2. The table shown below shows some values for functions f(x) and g(x). What is/are the solution(s)
when f(x) = g(x)? Explain your answer

The triangles are congruent by ASA theorem.

Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal. In other words, congruent triangles are triangles that have the same size and shape.

Therefore, If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent by ASA(angle side angle).

Therefore, the triangle are congruent by ASA(angle side angle)

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The distribution of z-scores would be a normal distribution centered at 0, with a standard deviation of 1.

The distribution of time it takes for people to solve a certain Sudoku puzzle is strongly skewed to the right. This means that most people take a shorter amount of time to solve the puzzle, but some take a longer amount of time. The mean (average) of this distribution is 30 minutes and the standard deviation is 15 minutes.

To find the distribution of z-scores, we need to convert the times into z-scores, which is done by subtracting the mean (30) from each time and then dividing by the standard deviation (15). This gives us a new distribution of z-scores, which is centered at 0 (since the mean of the times was subtracted from each time) and has a standard deviation of 1.

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From the given numbers ,The order from largest to smallest is 105,100,7.6,5.6,4.9,0.51,0.001

What is Descending order?

Descending order can be defined in such a way that the order is from largest to smallest.

Given numbers are ,

0.51 , 7.6 , 10^2 , 5.6 , 105 , 4.9 , 10^-3

10^2 = 10*10 = 100 .

so a^m = a multiplied by m times .

a^-m = 1/ a^m.

10^-3 = 1/1000 = 0.001

So,

We have to write from largest to smallest

we get,

105,100,7.6,5.6,4.9,0.51,0.001

Hence, From the given numbers ,The order from largest to smallest is 105,100,7.6,5.6,4.9,0.51,0.001

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Answer:

5.35%

Step-by-step explanation:

3 month 5.25%

So 4 times a year

(1+5.25%/4)^4 = 1.0535

So effective rate is 5.35%

Step-by-step explanation:

2/2

23/23

749876/749876

...

you did not show us any fractions to select.

a fraction is always 1, when the value on the top is the same value as on the bottom.

The minimum distance from the giant pumpkin is 8.9 yards.

We will use the minimum distance formula between a line and a point to obtain the distance in this case.

A linear function is given according to the standard notation  by:

Ax+By+C=0

A point with 'x' and 'y' coordinates are given by:

P(x*,y*)

The formula to find the shortest distance between a point and a line is denoted by the formula:

d=|Ax*+By*+C|/√(A²+B²)

In this issue, the path's line includes:

When x = 0, and y = 0, the intercept is 0.

0.5 slope means that when x rises by 4, y rises by 2.

Thus, y=1/2x

-1/2x+y=0

or, -x+2y=0

The coefficients of the line are:

A=-1 and B=2

Coordinates of the giant pumpkin is (x*,y*)=(-4,-3)

Therefore, the minimum distance is:

d=|(-1)(-4)+2(-3)|/√5

or,d=2/√5

or, d=0.89 units

We know, 1 unit=10 yards

or, 0.89 units=8.9 yards

Thus, the minimum distance between a point and a line is 8.9 yards.

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The reason studying the rainfall on the first day of September, October, and  November is not a random sample is: These are three consecutive months.

Random sample can be defined as the type of  sample in which some number of people  or group of people are choose from a large population when conducting a test.

The reason why studying the rainfall on the first day of September, October, and  November is not a random sample was because the September, October and November are  three consecutive months.

Based on this the sample should be spread out  to the entire year and should include more than three months.

Therefore these are three consecutive months.

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Answer: 12/4

Step-by-step explanation: 12/4 = 3/1 = 3

The length of sides in congruent triangles are MN=30, MP=18, PN=30

QR=30, RS=30,  SQ=18

In the diagram two congruent triangles are given ΔPMN ≅ ΔQSR.

So by CPCTC (corresponding parts of congruent triangles are congruent)

In ΔPMN and ΔQSR

PN=QR=30 in.

PM=SQ=18 in.

MN=RS= 30 in.

PN=QR=30 then PN=30

PM=SQ =18 then PM=18

MN=RS =30 then MN=30

Congruent triangles are the triangles of which all the sides and all the angles are congruent.

If two triangles are said to be congruent then its all corresponding parts must be equal.

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The amount of hardwood floor that Jahidel waxed is 3 8/9 yards²

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of hardwood floor that Jahidel waxed be A

Now , the equation will be

The total area of the hardwood floor is = 4 3/8 yards²

The total area of the hardwood floor is = 35/8 yards²

The amount of floor waxed by Jahidel A = ( 8/9 ) x total area of the hardwood floor

Substituting the values in the equation , we get

The amount of floor waxed by Jahidel A = ( 8/9 ) x ( 35/8 ) yards²

On simplifying the equation , we get

The amount of floor waxed by Jahidel A = ( 35/9 ) yards²

The amount of floor waxed by Jahidel A = 3 8/9 yards²

Hence , the amount of floor waxed is 3 8/9 yards²

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The answer for lateral surface area of the Triangular prism is 180 cm²

Any solid object's lateral area can be calculated using the lateral area formula. Any figure's lateral area only includes the non-base faces. Calculating the lateral surface area of various forms, such as the cuboid, cube, cylinder, cone, and sphere, is made easier using lateral area formulas.

The lateral area for a triangular prism

A triangular prism's lateral area is equal to the sum of its side faces' areas (which are 3 rectangles). Specifically, it is the total surface area less the surface areas of the two bases. Additionally called the lateral surface area (LSA). Due to the two dimensions involved in its calculation, we measure it in square units.

The total of the three regions is the triangular prism's lateral area. Consequently, the triangular prism's lateral area formula is

Triangular prism lateral surface area (LSA) = ah + bh + ch (or) (a + b + c) h.

We are aware that the perimeter of the base is (a + b + c) (triangle). Hence,

Triangular prism's lateral surface area (LSA) is equal to the product of the base's perimeter and the prism's height.

base perimeter × height

Explanation

The Given Image of the solid is Matching to a prism.so we are calculating the lateral surface area of the prism

The dimensions of each base are:

a = 5cm

b = 4 cm

c = 3 cm

The height of the triangular prism = 15cm.

Thus, the lateral area of triangular prism = (a + b + c ) h

= (5 + 4 + 3) 15

= (12) 15

= 180 cm²

Answer: The lateral area of the given triangular prism = 180 cm²

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The direction vector from the point (-4,8,7) to the point (6,5,5) is (10, -3, -2). The equations which represent the line are: 1. True 2. True 3. False 4. True 5. False.

The direction vector for the line that passes through the two points A (-4,8,7) and B (6,5,5), the position vector of point A is subtracted from the position vector of point B, hence:

v = AB = (6 –(-4), 5 – 8, 5 – 7) = (10, -3, -2)

The vector equation of the line is given by:

r = r0 + tv

where r0 is position vector, t is a scalar parameter, and v is position vector.

Considering the vector equation, the equation which represents the line are:

1. (x,y,z) = (-4,8,7) + t (-10,+3,+2); True

2. (x,y,z) = (6,5,5) + t (10,-3,-2); True

3. (x,y,z) = (-4,8,7) + t (6,5,5); False

4. (x,y,z) = (-4,8,7) + t (10,-3,-2); True

5. (x,y,z) = (6,5,5) + t (-4,8,7); False

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If the proportion of people from the population who read a novel in the past year is 0.40, then a binomial variable with 25 independent trials is the best interpretation of random variable R. So the option 2 is correct.

If the proportion of people from the population who read a novel in the past year is 0.40, then we have define which of the following is the best interpretation of random variable R.

The variance of random variable R is 6.

The variance of binomial distribution is:

var = np(1-p)

n = number of trials

p = the probability

6 = n × 0.40 × (1-0.40)

6 = n × 0.40 × 0.60

6 = n × 0.24

Divide by 0.24 on both side, we get

n = 25

The number of binomial trails is 25.

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The complete question is:

A random sample of n people selected from a large population will be asked whether they have read a novel in the past year. Let the random variable R represent the number of people from the sample who answer yes. The variance of random variable R is 6. Assume the responses are independent of each other. If the proportion of people from the population who read a novel in the past year is 0.40, which of the following is the best interpretation of random variable R ?

1. A binomial variable with 15 independent trials

2. A binomial variable with 25 independent trials

3. A variable that is not binomial with 25 independent trials

4. A binomial variable with 40 independent trials

5. A variable that is not binomial with 40 independent trials

Answer:

In a right triangle, the angle opposite the hypotenuse (side c) is always 90 degrees, so we can use the trigonometric function sine to find the length of side c.

sin(A) = opposite / hypotenuse

sin(50) = b / c

so c = b / sin(50)

c = 13 m / sin(50)

c ≈ 22.361 m

So the length of side c is approximately 22.361 meters

Answer:

$6.50

Step-by-step explanation:

So writing out everything

1 Pizza = $17.50

1 soda = $1.25

1 salad = $1.75

Exception; Salad is buy 1 get 1 free, so only 2 salads were paid for

Now we multiple

1 Pizza * 17.50 = 17.50

4 soda * 1.25 = 5

2 salad * 1.75 = 3.50

Now we add

17.50 + 5 = 22.50 + 3.50 = $26.00

Now lastly, we divide by 4 since there are 4 friends

26/4 = 6.5

Giving us a answer of $6.50

Classes           Frequency

0-4                7

5-9                5

10-14              2

15-19              4

20-24              1

The frequency of each class is determined by counting the number of waiting times that fall within each range. For example, the class 0-4 has a frequency of 7, meaning 7 customers waited between 0 to 4 minutes for their oil change.

The number of times a specific value appears in the data is its frequency (f). A variable's distribution is its frequency pattern, or the collection of all conceivable values and the frequencies corresponding to those values.

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HE hundred digit less than the tens digit ,the tens digit is has to 9 .This is because of 9is the only positive integer less than 10 and only it also greater than 8 in one digit numbers. result when 8 is subtracted from it.

When you have an optimistic outlook on life, you have optimism and confidence and focus more on the positives than the negatives.

Be optimistic about the future and carry on with your normal life.

A positive person chooses to focus on the positive aspects of their life, finds delight in the little things, and adopts the mindset that while there are many things outside of their direct control, they can select what they choose to give their attention to.

According to one idea, having a positive outlook makes it easier for you to handle stressful situations, which lessens the negative consequences of stress on your body's health.

we already know that ones digit is 5 less than the tens digit, so it is 9-5=4,and the hundreds digital has to be 1, so the answer is 194.

so, let we can solve it as by the problem,

by the problem

units will be considered as a x

ok

x greater than or equal 9

tens digit digit is more than 5 units

we know that,

so, tens digit value is 9

hundreds digit value is 1

let we find ones digit value x+5<=9

x<=4

hundreds digit is less than

x+5

x+5-8>=0

x-3>=0

x>=3

>3=4

thus the x is 4

then the number is 194

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The translation of point A to point B is done by translation vector (- 3, - 6).

In this problem we find the a point that is part of a rectangle and that must be translated by means of a rigid transformation formula, that is, a translation formula that does not alter the features of the rectangle. We need to determine the translation vector by means of the following formula:

T(x, y) = B(x, y)  - A(x, y)

Where:

If we know that A(x, y) = (6, 9) and B(x, y) = (3, 3), then the translation vector is:

T(x, y) = (3, 3) - (6, 9)

T(x, y) = (- 3, - 6)

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According to the figure the two triangles congruency state cannot be determined

Triangles are considered congruent when their sides and angles match those specified by the triangle congruency rules.

The triangle congruency rules.

Side - Side - Side = SSS.

Angle - Side - Side = SAS

Side - Angle - Angle = ASA

Angle, Angle, and Side = AAS

Hypotenuse plus one leg = HL

To demonstrate that the triangles are congruent, the is need for three parameters to be known except for right triangle

In the problem, only two parameters can be deduced the side and the angle equal by vertical angle theorem

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The number of dimes more than nickels in the jar is 17.

The first step is to determine the total number of coins in the jar.

Total number of coins in the jar = (sum of ratios x number of quarters) / ratio that represents the number of quarters

Sum of ratios = 2 + 3 + 5 = 10

Total number of coins in the jar = (10 x 85) / 5 = 170

Number of dimes in excess of nickels = [(ratio representing dimes - ratio representing quarters) / sum of ratios) x total number coins

[(3 - 2) / 10] x 170

(1/10) x 170 = 17

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The number of tens that he regrouped as ones is equal to 2 tens.

The number of books that are on each shelf is equal to 66 books.

In Mathematics, a quotient simply refers to a mathematical expression that is typically used for the representation of the division of a number by another number.

Based on the information provided above, the number of books on each shelf is given by this quotient:

Quotient = 264/4

Quotient = 66

For the number of tens that Mr. Kent regrouped as ones on the shelf, we have the following:

26/4 = 24/4 + 2 = 2 tens.

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Answer:

114 cents

Step-by-step explanation:

1. 66÷22=3 cents per inch

2. 3×38=114

3. 114 cents ($1.14) for 38 inches

In the triangle, we will use the Law of Cosines to find the value of angle q. angle q in the triangle is approximately 61.2° (rounded to one decimal place).

The Law of Cosines is a mathematical formula used in trigonometry to find the length of a side or an angle in a triangle.

The formula can be used to find the length of a side or an angle in a triangle, given the length of the other sides and angles.

The Law of Cosines is particularly useful when only two sides and the angle between them are known, or when only two angles and the side between them are known.

To use the Law of Cosines, you need to identify the sides and angles that you know and plug them into the formula. Then, you can use algebra to solve for the unknown side or angle.

The Law of Cosines is related to the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side.

The Law of Cosines can also be used in three-dimensional geometry to find the distance between two points in space.

The Law of Cosines is a useful tool in many fields, including engineering, physics, and computer graphics, and is widely used in solving geometric problems.

In this triangle, we have x = 66.1 cm, y = 22.8 cm, and angle f = 23.3º. We want to find angle q, which is opposite side x.

We can use the Law of Cosines to find the value of cos(q), and then use the inverse cosine function to find the value of q in degrees.

cos(q) = (x² + y² - x²)/(2xy)

cos(q) = (66.1² + 22.8² - 22.8²)/(2 * 66.1 * 22.8)

cos(q) = 67.8664/150.6448

cos(q) = 0.449

q = cos⁻¹(0.449)

q = 61.2°

Therefore, angle q in the triangle is approximately 61.2° (rounded to one decimal place).

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If there are 4 boys and 4 girls , then the number of ways in which

(i) there is no restriction is 40320 ways  ,

(ii) not all girls sit together is 37440 ways  ,

(iii) no two girls sit together is 2880 ways  .

the number of boys in the class is =  4 boys ;

the number of girls in the class is = 4 girls ;

Part(i) ,

we have to find number of ways in which they can sit in a row where there is no restriction .

there are total of 8 persons ,

So ,the number of ways in which 8 persons can be arranged without any restrictions is = 8! ways.

= 40320 ways

Part(ii) ,

we have to find number of ways in which they can sit in a row where not all girls sit together.

the cases where all gets sit together is written as :

= B₁ , B₂ , B₃ , B₄ , G ⇒ 5! ways ;

= B: G₁ , G₂ , G₃ , G₄ ⇒ 4! ways ;

the number of ways all girls are together is = 5! × 4! ;

So , the number of ways not all girls are together is = 8! - 5!×4!  ;

= 37440 ways

Part(iii) ,

we have to find number of ways in which they can sit in a row where no two girls sit together.

this case can be denoted as : G , B₁ , G , B₂ , G , B₃ , G , B₄ .

So , the boys can be arranged in 4! ways ;

and there will be 5 places for 4 girls , which can be arranged in ⁵P₄ ways ;

total number of ways is = 5!×4! =  2880 ways .

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Answer:

[z+(-1( z-x))]

given,

z=5 X=4

[5+(-1(5-4))]

[5+(-1x(1))]

5+(-1)

5-1

4

This means x = 5a pairs up with y = 0.

=========================================================

Explanation:

The two lines have the same x-intercept, which means they cross the x axis at the same location. This is the solution to the system since this point is on both lines simultaneously.

To find the x-intercept, plug in y = 0 and solve for x.

(1/5)x+4y = a

(1/5)x+4*0 = a

(1/5)x = a

x = 5a

We don't know the value of 'a', so we cannot determine the numeric value of x.

The x-intercept is located at (x,y) = (5a,0) and this is the solution to the system.

Answer:

  75 minutes

Step-by-step explanation:

You want to know when both buses will be at the stop again if bus A arrives every 25 minutes, and bus B arrives every 15 minutes.

The number of minutes until both buses are at the stop again is the least common multiple (LCM) of their arrival times.

Factors of the times are ...

  25 = 5·5

  15 = 3·5

A common multiple must have all of these factors, so will have factors ...

  LCM = 3·5·5 = 75

After 75 minutes, both buses will be at the stop again.

__

Additional comment

You can see that 5 is a common factor of the two numbers. The LCM can also be found as the product of the two numbers, divided by their greatest common factor (GCF).

  LCM(a, b) = a·b/GCF(a, b)

  LCM(15, 25) = 15·25/5 = 75

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The value of x is -20 and can be calculated using basic proportionality theorem.

The Basic Proportionality Theorem, often known as the Thales Theorem, was developed by the well-known Greek mathematician Thales.

Basic Proportionality Theorem asserted that the ratio of any two related sides is always the same for any two equiangular triangles.

Thales provided the basic proportionality theorem based on this idea (BPT). Similar triangles have introduced this idea before. If two triangles resemble one another, then

The corresponding angles of both triangles are equal.

The corresponding sides of both triangles are proportional to one another.

Since the ratio of other side pair is 1:1, similarly 4x+20 = 3x

20 = 3x-4x

20 = -x

x = -20

Therefore, the value of x is -20

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The values of x and y that makes the figure a parallelogram are x = 17 and y = 26

A parallelogram is a four-sided geometric shape that has opposite sides that are parallel to each other.

The opposite sides of a parallelogram have the same length, and the opposite angles are also equal. The opposite sides of a parallelogram are also known as the bases, and the other two sides are known as the legs.

Since the opposite sides of a parallelogram are equal in length, we can say:

3x + 6 = 4 - x

3x + x = 4 - 6

4x = -2

x = -2/4

x = -1/2 = -0.5

y + 2 = 2y - 3

2 + 3 = 2y - y

5 = y

y = 5

Likewise, the opposite angles of a parallelogram are equal, so we can say:

(4x - 12)° = (3x + 5)°

4x - 12 = 3x + 5

4x - 3x = 5 + 12

x = 17

(3y + 46)° = (5y - 6)°

3y + 46 = 5y - 6

46 + 6 = 5y - 3y

52 = 2y

2y = 52

y = 52/2

y = 26

Thus, x = 17 and y = 26 makes the figure a parallelogram

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