a college student earned $3,600 one summer during this semester she spent $2,500 for tuition what fraction shows what she spent on tuition

Answer:

A- 6/x^2

Step-by-step explanation:

Answer:

74-2c

Step-by-step explanation:

you know that craig's age is c. You multiply c by two, which is twice craig's age. Then you subtract that from c.

There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (amount in the account after 25 years)

P = Principal amount (amount deposited every 2 months)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.

Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.

Now, we can substitute these values into the formula:

A = 940(1 + 0.0399/4)^(4*25)

Calculating the exponent first:

(1 + 0.0399/4)^(4*25) ≈ 2.703236

Now, substituting the calculated exponent and the number of deposits into the formula:

A = 940 * 2.703236 * 150 ≈ $594,311.34

Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.

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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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\(f(x)=x\) for \(x\leq0\), therfore \(f(0)=0\).

the first domain is true for f(0) so we substitute value of x in the first function

\(f(x) = x \\ f(0) = 0\)

Answer:

Step-by-step explanat

126

612

126

The Equation of a Circle

If a circle has its center at the point (h, k) and has a radius r, the equation of the circle is:

We are only given the endpoints of the diameter of the circle (3, -2) and (-5, 8). We need to find its center and radius.

These facts will help us to find both parameters:

* The diameter passes through the center of the circle.

* The center of the circle is the midpoint of the diameter.

* The radius of the circle is half the length of the diameter.

The midpoint of the diameter can be calculated as:

The coordinates of the midpoint are (-1, 3) and it happens to be the center of the circle, thus h = -1 and k = 3.

To find the radius, we need to calculate the distance from the center to any of the endpoints. Let's use the points (-1, 3) and (3, -2) and use the formula of the distance:

We don't need to calculate the value of r. Its square is enough to substitute in the general form of the circle to get:

The slope of the line passing through the points (5, 3) and (8, 2) is -1/3.

To find the slope of the line passing through the points (5, 3) and (8, 2), we can use the formula for slope:

slope = (y2 - y1) / (x2 - x1)

Let's substitute the coordinates of the given points into the formula:

x1 = 5, y1 = 3

x2 = 8, y2 = 2

slope = (2 - 3) / (8 - 5)

Calculating the numerator and denominator:

slope = -1 / 3

Therefore, the slope of the line passing through the points (5, 3) and (8, 2) is -1/3.

Note: The slope represents the rate of change between the y-coordinates and x-coordinates of two points on a line. In this case, for every 3 units increase in the x-coordinate, the y-coordinate decreases by 1 unit.

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The first step is to find the diameter of the circle. We would do this by applying the formula for finding the distance between two points which is expressed as

From the points given,

x1 = 3, y1 = 0

x2 = 4,y2 = 0

Thus,

Diameter = 1

Recall,

radius = diameter/2 = 1/2 = 0.5

The standard form of the equation of a circle is expressed as

(x - h)^2 + (y - k)^2 = r^2

h and k are the x and y coordinates of the center of the circle

r is the radius

To find the x and y coordinates of the circle, we would find the midpoint of the diameter. The formula for determining midpoint is expressed as

Midpoint = [(x1 + x2)/2, (y1 + y2)/2

Midpoint = [(3 + 4)/2, (0 + 0)/2)

Midpoint = 7/2, 0

Midpoint = 3.5, 0

Thus,

h = 3.5, k = 0

Substituting these values into the standard equation, we have

(x - 3.5)^2 + (y - 0)^2 = 0.5^2

(x - 3.5)^2 + y^2 = 0.25

Answer: -2

Step-by-step explanation:

Subtract 13 on both sides

-7x = 14

Divide by -7 on both sides

x = -2

Answer:

Step-by-step explanation:

Solution and how to convert 80 / 50 into a percentage

1.6 times 100 = 160. That's all there is to it!

To determine the function that models the data, we need to analyze the relationship between the cost per photo and the number of photos a customer buys. From the given information, we can observe that the cost per photo varies inversely with the number of photos. This implies that as the number of photos increases, the cost per photo decreases, and vice versa.

To model this relationship, we can use the inverse variation equation, which can be expressed as:

y = k/x

Here, y represents the cost per photo, x represents the number of photos, and k is the constant of variation.

Let's examine the data given in the table to find the value of k:

Number of Photos (x) Cost per Photo (y)

10 10

25 4

50 2

100 1

We can see that as the number of photos increases, the cost per photo decreases. We can use any pair of values from the table to solve for k. Let's choose the pair (50, 2):

2 = k/50

Solving for k:

k = 2 * 50 = 100

Now that we have the value of k, we can write the function that models the data:

y = 100/x

Therefore, the function that models the data is y = 100/x, where y represents the cost per photo and x represents the number of photos a customer buys.

Answer:

The answer is thirty - seven hundredths

Step-by-step explanation:

Answer:

Least to greatest:

D.  5, -2, 20, -1 = -2, -1, 5, 20

E.  20, -3, -13, 2 = -13, -3, 2, 20

Answer:

The 10th percentile is 66.42.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

X ~ N(70, 14).

This means that \(\mu = 70, \sigma = 14\)

Suppose that you form random samples of 25 from this distribution.

This means that \(n = 25, s = \frac{14}{\sqrt{25}} = 2.8\)

Find the 10th percentile.

This is X when Z has a pvalue of 0.1, so X when Z = -1.28.

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(-1.28 = \frac{X - 70}{2.8}\)

\(X - 70 = -1.28*2.8\)

\(X = 66.42\)

The 10th percentile is 66.42.

Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

The prove to show that ΔABC is similar to ΔMNC is explained below.

Similar triangles are triangles that have the same shape but are not necessarily the same size. More precisely, two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.

Considering the given diagram, we can say:

AM = MC    (Given)

BN = NC     (Given)

BC = BN + NC (addition property of a line segment)

AC = AM + MC (addition property of a line segment)

NC/ BC = MC/ AC = constant

∠ACB = ∠MCN  (Reflexive property)

Thus, ΔABC ~ ΔMNC (Side-Angle-Side theorem)

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Answer:

a

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

this is because both number are to the left of zero which makes both numbers negative which leaves you with one answer.

Answer:

Step-by-step explanation:

it think it 23 becasue u add

1 divide it by 2

Answer:

25a-20

Step-by-step explanation:

15a+10a-20=

25a-20

Answer:

-8d-5

HOPE THIS HELPS

- Todo ❤️

Step-by-step explanation:

-6d-2d=-8d

2-7=-5

Answer:

-8d-5

Step-by-step explanation:

Answer:

a.) 0.5

b.) 0.66

c.) 0.83

Step-by-step explanation:

As given,

Total Number of Batteries in the drawer = 10

Total Number of defective Batteries in the drawer = 4

⇒Total Number of non - defective Batteries in the drawer = 10 - 4 = 6

Now,

As, a sample of 3 is taken at random without replacement.

a.)

Getting exactly one defective battery means -

1 - from defective battery

2 - from non-defective battery

So,

Getting exactly 1 defective battery = ⁴C₁ × ⁶C₂ =  \(\frac{4!}{1! (4 - 1 )!}\) × \(\frac{6!}{2! (6 - 2 )!}\)

                                                                            = \(\frac{4!}{(3)!}\) × \(\frac{6!}{2! (4)!}\)

                                                                            = \(\frac{4.3!}{(3)!}\) × \(\frac{6.5.4!}{2! (4)!}\)

                                                                            = \(4\) × \(\frac{6.5}{2.1! }\)

                                                                            = \(4\) × \(15\) = 60

Total Number of possibility = ¹⁰C₃ = \(\frac{10!}{3! (10-3)!}\)

                                                        = \(\frac{10!}{3! (7)!}\)

                                                        = \(\frac{10.9.8.7!}{3! (7)!}\)

                                                        = \(\frac{10.9.8}{3.2.1!}\)

                                                        = 120

So, probability = \(\frac{60}{120} = \frac{1}{2} = 0.5\)

b.)

at most one defective battery :

⇒either the defective battery is 1 or 0

If the defective battery is 1 , then 2 non defective

Possibility  = ⁴C₁ × ⁶C₂ = 60

If the defective battery is 0 , then 3 non defective

Possibility   = ⁴C₀ × ⁶C₃

                   =  \(\frac{4!}{0! (4 - 0)!}\) × \(\frac{6!}{3! (6 - 3)!}\)

                   = \(\frac{4!}{(4)!}\) × \(\frac{6!}{3! (3)!}\)

                   = 1 × \(\frac{6.5.4.3!}{3.2.1! (3)!}\)

                   = 1× \(\frac{6.5.4}{3.2.1! }\)

                   = 1 × 20 = 20

getting at most 1 defective battery = 60 + 20 = 80

Probability = \(\frac{80}{120} = \frac{8}{12} = 0.66\)

c.)

at least one defective battery :

⇒either the defective battery is 1 or 2 or 3

If the defective battery is 1 , then 2 non defective

Possibility  = ⁴C₁ × ⁶C₂ = 60

If the defective battery is 2 , then 1 non defective

Possibility   = ⁴C₂ × ⁶C₁

                   =  \(\frac{4!}{2! (4 - 2)!}\) × \(\frac{6!}{1! (6 - 1)!}\)

                   = \(\frac{4!}{2! (2)!}\) × \(\frac{6!}{1! (5)!}\)

                   = \(\frac{4.3.2!}{2! (2)!}\) × \(\frac{6.5!}{1! (5)!}\)

                   = \(\frac{4.3}{2.1!}\) × \(\frac{6}{1}\)

                   = 6 × 6 = 36

If the defective battery is 3 , then 0 non defective

Possibility   = ⁴C₃ × ⁶C₀

                   =  \(\frac{4!}{3! (4 - 3)!}\) × \(\frac{6!}{0! (6 - 0)!}\)

                   = \(\frac{4!}{3! (1)!}\) × \(\frac{6!}{(6)!}\)

                   = \(\frac{4.3!}{3!}\) × 1

                   = 4×1 = 4

getting at most 1 defective battery = 60 + 36 + 4 = 100

Probability = \(\frac{100}{120} = \frac{10}{12} = 0.83\)

Answer:

X = 81.20º

Step-by-step explanation:

sinX = opp/hyp

sinX = 84/85

X = arcsin(84/85)

use calculator

X = 81.20º

The only rule to follow is

Divide dividend by divisor and the mention the quotient and things left after remains in place of remainder

Here is a sample

\(\sf\Large\qquad\quad16\\ \begin{array}{cc} \cline{2 - 2}\sf 20 )&\sf \ 327\\&\sf - 20 \downarrow\\ \cline{2-2}& \sf \ \ \ \ 127\\ &\sf \ - 120 \\ \cline{2-2} & \sf \ \007 \\ \cline{2-2} \end{array}\\\\\\ \sf Divisor \rightarrow 20 \\ \\ \sf Quotient \rightarrow 16\\\\ \sf Remainder \rightarrow 7\)

The solution of the inequality is 8 ≥  x  or x > 10. The graph of the solution is attached

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Solving for x:

11≥ 2x - 5 or 2x - 5 > 15

Collect like terms:

11 + 5 ≥ 2x  or 2x > 15 + 5

16 ≥ 2x  or 2x > 20

8 ≥  x  or x > 10

Note:  8 ≥  x can also be written as x ≤ 8

We can combine the two as follow:

Inequality notation: 8 ≥  x > 10

The graph of the solution is attached

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Answer:

I think its the 3rd one sorry if im whrong

Answer:

It is C

Step-by-step explanation:

Please give me brainliest :)

Answer:

To calculate the value of each investment at the end of 2010, we need to use the compound interest formula:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the initial investment

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

For the investment in the fund tracking stocks:

P = $300

r = 6.4% = 0.064

n = 1 (assuming the interest is compounded annually)

t = 2010 - 1900 = 110

A = 300(1 + 0.064/1)^(1*110) = $208,884.78 (rounded to the nearest cent)

For the investment in the fund tracking bonds:

P = $300

r = 1.7% = 0.017

n = 1

t = 2010 - 1900 = 110

A = 300(1 + 0.017/1)^(1*110) = $2,326.34 (rounded to the nearest cent)

For the investment in the fund tracking cash:

P = $300

r = 0.7% = 0.007

n = 1

t = 2010 - 1900 = 110

A = 300(1 + 0.007/1)^(1*110) = $862.38 (rounded to the nearest cent)

Therefore, the investment in the fund tracking stocks would be worth approximately $208,884.78 at the end of 2010, the investment in the fund tracking bonds would be worth approximately $2,326.34, and the investment in the fund tracking cash would be worth approximately $862.38.

Answer:

-7-63a

Step-by-step explanation:

-7(1 + 9a)

(use the distributive property of multiplication to simplify)

-7-63a

Answer:

is x multiplied by p/q??