For each of the following systems, determine whether the system is independent, dependent, or
inconsistent. Justify your answers.
2x + 3y = 7 -2x-3y= -7

A is the set of integers greater than -14 and less than -5. B={h, i, s, x, z}. The cardinalities of A and B are, n(A) = 8 and n(B) = 5.

-12 ∈ A, s ∈ B, and m ∉ B are True statements. Since, -21 does not belong to A, 21 ∈ A is a False statement.

Cardinalities of A and B

It is given that,

A = {n : -14 < n < -5, n ∈ Z}  ............ (1)

B = {h, i, s, x, z} ......... (2)

Thus, from (1),

A = {-13, -12, -11, -10, -9, -8, -7, -6} ........... (3)

Cardinalities of A and B are the number of members in the set A and B, respectively. Therefore,

n(A) = 8

n(B) =5

Reason Behind True or False

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Ratio remains same

\(\\ \sf\longmapsto \dfrac{18}{27}=\dfrac{x}{45}\)

\(\\ \sf\longmapsto 2/3=x/45\)

\(\\ \sf\longmapsto 3x=90\)

\(\\ \sf\longmapsto x=30\)

The highest height for the daily rainfall were for 5 and 6 inches

Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.

From the given dot plot, we see the number of times for each height of rainfall.

Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.

Thus, we conclude those were the highest heights for the daily rainfall.

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The sixth term of the geometric sequence is 2048.

The given geometric sequence is 2, 8, 32, 128. We can observe that each term is obtained by multiplying the previous term by 4. Therefore, the common ratio (r) of the sequence is 4.

The formula for the nth term (an) of a geometric sequence is given by:

an = a1 * r^(n-1)

where a1 is the first term and r is the common ratio.

For this sequence, a1 = 2 and r = 4. Plugging in these values into the formula, we get:

an = 2 * 4^(n-1)

To find a6, we substitute n = 6 into the formula:

a6 = 2 * 4^(6-1)

  = 2 * 4^5

  = 2 * 1024

  = 2048

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The Probable question may be:
Write an equation for the nth term of the geometric sequence 2, 8, 32, 128,

Then find a6. Round to the nearest tenth if necessary.

a = 5×4 X

a1 = n-1 X

The Broadway theater had 100 Orchestra, 220 main seat and 190 balcony seats.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the number of Orchestra, y represent the main seat and z represent the balcony seat.

A Broadway theater has 510 ​seats, Hence:

x + y + z = 510    (1)

Also:

140x + 135y + 100z = 62700    (2)

And:

135y + 100z + (1/2)(140)x = 55700    (3)

From the three equations:

x = 100, y = 220, z = 190

The Broadway theater had 100 Orchestra, 220 main seat and 190 balcony seats.

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Answer:

12 feet

Step-by-step explanation:

For an inclined roof, the rise is the vertical distance from the roof rafter to the vertical top plate while the run is the distance from the edge of the wall to half of the center of the ridge.

The slope is the ratio of the rise to run. Given a rise to run ratio of 3 to 4. The house is 32 feet wide.

The run of the roof =  half of the width of the roof = 1/2 × 32 feet = 16 feet

Let the rise of the roof (height of the attic) be x, hence:

rise to run ratio = height of attic/ run of roof

3/4 = x/16

x = 3/4 × 16

x = 12 feet

The height of the attic is 12 feet

Answer:

Mean = The numbers added up and divided by the number of numbers.

Step-by-step explanation:

= (13 + 8 + 9 + 6 + 10 + 8) / 6

= 54 / 6

= 9

The mean is 9.

Answer:

190 students

Step-by-step explanation:

Just focus on the first half of the problem: 80 english, 60 French, and 50 German. Added together this gives you 190

Given a table shows the number of computers and the number of students

We need to find the ratio between them:

So,

using the data of any row to find the ratio

So, the ratio of students to computers =

It can be written 6 or 6 : 1

The area of ΔQRS is 26.10 square units.

What is triangle?

A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles.

To find the area of \($\triangle QRS$\), we can use the formula:

\($Area = \frac{1}{2} \times base \times height$\)

where the base and height are the length of two sides of the triangle that are perpendicular to each other. We can find these sides using trigonometry.

First, we need to find the length of side \($QR$\). We can use the Law of Cosines:

\($QR^2 = QS^2 + RS^2 - 2(QS)(RS)\cos(R)$\)

where \($R$\) is the angle at vertex \($R$\). Substituting the given values, we get:

\($QR^2 = 9^2 + 5^2 - 2(9)(5)\cos(57^\circ)$\)

\($QR \approx 8.02$\)

Next, we need to find the height of the triangle, which is the perpendicular distance from vertex \($R$\) to side \($QS$\). We can use the sine function:

\($\sin(R) = \frac{opposite}{hypotenuse}$\)

\($\sin(57^\circ) = \frac{height}{8.02}$\)

\($height \approx 6.51$\)

Now we can find the area of the triangle:

\($Area = \frac{1}{2} \times QR \times height$\)

\($Area = \frac{1}{2} \times 8.02 \times 6.51$\)

\($Area \approx 26.10$\) square units

Therefore, the area of \($\triangle QRS$\) is approximately \($26.10$\) square units.

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Answer:

Let's assume that the total number of students in the school is "x". We can create a proportion to estimate how many students would choose the aquarium based on the given information:

Number of students who chose aquarium / Total number of students in the school = Percentage of students who chose aquarium / 100

We can plug in the values we know:

80 / x = p / 100

where "p" is the percentage of students who would choose the aquarium if the entire school were surveyed.

We can solve for "x" by cross-multiplying and simplifying:

8000 = px

x = 8000 / p

Now, we need to estimate the value of "p". We can do this by finding the average percentage of students who chose the aquarium, science center, planetarium, and farm:

(80 + 60 + 30 + 40) / x = (210 / x) = Average percentage of students who chose an attraction

This tells us that, on average, 210 out of every "x" students would choose one of the attractions. We can estimate that a similar percentage of the entire school would choose the aquarium:

p / 100 = 80 / 210

p = 38.1

So, we can estimate that approximately 38.1% of the students in the whole school would choose the aquarium. To find the estimated number of students who would choose the aquarium, we can plug in this value for "p" in our original proportion:

80 / x = 38.1 / 100

Cross-multiplying and solving for "x", we get:

x = 209.71

Rounding to the nearest whole number, we can estimate that approximately 210 students in the whole school would choose the aquarium.

Step-by-step explanation:

Answer:

The teacher surveyed a total of:

80 + 60 + 30 + 40 = 210 students.

If we assume that the sample of 210 students surveyed is representative of the entire population of 1000 students at Lake Middle School, we can use the relative frequency of students choosing the aquarium in the sample to estimate the number of students in the whole school who would choose the aquarium.

The relative frequency of students choosing the aquarium in the sample is:

80/210 = 0.38

This means that approximately 38% of the students in the sample chose the aquarium.

To estimate the number of students in the whole school who would choose the aquarium, we can multiply the relative frequency by the total number of students at the school:

0.38 x 1000 = 380

Therefore, the teacher can estimate that approximately 380 students out of 1000 at Lake Middle School would choose the aquarium for a field trip.

Answer:

The game should cost 25$  

Step-by-step explanation:

Answer:

The total cost is $25.00

Step-by-step explanation:

Answer:

Step-by-step explanation:

67

Alijah's taxable income puts him in the first tax bracket, over $8,350 but not surpassing $33,950. Hence, his tax due is a base of $835 plus 15% of the income that exceeds $8,350. This results in a total tax payable of $850. Option B is the correct answer.

Alijah's taxable income falls within the first bracket of the tax table given, being over $8,350 but not over $33,950.

This bracket requires him to pay a tax of $835.00 plus 15% of the amount over $8,350.

He has a surplus of $100 over the $8,350 threshold (i.e., $8,450 - $8,350), and 15% of $100 equals $15.

Therefore, the total tax he owes would be the fixed amount of $835.00 plus the $15.00 calculated, which sums up to $850.00.

Thus, looking at the provided options, option B ($850.00) would be the correct answer.

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None of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

To find the slope of the red line given that it is perpendicular to the green line with a slope of 2, we can use the property that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the green line is 2. To find the slope of the red line, we take the negative reciprocal of 2. The negative reciprocal is obtained by taking the reciprocal (flipping the fraction) and changing the sign.

Reciprocal of 2: 1/2

Negative reciprocal: -1/2

Therefore, the slope of the red line is -1/2.

However, none of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

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Answer: (x+6)(x-3)

Step-by-step explanation:

y=x^2+3x-18

(x+6)(x-3 )

Answer:

-0.750

Step-by-step explanation:

The triangles are congruent by AAS.

When two geometrical figures are completely same, they are said to be congruent. Congruent refers to objects that are the same size and shape. The concept of congruence can be applied to figures, angles, and line segments. Any two line segments are deemed to be congruent if their lengths are the same. If the measure of two angles is the same, they are said to be congruent. The sides and angles of two triangles are said to be equal if they are congruent. Congruent refers to objects that are precisely similar in size and shape. The forms stay equal no matter how they are rotated, flipped, or turned. For instance, create two circles with the same radius, cut them out, and stack them.

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Answer:

Step-by-step explanation:

100%

Answer:

the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.

Answer:

9.42

Step-by-step explanation:

Answer:

$375

Step-by-step explanation:

Divide $225 by 4.5

The answer is 50.

So the recycling center pays $50 for 1 ton of newspapers.

Multiply $50 by 7.5

$375

Hope I helped :)

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Answer:

i got -125

Step-by-step explanation:

Each year, the number of visitors is 1.4 times the number the year before. The correct option is B.

A function is simply used to illustrate the relationship that's exists between the variables that are given.  A function is an expression, rule, or law in mathematics that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.

In this case, the function f(x) = 12,419(1.4)x represents the number of visitors to a website x years after it was launched.

Therefore, it can be seen that the 1.4 in parentheses illustrates the number of visitors.

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Answer:

1.8

Step-by-step explanation:

Answer:

M and N are similar but not congruent

Step-by-step explanation:

M is width 1 length 2

N is width 2 length 4

1x2=2

2x2=4

the other options don't make sense so it's the fourth one.

The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.

To determine the dividends per share for preferred and common stock for each year, we need to divide the total dividends by the number of shares for each type of stock.

Preferred Stock:

Dividends per share of preferred stock = Total dividends for preferred stock / Number of preferred shares

Year 1:

Dividends per share of preferred stock for Year 1 = $50,000 / 40,000 shares = $1.25

Year 2:

Dividends per share of preferred stock for Year 2 = $90,000 / 40,000 shares = $2.25

Year 3:

Dividends per share of preferred stock for Year 3 = $130,000 / 40,000 shares = $3.25

Common Stock:

Dividends per share of common stock = Total dividends for common stock / Number of common shares

Year 1:

Dividends per share of common stock for Year 1 = ($50,000 - Total dividends for preferred stock) / 100,000 shares = ($50,000 - $50,000) / 100,000 shares = $0

Year 2:

Dividends per share of common stock for Year 2 = ($90,000 - Total dividends for preferred stock) / 100,000 shares = ($90,000 - $90,000) / 100,000 shares = $0

Year 3:

Dividends per share of common stock for Year 3 = ($130,000 - Total dividends for preferred stock) / 100,000 shares = ($130,000 - $130,000) / 100,000 shares = $0

The dividends per share for preferred stock for each year are: Year 1 - $1.25, Year 2 - $2.25, Year 3 - $3.25. The dividends per share for common stock for each year are all $0.

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Answer:

True, True, False

Step-by-step explanation:

16.284 to whole is 16

16.284 to tenth is 16.3

16.284 to hundredth is 16.28

Answer:

Step-by-step explanation:

Let's call the number of books printed this year "x".

The profit for this year can be represented as:

Profit = (Revenue from book sales) - (Cost of printing)

Revenue from book sales = x * selling price

Cost of printing = 10,000 + 8 * x

So, Profit = x * selling price - (10,000 + 8 * x) = (selling price - 8) * x - 10,000

To maximize the profit, we need to find the value of x and the selling price that maximizes the expression (selling price - 8) * x - 10,000.

Taking the derivative of the expression with respect to x, we get:

d(Profit)/dx = (selling price - 8)

Setting this equal to 0 and solving for the selling price, we get:

selling price = 8

So, the maximum profit is obtained when the selling price is 8 Birr and x is such that the total cost of printing is equal to the total revenue from book sales.

Substituting x = 10,000 and the selling price = 8 Birr into the equation for profit, we get:

Profit = (8 * 10,000) - (10,000 + 8 * 10,000) = 80,000 - 18,000 = 62,000 Birr

Therefore, the maximum profit is Birr 62,000 and the optimal selling price is Birr 8.

Answer:

15.85

Explanation:

Po = D1 / (k-g)

Po = purchase price,D1 = Dividend in paid in next year,k = required rate of return,g= growth rate

Po = (5.10 (1-0.13)) / (0.15-(-0.13))

Po= 15.85