A company sells build-your-own robot kits. The profit (in thousands of dollars) for the first 500 kits sold can be modeled by the function P(x), where x is the number of kits sold (in hundreds).

Use synthetic substitution to determine the total profit from the sale of 120 robot kits.​

Answer:

Explanation:

There are three right angled triangles are in the diagram of three different sizes.

Identify the right angles.

In the first triangle, the right angle is angle M. In the second one, the right angle is angle K and in the third triangle, it is angle K.

Now, identify the shortest sides of each.

The shortest side in the first triangle is MJ, in the second triangle, it is JK and in the third triangle, it is MK.

In the given triangle JKM, notice that JK is the shortest side and angle K is the right angle. Write the other two tringles also in the similar form with the first two letters gives the short side and middle letter represents the right angle.

So, the similarity statement is

Each flight has a probability of 60% or 0.6 of being on time. This means that its complement, or the probability that the flight isn't on time is:

It is 40% or 0.4. "~P(on time)" stands for the probability of the flight not being on time.

1. The probability that at least 2 flights are on time is:

To find the probability that 2 or more flights are on time we can fight the probability that "0" or "1" are not on time.

The probability of 2 or more flights are on time is:

The probability of 2 flights or more are on time is 0.996198912

2.

We need to calculate the probabilities of 7,8 and 9 flights are on time and then subtract by 1.

The probability of at most 6 flights are on time is:

The probability of 6 or less are on time is 0.768212992.

3.

The probability of exactly 5 flights are on time is:

The probability of exactly 5 flights are on time is 0.250822656.

The diameter of the circle is 5.2m.

The area of circular pond is 21.5 m2

area of a circle is given by the formula

area = πr²

21.5 = 3.14 r²

r² = 6.84

r = ±2.6

r is a length and it cannot be negative

So, r = 2.6

Diameter is twice of radius

d = 2r

d = 2(2.6)

d = 5.2

Therefore, the diameter of the circle is 5.2m.

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we have that the arithmetic sequence have:

so we can replace for n=2,3,and 4 to find the first four terms so:

for n=2

for n=3

and for n=4

So the first four numbers are

Answer:

5i + 2

Step-by-step explanation:

(5-2i)(i)

5i - 2i^2

i^2= -1

5i -2(-1)

= 5i + 2

The total number of pages they read by the end of November is 2916 pages.

As the question, Chapter 1 has 35 pages, Chapter 2 has 38 pages and Chapter 3 has 35 pages. All these pages are read by all 27 students by the end of November.

⇒   Total number of pages in Three chapters  [tex]=35+38+35[/tex]

                                                                             [tex]=108[/tex]

⇒   Total number of pages in all three chapters read by one student = 108

⇒   Total number of pages read by 27 students  

                                      [tex]= total number of pages in three chapters * 27[/tex]

                                      [tex]=108*27[/tex]

                                      [tex]=2916[/tex]

Therefore, The total number of pages 27 students read by the end of November = 2916.

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The full question is

There are 27 students in Mrs. Mello's class. fin the total number of pages they read by the end of November.

Answer: we would need to see the graphs to address this question fully, but you should look for the graph that starts at x = 0, 1250 and decreases by 14% compared to the previous year

so for example, x = 1, the y value should be 1250 - (0.14)(1250)

Step-by-step explanation:

Given:

The given point is (-4,1)

Let's check the ordered pair (-4,1) in the first equation

Hence, (-4,1) is a solution of the first equation x-5y=-9.

Now, let's check (-4,1) in the second equation.

So, (-4,1) is a solution of the second equation 4x+4y=-12.

Hence, (-4,1) is a solution of both equation in the system, then it is a solution to the overall system.

The statement that explains why Charlotte's submission is correct is that (4³)³ simplifies to (4⁹) and (4⁹) simplifies to 2¹⁸

From the question, the expression is given as

(43)3

Rewrite the expression properly

So, we have the following representation

(4³)³

Apply the law of indices to rewrite the exponents in the expression properly

So, we have

(4³)³ = 4³*³

Next, we evaluate the products

So, we have the following notation

(4³)³ = 4⁹

Solving further, we need to express 4 as the square of 2

So, we have

(4³)³ = (2²)⁹

Apply the law of indices to rewrite the exponents in the expression properly

So, we have

(4³)³ = 2²*⁹

Next, we evaluate the products

So, we have the following notation

(4³)³ = 2¹⁸

Hence, Charlotte's expression is correct

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Possible question

Charlotte states that (4³)³ can be rewritten as 2¹⁸. Which of the following explains how she is correct? Select all that apply.

Answer: The number of pencils Brian has is p+4

Step-by-step explanation:

Because p is the original number of the pencil ( we don't know how many are there so we keep it p). Then he bought 4 more which mean +4, so the answer is p+4

We have a figure ABCD that is dilated by a factor of 2.

We have to find the coordinate of the image point B'.

If the center of dilation is the origin (0,0) and the factor is k = 2, we can write the rule:

Then, for B(-1,1), we will get:

Answer: B' = (-2,2)

Answer:

about 3.09

Step-by-step explanation:

A = l  x w

A = 13/7 x 7/6

A = 1.857 x 1.666

A = 3.09

Hope it helps!

Given:

Annual earnings = $17,500

Asked: What is the gross amount of her semimonthly paycheck?

Solution:

To find the answer, we need to divide first the annual earnings by 12 to get the monthly paycheck. After that, we will divide it by 2 because we are looking for the semimonthly paycheck.

ANSWER: C. $729.17

The percent change in river depth is 52%

From the information, the depth of the river was 5 feet deep, it dropped to 3.8 feet and in 1848, it rose to 6.4 feet. The new feet will be:

= -5 - 3.8 + 6.4

= 2.4

Therefore, the percentage change will be:

= New feet / Initial feet × 100

= (5 - 2.4) / 5 × 100

= 2.6 / 5 × 100

= 52%

Note that there was no table given.

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Manuel will attend the quarter in 9 weeks.

Given,

In the question:

Total taken quizzes is 90

Manuel took a total of 20 quizzes over the course of 2 weeks.

To find the how many weeks of school will Manuel have to attend this quarter ?

Now, According to the question:
Based on the given conditions :

Formulate:

Let the no. of weeks be x

Total quizzes = 90

Here, The relationship is directly proportional.​

20/2 = 90/x

If the fraction is defined, the denominator cannot be equal 0.

Solve the equation:

10 = 90/x

10x = 90

x = 9

Hence, Manuel will attend the quarter in 9 weeks.

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Answer:

answer Is -9/40

Step-by-step explanation:

the formula Is

tan0= sin0/cos0

tan0= (9/41)/(-40/41)

tan0=(9/41)*(-41/40)

tan0= -9/40

The length of short side x is 4.5 units, the length of short side x+5 is 9.5 units and the length of longest side is 10.5 units.

By Pythagorean theorem,

[tex]( Hypotenuse)^{2} = (Base)^{2}+ (Perpendicular)^{2}[/tex]

Let                base = x+5

     perpendicular = x

        Hypotenuse = x+6

                                    [tex](x+6)^{2} = x^{2} +(x+5)^{2}[/tex]

                           [tex]x^{2} +12x+36 = x^{2} +x^{2}+10x+25[/tex][tex]2x^{2} +10x+25-x^{2} -12x-36=0[/tex]

                             [tex]x^{2} -2x-11=0[/tex]

                                               [tex]x = \frac{-(-2) + \sqrt{4 - 4(1)(-11)} }{2*1}[/tex] or [tex]\frac{-(-2) - \sqrt{4 - 4(1)(-11)} }{2*1}[/tex]

                                               [tex]x=\frac{2 + \sqrt{4 +44} }{2}[/tex] or  [tex]\frac{2 - \sqrt{4 +44} }{2}[/tex]

                                               [tex]x = \frac{2 + \sqrt{48} }{2}[/tex] or [tex]\frac{2 - \sqrt{48} }{2}[/tex]

                                               [tex]x = \frac{2+2\sqrt{12} }{2}[/tex] or [tex]\frac{2-2\sqrt{12} }{2}[/tex]

                                               [tex]x = 1+\sqrt{12}[/tex] or [tex]1-\sqrt{12}[/tex]

                                               [tex]x = 1+3.5[/tex] or [tex]1-3.5[/tex]

                                               [tex]x = 4.5[/tex] or [tex]-2.5[/tex]

As, length can't be negative, we will take x = 4.5

Therefore, x = 4.5

            x + 5 = 4.5 + 5

                      = 9.5

             x + 6 = 4.5 + 6

                       = 10.5

Hence, the length of short side x is 4.5 units, the length of short side x+5 is 9.5 units and the length of longest side is 10.5 units.

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The acceleration of the car will be 0.002 m / s².

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The velocity of the car = 35.9 m/hr

The time take by car = 8.2 seconds

Now,

Since, We know that;

⇒ Acceleration = (Final velocity - Initial velocity) / Time

Since, The driver accelerates her car from rest to a velocity of 35.9 mi/hr.

So, Initial velocity = 0

And, Final velocity = 35.9 m / hr

                             = (35.9 / 3600) m/s

                             = 0.01 m / s

So, We get;

⇒ Acceleration = (Final velocity - Initial velocity) / Time

⇒ Acceleration = (0.01 - 0) / 8.2

⇒ Acceleration = 0.01 / 8.2

⇒ Acceleration = 0.002 m / s²

Thus, The acceleration of the car will be 0.002 m / s².

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a) The area of the rectangle has the following inequality: 12 ≤ 6 · x ≤ 36.

b) The value of the variable x has the following inequality: 2 ≤ x ≤ 6.

The area of a rectangle (A) is described by the following formula:

A = b · h

Where:

a) If we know that b = 2 · x and h = 3, then the area of the rectangle is:

A = (2 · x) · 3

A = 6 · x

And the inequality is:

12 ≤ 6 · x ≤ 36

b) And the solutions for the values of x are represented by the following inequality:

2 ≤ x ≤ 6

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while shopping for clothes, Daniel spent $26 less than 2 times what curtis spent. Daniel spent $10. write and solve an equation to find how much curtis spent. let x represent how much curtis spent​

Let

x ------> amount that Curtis spent

we have that

10=2x-26 ------> equation that represent this situation

solve for x

2x=10+26

2x=36

x=$18

therefore

Answer:

1000

Step-by-step explanation:

The easiest way to go about this is by turning our number into ABCD.

A will be in the 1000th spot, B 100th, C 10th, and D 1st.

A has to be ≥ 5. So 5, 6, 7, 8, 9.

B has to be a prime number. 2, 3, 5, 7.

C is able to be any number it wants, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Since the number is odd, D has to be 1, 3, 5, 7, 9.

A has 5 different possibilities. B has 4, C has 10, and D has 5.
You'll then multiply all of these numbers for your answer.
5 * 4 * 10 * 5 = 1000

The function’s equation written in factored form and in vertex form are respectively;

f(x) = 2x(x - 4)

f(x) = 2(x - 2)² - 8

The factored form of a quadratic function is;

f(x) = a(x - p)(x - q)

where:

p and q are the x-intercepts

a is a constant

Now, we are given x-intercepts as; (0, 0) and (4, 0)

Thus;

f(x) = a(x - 0)(x - 4)

f(x) = ax(x - 4)

To find a, substitute the given vertex (2, -8) into the equation and solve for a:

2a(2 - 4) = -8

-4a = -8

a = 2

Thus;

f(x) = 2x(x - 4)

The vertex form of a quadratic equation is;

f(x) = a(x - h)² + k

where:

(h, k) is the vertex

a is constant

Since vertex is (2, -8), then we have;

f(x) = a(x - 2)² - 8

Put the coordinate (0, 0) to find a;

0 = a(0 - 2)² - 8

4a = 8

a = 2

Thus;

f(x) = 2(x - 2)² - 8

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Answer:

-64x^12

Explanation:

Given the expression

m = -4x^4

You are to look for m^3 as shown;

Open the bracket:

THe correct answer is -64x^12

Answer:

We have to use to elimination method to solve the provided system of equations, this method essentially involves eliminating one of the variables in the first equation by adding or subtracting a multiple of the second equation:

The elimination of the variable y in equation (1) is achieved by adding the 4 times the equation 2 into the equation (1), the steps of the process are as follows:

We have found the x value, the last step is to plug in the variable x value in any of the (1) or (2) equations, and solve for the y variable, the steps are as follows:

The final answer is as follows:

Therefore the answer is Option(B).

The digit in the hundreds place is 4

From the question, we have

(21 × 10¹)+(3×10²) + (9 × 10²)

=210+300+900

=1410

The digit in the hundreds place is 4 and the value is 400.

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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In the given triangle ABC where BD bisects ABC and according to the values of the given angles, the value of x is found out to be 3.5.

It is given to us that -

BD bisects ABC.

m/ABD = 2(3x) ----- (1)

and, m/ABC = 42 ------- (2)

We need to find out the value of x.

Since BD bisects triangle ABC,

The angles created with respect to the bisector are equal.

=> m/ABD = m/CBD ----- (3)

Also, it is also known that -

m/ABD + m/CBD = m/ABC ----- (4)

Substituting equation (3) in equation (4),

m/ABD + m/CBD = m/ABC

=> m/ABD + m/ABD = m/ABC

=> 2 m/ABD = m/ABC ----- (5)

Substituting the values of m/ABD and m/ABC from equation (1) and (2) in equation (5), we get

2 m/ABD = m/ABC

=> 2*2(3x) = 42

=> 12x = 42

=> x = 3.5

Thus, according to the values of the angles of the triangle, the value of x is 3.5.

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Answer:

7.5/3

Step-by-step explanation:

set AC and BD equal to eachother because they are equal and solve

Let's call the first odd number x.

The next odd number will be x + 2, and the last one will be x + 4.

If the sum of the first number and the last one is 26, we have that:

So the numbers are:

11, 13 and 15.

Answer:

(-2,4)

Explanation:

Given the inequality:

The solution set is graphed on the number line below: