1. A log cabin in the shape of a rectangular prism is modeled using a scale of 1 to 0.5 meter. If the model is 14x19x11 centimeters, what is the volume of the actual log cabin?
a) 182.875 m^3
b) 365.75 m^3
c) 548. 625 m^3
d) 1463 m^3

2. A circle graph below represents a family's monthly budget. If the total monthly income is $2000, how much money is spent on food?
(graph) food=35% other=25% housing=40%
a) $700
b) $800
c) $350
d) $400

3. solve the equation. round the result to two decimal places.
4.8x-1.3=1.7
a) 0.83
b) -1.80
c) 0.63
d) 0.08

Answer:   24/25

Step-by-step explanation:  sinB= perpendicular/hypotenuse

                                                      =  side opposite to angle B/hypotenuse

                                                      = AC/AB

                                                      = 24/25

x+x+2+x+4 =4x

3x+6 =4x

x=6

6 +8+10 = 24

ages are 6, 8 & 10

The Brady boys' ages are consecutive even integers, and their respective ages are 6, 8, and 10 years old, as derived from setting up and solving an equation based on the given sum and multiple conditions.

We have a mathematical problem involving consecutive even integers and the relationship between their sum and a single integer's multiple. Since the Brady boys' ages are consecutive even integers, we can represent the youngest boy's age as x. The ages of the other two boys would then be x + 2 and x + 4 respectively, because even integers are two units apart.

The information given states that the sum of the boys' ages equals four times the youngest boy's age. This gives us the equation:
x + (x + 2) + (x + 4) = 4x. Simplifying this equation,
3x + 6 = 4x
3x - 4x + 6 = 0
-x + 6 = 0
x = 6.

Therefore, the youngest Brady boy is 6 years old, the middle boy is 8 years old, and the oldest is 10 years old

Answer:

D. No solution

Step-by-step explanation:

Since, if an equation after solving gives a true statement,

Then the equation has infinitely many solution,

While, after solving the equation,

We get, a false statement,

Then the equation has no solution,

Given equation,

3 + 6z = 13 + 6z

⇒ 3 = 13

Which is a FALSE statement,

Hence, the given equation has no solution.

OPTION D is correct.

Answer:

[tex]-7\geq x<12[/tex] and [tex][-7,12)[/tex] in interval notation.

Step-by-step explanation:

We have been given a compound inequality [tex]-7x-50\leq -1\text{ and }-6x+70>-2[/tex]. We are supposed to find the solution of our given inequality.

First of all, we will solve both inequalities separately, then we will combine both solution merging overlapping intervals.

[tex]-7x-50\leq -1[/tex]

[tex]-7x-50+50\leq -1+50[/tex]

[tex]-7x\leq 49[/tex]

Dividing by negative number, flip the inequality sign:

[tex]\frac{-7x}{-7}\geq \frac{49}{-7}[/tex]

[tex]x\geq -7[/tex]

[tex]-6x+70>-2[/tex]

[tex]-6x+70-70>-2-70[/tex]

[tex]-6x>-72[/tex]

Dividing by negative number, flip the inequality sign:

[tex]\frac{-6x}{-6}<\frac{-72}{-6}[/tex]

[tex]x<12[/tex]

Upon merging both intervals, we will get:

[tex]-7\geq x<12[/tex]

Therefore, the solution for our given inequality would be [tex]-7\geq x<12[/tex] and [tex][-7,12)[/tex] in interval notation.

Answer:     Between $3 and $5, inclusive

Step-by-step explanation:

The total cost of fencing is $996.

Given that David wants to install a fence fence around his garden, and the garden is rectangular and has an area of 240 square feet, and one side of the garden is along the street and is 12 feet long, and for this side of the garden , David will use fencing that costs 18$ per linear foot, while for the other three sides of the garden, David will use fencing that costs 15$ per linear foot, to determine what is the total cost of fencing the following calculation must be made :

Therefore, the total cost of fencing is $996.

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Answer:

56.

Step-by-step explanation:

We are asked to find 35% of 160.

To 35% of 160, we will divide 35 by 100 and multiply the result by 160 as:

[tex]35\%\text{ of 160}=\frac{35}{100}\times 160[/tex]

[tex]35\%\text{ of 160}=0.35\times 160[/tex]

[tex]35\%\text{ of 160}=56[/tex]

Therefore, 56 is 35% of 160.

Final answer:

To find the decibel rating of sound b, we calculate the decibel difference between sound a and sound b, which is 9.031 decibels. Adding this to the decibel rating of sound a gives us an approximate decibel rating of 34 for sound b.

Explanation:

To find the decibel rating of sound b, we need to determine how many decibels louder it is compared to sound a. We know that sound b is 8 times as loud as sound a, so we can use the formula for decibel difference:

Decibel difference = 10 * log10(intensity ratio)

Since sound b is 8 times as loud as sound a, the intensity ratio is 8. Plugging this into the formula gives:

Decibel difference = 10 * log10(8) = 10 * 0.9031 = 9.031 decibels

To find the decibel rating of sound b, we add the decibel difference to the decibel rating of sound a:

Decibel rating of sound b = Decibel rating of sound a + Decibel difference = 25 + 9.031 ≈ 34 decibels

To find the cost of 11 rubber stamps, we calculate the unit price by dividing the given cost of 5 stamps by 5 and then multiply the unit price by 11.

To determine the cost of 11 rubber stamps when 5 stamps cost $9.70, first we need to find the cost of one rubber stamp. We divide the total cost by the number of stamps to find the unit price, which is $9.70 ÷ 5 = $1.94 per stamp. Using this unit price, we can then multiply by the desired number of stamps to find the total cost for 11 stamps. The equation to determine the cost of 11 rubber stamps is:

Cost of 11 stamps = 11 × $1.94

By calculating this, we find that 11 stamps will cost $21.34.

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Answer:

The correct option is 2.

Step-by-step explanation:

The point slope form of a line is

[tex]y-y_1=m(x-x_1)[/tex]

Where, m is slope.

The line passes through (4, 1/3 ) and has a slope of 3/4.

The equation of line is

[tex]y-\frac{1}{3}=\frac{3}{4}(x-4)[/tex]

Therefore the correct option is 2.

1. intersection is all the numbers both sets have in common

 so 3, ,7 , 13

2. union is all the numbers from both sets so 1, 5, 8, 12, 17

Answer:

Step-by-step explanation:

Given is the polynomials as

1) [tex]f(x) = x^3+2x^2-x-2[/tex]

The graph of this function has x intercepts as

-2, -1 and 0

Since f(x) =0 has solutions equivalent to x intercepts we see that the roots are

-2,-1 and 0

2) Given is a polynomial as

[tex]f(x) = 2x^3+5x^2-8x-20 =0[/tex]

Using rational roots theorem we find that

the roots possible are ±1.±2,±4,±5,±10,±20,±1/2,±5/2

Using remainder theorem we see that

f(2) =f(-2)=0

By using division, we find that the other factor is 2x+5

Hence roots are 2,-2, -2.5

Answers:

  A. If two angles are linear pairs, the angles are supplementary. The two angles are linear pairs. Therefore, the angles are supplementary.  

 B. If an object is a square, it is a parallelogram. The object is a square. The object is a parallelogram.

 C. If it is snowing, the play will be cancelled. It is snowing. Therefore, the play is cancelled.

  These are right.

Answer:

Law of detachment:

Statement 1: If a, then b

Statement 2: a

Conclusion: b

(A)

1. If two angles are linear pairs, then the angles are supplementary.

2. The two angles are linear pairs.

Let a be the statement " two angles are linear pairs"

let b be the statement "the angles are supplementary"

then, 1 and 2 can be written as;

1. if a , then b

2. a

So, by the law of detachment we can deduce that b is true.

i.e, The angles are supplementary.

(B)

1. If an object is a square, then it is a parallelogram.

2. The object is a square.

Let a be the statement " an object is a square"

let b be the statement "The object is a square"

then, 1 and 2 can be written as;

1. if a , then b

2. a

So, by the law of detachment we can deduce that b is true.

i.e, The object is a parallelogram.

(C)

1. If  it is snowing, then the play will be cancelled.

2. It is snowing.

Let a be the statement "it is snowing"

let b be the statement "the play will be cancelled"

then, 1 and 2 can be written as;

1. if a , then b

2. a

So, by the law of detachment we can deduce that b is true.

i.e, The play is cancelled.

Only option A, B and C  are examples of the Law of Detachment.