Answer:
\(x = 33\)
Step-by-step explanation:
\(65 + 4x - 17 = 180\)
\(4x + 48 = 180\)
\(4x = 132\)
\(x = 33\)
An electronics company has determined that the cost of producing MP3 players is $16 per MP3 player plus $16,380 per month and fixed cost the electronic company sells each MP3 player for $250 find the revenue function
Revenue function will be 17352.5
What do you mean by algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
It is given that,
Cost of each MP3 player plus = $16
Additional cost = $16380
Fixed cost for each MP3 player = $250
Let C(x),P(x), R(x) be the cost function, profit function and revenue function respectively.
Let x be number of units of mp3 produced and sold
R(x)= 250x is required revenue function
We know that, C(x)= variable cost+ fixed cost
C(x)=16x+16380 is the required cost function
We know that, profit= revenue-cost
P(x)=R(x)-C(x)
P(x)= 250x-[16x+16380]=250x-16x-16380 = 236x-16380
We know that break even point occur when revenue function and cost function has same value.
R(x)=C(x)
250x=16x+16380
250x-16x=16380
236x=16380
x = 16380/236 = 69.41
Revenue function, R(x) = 250x = 250(69.41) = 17352.5
Therefore, revenue will be $17352.5
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Trey randomly selects one card a from a standard 52-card deck.
The probability that Treys cards will be a heart or a black-suited card is because the set of hearts and the set of black-suited
The probability that Trey's card will be a heart or a black-suited card is
cards are
sets
Answer:
3/4 AND MUTUALLY EXCLUSIVE
Step-by-step explanation:
PLATO
The probability that Trey's card will be a heart or a black-suited card is
3/4
What is probability?Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Deck of cards contains,
spade=13, heart=13, diamonds=13, clubs= 13
In which clubs and spades are black and hearts and diamonds are red.
Total (Black suited card with a heart) =26+13= 39
P( heart or a black-suited card)=39/52
=3/4.
Hence, probability of heart or a black-suited card is 3/4
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Angela runs 2 1/2 hours a day. It takes her 3 1/4 hours to took and she sleeps 5 1/6 hours. How much time is left in Angela’s day
Answer:
this is not the full question I think im sorry
I don't understand it I'm sorry
can someone answer 15 16 and 17 with steps?
The required measure of side GH is 23.25, and measures of angles G and H are 64.5° and 25.5°.
From the given figure,
The measure of GH is given by, the Pythagorean theorem,
GH = √[10² + 21²]
GH = 23.25
Now applying the trig ratio to determine, angles H and G,
tang=21/10
G = tan⁻¹[21/10]
G = 64.53°
Similarly,
H = 25.5°
Thus, the required measure of side GH is 23.25, and measures of angles G and H are 64.5° and 25.5°.
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The time needed to travel a certain distancevaries inversely with the rate of speed. If ittakes 8 hours to travel a certain distance at 36miles per hour, how long will it take to travel thesame distance at 60 miles per hour?
We know that
• It takes 8 hours to travel a certain distance at 36 miles per hour.
,• At 60 miles per hour, how long would it take?
We solve this problem using the rule of three, or proportions. The image below shows the given relations.
We form the proportion. We have to write down 60 as numerator because it has an inverse relationship, that is, the more speed the least time needed.
\(\begin{gathered} \frac{8}{x}=\frac{60}{36} \\ x=\frac{36\cdot8}{60} \\ x=\frac{288}{60} \\ x=4.8 \end{gathered}\)Therefore, it would take 4.8 hours to travel the same distance at 60 miles per hour.Salim has a picture book with 124 pages in it. He read 1/4 of the book to his little brother. How many pages did he read?
Answer:
31
Step-by-step explanation:
124/4 = 31 pages per one fourth of the book
If your brother reads one fourth of the book then he reads 31 pages.
31
Step-by-step explanation:
divide 1/4 by 24 and 31 should be the answer
Can you help me with this please?
The half-life of the given exponential function is of 346.57 years.
What is the half-life of an exponential function?It is the value of t when A(t) = 0.5A(0).
In this problem, the equation is:
\(A(t) = A(0)e^{-0.002t}\).
In which t is measured in years.
Hence the half-life is found as follows:
\(0.5A(0) = A(0)e^{-0.002t}\)
\(e^{-0.002t} = 0.5\)
\(\ln{e^{-0.002t}} = \ln{0.5}\)
\(0.002t = -\ln{0.5}\)
\(t = -\frac{\ln{0.5}}{0.002}\)
t = 346.57 years.
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State a and d for the arithmetic sequence below:
3,9, 15, 21...
a
d=
Answer:
6 if I am correct I hope this helps
NEED HELP NEED ANSWERED TODAY
By composite compostion f(x) = 5x-6 and f⁻¹(x) = (x+6)/5 are inverse functions
How to show that f(x) and f⁻¹(x) are inverse functions using composite composition?
A function is a relationship between inputs where each input is related to exactly one output.
Given: f(x) = 5x-6 and f⁻¹(x) = (x+6)/5
To show the inverse relationship exists using composite composition, f(f⁻¹(x)) must be equal to f⁻¹(f(x))
Let's check:
f(f⁻¹(x)) = f((x+6)/5)
Substitute x = (x+6)/5 into f(x) = 5x-6:
f(f⁻¹(x)) = 5((x+6)/5) - 6
f(f⁻¹(x)) = (x+6)- 6
f(f⁻¹(x)) = x
Also,
f⁻¹(f(x)) = f⁻¹(5x-6)
Substitute x = 5x-6 into f⁻¹(x) = (x+6)/5:
f⁻¹(f(x)) = ((5x-6)+6)/5
f⁻¹(f(x)) = 5x/5
f⁻¹(f(x)) = x
Since f(f⁻¹(x)) = f⁻¹(f(x)). Therefore, f(x) = 5x-6 and f⁻¹(x) = (x+6)/5 are inverse functions
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An equivalent ratio to the tape diagram shown is
to pls i need a answer
An equivalent ratio to the tape diagram shown is 1 to 2
How to determine the equivalent ratio?From the tape diagram, we have:
Red = 2
Blue = 4
Express as a ratio
Red : Blue = 2 : 4
Divide by 2
Red : Blue = 1 : 2
Hence, an equivalent ratio to the tape diagram shown is 1 to 2
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rewrite without an exponent
Answer:
\(\frac{1}{3^{4} } \\\\\frac{1}{81}\)
Step-by-step explanation:
Answer: -81, the product would just be 3∧4 but negative
Ten years ago, P was half of Q's age. If the ratio of their present age is 3:4, what will be the total of their present ages.
The total of their present ages is 35 .
Steps to solve question on ages :
1. Choose age of any one to be x .
2. Write age of other in terms of the first one .
3. By using the conditions form an equation and solve for the variable .
According to question :
The ratio of ages is 3 : 4 .
Let the present age of P be 3x and Q be 4x .
Ten years ago , P was half of Q's age :
⇒ (3x-10) = (1/2)*(4x-10)
3x-10 = 2x -5
x=5
⇒ Present age of P = 3*5 = 15 and present age of Q = 4*5 = 20 .
Hence , sum of their present ages = 15+20 =35.
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A farmer wants to construct a fence around his rectangular garden which is 204 feet long by 142 wide. How many linear feet of fencing is required?
The linear feet of fencing in the rectangular garden s 692 feet
How many linear feet of fencing is required?From the question, we have the following parameters that can be used in our computation:
Length = 204 feet
Width = 142 feet
To calculate the amount of linear feet of fencing that is required, we make use of the following perimeter equation
Linear feet of fencing = 2 * (Length + Width)
Substitute the known values in the above equation, so, we have the following representation
Linear feet of fencing = 2 * (204 + 142)
Evaluate
Linear feet of fencing = 692
Hence, the linear feet of fencing is 692 feet
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10. A pipe whose diameter measures 1 1/4 inches should have less threads per inch than a pipe with a diameter of _______ inch.
A. 3
B. 1/2
C. 1
D. 11/2
A pipe whose diameter measures 1 1/4 inches should have less threads per inch than a pipe with a diameter of 11/2 inch. So, the correct answer is (D).
To determine the correct answer, we need to compare the diameters of the two pipes and understand the relationship between pipe diameter and threads per inch.
The number of threads per inch generally decreases as the pipe diameter increases. This means that a larger pipe diameter will have fewer threads per inch compared to a smaller pipe diameter.
Given that the first pipe has a diameter of 1 1/4 inches, we need to find the pipe diameter from the options that is larger than 1 1/4 inches.
The option that meets this requirement is D. 11/2. This represents a pipe diameter of 1 1/2 inches. Therefore, a pipe with a diameter of 1 1/2 inches should have fewer threads per inch than a pipe with a diameter of 1 1/4 inches. Therefore, the correct answer is D. 11/2.
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HELP. Use the grouping method to factor the polynomial below completely.
x^3 – 5x^2 + 3x - 15
A. (x^2 + 5)(x-3)
B. (x^2 - 3)(x+5)
C. (x^2 - 5)(x+3)
D. (x^2 + 3)(x - 5)
Answer:
D
Step-by-step explanation:
(x^2+3)(x-5)
That's the answer
25d^3 +210d^2-640=0
solve for d with steps please
Answer:
Step-by-step explanation:
The equation 25d^3 + 210d^2 - 640 = 0 can be reduced to a quadratic equation by using the factor theorem:
(d - 8)(25d^2 + 182d + 80) = 0
So, one root of the equation is d = 8. To find the other two roots, you can solve the quadratic equation:
25d^2 + 182d + 80 = 0
Using the quadratic formula, the roots can be calculated as:
d = (-b ± √(b^2 - 4ac)) / 2a
Where a = 25, b = 182, and c = 80.
So,
d = (-182 ± √(182^2 - 4 * 25 * 80)) / 2 * 25
d = (-182 ± √(33124 - 8000)) / 50
d = (-182 ± √(25124)) / 50
d = (-182 ± 158) / 50
Therefore, the roots of the equation are:
d = (-340 + 158) / 50 = (-182 + 158) / 50 = (-24) / 50 = -0.48
d = (-340 - 158) / 50 = (-182 - 158) / 50 = -340 / 50 = -6.8
So, the solutions to the equation are d = 8, -0.48, and -6.8.
how many 36-passenger busses will it take to carry 144 people?
Solution
how many 36-passenger busses will it take to carry 144 people?
Step by step explanation:
To solve this divide.
\(\frac{144}{36}=4\)144/36
and that =4
So it takes 4 buses.
Solve for b
B=??????
Answer:
\(\frac{b-7}{b+1}=\frac{b-10}{b+4}\)
\(\left(b-7\right)\left(b+4\right)=\left(b+1\right)\left(b-10\right)\)
\(\left(b-7\right)\left(b+4\right)=b^2-3b-28\)
\(\left(b+1\right)\left(b-10\right)=b^2-9b-10\)
\(b^2-3b-28=b^2-9b-10\)
\(b^2-3b-28+28=b^2-9b-10+28\)
\(b^2-3b=b^2-9b+18\)
\(b^2-3b-\left(b^2-9b\right)=b^2-9b+18-\left(b^2-9b\right)\)
\(6b=18\)
\(\frac{6b}{6}=\frac{18}{6}\)
\(b=3\)
The Price of Pollo
In El Salvador, "Country Chicken" is the most popular fried chicken franchise
in the country. Like most fast-food establishments, they provide a carry-out
service on their menu. You can buy their chicken in several different
quantities: 2, 6, 9, 15, or 21 pieces per box.
Over the years, prices have steadily risen, as things have a way of doing in
many areas of modern life. For example, on July 1, 1993, a box of two
pieces cost 8.35 colones, and on December 31, 1995, that same purchase
would cost you 11.25 colones.
(Note: prices are given in their original Salvadorean currency, colones; $1 U.S
colones.)
Using these two data 'points', you can form a linear equation of the slope-inter
mx + b. The independent variable x is time; the dependent variable y represe
Your task for this problem is to:
1. Find this equation.
2. Use your equation to predict what the price should have been for a 2
July 1, 1999.
Answer:
Hope I helped!~
Step-by-step explanation:
To find the equation of the line, we can use the slope-intercept form of the equation:
y = mx + b
where m is the slope of the line and b is the y-intercept.
Using the two data points given, we can calculate the slope:
m = (11.25 - 8.35) / (1995 - 1993) = 1.95
To find the y-intercept, we can use one of the data points:
8.35 = 1.95(1993) + b
b = -3884.65
So the equation of the line is:
y = 1.95x - 3884.65
To predict the price of a box of two pieces on July 1, 1999, we can substitute x = 6 (since 1999 is 6 years after 1993) into the equation:
y = 1.95(6) - 3884.65
y = 11.7 - 3884.65
y = -3872.95
This gives us a negative price, which obviously does not make sense. It is likely that the price of a box of two pieces was not linearly increasing during this time period, or that there were other factors influencing the price. Therefore, we cannot use this equation to accurately predict the price of a box of two pieces on July 1, 1999.
What is the value of the expression below?
-8+19+8
ОО
O 11
O 19
O 35
Answer:
the answer would be 19.
Step-by-step explanation:
-8+8=0
0+19=19
Answer:
19
Step-by-step explanation:
Find the distance between I and J on the number line below.
The position of I on the number line is -11.
The position of J on the number line is -3.
The distance between I and J can be determined as,
\(\begin{gathered} IJ=-3-(-11) \\ =-3+11 \\ =8 \end{gathered}\)Thus, the required distance is 8.
Determine the probability of rolling a die and getting a 2
then a 5.
The probability of rolling a die and getting a 2, then a 5, is 1/36.
To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.
First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.
Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.
To find the probability of both events happening, we multiply the probabilities:
Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.
Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.
It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.
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Determine whether the mean, median, or mode would be the best choice to describe the center of the following set of data. An elementary school has 92 first graders. They take a vocabulary test that estimates the number of vocabulary words they know. Most of the first-graders had a good start on language acquisition and knew between about 15,000 and 20,000 words. However, there were a few first-graders who were a little behind in language acquisition and only knew about 7,000 words. Would it be best to use the mean, median, or mode to describe the number of vocabulary words that are understood by the first-graders?
Answer:
Median
Step-by-step explanation:
The best measure of center in this case would be the median, as the presence of a few outliers (first-graders who were behind in language acquisition) would greatly affect the mean, while the median would provide a better representation of the typical vocabulary knowledge of first-graders in the group.
Find f(2), f(1), f(0), and f(-1) for f(x) = 3x + 8.
Answer:
Step-by-step explanation:
Solution
When, x=2
f(2)=3×2+8
=14
Again,
When, x=1
f(1)=3×1+8
=11
When, x=0
f(0)=3×0+8
=8
When, x=-1
f(-1)= 3×(-1)+8
=5
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I need help with this one
The mixed numbers are subtracted to get 6 4/5
How to perform the subtractionTo subtract mixed numbers we follow the following steps
convert the mixed numbers to improper fractions.
9 3/5 = (9 × 5 + 3) /5 = 48/5
2 4/5 = (2 × 5 + 4 )/5 = 14/5
Subtract the fractions.
= 48/5 - 14/5
= (48 - 14)/5
= 34/5
convert the improper fraction back to a mixed number
34/5 = 6 4/5
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Congratulations. You received a score of 3.4 on your annual review. Merit increases are given out starting at .5% at a score of 2.6 and it goes up 1% every .4 points. So, I will be receiving an increase of what?
To calculate the merit increase based on your annual review score, we can use the given information that merit increases start at 0.5% for a score of 2.6 and increase by 1% every 0.4 points.
First, we need to determine the difference between your score and the starting score of 2.6:
3.4 - 2.6 = 0.8
Next, we divide this difference by 0.4 to determine the number of 0.4-point intervals:
0.8 / 0.4 = 2
Since each 0.4-point interval corresponds to a 1% increase, we multiply the number of intervals by 1% to find the total increase:
2 * 1% = 2%
Therefore, you will be receiving a merit increase of 2%.
The blue object (D) has been rotated 270° clockwise about the point (1, 2). Which is the correct image?
The correct image include the following: B. Green: image A.
What is a rotation?In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
By applying a rotation of 270° clockwise about the point (1, 2) to the coordinate of the vertices of blue block D, the coordinate the vertices of of its image would be located at the position of the Green: image A.
In this context, we can reasonably infer and logically deduce that Green: image A is the correct transformed shape.
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Application
3. Compare the variety of vehicles detailed below. Each vehicle travels 15,000 km per year.
a. Complete the following table and graph the points on the given grid.
The completed table of values obtained by using the data and the values per 100 km is presented as follows;
3 a. \(\begin{array}{|c|c|c|c|}L \ per \, 100\, km & Litres \ used&L\, per \, 100\, km&Litres\ used \\23.5 &3525&3.9&585 \\11.7 & 1755 & 3.4&510\\7.8 & 1170&2.9&435 \\5.9 &885&2.6&390 \\ 4.7&705&2.3&345 \\\end{matrix}\)
What is a data set?A dataset is a collection of information which are related but contains elements of different values, and can be analyzed or manipulated through the use of computation methods.
The table of values is completed using the following calculations;
The distance each vehicle travels in a year = 15,000 km
The amount of fuel each vehicle uses is calculated as follows;
First car;
1. L per 100 km = 23.5 L
Liter used per year = 15,000 km/(100 km) × 23.5 L = 3525 L
2. L per 100 km = 11.7 L
Liter used per year = 15,000 km/(100 km) × 11.7 L = 1755 L
3. L per 100 km = 7.8 L
Liter used per year = 15,000 km/(100 km) × 7.8 L = 1170 L
4. L per 100 km = 5.9 L
Liter used per year = 15,000 km/(100 km) × 5.9 L = 885 L
5. L per 100 km = 4.7 L
Liter used per year = 15,000 km/(100 km) × 4.7 L = 705 L
6. L per 100 km = 3.9 L
Liter used per year = 15,000 km/(100 km) × 3.9 L = 585 L
7. L per 100 km = 3.4 L
Liter used per year = 15,000 km/(100 km) × 3.4 L = 510 L
8. L per 100 km = 2.9 L
Liter used per year = 15,000 km/(100 km) × 2.9 L = 435 L
9. L per 100 km = 2.6 L
Liter used per year = 15,000 km/(100 km) × 2.6 L = 390 L
10. L per 100 km = 2.3 L
Liter used per year = 15,000 km/(100 km) × 2.3 L = 345 L
The above values are used to complete the table as shown in the main section of the page above;
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uhm help pleaseeee <3
They can buy 20 pumpkins
Answer:
they can buy 20 pumpkin
Step-by-step explanation:
250/12.32=20.29222077922
so 20 pumpkin they can buy
7 milliliters is how many teaspoons? Hint: 1 mL ≈ 0.2 tsp Round your answer to the nearest tenth. Submit
Answer:
1.4 Teaspoons
Step-by-step explanation:
7 times .2 = 1.4
1.4 tsp
7 x .2 = 1.4 tsp