Practice & Problem Solving
Identify the domain and range

{(2, 1), (4, 2), (6, 3), (8, 4), (10,5)}

The price of the old model is ₱42,656.00. This answer is found by using the equation that the price of the old model is twice the price of the new model, minus the difference in price of ₱15,500.

Equations can be written using symbols, numbers, and letters, and includes an equal sign (=) to show that two sides of the equation are equal in value.

The price of the old model can be calculated using the following equation:

Old Model Price = 2(New Model Price) - 15,500

Old Model Price = 2 (29,078) - 15,500

Old Model Price = 58,156 - 15,500

Old Model Price = ₱42,656.00

Therefore, the price of the old model is ₱42,656.00

This equation can be used in general when comparing the price of a new and old model of the same item. By subtracting the difference in price of the two models from twice the price of the new model, we can find the price of the old model.

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\({ \red{\boxed{ \tt{Step-by-step-explaination}}}}\)

Perimeter of a rectangle : \({ \purple{ \tt{2(l+b)}}}\)

length = \({ \red{ \tt{17cm}}}\)

breadth= \({ \red{ \tt{?}}}\)

now,

according to the rule.

perimeter = 2(l+b)

66 = 2(17+b)

66 = 34 + 2b

66 - 34 = 2b

32 = 2b

32/2 = b

16 cm = b

hence b = \({ \pink{ \sf{16cm}}}\)

Answer:

false

Step-by-step explanation:

Call the persons 1 through 7.

1,2

1,3

1,4

1,5

1,6

1,7

2,3

2,4

2,5

2,6

2,7

3,4

3,5

3,6

3,7

4,5

4,6

4,7

5,6

5,7

6,7

There are 21 handshakes.

1 handshaking 2 is the same as 2 handshaking 1.

6 × 7/2 = 21

Answer: false

Answer: (0,-1)

Step-by-step explanation:

Let's start with the first inequality, \(y < -x^{2}+x\). To check which points satisfy this inequality, we can substitute the x- and y-coordinates and see if they satisfy the inequality.

Once again, we can repeat this for the second inequality (but this time, we only need to check the points that satisfy the first inequality).

Therefore, the answer is (A) (0, -1).

The quadratic equation has two solutions, x1 = 3.44 and x2 = 0.56

Quadratic equations are the ones with degree 2. The standard form of a quadratic equation with variable x is ax2 + bx + c = 0, where a ≠ 0. These equations can be solved by splitting the factorisation, completing the square, or by quadratic formula method.

2x²-8x+8 = -3

2x²-8x+8+3 = 0

2x²-8x+11=0

Using the quadratic formula

x = (- b ± √(b² - 4ac)) / 2a

where a = 2

b = -8

c = 11

x = (-(-8) ± √(11² - 4(2)(11))) / 2(2)

x = (8 ± √(121 - 88)) / 4

x = (8 ± √(33))/4

x 1 = (8 + √(33))/4

x1 = (8 + √(33))/4

x1 = (8 + 5.75)/4

x1 = 13.75 / 4

x1 = 3.44

x2 = (8 - √(33))/4

x2 = (8 - 5.75)/4

x2 = 2.25/4

x2 = 0.56

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Answer:

It would be the first answer choice, 18+54

Step-by-step explanation:

6(3+9

6x3=18

6x9=54

18+54 would be the equation.

Please pick me for brainliest

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

Option D cannot be evaluated to determine if -286 is its 50th term.

Based on the information provided, none of the given sequences can be identified as having -286 as its 50th term.

Let's evaluate each option to determine which sequence has -286 as its 50th term.

A) An alternating geometric sequence where the 43rd term is 4 and the 45th term is 16:

To determine the common ratio, we divide the 45th term by the 43rd term:

16 / 4 = 4.

Since this is an alternating geometric sequence, the terms alternate between positive and negative. However, since the common ratio is positive, this sequence will only have positive terms.

Therefore, option A cannot have -286 as its 50th term.

B) An arithmetic sequence where the 5th term is 7 and the 6th term is 10:

To determine the common difference, we subtract the 5th term from the 6th term:

10 - 7 = 3.

To find the 50th term, we use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1) * d,

where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference.

a_50 = 7 + (50 - 1) * 3

a_50 = 7 + 49 * 3

a_50 = 7 + 147

a_50 = 154.

Since the 50th term of this arithmetic sequence is 154, option B cannot have -286 as its 50th term.

C) -8, 2, -4...

This sequence alternates between -8 and 2. To find the pattern, we can observe that each term is multiplied by -1 to get the next term. However, there is no indication of a geometric or arithmetic relationship between terms.

Therefore, option C cannot have -286 as its 50th term.

D) P, -326, -324, 322...

Since the sequence starts with P and there is no information given about its value, we cannot determine the specific value of the 50th term.

Therefore, Option D cannot be tested to see if -286 is the 50th term.

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Answer:

The height of the flagpole is approximately 5.774 meters.

Step-by-step explanation:

Let's call the height of the flagpole h. We can use trigonometry to set up the following equation:

tan(30°) = h/10

Simplifying this equation, we get:

h = 10 tan(30°)

Using a calculator, we find that tan(30°) ≈ 0.5774, so:

h ≈ 5.774 meters

Therefore, the height of the flagpole is approximately 5.774 meters.

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The mean of a dataset is the average of the dataset.

The given parameters are:

\(\mathbf{x = 0, 0, 0, 1, 1, 1, 2, 2, 3, 5}\)

(a) Mean and Standard deviation

The mean of the dataset is calculated using:

\(\mathbf{\bar x = \frac{\sum x}{n}}\)

So, we have:

\(\mathbf{\bar x = \frac{0+ 0+ 0+ 1+ 1+ 1+ 2+ 2+ 3+ 5}{10}}\)

\(\mathbf{\bar x = \frac{15}{10}}\)

\(\mathbf{\bar x = 1.5}\)

Hence, the mean is 1.5

The standard deviation is calculated using:

\(\mathbf{\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n - 1}}}}\)

So, we have:

\(\mathbf{\sigma_x = \sqrt{\frac{(0 - 1.5)^2 + (0- 1.5)^2 + (0- 1.5)^2 + (1- 1.5)^2 + (1- 1.5)^2 + (1- 1.5)^2 + (2- 1.5)^2 + (2- 1.5)^2 + (3- 1.5)^2 + (5- 1.5)^2}{10 - 1}}}\)

\(\mathbf{\sigma_x = \sqrt{\frac{22.5}{9}}}\)

\(\mathbf{\sigma_x = \sqrt{2.5}}\)

\(\mathbf{\sigma_x = 1.58}\)

Hence, the standard deviation is 1.58

(b) When 5 is increased to a larger value

When 5 is increased:

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Answer:

1) true

2) false

3) false

4)True

Answer: my name is pro this is the answer

Step-by-step explanation:

2+1= 3

Answer:

x = 24, y = 54

Explanation:

As AE and BC is parallel, angle DAE and ABC is equal.

Hence: x + 19 = y - 11

            x + 19 + 11 = y

            y = x + 30

A Triangle's Interior Angle's sum up to 180°

Hence: 2x + y + y - 11 + x + 11 = 180°

            2x + x + 30 + x + 30 - 11 + x + 11 = 180

            5x + 60 = 180

            5x = 120

              x = 24

Then find y:  x + 30 = 24 + 30 = 54

the answer is 975

Step-by-step explanation:

find out what 1.3% of 2500 then multiply it by 30

The equation in slope-intercept form for the line is y = -3/2x + 5.

We have,

In slope-intercept form,

The equation of a line is written as y = mx + b, where m represents the slope of the line and b represents the y-intercept (the point where the line crosses the y-axis).

Given that the slope is -3/2 and the y-intercept is 5, we can substitute these values into the equation to obtain:

y = -3/2x + 5.

This equation tells us that for every increase of 1 unit in the x-coordinate, the y-coordinate decreases by 3/2 units.

The y-intercept of 5 indicates that the line passes through the point (0, 5).

Thus,

The equation in slope-intercept form for the line is y = -3/2x + 5.

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Answer: 35,000 · 0.87t

Step-by-step explanation: A coefficient is multiplying

The new volume of the air leaving the compressor can be calculated using Boyle's Law, which states that for a fixed amount of gas at a constant temperature, the product of pressure and volume is constant.

According to Boyle's Law,\(P1V1 = P2V2\), where \(P1 and V1\) are the initial pressure and volume, and \(P2 and V2\) are the final pressure and volume, respectively. In this case, we are given the initial volume (V1 = 0.8 cu in) and the initial pressure (P1 = 14.7 psi), as well as the final pressure (P2 = 42 psia).

Using Boyle's Law, we can rearrange the formula to solve for \(V2:\)

\(V2 = (P1 * V1) / P2\)

Plugging in the values, we get:

V2 = (14.7 psi * 0.8 cu in) / 42 psia

Simplifying the equation, we find:

\(V2\) ≈ 0.280 cu in

Therefore, the new volume of the air leaving the compressor is approximately 0.280 cubic inches. It's important to note that this calculation assumes the temperature remains constant throughout the process.

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Answer:

A = 3, 4 B = 2, 6 C = -20, -24 D = 4, 8

Step-by-step explanation:

A is plus 1 B is plus 4 C is -4 and D is +4 :)

Using the Sine-Law, value of c=18.5 units using ∠A= 47° , ∠C=74° and the side a = 14.1 units in the triangle.

What is Sine-Law?

The ratio of the sine of the angle to the length of the opposite side is known as the sine law. About their sides and angles, it applies to all three triangle sides. The triangle's sine rule The sine of angle A is divided by side A in the triangle ABC, which is equal to the sine of angle B divided by side B, which is equal to the sine of angle C divided by side C.

Sine Law:\(\frac{a}{SinA} =\frac{b}{SinB} =\frac{c}{SinC}\)  or  \(\frac{SinA}{a} =\frac{SinB}{b} =\frac{SInC}{c}\)

Given that: ∠A= 47° , ∠C=74° and the side a = 14.1

By taking, \(\frac{a}{SinA} =\frac{c}{SinC}\)

                 \(\frac{14.1}{Sin 47} =\frac{c}{Sin74}\)

                  \(\frac{14.1}{0.731}\)  = \(\frac{c}{0.961}\)

                        c =     \(\frac{14.1}{0.731}\)  × 0.961

                           = 18.536 units

The value of c is 18.536, when rounded off to one decimal place is 18.5 units Option-C.

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The length of the rectangular solar panel the electrician is installing is 25m

The length of the panel is calculated from the Area of the panel which is given by the formula

Ares of rectangle = length * width

given units

area = 180 squared meters

width of the section = 7 1/5

From area = length  * width

length  = are / width

length  = 180 / 7 1/5

length = 25 m

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Answer:

25m

Step-by-step explanation:

25m

Answer:

Statements #5. P(ABCD) = AB + AB + AB + AB

Statements #6. P(ABCD) = 4•AB

Reasons #1. Give

Reasons #2. Def. Congruent Segments

Reasons #3. Transitive Prop. ≅

Reasons #4. Definition of Perimeter

The probability of outcome to be a 5 is 1/13. The probability of outcome not be 5 is 12/13. The probability of outcome to be a diamond or a king is 4/13. The probability of the outcomes to be a jack or a queen is 2/13. The probability of The outcome to be a heart and a club is 0 and the probability of the outcomes to be a card greater than 6 and less than 9 is  2/13.

A deck contains a total of 52 cards.

Total outcomes if the selected number of cards is one=52

Case A:

Each suit contain one 5 numbered card. There are four suits. Therefore, The required outcome would be 4.

Probability of an outcome is the ratio of desired outcomes to the total outcomes.

The probability of outcome to be 5, P(A):
P(A)=4/52

P(A)=1/13

Case B:

The total probability of outcomes=52/52=1

The probability of the outcome to be 5=1/13

Therefore, the probability of the outcome not to be 5, P(B):

P(B)=1-(1/13)

P(B)=12/13

Case C:

Each suit carries a king. Therefore, the probability of the outcome to be a king, P(M):

P(M)=4/52

P(M)=1/13

A suit carries 13 cards. Therefore, there will be 13 cards of diamonds.

The probability of the outcome to be a diamond, P(N):

P(N)=13/52

P(N)=1/4

The probability that the outcome is a king of diamonds, P(M\(\cap\)N):

P(M\(\cap\)N)=1/52

Hence, the probability that the outcome is a diamond or a king, P(M\(\cup\)N):

P(M\(\cup\)N)=P(M)+P(N)-P(M\(\cap\)N)

P(M\(\cup\)N)=(1/13)+(1/4)-(1/52)

P(M\(\cup\)N)=16/52

P(M\(\cup\)N)=4/13

Case D:

Each suit carries a Jack. Therefore, the probability of the outcome to be a jack, P(P):

P(P)=4/52

P(P)=1/13

Each suit carries a Queen. Therefore, the probability of the outcome to be a Queen, P(Q):

P(Q)=4/52

P(Q)=1/13

The probability that the outcome is a jack and a queen, P(P\(\cap\)Q):

P(P\(\cap\)Q)=0/52

P(P\(\cap\)Q)=0

Hence, the probability that the outcome is a jack or a queen, P(P\(\cup\)Q):

P(P\(\cup\)Q)=P(P)+P(Q)-P(P\(\cap\)Q)

P(P\(\cup\)Q)=(1/13)+(1/13)-0

P(P\(\cup\)Q)=2/13

Case E:

A card is never a heart and a club. Therefore, the probability of a card to be a heart and a club is 0.

Case F:

The numbers greater than 6 and less than 9 are the numbers between 6 and 9. The numbers between 6 and 9 are 7 and 8.

Each suit carries one 7 numbered card and one 8 numbered card. There is a total of 4 suits.

Therefore the desirable outcomes=8

The probability of the outcome required=8/52

=2/13

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a. The probability that component A will fail within the guarantee period given that component B has failed already within the guarantee period is 0.2 or 20%.

b. It is likely that around 71 bottles out of the batch of 1500 will contain less than 750 ml.

a. To find the probability that component A will fail within the guarantee period given that component B has already failed, we can use conditional probability.

The probability of component A failing within the guarantee period is 0.2, and the probability of component B failing within the guarantee period is 0.15. Since the components operate independently, we can multiply these probabilities to find the joint probability of both components failing within the guarantee period: P(A and B) = P(A) * P(B) = 0.2 * 0.15 = 0.03.

Now, to find the conditional probability of component A failing given that component B has failed, we use the formula for conditional probability: P(A|B) = P(A and B) / P(B).

Substituting the values we have: P(A|B) = 0.03 / 0.15 = 0.2.

Therefore, the probability that component A will fail within the guarantee period given that component B has already failed within the guarantee period is 0.2 or 20%.

b. To find the number of bottles likely to contain less than 750 ml, we need to convert the given information into a standard normal distribution.

The average volume of the contents is 753 ml, and the standard deviation is 1.8 ml. We can calculate the z-score for 750 ml using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

Calculating the z-score: z = (750 - 753) / 1.8 ≈ -1.667.

Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of -1.667, which is the probability of a bottle containing less than 750 ml.

Looking up the z-score in the standard normal distribution table, we find that the probability is approximately 0.0475.

To find the number of bottles likely to contain less than 750 ml, we multiply the probability by the total number of bottles: 0.0475 * 1500 = 71.25.

Therefore, it is likely that around 71 bottles out of the batch of 1500 will contain less than 750 ml.

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The right triangle, like the other triangles, has three sides, three vertices, and three angles. The difference between the other triangles and the right triangle is that the right triangle has a 90  angle.

To find missing angles and sides and round to the nearest tenth, you can use different methods depending on the given information and the type of triangle or shape involved.

Some common methods include:
Trigonometric ratios (sine, cosine, tangent) for right triangles.
Angle sum property or exterior angle property for triangles.
Pythagorean theorem for right triangles.
Law of cosines and law of sines for non-right triangles.
To help find the missing angles and sides of a triangle, you need certain information about the triangle, such as known angle and side measurements, or information about the properties of the triangle.

Without this information, no concrete calculations can be made.

Provide the necessary information or describe the problem in more detail and we will help you find the missing corners and sides of the triangle and round it to tenths.

Remember to always check if any additional information is given, such as side lengths or angles ' 7 and to apply the appropriate formula or property to find the missing value.

Round your answer to the nearest tenth as specified.

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The minimum sample size needed for 95% confidence that the sample variance is within 5% of the population variance is given by n = (1.96² * σ²) / (0.05²).

The minimum sample size needed to be 95% confident that the sample variance is within 5% of the population variance can be calculated using the formula:

n = (Z² * σ²) / (E²)

where:

n is the minimum sample size,

Z is the z-score corresponding to the desired confidence level (in this case, 95% confidence corresponds to a z-score of approximately 1.96),

σ² is the population variance, and

E is the maximum allowable difference between the sample variance and the population variance (expressed as a proportion of the population variance).

The formula ensures that the desired confidence level is achieved while limiting the difference between the sample and population variances within the specified threshold.

In summary, to determine the minimum sample size needed to be 95% confident that the sample variance is within 5% of the population variance, you can use the formula n = (1.96² * σ²) / (0.05²), where σ² represents the population variance.

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To interpret this line plot with fraction addition and subtraction, we need to understand how to read the plot and how to perform the necessary calculations with fractions.

Looking at the line plot above, we can see that each horizontal line represents one pound, and each vertical line represents one baby's weight. The numbers on the vertical axis show the weights of the babies in pounds. For example, there are two babies that weigh 6 pounds, three babies that weigh 7 pounds, two babies that weigh 8 pounds, and so on. To find the difference in weight between the two heaviest babies, we need to first determine which babies are the heaviest. From the line plot, we can see that the two heaviest babies are the ones at the top of the plot, which both weigh 9 pounds. Converting the weight of the heaviest baby to a fraction with a denominator of 72 gives us 9/1 x 72/72 = 648/72. Converting the weight of the second heaviest baby to a fraction with a denominator of 72 gives us 8/1 x 72/72 = 576/72. Now that both weights are expressed as fractions with a common denominator, we can subtract them to find the difference: 648/72 - 576/72 = 72/72 = 1

Therefore, the difference in weight between the two heaviest babies is 1 pound, or 1/72 of a hundredweight (since there are 100 pounds in a hundredweight). The answer we were asked to provide is a proper fraction, so we can express this as 1/72. In summary, to interpret a line plot with fraction addition and subtraction, we need to understand how to read the plot to determine the weights of the babies, how to perform the necessary calculations with fractions, and how to express our answer as a proper fraction if required.

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The cost of ordering shirts for a club is 268 units.

Define Function.

A function, according to a technical definition, is a relationship between a set of inputs and a set of possible outputs, where each input is connected to precisely one output.

 This means that a function f will map an object x exactly to one object f(x) in the set of possible outputs if the object x is in the set of inputs (called the codomain).

The statement that f is a function from X to Y using the function notation f: X→Y

The function that represents the cost of the shirts(x) is f(x) = 8x+12

Now, for x = 32

 f(x) = 8x+12

f(32) = 8(32) + 12

        = 256 +12

f(32) = 268 units

.

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Answer:

Step-by-step explanation:

2 subtraction symbols equals a plus

so the answer is 9