You have $4000 to invest. If you'd like to earn exactly $638
in interest each year, how much should you invest in each of
two accounts, one that earns 8% per year and one that
earns 21% per year. (Round your answer to the nearest
dollar)
8%: $
21%: $

Answer:

2 and 4

Step-by-step explanation:

just anwser it  and a prime number is a  whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Numbers that have more than two factors are called composite numbers.

Answer:

A

Step-by-step explanation:

\(\dfrac{f(x)}{g(x)}=\dfrac{x+1}{x^{2}-x}\\f(x) = \dfrac{x+1}{x^{2}-x}*g(x)\\\\\dfrac{2}{x}*\dfrac{x^{2}-x}{x+1}=g(x)\\\\\\\dfrac{2}{x}*\dfrac{x(x-1)}{x+1}=g(x)\\\\\\\dfrac{2(x-1)}{x+1}=g(x)\\\\\\)

Answer: 69.6 Hope That helps!

Step-by-step explanation:

For the time period of  the projectile at least 192 feet above the ground is between 2 second and 6 second

Since s=128t-16t2, we want to know the 2 times where 128t-16t2=192, as those two values will be the begin and end times of the interval in question. We can rewrite that equation in standard quadratic equation form:

16t2-128t+192=0 or, simplified, 8t2-64t+96=0

or t2-8t+12=0

since it is now in quadratic form, we can solve using the quadratic formula:

t = 2 and 6

So the time period from approximately 2 second and 6 second has the projectile above 192 feet.

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The data in the table can be modeled by this linear equation in slope-intercept form: y = 8x - 5.

The slope is 8, which means the wages earned increases at rate of 8 dollars per hour as the time increases.

The y-intercept is -5 and it represent the initial wages earned.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (24.00 - 8.00)/(3 - 1)

Slope (m) = 16.00/2

Slope (m) = 8

At data point (1, 3), a linear equation in slope-intercept form for this line can be calculated as follows:

y - y₁ = m(x - x₁)

y - 3 = 8(x - 1)

y = 8x - 8 + 3

y = 8x - 5

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Answer:

\(m=-3\)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point (-1, 0)

Point (0, -3)

Step 2: Find slope m

The equation of the variable u is u = t/1

From the question, we have the following parameters that can be used in our computation:

t = 10u

To determine the value of u, we divide both sides of the equation by 10

So, we have the following representation

t/10 = u

Rewrite the equation as follows

So, we have the following representation

u = t/10

Hence, the solution is

u = t/10

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Complete question

Solve for u in t = 10u

Answer: 0.4714

Step-by-step explanation: square root of 8 is 2.8284 divided by 6 = 0.4714.

\( \frac{6}{ \sqrt{8x} } \\ \frac{ {6}^{2} }{ {( \sqrt{8x)} }^{2} } \\ \\ \frac{36}{8x} \\ \ \\ \frac{36 \div 4}{8x \div 4} \\ \\ \frac{9}{2x} \)

this is one of the ways to simplify it

you can divide 9 by 2 the answer will be 4.5x

The applied overhead cost for job 201 is $36,000 and total cost for job 201 under direct materials cost as allocation base is $86,000.

Allocation base is a technique utilized in accounting to designate the cost of something to its use or product to recognize the price of the finished product.

Example provides the total overhead cost at $120,000 for the period, the base data of $100,000 direct material cost and 500 direct labor hours. The base data are used to calculate the predetermined factory overhead rate, which is used to apply overhead costs to work in progress.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the base data. The predetermined factory overhead rate is multiplied by the actual activity in the allocation base to obtain the applied overhead cost.

Direct materials cost as allocation base $30,000 is the actual direct material cost used in job 201. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct material cost, which is $120,000/$100,000=120%.

The applied overhead cost for job 201 is $30,000*120% = $36,000.

Total cost for job 201 under direct materials cost as allocation base is $30,000+$20,000+$36,000 = $86,000.

-Direct labor cost as allocation base:

The actual direct labor cost used in job 201 is $20,000. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor cost, which is $120,000/$100,000=120%.

The applied overhead cost for job 201 is $20,000*120% = $24,000.

Total cost for job 201 under direct labor cost as allocation base is $30,000+$20,000+$24,000 = $74,000.

-Direct labor hours as allocation base:

The actual direct labor hours used in job 201 is 400 hours.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor hours, which is $120,000/500 hours = $240 per hour.The applied overhead cost for job 201 is $240*400 hours = $96,000.

Total cost for job 201 under direct labor hours as allocation base is $30,000+$20,000+$96,000 = $146,000.

-Physical output as allocation base: The actual output in units completed for job 201 is 2,000 shirts.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the output in units, which is $120,000/10,000 units = $12 per unit.

The applied overhead cost for job 201 is $12*2,000 units = $24,000.Total cost for job 201 under physical output as allocation base is $30,000+$20,000+$24,000 = $74,000.

-Machine hours as allocation base: The actual machine hours used in job 201 is 240 hours.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the machine hours, which is $120,000/5,000 hours = $24 per hour.

The applied overhead cost for job 201 is $24*240 hours = $5,760.

Total cost for job 201 under machine hours as allocation base is $30,000+$20,000+$5,760 = $55,760.

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Answer:384

Step-by-step explanation:

first you multiply 2 times 2= 4 then 4 times 4 times 4= 64 then you multiply 3 times 2= 6 lastly you multiply 6 and 64. your welcome:)

Answer:

False

Step-by-step explanation:

This is false although most prime numbers are not divisible two, but there is one exception to this... the number 2! The number 2 is prime and is divisible by 2. All other prime numbers cannot be divisible by 2 otherwise they would not be prime as prime numbers are only divisible by 1 and the number it self (this excludes 1).

The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

\(a(1) = 144\)

\(a(n) = 144{( - \frac{1}{6} )}^{n - 1} \)

\(a(n) = - \frac{1}{6} a(n - 1)\)

Step-by-step explanation:

area of rec= length×width

=10×4

= 40

radius= diameter/2

=4/2 = 2

area of semicircle= πr²/2

=22/7×2×2×1/2

=6.28

=6.3

adding both

we get,

=40+6.3

= 46.3

Answer:

1.11 will be the answer

Step-by-step explanation:

Answer:

bfc = 64, afb = 126

Step-by-step explanation:

I solved in the picture

Hope this helps ^-^

Answer:

The perimeter of an equilateral traingle with height 42cm is 126cm.

Step-by-step explanation:

Given that the height or edge of an equilateral traingle is 42cm. With this information, we are asked to find the perimeter of an equilateral traingle.

The perimeter of equilateral traingle is defined as the three times of the length of edge. Mathematically;

→ Perimeter = 3a

By substituting the given values in the formula, we get the following results:

→ Perimeter = 3(42)

→ Perimeter = 126

Hence, the perimeter of an equilateral traingle with height 42cm is 126cm.

Additional information:

Answer:

i think that all of them EXCEPT the last one are correct. Explained below

The Equivalent ratio to 8/2 is 4/1, 24/6, 32/8 and 48/12.

We have,

Cylinder and prism.

Here we have to find the equivalent ratio to 8/2.

First simplifying the given ratio as

8/2

= (4 x 2)/2

= 4 /1

Now, some more ratios equivalent to 8/2.

1. 8/2 x 3/3 = 24/ 6

2. 8/2 x 4/4 = 32/8

3. 8/2 x 6/6= 48/12

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Answer:

21.6

Step-by-step explanation:

44-27.5=16.5

line segment VX-36= line segment VW we will call line segment VW C

C-36=VX we will call line segment VX H for Hypotenuse

Ratio 27.5/44 = 0.625 the ratio must be the same.

So 36/0.625=57.6 so 57.6-36= 21.6

I got three different answers. This checked out twice../

The number N whose forty percent is 240 is 600, or we say that 40% of 600 is 240

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

\(\dfrac{a}{100} \times b\)

For this case, we are specified that:

40% of N = 240

Since 40% of N is \(\dfrac{N}{100} \times 40\), thus, we get

\(\dfrac{N}{100} \times 40 = 240\) (as they both are same quantity, ie. 40% of N)

Now, solving it further to get value of N:

\(\dfrac{N}{100} \times 40 = 240\\\\\text{Multiplying 100 on both the sides}\\\\N \times 40 = 24000\\\\\text{Dividing both the sides by 40}\\\\N = 24000/40 = 600\)

Thus,  40% of 600 is 240 or we say that the number N whose forty percent is 240 is 600

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the total number of students in class is given by the equation x - 1 / 2 x - 1 / 4 x - 1 / 7 x = 3 and is equal to 28.

Let the total number of students be x

Mathematics = 1 / 2 x

natural philosophy = 1 / 4 x

Silence = 1 / 7 x

Remaining = 3

So, we get the equation as:

x - 1 / 2 x - 1 / 4 x - 1 / 7 x = 3

(28 x - 14 x - 7 x - 4 x) / 28 = 3

3 x / 28

x = (3 × 28) / 3

x = 28

Number of students in class = 28.

Therefore, the total number of students in class is given by the equation x - 1 / 2 x - 1 / 4 x - 1 / 7 x = 3 and is equal to 28.

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Answer:

x¹= -4 , x²= 7

Step-by-step explanation:

1) Determine the defined range

¼x-¾=7/x =/ 0

2) Move the expression to the left-hand side and change its sign

\( \frac{1}{4} x - \frac{3}{4} - \frac{7}{x} = 0 \\ \\ \)

3) Write all numerators above the least common denominator 4x

\( \frac{ {x}^{2} - 3x - 28 }{4x} = 0\)

4) When the quotient of expressions equals 0, the numerator has to be 0

x²-3x-28=0

5) Write -3x as a difference

x²+4x-7x-28=0

6) Factor out x from the expression

x(x+4)-7x-28=0

7) Factor out -7 from the expression

×(x+4)-7(x+4)=0

8) Factor out x+4 from the expression

(x+4)×(x-7)=0

9) When the product of the factors equals 0, at least one factor is 0

x+4=0

x-7=0

10) Solve for the x

x+4=0 -> x= -4

x-7=0 -> x=7

11) Check if the solution has defined range

x= -4

x=7

12) The solution has 2 solutions

\(x1 = - 4 \: \: x2 = 7\)

Answer:

The correct answer is -9

Answer:

12kg=7.68

1.5=87

Step-by-step explanation:

I found the cost per kg

Answer:

Step-by-step explanation:

Answer:

\(\frac{2\sqrt{3} + 6}{12}\)

Step-by-step explanation:

Simplify the denominator of \(\frac{1 + \sqrt{3} }{\sqrt{12} }\) completely.

\(=> \frac{1 + \sqrt{3} }{ \sqrt{(4 \times 3)} } = \frac{1 + \sqrt{3} }{\sqrt{4} \times \sqrt{3} } = \frac{1 + \sqrt{3} }{2\sqrt{3} }\)

Now, to rationalise it you need to make the denominator rational.

\(=> \frac{1 + \sqrt{3} }{2\sqrt{3} } \times \frac{2\sqrt{3} }{2\sqrt{3} }\)

\(=> \frac{(1 + \sqrt{3})\times 2\sqrt{3} }{2\sqrt{3} \times 2\sqrt{3} }\)

\(=> \frac{2\sqrt{3} + 6 }{12}\)

Step-by-step explanation:

=(7x)^2-(y)^2

=(7x+y) (7x-y)

Therefore, a^2-b^3

=(a+b) (a-b)

Answer:

A: the probability that a 1 is received is 0.56.

B:  the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

Step-by-step explanation:

To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.

a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.

Let's denote:

P(1 sent) = 0.6 (probability a 1 is sent)

P(0→1) = 0.2 (probability a 0 is flipped to 1)

P(1 received) = ?

P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)

= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)

= 0.6 * (1 - 0.2) + 0.4 * 0.2

= 0.6 * 0.8 + 0.4 * 0.2

= 0.48 + 0.08

= 0.56

Therefore, the probability that a 1 is received is 0.56.

b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.

Let's denote:

P(0 sent) = ?

P(1 received) = 0.56

We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).

Using Bayes' theorem:

P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)

P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08

P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56

Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):

P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56

Simplifying:

P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56

= 0.08 * (1 - P(0 sent)) * (1 / 0.56)

= 0.08 * (1 - P(0 sent)) * (25/14)

= (2/25) * (1 - P(0 sent))

Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?

Answer:

20

Step-by-step explanation:

percentage error = predictions - actual ÷actual × 100

error

\( \frac{82 - 52 \\ }{52} \times 100\)

=

20

dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.

The autonomous differential equation that satisfies all of the given properties is dy/dx = (y-3)(y+3). This equation has two equilibrium solutions at y = 0 and y = 3, and is positive for -inf < y < 0, and negative for 0 < y < 3, and positive for 3 < y < inf.

To demonstrate this, let's consider the equation at y=-3. Since y=-3 is less than 0, the equation can be simplified to dy/dx = 6. Since 6 is positive, y' is also positive, meaning that y is increasing. Similarly, if y=3, dy/dx = 0 which is neither positive nor negative, so y remains constant. Finally, for y>3, dy/dx = -6, which is negative, so y is decreasing.

Therefore, dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.

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