[tex]\boldsymbol{\mathbf{Answer}}[/tex]
[tex]\boldsymbol{\mathbf{Machine \, A \,will\, take \,6 \,hours\, to \,produce\, 1 \,widget \,on\, its\, own.}}[/tex]
[tex]\boldsymbol{\mathbf{Step-by-step \,explanation:}}[/tex]
Let,
performance rate of machine A is x widget per hour.
performance rate of machine A is y widget per hour.
As given, Machine A and Machine B can produce 1 widget in 3 hours working together.
I.e mathemetically,
[tex]\boldsymbol{x + y=\frac{1}{3}......(1)}[/tex]
lly for second statement, Machine A’s speed were doubled, the two machines could produce 1 widget in 2 hours working together.
i.e mathematically,
[tex]\boldsymbol{2x + y=\frac{1}{2}......(2)}[/tex]
Substact equation (1) in (2)
[tex]x + y=\frac{1}{3}[/tex]
[tex]-2x + y=\frac{1}{2}[/tex]
Resultant equation will be,
[tex]-x=\frac{-1}{6}[/tex]
[tex]\boldsymbol{x = \frac{1}{6}}[/tex]
Performance rate of machine A is \frac{1}{6} widget per hour.
what is time Machine A will take to produce 1 widget on its own.
i.e = [tex]\frac{1}{\frac{1}{6}}[/tex]
[tex]\boldsymbol\mathbf{{=\, 6 \,hours.}}[/tex]
Why does math get so hard that you have an answer but you forget what your answer was because it was so so so so so so so so so so so so so so hard.Why is it hard?
Answer:
because if u write down the steps that u took to get the answer it wont be sosososososososo hard
Step-by-step explanation:
A jar contains six blue marbles and five red marbles. Suppose you choose a marble at random, and do not replace it. Then you choose a second marble. Find the probability of the following event. Both of the selected marbles are red.
The jar has 6+5=11 marbles.
We have to find the probability of the following event:
1.We pick a marble from a jar that has 11 marbles in total, 5 of them are red
2.We pick a marble from a jar that has now 10 marbles in total, 4 of them are red (because in the previous step we picked a red marble and did not put it back in the jar)
The probability of the first event is:
[tex]P_1=\frac{5}{11}[/tex]
The probability of the second event is:
[tex]P_2=\frac{4}{10}=\frac{2}{5}[/tex]
The probability of the both events to happen is:
[tex]P=P_1\cdot P_2=\frac{5}{11}\cdot \frac{2}{5}=\frac{2}{11}=0.1818[/tex]
Lauren coordinates a construction projects for a cement company. A government project requires constructing two rectangular concrete slabs of dimensions 24× 24× 1 feet. Additionally, the company sends a 20% surplus of concrete to ensure the job can be completed. If a cement truck can carry a maximum of 8 cubic yards of cement, what's the fewest number of trucks that Lauren should send? A)1 B)2 C)3 D)4 E)5lar
The fewest number of trucks Lauren should send is D) 4 trucks.
Step-by-step explanation:
Step 1:
The rectangular slab's dimensions are [tex]24 \times 24 \times 1[/tex] feet. Each truck can carry 8 cubic yards of cement.
First, we need to determine the volume of the slabs in yards. 1 foot = 0.333 yards. So 24 feet = [tex]24\times 0.3333[/tex] = 8 yards.
The volume of the slab = [tex]8 \times 8 \times 0.3333[/tex] = 21.3312 cubic yards.
Step 2:
The company sends a surplus of 20% to make sure the job can be completed. So the total cement sent is the required volume and an extra 20%.
The total cement sent = The required cement + 20%.
= 21.3312 + 20% = 25.597 cubic yards.
Step 3:
So to find the number of trucks needed, we divide the cement sent by the load each truck can carry. Each truck can carry 8 cubic yards of cement. So
The number of trucks needed = [tex]\frac{therequiredload}{load per truck} = \frac{25.597}{8} = 3.199625.[/tex]
If 3.199 trucks are needed, it means 4 trucks are needed which is option D.
________________shapes are radical alterations of visible reality simplifications, exaggerations, or transmutation that sometimes bear little resemblance to the original entities from which they were derived.1. geomatric2. organic3. contour4. abstract5. amorphous
Answer:4. Abstract.
Step-by-step explanation: Abstraction is a term used to describe a departure from reality in the expressions of image in art.
This kind of departure from accurate and actual representation can be slight,can be partial, or complete or total.
Abstract shapes are shapes used in depicting the virtual images of certain objects or people,it usually does not actually display reality or, it only shows the radical altering of the visual realities of different things.
Using the formula A=P(1+r)^t calculate the value of an initial investment of $4,500 after 10 years at 4% interest.
The solution is [tex]\$ 6661[/tex]
Explanation:
The initial investment is $4500
The time taken is 10 years.
The rate of interest is 4%
We shall determine the value of A using the formula [tex]A=P(1+r)^t[/tex]
where P is the initial investment,
r is the rate of interest and
t is time
Let us substitute the values [tex]P=4500[/tex] , [tex]t=10[/tex] and [tex]r=4 \%[/tex] in the formula [tex]A=P(1+r)^t[/tex]
Thus, we have,
[tex]A=4500(1+0.04)^{10}[/tex]
Adding the values within the bracket, we have,
[tex]A=4500(1.04)^{10}[/tex]
Simplifying, we get,
[tex]A=4500(1.4802)[/tex]
Multiplying, we have,
[tex]A=6661[/tex]
Thus, the value is $6661
Dan and Carl share a 18-ounce box of cereal. By the end of the week, Dan has eaten 1 6 of the box, and Carl has eaten 2 3 of the box of cereal. How many ounces are left in the box?
Answer: 3 ounces of cereals was left in the box.
Step-by-step explanation:
Dan and Carl share a 18-ounce box of cereal. By the end of the week, Dan has eaten 1/6 of the box. This means that the amount of cereals that Dan ate is
1/6 × 18 = 3 ounces of cereals
Also, by the end of the week, Carl has eaten 2/3 of the box of cereal. This means that the amount of cereals that Carl ate is
2/3 × 18 = 12 ounces of cereals
The total amount of cereals that they ate is 12 + 3 = 15 ounces
Therefore, the amount of cereals left in the box is
18 - 15 = 3 ounces
PLEASE HELP
Find the range of the function f(n) = 5n −4 for the domain {−3, 0, 4}. List the values in order from least to greatest and use a comma to separate each value..
range: { }
The range of the function is [tex]\{-19,-4,16\}[/tex]
Explanation:
The function is [tex]f(n)=5n-4[/tex]
The domain of the function is [tex]\{-3,0,4\}[/tex]
We need to find the range of the function.
The range can be determined by substituting the values of domain in the function.
Thus, the range of the function when the domain is -3 is given by
[tex]f(-3)=5(-3)-4[/tex]
[tex]=-15-4[/tex]
[tex]=-19[/tex]
Thus, the range is -19 when [tex]n=-3[/tex]
The range of the function when the domain is 0 is given by
[tex]f(0)=5(0)-4[/tex]
[tex]=0-4[/tex]
[tex]=-4[/tex]
Thus, the range is -4 when [tex]n=0[/tex]
The range of the function when the domain is 4 is given by
[tex]f(4)=5(4)-4[/tex]
[tex]=20-4[/tex]
[tex]=16[/tex]
Thus, the range is 16 when [tex]n=4[/tex]
Thus, the range of the function is [tex]\{-19,-4,16\}[/tex] when their corresponding domain is [tex]\{-3,0,4\}[/tex]
Arranging the range in order from least to greatest is given by
[tex]\{-19,-4,16\}[/tex]
Hence, the range of the function is [tex]\{-19,-4,16\}[/tex]
student enrollment at a local school is concerning the community because the number of students has dropped to 504 which is a 20% decrease from the previous year. what was the student enrollment the previous year?
Answer:
The answer is 630 students
Step-by-step explanation:
For this case, we have 504 students and the student enrollment has decrease 20%, which mean 504 is the 80% of the total student enrollment of the previous year.
[tex]100 - 20 = 80[/tex]%
This is a direct proportion problem. As shown bellow:
504 -> 80%
x -> 100%
For solving this we use the Mathematical Rule of Three, a method of having three numbers to help calculate the unknown.
b -> c
x -> a
The algorithm for rule of three is the following:
[tex]x = \frac{a * b}{c} \\\\x= \frac{504*100}{80} =\frac{50400}{80}=630\\ \\x=630[/tex]
What is the length of the missing side FP? Round answer to the nearest tenth.
Answer:
Step-by-step explanation:
Considering the given triangle KFP, to determine FP, we would apply the sine rule. It is expressed as
a/SinA = b/SinB = c/SinC
Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes
FP/SinK = FK/SinP = KP/SinF
Therefore
FP/Sin 49 = 66/Sin 85
Cross multiplying, it becomes
FPSin85 = 66Sin49
0.996FP = 45 × 0.7547
0.996FP = 33.9615
FP = 33.9615/0.996
FP = 34.1
A purchaser paid $1,539.13 for a computer system that originally cost $1,215.91. If the markup was 21% of the $1,539.13 selling price, then what is the percent markup based on cost?
Answer:
$1272.008264
Step-by-step explanation:
If the mark-up was 21%, then the final price is 121% of the original price. Simply divide $1,539.13 by 1.21 to get the original price of $1272.008264
The percent markup based on cost is calculated by finding the amount of the markup, dividing it by the original cost and multiplying by 100. In this case, the markup was 21% of the sale price, or $323.12. This correlates to a 26.56% markup based on the original cost ($1,215.91).
Explanation:The percent markup based on cost can be calculated by first determining the amount of the markup, then dividing the markup by the original cost of the item, and finally multiplying the result by 100 to express it as a percentage. According to the question, the markup is 21% of the $1,539.13 selling price. Therefore, to calculate the markup we multiply $1,539.13 by 0.21 which results in $323.12. This is the amount by which the original price was increased to get the selling price. To calculate the percent markup based on cost, we divide the markup amount ($323.12) by the original cost of the item ($1,215.91) and then multiply by 100. This gives us a percentage markup of approximately 26.56%. So, the percent markup based on cost is 26.56%.
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Use the given functions f and g to find f + g, f − g, fg, and f g . State the domain of each. (Enter your answer for the domain in interval notation.) f(x) = 3x + 6, g(x) = x + 2.
Find the domain of each problem.
f + g = Domain=
f-g= Domain=
(f)(g)= Domain=
f/g=Domain=
2.) Find (g ○ f)(x) and (f ○ g)(x) for the given functions f and g.
f(x) = 3/(x+5), g(x) = 3x − 6
(g ○ f)(x) =
(f ○ g)(x) =
3.) Use the method of completing the square to find the standard form of the quadratic function.
f(x) = x2 − 8x + 2
y =
4.) Use the vertex formula to determine the vertex of the graph of the function.
f(x) = x2 − 14x Write the function in standard form.
f(x) =
5.) Use the vertex formula to determine the vertex of the graph of the function.
f(x) = 3x2 − 10x + 1 Write the function in standard form.
f(x) =
Answer: The answers are stated below
Step-by-step explanation: Attached below is the explaination of the solution.
f + g =4x + 8 Domain - (-∞, ∞)
f - g = 2x + 4 Domain - (-∞, ∞)
(f)(g) = 3x² + 12x + 12 Domain - (-∞, ∞)
f/g = [tex]\frac{3x + 6}{x + 2}[/tex] Domain - [tex](-\infty, -2) \cup (-2, \infty)[/tex]
To solve the problems involving the functions f and g, we start by defining the functions:
Given functions:
[tex]f(x) = 3x + 6[/tex]
[tex]g(x) = x + 2[/tex]
1. Finding f + g, f - g, fg, and f/g:
f + g:
[tex]f + g = (3x + 6) + (x + 2) = 4x + 8[/tex]
Domain: All real numbers, [tex](-\infty, \infty)[/tex]
f - g:
[tex]f - g = (3x + 6) - (x + 2) = 2x + 4[/tex]
Domain: All real numbers, [tex](-\infty, \infty)[/tex]
fg:
[tex]fg = (3x + 6)(x + 2) = 3x^2 + 12x + 12[/tex]
Domain: All real numbers, [tex](-\infty, \infty)[/tex]
f/g:
[tex]f/g = \frac{3x + 6}{x + 2}[/tex]
However, g(x) cannot be zero: [tex]g(x) = 0[/tex] for [tex]x = -2[/tex].
Domain: All real numbers except [tex]x = -2[/tex] , which is [tex](-\infty, -2) \cup (-2, \infty)[/tex]
2. Finding (g ◦ f)(x) and (f ◦ g)(x):
(g ◦ f)(x):
[tex]g(f(x)) = g(3x + 6) = (3x + 6) + 2 = 3x + 8[/tex]
(f ◦ g)(x):
[tex]f(g(x)) = f(x + 2) = 3(x + 2) + 6 = 3x + 12[/tex]
3. Completing the square for f(x) = x² - 8x + 2:
First, take the coefficient of [tex]-8[/tex], halve it to get [tex]-4[/tex], and square it to get [tex]16[/tex].
Therefore:
[tex]f(x) = (x^{2} - 8x + 16) - 16 + 2 = (x - 4)^{2} - 14[/tex]
Now in standard form:
[tex]y = (x - 4)² - 14[/tex]
4. Vertex formula for f(x) = x² - 14x:
Vertex formula: [tex]x = -\frac{b}{2a}[/tex] where [tex]a=1, b=-14[/tex].
Therefore:
[tex]x = -\frac{-14}{2(1)} = 7[/tex]
Substituting [tex]x=7[/tex] back to find y:
[tex]f(7) = 7^{2} - 14(7) = 49 - 98 = -49[/tex]
Standard form:
[tex]f(x) = (x - 7)^{2} - 49[/tex]
5. Vertex for f(x) = 3x² - 10x + 1:
Vertex x-coordinate:
[tex]x = -\frac{-10}{2(3)} = \frac{10}{6} = \frac{5}{3}[/tex]
Substitute [tex]x=\frac{5}{3}[/tex] back to find y:
[tex]f(\frac{5}{3}) = 3(\frac{5}{3})^{2} - 10(\frac{5}{3}) + 1[/tex]
Calculate the value:
[tex]3(\frac{25}{9}) - \frac{50}{3} + 1 = \frac{75}{9} - \frac{150}{9} + \frac{9}{9} = -\frac{66}{9} = -\frac{22}{3}[/tex]
The standard form becomes:
[tex]f(x) = 3(x - \frac{5}{3})^{2} - \frac{22}{3}[/tex]