how do you know that 8:12 is equivalent to 4:6

The probability is approximately 0.8185 or 81.85%.

Normal distribution, also known as Gaussian distribution, is a probability distribution that is commonly used in statistics, mathematics, and the natural sciences to describe real-valued random variables whose distributions are not known.

To find the probability that a randomly selected x-value from a normal distribution with a mean of 48 and a standard deviation of 7 is between 34 and 55, we need to standardize the values using the z-score formula:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

For x = 34:

z = (34 - 48) / 7 = -2

For x = 55:

z = (55 - 48) / 7 = 1

We can use a standard normal distribution table or a calculator to find the area under the standard normal distribution curve between z = -2 and z = 1. This area represents the probability that a randomly selected x-value from the given normal distribution is between 34 and 55.

Using a standard normal distribution table, we can find the probabilities as follows:

P(z < -2) = 0.0228 (from the table)

P(z < 1) = 0.8413 (from the table)

Therefore, the probability that a randomly selected x-value from the given normal distribution is between 34 and 55 is:

P(-2 < z < 1) = P(z < 1) - P(z < -2) = 0.8413 - 0.0228 = 0.8185

So, the probability is approximately 0.8185 or 81.85%.

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Answer:

First: P, R. Second: 3.

Step-by-step explanation:

In this, you can see the first tree diagram with C,R C,B and C,W.

Then when you go to the other diagram it's P,R P,B and P,W.

Therefore the combination P,R is missing from the tree diagram and belongs to the box.

When you count the number of combinations:

1, P,R

2, P,B

3, P,W

Therefore they are a total of 3 combinations.

ANSWER: 16FT  

SOLUTION IN IMAGES

The value of the given expression √8/81 = 2√2/81.

The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number may be found by looking for a number that, when squared, yields the original value. The equation a a = b is true if 'a' is the square root of 'b'. Every integer has two square roots, one of a positive value and one of a negative value, because the square of any number is always a positive number. For instance, the square roots of 4 are both 2 and -2.

Given that,

√8/81

We can write the value of √8 = √(2)(2)(2) = 2√2.

Thus, we have the value of √8/81 = 2√2/81.

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We have no control over our cravings, affection, passion, or avarice. Humans and plants have many characteristics. You eat human flesh because you are a plant. Our way of life is represented by the plant.

Whether by hunting or scavenging, an animal or plant that consumes meat gets its food and energy needs from animal tissues (primarily muscle, fat, and other soft tissues).

The majority of the member species of the order Carnivora are known by the technical term "carnivoran," although confusion is often caused by the resemblance between the name of the order and the name of the diet.

So, in the given situation as the grows and as the money grows, it demonstrates that we are all looking out for one another.

In some ways, we are all carnivorous plants.

We all commit murder.

We are powerless against our hunger, love, passion, and greed. Plants and humans are similar in many ways.

What we desire is to live, and to exist in this world. You are a plant that consumes human flesh.

The plant represents our way of life.

Therefore, we have no control over our cravings, affection, passion, or avarice. Humans and plants have many characteristics. You eat human flesh because you are a plant. Our way of life is represented by the plant.

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Complete question:

Carnivorous plants have some unique and amazing characteristics. What do these characteristics suggest about life and the world that we live in? In other words, what can carnivorous plants teach us about the world?? Make a point and support it with an example from the text. Explain what your support shows.

The measure of angle x in the hexagon is 140 degree.

The formula for calculating the sum of interior angles of a polygon is ( n − 2 ) × 180 degree.

where is the number of sides

Since the number of sides of the polygon in the diagram is 6, we can find the sum of the interior angle.

Sum of interior angle = ( n − 2 ) × 180

Plug in n = 6

Sum of interior angle = ( 6 − 2 ) × 180

Sum of interior angle = ( 4 ) × 180

Sum of interior angle = 720°

Next, we sum up the interior angles given in the diagram equate to 720 degree and solve for x.

108 + 155 + 123 + 104 + 90 + x = 720

Collect and add like terms

580 + x = 720

Subtract 580 from both sides

580 - 580 + x = 720 - 580

x = 720 - 580

x = 140°

Therefore, the value of x is 140 degree.

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Part a: Compounded Semiannually: A = 20,771.75.

Part b: Compounded quarterly: A = 20817.66.

Part c: Compounded monthly: A = 20848.76

Part d: Compounded continuously :A = 407,538.49

Compound interest formula:

A = P[tex](1 + \frac{r}{n} )^{nt}[/tex]

And

A = P[tex]e^{rt}[/tex]

Principal P : $15,000

Time t = 6 years

Rate of interest r = 5.5%

number of time compounded - n

Part a: Compounded Semiannually:

r --> r/2

n = 2

A = 15,000[tex](1 + \frac{0.055}{2} )^{2*6}[/tex]

A = 20,771.75

Part b: Compounded quarterly:

r --> r/4

n = 4

A = 15,000[tex](1 + \frac{0.055}{4} )^{4*6}[/tex]

A = 20817.66

Part c: Compounded monthly:

r --> r/12

n = 12

A = 15,000[tex](1 + \frac{0.055}{12} )^{12*6}[/tex]

A = 20848.76

Part d: Compounded continuously

A = Pe∧(rt)

A = 15,000(2.72)∧(0.55*6)

A = 407,538.49

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Answer: Let's use variables to represent the three digits of the number. We can use d1 for the first digit, d2 for the second digit, and d3 for the third digit. Based on the given information, we can write the following equations:

d1 > d2 + 4 (the first digit is greater than the second by 4)

d3 > d1 + 2 (the third digit is greater than the first by 2)

We also know that the three digits combine to form a three-digit number. We can write this number as:

100d1 + 10d2 + d3

To solve for the digits, we can use the information we have to write expressions for d1, d2, and d3 in terms of a single variable, and then use that to find the digits. Let's start with the first equation:

d1 > d2 + 4

Subtracting 4 from both sides, we get:

d1 - 4 > d2

Now we can substitute this expression for d2 in the second equation:

d3 > d1 + 2

d3 > (d1 - 4) + 2

d3 > d1 - 2

So we have the following inequalities:

d1 > d2 + 4

d3 > d1 - 2

We can use these to write expressions for d1, d2, and d3 in terms of a single variable, say x:

d1 = x + 4

d2 = x

d3 = x + 2 + 4 = x + 6

Now we can substitute these expressions into the equation for the three-digit number:

100d1 + 10d2 + d3 = 100(x+4) + 10x + (x+6) = 111x + 406

So the three-digit number can be written as 111x + 406. To find the digits, we need to choose a value of x that satisfies the inequalities we derived. Let's start with the first inequality:

d1 > d2 + 4

x + 4 > x + 4

x > 0

So x must be greater than 0. Now let's check the second inequality:

d3 > d1 - 2

x + 6 > x + 2

6 > 2

This inequality is always true, so we don't need to worry about it. Therefore, any value of x greater than 0 will satisfy the given conditions. For example, if we choose x = 1, then the digits are:

d1 = 5

d2 = 1

d3 = 7

And the three-digit number is:

100d1 + 10d2 + d3 = 500 + 10 + 7 = 517

So the number is 517.

Step-by-step explanation:

The table which represents a linear function is answer B. By calculating the slope between any two points on the table.

A linear function is a mathematical function that produces a straight line when graphed. It is a type of function where the input variable (x) and output variable (y) are related in a way that can be represented by a straight line.

To determine which table represents a linear function, we need to check whether the change in the output variable (y) is proportional to the change in the input variable (x) for any two points on the table.

Answer A:

When we compare the difference between each value of y, we see that each subsequent value of y is multiplied by 2. For example, 2 x 2 = 4, 4 x 2 = 8, and so on. This means that there is a constant rate of change between each pair of x and y values, but the rate of change is not constant. Therefore, the function is not linear.

Answer B:

When we compare the difference between each value of y and x, we see that the difference between any two values of y is proportional to the difference between the corresponding x values. Specifically, when x increases by 1, y increases by 1, except for the first two values. This means that the rate of change between each pair of x and y values is constant, and the function is linear.

Answer C:

When we compare the difference between each value of y, we see that the difference between any two values of y is not proportional to the difference between the corresponding x values. Specifically, the rate of change is not constant. Therefore, the function is not linear.

Answer D:

When we compare the difference between each value of y, we see that the rate of change is not constant. Specifically, the rate of change from x = 1 to x = 2 is different from the rate of change from x = 2 to x = 3. The function is not linear.

Therefore, only answer B represents a linear function.

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Answer:

To find the scale of the photograph, we need to determine the ratio between the actual height of the man and the height of the man in the photograph.

First, we convert the height of the man from feet to inches:

6 feet = 6 x 12 = 72 inches

Next, we can set up a proportion:

actual height of man / height of man in photograph = scale factor

Substituting the given values, we get:

72 inches / 1.5 inches = scale factor

Simplifying, we get:

scale factor = 48

Therefore, the scale of the photograph is 1:48, which means that one inch in the photograph represents 48 inches (or 4 feet) in real life.

The mean and standard deviation for Brett Favre's per game pass completions were 21.4 and 6.47, respectively, and all measurements fall within two standard deviations of the mean.

What is standard deviation ?

Standard deviation is a measure of the amount of variation or dispersion in a set of data. It is a statistic that indicates how much the individual data points deviate from the mean or average of the dataset.

a. Here's a stem-and-leaf plot for the number of passes completed by Brett Favre for each of the 16 regular season games in the fall of 2006:

Each stem represents the tens digit of the number of passes completed, and each leaf represents the ones digit.

b. To calculate the mean and standard deviation for Brett Favre's per game pass completions, we can use the following formulas:

mean = (sum of all values) / (number of values)

standard deviation = sqrt[(sum of (each value minus the mean) squared) / (number of values - 1)]

Using these formulas, we get:

mean = (15 + 31 + 25 + 22 + 22 + 19 + 17 + 28 + 24 + 5 + 22 + 24 + 22 + 20 + 26 + 21) / 16 = 21.4

standard deviation = [tex]sqrt[((15-21.4)^2 + (31-21.4)^2 + (25-21.4)^2 + (22-21.4)^2 + (22-21.4)^2 + (19-21.4)^2 + (17-21.4)^2 + (28-21.4)^2 + (24-21.4)^2 + (5-21.4)^2 + (22-21.4)^2 + (24-21.4)^2 + (22-21.4)^2 + (20-21.4)^2 + (26-21.4)^2 + (21-21.4)^2) / (16-1)] = 6.47 \\ \\= 6.47[/tex] (rounded to two decimal places)

Therefore, Brett Favre's per game pass completions had a mean of 21.4 and a standard deviation of 6.47.

c. To find the proportion of the measurements that lie within two standard deviations of the mean, we need to find the range of values that fall within two standard deviations above and below the mean. We can use the following formula:

range = mean ± (2 × standard deviation)

Plugging in the values we calculated in part b, we get:

range = 21.4 ± (2 × 6.47) = 8.46 to 34.34

Therefore, the mean and standard deviation for Brett Favre's per game pass completions were 21.4 and 6.47, respectively, and all measurements fall within two standard deviations of the mean.

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The DRD for Jazz Corporation on the dividend it received from Williams Corp. is $4,000.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To calculate the dividends received deduction (DRD) for Jazz Corporation on the dividend it received from Williams Corp., we need to determine the taxable income limit for the deduction.

The taxable income limit is based on the percentage of ownership in the company. Since Jazz Corporation owns 10% of Williams Corp. stock, the taxable income limit is 50% of its taxable income, or $4,000 ($8,000 x 50%).

The DRD is then calculated as the lesser of the dividend received or the taxable income limit. In this case, Jazz Corporation received a dividend of $12,900, which exceeds the taxable income limit of $4,000.

Therefore, the DRD for Jazz Corporation on the dividend it received from Williams Corp. is $4,000.

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The slope of the secant line  PQ is -11.6

To find the slope of the secant line PQ, we need to find the coordinates of point Q, and then calculate the slope using the formula:

slope of PQ = (yQ - yP)/(xQ - xP)

where (xP, yP) = (0, 9) and (xQ, yQ) = (0.1, y(0.1)).

First, we need to find y(0.1) by substituting x = 0.1 into the equation y = (3 - 2x)^2:

y(0.1) = (3 - 2(0.1))^2 = (2.8)^2 = 7.84

Therefore, point Q is (0.1, 7.84).

Now we can calculate the slope of PQ:

slope of PQ = (yQ - yP)/(xQ - xP) = (7.84 - 9)/(0.1 - 0) = -11.6

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After the rotation, the coordinates of each point will be:Point R: (x,y) = (-y,x)Point S: (x,y) = (-x,-y)Point T: (x,y) = (y,-x)Point U: (x,y) = (x,y)

Coordinates are a set of two or more numbers or variables that indicate the position of a point, line, or object in space. Coordinates are used in many fields, from mathematics and science to navigation and cartography. Coordinates are essential for accurately mapping and measuring the location of objects on Earth and in the universe. Coordinates can also be used to calculate the area of a region or the volume of an object. Coordinates are one of the most important tools for understanding and manipulating the physical world.

Quadrilateral RSTU has a rotation of 90 degrees about the origin. After the rotation, the coordinates of each point will be:

Point R: (x,y) = (-y,x)
Point S: (x,y) = (-x,-y)
Point T: (x,y) = (y,-x)
Point U: (x,y) = (x,y)

This occurs because when rotating a point around the origin, the x-coordinates and y-coordinates change places. The sign also changes for the x-coordinate and the y-coordinate in order to preserve the direction of the rotation.

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Answer:

Step-by-step explanation:

To determine if the graphs of two linear equations are parallel, we need to compare their slopes. If the slopes are equal, then the lines are parallel. If the slopes are not equal, then the lines are not parallel.

In case (a), the two equations are y = x + 3 and y = x + 6. Both equations have a slope of 1, which means the lines have the same steepness. However, the y-intercepts are different (3 and 6), which means the lines are shifted up or down relative to each other. Since the slopes are equal, but the y-intercepts are different, the lines are parallel.

In case (b), the two equations are y = 4x - 1 and y = 1 - 4x. Both equations have a slope of -4, which means the lines have the same steepness. However, the y-intercepts are different (-1 and 1), which means the lines are shifted up or down relative to each other. Since the slopes are equal, but the y-intercepts are different, the lines are not parallel.

In case (c), the two equations are y = 2x - 3 and y = -2x + 3. The slopes of the two equations are 2 and -2, which are negative reciprocals of each other. This means the lines are perpendicular, not parallel.

In case (d), the two equations are 3y = x - 12 and 6y = 2x + 12. We can rewrite these equations in slope-intercept form by solving for y. The first equation becomes y = (1/3)x - 4 and the second equation becomes y = (1/2)x + 2. The slopes of the two equations are 1/3 and 1/2, which are not equal. Therefore, the lines are not parallel.

Answer:

22. Parallel

23. Not parallel

24. Not parallel

25. Parallel

Step-by-step explanation:

The slope equation form of a line is

y = mx + b

where

m = slope

b = y-intercept

If two lines are parallel their slopes, the value of m will be the same, in slope-intercept form

Q22

y = x + 33 → slope = 1
y = x + 6 →  slope = 1

Slopes are the same with = 1
Hence  the lines are parallel

Q23
y = 2x - 3  →  slope m = 2
y = -2x + 3  →  slope m = -2
Slopes not equal hence not parallel

Q24
y = 4x - 1 →  slope = 4
y = 1 --4x or y = - 4x + 1  → slope = - 4  

Slopes are different, hence not parallel

Q25
3y = x - 12
6y = 2x + 12

Divide the first equation by 3
=> 3y/3 = x/3 - 12/3
=> y = x/3 -4    →   slope = 1/3

Divide the second equation by 6
6y/6 = 2x/6 + 12/6
y = x/3 + 2  →   slope = 1/3

Slopes are same, hence parallel

Answer:

[tex]4992 \text{ cm}^2[/tex]

Step-by-step explanation:

We can model the amount of metal, in square centimeters, that is needed to make a soup can with the expression:

[tex](2 \cdot \text{area of base}) + (\text{area of side})[/tex]

We can first solve for the surface area of a soup can, using the fact that its bases are circles.

[tex]A_{\text{circle}} = \pi r^2[/tex]

↓ substituting 3 for π

[tex]A_{\text{base}} = 3r^2[/tex]

↓ plugging in radius (which is 1/2 of diameter, given as 8)

[tex]A_{\text{base}} = 3(4)^2[/tex]

↓ simplifying

[tex]A_{\text{base}} = 48 \text{ cm}^2[/tex]

Then, we can solve for the area of its side, which we can think of as an elongated circumference (circumference multiplied by height).

[tex]A_{\text{circumference}} = \pi d[/tex]

[tex]A_{\text{side}} = h(\pi d)[/tex]

↓ substituting 3 for π

[tex]A_{\text{side}} = h(3d)[/tex]

↓ plugging in height and diameter

[tex]A_{\text{side}} = 9(3 \cdot 8)[/tex]

↓ simplifying

[tex]A_{\text{side}} = 216 \text{ cm}^2[/tex]

Next, we can solve for the surface area of one soup can.

[tex](2 \cdot \text{area of base}) + (\text{area of side})[/tex]

↓ plugging in solved values

[tex](2 \cdot 48 \text{ cm}^2) + 216 \text{ cm}^2[/tex]

↓ simplifying

[tex]96 \text{ cm}^2 + 216 \text{ cm}^2[/tex]

↓ performing addition

[tex]312 \text{ cm}^2[/tex]

Finally, we can solve for the amount of metal needed for 16 cans by multiplying the amount for 1 can by 16.

[tex]16 \cdot 312 \text{ cm}^2[/tex]

↓ performing multiplication

[tex]\boxed{4992 \text{ cm}^2}[/tex]

Step-by-step explanation:

Refer to pic............

The value of x and y in the trapezium are 118 and 35 degrees respectively.

The diagram above is a trapezium. A trapezium is a quadrilateral with 4 sides.  The sum of all the four angles of the trapezium is equal to 360°.

A trapezium has two parallel sides and two non-parallel sides.

Therefore, let's find x and y as follows:

x = 180 - 62(supplementary angles)

x = 118 degrees

y = 180 - 145(supplementary angles)

y = 35 degrees

Therefore,

x = 118 degrees

y = 35 degrees

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The area of the garden alone is 21 yd²

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The total length of the patio and garden is 6 yards while the total width is 5 yard. Hence:

Area of garden and patio = length * width = 6 yards * 5 yards = 30 yd²

The length of patio is 3 yard and width of the patio is 3 yard, hence:

Area of Patio = length * width = 3 yd. * 3 yd. = 9 yd²

Therefore:

Area of garden = Area of garden and patio - Area of Patio = 30 yd² - 9 yd² = 21 yd²

The area of the garden is 21 yd²

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The domain is the set of all x-values greater than or equal to 1, and the range is the set of all y-values greater than or equal to -2.

A coordinate plane is a two-dimensional graph that is used to locate points in a given space. The two axes intersect at a point called the origin, which is located at the coordinates (0, 0). Points on the coordinate plane can be labeled using their x and y coordinates, which are written in the form (x, y).

The graph below shows a function in the coordinate plane, which is made up of a curved line that begins at the point (1, -2) and rises as it moves to the right. The domain of the function is all x-values, or inputs, which are greater than or equal to 1. The range of the function is all y-values, or outputs, which are greater than or equal to -2.

When determining the domain and range of a function, it is important to remember that the domain is the set of all possible inputs, while the range is the set of all possible outputs. In the case of the graph below, the domain is the set of all x-values greater than or equal to 1, and the range is the set of all y-values greater than or equal to -2.

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Answer:

Question 3
Equation for Malik:
y = 350 + 7x

Equation for Saraiah:
y = 400 + 4x

Question 4
Both of them will have the same amount of money after
50/3 years
or
16 2/3 years
or
16 years 8 months

Step-by-step explanation:

#3

Amount in Malik's account after x years given 2% interest
y = 350(1 + 0.02x)
y = 350 + 7x

For Saraiah's account:
y = 400(1 + 0.01x)
y = 400 + 4x

#4

If both Malik and Saraiah have the same amount of money after x years, then the right side of both their equations must be equal

Therefore

[tex]350+7x = 400+4x\\\\\mathrm{Move}\:350\:\mathrm{to\:the\:right\:side \:by \:subtracting\: 350 \:from\:both\: sides}\\350+7x-350=400+4x-350\\\\\mathrm{Simplify}\\7x=4x+50\\\\[/tex]

[tex]\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}\\\\7x-4x=4x+50-4x\\3x=50\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\dfrac{3x}{3}=\dfrac{50}{3}\\\\x=\dfrac{50}{3}[/tex]

Therefore both of them will have the same amount of money after [tex]\dfrac{50}{3}[/tex] years which is [tex]{16\dfrac{2}{3}[/tex] years

2/3 year = 2/3 x 12 months = 8 months

So both of them will have the same amount of money after [tex]{16\dfrac{2}{3}[/tex] years or 16 years and 8 months

The symmetry of the functions are

In mathematics, the symmetry of a function refers to the property that the function remains unchanged under a certain transformation

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

Graph 1

Under any transformation, the function would not remain the same when transformed

Graph 2

This function is a circle equation and it would remain the same when reflected or rotated across the axes and the origin

Graph 3

This function would only remain the same when reflected across the x-axis

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Using basic arithmetic operation, Ann's stock investment has increased in value more, by $331.25, compared to her bond investment, which has increased in value by $378.66.

The current value of Ann's bond investment can be calculated using the following formula:

Current Value of Bonds = Par Value x Market Rate

Since Ann has 7 bonds with a par value of $500 each, the total par value of her bond investment is:

$500 x 7 = $3,500

Using the market rate of 106.384, we can calculate the current value of Ann's bond investment as:

Current Value of Bonds = $3,500 x 1.06384 = $3,725.44

The current value of Ann's stock investment can be calculated by multiplying the number of shares she owns by the current stock price:

Current Value of Stock = Number of Shares x Stock Price

Since Ann owns 125 shares of Cilla Shipping stock and the current stock price is $30.65, the current value of her stock investment is:

Current Value of Stock = 125 x $30.65 = $3,831.25

To determine which investment has increased in value more, we need to compare the difference between the current and original values of each investment. The original value of Ann's bond investment is:

Original Value of Bonds = Par Value x Market Rate = $500 x 7 x 0.95626 = $3,346.78

The difference between the current and original value of Ann's bond investment is:

$3,725.44 - $3,346.78 = $378.66

The original value of Ann's stock investment is:

Original Value of Stock = Number of Shares x Stock Price = 125 x $28.00 = $3,500

The difference between the current and original value of Ann's stock investment is:

$3,831.25 - $3,500 = $331.25

Hence, Ann's stock investment has increased in value more, by $331.25, compared to her bond investment, which has increased in value by $378.66.

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Therefore, the correct answer is option 4: 5x + 3y = 80.

A mathematical statement that shows the equivalence of two formulas is what an equation through algebra means. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.

Let the number of 3-point questions answered correctly be x, and the number of 5-point questions answered correctly be y. Then, we can form two equations based on the information given:

3x + 5y = 80 (total score equation)

x + y = ?? (number of questions answered equation)

We cannot determine the exact value of x + y from the given information, so we will leave it as an unknown.

The correct equation that represents the number of 33-point questions, x, and the number of 5-point questions, y, he answered correctly is:

5x + 3y = 80

This equation comes from the fact that the student only answered 3-point and 5-point questions correctly. Therefore, the only way for the student to get a score of 80 is if the number of 3-point questions he answered correctly is a multiple of 3 and the number of 5-point questions he answered correctly is a multiple of 5. Thus, we can write:

x = 33n, where n is a non-negative integer (since the number of 3-point questions he answered correctly must be a multiple of 33)

y = 5m, where m is a non-negative integer (since the number of 5-point questions he answered correctly must be a multiple of 5)

Substituting these expressions into the total score equation, we get:

3(33n) + 5(5m) = 99n + 25m = 80

Simplifying this equation, we get:

5x + 3y = 80

Therefore, the correct answer is option 4: 5x + 3y = 80.

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By rewriting the 3 given systems, we will see that:

1) Independent and consistent.

2) Independent and inconsistent.

3) Dependent.

What is the system of equations?

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Let's look at the first one, we can rewrite it as:

y = 2x + 3

y = -x - 3

So, the slopes are different, meaning that we have one solution, so this system is consistent and independent.

Now let's look at the second system, we can rewrite it as:

y = 3x - 2

y = 3x + 2

Here both lines have the same slope, so the lines never do intersect, meaning that the system is inconsistent and independent.

For the final system, we have:

y = (-1/2)×x + 2

y = (-1/2)×x + 2

Hence, we have two equal lines, so this system is dependent.

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The correct answer is (C) the total number of rolls sold (small and large).

What are algebraic equations?

An algebraic equation is a mathematical expression that includes one or more variables and mathematical operations such as addition, subtraction, multiplication, and division. The equation asserts that two expressions are equal.

The goal in solving an algebraic equation is to determine the value(s) of the variable(s) that make the equation true. Algebraic equations are used to solve problems in various fields such as physics, engineering, economics, and finance.

In the equation 3s + 135 = 4.5(s + 10), the expression (s + 10) represents the total number of rolls sold (small and large).

To see why, let's break down the equation:

3s represents the total amount earned from selling small rolls (since the

club earns $3.00 for every small roll sold).

4.5(s + 10) represents the total amount earned from selling all the rolls (small and large). The (s + 10) part represents the total number of rolls sold, since the club sold 10 more large rolls than small rolls, which is represented by adding 10 to the number of small rolls sold (s).

Therefore, the correct answer is (C) the total number of rolls sold (small and large).

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The value of the given function for x=4 is 82.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is y+√x=5x+(x+4)².

Here, y=5x+(x+4)²-√x

f(x)=5x+(x+4)²-√x

Substitute x=4 in the function, we get

f(4)=5(4)+(4+4)²-√4

= 20+64-2

= 82

Therefore, the value of function is 82.

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The required final amount and interest are 3311.05 and 311.05

When you make interest on both the money you've saved and the interest you've earned, this is known as compound interest.

A. To find the amount of money in the account after 5 years, we can use the formula for compound interest:

[tex]$$A = P \left(1 + \frac{r}{n}\right)^{nt}$$[/tex]

where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $3000, r = 0.02 (2%), n = 4 (compounded quarterly), and t = 5. Plugging in these values, we get:

[tex]$$A = 3000\left(1 + \frac{0.02}{4}\right)^{4\cdot5} \approx $3311.05$$[/tex]

Therefore, there will be approximately 3311.05 in the account after 5 years.

B. To find the interest earned, we can subtract the principal from the final amount:

[tex]$$I = A - P = $3311.05 - $3000 = $311.05$$[/tex]

Therefore, the interest earned is 311.05.

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Answers:

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Explanation:

Problem 1

Each time x goes up by 1, y goes down by 5. This constant rate of change leads to the equation being linear. The slope is m = -5/1 = -5. You can use the slope formula for any two points in the table to confirm this is the correct slope.

The y intercept is b = 15 because we have x = 0 lead to y = 15.

Therefore, we go from y = mx+b to y = -5x+15

-----------------------------------

Problem 2

Each time x goes up by 3, the y coordinate goes down by 3. Therefore, we have another linear equation here. The slope is m = -3/3 = -1.

The y intercept is b = 4 because x = 0 leads to y = 4.

y = mx+b turns into y = -x+4

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Problem 3

Each time x goes up by 1, y is NOT going up the same amount. The jump from 10 to 20 is +10. The jump from 20 to 40 is +20. And so on.

Therefore, this equation isn't linear. Instead it's exponential. Each y term doubles when x increases by 1, so that's why the b term is b = 2.

The initial term is a = 80 because x = 0 leads to y = 80.

We go from y = a*b^x to y = 80*2^x

-----------------------------------

You can use a tool like Desmos or GeoGebra to visually confirm each of the answers. Both also offer support for function tables.

Answer:

1.  y = -5x + 15.

2. y = -x + 4.

3. y = 80(2^(x/3))

Step-by-step explanation:

1.

From the given data, we can see that as x increases by 1, y decreases by a fixed amount of 5. This means that the relationship between x and y is linear, specifically a decreasing linear relationship.

To write the equation for a linear relationship, we need to find the slope (m) and y-intercept (b).

Using the formula for slope:

m = (change in y) / (change in x)

m = (0 - 30) / (3 - (-3))

m = -5

Using the point-slope form of a linear equation:

y - y1 = m(x - x1)

y - 30 = -5(x - (-3))

y - 30 = -5x - 15

y = -5x + 15

So the equation for this linear relationship is y = -5x + 15.

2.

From the given data, we can see that as x increases by 3, y decreases by a fixed amount of 3. This means that the relationship between x and y is linear, specifically a decreasing linear relationship.

To write the equation for a linear relationship, we need to find the slope (m) and y-intercept (b).

Using the formula for slope:

m = (change in y) / (change in x)

m = (-5 - 13) / (9 - (-9))

m = -18 / 18

m = -1

Using the point-slope form of a linear equation:

y - y1 = m(x - x1)

y - 13 = -1(x - (-9))

y - 13 = -1(x + 9)

y = -x + 4

So the equation for this linear relationship is y = -x + 4.

3.

From the given data, we can see that as x increases by 1, y doubles. This means that the relationship between x and y is exponential.

To write the equation for an exponential relationship, we can use the general form of an exponential function:

y = ab^x

where a is the initial value, b is the base, and x is the exponent.

To find a and b, we can use the first and fourth data points since they have the smallest and largest values of y, respectively.

When x = -3, y = 10, so we have:

10 = ab^(-3)

When x = 0, y = 80, so we have:

80 = ab^(0)

From the second equation, we can see that a = 80. Substituting this into the first equation, we get:

10 = 80b^(-3)

Simplifying, we get:

b = 2^(1/3)

So the equation for this exponential relationship is:

y = 80(2^(1/3))^x

Simplifying further:

y = 80(2^(x/3))