A certain company reported selling 5,000 toys during the month of January and expects sales to grow at a rate of 7.5% per month until the end of that year. How many toys should the company expect to sell by the end of June of that year?

a) The cost of the stereo system is $4,760.

b) The total amount of interest paid is $1,760.

To find the cost of the stereo system, we need to calculate the sum of the down payment and the total of monthly payments over 4 years. The down payment is $400, and the monthly payment is $90 for 48 months (4 years). Thus, the total cost of the stereo system is $400 + ($90 × 48) = $4,760.

To calculate the total amount of interest paid, we need to subtract the initial principal amount (down payment) from the total cost of the stereo system. The initial principal amount is $400, and the total cost is $4,760. Therefore, the total interest paid is $4,760 - $400 = $1,760.

In summary, the cost of the stereo system is $4,760, and the total amount of interest paid is $1,760.

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The correct answer is option c) infinitely many solutions..

To solve the system of equations using the substitution method, we'll substitute the value of y from the second equation into the first equation and solve for x.

Given:

-6x + 2y = 8 ---(1)

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

Substitute equation (2) into equation (1):

-6x + 2(3x + 4) = 8

Simplify:

-6x + 6x + 8 = 8

8 = 8

We obtained a true statement (8 = 8), which means the two equations are equivalent. This solution shows that the system has infinitely many solutions.

Therefore, the correct answer is option c) infinitely many solutions..

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By working with percentages, we conclude that the total number of students surveyed is 880.

First, we know that a total of N students were surveyed about what color they preferred, blue or purple.

Then the other 55% preferred purple, which means that the 55% of the total number of students surveyed, N, is equal to 484.

So we just need to use what we know about percentages, we will get:

484 = N*(55%/100%) = N*0.55

Now we can solve this simple linear equation to find the value of N, we will get:

484/0.55 = N = 880

In this way, we conclude that the total number of students surveyed is 880.

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Answer:

The answer is 1

Step-by-step explanation:

The dot product of vectors a and b  || a |= 6,|| b ||= 4 and the angle between the vectors θ = π/3 is (c) 12.

The dot product of two vectors, we can use the formula:

a · b = ||a|| ||b|| cos(theta)

where ||a|| and ||b|| represent the magnitudes of vectors a and b, respectively, and theta is the angle between the vectors.

In this case, we are given that ||a|| = 6, ||b|| = 4, and the angle between the vectors is theta = π/3.

Substituting these values into the formula, we have:

a · b = 6 × 4 × cos(π/3)

To evaluate cos(π/3), we can use the fact that it is equal to 1/2. So we have:

a · b = 6 × 4 × 1/2

= 12

Therefore, the dot product of vectors a and b is 12.

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Answer:

70

Step-by-step explanation:

first step (4+3)=7

second step 10×7=70

The study would use a simple random sampling because it would be easy to randomly select. The study would use cluster sampling because the of fall into naturally occurring subgroups. The study would use stratified sampling because it would be important to have members from each segment of the population.

The study is a sample survey, because the population is for it to be practical to record all of the responses.

a. The study would use a simple random sampling because it would be easy to randomly select members of the population. Simple random sampling is a type of probability sampling that is used when the population is homogenous and every member has an equal chance of being selected for the sample.

b. The study would use cluster sampling because the members of the population fall into naturally occurring subgroups. Cluster sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into naturally occurring subgroups.

c. The study would use stratified sampling because it would be important to have members from each segment of the population. Stratified sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into segments or strata based on certain characteristics.

d. The study is a sample survey, because the population is too large for it to be practical to record all of the responses. Sample survey is a type of survey that collects data from a sample of the population, rather than the entire population. This is often done when the population is too large or when it is not practical to survey the entire population.

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Q1. (a) The Laplace transform of cosh(2t) + cos(2t) can be obtained as follows:

L{cosh(2t)} = 1/(s - 2) + 1/(s + 2) [Using the Laplace transform table]

L{cos(2t)} = s/(s^2 + 4) [Using the Laplace transform table]

Combining these results:

L{cosh(2t) + cos(2t)} = 1/(s - 2) + 1/(s + 2) + s/(s^2 + 4)

Simplifying further, we get:

L{cosh(2t) + cos(2t)} = (s^3 + 4s)/(s^3 + 4s^2 - 4s - 16)

(b) The Laplace transform of 3e^(-5t) + 4 - 4sin(4t) can be obtained as follows:

L{3e^(-5t)} = 3/(s + 5) [Using the Laplace transform table]

L{4} = 4/s [Using the Laplace transform table]

L{-4sin(4t)} = -16/(s^2 + 16) [Using the Laplace transform table]

Combining these results:

L{3e^(-5t) + 4 - 4sin(4t)} = 3/(s + 5) + 4/s - 16/(s^2 + 16)

Simplifying further, we get:

L{3e^(-5t) + 4 - 4sin(4t)} = (12s^2 + 152s + 106)/(s(s + 5)(s^2 + 16))

Q2. (a) The Laplace transform of t + tsin(2t) + t^2cos(3t) can be obtained as follows:

L{t} = 1/s^2 [Using the Laplace transform table]

L{tsin(2t)} = 2/(s^2 - 4) [Using the Laplace transform table]

L{t^2cos(3t)} = 2/(s^3 - 9s) [Using the Laplace transform table]

Combining these results:

L{t + tsin(2t) + t^2cos(3t)} = 1/s^2 + 2/(s^2 - 4) + 2/(s^3 - 9s)

Simplifying further, we get:

L{t + tsin(2t) + t^2cos(3t)} = (s^3 - 5s^2 + 8s + 8)/(s^3(s - 3)(s + 2))

(b) The Laplace transform of te^2 + sin(3t) can be obtained as follows:

L{te^2} = 48/(s - 2)^5 [Using the Laplace transform table]

L{sin(3t)} = 3/(s^2 + 9) [Using the Laplace transform table]

Combining these results:

L{te^2 + sin(3t)} = 48/(s - 2)^5 + 3/(s^2 + 9)

Simplifying further, we get:

L{te^2 + sin(3t)} = (s^4 - 10s^3 + 40s^2 -

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Ariel is not correct because mockingbird beats its wings 14 times per second.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

From the table the slope of the data is

= (1260 - 420)/ (90-30)

= 840 - 60

= 14

So, the mockingbird beats its wings approximately 14 times per second.

Thus, ariel is not correct.

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Either take the photo of that question or take screenshot and attach it. The question is not complete.

Answer:

2x + y = -2, x + 2y = 2

4x + y - 2z = 0, 2x+ 3z = 9 , -6x - 2y + z = 0

x + y = 4 , x - y = 2

Step-by-step explanation:

Answer:

x=2 and y=−5

Step-by-step explanation:

Let's solve your system by elimination.

7x−y=19;2x−3y=19

Multiply the first equation by -3,and multiply the second equation by 1.

−3(7x−y=19)

1(2x−3y=19)

Becomes:

−21x+3y=−57

2x−3y=19

Add these equations to eliminate y:

−19x=−38

Then solve−19x=−38for x:

−19x=−38

(Divide both sides by -19)

x=2

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

7x−y=19

Substitute2forxin7x−y=19:

(7)(2)−y=19

−y+14=19(Simplify both sides of the equation)

−y+14+−14=19+−14(Add -14 to both sides)

−y=5

y=-5

Answer:

x = 3, x = \(\frac{2}{7}\)

Step-by-step explanation:

(a)

The first step is to subtract 23x from both sides, that is

7x² - 23x + 6 = 0 ← in standard form

(b)

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 7 × 6 = 42 and sum = - 23

The factors are - 21 and - 2

Use these factors to split the x- term

7x² - 21x - 2x + 6 = 0 ( factor the first/second and third/fourth terms )

7x(x - 3) - 2(x - 3) = 0 ← factor out (x - 3) from each term

(x - 3)(7x - 2) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

7x - 2 = 0 ⇒ 7x = 2 ⇒ x = \(\frac{2}{7}\)

The exponential model is the most appropriate model for the given data.

The table of values is given as:

x  0  1  2      3    4     5

y  4  8 15.9 32 65.2 128

From the above table, we have the following highlights:

The above highlights is similar to an exponential model, because an exponential model has a constant multiplicative rate

Hence, the appropriate model is the exponential model

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Answer:

y = -3x + 22

Step-by-step explanation:

To find m, find the change in y and divide it by the change in x.

For example, the change in y between 19 and 13 is -6. Then determine the change in x. For example, since we determined the change in 19 and 13, let's look at the change in the x coordinates that pair with 19 and 13: 1 and 3. The change in x between 1 and 3 is 2. Now divide the change in y by the change in x: -6/2 = -3. So now we have the equation y = -3x + b, but we still need to figure out b, or the y-intercept. To do this, we need to figure out a pattern in the table to find out what y is equal to when x = 0, the definition of a y-intercept. From just the table alone, it looks like for every 2 units the x-coordinate decreases, the y-coordinates increases by 6. We could also just as easily say that for every 1 unit the x-coordinate decreases, the y-coordinate increases by 3. From this definition, if we look at the coordinate (1, 19), if we were to decrease 1 from the x-coordinate, we would have to increase the y-coordinate by 3 which we can write as (x - 1, y + 3). So, we would get (0, 22). So, when x = 0, y = 22.

Answer:

Total Surface Area = 24.887864491364 inches^2

itz pretty ez unless ur lazy tho

Answer:

To divide 1.7 by 8.5, you will need to move the decimal point one place to the right in the divisor and the dividend. This would result in 17 and 85 as the new divisor and dividend respectively, and the division would be performed as 17/85.

Answer:

the slope in line 1 is a

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

→ Utilise the gradient formula

(y₂ - y₁) ÷ (x₂ - x₁)

→ Substitute in the numbers

(2 - -6) ÷ (1--1)

→ Simplify

4

The sum of the first 7 terms of the following series round to the nearest whole number is 26.

When all the terms of a geometric sequence are added, then that expression is called geometric series.

Lets suppose its initial term is   , multiplication factor is  r

and let it has total n terms, then, its sum is given as:

\(S_n = \dfrac{a(r^n-1)}{r-1}\)

(sum till nth term)

We are given that;

The series= 8, 6, 9/2, …

n=7

Now To find the sum of the first 7 terms of the series, we need to add up the first 7 terms. The first term is 8, the second term is 6, and the third term is 9/2. We can see that each term is obtained by subtracting 2 from the previous term and then dividing by 2. So we can write out the first few terms:

8, 6, 9/2, 7/4, 5/8, 9/16, 7/32, ...

To find the sum of the first 7 terms, we can add them up:

8 + 6 + 9/2 + 7/4 + 5/8 + 9/16 + 7/32 = 25.625

Rounding to the nearest whole number, we get a sum of 26.

Therefore, answer of the given series will be 26.

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To evaluate the iterated integral ∫∫∫ 2z ln(x) xe^(-y) dy dx dz over the limits 0 ≤ y ≤ 6, 0 ≤ x ≤ 8, and 0 ≤ z ≤ 1, we begin by integrating the innermost integral with respect to y first, then the middle integral with respect to x, and finally the outermost integral with respect to z.

So, integrating with respect to y first, we get:
∫∫∫ 2z ln(x) xe^(-y) dy dx dz = ∫∫∫ 2z ln(x) (-e^(-y) + C) dx dz
where C is the constant of integration.
Next, integrating with respect to x, we get:
∫∫∫ 2z ln(x) (-e^(-y) + C) dx dz = ∫∫ 2z (-ln(x)e^(-y) + Cx) |_0^8 dz
= ∫∫ 16z(ln(8)e^(-y) - C) dz
= 16(ln(8)e^(-y) - C)z^2/2 |_0^1
= 8(ln(8)e^(-y) - C)
Finally, integrating with respect to z, we get:
∫∫ 8(ln(8)e^(-y) - C) dz = (8/2)(ln(8)e^(-y) - C)(1^2 - 0^2)
= 4(ln(8)e^(-y) - C)
Therefore, the value of the iterated integral over the given limits is 4(ln(8)e^(-6) - C), where C is a constant of integration.

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To prove that AΔB = CΔD if and only if AΔC = BΔD, we need to show two implications:

If AΔB = CΔD, then AΔC = BΔD

If AΔC = BΔD, then AΔB = CΔD

Let's start with implication 1:

Suppose AΔB = CΔD. This means that every element that is in A or B, but not both, is also in C or D, but not both. Similarly, every element that is in C or D, but not both, is also in A or B, but not both.

Now consider AΔC. This is the set of elements that are in A or C, but not both. We can split this set into two parts: (i) the elements that are in A but not in C, and (ii) the elements that are in C but not in A.

For part (i), we know that these elements are either in B or not in B, because if an element is in A but not in C, it must be in B (since B is the set of elements that are in A but not in AΔB). Similarly, for part (ii), we know that these elements are either in D or not in D.

Therefore, we can write AΔC = (A∩B')∪(C∩D').

Similarly, we can write BΔD = (B∩A')∪(D∩C').

Now, since AΔB = CΔD, we have that (A∩B')∪(C∩D') = (B∩A')∪(D∩C'). Rearranging this equation, we get (A∩C')∪(C∩A') = (B∩D')∪(D∩B'). This means that AΔC = BΔD, which proves implication 1.

Now let's move on to implication 2:

Suppose AΔC = BΔD. This means that every element that is in A or C, but not both, is also in B or D, but not both. Similarly, every element that is in B or D, but not both, is also in A or C, but not both.

Now consider AΔB. This is the set of elements that are in A or B, but not both. We can split this set into two parts: (i) the elements that are in A but not in B, and (ii) the elements that are in B but not in A.

For part (i), we know that these elements are either in C or not in C, because if an element is in A but not in B, it must be in C (since C is the set of elements that are in A but not in AΔC). Similarly, for part (ii), we know that these elements are either in D or not in D.

Therefore, we can write AΔB = (A∩C')∪(B∩D').

Similarly, we can write CΔD = (C∩A')∪(D∩B').

Now, since AΔC = BΔD, we have that (A∩C')∪(B∩D') = (C∩A')∪(D∩B'). Rearranging this equation, we get (A∩D')

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Answer:

1. 1.25 \(g/cm^{3}\)

2. 1.36 \(g/cm^{3}\)

3. 1.04 \(g/cm^{3}\)

4. 0.79 \(g/cm^{3}\)

Step-by-step explanation:

Density = Mass/Volume

1. 15g/\(12cm^{3}\) = 1.25 \(g/cm^{3}\)

2. 7.5g/\(5.5cm^{3}\) = 1.36 \(g/cm^{3}\)

3. 26g/\(25cm^{3}\) = 1.04 \(g/cm^{3}\)

4.  1350g/\(1700cm^{3}\) = 0.79 \(g/cm^{3}\)

Answer:

1. 1.25

2. 1.36

3. 1.04

4. 0.79

Answer:

Equilateral

Step-by-step explanation:

Cause all the sides are equal which implies all the angles are equal...

Answer:

B

Step-by-step explanation:

Equilateral because all the three sides are equal

Step-by-step explanation:

Simplify for m by using algebra.

Divide each side by 3:

\( \frac{3m}{3} = \frac{0.95}{3} \)

\( m = \frac{19}{60} \)

Answer:

2 quarts= 4 pints

Step-by-step explanation:

multiply the volume value by 2

We have found that dy/dx = -4xsin(4x) + cos(4x) + 10e23 for y = x cos(4x) + 10e23.

We can use the product rule of differentiation to find dy/dx for y = x cos(4x) + 10e23.

The product rule states that if y = u(x)v(x), then

dy/dx = u(x)dv/dx + v(x)du/dx.

In this case, we have u(x) = x and v(x) = cos(4x) + 10e23. We can differentiate each factor separately to get:

du/dx = 1

dv/dx = -4sin(4x)

Substituting these values into the product rule formula, we get:

dy/dx = x(-4sin(4x)) + (cos(4x) + 10e23)(1)

Simplifying, we have:

dy/dx = -4xsin(4x) + cos(4x) + 10e23

Therefore, we have found that dy/dx = -4xsin(4x) + cos(4x) + 10e23 for y = x cos(4x) + 10e23.

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Answer:

x = 13

Step-by-step explanation:

→ Remember the amount of degrees a triangle sums to

180°

→ Make an equation

8x - 44 + 8x - 44 + 8x - 44 = 180

→ Simplify

24x - 132 = 180

→ Add 132 to both sides

24x = 312

→ Divide both sides by 24

x = 13

If x = 1 2 , then f( 1 2) = 0. this is the same as = 0. in completely factored form, f(x) = x-12.

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

then f(x) = x-12

because if we put x= 12

then we get f(x) = 0

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The cone should have its maximum volume. V=1/*3r2h is the formula for calculating the volume V of a cone with height h and radius r.

The cone has a volume of

V=πr2h/3

Therefore, we must calculate the values of r and h in terms of R. R is the diameter of the cone's top-circular circle, and h is the cone's height.

R is the cone's slant height, and it serves as the hypotenuse of a right triangle.

R2 = h2 + r2, or r2 = R2-h2.

So V = (1/3)π

[R2-h2]

h = (π/3)[R2h-h3]

You must take the derivative of the cone's volume, set it to zero, then solve for h to determine the cone's maximum volume.

dV/dh=(π/3)[R2-3h2]

R2-3h2=0 --> h2=R2/3 -> h = R/√3

Now we can determine r:

r2=R2-R2/3 = (2/3)R2

The volume formula with r and h substituted:

V = (π/3)

r2h = (π/3)(2R2/3)

(R/√3)

V(R)=2πR3/(9√3)

The complete question is:

A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup (Your answer may depend on R).

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