The minimum total cost for the company if all of the order constraints are fulfilled is given as follows:
$25.
How to obtain the minimum total cost?The cost function is given as follows:
C = 3x + 2y.
Meaning that:
Each item x costs $3.Each item y costs $2.The relevant restrictions to minimize the costs are given as follows:
x+y≥10: at least 10 items.x−y≥0: x equals or greater than y.Since an item y costs less than an item x, considering the second bullet point above, the cost is minimized with an equal amount of x and y.
From the first restriction, they must have at least 10 amounts, hence the cost is minimized with:
x = 5 and y = 5.
And the cost is of:
C = 3 x 5 + 2 x 5
C = $25.
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bacteria growth the number of bacteria in a culture is increasing according to the law of exponential growth. there are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours. (a) find the initial population. (b) write an exponential growth model for the bacteria population. let represent time in hours. (c) use the model to determine the number of bacteria after 8 hours. (d) after how many hours will the bacteria count be 25,000
a) The initial population is [tex]N_0[/tex] = 125 / [tex]e^{(2k)}[/tex].
b) The exponential growth model for the bacteria population is N = [tex]N_0[/tex] × [tex]e^{(kt)}[/tex].
c) The number of bacteria after 8 hours is N = [tex]N_0[/tex] × [tex]e^{(8k)}[/tex].
d) After t = ln(25,000 / [tex]N_0[/tex]) / k hours the bacteria count will be 25,000.
(a) To calculate the beginning population, we must first establish the bacterium population's exponential growth rate. Assume that the initial bacterial population is [tex]N_0[/tex]. The exponential growth model is given by:
N = [tex]N_0[/tex] × [tex]e^{(kt)}[/tex]
Where N is the number of bacteria at time t, [tex]N_0[/tex] is the starting population, e is the natural logarithm base, k is the growth rate constant, and t is time in hours.
We have two data sets: N = 125 after two hours and N = 350 after four hours. We can solve using these two equations [tex]N_0[/tex] and k.
(125) = [tex]N_0[/tex] × [tex]e^{(2k)}[/tex]
(350) = [tex]N_0[/tex] × [tex]e^{(4k)}[/tex]
Dividing the second equation by the first equation:
(350/125) = [tex]e^{(2k)}[/tex]
Taking the natural logarithm of both sides:
ln(350/125) = 2k
Solving for k:
k = ln(350/125) / 2
Now that we have k, we can plug it into either equation and solve for it. [tex]N_0[/tex]:
[tex]N_0[/tex] = 125 / [tex]e^{(2k)}[/tex]
(b) The bacterium population's exponential growth model is:
N = [tex]N_0[/tex] × [tex]e^{(kt)}[/tex]
Where [tex]N_0[/tex] = 125 / [tex]e^{(2k)}[/tex] and k = ln(350/125) / 2
(c) To calculate the number of bacteria present after 8 hours, we use the exponential growth model with t = 8:
N = [tex]N_0[/tex] × [tex]e^{(8k)}[/tex]
(d) To calculate the time when the bacterium count reaches 25,000, enter N = 25,000 into the exponentially growing model and solve for t:
25,000 = [tex]N_0[/tex] × [tex]e^{(kt)}[/tex]
t = ln(25,000 / [tex]N_0[/tex]) / k
However, in the absence of a specified growth rate constant (k) and starting population ([tex]N_0[/tex]), we are unable to determine a precise value for t.
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The question is -
The number of bacteria in the culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours.
(a) Find the initial population.
(b) Write an exponential growth model for the bacteria population. (Let t represent time in hours)
(c) Use the model to determine the number of bacteria after 8 hours.
(d) After how many hours will the bacteria count be 25,000?
heart failure is due to either natural occurrences (89%) or outside factors (11%). outside factors are related to induced substances or foreign objects. natural occurrences are caused by arterial blockage, disease, and infection. suppose that 15 patients will visit an emergency room with heart failure. assume that causes of heart failure between individuals are independent. (a) what is the probability that 3 individuals have conditions caused by outside factors? round your answers to three decimal places (e.g. 0.987). probability
The probability that 3 individuals have conditions caused by outside factors is 0.1496
The proportion of heart failures due to outside factors, p = 11% = 0.11
Sample size, n = 15
The formula for binomial distribution is:
P(x) = ⁿCₓ pˣ (1 - p)ⁿ⁻ˣ
Here, x = Number of heart failures.
We are asked to determine the probability that 3 individuals have conditions caused by outside factors
So, here x = 3
P(3) = ¹⁵C₃ p³ (1 - p)¹⁵⁻³
P(3) = ¹⁵C₃ (0.11)³ (1 - 0.11)¹²
P(3) = ¹⁵C₃ (0.11)³ (0.89)¹²
P(3) = 455 (0.11)³ (0.89)¹²
P(3) = 0.1496
Hence, the probability that 3 individuals have conditions caused by outside factors is 0.1496
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Please help.
Graph RST with vertices R(4,1), S(7,3), and T(6, 4) and its image after the glide reflection.
Translation: (x,y) →(x, y-1)
Reflection: in the y -axis.
Answer:
Points R(4,1) S(7,3) T(6,4) after translation
R(4-3, 1) S(7-3, 3) T(6-3, 4)
R'(1, 1) S'(4, 3) T'(3, 4)
Points R'(1, 1) S'(4, 3) T'(3, 4) after reflection
R''(1, -3) S''(4, -5) T''(3, -6)
Step-by-step explanation:
Answer:Step-by-step explanation:Points R(4,1) S(7,3) T(6,4) after translation R(4-3, 1) S(7-3, 3) T(6-3, 4) R'(1, 1) S'(4, 3) T'(3, 4) Points R'(1, 1) ...
the set of complex numbers $z$ such that the real part of $1/z$ is equal to 1/6 forms a curve. find the area of the region inside the curve.
The area of this region is equal to [tex]\pi \cdot (\sqrt{35})^2 = 35\pi[/tex]
The equation for the set of complex numbers z such that the real part of 1/z is equal to 1/6 is given by:
Re(1/z) = 1/6
Since 1/z = 1/x + i/y,
Where x and y are the real and imaginary parts of z, respectively,
we can write the equation as:
(1/x)=(1/6) and [tex]$\frac{y}{x^2 + y^2} = \frac{1}{6}$[/tex]
From the first equation,
we have x = 6.
Substituting this value into the second equation, we get:
[tex]$\frac{y}{36 + y^2} = \frac{1}{6}$[/tex]
Solving for y,
we find that [tex]$y = \pm \sqrt{35}$[/tex].
So, the set of complex numbers z that satisfies the equation forms a circle centred at 6 + 0i with radius [tex]$\sqrt{35}$[/tex].
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an electrocardiogram is recorded on mm grid paper moving at a speed of 25mm per second. if the distance between the cycles as recorded is 15mm, what is the subject's heart rate in beats per minute?
The subject's heart rate is 100 beats per minute.
There are three main methods of calculating ECG rate. There is no specific best method, and preference varies between clinicians. However, certain methods may be better suited for rhythms such bradyarrhythmia's or tachyarrhythmias.
Rate = Number of R waves (rhythm strip) X 6The number of complexes (count R waves) on the rhythm strip gives the average rate over a ten-second period. This is multiplied by 6 (10 seconds x 6 = 1 minute) to give the average beats per minute (bpm)Useful for slow and/or irregular rhythmsTo calculate the heart rate from an ECG recorded on millimeter grid paper, you can use the following formula:
Heart rate (beats per minute) = (recording speed (mm/s) / distance between cycles (mm)) x 60 s/min
Using the given information, the calculation would be:
Heart rate (beats per minute) = (25 mm/s / 15 mm) x 60 s/min = 100 beats per minute
Therefore, the subject's heart rate is 100 beats per minute.
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how many nickels and dimes
Answer:
12 nickles and 9 dimes
Step-by-step explanation:
First, let's use the first equation, n + d = 21, to solve for d in terms of n:
n + d = 21 [Subtract n from both sides]
d = 21 - n
Now that we have found d in terms of n, let's plug d into the second equation, 0.05n + 0.1d = 1.5:
0.05n + 0.1d = 1.5 [Plug in d]
0.05n + 0.1(21 - n) = 1.5 [Distribute 0.1 to (21-n)]
0.05n + 2.1 - 0.1n = 1.5 [Combine like terms]
-0.05n + 2.1 = 1.5 [Subtract 2.1 from both sides]
-0.05n = -0.6 [Divide both sides by -0.05]
n = 12
Now that we have found the amount of nickles Donna had, let's use the first equation, n + d = 21, to solve for d, the amount of dimes she used.
n + d = 21 [Plug in n]
12 + d = 21 [Subtract 12 from both sides]
d = 9
So, Donna must have bought her candy bar using 12 nickles and 9 dimes.
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If Ashley bought 2 rotis and 3 pies for $10.00.
How much for one roti and how much for one pie?
One roti costs $20.00 and one pie costs $3.33.
How was the equation solved?Let x be the cost of one roti. Then, the cost of one pie is (10 - 2x) / 3.
Since the total cost is $10.00, we can set up an equation:
2x + (10 - 2x) / 3 = 10
Expanding the right-hand side:
2x + 3.33 - 2x = 10
0.33x = 6.67
Finally, dividing both sides by 0.33:
x = 20.00
So, one roti costs $20.00 and one pie costs (10 - 2 * 20) / 3 = $3.33.
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To select 10 students our of the class of 40 students, 40 names are placed in a hat and 10 names are drawn out of the hat. What type of sample is this? A. Stratified Random Sample B. Multistage Sample C. Simple Random Sample D. Cluster Sample E. Systematic Random Sample
Simple Random sampling as each student is getting equal opportunity to get selected.
Describe random sampling.
A selection of participants from a community are chosen at random by the investigator using simple random sampling, a sort of sampling techniques. Every individual in the population has the same chance of being chosen. Then, information is gathered from as much of this randomly selected subgroup as possible.
Which four forms of random sampling are there?
Simple random sampling, systematic sampling, stratified sampling, and cluster sampling are the four main random (probability) sampling techniques.
What benefit may simple random sampling provide?
The benefits of a simple random sample include its simplicity and accuracy of depiction. Simple random sampling is the easiest way to select a study sample from a bigger population.
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simplify the ratio 27:63
The hypotenuse of a 45°-45°-90° triangle measures 10 StartRoot 5 EndRoot in.
A right triangle is shown. The hypotenuse has a length of 10 StartRoot 5 EndRoot and the lengths of the other 2 sides are congruent.
What is the length of one leg of the triangle?
Answer:
5 StartRoot 10 EndRoot
Step-by-step explanation:
we know that
The legs of a 45°-45°-90° triangle are congruent
Let
x ----> the length of one leg of the triangle
Applying the Pythagorean Theorem
where
c is the hypotenuse
a and b are the legs
we have
substitute
Simplify
5 StartRoot 10 EndRoot
Sally is near the end of a three year lease on a car with an original msrp of $38,000. her leasing company claims that the car is now worth only $28,500. which percentage represents the residual value of sally’s leased car? a. 25% b. 33% c. 67% d. 75% please select the best answer from the choices provided a b c d
The right answer is D.
Detailed explanation:
$35,000. Original cost of the vehicle
The car's current value is $28,500.
The residual worth of Sally's leased vehicle is equal to x.
Current Price x * 38,000 = 28,500 x = 28,500/38,000 x = 0.75 Residual value * Original Price
Since we must determine the proportion
Divide the residual value by 100, or 0.75 * 100, to get 75%.
The right answer is D.
What exactly does leasing mean?A lease is a contract in which the owner of an asset (the lessor) agrees to let the lessee use it in exchange for a specific amount of money (the rent), which may or may not be based on any factors, for a specified amount of time (the lease term), which may or may not be flexible.
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what is the largest even integer which cannot be written as the sum of two odd composite numbers? (recall that a positive integer is said to be composite if it is divisible by at least one positive integer other than 1 and itself.)
Largest even integer which cannot be written as the sum of two odd composite numbers is 38 if it is divisible by at least one positive integer other than 1 and itself.
The positive even integers which cannot be expressed as the sum of 2 composite odd numbers are: 2,4,6,8,10,12,14,16,20,22,26,28,32,38. This sequence is A118081.
All we have to do now is check the even numbers smaller than 44
. The largest, 42 is a multiple of 3 so it’s handled as 42=9+33 and the next one down, 40 is handled as 40=25+15.But the next one down is our culprit: 38 is not the sum of two odd composite numbers, as you can readily check.
First, what are these “odd composite numbers” anyway? The number 1is considered neither prime nor composite (it’s a unit), so it’s out. 3,5 and 7 are prime. The smallest odd composite number is, therefore, 9 and the next one is 15 .So we have 18=9+9 24=9+1 and 30=15+15 as some even numbers which can be written as a sum of two odd composites, but so far it doesn’t look promising: plenty of even numbers, like 10 or 20 or 32 cannot be so written.
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The table shows values for functions f(x) and g(x) .
What are the known solutions to f(x)=g(x) ?
Select each correct answer.
1
3
7
9
11
The solution is, The value of x where f(x) = g(x) is 3.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
Functions and values
According to the given question, we are to find the value of x for which the function f(x) is equal to g(x)
From the given table, we need to find the point where the values of f(x) = g(x). The value of x at this point is the solution.
Therefore from the table, the value of x where f(x) = g(x) is 3
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The diameter of a circle measures 18cm. What is the circumference of the circle?
Use 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
56.52cm
Step-by-step explanation:
2r = 18cm
r = 9cm
[tex]c = 2r\pi[/tex]
C = 2 × 9 × 3.14
C = 56.52cm
Question 13
Subtract and simplify: 81xy4 - yx, where x ≥ 0 and y ≥ 0.
O 2xy
3√√xy4-y√√x
03
3xy-xy
The expression 81xy^4 - yx cannot be simplified
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
81xy4 - yx
Express properly
So, we have the following representation
81xy^4 - yx
This expression can be rewritten a
81xy^4 - xy
There are no like terms in the above expression
This means that the expression cannot be simplified
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Stacey is designing a custom rug for a client. the current design is a rectangle with a width of 8 feet and a length of 5 feet. the client wants the rug to be larger but doesn't want the width to exceed 12 feet. select any of the scale factors that stacey could use to dilate the current dimensions and meet the customer's requests.
Answer:87
Step-by-step explanation:
the mid point of AB = (?,?) A=(-2,1) B=(1,-1)
Answer:
The midpoint of AB is (-0.5, 0)
Step-by-step explanation:
( X1 plus X2 = -1/2 = -0.5, Y1 plus Y2 = 0
If you help you get a ice cream cake
1: The number of dogs is greater than 20
2: The temperature was less than 80°
3: The cost of the bike is atleast $100.
4: The grocery list does not exceed 15 items. The speed limit is not more than 40mph
market research indicates that a new product has the potential to make the company an additional $3.8 million, with a standard deviation of $1.8 million. if this estimate was based on a sample of 10 customers, what would be the 90% confidence interval?
The 90% confidence interval is (2.76, 4.84).
The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Standard deviation may be abbreviated SD and is most commonly represented in mathematical texts and equations by the lower-case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.
Mean [tex]$(\overline{\mathbf{x}})[/tex] =3.8, sample standard deviation [tex]$(\mathrm{s})[/tex] =1.8, sample size [tex]$(\mathrm{n})[/tex] = 10
since population standard deviation [tex]$(\sigma)$[/tex] is unknown and the value of [tex]$\mathrm{n}$[/tex] is less than 30, use. [tex]$\mathrm{t}$[/tex] - distribution
degrees of freedom =10-1=9
for 90% confidence level with degrees of freedom = 9
[tex]$t_{\frac{\alpha}{2}}=1.833[/tex] (from t- table)
formula: confidence interval for population mean. [tex]$\mu=\bar{x} \pm t_{\frac{\alpha}{2}} *\left\{\frac{s}{\sqrt{n}}\right\}$[/tex]
= 3.8 ± 1.833×[tex]\left\{\frac{1.8}{\sqrt{10}}\right\}$[/tex]
= 3.8 ± 1.04
= (3.8 - 1.04, 3.8 + 1.04)
= (2.76, 4.84)
Therefore, the 90% confidence interval is (2.76, 4.84).
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a football field is supposed to be exactly 120yd long, including the end zones. how many inches is this? (1yd
The length of a football field, including the end zones, is 120 yards, which is equal to 4320 inches.
To calculate this, we can use the conversion rate of 1 yard equal to 3 feet and 1 foot equal to 12 inches. This means that 1 yard is equal to 36 inches. To convert 120 yards to inches, we can multiply 120 by 36, resulting in 4320 inches.
To explain this mathematically, we can use the formula:
Inches = Yards x (Feet/Yard) x (Inches/Foot)where Inches/Foot = 12 and Feet/Yard = 3.
Plugging in the appropriate variables, we can calculate the number of inches in a football field as:
Inches = 120 x 3 x 12 = 4320 inches.
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Starting at noon, Justin observed the amount of snow on his lawn during a blizzard. He created a graph to represent how many inches of snow were on the lawn at � x minutes past noon. What does the y-intercept in the graph represent?
The y intercept represents the amount of snow in inches on his lawn at noon
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
The standard form of a linear equation is:
Ax + By = C
Where A, B and C are constants
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
If y represents the number of inches of snow on the lawn at x minutes past noon.
The y intercept represents the amount of snow on his lawn at noon
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A new product price is increased from $5 to $6. What is the percent of change?
Answer:
Step 1: $5 to $6 is a $1 increase
Step 2: Divide by the old value: $1/$5 = 0.2
Step 3: Convert 0.2 to percentage: 0.2×100 = 20% rise.
Or you could do it this way:
Step 1: Divide new value by old value: $6/$5 = 1.2
Step 2: Convert to percentage: 1.2×100 = 120% (i.e. $6 is 120% of $5)
Step 3: Subtract 100%: 120% − 100% = 20%, and that means a 20% rise.
Answer:
20%
Step-by-step explanation:
$5 to $6 is a $1 increase
Divide by old value: $1/$5=.2=20%
To check: $5 times 1.2 (120%)=6
2nd Method:
Divide by new vlaue: $6/$5=1.2
1.2=120%
120%-100%=20%
which equation is true??? A 3/4 = 9/16 B 6/8 = 4/3 C 3/5 = 8/10 D 12/16 = 36/48
Answer:
D) 12/16 = 36/48
Step-by-step explanation:
They are equivalent fractions, unlike the other options. Both of these fractions simplify to 1/3 so they are indeed equivalent.
Answer:
12/16 = 36/48
Step-by-step explanation:
because 12/16 multiplyed by 3 is 36/48
Which graph represents the inequality y is less than negative one-third times x plus 1? The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line. The graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line. The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line. The graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line.
The graph represents the inequality, the graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line.
What is linear inequality?According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. Any of the symbols for inequality, including greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).
Given the phrase, y is less than negative one-third times x plus 1
negative one-third times x plus 1,
-1/3x + 1
y < -1/3x + 1
to plot the coordinates consider,
y = -1/3x + 1
when x = 0, y = 1
and when y = 0,
0 = -1/3x + 1
-1/3x = -1
x = 3
x 0 3
y 1 0
and the graph says y is less than negative one-third times x plus 1,
so the shaded portion will be below the line, and the graph is attached for the condition.
Hence option D is correct.
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Help I’ll mark you, find x y and z
Answer:
x=54⁰ y= 43⁰ z= 83⁰
Step-by-step explanation:
z=180⁰-97⁰
83⁰ opposite angles add upto 180⁰
y= 43⁰
x= 83⁰+43⁰=126⁰
180⁰-126⁰= 54⁰ (alternate angles)
Identify the graph of the solution set of 13 > 5 + 4x.
The requried graph of the solution of a set of given inequality 13 > 5+ 4x is shown.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
here,
Given inequality,
13 > 5 + 4x
Simplify the above expression,
Subtract -5 from both sides,
13 - 5 > 5 - 5 + 4x
8 > 4x
Divide by 4 into both sides
2 > x
The graph of the solution to the given inequality is less than 2, and line x = 2 will be a dotted line [value no included in x < 2]
Thus, the graph of the inequality has been shown.
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Consider the function. what is the x-intercept of f–1(x)?
The x intercept of f-1(x) is the y intercept of f(x). The y intercept of f-1(x) is the x intercept of f(x). A horizontal asymptote for f(x) produces a vertical asymptote for f-1(x). A vertical asymptote for f(x) produces a horizontal asymptote for f-1(x).
(2 1/2, 0)
f(x) = 2 1/2 - 3 1/3 * x
or
f(x) = 5/2 - (10/3)*x
f^-1(x) is the inverse of f(x), which is obtained replacing f(x) by x, and x by y, and solving for y, as follows:
x = 5/2 - (10/3)*y
(10/3)*y = 5/2 - x
y = (5/2)*(3/10) - x*(3/10)
y = (3/4) - (3/10)*x
f^-1(x) = (3/4) - (3/10)*x
at x-intercept, f^-1(x) = 0,
(3/4) - (3/10)*x = 0
(3/4) = (3/10)*x
x = (3/4)*(10/3)
x = 5/2 or 2 1/2
Graph a quadratic function with a vertex of (3, -7). Type your equation below.
The quadratic equation can be written in vertex form as:
y = (x - 3)^2 - 7
How to write the quadratic equation?A general quadratic equation with a leading coefficient a and a vertex (h, k) can be written as:
y = a*(x - h)^2 + k
If particularly we take a = 1 (we could take any value here, because the problem doesn't say anything about the leading coefficient).
And the vertex is (3, -7)
Then the quadratic equation can be:
y = (x - 3)^2 - 7
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The length of a rectangle is 3 times the width, w. Which expressions represent the perimeter of the rectangle?
Select all the correct expressions.
Responses
4w4 w
8w8 w
3w+w3 w plus w
6w+2w6 w plus 2 w
3(w+w)3 times open paren w plus w close paren
2(3w+w)2 times open paren 3 w plus w close paren
the correct expression for the Perimeter of the Rectangle will be 8w, 2w + 6w, and 2 (w + 3w).
What is Perimeter?The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
Given, The length of a rectangle is 3 times the width, w
Since,
width of the rectangle = w
Length of the rectangle = 3w
From the general formula of the Perimeter of the Rectangle:
Perimeter = 2(Length + width)
Perimeter = 2 (w + 3w)
Perimeter = 2w + 6w
Perimeter = 8w
Therefore, the correct expression for the Perimeter of the Rectangle will be 8w, 2w + 6w, and 2 (w + 3w).
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n is an integer
write the values of n such that -15<3n<6
The values of n in -15<3n<6 are -4, -3, -2, 1, 0 and 1
How to determine the values of nFrom the question, we have the following parameters that can be used in our computation:
-15<3n<6
Divide through by 3
So, we have the following representation
-5 < n < 2
The values in this range are -4, -3, -2, 1, 0 and 1
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