How many solutions exist for the system of equations below?
[3x+y=18
13x+y=16

a. $456 would be the amount a customer could save during the first year by switching from Cable Zone to Super Vision.

b. Super Vision raises the rates 23% after a new customer's first year,  a customer who switched from Super Vision save $180 in the second year.

c. Super Vision raises the rates 18% for the third year compared to the second year, for the third year, Cable Zone would be cheaper.

a. To calculate how much a customer could save during the first year by switching from Cable Zone to Super Vision, we need to compare the costs of the two providers.

Cable Zone charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for monthly cable television. Therefore, the total cost per month with Cable Zone is:

$46 (home phone) + $36 (Internet) + $56 (cable television) = $138

Super Vision, on the other hand, offers all three services for a flat $100 monthly fee. So, the customer would save:

$138 (Cable Zone cost) - $100 (Super Vision cost) = $38 per month

Therefore, during the first year, the customer could save:

$38 (monthly savings) * 12 (number of months) = $456

b. After the first year, Super Vision raises the rates by 23%. The new monthly fee would be:

$100 (original fee) + 23% (rate increase) * $100 (original fee) = $123

To calculate the savings in the second year, we need to compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $123 (Super Vision cost) = $15 per month

Therefore, in the second year, the customer would save:

$15 (monthly savings) * 12 (number of months) = $180

c. If Super Vision raises the rates by 18% for the third year compared to the second year, we need to calculate the new monthly fee. The new Super Vision fee would be:

$123 (second-year fee) + 18% (rate increase) * $123 (second-year fee) = $145.14

To determine which company is cheaper for the third year, we compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $145.14 (Super Vision cost) = -$7.14

In this case, the Super Vision cost is higher than the Cable Zone cost by $7.14 per month. Therefore, for the third year, Cable Zone would be cheaper.

Overall, during the three-year period, the customer would save a total of $456 (first year) + $180 (second year) = $636 by switching to Super Vision.

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Answer:

B

Step-by-step explanation:

x * ( 7 - x ) > 8

Substitute the number and if the expression is True then that number is a solution.

A substitute x=8

x * ( 7 - x ) > 8

8 * ( 7 - 8 ) > 8

8 * ( -1 ) > 8

-8 > 8

This statement is FALSE so the number is not a solution of the inequality.

B substitute x=2

x * ( 7 - x ) > 8

2 * ( 7 - 2 ) > 8

2 * ( 5 ) > 8

10 > 8

This statement is True so the number is a solution of the inequality.

C substitute x=-1

x * ( 7 - x ) > 8

-1 * ( 7 - -1 ) > 8

-1 * ( 7 + 1 ) > 8

-8 > 8

This statement is FALSE so the number is not a solution of the inequality.

D substitute x=0

x * ( 7 - x ) > 8

0 * ( 7 - 0 ) > 8

0 * ( 7 ) > 8

0 > 8

This statement is FALSE so the number is not a solution of the inequality.

After answering the presented question, we can conclude that We only coordinates need the positive solution, so t = 1.259

A coordinate in mathematics is a number or combination of integers that indicates the position of a point or object in space. Coordinates are often used to define the position of a point or object in a certain coordinate system, such as the Cartesian or polar coordinate systems. A point, for example, is located in the Cartesian coordinate system by its distance from the origin along the x-axis and its distance from the origin along the y-axis. These distances are denoted by two numbers, the x-coordinate and the y-coordinate, respectively. The two coordinates specify the point's position in the plane.

To find the point that is 2/5 of the way from V to W, w

\(d = \sqrt((x2 - x1)^2 + (y2 - y1)^2)\\\)

where (x1, y1) = (-4, -4) and (x2, y2) = (11, 2).\\

\(d = \sqrt((11 - (-4))^2 + (2 - (-4))^2)\\= \sqrt(15^2 + 6^2)\\= \sqrt(225 + 36)\\= \sqrt(261)\\\)

\(d1 = (2/5) * \sqrt(261)\\x = -4 + t * (11 - (-4))\\d1 = s\qrt((x - (-4))^2 + (y - (-4))^2)\\= \sqrt((x + 4)^2 + y^2 - 8x - 8y + 32)\\\)

\(d1^2 = (x + 4)^2 + y^2 - 8x - 8y + 32\\d1^2 = (x + 4)^2 + y^2 - 8x - 8y + 32\\= (x + 4)^2 + y^2 - 8(x + 4) - 8y + 64 \\d1^2 = (x + 4)^2 + y^2 - 8(x + 4) - 8y + 64\\= (x + 4)^2 + (y - 4)^2 + 4 )\\(2/5)^2 * 261 = (x + 4)^2 + (y - 4)^2 + 4\\\)

\(52.2 = (x + 4)^2 + (y - 4)^2 + 4\\(x + 4)^2 + (y - 4)^2 = 48.2\\(x + 4)^2 + y^2 - 8x - 8y + 32 = 48.2 \\(x + 4)^2 + (-4 + 6t)^2 - 8x + 48t - 32 = 48.2\\(x + 4)^2 + 36t^2 - 48t + 32 = 48.2\\(x + 4)^2 + 36t^2 - 48t - 16.2 = 0\\\)

Using the quadratic formula:

\(t = (48 + sqrt(48^2 - 4 * 36 * (-16.2))) / (2 * 36)\\= (48 + sqrt(2596.8)) / 72\\= (48 + 50.956) / 72\\t = 1.259 or t = -0.705\\\)

We only need the positive solution, so t = 1.259

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To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

Answer:

Step-by-step explanation:

Hello!

Since you didn't upload the data, I'll use my own data to solve the example. The steps will be the same, only the results will change. (see attachment) The hypothesis test will be made using a 5% significance level.

The objective of this exercise is to test if there is an association between two variables:

X₁: The subject is vaccinated, categorized "Yes" and "No"

X₂: The subject got the disease, categorized "Yes" and "No"

These two variables of interest are qualitative categorical and each one of them has two categories.

To test if the variables are associated, considering the type of variables they are, you have to apply a Chi Square test of Independence, where the statistic hypotheses are:

H₀: \(P_{ij}= P_{i.} * P_{.j}\) ∀ i= 1, 2 and j= 1, 2

H₁: The variables, vaccination and disease status, are not independent.

α: 0.05

The statistic is

X²= \({r} \atop {i=1} \right.\)∑\({c} \atop {j=1} \right.\)∑\(\frac{(O_{ij}-E_{ij})^2}{E_{ij}}\)≈\(X^2_{(r-1)(c-1)}\)

i= values in rows

j= values in columns

r= total number of rows

c= total number of columns

This type of test is always one-tailed to the right, meaning that you will reject the null hypothesis to high values of Chi Square. There is only one critical value:

\(X^2_{(r-1)(c-1);1-\alpha }= X^2_{(2-1)(2-1);1-0.05}= X^2_{1*1;0.95}= 3.841\)

The decision rule will be:

If \(X^2_{H_0}\) ≥ 3.841, reject the null hypothesis.

If \(X^2_{H_0}\) < 3.841, do not reject the null hypothesis.

Using the p-value approach, the decision rule is always the same:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

Before calculating \(X^2_{H_0}\), you have to calculate the expected frequencies for all categories using the formula:

Ê\(_{ij}\)= \(\frac{O_{i.}*O_{.j}}{n}\)

Ê₁₁= \(\frac{O_{1.}*O_{.1}}{n}= \frac{82*100}{200} = 41\)

Ê₁₂= \(\frac{O_{1.}*O_{.2}}{n}= \frac{82*100}{200} = 41\)

Ê₂₁= \(\frac{O_{2.}*O_{.1}}{n}= \frac{118*100}{200} = 59\)

Ê₂₂= \(\frac{O_{2.}*O_{.2}}{n}= \frac{118*100}{200} = 59\)

\(X^2_{H_0}= \frac{(42-41)^2}{41} + \frac{(40-41)^2}{41} + \frac{(58-59)^2}{59} + \frac{(60-59)^2}{59}= 0.0827\)

The p-value for this test is the probability of obtaining a value as extreme as \(X^2_{H_0}\)= 0.0827:

P(X₁² ≥ 0.0827)= 1 - P(X₁² < 0.0827)= 1 - 0.2264= 0.7736

Ata 5% significance level, the decision is to not reject the null hypothesis. You can conclude that the vaccination and the disease status of the subjects are not related. The new vaccine does not affect the chances of the subjects getting the disease.

I hope this helps!

Given,

The coordinates of the points are (2,6) and (7, 2).

Required:

The distance between the points and the midpoint of the points.

The distance between two points is calculated as,

Hence, the distance between the points is 6.4

The midpoint is calculated as,

Hence, the midpoint is (4.5,4).

Answer:

222 mL

Step-by-step explanation:

okay so lets multply them lets call the quantity of hydrocloric acid x

so 61x+ 21(277.5-x)= 53*277.5

61x+ 21*277.5-21x= 53*277.5

40x=(53-21)(277.5)

40x= (32)(277.5)

x= 222 mL

if my answer helps please mark as brainliest.

Answer:

  14

Step-by-step explanation:

You want to know the size of the universal set if ...

The given sets are mutually exclusive and exhaustive, so the sum of their sizes is the size of the universal set:

  n(u) = 3 + 4 + 7

  n(u) = 14

__

Additional comment

  (r'∩s') ∪ (r'∩s) = r'∩(s' ∪ s) = r' . . . . n(r') = 3

  (r∩s) ∪ (r∩s') = r∩(s ∪ s') = r . . . . . . n(r) = 4 +7 = 11

Then r' ∪ r = u, the universal set.  . . . . n(u) = 3 +11 = 14

The height of the plane sighted by the two observer is 13.5 km.

The plane is sighted by two observers 1 km apart at angles 74 degrees and 78 degrees.

The height of the plane can be calculated as follows:

The side of the triangle can be gotten using sine law.

The law of sine or the sine law states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides

a / sin A = b / sin B = c / sin C

Hence,

x / sin 74 = 1 / sin 4

cross multiply

x sin 4 = 1 sin 74

divide both sides by sin 4

x = 1 sin 74 / sin 4

x = 0.96126169593 / 0.06975647374

x = 13.7794598314

Therefore, let's find the height of the plane using trigonometric ratio,

sin 78° = opposite / hypotenuse

sin 78° = h / 13.8

cross multiply

h = 13.8 × sin 78

h = 13.4984368901

h = 13.5 km

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Answer:  The correct answer is the plane is flying at a height of 13.5 km.

Step-by-step explanation:

Using the Sine Law, you can find the side of the triangle as it has been defined.

Angles A+B+C=180

Angle A = 74

Angle B = 78

Angle C = 28

x/sin74 = 1/sin4

xsin4 = 1sin74

x = 1sin74/sin4

x = 13.7794598

Height = 13.779*sin 78

Height = 13.4984 rounded to 13.5 km

If Leila makes a dot plot of the heights of the girls in her class to the nearest ¹/₂ inch, the number of different heights that will include on the number line is 5.

A dot plot is a data visualization tool that consists of data points plotted as dots on a graph with an x- and y-axis.

The number of dots plotted on each number line shows the frequency of the data group.

Height    Frequency   Cumulative Frequency

56¹/₂             2                               2

57                 2                               4

57¹/₂             2                               6

58                2                               8

58¹/₂             1                               9

Thus, arranging the heights according to groups, the different heights on the number line can be classified into 5.

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The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Answer:

I dont give the answer right away so you read what i write and fully understand :D

Step-by-step explanation:

The reciprocal of something is basically when you flip something over. Since 17h/46j is a fraction, the reciprocal is 46j/17h. Remember, a number times the reciprocal is always equal to one.

Answer:

46j over 17h

Step-by-step explanation:

a reciprocal fraction is formed by flipping the fraction around

for example:

2/3

reciprocal= 3/2 or 1.5

HOPE THIS HELPS!!! :)

\((\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{8}}} \implies \cfrac{ 3 }{ -3 } \implies - 1\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{8}) \\\\\\ y-5=-x+8\implies {\Large \begin{array}{llll} y=-x+13 \end{array}}\)

Based on the information given about the combination, the number of different parts of fruits that can be selected from the bowl will be 6.

Since the bowl contains an apple, a plum, a pear, and a banana, the different pairs of fruit that can be selected from the bowl will be 4C2.

We can solve this further which will be:

= 4C2

= 4! /2! (4 - 2)!

= 4! / 2!2!

= (4 × 3 × 2)/ 2 × 2

= 24/4

= 6

Therefore, 6 different pairs of fruit can be selected.

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It's the last option again. You have 1 linear factor (3x) and 2 copies of a quadratic factor (x² + 10), and the partial fractions with the quadratic factor need to have a linear polynomial in the numerator.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Answer:-3x - 12 + 5x

Step-by-step explanation:

Answer:

a = -5

Step-by-step explanation:

15 - a = 20

Move the constant of 15 to the other side by subtracting it.

-a = 5

Divide by -1 to make a positive.

a = -5

Check.

15 - (-5) = 20

15 + 5 = 20

20 = 20

Answer:

-5

Step-by-step explanation:

15-(-5)=20

5 turns into a positive

15+5=20

Answer:

the percentage of the company works on the weekend is 50%

Step-by-step explanation:

The computation of the percentage of the company works on the weekend is shown below:

= Total number of employees working on weekends ÷ number of employees in a company

= 250 employees ÷ 500 employees

= 0.50

= 50%

hence, the percentage of the company works on the weekend is 50%

Answer:

9m  +3

Step-by-step explanation:

6m-4+3m+7

Combine like terms

6m+3m    -4+7

9m  +3

Answer:

−3⋅(5m+7)

Step-by-step explanation:

(f/g)(-5) is equal to 1/4, and the value -1 is not in the domain of f/g.

To find (f/g)(-5), we need to substitute -5 into the functions f(x) and g(x) and then divide f(-5) by g(-5).

Given:

f(x) = (4+x)(6+x)

g(x) = 1+x

Substituting -5 into the functions:

f(-5) = (4+(-5))(6+(-5)) = (-1)(1) = -1

g(-5) = 1+(-5) = -4

Now, we can calculate (f/g)(-5):

(f/g)(-5) = f(-5) / g(-5) = -1 / -4 = 1/4

Therefore, (f/g)(-5) equals 1/4.

Now let's determine the values that are not in the domain of f/g. The values that are not in the domain of f/g are the values that make the denominator g(x) equal to zero. In this case, the denominator is g(x) = 1+x.

To find the values that make the denominator zero, we solve the equation:

1 + x = 0

Subtracting 1 from both sides, we get:

x = -1

So, the value x = -1 is not in the domain of f/g because it would make the denominator equal to zero.

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Answer:

Row D

Step-by-step explanation:

y = 2x - 3

if x = 10

y = 2 * 10 - 3

= 20 - 3

= 17

so row d is incorrect.

Answer:

8(3+4p)

Step-by-step explanation:

8 goes into 24 and 32, so it can be factored out:

\(24+32p=8(3+4p)\)

Answer:

8(3 + 4p)

Step-by-step explanation:

Factor 24 + 32p

First, factor out the GCF. In this case, the GCF is 8, and we have

8(3 + 4p)

We can't factor anymore so the answer is 8(3 + 4p)

Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

The volume of the given figure is 1176 cubic cm.

The value of the figure is calculated by multiplying all three side areas. Volume is a measure of the amount of space that an object or a substance occupies. It is typically expressed in cubic units such as cubic meters (m³), cubic centimetres (cm³), or cubic feet (ft³).

The volume of the figure is calculated as,

Volume = 2 ( 15 x 6 + 20 x 6 + 20 x 18 )

Volume = 1176 Cubic cm

Hence, the volume of the figure will be equal to 1176 Cubic cm.

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Answer:

m∠JLK° = 62°

Step-by-step explanation:

∠JLK = ∠KJL

SO

56°+2(∠JLK)° = 180°

2(∠JLK)° = 180-56

2(∠JLK)° = 124

∠JLK° = 62°

so m∠JLK° = 62°

Answer:

m∠JLK = 62°

Step-by-step explanation:

180 - 56 = 124

124 ÷ 2 = 62

The price per foot is $3.09

A 3 yard roll of butcher paper costs $9.27

= 9.27/3

= $3.09

Hence the price per foot is $3.09

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\(\sqrt[3]{a^2+b^2} = (a^2+b^2)^{\frac{1}{3}}\)