The end behavior of y as x goes to negative infinity in the equation y = -3x^5 + 4x^2 – 7 can be determined by looking at the leading term of the polynomial, which is -3x^5. As x goes to negative infinity, this term will dominate the other terms and determine the end behavior of the function.
Since the degree of the leading term is 5, which is an odd number, and the coefficient is negative, the end behavior of the function will be that y goes to positive infinity as x goes to negative infinity. This can be written in notation as:
lim(x→-∞) y = +∞
In conclusion, the end behavior of y as x goes to negative infinity in the equation y = -3x^5 + 4x^2 – 7 is that y goes to positive infinity.
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What the greatest common factor of 10x and 25
Answer:
5
Step-by-step explanation:
How many numbers cansisting of 3 digits can be made from 1,2,3,4,5, and 6 if letter A repitition is allowed, letfer B repitition is not allowed.
Answer:
If repetition of letter A is allowed and letter B cannot be repeated, then there are two cases to consider when constructing a 3-digit number:
Case 1: The first digit is letter A. In this case, there are 6 options for the first digit (since any of the 6 digits can be used), and there are 5 options for each of the remaining digits (since letter B cannot be repeated). Therefore, the total number of 3-digit numbers that can be formed in this case is:
6 x 5 x 5 = 150
Case 2: The first digit is not letter A. In this case, there are 5 options for the first digit (since letter A cannot be repeated), and there are 5 options for each of the remaining digits (since letter B cannot be repeated). Therefore, the total number of 3-digit numbers that can be formed in this case is:
5 x 5 x 4 = 100
To get the total number of 3-digit numbers that can be made from 1, 2, 3, 4, 5, and 6 with letter A repetition allowed and letter B repetition not allowed, we add the number of possibilities from Case 1 and Case 2:
Total = 150 + 100 = 250
Therefore, there are 250 different 3-digit numbers that can be made from 1, 2, 3, 4, 5, and 6 with letter A repetition allowed and letter B repetition not allowed.
There are 720 numbers consisting of 3 digits that can be made from 1, 2, 3, 4, 5, and 6 if letter A repetition is allowed and letter B repetition is not allowed.
This can be calculated by taking the number of possible combinations for each digit (6 for A, 5 for B, 4 for C) and multiplying them together: 6 x 5 x 4 = 120. Since there are 6 possible numbers for each digit, there are 120 combinations for a 3-digit number. Then, multiplying 120 by 6 (since repetition is allowed) yields 720 possible 3-digit numbers.
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The wind farms in southern California contain wind generators whose power production varies directly with the cube of the wind's speed. one such generator produces 1000W of power in a 25mph wind, find the power it generate in a 35mph wind.
The wind generator will produce 2744W of power in a 35mph wind.
Determine the generate powerTo find the power generated by the wind generator in a 35mph wind, we can use the formula P = kV³, where P is the power generated, k is a constant, and V is the wind's speed.
First, we need to find the value of k. We can do this by plugging in the given values of P and V into the formula and solving for k:
1000W = k(25mph)³ 1000W = k(15625mph³)
k = 1000W/15625mph³
k = 0.064W/mph³
Now that we have the value of k, we can plug it back into the formula along with the new wind speed of 35mph to find the power generated:
P = (0.064W/mph³)(35mph)³
P = (0.064W/mph³)(42875mph³)
P = 2744W
Therefore, the wind generator will produce 2744W of power in a 35mph wind.
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The table lists the ring size S for a finger with circumference x in centimeters. x (cm) 4.87 5.66 5.92 6.71 S (size) 4 7 8 11 a. Find a linear function S that models the data. b. Find the circumference of a finger with a ring size of 6.
The linear function that models the data is S = 3.8x - 14.506 and the circumference of a finger with a ring size of 6 is 5.4 cm.
a. To find a linear function S that models the data, we need to find the slope and y-intercept of the line that best fits the data. The slope can be found by using the formula:
m = (y2 - y1) / (x2 - x1)
Using the first two data points, we can find the slope:
m = (7 - 4) / (5.66 - 4.87)
m = 3 / 0.79
m = 3.8
To find the y-intercept, we can use the formula:
y = mx + b
Substituting one of the data points and the slope into the formula and solving for b:
4 = (3.8)(4.87) + b
b = 4 - (3.8)(4.87)
b = -14.506
So the linear function that models the data is:
S = 3.8x - 14.506
b. To find the circumference of a finger with a ring size of 6, we can substitute S = 6 into the linear function and solve for x:
6 = 3.8x - 14.506
3.8x = 20.506
x = 5.4 cm
So the circumference of a finger with a ring size of 6 is 5.4 cm.
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How do u change this from vertex form y=2(x-2)^2+5 to standard form?
The standard form for the quadratic equation written in vertex form y = 2(x - 2)² + 5 is y = 2x² - 8x + 13.
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. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
To change the equation y = 2(x - 2)² + 5 from vertex form to standard form, we need to expand the squared term and simplify the expression.
Here are the steps -
Start with the vertex form: y = 2(x - 2)² + 5.
Expand the squared term using the formula (a - b)² = a² - 2ab + b².
In this case, a = x and b = 2, so we have -
y = 2(x - 2)(x - 2) + 5
y = 2(x² - 4x + 4) + 5
Multiply the coefficient 2 by each term inside the parentheses -
y = 2x² - 8x + 8 + 5
Combine the constant terms -
y = 2x² - 8x + 13
This is the standard form of the quadratic equation.
In standard form, the quadratic equation is written as y = ax² + bx + c, where a, b, and c are constants.
In this case, a = 2, b = -8, and c = 13.
Therefore, the standard form is y = 2x² - 8x + 13.
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Weighted
grade is 89%. Final is worth 35%. What is the minimum final score
that I need to get a 77%?
To find the minimum final score you need to get a 77%,
you can use the following formula:
(weight of weighted grade * weighted grade) + (weight of final * final grade) = desired overall grade
Plug in the given values:
(0.65 * 89) + (0.35 * final grade) = 77
Solve for the final grade:
57.85 + 0.35 * final grade = 77
0.35 * final grade = 19.15
final grade = 19.15 / 0.35
final grade = 54.71
Therefore, the minimum final score you need to get a 77% overall is 54.71%.
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Question 3(Multiple Choice Worth 2 points)
(Theoretical Probability MC)
When rolling a 6-sided die twice, determine P(sum of 5).
O
2/6
4/36
5/36
10/36
The probability of rolling a sum of 5 when rolling a 6-sided die twice is 1/9.
The Law of Big Numbers is what?According to the Law of Large Numbers, a fundamental tenet of probability theory, the average of the results of an experiment approaches the predicted value of the random variable being measured as the number of trials in the experiment rises. In other words, the Law of Big Numbers states that the observed results will be closer to the predicted outcomes the more times an experiment is conducted.
The total number of outcomes when a die is rolled two times is 36.
The sum of 5 is obtained for the following outcomes:
(1,4), (2,3), (3,2), and (4,1)
Thus,
P(sum of 5) = 4/36 = 1/9
Hence, the probability of rolling a sum of 5 when rolling a 6-sided die twice is 1/9.
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Perform the addition or subtraction and simplify.
x
x − 4
−
3
x + 8
The simplified expression after doing this calculation is -1/3. To perform the addition or subtraction and simplify the given expression, we need to find a common denominator for the two fractions. The common denominator for x and 3 is 3x.
Multiply each fraction by the necessary factor to get the common denominator. For the first fraction, we multiply by 3/3, and for the second fraction, we multiply by x/x.
3/3 * (x/x) - x/x * (4/3) = (3x - 4x)/3x = (-x)/3x. Now, we can simplify the expression by canceling out the common factor of x in the numerator and denominator. (-x)/3x = -1/3
The simplified expression is -1/3.
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Training neural networks requires two steps. In the forward pass we compute the output of the network and the loss given the input, and in the backward pass we compute the derivatives for all the parameters given the loss, and the values computed in the forward pass. Take the regression network of slide 10 of lecture 6 ("Beyond linear models") and assume you have some instance, some target value and, and that you are using squared error loss. Write pseudocode for the forward and backward pass. You may use a separate variable for each node in the network, or store all the values of one layer in a list or similar datastructure. You can use whatever form of pseudocode seems most appropriate, but the more detailed it is, the better. When in doubt, we suggest making it as close to runnable python code as you can.
Training a regression network with squared error loss requires two steps: the forward pass and the backward pass.
Forward Pass:
Let x be the input to the neural network, y be the target value, w be the weights of the neural network, and h be the output of the neural network.Initialize an empty array l to store the output of each layer.Compute the output of the first layer l[0] with the weights w[0] and the input x, and store it in l[0].Compute the output of the second layer l[1] with the weights w[1] and the input l[0], and store it in l[1].Compute the output of the third layer h with the weights w[2] and the input l[1], and store it in h.Compute the loss between y and h, using the squared error loss function.Backward Pass:
Let delta be the derivative of the loss with respect to h.Compute the derivative of the loss with respect to l[2] with delta and the weights w[2].Compute the derivative of the loss with respect to l[1] with the derivative of the loss with respect to l[2] and the weights w[1].Compute the derivative of the loss with respect to l[0] with the derivative of the loss with respect to l[1] and the weights w[0].Compute the derivative of the loss with respect to w[2] with delta and the input l[1].Compute the derivative of the loss with respect to w[1] with the derivative of the loss with respect to l[2] and the input l[0].Compute the derivative of the loss with respect to w[0] with the derivative of the loss with respect to l[1] and the input x.Learn more about derivative
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Score on last try:
4.74
of 5 pts. See Details for more. You can retry this quest Round all ainsurers to 3 decintal places. The vertex of kis
The vertex of this function would be (-1, -8).
The question seems to be incomplete and there are some typos in it. However, I will try to provide a general answer based on the given information.
When finding the vertex of a function, you can use the formula -b/2a to find the x-coordinate of the vertex. Once you have the x-coordinate, you can plug it back into the original function to find the y-coordinate of the vertex.
For example, if the function is y = 2x^2 + 4x - 6, the formula for the x-coordinate of the vertex would be -4/(2*2) = -1. The y-coordinate of the vertex would be 2(-1)^2 + 4(-1) - 6 = -8.
So the vertex of this function would be (-1, -8).
Remember to Round all answers to 3 decimal places, as instructed in the question.
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43.5 and a number, n, is no greater than 50. possible values of n? Show your work.
Answer:
n ≤ 6.5
Step-by-step explanation:
43.5 + n ≤ 50
43.5 + n - 43.5 ≤ 50 - 43.5
n ≤ 6.5
Helppppppppp pleaseeeeeeeeeeeee
Answer:
Step-by-step explanation:
As before, I'll put slope-intercept first:
5. y = 1/4x + 1 ; y-2 = 1/4(x-4)
6. y = -1/2x + 2 ; y-1 = -1/2(x-2)
7. y = 1/3x + 1 ; y-2 = 1/3(x-3)
8. y = -x ; y-1 = 1(-x+1)
9. y = 2/3x -1 ; y-1 = 2/3(x-3)
Hope this helps!
biologist is studying diseases in chimpanzees. He takes three random samples of the same size from a troop of 150 chimpanzees. One sample indicates that 3% of the chimpanzees are hairless, another sample indicates that 5% are hairless, and a third sample indicates that 4% are hairless. How many hairless chimpanzees should the biologist expect to find in the troop?
6 hairless chimpanzees should the biologist expect to find in the troop.
What is the percentage?
A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a part per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
The sample number is 150.
Given that 3% of the chimpanzees are hairless, another sample indicates that 5% are hairless, and a third sample indicates that 4% are hairless.
The average percentage of chimpanzees of hairless is
(3% + 5% + 4%)/3
= 12%/3
= 4%
Now calculate 4% of 150:
4% of 150
= (4/100) × 150
= 6
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Use a graphing Utility to approximate the local macmum value and local minimum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6
1. the local maximum is y=__and it occurs at x=__
2. the local minimun is y=___ and it occurs at x=__
please explain process
if its possible please ans thank you
The local maximum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6 is y=2.2 and it occurs at x=-1.2, and the local minimum value is y=-4.6 and it occurs at x=-4.8.
Using a graphing Utility, we can approximate the local maximum value and local minimum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6.
1. The local maximum value occurs at the highest point on the graph within the given interval of -6. By observing the graph, we can see that the local maximum value is y=2.2 and it occurs at x=-1.2.
2. The local minimum value occurs at the lowest point on the graph within the given interval of -6. By observing the graph, we can see that the local minimum value is y=-4.6 and it occurs at x=-4.8.
It is important to note that these values are approximations and may not be exact. The graphing Utility is a useful tool for visualizing the function and finding approximate values, but it is not always precise.
the local maximum value of the function F(x) = -0.2x^3 – 0.5x^2 + 3x - 4 for -6 is y=2.2 and it occurs at x=-1.2, and the local minimum value is y=-4.6 and it occurs at x=-4.8.
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A store scanner has a red laser wavelength of 650 nm. While a
green laser pointer has a wavelength of 502 μm. Find the ratio of
green to red wavelengths for these lasers. Round to the nearest
tenth.
A store scanner has a red laser wavelength of 650 nm. While a green laser pointer has a wavelength of 502 μm. The ratio of green to red wavelengths is 0.77.
To find this ratio, we need to divide the wavelength of the green laser by the wavelength of the red laser:
502 μm / 650 nm = 0.77
Note that we need to convert the units of the green laser wavelength from micrometers (μm) to nanometers (nm) in order to divide it by the red laser wavelength, which is already in nanometers. To do this, we multiply the green laser wavelength by 1000:
502 μm * 1000 = 502000 nm
So the ratio of green to red wavelengths is 502000 nm / 650 nm = 0.77.
This ratio indicates that the green laser has a shorter wavelength than the red laser. Generally, shorter wavelengths correspond to higher energy and higher frequency light. In the case of lasers, this means that the green laser is capable of producing a more intense and focused beam of light than the red laser.
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Kobe scored 82 points in a basketball game. That was 1/8 of the points that he scored for the season. How many points did Kobe score in the season
Kobe scored 656 points in the season.
How to find and what is basketball?
If Kobe scored 82 points in a basketball game and that was 1/8 of the points he scored for the season, we can find the total points he scored in the season by multiplying 82 by 8, since 82 represents 1/8 of the total points:
Total points = 82 x 8
= 656
Therefore, Kobe scored 656 points in the season.
Basketball is a team sport played between two teams of five players each. The objective of the game is to shoot a ball through a hoop or basket that is mounted on a backboard at each end of the court, while also preventing the opposing team from doing the same.
The game is played on a rectangular court with standardized dimensions and various markings, including a center circle, free-throw lines, and three-point lines. Basketball is a fast-paced and physically demanding sport that involves a combination of offensive and defensive skills, including shooting, dribbling, passing, and rebounding.
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HELPPPPPP!!!!!!!!!!!!!!!!
Answer:
The answer is -3 because it passes through (0,0) and (2,-6).
Suppose the annual interest rate is 7.5% and the interest is compounded annually. How much will an investment of $1,000 be worth after 3 years?
The value of an investment with $1000 as principal amount compounding annually for 3 years with interest rate 7.5% is $1242.29
What is interest rate?The interest rate is the amount that the lender charges the borrower and is the principal - a percentage of the loan amount. Loan interest rates are usually quoted on an annual basis known as the annual rate (APR).
Solution according to the given information in the question:
Given, Principal = $1000
Time = 3 years
Interest rate = 7.5%
∴ Amount = P×(1 + r/100)³
= 1000×(1 + 7.5/100)³
= 1000×(1 + 0.075)³
= 1000×(1.075)³
= 1000 × 1.24
Amount = $1242.29
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Find the average rate of change of the given function on the
interval [5,10].
h(x)=3x2+6x−7
The average rate of change of the function h(x)=3x2+6x−7 on the interval [5,10] is 94.6.
The average rate of change of the function h(x)=3x2+6x−7 on the interval [5,10] is calculated by taking the change in the y-value (h(10) - h(5)) and dividing it by the change in the x-value (10-5):
Average rate of change = (h(10)-h(5))/(10-5)
= (3(10)2+6(10)-7 - (3(5)2+6(5)-7))/(10-5)
= (745-272)/5
= 473/5
= 94.6
Therefore, the average rate of change of the function h(x)=3x2+6x−7 on the interval [5,10] is 94.6.
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Question 4: Abstract Vector Spaces LetWbe the set of all vectorsu=(x,y)inR2such that the product of its componentsxandysatisfy the equationx⋅y=0. Check whether this set (a) is closed under operation of standard scalar multiplication in the plane. (b) is closed under operation of standard vector addition in the plane. Is the information you found is sufficient to conclude whether this set forms a vector space or not? Explain why yes or why not. What does this set represent geometrically?
The set W represents the x-axis and y-axis in the plane. Any vector with one of its components equal to 0 will satisfy the equation x⋅y = 0, and these vectors lie on either the x-axis or y-axis.
(a) The set W is closed under standard scalar multiplication in the plane. This is because for any scalar c and any vector u = (x,y) in W, the product of the components of cu = (cx,cy) is (cx)(cy) = c2(xy) = c2(0) = 0, so cu is also in W.
(b) The set W is not closed under standard vector addition in the plane. For example, the vectors u = (1,0) and v = (0,1) are both in W, but their sum u + v = (1,1) is not in W because the product of its components is 1(1) = 1, which does not satisfy the equation x⋅y = 0.
Since the set W is not closed under standard vector addition, it does not form a vector space. A set must be closed under both scalar multiplication and vector addition in order to be a vector space.
Geometrically, the set W represents the x-axis and y-axis in the plane. Any vector with one of its components equal to 0 will satisfy the equation x⋅y = 0, and these vectors lie on either the x-axis or y-axis.
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2x°
(3x + 25)°
Please helppppppp
The answer of the given question based on the sum of the two angles is ,the answer is 5x + 25° degrees.
What is Distributive property?The distributive property is fundamental property of arithmetic and algebra that allows us to multiply single term or sum by factor. The property states that:
a×(b+c)=a×b+a×c
In words, this means that the when number or variable (a) is multiplied by sum of two other numbers or variables (b + c), it is same as multiplying a by each term of sum (b and c) and then adding two products. The distributive property can be used in reverse to factor out common factor from sum of terms.
The sum of these two angles is:
2x° + (3x + 25)°
= 2x° + 3x° + 25° (using the distributive property of multiplication)
= 5x° + 25°
Therefore, the sum of the two angles is 5x + 25° degrees.
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Choose 1 answer:
A: Replace one equation with the sum/difference of both equations.
B: Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations.
C: Replace one equation with a multiple of itself.
D: Replace one equation with a multiple of the other equation.
Answer:
Step-by-step explanation:
Answer is (A)
Replace [tex]6x-5y=1[/tex] with the sum of both equations in System A
Rogelio watches a movie that is 1 3/4 hours
long. He stops for dinner after watching 3/5
of the movie. How many hours of the
movie has he watched?
Rogelio has watched 23/20 hours of the movie.
What is a fraction?
A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.
Movie duration = 1 3/4 = 7/4
Duration of movie watched = 3/5
Duration watched = 7/4 - 3/5
Duration watched = 23/20
Duration watched = 1 3/20 (mixed fraction)
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Find a model for the Body Mass Index (BMI) of a person, given
that BMI varies directly as a person’s weight in pounds and
inversely as the square of the person’s height in inches. If a
6ft6ft t
The model for the BMI of a person is:
BMI = (152100/weight in pounds)/(height in inches)^2
The Body Mass Index (BMI) of a person can be calculated using the formula:
BMI = (weight in pounds)/(height in inches)^2
In this case, the BMI varies directly as a person's weight in pounds and inversely as the square of the person's height in inches. This means that as the weight increases, the BMI increases and as the height increases, the BMI decreases.
To find a model for the BMI of a person, we can use the formula:
BMI = k(weight in pounds)/(height in inches)^2
Where k is a constant of proportionality. To find the value of k, we can use the given information that a 6ft 6in tall person has a BMI of 25.
First, we need to convert the height from feet and inches to inches. 6ft 6in is equivalent to 78 inches. Then, we can plug in the values into the formula and solve for k:
25 = k(weight in pounds)/(78 inches)^2
25(78 inches)^2 = k(weight in pounds)
152100 = k(weight in pounds)
Therefore, the model for the BMI of a person is:
BMI = (152100/weight in pounds)/(height in inches)^2
This model can be used to calculate the BMI of a person given their weight in pounds and height in inches.
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Part 3 B 3.1 Given: P = 2 2x+5 + 2x 3.1.1 Show that P is a rational number if x = 1.5 3.1.2 Determine the values of for which P is a real number. (3) (2)
P is rational number from the given equation P=2(2x+5)+2x.
What is the rational number?Rational numbers are in the form of p/q, where p and q can be any integer and q ≠ 0. This means that rational numbers include natural numbers, whole numbers, integers, fractions of integers, and decimals (terminating decimals and recurring decimals).
The given equation is P=2(2x+5)+2x.
Here, P=2(2x+5)+2x
P=4x+10+2x
P=6x+10
Given that, x=1.5, 3 and 1.2
Substitute, x=1.5 in P=6x+10, we get
P=6×1.5+10
P=9+10
P=19
So, 19 is rational number
Substitute, x=3 in P=6x+10, we get
P=6×3+10
P=18+10
P=28
So, 28 is rational number
Substitute, x=1.2 in P=6x+10, we get
P=6×1.2+10
P=7.2+10
P=17.2
So, 17.2 is rational number
Therefore, P is rational number from the given equation P=2(2x+5)+2x.
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Ms summers has 1/4 gallon of milk. She drinks 1/8 gallon of the milk then splits the remaining milk equally between her two children. How much milk does ms summer give each child
Ms. Summers will give each child 1/16 gallon of milk.
Beginning with a quarter gallon of milk, Ms. Summers. She consumes a quarter of a gallon of milk, leaving her with:
1/8 gallon divided by 2/8 gallon is equal to 1/8 gallon.
Mrs. Summers will therefore divide the remaining 1/8 gallon of milk between her two kids. She needs to divide it by 2 to distribute it equally amongst the two kids.
Hence, each kid will get:
(1/8 gallon x 2) yields 1/16 gallon
Ms. Summers will thus provide each youngster with 1/16 of a gallon of milk.
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See Solution Bcore: 5 Penalty: None gleton Operations on Functions 6:13PM f(x)=x^(2)-5x-50 and g(x)=x+5, find (f-g)(x)
The value of (f-g)(x) is x^(2)-6x-55.
What are Mathematical operations on a function?Mathematical operations on a function involve the manipulation or transformation of the function, such as adding, subtracting, multiplying, dividing, and integrating the function. These operations can be done either to the function itself or to the domain or range of the function. This can be used to find the inverse of a function, calculate the area under the curve, or find the first or second derivative of a function.
To find (f-g)(x), we need to subtract the function g(x) from the function f(x).
(f-g)(x) = f(x) - g(x)
= (x^(2)-5x-50) - (x+5)
= x^(2)-5x-50 - x - 5
= x^(2)-6x-55
Therefore, (f-g)(x) = x^(2)-6x-55.
This is the final answer for the difference between the two functions f(x) and g(x).
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The current temperature is 48\deg F. It is expected to drop 1.5\deg F each hour. Which equation can be used to find in how many hours, h, the temperature will be 36\deg F?
Answer:
Let's start by defining some variables to represent the given information:
T0 = 48°F (the current temperature)
deltaT = -1.5°F/hour (the rate of change in temperature)
T = 36°F (the target temperature)
We want to find how many hours it will take for the temperature to drop from 48°F to 36°F, so let's call that time h. We can use the formula for the linear relationship between temperature and time:
T = T0 + deltaT * h
We want to solve for h when T = 36°F, so we can substitute the given values and solve for h:
36 = 48 + (-1.5) * h
-12 = -1.5h
h = 8
Therefore, it will take 8 hours for the temperature to drop from 48°F to 36°F, assuming the temperature continues to decrease at a rate of 1.5°F per hour.
Find the sides of a triangle circumscribed about a circle of
radius 4 and divided on one side by the circle into segments of
length 6 and 8.
The sides of the triangle circumscribed about a circle of radius 4 and divided on one side by the circle into segments of length 6 and 8 are 6, 8, and 4.
The triangle circumscribed about a circle of radius 4 and divided on one side by the circle into segments of length 6 and 8 can be found using the Law of Cosines. The Law of Cosines states that c2 = a2 + b2 - 2ab cos C, where c is the length of the hypotenuse, a and b are the lengths of the other sides, and C is the angle opposite side c.
We know the hypotenuse of this triangle is 8, as it is the length of one of the segments on the side of the triangle. We also know that angle C is 90° as it is a right triangle.
Therefore, using the Law of Cosines we can find the length of the other side of the triangle, which is 6. The equation is 82 = 62 + a2 - 2(6)(a)cos(90°). Solving this equation, we find that a = 4.
Therefore, the sides of the triangle circumscribed about a circle of radius 4 and divided on one side by the circle into segments of length 6 and 8 are 6, 8, and 4.
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In the coordinate plane, the point A (0, 0) is translated to the point A '(1, 3). Under the same translation, the points B (-3, -2) and C (3, 3) are translated to B' and C', respectively. What are the coordinates of B' and C'?
Therefore , the solution of the given problem of coordinates comes out to be B' = (-2, 1) and C' = (4, 6) .
What is coordinates ?A coordinate system is a method that employs one or more values or coordinates to accurately locate points or even other mathematical objects on a space, such as Euclidean space. Coordinates, that are pairs of numbers, are used to locate a point or object on a double plane. The y and x vectors are two integers that specify where a point is situated on a two - dimensional plane. a group of numerals designating particular places. Usually, the number has two numbers.
Here,
By adding 1 to the x-coordinate and 3 to the y-coordinate, we can determine that position A is translated to point A'. As a result, we can determine the values of B' and C' using the same translation vector.
We increase the x-coordinate for position B by one
=> (-3 + 1 = -2) and
the y-coordinate by three
=> (-2 + 3 = 1). Consequently, B"s values are (-2, 1).
We increase the x-coordinate for position C by one
=> (3 + 1 = 4) and
the y-coordinate by three
=>(3 + 3 = 6). Consequently, C"s dimensions are (4, 6).
Consequently, the translated locations' coordinates are as follows:
=> B' = (-2, 1)
=> C' = (4, 6)
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