If m∠ATB = 20°, m∠BTD = 72°, and m∠CTD = 38°, what is m∠ATC?

Answer:

number of nickel = 60

number of dimes  = 20

Step-by-step explanation:

1 nickel = 5 cents

1 dimes = 10 cents

$1 = 100 cents

we will use these value to solve the questions

_______________________________

Total no of coins = 80

let the number of nickels be x

let the number of dimes be y

thus,

x+y = 80

y = 80-x   equation 2

value of x nickels = 5x

value of y dimes = 10y

Total value of x nickels and y dimes = 5x+10y

The total value of the coins is $5.00

total value of the coins in cents = 5*100 = 500

thus

5x+10y = 500

using y = 80-x   from equation 2

5x + 10(80 - x) = 500

5x + 800 - 10x = 500

-5x = 500 - 800 = -300

x = -300/-5 = 60

Thus,

number of nickel = 60

number of dimes = 80-60 = 20

Answer:

see explanation

Step-by-step explanation:

SQ = SP + PQ = - b + a

Since SN : NQ = 3 : 2 then SQ = 3 + 2 = 5 parts , thus

SN = [tex]\frac{3}{5}[/tex] SQ = [tex]\frac{3}{5}[/tex] ( - b + a) = - [tex]\frac{3}{5}[/tex]b + [tex]\frac{3}{5}[/tex] a

Thus

NR = NS + SR

     = - (- [tex]\frac{3}{5}[/tex] b + [tex]\frac{3}{5}[/tex] a) + a

     = [tex]\frac{3}{5}[/tex] b - [tex]\frac{3}{5}[/tex] a + a

     = [tex]\frac{2}{5}[/tex] a + [tex]\frac{3}{5}[/tex] b

Answer:

Yeah

Step-by-step explanation:

Very simple

It was said that

SN:NQ=3:2

→2SN = 3NQ

SN=SR-NR

SN=a - NR

NQ = NR - QR

NQ=NR - b

SQ = SN + NQ

Recall that SN=(3NQ)/2

SQ = (3NQ)/2 + NQ

SQ = (5/2)NQ

a - b = (5/2)(NR - b)

After simplification

NR = (2/5)a - (2/5)b +b

Factorize

NR = (2/5)a + (-2/5 + 1)b

NR = (2/5)a + (3/5)b

Answer:

x = (h+g)/-f

Step-by-step explanation:

-fx-g = h

Add g to each side

-fx-g+g = h+g

-fx = h+g

Divide each side by -f

-fx/-f = (h+g)/-f

x = (h+g)/-f

Answer:

The standard error of the sample mean is [tex]\sigma_{\= x } = 0.40[/tex]

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 5.30 \ hours[/tex]

     The population standard deviation is [tex]\sigma = 3.20 \ hours[/tex]

      The sample size is  [tex]n = 64[/tex]

Generally the standard error of the sample mean is mathematically represented as

               [tex]\sigma_{\= x } = \frac{\sigma}{\sqrt{n} }[/tex]

substituting values

                [tex]\sigma_{\= x } = \frac{3.20}{\sqrt{64} }[/tex]

                [tex]\sigma_{\= x } = 0.40[/tex]

Answer:

The  null hypothesis is  [tex]H_o : \mu = 445[/tex]

The  alternative hypothesis  [tex]H_a : \mu < 445[/tex]  (This is the original claim[ It is believed that the machine is under filling the bags] )

Step-by-step explanation:

From the question we are told that  

    The population mean is   [tex]\mu = 445 \ g[/tex]

    The  sample size is  [tex]n = 12[/tex]

    The  sample mean is  [tex]\= x = 442 \ g[/tex]

     The  standard deviation is  [tex]\sigma = 20[/tex]

     The  level of significance is  [tex]\alpha = 0.05[/tex]

The  null hypothesis is  [tex]H_o : \mu = 445[/tex]

The  alternative hypothesis  [tex]H_a : \mu < 445[/tex]  (This is the original claim )

Answer:

The diagonals of all parallelograms do not bisect each other at 90 degree angles.

Step-by-step explanation:

Answer:

C. $4.12

Step-by-step explanation:

From 9 a.m. to noon, it's 3 hours.

From noon to 4 p.m. it's 4 hours.

Total rental time: 3 hours + 4 hours = 7 hours

Total rental cost: $28.84

rental cost per hour = (rental cost)/(number of hours)

rental cost per hour = $28.84/(7 hours) = $4.12/hour

Answer:

seeed

Step-by-step] explanation:

ddd~!`

Answer:

  4/9

Step-by-step explanation:

The scale factor for the linear dimensions of the ball bearings will be the cube root of the volume scale factor:

  k = ∛(1.6/5.4) = 2/3

Then the scale factor for the areas will be the square of this scale factor:

  ratio of surface area = (2/3)² = 4/9

_____

The area is the product of two linear dimensions, so its scale factor is the product of the linear dimension scale factors. That is, the scale factor for area is the square of the linear dimension scale factor.

Similarly, volume is the product of three linear dimensions, so its scale factor is the cube of the linear dimension scale factor.

The correct answer is B. 0.00

Explanation:

In statistics, two events are mutually exclusive if only one event can occur at one time. For example, if you have a deck of cards with Hearts and Spades, every time you choose a card you will have either Hearts or Spades but not both at the same time as there is not any card that combines Hearts and Spades in the same card. This means it is statistically impossible for two mutually exclusive events to occur at the same time, which means the probability is 0.00.

Step-by-step explanation:

Hi, there!!!

According to the question we must find the area of shaded region, but we must find area of circle and rectangle to find area of shaded region,

So, let's simply work with it,

Firstly, finding the area of rectangle,

length = 11cm.

breadth = 11cm.

now, area= length× breadth.

or, a = 11cm× 11cm.

a= 121cm^2

Now, let's work out the area of circle.

radius= 5cm

and pi. = 3.14 {using pi value as 3.14}

now,

area of a circle = pi× r^2

or, a= 3.14×5^2

or, a = 78.5 cm^2.

Therefore, The area of a circle is 78.5cm^2.

Now lastly finding the area of shadedregion,

area of shaded region = area of rectangle - area of circle.

or, area of shaded region = 121cm^2 - 78.5cm^2

Therefore, the area of shaded region is 42.5 cm^2.

Hope it helps...

Answer:

3/4

Step-by-step explanation:

find a common number that 18 and 24 are both divisible by. I chose 6. So when i divide 6 by 18, I got 3. Which I put on my numerator, when I divided 24 by 6 I got 4 which I put on my denominator. My end result was 3/4

Answer:

3/4

Step-by-step explanation:

18/24

=2*9=18

=2*12=24

=9/12

=3/4

Answer:

After 7 days the crystals will be 57.57 grams.

Step-by-step explanation:

In this the continuous exponential growth formula will be used.

y = A e ^rt

Where A = original amount = 10 grams

y is the growth after 7 days

e is Euler's number= 2.719

t is the time in hours , weeks, years etc.= 7 days

r  is the rate in decimals = 25% = 0.25

Putting the values in the formula:

y = A e ^rt

y = 10 e ^0.25 (7)

Calculating with the calculator

y = 10* 2.719^1.75

y= 57.57 grams.

After 7 days the crystals will be 57.57 grams.

Answer:

57.55g

Step-by-step explanation:

Use the formula f(t) = aert, where a = 10, r = 0.25, and t = 7. This gives f(7) = 10e(0.25)(7) = 10e1.75 ≈ 10(5.755) ≈ 57.55.

Answer:

x^2 +3x -3

Step-by-step explanation:

f(x) = 3х – 5

g(x) = х^2+ 2,

(f+g)(x) = 3х – 5 +х^2+ 2

Combine like terms

         = x^2 +3x -3

Answer: 7

Step-by-step explanation:

f(0) means that x is equal to zero and so you substitute all the x's for zeros which means -3 times 0 plus 7 is equal to 7

Answer:

[tex]x=\frac{7}{3}[/tex]

Step-by-step explanation:

Since any number multiplied by zero equals zero, our equation is really:

0 = -3x+7

First, we'd have to subtract the 7 from both sides:

-7 = -3x

Now we need to divide the negative three from both sides to isolate the x.

7/3 = x

So, our answer is x=7/3

Hope this helps!! <3 :)

Answer:  [tex]\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]

Step-by-step explanation:

[tex]n^2+\dfrac{5}{2}n+\underline{\qquad}\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{2\cdot 2}\bigg)^2\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{4}\bigg)^2\\\\\\=\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]

Answer:

The answer to this question depends, in part, on the kinds of questions that you want to ask them. If the purpose of the survey is to try and figure out what concert patrons are thinking, then you want to try to get a good variety of ideas. In that case, you're no so interested in having a sample of individuals that's exactly representative of the population of concert goers. You only want to get a wide variety of the ideas that are out there. This is called heterogeneity sampling. That is, in this case, we'll be trying to get a sample not of people, but of ideas. In this case, we'd use brainstorming groups, panel sessions, and other group discussion methods to get all the ideas out there.

This approach is not an appropriate one if the purpose of the questions is to determine the preferences of the population of theater goers. That's because it doesn't communicate the popularity or prevalence of ideas in the sample. If this is a problem, and it likely is, it seems more appropriate to use some sort of purposive sampling method like modal interest sampling. This approach requires determining what the typical concert goer is like . If the company determines that the typical (or modal) attender is a young single person in college, then those people are sought out and interviewed. This is the sort of polling that is used in election polls where they interview "typical voters." For different genres of music and concert, a different typical concert goer could be postulated and different surveys and interview styles determined.

Probably most appropriate to this problem, though, is quota sampling. This form of purposive sampling uses demographic and other information to determine how many of different kinds of people to interview. For instance, if it is determined that only 20% of concert goers for a particular concert were women, then only 20% of the nonprobability sample should be made up of women. As long as these quotas are met, the sample can be sufficiently random.

I recommend using a combination of quota sampling and modal instance sampling. It seems to me that the kinds of people who attend concerts are idiosyncratic in some ways. Inasmuch as we can define universal characteristics of concert goers, we should seek to include only those people in the sample, but since we have demographic data as well, we should use these proportions as quotas as we select typical concert goers. For example, suppose we determine that the vast majority of people who attend operas make over $80,000/year, then we should limit our sample to people with that income level, but if we also know that 80% of opera attenders are women, we should work to insure that not more than 20% of our sample is men.

Answer:

D

Step-by-step explanation:

To determine if a function is exponential decay or growth, simply look at the rate. If the rate is less than one, it is decay. It it's greater than one, it's growth.

The rate in the given function is 0.75 or 75%. 0.75 is less than one so it's exponential decay.

To determine the percent decrease, simply subtract the rate into 1 or 100%. Thus:

[tex]1-0.75=0.25[/tex]

Therefore, it is a 0.25 or 25% decrease.

The answer is D.

Answer: D

Step-by-step explanation:

1-0.75=0.25

Therefore, it decreases Exponential decay,25 percent decrease  

Answer:

The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]

The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]

Step-by-step explanation:

The summary of the given statistics is:

Population Mean = 26,500

Sample Mean = 30,150

Standard deviation = 10560

sample size = 24

The objective is to state the null hypothesis and the alternate hypothesis.

An hypothesis is a claim with  insufficient information which tends to be challenged into  further testing and experimentation in order to determine if such claim is significant or not.

The null hypothesis is a default hypothesis where there is no statistical significance between the two variables in the hypothesis.

The alternative hypothesis is the research hypothesis that the  researcher is trying to prove.

The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]

The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]

The test statistic can be  computed as follows:

[tex]z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \dfrac{30150 - 26500}{\dfrac{10560}{\sqrt{24}}}[/tex]

[tex]z = \dfrac{3650}{\dfrac{10560}{4.8989}}[/tex]

[tex]z = \dfrac{3650 \times 4.8989 }{{10560}}[/tex]

z = 1.6933

This question is incomplete.

Complete Question

Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?

Answer:

280 tons of wood.

Step-by-step explanation:

From the above question:

To make 1 ship = we require 40 tons of wood.

1 ship = can accommodate 300 sailors.

Step 1

If :

300 sailors = 1 ship

2100 sailors = y ships

Cross Multiply

300 × y ships = 1 ship × 2100 sailors

y ships = 2100 / 300

y ships = 7

Hence, 2100 sailors can occupy 7 ships.

Step 2

We are told in the question that:

Astrid wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?

If:

1 ship = 40 tons of wood

Since 7 ships can accommodate 2100 sailors,

7 ships =

7 × 40 tons of wood = 280 tons of wood.

Therefore , Astrid needs 280 tons of wood to accommodate 2100 sailors.

Answer:

1/2

Step-by-step explanation:

● 1/4 + 4(1/2 - 3/4 )^2

To make it easier convert the fractions to decimal numbers.

● 1/4 = 0.25

● 1/2 = 0.5

● 3/4 = 0.75

So the expression will be:

● 0.25 + 4(0.5 - 0.75)^2

Calculte first 0.5-0.75 (0.5-0.75= -0.25)

● 0.25 + 4 × (-0.25)^2

-0.25^2 is the same as 0.25^2

● 0.25 + 4 × (0.25)^2

0.25^2 is 0.0625

● 0.25 + 4×0.0625

Multiplication has the priority (4 ×0.0625) wich is 0.25

● 0.25 + 0.25

● 0.5

0.5 is 1/2

So the answer 1/2

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\frac{1}{4}+4(\frac{1}{2}-\frac{3}{4})^2\\\frac{1}{4}+4(\frac{2-3}{4})^2\\\frac{1}{4}+4(\frac{-1}{4})^2\\\frac{1}{4}+4(\frac{1}{16})\\\frac{1}{4}+\frac{1}{4}=\frac{2}{4}=\frac{1}{2}[/tex]

Answer:

  0.4 meters

Step-by-step explanation:

The volume is ...

  V = LHB

  12.8 m³ = (8(5B))(5B)(B) = 200B³ . . . fill in given values

  0.064 m³ = B³ . . . . . simplify

  ∛0.064 m = B = 0.4 m

The breadth of the wall is 0.4 meters.

Answer:

D

Step-by-step explanation:

Option D is correct. Slope of the line shown in the graph is 3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run.

It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=(y₂-y₁)/(x₂-x₁)

The line is passing through point (2, 2) and (4, 8).

Lets find the corresponding point values y₂= 8, y₁ = 2, x₂= 4 and x₁ =2.

Plug in the values in slope formula:

Slope = (8-2)/(4-2)  

=6/2

=3

Hence, slope of the line shown in the graph is 3. Option D is correct.

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Answer:

See answer and graph below

Step-by-step explanation:

∬Ry2x2+y2dA

=∫Ry.2x.2+y.2dA

=A(2y+4Ryx)+c

=∫Ry.2x.2+y.2dA

Integral of a constant ∫pdx=px

=(2x+2.2Ryx)A

=A(2y+4Ryx)

=A(2y+4Ryx)+c

The graph of y=A(2y+4Ryx)+c assuming A=1 and c=2

The evaluation of the double integral is [tex]\mathbf{ \dfrac{105}{2}\pi }[/tex]

The double integral [tex]\mathbf{\int \int _R\ \dfrac{y^2}{x^2+y^2} \ dA}[/tex], where R is the region that lies between

the circles [tex]\mathbf{x^2 +y^2 = 16 \ and \ x^2 + y^2 = 121}[/tex].

Let consider x = rcosθ and y = rsinθ because x² + y² = r²;

Now, the double integral can be written in polar coordinates as:

[tex]\mathbf{\implies \int \int _R\ \dfrac{y^2}{x^2+y^2} \ dxdy}[/tex]

[tex]\mathbf{\implies \int \int _R\ \dfrac{r^2 \ sin^2 \theta}{r^2} \ rdrd\theta}[/tex]

[tex]\mathbf{\implies \int \int _R\ \ sin^2 \theta \ r \ drd\theta}[/tex]

Thus, the integral becomes:

[tex]\mathbf{=\int^{2 \pi}_{0} sin^2 \theta d\theta \int ^{11}_{4} rdr }[/tex]

∴

[tex]\mathbf{=\int^{2 \pi}_{0} \dfrac{1-cos 2 \theta }{2} \ \theta \ d\theta\dfrac{r}{2} \Big|^{11}_{4}dr }[/tex]  

[tex]\mathbf{\implies \dfrac{1}{2} \Big[\theta - \dfrac{sin \ 2 \theta}{2}\Big]^{2 \pi}_{0} \ \times\Big[ \dfrac{11^2-4^2}{2}\Big]}[/tex]

[tex]\mathbf{\implies \dfrac{\pi}{2} \times\Big[ 121-16\Big]}[/tex]

[tex]\mathbf{\implies \dfrac{105}{2}\pi }[/tex]

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Answer:

4x^2-22x+30

=2(2x^2 - 11x + 15)

=2(2x^2 -6x -5x +15)

= 2 { 2x(x-3) - 5(x-3) }

= 2 (x-3) (2x - 5)

Step-by-step explanation:

Hey, there!!!

The answer is option B

here, we have;

=4x^2-22x+30

=4x^2-(10+12)x+30

= 4x^2-10x-12x+30

now, taking common,

=2x(2x-5) -6(2x-5)

= 2(x-3)(2x-5).

Hope it helps

Answer:

Option (D)

Step-by-step explanation:

By applying Sine rule in the given triangle WXY,

[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinY}}{\text{XW}}=\frac{\text{SinX}}{\text{WY}}[/tex]

[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}=\frac{\text{Sin39}}{\text{WY}}[/tex]

[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}[/tex]

[tex]\frac{\text{XW}}{\text{XY}}=\frac{\text{Sin82}}{\text{Sin59}}[/tex]

      = 1.1489

XW : XY ≈ 1.15 : 1

[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin39}}{\text{WY}}[/tex]

[tex]\frac{\text{XY}}{\text{WY}}=\frac{\text{Sin59}}{\text{Sin39}}[/tex]

[tex]\frac{\text{XY}}{\text{WY}}=\frac{1.36}{1}[/tex]

[tex]\frac{\text{XY}}{\text{WY}}=\frac{\frac{1}{1}}{\frac{1}{1.36} }[/tex]

[tex]\frac{\text{XY}}{\text{WY}}=\frac{1}{0.7342}[/tex]

XY : WY = 1 : 0.7342

XW : XY : WY = 1.15 : 1 : 0.7342

Therefore, WX > XY > WY

Option (D). will be the correct option.

Part a)

There are 52 letters (26 lowercase and 26 uppercase), 10 digits, and 6 symbols. There are 52+10+6 = 68 different characters to choose from.

Adding up those subtotals gives

68^8+68^9+68^10+68^11+68^12 = 9.9207 * 10^21

different passwords possible.

======================================================

Part b)

Let's find the number of passwords where we don't have a special symbol

There are 52+10 = 62 different characters to pick from

Adding those subtotals gives

62^8+62^9+62^10+62^11+62^12 = 3.2792 * 10^21

different passwords where we do not have a special character. Subtract this from the answer in part a) above

( 9.9207 * 10^21)  - (3.2792 * 10^21) = 6.6415 * 10^21

which represents the number of passwords where we have one or more character that is a special symbol. I'm using the idea that we either have a password with no symbols, or we have a password with at least one symbol. Adding up those two cases leads to the total number of passwords possible.

======================================================

Part c)

The answer from part a) was roughly 9.9207 * 10^21

It will take about 9.9207 * 10^21  nanoseconds to try every possible password from part a).

Divide 9.9207 * 10^21  over 1*10^9 to convert to seconds

(9.9207 * 10^21 )/(1*10^9) = 9,920,700,000,000

This number is 9.9 trillion roughly.

It will take about 9.9 trillion seconds to try every password, if you try a password per second.

------

To convert to hours, divide by 3600 and you should get

(9,920,700,000,000)/3600 = 2,755,750,000

So it will take about 2,755,750,000 hours to try all the passwords.

------

Divide by 24 to convert to days

(2,755,750,000)/24= 114,822,916.666667

which rounds to 114,822,917

So it will take roughly 114,822,917 days to try all the passwords.

------

Then divide that over 365 to convert to years

314,583.334246576

which rounds to 314,583

It will take roughly 314,583 years to try all the passwords

------------------------------

All values are approximate, and are roughly equivalent to one another.

A) 9,920,671,339,261,325,541,376 different passwords are available for this computer system.

B) 875,353,353,464,234,606,592 of these passwords contain at least one occurrence of at least one of the six special characters.

C) It would take 314,582.42 years for a hacker to try every possible password.

To determine how many different passwords are available for this computer system; how many of these passwords contain at least one occurrence of at least one of the six special characters; and how long it takes a hacker to try every possible password, assuming that it takes one nanosecond for a hacker to check each possible password, the following calculations must be performed:

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Answer:

X= 1/2

Step-by-step explanation:

7^2x+3 =2401

7^(2x+3 )=2401

7^(2x+3 )= 7^4

Taking away the base because its equal to 7

Then solving the power as an equation

2x+3= 4

2x= 4-3

2x= 1

X=1/2

Now substituting x into the equation to know if we are correct

7^(2x+3 )=2401

Where x= 1/2

7^(2*(1/2) +3)= 7^4

7^(1+3)= 7^4

7^4= 7^4

7^4= 2401

proving statements!

it's the very definition of it

x  ≤  −  4

Step-by-step explanation:

Answer:

x ≤ -4

Step-by-step explanation:

16x − 7 ≤ − 71

Add 7 to both sides.

16x ≤ -64

Divide both sides by 16.

x ≤ -4