Solve for AC and AB. 10 points.

Answer:

PV= Max Loan amount = PMT*B(i,T) and PMT = 1200. Calculate B(i,T) = B(6%/12, 360)

=(12/.06)(1-(1/(1.005))360)  I will let you complete the calculation

Step-by-step explanation:

Answer:

Step-by-step explanation:

15+5x=20x

   -5x  -5x  => Subtract 5x from each side

You get

15 = 15x

Divide both sides by 15

1=x

Answer:

a) P(x = 0) = 64.69%

b) P(x ≥ 1) = 35.31%

c) E(x) = 0.42

d) var(x) = 0.3906

Step-by-step explanation:

The given problem can be solved using binomial distribution since:

The binomial distribution is given by

P(x) = ⁿCₓ pˣ (1 - p)ⁿ⁻ˣ

Where n is the number of trials, x is the variable of interest and p is the probability of success.

For the given scenario. the six daily arrivals are the number of trials

Number of trials = n = 6

The probability of success = 7% = 0.07

a) Find the probability that on one day no planes have an exceedence.

Here we have x = 0, n = 6 and p = 0.07

P(x = 0) = ⁶C₀(0.07⁰)(1 - 0.07)⁶⁻⁰

P(x = 0) = (1)(0.07⁰)(0.93)⁶

P(x = 0) = 0.6469

P(x = 0) = 64.69%

b) Find the probability that at least 1 plane exceeds the localizer.

The probability that at least 1 plane exceeds the localizer is given by

P(x ≥ 1) = 1 - P(x < 1)

But we know that P(x < 1) = P(x = 0) so,

P(x ≥ 1) = 1 - P(x = 0)

We have already calculated P(x = 0) in part (a)

P(x ≥ 1) = 1 - 0.6469

P(x ≥ 1) = 0.3531

P(x ≥ 1) = 35.31%

c) What is the expected number of planes to exceed the localizer on any given day?

The expected number of planes to exceed the localizer is given by

E(x) = n×p

Where n is the number of trials and p is the probability of success

E(x) = 6×0.07

E(x) = 0.42

Therefore, the expected number of planes to exceed the localizer on any given day is 0.42

d) What is the variance for the number of planes to exceed the localizer on any given day?

The variance for the number of planes to exceed the localizer is given by

var(x) = n×p×q

Where n is the number of trials and p is the probability of success and q is the probability of failure.

var(x) = 6×0.07×(1 - 0.07)

var(x) = 6×0.07×(0.93)

var(x) = 0.3906

Therefore, the variance for the number of planes to exceed the localizer on any given day is 0.3906.

(A) The required down payment is $48,000.

(B) The amount of the mortgage is $192,000.

(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

(a) To find the required down payment, we need to calculate 20% of the house price.

Down payment = 20% of $240,000

Down payment = 0.2 * $240,000

Down payment = $48,000

The required down payment is $48,000.

(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.

Mortgage amount = Total cost of the house - Down payment

Mortgage amount = $240,000 - $48,000

Mortgage amount = $192,000

The amount of the mortgage is $192,000.

(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal amount (mortgage amount)

r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)

n = Total number of monthly payments (30 years multiplied by 12 months)

Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

Using this formula and performing the calculation will give you the monthly payment amount.

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(a) The mean of the data item from the group data is 161.

(b) The deviation from the mean for each data is -6,-5,1,3 and 7. respectively.

(c) The sum of the deviation is 0

Grouped data are data formed by aggregating individual observations of a variable into groups, so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data.

(a) To find the mean of the data, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

(b) To calculate the deviation from the mean (M') for each of the data item we use the formula below.

M' = x-M

For data 115,

For data 156,

For data 162,

For data 164,

For data 168,

(c) The sum of the deviation is

Hence, the mean, the diaviation from the mean is -6,-5,1,3 and 7  and the sum of the deviation of the data is 161 and 0 respectively,

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The required next term at the end of the sequence is 43.

Arithmetic progression is the series of numbers that have common differences between adjacent values are equal.

here,
1, 2, 4, 7, 12, 19, 30,
As
the sequence is the prime addition of the number, as.
1,
1 + 1 = 2
2 + 2 = 4,

4 + 3 = 7
7 +  5 = 12
12 + 7 = 19
19 + 11 = 30
30 + 13 = 43

Thus, At the end of the sequence, the required next term is 43.

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Applying the definition of complementary and supplementary angles, the measures are:

24. a. x = 23; b. m∠ECH = 28°; m∠HCD = 62°; d. m∠GCF = 28°; e. m∠ECG = 152°; f.  m∠GCD = 118°

25.  m∠F = 74°; 26. m∠1 = 41°; 27. x = 18; 28. m∠PQT = 94°

29. m∠H = 28°

30. m∠2 = 148°

Two angles that have a sum of 90 degrees are complementary, while two angles that have a sum of 180 degrees are supplementary.

24. a. m∠ECH + m∠HCD = 90° [complementary angles]

Substitute

x + 5 + 3x - 7 = 90

4x - 2 = 90

4x = 90 + 2

4x = 92

x = 23

b. m∠ECH = x + 5 = 23 + 5

m∠ECH = 28°

c. m∠HCD = 3x - 7 = 3(23) - 7

m∠HCD = 62°

d. m∠GCF = m∠ECH [vertical angles]

m∠GCF = 28°

e. m∠ECG = 180 - m∠GCF [supplementary angles]

m∠ECG = 180 - 28

m∠ECG = 152°

f. m∠GCD = 90 + m∠GCF

m∠GCD = 90 + 28

m∠GCD = 118°

25.  m∠E +  m∠F = 180 [supplementary angles]

Substitute

9x - 38 + 2x + 42 = 180

11x + 4 = 180

11x = 180 - 4

11x = 176

x = 16

m∠F = 2x + 42 = 2(16) + 42

m∠F = 74°

26. 6x + 11 = 10x - 9 [vertical angles]

6x - 10x = -11 - 9

-4x = -20

x = 5

m∠1 = 6x + 11 = 6(5) + 11

m∠1 = 41°

27. m∠ABC = 2(m∠DBC)

Substitute

9x - 4 = 2(79)

9x - 4 = 158

9x - 4 + 4 = 158 + 4

9x = 162

x = 18

28. m∠PQS = m∠SQR

Substitute

7x - 6 = 4x + 15

7x - 4x = 6 + 15

3x = 21

x = 7

m∠PQT = 180 - 2(m∠PQS)

m∠PQT = 180 - 2(7x - 6)

m∠PQT = 180 - 2(7(7) - 6)

m∠PQT = 94°

29. m∠G = 2(m∠H) + 6

m∠G + m∠H = 90 [complementary angles]

Substitute

2(m∠H) + 6 + m∠H = 90

3(m∠H) + 6 = 90

3(m∠H) = 90 - 6

3(m∠H) = 84

m∠H = 84/3

m∠H = 28°

30. m∠2 = 5(m∠1) - 12

m∠1 + m∠2 = 180 [linear pair]

Substitute

m∠1 + 5(m∠1) - 12 = 180

6(m∠1) - 12 = 180

6(m∠1) = 180 + 12

6(m∠1) = 192

m∠1 = 192/6

m∠1 = 32°

m∠2 = 5(m∠1) - 12 = 5(32) - 12

m∠2 = 148°

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So, b) and e) are subspaces of R3, and a), c), and d) are not.

a) {(x,y,z) ∈R3 : x = 0} is not a subspace of R3, because it doesn't contain the zero vector (0,0,0) which is a requirement for a subspace. It's also not closed under scalar multiplication.

b) {(x,y,z) ∈R3: x + y = 0} is a subspace of R3, because it's closed under scalar multiplication and addition and it contains the zero vector (0,0,0).

c) {(x,y,z) ∈R3 : xz = 0} is not a subspace of R3, because it's not closed under scalar multiplication and it's not closed under addition

d) {(x,y,z) ∈ R3: y ≥0} is not a subspace of R3, because it's not closed under addition, it doesn't contain the zero vector (0,0,0) and it's not closed under scalar multiplication.

e) {(x,y,z) ∈ R3: x = y = z} is a subspace of R3 because it satisfies all the properties of a subspace, it is closed under addition, scalar multiplication, it contains the zero vector (0,0,0) and the negative of any vector in the set is also in the set. This set contains all the vectors that are multiples of (1,1,1) which forms a subspace.

So, b) and e) are subspaces of R3, and a), c), and d) are not.

Complete Question: For each of the following subsets of R3 determine whether it is a vector subspace of R3 or not. Justify your answer.                                                                                                                                                      

a) {(x,y,z) ∈R3 : x = 0}

b) {(x,y,z) ∈R3: x + y = 0}

c) {(x,y,z) ∈R3 : xz = 0}

d) {(x,y,z) ∈ R3: y ≥0}

e) {(x,y,z) ∈ R3: x = y = z}

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The area under the standard normal curve between z=0 and z=3 is 0.4987.

It should be noted that because the normal distribution is symmetrical on both sides of the mean and is a continuous probability distribution, the right side of the center is the opposite of the left side.

The normal distribution was first termed by early statisticians who observed that the same shape repeatedly appeared in many distributions. The characteristics of normal distributions are as follows: Bell-like in its symmetry. The distribution's mean and median, which are both at its center, are equal.

The area will be illustrated as:

P(0 < Z < 3)

From the distribution table. In this case, it's important to look at the normal distribution table under the z score for the values of zero less than Z and Z less than 3. This will be:

= 0.9987 - 0.5

= 0.4987

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Answer:

.048

Step-by-step explanation:

6 thousandths = 0.006

So, 0.006 times 8 would be...

.006

x    8

.048

Hope this helps you out! I'm not exactly sure how to explain how to multiply, but if you're confused, you can always ask someone for help...have a great day :)

Answer:

0.8413

Step-by-step explanation:

Find the z score.

z = (x − μ) / σ

z = (992 − 999) / 7

z = -1

Use a chart or calculator to find the probability.

P(Z > -1)

= 1 − P(Z < -1)

= 1 − 0.1587

= 0.8413

The required probability that a bottle has a volume greater than 992 mL is 0.84134. Option C is correct

Given that,
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and a standard deviation of 7 ml. The fill volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL, is to be determined

Probability can be defined as the ratio of favorable outcomes to the total number of events.

We use Z-statistic to find out the probability,

z = (x − μ) / σ

x = raw score = 992 mL
μ = population mean = 999 mL
σ = standard deviation
z = [992 − 999]/7
z = -1

P-value from Z-Table:

P(x<992) = 0.15866

P(x>992) = 1 - P(x<992) = 0.84134

Thus, the required probability that a bottle has a volume greater than 992 mL is 0.84134

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The probability that X is between 17 and 27 is given as follows:

0.6826.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for this problem are given as follows:

\(\mu = 22, \sigma = 5\)

The probability that X is between 17 and 27 is the p-value of Z when X = 27 subtracted by the p-value of Z when X = 17, hence:

Z = (27 - 22)/5

Z = 1

Z = 1 has a p-value of 0.8413.

Z = (17 - 22)/5

Z = -1

Z = -1 has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826.

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The Total volume of sand in cubic inches needed for the playground when the height of the sand in each sandbox is 4.5 in is; 2700 in³

We are told that the height of the sand, in inches (in.), is proportional to

the volume of sand.

Let the volume be denoted as V

Let the height be denoted as h

Thus;

V ∝ h

Then to equate this, we will have a constant of proportionality;

V = kh

where k is constant of proportionality

When the height of the sand is 1.25 in., the volume of the sand is 280 in³ and this gives;

280 = 1.25k

k = 250/1.25

k = 200

Now, ware told that the height of sand in a box is now 4.5 inches and so;

V = 200 * 4.5

V = 900 in³

Since the playground has 3 of such boxes, then we can say that;

Total volume of sand on the playground = 900 * 3 = 2700 in³

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To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.

The function value at x = 10 is:

f(10) = 1.85(10)^2 = 185

The function value at x = 20 is:

f(20) = 1.85(20)^2 = 740

The length of the interval is:

20 - 10 = 10

So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:

(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5

Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.

Answer:

y=(x-1)(x-6)

so x=1 or x=6

Answer:

Step-by-step explanation:

45

Answer:

Step-by-step explanation:

5

*Answer*

15:47

Step-by-step explanation:

He left; 15:03

Walk for; 12mins

Spends extra;4min

So by my side,

I'll sum up those values we're having to find the total time that was spent

12+4= 16mins

So, at that time when he reached at the station it was 15:19 when we add those extra mins

And so I think it'll 15:47

My thought told me so though

The time it will take for about a fourth of the original amount of P-32 remain is given as follows:

27 days.

An exponential function is defined as follows:

y = ab^x.

In which:

Considering that the initial amount is of 100, while after one day the amount was of 95, the parameters are given as follows:

a = 100, b = 95/100 = 0.95.

Hence the function for the amount remaining after x days is given as follows:

y = 100(0.95)^x.

One fourth of the amount will be remaining when y = 25, hence:

25 = 100(0.95)^x.

(0.95)^x = 0.25

xlog(0.95) = log(0.25)

x = log(0.25)/log(0.95)

x = 27 days.

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The maximum value of the objective function is 26 and the minimum is -10

The objective function is given as:

z=−3x+5y

The constraints are

x+y≥−2

3x−y≤2

x−y≥−4

Start by plotting the constraints on a graph (see attachment)

From the attached graph, the vertices of the feasible region are

(3, 7), (0, -2), (-3, 1)

Substitute these values in the objective function

So, we have

z= −3 * 3 + 5 * 7 = 26

z= −3 * 0 + 5 * -2 = -10

z= −3 * -3 + 5 * 1 =14

Using the above values, we have:

The maximum value of the objective function is 26 and the minimum is -10

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Answer:

0+4

Step-by-step explanation:

5 and 11 are the only prime number here so I am not sure I am answering your question, sorry if this is not right or you can explain what it is asking so I can help you better.

Hope this helps :)

Answer:

\(= 2 \frac{1}{9} \\ \)

Step-by-step explanation:

\(4 \frac{7}{9} - 2 \frac{2}{3} \\ \frac{43}{9} - \frac{8}{3} \\ \frac{43 - 24}{9} \\ = \frac{19}{9} \\ = 2 \frac{1}{9} \)

hope this helps

brainliest appreciated

good luck! have a nice day!

The correct answer is Option A: Proposition I is true and Proposition II is true.

A researcher can use Pearson's chi square test of independence to determine if two nominal variables are independent or not. In this case, the researcher observed a chi-square value of 10.00430.

To determine whether the null hypothesis should be accepted or rejected, the researcher must compare the chi-square value to a critical value associated with the desired level of significance.

At the 5% significance level, the critical value is usually around 7.815, and at the 1% significance level, the critical value is usually around 10.827. Since the observed chi-square value (10.00430) is higher than the critical values for both the 5% and 1% significance levels, the appropriate decision could be a Type II Error for both levels of significance.

In other words, Proposition I (At the 5% significance level the appropriate decision could be a Type II Error) and Proposition II (At the 1% significance level the appropriate decision could be a Type II Error) are both true.

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Answer:

10.3923

Step-by-step explanation:

= ( 12 x 9 )^1/2

= ( 108 )^0.5

= 10.3923

Answer:

10.3923

Step-by-step explanation:

= ( 12 x 9 )0.5

= ( 108 )0.5

= 10.3923

The loan for Gail under this assumption will be $14888.90.

It should be noted that the maturity value is the addition of the simple interest and the principal. The time based on the complete information will be:

= (239 + 70)/365

= 0.075

The interest will be:

= 14000 × 0.075 × 309/365

= $888.90

Therefore, the maturity value will be:

= $14000 + $888.90

= $14888.90

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Answer:

m∠C = 122°

Step-by-step explanation:

Opposite angles of a quadrilateral inscribed in a circle are supplementary. This means

m∠A + m∠C = 180°

m∠B + m∠D = 180°

To find angle C we need to find x, then subtract m∠A from 180°

x+20=3x

20=2x

x=10

Now we substitute 10 in for x

m∠A=2(10)+38

m∠A=20+38

m∠A=58°

Now we subtract this value from 180.

m∠C=180-58

m∠C=122°

Answer:

62°

i took the test and this is the right answer

Answer: