{Odd counting numbers less than 11}

Henry opens a savings account with an annual interest rate of 4.5 percent. After a year, he gets $75,000 in payment. He made a deposit into the savings account of $72,831.68.

Here are the steps on how to calculate the amount Henry invested:

Convert the annual interest rate to a monthly rate.

\(\begin{equation}4.5\% \div 12 = 0.375\%\end{equation}\)

Calculate the number of years.

\(\begin{equation}\frac{18 \text{ months}}{12 \text{ months/year}} = 1.5 \text{ years}\end{equation}\)

Use the compound interest formula to calculate the amount Henry invested.

\(\begin{equation}FV = PV * (1 + r)^t\end{equation}\)

where:

FV is the future value ($75,000)

PV is the present value (unknown)

r is the interest rate (0.375%)

t is the number of years (1.5 years)

\(\begin{equation}\$75,000 = PV \cdot (1 + 0.00375)^{1.5}\end{equation}\)

\$75,000 = PV * 1.0297

\(\begin{equation}PV = \frac{\$75,000}{1.0297}\end{equation}\)

PV = \$72,831.68

Therefore, Henry invested \$72,831.68 in the savings account.

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Answer:

I got you :)

Step-by-step explanation:

Remember the formula for the lateral surface area of a cylinder?

it is 2 x pi x radius x height

2·π·2·5 = 62.83185

Answer: 62.83in^3  

the in^3 is because its in square inches

Hope this helps!

Answer:

\(\rm\hookrightarrow Lateral\: surface\: area=\)62.8in²

Step-by-step explanation:

\(Solution,\\\\Here,\\\\Radius(r)=2in\\\\Height(h)=5in\\\\Now,\\\\\rm\hookrightarrow Lateral\: surface\: area=2\pi rh\\\\\rm\hookrightarrow Lateral\: surface\: area=2\times3.14\times2in\times5in\\\\\rm\hookrightarrow Lateral\: surface\: area=62.8in^{2}\)

30 percent of the 90-gallon is 27 gallons and the average person consumes this much of water as well.

The amount of water used overall must be multiplied by the proportion utilized outside to determine how much water is used outside:

27 gallons from 0.3 x 90 gallons.

Hence, each day the average person consumes around 27 gallons of water outside.

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The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is \($\sqrt{301}$\).

For part (a), we can find a nonzero vector orthogonal to the plane through the points P, Q, and R by constructing a normal vector to the plane using the cross product of two vectors in the plane. The two vectors in the plane are \($\vec{PQ} = (1- (-2), 0-1, 1-3) = (3, -1, -2)$\) and \($\vec{PR} = (1-4, 0-2, 1-5) = (-3, -2, -4)$\). Taking the cross product of the two vectors gives us the normal vector to the plane, \($\vec{n} = \vec{PQ} \times \vec{PR} = (8, -8, 12)$\). Therefore, the vector orthogonal to the plane is \($\vec{n} = (8, -8, 12)$.\)

For part (b), the area of triangle PQR can be found using the formula for Heron's Formula, which states that the area of a triangle with sides a, b,and c is given by

\($A = \sqrt{s(s-a)(s-b)(s-c)}$\)

where \($s = \frac{a+b+c}{2}$\) . In this case, the sides are \($a = \|\vec{PQ}\| = \sqrt{3^2 + (-1)^2 + (-2)^2} = \sqrt{14}$, $b = \|\vec{QR}\| = \sqrt{(-2-4)^2 + (1-2)^2 + (3-5)^2} = \sqrt{14}$\), and\($c = \|\vec{PR}\| = \sqrt{(-3)^2 + (-2)^2 + (-4)^2} = \sqrt{29}$\). Plugging these values into the formula, we get

\(= \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{\frac{7(7-\sqrt{14})(7-\sqrt{14})(7-\sqrt{29})}{4}} = \sqrt{7(7-\sqrt{14})^2(7-\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2(\sqrt{14}+\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2\sqrt{43}} = \sqrt{301}$\)Therefore, the area of triangle PQR is \($\sqrt{301}$\)

The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is \($\sqrt{301}$\).

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Answer:

domain is all real numberange

Answer: The answer is 8

Step-by-step explanation: 8 x 25 =200

Answer:

12/13

Step-by-step explanation:

The probability of not drawing an ace is =

1 minus the probability of drawing an ace.

there are 4 aces in a deck

hence the probability of not drawing an ace =

1 - \(\frac{4}{52}\)

= 48/52 = 12/13

The required probability of not drawing an ace would be 12/13.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

You draw a card from a standard deck of 52 playing cards.

The probability of not drawing an ace is P(E)

There are 4 aces in a deck

So the number of favorable outcomes n(E)= 4

And the total number of outcomes n(S) = 52

Thus, the probability of drawing an ace = n(E)/n(S) = 4 / 52

The probability of not drawing an ace will be:

⇒ P(E) = 1 - n(E)/n(S)

⇒ P(E) = 1 - 4 / 52

⇒ P(E) = 48/52

⇒ P(E) = 12/13

Therefore, the required probability of not drawing an ace would be 12/13.

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The answer to the question is no, there is not convincing evidence of a difference between the population proportions.

Confidence intervals are used to estimate the range of possible values of an unknown population parameter based on a sample. If the confidence interval does not contain 0, it means that the difference between the sample proportions is statistically significant, which suggests that the difference between the population proportions may also be statistically significant. However, to conclude that there is convincing evidence of a difference between the population proportions, it is important to make sure that the conditions for performing the hypothesis test have been met, such as the independence of the sample and the normality of the population.

In this case, it seems that the conditions have not been met, so we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify Egypt on the map is different from the true proportion of women that can identify Egypt on a map.

Therefore, the answer to the question is no, there is no convincing evidence of a difference between the population proportions.

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The answer to the question is no, there is not convincing evidence of a difference between the population proportions.

Confidence intervals are used to estimate the range of possible values of an unknown population parameter based on a sample. If the confidence interval does not contain 0, it means that the difference between the sample proportions is statistically significant, which suggests that the difference between the population proportions may also be statistically significant. However, to conclude that there is convincing evidence of a difference between the population proportions, it is important to make sure that the conditions for performing the hypothesis test have been met, such as the independence of the sample and the normality of the population.

In this case, it seems that the conditions have not been met, so we cannot use this interval to conclude that there is convincing evidence that the true proportion of men who can identify Egypt on the map is different from the true proportion of women that can identify Egypt on a map.

Therefore, the answer to the question is no, there is no convincing evidence of a difference between the population proportions.

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The value of r is 4 feet, the correct option is A.

The area of a circle is the region occupied by the circle in a two-dimensional plane.

Given

The area of circle Z is 64 ft2.

According to the following formula, we must find the radius of the circle:

\(\rm r =\sqrt{\dfrac{Area}{\pi }}\)

Substitute all the values in the formula

\(\rm r =\sqrt{\dfrac{Area}{\pi }}\\\\\rm r =\sqrt{\dfrac{64}{3.14}}\\\\\rm r =\sqrt{20.38}\\\\r=4.5\)

Hence, the value of r is 4 feet.

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The n circles divides the plane into six parts.

Let the number of circles given be n, and their intersection points be k. Now, let's draw the first few figures, noting the number of intersections between circles as we go.

First, we'll look at a single circle. There are two regions in the area of a single circle. Now, let's look at two circles. When we have two circles, we have four parts.

There are two regions inside each circle and two regions outside each circle. If we add one more circle, we will get a total of seven parts.

As we can see, when we add a circle, we create new regions. The number of new parts added is equivalent to the number of old regions that intersect the circle.

This suggests that the formula for the number of regions created by n circles, each of which intersects every other circle, is as follows:

R(n)=R(n−1)+n−1

Here, R(n) is the number of areas divided by n circles.

In other words, the number of parts into which the plane is divided. Let's apply this formula to our example. The number of areas divided by three circles that intersect each other is given by

R(3)=R(2)+2=4+2=6

Thus, the three circles divide the plane into 6 regions. Therefore, the answer is 6 parts.

A circle is a fundamental geometric shape defined as the set of all points in a plane that are equidistant from a fixed center point. It is a closed curve consisting of points that are all at a constant distance, called the radius, from the center.

Circles have numerous applications in geometry, trigonometry, physics, and engineering. They are used to represent and analyze curved objects, orbits, angles, and many other phenomena.

The properties and equations associated with circles play a significant role in various mathematical and scientific fields.

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Answer:

D- -1 <_y<_4

Step-by-step explanation:

When computing the elasticity of demand for the given demand equation, we get ε = [dp/dx * x/p]

Given the equation for the demand p = 148 - x² and given the price p = 296/3

We know that demand is elastic when the absolute value of ε > 1, inelastic when the absolute value of ε < 1, and unitary when the absolute value of ε = 1.

Thus, let us first compute the derivative of p with respect to x as follows dp/dx = -2x

Next, let us substitute the given price p, and then solve for x in the equation p = 148 - x²:296/3 = 148 - x²

x² = 148 - 296/3x² = 296/3

Thus, x = ± sqrt(296/3)

Now, we will substitute this value of x into the expression for the elasticity of demand to determine the elasticity of demand.

ε = [dp/dx * x/p]

For x = sqrt(296/3), ε = [-2(sqrt(296/3)) / (148 - (296/3))]

ε = -1.030

Since the absolute value of ε > 1, the demand is elastic. Therefore, the given demand is elastic at a price of 296/3.

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The lines having linear equation y=4x+1 and y=2x-1 intersect at the point (-1, -3).

What is a linear equation, exactly?

A linear equation is an algebraic equation of the first degree that describes a line in a two-dimensional plane. It is an equation of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept. The slope represents the rate of change of y with respect to x, while the y-intercept represents the point at which the line crosses the y-axis

Now,

To find the point of intersection between the lines y=4x+1 and y=2x-1, we can set the two equations equal to each other or we can graph these and find the intersection point.

1.

4x+1 = 2x-1

Simplifying this equation, we get:

2x = -2

x = -1

Now, we can substitute this value of x into either equation to find the corresponding value of y:

y = 4x+1 = 4(-1)+1 = -3

Therefore,

               the lines y=4x+1 and y=2x-1 intersect at the point (-1, -3).

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Answer:

$1.25

Step-by-step explanation:

30*2=15

15/12=1.25

Answer:

300 grapes

Step-by-step explanation:

This is done through ratios.

10 grapes:2 mg

x grapes : 60 mg

If you cross multiply, you get 300 grapes

Answer:

If ℓ, b and h denote respectively the length, breadth and height of a cuboid, then Total surface area of the cuboid = 2 (ℓb + bh + ℓh) square units. Volume of the cuboid = Area of the base × height = ℓ × b × h cubic units. where base area = Breadth × length

Hopefully, this helps! :D

Therefore, the change in profit is approximately 0.60 and the percent change in profit is approximately 0.81%.

The given function is P = 100xe–x/400, where is sales.

The change in profit as sales increase from x = 115 to x = 120 units is to be determined.

To find the change in profit, we need to calculate the profit at x = 115 and x = 120 and then find the difference between them.

P(115) = 100 * 115e^(–115/400) ≈ 73.99

P(120) = 100 * 120e^(–120/400) ≈ 73.39

The change in profit = P(120) - P(115) ≈ 0.60

Approximate percent change in profit as sales increase from

x = 115 to x = 120 units = (change in profit / initial profit) × 100%≈ (0.60/73.99) × 100%≈ 0.81%.

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Answer:

either 5 or 6 months

Step-by-step explanation:

Tom   M    Jerry

500    1     125

475     2   175

450     3    225

425     4    275

400     5    325

375     6    375

Sixteen teachers ordered a book to be used in their classrooms. The book costs $350, which is to be shared equally. The most appropriate representation of how much each teacher will pay is $350 / 16 = $ 21.88.

Since there are a total of sixteen teachers who placed an order for a book and the cost of the book is $ 350.

Thus, in order to determine the amount to be paid by each teacher equally is calculated by dividing the total cost of the book by the number of teachers, as follows

=  $ 350 / 16

=  $  21.875

After rounding off, it is

=   $ 21.88

Thus, each teacher will pay $ 21.88 for the book.

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Answer:

f(t)=4800(1.0378)^4t

3.78%

Step-by-step explanation:

f(t)=

f(t)=a(1+r)^t

f(t)=4800(1+0.16)^t

f(t)=4800(1.16)^t

Answer:

What? Retype the question below and ill answer it, but this isnt answerable.

Step-by-step explanation:

What is \redD{\text{A}}Astart color #e84d39, start text, A, end text, end color #e84d39 rounded to the nearest ten? What is \redD{\text{A}}Astart color #e84d39, start text, A, end text, end color #e84d39 rounded to the nearest hundred?

Like what kind of language is this ;--;

Answer:A) 8 miles

Step-by-step explanation:

8 miles

Answer:

Step-by-step explanation:

25, i think

The probability that at least 2 people have the same birthday when 27 people are selected at random can be calculated using the complement rule.

Assuming that birthdays are uniformly distributed throughout the year and that there are 365 days in a year (ignoring leap years), the probability that the first person has a unique birthday is 365/365. The probability that the second person has a different birthday is 364/365, and so on. Therefore, the probability that all 27 people have different birthdays is:

P(all different) = (365/365) * (364/365) * ... * (339/365)

To find the probability that at least 2 people have the same birthday, we subtract P(all different) from 1:

P(at least 2 have same birthday) = 1 - P(all different)

Calculating the values, we can find the probability. However, since the calculation involves a large number of fractions, it's not possible to generate the exact answer within the given 100-word limit.

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Answer:

i think it is the 0 property of addition. i hope this helps

Answer: Property of Addition

Step-by-step explanation: property of addition: Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4. Associative property of addition: Changing the grouping of addends does not change the sum.

Answer:

19

Step-by-step explanation:

The answer is B. 7x + 27 units.

Area is length multiplied by width, so to find the length, simply divide the expression 21x + 81 by the width --> 3.

21x becomes 7x, and 81 becomes 27.

To find the particular solution to the differential equation y′=3x3 that passes through (1,4.75), we need to use the given general solution y=c 3x44.

First, we differentiate the general solution to get y′=12cx33.

Next, we substitute the point (1,4.75) into the equation:

4.75 = c 3(1)^4 + C

where C is the constant of integration.

Simplifying this equation, we get:

4.75 = 3c + C

To find the value of C, we need to solve for it. We can do this by using the fact that the particular solution passes through the point (1,4.75). Substituting these values into the equation above, we get:

4.75 = 3c + C

4.75 = 3c + C

4.75 - 3c = C

So C = 4.75 - 3c.

Now we substitute this value of C back into the general solution to get the particular solution:

y = c 3x44

y = (4.75 - 3c) 3x44

Therefore, the particular solution to the differential equation y′=3x3 that passes through (1,4.75), given that y=c 3x44 is a general solution, is y = (4.75 - 3c) 3x44.

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Answer:

The car must go at 108 km per hour

Step-by-step explanation:

Let us solve the question

∵ A journey by bus takes 45 minutes at 60 km per hour

∴ The speed of the bus = 60 km per hour

∴ The time of the journey = 45 minutes

→ Change the time from minutes to hours

∵ 1 hour = 60 minutes

∴ 45 minutes = 45 ÷ 60 = 0.75 hour

∴ The time of the journey = 0.75 hour

∵ Distance = Speed × Time

→ Substitute the speed by 60 and the time by 0.75

∵ The distance that the bus traveled = 60 × 0.75

∴ The distance that the bus traveled = 45 km

∵ A car goes to do the same journey in 25 minutes

∴ The distance that the car travels = 45 km

∴ The time that the car takes = 25 minutes

→ Divide it by 60 to change it to hours

∵ 25 minutes = 25 ÷ 60 = \(\frac{5}{12}\) hour

∴ The time that the car takes =  \(\frac{5}{12}\) hour

→ Use the rule of the distance above to find the speed of the car

∵ 45 = the car's speed ×  \(\frac{5}{12}\)

→ Divide both sides by  \(\frac{5}{12}\)

∴ 108 = the car's speed

∴ The car's speed = 108 km per hour

∴ The car must go at 108 km per hour