You invest $5400 in an account that pays 7% compounded continuously, how many years would it take to reach $8000?

The total erasing cost is 5.

The erasing cost refers to the cost associated with removing or eliminating something. In this case, the question states that the total erasing cost is 5. However, without further context or information, it is unclear what specifically is being erased and what the units of the cost are.

To provide a more detailed explanation, it would be helpful to have additional information about the context or problem at hand. Please provide more details or clarify the question so that I can assist you more effectively in determining the specific meaning and explanation behind the total erasing cost of 5.

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Answer:

3 is 1

4. 7^-2

Step-by-step explanation:

Answer:

0.016328

Step-by-step explanation:

7^-6 = 0.000008

7^4 = 2041

Multiply em' both together and you get... 0.016328

Hope it helps

The purpose of using prefix in the metric system is to properly sale the basis of the unit so large numeric values can be used effectively.

If the metric system is not properly prefixed it can lead to various inconsistencies in the the numeric values. for example if you go to a computer store and you do not know the scale like (kb, mb, gb, tb) you will get quite confused about what is the sales representative saying

Consider you went to a store to get sugar and you do not know the metric system say(gram, kg, mg) you would not know how much sugar you need directly by taking it in your hands.

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Ellen can make a maximum of 6 batches of Cardamom cookies with her 2 fluid ounces of cardamom.

Ellen has 2 fluid ounces of cardamom in a jar. Her recipe requires 3/10 of a fluid ounce of cardamom for each batch of cardamom cookies.

We can use division to find the number of batches of cardamom cookies that Ellen can make with all of her cardamom:

2 fluid ounces ÷ (3/10 fluid ounce per batch) = (2/1) ÷ (3/10)

= (2/1) x (10/3)

= 20/3

= 6 2/3

Therefore, Ellen can make 6 batches of cardamom cookies with her 2 fluid ounces of cardamom, with 2/3 of a batch remaining.

Since she cannot make a fraction of a batch, Ellen can make a maximum of 6 batches of cardamom cookies with her 2 fluid ounces of cardamom.

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Considering a sinusoidal equation, and the concept of amplitude, if it found that the equation's amplitude is of 3 hours.

It is given by half the difference between the greatest and the smallest value.

In this problem:

0.5 x (15 - 9) = 3.

Hence, the equation's amplitude is of 3 hours.

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Answer :

$456

Step-by-step explanation:

Donation by local business :\( \frac{15}{100} \times 380 \\ \\ \frac{15 \times 38}{10} = 57\)

= $57

Donation by the principal of the student's school :

\( \frac{5}{100} \times 380 \\ \\ = \frac{5 \times 38}{10} = 19\)

= $19

The total money received by the food pantry :

$380 + $57 + $19

= $456

0.15 (380) = 57

0.05 (380) = 19

Let p = Food Pantry money in total

p = 380 + 57 + 19

p = $456

Answer:

0

Step-by-step explanation:

because

k  c  r

10 + (-10)

10 - 10=0

Answer:

☛☚um its 0

Step-by-step explanation:

Given:

Diameter of the hole = 30 cm

To find:

The area of the hole.

Solution:

The radius of a circle is always half of the diameter. It is given that the diameter of the hole is 30 cm. So, the radius of the hole is:

\(r=\dfrac{30}{2}\)

\(r=15\)

Area of a circle is:

\(A=\pi r^2\)

Putting \(\pi = 3.14\) and \(r=15\) in the above formula, we get

\(A=(3.14)(15)^2\)

\(A=(3.14)(225)\)

\(A=706.5\)

Therefore, the area of the hold is 706.5 square cm.

In a proportional relationship between two quantities, the constant of proportionality, often denoted by the letter "k," represents the value that relates the two quantities. The equation y = kx is the standard form for expressing a proportional relationship, where "y" and "x" are the variables representing the two quantities.

Here's a breakdown of the components in the equation:

y: Represents the dependent variable, which is the quantity that depends on the other variable. It is usually the output or the variable being measured.

x: Represents the independent variable, which is the quantity that determines or influences the other variable. It is typically the input or the variable being controlled.

k: Represents the constant of proportionality. It indicates the ratio between the values of y and x. For any given value of x, multiplying it by k will give you the corresponding value of y.

The constant of proportionality, k, is specific to the particular proportional relationship being considered. It remains constant as long as the relationship between x and y remains proportional. If the relationship is linear, k also represents the slope of the line.

For example, if we have a proportional relationship between the distance traveled, y, and the time taken, x, with a constant of proportionality, k = 60 (representing 60 miles per hour), the equation would be y = 60x. This equation implies that for each unit increase in x (in hours), y (in miles) will increase by 60 units.

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The number of miles where half a gallon is used is 15.5 miles.

From the information, it can be seen that the number of gallons that was used for 62 miles is 2 gallons.

Therefore, let the number of miles that will be used for 1/2 gallon = 0.5 x.

This will be represented as:

0.5 / 2 = x / 62

Cross multiply

2x = 62 × 0.5

2x = 31

Divide

x = 31 / 2

x = 15.5

The miles is 15.5 miles

The picture is attached.

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Answer:

b = 93° , c = 87°

Step-by-step explanation:

b and 93° are vertically opposite angles and are congruent , then

b = 93°

c and 93° are a linear pair and sum to 180° , that is

c + 93° = 180° ( subtract 93° from both sides )

c = 87°

Answer:

b=93

c=87

Step-by-step explanation:

1. For b, the angle is 93 degrees because of the vertical angle theorem, where two straight lines intersect, forming two sets of linear pairs with congruent angles.

Therefore, that angle is 90 degrees.

2. For c, use the given angle that is provided, since angle C and the given angle are supplementary (equaling 180 degrees), we can subtract the total (180) from the part (93)

180 - 93 = 87

We can see here that the solutions to the triangles are:

1. 62.2°.

2. 35.9°

3. 61.9°

4. 53.1°

We can see here that using trigonometric ratio formula, we find the values of x.

We see the following:

1. Cos x = 7/15 = 0.4666

x = \(cos^{-1}\) 0.4666 = 62.2°.

2. Sin x = 27/46 = 0.5869

x° = \(sin^{-1}\)  0.5869  = 35.9°

3. Sin x = 30/34 = 0.8823

x° = \(sin^{-1}\) 0.8823 = 61.9°

4. Tan x = 8/6 = 1.3333

x° = 1.3333 = 53.1°

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The potential differences δV12, δV23, δV34, and δV41 represent the differences in electric potential between specific pairs of points in a circuit or electrical system.

In an electrical circuit, potential difference refers to the difference in electric potential between two points. It represents the work done per unit charge in moving a charge from one point to another. The potential differences δV12, δV23, δV34, and δV41 are defined as follows:

δV12 (or V2 - V1) represents the potential difference between points 1 and 2.

δV23 (or V3 - V2) represents the potential difference between points 2 and 3.

δV34 (or V4 - V3) represents the potential difference between points 3 and 4.

δV41 (or V1 - V4) represents the potential difference between points 4 and 1.

The specific values of these potential differences depend on the configuration of the circuit or electrical system and the distribution of electric potential.

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Answer: \(28.3\ hr\)

Step-by-step explanation:

Given

Charge of the site visit \(\$45\)

Additional charge per hour is \(\$24\ \text{per hour}\)

He eaned \(\$810\)

Suppose he worked for x hours

\(\therefore 810=45+24x\\\text{On solving}\)

\(\Rightarrow 765=24x\\\Rightarrow x=28.3\ hr\)

Answer:

3(4) - 2 is 10 the value is 10

5(2) + 6 is 16 the value is 16

I hope this helps have a good day or night!

The mean amount spent on breakfast weekly is approximately $11.14, and the standard deviation is approximately $2.23.

To calculate the mean and standard deviation of the amount she spends on breakfast weekly (7 days), we need the individual daily expenditures data. Let's assume we have the following daily expenditure values in dollars: $10, $12, $15, $8, $9, $11, and $13.

To find the mean, we sum up all the daily expenditures and divide by the number of days:

Mean = (10 + 12 + 15 + 8 + 9 + 11 + 13) / 7 = 78 / 7 ≈ $11.14

The mean represents the average amount spent on breakfast per day.

To calculate the standard deviation, we need to follow these steps:

1. Calculate the difference between each daily expenditure and the mean.

  Differences: (-1.14, 0.86, 3.86, -3.14, -2.14, -0.14, 1.86)

2. Square each difference: (1.2996, 0.7396, 14.8996, 9.8596, 4.5796, 0.0196, 3.4596)

3. Calculate the sum of the squared differences: 34.8572

4. Divide the sum by the number of days (7): 34.8572 / 7 ≈ 4.98

5. Take the square root of the result to find the standard deviation: \(\sqrt{(4.98) }\)≈ $2.23 (rounded to the nearest cent)

The standard deviation measures the average amount of variation or dispersion from the mean. In this case, it tells us how much the daily expenditures on breakfast vary from the mean expenditure.

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Answer:

I don't, get it

a. The statement is true.

b. The statement is false.

c. The statement is false.

  a. When the null hypothesis of equal means for four groups is rejected using ANOVA at a significance level of 0.05, it implies that there is sufficient evidence to suggest differences between the group means. ANOVA compares the variability between groups to the variability within groups. If the null hypothesis is rejected, it means that the standardized variability between the groups is higher than the standardized variability within the groups.

b. The appropriate significance level for pairwise comparisons of group means, also known as post hoc tests, is not simply divided by the number of groups. Dividing the significance level by the number of groups, as stated in option b, is not a valid approach. To appropriately account for multiple comparisons, adjustments like the Bonferroni correction, Tukey's HSD, or the Sidak correction are commonly used. These methods ensure that the overall Type I error rate is controlled.

c. Rejecting the null hypothesis using ANOVA only indicates that there are differences between at least two group means. It does not provide information about which specific group means differ from each other. To identify which group means are significantly different, additional post hoc tests or pairwise comparisons are required. These tests allow for a more detailed analysis of specific group differences and provide insights into which pairs of group means are statistically significant.

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To evaluate the integral ∫132x2 5x dx using the fundamental theorem of calculus, we first need to find the antiderivative of the integrand.

Using the power rule of integration, we have:

∫132x2 5x dx = ∫13(5x)(x2) dx
= 5∫x3 dx
= 5 * (1/4)x4 + C  (where C is the constant of integration)

Thus, the antiderivative of the integrand is (1/4)x4, and the definite integral from x = 1 to x = 3 is:

(1/4)(3^4 - 1^4) = (1/4)(80) = 20

Therefore, using the fundamental theorem of calculus, we can evaluate the integral as:

∫132x2 5x dx = 20

where the fundamental theorem of calculus states that the definite integral of a function is equal to the difference between its antiderivative evaluated at the upper and lower limits of integration.
Hi! I'd be happy to help you evaluate the integral using the Fundamental Theorem of Calculus. The given integral is: ∫(13x^2 + 5x) dx.

Step 1: Find the antiderivative of the given function.
The antiderivative of 13x^2 is (13/3)x^3, and the antiderivative of 5x is (5/2)x^2. So, the antiderivative of the function is F(x) = (13/3)x^3 + (5/2)x^2 + C, where C is the constant of integration.

Step 2: Apply the Fundamental Theorem of Calculus.
The Fundamental Theorem of Calculus states that if F(x) is the antiderivative of a continuous function f(x) on the interval [a, b], then the definite integral of f(x) from a to b is equal to F(b) - F(a).

In this case, you didn't provide the limits of integration (a and b), so we can't complete the evaluation. However, if you have specific limits, simply substitute them into the antiderivative F(x) and find the difference F(b) - F(a) to get the final result.

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The probability of x taking on a value between 75 to 90 is 0.25.

Given that x is a continuous random variable uniformly distributed between 65 and 85.To find the probability that x lies between 75 and 90, we need to find the area under the curve between the values 75 and 85, and add to that the area under the curve between 85 and 90.

The curve represents a rectangular shape, the height of which is the maximum probability. So, the height is given by the formula height of the curve = 1/ (b-a) = 1/ (85-65) = 1/20.Area under the curve between 75 and 85 is = (85-75) * (1/20) = (10/20) = 0.5Area under the curve between 85 and 90 is = (90-85) * (1/20) = (5/20) = 0.25.

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By using  the sum or difference formula of cosine to solve cos(525°) we get cos(525°) = -0.465

The formula to find the value of cos(A ± B) is given as,

cos(A + B) = cosA cosB − sinA sinBcos(A − B) = cosA cosB + sinA sinB

Here, A = 450° and B = 75°

We can write 525° as the sum of 450° and 75°.

Therefore,cos(525°) = cos(450° + 75°)

Now, we can apply the formula for cos(A + B) and solve it.

cos(A + B) = cosA cosB − sinA sinBcos(450° + 75°) = cos450° cos75° − sin450° sin75°= 0.707 × 0.259 − 0.707 × 0.966= -0.465

Substituting the values in the above equation, we get

cos(525°) = 0.707 × 0.259 − 0.707 × 0.966= -0.465

Thus, cos(525°) = -0.465.

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Answer:

77.5

Step-by-step explanation:

55 and 100 average provides comprehensive information about what is the average of 55 and 100, and how it is being calculated mathematically. To calculate the average, the given quantities 55 and 100 can be of any physical quantity but both should have been expressed in the same measurement units.

55 and 100 average:

= (55 + 100)/2,

= 155/2,

= 77.5

Answer:

1). 30m. 2). 21m

Step-by-step explanation:

6 x 5 = 30 and 7 x 3 = 21. Have a great day!

Answer:

Use Area, which means multiply.

Step-by-step explanation:

1)      6 x 5 = 30

2)     7 x 3= 21

Hope this Helps!!

God Bless!!

~DuffyDuck~

The triangle C is reduced by a scale factor of 0.36 to form triangle D.

Given,

There are two triangles are C and D.

All sides of C are 35 in, 25 in, 45 in and all sides of D are 7 in, 9 in,5 in.

To find the scale factor by which triangle C is dilated or reduced to form triangle D, we need to compare the corresponding sides of both triangles.

The corresponding sides of triangle C and D are:

35 in : 7 in (longest sides of each triangle)

25 in : 9 in

45 in : 5 in

To find the scale factor, we can choose any pair of corresponding sides and divide the length of the side in triangle D by the length of the corresponding side in triangle C.

Let's choose the second pair of corresponding sides, which are 25 in and 9 in.

scale factor = length of corresponding side in triangle D / length of corresponding side in triangle C

scale factor = \( \frac{9 \: in}{25 \: in} \)

scale factor = 0.36

Therefore, triangle C is reduced by a scale factor of 0.36 to form triangle D.

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Answer: r=9

Step-by-step explanation: -3(4-r)=15                                                                 -12+3r+12=15+12                                                                                                     3r/3=27/3                                                                                                             r=9                                                                                                                    

The error is that after multiplying -3 by -r the negative sign was supposed to be removed from -3r because when you multiply two negative numbers because they are similar signs the product must be inverse of the two numbers so that is why the product becomes a positive number. And the error gotten is r=-9 because of the reason I listed above. The correct solution is r=9.

Using the scale 1/4 inch = 1 foot, a room that is 10 feet by 20 feet would be represented by a scale drawing that is 2.5 inches by 5 inches.

The dimensions of the room in the scale drawing would be:

Width: 2.5 inches

Length: 5 inches

Please find the sketch below.

A scale drawing is a drawing that represents an object or space in proportion to its actual size.

It is used to show the relationship between different parts of an object or space, and to provide accurate measurements of its dimensions.

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A rough sketch of what the room might look like in scale:

_________________________

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                  BED                             |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|                                                     |

|_________________________

Please note that this is a rough sketch and the furniture placement is just an approximation.

Also, the furniture is not to scale, but just a representation of where it might be placed in the room.

Answer:

Find other solutions in explanation

x = 250

y = 1750

Step-by-step explanation:

x = cost per copybook

y = cost per pen

2. Sum of the cost of 4 copy books and 3 pen is equal to 7750

3.)

2x+y=2750 - - (1)

4x + 3y = 7750 - - - (2)

From (1)

y = 2750 - 2x

Substitute y = 2750 - 2x into (2)

4x + 3(2750 - 2x) = 7750

4x + 8250 - 6x = 7750

-2x = - 500

x = 500/2

x = 250

y = 2750 - 2(500)

y = 2750 - 1000

y = 1750

The four functions can be described as follows: a) rect(x/8) - rectangular pulse centered at the origin with a width of 8 units, b) Δ(ω/10) - Dirac delta function with a spike at ω = 0 and zero everywhere else, c) rect(t-3/4) - rectangular pulse centered at t = 3/4 with a width of 1 unit, d) sinc(t) * rect(t/4) - modulated sinc function by a rectangular pulse of width 4 units centered at the origin.

a) rect(x/8):

The function rect(x/8) represents a rectangle function with a width of 8 units centered at the origin. It has a value of 1 within the interval [-4, 4] and a value of 0 outside this interval. The graph of rect(x/8) will consist of a rectangular pulse centered at the origin with a width of 8 units.

b) Δ(ω/10):

The function Δ(ω/10) represents a Dirac delta function with an argument ω/10. The Dirac delta function is a mathematical construct that is zero everywhere except at the origin, where it is infinitely tall and its integral is equal to 1. The graph of Δ(ω/10) will be a spike at ω = 0. The value of Δ(ω/10) at ω ≠ 0 is zero.

c) rect(t-3/4):

The function rect(t-3/4) represents a rectangle function with a width of 1 centered at t = 3/4. It has a value of 1 within the interval [3/4 - 1/2, 3/4 + 1/2] = [1/4, 5/4] and a value of 0 outside this interval. The graph of rect(t-3/4) will consist of a rectangular pulse centered at t = 3/4 with a width of 1 unit.

d) sinc(t) * rect(t/4):

The function sinc(t) * rect(t/4) represents the product of the sinc function and a rectangle function. The sinc function is defined as sinc(t) = sin(t)/t. The rectangle function rect(t/4) has a width of 4 units centered at the origin. The graph of sinc(t) * rect(t/4) will be the multiplication of the two functions, resulting in a modulated sinc function where the rectangular pulse shapes the sinc function.

Therefore, the four functions can be described as follows:

a) rect(x/8) - rectangular pulse centered at the origin with a width of 8 units.

b) Δ(ω/10) - Dirac delta function with a spike at ω = 0 and zero everywhere else.

c) rect(t-3/4) - rectangular pulse centered at t = 3/4 with a width of 1 unit.

d) sinc(t) * rect(t/4) - modulated sinc function by a rectangular pulse of width 4 units centered at the origin.

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