Rose invests $80 in an account that pays 1% annual interest, compounded monthly.
Emily invests $50 in an account that pays 2% annual interest, compounded weekly.
Whose balance is greater after 10 years?
Type Rose or Emily

[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3(ab^2)^2}{6a^3b^{-3}}\implies \cfrac{3}{6}\cdot \cfrac{(ab^2)^2}{a^3b^{-3}}\implies \cfrac{1}{2}\cdot \cfrac{(a^2b^4)}{a^3b^{-3}}\implies \cfrac{1}{2}\cdot \cfrac{b^4 b^3}{a^{-2}a^3} \\\\\\ \cfrac{1}{2}\cdot \cfrac{b^{4+3}}{a^{-2+3}}\implies \cfrac{1}{2}\cdot\cfrac{b^7}{a^1}\implies \cfrac{b^7}{2a}[/tex]

The location of B such that the ratio of AB to BC is given as follows:

B = 28.

The location of B in the context of this problem is obtained applying the proportion, which is the ratio between the locations.

The coordinates of each point in this problem are given as follows:

The length of each segment in this problem is given as follows:

The ratio of AB to BC is 3 to 1, hence the following proportional relationship is established:

AB/BC = 3.

(x - 4)/(36 - x) = 3.

Applying cross multiplication, we can solve to obtain the value of x, representing the location of B, as follows:

x - 4 = 108 - 3x

4x = 112

x = 112/4

x = 28.

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Part 1: A = 0, B = 2, C = 3, D = 0, E = -2

Part 2: The derivative f'(3) is 6.

Part 3: The equation of the tangent line to the curve y = f(x) at x = 3 is y = 6x – 15.

This equation of the tangent line can be found by substituting x = 3 into the simplified difference quotient expression C + Dh + Eh2 , and then taking the limit as h approaches 0.

This expression can then be rearranged to give the equation of the line, which is y = 6x – 15. The equation of the tangent line gives the slope of the line at the given point, in this case x = 3. The slope of the line is 6, which is the same as the derivative of the function at the given point.

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Therefore the numerical order of the dimensions of rectangular prism is 8, 12

The minimal set of coordinates required to represent any point inside a mathematical space is known as the dimension of the space in physics and mathematics. As a result, a line has a dimension of one since a point on it may be specified by a single coordinate, such as the point at 5 on a number line.

We have a minimum set when a group of words can all be distinguished from one another by altering one phoneme (always in the same location in the word). feat, fit, fat, fate, and foot were used. Big, Pig, Rig, Fig, Dig, and Wig might be included in another minimum list based on consonant phonemes.

The equation for the volume of a rectangular prism:

V = l × w × h

Given dimensions are x, x-2, and x+8

V = (x)(x-2)(x+8) = 96

x^3 - 2x^2 + 8x = 96

x^3 - 2x^2 + 8x - 96 = 0

(x-12)(x+4)(x-8) = 0

Therefore, x = 12, -4, 8

As the dimension of prism can't be negative, we can discard -4 as one of the dimension.

Thus, the numerical order of the dimensions of rectangular prism is 8, 12

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Jim will need to sail 4 miles across the lake from the marina to Kingston.

Miles is a unit of measurement used to measure the distance between two locations. It is equal to 1.609 kilometers and is commonly used in the United States and the United Kingdom. Miles are frequently used to measure the distance between two cities, the distance a person has traveled, or the length of a road or highway. It is also sometimes used to measure the distance of a flight.

Since he is driving 16 miles from the boat launch to the marina, he will have covered a total of 20 miles by the time he arrives at the marina. From there, it is 4 more miles to Kingston. Therefore, he will need to sail a total of 4 miles to reach his destination.

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312%, 312' 4', 13, 9, 4.2 x 10-2. This is a decending order.

What is meant by decending?

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Answer:

2001

Step-by-step explanation:

First, let us find the circumference of the wheel ( circle ) using the below formula.

C = 2πr

Here,

r ⇒ radius ⇒ 28 cm

Let us solve it now.

C = 2 × π × 28

C = 175.93 cm

And now let us covert the travelling distance to centimeters.

( For that, multiply km by 100000 )

3.52km = 352000 cm

Now, to find the number of revolution, divide the total distance travelled by its circumference.

352000/175.93 = 2000.79

Approximately, 2001 revolutions

The number of revolutions made by a wheel of 28cm radius covering a distance of 3.52km is 2000.8.

Given,

Radius, r = 28cm

Circumference = 2πr = 56π cm

Circumference = Distance traveled in one revolution

The distance traveled by wheel = 3.52km = 3520m = 352000cm

Let N = number of revolution

Now we know that,

Total distance = Number of revolutions × 1 revolution distance(circumference)

or 352000 = N × 56π

or N = 352000/56π

or N = 2000.8

Therefore, the number of revolutions made by a wheel of 28cm radius covering a distance of 3.52km is 2000.8.

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For given parametric curve the equations of both tangents at point where it crosses itself are: y = ± (√15x + 2√15)

The graph of parametric curve x = cos t + 2 cos 2t, y = sin t + 2 sin 2t (t ∈ [0, 2π]) is as shown below.

From the graph we can observe that, the curve crosses itself at (-2, 0).

Let x = -2

cos t + 2 cos 2t = -2,

and y = 0

sin t + 2 sin 2t = 0

sin t + 2 (2 sin(t) cos(t)) = 0

sin t + 4 sin t cos t = 0

sin t(1 + 4 cos t) = 0

sin(t) = 0   OR   1 + 4 cos(t) = 0

sin(t) = 0   OR   cos(t) = -1/4

From sin(t) = 0

⇒ t = 0 or t = π,

but for these values of t, cos t + 2 cos 2t = -2 is not true.

This means, the point (-2, 0) must corresponds to cos(t) = -1/4

[tex]\Rightarrow t=cos^{-1}(\frac{1}{4} )[/tex]

When cos(t) = -1/4,

sin(t) = [tex]\frac{\sqrt{15} }{4}[/tex]                ..............(by identity sin²(t) + cos²(t) = 1)

And

[tex]sin(2t) = 2sin(t)cos (t)\\sin(2t) = 2\times \frac{\sqrt{15} }{4} \times (\frac{-1}{4} )\\\\sin(2t) = -\frac{\sqrt{15} }{8}[/tex]

[tex]\\\\cos(2t)=2cos^2{t} - 1\\\\cos(2t)=2(\frac{-1}{4} )^2 - 1\\\\cos(2t)=\frac{1}{8}-1\\\\ cos(2t)=\frac{-7}{8}[/tex]

Now we find derivative of given parametric equations with respect to t.

for x = cos t + 2 cos 2t,

dx/dt = -sin(t) -4 sin(2t)

y = sin t + 2 sin 2t

dy/dt = cos(t) + 4 cos(2t)

Consider dy/dx

[tex]= \frac{\frac{dy}{dt} }{\frac{dx}{dt} }\\\\= \frac{cos(t) + 4 cos(2t) }{-sin(t) -4 sin(2t)}\\\\=\frac{\frac{-1}{4}+4~\frac{-7}{8} }{-\frac{\sqrt{15} }{4}-4~\frac{\sqrt{15} }{8} }\\\\=-\sqrt{15}[/tex]

This means, slope m = -√15

We have the point (−2,0)

Using equation of line y=mx+b the y-intercept would be,

0 = -√15 (−2) + b

b = -2√15

So, the equation for this tangent line :

y = -√15x - 2√15

And the equation of other tangent would be,

y = √15x + 2√15

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The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) is y = -2x - 18.

Therefore, the answer is b) y = −2x − 18.

The slope-intercept form of a line's equation is y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.

To find the equation of a line that is perpendicular to another line, we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other. This means that if the slope of one line is m, the slope of a line perpendicular to it is -1/m.

The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) can be found by first finding the slope of the line 2x – 4y = 17. We can do this by rearranging the equation to the slope-intercept form:

2x – 4y = 17

-4y = -2x + 17

y = (1/2)x - (17/4)

The slope of the line 2x – 4y = 17 is (1/2). Therefore, the slope of a line perpendicular to it is -2.

To find the equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2), we can use the slope-intercept form of a line's equation and plug in the slope (-2) and the coordinates of the point p(-8, -2):

y = -2x + b

-2 = -2×(-8) + b

b = -18

--The question is incomplete, the complete question is given below--

"Give the slope-intercept form of the equation of the line that is perpendicular to 2x – 4y = 17 and contains p(–8, –2).

a. y = −2x + 8

b. y = −2x − 18

c. y = −2x − 12

d. y = −2x + 2"

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The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) is y = -2x – 18

y = mx + b is the slope intercept form of a line’s equation. Here, m = slope of the line and b = y-intercept.

The equation of the line that is perpendicular to 2x – 4y = 17 and contains p(-8, -2) can be found by first finding the slope of the line 2x – 4y = 17. We can do this by rearranging the equation to the slope-intercept form:

2x – 4y = 17

-4y = -2x + 17

y = (1/2)x - (17/4)

The slope of the line is 1/2. Hence m = ½

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The area of triangle will be 140 square units.

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

K is the scaling factor for x in the equation y = Kx. This expression can also be visualised in terms of proportionality:

y ∝ x

K can therefore be regarded as a proportionality constant in this context.

Given the area of triangle = 35 sq. units

and scale factor is 2

The base times the height of a triangle equals its area. Triangle ABC's base and height each double when a scale factor of 2 with centre A is used, increasing the area by a factor of 4 as a result.

area of triangle = 1/2bh

where b = base and h = height

given 1/2bh = 35

when scale factor is 2

new base = 2b

new height = 2h

area will be 1/2(2b)(2h) = 4/2bh

so  1/2bh = 35

4/2bh = 35 x 4 = 140 square units.

Hence the area is 140 square units.

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Answer:

i think it's true am a 6 grader i really try

Step-by-step explanation:

The domain of (f/g)(x) in interval notation is [-3, 6].

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

From the graph,

f(x) has x values from x = -1 to x = 6

g(x) has x values from x = -3 to x = 5

The function f(x) is f(x) = mx + c

Find two coordinates from the graph of f(x).

= (-1, 3) and (6, 4)

m = (4 - 3) / (6 + 1) = 1/7

Now,

3 = (1/7) x -1 + c

3 = -1/7 + c
c = 3 + 1/7

c = 22/7

f(x) = (1/7)x + 22/7  _____(1)

The function g(x) is f(x) = mx + c

Find two coordinates from the graph of g(x).

= (-3, 2) and (5, 4)

m = (4 - 2) / (5 +3) = 2/8 = 1/4

Now,

2 = 1/4 x (-3) + c

2 = -3/4 + c
c = 2 + 3/4

c = 11/4

g(x) = (1/4)x + 11/4  _______(2)

Now,

From (1) and (2)

(f/g)(x)

= f(x)/g(x)

= ((1/7)x + 22/7) / ((1/4)x + 11/4)

The domain of f(x) and g(x) will include the domain of both f(x) and g(x).

So,

x = -1 to x = 6 and x = -3 to x = 5

This can be written as,

[-3, 6]

Thus,

The domain of (f/g)(x) is [-3, 6].

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The probability that a two-digit number selected at random has a tens digit less than its units digit is 0.2667 (4/15).

What is a probability simple definition?

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%

P= A/B

  = 4/15

There are 90 two-digit numbers (99-9). Of these, six numbers are divisible by 15 (15, 30, 45, 60, 75, 90). This is also divisible by 5. Therefore, the preferred case is 30-6 = 24. Therefore, the required probability is 24/90 = 4/15.

The probability of an event can be calculated by simply dividing the number of favorable results by the total number of possible results using a probabilistic expression. Whenever you are uncertain about the outcome of an event, you can talk about the probability of a particular outcome, that is, its potential.

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Answer:

It is 63 cm

Step-by-step explanation:

Take 28/4 = 7. That is what1 equals in the proportion. So, we take 2 x 7, 3 x 7, and 4 x 7. Then you just add the sides together and it equals 63 cm.

Answer: 63

Step-by-step explanation:

In the ratio, the longest side is 4. 4x7 is 28, so to make the ratios proportional again, you multiply all the sides by 7, getting 14:21:28.

These are the side lengths of the triangle, and to find the perieter you add all of them up, getting 63.

Hope this helps :)

(a) The impulse of the car of mass 1200 kg is 12000 Ns.

(b) The change in velocity of the car is 10 m/s.

Impulse is the product of force and time.

(a) To calculate the impulse of the force, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

(b) To calculate the change in velocity of the car, we use the formula below

Where:

From the question,

Given:

Substitute these values into equation 2

Hence the change in velocity of the car is 10 m/s.

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Answer: it's not its  [tex]\frac{1}{27}[/tex]

Step-by-step explanation:

Because the negative in the exponent moves it to the denominator then just cube 3 in the denominator

[tex]\frac{1}{3^{3} }[/tex]

[tex]\frac{1}{27}[/tex]

But [tex]2^{-3} =\frac{1}{8}[/tex]

because [tex]\frac{1}{2^{3} }[/tex] = [tex]\frac{1}{8}[/tex]

The number of revolution each wheel make is 5605.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is given as πr².

We have,

Diameter of the wheel = 36 inches

The radius of the wheel = 18 inches

The circumference of the wheel = 2πr.

The total distance traveled = Circumference of the wheel x Number of revolutions (N).

Now,

10 miles = 10 x 5280 ft = 10 x 5280 x 12 inches

10 miles = 2πr x N

N = (10 x 5280 x 12) / (2 x 3.145 x 18)

N = 633600 / 113.04

N = 5605

Thus,

The number of revolutions is 5605.

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Answer:

You know that x = -9, and 3 or The first number is 3, the other -9

Step-by-step explanation:

First number: x

Second: x + 6

(x)^2 + (x + 6)^2 = 90

x^2 + x^2 + 6x + 6x + 36 = 90

Simplify more

2x^2 + 12x + 36 = 90

2x^2 + 12x - 54 = 0

2(x + 9)(x - 3) = 0

From the given data about population, we found out answers:

a) The percentage of the panels that will be scrapped is 4.55%.

b) The percentage of the panels that will need rework is 45.45%.

c) In order to reduce the scrap percentage to 1%, the manufacturer must re-center the process with a new mean value of 10.50 mm.

d) The rework percentage with the new mean value is 0.33%.

This is because the new mean value (10.60 mm) is within the specified range (10.50 +0.50 mm). Thus, there will be no rework or scraped panels due to the mean being outside of the specified limits.

To better understand this, it is important to consider the normal distribution of the data and the specified limits for the hole size. The normal distribution of the data means that the majority of the holes will be of the mean size, with very few being either significantly larger or smaller.

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If you divided the number of letters in “Merry Christmas” by the number of thieves in the first “Home Alone” movie, then the answer will be 7.

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 split into 3 groups of equal size results in 4 in each group. Creating equal groupings or determining how many people are in each group after a fair distribution is the basic objective of division.

One of the four fundamental arithmetic operations, or how numbers are joined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

A division problem has three primary components: the dividend, the divisor, and the quotient. The amount that will be shared is the dividend. The quantity of "people" among whom the number is split is referred to as the divisor. The answer is the quotient.

Number of letters in Merry Christmas is 14

Number of thieves in Home Alone is 2

The quotient is given as 14/2 = 7

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The charge for the t-shirt earlier than the cut price of 25 percent is $20.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, the 25% discount, the price of a t-shirt was 15$.

Since, After 25% discount price of t-shirt = 15

Thus

Original price of t-shirt = 15 * 100/75

Original price of t-shirt = 20

Therefore, the price before the discount of 25 percent is $20.

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Answer:

[tex]y=1[/tex]

Step-by-step explanation:

Adding the equations yields [tex]4y=4[/tex]. Therefore, [tex]y=1[/tex].

The square feet of the garden that could contain flowers, given the side lengths of the stepping stone and the garden, is C. 16 ft².

To find the portion of the garden that could contain flowers, first find the total area of the entire garden ;

= Length of garden x Width

= 4 x 6

= 24 ft ²

The stepping stones will not contain flowers so their area should be deducted from the area of the garden :

= 24 - ( 2 x ( 2 x 2 ))

= 24 - ( 2 x 4 )

= 24 - 8

= 16 ft²

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Answer:

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

100 dozen add 20% is:

The value of x of the quadrilateral using the concept of similar quadrilaterals is; x = 1.5

Two quadrilaterals are referred to as similar quadrilaterals when the three corresponding angles are the same and as a result the fourth angles automatically become the same due to the fact that the interior angles of a quadrilateral sum up to 360 degrees and two adjacent sides have equal ratios.

Thus, we can say by the concept of similar quadrilaterals that;

AB/LM = BC/MN

Thus;

14/(x + 9) = 10/(x + 6)

14(x + 6) = 10(x + 9)

14x + 84 = 10x + 90

14x - 10x = 90 - 84

4x = 6

x = 1.5

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Answer:

1_ones and 2 _tenth

Step-by-step explanation:

the number in front of the point they start from ones continues

The equation of the parabola shown with its focus on this graph is D. y = [tex]-\frac{1}{12} \text x^2[/tex] + 1.

A parabola is a mirror-symmetrical, roughly U-shaped plane curve that is used in mathematics. It corresponds to a number of mathematical explanations that appear to differ on the surface but which all define the same curves.

A line and a point (the focus) are two ways to describe a parabola (the directrix). Not the directrix is the main focus. The location of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

Conic sections, which are formed when a right circular conical surface and a plane perpendicular to another plane that is tangential to the conical surface intersect, are another way to describe parabolas.

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