Russel wants to buy 3 identical gift cards. He wants to make sure the total cost is no more than $2 above or below $60. Which of the following inequalities represents the situation?

Answer:

5000

Step-by-step explanation:

1000 ÷ 2 = 500 x 10 = 5000

Answer:

Step-by-step explanation:

Formula for compound interest:

A= P(1+r/n)^n x t

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

We know that Serena pays annually meaning yearly (12 months or 1 year)

So after substituting all the numbers in,

A= 1000(1+0.02/12)^(12x10)

We change the rate to 0.02 because we must divide 2% by 100%. And divide the rate by number of times applied per time (n).

DISCLAIMER:

I have not done compound interest questions in a long time but if you want to confirm my answer, go to a calculator site and just input the numbers on there.

The velocity of the cylinder when it reaches the bottom of the incline is v = sqrt(4gh/3).

The velocity of the cylinder when it reaches the bottom of the incline can be calculated using the principle of conservation of energy. The velocity of the cylinder is given by the formula v = sqrt(2gh/(1+I/(mr^2))), where g is the acceleration due to gravity, h is the height of the incline, and I is the moment of inertia of the cylinder.

In this case, the cylinder is released from rest at a height h on an incline without slipping, which means that all the potential energy at the top of the incline is converted to kinetic energy at the bottom of the incline. Therefore, we can write:

1/2 mv^2 = mgh

where v is the velocity of the cylinder at the bottom of the incline.

The moment of inertia of the cylinder is given as 1/2mr^2. Substituting this into the formula for v and simplifying, we get:

v = sqrt(2gh/(1+1/2)) = sqrt(4gh/3)

Therefore, the velocity of the cylinder when it reaches the bottom of the incline is v = sqrt(4gh/3).

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The radius of the spherical part is 3 inches and the length of the tube is 21 cm.

The capacity of a cylinder, which determines how much material it can hold, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, can be immersed in it uniformly.

Given that the volume when the water is fully dipped is 4554 / 7 cm³. The volume when the length is 9 cm empty is 396 cm³.

The two equations can be formed as below:-

4554 / 7 = πr²l + (2/3)πr³

396 = πr²( l - 9 ) + (2/3)πr³

Subtract the second equation from the first,

( 4554 / 7 ) - 396 = 9πr²

9πr² = 254.5

r² = 9

r = 3 cm

The length will be calculated as:-

4554 / 7 = πr²l + (2/3)πr³

4554 / 7 = π( 3 )²l + (2/3)π(3)³

l = 21 cm

Therefore, the tube's length is 21 cm, and the spherical part's radius is 3 inches.

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a. The resultant magnetic field at point P due to currents in the two wires can be determined by vector addition of the individual magnetic fields.

b. Reversing the direction of currents in both wires would result in a reversed direction of the resultant magnetic field at point P.

a. To construct the vector diagram showing the direction of the resultant magnetic field at point P due to currents in the two wires, we can use the right-hand rule for determining the magnetic field direction around a wire carrying current.

For Wire 1, which has the current coming towards us (out of the plane of the paper), the magnetic field direction can be determined by wrapping the right-hand fingers around the wire in the direction of the current, and the thumb will point in the direction of the magnetic field. Let's say the direction of the magnetic field for Wire 1 is from left to right.

For Wire 2, which has the current going into the plane of the paper, we apply the right-hand rule again. Wrapping the right-hand fingers around the wire in the direction opposite to the current, the thumb will point in the direction of the magnetic field. Let's say the direction of the magnetic field for Wire 2 is from right to left.

At point P, which is equidistant from the two wires, the magnetic fields due to the currents in the wires will combine. The resultant magnetic field direction at point P can be found by vector addition. Drawing the vectors representing the magnetic fields for Wire 1 and Wire 2, with opposite directions, we can add them head-to-tail. The resultant vector will show the direction of the resultant magnetic field at point P.

b. If the currents in both wires were instead directed into the plane of the page (such that the current moved away from us), the directions of the magnetic fields due to the currents in the wires would be reversed compared to the previous case.

For Wire 1, the magnetic field direction would be from right to left, and for Wire 2, it would be from left to right. Following the same process as in part a, we would draw the vectors representing the magnetic fields for Wire 1 and Wire 2 in their respective reversed directions. Adding them head-to-tail would give us the resultant vector indicating the direction of the resultant magnetic field at point P in this scenario.

Complete Question:

Two wires lie perpendicular to the plane of the paper, and equal electric currents pass through the paper in the directions shown. Point P is equidistant from the two wires.

a. Construct a vector diagram showing the direction of the resultant magnetic field at point P due to currents in these two wires. Explain your reasoning.

b. If the currents in both wires were instead directed into the plane of the page (such that the current moved away from us), show the resultant magnetic field at point P.

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Answer:

definition of perpendicular bisector

Step-by-step explanation:

You need to show the entire problem including the given.

I assume the given info states that

Segment MP is the perpendicular bisector of segment NO.

If that's the case, then the reason for lengths NP and OP being equal is

"definition of perpendicular bisector"

Calvin's age is now 23 years old.

9 years ago, Dallas was 3 times Calvin's age, which was 11.

Therefore, 9 years ago, Dallas was 33. 32 years ago, when Calvin was 0, Dallas was 32.

Since then, Dallas has aged 1 year for every year Calvin has aged, so Calvin is now 23 and Dallas is 55.

This problem can also be solved using algebra. Let x be Calvin's age now, and y be Dallas' age 9 years ago. We can then set up the following equation:

x + 32 = 3(y - 9)

We can simplify this to x + 32 = 3y - 27 and solve for x:

x = 3y - 27 - 32

Plugging in the given information that y = 33, we get:

x = 3(33) - 27 - 32 = 23

Therefore, Calvin is currently 23 years old.

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Answer:

31.4 cm , just did the quiz

Step-by-step explanation:

The length of the minor arc is 31.4 cm of the given circle.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Arc length is the distance between two points along a section of a curve.

The formula for arc length is θ/360×2πr

Arc length =  θ/360×2πr

Where θ is the central angle and r is the radius of the circle.

θ = 60 degrees and r is 30 cm

Plug in the value of θ and r

Arc length = 60/360 × 2×3.14×30

=1/6×60×3.14

=188.4/6

=31.4

Hence, the length of the minor arc is 31.4 cm of the given circle.

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Using the property that the Fourier Transform of the nth derivative of a function is given by (iω)^n times the Fourier Transform of the original function, we get:

F(ω) = (-iω)^3 F(ω)'

(a) To find the Fourier Transform of the given function, we can use the definition of the Fourier Transform:

\(F(ω) = ∫[-∞,∞] f(t) e^(-iωt) dt\)

where f(t) is the input signal and F(ω) is its Fourier Transform.

For the given function, f(t) is equal to 1 for 0 < t < 1 and 0 otherwise. We can write this as:

f(t) = u(t) - u(t-1)

where u(t) is the unit step function, defined as u(t) = 1 for t > 0 and u(t) = 0 for t < 0.

Substituting this expression for f(t) into the Fourier Transform integral, we get:

\(F(ω) = ∫[0,1] e^(-iωt) dt - ∫[1,∞] e^(-iωt) dt\)

Using integration by parts with u = e^(-iωt) and dv/dt = 1, we get:

\(∫ e^(-iωt) dt = -iω e^(-iωt) / ω^2 + C\)

where C is the constant of integration. Substituting this into the Fourier Transform integral, we get:

\(F(ω) = [(-iω e^(-iωt) / ω^2 + C)]_0^1 - [(-iω e^(-iωt) / ω^2 + C)]_1^∞\)

Simplifying this expression, we get:

\(F(ω) = (-iω e^(-iω) / ω^2 + C) - C - (-iω e^(-iω) / ω^2 + C)= -iω e^(-iω) / ω^2\)

Therefore, the Fourier Transform of the given function is F(ω) = -iω e^(-iω) / ω^2.

(b) To find the Fourier Transform of the given function using differentiation, we can differentiate the function three times and use the property that the Fourier Transform of the nth derivative of a function is given by (iω)^n times the Fourier Transform of the original function.

The first derivative of the function is:

f'(t) = δ(t) - δ(t-1)

where δ(t) is the Dirac delta function, which has a value of infinity at t = 0 and 0 elsewhere. The second derivative of the function is:

f''(t) = δ'(t) - δ'(t-1) = -δ(t) + δ(t-1)

where δ'(t) is the derivative of the Dirac delta function, which is defined as δ'(t) = d/dt δ(t).

The third derivative of the function is:

f'''(t) = -δ'(t) + δ'(t-1) = -δ''(t) + δ''(t-1)

where δ''(t) is the second derivative of the Fourier Transform which is defined as\(δ''(t) = d^2/dt^2 δ(t).\)

where F(ω)' is the Fourier Transform of f'(t). To find F(ω)', we can use the fact that the Fourier Transform of the Dirac delta function is 1, and the   Fourier Transform

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The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Answer:

False

Step-by-step explanation:

Dividing integers is opposite operation of multiplication. But the rules for division of integers are same as multiplication rules. Though, it is not always necessary that the quotient will always be an integer.

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Answer: 1 4/5 feet

Step-by-step explanation:

Here's the complete question:

Taylor is decorating for a party. She cuts 5 equal-length streamers from a strip of yellow paper that is 9 feet long. How long is each streamer in fraction form?

The length of each streamer will be gotten by dividing the length of the strip of yellow paper by the number of streamers. This will be:

= 9 feet / 5

= 1 4/5 feet

Therefore, the length of each streamer is 1 4/5 feet.

Answer:

Step-by-step explanation:

Answer:

103 is my answer.

Step-by-step explanation:

hope it helps

a.  If we let u = (3 - 2x), then the derivative du/dx would be -2, which is not equal to zero. This indicates that the substitution does not satisfy the requirement for u to be differentiable.

b. Michael's substitution satisfies the requirement for u to be differentiable.

(a) i. Kayla's proposed substitution of u as (3 - 2x) will not work in this case. The reason is that when using the u-substitution method, it is necessary for the chosen u to be differentiable, meaning that its derivative du/dx should exist and be non-zero. However, if we let u = (3 - 2x), then the derivative du/dx would be -2, which is not equal to zero. This indicates that the substitution does not satisfy the requirement for u to be differentiable.

ii. Kayla's idea of always picking the most inside factor as u does not work for all u-substitutions. There can be cases where choosing the most inside factor may not lead to a valid substitution that simplifies the problem or makes integration easier. It is important to consider the properties of the function and choose a suitable substitution accordingly.

(b) i. Michael's proposed substitution of u as 3√3 - 2x will work in this case. If we let u = 3√3 - 2x, then the derivative du/dx would be -2, which is non-zero. Therefore, Michael's substitution satisfies the requirement for u to be differentiable.

ii. Michael's idea of always picking the most complicated factor as u also does not hold true for all u-substitutions. The choice of u depends on various factors, including the structure of the function, simplification possibilities, and making the integration process more manageable. It is not necessarily the case that the most complex factor will always result in a successful substitution.

It is important to consider the specific characteristics of the function and apply appropriate judgment in choosing the substitution u to simplify the problem effectively.

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The question asks to estimate the rainfall at station D in the year 1980 based on the rainfall data of other stations. The answer is that station D's rainfall in 1980 can be estimated by comparing the rainfall patterns of all stations in the basin.

To estimate the rainfall at station D in 1980, we can analyze the relationship between the rainfall at different stations. In this case, we can observe that there is a correlation between the annual rainfall at stations A, B, C, and D. By comparing the rainfall patterns of these stations, we can make an estimation for station D.

In the given data, station D is inoperative in 1980, but the rainfall data for stations A, B, and C are available. By analyzing the rainfall patterns in previous years and considering the correlation between the stations, we can estimate the rainfall at station D in 1980 based on the rainfall data of the other stations in the basin.

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Using a system of equations to find variables for a parallelogram requires a long answer because there are several steps involved. However, once you understand the properties of parallelograms and how to set up the equations, it becomes a straightforward process.

To find variables for a parallelogram using a system of equations, you will need to use the properties of parallelograms. One important property of a parallelogram is that opposite sides are parallel. Therefore, you can use the slope formula to find the slope of each side of the parallelogram.
Once you have the slopes of the sides, you can set up two equations in point-slope form for the two pairs of opposite sides. For example, if one pair of opposite sides has slopes m1 and m2, and one of the sides passes through point (x1, y1), the equation for that side would be y - y1 = m1(x - x1). You can set up a similar equation for the other side.
Next, you can solve the system of equations to find the values of the variables. This will give you the coordinates of the vertices of the parallelogram. You can then use the distance formula to find the lengths of the sides and the Pythagorean theorem to find the diagonals.

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The percentage of people who earn less than $50,000 is approximately 15.87%.

To find the percentage of people who earn less than $50,000, we can use the properties of the normal distribution.

Given that the salaries follow a normal distribution with a mean of $60,000 and a standard deviation of $10,000, we can use this information to calculate the z-score for the salary of $50,000.

The z-score is calculated as:

z = (x - μ) / σ,

where x is the value we want to find the percentage for, μ is the mean of the distribution, and σ is the standard deviation.

Plugging in the values, we get:

z = ($50,000 - $60,000) / $10,000 = -1.

Now, we need to find the area under the normal distribution curve to the left of the z-score of -1. This represents the percentage of people who earn less than $50,000.

Using a standard normal distribution table or a calculator, we can find that the area to the left of a z-score of -1 is approximately 0.1587. This means that approximately 15.87% of people earn less than $50,000.

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The probability of getting a 4, and taking a green ball is 1/48.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

The probability of flipping a coin and getting a head is 1/2. The probability of tossing a die and getting a 4 is 1/6. The probability of taking a green ball out of a bag is 1/4. Therefore, the probability of flipping a coin and getting a head, tossing the die and getting a 4, and taking a green ball out of a bag is (1/2) * (1/6) * (1/4) = 1/48.

Hence, the probability of getting a 4, and taking a green ball is 1/48.

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Answer:

\( \boxed{n = 8} \)

Step-by-step explanation:

\( = > 9n - 7 = 3 + 8n - 2 \\ \\ = > 9n - 7 = 8n + 3 - 2 \\ \\ = > 9n - 8n = 1 + 7 \\ \\ = > n = 8\)

Answer:

8

Step-by-step explanation:

9n - 7 = 3 + 8n - 2

Combine like factors.

9n - 7 = 8n + 1

Subtract 8n from both sides

n - 7 = 1

Add 7 to both sides.

n = 8

Answer:

A, C, D

Step-by-step explanation:

One rule of thumb is just add up two sides and if its greater than the third value that side works. (make sure to test it for all of the sides though)

The missing value for the letter b can be determined by finding the ratio of pencils to pens and applying it to the known value of pencils. The value of b is 168.

To find the missing value for the letter b, we need to determine the ratio of pencils to pens based on the given information. We can do this by dividing the number of pencils by the number of pens in each case.

In the first case, the ratio is 18/72 = 1/4.

In the second case, the ratio is 29/35 = 1/5.

To find the missing value for b, we need to apply the same ratio to the number of pens in the third case, which is 140.

Using the ratio 1/5, we can calculate b as follows:

b = (1/5) * 140 = 28.

However, there seems to be a mistake in the given answer choices. The correct value of b based on the calculations is 28, not 168. Therefore, the missing value for the letter b is 28.

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Answer:

x = √21, x = -√21

The mean and variance of the number of accepted applications by the banker in a day are 10 and 7.5 respectively.

Given that a banker reviews 40 loan applications a day and the acceptance rate of a loan application is 25%. We have to find the mean and variance of the number of accepted applications by the banker in a day.

Let X be the random variable that represents the number of applications accepted by the banker in a day. As given, the acceptance decision is independent across applications.

The probability of accepting a loan application is 0.25. Then, the probability of rejecting the loan application is 1 - 0.25 = 0.75.

We know that mean of a binomial distribution with parameters n and p is given by μ = np and the variance is given by σ^2 = np(1 - p).

Therefore,

Mean:

μ = np

Where n = 40 and p = 0.25

μ = 40 * 0.25

μ = 10

Variance:

σ^2 = np(1 - p)

Where n = 40 and p = 0.25

σ^2 = 40 * 0.25 * (1 - 0.25)

σ^2 = 7.5
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Answer: 4/5

Step-by-step explanation:

\(6 \cdot \frac{2}{15}=(2)(3) \cdot \frac{2}{3(5)}=\frac{4}{5}\)