Jeff, Gene, and Mike need to eat an entire cake before it goes bad. The cake is cut into 8 pieces.

- Jeff could eat 6 pieces of cake in 2 hours
- Gene can eat 2 pieces of cake in 30 minutes
- Mike can eat 4 pieces of cake in 48 minutes

The pieces can be divided into smaller pieces as necessary - the rates are based on the size of pieces that result when dividing the cake into 8 equal pieces.

Answer these questions below:

1) How many pieces of cake can jeff eat in 1 hour? _________________

2) How many pieces of cake can Gene eat in 1 hour? _____________________

3) How many pieces of cake can Mike eat in 60 minutes? ____________________

4) Will it take Mike, Gene, and Jeff more than 1 hour to each eat the cake, or less that an hour to eat the cake? Explain how you know.

The equation solved in terms of a is 10x + 15/ 2x + 13

The subject of a formula is defined as the variable that is expressed in terms of the other variables in an equation or given expression.

It is also described as the variable that is being worked out in a given equation.

Given the equation;

a(2x + 3) = 9x + 15 + x

collect like terms

a(2x + 3) = 10x + 15

To make 'a' the subject, divide both sides by the coefficient of a which is (2x + 3)

a = 10x + 15/ 2x + 13

Thus, the equation solved in terms of a is 10x + 15/ 2x + 13

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Answer:

True

Step-by-step explanation:

The location on the number line to plot the sum will be between -1 1/2 and -2.

It should be noted that the number line is a straight line that is a visual representation of the numbers. It can be used for addition and subtraction.

In this case, the addition of 3/4 + (-2 1/2) will be:

= 3/4 - 2 1/2

= - 1 3/4

Therefore, the location on the number line to plot the sum will be between -1 1/2 and -2.

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       Round 98984 to 1 significant figure.

       100000.

Answer:

a

Step-by-step explanation:

Determine the amount of sales she made that month

a. The total amount of sales is Ksh 450,000

b. Her commission in february is  Ksh 34,480

Total earning is Ksh 43,860

a) Jane's total earnings in January were Ksh 48,000, and her base salary is Ksh 20,000. This means that she earned an additional Ksh 28,000 in commissions.

Since her commission rate is 8% for sales in excess of Ksh 100,000, we can calculate the amount of sales she made in January by first calculating the sales over which she got a commission.

Ksh 28,000 is 8% of the sales over Ksh 100,000. So we can set up the following equation and solve for the sales:

0.08 * sales = 28,000

Solving for sales:

sales = 28,000 / 0.08 = Ksh 350,000

Since she only earns a commission on sales in excess of Ksh 100,000, the total amount of sales she made in January would be:

Ksh 100,000 (no commission threshold) + Ksh 350,000 (sales over the threshold) = Ksh 450,000

b) i) If her total sales in February increased by 18%, her sales in February were:

1.18 * Ksh 450,000 = Ksh 531,000

But remember, she only gets a commission on sales over Ksh 100,000. So the sales that will earn a commission in February are:

Ksh 531,000 - Ksh 100,000 = Ksh 431,000

Her commission in February is 8% of this amount:

0.08 * Ksh 431,000 = Ksh 34,480

ii) If her sales in March then dropped by 25%, her sales in March were:

0.75 * Ksh 531,000 = Ksh 398,250

The sales that will earn a commission in March are:

Ksh 398,250 - Ksh 100,000 = Ksh 298,250

Her commission in March is 8% of this amount:

0.08 * Ksh 298,250 = Ksh 23,860

So, her total earnings in March (her base salary plus her commission) would be:

Ksh 20,000 + Ksh 23,860 = Ksh 43,860

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Answer: 106.6 is the correct answer

Step-by-step explanation:

The arithmetic sequence AP's 32nd term is calculated to be 225.

An arithmetic progression (AP) in mathematics is a list and maybe sequence of numbers with each term is obtained by adding a sequence to the term before it.

Finally, the solution to the question is as follows:

The numbers in the displayed sequence are as follows:

101,105,109,113, ...........

We must explore the 32nd number in the series because it contains 32 terms.

The common difference with both two consecutive terms of an AP which are equal is denoted by 'd.'

Let's assume the first term is'a₁' = 101.

Let's assume 'a₂' = 105 is the second term.

Let's assume the third term is 'a₃' = 109

Substitute the values the preceding equation; the 32nd term is-

d = a₂ - a₁  

Obtain the common difference;

d = 105 - 101

d = 4

Put the values in the preceding formula; the 32nd term is

The formula finds the nth term equation;

Put the given values in nth term formula;

a₃₂ = a + (n - 1) d

a₃₂ = 101 + (32 - 1)(4)

a₃₂ = 101 + 128 - 4

a₃₂ = 225

Thus, the 32nd term value of the arithmetic sequence is calculated to be 225.

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The equation [tex]A(x)=\frac{18+0.15x}{x}[/tex] represents the correct expression for the Average cost.

What is a mathematical expression?

In mathematics, an expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. Mathematical symbols can represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to aid in determining the sequence of operations and other features of logical grammar.

The store charges $18 for design setting and $0.15 per print out of business card.

Let the number of cards be [tex]x[/tex]

Then, total cost of printing of [tex]x[/tex] cards = $ [tex]0.15x[/tex]

Thus, the expression for the average cost [tex]A(x)[/tex] is given as,

[tex]A(x)=\frac{18+0.15x}{x}[/tex]

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The value of x makes the triangle a right triangle is 15 .

Pythagoras Theorem states that sum of square of two sides of triangle  is equal to the square of longest side of the right angle triangle.

In the given question

the length of longest side = 25.

length of other two side= x and x+5.

By Pythagoras Theorem

[tex]x^{2} +(x+5)^{2} =25^{2}[/tex]

[tex]x^{2} +x^{2} +25+10x=625[/tex]

[tex]2x^{2} +10x-600=0[/tex]

[tex]2x^{2} +40x-30x-600=0[/tex]  ( By Splitting the middle term)

[tex]2x(x+20)-30(x+20)=0\\ \\ (2x-30)(x+20)=0\\[/tex]

solving 2x-30=0   and  x+20=0

we get x=15 and x= -20 ( not possible as distance can't be negative)

x=15.

Therefore , the value of x makes the triangle a right triangle is 15 .

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Square feet of cardboard are used to make each barrel = 23.4558 sq. ft.

The recycling barrels are cylindrical.

Height of the cylinder, h = 3ft

Diameter of the base circle of the cylinder = 30 inches

So radius, r = 15 inches = 15 x 0.083 ft = 1.245 ft

The total surface area of the cylinder is the sum of its lateral surface area and the area of the base and lid circles.

Here the base and lid of the cylinder is made of plastic and sides made of cardboard. So to find the square feet of cardboard required, we need only to find the lateral surface area of the cylinder.

Lateral surface area of the cylinder = 2πrh

                                                           = 2 x 3.14 x 1.245 x 3

                                                           = 23.4558 square feet

So 23.4558 square feet of cardboard is used to make each barrel

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The relation is a function because it is a one-to-one relation

The relation is given as

y = -3x

The inputs are given as

x = 0, x = 1 and x = 2

Substitute the values of x i.e. x = 0, x = 1 and x = 2 in the equation of the function y = -3x

So, we have

y = -3(0) = 0

y = -3(1) = -3

y = -3(2) = -6

From the above computations, we can see that the y values are different for the inputs

Hence, the relation is a function because it is a one-to-one relation

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There are 13 diamonds in the deck (as well as other colors). Since there are 52 cards, the probability of getting a diamond on the first draw is 13/52. After the first card is drawn, all that's left are his 12 diamonds. Therefore, the probability of drawing a diamond is 12/51 (note that he has only 51 cards left after pulling/removing the first card since there are no replacement cards). The overall probability is the product of two possibilities. The odds of drawing diamonds from the original deck are 13/52 times the odds of drawing diamonds from his remaining 51 cards. Assuming the first card drawn is a diamond, 12/51.

P=13/52*12/51=1/4*4/17=1/17.

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The approximate distance that Pluto is from the sun will be 3.72 × 10⁹ miles. Then the correct option is A.

Conversion means to convert the same thing into different units.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The average distance between the centers of the Earth and the Sun is measured in astronomical units.

We know that One astronomical unit is about 9.3 × 10⁷ miles.

Pluto is about 40 astronomical units from the sun. Then the approximate distance that Pluto is from the sun will be

⇒ 40 × 9.3 × 10⁷

⇒ 372 × 10⁷

⇒ 3.72 × 10⁹ miles

The approximate distance that Pluto is from the sun will be 3.72 × 10⁹ miles. Then the correct option is A.

Your question was incomplete, but the complete question was given below.

An astronomical unit is the mean distance from the center of Earth to the center of the sun. One astronomical unit is about 9.3 × 10⁷ miles. Pluto is about 40 astronomical units from the sun. What is the approximate distance that Pluto is from the sun?

A. 3.72 × 10⁹ miles

B. 4.30 × 10⁹ miles

C. 3.72 × 10⁷ miles

D. 4.30 × 10⁷ miles

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The sum of finite arithmetic series 10+20+30+ . . . . . +110+120 is 780

Suppose we are given an arithmetic series:

   a(1) + a(2) + a(3) + ... + a(n)

The sum of the first nth terms is given by:

S(n) = n/2 [a(1) + a(n)]

Where:

a(1) is the first term and a(n) is the nth term.

The given series is:

    10+20+30+ . . . . . +110+120

We get, then,

a(1) = 10

a(n) = 120

To find n, recall the formula of the nth term of an arithmetic sequence:

a(n) = a(1) + (n-1) . d

where d is the common difference.

From the given series, we get:

d = 20 - 10 = 10

Substitute a(1) =10, d = 10, and a(n) = 120 into the formula:

120 = 10 + (n-1) . 10

120 = 10 n

n = 12

Substitute n = 12 into the sum formula:

S(n) = n/2 [a(1) + a(n)]

S(12) = 12/2 (10 + 120)

         = 6. 130 = 780

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The geometric mean of 8 and 22 in simplest form is 4√11. The answer is letter A.

Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.

To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.

The formula for the geometric mean is given by:

GM = n√x1 x2 . . . xn

Solving for the geometric mean between 18 and 1.5 using the formula:

GM = n√x1 x2 . . . xn

where n = 2, x1 = 8, and x2 = 22

GM = √(8)(22)

GM = √176

GM = 4√11

Hence, the geometric mean of 8 and 22 is A. 4 √11.

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Quantum numbers are:

Quantum numbers:

(A) n = 1

(B) n = 2

Therefore, Quantum numbers are:

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The y-coordinate is 4 and the y-intercept is (0,4)

The given equation is 4x + 3y = 12

Comparing the equation with the equation of line ax + by = c

where a = 4, b = 3, c = 12

The y-intercept is the point where the graph intersects the y-axis. To graph, any function that is of the form y = f(x) finding the intercepts is really important. There are two types of intercepts that a function can have. They are the x-intercept and the y-intercept. An intercept of a function is a point where the graph of the function cuts the axis.

for y-intercept,

x coordinate is 0

that is x=0

4(0) + 3y = 12

3y = 12

y = 12/3

y = 4

Hence the y-coordinate is 4 and the y-intercept is (0,4)

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Answer:

ah²+k

Step-by-step explanation:

The y-intercept is when x=0.

[tex]y=a(0-h)^2+k=ah^2+k[/tex]

The two possible locations of the point C are (1, 1) and (- 2, - 5).

According to the statement, we find the coordinates of the ends of a line segment and a partition ratio. There are two possible solutions concening the location of the point B:

Thus, we have the corresponding expressions for each case:

Case 1

C(x, y) = A(x, y) + (4 / 5) · [B(x, y) - A(x, y)]

C(x, y) = (- 3, - 7) + (4 / 5) · [(2, 3) - (- 3, - 7)]

C(x, y) = (- 3, - 7) + (4 / 5) · (5, 10)

C(x, y) = (- 3, - 7) + (4, 8)

C(x, y) = (1, 1)

Case 2

C(x, y) = A(x, y) + (1 / 5) · [B(x, y) - A(x, y)]

C(x, y) = (- 3, - 7) + (1 / 5) · [(2, 3) - (- 3, - 7)]

C(x, y) = (- 3, - 7) + (1 / 5) · (5, 10)

C(x, y) = (- 3, - 7) + (1, 2)

C(x, y) = (- 2, - 5)

The two possible locations of the point C are (1, 1) and (- 2, - 5).

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If Landon left his automobile alone for 4 hours, he would be charged $13.

If Landon left his car for t hours, he would be charged 5 + 2t.

It is best to create a phrase for such inquiries.

The set cost of the parking fee is $5.

Additionally, it costs $2 each hour.

In other words, if someone uses the parking lot for t hours, they must pay $2 per hour for those t hours.

Formula = 2 x t = 2 t

Including the set amount, the entire phrase is:

5 + 2t

So, if Landon parked for six hours, he would have to pay:

= 5 + 2 t

= 5 + 2 x 4

= $13

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The triangle with vertices A(0 , 0), B(0 , 6), and C(10 , 0) has its circumcenter located at (5 , 3).

Circumcenter of a triangle refers to the point inside a triangle at which the perpendicular bisectors of the sides of a triangle intersect. This point is also equidistant from the three vertices.

Given the location of the three vertices, there are different methods that can be used to locate the circumcenter of the triangle.

First, try to graph and visualize the triangle formed by the three vertices. (see photo)

From there, we can say that triangle ABC is a right-angled triangle with line BC as the hypotenuse.

One of the properties of the circumcenter of a triangle states that the circumcenter lies in the middle of a hypotenuse if it is a right-angled triangle.

To get the circumcenter, find the midpoint of the line BC.

midpoint = M(xm ,ym) = [(x1 + x2)/2 , (y1 + y2)/2]

M(xm ,ym) = [(0 + 10)/2 , (6 + 0)/2]

M(xm ,ym) = (5 , 3)

Hence, the circumcenter is located at (5 , 3).

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Answer: A and E

Step-by-step explanation:

A. 21/25 × 50/63=

(21*50)/(25*63)=

21/63 * 50/25 =

1/3 * 2 =2/3

B. 7/8×9/25=

(7*9)/(8*25)=

63/200 [tex]\neq[/tex] 2/3

C. 1/30×2/3=

(1*2)/(30*3)=

2/90=

1/45 [tex]\neq[/tex] 2/3

D. 3/25×7/12=

(3*7)/(12*25)=

3/12 * 7/25 =

1/4 * 7/25 =

(1*7)/(4*25)=

7/100 [tex]\neq[/tex] 2/3

E. 20/27×27/30=

(20*27)/(27*30)=

27/27 * 20/30=

1 * 2/3 = 2/3

A and E

The equation of the line that passes through (0,-b) and (c,0) is 7y - 8x = 28

The relationship between each x and each matching y is expressed in the equation of a line to produce an ordered pair (x, y) that lies on the line. The equation won't be satisfied by ordered pairs (x, y) that don't lie on the line.

The equation of a line in point-slope form is calculated using the following formula:

y-y₀=m(x-x₀)

where, m is the slope of the line and (x₀, y₀) is any point on the line.

Given data: A line G passes through the points (-2.6,1) and (-1.4,2.5). Let the points (-2.6,1) be (x₀,y₀) and (-1.4,2.5) be (x,y).

Slope of the equation (m)= y-y₀/ (x-x₀)

Slope of the equation (m)=2.5-1/{-1.4-(-2.6)}

Slope of the equation (m)=1.5/(-1.4+2.6)

Slope of the equation (m)=1.5/1.2

Slope of the equation (m)=5/4

Slope of the equation (m)=1.25

The formula y= ax + b can be used to determine the equation of line.

y= 1.25x+b

To find the value of b, let's replace the point (-2.6,1) in the equation above.

1=1.25(-2.6)+b

1=-3.25 +b

b= 1+3.25

b=4.25

let y=0

0=1.25x+4.25

x=-3.4

Therefore, the equation's points are (0,-4.25) and (-3.4,0).

let y =  kx+ b

0=k(-3.4)+(-4.25)

k=-1.25

In light of this, the equation for the line through points (0,-4.25) and (-3.4,0) is y=-1.25x-4.25

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Answer:

8

Step-by-step explanation:

answer:

9

explanation:

9*9=81

81 sqrt= 9

The number of people that are in the Kariang tribe is; 420000 people

We are given;

Total Population of Akha Tribe in Thailand = 7 * 10⁴ people

Kariang tribe population is a total of 6 times larger than that of Akha Tribe

Thus, for us to be able to get how many people are in the Kariang tribe, we will just multiply both values to get;

6 * 7 * 10⁴ = 42 * 10⁴ = 420000

Therefore, since Thailand is home to numerous indigenous tribes, we can conclude from the calculation above and using the given parameters in the question that the number of people that are in the Kariang tribe is; 420000 people

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