Write a polynomial function of least degree with zeroes 0 and - 2. write your answer using the variable x and in standard form with a leading coefficient of 1.
Brain weight bb as a function of body weight ww in fish has been modeled by the power function b=.007w2/3b=.007w2/3, where bb and ww are measured in grams. a model for body weight as a function of body length ll (measured in cmcm) is w=.12l2.53w=.12l2.53. if, over 1010 million years, the average length of a certain species of fish evolved from 15cm15cm to 20cm20cm at a constant rate, how fast was the species' brain growing when the average length was 18cm18cm? round your answer to the nearest hundredth.
To find the rate of brain growth, we calculate the derivatives of the brain weight and body weight functions. Then, we find the rate by multiplying the derivatives and substituting the average length of 18cm. The rate of brain growth is approximately 0.04 grams/cm.
Explanation:To find the rate at which the species' brain was growing when the average length was 18cm, we need to find the derivative of the brain weight function with respect to body weight and then multiply it by the derivative of body weight with respect to body length.
First, let's find the derivative of the brain weight function, b = 0.007w^(2/3), with respect to body weight, w.
Taking the derivative, we get db/dw = (2/3) * 0.007 * w^(-1/3).
Next, let's find the derivative of the body weight function, w = 0.12l^(2.53), with respect to body length, l.
Taking the derivative, we get dw/dl = 2.53 * 0.12 * l^(1.53).
Finally, to find the rate of brain growth when the average length was 18cm, we plug in the value 18 for l in the derivative of the body weight function and multiply it by the derivative of the brain weight function:
Rate of brain growth = (2/3) * 0.007 * (18)^(-1/3) * 2.53 * 0.12 * (18)^(1.53).
Rounding to the nearest hundredth, the rate of brain growth when the average length was 18cm is approximately 0.04 grams/cm.
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What is the measure of A and what is the measure of B
(5y-3) = (3y+27) -3y from both sides
2y-3 = 27 +3 to both sides
2y= 30 divide both sides by 2
y=15
check
5X15-3 = 3x15+27
72 = 72
correct that y=15 and that each angle is 72
in that shape correlating angles are the same so...
360-72-72= 216
216 divided by 2= 108 degrees
B is equal to 108 degrees
A is equal to 72 degrees
An integer x is divided by an integer y, and quotient is 24.the sum of these two integers is 75. what is the value of x?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The value of x is 72.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Let the integer be x and y.
An integer x is divided by an integer y, and the quotient is 24.
This can be written as:
x ÷ y
x/y = 24
x = 24y _____(1)
Now,
The sum of the integer is 75.
x + y = 75
From (1) we get,
24y + y = 75
25y = 75
Divide both sides by 25.
y = 3
Now,
From (2 ) we get,
x + y = 75
x + 3 = 75
Subtracting 3 on both sides.
x = 75 - 3
x = 72
We can also cross-check:
x = 72 and y = 3
= x ÷ y
= 72/3
= 24
Thus,
The value of x is 72.
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How to find the equation of a parabola given the vertex and one point?
To find the equation of a parabola given the vertex and one point, use the vertex form of a parabola equation: y = a(x - h)² + k.
Explanation:To find the equation of a parabola given the vertex and one point, you can use the vertex form of a parabola equation: y = a(x - h)² + k. Here's how:
Determine the values of h and k from the given vertex.Use the given point to substitute the values of x and y in the vertex form.Solve for a to find the equation of the parabola.For example, if the vertex is (2, 3) and the point is (4, 5), the equation of the parabola would be y = 1(x - 2)² + 3.
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What form would you use to write the equation of a line if you knew the slope and x-intercept? Explain.
The form used to write the equation of a line if you knew the slope and x-intercept y=mx−k/m
What is slope?The slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it
According to the given situation we have given :a slope of 'm' and an x-intercept of 'k'
we can write
y=mx−k/m
and generally, To find the x-intercept, set y = 0 and solve for x.
For example,
Let k be some constant such that
y=mx + k
where
m is the slope.
m=3/4 and the x-intercept is 4
If the x-intercept is 4 this means that x=4 when y=0
So equation:
y=mx + k becomes
0=3/4+ k
k=−3
and our equation is
y=3/4x−3
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The glee club has a set of 48 classical cds and a set of 42 show tune cds. each set can be divided equally among the club members. what is the greatest possible number of club members?
The greatest possible number of club members that we can divide 48 classical CDs and 42 show tune CDs is 6.
What is HCF?HCF is the highest common number or factor that divides two or more than two given numbers completely.
These types of questions can be solved by the concept of HCF.
Given that the glee club has a set of 48 classical CDs and a set of 42 show tune CDs and we have to determine the highest number of club members so that we can distribute these two types of CDs to the club members equally.
∴ The HCF of 42 and 48 is 6, we know 2 and 3 also divides 42 and 48 but they are not the largest number.
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Jina purchased a prepaid phone card for $30 . Long distance calls cost 22 cents a minute using this card. Jina used her card only once to make a long distance call. If the remaining credit on her card is $25.82 , how many minutes did her call last?
We _____ when calculating the average deviation, because the sum of all deviation scores around the mean equals zero.
We do not square the deviations when calculating the average deviation, because the sum of all deviation scores around the mean equals zero.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
The average deviation is calculated by taking the absolute value of the deviations from the mean, summing them, and then dividing by the total number of observations.
This gives us a measure of the average distance between each observation and the mean.
The formula for the average deviation is:
average deviation = Σ |x - mean| / n
where x is an observation, mean is the mean of the observations, and n is the total number of observations.
By taking the absolute value of the deviations, we ensure that negative and positive deviations do not cancel each other out when we sum them.
Thus,
We do not square the deviations when calculating the average deviation, because the sum of all deviation scores around the mean equals zero.
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Triangle ABC has vertices A(–2, –3), B(–5, –3), and C(–4, –2). The triangle is rotated 90° counterclockwise around the origin.
A) A’(3, 2), B’(3, 5), C’(2, 4)
B) A’(3, –2), B’(3, –5), C’(2, –4)
C) A’(–3, –2), B’(–3, –5), C’(–2, –4)
D) A’(–3, 2), B’(–3, 5), C’(–2, 4)
Long Beach California has an elevation of -7 ft New Orleans Louisiana is 8 feet below sea level which city has lower elevation
New Orleans has the lower elevation at -8 feet compared to Long Beach, which is at -7 feet, since a lower numerical value below zero indicates a further drop below sea level.
To determine which city has the lower elevation, we need to compare the elevations of Long Beach, California and New Orleans, Louisiana. A lower elevation means that it is further below sea level. Long Beach is at an elevation of -7 feet, while New Orleans is at 8 feet below sea level. In numerical terms, New Orleans’ elevation can be considered as -8 feet because the word 'below' indicates a negative elevation.
Comparing the two elevations:
Long Beach, California: -7 feet
New Orleans, Louisiana: -8 feet
Since -8 is less than -7, we determine that New Orleans has the lower elevation compared to Long Beach.
PLEASE HELP ASAP!
Write each equation in slope-intercept form of the equation of a line. Underline the slope and circle the y-intercept in each equation.
a)2x–y=4
b) 2x–y=0
c) x+3y=0
d) 2y–6=0
Final answer:
To write each equation in slope-intercept form and identify the slope and y-intercept, rearrange the given equations. a) 2x - y = 4: slope = 2, y-intercept = -4. b) 2x - y = 0: slope = 2, y-intercept = 0. c) x + 3y = 0: slope = -1/3, y-intercept = 0. d) 2y - 6 = 0: slope = 0, y-intercept = 3.
Explanation:
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. To write each equation in slope-intercept form and identify the slope and y-intercept, we can rearrange the given equations.
a) 2x - y = 4
First, we rearrange the equation to isolate y: -y = -2x + 4, then we rewrite as y = 2x - 4. Therefore, the slope is 2 and the y-intercept is -4.
b) 2x - y = 0
Rearranging the equation gives y = 2x. The slope is 2 and the y-intercept is 0.
c) x + 3y = 0
Isolating y, we get y = -1/3x. The slope is -1/3 and the y-intercept is 0.
d) 2y - 6 = 0
Solving for y, we find y = 3. The slope is 0 and the y-intercept is 3.
What is the area of a section of pavement that is 20 ft wide and 50 yd long? give your answer in square feet?
you pay $14.82 for 1.5 pound of ham. you buy 2.25 pounds of roast beef for $12.40 per pound. How much less does ham cost per pound than roast beef?
Consider the probability distribution of a random variable x. is the expected value of the distribution necessarily one of the possible values of x?
Answer:
No. The expected value can be a value different from the exact value of x.
solve and graph |2x+10|>26
In a shopping mall, shoppers who use a reward points card get a 10% discount on every transaction. If the average transaction is $450 for customers with these cards, and $500 for other customers, what happens to the expected value of a transaction?
Final answer:
The expected value of a transaction decreases by 10% for customers using a rewards points card, going from $500 to $450 per transaction as they receive a 10% discount.
Explanation:
The question pertains to the expected value of a transaction at a shopping mall considering different discounts for customers who use a rewards points card. The expected value takes into account the average (mean) value of transactions and the discounts applied to those transactions. With shoppers using the rewards card receiving a 10% discount, the average transaction value for these customers is $450, compared to $500 for those without the card.
If we calculate the expected value for a transaction without considering the card, it would simply be the average transaction amount of $500. However, when including the rewards card usage, we have to account for the discount. Therefore, the expected value for a transaction from a customer using the rewards card is 10% less than $500, which equals $450. This means the expected value for a transaction with the card has decreased by $50 compared to customers without the card.
To summarize the effect, use of the rewards card reduces the expected value of transactions for the business, given that a discount is provided. On the other hand, it incentivizes customers with savings, potentially increasing customer loyalty and the frequency of visits, which might offset the decrease in expected transaction value in a broader business strategy.
An aircraft travels with the wind for 120 miles in 0.75 of an hour. The return trip is flown against the wind and takes exactly 1 hour. Which system of linear equations represents x, the speed of the plane in miles per hour, and y, the speed of the wind in miles per hour? Recall the formula d = rt. 0.75(x + y) = 120 x − y = 120 0.75(x − y)= 120 x + y = 120 120(x + y) = 0.75 120(x − y) = 1 120(x − y) = 0.75 120(x + y) = 1 Mark this and return
Answer:
System of equation: 0.75(x+y)=120 and x-y=120
A is correct
Step-by-step explanation:
An aircraft travels with the wind for 120 miles in 0.75 of an hour.
The return trip is flown against the wind and takes exactly 1 hour.
Let speed of aircraft be x mph and speed of wind y mph
Formula:
[tex]speed=\dfrac{Distance}{Time}[/tex]
Case 1: When aircraft along with wind
Speed = x+y
Time = 0.75
Distance = 120
[tex]x+y=\dfrac{120}{0.75}[/tex]
[tex]0.75(x+y)=120[/tex]
0.75(x+y)=120
Case 2: When aircraft against with wind
Speed = x-y
Time = 1
Distance = 120
[tex]x-y=\dfrac{120}{1}=120[/tex]
x-y=120
Hence, The system of equation are 0.75(x+y)=120 and x-y=120
He area of a rectangle is 27 m2 , and the length of the rectangle is 3 m less than twice the width. find the dimensions of the rectangle.
The width of the rectangle is 4.5 meters, and the length is 6 meters.
Let's denote the width of the rectangle as [tex]\( w \)[/tex] and the length as [tex]\( l \)[/tex].
1. The area [tex]\( A \)[/tex] of a rectangle is given by the product of its length and width, so we have the equation:
[tex]\[ A = l \times w \][/tex]
Since the area is given to be 27 square meters, we can write:
[tex]\[ l \times w = 27 \][/tex]
2. The length of the rectangle is 3 meters less than twice the width.
This relationship can be expressed as:
[tex]\[ l = 2w - 3 \][/tex]
This is our second equation.
Now we have a system of two equations with two variables:
[tex]\[ \begin{cases} l \times w = 27 \\ l = 2w - 3 \end{cases} \][/tex]
We can substitute the expression for [tex]\( l \)[/tex] from the second equation into the first equation:
[tex]\[ (2w - 3) \times w = 27 \][/tex]
Expanding the equation, we get:
[tex]\[ 2w^2 - 3w - 27 = 0 \][/tex]
To solve this quadratic equation, we can factor it:
[tex]\[ (2w - 9)(w + 3) = 0 \][/tex]
Setting each factor equal to zero gives us two possible solutions for [tex]\( w \)[/tex]:
[tex]\[ 2w - 9 = 0 \quad \text{or} \quad w + 3 = 0 \][/tex]
Solving for [tex]\( w \)[/tex], we get:
[tex]\[ w = \frac{9}{2} \quad \text{or} \quad w = -3 \][/tex]
Since the width of a rectangle cannot be negative, we discard [tex]\( w = -3 \)[/tex].
Thus, [tex]\( w = \frac{9}{2} \)[/tex] meters, which simplifies to [tex]\( w = 4.5 \)[/tex] meters.
Now we can find the length [tex]\( l \)[/tex] by substituting [tex]\( w = 4.5 \)[/tex] into the second equation:
[tex]\[ l = 2(4.5) - 3 \][/tex]
[tex]\[ l = 9 - 3 \][/tex]
[tex]\[ l = 6 \][/tex]
What is the sum of the coefficients of the expression 3x4+5x2+x3x4+5x2+x?
add like terms
x^3x^4 = x^7
5x^2 + 5x^2 = 10x^2
you end up with x^7 +3x^4 + 10x^2 +x
Find the product (x-y) (3x-4y)
If a number is divisible by both two and three then we can say the number is divisible by
simple it is divisible by both
is the answer is both 2 and 3
Evaluate 4(6) + 7 (5 - 3 )
A: 118
B: 80
C: 10
D: 38
The average of your first three test grades is 78. what grade must you get on your fourth and final test to make your average 80?
Calculate the loss on selling 50 shares of stock originally bought at 13 3/4 and sold at 12
Mr. Mask suggested contacting a travel agent to see whether they could get a lower price. The agent found a price that was 30% lower than $2075. What was the price the travel agent found? Explain and Show your work.
Tanner walked a total of 8 kilometers by making 2 trips to school. How many trips will Tanner have to make in all to walk a total of 12 kilometers?
The total number of trips is x to walk a total of 12 kilometers is 3 trips if Tanner walked a total of 8 kilometers by making 2 trips to school.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
Tanner walked a total of 8 kilometers by making 2 trips to school.
Let the total number of trips be x to walk a total of 12 kilometers.
8 km → 2 trips
12 km → x trips
8x = 24
x = 24/8
x = 3 trips
Thus, the total number of trips is x to walk a total of 12 kilometers is 3 trips if Tanner walked a total of 8 kilometers by making 2 trips to school.
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1.For the function y = f(x), what is the ordered pair for the point on the graph when x = b - 2? (3 points)
a. (b - 2, f(b -2))
b. (x, f(b))
c. (x, b - 2)
d. (b - 2, f(b))
Answer:
A
Step-by-step explanation:
BIG BRAIN
If f(x)=x+8 and g(x) = -4x - 3, find (f+g)(x)
(f + g) (x)= -3 x+ 5
(f + g)(x) = -3x + 5
What is function?"It defines a relation between input and output values.""In function, for each input there is exactly one output."For given question,
We have been given two functions.
f(x) = x+8 and g(x) = -4x - 3
We need to find the value of (f + g)(x)
This means, we need to find the addition of functions f(x) and g(x)
⇒ (f + g)(x) = f(x) + g(x)
⇒ (f + g)(x) = (x + 8) + (-4x - 3)
⇒ (f + g)(x) = x - 4x + 8 -3
⇒ (f + g)(x) = -3x + 5
Therefore, (f + g)(x) = -3x + 5
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What is the area of a triangle with vertices at (0, −2) , (8, −2) , and (9, 1) ? Enter your answer in the box
Answer:
12 square unit.
Step-by-step explanation:
Since, the area of a triangle having vertices [tex](x_1, y_1)[/tex], [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] is,
[tex]A=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
Here, the vertices of the triangle are (0, −2), (8, −2) and (9, 1),
Hence, area of the given triangle is,
[tex]A=\frac{1}{2}|0(-2-1)+8(1+2)+9(-2+2)|[/tex]
[tex]=\frac{1}{2}| 0+24+0|[/tex]
[tex]=\frac{24}{2}[/tex]
[tex]=12\text{ square unit}[/tex]