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 = 1a = 3·b + 1
a = 3 × 1 + 1 = 4
a = 4[tex]c = \dfrac{45-25\times 1}{4} = \mathbf{ 5}[/tex]
c = 5Number 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 = 52.) The person that can be fired is the one that finds the least number of gold nuggets per hour, which is Kevin
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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
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
Which of the following is equivalent to 23 X^-1/2
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.
What is the solution to |2x-8|=6?
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
is a rectangle. and . What is ?
A.
12
B.
6
C.
15
D.
24
Answer:
6
Step-by-step explanation:
diagonals bisect each other in rectangle
3x-6 = 2x
x=6
the sum of a numner x and 4 equals 12
SOLUTION:
=) x + 4 = 12
=) x = 12 - 4
=) x = 8
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?
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.
How far to get to the the coldest place on Earth?
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
How do I find the value of x?? please help
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 two ways to rewrite 21x^2 -42x +14 in equvalent form? i really need help here lol-
Answer:
7(3x^2-6x+2)
Step-by-step explanation:
21, 42, 14 they can be divided by 7 so we put 7 out
4(x+1 1/3) =9 2/3 enter your answer as a mixed number in simplest from
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! :)
Essay about how we use math in our every day life. Give me a paragraph or something pleaseee
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:
bntu segera y mksh.
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.
what is the gradient of the blue line ??
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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Im du.mb at this stuff, i dont know how to do it
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]
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).
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?
What is the percent of change if 38 is decreased to 25? round to the nearest whole number
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
3ab+4ab^3 I really need help please help meeeee!!!!
Answer:
ab times (3+4b^2)
Step-by-step explanation:
You would factor the equation.
Which could be the function? f(x) = (x 4)2 f(x) = x2 4 f(x) = (x – 4)2 f(x) = x2 – 4.
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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what is ratio of perimiters
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.
3. ^2x + 6 = 2
solve radical equations?
Answer:
x = - 2
Step-by-step explanation:
2x + 6 = 2
2x = 2 - 6
2x = -4
x = -4/2
x = - 2
Hope it helps ⚜
If the sum of two
prime numbers is 2013,
what is their product?
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
find any 4 rational numbers between -1/2 and 1/2
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 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.
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-
What is slope and how do you find it?
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-x1If a line be ax+by+c=0
Slope'-
m=-a/bDescribe how to determine f(x) and g(x) when x=5
Answer:
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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?
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
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).
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
Answer:
-5
Step-by-step explanation:
when something is squared it can be positive or negative
What is the solution 2/3 a +6 > 0
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]
The area of a rectangular rug is 21 square feet. The perimeter is 20 feet. What are the dimensions of the rug?
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.