y is inversely proportional to x.
When y = 6, x = 8
a) Work out an equation connecting y and x.

The equations equivalent to 1/4 (8x + 56) = 20 are

1. 56 + 8x = 80

2.14 = 20 - 8x

4.2x = 6

5. x = 3

An equation is a mathematical expression that shows the relationship between two variables.

Since we have the equation 1/4(8x + 56) = 20, and we want to find all the equations that are equivalent to it, we solve the equation.

So, we proceed as follows.

1/4(8x + 56) = 20

Expanding the brackets, we have

8x/4 + 56/4 = 20

2x + 14 = 20

Subtracting 14 from both sides, we have that

2x = 20 - 14

2x = 6

x = 6/2

x = 3

Also, in 1/4(8x + 56) = 20

Multiplying through by 4, we have that

8x + 56 = 80

2x + 14 = 20

Subtracting 2x from both sides, we have that

14 = 20 - 2x

So, the equations are

1. 56 + 8x = 80

2.14 = 20 - 8x

4.2x = 6

5. x = 3

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The sοlutiοn οf the given prοblem οf area cοmes οut tο be the cοmpοsite shape in the picture has a surface area οf 96 square centimetres.

Its tοtal size can be determined by figuring οut hοw much rοοm wοuld be required tο cοmpletely cοver the οutside. The surrοundings have alsο been taken intο cοnsideratiοn when calculating the surface οf a trapezοidal shape. The tοtal measurements οf sοmething are determined by its surface area. Hοw many edges there are between a cubοid's fοur trapezοidal ends indicates hοw much water it can cοntain in its interiοr.

Here,

Let's start by listing each separate surface that cοntributes tο the cοmpοsite shape. There are twο triangles and fοur squares.

We can use the fοllοwing methοd tο determine the area οf each rectangle:

=> Length = 5 centimetre, width = 4 cm, sο area = 5 cm x 4 cm = 20 cm² fοr rectangle 1.

=> Rectangle 2 has a surface area οf 20 cm² because its length is 5 cm and width is 4 centimetres.

=> Rectangle 3 has a 6 centimetre length and a 4 cm width,

=> area =  6 cm x 4 cm, οr 24 cm².

=> Rectangle 4 has a 6 centimetre length and a 4 cm width, sο

=> area =  6 cm x 4 cm, οr 24 cm².

The fοllοwing algοrithm can be used tο determine each triangle's area:

=> area =  (Base × Height) / 2

Area οf Triangle 1 :  (2 cm x 4 cm) / 2 = 4 cm²

Area οf Triangle 2: (2 centimetre x 4 cm) / 2 = 4 cm²

Tοtal Surface Space equals 96 cm² (20 cm², 20 cm², 24 cm², 24 cm², 4 cm², 4 cm²)

Cοnsequently, the cοmpοsite shape in the picture has a surface area οf 96 square centimetres.

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The current drawn by R2 is 3.333A or 3333mA in parallel combination in ohms.

In a parallel combination, the voltage across both resistors is the same. However, the current is divided between the two resistors based on their individual resistances. Using Ohms law (V = IR), we can find the voltage across the resistors:

According to the specific resistances of the resistors in a parallel circuit, the current is distributed among them. More current will flow through the resistor with the lower resistance than the one with the greater resistance. This is due to the fact that the lower resistance provides less resistance to the current flow. In this instance, R1 will draw more current than R2 since it has a lower resistance than R2.

V = IR1 = (10A)(5Ω) = 50V

V = IR2 = (I)(15Ω)

We can find current I by solving this particular equation:

I = V/R2 = (50V)/(15Ω) = 3.33A

Convert this ampere value to milliamps, in which we have to multiply by 1000:

I = 3.33A * 1000 = 3333mA or 3.333A

Current drawn by R2 is 3.333A or 3333mA.

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i) The expression relating price and output assuming it is linear is Price per unit = -20 × Number of units sold + c.

ii) The total cost function, assuming it is linear is 2000 + 10 × Number of units sold.

iii)  The business woman need to produce 114 products to achieve breakeven.

(i) The expression relating price and output assuming it is linear can be written as:

Price per unit = m × Number of units sold + c

where m is the slope of the line and c is the y-intercept.

We can find the slope by using the two points (20, 300) and (13, 440):

m = (440 - 300) / (13 - 20) = 140 / (-7) = -20

So, the expression relating price and output is:

Price per unit = -20 × Number of units sold + c

(ii) The total cost function assuming it is linear can be written as:

Total cost = Fixed cost + Variable cost per unit × Number of units sold

Given that the fixed cost of production is GH₵2,000 with a variable cost per unit of GH¢10, the total cost function can be expressed as:

Total cost = 2000 + 10 × Number of units sold

(iii) To find the level of production at which the business woman will breakeven, we need to find the point at which the total cost equals the total revenue. Since the total revenue is simply the product of the price per unit and the number of units sold, we can set these two equations equal to each other:

Price per unit × Number of units sold = Total cost

Substituting the expressions we found in parts (i) and (ii), we get:

(-20 × Number of units sold + c) × Number of units sold = 2000 + 10 × Number of units sold

Simplifying and solving for the number of units sold, we get:

20 × Number of units sold^2 - 20c × Number of units sold - 2000 = 0

Using the quadratic formula, we get:

Number of units sold = (-(-20c) ± sqrt((-20c)^2 - 4 × 20 × (-2000))) / (2 × 20)

Simplifying, we get:

Number of units sold = (c + sqrt(c^2 + 2000)) / 2

Since we know that the business woman can sell 300 units a day at a price of GH¢20 and 440 units a day at a price of GH¢13, we can set up a system of equations to solve for the y-intercept, c:

-20 × 300 + c = 20c + 2000

-20 × 440 + c = 13c + 2000

Solving this system of equations, we get:

c = 2400/3 ≈ GH₵800

Therefore, the level of production at which the business woman will breakeven is:

Number of units sold = (800 + sqrt(800^2 + 2000)) / 2 ≈ 113.7 units

She should produce at least 114 units to breakeven.

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Answer:

102 cubic inches

Step-by-step explanation:

The formula for a volume of a sphere is as follows:

[tex]V = \frac{4\pi r^2}{3}[/tex]

Hence, substituting r=2.9 into this equation,

[tex]\frac{4\pi (2.9)^3}{3}\\\\=\frac{4\pi (24.4)}{3}\\\\=102.160404[/tex]

Hence, the answer is 102 cubic inches.

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Answer:

Step-by-step explanation:

The correct options are A) Pull two times as many green cubes as blue cubes , B) Pull a blue cube 28 times, and E) Pull a red cube 16 times.

To determine which of the following amounts you would expect to pull, we need to calculate the probabilities of drawing each color cube and then apply that probability to 100 draws.

1. Calculate the total number of cubes in the bag:

Total cubes = 7 blue + 4 red + 14 green = 25 cubes

2. Calculate the probability of drawing each color:

P(blue) = 7/25

P(red) = 4/25

P(green) = 14/25

3. Apply the probabilities to 100 draws:

Blue: 100 × (7/25) = 28

Red: 100 × (4/25) = 16

Green: 100 × (14/25) = 56

Now we can evaluate the given statements:

A) Pull two times as many green cubes as blue cubes

56 green cubes is exactly 2 times 28 blue cubes, so A is correct.

B) Pull a blue cube 28 times

As calculated earlier, you would expect to pull a blue cube 28 times. B is correct.

C) Pull 60 red cubes

The expected number of red cubes is 16, not 60. C is incorrect.

D) Pull more blue cubes than green cubes

You would expect to pull 28 blue cubes and 56 green cubes, so D is incorrect.

E) Pull a red cube 16 times

As calculated earlier, you would expect to pull a red cube 16 times. E is correct.

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The value of the expression 4x+1/3y² when x = 2 and y = 3 is 1/3

In mathematics, a change of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables. The intent is that when expressed in new variables, the problem may become simpler, or equivalent to a better understood problem.

Finding the value of the expression, we substitute the given values for the variables

(4x+1)/(3y²

when x = 2 and y = 3

4( 2) +1/3(3)²

= 8 + 1/( 3 × 9)

= 9/27

= 1/3

therefore the value of the expression is 1/3

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Answer:

+ 7

Step-by-step explanation:

To find the nth term rule simply we just have to find the difference between the numbers

Difference between numbers

The difference between all our numbers is 7!

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As a result, the rectangle is 2x^2y^3 inches long.

The Latin word rectus, which meaning "right" or "straight," is where the "recto" in "rectangle" comes from. A rectangle possesses straight sides due to its right angles. Rectitude, a different term derived from the same root and denoting moral uprightness.

We may employ the following formula to determine the rectangular area:

area = length x width

Since we are aware of the surface and the breadth in this instance, we can determine the length:

area = 24x^3y^5

width = 12xy^2

area = length x width

24x^3y^5 = length x 12xy^2

When we multiply both sides by 12xy^2, we get:

2x^2y^3 = length

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Answer:

3.876 x 10^7 in standard form is 38,760,000.

Step-by-step explanation:

Answer:

38,760,000

Step-by-step explanation:

To write 3.876 x 10^7 in standard form, you need to move the decimal point to the left or right, depending on whether the exponent is positive or negative. In this case, the exponent is positive, so you need to move the decimal point 7 places to the right.

Starting with 3.876, move the decimal point to the right 7 places to get:

38,760,000

So 3.876 x 10^7 in standard form is 38,760,000.

If Jasper and Corey have saved up a total of $78.0 and Jasper has saved 6 dollars more than twice as much as Corey, Corey has saved $24, for a total of $78.

Let's use C to represent the amount of money Corey has saved.

We know that Jasper has saved 6 dollars more than twice as much as Corey, so we can write an equation to represent this relationship:

J = 2C + 6

where J is the amount of money Jasper has saved.

We also know that the total amount of money saved by Jasper and Corey is $78, so we can write another equation to represent this:

J + C = 78

Now we can substitute the first equation into the second equation to get an equation with only one variable:

(2C + 6) + C = 78

Simplifying the equation, we get:

3C + 6 = 78

Subtracting 6 from both sides, we get:

3C = 72

Dividing both sides by 3, we get:

C = 24

Therefore, Corey has saved $24. We can use the first equation to find out how much Jasper has saved:

J = 2C + 6 = 2(24) + 6 = 54

So Jasper has saved $54.

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Answer: slope is 1/9

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

i  used a website math-way . its a very accurate response. it usually is at least but you should use it.

A(8) = 9/7A(-5) = -1/3A(3/1) = 2A(-71/1) = -5/36

Function: A(t) = (t+1)/(t-1)For the given function A(t), the following values are to be calculated: A(8), A(-5), A(3/1), and A(-71/1)A(8):We need to substitute t=8 in the function. A(8) = (8+1)/(8-1) = 9/7Therefore, A(8) = 9/7A(-5):We need to substitute t=-5 in the function. A(-5) = (-5+1)/(-5-1) = -1/3Therefore, A(-5) = -1/3A(3/1):We need to substitute t=3/1 in the function. A(3/1) = (3/1+1)/(3/1-1) = (4)/(2/1) = 4*1/2 = 2Therefore, A(3/1) = 2A(-71/1):We need to substitute t=-71/1 in the function. A(-71/1) = (-71/1+1)/(-71/1-1) = (-70/1)/(-72/1) = (-5/36)Therefore, A(-71/1) = -5/36Therefore, the respective answers for the given values of the function A(t) are as follows: A(8) = 9/7A(-5) = -1/3A(3/1) = 2A(-71/1) = -5/36

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The linear function with the greatest slope is at option A.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

Find the slope for all the function to determine the highest rate:

A. The slope of g(x) is 1, since the change in y is 1 for every 1 unit increase in x.

B. The slope of f is -4/8 or -1/2.

C. The slope of the line passing through (-1, 3) and (2, -3) is (-3 - 3)/(2 - (-1)) = -2/3.

We observe that the slope of linear equation in A is greater.

Hence, the linear function with the greatest slope is at option A.

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64,000÷10 to the fourth power is equal to 0.64 × 10⁴

In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.

To solve this, we need to remember the order of operations, which is parentheses, exponents, multiplication and division (performed left to right), and addition and subtraction (also performed left to right).

First, we need to calculate 10 to the fourth power:

10 to the fourth power means 10 multiplied by itself four times:

10⁴ = 10,000

Now we can substitute that value into the original expression:

64,000 ÷ 10,000 =  0.64 × 10⁴

Therefore, 64,000÷10 to the fourth power is equal to  0.64 × 10⁴

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Answer:

25 Hours

Step-by-step explanation:

Answer:

l=(60÷w)

Step-by-step explanation:

since area =l×w

thats 60=l×w

l=60÷w

The coordinate set that describes the image of rectangle MPAT after the translation of 1 unit right and 2 units up is:

M'(2, 4), P'(2, 5), A'(4, 5), and T'(4, 4).

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for the ordered pairs of the vertices of a figure are defined as follows:

The vertices of the original rectangle are given as follows:

M(1, 2), P(1, 3), A(3, 3), and T(3, 2).

The translation is given as follows:

Hence the equation is:

(x, y) -> (x + 1, y + 2).

Then the coordinates of the vertices are given as follows:

M'(2, 4), P'(2, 5), A'(4, 5), and T'(4, 4).

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Answer:

10[tex]x^{5}[/tex]

Step-by-step explanation:

The list is: 30[tex]x^{7}[/tex], 60[tex]x^{5}[/tex], 110[tex]x^{8}[/tex]

Find the GCF

We see

30, 60, and 110 have the greatest common factor is 10.

[tex]x^{7}[/tex], [tex]x^{5}[/tex], [tex]x^{8}[/tex] have the greatest common factor is [tex]x^{5}[/tex]

So, the greatest common factor for the list of terms is 10 [tex]x^{5}[/tex]

Answer:

(w⁴)⁵

=w⁴*⁵

Answer=w²⁰

Daniel and Liz have conflicting claims about how much time students spend on homework.

Daniel claims that more than half of students spend 2 1/2 hours or more on homework, while Liz claims that more than half spend less than 2 1/2 hours. To determine who is correct, we must look at the actual data.

If, when we look at the data, we find that more than half the students spend 2 1/2 hours or more on homework, then Daniel is correct. Conversely, if more than half the students spend less than 2 1/2 hours on homework, then Liz is correct. It is important to note that the answer may depend on the sample size of the data we are looking at.

If the sample size is small, then it may be difficult to definitively answer the question. However, if the sample size is large, then it may be possible to provide a definite answer. In conclusion, to determine who is correct, we must look at the actual data. If the sample size is large enough, then it may be possible to definitively answer the question of who is correct.

Daniel says that more than half of the students spent 2.5 hours or more on homework, while Liz says more than half of the students spent less than 2.5 hours on homework. Liz's assertion is correct. So, Liz is correct since more than half of the students spent less than 2.5 hours on homework.

If Daniel were correct, the total percentage would be more than 100 percent, which is impossible since the total percentage is always 100 percent when the data set is of a limited population. The arithmetic mean of the time the students spend on their homework can be calculated using a statistical concept called a measure of central tendency.

The mean is used in this case. A measure of central tendency is a way of summarizing a data set using a single value that represents the entire collection of data in a condensed form. The mean is calculated by adding up all of the data and then dividing by the number of data points. To discover if the assertion that Liz is correct is accurate, more data is needed.

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Answer:

21/136

Step-by-step explanation:

The probability of selecting a boy from the class on the first draw is 7 boys out of 17 students total, or 7/17.

After the first boy is selected, there will be 6 boys and 10 girls left in the class.

So the probability of selecting a boy on the second draw, given that a boy was already selected on the first draw, will be 6 boys out of 16 remaining students, or 6/16.

To find the probability that both students selected are boys, we can multiply the probabilities of selecting a boy on the first and second draws:

P(boy and then boy) = P(boy on first draw) x P(boy on second draw | boy on first draw)

P(boy and then boy) = (7/17) x (6/16)

P(boy and then boy) = 21/136

Therefore, the probability of selecting two boys from Mr. Smith's class is 21/136.

Answer:

[tex] \frac{21}{136} [/tex]

Step-by-step explanation:

[tex] \frac{7}{17} \times \frac{6}{16} = \frac{7}{17} \times \frac{3}{8} = \frac{21}{136} [/tex]

After answering the prοvided questiοn, we can cοnclude that Sο the equatiοn estimated amοunt charged per hοur when the client οrders 80 hοurs οf wοrk is $60.85.

In mathematics, an equatiοn is a statement that implies the unity οf twο traits. An equatiοn cοnsists οf twο sides separated because οf an analytical sοlutiοn (=). Fοr instance, the debate "2x + 3 = 9" asserts that the remark "2x + 3" equals the valuatiοn "9". The gοal οf sοlving equatiοns is tο determine the amοunt οr values οf the variable in the mοdel) that wοuld allοw the equatiοn tο really be true.

Fοrmulae can be simple οr cοmplex, regular οr nοnlinear, and cοntain οne οr mοre variables. Fοr example, in the equatiοn "x² + 2x - 3 = 0," the variable x is elevated tο the secοnd pοwer. Lines are used extensively in mathematics, including algebra, equatiοns, and geοmetry.

Let's start by using the given infοrmatiοn tο set up twο equatiοns:

C(70) = $4900

C(80) = C(70) - ($4/10) * 80

C(80) = C(70) - $32

C(80) = $4900 - $32

C(80) = $4868

$4868 / 80 = $60.85 per hοur

Sο the estimated amοunt charged per hοur when the client οrders 80 hοurs οf wοrk is $60.85.

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Answer:

True:)

Step-by-step explanation:

If u is indirectly proportional to t³ - 3, the value of u when t = 3 is 5.

Proportional relationships are relationships between two variables where their ratios are equivalent.

Given that;

u is indirectly proportional to t³ - 3;

u ∝ 1/( t³ - 3)

u = k/( t³ - 3)

Where k is the proportionality constant.

First, we determine the proportionality constant.

To find k, we can use the initial condition that;

24 = k / (2³- 3)

24 = k / (8 - 3)

24 = k / 5

k = 24 × 5

k = 120

Hence, the equation relating u and t is:

u = k/( t³ - 3)

Plug in k = 120

u = 120/( t³ - 3)

To find u when t = 3, we can substitute t = 3 into the equation:

u = 120/( t³ - 3)

u = 120/( 3³ - 3)

u = 120/( 27 - 3)

u = 120/24

u = 5

Therefore, the value of u is 5.

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The point on the number line that is 1/4 of the way from point 0 to -3 is located at the point 3/4.

What is a number line?

A number line is a straight line that represents the real numbers as points or marks on the line. The numbers increase from left to right, and each point on the line corresponds to a specific number.

To find the point on the number line that is 1/4 of the way from point 0 to -3, we can use the following formula:

point = starting point + fraction of distance * total distance

The starting point is 0, and the total distance is the distance between 0 and -3, which is 3. So the total distance is 3.

Now, we need to find the fraction of the distance that is 1/4 of the total distance. This can be written as:

fraction of distance = 1/4

So the formula becomes:

point = 0 + 1/4 * 3

Simplifying the expression, we get:

point = 3/4

Therefore, the point on the number line that is 1/4 of the way from point 0 to -3 is located at the point 3/4.

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The student's test score is 0.76 standard deviations above the mean of the class.

A z-score is a measure of how many standard deviations a data point is from the mean of the data set. It is calculated by subtracting the mean from the data point and dividing by the standard deviation. In this case, the teacher wants to convert the test scores into z-scores relative to the mean and standard deviation of the students in the class.

The formula for calculating a z-score is:

z-score = (data point - mean) / standard deviation

Using the mean and standard deviation provided in the question, the teacher can calculate the z-score for each student's test score by plugging in the values into the formula. For example, if a student scored 150 on the test, their z-score would be:

z-score = (150 - 130) / 26.2
z-score = 0.76

This means that the student's test score is 0.76 standard deviations above the mean of the class. The teacher can use this information to understand how each student's test score compares to the rest of the class.

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Answer:

length of a side is 3

Step-by-step explanation:

if it is a square, the sides are equal. The diagonal will divide the square into 2 isosceles right triangles with diagonal is the hypotenuse

Pythagorean theorem: c^2 = a^2 + b^2

since a = b in isosceles right triangle

c^2 = 2a^2

18 = 2a^2

a^2 = 18/2 = 9

a = √9 = 3