Maggie's brother is 5 years younger than three times her
age. The sum of their ages IS 43.
How old is Maggie?

1) Find the sample space for the experiment of tossing a six-sided die three times and recording the sum:
The minimum sum occurs when you roll a 1 on each toss (1+1+1=3), and the maximum sum occurs when you roll a 6 on each toss (6+6+6=18). So, the sample space for this experiment is {3, 4, 5, ..., 18}.

2) Find the sample space for the experiment of a taste tester ranking three varieties of yogurt, A, B, and C, according to preference:
The taste tester can rank the yogurts in any order, so there are 3! (3 factorial) or 6 possible rankings. The sample space for this experiment is {ABC, ACB, BAC, BCA, CAB, CBA}.

3) Find the sample space for the experiment of selecting two county supervisors from five supervisors, A, B, C, D, and E, to study a recycling plan:
There are C(5, 2) or 10 possible combinations of supervisors. The sample space for this experiment is {AB, AC, AD, AE, BC, BD, BE, CD, CE, DE}.

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132 cm² is the area of the given figure.

To find the area of the figure we need to divide it into two parts such as a rectangle with the dimension of 20 * 6 and a triangle with the dimension of  (10 - 6) * (20 - (8 + 6)).

So,

the height of the triangle = 10 - 6 = 4 cm

the base of the triangle = 20 - (8 + 6) = 20 - 14 = 6 cm

Thus,

the area of the triangle = 1/2 * base * height

= 1/2 * 6 * 4

= 12 square cm

Area of the rectangle = length * width

= 20 * 6

= 120 square cm

Thus, the area of the figure will be = 120 + 12  = 132 square cm.

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Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

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Answer:c

Step-by-step explanation:

Answer:

(3x-16)(2x+15)=0

I'm not 100% positive, but from my calculatons, the answer is C.

The expression that results in a sum of eight and eleven twenty fourths is four and one eighth plus four and one third and this can be determined by using the arithmetic operations.

Check all options in order to determine which option gives the result in a sum or difference of eight and eleven twenty fourths.

a) Six and two twelves plus two and one half

The mathematical expression of the above statement is given by:

\(=6\dfrac{2}{12}+2\dfrac{1}{2}\)

Simplify the above expression.

\(=\dfrac{74}{12}+\dfrac{5}{2} = \dfrac{104}{12}\)

b) Four and one eighth plus four and one third

The mathematical expression of the above statement is given by:

\(=4\dfrac{1}{8}+4\dfrac{1}{3}\)

Simplify the above expression.

\(=\dfrac{33}{8}+\dfrac{13}{3} = \dfrac{203}{24}=8\dfrac{11}{24}\)

c) Ten and five sixth minus two and three quarters

The mathematical expression of the above statement is given by:

\(=10\dfrac{5}{6}-2\dfrac{3}{4}\)

Simplify the above expression.

\(=\dfrac{65}{6}-\dfrac{11}{4} = \dfrac{194}{24}\)

d) Nine and two thirds minus one and three eighths

The mathematical expression of the above statement is given by:

\(=9\dfrac{2}{3}-1\dfrac{3}{8}\)

Simplify the above expression.

\(=\dfrac{29}{3}-\dfrac{11}{8} = \dfrac{199}{24}\)

So, the correct option is b).

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If the value of θ is 46.4°. Then the value of the cosine of θ will be 20/29.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The value of sine of θ is 21/29.

Then the value of θ will be

sin θ = 21/29

     θ = sin⁻¹(21 / 29)

     θ = 46.4°

Then the value of the cosine of θ will be

cos θ = cos 46.4°

cos θ = 20/29

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1. Building Supply Company:

Let's define the variables:

Let B represent the number of pallets of bricks.

Let R represent the number of pallets of roofing material.

According to the problem, we have the following restrictions:

At least 30 pallets of brick: B ≥ 30

Each brick pallet weighs 900 pounds: 900B ≤ 34,000 (load capacity of the truck)

At least 20 pallets of roofing material: R ≥ 20

Each roofing material pallet weighs 650 pounds: 650R ≤ 34,000

The first inequality ensures that the company has at least 30 pallets of bricks.

The second inequality guarantees that the total weight of bricks (900B) does not exceed the load capacity of the truck, which is 34,000 pounds.

The third inequality ensures that the company has at least 20 pallets of roofing material.

The fourth inequality guarantees that the total weight of roofing material (650R) does not exceed the load capacity of the truck.

2. Effective Interest Rate Calculation:

To calculate the effective interest rate compounded monthly, we use the formula:

Effective Interest Rate = (1 + (Annual Interest Rate / Number of Compounding Periods)) ^ Number of Compounding Periods - 1

In this case, the annual interest rate is 8.1% (0.081) and it is compounded monthly. Therefore, we have:

Effective Interest Rate = (1 + (0.081 / 12))^12 - 1 = 8.44%

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Answer:

x - 3 = 6

Step-by-step explanation:

In all of the other equations... when you solve for x... you get x = 6.

x -3 = 6 does not end up with x = 6... rather x = 9 in that equation

Answer:

the 2nd one

Step-by-step explanation:

1. 6-2=4

2.9-3=6

3.6-5=1

4.6-6=0

all 6's except 2nd

The numeric values of the functions are given as follows:

(g-f)(-1) = √15

(g x f)(2) =  -3√3

(g + f)(2) =  3 -√3

(f/g)(-1) = 0

We have the function,

f(x) = 1 - x²

g(x) = √11-4x

1. (g-f)(-1)

= g(-1) - f(-1)

= (√ 11 - 4(1)) - (1- 1²)

= √15- 0

= √15

2. (g. f)(2)

= g(2). f(2)

= (√11- 8) . (1 -4)

= (√3) (-3)

= -3√3

3. (g+f)(2)

= g(2) + f(2)

= (√11-8) + (1-4)

= √3 - 3

4. (f/g)(-1)

= f(-1)/ g(-1)

= (1-1)/ (√11 + 4)

= 0/√15

= 0

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The recursive rule for the sequence in the graph is aₙ = aₙ₊₁ + 4

Recursive rule are the rules that continually takes a previous number and changes it to get to a next number.

It gives first term or terms of sequence and describes how term is related to previous term with an equation.

Looking at the graph ,

taking first two point  ,n = 1 and n = 2

At n = 1 , a(n) = 13

At n = 2 , a(n) = 9

so , 9 = 13 - 4

we can write it as,

a₂ = a₁ - 4

Hence , recursive formula for sequence :

aₙ₊₁ = aₙ - 4

bring aₙ to the left

=>  aₙ = aₙ₊₁ + 4 is required recursive formula

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Step-by-step explanation:

make the number or start the number which addition

Answer:

2011: 567 2012: 567*(1-.015) 2013: 567*(1-.015)*(1-.015) 2014: 567*(1-.015)567*(1-.015)*(1-.015) you see the pattern; and, if so, you can build an little equation giving you the answer

Answer:

339

Step-by-step explanation:

a = 567 (.95)¹⁰

a = 339.4838445482

Rounded

339

Answer:

3 and -14

Step-by-step explanation:

Find the factors of -42 and add them to see what they give:

1 × -42 = 42, -41

2 × -21 = 42, -19

3 × -14 = 42, -11

6 × -7 = 42, -1

The second to last is right so the numbers are 3 and -14

After calculating the individual discount and coupon percentages of the actual price, we find out that the final price of the new computer monitor is $40.

It is given to us that -

The new computer monitor is regularly priced at $200

It is now on sale for 25% off

After the sale discount, we can also use 20% off coupon

We have to find out the final price of the computer monitor.

The initial price of the new computer monitor = $200

After the sale discount of 25% off is applied to the product, the new price of the monitor can be calculated by finding out

25% of $200 = 0.25 * 200 = $50

Now, after calculating the price of the monitor after the sales discount, we have to find out the final price after the 20% off coupon is applied.

So, 20% of $50 = 0.20 * 50 = $10

So, we can conclude that after the sales discount and after a coupon of $10 off is applied, the final price of the computer monitor is -

$50 - $10

= $40

Thus, calculating the individual discount and coupon percentages of the actual price, we find out that the final price of the new computer monitor is $40.

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Answer:

Fractions?

Step-by-step explanation:

Um, please try to put in a little more to put forth an effort with the question, this looks like random nonsense. :|

Cofunction pairs are shifted by π/2 radians (90 degrees) from each other.

Cofunction pairs are shifted by π/2 radians (90 degrees) from one another. It means that the value of one function at an angle is equal to the other function at that angle plus π/2 radians.

For example, the sine function and cosine function are cofunctions, and they are shifted by π/2 radians from each other. The same is true for other cofunction pairs such as tangent and cotangent, and secant and cosecant.

This means that the value of the sine function at a certain angle is equal to the cosine function at that angle plus π/2 radians (90 degrees), and vice versa. Similarly, the same for value of the tangent function, secant function at a certain angle.

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Step-by-step explanation:

3 - 4 + 16 - 10 + 2

= 7

hope it helps :)

Step-by-step explanation:

3 − 4 + 16 − 10 + 2 [B.O.D.M.A.S rule] (First addition)

= 3 + 16 + 2 - 4 -10

= 21 - 14. (Then subtraction)

= 7 (Ans)

Answer:

  86 ft

Step-by-step explanation:

You want the straight line distance from a location 50 ft from a hotel to a window that has an angle of elevation of 54.5°.

The cosine relation between sides and angles in a right triangle is ...

  Cos = Adjacent/Hypotenuse

The 50 ft distance is adjacent to the angle, and we want to find the hypotenuse. Using this equation, we can solve for the length we want:

  Hypotenuse = Adjacent/Cos

Using the numbers in the problem statement, we find the straight-line distance to be ...

  LW = LH/cos(54.5°) = (50 ft)/0.580703 ≈ 86 ft

The distance between Penny and Lisa is about 86 feet.

__

Additional comment

We don't know what drawing tools you have available. The attached diagram was drawn by locating the window at 50tan(54.5°) up from the base of the hotel. The tool provided the length of LW as 86.1.

We could have use a rotation tool to create the angle of 54.5°, or a line graphing tool to draw the line through (50, 0) with slope tan(-54.5°). Then an intersection tool could have located the window at the point of intersection of that line and the y-axis.

The calculation we did above is about the easiest for determining the distance mathematically (not having the tool measure it).

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Answer:

D,B or E

Step-by-step explanation:

Im dumb always

Answer:

x = 3

Step-by-step explanation:

x+5=8

x+5-5=8-5

X=3

Answer:

x = 3

Step-by-step explanation:

basically 2 ways

1st: Transposing

1) x + 5 = 8

2) transpose or transfer +5 to the other side

NOTE: transposing numbers and variables switches the signs (positive -> negative and vice versa)

3) x = 8 - 5

x = 3

2nd: Property of Equality (whatever u do one one side, you do the same to the other)

1) x + 5 = 8

2) x + 5 - 5 = 8 - 5

x = 3

the main focus is to isolate x, or to make it be alone in one side of the equation

The choose (D)

(0,-4) and (2,0)

The scale factor between the map and the wilderness area is :

1:7500

Given, the scale on a map of a wilderness area shows that 2 cm represent 3 km.

Whereas the camp store is 20 cm from the beach on the map.

Calculating scale factor

From the question, we are to determine what the scale factor from the map to the wilderness area is:

we know that, the scale on a map of a wilderness area shows that 2 cm represent 3 km.

so, convert km to cm.

2cm = 3 km

1 cm = 3 km/ 2 cm

cm = 3×100000/2

cm = 3×50000

cm = 150000

= 150000 cm

scale factor between the map and the wilderness area :

⇒ 20 cm : 150000 cm

⇒ 2 : 15000

⇒ 1 : 7500

Hence the scale factor between the map and the wilderness area

is 1:7500

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The Height and volume of the pyramid is ,

i) Height = 15.35cm

ii) Volume= 690.75 \(cm^3\).

What is pyramid ?

 A three-dimensional shape is a pyramid. Flat triangular sides that are joined at a common point known as the apex define the polygonal base of a pyramid. By fusing the bases together at the peak, a pyramid is created. The lateral face, a triangular feature formed by the connection of each base edge to the apex, is present.

Here slant height l = 16cm and sides of the rectangular base is ,

length l = 15cm and width w = 9 cm.

Side length = 9/2 = 4.5cm

Using Pythagorean theorem ,

=> Height h =  \(\sqrt{16^2-4.5^2}\)

=> height h = 15.35 cm

Now volume of pyramid is ,

=> V = 1/3 * Base area * height cubic unit

=> V = 1/3 *15*9*15.35

=> V = 690.75 \(cm^3\)

Hence the Height and volume of the pyramid is ,

i) Height = 15.35cm

ii) Volume= 690.75 \(cm^3\).

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There are two free variables, so the dimension of the eigenspace is 2. So the dimensions of the associated eigenspaces are 2 for all three eigenspace.

To determine which of the given values are complete eigenvalues, we need to find the characteristic polynomial of the matrix. This is done by finding the determinant of (A - λI), where A is the matrix and λ is the eigenvalue:

| 3-λ   2    0   -4    1 |
| 0     1-λ  3    1    0 |
| 1     -1   -1-λ 4    0 |
| -1    0    2    -4-λ 0 |
| 1     1    -1   0    1-λ|

Expanding along the first row, we get:

(3-λ) | 1-λ  3   1   0 |
    |-1   2-λ 4   0 |
    |1    -1  -4-λ 0 |
    |1    -1  0    1-λ |

= (3-λ)[(2-λ)(1-λ)(1-λ) + 4(-1)(1-λ) + 0(4-λ)] - (-1)[(1-λ)(1-λ)(4-λ) + 0(1-λ) + 0(-1)] + (1)[(1-λ)(4-λ)(0) - (2-λ)(1-λ)(-1)] - (1)[(1-λ)(-1)(-1) - (2-λ)(-1)(0)]

= (3-λ)[λ^3 - 6λ^2 + 9λ - 4] + (λ-1)[4λ^2 - 10λ + 6] + (λ-1)(λ-4) - (λ-2)

= λ^5 - 11λ^4 + 44λ^3 - 78λ^2 + 60λ - 16

Now we can check which of the given values satisfy the characteristic polynomial:

(a) 3, († 2), 0, 1
Substituting each value into the polynomial, we get:
3^5 - 11(3^4) + 44(3^3) - 78(3^2) + 60(3) - 16 = 0
2^5 - 11(2^4) + 44(2^3) - 78(2^2) + 60(2) - 16 ≠ 0
0^5 - 11(0^4) + 44(0^3) - 78(0^2) + 60(0) - 16 ≠ 0
1^5 - 11(1^4) + 44(1^3) - 78(1^2) + 60(1) - 16 = 0

So the complete eigenvalues for this matrix are 3, 0, 1.

To find the dimension of the associated eigenspace for each eigenvalue, we need to find the nullspace of (A - λI). For each eigenvalue, we can do this by row reducing the matrix (A - λI) and finding the number of free variables. The dimension of the associated eigenspace is then equal to the number of free variables.

(a) λ = 3:

| 0 -1  1  1 -1 |
| 0 -2  4  0  1 |
| 1 -1 -4  2  1 |
|-1  0  2 -7  1 |
| 1  1 -1  0 -2 |

RREF:

| 1  0 -2  0  0 |
| 0  1 -2  0  0 |
| 0  0  0  1  0 |
| 0  0  0  0  1 |
| 0  0  0  0  0 |

There are two free variables, so the dimension of the eigenspace is 2.

(a) λ = 0:

| 3  2  0 -4  1 |
| 0  1  3  1  0 |
| 1 -1 -1  4  0 |
|-1  0  2 -4  0 |
| 1  1 -1  0  1 |

RREF:

| 1  0 -2  0  0 |
| 0  1 -2  0  0 |
| 0  0  0  1  0 |
| 0  0  0  0  0 |
| 0  0  0  0  0 |

There are two free variables, so the dimension of the eigenspace is 2.

(a) λ = 1:

| 2  2  0 -4  1 |
| 0  0  3  1  0 |
| 1 -1 -2  4  0 |
|-1  0  2 -5  1 |
| 1  1 -1  0  0 |

RREF:

| 1  0 -1  0  0 |
| 0  1 -1  0  0 |
| 0  0  0  1 -1 |
| 0  0  0  0  0 |
| 0  0  0  0  0 |

There are two free variables, so the dimension of the eigenspace is 2.

So, the dimensions of the associated eigenspaces are 2 for all three eigenvalues.

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Answer:

did you ever solve it ?

Step-by-step explanation:

The acceptable row operation when conducting Gaussian Elimination is;

Multiplying an entire row by four

     Gaussian Elimination is defined as row reduction, is a method used for solving  a system of linear equations.

Now, let us look at the options;

Option A; This option is wrong because multiplying an entire row by zero eliminates the entire equation and as such makes it invalid.

Option B; This statement is not correct because in gaussian eliminiation, we try to make an equation easy to add to another one to eliminate one of the variables. But in this case replacing with reciprocal does not achive that purpose.

Option C; This statement is wrong because we only add or subtract one equation from another and not subtract a number from an equation.

Option D; This statement is correct because it means that by multiplying the entire row by 4, it means we are following the process of trying to make the equation easy to add or subtract from another equation to eliminate one of the variables.

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The Taylor expansion of the function ln(4 + z^2) on the region |z| < 2 can be obtained by using the basic Taylor expansion formula and integrating all the terms of the series.

To find the Taylor expansion of ln(4 + z^2), we start by expanding ln(4 + z^2) using the basic Taylor expansion formula for ln(1 + u), which is given by ∑[infinity]n=0 (−1)^n u^n.

Substituting u = z^2/4 into the formula, we have ln(4 + z^2) = ln(4(1 + z^2/4)) = ln(4) + ln(1 + z^2/4).

The term ln(4) is a constant, so we can ignore it in the Taylor expansion. Now, we focus on finding the Taylor expansion of ln(1 + z^2/4).

Expanding ln(1 + z^2/4) using the basic Taylor expansion formula, we have ln(1 + z^2/4) = ∑[infinity]n=0 (−1)^n (z^2/4)^n.

Integrating each term of the series, we get ∫(ln(1 + z^2/4)) = ∑[infinity]n=0 (−1)^n ∫((z^2/4)^n).

By integrating each term, we obtain the Taylor expansion of ln(4 + z^2).

It's important to note that the Taylor expansion will be an infinite series, as indicated by the ∑[infinity] notation. The expansion will include terms with higher powers of z, which become smaller as the power increases. The number of terms considered in practice depends on the desired level of accuracy in the approximation.

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