Suppose you deposit $1000 in an account earning 6% simple interest each year. How much would you earn in interest after 6 months?

Answer:

3x

Step-by-step explanation:

x = number of weeks.

When you plug in the number of weeks for x you'll get the amount of hours she had for dance classes.

Example: She has been doing classes for 3 weeks, how many hours did she do?

3x

3(3)

= 9(She had 9 hours of dance class combined for the past three weeks).

The shortest distance from the given surface function to the origin is 9 units.

What is function?

A function in mathematics is nothing but a relationship among the inputs i.e. the domain and their outputs i.e. the codomain where each input has exactly one output, and the output can be find by tracing back to its input.

Let us take the square of distance function be f(x, y, z)= x² + y² +z²

Given function is g(x, y, z)= xy+12x+z²

Now applying Lagrange multiplier as ,

∇f(x, y, z)= λg(x, y, z)

Now finding the gradient to both sides ,

< 2x, 2y, 2z>=λ <y+12, x, 2z>

Now equating both sides we get,

2x= λ(y+12), 2y= λx, 2z= 2λz

So solving we get,

λ=1

putting the value of λ in 2x= λ(y+12) and 2y= λx we get,

2x= y+12 and 2y= x

solving these two equations we will get,

x= 8 and y=4

Now plugging all these values in the equation

xy+12x+z²= 129 and solve for z,

32+96+z² =129

z²= 129-128

z²=1

z=±1

Now for x= 8, y=4 and z= ±1 the function f(x, y, z) becomes

(8)²+(4)²+(1)²

= 64+16+1

= 81

d=√81

Hence, the shortest distance from the given surface to the origin is 9 units.

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Answer:

Your answer is <, Hope it helps.

By making an initial deposit of $12,000 followed by annual deposits of $6,000 for the next 7 years into an account earning 2.1% interest, you will have approximately $63,274 in the account after 10 years.

To calculate the total amount in the account after 10 years, we need to consider the initial deposit, the annual deposits, and the interest earned.

The initial deposit of $12,000 will contribute to the account's value immediately.

For the annual deposits of $6,000 for the next 7 years, we can calculate the future value using the future value of an ordinary annuity formula:

\(FV = P * [(1 + r)^{n - 1}] / r\)

where FV is the future value, P is the annual payment, r is the interest rate per period, and n is the number of periods.

Using the formula, we can calculate the future value of the annual deposits:

\(FV = $6,000 * [(1 + 2.1\% / 100)^{7 - 1}] / (2.1\% / 100) = $42,274\)

(rounded to the nearest dollar).

To calculate the total amount in the account after 10 years, we need to add the initial deposit, the future value of the annual deposits, and any interest earned on these amounts over the 10-year period.

The interest earned on the initial deposit can be calculated as:

Interest = $12,000 * (2.1% / 100) * 10 = $2,520.

Adding the initial deposit, the future value of the annual deposits, and the interest earned, we get:

Total amount = $12,000 + $42,274 + $2,520 = $56,794.

However, we need to consider the interest earned on the account value over the last 3 years. Using compound interest, the interest earned on the total amount can be calculated as:

Interest = $56,794 * (2.1% / 100) * 3 = $3,576.

Adding the interest earned on the total amount, the final balance after 10 years is:

Final balance = $56,794 + $3,576 = $60,370.

Rounding to the nearest dollar, the total amount in the account after 10 years is approximately $63,274.

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t=2 hrs-------so 2 hrs after the second plane leaves it will catch the first plane

CK

720+240*2=600*2

720+480=1200

1200=1200

the distance from (4,-4) to (-7,-8) is 11.70

Answer: 5

Step-by-step explanation:

use distance formula for these types of equations x1-x2 squared plus y1 -y2 squared. add both sides together square them and then get a total and then square your total for the answer. In this case 5

Answer:

Step-by-step explanation:

2^4*m^4*n^(4*4)

16 m^4 n^16

Answer:

Area of B =80

I hope it's helps you

the end behavior of the polynomial \($-2 x^4-3 x^2-x+5$\) is: The polynomial decreases without bound as \($x$\) get closer to positive infinity. The polynomial grows without bound as \($x$\) gets closer to negative infinity.

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. \($x^2+x-12$\) is an illustration of a polynomial with a single variable.

from the question:

The degree and leading coefficient of the polynomial \($-2 x^4-3 x^2-x+5$\)must be examined in order to determine its final behavior.

As the polynomial has a degree of 4 , it will expand or decay at a pace dictated by the leading coefficient as x gets closer to positive or negative infinity. The negative (leading) coefficient is -2 .

As in this instance, the final behavior of a polynomial with a negative leading coefficient and an even degree is as follows:

- The polynomial will decrement without bound as x approaches positive infinity, causing the y values to decrement steadily. This is due to the fact that as x increases significantly, the term with the highest degree takes over the polynomial, and since the leading coefficient is negative, the polynomial reduces.

- The polynomial will grow without bound as x gets closer to negative infinity, which causes the y-values to get steadily increasingly positive. This is because as x gets very tiny and negative, the term with the highest degree dominates the polynomial, and since the leading coefficient is negative, the polynomial rises.

Hence, the polynomial \($-2 x^4-3 x^2-x+5$\) has the following final behavior:

- The polynomial decreases without bound as x get closer to positive infinity.

- The polynomial grows without bound as x gets closer to negative infinity.

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5. 24 hours over 7 days (Because 1 day = 4 hrs)

6. 16 limes over 2 bags (1 bag = 8 limes)

7. 54 cups over 9 boxes (6 cups = 1 box)

8. 27 meters (or minutes) over 3 seconds (9 meters over 1 second)

9. 36 lbs over $24 ($1 = 1.5lbs)

Answer:

6

Step-by-step explanation:

Answer:

D. 68+(6x+4)=180

x = 18

Step-by-step explanation:

"Supplementary angles" are angles that add up to 180°

So we add the twi angles 68+(6x+4) and that equals to 180°.

68 + 6x + 4 = 180

add 68 and 4

72 + 6x = 180

subtract 72.

6x = 108

divide by 6.

x = 18

Answer:

At x=5 both functions have the same value: 7

Step-by-step explanation:

Table:

f(1) = 15; f(2) = 16 ; f(3) = 15 ;  f(4) = 12;  f(5) = 7 ; f(6) = 0

g(1) = 3; g(2) = 4; g(3) = 5; g(4) = 6 ; g(5) = 7; g(6) = 8

If we denote the probability of hitting a bullseye on a dartboard with radius 12 inches as a function of the size of the bullseye, we can refer to this function as PS.

The function PS represents the probability of hitting the bullseye and is dependent on the size of the bullseye. The larger the bullseye, the higher the probability of hitting it, and vice versa. By adjusting the size of the bullseye, we can determine the corresponding probability of hitting it using the function PS.

It's important to note that without specific information about the relationship between the bullseye size and the probability, it's not possible to provide a specific mathematical expression or further details about the PS function. The function would need to be defined or provided to calculate the probability accurately.

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Answer:

Volume = 1099 cm³

Step-by-step explanation:

Volume = πr²h = 3.14(5²)(14) = 1099 cm³

Answer:

10 steps

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

17+(8-5)x5

17+3×5

17+15

22

Answer:

255

Step-by-step explanation:

B stands for brackets

O stands for order

D stands for devision

M stands for multiplication

A stands for addition

S stands for subtraction

If you follow it in the right order then you will find your answer so just follow it in the right order...

The cost of direct labor per unit is $5.628 per apple.

To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.

Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".

The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:

L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)

The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:

L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)

Now, let's calculate the total labor hours required per unit:

Total labor hours per unit = L₁ (first resource) + L₂ (second resource)

= 0.4762 hours/apple + 0.2273 hours/apple

= 0.7035 hours/apple (rounded to 4 decimal places)

Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:

Cost of direct labor per unit = Total labor hours per unit * Wage rate

= 0.7035 hours/apple * $8/hour

= $5.628 per apple (rounded to 3 decimal places)

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Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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The one-sample z-statistic for evaluating the hypothesis that unvaccinated people get COVID-19 is not 0.03 is -85.7. This statistic tested the hypothesis that unvaccinated people do not get COVID-19 at 0.03%.

In order to compute the one-sample z-statistic, we must first do a comparison between the observed proportion of COVID-19 instances in the placebo group and the expected proportion of 0.03. (p - p0) / [(p0(1-p0)) / n is the formula for the one-sample z-statistic. In this formula, p represents the actual proportion, p0 represents the predicted proportion, and n represents the sample size.

The observed proportion of COVID-19 instances among those who received the placebo is 162/18325 less than 0.0088. According to the received wisdom, the proportion that should be anticipated is 0.03. The total number of people sampled is 18325. After entering these numbers into the formula, we receive the following results:

z = (0.0088 - 0.03) / √[(0.03(1-0.03)) / 18325] ≈ (-0.0212) / √[(0.0291) / 18325] ≈ -85.7

As a result, the value of the z-statistic for just one sample is about -85.7. This demonstrates that the observed proportion of COVID-19 cases in the unvaccinated population is significantly different from the expected proportion of COVID-19 cases in that population.

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Answer:

Circumference, C = 62.8 ft

Area, A = 314 ft²

Step-by-step explanation:

where π = 3.14

Circumference, C = 2π(r)

= 2π(10ft)

= 20π ft

= 62.8 ft

Area, A = π(r²)

= π(10ft)²

= 100π ft²

= 314.1593654 ft²

= 314 ft²

Answer:

C

Step-by-step explanation:

The distance between the two points can be found using the distance formula, which is:

d = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the two points are located at (15, -10) and (15, 22), so:

x1 = 15

y1 = -10

x2 = 15

y2 = 22

Substituting these values into the formula, we get:

d = √((15 - 15)^2 + (22 - (-10))^2)

= √(0 + 32^2)

= √1024

= 32

Therefore, the distance between the two points is 32 units.

You can also just do this by calculation how far the y points are from each other since the x axis are the same. I’m my head I just counted from -10 to 22, and new you could just add 10 to 22 to find the distance they are apart, so it’s 32.

Answer: I think it’s true

Step-by-step explanation:

Using the inscribed angle theorems, the measure of the indicated angles are:

1. m∠BOA = 26°

2. m∠BDA = 13°

3. m∠BCA = 13°

Based on the inscribed angle theorem, the following relationships are established:

Given:

Intercepted arc BA = 26°

1. ∠BOA is central angle

Thus:

m∠BOA = 26° (inscribed angle theorems)

2. ∠BDA is inscribed angle.

m∠BDA = 1/2(30) = 13° (inscribed angle theorems)

3. m∠BCA = m∠BDA = 13° (inscribed angle theorems)

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The "d" format specifier is used to denote a signed decimal integer in various programming languages and formatting systems.

When used in format strings or printf-style functions, the "d" specifier indicates that the corresponding argument should be formatted as a signed decimal integer. It allows for the representation of both positive and negative whole numbers, including zero.

For example, in C programming, the printf function can be used with the "%d" format specifier to display a signed decimal integer value. Similarly, in other languages such as Python, the "{:d}" format specifier can be used with the format() function or string interpolation to represent a signed decimal integer.

Using the "d" specifier ensures that the output is formatted as a base-10 representation of a signed integer, taking into account the sign of the number.

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Answer:

so whats the question

Step-by-step explanation: