Find the surface area for the triangular prism below if AB = 16 m, AC = 33 m, AD = 12 m, and DP = 9 m. (Note: the bases are isosceles triangles.)

The technique of repeated addition involves combining equal groups.

4 x ( -3) = 12.

Repeated addition is the combining of equal groupings. It offers a basis for comprehending multiplication. For instance, 3 x 5 can be expressed as 5 + 5 + 5 to represent 3 groups of 5 counters.

We have been given that

4 x ( -3) = 12

By using repeated addition for multiplication

Add 4 three times or add 3 for times ..

In question negative 3 is given so we add negative 4 , three times

(-4) + (-4) + (-4)

-12.

Or

Add negative 3 , four times

(-3) + (-3 )+ (-3) + (-3)

-12.

Hence, we solved given multiplication by the using repeated addition method.

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First, let's calculate the area of the triangle.

Now let's calculate the area of the semicircle.

The total area of the figure is:

24+25.12 ft2 = 49.12 ft2

Given,

1)P(A) = 0.25

P(B) = 0.65

The value of P( A or B) is,

Hence, option d is correct.

2)P(A) = 0.45

P(B) = 0.35

The value of P( A or B) is,

Hence, option c is correct.

We are given the following expression:

To simplify the expression, we will first use the distributive property on the parenthesis, like this:

Solving the operations:

Now we add like terms:

Solving the operations:

This is the most simplified form of the equation

With the help of Linear equation we can say that  Damion added 12 on both sides.

The given equation was,

If we will add 12 on both sides ,

Hence we can say that Damion added 12 to both sides.

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Answer:

  (a) graph with line through (90, 60)

Step-by-step explanation:

You want a graph of the proportional relationship between sit-ups and seconds if a student can do 40 sit-ups in 60 seconds.

Seconds are plotted on the x-axis, and sit-ups are plotted on the y-axis The graph will match that shown in the attachment.

<95141404393>

The value of x is the answer to the equation x - 2 = 16 which is 18.

An equation is an expression that shows the relationship between two or more numbers and variables. The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of that variable would give a true mathematical statement.

We have been given a linear equation as;  x - 2 = 16

We need to find the value of x as the answer to the equation x - 2 = 16.

Therefore, we will eliminate the 2.

x - 2 = 16

Add 2 on both sides of the equation;

x - 2 + 2= 16+ 2

Then ;

x = 18

Hence, the value of x is the answer to the equation x - 2 = 16 which is 18.

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The given statement is false: vertical angle do not depend on the line being parallel. A pair of vertical angles are always congruent.

Vertical angle:

Vertical angle means that the angles opposite each other when two lines cross.

Given,

Here we have the diagram and we also know that angle 7 is congruent to angle 5.

Now we need to find the given statement is true or not.

Through the given diagram, we have identified that, the eight angles will together form four pairs of corresponding angles.

Angles 1 and 5 constitutes one of the pairs.

We know that all the corresponding angles are congruent.

All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs e.g. 3 + 7, 4 + 8 and 2 + 6.

Through that we know that basically, the vertical angles are always congruent, which means that they are equal. So, it is not necessary for them to be parallel.

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The given expression is,

Opening the brackets and multiplying each term inside the bracket with 5, we get,

The simplified expression is 15k = 35 and the value of k is 2.33.

The safe load, L of a wooden a beam 3 in. wide 9 in. deep and 11 ft long of the same material support is 307.17

Analyzing the given conditions in the question, we get

The safe load, L is directly proportional to width (w) and square of depth (d²)

also,

L is inversely as length (l) i.e L = k/l

combining the above conditions, we get an equation as:

L = k(wd²/l)

now, for the first case we have been given

w = 8 in

d = 6 in

l = 10 ft

L = 1966 lbs

thus,

1966 lb = k ((8 × 6²)/10)

or

k = 68.26 lbs/(ft.in³)  

Now,

Using the calculated value of k to calculate the value of L in the second case  

in the second case, we have

w = 3 in

d =9 in

l = 11 ft

Final Safe load L' =  68.26 × (6 × 3²/12)

or

L' =307.17 lb

Therefore, The safe load, L of a wooden a beam 3 in. wide 9 in. deep and 11 ft long of the same material support is 307.17

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Answer:

Step-by-step explanation:

[tex]\frac{150}{x} =tan72 \\x=150 cot~72=150 cot(90-18)=150 ~tan ~18 \approx 48.74 ~meteres[/tex]

The amount paid for each is;

1) Amount earned per game = $215625 per game

2) Amount earned per minute played = $4492.1875

3) Amount earned each minute for 2/3 games = $6738.28

4) Amount earned per hour = 4492.1875 * 60 = $269531.25

We are given;

Amount earned by athlete = $17,250,000

Number of games played = 80 Games

Number of minutes per game = 48 minutes

1) Amount earned per game = Amount earned by athlete/Number of games played = 17250000/80 = $215625 per game

2) If he played entire games for the entire minutes;

Amount earned per minute played = 17250000/(80 * 48)

Amount earned per minute played = $4492.1875

3) He played 2/3 of every game. Thus;

Amount earned each minute for 2/3 games = 17250000/((2/3) * 80 * 48)

Amount earned each minute for 2/3 games = $6738.28

4) Since amount earned for every minute is $4492.1875, then we say that;

Amount earned per hour = 4492.1875 * 60 = $269531.25

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Answer:

-3/9 or -1/3

Step-by-step explanation:

:]

Answer:   -1/3

Step-by-step explanation- To subtract fractions, you first make the the denominators the same. The denominator is the bottom number. To make the denominator the same, you look for the lowest common denominator. Making the answer -1/3

The cost of Apple A: $1.225

What is Weight?

The weight of an object is the force exerted on it by gravity. Some standard textbooks define weight as a vector quantity, the force of gravity acting on an object. Some define weight as a scalar quantity that is the magnitude of gravity.

Cost of the different types of the apple have been given as,

Apple A = costing $4.90 for 4 lb

Apple B = costing $1.00 for 10 oz

Apple C = costing $0.45 for 1/2 lb

For Apple A,

Since, cost of 4 lb = $4.90

Therefore, cost of 1 lb = 4.90/4

                                    = $1.225

For Apple B,

Since, 1 oz = 0.0625 lb

Therefore, 10 oz = 0.0625 × 10

                            = 0.625 lb

Since, cost of 10 oz = $1.00          

Therefore, cost of 0.625 lb = $1.00

And cost of 1 lb = 1/0.625

                          = $1.6

For Apple C,

Since, cost of 1/2 lb = $0.45

Therefore, cost of 1 lb = 0.45 × 2

                                   = $0.90

 Hence, Cost of Apple A will be the least with $1.225 per pound.

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In an isosceles triangle, there are

2 legs (equal sides)

1 base

The 2 legs are the equal sides

The base is the third side

In the isosceles triangle ABC:

Since AB = BC, then

AB and BC are the legs of the triangle, then

AB and BC are called legs

The answer is d

As per the concept of probability, there are 7776 different lottery numbers are possible.

Probability:

Probability means the concept that is based on the possible chances of something to happen.

Given,

Lottery numbers in a particular state consist of 5 digits. Each lottery cube that is drawn/rolled has six sides, numbered 1-6.

Here we need to find how many different lottery numbers are possible.

Through the given question we know that,

The number of digits in a lottery ticket = 5

Side in cube = 6

So, in each time they will roll the dice 5 times to get one number.

So, the possible options of that event are,

For the first time we have 6 options

Second time we got 6 options

Third time also we got six option

Fourth time = 6 options

Fifth time = 6 options.

Therefore, it can be written as,

=> 6 x 6 x 6 x 6 x 6

=> 6⁵

=> 7776.

Therefore, there are 7776 different lottery numbers are possible.

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we have that

TLy+TRy=20,290 ------> equation A

and

sin(24.3)=TLy/TL

TLy=TLsin(24.3) ------> equation B

sin(44.5)=TRy/TR

TRy=TRsin(44.5) ------> equation C

and

TLx=TRx

TLcos(24.3)=TRcos(44.5)

TL=TRcos(44.5)/cos(24.3) --------> equation D

substitute equation B and equation C in equation A

TLsin(24.3)+TRsin(44.5)=20,290 -------> equation E

substitute equation D in equation E

(TRcos(44.5)/cos(24.3))sin(24.3)+TRsin(44.5)=20,290

solve for TR

factor TR

TR[cos(44.5)/cos(24.3))sin(24.3)+sin(44.5)]=20,290

TR=19,835 pounds

Find TL

TL=(19,835)cos(44.5)/cos(24.3)

TL=

Given:

The initial investment is, P = $720.

The rate of interest is, r = 7.8% = 0.078.

The number of years of investment is, t = 6 years.

Explanation:

The general formula to find the compound interest is,

Here, n represents the number of times compounded in a year. It is given that the amount is compounded monthly, so the value of n = 12.

To find total amount after 6 years:

Now, substitute the given values in the general equation.

Thus, the total amount earned is $1147.95.

To fnd interest amount:

Now, the amount of interest can be calculated as,

Hence, the interest amount earned is $427.95 and the total amount earned is $1147.95.

F is the correct answer (option A) that is, the relation is like many to one. So, it is a function.

Given mapping diagram that represents the relation.

We have to determine whether the relation is a function.

(-8, -6), (-5, 2), (-8, 1), (7, 3)

Here,

Domain = (-8, -5, 7)

Range = (-6, 2, 1, 3)

A function is a relation where each input has only one output.

Here,

F. The relation is like many to one. So, it is a function.

G. The relation is many to one. So, it is a function.

H. The relation is one to many. It is not a function.

G. The relation is one to many. It is not a function.

So, F is the correct answer (option A) that is, the relation is like many to one. So, it is a function.

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Slope of a parallel line: 6

Slope of a perpendicular line: -1/6

What is Slope ?

slope, The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytical geometry ("slope equals rise over run").

Given equation,

y=6x-4

The equation of a line with slope  m  is given as:

y=mx+c

Rearranging the given equation:

y=(6)x+(-4)

By equating the equations we get,

m= 6

Which is slope of a parallel line

Now any parallel line would have the same slope.

And slope of a perpendicular line would be  −1/m.

i.e.  m(perpendicular)= -1/6

Hence, Slope of a parallel line is 6 and Slope of a perpendicular line is -1/6

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Answer:

a = 12.5 m/s2

Step-by-step explanation:

anwser 12.5

The formula for the margin of error is

The critical value for 95% confidence interval is 1.96

The standard error is

To know which of the list of options will yield approximately the desired margin of error, we will have to calculate the margin of error with the following values

For 110 trees, n= 110, standard dev. =16

For 144 trees, n=144, standard dev=16

For 43 trees, n=43 , standard dev.=16

For 87 trees, n= 87, standard dev=16

Hence, from the above calculations, the most prefered is the sample size of 110 trees (because the margin of error of 2.9988 is approximately 3 )

Answer is 110 trees

Answer:

Step-by-step explanation:

9*(15/2)[2+14] = 9*15*16 = 2160.

The amount of bond amortization for each six month period is [tex]\$225[/tex].

In the given question,

Towson Corporation issued [tex]\$150,000[/tex] of [tex]7\%[/tex] ten year bonds at [tex]103[/tex] on the semi-annual interest date.

Towson uses the straight line method to amortize any bond premium or discount.

We have to find the amount of bond amortization for each six month period.

Cash issued [tex]=\$150,000[/tex]

Rate [tex]=7\%[/tex] ten year bond at [tex]103[/tex] n the semi-annual interest date.

So the cash proceed on issue of bond = Cash issued [tex]\times103[/tex] [tex]/100[/tex]

Cash proceed on issue of bond [tex]=\$150,000\times\frac{103}{100}[/tex]

Firstly simplifying ratio

After simplification of ratio

Cash proceed on issue of bond [tex]=\$150,000\times1.03[/tex]

Now simplifying after multiplication

Cash proceed on issue of bond [tex]=\$154,500[/tex]

Hence, the cash proceed on issue of bond is [tex]\$154,500[/tex].

Now we find the premium that issued in the bond.

Premium on issue of bond [tex]=\$154,500-\$150,000[/tex]

Simplifying

Premium on issue of bond [tex]=\$4,500[/tex]

Hence, the premium on issue of bond is [tex]\$4,500[/tex]

Now finding the amount of bond amortization for each six month period.

Bond Amortization = (Premium on issue of bond/10 years) * 1/2

Bond Amortization [tex]=(\frac{\$4500}{10})\times\frac{1}{2}[/tex]

Simplifying the ratio

Bond Amortization [tex]=\$450\times0.5[/tex]

Bond Amortization [tex]=\$225[/tex]

Hence, the amount of bond amortization for each six month period is [tex]\$225[/tex].

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Let's list down the pieces of information given the scenario:

Cost of bike parts = $17.50

Bike parts and labor together = not more than $40/ lesser than or equal to $40.

Let's now generate the equation based on the given information,

Let,

L = Labor cost

Let's now generate the inequality showing the possible labor cost, L

Therefore, the cost of labor must not be more than $22.50.

Answer:

A" (2, 12)

B" (8,8)

C" (6, 4)

Step-by-step explanation:

For each point P(x, y) of the image, the translations are as follows:

Translate P(x, y) by <2, 3> [tex]\longrightarrow[/tex] P'(x + 2, y + 3) [tex]\longrightarrow[/tex] P'(x', y')

Dilate P'(x', y') by 2 [tex]\longrightarrow[/tex] P'' (x'', y'') [tex]\longrightarrow[/tex] P(2x', 2y')

Point      [tex]\longrightarrow[/tex]           Translate <2, 3>                   [tex]\longrightarrow[/tex]       Dilate by 2

A(-1, 3)    [tex]\longrightarrow[/tex]         A'(-1 +2, 3 + 3) =>  A'(1, 6)       [tex]\longrightarrow[/tex]            A''(2, 12)

B(2, 1)     [tex]\longrightarrow[/tex]         B'(2 + 2, 1 + 3) =>  B'(4, 4)       [tex]\longrightarrow[/tex]           B"(8, 8)

C(1, -1)    [tex]\longrightarrow[/tex]          C'(1 + 2, -1 + 3) =>  C'(3, 2)     [tex]\longrightarrow[/tex]            C"(6, 4)