The equation A equals P quantity 1 plus 0.06 over 4 end quantity all raised to the power of 4 times t represents the amount of money earned on a compound interest savings account with an annual interest rate of 6% compounded quarterly. If after 15 years the amount in the account is $16,497.06, what is the value of the principal investment? Round the answer to the nearest hundredths place.

Answer:42

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Volume = height x width x length

6 x 10 = 60

480 divided by 60 = 14

Answer:

Saanvi recorded the number of math problems she did for homework each night for 10 days.

Step-by-step explanation:

Here's what you need to do:

We know that Ryan can install 144 square feet of flooring in 3 hours.

So, if we take 144 square feet, and divide by 3 hours, 144 / 3, we end up with 48, meaning Ryan can install 48 square feet of flooring every hour.

Then, simply multiply 48 by 18, 48 x 18, and you end up with 864.

Meaning, in 18 hours, Ryan can install 864 square feet of flooring.

Answer: 864 square feet.

The function f(x) = 81 − x2 is increasing on the interval (−∞, 9) and decreasing on the interval (9, ∞).

Parabola is a type of curve which is defined by the quadratic equation. It has a distinct "U" shape, with the vertex of the curve being the highest or lowest point.

The point x = 9 is the vertex of the parabola, which marks the point at which the function changes from increasing to decreasing.

Since the function is a parabola, it is also a polynomial of degree 2, and it is always decreasing for points greater than the vertex, and increasing for points less than the vertex.

This means that the function is increasing on the interval (−∞, 9) and decreasing on the interval (9, ∞).

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Answer:

-4y2 +y - 12

Step-by-step explanation:

-3y2 - y2= -4y2

-y+2y= y

-8 - 4= -12

-4y2 + y - 12

Answer:

Step-by-step explanation:

The expression in standard form that represents the area of the square with side length s is given by:

A = s^2

However, if you want to substitute the value of s with the expression 5y+3, then the area expression becomes:

A = (5y+3)^2

Expanding the expression, we get:

A = 25y^2 + 30y + 9

Therefore, the expression in standard form that represents the area of the square with side length 5y+3 is 25y^2 + 30y + 9.

Answer:

a) There are four prime numbers between 1 and 10: 2, 3, 5, and 7. So the probability of drawing a prime number is 4/10 or 2/5, which is 20% and not 10%. Therefore, option (a) is not correct.

b) As we saw in part (a), the probability of drawing a prime number is 2/5 or 40% (since 2/5 is equivalent to 0.4). Therefore, option (b) is correct.

c) The probability of drawing a prime number is 2/5 or 40%, which is not 25%. Therefore, option (c) is not correct.

d) As we saw in part (a) and (b), the probability of drawing a prime number is 2/5 or 40%, which is not 50%. Therefore, option (d) is not correct.

So, the correct answer is (b) 25%.

Hope This Helps!

The vertex is ( 6 , 1 ). The vertex of the graph of the equation maximum.

What is parabola in math?

Each point on a parabola, which has the shape of a U, is situated at an equal distance from the focus, a fixed point, and the directrix, a fixed line. All of the parabola-related ideas are discussed here since it is a crucial component of the conic section subject.

the equation  y = -x² + 6x + 1

  Use the formula: -b/2a

       = -6/-1

       = 6

The x-coordinate of the vertex is 6

Plug the x value back into the original equation to find the y-coordinate of the vertex

     y = -x² + 6x + 1

        = -(6)² + 6 * 6 + 1

        = -36 + 36 + 1

        = 1

The vertex is = ( 6 , 1 )

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Answer:

[tex]16-(6.25+2*2.25)[/tex]

Step-by-step explanation:

To find the amount of money she has left, you want to subtract the price of the ticket and the price of the two snacks from the amount of money she starts with.

So we want to subtract 6.25 once and subtract 2.25 twice (because she bought two snacks) from 16

16-6.25-2*2.25

Or you can also do this by adding up the monetary value of the ticket and the snacks and subtract that from the initial amount of money that Parvati has

16-(6.25+2*2.25)

(I am assuming that the "2.2.25" is supposed to say [tex]2*2.25[/tex])

We can cut 6 pieces of rope measuring 5/8 of a foot from a rope of 4 3/8 feet, with some rope left over.

Area is a measurement of the size of a surface or a region in a two-dimensional space. It is expressed in square units, such as square inches (in²), square meters (m²), or square feet (ft²). To find the area of a shape, you need to multiply its length by its width, or use an appropriate formula depending on the shape. For example, the formula for the area of a rectangle is A = l × w, where A is the area, l is the length, and w is the width.

To find the number of pieces of rope measuring 5/8 of a foot that can be cut from a rope of 4 3/8 feet, we need to divide the length of the rope by the length of each piece of rope:

4 3/8 feet = 4 + 3/8 feet = 4 feet + (3/8) x 12 inches = 4 feet + 3 inches = 51 inches

Each piece of rope measures 5/8 of a foot, which is equivalent to 5/8 x 12 inches = 7.5 inches.

Now we can divide the length of the rope (in inches) by the length of each piece of rope (in inches) to find the number of pieces:

51 inches ÷ 7.5 inches ≈ 6.8

Therefore, we can cut 6 pieces of rope measuring 5/8 of a foot from a rope of 4 3/8 feet, with some rope left over.

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The solution will be b=4, the number b such that the average rate of change of f on the interval [2, b] is - 1/18 if the provided assertion is correct.

For instance, a range between 0 and 10 would include all of the integers between them, not just 1, 2, 3, 4, 5, 6, 7, 8, and 9. These would additionally incorporate fractional numbers like 1.3 and components like 1/10. We therefore have the job. We must determine b to the extent that the interval [2, b]'s average percentage of change or slope is -1/8. Discover f first(2).

f(2) = 1/(2) = 1/2

So, we have the point (2, 1/2)

At point b, f(b) = 1/b.

Let's plug this into the slope formula

We simply have to figure out b now. Let's start by multiplying the divisor and fraction by b.

Now, cross multiply.

Solve for b. Use the factors -4 and -2 to multiply.

Thus, b=4 or b=2.

However, b=2 cannot be the answer because the range [2,2] has no significance. Thus, b=4.

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Answer:   76.67%

Step-by-step explanation:

Answer:

f(x) = - [tex]\frac{1}{2}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 0 ) , x- intercept and (x₂. y₂ ) = (0, - 4) , y- intercept

m = [tex]\frac{-4-0}{0-2}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , then

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute (- 4, 7 ) into the partial equation

7 = - [tex]\frac{1}{2}[/tex] (- 4) + c = 2 + c ( subtract 2 from both sides )

5 = c

y = f(x) = - [tex]\frac{1}{2}[/tex] x + 5 ← equation of function

Answer:

Step-by-step explanation:

Solution:

We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).

The GCF of 305 and 60 is 5.

Divide both terms by 5.

305 ÷ 5 = 61

60 ÷ 5 = 12

Therefore:

305 : 60 = 61 : 12

The surface area of the rectangular prism graphed is given as follows:

10.12 ft³.

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

Converting the mixed numbers to decimal, the dimensions of the rectangular prism are given as follows:

1.3 ft, 1.4 ft and 1.2 ft.

Hence the surface area of the prism is given as follows:

S = 2 x (1.3 x 1.4 + 1.3 x 1.2 + 1.4 x 1.2)

S = 10.12 ft³.

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Using the graph of the picewise function we can see that:

Here we have a piecewise function and we want to evaluate it in different values of x.

First we want to get:

i(-3)

Notice that at x = -3 we have a closed circle in the second line, the one constant at y = 2, so we need to use that value here:

i(-3) = 2

The closed dot means that the value belongs to that line, while a open one (like the one that is just above) means that the value does not belong.

For the second evaluation:

i(-4)

This time we just need to look at the line in the left, here we can see that: i(-4) = 3

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There is a 15.74% chance that a randomly chosen employee will earn between $450 and $550.

The study of random occurrences or phenomena falls under the umbrella of the mathematic discipline known as probability. It is the measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

To find : the probability that a worker selected at random makes between $450 and $550

z = (x - μ) / б

where б is the standard deviation, μ is the mean, and x is the value we wish to normalize.

For $450, we have:

z₁ = (450 - 400) / 50 = 1

For $550, we have:

z₂ = (550 - 400) / 50 = 3

We can then use a standard normal distribution table or calculator to find the area under the standard normal curve between z₁and z₂:

P(z₁< z < z₂) = P(1 < z < 3) = 0.1574

This means that the probability that a worker selected at random makes between $450 and $550 is 15.74%.

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Answer: x=6.5

Step-by-step explanation: 13 x 10=130

845/130= 6.5

The measure of arc CD is equal to the measure of angle BCD, which is 240 degrees.

In the given diagram, we can see that angle ACD is a right angle, since it is formed by the radius AC and tangent CD at point C.

Therefore, angle BCD is equal to angle ACD, which is 90 degrees.

Since angle BCD is an exterior angle of triangle BCF, it is equal to the sum of the two remote interior angles, which are angles BFC and FCB.

Angle BFC is equal to angle ABC (since they are opposite angles), which is 60 degrees.

Similarly, angle FCB is equal to angle ACF, which is also 60 degrees.

Therefore, angle BCD is equal to angle BFC + angle FCB, which is 60 + 60 = 120 degrees.

Now, since arc CD is subtended by angle BCD, its measure is also equal to 120 degrees.

Hence, the measure of arc CD is 120 degrees.

Similarly, angles ACF and FCB are opposite angles in the cyclic quadrilateral AFCB, so they are supplementary. Therefore, angle FCB is equal to 180 - angle ACF,

Which is also 180 - 60 = 120 degrees.

Now we can apply the exterior angle theorem to find the measure of angle BCD. We have:

angle BCD = angle BFC + angle FCB

= 120 + 120

= 240 degrees

Finally, we can conclude that the measure of arc CD is equal to the measure of angle BCD, which is 240 degrees.

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Answer:249.98

Step-by-step explanation: i had a question like this before.

In a regular hexagon, where FGHIJK shares a common center with square ABCD on a coordinate plane. ||. It is Across any of the perpendicular bisectors of the sides of the square that the combined figure can reflect onto itself.

In Regular Hexagon FGHIJK, we have 6 lines of reflection across which the hexagon reflects onto itself. Those lines are:

3 perpendicular bisectors of sides i.e. perpendicular bisector of IJ , IH and GH

3 lines passing through vertices i.e. HK, IF and GJ.

While in Square, we have 4 line of reflection across which the square reflects onto itself. Those lines are:

2 perpendicular bisectors of sides AB and BC i.e. HK and perpendicular bisector of CD

2 diagonals of square i.e. AC and BD

Note as well that from figure we know that perpendicular bisector of CD and perpendicular bisector of IJ is the same line.

So, for combined figure we have to take common lines from both figures i.e. perpendicular of sides CD or IJ and line HK.

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Full Question:

Although part of your question is missing, you might be referring to this full question: See the attached image and the questions below.


In a regular hexagon, FGHIJK shares a common center with square ABCD on a coordinate plane. || . Across which lines can the combined figure reflect onto itself?
A. any of the perpendicular bisectors of the sides of the hexagon
B. either diagonal of the square
C. any of the perpendicular bisectors of the sides of the square
D. there are no lines across which this figure can reflect onto itself

The perimeter of the circle formed by bending the rectangular wire will be equal to the length of the wire.

Perimeter of the circle = Length of the wire

2πr = 2(l+b) where r is the radius of the circle, l is the length of the wire, and b is the breadth of the wire.

Substituting the given values, we get:

2 x 3.14 x r = 2(32 + 12)

6.28r = 88

r = 14 cm

Therefore, the radius of the circle is 14 cm.

Answer:

14.01 cm

Step-by-step explanation:

The length of the wire is equal to the perimeter of the rectangle. So, the length of the wire is:

When this wire is bent into a circle, its length becomes equal to the circumference of the circle. The formula for the circumference of a circle is:

(let r = radius)

So, we can write:

Solving for r, we get:

So, the exact value of the radius of the circle formed by bending this rectangular wire is 14.01 cm.

The relation is not a function, but rather a circle with center at the origin and radius 2.

Given the relation in the question;

x² + y² = 4.

First, lets solve for y.

x² + y² = 4

Subtract x² from both sides

x² - x² + y² = 4 - x²

y² =  4 - x²

Take the squre root of both sides

y = ±√( 4 - x² )

This shows that for a given value of x, there are two possible values of y. One positive and one negative, that satisfy the equation.

Therefore, the relation is not a function.

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Answer:

Positive

Step-by-step explanation:

It's a positive number

If it doesn't have a (-) it's a positive number

Step-by-step explanation:

5(2 + 1) can be simplified using the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Using this property, we get:

5(2 + 1) = 5(2) + 5(1)

Simplifying the expression further, we get:

5(2) + 5(1) = 10 + 5 = 15

Therefore, 5(2 + 1) is equivalent to 15.

According to the solving $310 money you have in savings after 26 weeks, we can use either the recursive or explicit formula:

The explicit equations for L-functions are Riemann's relations between sums over an L-function's complex number zeroes and sums over prime powers for the Riemann zeta function.

a) Recursive formula:

Let S(n) be the amount of money in savings after n weeks. Then:

S(0) = 50 (initial amount)

S(n) = S(n-1) + 10 (deposit of $10 per week)

b) Explicit formula:

The explicit formula for this sequence is:

S(n) = 50 + 10n, where n is the number of weeks.

c) To find how much money you have in savings after 26 weeks, we can use either the recursive or explicit formula:

Using the recursive formula:

S(0) = 50 (initial amount)

S(1) = S(0) + 10 = 50 + 10 = 60

S(2) = S(1) + 10 = 60 + 10 = 70

S(3) = S(2) + 10 = 70 + 10 = 80

and so on, until:

S(26) = S(25) + 10 = 310

Therefore, after 26 weeks, you have $310 in savings.

Using the explicit formula:

S(26) = 50 + 10(26) = 50 + 260 = 310

after 26 weeks, you have $310 in savings.

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Answer:

The answer to your problem is, A. 536,866,822

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

If a fair coin is tossed 29 times, the total number of outcomes will be expressed as: [tex]2^{29} = 536,870,476[/tex]

If at least 2 tails occur, the expected outcome will be 29 times

Pr(at least 2 tails occur) = [tex]2^{29} - 29 - 1[/tex]

Pr(at least 2 tails occur) = [tex]536,870,912 - 30 = 536,866,822[/tex]

Thus the answer to your problem is, A. 536,866,822