Evaluate the determinant for the following matrix 1, 4, 4, 5, 2, 2, 1, 5, 5

Answer:

the rate at which total personal income was rising in the area in 1999 is $1,580,507,200 billion

Step-by-step explanation:

From the given information:

Let consider y to represent the number of years after 1999

Then the population in time (y) can be expressed as:

P(y) = 9400y + 924900

The average annual income can be written as:

A(y) = 1400y + 30388

The total personal income = P(y)  ×  A(y)

The rate at which the total personal income is rising is T'(y) :

T'(y) = P'(y)  ×  A(y)  + P(y)  ×  A'(y)

T'(y) = (9400y + 924900)' (1400y + 30388) + (9400y + 924900) (1400y + 30388)'

T'(y) = 9400(1400y + 30388) + (9400y + 924900) 1400

Since in 1999 y =0

Then:

T'(0) = 9400(1400(0) + 30388) + (9400(0) + 924900) 1400

T'(0) = 9400(30388) + (924900)1400

T'(0) = $1,580,507,200 billion

Therefore; the rate at which total personal income was rising in the area in 1999 is $1,580,507,200 billion

Answer:

answer D

Step-by-step explanation:

Lets have a look to the graph and to the  each of given functions.

As we can see in graph it intersects X in points (-3;0) and (-6;0) that means the function has the roots x1=-3 and x2=-6

Function A  has the roots x1=+3 and x2=+6 => doesn' t fit

Function B has only 1 root x=2 , so can be factorized y=(x-2)^2 => doesn' t fit

Function C has 2 roots  x1=4  and x2=-5 => doesn' t fit

Function D can be factotized as y=(x+6)*(x+3) so has 2 roots x1=-6 x2=-3 => exactly what we need!!!

We can also notice that the coefficient near x²  is equal to 1  and is positive.

That means the legs of the graph directed up,- this is exactly like in our graph. It gives us extra argument why we choose D.

Answer: 97

Step-by-step explanation:

Formula to compute the required sample size :

[tex]n= (\dfrac{\sigma\times z_{\alpha/2}}{E})^2[/tex]

, where [tex]\sigma[/tex] = standard deviation

E= Margin of error

[tex]z_{\alpha/2}[/tex] = Two tailed z-value.

Here, E= 20

[tex]\sigma[/tex] = 100

For 95% confidence level: [tex]z_{\alpha/2}[/tex] =1.96

Required sample size:

[tex]n=(\dfrac{100\times1.96}{20})^2\\\\=(5\times1.96)^2\\\\=96.04\approx97[/tex]

Hence, the required sample size : 97

Answer: answer is: 1000000/19

Step-by-step explanation:

10/19 - 40k -> 10/19*40k= 400000/19

6/19- 60k -> 6/19*60k= 360000/19

3/19 - 80k -> 3/19*80k=240000/19

400000/19+360000/19+240000/19=1000000/19

answer is: 1000000/19

Answer:

A. -9

Step-by-step explanation:

If one of the variables were negative than, it would not be able to equal 2/7.

Answer:

Im not 100% sure, but I think it is:

No

No

No

Yes

Answer:

a) $3700

b) $555

Step-by-step explanation:

The length of the loan is 3 years.

The interest after 3 years is $444.

The rate of the Simple Interest is 4%.

Simple Interest is given as:

I = (P * R * T) / 100

where P = principal (amount borrowed)

R = rate

T = length of years

Therefore:

[tex]444 = (P * 3 * 4) / 100\\\\444 = 12P / 100\\\\12P = 444 * 100\\\\12P = 44400\\\\P = 44400 / 12\\[/tex]

P = $3700

She borrowed $3700

b) If the simple interest was 5%, then:

I = (3700 * 5 * 3) / 100 = $555

The interest would be $555.

Answer:

The dentist should fail to reject the Null hypothesis

Step-by-step explanation:

From the question we are told that

       The sample size is  n =  400

       The  sample  mean is  [tex]\= x = 149[/tex]

       The  level of significance is  5%  = 0.05  

       The  Null hypothesis is  [tex]H_o : p = 0.40[/tex]

        The Alternative  hypothesis is  [tex]H_a : p < 0.40[/tex]

         The  p-value is  [tex]p-value = 0.131[/tex]

Looking at the given data we can see that the p-value is greater than the level of significance hence the dentist should fail to reject the Null hypothesis  

Answer:

Step-by-step explanation:

Using the following data:

H0:p=0.40 (null hypothesis)

Ha:p>0.40 (alternative hypothesis)

The p-value was determined to be 0.001.

a significance level of 5%

Since the p value (0.001) is less than the significance level (0.05), we will reject the null hypothesis and then we would conclude that the proportion of students that are nursing majors is greater than 0.4.

Answer:

p value= 0.131

Step-by-step explanation:

Since we have calculated the test statistic, we can now proceed to find the p-value for this hypothesis test.Using the test statistic and since the hypothesis test is a left tailed test, the p-value will then be the area under the standard normal curve to the left of the test statistic of -1.12.Using the Standard Normal table given above, the area under the standard normal curve to the left of the test statistic of -1.12 is 0.131 (rounded to 3 decimal places.Thus the p-value = 0.131.

Answer:

The amount necessary to fund the withdrawal is $8798.820

Step-by-step explanation:

Here, we are interested in calculating the necessary amount to fund the withdrawal given in the question.

From the question, we can identify the following;

Principal amount, P= $850

Here, Period rate, i = 0.047/ 2 =0.0235

n = 6*2 = 12

Mathematically;

Present Value of an annuity, Ao=P* [1-(1+i)^{-n}]/i

Ao=850* [1-(1+0.0235)^{-12}] /0.0235

Ao = $8798.820

Answer:

Step-by-step explanation:

B. ​No, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually​ exclusive, then when one of them​ occurs, the probability of the other must be zero.

For two mutually exclusive events , with non- zero probabilities , when one occurs , the other can not happen . In this way they become dependent events . In this way , for two events to be both independent and mutually exclusive , at least one of the two events must have zero probability .

It should be noted that two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually​ exclusive, then when one of them​ occurs, the probability of the other must be zero.

Mutually exclusive events simply means the events that cannot take place at the same time. The occurrence of one of the events will prevent the other event from occuring.

Therefore, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually​ exclusive, then when one of them​ occurs, the probability of the other must be zero.

Read related link on:

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Answer:

The z-score is  [tex]z = 2.65[/tex]

The length of days is not unusual

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 267.6 \ days[/tex]

     The standard deviation is  [tex]\sigma = 15.4 \ days[/tex]

      The value considered is  [tex]x = 309 \ days[/tex]

The z-score is mathematically represented as

           [tex]z = \frac{x - \mu}{\sigma }[/tex]

            [tex]z = \frac{309 - 267.6}{15.6 }[/tex]

           [tex]z = 2.65[/tex]

Now given that the z-score is not greater than 3  then we can say that the length of days is not unusual

(reference khan academy)

Answer:

Step-by-step explanation:

  D=4300x /x² + 40.

x = 1

D = 4300 / 41 = 104.88 p / mi²

x = 6

D = 25800 / 76

= 339.47  p / mi²

Population density increases as we go away from city's centre .

b )

x = 10

D=4300x /x² + 40.

D = 307.14 p/ mi²

x = 30

D = 137.23 p / mi²

Population decreases .

c )

when x is very high , density will decrease due to squared denominator whose value increases very fast .

d )

D < 200

4300x /x² + 40 < 200

4300 x < 200 x² + 8000

43 x < 2 x² + 80

2 x² - 43 x + 80 > 0

( x - 19.44 ) ( x - 2.05 ) > 0

Range x <  2.05

x > 19.44

Answer:

The correct option is C

Step-by-step explanation:

From the question we are told that

   The  sample mean is  [tex]\= x =[/tex]$21.51

    The 95%  confidence level interval  is  [$ 20.52 , $22.48]

Generally the 95%  confidence level interval is mathematically represented as

      [tex]\= x - MOE < \mu < \= x + MOE[/tex]

Where  MOE  is the margin of error which defines in percentage the amount by which the sample mean taxi fare(for the 7 taxi  ) will differ from the average taxi fare between Logan Airport and downtown Boston will fall between

Also  [tex]\mu[/tex] is the  average taxi fare between Logan Airport and downtown Boston

So we see that the this 95%  confidence level interval tells us  that  the average taxi fare between Logan Airport and downtown Boston will fall between $20.52 and $22.48.

Answer:

[tex]\boxed{Option \ B}[/tex]

Step-by-step explanation:

In the triangle,

Hypotenuse = 13

Opposite = Perpendicular = 5

Adjacent = Base = 12

Now,

Cos B = [tex]\frac{Adjacent}{Hypotenuse}[/tex]

Cos B = 12/13

If the triangle is just like in the attached file!

Answer:

B) 12/13

Step-by-step explanation:

Answer:

Step-by-step explanation:

Equation given

tan(3B-32 ) = cot ( 5B +10 ) = tan [ 90 - ( 5B + 10 ) ]

tan(3B-32 ) = tan  (90 - 5B - 10 )

(3B-32 ) =  (90 - 5B - 10 )

8B = 32 + 80

B = 14° .

Answer:

42

Step-by-step explanation:

The permutation formula is P(n, r) = n! / (n - r)!. We know that n = 7 and r = 2 so we can write:

7! / (7 - 2)!

= 7! / 5!

= 7 * 6 * 5 * 4 * 3 * 2 * 1 / 5 * 4 * 3 * 2 * 1

= 7 * 6 (5 * 4 * 3 * 2 * 1 cancels out)

= 42

Answer:

[tex]\boxed{42}[/tex]

Step-by-step explanation:

Apply the permutation formula.

[tex]P(n,r)=\frac{n!}{ (n-r)!}[/tex]

[tex]P=number \: of \: permutations\\n=total \: number \: of \: objects \: in \: the \: set\\r=number \: of \: choosing \: objects \: from \: the \: set\\[/tex]

[tex]n=7\\r=2[/tex]

Plug in the values and evaluate.

[tex]P(7,2)=\frac{7!}{ (7-2)!}[/tex]

[tex]P(7,2)=\frac{7!}{ (5)!}[/tex]

[tex]P(7,2)=\frac{5040}{120}[/tex]

[tex]P(7,2)=42[/tex]

Answer:

y < -12

Step-by-step explanation:

Step 1: Subtract 15 on both sides

y + 15 - 15 < 3 - 15

y < -12

This inequality means the any number smaller than -12 would work. So:

-123415235 would work

-1234 would work

-46527 would work

2 would NOT work

6 would NOT work

Answer:

Step-by-step explanation:

[tex]y + 15 < 3[/tex]

Move constant to RHS and change its sign:

[tex]y < 3 - 15[/tex]

Calculate the difference

[tex]y < - 12[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

[tex] P(X \geq 6) = P(X=6) +P(X=7) +P(X=8) +P(X=9) +P(X=10)[/tex]

And using the probability mass function we got:

[tex]P(X=6)=(10C6)(0.5)^6 (1-0.5)^{10-6}=0.205[/tex]

[tex]P(X=7)=(10C7)(0.5)^7 (1-0.5)^{10-7}=0.117[/tex]

[tex]P(X=8)=(10C8)(0.5)^8 (1-0.5)^{10-8}=0.0439[/tex]

[tex]P(X=9)=(10C9)(0.5)^9 (1-0.5)^{10-9}=0.0098[/tex]

[tex]P(X=10)=(10C10)(0.5)^{10} (1-0.5)^{10-10}=0.000977[/tex]

And adding the values we got:

[tex] P(X\geq 6) = 0.377[/tex]

The best answer would be:

D. 0.377

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=10, p=0.5)[/tex]

The probability mass function for the Binomial distribution is given as:

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

Where (nCx) means combinatory and it's given by this formula:

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

For this case in order to pass he needs to answer at leat 6 questions and we can rewrite this:

[tex] P(X \geq 6) = P(X=6) +P(X=7) +P(X=8) +P(X=9) +P(X=10)[/tex]

And using the probability mass function we got:

[tex]P(X=6)=(10C6)(0.5)^6 (1-0.5)^{10-6}=0.205[/tex]

[tex]P(X=7)=(10C7)(0.5)^7 (1-0.5)^{10-7}=0.117[/tex]

[tex]P(X=8)=(10C8)(0.5)^8 (1-0.5)^{10-8}=0.0439[/tex]

[tex]P(X=9)=(10C9)(0.5)^9 (1-0.5)^{10-9}=0.0098[/tex]

[tex]P(X=10)=(10C10)(0.5)^{10} (1-0.5)^{10-10}=0.000977[/tex]

And adding the values we got:

[tex] P(X\geq 6) = 0.377[/tex]

The best answer would be:

D. 0.377

Answer:

P(A|B) = 1 / 6

Step-by-step explanation:

Assuming two fair sided dice with faces numbered 1 to 6.

By intuition, there can only be 6 possible outcomes, so probability is 1/6.

Illustration how to use conditional probability.

Given two events A, B, following is the equation of conditional probability

that A happens given B has already happened and observed.

P(A|B) = P( A intersect B ) / P(B)

In the given problem,

A = casting a double-six

B = casting a double

P(A) = (1 / 6) * (1 / 6) = 1/36

P(B) = (6/6) * (1/6) = 1/6

P(A|B) = 1/36 / (1/6) = 1/6

Answer: Its coefficient of variation = 0.316

Step-by-step explanation:

The formula to find the coefficient of variations:

Coefficient of variation: [tex](\dfrac{\sqrt{\text{variance}}}{\text{return}})[/tex]

Given: Asset X has

Variance = 10

Expected return = 10

then, coefficient of variation [tex]=\dfrac{\sqrt{10}}{10}=\dfrac{1}{\sqrt{10}}\approx0.316[/tex]

Hence, its coefficient of variation = 0.316

The complete part of the first sentence is;

A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by at least 12 kilograms.

Answer:

we fail to reject the null hypothesis and conclude that the difference of the average tensile strength of thread A and thread B is less than 12

Step-by-step explanation:

We are given;

n_A = 16

n_B = 16

x'_A = 185 kg

x'_B = 178 kg

s_A = 6 kg

s_B = 9 kg

Let μ_A denote the population average tensile strength of thread A

Also, Let μ_B represent the population average tensile strength of thread B

Thus;

Null Hypothesis; H0;μ_A - μ_B ≤ 12

Alternative hypothesis;H1; μ_A - μ_B > 12

From the image attached, with a significance level of 0.05, the critical value for right tailed is 1.645. So we will reject the hypothesis is z > 1.645

Formula for z is;

z = (x'_A - x'_B - d_o)/√((s_A²/n_A) + (s_B²/n_B))

Plugging in the relevant values, we have;

z = (185 - 178 - 12)/√((6²/16) + (9²/16))

z = -5/2.7041634566

z = - 1.849

Since the z-value is less than 1.645,we fail to reject the null hypothesis and conclude that the difference of the average tensile strength of thread A and thread B is less than 12

Answer:

A

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = [tex]\frac{19}{x^3}[/tex] ( multiply both sides by x³ )

x³y = 19 ( divide both sides by y )

x³ = [tex]\frac{19}{y}[/tex] ( take the cube root of both sides )

x = [tex]\sqrt[3]{\frac{19}{y} }[/tex]

Change y back into terms of x, then

[tex]f^{-1}[/tex] (x) = [tex]\sqrt[3]{\frac{19}{x} }[/tex] = [tex]\frac{\sqrt[3]{19} }{\sqrt[3]{x} }[/tex] → A

Answer:

The domain of the graph is all real numbers less than or equal to 0.

Step-by-step explanation:

Hello,

We know that we cannot take square root of negative numbers, so we must have

[tex]-x\geq 0 \ \text{ ***multiply by -1, it changes the inequality, so*** } \\ \\\large \boxed{\sf \ \ x\leq0 \ \ }[/tex]

So the domain of the graph is all real numbers less than or equal to 0.

For information, I attached the graph so that we can verify it.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

  (T, C, J) = (in dollars)

     (10000, 10000, 0),

     (15000, 4915.97, 84.03),

     (18181.82, 1680.67, 137.51)

Step-by-step explanation:

There are a number of ways to approach this question. We have chosen an approach that determines the investments required to achieve interest rate targets.

__

For an overall interest rate of I, the proportion that must be invested at rate I1 < I < I2 is ...

  proportion at I1 = (I2 -I)/(I2 -I1)

Similarly, the proportion that must be invested at I2 is what's left over. It can be computed similarly:

  proportion at I2 = (I -I1)/(I2 -I1)

__

We want an overall interest rate of $2000/$20000 = 10%.

Given available interest rates of 9%, 11%, and 130%, we need to have investments at a rate lower than 10% and at a rate higher than 10%.

If we use only the options for 9% and 11% (no junk bonds), then we can compute ...

  proportion at 9% = (11 -10)/(11 -9) = 1/2

  proportion at 11% = (10 -9)/(11 -9) = 1/2

1st Option:

  $10,000 in treasury bills; $10,000 in corporate bonds

__

Suppose we want to achieve a 13% return on our investments at 11% and 130%. Then the proportion invested at 9% will use this value for I2:

  proportion at 9% = (13 -10)/(13 -9) = 3/4

Of the remaining 1/4 of the money, we can achieve a 13% return by mixing the investments like this:

  proportion at 11% = (130 -13)/(130 -11) = 117/119

  proportion at 130% = (13 -11)/(130 -11) = 2/119

2nd option:

  $20,000 × 3/4 = $15,000 in treasury bills

  $5000 × 117/119 = $4,915.97 in corporate bonds

  The remaining amount, $84.03 in junk bonds

__

Let's suppose we want a 20% return on our investment in junk bonds and corporate bonds. Then the proportion of the money invested at 9% will be ...

  proportion at 9% = (20 -10)/(20 -9) = 10/11

And the proportion at 11% will be ...

  proportion at 11% = (130 -20)/(130 -11) = 110/119 . . . (of the remaining 1/11 of the funds)

3rd option:

  $20,000 × 10/11 = $18,181.82 in treasury bills

  $1,818.18 × 110/119 = $1,680.67 in corporate bonds

  The remaining amount, $137.51 in junk bonds

_____

Additional comment

The most that could be invested in Junk Bonds is $165.29. If the remainder is invested in Treasury Bills, then the overall return will be $2000. (You could consider this to be a 4th option.)

Answer:

This is an arithmetic sequence.

Step-by-step explanation:

The difference between the consecutive terms is constant => sequence is arithmetic.

4-2 = 2

6-4= 2

8-6 = 2

10-8 = 2

Step-by-step explanation:

It's an arithmetic sequences.

Formed by the n th term 2n.

As the difference is 2 between them.

let's find it, by formulae.

n th term = 2n

and so on.....

Therefore, it's an arithmetic sequence.

Hope it helps..

Answer:

J = 32

E = 0

Step-by-step explanation:

E is the number of hours for the Escobar family

J is the number of hours for the Johnson family

E + J = 32

E * 20 + J * 30 = 960

Multiply the first equation by -20 so we can use elimination

-20 E -20 J = -640

Add this to the second equation

E * 20 + J * 30 = 960

-20 E -20 J = -640

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

         10 J = 320

Divide by 10

J = 32

Now find E

E + J = 32

E  + 32 = 32

E = 0

Let's take a look at each term separately.

15a^2b^2:

15 has factors 1, 3, 5, 15

a x a

b x b

-24ab

-24 has factors 1, 2, 3, 4, 6, 8, 12, 24

a

b

Now, we can see what each of these terms has in common. Both have a 3 in their factor lists, as well as one a and one b.

Therefore, the greatest common factor is 3ab.

Hope this helps!! :)

Answer:

3ab

Step-by-step explanation:

[tex]15a^{2} b^{2} - 24ab[/tex] is divided by 3

[tex]5a^{2} b^{2} - 8ab[/tex] take away a and b once

hope this helped!!!

[tex]5ab - 8[/tex]

= 3ab

Answer: x = 5, x = -7/2

Step-by-step explanation:

2x² - 3x - 35 = 0

Step 1: Find two values whose product = 2(-35) and sum = -3:  -10 & 7

Step 2: Replace the b-value of -3x with  -10x + 7x:

2x² - 10x   + 7x - 35 = 0

Step 3: Factor the first two terms and the second two terms:

2x(x - 5)  +7(x - 5) = 0

Step 4: Write the factored form:

Notice that the parenthesis are identical.  This is one of the factors. The outside values are the other factor:

Parenthesis: (x - 5)

Outside: (2x + 7)

Factored form: (x - 5)(2x + 7) = 0

Step 5: Set each factor each to zero and solve for x:

x - 5 = 0             2x + 7 = 0

   x - 5                      [tex]x=-\dfrac{7}{2}[/tex]

The solutions of the quadratic equation given as 2x² - 3x - 35 = 0 are x=5 and x =-3.5.

Given that:

2x² - 3x - 35 = 0

This is a quadratic equation.

It is required to find the solutions of this equation.

The solution of the quadratic equation of the form ax² + bx + c = 0 can be found using the quadratic formula:

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

From the given equation:

a = 2

b = -3

c = -35

Substitute to the quadratic formula.

[tex]x=\frac{-(-3)\pm \sqrt{(-3)^2-4(2)(-35)}}{2(2)}[/tex]

  [tex]=\frac{3\pm \sqrt{9+280}}{4}[/tex]

  [tex]=\frac{3\pm \sqrt{289}}{4}[/tex]

  [tex]=\frac{3\pm 17}{4}[/tex]

So, the solutions are:

[tex]x=\frac{3+ 17}{4}=5[/tex], and [tex]x=\frac{3-17}{4}=-3.5[/tex]

Hence, the solutions are x =5, -3.5.

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Answer:

The probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points is 0.67

Step-by-step explanation:

Please check attachment for complete solution and step by step explanation