Give the expression in terms of a, k, and t is g(t+1/k) = a2^(k(t+1/k)) = a2^kt * 2^(1/k)
The population doubles when P(t) = 2 * P(0), so we can set up the equation:
2 * 55 = 20^(5t)
Solving for t:
t = log(2)/(5 * log(20)) = log(2)/log(400)
The population doubles after approximately 0.173 years or 63.1 days.
g(t+1/k) = a2^(k(t+1/k)) = a2^kt * 2^(1/k)
Interpretation: g(t+1/k) is the population at time t+1/k, where a and k are positive constants. The population at t+1/k is equal to the population at time t multiplied by 2^(1/k). This means that if k is a large number, the population will change very little over time, if k is a small number, the population will change more quickly.
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HELP PLEASE someone ?????
event a occurs with probability 0.. teh conditional probability that event b occurs, given that a occurs is 0.5. the probability that both a and b occurs is
The probability of event a occurring is 0 and the conditional probability of event b occurring given that event a has occurred is 0.5.
The probability that both event A and event B occur is calculated using the formula P(A and B) = P(A) x P(B|A).
In this case, P(A) = 0 and P(B|A) = 0.5. When we plug these values into the equation, P(A and B) = 0 x 0.5 = 0. Therefore, the probability of both event A and event B occurring is 0. The probability that both events a and b occur is determined by multiplying the probability of event a occurring with the conditional probability of event b occurring given that event a has already occurred. This can be expressed mathematically as P(A∩B)=P(A)*P(B|A). In this case, the probability of both events a and b occurring is 0.5*0.5=0.25, since the probability of event a occurring is 0 and the conditional probability of event b occurring given that event a has occurred is 0.5.
This makes sense, since event A has a probability of 0 and cannot occur in the first place, so the probability of both events occurring together is 0.
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c x 3 c 9 7. followingis a statement of a theorem which can be proven using the quadratic formula. for this theorem, a, b, and c are real numbers. theorem if f is a quadratic function of the form f .x/ d ax2 c bx c c and ac < 0, then the function f has two x-intercepts. using only this theorem, what can be concluded about the functions given by the follo
The conclusion about given functions are given below.
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
We have the following theorem:
If f is a quadratic function of the form f(x) = ax²+bx+c and ac < 0 , then the function f has two x-intercepts.
(a) g(x) = -8x²+5x-2
For this function a = -8 and c = -2, then -8 × -2 = 16 is greater than zero. Therefore, we cannot conclude anything.
(b) h(x) = [tex]-\frac{1}{3}x^{2} + 3x[/tex]
For this function a = -8 and we don't know the value of c. Therefore, we cannot conclude anything.
(c) k(x) = 8x²-5x-7
For this function a = 8 and c = -7, then 8 × -7 = -56 is less than zero. Therefore, we can conclude that the function k has two x-intercepts.
(d) j(x) = [tex]-\frac{71}{99}x^{2} + 210[/tex]
For this function a = [tex]-\frac{71}{99}[/tex] and c = 210, then [tex]-\frac{71}{99}[/tex] × 210 = [tex]-\frac{4970}{33}[/tex] is less than zero. Therefore, we can conclude that the function k has two x-intercepts.
(e) f(x) = 4x²-3x+7
For this function a = 4 and c = 7, then 4×7 = 28 is greater than zero. Therefore, we cannot conclude anything.
(f) F(x) = [tex]-x^{4} + x^{3} + 9[/tex]
We cannot conclude anything because this is not a quadratic function.
The conclusion about given functions are given above in explanation.
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complete question : Following is a statement of a theorem which can be proven using the quadratic formula. For this theorem, a, b, and c are real numbers. Theorem If f is a quadratic function of the form f .x/ D ax2 C bx Cc and ac < 0, then the function f has two x-intercepts. Using only this theorem, what can be concluded about the functions given by the following formulas(a) g (x) = -8x^2 + 5x - 2 (b) h (x) = -(1/3)x^2 + 3x (c) k (x) = 8x^2 - 5x - 7 (d) j (x) = -(71/99)x^2 + 210 (e) f (x) = 4x^2 - 3x + 7 (f) F (x) = -x^4 + x^3 + 9
3 c 9 8. following is a statement of a theorem about certain cubic equations. for this theorem, b represents a real number. theorem a. if f is a cubic function of the form f .x/ d x 3 x c b and b > 1, then the function f has exactly one x-intercept. following is another theorem about x-intercepts of functions: theorem b. if f and g are functions with g.x/ d k f .x/, where k is a nonzero real number, then f and g have exactly the same x-intercepts. using only these two theorems and some simple algebraic manipulations, what can be concluded about the functions given by the following
Both f(x) and g(x) have one x-intercept at x = -1/3.
Theorem A states that for a cubic function of the form f(x) = x^3 + x + b, with b > 1, the function f has exactly one x-intercept. Using Theorem B, we can conclude that for any nonzero real number k, the function g(x) = kf(x) = kx^3 + kx + bk also has exactly one x-intercept.
For example, if f(x) = x^3 + x + 5 and k = 2, then g(x) = 2x^3 + 2x + 10. Both f(x) and g(x) have exactly one x-intercept. This can be shown by solving the quadratic equation formed by setting f(x) = 0 or g(x) = 0. Doing this yields x = -1/3. Therefore, both f(x) and g(x) have one x-intercept at x = -1/3.4
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A town has a population of 1600 people at time t=0. In each of the following cases, write a formula for the population P, of the town as a function of year t.(a) The population increases by 70 people per year.(b) The population increases by 9 percent a year.
The population of the town at any given time t can be determined using the formulas provided. For example, if the town's population at time t=5 years is desired, the population can be calculated as follows:(a) P(5) = 1600 + 70(5) = 2100 people (b) P(5) = 1600(1.09)^5 = 2266.05 people
(a) P(t) = 1600 + 70t
(b) P(t) = 1600(1.09)^t
(a) In this case, the population increases by 70 people per year, so the formula for the population as a function of time is P(t) = 1600 + 70t. This means that the population is 1600 people at time t=0 and increases by 70 people for each additional year.
(b) In this case, the population increases by 9 percent each year, so the formula for the population as a function of time is P(t) = 1600(1.09)^t. This means that the population is 1600 people at time t=0 and increases by a factor of 1.09 (9 percent) for each additional year.
The population of the town at any given time t can be determined using the formulas provided. For example, if the town's population at time t=5 years is desired, the population can be calculated as follows:
(a) P(5) = 1600 + 70(5) = 2100 people
(b) P(5) = 1600(1.09)^5 = 2266.05 people
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The quadratic functions f(x) and g(x) are described in the table.
x f(x) g(x)
−6 36 4
−5 25 1
−4 16 0
−3 9 1
−2 4 4
−1 1 9
0 0 16
1 1 25
2 4 36
In which direction and by how many units should f(x) be shifted to match g(x)?
Left by 4 units
Right by 4 units
Left by 8 units
Right by 8 units
In the horizontal direction and by 4 units to the left, f(x) should be shifted to match g(x).
The correct option is A.
What is transformation on the graphs?The function provided by the basic function f(x) and the constant
g(x) = f(x - k),
may be drawn by horizontally moving the f(x) k unit coordinates.
The shift's direction depends on the value of k. Specifically,
The base graph moves k units to the right if k > 0, and
The base graph moves k units to the left if k < 0.
Given:
The quadratic functions f(x) and g(x) are described in the table.
From the table, the functions,
f(x) = x².
And g(x) = (x + 4)².
In the attached image,
the blue curve is the function of f(x).
And red line is the function of g(x).
From the graph,
Left by 4 units, f(x) should be shifted to match g(x).
Therefore, left by 4 units, f(x) should be shifted to match g(x).
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Answer: A
Step-by-step explanation: took the test
Please help i need it quickly too please
B. In square EFGH, find the length of EG.
Answer:
6√2
Step-by-step explanation:
You want one side of a square whose half-diagonal has length 6.
Right triangleIf X is the center point of the square where the diagonals cross at right angles, triangle EXG is an isosceles right triangle with leg length 6. The hypotenuse of an isosceles right triangle is √2 times the leg length, so ...
EG = 6√2
__
Additional comment
If you like, you can use the Pythagorean theorem to prove that.
EG² + EX² +GX² = 6² +6² = 72
EG = √72 = √(36·2) = 6√2
A square is a rhombus, so the diagonals cross at right angles. A square is a rectangle, so the diagonals are the same length. A square is a parallelogram, so the diagonals bisect each other.
A local art group wishes to raise $8,000. Currently, they have raised $4,200. what percent has the art group raised
Answer:
raised 53%
Step-by-step explanation:
goal = $8,000
raised = $4,200
$4,200/$8,000 = 0.525 = about 53%
Three friends each ordered a large cheese pizza. Shauntee ate $\frac{2}{3}$ of her pizza, Carlos ate $\frac{8}{9}$ of his pizza and Rocco ate $\frac{26}
{27}$ of his pizza. If the remaining portions from the three pizzas are put together, what fraction of a large pizza do they make? Express your answer as a common fraction.
The remaining portions from the three pizzas together make up 13/27 of a large pizza.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
Shauntee ate 2/3 of her pizza, so she has 1/3 left.
Carlos ate 8/9 of his pizza, so he has 1/9 left.
Rocco ate 26/27 of his pizza, so he has 1/27 left.
To determine the combined fraction of the remaining portions of the three pizzas, we add the fractions that are left:
1/3 + 1/9 + 1/27 = (1/3) + (1/9) + (1/27)
Simplifying this fraction by finding the least common denominator, which is 27:
(1/3) + (1/9) + (1/27) = (9/27) + (3/27) + (1/27) = 13/27
So they together make up 13/27 of a large pizza.
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8.498 ? 8.478 use >,<,=
The inequality equation is 8.498 > 8.478
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Let the first number be represented as = p
Let the second number be represented as = q
Now , the value of p = 8.498
The value of q = 8.478
And , the hundredths value in the number 8.498 is greater than the hundredths value in the number 8.478
So , the value of p is greater than q
Therefore , 8.498 > 8.478
Hence , the inequality is 8.498 > 8.478
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1. The normal temperature for the human body is 37 °C (degrees Celsius). A patient suffering from malaria has a temperature of 40,2 °C. How many °C must his temperature decrease to reach a normal temperature?
Answer:
3,2 °C
Step-by-step explanation:
40,2 °C - 37 °C = 3,2 °C
Write an algebraic expression that Marshall can use to determine the total cost of buying a watermelon that weigh w pounds and some tomatoes that weigh t pounds. How much will it cost to buy a watermelon that weighs 18.5 pounds and 5 pounds of tomatoes? Tomatoes are $3.25 / lb and Watermelon is $0.68 / lb
The algebraic expression which represents the total cost of buying watermelons and tomatoes as described is; C = 0.68w + 3.25t.
The cost of buying a watermelon that weighs 18.5 pounds and 5 pounds of tomatoes is; $28.83.
What is the cost of buying watermelons and tomatoes?It follows from the task content that the cost of buying Tomatoes are $3.25 / lb and Watermelon is $0.68 / lb.
Hence, the algebraic expression which represents the cost of buying a watermelon that weighs, w pounds and tomatoes that weigh t pounds is;
C = 0.68w + 3.25t.
Hence, if the watermelon bought weighs 18.5 pounds and tomatoes weigh 5 pounds,
C = 0.68 (18.5) + 3.25 (5)
C = 12.58 + 16.25
C = $28.83.
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what are the factors and zeros of the function f(x)=x2-5x+6
The factors and zeros of the function f(x)=x2-5x+6 are x-3, x-2 and 3 and 2 respectively
How to determine the zeros of the functionGiven the quadratic function as;
f(x) = x² - 5x + 6
Using the factorization method of solving quadratic function, we have to multiply the coefficient of x² by the constant of the function
Then find the pair factors of the function that sums up to -5
The pair factors area -2 and -3
Substitute the values, we get;
x²- 2x - 3x + 6
Pair the expression
(x² -2x) - (3x + 6)
Factorize the value
x(x -2) -3(x - 2)
The zeros are;
x-3 = 0
x = 3
Then,
x -2 = 0
x =2
Hence, the values are 2 and 3
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You mix 1 half cup of salt with 3 cups of sugar. Which below is the ratio of salt to sugar.
In a case whereby you mix 1 half cup of salt with 3 cups of sugar the ratio of salt to sugar.
What is ratio?The concept that will be used is ratio. An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
we were told that there were 1 half cup of salt with 3 cups of sugar
Then the ratio can be written as
salt/sugar
= (1 1/2)/3
Since the amount of the salt is in mixed fraction, we can reduce to improper fraction for easy calculation.
=( 3/2)/ 3
= 3/6
=1/2
Hence, the ratio is 1:2
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missing options:
A. 2:3
B.1:2
C.2:1
D. 5:6
42.735 rounded to the nearest ones places
Answer: 43 because 7 is greater than 5 so you round up. Have a nice day ;)
The correct answer is 43. 0.735 is greater than 0.5, so you round it up to 43
FILL IN THE BLANK When aligning tow shafts, the reason to rotate the coupling hubs before making each measurement is so each measurement is ____________
When we are aligning two shafts, the reason behind rotating the coupling hubs before taking each measurement is so that each of the measurements is taken from the same place on the hub every time.
Shafts are basically a component of circular cross section which rotates and transmits the power from a driving device like an engine or a motor through a particular machine. Coupling hubs are basically the attachment of the coupling to shaft in a device.
During the alignment of two shafts, the angular as well as parallel misalignment is thoroughly checked. The coupling hubs are rotated before taking each measurement is so that each of the measurements is taken from the same place on the hub every time.
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help asap! Giving brainliest
The table below shows the ratio of a bird's brain to body weight.
Brain (part) 0.6 B 1.8 E
Body (part) A 14.3 19.8 33
Total (whole) 7.2 C D 36
Which table shows the correct missing values?
Brain (part) 0.6 1.3 1.8 3
Body (part) 6.6 14.3 19.8 33
Total (whole) 12.6 27.3 37.8 36
Brain (part) 0.6 1.2 1.8 3
Body (part) 1.2 14.3 19.8 33
Total (whole) 7.2 15.6 21.6 36
Brain (part) 0.6 1.2 1.8 3
Body (part) 6.0 14.3 19.8 33
Total (whole) 6.6 15.5 37.8 36
Brain (part) 0.6 1.3 1.8 3
Body (part) 6.6 14.3 19.8 33
Total (whole) 7.2 15.6 21.6 36
The complete table is given as follows -
Brain (part) 0.6 1.3 1.8 3
Body (part) 6.6 14.3 19.8 33
Total (whole) 7.2 15.6 21.6 36
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that an interior designer recently spent £1359.55 buying 25 kettles and 20 toasters for a smaller group of new houses. For her current assignment she needs 80 kettles and 56 toasters.
The given table is -
Brain (part) 0.6 B 1.8 E
Body (part) A 14.3 19.8 33
Total (whole) 7.2 C D 36
We can write the expressions as -
0.6 + A = 7.2 .... Eq( 1 )
A = 6.6
1.8 + 19.8 = D .... Eq( 2 )
21.6 = D
E + 33 = 36
E = 3 .... Eq( 3 )
Therefore, the complete table is given as follows -
Brain (part) 0.6 1.3 1.8 3
Body (part) 6.6 14.3 19.8 33
Total (whole) 7.2 15.6 21.6 36
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Which graph represents the solution set of the compound inequality below?
x+3<= (4x-12) < 20
OH
4 5 6 7 8 9 10 11 12
4 5 6 7 8 9 10 11 12
6 7 8 9 10 11 12 13 14
6 7 8 9 10 11 12 13 14
A graph that represents the solution set of the compound inequality is: graph D.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than (<).Greater than (>).Greater than or equal to (≥).Less than or equal to (≤).Next, we would solve the given compound inequality by making x the subject of formula as follows;
x + 3 < 1/2(4x - 12) < 20
Multiplying all through by 2, we have the following:
2x + 6 < 4x - 12 < 40
Next, we would solve the compound inequality in parts:
2x + 6 < 4x - 12
4x - 2x < 12 + 6
2x < 18
x < 18/2
x < 9.
4x - 12 < 40
4x < 40 + 12
4x < 52
x < 52/4
x < 13.
In conclusion, the line on a number line (graph) should be open when the inequality symbol is greater than (>) or less than (<).
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Please help ASAP or a huge cockroach will crawl into in your ear
In this figure, GH=12, GP=16, and FP=2.
What is EF?
Enter your answer in the box.
EF
Answer:
This is nonsense, if GP = 16 and GH = 12 then HP = 4 (16 - 12 = 4). FP is looking basically the same size as HP, so FP = 4, not 2.
Step-by-step explanation:
These are all lies, your teacher is a liar and EF must be around 12 too.
Answer:
30
Step-by-step explanation:
Provide explanation for how to solve this problem.
The numeric value of the function is given as follows:
2x + h + 9.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function in this problem is given as follows:
f(x) = x² + 9x.
At x = x + h, the function is defined as follows:
f(x + h) = (x + h)² + 9(x + h)
f(x + h) = x² + 2xh + h² + 9x + 9h
f(x + h) = x² + 2xh + h² + 9x + 9h.
Subtracting by f(x), we have that:
f(x + h) - f(x) = h² + 2xh + 9h.
f(x + h) - f(x) = h(h + 2x + 9).
Dividing by h, the numeric value is given as follows:
2x + h + 9.
Meaning that the first option is the correct option.
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suppose phone calls arrive at an office according a poisson process at a mean rate of 5 calls per hour. the expected waiting time in hours until the first call arrived is
The expected waiting time in hours until the first call arrived is 0.00045.
The formula for poisson distribution is expressed as
P(x = r) = (e^- µ × µ^r)/r!
Where ,
µ= represents the mean of the theoretical distribution.
r = represents the number of successes of the event.
According to the question,
µ = 5
For the probability that there are one in one hour, it is expressed as
P(x = 1) ,
Therefore,
P(x = 1)
= (e^- 10 × 10^1)/1! = 0.00045
Therefore,
P(x = 1)
= 0.00045
Poisson distribution
A Poisson distribution is a discrete probability distribution. It gives the probability of an event happening a certain number of times (k) within a given interval of time or space.
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Freshman and sophomores were surveyed during lunch about their favorite professional football team.
A bar graph with the first bar labeled Jaguars, divided into freshmen from 0 to 40 percent and sophomores from 40 to 100 percent. The second bar is labeled Dolphins, with freshman from 0 to 45 percent and sophomores from 45 to 100 percent, and the third bar is labeled Buccaneers, with freshmen from 0 to 45 percent and sophomores from 45 to 100 percent.
If 140 students selected Jaguars, how many of those students are freshman?
56 students
63 students
77 students
84 students
There are 56 students as freshmen. The correct answer would be an option (A).
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
A bar graph with the first bar labeled Jaguars, divided into freshmen from 0 to 40 percent and sophomores from 40 to 100 percent.
This can be determined by multiplying the percentage of freshmen who selected Jaguars (40%) by the total number of students surveyed (140).
⇒ 40% × 140 = 56
So there are 56 students as freshmen.
Hence, the correct answer would be option (A).
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Use the motion map to answer the question. A motion map. The position line is a long black arrow pointing right with x as the reference point at left. Above the line are 3 dots with short vector arrows moving toward x, then a dot, then 2 dots with longer vector arrows moving away from x. Describe the position and velocity of the object based on the motion map.
The direction and position of the fourth and fifth arrows indicate that the object then moves towards the origin, with a smaller velocity.
What are Motion maps?Motion maps are used to illustrate the direction and position of an object. Using the motion map, the description of the object position and velocity is as follows:
The object starts its movement from the origin with a large velocity, before moving back to the origin with a smaller velocity. It stops for 1 second in the origin, then moves away with a larger velocity, Finally, it moves back towards the origin with a smaller velocity.
See attachment for the motion map, where the number on each arrow in the map, represents the position of the object.
Note that; the long arrow means large velocity while the short arrow means small velocity.
We analyze the direction and position using the arrows
The first arrow shows that the object starts from the origin with a large velocity.The direction and length of the second arrow show that, the object then returned to the origin with a smaller velocity.There is a dot in front of the second arrow. This dot indicates that the object stops for one second.The third arrow means that, the object moved from the origin with a larger velocityThe direction and position of the fourth and fifth arrows indicate that the object then moves towards the origin, with a smaller velocity.Therefore, the direction and position of the fourth and fifth arrows indicate that the object then moves towards the origin, with a smaller velocity.
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Answer:
Based on the motion map, the object starts at the reference point "x" on the left side of the position line. The three dots with short vector arrows moving toward "x" indicate that the object is moving in the direction of the reference point and gaining speed. This suggests that the object is accelerating. Then, there is a single dot, which might indicate a momentary pause or a constant velocity. Afterward, the two dots with longer vector arrows moving away from "x" suggest that the object is decelerating or slowing down. In summary, the motion map shows an object that starts from rest, accelerates towards the reference point, maintains a constant velocity for a brief moment, and then decelerates away from the reference point.
Step-by-step explanation:
Use chat gpt to give you unique answer.
Which statements regarding Triangle E F G are true? Select three options. EF + FG > EG EG + FG > EF EG - FG < EF EF- FG > EG EG + EF < FG
we can conclude that option (A) , (B) and (C) are true.
We know that in a triangle,
• Sum of any to sides is greater than the third side.
• Difference between any two sides is smaller than the third side.
So, in ∆EFG, we have,
• EF + FG > EG
• FG + EG> EF
• EF + EG > FG
and,
• EF - FG <EG or FG - EF <EG
• FG - EG < EF or EG - FG < EF
• EF - EG <FG or EG - EF < FG
From options now we get,
A) EF + FG > EG is true
B)EG + FG > EF is true
C) EG - FG < EF is true
D) EF - FG > EG is false
E) EG + EF < FG is false
Therefore, we can conclude that option () , () and () are true.
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We can conclude that option (A) , (B) and (C) are true.
We know that in a triangle,
• Sum of any to sides is greater than the third side.
• Difference between any two sides is smaller than the third side.
So, in ∆EFG, we have,
• EF + FG > EG
• FG + EG> EF
• EF + EG > FG
and,
• EF - FG <EG or FG - EF <EG
• FG - EG < EF or EG - FG < EF
• EF - EG <FG or EG - EF < FG
From options now we get,
A) EF + FG > EG is true
B)EG + FG > EF is true
C) EG - FG < EF is true
D) EF - FG > EG is false
E) EG + EF < FG is false
Therefore, we can conclude option (A) , (B) and (C) are true.
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exercise 1.2.3 the augmented matrix of a system of linear equations has been carried to the following by row operations. in each case solve the system.1 2 1 3 1 | 10 1 -1 0 1 | 1c = 0 0 0 1 -1 | 00 0 0 0 0 | 0
The presented system of linear equations has no solution.
The final form of the augmented matrix suggests that the system of linear equations has no solution, as the last row represents an equation with 0 = 0, which is always true but doesn't provide any information about the variables.
To see this more clearly, let's use the augmented matrix to write out the system of linear equations:
1x - 1y + 2z = 4
2y + 1z = -1
z = 1
The first two equations are consistent and have a unique solution, but the last equation is trivial and provides no information about x and y. In other words, infinitely many pairs of x and y satisfy the first two equations, but none satisfy the third equation. Therefore, the given system of linear equations has no solution.
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need the answer please
Answer:
Step-by-step explanation:
Answer:
1.91 lb
Step-by-step explanation:
1 3/4 cups of pecans per pie = 1.75 cups.
For 5 pies, 5 × 1.75 cups = 8.75 cups are needed.
1 cup = 99 g
8.75 cup × (99 g) / (1 cup) = 866.25 g
Exact conversion: 453.59237 g = 1 lb
866.25 g × (1 lb)/(453.59237 g) = 1.91 lb
Answer: 1.91 lb
what is a system of linear equations whose solution is (6,19)
Answer:
A system of linear equations is a set of two or more equations containing two or more variables. The solution to a system of linear equations is the set of values for the variables that makes all the equations in the system true.
For example, a system of linear equations whose solution is (6,19) could be represented by the following equations:
x + 2y = 25
3x - 4y = 6
Solving this system would yield x = 6 and y = 19 as the solution.
The life span of fruit fly have a bell shaped distribution, with a mean of 32 days and a standard deviation of 5 days. What is the Z score of the fruit flys at 37 ,30 and 47 days
Answer:
The Z-score (also known as a standard score) represents the number of standard deviations a value is away from the mean of a distribution. The formula for the Z-score is:
Z = (X - μ) / σ
Where X is the value of interest, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
Given the information in the problem, we know that the mean of the fruit fly's lifespan is 32 days and the standard deviation is 5 days.
To find the Z-score of a fruit fly whose lifespan is 37 days:
Z = (37 - 32) / 5 = 1
To find the Z-score of a fruit fly whose lifespan is 30 days:
Z = (30 - 32) / 5 = -0.4
To find the Z-score of a fruit fly whose lifespan is 47 days:
Z = (47 - 32) / 5 = 2.4
Therefore, a fruit fly whose lifespan is 37 days has a Z-score of 1, a fruit fly whose lifespan is 30 days has a Z-score of -0.4, and a fruit fly whose lifespan is 47 days has a Z-score of 2.4.
in problems 21 through 30, first verify that the given vectors are solutions of the given system. then use the wronskian to show that they are linearly independent. finally, write the general solution of the system. 25
It is verified that the given vectors x₁ and x₂ are solutions of the given system. Using Wronskian it is shown that they are linearly independent. Then, [tex]W(t)=7e^{-3t}[/tex]. The general solution of the given system is written as [tex]x(t)=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right][/tex].
Wronskian analysis helps to determine whether a solution is linearly dependent or independent.
Given the system is [tex]x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x[/tex].
Let's differentiate x₁ concerning t, and we get,
[tex]\begin{aligned}x_1'&=\left[\begin{array}{c}\frac{d}{dt}(3e^{2t})&\\\frac{d}{dt}(2e^{2t})&\end{array}\right] \\&=\left[\begin{array}{c}6e^{2t}&\\4e^{2t}&\end{array}\right] \end{aligned}[/tex]
Now,
[tex]\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_1&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}12e^{2t}-6e^{2t}\\18e^{2t}-14e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}6e^{2t}\\4e^{2t}\end{array}\right]\\&=x_1'\end{aligned}[/tex]
From this, we can write,
[tex]x_1'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_1[/tex]
Therefore, we conclude that x₁ is a solution to the given system.
Let's differentiate x₂ concerning t, and we get,
[tex]\begin{aligned}x_2'&=\left[\begin{array}{c}\frac{d}{dt}(e^{-5t})&\\\frac{d}{dt}(3e^{-5t})&\end{array}\right] \\&=\left[\begin{array}{c}-5e^{-5t}&\\-15e^{-5t}&\end{array}\right] \end{aligned}[/tex]
Now,
[tex]\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_2&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}4e^{-5t}-9e^{-5t}\\6e^{-5t}-21e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}-5e^{-5t}\\-15e^{-5t}\end{array}\right]\\&=x_2'\end{aligned}[/tex]
From this, we can write,
[tex]x_2'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_2[/tex]
Therefore, we conclude that x₂ is also a solution to the given system.
Now, find the Wronskian of x₁ and x₂, we get,
[tex]\begin{aligned}W(t)&=\text{det}[x_1\;x_2]\\&=\text{det}\left[\begin{array}{cc}3e^{2t}&e^{-5t}\\2e^{2t}&3e^{-5t}\end{array}\right] \\&=(3e^{2t}\times3e^{-5t})-(e^{-5t}\times2e^{2t})\\&=9e^{2t-5t}-2e^{2t-5t}\\&=9e^{-3t}-2e^{-3t}\\&=7e^{-3t}\\&\neq0\end{aligned}[/tex]
From this, we can conclude that x₁ and x₂ are independent.
Finally, we write the general solution of the system as follows,
[tex]\begin{aligned}x(t)&=c_1x_1+c_2x_2\\&=c_1 \left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right] +c_2\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right] \\&=\left[\begin{array}{c}3c_1e^{2t}\\2c_1e^{2t}\end{array}\right] +\left[\begin{array}{c}c_2e^{-5t}\\3c_2e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right] \end{aligned}[/tex]
The complete question is -
First, verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system.
[tex]x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x;\; x_1=\left[\begin{array}{ccc}3e^{2t}\\2e^{2t}\end{array}\right], \;x_2=\left[\begin{array}{cc}e^{-5t}\\3e^{-5t}\end{array}\right][/tex]
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