What is the average rate of change of f(x), represented by the graph, over the interval [0,2]?
A: 2
B: 1
C: 0.5
D: -0.5
![What Is The Average Rate Of Change Of F(x), Represented By The Graph, Over The Interval [0,2]?A: 2B:](https://i5t5.c14.e2-1.dev/c-qa-images/contents/attachments/psWK9B7zO7Q84bIn3x0kMwvr0FOdgwMx.png)
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Indicate the equation of the given line in standard form. The line that is the perpendicular bisector of the segment whose endpoints are R(-1,6) and S(5,5)
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now, what the dickens is the midpoint of RS anyway?
[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) R&({{ -1}}\quad ,&{{ 6}})\quad % (c,d) S&({{ 5}}\quad ,&{{ 5}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left( \cfrac{5-1}{2}~~,~~\cfrac{5+6}{2} \right)\implies \stackrel{midpoint}{\left(2~~,~~\frac{11}{2} \right)}[/tex]
so, we know that perpendicular line, will have to go through (2, 11/2)
now, a perpendicular line to RS, will have a negative reciprocal slope to it. Well, what is the slope of RS anyway?
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -1}}\quad ,&{{ 6}})\quad % (c,d) &({{ 5}}\quad ,&{{ 5}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{5-6}{5-(-1)}\implies \cfrac{5-6}{5+1}\implies -\cfrac{1}{6}[/tex]
and let's check the reciprocal negative of that,
[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad -\cfrac{1}{6}\\\\ slope=-\cfrac{1}{{{ 6}}}\qquad negative\implies +\cfrac{1}{{{ 6}}}\qquad reciprocal\implies + \cfrac{{{ 6}}}{1}\implies 6[/tex]
so, then, what's is the equation of a line whose slope is 6, and goes through 2, 11/2?
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 2}}\quad ,&{{ \frac{11}{2}}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 6 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-\cfrac{11}{2}=6(x-2) \\\\\\ y-\cfrac{11}{2}=6x-12\implies -6x+y=-12+\cfrac{11}{2}\implies \stackrel{\textit{standard form}}{-6x+y=-\cfrac{13}{2}}[/tex]
The equation of the perpendicular bisector of the segment with endpoints R(-1,6) and S(5,5) is found by calculating the midpoint, slope, and using the negative reciprocal for the perpendicular slope. It is then written in point-slope form and converted to standard form, resulting in 12x - 2y = 13.
Explanation:To find the equation of a line that is the perpendicular bisector of a segment with endpoints R(-1,6) and S(5,5), we need to take the following steps:
Determine the midpoint of the segment RS which will be a point on our bisector.Calculate the slope of the line segment RS.Find the negative reciprocal of the slope from step 2, which will give us the slope of our perpendicular bisector.Write the equation of the bisector line using the point-slope form and then convert it into standard form.The midpoint of RS is given by ((-1+5)/2, (6+5)/2) = (2, 5.5). The slope of RS is (5-6)/(5-(-1)) = -1/6. The negative reciprocal of -1/6 is 6. Thus, the slope of our bisector is 6.
Using the point-slope form with the midpoint, y - 5.5 = 6(x - 2). Expanding and rearranging to standard form, we get:
6x - y = 12 - 5.5 -> 6x - y = 6.5.
Multiplying through by 2 (to clear the decimal), we obtain:
12x - 2y = 13, which is the standard form equation of the perpendicular bisector of segment RS.
What is the difference between 7,001 and 433?
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3.74 rounded to the nearest
hundredth
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What scale of measurement is being used when a teacher measures the number of correct answers out of 50 on a quiz for each student?
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p x qCovariance between 2 variablesCovariance is a measure of the linear association between 2 variables with the 2 variables represented in their original units (not standardized). Unlike a correlation coefficient that goes from -1 to +1, the value of a covariance can go from - infinity to + infinity.Pearson product moment correlation (r) between 2 variablesPearson correlation (r) is a measure of the linear association between 2 variables with the 2 variables being standardized (mean = 0, SD = 1). Correlation coefficient that goes from -1 to +1Variance-Covariance MatrixIn a variance-covariance matrix the variances of the variables are represented in the diagonal of the matrix; the covariances between pairs of variables are represented in the off diagonalConstructAn unobserved or latent variable that is used to explain some observed phenomenon or experience. Latent variables are represented by a circle in measurement models.Reflective Measurement ModelA measurement model that holds that holds that a construct is viewed as the cause of the observed or measured variables.Formative Measurement ModelA measurement model that holds that holds that the observed or measured variables are the cause of the latent variableOperational Definition of a ConstructA definition that is clear and detailed that defines the construct by specifying the procedures used to measure a constructContent ValidityOne of five sources of measurement validity evidence that often involves experts who are knowledgeable about the construct making evaluative judgments about whether the items used to measure the construct adequately reflect the definition of the construct.Convergent ValidityA construct measured by 2 methods should produce a moderate to strong correlation between the 2 measures (e.g., a person's anxiety determined by a questionnaire and a person's anxiety determined by a structured interview).Discriminant ValidityScores on the measure are not related to other measures that are theoretically different (if Grit is theoretically different from Conscientiousness, the correlation between these measures should not be strong)Nomological NetworkAn approach used as part of the process of gathering evidence of construct validity of educational and psychological measures. Similar to the research process, relationships based on theory between measures that the new measure should relate to and measures it should not relate to are tested.Reliability
When a decimal is written in word form, what indicates that the equivalent form is a mixed number and not a fraction
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A rectangular prism is completely packed with 90 cubes of edge length fraction 1 over 2 inch, without any gap or overlap. Which of the following describes the volume of this rectangular prism? 11 unit cubes and 1 smaller cube of volume fraction 1 over 8 cubic inch 22 unit cubes and 4 smaller cubes of volume fraction 1 over 8 cubic inch each 11 unit cubes and 2 smaller cubes of volume fraction 1 over 8 cubic inch each 22 unit cubes and 2 smaller cubes of volume fraction 1 over 8 cubic inch each Could someone teach me the steps please? I reviewed the lesson, I still don't understand
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ok, notice the volume of the smaller cube forming the larger cube. Keeping in mind that the larger cube has 90 of those small ones.
[tex]\bf \stackrel{\textit{larger cube}}{V}=90\stackrel{\textit{small cube}}{V}\implies \stackrel{\textit{larger cube}}{V}=90\cdot \cfrac{1}{8}[/tex]
Answer:
A
Step-by-step explanation:
ur welcomes
if y is directly proportional to x^2 and y=216 when x=9 find y if x=19
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Round 527 to the nearest hundred
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NEED HELP 25 POINTS PLEASE HELP.The students at Harrison Middle School are being split into groups for a community service project. The school faculty has decided that each grade (6th, 7th, and 8th) will be split up into their own set of groups. The faculty has also decided that it is important for each grade to be split evenly into groups, with no leftover students, so that each group in a grade has exactly the same number of boys and girls. For each of the following grades, determine the largest number of groups that can be made and the number of boys and girls that will be in each group. The 6th grade has 64 girls and 72 boys. The 7th grade has 81 girls and 63 boys. The 8th grade has 68 girls and 60 boys. Please list down how many groups each grade has for both boys and girls.
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6th grade :
64 girls = 8 * 8
72 boys = 8 * 9
There will be 8 groups consisting of 8 girls and 9 boys
7th grade :
81 girls = 9 * 9
63 boys = 9 * 7
There will be 9 groups consisting of 9 girls and 7 boys
8th grade :
68 girls = 4 * 17
60 boys = 4 * 12
There will be 4 groups consisting of 17 girls and 12 boys
5x - x + 12 +2x - 7 = 10
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6x+5=10
Subtract 5 from both sides
6x=5
Divide bith sides by 6
x=5/6
Final answer: B
We're simply just trying to isolate x :)
However, we must first simplify the equation by adding like terms.
(5x - x + 2x) + (12 - 7) = 10
Simplify.
6x + 5 = 10
Then, we must subtract 5 from both sides.
6x = 10 - 5
Simplify.
6x = 5
Divide both sides by 6.
6x ÷ 6 = 5 ÷ 6
Simplify.
x = 5/6
B. x = 5/6
~Hope I helped!~
What value of x will give the minimum value for x^2- 14x + 3?
Please help me!!
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a = 1
b = -14
Vertex Formula.
[tex]x = -\frac{b}{2a}[/tex]
[tex]x = -\frac{(-14)}{2(1)}[/tex]
Distrubute the negative to the -14 making it 14
[tex]x = \frac{(14)}{2(1)}[/tex]
Times the denominator 2 * 1 = 2
[tex]x = \frac{(14)}{2}[/tex]
[tex]x = 7[/tex]
So 7 will give the minimum value for x^2- 14x + 3
Graph the following lines and write the equation in slope-intercept form. Through the point (−8,1) with a slope of 3.
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y = 3x + b
use the point to solve for y-intercept b
1 = 3(-8) + b
1 = -24 + b
1 + 24 = b
25 = b
equation
y = 3x +25
Solve for y 1.2x - 4y = 28
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what times what equals 46
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hope this helps
What times what equals 46 is 2 times 23, or 2 x 23 = 46.
We have,
To find what times equal 46, we can look for pairs of numbers that, when multiplied together, result in 46.
We can start by listing the factors of 46:
1 x 46 = 46
2 x 23 = 46
From these factor pairs, we can see that 2 and 23 are the numbers that multiply to 46.
Therefore,
What times what equals 46 is 2 times 23, or 2 x 23 = 46.
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A restaurant uses 8 1/4 pounds of carrots to make 6 carrot cakes. Frank wants to use the same recipe. How many pounds of carrots does Frank need to make one carrot cake?
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Frank needs [tex]\( \frac{11}{8} \)[/tex] pounds of carrots to make one carrot cake.
To find out how many pounds of carrots Frank needs to make one carrot cake, we first need to determine how many pounds of carrots are used per carrot cake in the original recipe.
Given that the restaurant uses 8(1)/(4) pounds of carrots to make 6 carrot cakes, we divide the total pounds of carrots by the number of cakes to find the amount per cake.
[tex]\( \text{Carrots per cake} = \frac{8\frac{1}{4}}{6} \)[/tex]
First, we convert the mixed number [tex]\(8\frac{1}{4}\)[/tex] to an improper fraction:
[tex]\(8\frac{1}{4} = \frac{(8 \times 4) + 1}{4} = \frac{33}{4}\)[/tex]
Then, divide by 6:
[tex]\( \frac{33}{4} \div 6 = \frac{33}{4} \times \frac{1}{6} = \frac{33}{24} = \frac{11}{8} \)[/tex]
So, Frank needs [tex]\( \frac{11}{8} \)[/tex] pounds of carrots to make one carrot cake.
How much pizza will each person get if 4 people share 3/4 of a pizza equally?
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Evaluate the integral. 2 (6t i − t3 j + 2t3 k) dt 0
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The integral of the vector field 2 (6t i − t3 j + 2t3 k) from 0 to t can be broken down into three separate integrals for each component, yielding the resulting integral vector of (6t^2)i - (0.5t^4)j + (t^4)k.
Explanation:The integral you're asking about is a vector field integral, which comes up primarily in physics-related problems. The integral of a vector field, in this case, 2 (6t i − t3 j + 2t3 k) with respect to time, can be broken down into three separate integrals, each corresponding to a different component.
To solve, you would perform each integral separately:
Integral from 0 to t of 2*6t dt = 6t^2 between 0 and t = 6t^2 Integral from 0 to t of 2*-t^3 dt = -0.5*t^4 between 0 and t = -0.5t^4 Integral from 0 to t of 2*2t^3 dt = t^4 between 0 and t = t^4Combine these answers to yield the integral vector (6t^2)i - (0.5t^4)j + (t^4)k as the solution. Please remember to always check your calculations to ensure accuracy!
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One and two thirds times a right angle
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1 2/3 * 90 =
5/3 * 90 =
450/3 =
150 <===
Answer:
150 Degrees
Step-by-step explanation:
We have to find one and two third of a right angle.
That is we have to basically find [tex]1\displaystyle\frac{2}{3}\text{ of a right angle.}[/tex]
The measure of a right angle in degrees is 90 degrees.
[tex]1\displaystyle\frac{2}{3}\times 90[/tex]
We convert the mixed fraction into unlike fraction
[tex]\displaystyle\frac{5}{3}\times 90 = 150[/tex]
Thus, one and two third of a right angle is 150 degrees or [tex]150^\circ[/tex]
The perimeter of a college athletic field is 92 meters and the length is 18m more than the width. Find the length and width.
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width = 14
i did a lot of trial and error
Determine whether the statement is always, sometimes, or never true. If △ABC has angles that measure 10° and 40°, and △DEF has angles that measure 40° and 120°, then △ABC ≅ △DEF.
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The statement is sometimes true. If two triangles have congruent angles, they are similar but not necessarily congruent.
Explanation:The statement is sometimes true. If △ABC has angles that measure 10° and 40°, and △DEF has angles that measure 40° and 120°, we can determine their congruence by comparing their angles. If two triangles have congruent angles, they are similar but not necessarily congruent. Therefore, △ABC and △DEF are similar triangles but not necessarily congruent.
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A town's population is 43,200. About 100 people move out of the town each month. Each month, 125 people on average move into town. A nearby town has a population of 45,000. It has no one moving in and an average of 200 people moving away every month. In about how many months will the populations of the towns be equal?
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Describe sets of two or more matching integer cards that satisfy the criteria in each part below:
a. Cards increase the score by eight points.
b. Cards decrease the score by 9 points.
c. Removing cards that increase the score by 10 points.
d. Positive cards that decrease the score by 18 points.
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Answer:
a. Removing two (-4)'s
b. Picking up three (-3)'s or removing three 3's
c. Removing two (-3)'s and one (-4)'s
d. Removing three 5's and one 3's
Step-by-step explanation:
Cards available: 5, -3, -4, & 3
a. Score can be increased picking up positive cards or removing negative cards.
b. Score can be decreased picking up negative cards or removing positive cards.
c. As stated before, in order to increase the score removing cards, positive cards have to be removed.
d. As stated before, in order to decrease the score with positive cards, those cards have to be removed.
The ratio of a quarterback completed passes to attempted passes is 7 to 8. If he attempted 24 passes, how many did he complete? Round to nearest whole number if needed.
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If he attempted 24 passes, he completes 21 pass.
What is ratio?The numerical association of two values that shows how frequently one value includes or is contained inside another is called ratio.
Given, The ratio of a quarterback completed passes to attempted passes is 7 to 8.
If he attempted 24 passes.
To find the number of passes, he completes:
24 x 7/8
= 3 x7
= 21
Hence, he completes 21 passes.
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Standard form of 210 million, 64 thousands, and fifty
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The standard form of 210 million, 64 thousands, and fifty is 210,064,050. This is found by adding the values of each place: 210,000,000 for million, 64,000 for thousand, and 50 for the units.
The standard form of a number is a way of writing numbers that is commonly used in mathematics, especially in arithmetic and place value studies. To write the number 210 million, 64 thousands, and fifty in standard form, one combines these values considering their place values.
The value of 210 million is simply 210,000,000. The value of 64 thousands is 64,000, and the value of fifty is 50. When these are combined, we get:
210,000,000 (Two hundred and ten million)+ 64,000 (Sixty-four thousand)+ 50 (Fifty)Adding these together:
210,000,000 + 64,000 + 50 = 210,064,050
Therefore, the standard form of 210 million, 64 thousands, and fifty is 210,064,050.
21.12 subtracted by 12.2
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Complete the following proof. Given: 2x 11 = 15 Prove: x = 2
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Answer:
Hence, x = 2.
Step-by-step explanation:
Given : Given: 2x + 11 = 15 .
To find : Prove: x = 2.
Solution : We have given 2x + 11 = 15 .
On subtracting both sides by 11
2x = 15 - 11
2x = 4
On dividing both sides by 2
x = 2
Hence, x = 2.
Therefore, Hence, x = 2.
A rectangular rug is 12.5 feet long and 10 feet wide. The rug needs to be reduced by a factor of 1/5 to be placed near a door. What is the area of the reduced rug in square feet?
_______ft2
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Pamela wants to buy a suitcase whose dimensions are 1 1/2 times those of her 28 times 16 times 8 inch suitcase. How is the ratio of the volumes related to the ratio of corresponding dimensions? What is the ratio of the volumes?
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ok
volume=length times width times height
her current suitcase volume is 28*16*8=3584 cubic inches
her new one will have each dimention mulipled by 1 and 1/2 or 1.5
so
newV=(1.5*28)*(1.5*16)*(1.5*8)
newV=12096 cubic inches
ratio is 12096/3584=3.375=1.5*1.5*1.5
the ratio is new:old=3.375:1
Thus the required ratio is 3.375
Pamela wants to buy a suitcase whose dimensions are 1 1/2 times of her 28 times 16 times 8 inch suitcase.
What is the ratio of the volumes?
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
volume of former suitcase = 28 x 16 x 8
=3584 cubic inches
volume of latter suitcase
=1.5x28 x1.5x16 x1.5x8
=12096
ratio of volumes
= 12096/3584
=3.375
Thus the required ratio is 3.375 of volumes of suitcase.
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Which functions represent the arithmetic sequence 8, 1.5, –5, –11.5... ?
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Answer:
-6.5n+14.5 and 8,f(n+1)=f(n)-6.5
Step-by-step explanation:
When the r2 of a regression equation is very high, it indicates tha?