Tony is spending money at a constant rate. Suppose he initially has $1000, and after 4 months, he has $760,

Which of these expresses the rate at which Tony's amount of money is changing?

Answer:

a) 0.064

b) 0.002

Step-by-step explanation:

a) Assuming that  the batteries' voltage levels are independent

Probability = 0.8 * 0.8 = 0.64

b) batteries' voltage levels are dependent

20/19 (0.064)^19 *0.036  + 20/20 (0.064)^20 *0.036^0

= 0.002

Emily funded $6000 in stocks and $12,000 in bond funds. She also funded the remaining  $2,000 in her savings account.

Future value = $20,000

Simple interests rate = 1.5%

The return rate on bonds= 4.5%

The return rate on stocks = 6.2%

Total amount made on invests =  $942

Time period = 1 year

Let us assume that the amount of money Emily invested = x

Amount invested in stock = y

If the amount is twice = 2y

The interest earned = x * 0.015

Interest on bond = 2y * 0.045

Interest on stocks = y * 0.062

The equation will be:

(x * 0.015) + (2y * 0.045) + (y * 0.062) = 942

0.015x + 0.152y = 942  ------ Equation 1

Total future value is given as $20,000

x + 2y + y = 20000

x + 3y = 20000

x = 20000 - 3y

Substituting the x value in the first equation:

0.015(20000 - 3y) + 0.152y = 942

300 - 0.045y + 0.152y = 942

0.107y = 642

y = 6000

Therefore, we can conclude that Emily funded $6000 in stocks and $12,000 in bond funds.

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\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{\pi }{2}\\[1em] r=\frac{8}{3} \end{cases}\implies A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot\left( \cfrac{8}{3} \right)^2 \\\\\\ A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot \cfrac{64}{9}\implies A=\cfrac{16\pi }{9}\implies A\approx 5.59\)

Answer:

The correct option is A. Parallel line.

Answer:

y=x-2

Step-by-step explanation:

4-0=4 = (change in y)

2--2=4 = (change in x)

change in y/change in x=4/4=1=x

gradient = x

y=x+c

Subtitute any coordinate

2=4+c

c=-2

so

y=x-2

Answer:

y=x-2

Step-by-step explanation:

Slope Intercept Form

y=x-2

Find Slope using equation below

Chose points I chose 2 as y2 and -2 as y2

4 is x2 and 0 as x1

Slope is 1

now choose a point and plug it in for x and y and plug slope in Equation

I chose (4,2)

2=4+b

subtract 4 by both sides

-2=b

Slope Form

So... y=x-2 is the answer

Answer:

Below

Step-by-step explanation:

Line AB is of the form y = mx + b    where m is the slope = 2

 Line BC is perpendicular to this and will have slope - 1/m = - 1/2   and includes the point C (0,6)

 The point slope form of line BC will then be

     ( y-6) = - 1/2 ( x - 0)    which can be re-arranged to

       y = - 1/2x + 6     < ==== equation for line BC

Answer:

x = 32

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

100 = 68+x

Subtract 68 from each side

100 -68 = x

32 =x

\(\huge\bold{Given :}\)

Angle AOB = 100°

Angle OBC = 68°

Angle BCO = \(x°\)

\(\huge\bold{To\:find :}\)

The value of \(x°\).

\(\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}\)

\(\implies {\blue {\boxed {\boxed {\purple {\sf {C.\:x°\:=\:32°}}}}}}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

An exterior angle of a triangle is equal to sum of two opposite interior angles.

And so we have,

➪ ∠ AOB = ∠ OBC + ∠ BCO

➪ 100° = 68° + \(x°\)

➪ \(x°\) = 100° - 68°

➪ \(x°\) = 32°

Therefore, the value of \(x°\) is 32°.

\(\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}\)

∠ AOB = ∠ OBC + ∠ BCO

✒ 100° = 68° + 32°

✒ 180° = 100°

✒ L. H. S. = R. H. S.

\(\boxed{Hence\:verified.}\)

(Note: Kindly refer to the attached file.)

\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}\)

In the given similar triangles below, we have to find the measure of Dwrite. Triangle 1, ABC, is similar to Triangle 2, DEF. The two triangles are similar because their corresponding angles are congruent and their sides are proportional.

In order to find the measure of Dwrite, we can use the concept of proportionality. The sides of similar triangles are proportional to each other.

This means that if we know the ratio of the sides of one triangle, we can use that ratio to find the corresponding sides of the other triangle. We can use this property to find the value of Dwrite.

To start, let's write down the ratio of the sides of Triangle 1 and Triangle 2. We can choose any two corresponding sides to do this, but we'll choose AB and DE because they are easiest to measure: AB/DE = 6/8.5We know that the measure of AB is 6, so we can solve for the measure of DE: DE = AB x (DE/AB)DE = 6 x (8.5/6)DE = 8.5Now we know that the measure of DE is 8.5.

We can use this to find the measure of Dwrite. We know that DE and Dwrite are corresponding sides of Triangle 2 and Triangle 1, respectively.

So we can write a proportion using the ratio of DE to Dwrite: DE/Dwrite = 8.5/xWe know that DE is 8.5, so we can substitute that in:8.5/Dwrite = 8.5/Now we can solve for x by cross-multiplying:8.5x = 8.5Dwrite = 1Therefore, the measure of Dwrite is 1.

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Answer:   71º

Step-by-step explanation:

I cant remeber the therum but basically its just the opposite, super simple!!

The bearing of point Q from point P is 070 degrees.

1. The man starts at point P and walks 4 km on a bearing of 023 degrees. This means he is moving slightly to the northeast direction.

2. After walking 4 km, the man reaches point Q.

3. From point Q, we need to determine the bearing of Q from P. To do this, we imagine a straight line connecting P and Q.

4. The bearing is measured clockwise from the north direction. Therefore, we need to find the angle that the line PQ makes with the north direction.

5. We already know that the man walked 4 km from P to Q on a bearing of 113 degrees. Since bearings are measured clockwise, we can subtract 113 degrees from 180 degrees to find the angle that the line PQ makes with the north direction.

6. Subtracting 113 degrees from 180 degrees gives us 67 degrees. Therefore, the angle between the line PQ and the north direction is 67 degrees.

7. Finally, we add this angle to the initial bearing of 023 degrees to find the bearing of Q from P.

8. Adding 67 degrees to 023 degrees gives us 090 degrees.

9. However, bearings are typically represented in three digits, so we can drop the leading zero.

10. Therefore, the bearing of point Q from point P is 070 degrees.

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\(20^{\tfrac 52}\\\\=(20^5)^{\tfrac 12}\\\\=\left(20^4 \cdot 20 \right)^{\tfrac 12}\\\\=20^{\tfrac 42} \cdot 20^{\tfrac 12}\\\\=20^2 \sqrt{20}\\\\=400\sqrt{4 \times 5}\\\\=400 \times 2\sqrt 5\\\\=800\sqrt 5\)

Answer:

\(800\sqrt{5}\)

Step-by-step explanation:

Given: \(\large (20)^\text{$ \dfrac{5}{2} $}\)

Properties of Exponents:

Rational Exponent Property: \(\large x^\text{$ \dfrac{m}{n} $} = \large \text{$ \sqrt[n]{x^m} $}\)

Product of Powers Property:

1. Convert into a radical:

\(\sqrt[2]{20^5} \implies \sqrt{20^5}\)

2. Simplify the expression:

\(\sqrt{20^2\times20^2\times20^1}\\\\\implies \sqrt{20^4\times20}\\\\\implies 20^2\sqrt{20}\\\\\implies 20^2\sqrt{4\times5}\\\\\implies 20^2\times2\sqrt{5}\)

3. Evaluate the power:

\(20\times20\times2\sqrt{5}\\\\\implies 400\times2\sqrt{5}\)

4. Multiply:

\((400\times2)\sqrt{5}\\\\\implies800\sqrt{5}\)

More than once a week: 0.11

Once a week: 0.51

Every other week: 0.26

Every three weeks: 0.05

Less often than every three weeks: 0.07

To make a relative frequency distribution, follow these steps:

Count the number of occurrences of each category in the data. In this case, 11% of the 251 participants responded "more than once a week", so the number of occurrences for this category is 0.11 * 251 = 27.61 (rounded to 28). Similarly, 51% of the participants responded "once a week", so the number of occurrences for this category is 0.51 * 251 = 127.51 (rounded to 128). And so on for the other categories.

Divide the number of occurrences for each category by the total number of participants. In this case, the total number of participants is 251, so the relative frequency for "more than once a week" is 28 / 251 = 0.11. The relative frequency for "once a week" is 128 / 251 = 0.51. And so on for the other categories.

And that's it! These are the relative frequencies for each category in the data.

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Answer:

\( q = - \: \frac{s}{ tr} \)

I hope I helped you^_^

Answer:

\(s = - trq \\ \boxed{ q = - \frac{s}{tr} }\)

The equation to find the number of servings of trail mix that had been eaten during the month will be x = 71 - 49.

It It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, Shiloh made 71 servings of trail mix and by the end of the month, she had 49 servings of trail mix left.

The equation to find the serving eaten will be:

x = Beginning amount - Ending amount

x = 71 - 49

This depcits the equation.

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Answer:

Step-by-step explanation:

37.087 is less than 32.78 because of the zero in the hundreds spot.

Answer:

no

Step-by-step explanation:

this is because in 32.087 the right side of the decimal starts  in the hundreths place. but in 32.78 the right side of the decimal starts in the tenths place which would make 32.78 greater than 32.087

Step-by-step explanation:

2.25

6.4

4

1.333

Hope is will help you

We want to calculate the temperature difference between Winnipeg and Fairbanks. To do , we take the temperature of Winnipeg and subtract the temperature of fairbanks. So we get

So, this means that the difference between both temperatures is 16 degrees. Since Winnipeg has a higher temperature, that means that the temperature was 16 degrees higher.

Answer:

54

Step-by-step explanation:

Answer:

4/5=8/10=16/15=20/30

Step-by-step explanation:

there you go may u help me on my question now pls i rlly need help.

Answer:

The answer is 20 because when you divide 56 by 2.8 you get 20

Answer:

10

Step-by-step explanation:

(4 y + 8 x + 6) + 25 + (4x + 6 y + 7)

(10 y + 6) + 25 + (12 x + 7)

10 y + 38 + 12 x

The simplified expression:

10 y + 38 + 12 x

Answer:

10

Step-by-step explanation:

(4y + 8x + 6) + 25 + (4x + 6y + 7).

Combine like terms

4y+6y  + 8x+4x  + 6+25+7

10y+12x+38

The cost for a new customer to rent a bay for 6 hours at Top Golf is $22, which includes a $10 player card fee and a $12 bay rental fee at $2 per hour.

Let's let "x" be the total cost for a new customer to rent a bay for 6 hours.

We know that there is a flat fee of $10 for the player card, and then an additional $2 per hour for the bay rental.

So, the equation for the cost "x" can be written as

x = 10 + 2(6)

The expression 2(6) represents the cost of the bay rental for 6 hours. We can simplify the expression by multiplying 2 and 6, which gives us

x = 10 + 12

Now, we can combine like terms to find the final cost

x = 22

Therefore, the cost for a new customer to rent a bay for 6 hours at Top Golf is $22.

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

" For a new customer top golf charges $10 for a player card and $2 per hour. Write and solve a linear equation to find the cost for a new customer to rent a bay for 6 hours."--

Answer:

2

Step-by-step explanation:

Since it is AP, the common difference is same for any term:

The first 3 terms are:

Since the last term is 18, it means this AP has 6 terms:

Answer: as we need to find the value of x only, it is = 2

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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Answer:

Its C

Step-by-step explanation:

The equivalent expression for (f .g)(x) is given as √2x+3

Composite functions are also known as function of a function. It is way of substituting a function into another function.

Given the following functions below:

f(x) = √x

g(x) = 2x + 3

Required

Composite function f(g(x))

f(g(x)) = f(2x+3)

Replace x as 2x+3 in the function f(x)

f(g(x)) = √2x+3

Hence the composite function f(g(x)) is equivalent to √2x+3

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The money Jena will have after buying a set of markers in algebra expression is y = 15 - x.

Arithmetic operations like subtraction, addition, division, multiplication, and exponentiation are used to combine variables and integers to produce any algebraic expression. A variable, a number, or a variable and number with an exponent as a product can all be used as the phrase.

Cost is the amount of money spent by a business to produce or create goods or services.

The cost of one set of markers is x dollars.

Now Jen has a total of $15.

Then, the amount of money "y" Jena will have after buying one set of markers will be:

y = 15 - x

Hence, the algebraic expression after buying one set of markers is y = 15 - x.

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At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

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