30*8000(5-)1800=?
1500(800-)15000*18000=?

The sum of the first 5 terms of the series is 121.

An infinite number of terms with a fixed ratio between them are added to form a geometric series.

The series is a geometric series with the first term (a) equal to 1 and the common ratio (r) equal to 3.

To find the sum of the first 5 terms of the series, we can use the formula:

[tex]\rm S = a(1 - r^n) / (1 - r)[/tex]

where S is the sum of the first n terms of the series. Substituting the values we get:

[tex]\rm S = 1(1 - 3^5) / (1 - 3) \\\\= 1(1 - 243) / (-2)\\\\ = -242 / -2 \\\\= 121[/tex]

Therefore, the sum of the first 5 terms of the series is 121.

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Answer: The formula needed to find the amount of border needed is the perimeter formula for a rectangle:

Perimeter = 2(length + width)

Step-by-step explanation:

To find the median of the data, we need to first arrange the numbers in order from smallest to largest:

65, 65, 124, 129, 180, 190, 228, 285, 285, 316, 370, 370

There are 12 numbers in the sample, so the median will be the middle value. In this case, there are two middle values because there are an even number of data points. To find the median, we take the average of the two middle values:

median = (180 + 190)/2 = 185

So the median number of pieces in the sample of building toys is 185.

Answer

Step-by-step explanation:

what's the question?

Answer:

look in explanation

Step-by-step explanation:

The formula to find the surface area of a cylinder is as follows: SA= (2*π*r*h) + (2*π*r²)

You need to know the height of the cylinder in order to input the number into the equation.

Also, if you are using nets, you need to know the height of the cylinder because you cannot calculate the area of the rectangle part of the cylinder's net without that measurement.

Answer:

d is the correct option

Step-by-step explanation:

when powers are raised to powers

they got multiplied

Answer:

Step-by-step explanation:

NOTE:

   [tex](x^p)^q=x^{p\times q}[/tex]

As a result of this law the correct solution is (d). )

His total annual cost for providing these insurance plans will be $ 5, 659 per employee for the year.

The total annual cost for providing these insurance plans will be $ 12, 500 per employee.

The annual cost of insurance to Bob for the insurance package that he wants to offer his employees is:

= Health Insurance + Dental Insurance + Vision Insurance

= 5, 179 + 360 + 120

= $ 5, 659

The total cost of the insurance plans per employee would be:

= Life Insurance + Disability insurance

= 9, 500 + 3, 000

= $ 12, 500

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The full question is:

Let's say Bob wants to offer an insurance package to his employees that will cover any outpatient surgery charges, tooth sealants, and glasses. His total annual cost for providing these insurance plans will be $ ____ per employee for the year. Let's assume that Schmidt wants to cover his employees' expenses in case of disability. He also wants to ensure that the family of an employee is provided for in the event of an employee's loss of life. The total annual cost for providing these insurance plans will be $ _____ per employee.

The correct classification(s) of the fractional number 15/3 is: whole, integer, rational.

What is fractional number?

A fractional number, also known as a fraction, is a number that represents a part of a whole. It consists of two parts: a numerator and a denominator, separated by a slash (/). The numerator is the number above the line, and the denominator is the number below the line.

The number 15/3 is a fraction. When we simplify this fraction, we divide 15 by 3 to get:

15/3 = 5

Therefore, the number 15/3 is equivalent to the whole number 5.

An integer is a number that can be expressed without fractions or decimals, and can be positive, negative, or zero. The number 5 is also an integer, because it is a positive whole number.

A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. In this case, 15/3 can be expressed as the ratio of two integers (15 and 3), so it is a rational number.

Therefore, the correct classification(s) of the number 15/3 is:

whole, integer, rational.

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Answer:

[tex]P(x)=3x^4-11x^3+71x^2-275x-100[/tex]

Step-by-step explanation:

Given information:

For any complex number  [tex]z=a+bi[/tex], the complex conjugate of the number is defined as  [tex]z*=a-bi[/tex].  

If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.

Therefore, if P(x) is a polynomial with real coefficients, and 5i is a root of P(x)=0, then its complex conjugate -5i is also a root of P(x)=0.

So the zeros of the function are: 5i, -5i, 4, and -1/3.

The zeros of a function P(x) are the x-values of the function such that the P(x)=0.  According to the Factor Theorem, if P(x) is a polynomial, and P(a)=0, then (x - a)  is a factor of P(x).

Therefore, the factors of the function are:

[tex]x=5i \implies (x-5i)[/tex]

[tex]x=-5i \implies (x+5i)[/tex]

[tex]x=4 \implies (x-4)[/tex]

[tex]x=-\dfrac{1}{3} \implies (3x+1)[/tex]

So the polynomial in factored form is:

[tex]P(x)=a(x-5i)(x+5i)(x-4)(3x+1)[/tex]

As we have not been given a specific leading coefficient, let us assume it is one.

[tex]P(x)=(x-5i)(x+5i)(x-4)(3x+1)[/tex]

To write the polynomial in standard form, expand and simplify.

[tex]\begin{aligned}P(x)&=(x-5i)(x+5i)(x-4)(3x+1)\\&=(x^2+5ix-5ix-25i^2)(3x^2+x-12x-4)\\&=(x^2-25(-1))(3x^2-11x-4)\\&=(x^2+25)(3x^2-11x-4)\\&=3x^4-11x^3-4x^2+75x^2-275x-100\\&=3x^4-11x^3+71x^2-275x-100\end{aligned}[/tex]

Answer:

y = -5x

Step-by-step explanation:

y = -5x;

[tex]\frac{y}{x}[/tex] = -5;

y:x=-5:1

a. The y-intercept of the line is 4.

b. The gradient of the line is 2.

The gradient of a line is the steepness of the line, which is determined by how much the line rises or falls for each unit of horizontal distance [m = change in y / change in x], while the y-intercept is the point where the line crosses the y-axis.

a. The line cuts the y-axis at 4, therefore, the y-intercept is 4.

b. Gradient of the line = rise/run = 2/1

Gradient = 2.

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The answer of the given question on the listing the critical numbers is  the critical numbers as x = 3, 6, and 9. and the function has an absolute maximum at x = 9. and the function has an absolute minimum at x = 2.

an absolute maximum occurs at the highest point on the graph of a function over its entire domain. It can be a local maximum or a global maximum, depending on whether there are any other points in the domain that have higher function values. Finding the absolute maximum of a function is important in optimization problems, where we want to find the maximum or minimum value of a function subject to certain constraints.

Based on the graph provided, we can approximate the critical numbers as x = 3, 6, and 9.

To determine whether there is relative maximum, relative minimum, absolute maximum, or absolute minimum at each critical number, we need to examine  behavior of function near each critical number.

At x = 3, the function has a relative maximum, since the graph changes from increasing to decreasing at that point.

At x = 6, the function has a relative minimum, since the graph changes from decreasing to increasing at that point.

At x = 9, the function has a relative maximum, since the graph changes from increasing to decreasing at that point.

Since the graph increases without bound as x approaches 10 from the left, but approaches a finite value as x approaches 10 from the right, the function has an absolute maximum at x = 9.

Since the graph decreases without bound as x approaches 2 from the right, but approaches a finite value as x approaches 2 from the left, the function has an absolute minimum at x = 2.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]6x+y=-10\implies y=-6x-10\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -6 \implies \cfrac{-6}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-6}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-6} \implies \cfrac{1}{ 6 }}}[/tex]

so we're really looking for the equation of a line whose slope is 1/6 and it passes through (1 , 1)

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{6} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{6}}(x-\stackrel{x_1}{1}) \\\\\\ y-1=\cfrac{1}{6}x-\cfrac{1}{6}\implies y=\cfrac{1}{6}x-\cfrac{1}{6}+1\implies {\Large \begin{array}{llll} y=\cfrac{1}{6}x+\cfrac{5}{6} \end{array}}[/tex]

The intersection points are: (0, -3) and (10, 2)

The bounded area is -20.83 unit²

(a) The  intersection points of the line and curve are the points where the line and curve meet. Thus, the intersection points are:

(0, -3) and (10, 2)

(b) The integral terms of y which gives the area bound are:

a = -3, b = 2 (These are the y values of the intersection points)

Since we have x = y² + 3y and x = 2y + 6, we can say:

y² + 3y = 2y + 6

y² + 3y - 2y - 6 = 0

y² + y - 6 = 0

Thus, h(y) =

Using a = -3 and b = 2  with h(y) = y² + y - 6, we have the bounded area as:

[tex]Area = \int\limits^b_a {y} \, dy[/tex]

[tex]Area = \int\limits^{2}_{-3} {(y^{2} + y - 6}) \, dy[/tex]

Integrating the area:

Area = [y³/3 + y²/2 - 6y + C]²₋₃

Area = [2³/3 + 2²/2 - 6(2)] - [(-3)³/3 + (-3)²/2 - 6(-3)]

Area = [8/3 + 2 - 12] - [-9 + 4.5 + 18]  

Area = [-22/3] - [27/2]

Area = -125/6

Area = -20.83 unit²

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m∠NOP = 90° is the value of angle .

What does a math angle mean?

An angle is made up of two rays (half-lines) that have a shared termination. The rays serve as the angle's sides, occasionally serving as the angle's legs and occasionally serving as its arms, while the latter is referred to as the vertex of the angle.

                                           A figure that is created by two rays or lines that have the same endpoint is known as an angle in plane geometry. The Latin word "angulus," which meaning "corner," is the source of the English term "angle". The vertex, which is the shared terminal of the two rays, is referred to as the side of an angle.

m∠NOP = 90° is the value of angle .

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Answer:

1/4(2^3 + 4^2) = 6

Step-by-step explanation:

I

Answer: The tank starts with 10 gallons of gas

Step-by-step explanation:

so the first thing that you are going to do is divide and multiply  what might you be dividing great question, you will divide 10 in to 9 then multiplying 160 into 15.

If you want to know how i got this answer please ask me in the commets below.

The equation solved for the variable x is:

[tex]x = e^{ W(ln(y))}[/tex]

In any equation of the form:

y = f(x), to make x the subject of the equation, we need to isolate x in one of the sides of the equation, then we will get:

x = g(y).

In this case we have:

xˣ = y

And we want to make x the subject of the equation.

We can start by apliying the natural logarithm in both sides to get:

ln(xˣ ) = ln(y)

x*ln(x) = ln(y)

We can rewrite:

[tex]x = e^{ln(x)}[/tex]

Then our equation becomes:

[tex]e^{ln(x)}*ln(x) = ln(y)[/tex]

Now the Lambert W function is defined as:

[tex]W(x*e^x) = x[/tex]

So if we apply this in both sides, we will get:

[tex]W(e^{ln(x)}*ln(x)) = W(ln(y))\\ln(x) = W(ln(y))[/tex]

Now apply the exponential in both sides and get:

[tex]ln(x) = W(ln(y))\\\\e^{ln(x)} = e^{ W(ln(y))}\\x = e^{ W(ln(y))}[/tex]

That is the equation solved for x.

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Complete question:

"How can you make x the subject in the equation? xˣ = y"

The range of possible values for x is approximately -14.7 to 14.7. However, since x represents a length, it cannot be negative. Thus, the range of possible values for x is approximately 0 to 14.7.

The range refers to the difference between the maximum and minimum values in a dataset.
The range is easy to calculate and provides a quick estimate of how much variation there is in the dataset.

We have:

∠ABC + ∠ABD + ∠BDA + ∠BAC = 360°

120° + 115° + ∠BDA + ∠BAC = 360° (substituting given values)

∠BDA + ∠BAC = 125°

Now, we can use the law of cosines to relate the sides and angles in each triangle:

AC² = AB² + BC² - 2ABBCcos(∠ABC)

(4x-10)² = AB² + 24² - 2AB24cos(120°)

(4x-10)² = AB² + 576 + 24AB

AD² = AB² + BD² - 2ABBDcos(∠ABD)

40² = AB² + 24² - 2AB24cos(115°)

AB² - 48AB + 496 = 0

Using the quadratic formula to solve for AB, we get:

AB = (48 ± √(48² - 4×496))/2

AB = 24 ± 2√211

Since AB = 24 + 2x, we have:

24 + 2x = 24 + 2√211 or 24 - 2√211

By Solving for x in each case, we get:

x = √211 + 0.5 ≈ 14.7 or x = -√211 + 0.5 ≈ -14.7

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There are three coefficients present in the expression: 5 for the x³ ;  2 for the x² and 6 is for x.

The integer or constant quantity put before a variable is known as a coefficient.

Thus, there are three coefficients present in the expression: 5 for the x³ ;  2 for the x² and 6 is for x.

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Complete question-

How many coefficients are in the expression 5x³ + 2x²+6x-4?

Answer:

If the entire mass of the Milky Way was due to gas and stars, how would you expect the rotational speed of a star near the edge of the galaxy to compare to the rotational speed of a star near the center?

Step-by-step explanation:

Answer:

the clock hands do not form a right angle at 5:00.

Step-by-step explanation:

Answer: one inch measured the the map represented 100 feet on the ground

Step-by-step explanation:

Answer: 10/20, 8/20, 4/20, 6/20

Step-by-step explanation:

Black: 10/20

Red: 8/20

White: 4/20

Blue: 6/20

There are 20 marbles in total the amount of colored marbles is the numerator and the denominator is the total.

Have a lovely day!!

Answer: $1.46 less

Step-by-step explanation:

Lets find how much each bottle is first for Store B, to do that divide 29.10 divided by 15 and you should get 1.94 meaning each bottle of juice is $1.94. Next, lets find how much each bottle costs in store A. You can take any number from the total cost and divide it by the bottles and you should get the same thing. Lets do the first one 2.40 divided by 5 equals 0.48. If you want to check you can multiply 0.48 by any number of bottles and you should get the total cost. Now we have to find how much less Store A costs, to do so we subtract store B (1.94) and store A (0.48) and you should get $1.46.

Answer:

(0,8)

Step-by-step explanation:

The slope intercept formula is set up as y=mx+b, where b is the y-intercept value. In the equation y=3x+8, we can see that 8 is the y-intercept. So we plug 8 for y in a coordinate, and 0 for x. The answer is (0,8)