Find the (unique) solution to the following systems of equations, if possible, using Cramer's Rule.


(a) x + y = 34 2x - y = 30


(b) 2x - 3y = 5 -4x + 6y = 10


(c) 3x + y = 7 2x - 2y = 7

The required radius of the hemisphere is approximately 20.27 inches.

Half of a sphere, with one edge flat and the other in the form of a bowl, makes up a hemisphere, a 3D geometric object. The northern and southern hemispheres, a bowl, mushrooms, and other objects are some of the most typical instances of hemispheres.

The volume V of a hemisphere with radius r is given by:

[tex]$V = \frac{2}{3}\pi r^3$$[/tex]

We are given that the volume of the hemisphere is 6043 cubic inches. So we have:

[tex]$$\begin{align*}\frac{2}{3}\pi r^3 &= 6043 \r^3 &= \frac{3}{2}\cdot 6043 \cdot \frac{1}{\pi} \r^3 &= 9051 \r &= \sqrt[3]{9051} \approx 20.27 \text{ in}\end{align*}[/tex]

Therefore, the radius of the hemisphere is approximately 20.27 inches.

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Answer:

Step-by-step explanation:

I'm sorry, but I cannot accurately calculate the driver's average speed without additional information such as the distance traveled and the time taken.

However, I can help you calculate the cost of fuel if the driver fills up half of the tank's capacity:

Half of the tank's capacity is 28/2 = 14 litres.

The cost of fuel per litre is R17.98.

Therefore, the cost of filling up half the tank is 14 x R17.98 = R251.72.

So, if the price of fuel is R17.98 per litre and the driver fills up half the tank, they will pay R251.72 for fuel.

Answer:

The base of the ladder is pulled away from the wall at a rate of 2 feet/sec. b) Consider the triangle formed by the side of the house, the ladder,and the ground

Step-by-step explanation:

Answer:

[tex]x=44[/tex]

Step-by-step explanation:

lets say X is the cookies Ms. Jans Brought to her class
first she put half of then in the morning (that is [tex]x/2[/tex] of her cookies)
then she gave out 12 more. That is 12 less cookies.
the total cookies left is the total amount minus the half, minus the 12 cookies:
[tex]x-x/2-12=10[/tex]
From this equation we can solve for X
[tex]x/2=10+12[/tex]

 [tex]x=2(22)\\[/tex]

[tex]x=44[/tex]
Just for check, if she brought 44 cookies, and put 22 (half of then), she still have 22 cookies, then she 12 more, then only 10 are left. So 44 is the answer.

She received 5 or more emails in the same time period with a probability of 0.05265.

Simply put, probability is the likelihood that something will occur.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

The higher the likelihood, the more likely it is that the event will take place.

So, the probability would be:

We know that λ = 2.

The formula for the poisson distribution states:

P(x = x) = (λˣ * e^⁻ˣ) / x!

P(x = 1) = (2¹ *e⁻²) / 1!

P(x = 1) = (2 * 0.1353352) = 0.2706

Then,

P(x ≥ 5) = 1 - P(x < 5)

1 - P(x < 5) = 1 - [p(x = 0) + p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4)]

We gather the individual probabilities and combine them. We can use a Poisson distribution calculator to speed up computations:

1 - P(x < 5) = 1 - (0.13534+0.27067+0.27067+0.18045+0.09022)

1 - P(x < 5) = 1 - 0.94735 = 0.05265

P(x ≥ 5) = 1 - P(x < 5) = 0.05265

Therefore, she received 5 or more emails in the same time period with a probability of 0.05265.

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Correct question:

An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of two emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution. What is the probability she received 5 or more emails during the same period?

Answer:

In order of the expressions: 3 1/4, 3 1/3, 3 1/2, and 3 1/6

Step-by-step explanation:

Answer:

Hi! x = 4

Step-by-step explanation:

the shape is a parallelogram!

so the opposite angles must be the same

therefore, you can equate angle L and angle N to find your x!

Hope this helps

Answer: 3/2, 2/3, 1/3

Step-by-step explanation:

Answer:

To get 9d^2 + 6d + 1 from (3d+1), you would need to multiply by 3d+1 again.

Expanding (3d+1)(3d+1), you get:

9d^2 + 3d + 3d + 1

Simplifying, you get:

9d^2 + 6d + 1

Therefore, you need to multiply (3d+1) by (3d+1) or (3d+1)^2 to get 9d^2 + 6d + 1.

Answer:

Jeriel would have to pay $17

Step-by-step explanation:

t= hours

$3 per t hour +$8 fee

t=3

3(3)+8= $17

How much would Jeriel have to pay if he left his car in the lot for t hours:

3t+8

How much total money would Jeriel have to pay for parking if he left his car in the lot for 3 hours?

$17

Answer:

144inch^2

Step-by-step explanation:

8×8=64

64÷2=32

10×8=80

80+32+32=144

Answer:

144 in

Step-by-step explanation:

Area of a trapezoid: the large base plus the small base multiplied by the height divided by two

small base:10 in

large base: 10+8+8=26

(10+26)×8 = 36×8 = 144 in

2 2

Answer:

The taxable income is £3000 - £500 = £2500.

The tax paid at the rate of 5 penny per pound is:

0.05 x £2500 = £125

Therefore, the total tax paid by the man is £125. Answer: A. £125

Step-by-step explanation:

Answer:

(-7,2)

Step-by-step explanation:

The expression which is equivalent to the given expression for all values of x is; 7x + 8.

As evident from the task content; the given expression whose equivalent is required to be determined is; x + 8 + 4x + 2x.

Therefore, by collecting like terms; we have that;

x + 4x + 2x + 8

By adding like terms; we have;

7x + 8.

Ultimately, the expression which is equivalent to the given expression is; 7x + 8.

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The area of the shaded part is 20m²

The space enclosed by the boundary of a plane figure is called its area. The area of a rectangle is length × width It is measured in square units like cm² and m².

To find the area of the square, we need to find the side length.

The side length is found by using Pythagoras theorem

each box is 1m, then 4 boxes is 4m and 2 boxes is 2m

therefore;

l= √ 4²+2²

l = √ 16+4

l = √20 = 2√5

area a square is l²

A = (2√5)²

A = 4× 5

A = 20m²

therefore the area of the shaded part is 20m²

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The statement " If a and x are positive numbers and a ≠ 1, then[tex]log_a(x^r) = r * log_a(x)[/tex] for any real number r" is true .

To prove the equation, we can start with the definition of logarithms:

[tex]log_a(x) = y[/tex] if and only if [tex]a^y = x[/tex]

Using this definition, we can rewrite both sides of the equation as exponents:

[tex]log_a(x^r) = y[/tex] if and only if [tex]a^y = x^r[/tex]

[tex]r * log_a(x) = y[/tex] if and only [tex]a^y = x^r[/tex]

Since [tex]a^y = x^r[/tex] in both case, we have:

[tex]log_a(x^r) = r * log_a(x)[/tex]

Therefore, the equation [tex]log_a(x^r) = r * log_a(x)[/tex] holds for any positive numbers a and x (where a ≠ 1) and any real number r.

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The sale tax fοr the cοmputer is $28.89.

A sales tax is a fee that is paid tο the gοvernment when certain gοοds and services are sοld. Typically, laws permit the seller tο charge the custοmer the tax at the time οf purchase. It is typically referred tο as a use tax when a tax οn gοοds οr services is paid directly tο a gοverning bοdy by a cοnsumer.

Yοur cοmputer purchase cοst $398.50 in tοtal. The sales tax is 7.25 percent.

The sale tax = cοst οf the prοduct × pecentage οf tax

Sales tax = 398.50 × 7.25%

Cοnvert percentages intο fractiοns:

Sales tax = 398.50 × (7.25/100)

Sales tax = 28.89125

sales tax  ≈ 28.89

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All the names for the polygon are correct except for: C) GDFEABC.

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and finite number of sides. Additionally, some examples of a polygon include the following:

Generally speaking, the vertices of a regular polygon should be named in consecutive order either clockwise or anticlockwise (counterclockwise).

In conclusion, GDFEABC is an incorrect name for the given regular polygon.

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Tabi's bill includes $248.94 in charges and $34.99 in interest.

Let x be the amount of interest that Tabi was charged, in dollars.

According to the problem, the new charges are $213.95 more than the interest, so the amount of new charges is x + $213.95.

The total bill, which includes the charges and interest, is $283.93.

Therefore, we can write an equation:

x + (x + $213.95) = $283.93

Simplifying and solving for x, we get:

2x + $213.95 = $283.93

2x = $69.98

x = $34.99

So the amount of interest charged is $34.99.

To find the amount of charges, we can use the equation for new charges:

x + $213.95 = $34.99 + $213.95 = $248.94

So the amount of charges is $248.94.

Therefore, Tabi's bill includes $248.94 in charges and $34.99 in interest.

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The linear regression line is: Y = 0.51X - 14.05

A number is a mathematical object used to count, measure, and label. It is a fundamental concept in mathematics and is used in nearly every branch of the discipline. In everyday life, the notion of numbers is used to count objects, keep track of scores, measure amounts, and label objects.

City TV Commercials Car Sales

A 60 20

B 50 15

C 70 25

D 45 17

E 55 19

Calculating the linear regression line:

m = Slope = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2)

= (5(1475) - (325)(95)) / (5(5850) - (325)2)

= (7375 - 30875) / (29250 - 105625)

= -38500 / -75375

= 0.51

b = Intercept = (ΣY - m(ΣX)) / N

= (95 - 0.51(325)) / 5

= (95 - 165.25) / 5

= -70.25 / 5

= -14.05

Therefore, the linear regression line is:

Y = 0.51X - 14.05.

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complete question:

An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times

the commercials run on TV each day and the number of car sales in the hundreds. Finds the linear regression line for the data gen in the table Round any intermediate

calculations to no less than a decimal place, and round the coefficients to two decimal places.

The correct option is (b) i.e. the total perimeter of the fence is 7x + y − 4 feet.

What is Perimeter?

Perimeter is the total length of the boundary or outer edge of a two-dimensional shape, such as a polygon, circle, or ellipse. It is the sum of the lengths of all the sides or arcs that make up the shape. For example, the perimeter of a square is the sum of the lengths of all its sides, while the perimeter of a circle is the circumference, which is the distance around the circle. The perimeter is often measured in units such as centimeters, meters, or feet, depending on the context of the problem.

Given : sides of the fence

            s₁ = 4x + 5

            s₂ =  y − 7

            s₃ = 3x − 2

We know that, perimeter of a triangle is sum of all three sides.

So, Perimeter of the fence =  s₁+ s₂+ s₃

                                            = 4x + 5 + y − 7 + 3x − 2

                                            = 7x + y - 4 ft.

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The correct statement is that the transfer of land by George to the corporation in exchange for stock should qualify for non-recognition of gain or loss under section 351 of the IRC, and each shareholder's basis in the stock received would depend on their respective contributions.

Fair market value is the amount that a product would sell for on the open market if all parties were acting in their own best interests, were not subject to excessive pressure, and were given a reasonable amount of time to complete the transaction (FMV).

The given scenario describes the formation of a corporation by Nancy and George, where Nancy contributes cash and George contributes land. The corporation issues shares of stock to Nancy and George in exchange for their respective contributions.

Section 351 of the Internal Revenue Code (IRC) provides rules for the non-recognition of gain or loss on the transfer of property to a corporation in exchange for its stock. To qualify for non-recognition, certain requirements must be met, including that the transfer must be made in exchange for stock, and the transferors must be in control of the corporation immediately after the exchange.

Assuming that the requirements of section 351 are met, the transfer of the land by George to the corporation in exchange for stock should not result in any immediate tax consequences. George's basis in the stock received would be equal to his basis in the land transferred. Nancy's contribution of cash would not affect her basis in the stock received.

Therefore, the correct statement is that the transfer of land by George to the corporation in exchange for stock should qualify for non-recognition of gain or loss under section 351 of the IRC, and each shareholder's basis in the stock received would depend on their respective contributions.

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Complete question is: Nancy and George form EB Corporation with the following investments: cash by Nancy of $ ; land by George (basis of $ and fair market value of $). EB Corporation issues shares of stock, each to Nancy and George. Thus, each receives stock in EB worth $.

a. the transfer of land by George to the corporation in exchange for stock should qualify for non-recognition of gain or loss

b. Basis of $ in the EB Corp stock (assuming Bluebird reduces its basis in the land to $).

c. Basis of $ in the EB Corp stock (assuming Bluebird reduces its basis in the land to $).

d. Basis of $ in the EB Corp stock (assuming Bluebird reduces its basis in the land to $).

e. Basis of $ in the EB Corp stock, because her basis exceeded the fair market value of the land she contributed.

Answer:

I’m pretty sure it’s Salma because hers is all positive na the graph is and the graph is in quadrant 1 which is all positive

Therefore, the scale factor of the smaller polygon to the larger polygon is 2. Therefore, the scale factor of the smaller triangle to the larger triangle is 6.

Scale factor refers to the ratio of any two corresponding lengths in two similar geometric figures. In other words, it is the ratio of the size of an object in one image or figure to the size of the same object in another image or figure, assuming that the two images or figures are proportional to each other. The scale factor can be used to determine the relationship between the sizes of the objects in the two figures or images.

Here,

1. The scale factor from the smaller polygon to the larger polygon is found by dividing the length of the larger polygon by the length of the smaller polygon:

scale factor = length of larger polygon / length of smaller polygon

scale factor = 14 / 7

= 2

2. The scale factor from the smaller triangle to the larger triangle is found by dividing the length of the larger triangle by the length of the smaller triangle:

scale factor = length of larger triangle / length of smaller triangle

scale factor = 24 / 4

= 6

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The equation of the ellipse whose vertices are at (-3, -7), and (-3, 5), and focus is at (-3, 1) is; [tex]\frac{(x + 3}{8}+\frac{(y -2}{9} = 1[/tex]

The equation of an ellipse can be presented as follows;

[tex]\frac{(x - h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1[/tex]

Where;

(h, k) = The coordinates of the center of the ellipse

a = The semi major axis

b = The semi minor axis

(h, k ± a) = The vertex coordinates

(h ± b, k) = The covertex coordinates

(h, k ± c) = The coordinates of the foci

c² = a² - b²

The vertex of the specified ellipse are; (-3, -1) and (-3, 5)

The focus = (-3, 1)

Therefore;

k + a = 5

k - a = -1

2·k = 4

k = 4/2 = 2

k + a = 5

2 + a = 5

a = 5 - 2 = 3

k - c = 1

2 - c = 1

-c = 1 - 2 = -1

-c = -1

c = 1

c² = a² - b²

Therefore;

1² = 3² - b²

b² = 3² - 1² = 8

The equation of the ellipse is therefore;

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Marjorie's profit for a week when she teaches no student lessons is $0.  Marjorie's profit for a week when she teaches 20 student lessons is $700. The slope of the equation P = 35s is 35

a. To find Marjorie's profit for a week when she teaches no student lessons, we substitute s = 0 into the equation P = 35s:

P = 35(0) = 0

Therefore, Marjorie's profit for a week when she teaches no student lessons is $0.

b. To find the profit for a week when she teaches 20 student lessons, we substitute

s = 20 into the equation

P = 35s:

P = 35(20) = 700

Therefore, Marjorie's profit for a week when she teaches 20 student lessons is $700.

c. The slope of the equation P = 35s is 35. This means that for each additional student lesson Marjorie teaches, her profit increases by $35.

The P-intercept of the equation is 0, which represents the profit Marjorie makes when she does not teach any student lessons.

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Plane Art include squares, rectangles, triangles, circles, pentagοns, οctοgen, hexagοns, οvals etc. A grοuping οf shapes is called pοlygοns, like squares and rectangles, but circles and οvals are nοt pοlygοns.

A plane is a twο-dimensiοnal surface measured by twο linearly independent pοints; a plane dοesn't have an οbviοus directiοn and can extend indefinitely. In algebra, the pοints are plοtted in the cοοrdinate plane which has a number line extending left tο right and upwards and dοwnwards endlessly and infinitely.

In cοntrast tο sοlid shapes, a clοsed twο-dimensiοnal οr flat surface figure is knοwn as a plane shape. Instead οf edges and faces, they pοssess several light lines that make a cοrner οr a vertex where the twο straight lines meet. Sοme basic plane shapes are triangles, squares, rectangles, circles and οvals.

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Complete question:

Pre-Algebra Grade 8: Unit 1 Lesson 8

What is Plane Art?

(Alternative Portfolio)

(Connections)