A rectangle 28 in. long has the same area as a square with 14 in. sides. What is the width of the rectangle?

The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

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Answer:

It would take you 18 minutes

Step-by-step explanation:

You have 10kil/3min and you also travel 60 kil. 10 to 60 is six times this distance to multiply the time taken to drive by 6. 6 times 3 is 18

3/10=18/60 18 minutes

Answer:

5 4/10 is the answers for the question

Step-by-step explanation:

please give me brainlest

Answer: the answer is 8 because

Step-by-step explanation:

The value of the missing data point is 10. Option C

The data set has 8 data points, and the median is given as 12. The median is the middle value when the data points are arranged in ascending or descending order.

Let's arrange the data set in ascending order:

6, 8, ?, 8, 14, 15, 16, 18

Since the median is 12, it should be the fourth data point when arranged in ascending order. Therefore, the missing data point must be the fourth value in the sorted data set.

From the given options, the only whole number that could fit as the fourth value in the data set is 10.

Thus, the value of the missing data point is C. 10.

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Answer:

1. s

2. c

3. (-8,6)

4. 3y and 8y

5. 11b + 2a

6. 11x-24

7.

8. 45y-44

Step-by-step explanation:

Answer:

15 more bags.

Step-by-step explanation:

360/6= 60.

270/6=45

60-45=15.

Hope this helps. <3

Answer:

The volume of the cube is 1/2 x 1/2 x 1/2 = 1/8

length x width x height = volume

1x2x2.5=5

2 1/2 = 2.5 because 1/2=0.5

to divide fractions multiply the reciprocal. The reciprocal is the fraction flipped over

5 / 1/8 = 5 x 8/1

5x8/1=40

40 cubes

Step-by-step explanation:

Answer:

\(\frac{1}{3}, \frac{2}{5} , \frac{3}{4} , \frac{4}{5}\)

Step-by-step explanation:

Start by making a common denominator. That way we can just compare the numerators of the fractions and easily order then from least to greatest. Start by finding the LCM(least-common-multiple) of the denominators.

The LCM of 3, 4, and 5, is 60.

So let's make each of the fractions have a denominator of 60.

Start with \(\frac{2}{5}\),

\(\frac{2}{5} =\frac{x}{60}\), no we have to solve for x, and since we multiply by 12 to get to 60 from 5, we multiply 2 by 12 as well.

So, \(x=24\).

Now do the same for each fraction.

\(\frac{1}{3} =\frac{x}{60}\), we multiply by 20, so \(x=20\)

\(\frac{4}{5} =\frac{x}{60}\), we multiply by 12, so \(x=48\)

\(\frac{3}{4}=\frac{x}{60}\), we multiply by 15, so \(x=45\)

So now are new fractions are \(\frac{24}{60} , \frac{20}{60} ,\frac{48}{60} , \frac{45}{60}\)

Now just order these like normal since they have a common denominator.

\(\frac{20}{60} ,\frac{24}{60} , \frac{45}{60} , \frac{48}{60}\)

Now revert them and make them there original values

\(\frac{1}{3}, \frac{2}{5} , \frac{3}{4} , \frac{4}{5}\)

Answer:

y=4x-5

Step-by-step explanation:

Slope-intercept form is y=mx+b where m is the slope and b is the y intercept.

Plug in what you know to solve for b.

3 = 4(2) + b

3 = 8 + b

3-8 = b

b = -5

now put b and m back into the slope- int form.

y = 4x-5

Soving the equations given below simultaneously,

Using elimination method,

The costs to buy 10 lb of rice and 50 lb of potatoes is $29.

Rice=x

Potatoes=y

We have two questions based on

(i) 20x+10y =16.60

(ii) 30x+12y= 23.52

To solve for the variables in equations (i) and (ii), we will use substitution.

From equation (iii)

y=( 16.60-20x):10= 1.66-2x

Substituting this into equation (ii):

• 30x + 12(1.66 - 2x) = 23.52

30x+19.92- 24x = 23.52

• 6x = 3.6

x= 3.6 : 6 = 0.6$

to find value y, we substitute to equation (iii)

y=1.66-2x

y=1.66-2(0.6$)

y=1.66-1.2

y=0.46$

Value x=0.6$ and y=0.46$

To buy 10 lb of rice and 50 lb of potatoes:

10x+50y= 10(0.6$) +50(0.46$) =6$+23$=29$

The Substitution Formula that is the formula used in Mathematics to solve a problem by combining known equations.

Most often found in mathematics lessons. This Substitution Formula is contained in the material on the System of Two Variable Linear Equations.

Your question is incomplete but most probably your full question was:

20 lb of rice and 10 lb of potatoes cost $16.60, and 30 lb of rice and 12 lb of potatoes cost $23.52, how much will 10 lb of rice and 50 lb of potatoes cost?

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Answer:

It takes takes them 31.67 secs to meet after Person A starts walking

OR

34.67 secs after Person B starts walking

Step-by-step explanation:

First, we will find the perimeter of the rectangle

From,

Perimeter of rectangle = 2 (\(l\) + \(b\))

Where \(l\) is the length

and \(b\) is the breadth

From the question, \(l\) = 100m

and \(b\) = 50m

Hence,

Perimeter of the rectangle = 2 (100+50)

= 2(150) = 300m

Hence, the perimeter of the rectangle is 300m

This is the total distance that will be covered by both persons by the time they meet.

Let the distance covered by person A be \(S_{1}\)

and the distance covered by person B be \(S_{2}\)

We can write that

\(S_{1}\) + \(S_{2}\) = 300m

Velocity of person A, \(V_{A}\) = 4 m/s

and velocity of person B, \(V_{B}\) = 5 m/s

From the question, Person A starts walking 3 seconds after person B,

This means, if person A spends \(t\) secs before they meet, then person B would spend (3 + \(t\)) secs.

For Person A,

Velocity = 4 m/s

Time = \(t\) secs

Distance = \(S_{1}\)

From,

\(Velocity = \frac{Distance}{Time}\)

Then,

\(Distance = Velocity \times time\)

\(S_{1} = 4 \times t\)

\(S_{1} = 4t\) ...... (1)

For Person B

Velocity = 5 m/s

Time = (t + 3) secs

Distance = \(S_{2}\)

Also, from

\(Distance = Velocity \times time\)

\(S_{2} = 5 \times (3+t)\)

\(S_{2} = 5(3+t)\) ...... (2)

Recall that, \(S_{1}\) + \(S_{2}\) = 300m

Then, \(S_{2}\) = 300m - \(S_{1}\)

We can then write that,

300m - \(S_{1}\) \(= 5(3+t)\)

Then,

\(S_{1} = 300 - 5(3+t)\) ..... (3)

Equating equations (1) and (3), we get

\(300 - 5(3+t) = 4t\)

\(300 - 15 -5t = 4t\\9t = 285\\t = \frac{285}{9}\\\)

\(t = 31.67 secs\)

This is the time spent by Person A

Hence, it takes takes them 31.67 secs to meet after Person A starts walking OR

34.67 secs after Person B starts walking

Answer:

I mistakenly rated Abdulazeez10's answer 2 stars because I thought he mixed up his variables, but I was actually the one who mixed up my variables.

Step-by-step explanation:

Sorry, Abdulazeez10 :( I can't change my rating, but just so everyone else knows, his answer is 100% correct!

To calculate the area of the triangle we need the length of the base and the height, being the height perpendicular to the base.

The base of the triangle has a length that is equal to the diameter of the circle. It can also be expressed as 2 times the radius r. So the base is:

The height is the segment perpendicular to the base that goes up to the vertex at the top. as it goes from the center of the circle to the border of the circle, it has a length that is equal to the radius r:

Then, we can calculate the area of the triangle as:

We can calculate the area of the circle as:

The probability that a randomly selected point within the circle falls in the white area is equal to the ratio of white area to the area of the circle.

The white area is equal to the area of the circle minus the area of the triangle.

Then, we can calculate the probability as:

Answer: The probability is p=0.68.

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer: \(-4\left(\frac{1}{2} \right)^{x}\)

Step-by-step explanation:

To reflect the graph of a function across the x-axis,

\(y=f(x) \longrightarrow y=-f(x)\)

Answer:

c

Step-by-step explanation:

Answer:

y^2 = 2x + 6

2x = y^2 - 6

x = 1/2(y^2 - 6)

The points of intersection of the  curves are  calculated:

y + 1 = 1/2( y^2 - 6)

2y + 2 = y^2 - 6

y^2 - 2y - 8 = 0

( y - 4)(y + 2) = 0

y = 4, -2

when y = 4, x = 5 and when y = -2 x = -1.

Integrating between  y = 4 and y = -2

     4

     INT  [ ( y + 1 + 1/2 (6 - y^2) ]dy

     -2

=    4

    {   y^2 / 2 + y + 3y - y^3/6 }

 -2

= 13 1/3 - (-4 2/3)

13 1/3 + 4 2/3

= 18  answer.

Answer:

i think its 18.

Step-by-step explanation:

h(x) = g(x) + 200, which means the average  new income tax is the sum of the original income tax and an additional flat fee of 200 dollars per taxpayer.

h(x) = g(x) + 200

h(x) is the new income tax for a single person with taxable income x dollars.

g(x) is the 2010 federal income tax for a single person with taxable income x dollars.

Therefore, h(x) = g(x) + 200, which means the new income tax is the sum of the original income tax and an additional flat fee of 200 dollars per taxpayer.

The new income tax plan consists of the 2010 income tax plus an additional 200 dollars per taxpayer. To represent this mathematically, we let g(x) be the function such that g(x) is the 2010 federal income tax for a single person with taxable income x dollars, and let h(x) be the corresponding function for the new income tax plan. By examining the new income tax plan, we can see that the new income tax is the sum of the original income tax plus an additional flat fee of 200 dollars per taxpayer. Thus, h(x) = g(x) + 200, which is a concise formula that captures the essence of the new income tax plan. This formula shows that the new income tax is simply the original income tax increased by a fixed amount of 200 dollars.

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Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

Answer:

rawl- 8 years old

mile- 24 years old

jerry- years old

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

d(5(x+2))/dx

d(5x+10)/dx

d(5x)/dx + d(10)/dx

5+0

5

The probability of passing at least one will be 0.70.

We know that,

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

here, we have,

Probability of passing history course = 0.59

Probability of passing math course = 0.60

Probability of passing both courses = 0.49

so, we get,

Probability of passing at least one will be

⇒ 0.59 + 0.60 – 0.49

⇒ 0.70

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complete question:

A student is taking two courses, history and math. the probability the student will pass the history course is 0.59, and the probability of passing the math course is 0.60. the probability of passing both is 0.49. what is the probability of passing at least one?

Answer:

a) The 90% confidence interval on the proportion of such graduates planning to continue their education is (0.2097, 0.2737).

b) The 95% confidence interval on the proportion of such graduates planning to continue their education is (0.2036, 0.2798).

c) Due to higher value of z, a 95% confidence interval, as in part b, is wider than a 90% confidence interval, found in part a, and is the difference between these two intervals.

d) Yes, because 0.25 is inside both intervals.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

117 of 484 new engineering graduates were planning to continue studying for an advanced degree.

This means that \(n = 484, \pi = \frac{117}{484} = 0.2417\)

90% confidence level

So \(\alpha = 0.1\), z is the value of Z that has a pvalue of \(1 - \frac{0.1}{2} = 0.95\), so \(Z = 1.645\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2417 - 1.645\sqrt{\frac{0.2417*0.7583}{484}} = 0.2097\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2417 + 1.645\sqrt{\frac{0.2417*0.7583}{484}} = 0.2737\)

The 90% confidence interval on the proportion of such graduates planning to continue their education is (0.2097, 0.2737).

Question b:

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a pvalue of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2417 - 1.96\sqrt{\frac{0.2417*0.7583}{484}} = 0.2036\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2417 + 1.96\sqrt{\frac{0.2417*0.7583}{484}} = 0.2798\)

The 95% confidence interval on the proportion of such graduates planning to continue their education is (0.2036, 0.2798).

(C) Compare your answers to parts (a) and (b) and explain why they are the same or different.

The margin of error of a confidence interval of proportions is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

This means that, due to higher value of z, a 95% confidence interval, as in part b, is wider than a 90% confidence interval, found in part a, and is the difference between these two intervals.

(D) Could you use either of these confidence intervals to determine whether the proportion is actually 0.25? Explain your answer. Hint: Use the normal approximation to the binomial.

Yes, because 0.25 is inside both intervals.

Answer:

Step-by-step explanatmkjion:

The Correct statements is \((\sqrt[m]{x^a})^b = \sqrt[m]{x^{ab}} \\\).

To determine which statement is true, let's evaluate each statement one by one:

\(\sqrt[m]{x} * \sqrt[m]{y} = 2\sqrt[m]{xy}\)

This statement is false. The correct product of two nth roots (\(\sqrt[m]{x}\) and \(\sqrt[m]{y}\)) is \(\sqrt[m]{x*y}\), not 2\(\sqrt[m]{x*y}\).

\((\sqrt[m]{x^a})^b = \sqrt[m]{x^{ab}} \\\).

This statement is true. When raising an nth root to a power, you can simply multiply the exponents. So, \((\sqrt[m]{x^a})^b = \sqrt[m]{x^{ab}} \\\)..

\(a \sqrt[n]{x}+ b \sqrt[n]{x} = ab \sqrt[n]{x}\)

This statement is false. The correct result of adding two nth roots is not the product of the coefficients. It's simply (a + b) \(\sqrt[n]{x}\).

\(\sqrt[m]{x} /\sqrt[m]{y} = \sqrt[m]{xy}\)

This statement is false. The correct division of two nth roots (\(\sqrt[m]{x}\) divided by \(\sqrt[m]{y}\)) is not equal to the product of the roots. The correct division is:

\(\sqrt[m]{x} /\sqrt[m]{y} = \sqrt[m]{x/y}\)

So, \(\sqrt[m]{x} /\sqrt[m]{y}\) is equal to \(\sqrt[m]{x/y}\), not \(\sqrt[m]{xy}\).

Correct statements:

\((\sqrt[m]{x^a})^b = \sqrt[m]{x^{ab}} \\\)

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