The line models the number of birch trees and oak trees that can expect to produce the most reliable predictions.
How the correlation coefficient is useful?
The correlation coefficient is a measure of the strength of an association between two variables.
As the absolute value of the correlation coefficient gets closer to 1 and farther from 0, the relationship grows stronger and predictions made using the line of best fit become more reliable.
Because the absolute value of the correlation coefficient is closest to 1 for the line modeling the numbers of birch trees and oak trees, the botanist can expect this line to produce the most reliable predictions.
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Find the number of students in the class if 2/3 of the students are girls and the number of boys is 21.
How do you solve this??
21 a(little 6) b(little 5)
————————————
7 a(little 3) b
\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)
To solve this problemWe can use the rules of exponents and simplify the terms with the same base.
Dividing the coefficients: 21 / 7 = 3.
For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)
Similarly,\(b^5 / b = b^(5-1) = b^4\).
Putting it all together, the simplified expression is:
\(3a^3b^4.\)
Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)
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A city holds an election for mayor every 2 years and an election for treasurer every 6 years. It held elections for both mayor and treasurer this year. How many years will
it be before the elections for mayor and treasurer both happen in the same year again?
Answer:
3years
Step-by-step explanation:
Answer:
It will take for about 6 six years for the election for both positions be taken
In DEF, sin D = 24/26 What is cos E?
A. 24 26
B. 10 24
C. 10 26
D. 26 10
Answer:
your answer will be option A. 24/26
Step-by-step explanation:
hope it helps....
In \(\triangle\) DEF, \(SinD = \frac{24}{26}\) , then \(Cos \ E\) will be equals to \(\frac{24}{26}\) .
What are trigonometric ratios ?Trigonometric ratios are defined as the sides and angles of a right-angled triangle are dealt with in Trigonometry.
We have,
\(\triangle\) DEF,
\(SinD = \frac{24}{26}\)
We know that,
\(SinD=\frac{Perpendicular}{Hypotenuse}=\frac{EF}{ED}\) and \(CosE=\frac{EF}{ED}\)
Using Pythagoras Theorem,
\(P^{2} +B^{2} =H^{2}\)
i.e.
\(EF^2+FD^2=EF^2\)
\(24^{2} +FD^2=26^2\)
\(FD^2=676-576\)
\(FD=10\)
But when we look from \(\angle E\) for \(Cos E\) then,
\(CosE=\frac{EF}{ED}\)
so,
\(CosE=\frac{24}{26}\)
So, the value of \(CosE=\frac{24}{26}\) is derived using the Trigonometric ratios.
Hence, we can say that In \(\triangle\) DEF, \(SinD = \frac{24}{26}\) , then \(Cos \ E\) will be equals to \(\frac{24}{26}\) .
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If 1/2 p = -5, then the value of p is
(a)-10
b) 10 c) 0 d) 2
Answer:
a
Step-by-step explanation:
\(\frac{1}{2}\) p = - 5 ( multiply both sides by 2 to clear the fraction )
p = 2 × - 5 = - 10
Answer: a -10
Step-by-step explanation:
\(\frac{1}{2} *\frac{-10}{1}\)
-10 divided by 2 is -5
Please look at the photo. Thank you!
The value of f(5) is positive
At f(x) = 0, the value of x is 1
For the interval f(x) ≤ 0, the values of x are [-2, 1]
How to determine the values of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have
f(5) = 1
This means that f(5) is positive
Also, we have
When f(x) = 0, the value of x is 1
For the interval f(x) ≤ 0, we have the values of x to be
-2 ≤ x ≤ 1
When represented as an interval, we have
[-2, 1]
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Find the product of polynomials (First Screenshot)
Problem 1.5 (Second Screenshot)
Polynomials have the following product: 3x5 + 2x4 + 5x3 + 2x2 - 32x + 14. An algebraic formula with variables is called a polynomial.
what is polynomials ?A polynomial is a mathematical expression consisting exclusively of additions, subtractions, multiplications, and positive integer powers of variables. It is an expression of coefficients and uncertainty. x2 4x + 7 represents a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that can be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic formula that includes variables and coefficients. Addition, subtraction, multiplication, and non-negative integer exponents are the only operations that can be included in an expression. This type of statement is known as a polynomial.
given
Multiply each combination of terms:
Combine like terms.
3x^5 + 2x^4 + (-7x^3 + 12x^3) + (8x^2 - 6x^2 ) + (-28x - 4x) +14=
3x^5 + 2x^4 + 5x^3 + 2x^2 - 32x + 14.
Polynomials have the following product: 3x5 + 2x4 + 5x3 + 2x2 - 32x + 14. An algebraic formula with variables is called a polynomial.
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the conference room can hold fewer than 100 people
What is the equation for this question
C = conference room capacity
we can write something along the lines of C < 100, namely C can hold is less than 100.
URGENT Erin is taking part in a play at the community theater. The cast and crew ordered T-shirts for all the volunteers. The cost of a T-shirt is $8, and the total delivery charge is $45 per order. If the center has no more than $325 to buy T-shirts, how many T-shirts can they buy?
Answer:
B is the correct answer. Less than or equal to 35 t shirts orders.
Step-by-step explanation:
3x^2+5x+2 help me solve this
Answer:
(3x +2)(x +1)
Step-by-step explanation:
A number of different ways are suggested for doing this. One that seems straightforward is this.
For ax^2 +bx +c, look for factors of ac that total b. Here we have ...
ac = 3·2 = 6
b = 5
It is easy to see that the factors we just multiplied to get 6 are ones that total 5: 3+2 = 5.
Now, rewrite the "bx" term using this sum.
3x^2 +3x +2x +2
Factor each pair of terms.
3x(x +1) +2(x +1)
And factor out the common factor:
(3x +2)(x +1)
Describe the series of rigid motion transformations which map polygon A to Polygon A'''. Are the two polygons congruent? Explain how you know.
(someone please help me!)
The series of rigid motion transformations that map polygon A to Polygon A''' are;
A rotation of 145° about the origin to map A to A'A reflection across the x-axis to map A' to A'A translation of four units to the right and one unit downWhat is a rigid transformation?A rigid transformation is a transformation in which the distance between all pairs of points on the pre-image is preserved following the transformation.
The series of rigid motion transformations that map polygon A to polygon A''' are;
Transformation from A to A'
The angle in the diagram in the question indicates the rotation of polygon A to produce polygon A' is a rotation of 145° about the origin.Transformation from A' to A''
The coordinates of the vertices of triangle, A' (0.9, 4.1), (3.1, 5.9), (5.5, (2.5) and the vertices of triangle A'' (0.9, -4.1), (3.1, -5.9), (5.5, -2.5), indicates that the transformation is a reflection about the x-axisTransformation from A'' to A'''
The arrow of the translation transformation indicates that the transformation is a translation of four units to the right and 1 unit down.Learn more about rigid transformations in geometry here:
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What is the value of the expression -(-6)?
A.-6 b.-1/6 c.1/6 d.6
Answer:
d. 6
Step-by-step explanation:
Answer:
D: 6
Step-by-step explanation:
The Main Rules Are:
1) A negative number times a negative number is a positive number.
2) A positive number times a positive number is a positive number.
3) A negative number times a positive number is a negative number.
This problem is read as negative 1 times negative 6. Any negative symbol in front of a parentheses would be read as negative 1. In other words, the problem reads -1(-6). Remember, a negative number times a negative number is a positive number. Multiplying negatives is no different than multiplying numbers greater than zero, you just change the sign of the answer. Lets read this as 1 times 6 which is 6. Therefore, -1 times -6 is 6.
Hope that helped, as well as explained the concept :)
Question 16 of 22 -
MYA-Math-Alg1-CBT-2020-2021: Section 1
Question: 1-16
In the city of Carmen, there is a drawbridge that is opened twice per hour over the summer. The graph below shows the number of feet that the top of the bridge w
minutes that the drawbridge was open.
40
30
Feet Above Water
20
10
+
1
2
3
4
Minutes
The city's engineer noticed that the bridge is not opening and closing at the same rate and wanted to determine the rate of change over these intervals. Complete th
drawbridge (in feet per minute) at each of the specified intervals.
-25 -12.5-5 -2.50 2.5 5 12.5 25
Answer:
25, 0, -12.5
Step-by-step explanation:
See attached
Rate of change is:
Interval 0 - 1 min
(40-15)/(1-0) = 25/1 = 25Interval 1 - 2 min
(40 - 40)/(2-1) = 0/1 = 0Interval 2- 5 min
(15 - 40)/(4-2) = -25/2 = -12.5Find the quotient and remainder using synthetic division.
x^4
-
3
x^3
+
9
x
+
6/
x
+
1
The quotient is
The remainder is
The quotient of x⁴ - 3x³ + 9x + 6 ÷ x + 1 using synthetic division is x³ + 2x² - 2x + 7 and the remainder is 13
Finding the quotient and remainder using synthetic divisionFrom the question, we have the following parameters that can be used in our computation:
x⁴ - 3x³ + 9x + 6 ÷ x + 1
The synthetic set up is
-1 | 1 3 0 9 6
|__________
Bring down the first coefficient, which is 1 and repeat the process
-1 | 1 3 0 9 6
|__-1_-2_-2_7____
1 2 -2 7 13
This means that the quotient is
x³ + 2x² - 2x + 7
And the remainder is 13
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Complete question
Find the quotient and remainder using synthetic division.
x^4-3x^3+9x+6/x+1
The quotient is
The remainder is
Answer:
Step-by-step explanation:
To use synthetic division, we need to set up the coefficients of the dividend polynomial in decreasing order of powers of x, including any missing terms with zero coefficients.
So we have:
Dividend: x^4 - 3x^3 + 9x + 6
Divisor: x + 1
We can represent the divisor as (x + 1) and set up the synthetic division table as follows:
-1 | 1 -3 9 0 6
| -1 4 -13 13
|___________________
| 1 -4 13 -13 19
The numbers on the first row of the table are the coefficients of the dividend polynomial in decreasing order of powers of x. The -1 on the left of the table is the opposite of the divisor, x + 1.
The first number in the second row is always 0, and we get it by bringing down the first coefficient, which is 1. To get the next number in the second row, we multiply the divisor, -1, by 1, and add the result to the second coefficient, which is -3. This gives us -1 x -3 = 3, which we write under -3 in the first row.
We repeat this process for the next numbers in the second row, always multiplying the divisor by the last number in the second row, and adding the result to the next coefficient in the first row. We continue until we reach the last coefficient in the first row.
The last number in the second row, 13, is the remainder of the division. The other numbers in the second row are the coefficients of the quotient polynomial in decreasing order of powers of x. So the quotient is:
x^3 - 4x^2 + 13x - 13
And the remainder is:
13
Therefore, the quotient is x^3 - 4x^2 + 13x - 13, and the remainder is 13.
si ABCD son los vertices de un cuadrado y A(2,2) y C (10,8) 2 vertices opuestos. Hallar los otros dos vertices, dar como respuesta la mayor de las ordenadas
The area of the square is given as 100 square unit
How to determine the area of square?You should be aware that the square has all its sides equal
The perpendicular from opposite vertices represent distance
The given vertices are
(2,2) and (10,8)
Using the formula for distance between two points
d=√(10-2)²+(8-2)²
d=√8²+6²
d = √64+36
d=√100
This implies that d=10
The area of a square is given as s²
Area = 10²
Atrea = 100 square units
In conclusion, the area of the square is 100 square units
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Translated question:
The vertices of a square ABCD are A(2,2) and B(10,8), Find the area of the square
Use the drawing tools) to form the correct answer on the provided graph
The graph of the function g(x)=+3-4 is shifted 5 units to the left. Plot the zeros of the new function on the
Drawing Tools
Select
Point
Click on a tool to begin drawing
Reset
k
a
F
Unu
The zeros of the new function are x = -9 and x = -4
Ploting the zeros of the new functionfrom the question, we have the following parameters that can be used in our computation:
g(x) = x² + 3x - 4
The transformation rule is given as
Shifted 5 units to the left
So, we have
h(x) = (x + 5)² + 3(x + 5) - 4
Next, we plot the graph of h(x)
See attachment
From the graph, we have the zeros to be
x = -9 and x = -4
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Suppose the prices of a certain model of new homes are normally distributed with a mean of 150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid between $149,000 and $151,000 if the standard deviation is $1000
The percentage of buyers is approximately 68.26% of buyers of new houses paid between \($149,000\) and \($151,000\) .
We are given that the prices of the new homes are normally distributed with a mean of \($150,000\) and a standard deviation of $1000.
Using the 68-95-99.7 rule, we know that: approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the data falls within two standard deviations of the mean, approximately 99.7% of the data falls within three standard deviations of the mean.
In order to determine the proportion of customers who spent between $149,000 and , we must first determine the z-scores for these values:
z1 = (149,000 - 150,000) / 1000 = -1 z2 = (151,000 - 150,000) / 1000 = 1
Now, we can determine the proportion of data that falls between z1 and z2 using the z-table or a calculator. The region to the left of z1 is 0.1587, and the area to the left of z2 is 0.8413, according to the z-table. Thus, the region bounded by z1 and z2 is:
0.8413 - 0.1587 = 0.6826
We can get the percentage of consumers who spent between by multiplying this by 100% is \($149,000\) and \($151,000\):
0.6826 x 100% = 68.26%
Therefore, the standard deviation of customers who paid between is \($149,000\) and \($151,000\) for this model of new homes.
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The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude,
in feet, of the airplane and x represents the number of minutes the plane has been descending:
y= -1025x + 30,750
Part A:
Create a table for the values when x = 0, 5, 8, 10, 30.
Include worked-out equations used to identify the values within the table.
Part B:
Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and
describe what is happening to the ajrplane at these time intervals.
Part C:
Which ordered pair(from the table in part A) represents the initial value? What does the initial value represent in this problem?
Part D:
What is the rate of change in this equation? What does the rate of change represent in this problem?
Answer:
Step-by-step explanation:
Part A:
To create the table, we substitute each of the given values of x into the equation and solve for y:
x y = -1025x + 30,750
0 30,750
5 25,375
8 21,050
10 18,725
30 -7,500
Part B:
The altitude after 5 minutes can be found by substituting x=5 into the equation:
y = -1025(5) + 30,750 = 25,375
The altitude after 30 minutes can be found by substituting x=30 into the equation:
y = -1025(30) + 30,750 = -7,500
After 5 minutes, the altitude of the airplane is 25,375 feet. After 30 minutes, the altitude of the airplane is -7,500 feet, which means the airplane is on the ground. This is because the altitude is decreasing by 1,025 feet every minute, and after 30 minutes, the altitude has decreased to 0 feet, which is the ground level.
Part C:
The ordered pair (0, 30,750) represents the initial value, where x=0. The initial value represents the altitude of the airplane before it started descending. In this problem, the initial value of 30,750 feet represents the altitude of the airplane when it was at cruising altitude.
Part D:
The rate of change in this equation is -1025. The rate of change represents the speed at which the altitude of the airplane is changing per minute. In this problem, the rate of change of -1025 feet per minute means that the altitude of the airplane is decreasing by 1025 feet every minute it descends.
PLEASE I'M NOT SURE WHAT TO DO: Write the following equation in point-slope form: 16. The cost to rent a video game at a rental store can be modeled by a linear function. Renting a game for 1 night costs $1.50 and renting a game for 2 nights cost $2.7%. Write a linear equation that models the total cost of renting a game, y, as a function of the number of nights rented, x. Hint: find your ordered pairs then slope, point slope form is y-yı = m(x - x1)
Answer:2.7 - 1.50 = 1.2(2-1)
Answer:
129.6 is the answer
Step-by-step explanation:
it takes matilda twice as long to complete a research project
The beginning balance of the check register was $492.88. During the month, deposits were made for $210 and $499.88. Checks were
written for $18.25, $19.82, and $309.82. What is the ending balance of the check register?
Note: Round your answer to 2 decimal places.
Answer:
$840.77
Step-by-step explanation:
Please see screenshot.
Answer:
See below
Step-by-step explanation:
Find the value of x in the triangle shown below
X=2
X=5
X= √5
X= √17
Answer:
the answer is \(\sqrt{17}\)
Step-by-step explanation:
the Pythagorean theorem is \(a^{2}\) + \(b^{2} = c^{2}\). c is always the hypotenuse (the longest side) and a and b are the legs (the shorter sides) so 1 squared plus 4 squared is 17. there is no whole square root of 17 so the answer is \(\sqrt{17}\)
Consumer Price Index, 1970-2002
Year
1970
1975
1980
1985
1990
1995
2002
Source: World Almanac 2003
CPI
116.3
161.2
248.8
322.2
391.4
456.5
535.8
Describe how the CPI is related to the year.
As the year increases, the CPI decreases and then increases.
As the year increases, the CPI increases and then decreases.
As the year increases, the CPI decreases.
d. As the year increases, the CPI increases.
C.
a.
b.
The computation of the increased in salary is $500.
Here, we have,
Explanation:
Data provided in the question
Salary for the first year = $50,000
CPI increase during the year = 4%
Overstated inflation = 1% i.e. 5%
The computation of the increased in salary is shown below:
= Salary of the first year × inflation rate - salary of the first year × CPI increase during the year
= $50,000 × 5% - $50,000 × 4%
= $2,500 - $2,000
= $500
Hence, The computation of the increased in salary is $500.
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complete question:
Mark's wage contract specifies a $50,000 salary for the first year, and specifies a salary increase equal to the percentage increase in the CPI during the second year. The increase in the CPI during the year was 4.0%. If the CPI overstates inflation by 1.0% (that is, the actual price increase was 3% and not 4%), at the end of the first year Mark's salary increased by $________ more than it would have without the upward bias.
Mary is having a birthday party. She invited 14 friends. Mary made 190 cookies. She wants to share them at her party but also wants to save 22 for her mother and father. How many cookies will each person get at the party?
please I need help with this
A. The following are sets A and B:
A = {2, 3, 5, 7, 11}
B = {1, 2, 3, 4, 6, 12}
C. Elements not in A or A' = ∅
B. The Venn diagram is attached
How to solve sets?A universal set is a set which consists of all elements related to the given sets. It is denoted by U.
A. Set A:
A = {2, 3, 5, 7, 11}
Set B:
B = {1, 2, 3, 4, 6, 12}
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A' = {1, 4, 6, 8, 9, 10, 12}
C. Elements not in A or A' = ∅
Complement of set A is refers to a set that contains the elements present in the universal set but not in set A.
Hence, the Venn diagram of sets A, B and U has been attached.
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The graph below shows the solution to which system of inequalities?
A bag contains 15 white balls and 10 black balls,another contains 20 white balls and 15 white balls.if two balls are drawn without replacement from each bag,find the probability that
a)all four are black
b)exactly one of the four are white
Answer:
exactly one of the four are white
Suppose that the credit remaining on a phone card (in dollars) is a linear function of the total calling time (in minutes). When graphed, the
function gives a line with a slope of -0.13. See the figure below.
There is $28.51 in credit remaining on the card after 27 minutes of calls. How much credit will there be after 36 minutes of calls?
After 36 minutes of calls, when the function returns a line with a slope of -0.13, there will be $27.56 credit.
what is function ?Mathematics deals with numbers and their variants, equations and related structures, shapes and their locations, and locations where they might be found. A function is an association between inputs and outputs where each input results in a single, unique output. A domain and a codomain, or scope, are assigned to each function. Functions are typically denoted by the letter f. (x). The input is an x. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four main categories of functions that are available.
given
Assume that the total calling time is a linear function of the credit left on a phone card (measured in dollars) (in minutes).
m(call time) + b = credit
The function produces a line with a slope of -0.14 when graphed.
After 43 minutes of calls, the card's balance is $26.02 left.
After 32 minutes of calls, there was 26.02 = -0.14(43) + b b = 26.02+6.02 b = 32.04 C(x) = -0.14x+32.04
credit?
C(32) = -0.14(32) + 32.04\sC(32) = $27.56
After 36 minutes of calls, when the function returns a line with a slope of -0.13, there will be $27.56 credit.
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y and z are whole numbers y<70 z 60 work out the largest possible value of y and z
Answer:
a) 12
b) 129
Step-by-step explanation:
a)
\(w, x \in \mathbb{Z}_{\ge 0}\)
\(w>50\\x<40\)
For the smallest value of \(w-x\), we gotta figure out the smallest value for w and the highest value for x.
\(w>50 \Rightarrow \text{ smallest value is } 51\)
For \(x\), once \(-(-x)=x\), we conclude that \(x\) cannot be negative and therefore, \(x=39\).
\(51-39=12\)
b)
\(y, z \in \mathbb{Z}_{\ge 0}\)
\(y<70\\z\leq 60\)
For the largest value of \(y+z\), we gotta figure out the highest value for y and z.
\(y<70 \Rightarrow \text{ highest value is } 69\)
\(z\leq 60 \Rightarrow \text{ highest value is } 60\)
\(y+z=69+60=129\)