The slope of the line and its meaning in terms of the real-world scenario is; C. The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
How to calculate or determine the rate of change or slope of a line?In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (0 - 24)/(6 - 0)
Slope (m) = -24/6
Slope (m) = -4.
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In this figure, FE←→
is parallel to AD¯¯¯¯¯
, and m∠A
= 158°. What is m∠FCA? m∠FCA
= °
Note that where the above conditions are given, m∠FCA is also = 158°. This is due to the principle of alternate angles.
What are alternate angles?A pair of angles that are created by a transversal intersecting two parallel lines, known as alternate angles, have key properties which contribute to their importance in geometry.
They take place on opposite sides of the transversal and have equal magnitudes.
These concepts aid in understanding vertical angles and parallel lines within geometrical systems.
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Answer: ur correct answer is 158
Step-by-step explanation: not doing this to tke points!!
The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 8.5% per hour. How many hours does it take for the size of the sample to double?
.54 oz of premium walnuts costs $12.95. what is cost per ounce
The cost per ounce of the premium walnut is $0. 23
What is proportion?To determine the value of the cost, we need to note that proportion is simply described as the comparison of numbers such that they are made equal to another.
From the information given, we have that;
54 ounces of premium walnuts costs $12.95
This is represented as;
54 ounces = $12. 95
Then 1 = x
cross multiply the values, we get;
x = $12.95/54
Divide the values, we get;
x = $0. 23
Hence, the value is $0. 23 per premium walnut
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Find and compare the domain and range of each function. f(x) = 5/8x + 1 g(x) = 2/3x^3 A. The domains and ranges of both functions are not restricted. B. The domain of f is restricted, but its range is not. The domain and range of g are not restricted. C. The range of f is restricted, but its domain is not. The domain and range of g are not restricted. D. Both the domain and range of f are restricted, but the domain and range of g are not.
A. The domains and ranges of both functions are not restricted.
For f(x) = 5/8x + 1, any real number can be plugged in for x, so the domain is (-∞, ∞). Similarly, any real number can be obtained by evaluating the function, so the range is also (-∞, ∞).
For g(x) = 2/3x^3, any real number can be plugged in for x, so the domain is (-∞, ∞). As x is cubed, the range can be negative or positive infinity, or any real number in between, so the range is also (-∞, ∞).
Therefore, both functions have unrestricted domains and ranges.
The correct answer is A.
Using the above supply/demand graph, what is the price at the point of equilibrium
The price at the point of equilibrium is 105
What is the price at the point of equilibrium?From the question, we have the following parameters that can be used in our computation:
The supply/demand graph
The price at the point of equilibrium is the price where the lines/curves of the supply and the demand functions intersect
Using the above and the graph as a guide, we have the following:
Price = 105 when demand = supply
Hence, the price at the point of equilibrium is 105
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Question
Using the above supply/demand graph, what is the price at the point of equilibrium? a. 105 b. 100 c. 95 d. 80
Differentiate y = x^3 ln 2x/e^x Sin x
Differentiating y = x^3 ln 2x/e^x Sin x is: y' = x^2 [(3 ln 2x/e^x Sin x + 3/x) - 2 ln 2x/e^x Sin x cos x + cos x].
What is Differentiation?Differentiate y can be find using the product and chain rule.
Using the chain rule
v'(x) = [1/(2x/e^x)] * (2e^x - e^x*2x) / (2x/e^x)^2
v'(x) = [e^x(2-e^x)] / (2x)^2
Using the product rule
y' = 3x^2 ln(2x/e^x) sin(x) + x^3 [e^x(2-e^x)] / (2x)^2 sin(x) + x^3 ln(2x/e^x) cos(x)
Simplifying
y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)
So,
derivative of y is:
y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)
Therefore the differentiate of y is 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x).
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Fill in the paragraph shown with the correct information from the answer choices provided.
Portland Rainfall
Seattle Rainfall
(inches)
(inches)
4
3
2
Week
1
2
3
4
5
5
10
1
4
7
6
5
A meteorologist tracks the rainfall in two cities.
variability
By calculating the
claim that Portland tends to receive more rainfall than Seattle.
of the data, the meteorologist can
mean
By calculating the median of the data, the meteorologist can claim that Portland tends to receive more rainfall than Seattle.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.
The ordered data-sets for each city are given as follows:
The median is the middle element for each data-set, hence it is given as follows:
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The Hullian learning model asserts that the probability p of mastering a task after t learning trials is approximated by p (t) = 1 - e -kt where k is a constant that depends on the task to be learned. Suppose that a new dance is taught to an aerobics class. For this particular dance, the constant k = 0.28.
a. What is the probability of mastering the dance's steps in 1 trial? 2 trials? 5 trials? 11 trials? 16 trials? 20 trials?
Find the rate of change, p'(t).
Sketch a graph of the function.
Answer:
Step-by-step explanation:
a. Using the formula p(t) = 1 - e^(-kt), where k = 0.28:
Probability of mastering the dance's steps in 1 trial: p(1) = 1 - e^(-0.28*1) ≈ 0.243
Probability of mastering the dance's steps in 2 trials: p(2) = 1 - e^(-0.28*2) ≈ 0.446
Probability of mastering the dance's steps in 5 trials: p(5) = 1 - e^(-0.28*5) ≈ 0.846
Probability of mastering the dance's steps in 11 trials: p(11) = 1 - e^(-0.28*11) ≈ 0.981
Probability of mastering the dance's steps in 16 trials: p(16) = 1 - e^(-0.28*16) ≈ 0.997
Probability of mastering the dance's steps in 20 trials: p(20) = 1 - e^(-0.28*20) ≈ 0.999
b. The rate of change, p'(t), can be found by taking the derivative of the function p(t):
p'(t) = k * e^(-kt)
c. Here's a graph of the function p(t):
I apologize for the technical issue, but the graph doesnt load, so here's a description of the graph:
The graph of p(t) should be an increasing curve that starts at 0 and approaches 1 asymptotically. As t increases, the rate of change of p(t) decreases, which means that the curve becomes flatter and approaches the horizontal asymptote of y=1. The curve is concave down, meaning that its rate of change is decreasing. At t=0, the rate of change is k, which is the steepest point of the curve.
_______________________
graph of p(t) = 1 - e^(-0.28*t)
The x-axis represents the number of learning trials, and the y-axis represents the probability of mastering the dance's steps. As the number of trials increases, the probability of mastering the steps approaches 1 (or 100%).
Gate posts are parallel and m<4 =47, what is m<1
The value of angle 1 given the value of angle 4 as 47° will be 133°
How to explain parallel linesParallel lines are two lines on a two-dimensional plane that, no matter how far they are extended, never collide. They always keep the same gap between them.
Parallel lines have the same slope, which means they have the same angle of inclination or steepness. In other words, they rise and fall at the same pace along their length.
The value will be:
= 180° - 47°
= 133°
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Medication with strength 125 mg/5 mL has been ordered at 5 mg/kg. The patient weighs 134 lb. How much should be administered? (If less than 1, round to the nearest hundredth; otherwise, round to the nearest tenth.)
Rounding to the closest hundredth, the final result is 12.16 mL, which is the amount of the drug that should be administered.
The patient's weight must first be converted from pounds to kilograms.
1 lb = 0.453592 kg
Therefore, 134 lb = 60.78 kg
The dose must then be determined depending on the patient's weight:
60.78 kg times 5 mg/kg equals 303.9 mg.
Now that we know the medication's concentration, we need to determine how much to deliver.
25 mg/mL x 125 mg/5 mL
The dosage for 303.9 mg is as follows:
303.9 mg x 25 mg/mL = 12.16 mL
The final result, rounded to the closest hundredth, is 12.16 mL.
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60 POINTS ANSWER FOR BRAINLIST AND HEARTS
Answer:
a. The given equation is (y - 3)^2 -10 = 71. To determine the number and type of solutions, we need to use the discriminant, which is given by b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in standard form (ax^2 + bx + c = 0). In this case, the equation can be rewritten as (y - 3)^2 = 81, which is in the form of (y - k)^2 = r^2, where k = 3 and r = 9. Therefore, the equation can be written as (y - k)^2 - r^2 = 0, which is a quadratic equation with a = 1, b = -6, and c = -72. The discriminant is then b^2 - 4ac = (-6)^2 - 4(1)(-72) = 300. Since the discriminant is positive, there are two real solutions.
b. To solve the equation (y - 3)^2 -10 = 71, we first add 10 to both sides to get (y - 3)^2 = 81. Then, we take the square root of both sides to get y - 3 = ±9. Adding 3 to both sides, we get y = 3 ± 9, which gives us two solutions: y = 12 and y = -6.
Therefore, the equation (y - 3)^2 -10 = 71 has two real solutions, which are y = 12 and y = -6.
Step-by-step explanation:
Answer: type: real number of solutions:2 y=12,-6
Step-by-step explanation:
see images for explanations
Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = x + 2 Complete the table on your own paper, then select the value that is a solution to f(x) = g(x). (2 points) Group of answer choices x = 2 x = 3 x = 5 x = 6
PLEASE HELP (WILL GIVE BRAINLIEST
Answer:
6.7 = π(r^2)(33.5/12)
r = .874
75/(2 × .874) = 42.9 = 42 barrels
6.7 = (3.14)(r^2)(33.5/12)
r = .874
75/(2 × .874) = 42.9 = 42 barrels
Highschool geometry please answer questions 8-10 in the attachment added
Solve the following for θ, in radians, where 0≤θ<2π.
3cos2(θ)+6cos(θ)−4=0
Answer:
0 ≤ < 2
Step-by-step explanation:
Answer:1.02 5.27 are correct
Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
3u^2 + 6u - 4 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 3, b = 6, and c = -4. Substituting these values, we get:
u = (-6 ± sqrt(6^2 - 4(3)(-4))) / 2(3)
u = (-6 ± sqrt(84)) / 6
u = (-3 ± sqrt(21)) / 3
Therefore, either:
Find the average of the numbers: 16 and 17
Answer:
16.5
Step-by-Step Explanation:
16.5 would be the average because it is right between 16 and 17. hope that helps :)
Given g(x)=x²-6x-16, which statement is true?
The zeros are -8 and 2, because the factors of gare (x+8) and (x-2).
The zeros are -8 and -2, because the factors of g are (x + 8) and(x+2).
The zeros are -2 and 8, because the factors of gare (x+2) and (x-
8).
The zeros are 2 and 8, because the factors of gare (x-2) and (x-
8).
Since g(x) = x² - 6x - 16, a statement which is true include the following: C. The zeros are -2 and 8, because the factors of g are (x+2) and (x-
8).
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would solve the quadratic function by using the factorization method as follows;
g(x) = x² - 6x - 16
0 = x² - 6x - 16
0 = x² - 8x + 2x - 16
0 = x(x - 8) + 2(x - 8)
(x - 8)(x + 2)
x = 8 or x = -2.
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Ethan correctly answers 80% of the total questions on his history test. He correctly answers 32 questions.
Answer: There are 40 questions on Ethan's test.
Step-by-step explanation: To find what 32 is 80% of, you must first convert 80% to a decimal (.8).
Next, divide 32 by .8.
[tex]32/.8 = 40[/tex]
I called at 11:45 pm been on the phone for 1 hour 24 minutes what time did that person hang up
Answer:
If you called at 11:45 pm and were on the phone for 1 hour 24 minutes, the call would have ended at 1:09 am.
A student argues that y=x/9 does not represent a proportional relationship between x and y because we need to multiply one variable by the same constant to get the other one and not divide it by a constant. Do you agree or disagree with this student? Explain why.
The student's argument that y=x/9 does not represent a proportional relationship between x and y is false because there is constant factor which shows the proportional relationship.
A proportional relationship exists between two variables if they are related by a constant factor, meaning that multiplying one variable by a constant results in the other variable. However, this constant can also be obtained by dividing one variable by the other, as in the case of y=x/9.
To see why, we can rearrange the equation to x=9y, which shows that x is proportional to y with a constant factor of 9. Multiplying y by 9 results in x, just as dividing x by 9 results in y. Therefore, the relationship between x and y is still proportional, regardless of whether we multiply or divide to obtain the constant factor.
In general, we can say that a relationship between two variables is proportional if it can be written in the form y=kx, where k is a constant. It does not matter whether we use multiplication or division to express this constant, as long as it is the same for all values of x and y.
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[tex]\frac{v-2}{2v^2+10v} + \frac{1}{2v+10}=\frac{1}{2}[/tex]
Show all steps
The value of variable 'v' in the expression ( v - 2 ) / (2v² + 10v ) + 1 / ( 2v + 10 ) = 1 / 2 is equal to -4.
The expression is equal to,
( v - 2 ) / (2v² + 10v ) + 1 / ( 2v + 10 ) = 1 / 2
Simplify the expression we have,
⇒ ( v - 2 ) / 2v ( v + 5 ) + 1 / 2( v+ 5 ) = 1 / 2
Take the least common multiple of the denominator we have,
⇒ [( v - 2 ) + 2 ] / 2v( v+ 5 ) = 1 / 2
⇒ v / 2v( v+ 5 ) = 1 / 2
Multiply both the sides of the expression by 2 we get,
⇒ 1 / 2( v+ 5 ) = 1 / 2
⇒ 1 /( v + 5 ) = 1
Cross multiply the expression we get,
⇒ v + 5 = 1
Subtract 5 from the both the sides of the equation we get,
⇒ v = -4
Therefore , the value of v in the given expression is equal to -4.
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log3 55=x
Use the base of formula to solve for x in logaritm experssion
The change of base formula log 55 / log 3. The base we use to solve via change of base formula is Base 10. The value of x = 55.
The logarithmic expression given is
log₃ 55 = x
To solve for x using the change of base formula, we can use the formula
logₐ b = log c / log a
where a, b, and c are positive real numbers and a ≠ 1.
Using this formula, we can rewrite the given expression as
log x / log 3 = log 55 / log 3
We can simplify this expression by canceling out log 3 on both sides
log x = log 55
Now, we can use the definition of logarithms, which states that if log a b = c, then [tex]a^c[/tex] = b. Using this definition, we get
x = 55
Therefore, the solution is x = 55, rounded to the nearest hundredth of a decimal.
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What is the next term in the pattern? 1,1,5,17,71,247
Answer: 1085
Step-by-step explanation:
Martina vence a Jelena en 2 juegos de un total de 3 en el tenis. ¿Cuál es la probabilidad de que Jelena gane un set de de tenis 6 juegos a 4?
Pista: ¿Cuál es el score que tendría que haber después de 9 juegos?
0.034141137 o sobre 17/500
a robotic vacum cleanervacumsonehotelroomin 3/10 hour. at this rate, how many rooms of the same size will it vaccum in 3 hours
The number of rooms of the same size it willl vaccum in 3 hours is 10
How many rooms of the same size will it vaccum in 3 hoursFrom the question, we have the following parameters that can be used in our computation:
Unit rate = 3/10 hour per room
Time = 3 hours
using the above as a guide, we have the following:
Number of rooms = Time/Unit rate
Substitute the known values in the above equation, so, we have the following representation
Number of rooms = 3/(3/10)
Evaluate the quotient
Number of rooms = 10
Hence, the number of rooms is 10
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18+(d+3)(d-3)(4)
How do I distribute?
Answer:
Step-by-step explanation:
To distribute the expression 18+(d+3)(d-3)(4), you can use the distributive property of multiplication, which states that a(b+c) = ab + ac.
Here's how you can apply the distributive property to the expression:
First, simplify the expression inside the parentheses by using the difference of squares formula: (d+3)(d-3) = d^2 - 3d + 3d -9
(d+3)(d-3) = d^2 - 9
So now the expression becomes:
18 + (d^2 - 9)(4)
Next, use the distributive property to multiply 4 by each term inside the parentheses:
18 + 4d^2 - 36
Simplify by combining like terms:
4d^2 - 18
So the final result is 4d^2 - 18
Help me please I don’t understand
Answer:16x-4-2x+8=14x+4
Step-by-step explanation:
In order to solve this question you first want to multiply everything inside the bracket by the number outside.
4(4x-1)
so 4 times 4x which is 16x and 4 times -1 which is -4 so the first bracket is
(16x-4)
then do the same for the second bracket
-2(x-4)
so -2 times x would be -2x and -2 times -4 would be 8
for the final step collect the like terms and solve
so your answer would be
16x-2x which would be 14x and -4+8 which would be 4
so in conclusion the answer is
14x+4
simplify the following expression:
(2x^3)^2 * (3x)^4
[tex](2x^3)^2\cdot (3x)^4\implies (2^2 x^{3\cdot 2})\cdot (3^4x^4)\implies 4x^6\cdot 81x^4 \\\\\\ (4)(81)x^{6+4}\implies 324x^{10}[/tex]
in a race in which 9 contestants are entered in how many ways can first second and third place be awarded
Answer: 504 different ways.
Step-by-step explanation:
This situation uses a permutation. We will use the given formula and simplify to solve. n is equal to the number of contestants and r is 3 since we are selecting and first-, second-, and third-place winner.
Given:
[tex]\displaystyle P = \frac{n!}{(n-r)!}[/tex]
Substitute values:
[tex]\displaystyle P = \frac{9!}{(9-3)!}[/tex]
Subtract:
[tex]\displaystyle P = \frac{9!}{6!}[/tex]
Multiply:
[tex]\displaystyle P = \frac{9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1}[/tex]
Simplify using the knowledge that something divided by itself is 1:
P = 9 * 8 * 7
Multiply:
P = 504
We can also think of it as 9 different people could win 1st, 8 different people could win 2nd, and 7 different people could win 3rd. 9 * 8 * 7 = 504. However, the steps above show why this works with the formula as well.
Can someone please help me with this, it’s super confusing and I can’t find help anywhere
Answer:
Step-by-step explanation:
ask ur teacher