Determine the present value P that must be invested to have the future value A at simple interest rate r after time t.
A = $8000.00, r = 10.5%, t = 9 months
$
(Round up to the nearest cent as needed.)

George should be 150 mm taller than Martha.

Since George's height is 1.75 meters and Martha's height is 160 centimeters.

So here we convert the meters to mm

So,

[tex]= 1.75\times 100\\\[/tex]

= 1750 mm

Now 160 cm to mm

So,

[tex]= 160\times 10[/tex]

= 1,600 mm

So, the difference should be

= 1,750 - 1,600

= 150 mm

Therefore, George should be 150 mm taller than Martha.

Learn more about height here: https://brainly.com/question/15810288

Complete question is;

Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device. If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?

Answer:

P(All three are not caused by firmware) = 83.84%

Probability that the entire batch will be accepted = 0.8384

Step-by-step explanation:

We are told that out of the 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware.

Thus,

Cases not caused by firmware = 8834 - 504 = 8330

So, probability of the first case not being affected by firmware is;

P(first case not caused by firmware) = 8330/8834

Also,

Probability of second case not being affected by firmware is given as;

P(second case not caused by firmware|first case not affected by firmware) = 8329/8833

Similarly,

Probability of third case not being affected by firmware is given as;

P(third case not caused by firmware|first and second not caused by firmware) = 8328/8832

Now, looking at the 3 Probabilities gotten, it is obvious that the events are not independent because the probability of occurence of one event depends on the probability of occurence of the other event.

Thus, we will make use of the general multiplication rule which is;

P(A & B) = P(B) × P(A|B)

Thus;

P(All three not caused by firmware) = P(first case not caused by firmware) × P(second case not caused by firmware|first case not affected by firmware) × P(third case not caused by firmware|first and second not caused by firmware)

Plugging in the relevant values, we have;

P(All three not caused by firmware) = (8330/8834) × (8329/8833) × (8328/8832)

P(All three are not caused by firmware) = 0.83840506679 ≈ 83.84%

Answer:

[tex]18\sqrt2[/tex]

Step-by-step explanation:

To simplify:

[tex]2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 }[/tex]

First of all, let us write 18 and 162 as product of prime factors:

[tex]18 = 2 \times \underline{3 \times 3}\\162 = 2 \times \underline{3 \times 3} \times \underline{3 \times 3}[/tex]

The pairs are underlined as above.

While taking roots, only one of the numbers from the pairs will be chosen.

Now, taking square roots.

[tex]\sqrt{18} =3 \sqrt2[/tex]

[tex]162 = 3 \times 3 \times \sqrt 2 = 9 \sqrt2[/tex]

So, the given expression becomes:

[tex]2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 } = 2 \times 3\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow 6\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow \sqrt2(6+3+9)\\\Rightarrow \bold{18\sqrt2}[/tex]

So, the answer is:

[tex]18\sqrt2[/tex] or 18 StartRoot 2 EndRoot

Answer:

its B. 18 sqrt(2)

Step-by-step explanation:

just took test

Answer:

Subtraction property

Step-by-step explanation:

Answer:

Subtraction

Step-by-step explanation:I took the test

Answer:

It means that above 0 degrees Celsius the water does not freeze, whereas 0 degrees are freezing teperatures of water.

Step-by-step explanation:

Water freezes at 0 degrees Celsius, but the freezing temperature can be lowered  by adding salt to the water. A student discovered that adding half a cup of salt to  a gallon of water lowers its freezing temperature by 7 degrees Celsius. What is  the freezing temperature of the gallon of salt water?

0° - 7° = -7°

Answer:

The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.

Step-by-step explanation:

Call X is the number of hours that the author uses on monthly basis.

Total bill value if the author uses Don’tTalkMuch service is $80 + $1 X.

Total bill value if the author uses TalkLots service is $20 + $4X

The total fees between 2 providers equal as:

$80 + $1 X = $20 + $4X => 3X = $60 => X = 20

Hence: The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.

Answer:

Show that the statement is true for n=1

Step-by-step explanation:

Hey,

Show that the statement is true for n=1

You can check my other answer there which explains a little bit more the ideas.

https://brainly.com/question/17162256

thank you

Answer:

Step-by-step explanation:

The comparison will be the same if you subtract the right side and compare to zero:

  a/b ?? c/d . . . . . . . using ?? for the unknown comparison symbol

  a/b - c/d ?? 0 . . . . subtract the fraction on the right

  (ad -bc)/bd ?? 0 . . . combine the two fractions

  ad - bc ?? 0 . . . . . . multiply by bd to make the job easier

__

5/6 and 2/5

  5(5) -6(2) = 25 -12 > 0   ⇒   5/6 > 2/5

4/10 and 7/8

  4(8) -10(7) = 48 - 70 < 0   ⇒   4/10 < 7/8

3/12 and 1/4

  3(4) -12(1) = 0   ⇒   3/12 = 1/4

_____

Of course, you can use your calculator (or your memory) to change each of these to a decimal equivalent. The comparison should be easy at that point.

  0.833 > 0.400

  0.400 < 0.875

  0.250 = 0.250

Answer:

a y = 2

b.y = 14

c. y =56

Step-by-step explanation:

a .6 (1)- 4=2

y=2

b. 6 (3)- 4

=18-4

y=14

c. 6 (10) - 4

= 60 - 4 =56

Answer:

Policeman A = 56 tickets

Step-by-step explanation:

Policemen A + B = 70

If Policeman B hands out x no of tickets...

Then Policeman A hands out 4x no of tickets

meaning...

x + 4x = 70

5x = 70

x = 70/5

x = 14

Therefore Policeman A hands out..

4x = 4 × 14 = 56 tickets

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome of event/Total outcome.

If a video rental store keeps a list of their top 15 movie rentals each week, the total outcome is 15.

If the list for the week includes 6 action, 4 comedies, 3 dramas, and 2 mysteries and the store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store, the probability that she selected 2 comedies and 1 action movie will be calculated as shown;

Probability of selecting 2 comedies  = 4/15*4/15 = 16/225 (Note that the expected outcome in this case is 4).

Probability of selecting 1 action movie = 6/15 = 2/5

Hence, the probability that she selected 2 comedies and 1 action movie will be equivalent to 16/225*2/5 = 32/1125

Note that the rented movies will have to be returned hence reason for the replacement.

Complete Question

In a genetics experiment on​ peas, one sample of offspring contained 372 green peas and 35 yellow peas. Based on those​ results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3/4 that was​ expected?

Answer:

The  probability is  [tex]P(g) = 0.9140[/tex]

No it is not close to the probability expected

Step-by-step explanation:

From the question we are told that

    The sample size is  [tex]n = 372 + 35= 407[/tex]

      The  number of  green peas is  [tex]n_g = 372[/tex]

    The  number of  yellow  peas is  [tex]n_y = 35[/tex]

The  probability of getting an offspring pea that is green is mathematically represented as

         [tex]P(g) = \frac{n_g}{n}[/tex]

substituting values

         [tex]P(g) = \frac{372}{ 407}[/tex]

         [tex]P(g) = 0.9140[/tex]

The  expected probability is  [tex]\frac{3}{4} = 0.75[/tex]

But what we got is  [tex]P(g) = 0.9140[/tex]

So we can say that the value obtained is not equal to the expected value

Answer:

71°

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle

m<x + m<y = m<z

4n - 18 + n + 9 = 151 - 5n

5n - 9 = 151 - 5n add like terms

10n = 160

n = 16

Since m<z = 151 - 5n we replace n with 16 and 151 - 5×16 = 71

Answer:

A. 71

Step-by-step explanation:

x + y = z

4n - 18 + n + 9 = 151 - 5n

5n - 9 = 151 - 5n

10n = 160

n = 16

Z = 151 - 5(16) = 71

[tex]2.232\approx2.32[/tex]

Answer:

f(x) = (x - 3)² - 5

Step-by-step explanation:

equate equation to 0

(x - 3)² = 0

take the square root on both sides

x - 3 = 0

add 3

x = 3

If x = 3 then you are moving to 3 units to the right.

- 5 means you are going downward 5 units.

Answer:

(a) 50%

(b) 47.5%

(c) 2.5%

Step-by-step explanation:

According to the honest coin principle, if the random variable X denotes the number of heads in n tosses of an honest coin (n ≥ 30), then X has an approximately normal distribution with mean, [tex]\mu=\frac{n}{2}[/tex] and standard deviation, [tex]\sigma=\frac{\sqrt{n}}{2}[/tex].

Here the number of tosses is, n = 2500.

Since n is too large, i.e. n = 2500 > 30, the random variable X follows a normal distribution.

The mean and standard deviation are:

[tex]\mu=\frac{n}{2}=\frac{2500}{2}=1250\\\\\sigma=\frac{\sqrt{n}}{2}=\frac{\sqrt{2500}}{2}=25[/tex]

(a)

To not lose any money the even rolls has to be 1250 or more.

Since, μ = 1250 it implies that the 50th percentile is also 1250.

Thus, the probability that by the end of the evening you will not have lost any money is 50%.

(b)

If the number of "even rolls" is 1250, it implies that the percentile of 1250 is 50th.

Then for number of "even rolls" as 1300,

1300 = 1250 + 2 × 25

        = μ + 2σ

Then P (μ + 2σ) for a normally distributed data is 0.975.

⇒ 1300 is at the 97.5th percentile.

Then the area between 1250 and 1300 is:

Area = 97.5% - 50%

        = 47.5%

Thus, the probability that the number of "even rolls" will fall between 1250 and 1300 is 47.5%.

(c)

To win $100 or more the number of even rolls has to at least 1300.

From part (b) we now 1300 is the 97.5th percentile.

Then the probability that you will win $100 or more is:

P (Win $100 or more) = 100% - 97.5%

                                   = 2.5%.

Thus, the probability that you will win $100 or more is 2.5%.

Answer:

14/20 or .7 or 70%

Step-by-step explanation:

Total Number of cards: 20

Number of Red cards: 6

The leftover cards: 20 -6 = 14

The probability of not getting a red = 14/20

14/20 as a decimal = 14/20 = 70/100 = .7

14/20 as a percent = 14/20 = 70/100 = 70%

Answer:  11 down and 9 right

Step-by-step explanation:

Slope IS rise over run where the top number of the fraction (numerator) determines the vertical distance --> positive is up, negative is down

and the bottom number of the fraction (denominator) determines the horizontal distance --> positive is right, negative is left.

Given slope = -11/9

the numerator is -11 so the "rise" is  DOWN 11 units

the denominator is 9 so the "run" is RIGHT 9 units

Lila will need to start the hike at 11: 55 a.m. to be back at exactly 6: 05 p.m. or at 11: 54 a.m. to be before 6: 05 p.m (6: 04 p.m.)

Explanation:

To solve this question, the first step is to calculate how much time does hiking to the lake, go fishing, and go back takes in total. This can be calculated by adding the time of the three activities. This means 1 hour 10 minutes + 3 hours 10 minutes + 1 hour 50 minutes which is equal to 6 hours 10 minutes. The detailed process is shown below.

Add the hours: 1 + 3 + 1 = 5

Add the minutes: 10+50 +10 = 70

Also, because the total of minutes is above 60 (each hour has 60 minutes) it is necessary to subtract 60 minutes and add 1 hour.

5 hours + 1 hour and 70 minutes - 60 minutes = 6 hours and 10 minutes

Now, to solve the question subtract the time of the activities to the time Lila needs to complete all the activities.

6: 05 p.m.  -  6 hours and 10 minutes = 11: 55 a.m

You can get this result by substracting first the hours and then the minutes

6: 05 p.m. - 6 hours = 12: 05 p.m.

12: 05 - 10 minutes = 11: 55 a.m.

According to this, Lila will need to start the hike at 11: 55 a.m. to be back at exactly 6: 05 p.m. or at 11: 54 a.m. to be before 6: 05 a.m because if she starts at 11: 54 a.m. she will be back at 6:04, which is a minute before 6:05 p.m.

Answer: 1, 2, 4, 8, 16, and 32.

Step-by-step explanation:

Factors are what we can multiply to get the number.

Factors of 32:

1 x 32=32

2 x 16=32

4 x 8=32

Therefore, the factors of 32 are 1, 2, 4, 8, 16, and 32.

Answer:

  5/2

Step-by-step explanation:

Let u = sin(t). Then this is the integral ...

  [tex]\displaystyle\int_0^{\frac{\pi}{2}}{5u}\,du=\left.\dfrac{5u^2}{2}\right|_0^{\frac{\pi}{2}}=\dfrac{5}{2}(\sin(\frac{\pi}{2})^2-\sin(0)^2)=\dfrac{5}{2}(1-0)=\boxed{\dfrac{5}{2}}[/tex]

Answer:

I thinksomething is wrong.

I'm getting another proving it's-tan thita.

I hope this is the one you are searching for..

Answer:

3 =x

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

3x(x+1) = 4x*x

Divide each side by x

3(x+1) = 4x

Distribute

3x+3 = 4x

Subtract 3x from each side

3x-3x +3 = 4x-3x

3 =x

Answer:

[tex]\bold{n =2t-1}[/tex]

Step-by-step explanation:

Given table is:

[tex]\begin{center}\begin{tabular}{ c c}Term Number (t) & Number of triangles (n) \\ 1 & 1 \\ 2 & 3 \\ 3 & 5 \\ 4 & 7 \\\end{tabular}\end{center}[/tex]

i.e. when term number, t = 1, number of triangles (n) = 1

when term number, t = 2, number of triangles (n) = 3

when term number, t = 3, number of triangles (n) = 5

when term number, t = 4, number of triangles (n) = 7

If we closely look at the pattern, number of triangles (n) in each row are 1 lesser than twice of term number (t).

i.e. for [tex]t=1, n = 2\times 1 -1=1[/tex]

[tex]t=2, n = 2\times 2 -1=3[/tex]

[tex]t=3, n = 2\times 3 -1=5[/tex]

[tex]t=4, n = 2\times 4 -1=7[/tex]

Therefore, the number of triangles in the nth term will be given as:

[tex]\bold{n =2t-1}[/tex]

Answer:

an = 2t -1

Step-by-step explanation:

We are adding 2 each time

1+2 =3

3+2 = 5

5+2 = 7

an is the nth term in the sequence  and t is the number of triangle

an =1+ 2(t-1)

Distribute

an = 1 +2t -2

an = 2t -1

Answer:

Standard deviation = 2.2360679774998

Step-by-step explanation:

We are asked to find the Standard deviation of a samples of speeches as an awards.

The formula for sample standard deviation is given as:

√[(x - μ)²/N - 1 ]

Step 1

We find the mean (μ)

The mean of the sample =>

= Sum of term/ Number of terms

= (3 + 7 + 5 + 4 + 1)/5

= 20/5

= 4

Step 2

Find the Standard deviation of the sample

√[(x - μ)²/N - 1 ]

N = number of samples or terms = 5

= √[(3 - 4) ² + (7 - 4)² + (5 - 4)² +(4 - 4)² +(1 - 4)²/ 4]

= √ (1 ² + 3² + -1² + 0² + -3²/4)

= √( 1 + 9 + 1 + 0 + 9/4)

= √20/5 - 1

= √5

= 2.2360679774998

The standard deviation of the sample = 2.2360679774998

Answer:

Following are the answer to this question:

Step-by-step explanation:

In the given statement, we don't agree with Ed’s conclusion, because it is not relevant simply since it is not statistically significant. The reduction of prostate cancer is the death risk, which is highly significant even if it decreases significantly. It can also be something statistically important without becoming important.

Answer:

D. F(x) = ( (1/5)x)^2 - 4

Step-by-step explanation:

The standard transformation with a stretch and a shift is

F(x) = f(x/b) + k

The red curve has a vertex at (0,-4), and cuts the x-axis at (10,0)

That means that before the vertical shift (of k=-4), the vertex was at (0,0), and the curves passes through (10,4).

Substituting in the equation

F(10) = (10/b)^2 -4 = 0

solve for b

(10/b)^2-4 = 0

(10/b)= sqrt(4) = 2

b = 10/2 = 5

Therefore the transformation equation is

F(x) = (x/5)^2-4

The answer is

F(x) = ( (1/5)x)^2 - 4

Answer:

2.7 in²

Step-by-step explanation:

Given:

∆BAC ~ ∆EDF

Area of BAC = 6 in²

EF = 2 in

BC = 3 in

Required:

Area of ∆EDF

SOLUTION:

Let x = area of ∆EDF

[tex] \frac{6 in^2}{x} = (\frac{3 in}{2 in})^2 [/tex] (theorem of area of similar triangles)

[tex] \frac{6 in^2}{x} = (\frac{3 in}{2 in})^2 [/tex]

[tex] \frac{6}{x} = \frac{9}{4} [/tex]

Cross multiply:

[tex] 6*4 = 9*x [/tex]

[tex] 24 = 9x [/tex]

Divide both sides by 9

[tex] \frac{24}{9} = x [/tex]

[tex] 2.67 = x [/tex]

Area of ∆EDF = 2.7 in²

Answer:

0.44

Step-by-step explanation:

11/25 = 0.44 = 44%

Answer:

11/25

Step-by-step explanation:

since there are 25 students, there will be 25 choices, and the 25 will be the denominator

and there are 11 guys so there will be 11 choices of guys and the 11 will go on top