We deposit $12000 into an account carning 3 % interest compounded continuously, How many years will it take
for the account to grow to $16800? Round to 2 decimal places,

Answer:

Yes, P(E1)=P(E2)

Step-by-step explanation:

We are given that

Number of dice=3

Total outcomes of 1 die=6

Therefore,

Total number of outcomes =[tex]6^3=216[/tex]

E1={{(1,4,6),(2,3,6),(1,5,5),(2,4,5),(3,3,5),(3,4,4)}

E2={(1,5,6),(2,4,6),(3,3,6),(2,5,5),(4,4,4),(3,4,5)}

We have to show that E1 and E2 have the same probability P(E1) = P(E2).

Probability, [tex]P(E)=\frac{Favorable\;outcomes}{Total\;outcomes}[/tex]

Using the formula

[tex]P(E_1)=\frac{6}{216}[/tex]

[tex]P(E_1)=0.0278[/tex]

[tex]P(E_2)=\frac{6}{216}[/tex]

[tex]P(E_2)=0.0278[/tex]

Hence, P(E1)=P(E2)

Answer:

Step-by-step explanation:

19.

The numbers are m and n

Sum of m and n = m + n

Sum is multiplied by 91 = 91 x ( m + n )

20.

Let the number be = m

Six subtracted from the number = m - 6

41 times the difference = 41 x ( m - 6)

21.

Let the number be = r

Difference between 83 and 10 = 83 - 10 = 73

[tex]The \ number\ divided \ by\ the \ difference \ = \frac{r}{73}[/tex]

22.

Total of p and 23 = p + 12

[tex]Total \ divided \ by \ 18 = \frac{p + 12 }{18}[/tex]

23.

The product of c and 3  = 3c

Sum of 9 and 12 = 21

Product is more than Sum = 3c + 21

24.

Sum of y  and 10 = y + 10

Number x decreased by 5 = x - 5

[tex]Sum \ divided \ by \ difference = \frac{ y + 10 }{x - 5}[/tex]

Answer:

The slope of diagonal AB is 0 and its equation is [tex]y=-2[/tex].

Step-by-step explanation:

Horizontal lines have zero slope. Since diagonal AB represents a horizontal line (same y-value regardless of x-value), the slope of diagonal AB is 0.

Horizontal lines can be expressed as [tex]y=n[/tex] where [tex]n[/tex] is some real number. In this case, diagonal AB sits on a line with only y-values of -2, and therefore the equation of the line the diagonal is on is [tex]\boxed{y=-2}[/tex].

Answer:

D is the answer

Step-by-step explanation:

plug the -2's in line 1 & 2 then 4 in 2 and 3

the 1&2 , and the 2 and 3 numbers have to match

Using the conditions for continuity, we find that the function D.) is continuous.

A function f(x) is said to be continuous at a point x = a, in its domain if the following three conditions are satisfied:

Since for -4 <= x < -2, -2 <= x < 4 and 4 <= x <= 8, the function f(x) is defined by straight lines , the function will be continuous for all x ≠ -2 and 4. Now for x = -2, 4, let us check all the three conditions:

A.

f(-2) = 0.5 * (-2)² = 2

left hand limit = -2 + 6 = 4

right hand limit = 0.5 * (-2)² = 2

Since, left hand limit is not equal to right hand limit, the function is not continuous at x = -2. No need to check further.

B.

f(-2) = 0.5 * (-2)² = 2

left hand limit = -2 -2 = -4

right hand limit = 0.5 * (-2)² = 2

Since, left hand limit is not equal to right hand limit, the function is not continuous at x = -2. No need to check further.

C.

f(-2) = 0.5 * (-2)² = 2

left hand limit = -2 + 4 = 2

right hand limit = 0.5 * (-2)² = 2

Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = -2.

f(4) = 25 - 3*4 = 13

left hand limit = 0.5 * (4)² = 8

right hand limit = 25 - 3*4 = 13

Since, left hand limit is not equal to right hand limit, the function is not continuous at x = 4.

D.

f(-2) = 0.5 * (-2)² = 2

left hand limit = -2 + 4 = 2

right hand limit = 0.5 * (-2)² = 2

Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = -2.

f(4) = 20 - 3*4 = 8

left hand limit = 0.5 * (4)² = 8

right hand limit = 20 - 3*4 = 8

Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = 4.

Thus, the function is continuous.

Learn more about continuity here

https://brainly.com/question/21447009

#SPJ2

Answer:

36.87

Step-by-step explanation:

sin(b)/12 = .05

arcsin(.6) = 36.87

Answer:

a) [tex]Z = 0.0085[/tex]

b) [tex]Z = 0.0095[/tex]

c)  ii. Amy

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Question a:

Nina took a test in English and earned a 71.8. In the English class had a mean of 71.7 and a standard deviation of 11.7.

This means that [tex]X = 71.8, \mu = 71.7, \sigma = 11.7[/tex]

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{71.8 - 71.7}{11.7}[/tex]

[tex]Z = 0.0085[/tex]

Question b:

Amy took a test in Social Studies and earned a 60.7. Students' test grades in Social Studies had a mean of 60.6 and a standard deviation of 10.5.

This means that [tex]X = 60.7, \mu = 60.6, \sigma = 10.5[/tex]

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{60.7 - 60.6}{10.5}[/tex]

[tex]Z = 0.0095[/tex]

c) Which person did relatively better?

Amy had a higher z-score, so she did relatively better.

Answer:

See explanation

Step-by-step explanation:

Required

The average

The data whose average is to be calculated are not given.

However, the formula to calculate the average is:

[tex]\bar x = \frac{\sum x}{n}[/tex]

Assume the data is:

[tex]1287\ 1215\ 1221\ 1229[/tex]

This means that the number of schools is 4

So:

[tex]\bar x = \frac{1287+ 1215+ 1221+ 1229}{4}[/tex]

[tex]\bar x = \frac{4952}{4}[/tex]

[tex]\bar x = 1238[/tex]

The average of the assumed data is 1238

Answer:

25

Step-by-step explanation:

im pretty sure i think only ok i think no saying bad things in the comment

The correct answer is the fourth one, as it pinpoints both dots perfectly

Answer: Analysis of variance

Step-by-step explanation:

Analysis of variance is the statistical test that's used in analyzing the differences among means. The analysis of variance is used to determine if a statistically significant differences exust between the means of the independent groups.

Based on the question given, the null hypothesis will be that no difference in the importance that's attached to shopping by the consumers living in different regions in the United States.

Answer:

irrational numbers

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q.

Hi there!  

»»————-　★　————-««

I believe your answer is:

Irrational Number

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

⸻⸻⸻⸻  

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

Step-by-step explanation:

A)

The opposite sides of a rectangle are equal. The width make this obvious because both of them are x.

B)

The lengths are not so obvious, but it is never the less true. The two sides are obvious and they are therefore true.

4x + 1 = 2x + 12                   Subtract 1 from both sides.

   - 1              -1

4x = 2x + 11                         Subtract 2x from both sides

-2x   -2x

2x  =  11                               Divide by 2

x = 11/2

x = 5.5

C)

P = L + L + w + w

P = 4(5.5) + 1  + 2(5.5) + 12 + 5.5 + 5.5

P = 22 + 1 + 11 + 12 + 11

P = 23 + 23 + 11

P = 57

Answer:

652 cases

Step-by-step explanation:

The formula for percentage increase is 100 times the final-initial/final value. If we plug the numbers in and calculate, we get 652 cases. Have a great day!

Answer:

146

Step-by-step explanation:

next number is the last -666

Answer:

1/4 *1/4*1/2 =0.03125

which as a fraction is 1/32

so the minimuim number of passes that will get him a goal is 1 since he could get it on the first try

Hope This Helps!!!

Answer:

less

Step-by-step explanation:

An increase of 20% makes the price 120% of the original price.

A discount of 20% makes the discounted price 80% of the previous price.

Original price: x

20% increase in price: 1.2 * x

20% discount over the raised price: 0.8 * 1.2 * x

Now we multiply the numbers in the last expression and compare the result with x.

0.8 * 1.2 * x = 0.96x

0.96 is less than x, so the customer pays less than the original price.

Answer:

739.2

Step-by-step explanation:

Answer:

-14-2i

Step-by-step explanation:

-9-i+(-5-i)

collect like terms(real-real, imaginary-imaginary)

=(-9-5)+(-i-i)

=-14-2i

Answer:

A. 18 calls

B. 0.9

C. 20

Step-by-step explanation:

Number of representatives=2,

Number of extension lines=2,

Average calls each representative can accommodate per hour = 15 calls,

Arrival rate per hour = 30 calls

(a) 90% of the arrival rate = 0.09 × 20 = 18 calls

To handle 18 calls immediately, 18 extension lines should be used

(b) Probability is given by number of possible outcomes ÷ number of total outcomes

Number of possible outcomes = 18, number of total outcomes = 20

Probability (call will receive busy signal) = 18/20 = 0.9

(c) For one extension line, numbers of calls to receive busy signal = 20 - 10 = 10 calls

Number of calls to receive busy signal for the current telephone system with two extension lines = 2 × 10 = 20 calls

Answer:

b) 6.68%

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean score on the scale is 50. The distribution has a standard deviation of 10.

This means that [tex]\mu = 50, \sigma = 10[/tex]

Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale?

The proportion is 1 subtracted by the p-value of Z when X = 65. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{65 - 50}{10}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a p-value of 0.9332.

1 - 0.9332 = 0.0668

0.0668*100% = 6.68%

So the correct answer is given by option b.

Answer: [tex]n=13[/tex]

Step-by-step explanation:

Given

Sum of the first 10 terms is equal to sum of 20, 21, and 22 term

[tex]\Rightarrow \dfrac{10}{2}[2a+(10-1)d]=[a+19d]+[a+20d]+[a+21d]\\\\\Rightarrow 5[2a+9d]=3a+60d\\\Rightarrow 10a+45d=3a+60d\\\Rightarrow 7a=15d[/tex]

No of terms to give a sum of 960

[tex]\Rightarrow 960=\dfrac{n}{2}[2a+(n-1)d]\\\\\Rightarrow 1920=n[2a+(n-1)\cdot \dfrac{7}{15}a]\\\\\Rightarrow 28,800=n[30a+7a(n-1)]\\\\\Rightarrow a=\dfrac{28,800}{n[30+7n-7]}\\\\\Rightarrow a=\dfrac{28,800}{n[23+7n]}[/tex]

Value of first term is less than 20

[tex]\therefore \dfrac{28,800}{n[23+7n]}<20\\\\\Rightarrow 28,800<20n[23+7n]\\\Rightarrow 0<460n+140n^2-28,800\\\Rightarrow 140n^2+460n-28,800>0\\\\\Rightarrow n>12.79\\\\\text{For integer value }\\\Rightarrow n=13[/tex]

Answer:

15

Step-by-step explanation:

In the previous answer halfway through they used the equation: 960 = (n÷2)×(2a+(n-1)×(7a÷15))

Using this equation we can substitute an number to replace n, the higher the number is the smaller a would be.

When we substitute 15 into a, then it leaves us with the answer to be a = 15 which is a positive integer and also is smaller than 20, this then let’s us know that 15 is how many terms can be summed up to make 960.

To double check this answer you can find that d = 7 by changing the a into 15 in the formula 7a/15 (found in the previous answer.

Then in the expression: (n÷2)×(2a+(n-1)×d)

substitute:

n = 14 (must be an even number for the equation to work)

a = 15

d = 7

This will give you an answer of 847, but this is only 14 terms as we changed n into 14. To add the final term you need to complete the following equation: 847+(a+(n-1)×d)

substituting:

n = 15

a = 15

d = 7

This will give you the answer of 960, again proving that it takes 15 terms to sum together to make the number 960.

I hope this has helped you.

P.S. Everything in the previous solution was right apart from the start of the last section and the answer

Divide 25 by 24:

25 / 24 = 1.0416

The hundredth place is the second decimal place, because the third decimal place is less than 5, the hundredths place stays the same:

Answer: 1.04

Answer:

= F^2 x^2

Step-by-step explanation:

(F(x))^2

Apply the rule: (a) =a     (x) = x

= (Fx)^2

Apply exonent rule: (a . b)^n = a^n b^n      (Fx)^2 = F^2 x^2

= F^2 x^2

Answer:

x = 3 , y = 4

Step-by-step explanation:

5x + y = 19 --------- ( 1 )

=> y = 19 - 5x

7x - 2y = 13 ------------ ( 2 )

Substitute y in ( 2 ) :

                        7x - 2( 19 - 5x ) = 13

                        7x - 38 + 10x = 13

                        17x = 13 + 38

                        17x = 51

                           x = 3

Substitute x in ( 1 ) :

                           5x + y = 19

                           5( 3 ) + y = 19

                            15 + y = 19

                              y = 19 - 15

                               y = 4

Hi there!

[tex]\large\boxed{C. \text{ } 1}[/tex]

csc (π/2)

π/2 is located at (0, 1)

csc is equal to 1/y, or the reciprocal of the y-value

Therefore:

csc(π/2) = 1/1 = 1. C is the correct answer.

can you show a picture of the symbols