Eight triangles are drawn within a square to create the shaded region in the figure.

Answer:

x = -2

x = 3

Step-by-step explanation:

They will be 72 km far apart after 2 hours. The solution has been obtained by using the concept of relative speed.

The speed of a moving body relative to another might be referred to as relative speed. The differential between two moving bodies is used to calculate their relative speed. Yet, the relative speed of two bodies travelling in opposition to one another is determined by summing their respective speeds.

We are given that the Serenity and the Mystic travels in the opposite direction at 16 mph and at 20 mph respectively.

So,

The relative speed = 16 + 20 = 36 mph

Now,

After 2 hours the distance between them will be as follows

36 × 2 = 72 mph

Hence, they will be 72 km far apart after 2 hours.

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427.

The proof for the question is as follows:

A(n) is the arithmetic mean of the (positive) factors of n.

We want to find the n for which A(n) = 124.

Let F be the set of (positive) factors of n, and let f1, f2,..., fm be the elements of F.

The arithmetic mean of F is defined as A(n) = (f1 + f2 + ... + fm)/m.

Now, we have A(n) = 124. So, 124 = (f1 + f2 + ... + fm)/m.

Therefore, 124m = f1 + f2 + ... + fm.

This implies that f1 + f2 + ... + fm = 124m = 427.

Thus, n = 427.

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Therefore , the solution of the given problem of slope comes out to be slope-intercept equation y = 2x + 1.

The y-intersection axis's with the slope of the line marks the inflection point in arithmetic where the y-axis intersects a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is the equation for the long line. The y-intercept (b) and slope (m) of the line are emphasised in the equation intercept form. An solution with the intersecting form (y=mx+b) has m and b as the slope and y-intercept, respectively.

Here,

Y = mx + b, where m is the line's slope and b is the y-intercept, is the slope-intercept version of a linear equation. Given two points (x1, y1) and (x2, y2), we can use the following method to determine the slope of the line:

=> m = (y2 - y1) / (x2 - x1) (x2 - x1)

For instance, if the two locations (2, 5) and (4, 9) are provided, we can determine the slope as follows:

=> m = (9 - 5) / (4 - 2) = 2

The y-intercept can then be determined by using one of the locations and the slope. Let's use points 2 and 5:

=> y = mx + b

=> 5 = 2(2) + b

=> 5 = 4 + b

=> b = 1

As a result, the line going through the points (2, 5) and (4, 9) has the slope-intercept equation y = 2x + 1.

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To find all the vectors that are in the subspace V of R³, we need to solve the system of equations given in the question. We can use the Gaussian elimination method to do this.

First, let's write the system of equations in matrix form:
\[ \begin{bmatrix} 1 & 2 & -3 \\ 0 & 1 & -2 \end{bmatrix} \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} \]

Now, we can use the Gaussian elimination method to find the solution:
Step 1: Subtract 2 times the second equation from the first equation to eliminate x₂:
\[ \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & -2 \end{bmatrix} \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} \]
Step 2: Solve for x₁ and x₂ in terms of x₃:
x₁ = -x₃
x₂ = 2x₃
Step 3: Write the solution in vector form:
\[ \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \end{bmatrix} = \begin{bmatrix} -x_{3} \\ 2x_{3} \\ x_{3} \end{bmatrix} = x_{3} \begin{bmatrix} -1 \\ 2 \\ 1 \end{bmatrix} \]

So, the subspace V is the set of all scalar multiples of the vector (-1, 2, 1). In other words, V = {x₃(-1, 2, 1) | x₃ ∈ R}.

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The probability of rolling a sum greater than 5 is 13/18.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

There are six different possible outcomes for a dice, the set (S) of all the outcomes can be listed as follows:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

a) The probability of rolling a sum of even number

Number of favorable outcomes = 9

Total number of outcomes = 36

Now, probability = 9/36

= 1/4

b) The probability of rolling a sum of odd numbers

Number of favorable outcomes = 9

Total number of outcomes = 36

Now, probability = 9/36

= 1/4

c) The probability of rolling a sum of greater than 5

Number of favorable outcomes = 26

Total number of outcomes = 36

Now, probability = 26/36

= 13/18

Therefore, the probability of rolling a sum greater than 5 is 13/18.

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Given:

What is the interest earned when $46,230 is invested for 9 years at 7.8% p.a?

To find:

The interest

Solution:

The answer of decimal number that has the specified place values is 964.8.

To write the decimal number, we need to understand the place value of each digit.

The place values are as follows:

- 9 hundreds = 900
- 6 tens = 60
- 4 ones = 4
- 8 tenths = 0.8
- 0 hundredths = 0.00

To write the decimal number, we add the place values together:

900 + 60 + 4 + 0.8 + 0.00 = 964.8

Therefore, the decimal number that has the specified place values is 964.8.

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The original list price for the product was $487.09.

To find the original list price for the product, we need to reverse the discounts and markup that were applied to it. Here is a step-by-step explanation:

Therefore, the original list price for the product was $487.09.

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Answer:

490 newtons

Step-by-step explanation:

The surface area to the nearest tenth value is somewhere around 285.9 cm². We can find it in the following manner,

Given the formula is S= 4πr²

And the volume of the regulation basketball is given as 456cm³

Since we know the formula for sphere is (4/3)πr³ we can find the radius from the volume of formula

V= (4/3)πr³

456cm³= (4/3)πr³

456= (4/3)(22/7)r³

r= 4.77 cm

Therefore the radius come out to be 4.77 cm

Now to find the surface area according to the first formula that is S= 4πr² where S represent surface area

S= 4πr²

S= 4 x (22/7) x (4.77)²

S= 285.92 cm²

Therefore the surface area to the nearest tenth value is somewhere around 285.9 cm²

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Answer:

  x = 1 or 5

Step-by-step explanation:

You want the value(s) of x that make 3x^2-x+1 and 2x^2+5x-4 have the same value.

Equating their values, we have ...

  3x² -x +1 = 2x² +5x -4

  x² -6x +5 = 0 . . . . . . . . . subtract (2x²+5x-4)

  (x -5)(x -1) = 0 . . . . . . . factor

  x = 1 or x = 5 . . . . . . values of x that make the factors zero

The two trinomials will have the same value for x=1 and for x=5.

__

Additional comment

The attached graph shows the points where the trinomials have the same value.

Answer:

Step-by-step explanation:

c

Answer:E

Step-by-step explanation:

The remainder when -233 is divided by 11 is 9. To find the remainder when a is divided by b, we can use the formula:

r = a % b

Where % is the modulo operator, which gives the remainder when one number is divided by another.

In this case, we have a = -233 and b = 11. Plugging these values into the formula, we get:

r = -233 % 11

Using a calculator or doing the division by hand, we find that the remainder is -2. However, since we are looking for the positive remainder, we can add b to this value to get the correct answer:

r = -2 + 11 = 9

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The area of an "A" sector with central angle 2.781 is 36.17 square units. The area of a "B" sector with central angle 1.54519 is 20.10 square units. The area of a "C" sector with central angle 112.128 degree is 49.81 square units. Grade in order of increasing likelihood: B, A, C. Likelihood that you will receive an "A" is 0.4427.

The area of a sector of a circle can be found using the formula A = (1/2)r^2θ, where r is the radius of the circle and θ is the central angle of the sector in radians. To find the area of each sector, we need to convert the central angles from degrees to radians by multiplying by π/180.

The area of an "A" sector with central angle 2.781 radians is A = (1/2)(5.1)^2(2.781) = 36.17 square units.

The area of a "B" sector with central angle 1.54519 radians is A = (1/2)(5.1)^2(1.54519) = 20.10 square units.

The area of a "C" sector with central angle 112.128 degrees is A = (1/2)(5.1)^2(112.128)(π/180) = 49.81 square units.

The total area of the circle is A = πr^2 = π(5.1)^2 = 81.71 square units.

The likelihood of receiving an "A" is the area of the "A" sector divided by the total area of the circle, or 36.17/81.71 = 0.4427.

The likelihood of receiving a "B" is the area of the "B" sector divided by the total area of the circle, or 20.10/81.71 = 0.2460.

The likelihood of receiving a "C" is the area of the "C" sector divided by the total area of the circle, or 49.81/81.71 = 0.6096.

Therefore, the grades in order of increasing likelihood are: B, A, C.

The likelihood that you will receive an "A" is 0.4427.

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There would be 40,320 ways can 8 people be arranged on 8 chairs in a row. There are 5,040 ways can 8 people be seated around a circular table. There are  128 committees can be selected from the people if ps has to be the chair of the committee

(a) The number of ways that 8 people can be arranged on 8 chairs in a row is 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320. This is because there are 8 choices for the first chair, 7 choices for the second chair, and so on until there is only one choice for the last chair.

(b) The number of ways that 8 people can be seated around a circular table is (8-1)! = 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040. This is because we can fix one person in one seat and then there are 7 choices for the next seat, 6 choices for the next seat, and so on until there is only one choice for the last seat.

(c) The number of committees that can be selected from the 8 people if Ps has to be the chair of the committee is 2^(8-1) = 2⁷ = 128. This is because there are 7 people left to choose from and each person can either be on the committee or not on the committee, which gives us 2 choices for each person.

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By answering the above question, we may state that We are unable to solve this equation for both l and w since it has only one solution and two unknowns.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

We are aware of the frame's 42-inch circumference but are unaware of the picture's or frame's shape, as well as if the frame's breadth fluctuates or is constant.

With the assumption that the frame is rectangular and has a constant width, we might create the equation shown below:

2l + 2w + 4x = 42

where L stands for the picture's length, W for its width, and X for the frame's width (assuming there are four sides with the same width).

We are unable to solve this equation for both l and w since it has only one solution and two unknowns.

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The derivative of √(x + 3) / (x + 1) with respect to x is:

[(√(x + 3)) / (x + 1)]' = [1 - (√(x + 3))  (x + 1)] / [2(x + 1)²  √(x + 3)]

To differentiate √(x + 3) / (x + 1) with respect to x, we need to use the quotient rule:

(f(x) / g(x))' = (f'(x) * g(x) - f(x) * g'(x)) / [g(x)]²

where f(x) = √(x + 3) and g(x) = x + 1.

Now, let's differentiate each term:

f'(x) = (1/2) * (x + 3)^(-1/2) * 1

= 1 / [2 * √(x + 3)]

g'(x) = 1

Substituting into the quotient rule formula:

[(√(x + 3)) / (x + 1)]' = [(1 / [2 * √(x + 3)]) * (x + 1) - (√(x + 3)) * 1] / [(x + 1)²]

Simplifying the expression:

[(√(x + 3)) / (x + 1)]' = [1 - (√(x + 3)) * (x + 1)] / [2 * (x + 1)² * √(x + 3)]

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The correct answer is E) approximately normal.

When the process of rolling a fair 20-sided die 60 times and computing the value of chi-square using expected counts of 3 for each face is repeated many times, the distribution of the values of chi-square should be approximately normal. This is because the chi-square distribution is a special case of the gamma distribution, and as the degrees of freedom increase, the chi-square distribution approaches a normal distribution. In this case, the degrees of freedom are 19 (20-1), which is a relatively large number, so the distribution should be approximately normal.

To summarize, the repeated process of rolling a fair 20-sided die 60 times and computing the value of chi-square using expected counts of 3 for each face will result in an approximately normal distribution of the values of chi-square.

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Answer: See attached.

Step-by-step explanation:

     The first one is incorrect because this equation shows 5 / 2, not 2/5.

     The second one is correct. 7/4 = 7/4.

     The third one is also correct. 12/4 = 12/4.

     It can help to rewrite both sides of the equation in the same format to make it easier to compare.

Answer:

We can start by simplifying each parentheses separately and then adding the resulting expressions:

(2^4 – 5^3 – 7) + (−5^5 − 5^2 + 9 + 17)

= (16 - 125 - 7) + (-3125 - 25 + 9 + 17) (using the fact that 2^4 = 16 and 5^3 = 125)

= (-116) + (-3124) (combining like terms)

= -3240

Therefore, the answer is -3240. To express this number in standard form, we write it as:

-3.24 x 10^3

The negative sign indicates that the number is less than zero, and the 3.24 tells us the value of the number. The "x 10^3" part means that we need to multiply 3.24 by 10^3 (which is 1000) to get the actual value of the number:

-3.24 x 10^3 = -3.24 * 1000 = -3240

So, the answer in standard form is -3.24 x 10^3.

Answer:

5

Step-by-step explanation:

Answer: C

Step-by-step explanation:

The percentage of yellow paint that has to be used is given as 0.45

The amount of seafoam paint is given as 1.5 quartz

The percentage of yellow paint in the seafoam paint is 30 percent

Hence the amount that would be in it that would be made of yellow paint is given as

1.5 x 30%

1.5 x 0.30

= 0.45

Hence we would conclude by saying that the amount of yellow paint that has to be used in order to make the paint should be 0.45

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Curt and Melanie are mixing blue and yellow paint to make seafoam green paint. 1.5 quarts of seafoam paint is made of 70% blue, 30% yellow. Use the percent equation to find how much yellow paint they should use.

Answer: 9

Step-by-step explanation:

Answer: D

Step-by-step explanation: Disregard the $ and solve algebraically.

[tex]4x+36\leq 52[/tex]

[tex]4x\leq 52-36[/tex]

[tex]4x\leq 16[/tex]

[tex]x\leq 4[/tex]

Answer: Choice D is the correct answer :)

Step-by-step explanation:

The slope of the line as shown in the image attached below is: 2/3.

The slope of a line represents the ratio of the change in y (vertical) to the change in x (horizontal). It is a measure of the steepness of the line and tells us how much the y-value changes for each unit change in the x-value.

It is given as:

Slope (m) = rise/run.

The rise (blue line) = 2 units

The run (red line) = 3 units

Slope (m) = -2/3

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The area of the triangle with the given vertices is 4.47.

To find the area of the triangle with the given vertices, we can use the formula:
Area = (1/2) * |(B-A) x (C-A)|
Where "x" represents the cross product of two vectors.
First, we need to find the vectors B-A and C-A:
B-A = (1-5, 1-(-1), 0-(-2)) = (-4, 2, 2)
C-A = (3-5, 2-(-1), -1-(-2)) = (-2, 3, 1)
Next, we need to find the cross product of these two vectors:
(B-A) x (C-A) = (2*1 - 2*3, 2*(-2) - (-4)*1, (-4)*3 - 2*(-2)) = (-4, 0, -8)
Finally, we can find the area of the triangle by plugging in the values into the formula:
Area = (1/2) * |(-4, 0, -8)|
Area = (1/2) * √((-4)^2 + 0^2 + (-8)^2)
Area = (1/2) * √(80)
Area = (1/2) * 8.94
Area = 4.47
Therefore, the area of the triangle with the given vertices is 4.47.

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Step-by-step explanation:

the ratio is 30/21600 = 3/2160 = 1/720

that means for every degree the hour hand moves, the second hand does 2 full rotations (2×360°).

h = s×30/21600 = s/720

FYI :

as there are 12 hours on a clock, every hour means 360/12 = 30° rotation for the hour hand.

so, for each hour the second hand moves 21600°.

that means 21600/360 = 60 full rotations.

that means one rotation of the second hand is 1 minute.

so, the second hand is truly a second hand (counting the seconds).

60 seconds in a minute (a full rotation by the second hand), that means each second corresponds to 360/60 = 6° rotation of the second hand.

Answer:

the answer is B. 2x(5x+1)