The total profit of F_1 in the week was $25920 and the total profit of F_2 in the week was $0.
The profit vector can be expressed as p = [35 62 30]. The total profit of F_1 and F_2 can be calculated by multiplying the matrix A by the vector p. The result, Ap, is a vector whose components give the total profits of the two stores in the week.
For example, the total profit of F_1 can be calculated as Ap_1 = [35 62 30] * [400 60 240] = [14000 3720 7200] = 25920.
Similarly, the total profit of F_2 can be calculated as Ap_2 = [35 62 30] * [0 0 0] = [0 0 0] = 0.
Therefore, the total profit of F_1 in the week was $25920 and the total profit of F_2 in the week was $0.
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a system of linear equations is graphed. which ordered pair is the best estimate for the solution to the system?
The best estimate for the solution to a system of linear equations can be found by using the Substitution Method.
To solve for the solution, the equations must be written in the form y = mx + b. The slope, m, and the y-intercept, b, of each equation can then be calculated. The x-coordinate of the solution can be found by setting the two equations equal to each other to create an equation in one variable. This equation can then be solved for x. The y-coordinate of the solution can be found by substituting the x-coordinate into one of the original two equations. The ordered pair that is the estimated solution can then be formed.
For example, consider the system of equations y = 3x + 2 and y = -x + 5. The slope of the first equation is m1 = 3, and the y-intercept is b1 = 2. The slope of the second equation is m2 = -1, and the y-intercept is b2 = 5. Setting the two equations equal to each other yields 3x + 2 = -x + 5. Solving for x gives x = 3. Substituting this x-coordinate into either of the original equations yields y = 3(3) + 2 = 11. The ordered pair that is the estimated solution to the system is (3, 11).
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inquiry HOW can you use a bar diagram to show a percent of change?
A bar diagram can be used to show a percent of change by the method of comparing two bars.
What is a bar diagram?
Bar graphs or bar charts are visual depictions of groups of data that are made up of vertical or horizontal rectangular bars with lengths that are equal to the data's measure.
A bar diagram can be used to show a percent of change by comparing the size of two or more bars. The bars can represent the original value and the final value, and the difference in size between the two bars will indicate the percent of change.
For example, if the original value is represented by a bar that is 10 units tall and the final value is represented by a bar that is 12 units tall, the percent of change would be 20% (the difference in height between the two bars divided by the original value).
The percent of change can also be labeled or annotated on the graph.
Therefore, bar graph is helpful in denoting the percent of change.
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A stunt motorcyclist makes a jump from one ramp 20 feet off the ground to another ramp 20 feet off the ground. The jump between the ramps can be modeled by y=-1/640 x to the power of 2 + 1/4 x + 20 where x is the horizontal distance (in feet) and y is the height above the ground (in feet).A) what is the motorcycle's height r when it lands on the ramp?B) what is the distance d between the ramps?C) what is the horizontal distance h the motorcycle has traveled when it reaches its maximum height?D) what is the motorcycle's maximum height k above the ground?
A) 20 ft B) 80 ft C) 40 ft D) 24 ft. The equation y=-1/640 x2 + 1/4 x + 20 can be used to calculate the height, distance, maximum height, and horizontal distance of the stunt motorcyclist's jump.
A) The motorcycle's height when it lands on the ramp is 20 feet. This can be calculated by plugging 0 in for x in the equation y=-1/640 x2 + 1/4 x + 20. When you plug in 0 for x, you get y=-1/640 (0)2 + 1/4 (0) + 20, which simplifies to y=20. This means that when the motorcycle lands on the ramp, it is 20 feet off the ground.
B) The distance between the ramps is 80 feet. This can be calculated by finding the value of x when y=20. Solve the equation y=-1/640 x2 + 1/4 x + 20 for x when y=20. When you solve this equation, you get x=80. This means that the distance between the ramps is 80 feet.
C) The horizontal distance the motorcycle has traveled when it reaches its maximum height is 40 feet. This can be calculated by finding the value of x when y=24. Solve the equation y=-1/640 x2 + 1/4 x + 20 for x when y=24. When you solve this equation, you get x=40. This means that the horizontal distance the motorcycle has traveled when it reaches its maximum height is 40 feet.
D) The motorcycle's maximum height above the ground is 24 feet. This can be calculated by finding the maximum value of y in the equation y=-1/640 x2 + 1/4 x + 20. When you calculate the maximum value of y, you get y=24. This means that the motorcycle's maximum height above the ground is 24 feet.
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Erik has $17,531 in a savings account that earns 14% interest per year. The interest is not compounded. How much interest will he earn in 1 year?
Answer:
$2454.34 in interest in a year
Step-by-step explanation:
Turn 14% into a decimal (0.14)
17,531x0.14 = 2453.34
This is calculated by multiplying values by the frequency of their occurrence, adding the total of all the products, and then dividing by the total number of occurrences.
a. mean
b. arithmetic mean
c. mode
d. weighted mean
The mean is calculated by taking the sum of all the values and then dividing by the total number of occurrences.
This is known as the arithmetic mean. The mode is the most frequently occurring value, and the weighted mean takes into account the frequency of each value when calculating the mean by multiplying each value by its frequency and then dividing by the total number of occurrences.
The mean is calculated by taking the sum of all the values and dividing by the total number of occurrences, which is known as the arithmetic mean. The mode is the most frequently occurring value, and the weighted mean takes into account the frequency of each value when calculating the mean by multiplying each value by its frequency and then dividing by the total number of occurrences.
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determine whether the relation represents y as a function of x. x^2 + y^2 = 25
Answer: The relation x^2 + y^2 = 25 does not represent y as a function of x. This is because for a given value of x, there are multiple values of y that would satisfy the equation. For example, for x = 3, y = 4 and y = -4 both satisfy the equation. In a function, each value of the independent variable (in this case, x) must correspond to only one value of the dependent variable (in this case, y).
It's an equation of a circle with a center (0,0) and a radius of 5.
Step-by-step explanation:
use differentials to estimate the amount of cubic meters of paint needed to apply a coat of paint 0.18 cm thick to a hemispherical dome with diameter 60 meters.
It requires 10.1833 cubic meter of paint to apply a coat of paint on the hemispherical shell.
What is volume of hemisphere?The volume of a hemisphere is (2/3)πr³, where r is the radius of the hemisphere. It is half of the volume of a sphere with the same radius.
Formula for Volume of a hemisphere, V = (2/3)πr³
radius = diameter/2
=>60/2
=>30 m
dr = 0.18 cm = 0.0018 m
dV/dr = (2*3)/3 * πr²
=> dV/dr = 2πr²
=> dV = 2πr² dr
so dV = 2π*(30)²*0.0018
=> 10.1833
So , it requires 10.1833 cubic meter of paint.
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Determine if f (x )is continuous at x equals 6. if not, select the option with the correct reasoning as to why not.
The limit of f(x), which must exist at x = 1 and be equal to k, is required for f(x) to be continuous at x = 1. (1).
What is meant by mathematical function?A mathematical function is a rule that determines the value of the dependent variable based on the values of the independent variables. A table, a formula, or a graph are just a few examples of how a function might be expressed. A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the function's codomain. Initially, functions were just an idealized representation of the relationship between two changing quantities.
The limit of f(x), which must exist at x = 1 and be equal to k, is required for f(x) to be continuous at x = 1. (1).
While the limit of f(x) is 1 - (1)2 = 0 as x approaches 1 from the left, it is 1+1 = 2 as x approaches 1 from the right. The limit of f(x) as x approaches 1 therefore does not exist because the one-sided limits are not the same.
As a result, at x = 1, f(x) is not continuous.
The function has a gap at x = 1, which can be seen if you graph it. Gaps and holes don't exist in continuous function graphs.
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Which function is best represented by this graph?
Responses
f(x)=x2+1
f(x)=x2−1
f(x)=−x2+1
f(x)=−x2+x−1
The function that best represented by this graph is f(x) = −x² + 1.
The correct option is C.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
A graph of a function is given in the image.
The parent function of the graph is g(x) = x².
And the graph is negative of the parent function.
And shifted upwards to 1 point.
That means, the function is f(x) = −x² + 1.
Therefore, the function is f(x) = −x² + 1.
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A company's 'dividend yield' is defined as the ratio between its dividend per share and share price, i.e. Dividend Yield =Dividend per SharePrice per Share. If a company has a dividend yield of 2.5%, a share price of $18 per share, how much will I receive in dividends if I own 10,000 shares? Do not include commas or the dollar sign in your answer.
So if you own 10,000 shares of the company, you would receive $4,500 in dividends.
How do we calculate the receivable dividend?A dividend is a portion of a company's profits and retained earnings that it distributes to its shareholders and owners. When a company makes a profit and accumulates retained earnings, those earnings can be reinvested in the company or distributed to shareholders as a dividend.
The amount of dividends you will receive if you own 10,000 shares can be calculated as follows:
Dividend per share = Share price * dividend yield
Dividend per share = $18 * 0.025
Dividend per share = $0.45
Total dividends received = number of shares * dividend per share
Total dividends received = 10,000 * $0.45
Total dividends received = $4,500
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7
The product of (a - b)(a - b) is a perfect square trinomial. (1 point)
Sometimes
Always
Never
Find the product of (x + 5)². (1 point)
Ox²-10x+25
Ox²-25
O x²+25
Ox²+10x+25
Product of (a - b)(a - b) is never a perfect square trinomial, the product of (x + 5)² is x² + 10x + 25.
An algebraic expression is what?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
The algebraic expression (a + b) (a b) should be multiplied.
(a + b) = a² - ab + ba - b² (a + b)
(a + b) = a² - b² (a b) [ - ab + ba = 0 ]
Since there are only 2 terms in the final formula, a² - b² is a binomial.
As a result, the result of (a + b) (a b) is not a trinomial with a perfect square.
product of (x + 5)²
⇒ (x+5)(x+5)
⇒ x² + 5x + 5x + 25
⇒ x² + 10x + 25
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a student sets up the following equation to convert a measurement. (the stands for a number the student is going to calculate.) fill in the missing part of this equation. note: your answer should be in the form of one or more fractions multiplied together
The missing part of the equation should be like 1000 g / 1 kg × 100 cm / 1 m
Given,
The set of units used in the final response is different. In particular, kilogram (kg) and meters (m) are converted to gramm(g) and centimeter (cm), respectively (cm). You must multiply the initial value by proportions to achieve this adjustment.
It is crucial to organize these proportions in a way that permits unit cancellation when writing them down. As an illustration, since kg and m are both in the numerator, they must be in the denominators of the conversions.
Proportions:
1 kg = 1,000 g
1 m = 100 cm
Here,
The complete equation is like;
-4.3 × 10⁴ (kg × m / s) × (1000 g / 1 kg) × (100 cm / 1 m) = ? (g × cm / s)
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Complete question is attached
4x-2 ≤ -22 i need a answer
Answer:
x < 5
Step-by-step explanation:
4x-2 < - 22
=4x < -22 + 2
=4x < -20
=4x/4 < -20/4
x < 5.
Three equal mass satellites A, B, and C are in coplanar orbits around a planet as shown in the figure. The magnitudes of the angular momenta of the satellites as measured about the planet are LA, LB, and LC. Which of the following statements is correct? (A) LA > LB > LC (B) LC > LB > LA (C) LB > LC > LA (D) LB > LA > LC (E) The relationship between the magnitudes is different at various instants in time
(B) LC > LB > LA is the correct statement for satellites
The magnitudes of the angular momenta of the satellites as measured about the planet are LA, LB, and LC.
The angular momentum of each satellite is conserved independently so we can compare the orbits at any location. Looking at the common point between orbit A and B shows that satellite A is moving faster at that point than satellite B, showing LA > LB. A similar analysis at the common point between B and C shows LB > L A because three equal mass satellites are in coplanar orbits around a planet
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At what rate was an investment made that obtains $50.40 on $210 over four years?
Answer:
Rate=6
Step-by-step explanation:
First multiply the interest by 100
50.40×100=5040
then multiply the investment by the number of years
210×4=840
then divide the two answers together
5040÷840=6
The density function for the random variable, T, that denotes the life time of a bulb (in years) is given by: 6 - t f(t) = 12,0
A continuous random variable takes on an uncountably infinite number of possible values. For a discrete random variable X that takes on a finite or countably infinite number of possible values, we determined p(X=x) for all of the possible values of X and called it the probability mass function ("p.m.f").
For continuous random variables, as we shall soon see, the probability that X takes on any particular value x is 0. That is, finding p(X=x) for a continuous random variable X is not going to work. Instead, we'll need to find the probability that X falls in some interval a,b that is, we'll need to find.
We will do that using a probability density function ("p.d.f."). We'll first motivate a p.d.f. with an example, and then we'll formally define it.
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2 Jai paddles 8 miles on a kayak
each day for 4 days. On the fifth
day, he paddles some more miles.
In 5 days, he paddles 40 miles.
How many miles does he paddle
on the kayak on the fifth day?
Jai paddles 8 miles each day for 4 days, a total of 8*4 = 32 miles.
What is an example of a unitary method?
A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.
We know that in 5 days he paddles 40 miles in total.
So on the fifth day he paddles 40-32 = 8 miles.
Therefore, Jai paddles 8 miles on the kayak on the fifth day.
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if a student scored 84, 72, and 83 on the quizzes, exams, and final respectively, calculate the student's final grade. express your answer to three significant figures.
The student's final grade is 78.9.
The final grade of the student is determined using the weight average. A weighted average refers to a type of mean that gives differing importance to the values in a dataset. It is used when the relative significance of values in a dataset are to be considered. The formula for finding the weighted average is the sum of all the variables multiplied by their weight, then divided by the sum of the weights.
Based on the provided information, as student score 84 on quizzes with weighted 30%, 72 on exams with weighted 40%, and 83 on final exam with weighted 30%, hence
Final grade = (84*0.3 + 72*0.4 + 83* 0.3)/(0.3 + 0.4 + 0.3) = (25.2 + 28.8 + 24.9)/1 = 78.9
Note: The question is incomplete. The complete question probably is: For a chemistry class, a student's grades are weighted as follows: quizzes are 30%, exams are 40%, and the final exam is 30%. If a student scored 84, 72, and 83 on the quizzes, exams, and final respectively, calculate the student's final grade. express your answer to three significant figures.
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Answer:
79.6
Step-by-step explanation:
(86x.3)+(73x.4)+(82x.3)
SAVE ME WITH MY MAAAAAAATH
Answer:
14.75
Step-by-step explanation:
If Shenelle has $25 and wants to see a $10.25 regular admissions showing of a 3D movie, she will have $14.75:
[tex]x + 10.25 \leq 25[/tex]
[tex]x \leq 14.75[/tex]
Anna bought a bike horn. She paid $11.59 and received $9.67 in change. How much did the bike horn cost?
Answer:
$1.92
Step-by-step explanation:
$11.59 - $9.67 = $1.92
by examining birth records, it has been determined that 12% of people are born in the winter (w), 28% are born in the spring (sp), 42% are born in the summer (su), and 18% are born in the fall (f). suppose we select a person at random. find each probability. p(w and f)
The probability of selecting a person at random is p(w and f) is 0.0216 or 2.16%.
The probability of an event occurring and another event occurring is found by using the multiplication rule of probability, which states that the probability of two events occurring together is equal to the product of the probabilities of each event occurring independently.
In this case, we are looking for the probability of a person being born in the winter (p(w)) and the probability of a person being born in the fall (p(f)), so we would calculate:
p(w and f) = p(w) * p(f)
Using the information provided, we know that:
p(w) = 12% = 0.12
p(f) = 18% = 0.18
So, to find p(w and f), we would multiply:
p(w and f) = 0.12 * 0.18 = 0.0216 or 2.16%
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Answer:
0
0.30
0.82
0.70
Step-by-step explanation:
nora's grandfather lived to be 87, and her father is still alive at the age of 98. nora concludes that longevity is inherited and anticipates a very long life. nora should know that . question 38 options: the lifespans of fraternal twins are just as similar as the lifespans of identical twins, indicating that longevity is probably not a heritable trait there is no reliable data on the heritability of longevity, so the cumulative effects of random events probably contributed to the long lives of her relatives the heritability of longevity is high, ranging from .75 to .95 for age at death, indicating that longevity is directly related to genetic factors rather than inheriting longevity directly, people probably inherit risk and protective factors that influence their chances of dying earlier or lat
Nora should know that rather than inheriting longevity directly, people probably inherit risk and protective factors that influence their chances of dying earlier or later. Hence, the correct answer is option C.
The given problem here requires knowledge of both biology and mathematics in order to solve the question. The mathematical component of this question is the probability of someone inheriting logetivuty or risk factors in their life.
The biological factor here is the inheritance of a trait. The traits in question are either longevity or risk factors. The probability of someone inheriting longevity is far less compared to the probability of inheriting a health condition that might be a risk factor for the person in the long run. Hence, option C is the correct answer.
The complete question that you might be looking for is given below-
Nora's grandfather lived to be 87, and her father is still alive at the age of 98. Nora concludes that longevity is inherited and anticipates a very long life. Nora should know that __________.
A) there is no reliable data on the heritability of longevity, so the cumulative effects of random events probably contributed to the long lives of her relatives
B) the lifespans of fraternal twins are just as similar as the lifespans of identical twins, indicating that longevity is probably not a heritable trait
C) rather than inheriting longevity directly, people probably inherit risk and protective factors that influence their chances of dying earlier or later
D) the heritability of longevity is high, ranging from .75 to .95 for age at death, indicating that longevity is directly related to genetic factors
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The set S={1,2,3,….,12} is to be partitioned into three sets A,B,C of equal size, thus A∪B∪C=S, A∩B=B∩C=A∩C=ϕ. Thus number of ways to partition S is
The number of ways to partition set S into three sets A, B, and C of equal sizes is 495.
The number of ways to partition S into three sets of equal sizes can be calculated using the formula: nPr=n!/(r!(n−r)!), where n is the total number of elements in the set and r is the number of elements in each partitioned set.
In this case, n=12 and r=4. Therefore, the number of ways to partition S into three sets A, B, and C of equal sizes is 12P4 = 12!/(4!(12−4)!) = 495.
In calculation way step by step,
We know that n = 12 and r = 4.
Calculate 12!.
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479001600
Calculate 4!.
4! = 4 x 3 x 2 x 1 = 24
Calculate (12 - 4)!
(12 - 4)! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320
Calculate nPr.
nPr = n!/(r!(n - r)!) = 479001600/(24 x 40320) = 495
Thus, the number of ways to partition set S into three sets A, B, and C of equal sizes is 495.
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Consider the problem of predicting Y using another variable, X, so that the prediction of Y is some function of X, say g(X). Suppose that the quality of the prediction is measured by the squared prediction error made on average over all predictions, that is, by E{[Y – g(x)]?}. This exercise provides a non-calculus proof that of all possible prediction functions g, the best predic- tion is made by the conditional expectation, E(Y|X). a. E(Y|X), and let u = Y – û denote its prediction error. Show that E(u) = 0. (Hint: Use the law of iterated expectations.) b. Show that E(uX) = 0. c. Let Ỹ = g(x) denote a different prediction of Y using X, and let v = Y Ỹ denote its error. Show that E[(Y – Ỹ)?] > E[(Y - Ỹ)2]. [Hint: Let h(X) = g(x) – E(Y|X), so that v = [Y - E(Y|X)] - h(X). Derive E(v2).] a. Let û =
E(Y|X) is the conditional expectation of Y given X. We can use the law of iterated expectations to show that E(u) = 0.
This law states that E(E(X|Y)) = E(X). Therefore, E(u) = E(Y - E(Y|X)) = E(Y) - E(E(Y|X)) = E(Y) - E(Y) = 0.
b. We can use the law of iterated expectations again to show that E(uX) = 0. This law states that E(E(XY|Z)) = E(X)E(Y|Z). Therefore, E(uX) = E(YX - E(YX|X)) = E(YX) - E(E(YX|X)) = E(YX) - E(Y)E(X) = 0.
c. Let Ỹ = g(x) denote a different prediction of Y using X and let v = Y - Ỹ denote its error. We can use the equation h(X) = g(x) - E(Y|X), so that v = [Y - E(Y|X)] - h(X). Using this equation, we can derive E(v2) = E[(Y - E(Y|X))2] - 2E[(Y - E(Y|X))h(X)] + E[h(X)2]. Since E(Y - E(Y|X)) = 0, this reduces to E(v2) = E[h(X)2] < E[(Y - Ỹ)2], which shows that E[(Y - Ỹ)?] > E[(Y - Ỹ)2].
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can you find the slope intercept???
the slope intercept form is y=mx+b m is the slope and b is your y intercept
A formula for calculating the magnitude of an earthquake is M=23log(EE0)
that uses the common (base 10) logarithm. This is called the Moment Magnitude Scale (MMS), an alternative to the more well known Richter Scale. One earthquake has magnitude 3.9
on the MMS. If a second earthquake has 700
times as much energy as the first, find the magnitude of the second quake.
Round to the nearest hundredth.
The magnitude of the second earthquake was
The magnitude of the second earthquake is given as follows:
5.80.
How to obtain the magnitude of the second earthquake?The magnitude of an earthquake is given by the equation presented as follows:
[tex]M = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]
The first earthquake has a magnitude of 3.9, hence it's energy is obtained as follows:
[tex]3.9 = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]
[tex]\log{\left(\frac{E}{E_0}\right)} = \frac{3.9 \times 3}{2}[/tex]
[tex]\log{\left(\frac{E}{E_0}\right)} = 5.85[/tex]
As the power of 10 is the inverse function of the logarithm, we have that:
[tex]\frac{E}{E_0} = 10^5.85[/tex]
[tex]\frac{E}{E_0} = 707946[/tex]
[tex]E = 707946E_0[/tex]
The second earthquake has 700 times as much energy as the first, hence the energy is of:
[tex]E = 700 \times 707946E_0[/tex]
[tex]E = 495562049E_0[/tex]
Then the magnitude of the second earthquake is given as follows:
[tex]M = \frac{2}{3}\log{\left(\frac{495562049E_0}{E_0}\right)}[/tex]
[tex]M = \frac{2}{3}\log{(495562049)}[/tex]
M = 5.80.
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Set up an equation and solve each of the following problems. The total surface area of a right circular cylinder is 54π square inches. If the altitude of the cylinder is twice the length of a radius, find the altitude of the cylinder.
The altitude of the cylinder is 6 inch.
what is surface area of cylinder?The surface area of a cylinder is given by 2πr(r + h) , where r is the radius of the base and h is the height of the cylinder. It is the sum of the areas of the two circular bases and the lateral surface.
The formula for surface area of cylinder is given by:
surface area = 2πr(r+h)
where r is radius of the cylinder and h is the altitude of the cylinder
given h = 2r
so , surface area = 2πr(r+2r)
=> 6πr²
given 6πr² = 54π
=> r² = (54π)/(6π)
=> r² = 9
=> r = 3
so the altitude of the cylinder = 2r
=>2*3
=> 6
so the altitude of the cylinder is 6 inch.
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5. Sadie drew a number line diagram to find the number
of fluid ounces in 4 cups. What numbers for fluid
ounces will complete the diagram?
cups 0
fluid ounces 0
8
2
3
4
Fluid ounces are usually measured in milliliters, but if Sadie is using ounces, then the numbers she will need to complete the diagram are 32, 64, 96, and 128.
What is number?Number is a mathematical concept that represents a quantity or amount. It is used to count, measure, and label objects and phenomena in the physical and natural world. Number can be divided into two categories: cardinal numbers and ordinal numbers. Cardinal numbers are used to denote the total number of items in a set, while ordinal numbers are used to indicate the position of an item within a set. Number is also used to represent relationships between quantities, such as addition, subtraction, multiplication, and division. Number is an essential part of mathematics and is used in a variety of ways in the real world.
This is because 1 cup is equal to 8 fluid ounces, and 4 cups is therefore equal to 32 ounces, which is the same as 64 milliliters. Similarly, 2 cups is equal to 16 ounces, or 96 milliliters, and 3 cups is equal to 24 ounces, or 128 milliliters.
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You purchase a new laptop today. The value of that laptop depreciates based on the function f(t) = 4,300(0.83)t, where t is measured in years after purchase. How much is the laptop worth after five halves years, rounded to the nearest dollar?
$2,105
$1,601
$2,699
$3,215
The laptop worth after five halves years will be $1,543. Then the correct option is E.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
You purchase a new laptop today. The value of that laptop depreciates based on the function is given below.
f(x) = 4,300(0.83)ˣ.
Where 'x' is the number of years.
The laptop worth after five halves years will be given as,
[tex]\rm f(x) = \$4,300 \times (0.83)^{5.5}[/tex]
f(x) = $4,300 × 0.35886
f(x) = $1,543
The laptop worth after five halves years will be $1,543. Then the correct option is E.
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The missing options are given below.
$2,105
$1,601
$2,699
$3,215
$1,543
The worth of the laptop after 2.5 years is $2,699.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(t) = 4,300 [tex](0.83)^t[/tex]
Now,
For t = 5/2,
t = 2.5
f(5) = 4300 x [tex]0.83^{2.5}[/tex]
f(5) = 2699
Thus,
The laptop is worth $2,699 after 2.5 years.
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Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the Tanzanian blend with the Gazebo blend, but always in the same proportion. Yesterday, you mixed 80 pounds of the Tanzanian blend with 24 pounds of the Gazebo blend. Today, there is 20 pounds of the Tanzanian coffee left in stock. How many pounds of the Gazebo coffee should you mix with it to get your secret blend?
6 pounds of Gazebo blend is required to be mixed with Tanzanian blend to get the secret blend.
What is a ratio?The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given here: A secret coffee blend requires 80 pounds of Tanzanian blend with 24 pound of Gazebo blend.
Now, A proportion is an equation in which two ratios are set equal to each other. Ratio of the required secret blend is 80:24=10:3
Amount of Tanzanian blend left in stock is 20 pounds and let x pounds of Gazebo blend be required to make the secret blend thus to preserve the proportion we must have;
10/3=20/x
x/3=20/10
x=6
Hence, 6 pounds of Gazebo blend is required to get the secret blend.
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