The value of a and b are 1 and -8 respectively.
What are Quadratic Expressions?Quadratic expressions are polynomial expressions of second degree.
The general form of a quadratic expression is ax² + b x + c.
The given quadratic expression is x² + 2x - 7.
We have to write this in the form (x + a)² + b.
We have the algebraic identity a² + 2ab + b² = (a + b)²
x² + 2x - 7 = x² + 2x - 7 + 1 - 1
= (x² + 2x + 1) - 7 - 1
= (x + 1)² - 8, which is in the form (x + a)² + b.
a = 1 and b = -8
Hence the value of a is 1 and the value of b is -8.
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Easy Question
A researcher found that students who spent more time exercising each week also had higher average test scores. Describe the correlation, if any, between time spent exercising and test scores.
The correct answer is a) No you cannot, because the lower boundary of the confidence interval is .131, which is less than .30, and so the true correlation could be less than .30.
What is the correlation analysis?Correlation analysis allows us to examine the strength, direction, and nature of the relationship between two variables, and to determine whether or not there is a statistically significant association between them.
Based on the information given, there appears to be a positive correlation between time spent exercising and test scores. This means that as the time spent exercising increases, the test scores also tend to increase. However, we cannot determine the strength or causality of this correlation without additional information or analysis. It is possible that other factors could be influencing both variables or that there could be confounding variables affecting the relationship.
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Correct question:
Assume a researcher found that the correlation between a test she had developed and exam performance was .5 in a study of 25 students. She had previously been informed that correlations under .30 are considered unacceptable. The 95% confidence interval was [0.131, 0.747]. Can you be confident that the true correlation is at least 0.30?
No you cannot, because the lower boundary of the confidence interval is .131, which is less than .30, and so the true correlation could be less than .30.Yes you can, because the correlation coefficient is .5 (which is above .30) and falls within the boundaries of the confidence interval.No you cannot, because the sample size was too small. Yes you can, because the upper boundary of the confidence interval is above .30 we can be 95% confident that the true correlation will be above .30Write an expression for C less than the product of k and y
Answer:
ky - c
Step-by-step explanation:
K(Y) - C
(K*Y) - C
Find each trigonometric ratio. Give your answer as a fraction
Show proofs
Help urgent
The side length QR = 34 derived using the Pythagoras rule, and the following are the values of the trigonometric ratio:
sin Q = 30/34, cos Q = 16/34 , tan Q = 30/16, sin Q = 30/34, cos Q = 16/34, and tan Q = 30/16
What is the Pythagoras ruleThe Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
QR² = 16² + 30²
QR = √(256 + 900) {take square root of both sides}
QR = √1156
QR = 34
since we have QR = 34, RS = 30, and SQ = 16, then:
Considering the angle Q for the right triangle;
sin Q = 30/34 {opposite/hypotenuse}
cos Q = 16/34 {adjacent/hypotenuse}
tan Q = 30/16 {opposite/adjacent}
Considering the angle R for the right triangle;
sin R = 16/34 {opposite/hypotenuse}
cos R = 30/34 {adjacent/hypotenuse}
tan R = 16/30 {opposite/adjacent}
Therefore, the side length QR = 34 derived using the Pythagoras rule, and the following are the values of the trigonometric ratio:
sin Q = 30/34, cos Q = 16/34 , tan Q = 30/16, sin Q = 30/34, cos Q = 16/34, and tan Q = 30/16.
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If a < b, what can you say about the locations of a and b on the number line?
There is not enough information given.
a is to the right of b.
a is to the left of b.
a and b are the same distance away from 0.
If a < b, we can say that b is to the right of a on the number line. In other words, a is to the left of b.
What exactly is the number line?A number line is a horizontal line with evenly spaced number increments. The numbers on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, such as plotting a point.
If a b, then b is to the right of a on the number line. To put it another way, an is to the left of b.
This is because the number line depicts the order of real numbers, with smaller numbers to the left and larger numbers to the right. Because an is less than b, it is a smaller number and must be to the left of b on the number line.
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Use the Associative Property of Addition to write an expression equivalent to (W+4)+2
Answer:W+6
Step-by-step explanation:
Solve for the equation below PLEASE
Solving the Question
[tex]\dfrac{2}{3}x=6[/tex]
Our goal is always to isolate x.We can do that by performing inverse operations⇒ ex. the inverse of addition is subtractionHere, we have to get rid of the [tex]\dfrac{2}{3}[/tex] by dividing both sides by it.[tex]\dfrac{\frac{2}{3}x}{\frac{2}{3}}=\dfrac{6}{\frac{2}{3}}\\\\x=\dfrac{6}{\frac{2}{3}}\\\\x=6\div\dfrac{2}{3}[/tex]
Dividing by a fraction is the same as multiplying by its reciprocal:[tex]x=6\times\dfrac{3}{2}\\\\x=\dfrac{18}{2}\\\\x=9[/tex]
Answerx = 9
a unit of measurement equal to one thousand meters is_____
A unit of measurement which is equal to one thousands meters is known as one kilometers.
Different units of measurements are meters , kilometers, centimeters, millimeters and so on.Measuring small length basically we use centimeters and very small length in millimeters.Measuring medium length we use unit known as meters.When we have measure long distance unit which is used is known as kilometers.Relation between different units of length are:1centimeters is equal to 10 millimeters1 meter is equal to 100 centimeters1 kilometers is equal to 1000 metersTherefore, the given units of measurement equal to one thousand meters is called one - kilometers.
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Distribute Solve for the variables 2(y+6)=8
The value of y is -2.
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,
2 (y + 6) = 8
Using the distributive operation of multiplication over addition.
2y + 12 = 8
2y = 8 - 12
2y = -4
y = -2
Thus,
y = -2.
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By rounding to one significant figure estimate the answer to 49x138
jacinda divides 19 cookies into 5 equal piles, using as many cookies as possible, but has some left over, how many are left?
Answer: Jacinda has 4 cookies left over.
Step-by-step explanation:
If Jacinda divides 19 cookies into 5 equal piles using as many cookies as possible, but has some left over, we can use integer division to determine how many cookies are in each pile. Integer division divides two numbers and rounds down to the nearest integer. In this case, the number of cookies in each pile is:
19 cookies ÷ 5 piles = 3 with a remainder of 4
Answer: 4
Step-by-step explanation:
Based on the given conditions, formulate: 19-5
Calculate the sum or difference: 14
Sale! 50% OFF
of the original price!
If a tent has a sale price of $39, what was the original price?
Answer:is this real
Step-by-step explanation:
1 =727
can factorials with algebraic expressions still be correct if you substitute the letter with a number
factorials with algebraic expressions still be correct if you substitute the letter with a number.
What are factorials?Factorial is a mathematical operation denoted by the exclamation mark (!). It is used to find the product of all positive integers from 1 to a given number. For example, the factorial of 4 (written as 4!) is:
4! = 4 × 3 × 2 × 1 = 24
Given by the question.
if you substitute a numerical value for the algebraic expression, the resulting factorial can be computed and evaluated as a numerical expression.
For example, consider the factorial expression n! where n is an algebraic expression such as n = x + 2. Substituting a numerical value for x, say x = 3, we get n = 3 + 2 = 5, and hence we can compute 5! = 5 x 4 x 3 x 2 x 1 = 120.
Similarly, if we have an expression like (n+1)! /(n-1)! where n is an algebraic expression, we can substitute a numerical value for n and compute the resulting value. For example, if we substitute n = 4, we get (4+1)!/(4-1)! = 5!/3! = (5 x 4 x 3 x 2 x 1)/(3 x 2 x 1) = 60.
It's important to note that substituting numerical values for algebraic expressions only works if the resulting expression is well-defined and doesn't lead to any undefined or indeterminate forms (such as division by zero).
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Anyone help me with this geometry hw?
The circles with the specified angle of internal sectors, indicates that we get the following arc and radial lengths;
2. m∠ADC = 160°
m∠BDC = 160°
3. Length of [tex]\widehat{CB}[/tex] ≈ 11.17 inches
4. Length of [tex]\widehat{ABC}[/tex] ≈ 13.96 inches
5. a. The radius of ⊙ Q ≈ 14.324 inches
What is the radius of a circle?The radius is the straight line extending from the circle center to the circumference. The radius is the shortest distance from the circle center to the circumference of the circle.
Angle ∠ADC is congruent to ∠BDC in the circle with center D
∠ADC ≅ ∠BDC
2. ∠ADC ≅ ∠BDC, therefore;
m∠ADC = m∠BDC
The angle sum property of the angle at the center of a circle, indicates that we get;
40° + m∠ADC + m∠BDC = 360°
Therefore by plugging in m∠ADC = m∠BDC, we get;
40° + m∠ADC + m∠ADC = 360° (substitution property)
40° + 2 × m∠ADC = 360°
2 × m∠ADC = 360° - 40° = 320°
m∠ADC = 320° ÷ 2 = 160°
m∠ADC = 160° = m∠BDC
m∠BDC = 160°
3. The length of the arc [tex]\widehat{CB}[/tex], can be obtained from the proportion of the circumference of the circle D represented by the sector BDC as follows;
Length of the arc [tex]\widehat{CB}[/tex] = ((m∠BDC)/360°) × 2·π·r
Where;
r = The radius of the circle
The radius of the circle, r = 4 inches
Therefore; Length of the arc [tex]\widehat{CB}[/tex] = (160°/360°) × 2 × π × 4 ≈ 11.17
The length of the arc [tex]\widehat{CB}[/tex] ≈ 11.17 inches4. The length of the arc [tex]\widehat{ABC}[/tex] can be found as follows;
The angle at the center of the arc [tex]\widehat{ABC}[/tex] = 40° + m∠BDC
Therefore; The angle at the center of the arc [tex]\widehat{ABC}[/tex] = 40° + 160° = 200°
Length of [tex]\widehat{ABC}[/tex] = (200°/360°) × 2 × π × 4 inches ≈ 13.96 inches5. The length of the arc [tex]\widehat{AB}[/tex] = 15 inches
The angle formed by the sides AQ and BQ of the sector AQB = 60°
Therefore, we get;
length of the arc [tex]\widehat{AB}[/tex] = (60°/360°) × 2 × π × r = 15 inches
r = 15/((60°/360°) × 2 × π) ≈ 14.324
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what is how do you find DAC
The value of DAC in the figure would be 47 degrees.
How to find the measure of DAC?From the question, we have the following parameters that can be used in our computation:
The angles EAD, DAC and CAB are all on a straight line which means they add up to 180 degrees.
Angle CAB is in a triangle which means all the angles add up to 180 degrees and the value of this angle is:
= 180 - 80 - 57 = 43 degrees
The value of DAC would then be;
= 180 - EAD - CAB
Substitute the known values in the above equation, so, we have the following representation
= 180 - 90 - 43
= 90 - 43 = 47 degrees
Hence, the angle is 47 degrees
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What sorting algorithms are not comparison based?
The sorting algorithms that are not comparison based are counting sort, bucket sort, and radix sort.
Counting sort works by counting the number of occurrences of each element in an array and then using this information to determine the position of each element in the sorted array.
Bucket sort works by dividing the array into a number of smaller arrays, called buckets, and then sorting each of these smaller arrays separately.
Radix sort works by sorting the elements of an array based on the individual digits of each element, starting with the least significant digit and working up to the most significant digit.
These algorithms do not rely on comparisons between elements, which is why they are not considered comparison based.
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Find integer matrices A,B not multiples of each other such that Nul(A)=Nul(B) and Col(A)=Col(B)
Nul(A) = Nul(B) , Col(A) = Col(B) in integer matrices.
Describe matrix using an example?
A matrix is a collection of numbers that have been put in rows and columns to make a rectangular array. The entries of the matrix are the numbers, which are referred to as its elements.
In addition to many other areas of mathematics, matrices have extensive applications in the fields of engineering, physics, economics, and statistics.
The null space of any matrix A consists of all the vectors
X such that Ax = 0
And the column space of a matrix A is the span of its column vectors.
Let A = [tex]\left[\begin{array}{ccc}1&0&0 \\0&1&0\\0&0&1\end{array}\right][/tex]
Therefore, Nul(A) = {(0,0,0,w ) w∈ Z }
Col(A) = span{ (1,0,0), (0,1,0) , (0,0,1) }
By using definition of Null space of matrix and column space of matrix.
Let B = [tex]\left[\begin{array}{ccc}1&1&0\\0&1&0\\0&0&1\end{array}\right][/tex]
Nul(A) = {(0,0,0,w ) w∈ Z }
Col(A) = span{ (1,0,0), (0,1,0) , (0,0,1) }
Hence Nul(A) = Nul(B) , Col(A) = Col(B)
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Jeanne has a piece of fabric in the shape of a square. She wants to cut the fabric in the shape of a circle.
The approximate area of the remaining part of the fabric is given as 17.415 square feet
How to solve for the area of the remaining fabricTo get the solution, we have to solve for the area of the square shape and the area of the circle
The area of a square is given as A = a²
The area of a circle is given as πr²
We would have area of remaining fabric as
a² - πr²
The square has its sides as a = 9 cm
the circle has π = 3.14
we are to find the radius. But first we have to determine the diameter
The circle runs from one end of the square to the other end. This should be the diameter, because it is the length of the square as well
Diameter = 9 cm
radius = diameter / 2
= 9 / 2
= 4.5
When we put the values in the formula a² - πr² we would have
9² - 3.14 * 4.5²
81 - 3.14 * 20.25
81 - 63.585
= 17.415
The area of the remaining part after the circle is cut is 17.415 square feet
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The table below shows the linear relationship between
the number of people at a picnic and the total cost of the
picnic.
Number of People
6
9
12
Intro
15
Total Cost ($)
52
58
64
70
Which statements about the function described by the
table are true? Check all that apply.
The independent variable is the number of people.
The initial value (initial fee) for the picnic is $40.
The rate of change is $8.67 per person.
As the number of people increases, the total cost of
the picnic increases.
If 4 people attended the picnic, the total cost would
be $46.
Done
The initial value (initial fee) for the picnic is $40. Then the correct options are A, B, and D.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
Let 'x' be the number of people and 'y' be the total cost.
From the table, the two points are (6, 52) and (9, 58). Then the equation of the line is given as,
(y - 52) = [(58 - 52) / (9 - 6)](x - 6)
y - 52 = 2x - 12
y = 2x + 40
The initial value (initial fee) for the picnic is $40. Then the correct options are A, B, and D.
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What is the value of 240 inches in feet?
Answer:
Step-by-step explanation:20
Triangle ABC is similar to triangle FGH. Given the following angle measures, find the missing angle measures.
m∠A = 63 degrees
m∠B = 82 degrees
Enter your answers as numbers only.
The measure of the angle m∠C = m∠H is equal to 35°.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
Given, Triangle ABC is similar to triangle FGH.
Therefore, m∠A = m∠F = 63° and m∠B = m∠G = 82°.
We know the sum of the measure of all the interior angles in a triangle is 180°.
Therefore, m∠C = m∠H = 180° - 63° - 82° = 35°.
Congruency can be applied to any two dimensional figure, For example,
Two circles are congruent if they have the same radius length.
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A Plus Landscaping Company has a big job where they need 83 bushes and 22 trees.They need to compare the costs from two similar suppliers; Pinedale Plants and Sierra Shrubs. Last month A Plus Landscaping placed two orders with Pinedale Plants. The first order was for 10 bushes and 5 trees and totaled $393.6 before taxes. The second order was for 5 bushes and 2 trees and totalled $177.32 before taxes. The bills from Pinedale Plants do not list the per-item price. A Plus Landscaping has an offer from Sierra Shrubs where similar bushes cost $18.27 and trees cost $41.96.
Answer: To compare the costs between the two suppliers, we need to find the total cost of 83 bushes and 22 trees from each supplier.
For Pinedale Plants:
The first order was for 10 bushes and 5 trees, so the cost per bush is $393.6 / 10 = $39.36.
The second order was for 5 bushes and 2 trees, so the cost per bush is $177.32 / 5 = $35.464.
To find the average cost per bush from Pinedale Plants, we can take the average of the two costs: ($39.36 + $35.464) / 2 = $37.412
The total cost from Pinedale Plants for 83 bushes would be 83 * $37.412 = $3108.976
The total cost from Pinedale Plants for 22 trees would be 22 * $35.464 (since the cost per tree was not specified), which is $777.75
The total cost from Pinedale Plants for 83 bushes and 22 trees would be $3108.976 + $777.75 = $3886.726
For Sierra Shrubs:
The cost per bush from Sierra Shrubs is $18.27
The total cost from Sierra Shrubs for 83 bushes would be 83 * $18.27 = $1510.01
The cost per tree from Sierra Shrubs is $41.96
The total cost from Sierra Shrubs for 22 trees would be 22 * $41.96 = $923.12
The total cost from Sierra Shrubs for 83 bushes and 22 trees would be $1510.01 + $923.12 = $2433.13
So, we can see that the total cost from Sierra Shrubs for 83 bushes and 22 trees is lower than the total cost from Pinedale Plants. The company would save $3886.726 - $2433.13 = $1453.596 by ordering from Sierra Shrubs.
Step-by-step explanation:
What is an example of multi stage sampling?
Multistage sampling is a probability sampling technique that involves sampling in stages or multiple steps. In this technique, a large population is divided into smaller subgroups, and then a random sample is selected from each subgroup.
Here is an example of multistage sampling:
Suppose we want to conduct a study on the prevalence of a certain disease among high school students in a particular country. The population of high school students in the country is very large, so it is not feasible to sample all of them. Instead, we can use multistage sampling to select a representative sample.
In the first stage, we randomly select a certain number of schools from different regions of the country. Let's say we select 20 schools.
In the second stage, we randomly select a certain number of classes from each of the selected schools. Let's say we select 2 classes from each of the 20 schools, resulting in a total of 40 classes.
In the third stage, we randomly select a certain number of students from each of the selected classes. Let's say we select 10 students from each of the 40 classes, resulting in a total of 400 students.
This process of selecting a sample in stages is an example of multistage sampling. By selecting schools, classes, and students in a random and systematic way, we can obtain a representative sample of high school students in the country, which can be used to estimate the prevalence of the disease.
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How do you find the symmetry of a distribution?
Analyzing a distribution's form and the placements of its mean, median, and mode in relation to one another can reveal its symmetry.
Therefore by analyzing a distribution's form and the placements of its mean, median, and mode in relation to one another can reveal its symmetry. The following techniques can be used to determine a distribution's symmetry: Examining a distribution's histogram, box plot, or probability density function visually is one technique to identify a distribution's symmetry. If the distribution's shape appears to be symmetrical, it probably is. The subjective nature of this approach means that it might not give an accurate indication of symmetry.
Skewness is a measurement of a distribution's asymmetry. It may be calculated manually or with the aid of statistical tools. Examining a distribution's histogram, box plot, or probability density function visually is one technique to identify a distribution's symmetry. If the distribution's shape appears to be symmetrical, it probably is. Skewness is zero for a symmetric distribution. When the skewness is positive, the distribution is skewed to.
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Audrey and David are reading the same book. Audrey reads 40 pages each day.
David reads 20 pages each day.
Which of the following is a true statement about the number of pages Audrey and David have read after each day?
Select all that apply.
A.
Audrey has always read twice as many pages as David.
B.
After 6 days, Audrey and David have read the same total number of pages.
C.
Audrey has always read a total of 20 pages more than David.
D.
After 2 days, Audrey has read 40 more pages than David.
E.
After 3 days, Audrey has read three times as many pages as David.
ITS MULTIPLE CHOICE BTW
How can I find the variable for this?
The values of x is 13.42, y is 12 and z is 26.83 for right angle triangle ABC shown below.
Describe the term right angle triangle?The Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides, is a fundamental property of right triangles.
By the figure apply Pythagorean theorem in right angle ΔABC;
x² + z² = (24+6)² = 30²
x² + z² = 900 (eq. 1)
Apply Pythagorean theorem in right angle ΔAEB;
y² + 24² = z²
z² - y² = 576 (eq. 2)
Apply Pythagorean theorem in right angle ΔAEC;
y² + 6² = x²
x² - y² = 36 (eq. 3)
subtract eq. 2 and 3; then we get,
z² - x² = 540 (add this eq. with eq. 1)
2z² = 1440
z = √720 = 26.83
put in eq. 1
x² + 720 = 900
x = √180 = 13.42
put x value in eq. 3
180 - y² = 36
y = 12
Therefore, the values of x is 13.42, y is 12 and z is 26.83
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What is the y-intercept of y=-3-7xy=−3−7xy, equals, minus, 3, minus, 7, x?
Answer:
-3
Step-by-step explanation:
If it took 4 hours to mow 7 lawns, then at that rate, how many lawns could be mowed in 16 hours?
Answer:
28 lawns
Step-by-step explanation
If there is 7 lawns for 4 hours there will be 14 lawns in 8 hours. and 28 lawns in 16 hours
I will give you a Brainliest
Answer:
B isa the answer for me it might be wrong for you or switch them
Step-by-step explanation:
Determine the slope and y-intercept of the line that passes through the points (14, -2) and (5,13)
Answer:
m = -5/3
Y-intercept: (0, 64/3)
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (14, -2) and (5,13)
We see the y increase by 15 and the x decrease by 9, so the slope is
m = -15/9 = -5/3
The y-intercept is located at ( 0, 64/3)
NATURE The locations of wildflowers and honeybee hives were plotted on a coordinate plane.
A beehive is located at (3, 7)
and its bees were found visiting flowers as far as a flower patch located at (−1, 2)
. The equation that models the circumference of the circular area the bees were foraging in is
(x− ?)^2+(y−?)^2=?
.
The equation of the circle that models the circumference of the circular area the bees were foraging in is given as follows:
(x - 3)² + (y - 7)² = 41.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
A beehive is located at (3, 7), hence the center is located at (3,7), thus:
(x - 3)² + (y - 7)² = r².
The farthest patched was located at (-1,2), hence the radius is obtained as follows:
(-1 - 3)² + (2 - 7)² = r²
r² = 41.
Hence the equation is:
(x - 3)² + (y - 7)² = 41.
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