonants) ÷ Number of events ( Number of letters in MUSIC)

P ( Consonant) = 3/5

Step 3

This is the final step

And we are to find the Probability of P(6 and consonant)

P( 6 and Consonant ) = P (6) × P ( Consonant)

P ( 6 and Consonant) = 1/6 × 3/5

= 3/30 = 1/10

Therefore, the Probability of obtaining P(6 and consonant) = 1/10.

Final answer:

The probability of rolling a 6 on a six-sided die and selecting a consonant from the word MUSIC is 1/10.

Explanation:

The probability of rolling a 6 on a number cube and selecting a consonant from the word MUSIC is found by multiplying the probabilities of the two independent events. The probability of rolling a 6 on a six-sided die is 1/6. The word MUSIC has three consonants: M, S, and C. The probability of choosing a consonant from MUSIC is 3/5, since there are 5 letters in total and 3 of them are consonants.

Therefore, the probability of both events occurring is:
P(6 and consonant) = P(6) × P(consonant) = (1/6) × (3/5) = 1/10.

Answer:

120 pixels wide by 70 pixels high

Step-by-step explanation:

Think about it...

The image is 600/350

that is equivalent to 12/7 or 7:12

The space provided is 120/70

that is equivalent to 12/7 or 7:12

Since the ratios are the same the largest possible size the image can be is 120/70

The largest image of the school mascot that will fit in the web page is 120 pixels wide by 70 pixels high, which is the same aspect ratio as the original image size of 600 pixels wide by 350 pixels high.

Your task is to determine the biggest possible size for the school mascot image on the school web page. The spot for the mascot on the webpage is restricted to 120 pixels wide by 70 pixels high, while the actual digital image is 600 pixels wide by 350 pixels high.

The image needs to keep its aspect ratio (the ratio of width to height) in order to prevent distortion. The aspect ratio of the digital image is 600/350 (or 60/35 when simplified), which equals 12/7. Therefore, the mascot image also needs to have a 12/7 ratio to fit in the webpage space perfectly.

The way to do this is to scale down the image. Scaling works equally on both width and height of the image, therefore, we can start by scaling down the width from 600 pixels to 120 pixels. To calculate the scale factor, we divide 120 (the width of the webpage space) by 600 (the width of the image). The scale factor is 0.2 or 20%.

Applying this scale factor to the height: Scale factor * height of image = 0.2 *350 = 70 pixels, which is exactly the height of the webpage space. So, the largest image of the mascot that will fit in the webpage is 120 pixels wide by 70 pixels high, which maintains the same aspect ratio as the digital image.

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Answer:

Step-by-step  expthe second term is −5. We include ... the like terms are 2x and 4x, 3y and −5y. What do we do ... b) What number is the coefficient of y ? −4. c) What ... m) 4x² − 5x² + x² = 0. Problem 5. ... d) (5xy − 3x + 2y − 1) − (2xy − 7x − 8y + 6) ... We can therefore state the following rule for subtraction. ... Subtract x² − 5x + 7 from 3x² − 8x − 2.lanation:

Answer: D

In(2x^5/y)

Step-by-step explanation:

Answer:

A) 5/7 and 2/6 B) 4/7

Step-by-step explanation:

First find the total and then establish probability for each color: 2+5 = 7 total marbles. [tex]\frac{2}{7}[/tex] for blue and [tex]\frac{5}{7}[/tex] for red. Because you don't replace the marble you took out the total will do down one but the number of blue will not be affected to it just changed from [tex]\frac{2}{7} to \frac{2}{6}[/tex]

On part b I'm a little confused, are you putting a blue marble in the bag and then finding red's probability? If so, you are in theory replacing the first red marble so the total will be 7 again but since it's a blue marble your probabilities change to [tex]\frac{3}{7}[/tex] for blue and [tex]\frac{4}{7}[/tex] for red.

Answer

We have,

Volume of pyramid = 4834 in³

Base area of the pyramid = ?

Assuming height of the pyramid = 20 in

We know that

Volume of pyramid =[tex]\dfrac{hlw}{3}[/tex]  

           [tex] 4834=\dfrac{20\time lw}{3}[/tex]  

           l w = 725.1 in²

Hence, area of the base of the pyramid is equal to 725.1 in².

Answer:

  5. yes

  6. no

Step-by-step explanation:

5. yes

You know this because you're familiar with the first few Pythagorean triples:

   (3, 4, 5), (5, 12, 13), (7, 24, 25), ...

If you're not, you can use the Pythagorean theorem to check. The sides will form a right triangle if and only if they satisfy the Pythagorean theorem.

  13^2 = 12^2 +5^2

  169 = 144 + 25 . . . . . . true

__

6. no

Your knowledge of numbers tells you that these numbers cannot satisfy the Pythagorean theorem.* The sum of an even and and odd number cannot be even. (The square of a number has the same parity as the number itself.)

_____

* Thanks to Brainly, I recently figured out that you can apply a parity test to candidates for right triangle sides. The number of odd-length sides must be even. There cannot be a right triangle with integer side lengths, only one of which is odd.