A lawn mower manufacturer incurs a total of $34,816 in overhead costs and $388 per lawn mower in production costs. How many lawn mowers were manufactured if the average cost of production is $660?

5 + 2*SQRT(x) = 15

 subtract 5 from each side

2*SQRT(x) = 10

(2*SQRT(x))^2 =10^2

2^2 *x = 100

4x=100

x=400/4

x = 25

Assuming a regularly shaped rectangle, the formula for the area is given as:

A = L * W

where L and W are the length and width respectively

A = 3.6 x 10^2 miles * 2.8 x 10^2 miles

A = 100,800 square miles

or

A = 10.08 x 10^2 miles

Answer: The area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]

Step-by-step explanation:

The shape of wyoming is rectangular with length , [tex]L=3.6\times 10^{2}\, miles[/tex]

and height , [tex]H=2.8\times 10^{2}\, miles[/tex]

Area of rectangle , [tex]A=L\times W[/tex]

=> [tex]A=(3.6\times 10^{2})\times (2.8\times 10^{2})\, miles^{2}[/tex]

=>[tex]A=1.008\times 10^{5}\, miles^{2}[/tex]

Thus the area of wyoming is [tex]A=1.008\times 10^{5}\, miles^{2}[/tex]

the sum of the first 8 terms of the series is [tex]\( -255 \)[/tex].

To find the sum [tex]\( S_8 \)[/tex] of the geometric series [tex]\( 3 - 6 + 12 - 24 + \ldots \)[/tex], we need to determine the common ratio [tex](\( r \))[/tex] and the first term [tex](\( a \)).[/tex]

The general form of a geometric series is [tex]\( a + ar + ar^2 + \ldots + ar^{n-1} \)[/tex], where:

- [tex]\( a \)[/tex] is the first term,

- [tex]\( r \)[/tex] is the common ratio,

- [tex]\( n \)[/tex] is the number of terms.

In our series:

- [tex]\( a = 3 \)[/tex] (the first term),

- To find the common ratio [tex](\( r \))[/tex], we can divide any term by its preceding term:

 - [tex]\( \frac{-6}{3} = -2 \)[/tex]

 - [tex]\( \frac{12}{-6} = -2 \)[/tex]

 - [tex]\( \frac{-24}{12} = -2 \)[/tex]

So, [tex]\( r = -2 \)[/tex].

Now, [tex]\( S_n \)[/tex], the sum of the first [tex]\( n \)[/tex] terms of a geometric series, is given by the formula:

[tex]\[ S_n = \frac{a(1 - r^n)}{1 - r} \][/tex]

Substituting the values of [tex]\( a \), \( r \)[/tex], and [tex]\( n = 8 \)[/tex], we get:

[tex]\[ S_8 = \frac{3(1 - (-2)^8)}{1 - (-2)} \][/tex]

[tex]\[ S_8 = \frac{3(1 - 256)}{1 + 2} \][/tex]

[tex]\[ S_8 = \frac{3(-255)}{3} \][/tex]

[tex]\[ S_8 = -255 \][/tex]

So, the sum of the first 8 terms of the series is [tex]\( -255 \)[/tex].

Answer: The all possible rational roots are [tex]x=\pm1,\pm2,\pm3,\pm4,\pm6,\pm12,\pm\frac{1}{2},\pm\frac{3}{2},\pm\frac{1}{4},\pm\frac{3}{4},\pm\frac{1}{10},\pm\frac{1}{5},\pm\frac{3}{5}\pm\frac{3}{10},\pm\frac{2}{5},\pm\frac{6}{5},\pm\frac{1}{20},\pm\frac{3}{20},\pm\frac{4}{5},\pm\frac{12}{5}[/tex].

Explanation:

The given polynomial is,

[tex]f(x)=20x^4+x^3+8x^2+x-12[/tex]

The Rational Root Theorem states that the all possible roots of a polynomial are in the form of a rational number,

[tex]x=\frac{p}{q}[/tex]

Where p is a factor of constant term and q is the factor of coefficient of leading term.

In the given polynomial the constant is -12 and the leading coefficient is 20.

All possible factor of -12 are [tex]\pm1,\pm2,\pm3,\pm4,\pm6,\pm12[/tex].

All possible factor of 20 are [tex]\pm1,\pm2,\pm4,\pm5,\pm10,\pm20[/tex].

So, the all possible rational roots of the given polynomial are,

[tex]x=\pm1,\pm2,\pm3,\pm4,\pm6,\pm12,\pm\frac{1}{2},\pm\frac{3}{2},\pm\frac{1}{4},\pm\frac{3}{4},\pm\frac{1}{10},\pm\frac{1}{5},\pm\frac{3}{5}\pm\frac{3}{10},\pm\frac{2}{5},\pm\frac{6}{5},\pm\frac{1}{20},\pm\frac{3}{20},\pm\frac{4}{5},\pm\frac{12}{5}[/tex]

Answer:

A.) -4/5 and 3/4

Step-by-step explanation:

Answer:

  B.  The amount spent on grapes compared with the weight of the purchase.

Step-by-step explanation:

Grapes are usually sold at some dollar amount per pound. That dollar amount is the "rate of change," and it is generally constant.

___

In the case of pizza delivery or bus ridership, it is hard to imagine what the "rate of change" might be, as the relationship is probably not a function.

The distance of the plane from the base of the tower is:

                    Option: D

                    D.  98 feet  

Let x denotes the distance of the plane from the base of the tower.

Now, in the right angled triangle we will need to use trignometric identity corresponding to 63°.

Based on the figure we have:

[tex]\tan 63=\dfrac{x}{50}\\\\\\x=50\times \tan 63[/tex]

[tex]x=50\times 1.9626\\\\\\x=98.13\ feet[/tex]

which to the nearest feet is:

                        98  feet

x=  standard

y = high quality

x +y = 1070

y=1070-x

2.8x + 4.9y =3521

2.8x +4.9(1070-x) = 3521

2.8x+5243-4.9x =3521

-2.1x=-1722

x=-1722/-2.1 = 820

820*2.8 =2296

1070-820 =250

250*4.9 = 1225

1225+2296 = 3521

there were 250 high quality downloads

Answer:

7 times during the first 15 minutes

Step-by-step explanation:

Remember that

[tex]1\ min=60\ sec[/tex]

so

[tex]15\ min=15(60)=900\ sec[/tex]

Decompose the numbers 18 and 42 in prime factors

we know that

[tex]18=(2)(3^2)[/tex]

[tex]42=(2)(3)(7)[/tex]

Find the least common multiple (LCM)

The LCM is

[tex](2)(3^2)(7)=126\ sec[/tex]

we need to find all multiples of 126 that are less than or equal 900.

[tex]126*1=126\ sec\\126*2=252\ sec\\126*3=378\ sec\\126*4=504\ sec\\126*5=630\ sec\\126*6=756\ sec\\126*7=882\ sec[/tex]

therefore

7 times during the first 15 minutes

The slope of a line perpendicular to x = -3 is 0. Option B is correct answer.

Perpendicular line slopes are the negative reciprocals of one another. In other words, if one line has a slope of m, a line perpendicular to it has a slope of -1/m. The definition of perpendicular lines, which states that the angles created by the lines are 90 degrees, may be used to demonstrate this relationship. The product of the slopes of perpendicular lines must be -1 in order to meet the requirement that the tangent of a 90 degree angle be specified.

Given the line x = -3.

Any line perpendicular to this line will have slopes of negative reciprocals of each other.

The slope of a horizontal line is 0, since the line does not change in the y-direction.

Hence, the slope of a line perpendicular to x = -3 is 0.

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Answer:

[tex]n=\frac{3}{2},\,\,n=2[/tex].

Step-by-step explanation:

The equation you have is a quadratic equation because the polynomial [tex]2n^{2}-7n+6[/tex] has degree 2. One of the methods available to solve kind of equations is  to factorize the polynomial  on the left hand side. To factorize you can do the following:

(1) [tex]2n^2-7n+6[/tex]. The given polinomial

(2) [tex]\frac{2\times(2n^2-7n+6)}{2}=\frac{(2n)^{2}-7(2n)+12}{2}[/tex].  Multiply and divide by 2, because it is the coeficient of [tex]n^{2}[/tex]

(3)  [tex]\frac{(2n)^{2}-7(2n)+12}{2}=\frac{(2n-\_\_)(2n-\_\_)}{2}[/tex]. Separate the polynomial in two factors, each one with [tex]2n[/tex] as a first term. The sign in the first factor is equal to the sign in the second term of the polynomial, that is to say, [tex]-7n[/tex]. The sign in the second factor is the sign of the second term multiplied by the sign of the third term, that is to say [tex](-)\times(+)=(-)[/tex] . In the blanks you should select two numbers whose sum is 7 and whose product is 12. Those numbers must be 3 and 4.

(4)The polynomial factorized is [tex]\frac{(2n-4)(2n-3)}{2}[/tex]

(5)Use the common factor in the numerator to cancel the number 2 in the denominator to obtain [tex](n-2)(2n-3)[/tex]

Then the given equation can be written as:

[tex]{(2n-3)(n-2)=0[/tex]

The product of two expression equals zero if and only if one of the expression is zero. From here we have that

[tex]2n-3=0[/tex] or [tex]n-2=0[/tex]

From the first equality we obtain that [tex]n=\frac{3}{2}[/tex]. From the second equality we obtain that [tex]n=2[/tex].

Final answer:

The magnitude of 6 + 2i is 2√10.

Explanation:

To find the magnitude of the complex number 6 + 2i, we can use the Pythagorean theorem. The magnitude, or absolute value, of a complex number is found by taking the square root of the sum of the squares of its real and imaginary parts. In this case, the real part is 6 and the imaginary part is 2. So the magnitude is:

|6 + 2i| = √(6^2 + 2^2) = √(36 + 4) = √40 = 2√10

Therefore, the magnitude of 6 + 2i is 2√10.

Length of arc VZX is 27.92 units.

The arc is a portion of the circumference of a circle.

Given,

Radius of circle = 8 units

∠VCX = 160°

Let length of arc VZX = x

x = area of circle×(360°- ∠VCX)/360°

x = 2π×8×(360-160)/360

x = 2π×8×(200)/360

x = 400π/45

x = 80π/9

x = 27.92 units

Hence, length of arc VZX is 27.92 units.

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Answer: C.The transfer rate of the USB stick is 200 times the transfer rate of the modem .

It is given in the question that

You will be charged 12.5% interest on a loan of $678.

So to find the interest, we have to find 12.5% of 678. And 12.5% = 0.125

So we have to find the value of 0.125 of 678.

[tex]0.125*678 = 84.75[/tex]

Therefore the interest that you will have to pay on loan is $84.75 .

Final answer:

The probability of drawing two yellow marbles in succession without replacement from a bag of 10 marbles, where 2 are yellow, is 1/45.

Explanation:

The student is asking about the probability of drawing two yellow marbles successively without replacement from a bag containing a total of 10 marbles with different colors. To solve this problem, we use conditional probability. The probability of drawing the first yellow marble is 2 out of 10 since there are 2 yellow marbles among 10 total marbles. This can be written as P(Y1) = 2/10 or 1/5. After the first yellow marble is drawn, there is only 1 yellow left among 9 total marbles, so the probability of drawing a second yellow marble is P(Y2|Y1) = 1/9.

The two events are dependent since the outcome of the first draw affects the second draw. Therefore, to find the overall probability of both events happening, we multiply their probabilities: P(Y1 and Y2) = P(Y1) × P(Y2|Y1) = (1/5) × (1/9) = 1/45. So, the probability of drawing two yellow marbles successively without replacement is 1/45.