A wooden plank is $5$ feet long and $1\frac{1}{2}$ inches thick. To make the plank $1\frac{1}{8}$ inches thick, a carpenter removes the same thickness of wood from the top and bottom of the plank. How many inches does the carpenter remove from the top of the plank

Answer:

Both A and B

Step-by-step explanation:

A set of ordered pairs is not a function if there is a repeating output (Y value.)

Y values of A= 5, 2, -2, -5.

Y values of B= 2, -2, 4, -3.

There are no repeating outputs.

The probability of getting tails on the coin and an even number on the number cube is 1/4

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The sample space of a coin is:

S = {H, T}

The sample space of a die is:

S = {1, 2, 3, 4, 5, 6}

The above means that:

A coin has 2 faces, one of which is the tail.

So, we have:

P(Tail) = 1/2

A number cube has 6 numbers, 3 or which are even.

So, we have

P(Even) = 3/6

The required probability is

P = P(Tail) * P(Even)

This gives

P = 1/2 * 3/6

Evaluate

P = 1/4

Evaluate the quotient

P = 0.25

Hence, the probability of getting tails on the coin and an even number on the number cube is 1/4 or 0.25

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The number of unique combinations that can be formed by picking one object from each set is =960. That is option C.

Number combination is a mathematical technique that shows the number of possible arrangements in a collection of items.

The first set of objects = 4. There are a total of 4 possibilities.

The second set of objects = 5. There are a total of 5 possibilities

Therefore from first and second set, the total number of possibilities = 4×5 = 20

For the whole set, the total possibilities;

= 4×5×6×8

= 960

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Answer:

X=4 easy blah blah blah it’s 4. jdjjdjfnfvbdnnfn

The area of the wings of the model is 100000 square centimeters

The given parameters are:

Scale factor, k = 1/2

Actual area of wings, A = 40 square meters

The model area is calculated as

Model area = Actual area * k^2

This gives

Model area = 40 * (1/2)^2

Evaluate

Model area = 10 square meters

Convert square meters to square centimeters

Model area = 10 * 10000 square centimeters

Evaluate

Model area = 100000 square centimeters

Hence, the area of the wings of the model is 100000 square centimeters

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Answer:

2nd, 3rd, and 6th option are correct

Step-by-step explanation:

using a²+b²=c² those are the obly that meet the criteria (im pretty sure)

In the given triangle equations AC² = AB² + BC², AB² = AD² + BD² and BC² = CD² + BD² are true.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or any angle is a right angle.

Given that,

ABC is a right angle triangle.

And BD is perpendicular to AC.

To show the equations which are true,

Use Pythagorean theorem,

(Hypotenuse)² = (base)² + (height)²

In triangle ABC,

AC² = AB² + BC²

In triangle ABD,

(AB)² = AD² + BD²

And in triangle BCD,

BC² = CD² + BD²

Therefore, option (2), (3) and (6) are correct.

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For each of the following distance matrices of graph, the

This is used to refer to the fact that there would be a maximum distance that exists between the pair of vertices.

This used to refer to the minimum eccentricities of the vertices

This is used to show all of the vertices that have minimum eccentricities.

We have

e 1 = 3

e 2 = 3

e3 = 2

e4 = 3

e 5 = 3

e 6 = 3

e 7 = 3

e8 = 2

e 9 = 3

e 10 = 2

Then the the diameter = maximum eccentricity = 3

The radius = minimum eccentricity = 2

center = [3, 8,10]

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The quotient of the polynomial exists 5x+6 + (4 / x+6).

The number of periods we have subtracted exists named the quotient (of the division of by ) The number that exists leftover after subtracting as usually as possible exists named the remainder (of the division of by ).

Given: (5x²+36x+40)/(x+6)

(5x²+36x+40)/(x+6) = 5x + (6x+40 / x+6)

Dividing the above equation

(6x+40) / (x+6) = 6+(4 / x+6)

Therefore, (5x²+36x+40)/(x+6) = 5x+6 + (4 / x+6)

The quotient of the polynomial exists 5x+6 + (4 / x+6).

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The length of JN from the figure is 108

A line is the shortest distance between two points. Given the following parameters

Required

We need the length of JN

JN = JK + KN

JN = 59 + 49

JN = 108

Hence the length of JN from the figure is 108

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The equivalent expression of the expression is 128x^5y^6/2x^7y^5

The expression is given as:

128x^5y^6/2x^7y^5

Divide 128 by 2

64x^5y^6/x^7y^5

Apply the law of indices

64y^(6-5)/x^(7-5)

Evaluate the differences

64y/x^2

Hence, the equivalent expression of the expression is 128x^5y^6/2x^7y^5

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Complete question

Select the correct answer. which expression is equivalent to 128x^5y^6/2x^7y^5 , if x > 0 and y > 0

Answer:

Sum is

Step-by-step explanation:

Part A

[tex]3x^2 -2x-1+9x+2x^2 -3=\boxed{5x^2 + 7x-4}[/tex]

Part B

[tex](5x^3 +4x^2 - x-3)-(5x^2 + 7x-4)=\boxed{5x^3 - x^2 - 8x+1}[/tex]

Part C

No, because although they provide examples for specific polynomials being closed under addition and subtraction, there is a loss of generality.

The partial sums are correct are  That is:  (2) and (28/9).

A partial sum would be:

2 + (2/3).

In this case, thus,

Series 1 = 2  - This is correct.

Series 2 = 2 + (2/3) = 8/3 - incorrect

Series 3 = (8/3) + (4/9) = (28/9) Correct

Series 4 = (28/9) + (8/27) = (92/27)

Series 5 = (92/27) + (16/81) = 292/81

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Answer:

k = 56

Step-by-step explanation:

2k + 68 = 180

2k = 112

112 ÷ 2 = 56

k = 56

Answer:

since those 2 lines are parrelel that means the angles are the same so

8x+6=4x+38

minus 6

8x=4x+32

minus 4x

4x=32

divide by 4

x=8

Hope This Helps!!!

The value of the x is 11 and the measure of the angle B is 82 degrees.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

We have:

The angle measurements in the diagram are represented by the following expressions:

Angle A = 8x - 6

Angle B = 4x + 38

By using the vertically opposite angle property in angle B

As we know the alternate exterior angle are equal

8x - 6 = 4x + 38

4x = 44

x =11

Measure of angle B = 4(11) + 38 = 82 degrees

Thus, the value of the x is 11 and the measure of the angle B is 82 degrees.

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The given sample's 95% confidence interval is 11.6 ± 0.5357. I.e., from the lower bound 11.06 to the upper bound 12.14. Its margin error is 0.5357.

To find the confidence interval C.I,

It is given that,

Sample size n = 225

Sample mean μ = 11.6

Standard deviation σ = 4.1

Since 95% confidence interval, z-score is 1.96

So, the required confidence interval is calculated by,

C. I = μ ± z(σ/√n) or mean ± margin error

On substituting,

C. I = 11.6 ± 1.96(4.1/√225)

     = 11.6 ± 1.96 × 0.2733

     = 11.6 ± 0.5357

So, the lower bound = 11.6 - 0.5357 = 11.065 and

the upper bound = 11.6 + 0.5357 = 12.135.

Thus, the confidence interval is from 11.06 to 12.14, and its margin error is 0.0537 for the population mean number of unoccupied seats per flight.

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Answer:

(32÷(10-8)÷2)-3

Step-by-step explanation:

(32÷(10-8)÷2)-3

(32÷2÷2)-3

(16÷2)-3

8-3 = 5

✅

Answer:

7

Step-by-step explanation:

By the AA Postulate, triangles JKL and MNP are similar. Segment JK corresponds to segment MN, and segment JL corresponds to segment MP.

JK/MN = JL/MP

25/30 = 20/(4x-4)

25(4x-4) = 20*30

100x - 100 = 600

100x = 700

x = 7

A function for the described sequence is; f(n) = 6• 3^(n-1) and the sixth term is; 1458.

Since, it follows that the first term of the sequence is; 6 and the common ratio is 3, it follows that the recursive function that represents the sequence is; f(n) = 6• 3^(n-1).

Additionally, by substitution of 6 for n; f(6) = 1,458.

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Answer:

500x - 300xp.

Step-by-step explanation:

100x(5 - 3p)

First distribute the 100x over the parentheses:

= 100x*5 - 100x * 3p

Now simplify:

= 500x - 300xp.

The exponential function that models this situation is:

[tex]D(t) = 10000(1.045)^t[/tex]

Using the function, in 2050, she will have $37,453.

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

For this problem, the parameters are:

A(0) = 10000, r = 0.045.

Hence the equation is:

[tex]D(t) = 10000(1.045)^t[/tex]

2050 is 30 years after 2020, hence the amount is:

[tex]D(30) = 10000(1.045)^{30} = 37453[/tex]

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The number of compounding per year is[tex]N = 920(1+0.03)^4t[/tex]

This can be calculated by making use of the formular;  920(1.03)^4t and use the  compound interest equation which is N=P( 1+r/n)^nt

We know that 12% was given as the rate per year, then to get the quarter rate we divide by factor of 4, which is  12/4= 3%

The compounding for t years = n*t = 4t where n=4.

and the Initial number of cars serviced=920

Then we can substitute the values into the above equation, we have Thus [tex]N = 920(1+0.03)^4t[/tex]

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CHECK THE COMPLETE QUESTION BELOW:

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. A car repair center services 920 cars in 2012. The number of cars serviced increases quarterly at a rate of 12% per year after 2012. Create an exponential expression to model the number of cars serviced after t years. Then, match each part of the exponential expression to what it represents in the context of the situation. 920(1.03) is the number of cars multiplied by 1.03. The quarterly rate of growth is 0.03 or 3%. The compound periods multiplied by the number of years is 4t. The initial number of cars serviced is 920. The growth factor is represented by 1.03. The growth rate is 1.03. Exponent arrowRight Base arrowRight Coefficient arrowRight Rate arrowRight

Answer:

d

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

(x - 5 )² + (y + 1)² = 4 ← is in standard form

with centre (5, - 1 ) and r = [tex]\sqrt{4}[/tex] = 2

For the males' data, we can logically deduce the following data elements:

Mathematically, the male IQR can be calculated by using this formula:

IQR = Q₃ - Q₁

IQR = 14 - 2

Male IQR = 12.

Next, we would find the difference between the median values:

Note: The median of male's data is equal to 10 while median of female's data is equal to 18.

Difference, d = 18 - 10

Difference, d = 8.

The male's data has an outlier probably due to sampling technique used while the female's data doesn't have an outlier. Thus, the median would be a better measure of center for the male's data and the mean being a better measure of center for the female's data.

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Answer: s

Step-by-step explanation:

Given that (p - 1/p) = 4, the value of p² + 1/p² is 18. Detail below

(p - 1/p) = 4

Square both sides

(p - 1/p)² = (4)²

(p - 1/p)² = 16 ....(1)

Recall

(a - b)² = a² + b² - 2ab

Thus,

(p - 1/p)² = p² + 1/p² - (2 × p × 1/p)

(p - 1/p)² = p² + 1/p² - 2

From equation (1) above,

(p - 1/p)² = 16

Therefore,

p² + 1/p² - 2 = 16

Rearrange

p² + 1/p² = 16 + 2

p² + 1/p² = 18

Thus, the value of p² + 1/p² is 18

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Answer:

x = 30

Step-by-step explanation:

110 and 3x - 20 are supplementary angles, sum to 180° , then

110 + 3x - 20 = 180

90 + 3x = 180 ( subtract 90 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30

Answer:

x = 30

Step-by-step explanation:

Please refer to the attached photo. (Apologies for the terrible drawing.)

For this question, you must be clear of the angle properties.

z + 110 = 180 (Sum of Angles on a straight line)

z = 180 - 110 = 70

z = 3x - 20 (Corresponding Angles)

3x - 20 = z

3x - 20 = 70

3x = 70 + 20

3x = 90

x = 90 / 3 = 30

In the given diagram, the value of x is 90°

From the question, we are to determine the value of x

In the given diagram,

Using the linear pair theorem, we can write that

x + 90° = 180°

x = 180° - 90°

x = 90°

Hence, the value of x is 90°

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Answer:

Step-by-step explanation:

    p=-12x^2 + 168 - 510        

   isolate the varible by diveding each side by factors that dont conatin the varible

x= square root of -p+342/3/2

x= - square root of  -p+ 342/3/2

I hope this has helped if you need any clarfcation just ask

Answer:

FIRST

To find the volume of rectangular prism is

Volume = Length x Width x Height

Volume = 20cm x 10cm x 13cm

= 40 x 13

= 520cm cubic or cube

520 is the volume of the rectangular prism

the you divide volume of rectangular prism and volume of solid ball.

Correct me if i am wrong guys.

Answer:

It will take approximately take 17 balls to overflow the container

Step-by-step explanation:

Volume of the rectangle = 20x13x10 = 2600[tex]cm^{3}[/tex]

Volume of the water = 20x10x11 = 2200[tex]cm^{2}[/tex]

Amount of empty space = 2600-2200 = 400[tex]cm^{3[/tex]

Solid ball volume = 23[tex]cm^{3}[/tex] each

To find how many balls can overflow the container = 400/23 = 17.39

All the events in the sample space that are not part of the specified event are called Complement of Event.

Complement of event:

The complement of an event is the subset of outcomes in the sample space that are not in the event. A complement is itself an event. The complement of an event A is denoted as A c A^c Ac or A′. An event and its complement are mutually exclusive and exhaustive.

Two events are said to be complementary when one event occurs if and only if the other does not. The probabilities of two complimentary events add up to 1. For example, rolling a 5 or greater and rolling a 4 or less on a die are complementary events, because a roll is 5 or greater if and only if it is not 4 or less.

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