Below is the previous 3-day work schedule for co-workers: Kate, Kevin, and Greg, who work at a gold
mine. Unfortunately, someone must be fired.
Monday
Tuesday
Wednesday
Kate
8am-2pm
9am-2pm
10am-2pm
Kevin
9am-4pm
8am-1pm
8am-4pm
Greg
8am-12pm
12pm-6pm
9am-3pm
If there were 51 gold nuggets found on Monday, 55 nuggets found on Tuesday, and 54 nuggets found on
Wednesday,
1.) How many nuggets per hour does each worker find? (These three numbers is the next code)
2.) Who should be fired?

Below Is The Previous 3-day Work Schedule For Co-workers: Kate, Kevin, And Greg, Who Work At A Goldmine.

Answers

Answer 1

The three workers working in different shifts, and the number of gold

nuggets found in three days give a system of three equations.

Response:

1) Kate finds 4 nuggets per hour, Kevin finds 1 nugget per hour and Greg finds 5 nuggets per hour.

2) Kevin

Which method can be used to solve for the number of nuggets each worker finds per hour?

Let a, b, and c represent the number of nuggets per hour that Kate, Kevin, and Greg finds, we have;

Kate, Kevin, and Greg works for 6, 7, and 4 hours respectively on Monday

On Tuesday, we have; 5, 5, and 6 hours respectively

On Wednesday, we have; 4, 8, and 6 hours respectively

Which gives the following system of simultaneous equations;

6·a + 7·b + 4·c = 51...(1)

5·a + 5·b + 6·c = 55...(2)

4·a + 8·b + 6·c = 54...(3)

Subtracting equation (2) from (3) gives;

4·a - 5·a + 8·b - 5·b + 6·c - 6·c = 54 - 55 = -1

3·b - a = -1

a = 3·b + 1

Which gives;

6·(3·b + 1) + 7·b + 4·c = 25·b + 4·c + 6 = 51

25·b + 4·c + 6 = 51

[tex]c = \dfrac{51 - 6 - 25\cdot b}{4} = \mathbf{ \dfrac{45 - 25\cdot b}{4}}[/tex]

5·(3·b + 1) + 5·b + 6·c = 20·b + 6·c + 5  = 55

20·b + 6·c + 5 = 55

Similarly;

[tex]c = \dfrac{55-5 - 20\cdot b}{6} = \mathbf{\dfrac{50 -20\cdot b}{6}}[/tex]

Which gives;

[tex]c = \dfrac{45-25\cdot b}{4} = \dfrac{50- 20\cdot b}{6}[/tex]

4 × (50 - 20·b) = 6 × (45 - 25·b)

200 - 80·b = 270 - 150·b

150·b - 80·b = 270 - 200 = 70

70·b = 70

b = 1

a = 3·b + 1

a = 3 × 1 + 1 = 4

a = 4

[tex]c = \dfrac{45-25\times 1}{4} = \mathbf{ 5}[/tex]

c = 5

Number of gold nuggets Kate finds per hour, a = 4Number of gold nuggets Kevin finds per hour, b = 1Number of gold nuggets Greg finds per hour, c = 5

2.) The person that can be fired is the one that finds the least number of gold nuggets per hour, which is Kevin

Learn more about simultaneous equations here:

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Related Questions

Essay about how we use math in our every day life. Give me a paragraph or something pleaseee

Answers

Answer:

Math is required in every day life. When you go to the grocery store determining which is the better deal. Or when cooking to figure out exactly what ingredients you need or hu=ow much. Math is required everyday to do very simple tasks

Step-by-step explanation:

Describe how to determine f(x) and g(x) when x=5

Answers

Answer:

brainly is the best study app in the world

bntu segera y mksh. ​

Answers

Step-by-step explanation:

1. Clean the floor now.

2. Clean the blackboard.

3. Make sure your friends never drives fast again

4. Go and serve a glass of juice to your friend

5. Tell your friend to not speak loud.

4(x+1 1/3) =9 2/3 enter your answer as a mixed number in simplest from​

Answers

Answer:

x = 13/12

x = 1 1/12

Step-by-step explanation:

4 (x + 1 1/3) = 9 2/3

4x + 5 1/3 = 9 2/3

subtract 5 1/3 from each side

4x = 4 1/3

divided by 4 on each side

x = 13/12

x = 1 1/2

hope this helps! :)

06.05 Data Observation
Instructions
For this activity, you will need two different coins. First, you will determine the theoretical probability of events. Then, you will flip the coins 100 times and determine the experimental probability of the events.

Flip two different coins 100 times, and record the results of each coin toss in a table like the one below:

Result Frequency
Two heads
Two tails
One head, one tail
Answer the following questions based on the data you gathered. You must show your work to receive credit.

What is the theoretical probability that a coin toss results in two heads showing?
What is the experimental probability that a coin toss results in two heads showing?
What is the theoretical probability that a coin toss results in two tails showing?
What is the experimental probability that a coin toss results in two tails showing?
What is the theoretical probability that a coin toss results in one head and one tail showing?
What is the experimental probability that a coin toss results in one head and one tail showing?
Compare the theoretical probabilities to your experimental probabilities. Why might there be a difference?

Answers

1. What is the theoretical probability that a coin toss results in two heads showing? 0.25

2. What is the experimental probability that a coin toss results in two heads showing? 0.5 x 0.5

3. What is the theoretical probability that a coin toss results in two tails showing?1/2

4.  What is the experimental probability that a coin toss results in two tails showing?1 in 4

5. What is the theoretical probability that a coin toss results in one head and one tail showing? 0.5

6. What is the experimental probability that a coin toss results in one head and one tail showing? .5

7.  Compare the theoretical probabilities to your experimental probabilities. Why might there be a difference? The theoretical is slightly higher than expected

What is the percent of change if 38 is decreased to 25? round to the nearest whole number

Answers

Answer:

7.89474% decrease

Step-by-step explanation:

Solution:

Calculate percentage change

from V1 = 38 to V2 = 35

(V2−V1)|V1|×100

=(35−38)|38|×100

=−338×100

=−0.0789474×100

=−7.89474%change

=7.89474%decrease

what is ratio of perimiters

Answers

Answer:

Ratio of their perimeters is equal to the ratio of their corresponding side lengths. the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

is a rectangle. and . What is ?


A.
12
B.
6
C.
15
D.
24

Answers

Answer:

6

Step-by-step explanation:

diagonals bisect each other in rectangle

3x-6 = 2x

x=6

find any 4 rational numbers between -1/2 and 1/2​

Answers

Answer:

Step-by-step explanation:

Multiply the numerator and denominator of rational numbers by 5

[tex]\dfrac{-1}{2}=\dfrac{(-1)*5}{2*5}=\dfrac{-5}{10}\\\\\\\dfrac{1}{2}=\dfrac{1*5}{2*5}=\dfrac{5}{10}\\\\\\In\ between \ rational \ numbers \\\\\dfrac{-4}{10} ; \dfrac{-3}{10}; \dfrac{-2}{10}; \dfrac{-1}{10}[/tex]

The area of a rectangular rug is 21 square feet. The perimeter is 20 feet. What are the dimensions of the rug?

Answers

Answer: The length is 7, the width is 3.

Step-by-step explanation:

7*3 = 21 which is the area, also 7 and 3 are the only factors of 21.

7+7 is 14,

3+3 is 6

14 + 6 is 20 which is the perimeter.

How far to get to the the coldest place on Earth?

Answers

Answer:

Oymyakon is the coldest permanently-inhabited place on Earth and is found in the Arctic Circle's Northern Pole of Cold. In 1933, it recorded its lowest temperature of -67.7°C.

hope it will help

the sum of a numner x and 4 equals 12

Answers

SOLUTION:

=) x + 4 = 12

=) x = 12 - 4

=) x = 8

Which could be the function? f(x) = (x 4)2 f(x) = x2 4 f(x) = (x – 4)2 f(x) = x2 – 4.

Answers

Answer:

C. f(x) = (x-4)^2

Step-by-step explanation:

The function among the given option is f(x) = (x – 4)² hence option (C) will be the correct.

What is a function?

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

Given that which one is a function so it is clear that f(x) = (x – 4)² is the best relation between x and f(x).

Hence this option will be the correct answer.

For more about the function

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A cafe makes ten 8-ounce fruit smoothies. Each smoothie is made with 4 ounces of soy milk and 1.3 ounces of banana flavoring. The rest is blueberry juice. How much of each ingredient will be necessary to make the smoothies?

Answers

Answer:

27 ounces of blueberry juice. 40 ounces of soy milk. 13 ounces of banana flavoring.

Step by Step:

4 + 1.3 = 5.3, This is how much of the smoothie is made up of the soy milk and banana flavoring, 5.3 ounces.

So to find the amount of blueberry juice in the smoothie you have to subtract 8-5.3. This finds the remaining part of the smoothie, which is the blueberry juice. 8-5.3 = 2.7

2.7 ounces of blueberry juice in each smoothie.

Now you have to multiply every ingredient by 10, since there are 10 smoothies.

4 * 10 = 40

1.3 * 10 = 13

2.7 * 10 = 27

You need 40 ounces of soymilk, 13 ounces of banana flavoring, and 27 ounces of blueberry juice to make 10, 8-ounce smoothies.

What is the solution to |2x-8|=6?

Answers

Answer:

x = 7, 1 (Multiple solutions)

Step-by-step explanation:

2(7) - 8 = 6

14 - 8 = 6

6 = 6

| 2(1) - 8 | = 6

| -6 | = 6

6 = 6

If the sum of two
prime numbers is 2013,
what is their product?

Answers

Answer:

2013 = 3 x 11 x 61

Step-by-step explanation:

3 x 11 x 61 are all prime. Their sum is 3+11+61 = 75

Answer:

2013 = 3 x 11 x 61

Step-by-step explanation:

Their sum is 3+11+61 = 75

3,11,61 are all prime numbers

hope this helps

Completely factor the polynomial 8x2 – 24x 20x – 60. 8x(x 3)(x – 5) (4x – 3)(2x – 5) 2(2x – 3)(2x 5) 4(x – 3)(2x 5).

Answers

Polynomials consist of both indeterminates and coefficients. The factor of the polynomial 8x² - 24x + 20x - 60 are 2(4x+10)(x-3).

What are polynomials?

A polynomial consists of both indeterminates and coefficients and involves mathematical operations such as addition, subtraction, multiplication, and division.

Given to us

8x² - 24x + 20x - 60

We can factorize the polynomial in the following manner,

[tex]8x^2 - 24x + 20x - 60[/tex]

taking two as the factor commons from the entire polynomial,

[tex]=2[4x^2 - 12x + 10x - 30][/tex]

Now, taking 4x as the common factor from the first two terms of the brackets, also, take 10 as the common factor from the last two terms of the brackets,

[tex]=2[4x(x - 3) + 10(x - 3)]\\\\=2[(4x+ 10)(x - 3)]\\\\= 2 (4x+10)(x-3)[/tex]

Hence, the factor of the polynomial 8x² - 24x + 20x - 60 are 2(4x+10)(x-3).

Learn more about Polynomials:

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Answer: 4(x – 3)(2x + 5)

Step-by-step explanation: did no one use the formula that was given to you?

Which of the following is equivalent to 23 X^-1/2

Answers

Answer:

The answer is 42/2

Step-by-step explanation:

I am so sorry if its not correct please tell me so i can fix my mistake if so.

3ab+4ab^3 I really need help please help meeeee!!!!

Answers

Answer:

ab times (3+4b^2)

Step-by-step explanation:

You would factor the equation.

The amusement park installed a new 260-foot-tall ride. This ride is 78 feet taller than the next tallest ride in the park.
Write an equation using the subtraction property of equality that results in the height of the second tallest ride in the park. Explain your equation.

Answers

Answer:-

[tex]\boxed{\huge \text{182 feet}}[/tex]

Step-by-step explanation:

Let the height of the next tallest rider be t feet

Since the 260-foot-tall ride is 78 feet taller than the next tallest;

That means t = 260 - 78 = 182 feet



Therefore, the height of the second tallest ride in the park = 182 feet.

[tex]\huge \text{hope this helps! :)}[/tex]

-InLoveWithNature-

3. ^2x + 6 = 2
solve radical equations?

Answers

Answer:

x = - 2

Step-by-step explanation:

2x + 6 = 2

2x = 2 - 6

2x = -4

x = -4/2

x = - 2

Hope it helps ⚜

Evelyn drew a marble at random from a bag containing 4 blue, 3 red, 2 yellow, and 5 green marbles. What is the probability that Evelyn selected a marble that is NOT red?

3/14
11/14
3/11
3/7
SHOW WORKK

Answers

Answer:

The probability that she picked a card that is not red is 11/14

Step-by-step explanation:

Number of blue marbles n(blue)=4

Number of red marbles n(red)=3

number of yellow marbles n(yellow)= 2

number of green marbles n(green)=5

total number of marbles n(S)=4+3+2+5=14

P(red)=n(red)/n(S)

P(red)=3/14

We have to determine the probability that the card picked is not red which means the card can be blue or yellow or green.

P(not red)=1-P(red)

               =1-3/14

                =11/14

Hope this helps

Excerpt from Brainly

Im du.mb at this stuff, i dont know how to do it

Answers

Answer:

the correct answer will be 88

Answer:

Area of the shaded region 45.76 cm².

Step-by-step explanation:

Firstly, finding the area of rectangle by substituting the values in the formula :

[tex]{\longrightarrow{\pmb{\sf{A_{(Rectangle)} = l \times b}}}}[/tex]

→ A = Area→ l = length → b = breadth

[tex]\begin{gathered} \qquad{\longrightarrow{\sf{A_{(Rectangle)} = l \times b}}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} = 12\times 8}}}\\\\\qquad{\longrightarrow{\sf{A_{(Rectangle)} = 96}}}\\\\\qquad{\star{\boxed{\sf{\pink{A_{(Rectangle)} = 96 \: {cm}^{2}}}}}} \end{gathered}[/tex]

Hence, the area of rectangle is 96 cm².

[tex]\rule{200}2[/tex]

Secondly, finding the area of circle by substituting the values in the formula :

[tex]{\longrightarrow{\pmb{\sf{A_{(Circle)} = \pi{r}^{2}}}}}[/tex]

→ A = Area → π = 3.14 → r = radius

[tex]\begin{gathered} \qquad{\longrightarrow{\sf{A_{(Circle)} = \pi{r}^{2}}}} \\ \\ \qquad{\longrightarrow{\sf{A_{(Circle)} = 3.14{(4)}^{2}}}} \\ \\ \qquad{\longrightarrow{\sf{A_{(Circle)} = 3.14{(4\times 4)}}}} \\ \\ \qquad{\longrightarrow{\sf{A_{(Circle)} = 3.14(16)}}} \\ \\ \qquad{\longrightarrow{\sf{A_{(Circle)} = 3.14 \times 16}}} \\ \\ \qquad{\longrightarrow{\sf{A_{(Circle)} \approx 50.24}}} \\ \\ \qquad{\star{\boxed{\sf{\purple{A_{(Circle)} \approx 50.24 \: {cm}^{2}}}}}} \end{gathered}[/tex]

Hence, the area of circle is 50.24 cm².

[tex]\rule{200}2[/tex]

Now, finding the area of shaded region by substituting the values in the formula :

[tex]\longrightarrow{\pmb{\sf{A_{(Shaded)} = A_{(Rectangle)} - A_{(Circle)}}}}[/tex]

→ A = Area→ Rectangle → Circle

[tex]\begin{gathered}{\quad{\longrightarrow{\sf{A_{(Shaded)} = A_{(Rectangle)} - A_{(Circle)}}}}}\\\\{\quad{\longrightarrow{\sf{A_{(Shaded)} = 96 - 50.24}}}}\\\\{\quad{\longrightarrow{\sf{A_{(Shaded)} \approx 45.76}}}}\\\\{\quad{\star{\boxed{\sf{\red{A_{(Shaded)} \approx 45.76 \: {cm}^{2}}}}}}} \end{gathered}[/tex]

Hence, the area of shaded region is 45.76 cm².

[tex]\rule{300}{2.5}[/tex]

What is slope and how do you find it?

Answers

Step-by-step explanation:

Slope = [tex]\frac{rise}{run}[/tex]

          = [tex]\frac{y2 - y1}{x2-x1}[/tex]

If two coordinates be (x1,y-1) and (X2,Y2)

Slope:-

m=y2-y1/x2-x1

If a line be ax+by+c=0

Slope'-

m=-a/b

what is two ways to rewrite 21x^2 -42x +14 in equvalent form? i really need help here lol-​

Answers

Answer:

7(3x^2-6x+2)

Step-by-step explanation:

21, 42, 14 they can be divided by 7 so we put 7 out

Which shows the domain and range of these functions? Domain: (Negative infinity, infinity) Range: (Negative infinity, infinity) Domain: (0, infinity) Range: (Negative infinity, infinity) Domain: (Negative infinity, infinity) Range: (0, infinity).

Answers

The domain (input values) and range (output values) of the function is, Domain: (Negative infinity, infinity), Range: (0, infinity).

What is domain and range of function?

Domain of a function is the set of all the possible input values which are valid for that function.

Range of a function is the set of all the possible output values which are valid for that function.

Given information-

The function given in the problem is,

[tex]y=f(x)\\y=h(x)\\y=g(x)\\y=k(x)[/tex]

As domain of a function is the set of all the possible input values which are valid for that function. Thus the function should accept all the values for the given function.

Here in the given function the function is takes the input for all the real number form positive to the negative infinite. Thus the domain of the function is,

Domain: (-∞, ∞).

Range of a function is the set of all the possible output values which are valid for that function.

Here the output for the given function gives the positive values to the infinite. thus the range of the function is,

Range: (0, ∞).

Thus, the domain and range of the function is, domain: (Negative infinity, infinity), range: (0, infinity).

Learn more about the domain and range of the function here;

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Answer:

Answers for entire slide:

1. B, and D

2. All of them

3. only correct one is C.

Step-by-step explanation:

Source: trust me bro

This is with tangents I have already figured out one portion of the prolem please help

Answers

Answer:

-5

Step-by-step explanation:

when something is squared it can be positive or negative

How do I find the value of x?? please help

Answers

Add the two angles and then subtract from 180* to find the missing angle

So,

145* + 15* = 160*

180* - 160* = 20*

Answer: x = 20*

what is the gradient of the blue line ??

Answers

Answer:-5

Step-by-step explanation:

The solution is in the attached file below

The gradient of the blue line that passes through the points (-1, 0) and (0, -5) is -5.

What is the slope ( gradient ) of the line?

The Slope (gradient) is simply expressed as a change in y over the change in x.

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

The blue line in the graph runs through points (-1, 0) and (0, -5).

To find the gradient (slope) of the blue line passing through the points (-1, 0) and (0, -5), we use the slope formula.

Point (-1,0): x₁ = -1 and y₁ = 0

Point (0, -5): x₂ = 0 and y₂ = -5

Plug the coordinates into the above formula:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}\\\\m = \frac{-5 - 0}{0 - (-1)}\\\\Simplify:\\\\m = \frac{-5 - 0}{0 + 1}\\\\m = \frac{-5}{ 1}\\\\m = -5[/tex]

Therefore, the slope is -5.

Learn more about slope formula here: brainly.com/question/24578307

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What is the solution 2/3 a +6 > 0

Answers

Answer:

a > -9

subtract 6 from both sides to get 2/3 a > -6. Then multiply both sides by 3 to get 2a > -18. Last, divide both sides by 2 to get your answer: a > -9

Answer:

a > (-9)

Step-by-step explanation:

[tex] \frac{2}{3} a + 6 > 0 \\ \frac{2}{3} a + 6 - 6 > 0 - 6 \\ \frac{2}{3} a > - 6 \\ \frac{2}{3} \times 3 \: \: a > - 6 \times 3 \\ 2a > - 18 \\ \frac{2a}{2} > \frac{ - 18}{2} \\ a > (- 9) \\ [/tex]

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