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Create your own puzzle problem similar to the problem at the beginning of the lesson. Post your original puzzle on the discussion board.

Original problem: The sum of three numbers is 12. The sum of the first number and the second number is 2 more than the third number. The second number minus the sum of the first number and third number is twice the third number.

The solutions to the equations are;

(-3, 8) and (34/10, 156/16)

1) We can see that;

2x+y=2  ---- (1)

5x+3y =  9 ----- (2)

Multiply (1) by 5 and (2) by (2)

10x + 5y = 10 --- (3)

10x + 6y = 18 ----- (4)

Subtract 3 from 4

y = 8

Now substitute y =8 in (1)

2x + 8 = 2

x = 2 - 8/2

x = -3

Solution is; (-3, 8)

For question 2;

5x - 2y = -2 ---- (1)

3x + 4y =  30 ---- (2)

Multiply 1 by 3 and 2 by 5

15x - 6y = -6 ---- (3)

15x + 20y = 150 ----- (4)

Subtract (3) from (4)

16y = 156

y = 156/16

5x - 2(156/16) = -2

5x - 156/8 = -2

5x = -2 + 156/8

x = 34/10

Solution; (34/10, 156/16)

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The graph of the inequality is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y < -1/2x + 4 1/2

3x - 4y ≥ 12

The above expressions are linear inequality

Next, we plot the graph

See attachment for the graph of the inequality

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The required number Justin could have bought 1 pair of jeans and 3 t-shirts.

If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

Let's assume Justin bought x pairs of jeans and y t-shirts.

We know that the cost of each pair of jeans is $40 and the cost of each t-shirt is $20.

So, the total cost of Justin's purchase can be represented as:

Total cost = 40x + 20y

We also know that Justin bought a total of 4 items. So:

x + y = 4

Now we can use these two equations to solve for x and y:

40x + 20y = 100 (divide both sides by 20)

2x + y = 5 (subtract x from both sides)

Now we have two equations with two variables. We can solve for y in the second equation:

y = 5 - 2x

And substitute this into the first equation:

40x + 20(5-2x) = 100

Simplifying, we get:

40x + 100 - 40x = 100

100 = 100

This equation is true for any value of x and y that satisfy the condition x + y = 4.

So, Justin could have bought 1 pair of jeans and 3 t-shirts.

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This is exponential growth

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

Explanation:

The exponential rule we need is:  a^(b*c) = (a^b)^c

Apply that rule and do a bit of rearranging:

y = 2(1.06)^(9t)

y = 2( (1.06)^9 )^t

y = 2( 1.68948 )^t

y = 2( 1 + 0.68948 )^t

y = 2( 1 + 0.69 )^t

The last equation fits the format of  y = a(1+r)^t  which tells us that...

Since r is positive, we have exponential growth. If r was negative, then we'd have exponential decay.

The temperature in Helena at 6 a.m. the next morning is 24∘C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

The temperature in Helena, MT was 0∘C at 6 a.m. on Tuesday morning.

The temperature rose at a rate of 78∘C per hour for 12 hours, then fell at a rate of 76∘C per hour for 12 hours.

Now,

Temperature first after 12 hours= 78*12=936

Temperature second after 12 hours= 76*12=912

=936-912

=24

Therefore, the answer will be 24∘C.

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The number of chocolates in the jar is given by the equation n = 21 chocolates

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 equation be represented as A

Let the number of chocolates be n

Substituting the values in the equation , we get

The number of strawberries in the jar = 18

The number of cherries in the jar = 24

The number of lime candies in the jar = 19

The total number of candies in the jar = 82 candies

So , the equation will be

Number of strawberries in the jar + number of cherries in the jar + number of candies in the jar + number of chocolates = 82

Substituting the values in the equation , we get

18 + 24 + 19 + n = 82

On simplifying the equation , we get

n + 61 = 82

Subtracting 61 on both sides of the equation , we get

n = 21 chocolates

Hence , the equation is n = 21 chocolates

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The required ratio of trombones to all the brass section members is 3 : 7.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Here,
The total number of members in the brass section of the jazz band is:

4 trumpets + 3 trombones = 7 members

The ratio of trombones to all the brass section members can be expressed as,

= 3 trombones / 7 brass section members

This ratio cannot be simplified further because the numbers are relatively prime.

Therefore, the ratio of trombones to all the brass section members is 3 : 7.

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240 gallons of a 50% antifreeze solution must be mixed with 80 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

Let's call the amount of 50% antifreeze solution that we want to mix with the 80 gallons of 10% antifreeze "x".

The total volume of the mixture after mixing x gallons of 50% antifreeze solution with 80 gallons of 10% antifreeze solution is given by (x + 80) gallons.

The concentration of antifreeze in the mixture is given by the weighted average of the antifreeze concentrations in the two solutions, where the weight for each solution is proportional to its volume:

(0.5x) + (0.1 * 80) = (0.4 * (x + 80))

Expanding and solving for x, we get:

0.5x + 8 = 0.4x + 32

0.1x = 24

x = 240

Therefore, we need to mix 240 gallons of 50% antifreeze solution with 80 gallons of 10% antifreeze solution to get a mixture that is 40% antifreeze.

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If a data set has an outlier, the median would be the best measure of central tendency to use as it is less sensitive to extreme values compared to the mean.

The presence of an outlier can heavily skew the mean in the direction of the outlier, causing it to become an inaccurate representation of the center of the data. On the other side, the median is less sensitive to extreme values and represents the middle value of the dataset. It is calculated by finding the middle value in a dataset after arranging it in numerical order.

Therefore using the median as the measure of central tendency in a dataset with an outlier can provide a better indication of the typical value compared to the mean.

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The acceleration due to gravity of a falling object is +9.8 m/s²

The acceleration an object experiences as a result of gravitational force is known as acceleration due to gravity. m/s² is its SI unit. Its nature which includes both magnitude and direction—makes it a vector quantity.

Given:

A linear expression we have

y= k x,

Here, Variation's constant is constant, or k.

The acceleration caused by gravity is stated to be the variational constant in the statement.

So, the linear expression becomes

y = g x, where g is a proportionality constant.

Now, Work is not done against gravity since an object falling downwards accelerates due to gravity at a rate of +9.8 m/s².

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The option that does not describe the Line GE is; B: Centroid

A triangle has three sides, three angles, and three vertices.

The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.

The sum of the length of any two sides of a triangle is greater than the length of the third side.

The point in which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all the three medians.

In this case, we see that the line GE divides DF into two equal parts and as such we can call this the median, perpendicular bisector or even angular bisector because it divides angle e into 2 equal angles for specific values of y.

Thus, this line cannot be the centroid

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Answer:

If the repayment period is the same length for both loans, the interest option that will result in the least amount of interest added to the loan is B. Option A will have the least amount of interest because simple interest generates earnings from principal only.

What is the simple interest?

The simple interest is the interest system that does not compute interest on accumulated interest.

Unlike simple interest, compound interest charges interest on accumulated interest.

Thus, the simple interest system applies the interest rate on the principal only for each period to determine the amount of interest.

Step-by-step explanation:

Have a nice day

Since it's a rhombus, the the diagonal intersection point is the middle point, so the diagonal should be

d1=5x2=10cm

d2=2x2=4cm

area=(d1xd2)/2=(10x4)/2=20cm^2

Median would be a better measure of central tendency to use in the employees perspective, the mean of data set is 12.5 and median is 10, and

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Let us find the mean and median of the given data set {11,6,32,7,18,4,9,1,15,9,5,27}.

To find mean, we add up all the numbers and divide by the total number of numbers:

(11 + 6 + 32 + 7 + 18 + 4 + 9 + 1 + 15 + 9 + 5 + 27) / 12 = 12.5

So the mean number of years of employment is 12.5.

To find the median, we first need to put the numbers in order:

1, 4, 5, 6, 7, 9, 9, 11, 15, 18, 27, 32

Since there are 12 numbers, the median is the average of the middle two numbers, which are 9 and 11.

So the median is (9 + 11) / 2 = 10.

The median would be a better measure of central tendency to use, because it is less sensitive to extreme values than the mean

Hence, the mean of data set is 12.5 and median is 10, and median would be a better measure of central tendency to use in the employees perspective.

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The angle is 144°.

In planar geometry, an angle is a shape made up of two rays or lines that share an endpoint. The English word "angle" derives from the Latin word "angulus," which means "corner." The vertex and the two rays are referred to as the sides of an angle, respectively, and are the shared termini of two rays. A shared terminal between two rays (half-lines) is joined to create an angle. The latter is referred to as the angle's vertex, and the rays are sometimes referred to as the angle's legs and other times as its arms.

Thus;

∠AOC + ∠COD + ∠BOD = 180°

Since AOB is a straight line:

⇒3x-10+50+x+20=180

⇒4x = 120°

⇒x = 30°

Thus, ∠AOC = 3x - 18

∠AOC = 3 × 30° - 18

∠AOC = 72°

2(72) = 144°

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The missing numbers for the respective rows are:

row 1: 4/5

row 2: -4/5 and -2/5

row 3: -3/5 and 6/5

Missing number for row 1(top row):

1 - 1/5 = 4/5

Missing number for row 2 (2nd number for last column):

3/5 - 1 = -2/5

Missing number for row 2 (1st number for first column):

-2/5 - 2/5 = -4/5

Missing number for row 3 (1st number for first column):

1/5 + (-4/5) = -3/5

Missing number for row 3 (2nd number for second column):

4/5 + 2/5 = 6/5

Therefore, row 1 have the missing number; 4/5. Row 2 missing numbers from left; -4/5 and -2/5. Row 3 missing number from left; -3/5 and 6/5

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Possible question:

If the sum of the first two numbers in row 1 is equal to 1 and the sum of the first two in last column to the right is equal to 3/5. Find the missing numbers.

Prove by contradiction that in a right triangle with integer sides, the two shorter sides cannot both be odd.

Assume that the two shorter sides, a and b, of a right triangle are both odd integers. Then the hypotenuse, c, must also be an integer. From the Pythagorean theorem, we know that c2 = a2 + b2. We can rewrite this as c2 = (2m + 1)2 + (2n + 1)2, where m and n are integers. We can expand the left-hand side of the equation to get c2 = 4m2 + 4n2 + 4m + 4n + 1. Since c2 is an even integer, 4m2 + 4n2 must be an even integer as well. But, since 4m + 4n + 1 is odd, the only way to make the left-hand side of the equation an even integer is if 4m2 + 4n2 is an odd integer, which is impossible.

Therefore, our initial assumption that a and b are both odd integers is false. Thus, in a right triangle with integer sides, the two shorter sides cannot both be odd.

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The valid inferences are (a) and (c)

From the data in the table, we can make the following valid inferences:

Using the above as a guide, we have the following:

Other inferences are invalid

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The correct answer is: 2.8 is greater than 2.58.

A decimal value is a number expressed in the decimal system, which is based on the number ten. It includes a decimal point that separates the whole number part from the fractional part. The digits to the left of the decimal point represent whole numbers, and the digits to the right of the decimal point represent fractional parts of a whole number, which are expressed in powers of ten (tenths, hundredths, thousandths, etc.). For example, in the decimal value 3.14, the digit 3 represents the whole number part, and the digits 1 and 4 represent the tenths and hundredths parts, respectively. Decimal values are commonly used in mathematics, science, and everyday life to represent quantities that are not whole numbers, such as measurements, percentages, and money values.

Given by the question.

because the digit in the tenths place is larger in 2.8 than in 2.58. In decimal notation, the digit immediately to the right of the decimal point represents tenths, and larger values in this place indicate a larger overall value. In this case, 2.8 has a digit of 8 in the tenths place, while 2.58 has a digit of 5 in the tenths place. Therefore, 2.8 is greater than 2.58. The location of the numbers on a number line is not relevant for comparing decimal values, unless they have the same digit in the tenths.

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The fraction of water Libby drinks is 1 6/8 more liters of water than Jack.

In mathematics, a fraction is represented by a numerical value that designates a portion of an entire. A fraction is a piece or section of a whole, where the whole can be any number, a particular value, or an object. Let's use an example to better comprehend this idea. A pizza cut into 8 equal pieces is depicted in the following diagram. Now, to describe a single portion of the pizza, we may use the notation 1/8, which indicates that, out of 8 equally sized portions, we are speaking of one portion.

Given that, Libby drinks 2 7/8 liters of water.

Coverting the mixed fraction into improper fraction:

2 7/8 = 2(8) + 7/ 8 = 23/8

Jack drinks 1 1/8 liters of water.

Coverting the mixed fraction into improper fraction:

1 1/8 = 8 + 1/8 = 9/8

The difference between is:

D = 23/8 - 9/8 = 14/8

14/8 = 1 6/8

Hence, Libby drinks 1 6/8 more liters of water than Jack.

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The height of the  building which casts a 103-foot shadow is 95.5 foot.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34.5-foot shadow

We need to find the height of the building.

Let us consider x be the height of building.

Form a proportional equation.

x/103=32/34.5

Apply cross multiplication

34.5x=32×103

34.5x=3296

Divide both sides by 34.5

x=3296/34.5

x=95.5

Hence, 95.5 foot be the height of the  building which casts a 103-foot shadow.

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(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R'  is 1/2

(B) Coordinates of Δ P"Q"R"

P" (-4,0)

Q"(-3,1)

R"(1,-2)

(C) Triangles PQR and P"Q"R" are not congruent.

Given

ΔPQR is transformed into ΔP'Q'R'

Coordinates of P, Q, R are

P (8,0),

Q(6,2)

R(-2,-4)

Coordinates of P'Q'R' are

P′(4, 0)

Q′(3, 1)

R′(−1, −2)

(A) By Distance formula we can find the distance between P Q and P'Q'

Distance formula = [tex]D = \sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]

Where D = Distance between two points

from distance formula we can write that

PQ = [tex]\sqrt{(6-8)^{2} +(2-0)^{2} } = \sqrt{4+4} =2 \sqrt{2}[/tex]

Similarly

P'Q'= √2

PQ /P'Q' = 2

hence the scale factor of dilation is 1/2 (Compression)

(B )The Coordinates of Reflection about y axis can be written for a point

(x,y) as (-x,y)

So the Coordinated of Δ P"Q"R" can be written as

P" (-4,0)

Q"(-3,1)

R"(1,-2)

(C) ΔPQR  and ΔP"Q"R" are similar triangles but they are not  congruent because their sides  are not equal in size.

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The result is (x + 8).

Polynomial is an equation written with terms of the form kx^n.

where k and n are positive integers.

There are quadratic polynomials and cubic polynomials.

Example:

2x³ + 4x² + 4x + 9 is a cubic polynomial.

4x² + 7x + 8 is a quadratic polynomial.

We have,

x² + 12x + 32 and g(x) = x + 4.

Now,

(f/g)(x)

= (x² + 12x + 32) / (x + 4) _____(1)

Now,

We can factorize x² + 12x + 32.

x² + 12x + 32

= x² + (8 + 4)x + 32

= x² + 8x + 4x + 32

= x(x + 8) + 4(x + 8)

= (x + 4) (x + 8) ______(2)

From (1) and (2),

(f/g)(x)

= (x² + 12x + 32) / (x + 4)

=  (x + 4) (x + 8) / (x + 4)

= x + 8

Thus,

The result is (x + 8).

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Answer:!(I think)! the answer might be 0

Step-by-step explanation:

6( 2 - 6o) = -24

6 times (2 - 6o) = -24

Answer:

x=1

Step-by-step explanation:

open bracket

12-36x=-24

-36x=-24-12

-36x=-36

divide both sides by -36

x=1

Answer:

1) Wendy

2) Paige

3) 15%

4) 27%

5) Wendy and Vanessa

Step-by-step explanation:

Wendy 29%

Vanessa 21%

Oliver x

Mike 14%

Luke 12%

Paige 9%

Total 100%

First, let's find Oliver's percentage.

29 + 21 + x + 14 + 12 + 9 = 100

x = 15

Now we have:

Wendy 29%

Vanessa 21%

Oliver 15%

Mike 14%

Luke 12%

Paige 9%

Total 100%

1) Wendy

2) Paige

3) 15%

4) 12% + 15% = 27%

5) 29% + 21% = 50%: Wendy and Vanessa

It will cost $2353.05 to pour concrete for the entire driveway

From the question, we have the following parameters that can be used in our computation:

Dimension = 15 3/4 yards by 3 yards.

Concrete costs $49.80 per square yar

The cost is calculated as

Total = Area * Cost

So, we have

Total = (15 3/4 * 3) * 49.8

Evaluate

Total = 2353.05

Hence, the cost is $2353.05

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The probability of obtaining a z-value less than 1.5 is 0.8531 or 85.31% using normal distribution table.

The probability of obtaining a z-value less than 1.5 can be calculated using the standard normal distribution table or by using software like Excel or statistical calculators.

The standard normal distribution is a probability distribution with a mean of zero and a standard deviation of one. It is denoted by the letter Z and is used to standardize normal random variables. The standard normal distribution table provides the probabilities for different values of Z, ranging from -3.4 to 3.4.

To find the probability of obtaining a z-value less than 1.5, we need to look up the value of 1.5 in the standard normal distribution table. The table provides the area under the standard normal curve to the left of a given Z-value.

Looking at the table, we find that the probability of obtaining a z-value less than 1.5 is 0.8531, which means that approximately 85.31% of the area under the standard normal curve is to the left of 1.5.

This means that if we have a normally distributed variable with a mean of zero and a standard deviation of one, there is a 85.31% chance that the z-value will be less than 1.5.

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The value that should go on the flyer from the environmental group can be found to be 60, 000 m ².

The reason why the building developer chose a different unit from the environmental group is to try to understate the amount of land they would be building on.

The conversion factor for square kilometers and meters squared is :

1 km ² = 100, 000 m²

0. 06 km ² would then be :

= 0. 6 x 100, 000

= 60, 000 m ²

The building developer chose to use square kilometers to make it seem as though the amount of land they were using was little so as not to have people being angry with the amount of land they would use. The environmental group chose meters squared for the opposite effect to make it seem like a lot of land was to be used.

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Answer:

1.5748 in

Step-by-step explanation:

Answer:

1 inch = 2.54 cm

4 / 2.54 = 1.5748031496 inches

Step-by-step explanation: