The Integer Root Theorem states that the possible integer roots of a polynomial are the divisors of the constant term (100). Therefore, the candidate integer roots for the polynomial [tex]f(x) = -x^5 + 22x^4 - 8x^3 - 8x^2 + 5x + 100[/tex] are: 1, -1, 2, -2, 4, -4, 5, -5, 10, -10, 20, -20, 25, -25, 50, and -50.
According to the integer root theorem, the possible integer roots of a polynomial f(x) are the factors of the constant term divided by the factors of the leading coefficient. In the case of f(x)=-x^(5)+22x^(4)-8x^(3)-8x^(2)+5x+100, the constant term is 100 and the leading coefficient is -1.
The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, and 100. The factors of -1 are: 1 and -1.
Therefore, the possible integer roots of f(x) are: ±1, ±2, ±4, ±5, ±10, ±20, ±25, ±50, and ±100.
So, the candidate integer roots of [tex]f(x) = -x^5 + 22x^4 - 8x^3 - 8x^2 + 5x + 100[/tex] are: 1, -1, 2, -2, 4, -4, 5, -5, 10, -10, 20, -20, 25, -25, 50, -50, 100, and -100.
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Guide
The table shows the height of a child, in contimeters, at different ages.
Height of a Child
Age (years)
2
3
5
7
15
12
Holght (cm)
84.5
90.5
105.0
119.0
125.5
151.5
Create an equation to model the relationship between the height, in centimeters, and the age, in years, of this child.
Show your work or explain your equation. Be sure to include the limitations of your equation.
Enter your equation, your work or explanation, and the limitations in the box provided.
The estimated height of the child at delivery is represented by the y-intercept, which is 72.66.
What is an equation to model the relationship between the height, in centimeters, and the age, in years, of this child?We may use linear regression to construct an equation that represents the link between this child's height and age. The line of best fit for the supplied data is determined by linear regression, which can be written as:
Age (years) + b * m * Height (cm)
where m denotes the line's slope and b its y-intercept.
The equation that most closely matches the above data can be determined using a calculator or spreadsheet software as follows:
Age (years) + 72.66 Height (cm) = 6.087
Thus, the height of the youngster increases by roughly 6.087 centimetres for every year that their age rises. The estimated height of the infant at delivery is represented by the y-intercept, which is 72.66.
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Pippin has a 32-ounce sports drink. She drinks 20 ounces.
Enter the percentage of ounces Pippin has left of her sports drink. HELP PLSS
THIS IS DUE TONIGHT AND IT COUNTS TOWARDS MY GRADE
Pippin has 37.5% of her sports drink left.
What is Percentage?
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Pippin has 32 - 20 = 12 ounces of sports drink left.
To find the percentage of ounces Pippin has left, you need to divide the number of ounces left by the original amount of sports drink (32) and then multiply by 100 to get the percentage:
(12/32) x 100 = 37.5%
Therefore, Pippin has 37.5% of her sports drink left.
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Order from greatest to least
Answer:
15, 3, -1, -12
Step-by-step explanation:
15, 3, -1, -12
Answer:
First answer (15, 3, -1, -12)
Step-by-step explanation:
ez
Points A and B have coordinates (-5, 16) and (3,12) respectively.
C is the point that lies of the way along AB. Find the coordinates of C.
A random sample of 100 soft drink consumers tasted an unmarked cup of pepsi and an unmarked cup of coke. Fifty-nine out of the 100 consumers stated that they prefer pepsi over coke.
A majority of the consumers in the sample prefer pepsi over coke.
Based on the given information, a random sample of 100 soft drink consumers tasted an unmarked cup of pepsi and an unmarked cup of coke. Fifty-nine out of the 100 consumers stated that they prefer pepsi over coke.
This means that the majority of the consumers in the sample, or 59%, preferred pepsi over coke. It is important to note that this is only a sample of consumers and may not necessarily reflect the preferences of the entire population of soft drink consumers. However, it does provide some insight into the preferences of a portion of the population.
In conclusion, the results of the taste test indicate that a majority of the consumers in the sample prefer pepsi over coke.
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Titanium-44 has a half life of 63 years. How much of a 10g sample will
be left after 50 years?
A 10gm sample of Titanium-44 will have 6.06 grams of mass left after 50 years.
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]
The formula for exponential decay is [tex]y = y_0e^{(-kt)}.[/tex]
From the information, Titanium-44 has a half-life of 63 years we can model,
[tex]5 = 10.e^{63k}.[/tex]
[tex]0.5 = e^{63k}.[/tex]
[tex]63k = ln0.5.[/tex]
63k = - 0.69.
k = - 0.01.
Therefore, The amount of mass left after 50 years is,
[tex]y_{50} = 10.e^{-0.01\times50}.[/tex]
[tex]y_{50} = 6.06[/tex] grams.
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If X ~ Exp^) with 1 2.0. Then Markov's inequality says that P(X > 1) < a where a is (choose the closest): (A) 1.0 (B) 0.25 (C) 0.5 (D) Can't tell. Not enough info. (E) 0.75
The probability that X is greater than 1 is less than or equal to 0.5, making the correct answer (C) 0.5.
Markov's inequality states that for a non-negative random variable X and a positive number a, the probability that X is greater than a is less than or equal to the expected value of X divided by a. In mathematical terms, this can be written as:
P(X > a) ≤ E(X) / a
In this case, X follows an exponential distribution with a mean of 1/2.0, or 0.5. Therefore, the expected value of X is 0.5. If we plug in the values for X and an into Markov's inequality, we get:
P(X > 1) ≤ 0.5 / 1
P(X > 1) ≤ 0.5
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Suppose that a, b and c are non-zero real numbers. Determine whether or not it is possible for each of the six quadratic equations
ax2 + bx + c = 0
ax2 + cx + b = 0
bx2 + ax + c = 0
bx2 + cx + a = 0
cx2 + ax + b = 0
cx2 + bx + a = 0
to have at least one real root.
It is possible for each of the six quadratic equations to have at least one real root.
This is because the discriminant of a quadratic equation determines the nature of its roots. The discriminant is given by the formula: D = b² - 4ac.
If D > 0, the equation has two distinct real roots.
If D = 0, the equation has one real root (a double root).
If D < 0, the equation has no real roots (two complex roots).
In each of the six equations, the coefficients a, b, and c are non-zero real numbers. This means that the discriminant can be positive, zero, or negative, depending on the values of a, b, and c. Therefore, it is possible for each of the six equations to have at least one real root.
For example, consider the equation ax² + bx + c = 0. If b² > 4ac, then the equation has two distinct real roots. If b² = 4ac, then the equation has one real root (a double root). If b² < 4ac, then the equation has no real roots (two complex roots).
Similarly, the other five equations can also have at least one real root, depending on the values of the coefficients a, b, and c.
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Rectangle
�
�
�
�
ABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle:
�
(
5
,
1
)
,
A(5,1),A, left parenthesis, 5, comma, 1, right parenthesis, comma
�
(
7
,
1
)
B(7,1)B, left parenthesis, 7, comma, 1, right parenthesis,
�
(
7
,
6
)
C(7,6)C, left parenthesis, 7, comma, 6, right parenthesis, and
�
(
5
,
6
)
D(5,6)D, left parenthesis, 5, comma, 6, right parenthesis.
What is the perimeter of rectangle
�
�
�
�
ABCDA, B, C, D?
units
The perimeter of this rectangle is equal to 14 units.
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;
P = 2(L + W)
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.For the width, we would determine the distance between the vertices (5, 6) and (5, 1)
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(5 - 5)² + (1 - 6)²]
Distance = √[(0² + (-5)²]
Distance = √25
Distance = 5 units.
For the length, we have:
Distance = √[(7 - 5)² + (6 - 6)²]
Distance = √[(2² + 0²]
Distance = √4
Length = 2 units.
Perimeter of this rectangle, P = 2(5 + 2)
Perimeter of this rectangle, P = 14 units.
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Complete Question:
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(5,1). B(7,1), C(7,6), and D(5,6). What is the perimeter of rectangle ABCD?
Please show your work.
We can write the perimeter of the equilateral triangle as -
P = 13x - 19.
What is line of best fit?A line of best fit is a straight line that minimizes the distance between it and some data. The line of best fit is used to express a relationship in a scatter plot of different data points. It is an output of regression analysis and can be used as a prediction tool for indicators and price movements.Given is a equilateral triangle.
We can write the perimeter of a equilateral triangle as -
Perimeter = (2x + 3) + (4x - 5) + (7x - 17)
Perimeter = 2x + 4x + 7x + 3 - 5 - 17
Perimeter = 13x - 19
Therefore, we can write the perimeter of the equilateral triangle as -
P = 13x - 19.
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ins all the integers from -7 through 4 , inclusive. Set Q contains the absolute values of all the numbers in Set P. numbers are in the intersection of sets P and Q ?
The numbers in the intersection of sets P and Q are 0, 1, 2, 3, and 4.
The integers in Set P are {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4}.
The absolute values of these integers are {7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4}, which make up Set Q. The intersection of Set P and Set Q are the integers that are in both sets, which are {0, 1, 2, 3, 4}.
Therefore, the numbers in the intersection of sets P and Q are 0, 1, 2, 3, and 4.
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Does anyone know how to solve this
y=-2x^(2) + 12x - 15 ;x=3
Cause when I try it I get y=-27
but answer is supposed to be y=3 and x=3
Pls explain how
Answer: Order of operations
Step-by-step explanation:
Plug in 3 for x so...
y = -2(3)² + 12(3) - 15
Don't forget the order of operations, exponents go first
y = -2(9) + 12(3) - 15
Then multiply
y = -18 + 36 - 15
Simplify
y = 3
Alexia took out a 12-year loan for $72,000 to renovate her home. If her monthly payments are $680, what is the interest rate?
Answer:
Finding the total accrued amount is necessary before we can determine the interest rate.
Simply multiplying the monthly payment by the number of months in a 12-year period will give us the accrued amount.
144 months in 12 years.
$680 x Monthly Payment
A = 680 * 144
A = $97920
We can use the following formula now that we know the total accrued sum:
A= 97920
P = 72000
t= 12
Let's replace them with our values now.
The percentage value is then obtained by multiplying the r value by 100.
0.03 x 100 = 3%
The interest rate for Alexia is 3%.
Using remainder theorem, find the value of k if on dividing 2x3+3x2−kx+5 by x−2, leaves a remainder 7
The value of k is 13.
Using the remainder theorem, we can find the value of k by substituting the value of x in the given polynomial equation with the value that makes the divisor equal to zero. In this case, the divisor is x-2, so the value of x that makes it equal to zero is x=2.
Substituting x=2 into the polynomial equation, we get:
2(2)^3 + 3(2)^2 - k(2) + 5 = 7
Simplifying the equation, we get:
16 + 12 - 2k + 5 = 7
33 - 2k = 7
-2k = -26
k = 13
Therefore, the value of k is 13.
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An animal reserve is home to 8 meerkats. It costs the reserve $1.50 per day to feed each meerkat. Write an equation with two variables that can be used to determine the total cost of feeding the reserve's meerkats for any number of days.
Answer: Okay, so it's $8 per day to feed all of them. So one way you could answer it could be to say; "It costs $8 per day to feed all of the meerkats,..." then pick a number of days to multiply $8 by.
I hope this helps some!
Where does the FDIC’s reserve fund come from?
a.
The FDIC has access to federal tax revenue.
b.
If an insured bank fails, the FDIC keeps the money at that bank that is beyond the insured limit.
c.
A certain amount of money goes directly from the Treasury to the FDIC’s reserve fund.
d.
Insured banks pay a premium on the money insured.
Answer:
d. Insured banks pay a premium on the money insured. The FDIC's reserve fund comes from premiums paid by insured banks. The premiums are paid based on the amount of deposits held by the bank and the level of risk the bank poses to the FDIC's insurance fund.
Felipe makes a bracelet with 30 beads. The table shows the number of beads of
each color on the bracelet. Write 3 ratios to represent the number of beads (part-
part, part-part, and part-whole)
Other fractions could represent the part of the beads on the bracelet that will be green are : 1/3, 2/6, 3/9, 4/12.
What is fraction?A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
here, we have,
The maximum number of beads the bracelet can have = 12 beads
The fraction of green beads in the bracelet = 1/3
⇒ 1 bead in every 3 bead is GREEN.
⇒The minimum number of total beads = Number of (green+ Other) bead = 2 + 1 = 3
Now, the possible number of total beads the bracelet can have is
3, 4, 5 , 6, 7, 8, 9 ,10, 11 and 12.
If there are total 3 beads, the fraction representing the green bead = 1/3
If there are total 6( =3 +3) beads, the fraction representing the green bead
= 1 green bead in first 3 beads + 1 green bead in next 3 beads
= 2 green beads in total 6 beads
= 2/6
If there are total 9( = 3 +3 +3) beads, the fraction representing the green bead = 3/9
If there are total 12( = 3 + 3 +3 +3) beads, the fraction representing the green bead = 4/12
Hence, other fractions could represent the part of the beads on the bracelet that will be green are :1/3, 2/6, 3/9, 4/12.
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A book sold 42800 copies in its first month of release. Suppose this represents 7.3 of the number of copies sold to date. How many copies have been sold to date?
The number of copies sold in total is 586,301
What is percentage?A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.
Given that, a book sold 42800 copies in its first month of release, this represents 7.3 of the number of copies sold to date, we need to find the number of the copies have been sold to date,
Let the number of copies sold in total be x,
Using the concept of percentage,
7.3 % of x = 42800
7.3 / 100 of x = 42800
x = 100/7.3 (42800)
x = 586,301
Hence, the number of copies sold in total is 586,301
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7x - 4y = -8
X + 2y = -14
Step-by-step explanation:
First of all sorry for the bad hand writing
so rn I'm using elimination method which I try to eliminate y by multiple number 2 equation with 2
in order to find x
I know my explanation is quite confusing but any way goodluck n hope u understand
Big ideas 7.5 question
The value of the line segment AB of the trapezoid ABCD will be 25.9 units.
What is a trapezoid?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.
The sum of the parallel sides of the trapezoid is equal to twice the line segment that divides the other two sides in the ratio of 1: 1.
Then the equation is given as,
MN = (AB + CD) / 2
18.7 = (AB + 11.5) / 2
37.4 = AB + 11.5
AB = 25.9 units
The value of the line segment AB of the trapezoid ABCD will be 25.9 units.
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Knowledge Check Question 13 Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 3.5cm:1.4cm
The ratio 3.5cm:1.4cm can be written as the fraction 5/2 in simplest form, with whole numbers in the numerator and denominator.
To write the ratio as a fraction in simplest form, we will follow the steps below:
Step 1: Write the ratio as a fraction. In this case, we have 3.5cm:1.4cm, which can be written as 3.5cm/1.4cm.
Step 2: Simplify the fraction by dividing both the numerator and denominator by the greatest common factor (GCF). In this case, the GCF of 3.5 and 1.4 is 0.7. So we will divide both the numerator and denominator by 0.7 to get:
(3.5cm/0.7) / (1.4cm/0.7) = 5/2
Step 3: Convert the fraction to simplest form with whole numbers in the numerator and denominator. In this case, we can multiply both the numerator and denominator by 10 to get:
(5*10)/(2*10) = 50/20
Step 4: Simplify the fraction by dividing both the numerator and denominator by the GCF. In this case, the GCF of 50 and 20 is 10. So we will divide both the numerator and denominator by 10 to get:
(50/10)/(20/10) = 5/2
Therefore, the ratio 3.5cm:1.4cm can be written as the fraction 5/2 in simplest form, with whole numbers in the numerator and denominator.
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Using the slope formula, find the slope of the line through the given points.
(2,9) and (4,5)
What is the slope of the line? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The slope of the line is
OB. The slope of the line is undefined.
(Type an integer or a simplified fraction.)
use the slope formula
5 - 9/4-2 = -4/2 = -2
slope = -2
Let a, b, c, and d be constants. Describe the possible solution sets of the inequality ax + b < cx + d.
The requried, possible solution sets of the inequality ax + b < cx + d is x < (d - b)/(a-c).
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
To describe the possible solution sets of the inequality ax + b < cx + d, we need to isolate the variable x on one side of the inequality and simplify.
ax + b < cx + d
ax - cx < d - b
x(a-c) < d - b
x < (d - b)/(a-c)
So the solution set for the inequality is all values of x that are less than the quotient of (d - b) divided by (a-c).
Therefore, the possible solution sets of the inequality ax + b < cx + d is x < (d - b)/(a-c).
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How many solutions exist for 1/1-x^2=-|3x-2|+5
A. 1
B. 2
C. 3
D. 4
23 POINTS!
Answer:
4 !!!!
Step-by-step explanation:
f (x) = 1/1-x2 g (x) = -(3 x -2 ) - 5 then the number of solutions if the number of intersections of f(x) and g (x) i drew a graph and there was 4 intersections so thats how i got this answer
I hope i was right
There are two solutions to the equation 1/(1 - x²) = -|3x - 2| + 5.
What is Equation?An equation is a statement that shows that two mathematical expressions are equal to each other. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponents.
We can start by considering the case where the expression inside the absolute value is non-negative, i.e., 3x - 2 ≥ 0, which implies x ≥ 2/3. In this case, the equation becomes:
1/(1 - x²) = 3x - 2 + 5
1/(1 - x) = 3x + 3
Multiplying both sides by 1 - x², we get:
1 = (3x + 3)(1 - x²)
3x³ + x² - 3x - 2 = 0
This equation has one real root.
The root is approximately x = 0.727.
Next, we consider the case where the expression inside the absolute value is negative, i.e., 3x - 2 < 0, which implies x < 2/3. In this case, the equation becomes:
1/(1 - x²) = -(3x - 2) + 5
Simplifying this equation, we get:
1/(1 - x) = -3x + 3
1 = (-3x + 3)(1 - x²)
3x³ - x² - 3x + 2 = 0
This equation also has one real root, which we can find using the same methods as before. The root is approximately x = -0.727. \
Therefore, there are two solutions to the equation 1/(1 - x²) = -|3x - 2| + 5.
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PLEASE HELP THIS IS DUE AT 7 Name the coordinates of two points so that the line segment drawn from one to the other will intersect the y-axis.
The coordinates of the two points that intersect with the y-axis are (2, 3) and (-2, 4)
How to determine the coordinates of the two pointsRepresent the points with P and Q
When a line is drawn from a point to another would intersect with the y-axis, as long as the line is not a vertical lineAlso, the line would intersect with the y-axis if the points are in different quadrants other than vertical quadrantsA vertical line is a line whose endpoints have the same x-coordinate
i.e. (x, y1) and (x, y2)
Using the above as a guide, we have the following:
We can make use of the coordinates (x1, y1) and (x2, y2), where the values of x's and y's are not the same
An instance of these points is (2, 3) and (-2, 4)
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i need assistance i am slow in the head
Answer:
Step-by-step explanation:
31 degreese
add 59 with 90 you get 149 then you subtract 149 with 180 a
nd then get 31
I’m not sure how to do question 5.
Question Number 5.
The first and second numbers in the exponential sequence are 10 and 5, respectively.
How do we solve this?In the exponential sequence given by a, b, c, d, ..., where a and b are the first two numbers. We know that the third number is given by b * c/a, and the fourth number is given by c * d/b.
the third number = 100
the fourth number = 500,
So b * c/a = 100
c * d/b = 500
rearranging the first equation :
c = 100a/b
Substituting this into the second equation, we then have
d = 500b/a
The sequence is then written as a, b, 100a/b, 500b/a, ...
We then proceed to find a and b,
a, b, 100a/b, 500b/a, ...
a, b, 100a/b, 500b/a, ... = a, b, 100a/b, 500b/a, ...
100a/b = 100
500b/a = 500
Solving for a and b, we have:
a = 10
b = 5
In conclusion, the first and second numbers in the exponential sequence are 10 and 5.
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Select the correct answer.
What is the end behavior of this radical function?
f(x) = 3√x-4
As x approaches positive infinity, f(x) approaches positive infinity.
As x approaches negative infinity, f(x) approaches positive infinity.
As x approaches positive infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches 0.
Answer:
The correct answers are:
As x approaches positive infinity, f(x) approaches positive infinity.
As x approaches negative infinity, f(x) approaches 0.
Step-by-step explanation:
Data was collected on the weight, in ounces, of kittens for the first three months after birth. A line of fit was drawn through the scatter plot and had the equation w = 2.75 + 0.2d, where w is the weight of the kitten in ounces and d is the age of the kitten in days.
What is the w-intercept of the line of fit and its meaning in terms of the scenario?
0.2; a kitten who is just born is predicted to weigh 0.2 ounces
0.2; for each additional day after the kitten is born, its weight is predicted to increase by 0.2 ounces
2.75; a kitten who is just born is predicted to weigh 2.75 ounces
2.75; for each additional day after the kitten is born, its weight is predicted to increase by 2.75 ounces
2.75; a kitten who is just born is predicted to weigh 2.75 ounces.
What is Statistics?
Statistics is a branch of mathematics that involves collecting, analyzing, interpreting, presenting, and organizing data. It enables the identification of trends, patterns, and relationships within the data. The goal of statistics is to make meaningful inferences and predictions based on the data.
It is used in a wide range of fields, including business, economics, social sciences, healthcare, and engineering. The main tools of statistics include probability theory, statistical inference, and statistical modeling.
2.75; a kitten who is just born is predicted to weigh 2.75 ounces.
The w-intercept of the line of fit represents the weight of a kitten at birth, which is the value of w when d equals zero. In this case, the intercept is 2.75, which means that a kitten who is just born is predicted to weigh 2.75 ounces.
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Can someone solve this ??
I need help ASAP
Answer:
1. 2430 feet
2. 1.8 m/s^2
Step-by-step explanation:
See the attached worksheet.
A time versus speed graph contains a small treasure of mathematical rewards. The area under the graph is equal to the distance travelled. The slope of the line segments represents acceleration.
For total distance: If we break the graph into three sections (2 triangles and a rectangle) we can calculate the areas for each. Each area is the distance travelled for that segment. As shown on the workseet, the total area is 2430 miles, the distance travelled by the train for this question.
The slope of the line in the first 10 seconds is 1.8 meters/sec^2, the acceleration of the train over that period.