A trapezoid was broken into two congruent triangles and a rectangle. A trapezoid is broken into 2 triangles and 1 rectangle. The triangles both have a base of 3 centimeters and a height of 12 centimeters. The rectangle has a height of 12 centimeters and a width of 14 centimeters. What is the base length, b, of one of the triangles? 3 cm 4 cm 6 cm 7 cm

Answer:

x=36 degrees

Step-by-step explanation:

Remember that all angles of a triangle must add up to 180 degrees due to the Angle Addition Postulate. So let's plug it in! x+65+79=180

Now you solve, x=180-79-65

x=36!

x=36 degrees

Answer:

Option B

Step-by-step explanation:

All interior angles of a triangle add up to 180°.

[tex]79+65+x=180\\144+x=180 \\144-144+x=180-144\\\boxed {x=36}[/tex]

The missing angle is 36°.

Option B should be your correct answer.

Answer:

[tex]t \approx 36.1\,min[/tex]

Step-by-step explanation:

The time constant for the isotope decay is:

[tex]\tau = \frac{8\min}{\ln 2}[/tex]

[tex]\tau \approx 11.542\,min[/tex]

Now, the decay of the isotope is modelled after the following expression:

[tex]m (t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex]

The time is now cleared with some algebraic handling:

[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]

[tex]t = -\tau \cdot \ln \frac{m(t)}{m_{o}}[/tex]

Finally, the time need for the element X to decay to 43 grams is:

[tex]t = - (11.542\,min)\cdot \ln\left(\frac{43\,g}{980\,g} \right)[/tex]

[tex]t \approx 36.1\,min[/tex]

Answer:

number of minutes to drain the entire tower = 241 minutes(nearest minutes)

Step-by-step explanation:

The water tower has the shape of  a cylinder with a cone on top . The volume of the water tower can be find when you find the sum of the volume of the cylinder and the cone.

Therefore,

volume of the cylinder = πr²h

where

r = 12/2 = 6 ft

h = 15 ft

volume = π × 6² × 15

volume = π × 36 × 15

volume of the cylinder = 540π

Volume of the cone = 1/3πr²h

r = 6 ft

Using tangential ratio we can find the height which is the opposite side of the triangle

tan 25° = opposite/adjacent

tan 25° = h/6

cross multiply

h = 6 tan 25°

h = 6 × 0.46630765815

h = 2.79784594893

h = 2.8 ft

volume of the cone  =  1/3πr²h

volume = 1/3 × π × 36 × 2.8

volume = 100.8π/3

volume = 33.6π

Volume of the tower system = 540π + 33.6π =  573.6π

volume of the tower system = 573.6 × 3.14 = 1801.104 ft³

1 cubic ft  = 7.48 gallons

1801.104 cubic fit = ? gallons

cross multiply

gallons = 1801.104 × 7.48

gallons = 13472.25792  gallons

The residents drains the water at the rate of 56 gallons per minute. Therefore,

56 gallons = 1 minutes

13472.25792  gallons = ? minutes

number of minutes = 13472.25792  /56

number of minutes = 240.576034286

number of minutes to drain the entire tower = 241 minutes(nearest minutes)

Answer:

The Net Present Value =  $451180.733

Step-by-step explanation:

Given that:

the initial cost of the project is $1670000

the initial increase in working capital is $198000

The total investment will be ; initial cost of the project + initial increase in working capital

The total investment = $1670000 + $198000

The total investment = $1868000

So, This investment cost is amortised to zero over four years; This implies that the project will depreciate in four years;

Now; lets determine the rate of the annual depreciation

The annual depreciation = [tex]\dfrac{Initial \ cost \ of \ project }{life \ of \ project}[/tex]

The annual depreciation = [tex]\dfrac{1670000}{4}[/tex]

The annual depreciation = $417500

Over to the annual operating cash flow; the annual operating cash flow can be calculated as follows:

annual operating cash flow = (sales - cost) × (1 - tax rate )+ (annual depreciation × tax rate )

Given that the tax rate = 21% = 0.21

annual operating cash flow = (1850000 -1038000)×(1-0.21)+(417500× 0.21)

annual operating cash flow = 812000 × 0.79 + 87675

annual operating cash flow = 641480 +  87675

annual operating cash flow = $729155

So; let's calculate the after tax salvage value for the project

We know that the sales values for the project in four years is $435,000 (i.e the disposal rate of the asset after four years)

Thus; the book value is zero

The after tax salvage value for the project can now be determined by the relation:

after tax salvage value = sale value - tax (sale value - book value)

after tax salvage value =  435000  - 0.21 (435,000 -0)

after tax salvage value = 435000 - 91350

after tax salvage value = $343650

Similarly; given that the recovering rate of the project is $198000;

The cash flow in year 4 will be: annual operating cash flow + after tax salvage + recovery working capital

cash flow in year 4 = $(729155 + 343650 + 198000)

cash flow in year 4 = $ 1270805

This implies that the cash flow from year one to three is : 729155

the cash flow in year four is : 1270805

Given that the Required return rate = 16.4% = 0.164

We can therefore determine the Present cash inflows by using the relation:

[tex]Present \ Value = \dfrac{c_1}{(1+r)^1}+ \dfrac{c_2}{(1+r)^2}+ \dfrac{c_3}{(1+r)^3}+ \dfrac{c_4}{(1+r)^4}[/tex]

[tex]Present \ Value = \dfrac{729155}{(1+0.164)^1}+ \dfrac{729155}{(1+0.164)^2}+ \dfrac{729155}{(1+0.164)^3}+ \dfrac{1270805}{(1+0.164)^4}[/tex]

[tex]Present \ Value = \dfrac{729155}{1.164^1}+ \dfrac{729155}{1.164^2}+ \dfrac{729155}{1.164^3}+ \dfrac{1270805}{1.164^4}[/tex]

Present Value = $(626421.8213 + 538163.0767 + 462339.413+692256.4225)

Present Value = $2319180.733

Finally, The net present value = Present Value - Total Investment

Net Present Value = $(2319180.733 - 1868000)

Net Present Value =  $451180.733

Therefore; The Net Present Value =  $451180.733

Answer:

[tex]3(-4a-3)(2a-1)[/tex]

Step-by-step explanation:

[tex]-24a^2-6a+9[/tex]

[tex](-12a-9)(2a-1)[/tex]

[tex]3(-4a-3)(2a-1)[/tex]

Answer:

−3(2a−1)(4a+3)

Step-by-step explanation:

9 - 6a - 24a^2

24a²-6a-9=

−3(2a−1)(4a+3)

We get this because −3(2a−1)(4a+3) equals out to 24a²-6a-9. If you need more explanation, reply to this answer.

Answer:

x is 4 and y is 3.

Step-by-step explanation:

The scale factor between the triangles is 2, as you can see. The hypotenuse of the small triangle is 5 while the hypotenuse of the larger one is 10, so the scale factor between the triangles is 2. This means you can divide the other leg lengths of the large triangle by 2 to find the lengths for the corresponding legs of the small one.

Answer:

50

Step-by-step explanation:

First things first, use PEMDAS.

Parenthesis is first.

(9+8) is in parenthesis. 9+8 is obviously 17.

The equation now looks like this:

6 x 14 - 17 x 2

There is no exponents, but there is multiplication. 6 x 14 is 84 and 17 x 2 is 34. They both are multiplication equations.

The equation now looks like this:

84 - 34

84-34 is 50. 50 is your answer.

Answer:

21/100

Step-by-step explanation:

By looking at the table, we can find the box that has information on people who have dogs but do not walk. The number is 21. The total number of people is 100. To find probability, divide 21 by 100.

21/100

This fraction is in its simplest form and cannot be simplified any further.

The answer is [-1/2-1/2]

The range of the function f(x) is [-1/2, 1/2].

The range is the set of possible output values, which are shown on the y-axis. The range of a function, f is the set of all values f(x) , such that x is in the domain of f. Graphically speaking, the range is the set of all y such that (x,y) is a point on the graph of f.

For the given situation,

The function f(x) = 1/2sin(2x-π)

The graph below shows the range of the function f(x) = 1/2sin(2x-π) graphically.

As the range of sinx function is [-1, 1], the range of sin2x is also [-1, 1].

Let us consider [tex]\theta = 2x-\pi[/tex]

⇒ Then, [tex]sin \theta[/tex] lies in the range [tex][-1,1][/tex]

⇒ [tex]-1\leq sin(2x-\pi )\leq 1[/tex]

⇒ [tex](\frac{1}{2} )(-1)\leq sin(2x-\pi )\leq( 1)(\frac{1}{2} )[/tex]

⇒ [tex]\frac{-1}{2} \leq sin(2x-\pi )\leq\frac{1}{2}[/tex]

Hence we can conclude that the range of the function f(x) is [-1/2, 1/2].

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Answer:

2.12

Step-by-step explanation:

He spent 4*0.53 on pie molds.

4*0.53=2.12

Answer:

c+r+d= 200

1.50c+5.75r+2.60d= 589.50

r=d-20

Step-by-step explanation:

From the information given you have that Billy's restaurant ordered roses, daisies and carnations that total 200 flowers. The first equation is:

c+r+d= 200

c= number of carnations

r= number of roses

d= number of daisies

Also, you can say that the sum of the results of multiplying the price of each flower for its quantity is equal to $589.50. The second equation is:

1.50c+5.75r+2.60d= 589.50

Besides, from the statement you know there are 20 fewer roses than daisies and from that you can write the third equation:

r= d-20

The system of linear equations that can be used to find c, the number of carnations, r,  the number of roses, and d, the number of daisies is:

c+r+d= 200

1.50c+5.75r+2.60d= 589.50

r=d-20

Answer/Step-by-step explanation:

The length of the boxes and whiskers of a box plot tells us more about the spread the data being represented is and as well as the shape of the spread.

Invariably, if the length of the left box and left whiskers is of the same length as the right box and right whiskers, this implies that the distribution of the data point is close to being symmetric, or approximately symmetrical.

Answer:

Incorrect

Step-by-step explanation:

It is incorrect because all even numbers have a factor of 1.

That is odd.

Answer:

False

Step-by-step explanation:

even numbers has odd  & even factors

6 is an even number

Factors of 6 = 2 , 3

Where 3 is a odd number

Answer:

Step-by-step explanation:

A = P[1 + (r/n)]^(nt)

Look the formula up online to find out what each variable represents if needed.

We are solving for P, which is the principal amount 5 years back.

Substitute 11,000 for A (total amount), 4.5% for r(rate), 2 for n(number of times -- in this case, semiannually), and 5 for t(time -- 5 years).

11000 = P[1+(0.045/2)]^(2x5)

11000 = P (1.0225)^10

11000 = P (1.2492)   approx.

Divide both sides by 1.2492 to find P.

P = $8805.64  (approx)

I know that the answer I got is not an option listed. However, I feel that my workings may help other people to answer this question or give them inspiration to answer similar questions. Therefore, I will leave this answer up.

Thanks, and sorry I couldn't do much.

Answer:

1250 milliliters

Step-by-step explanation:

Omar has 5 liters of water. He divides evenly between 4 buckets.

5/4 = 1.25

He pours 1.25 liters in each bucket.

Convert 1.25 liters into milliters.

1.25 × 1000

1250 milliliters.

Omar pours 1250 milliliters in each bucket.

Answer:

[tex]\angle ADC=62^\circ[/tex]

Step-by-step explanation:

Given the circle centered on point B with points A, C and D on its circumference.

[tex]\angle ABC[/tex] is the angle subtended by arc AC at the centre.

Since D is on the circumference, [tex]\angle ADC[/tex] is the angle subtended by arc AC on the circumference.

Circle Theorem: The measure of the angle subtended by an arc at the center is twice the measure of the angle subtended by same arc at the circumference.

By the theorem stated above:

[tex]\angle ABC = 2 X \angle ADC\\Since \angle ABC=124^\circ\\124^\circ = 2 X \angle ADC\\ \angle ADC=124^\circ \div 2\\\\ \angle ADC=62^\circ[/tex]

Answer:

The real answer is 20 its not that high of a number

Step-by-step explanation:

Answer:

11.5

Step-by-step explanation:

using Pythagoras theorem

the square of 13 equals the square of 6 and the unknown side

Answer:

11.5 feet

Step-by-step explanation:

I just took the quiz on edge

Answer:

Area = 2.33 mm²

Explanation:

Perimeter of quarter circle = 14.28

But

Perimeter of quarter circle = 2πr+2r

So

2πr+2r = 14.28

6.3r+2r = 14.28

8.3r = 14.28

r = 14.28/8.3

r = 1.7 mm

Now the Area

Area of quarter circle = 1/4(πr²)

= 1/4(3.14)(1.7)²

= 1/4(3.14)(2.97)

= 1/4(9.34)

= 2.33 mm²

Answer:

2.34-1.7*0.2=2

Step-by-step explanation:

Well to solve this, we need to use PEMDAS:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Multiplication comes first before subtraction. You can do long multiplication for this and multiply 1.7 and 0.2 together. Once done that, the product of those 2 numbers are 0.34.

Now 2.34-0.34=2.00

Our answer is 2.

Answer:

2

Step-by-step explanation

1.7 x 0.2 = 0.34

2.34-0.34=2

Answer:

Answer:

Two rhombuses are not necessarily similar , No

Two circles are always similar , Yes

Two isosceles are similar , Yes

Two regular hexagons will be similar , Yes

The similar figures are Circle, Isosceles triangle and regular hexagons.

Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.

Therefore the similar figures are Circle, Isosceles triangle and regular hexagons.

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Answer:

Step-by-step explanation: true

Answer:

The amount he will have at the end of five years is $11,616.8

Interest on the amount is $1,616.8

Step-by-step explanation:

Kindly check the attached picture for explanation.

Answer:

1/52

Step-by-step explanation:

Answer:

Take u1 = average number of mosquitoes attracted after drinking beer

u2 = average number of mosquitoes attracted after drinking water

a) The null and alternative hypotheses:

H0 : u1 = u2

H1 : u1 > u2

b) i) The average number of mosquitoes per volunteer before drinking (beer group) :

[tex] x'1 = \frac{x_1}{n} = \frac{434}{25} = 17.36 [/tex]

Sample mean for mosquitoes attracted before consumption for beer group is 17.36

The average number of mosquitoes per volunteer before drinking (water group) :

[tex] x'2 = \frac{x_2}{n} = \frac{337}{18} = 18.72 [/tex]

Sample mean for mosquitoes attracted before consumption for water group is 18.72

The two means are different.

The difference in the two means are as a result of random choice.

c) i) The average number of mosquitoes per volunteer after drinking (beer group) :

[tex] x'1 = \frac{x_1}{n} = \frac{590}{25} = 23.60 [/tex]

Sample mean for mosquitoes attracted after consumption for beer group is 23.60

ii) The average number of mosquitoes per volunteer after drinking (water group) :

[tex] x'2 = \frac{x_2}{n} = \frac{345}{18} = 19.17[/tex]

Sample mean for mosquitoes attracted after consumption for water group is 19.17

The two sample means are different.

This difference here is likely not to be as a result of random choice, because the mean difference here is greater than the mean difference before consumption.

d) A statistically significant difference provides evidence that beer consumption increases mosquito attraction, as the average number of mosquitoes attracted when drinking beer is higher than the mean number of mosquitoes attracted when drinking water.

Answer:

Step-by-step explanation:

(2 + 3)/(4 - 2)= 5/2

y + 3 = 5/2(x - 2)

y + 3 = 5/2x - 5

y = 5/2x - 8

2y = 5x - 16

5x - 2y = 16

Answer:

Range : { -3,0,4,6}

Step-by-step explanation:

The range of the function is the output values

Range : { -3,0,4,6}

Answer:

C. {-3, 0 ,4, 6}

Step-by-step explanation:

→The range is the total of y-intercepts/outputs. In this case, looking at the function, you can see that the y-intercepts/outputs are 0, -3, 4, and 6.

→The others numbers are the x-intercepts/inputs, which would be the domain of the function.

1000ML = 1 L

78ML ?

78*1/1000 = 0.078 L

Answer:

See below.

Step-by-step explanation:

For the first one:

[tex]f(x)=\frac{4x+3}{5x+2}[/tex]        

[tex]f(\frac{1}{x})= \frac{4(\frac{1}{x})+3}{5(\frac{1}{x})+2 }[/tex]

First, multiply both top and bottom by [tex]x[/tex].

Thus:

[tex](\frac{4(\frac{1}{x})+3}{5(\frac{1}{x})+2 } )\cdot \frac{x}{x}[/tex][tex]=\frac{4+3x}{5+2x}[/tex]

It cannot be simplified further.

For the second one:

[tex]g(x)=\sqrt{x^2-8x}[/tex]

[tex]g(x-2)=\sqrt{(x-2)^2-8(x-2)}[/tex]

[tex]\sqrt{(x^2-4x+4)-8x+16}[/tex]

[tex]\sqrt{x^2-12x+20}[/tex]

And that cannot be simplified further.

Answer:

a) 0.164 = 16.4% probability that a disk has exactly one missing pulse

b) 0.017 = 1.7% probability that a disk has at least two missing pulses

c) 0.671 = 67.1% probability that neither contains a missing pulse

Step-by-step explanation:

To solve this question, we need to understand the Poisson distribution and the binomial distribution(for item c).

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!} [/tex]

In which

x is the number of sucesses

[tex] e = 2.71828[/tex] is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Binomial distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Poisson mean:

[tex]\mu = 0.2[/tex]

a. What is the probability that a disk has exactly one missing pulse?

One disk, so Poisson.

This is P(X = 1).

[tex]P(X = 1) = \frac{e^{-0.2}*0.2^{1}}{(1)!} = 0.164 [/tex]

0.164 = 16.4% probability that a disk has exactly one missing pulse

b. What is the probability that a disk has at least two missing pulses?

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which

[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!} [/tex]

[tex]P(X = 0) = \frac{e^{-0.2}*0.2^{0}}{(0)!} = 0.819[/tex]

[tex]P(X = 1) = \frac{e^{-0.2}*0.2^{1}}{(1)!} = 0.164 [/tex]

[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.819 + 0.164 = 0.983[/tex]

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.983 = 0.017[/tex]

0.017 = 1.7% probability that a disk has at least two missing pulses

c. If two disks are independently selected, what is the probability that neither contains a missing pulse?

Two disks, so binomial with n = 2.

A disk has a 0.819 probability of containing no missing pulse, and a 1 - 0.819 = 0.181 probability of containing a missing pulse, so [tex]p = 0.181[/tex]

We want to find P(X = 0).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{2,0}.(0.181)^{0}.(0.819)^{2} = 0.671[/tex]

0.671 = 67.1% probability that neither contains a missing pulse