5. Carrie Burnside is single, earns $350. 15 weekly, and claims 1 allowance.

6. Ray Barbee, a radio announcer, is single, earns $300. 74 weekly, and

claims 2 allowances.

7. Stephen Jensen, a pharmacist, is married, earns $369. 23 weekly, and

claims 2 allowances.

8. Lisa Steamer is married, earns $290. 34 weekly as a receptionist, and

claims no allowances.

9. Catherine Hall, a restaurant hostess, earns $208. 35 a week. She is single

and claims 2 allowances.

10. Veterinarian Ike Stone earns $925. 32 a week. He is single and claims

1 allowance.

11. Doug Smalley, a meteorologist, is married and earns $1,304. 30 a week.

He claims 2 allowances.

12. Kristen Martinez, a dentist, is married, earns $1,352. 75 a week, and

claims 1 allowance.

The determinant of nxn matrix A  2’s on the diagonal, 1’s above the diagonal, and 0’s below the diagonal is 2^n.

From the given information, the matrix will appear as follows

\(A= \left[\begin{array}{ccccc}2&1&......&1 &1\\0&2&......&1 &1\\0&0&2 ......&1 &1\\0&0&0 ......&2 &1\\0&0&0 ......&2 &1\\0&0&0 ......&0 &2\end{array}\right]\)

The matrix is nxn, there are n rows and n columns. As we can see, this matrix has an upper diagonal, and in terms of linear algebra, its determinant is the sum of all its principal diagonal members. As a result, the matrix's determinant is: 2^n

Therefore, the determinant of a n x n matrix A with 2’s on the diagonal, 1’s above the diagonal, and 0’s below the diagonal is 2^n.

To learn more on determinant here:

https://brainly.com/question/4470545#

#SPJ4

To find P(A | B),  first we use the formula P(A | B) = P(A ∩ B) / P(B).To find P(B | A), we use the formula P(B | A) = P(A ∩ B) / P(A).  To determine if A and B are independent, we need to compare P(A ∩ B) with P(A)P(B). If P(A ∩ B) = P(A)P(B), then A and B are independent. If P(A ∩ B) ≠ P(A)P(B), then A and B are dependent.

a. Plugging in the given values, we have:
P(A | B) = 0.20 / 0.50 = 0.40
So, P(A | B) = 0.4000 (to 4 decimals).

b. Plugging in the given values, we have:
P(B | A) = 0.20 / 0.50 = 0.40
So, P(B | A) = 0.4000 (to 4 decimals).

c. Given values are:
P(A) = 0.50
P(B) = 0.50
P(A ∩ B) = 0.20
Calculating P(A) * P(B):
0.50 * 0.50 = 0.25

Since P(A ∩ B) ≠ P(A) * P(B), events A and B are not independent. The occurrence of one event affects the probability of the other event occurring.

To learn more about probability : brainly.com/question/30034780

#SPJ11

Answer:

-16

-2

-2

-2

Step-by-step explanation:

-32/2 = -16

-8/4 = -2

-8^2 / -32 = 64/-32 = -2

-8/(2^2) = -8/4 = /-2

The number of different license plate combinations that are possible if exactly one letter is repeated exactly once, but digits cannot be repeated is 8,424,000.

A combination is just a mathematical technique for determining the number of potential arrangements in a set of objects where the order of a selection is irrelevant.

You can choose the components in any order in combinations. Permutations and combinations are often mistaken.

Now according to the question,

Possible letter combinations

Choose any letter and make it a repeat letter = 26 ways

But, there are ⁴C₂ = 6 spots available for the identical letters.

And there are (25)×(24) other methods for selecting the other two letters.

The total amount of "words" equals ⁴C₂ × 26 × 25 × 24 = 93600.

Furthermore, because the numerals cannot be repeated = 10 × 9 = 90

So, the total number of choices = 93600 × 90 = 8,424,000

Therefore, the total combinations in which the letters can be chosen for the license plates is  8,424,000.

To know more about the combination, here

https://brainly.com/question/11732255

#SPJ4

The expression for the amount of change Zina should receive would then be 20 - (0.30 x 10) = 17.00. This means that Zina should receive 17.00 in change from the clerk.

What is amount?

Amount is the quantity or amount of something that is available, measurable, or given. It is a numerical value. Amount can refer to a quantity of money, goods, or services that is owed, requested, or given. It can also refer to the total cost of items or services. Amounts can be measured in both the physical and digital world. Amount is used in accounting, finance, and other fields to measure and keep track of assets and liabilities.

The expression that represents the amount of change Zina should receive is 20 - (0.30p). This expression takes the original amount of money given to the clerk, twenty dollars, and subtracts out the total cost of the bananas, which is 0.30p. The 'p' in this expression represents the number of pounds of bananas Zina purchased.

To determine the amount of change Zina should receive, the clerk must first calculate the total cost of the bananas. This is done by multiplying the number of pounds of bananas purchased by the cost per pound. Once the total cost of the bananas is calculated, it is then subtracted from the twenty dollars given. The resulting number is the amount of change Zina should receive.

For example, if Zina purchased 10 pounds of bananas at 30 cents per pound, the total cost of the bananas would be 10 x 0.30 = 3.00. The expression for the amount of change Zina should receive would then be 20 - (0.30 x 10) = 17.00. This means that Zina should receive 17.00 in change from the clerk.

For more questions related to assets,

https://brainly.com/question/27972503

#SPJ1

Answer:

6 I think.

Step-by-step explanation:

6 I think. think

Based on the fact that Jessica and her best friend split the money and were able to get $16.32, the total amount that they found was $32.64

The fact that they split the money evenly means that they split it in half which each person getting the same amount.

This means that the total amount they found was twice the amount that Jessica and her best friend got.

The total amount found is therefore:

= Jessica's share + Best friend's share

= 16.32 + 16.32

= $32.64

Find out more on money addition problems at https://brainly.com/question/20460989.

#SPJ1

The general solution is given by y = y_c + y_p = Ae^(12x) - x/8 + B + e^x.the equation P(r) = Be^(k(r - 2010)) and solve for B and k.AND the equation P(r) = Be^(k(r - 2010)) to draw the curve that fits the data.

1. To solve the differential equation 3y' - 36y = 3x + e^x, we first find the complementary solution by solving the homogeneous equation 3y' - 36y = 0. The characteristic equation is 3r - 36 = 0, which gives r = 12. So the complementary solution is y_c = Ae^(12x).

Next, we assume a particular solution in the form of y_p = Ax + B + Ce^x, where A, B, and C are constants to be determined. Substituting this into the original equation, we get -24A + Ce^x = 3x + e^x. Equating the coefficients of like terms, we have -24A = 3 and C = 1. Thus, A = -1/8.

The general solution is given by y = y_c + y_p = Ae^(12x) - x/8 + B + e^x.

2. (a) To solve the differential equation dP/dt = kP, we separate the variables and integrate both sides: (1/P) dP = k dt. Integrating gives ln|P| = kt + C, where C is the constant of integration. Exponentiating both sides, we have |P| = e^(kt + C), and by removing the absolute value, we get P = Be^(kt), where B = ±e^C.

Substituting t = 1, we have P(1) = Be^k. So, the solution for P(1) is P(1) = Be^k.

(b) (i) Based on the data in Table 1, we have two points (2010, 3.2 million) and (2015, 6.2 million). Using these points, we can set up the equation P(r) = Be^(k(r - 2010)) and solve for B and k.

(ii) To estimate when the immigrant population in Country C will become 12 million people, we can plug in P(r) = 12 million into the equation P(r) = Be^(k(r - 2010)) and solve for r.

(iii) To sketch a graph illustrating the population growth, we can plot the points from Table 1 and use the equation P(r) = Be^(k(r - 2010)) to draw the curve that fits the data.

 To  learn more about differential equation:brainly.com/question/32538700

#SPJ11

Answer:

54months

Step-by-step explanation:

30,000-3000=27000.

27000/500=54.

answer=54 more months.

The function f(x) = \((x^3)/(4 - x^2)\) vertical asymptotes are x = 2 and x = -2 and the function has no horizontal asymptotes.

Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a particular value.

Determine the values of x that make the denominator equal to zero to know vertical asymptotes.

Setting the denominator equal to zero:

4 - x² = 0

Rearranging the equation:

x² = 4

Taking the square root of both sides:

x = ±2

Therefore, there are two vertical asymptotes at x = 2 and x = -2.

Horizontal asymptotes occur when the function approaches a particular value as x approaches positive or negative infinity. The degree of the numerator is 3 (highest power of x) and the degree of the denominator is 2 (highest power of x). When the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

Therefore, the function f(x) = \((x^3)/(4 - x^2)\) does not have a horizontal asymptote, but have two vertical asymptotes at x = 2 and x = -2.

Learn more about asymptotes https://brainly.com/question/32038756

#SPJ11

The given series Σ(1 - 11)^n converges for certain values of x. The series converges from -1 to 2, including the left end and excluding the right end. The Alternating Series Test tells us that the series converges.

In more detail, the given series can be written as Σ(-10)^n. When |(-10)| < 1, the series converges. This condition is satisfied when -1 < x < 1. Therefore, the series converges for all x in the interval (-1, 1). Now, the given interval is from 0 to 11, so we need to determine whether the series converges at the endpoints. When x = 0, the series becomes Σ(1 - 11)^n = Σ(-10)^n, which is an alternating series. In this case, the series converges by the Alternating Series Test. When x = 11, the series becomes Σ(1 - 11)^n = Σ(-10)^n, which is again an alternating series. The Alternating Series Test tells us that the series converges when |(-10)| < 1, which is true. Therefore, the series converges at the right endpoint. In summary, the given series converges from -1 to 2, including the left end and excluding the right end ([-1, 2)).

Learn more about Alternating Series Test here: https://brainly.com/question/30400869

#SPJ11

The required perimeter of the polygon is 92 cm.

Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,

Examples of polygons, equilateral triangles, squares, pentagons etc

here,
∠B ≅ ∠C

tangent drawn from D = tangent drawn from B
tangent drawn from D = 11.5 cm

The perimeter of the polygon is given = as the sum of a tangent from all points
= 11.5 + 11.5 + 11.5 + 11.5 + 10.5 + 10.5 + 12.5 + 12.5
= 92 cm

Thus, the required perimeter of the polygon is 92 cm.

Learn more about polygon here:
https://brainly.com/question/24464711
#SPJ1

The given statement "the function g(x)=x3 is a linear transformation from r into r." is false. . A linear transformation must satisfy additivity and homogeneity properties, but the function g(x)=x^3 does not satisfy homogeneity, making it nonlinear.

A linear transformation from R into R is a function that satisfies two properties

Additivity T(u + v) = T(u) + T(v) for all u, v in R

Homogeneity T(cu) = cT(u) for all u in R and all scalars c.

However, the function g(x) = x^3 is not linear because it violates the second property, homogeneity. Specifically, g(cx) = (cx)^3 = c^3x^3, which is not equal to cg(x) = c*x^3, unless c = 1. Therefore, g(x) = x^3 is a nonlinear transformation from R into R.

To know more linear transformation:

https://brainly.com/question/30514241

#SPJ4

--The given question is incomplete, the complete question is given

" the function g(x)=x3 is a linear transformation from r into r. True or false"--

Answer:

1375 miles

Step-by-step explanation:

0.20x+95=370

0.20x=275

x=1375

The exact values of the remaining trigonometric functions are listed below:

Case 3: cos θ = 3 / 5, tan θ = 4 / 3, cot θ = 3 / 4, sec θ = 5 / 3, csc θ = 5 / 4

Case 4: sin θ = √11 / 6, tan θ = √11 / 5, cot θ = 5√11 / 5, sec θ = 6 / 5, csc θ = 6√11 / 11

Case 5: cos θ = 8√73 / 73, sin θ = 3√73 / 73, tan θ = 3 / 8, cot θ = 8 / 3, csc θ = √73 / 3

Case 6: sin θ = 1 / 2, cos θ = √3 / 2, tan θ = √3 / 3, sec θ = 2√3 / 3, csc θ = 2

In this problem we find four cases of trigonometric functions, whose exact values of remaining trigonometric functions must be found. The trigonometric functions are defined below:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

Now we proceed to determine the exact values of the trigonometric functions:

Case 3: y = 4, √(x² + y²) = 5

x = √(5² - 4²)

x = 3

cos θ = 3 / 5

tan θ = 4 / 3

cot θ = 3 / 4

sec θ = 5 / 3

csc θ = 5 / 4

Case 4: x = 5, √(x² + y²) = 6

y = √(6² - 5²)

y = √11

sin θ = √11 / 6

tan θ = √11 / 5

cot θ = 5√11 / 5

sec θ = 6 / 5

csc θ = 6√11 / 11

Case 5: x = 8, √(x² + y²) = √73

y = √(73 - 8²)

y = 3

cos θ = 8√73 / 73

sin θ = 3√73 / 73

tan θ = 3 / 8

cot θ = 8 / 3

csc θ = √73 / 3

Case 6: x = √3, y = 1

sin θ = 1 / 2

cos θ = √3 / 2

tan θ = √3 / 3

sec θ = 2√3 / 3

csc θ = 2

To learn more on trigonometric functions: https://brainly.com/question/25618616

#SPJ1

Ok, so

We have that, for option 1:

The total cost of the service will be:

20x + 45. Where x is the number of months.

Fot option 2, the total cost will be:

35x + 0. Where x is the number of months.

If we equal both equations, we obtain:

20x + 45 = 35x.

Now, we have to solve this equation to find the number of months in which the cost will be the same for two options.

Then, 45 = 15x and x=3.

So, the number of months is 3.

Then, that cost can be found, if we replace x=3 in any equation. For example, in equation 2:

Cost = 35x which is equal to 35*3 and this is 105.

So, after 6 months:

Option 1 will be equal to: 20(6) + 45 and this is: 165$.

Option 2 will be equal to 35(6) and this is: 210$.

Then, Option 1 will be the cheaper option.

Using the values given in the table to evaluate each expression, the value of each expression is (a) 5, (b) 8, (c) -7, (d) -3, (e) 1, and (f) 3.

To evaluate the expressions, we need to use the values given in the table for f(x) and g(x). The composition of functions (f∘g)(x) means that we plug the value of g(x) into the function f(x).

a. (f∘g)(1) = f(g(1)) = f(0) = 5

b. (f∘g)(2) = f(g(2)) = f(-3) = 8

c. (g∘f)(2) = g(f(2)) = g(3) = -7

d. (g∘f)(3) = g(f(3)) = g(2) = -3

e. (g∘g)(1) = g(g(1)) = g(0) = 1

f. (f∘f)(3) = f(f(3)) = f(2) = 3

Therefore, the answers are (a) 5, (b) 8, (c) -7, (d) -3, (e) 1, and (f) 3.

Learn more about composition of functions here: https://brainly.com/question/10687170.

#SPJ11

Did you know that 1 = 2? Think that sounds ridiculous? OK, I'll prove it to you. Then I'll show you why this "proof" is indeed, as you suspected, ridiculous. And we'll see what it all has to do with the number zero.

How to “Prove” That 2 = 1

Let’s begin our journey into the bizarre world of apparently correct, yet obviously absurd, mathematical proofs by convincing ourselves that 1 + 1 = 1. And therefore that 2 = 1. I know this sounds crazy, but if you follow the logic (and don’t already know the trick), I think you’ll find that the “proof” is pretty convincing.

Step-by-step explanation:

Here’s how it works:

Answer:

1433.09

Step-by-step explanation:

4,000,000 divided by 64 = 62,500

62,500 divided by 42 1,433.09

He makes 1433.09 per minute

Answer:

10%

Step-by-step explanation:

40 times 1% equals 4 (inverse operation)

Answer:

62789

Step-by-step explanation:

Answer:

9/10

Step-by-step explanation:

9/10 is equal to .9 and 5/6 is equal to .833333 and .9 is greater than .833333

Answer: 5/6

Step-by-step explanation:

because with fractions if the bottom is less than it is more than a number bigger tha it

Answer:

Step-by-step explanation:

Given - This is the start of the proof. Use this for the information given from the start.

Addition property of equality - Use this when adding terms on both sides of an equation.

Division property of equality - Use this when dividing terms on both sides of an equation.

The length of the base of the parallelogram twisted to form the tube for a roll of paper towels will be 5 inches.

What is a parallelogram?

A parallelogram is a flat figure with two sets of parallel lines. Opposite sides of a parallelogram have the same length and are parallel to one another.

A square, a rectangle, a diamond, and a rhombus are all types of parallelograms.

According to the question,

The area of the parallelogram is 60 sq in.

h = b + 7 (the height of the parallelogram is 7 more than the length of the base).

We know that the formula for calculating the area of a parallelogram is given as follows:

A = bh

We have A = 60 square inches, and we're looking for b, so we'll substitute that into the formula to solve for b.

60 = b(b + 7)60 = b² + 7b0 = b² + 7b - 60

Using the quadratic formula to solve the equation,

b = (-b ± √(b² - 4ac)) / 2a

Where a = 1, b = 7, and c = -60.

b = (-7 ± √(7² - 4(1)(-60))) / 2(1)b = (-7 ± √(49 + 240)) / 2b = (-7 ± √289) / 2

Since we are only interested in the positive value of b,

b = (-7 + 17) / 2b = 10 / 2b = 5

Therefore, the length of the base of the parallelogram is 5 inches.

Learn more about parallelogram here:

https://brainly.com/question/28854514

#SPJ11

Answer:

4986 ounces/m³

Step-by-step explanation:

1 kilogram = 35.274 ounces

1 cubic foot = 0.0283 cubic metre

We are converting kg/ft³ to ounces/m³

Hence:

4kg/ft³ × 35.274 ounces/ 1 kg × 1 ft³/0.0283m³

= 4985.7243816 ounces/m³

Approximately to the nearest whole number = 4986 ounces/m³

Answer:

the original price was $500

hopefully that solves your problems