Answers
a. -4
Explanation
the average rate of change is given by:
[tex]\begin{gathered} rateofch=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ where \\ P1(x_1,y_1)\text{ is the start point} \\ P2(x_2,y_2)\text{ is the end point} \end{gathered}[/tex]then
Let
[tex]\begin{gathered} x_1=1 \\ f(x_1)=0 \end{gathered}[/tex]and
[tex]\begin{gathered} x_2=3 \\ f(x_2)=-8 \end{gathered}[/tex]hence
P1(1,0)
P2(3,-8)
now, replace in the formula
[tex]\begin{gathered} rateofch=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ \text{rate of change=}\frac{-8-0}{3-1}=\frac{-8}{2}=-4 \\ \text{rate of change=-}4 \end{gathered}[/tex]therefore, the answer is
a. -4
I hope th
Related Questions
Area of a cylinder: S = 2лr² + 2лrh; solve for h.
Answers
The given equation for the area of a cylinder is:
S = 2πr² + 2лrh
Subtract 2πr² from both sides
S - 2πr² = 2πr² - 2πr² + 2лrh
S - 2πr² = 2лrh
Divide both sides 2лr
[tex]\begin{gathered} \frac{S-2\pi r^2}{2\pi r}=\frac{2\pi rh}{2\pi r} \\ \\ h=\frac{S-2\pi r^{2}}{2\pi r} \end{gathered}[/tex]what is 7^3? Describe the strategy you used and explain why you used that approach
Answers
Given expression is
[tex]7^3[/tex]We can expand the given expression as follows.
[tex]7^3=7\times7\times7[/tex]Multiplying 7 and 7, we get
[tex]=49\times7[/tex]Multiplying 49 and 7, we get
[tex]=343[/tex]Hence 7^3 is 343.
We multiply the number twice by itself to find the cube of 7.
This strategy is easy and basic to find the cube of the number.
6(__+x)-8(-3+8x) = 30-58xfill in the blank
Answers
In this expression, we have the same value on the left side is equal to the same amount on the right side.
So, let's start operating it to simplify it
6(_+x) -8(-3+8x)=30-58x
6(_+x)+24-64x=30-58x
6( ) +6x +24 -64x =30 -58x
6( ) -58x+24=30-58x
6( )-58x +58x=30-24
6( ) =14 DIviding both sides by six
( ) =7/3
Testing:
6(7/3 +x) -8(-3+8x)=30-58x
14+6x +24 -64x =30-58x
38
express 0.004 in scientific notation
Answers
We are asked to express 0.004 in scientific notation
The number 0.004 has the decimal point at the start, so we move this decimal point to the right until there is only one non-zero digit is left (4 in this case) and then count the number of times we moved.
[tex]0.0004=4\times10^{-3}[/tex]In this case, we moved 3 times so the exponent (power) is -3
The sign of exponent is negative when we move to the right (like in this case)
The sign of exponent is positive when we move to the left.
Find each probability of the events and place them in order
Answers
Considering Box A,
Total number of pens = 3 + 5 = 8 pens
Probability of picking a purple (P) and black (B) pen is given below as,
[tex]\begin{gathered} P(P)=\frac{3}{8} \\ P(B)=\frac{5}{8} \end{gathered}[/tex]Considering Box B,
Total number of pens = 15 + 5 = 20 pens
Probability of picking a purple and black pen is given below as,
[tex]\begin{gathered} P(P)=\frac{15}{20} \\ P(B)=\frac{5}{20} \end{gathered}[/tex]For event 1, probability of choosing a red (R) pen from Box B is zero because there is no red pen in the Box.
Event 1 P(R) = 0
For event 2, probability of choosing a purple or black pen from Box A is,
[tex]P(P\text{ or B)=}\frac{3}{8}+\frac{5}{8}=\frac{3+5}{8}=\frac{8}{8}=1[/tex]Event 2 P(P or B) = 1
For event 3, probability of choosing a purple pen from Box A is,
[tex]P(P)=\frac{3}{8}[/tex]Event 3 (P) = 3/8
For event 4, probability of choosing a black pen from Box B is given below as,
[tex]P(B)=\frac{5}{20}=\frac{1}{4}[/tex]Event 4 P(B) = 1/4
Arranging each events from the least likely to the most likely is in the order below
[tex]\text{Event 1, Event 4, Event 3, Event 2}[/tex]Answer deduced above.
Yael used to have a square garage with 222 ft2 of floor space. She recently built an addition to it. The garage is still a square, but now it has 50% more floor space. What was the length of one side of the garage originally? What is the length of one side of the garage now
Answers
• The length of one side of the garage originally is approximately 14.9 ft
,• The length of one side of the garage now is approximately 18.3 ft
Explanation:Old garage = 222 sq. ft
New garage has 50% more floor space.
50% of 222 = 111
Therefore, the new garage is (222 + 111) sq. ft = 333 sq. ft
Since the garage is square,
one side of the old garage is:
[tex]\sqrt[]{222}=14.9\text{ ft}[/tex]One side of the new garage is:
[tex]\sqrt[]{333}=18.3\text{ ft}[/tex]Sailor SheftalSimilar Figures / Proportion (Level 1)Aug 02, 10:17:02 AM?Triangle EFG is similar to triangle HIJ. Find the measure of side HI. Round youranswer to the nearest tenth if necessary.G94425Submit AnswerAnswer:attempt 1 out of 2
Answers
If we have two similar triangles, that ratio of the corresponding sides are all the same. This means that:
[tex]\frac{GF}{JI}=\frac{EF}{HI}[/tex]Substituting the lengths, we get:
[tex]\begin{gathered} \frac{44}{9}=\frac{25}{HI} \\ HI=25\cdot\frac{9}{44}=5.1136\ldots\approx5.1 \end{gathered}[/tex]please answer quickly I'm just trying to confirm my answer
Answers
Given the following vector:
[tex]v=<-\sqrt{3},2\sqrt{3}>[/tex]The magnitude of the vector will be as follows:
[tex]||v||=\sqrt{(-\sqrt{3})^2+(2\sqrt{3})^2}=\sqrt{3+12}=\sqrt{15}[/tex]So, the answer will be option 2) ||v|| = √15
The length of a rectangle is 5 times its width if the perimeter is at most 96 cm what is the greatest possible value for the width
Answers
The value of the width in the rectangle is 8cm.
How to calculate the width?Based on the information, let the width be represented as w.
Let the width be represented as 5 × w = 5w
Perimeter = 96cm
Perimeter of a rectangle = 2(length + width)
Perimeter = 2(5w + w)
96 = 12w
Divide
w = 96/12
w = 8
The value of the width is 8cm.
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u= ak - b solve for a
Answers
To solve it for "a" is to isolate "a' in one side, by doing some algebraic operations.
U =ak -b
1) Let's rewrite it
-b+ak=u
2) Add b to both sides
-b +b +ak = u +b
ak = u+b
3) Divide both sides by k
[tex]\frac{ak}{k}=\frac{u+b}{k}[/tex]4) Finally, we have it for 'a':
[tex]a\text{ =}\frac{u}{k}\text{ + }\frac{b}{k}[/tex]Solve the following problems.a. After 6 points have been added to every score ina sample, the mean is found to be M=70 and thestandard deviation is s= 13. What were the valuesfor the mean and standard deviation for the originalsample?b. After every score in a sample is multiplied by 3, themean is found to be M=48 and the standard devia-tion is s=18. What were the values for the meanand standard deviation for the original sample?
Answers
Original mean = 64
standand deviation = 13
Explanations:Let the value of of the originalmean be X. If after 6 points have been added to every score in a sample, the mean is found to be M = 70, then;
X + 6 = 70
Subtract 6 from both sides
X + 6 - 6 = 70 - 6
X = 70 - 6
X = 64
Hence the mean of the original sample will be 64.
The standard deviation of the data will remain unchanged since the distance from the mean will remain the same no matter the change in mean. Therefore the standard deviation of the sample will be 13.
If V1 = (2,4) and V2 = (-1,5), then V1*V2is equal to which of the following? A. (-2,20) , B. 18 , C. 22 , D. (8,-5)
Answers
B. 18
Explanation
The dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number
it is given by.
[tex]\begin{gathered} u=(u_x,u_y) \\ v=(v_{_x},v_y) \\ u\cdot v=(u_xv_x+u_yv_y) \end{gathered}[/tex]so, we can find the dot product by multiplying the corresponding values in each vector and adding them together
Step 1
get the dot product
let
[tex]\begin{gathered} v_1=(2,4) \\ v_2=(-1,5) \end{gathered}[/tex]then
[tex]\begin{gathered} v_1\cdot v_2=(2\cdot-1)+(4\cdot5) \\ v_1\cdot v_2=-2+20 \\ v_1\cdot v_2=18 \end{gathered}[/tex]therefore, the answer is
B. 18
I hope this helps you
A bowl has 4 green marbles 3 red marbles and 2yellow marbles what is the probability that you are going to select a red marble and a yellow marble. You replace the marble before another marble is selected
Answers
ANSWER
2/27
EXPLANATION
There are a total of 9 marbles in the bowl. The probability of drawing a red marble is,
[tex]P(red)=\frac{\#red.marbles}{\#total.marbles}=\frac{3}{9}=\frac{1}{3}[/tex]Then you draw another marble, but you put the first back in the bowl, so the total number of marbles is the same. The probability of drawing a yellow marble is,
[tex]P(yellow)=\frac{\#yellow.marbles}{\#total.marbles}=\frac{2}{9}[/tex]The probability of drawing a red marble and a yellow marble is,
[tex]P(red.and.yellow)=P(red)\cdot P(yellow)=\frac{1}{3}\cdot\frac{2}{9}=\frac{2}{27}[/tex]determine the degree of the polynomial -56a^2y^3+23a^2y-29a+17
Answers
The degree a polynomial is determine by the highest highest power of variable in the equation.
However, for a multivariable polynomial, the degree is the highest sum of powers of different variables in any of the terms in the expression.
For this polynomial,
[tex]-56a^2y^3+23a^2y\text{ - 29a + 17}[/tex]The degree of polynomial is 5 at the term -56^2y^3 which has 2 and 3 exponent at variable a and y respectively.
An equilateral triangle is folded in half.IN60° 60°14 cm-4What is x, the height of the equilateral triangle?O 14V301407307
Answers
An equilateral triangle is a triangle that has the same length on all its three sides. Therefore, we can say that:
Since the triangle is folded in half, then we can say that:
From this, we can solve "x" using the Pythagorean Theorem.
[tex]c^2=a^{2^{}}+b^2[/tex]where "c" = hypotenuse and "a" and "b" can be either of the remaining sides.
[tex]\begin{gathered} 14^2=7^2+x^2 \\ 196=49+x^2 \\ 196-49=49+x^2-49 \\ 147=x^2 \\ \sqrt[]{147}=\sqrt[]{x^2} \\ 7\sqrt[]{3}=x \end{gathered}[/tex]Therefore, the height of our equilateral triangle is 7√3. This is found in the third option.
If $4,780 is deposited in an account that pays 1.25% interest compounded annually, how much interest is in the account at the end of 8 years? A $5,279.44 B $500.44 C$ 478.00 D $499.44
Answers
We can calculate the interest as the difference between the future and the present value of the investment:
[tex]I=FV-PV[/tex]The present value is $4780.
The annual interest rate is r=1.25/100=0.0125.
The number of years is 8, so n=8.
We can calculate the future value as:
[tex]\begin{gathered} FV=PV(1+r)^n \\ FV=4780\cdot(1+0.0125)^8 \\ FV=4780\cdot1.0125^8 \\ FV\approx4780\cdot1.1045 \\ FV\approx5279.44 \end{gathered}[/tex]Then, we can calculate the interest as:
[tex]I=FV-PV=5279.44-4780=499.44[/tex]Answer: D. $499.44
In a music class of 20 students, there are 12 who play the Guitar (G), 7 who play the piano (P) and 4 who do not play any of his instruments.A) Represent the situation using a Venn diagram.B) What is the probability that a randomly selected student will play guitar and piano?C) What is the probability that a randomly selected student will play one of these two instruments?D) What is the probability that a randomly selected student will not play the piano?
Answers
n(U) = 20
n(G) = 12
n(P) = 7
[tex]\text{ n(G u P)}^1=4[/tex]Let x represent students that play both instruments
n(PuG) = x
A. Venn diagram
B. What is the probability that a randomly selected student will play guitar and piano?
Firstly solve for x
12-x + x + 7-x + 4 = 20
23-x = 20
-x = 20 - 23
-x = -3
x = 3
Number of students that play guitar and piano = x = 3
Total students = 20
Probability that a randomly selected student will play guitar and piano = 3/20
C. What is the probability that a randomly selected student will play one of these two instruments?
[tex]\begin{gathered} \text{ = }\frac{12-x}{20}\text{ +}\frac{7-x}{20} \\ =\frac{12-3}{20}+\frac{7-3}{20} \\ =\frac{9}{20}+\frac{4}{20} \\ =\frac{13}{20} \end{gathered}[/tex]D. What is the probability that a randomly selected student will not play the piano?
Students who do not play piano are students that play guitar only and students who do not play any instrument
students that play guitar only = 12 -x = 12 -3 = 9 students
students who do not play any instrument = 4
Probability that a randomly selected student will not play the piano =
[tex]\frac{9}{20}+\frac{4}{20}\text{ = }\frac{13}{20}[/tex]
r-9<-25. on a graph bar
Answers
r-9<-25 is equal to solution: [tex]$\quad R < -16$[/tex], Interval Notation: [tex]$\quad(-\infty,-16)$[/tex]. The graph is shown in attachement.
R-9<-25
Add 9 to both sides
R-9+9<-25+9
Simplify
R<-16
A graph is simply an orderly representation of data. It aids us in comprehending the info. The numerical information gathered through observation is referred to as data.
Data is derived from the Latin term Datum, which meaning "anything supplied."
Data is collected continuously through observation when a research question is formulated. It is then organized, summarized, categorised, and graphically shown.
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1.) twenty-five and five hundred seventy-eight thousandths
2.) Six thousand one and one hundreadths
Answers
Answer:
Here are the numbers:
1) 25.578
2) 6,001.01
Which of the following expressions is equivalent to the one shown below?71377OA. 791OB. 720O C. 76O D. 75
Answers
Given
[tex]\frac{7^{13}}{7^7}[/tex]Find
Equivalent expression
Explanation
Here , we use laws of exponents
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]so ,
[tex]\begin{gathered} =\frac{7^{13}}{7^7} \\ \\ =7^{13-7} \\ \\ =7^6 \end{gathered}[/tex]Final Answer
Therefore , the correct option is C
For the following set of data, find the percentage of data within population standarddeviations of the mean, to the nearest percent.88, 92, 57, 62, 57, 56, 58, 57Copy Values for CalculatorOpen Statistics Calculator
Answers
Answer: 100 %
Explanation:
The first step is to rearrange the numbes in ascending order. It becomes
56, 57, 57, 57, 58, 62, 88, 92
The next step is to calculate the population μ, mean.
μ = sum of terms/number of terms
From the information given
n = number of terms = 8
μ = (56 + 57 + 57 + 57 + 58 + 62 + 88 + 92)/8 = 65.875
μ = 65.875
The formula for calculating the population standard deviation, σ is
σ = √[Σ(x - μ)^2]/n
Σ(x - μ)^2/n = [(56 - 65.875)^2 + (57 - 65.875)^2 + (57 - 65.875)^2 + (57 - 65.875)^2 + (58 - 65.875)^2 + (62 - 65.875)^2 + (88 - 65.875)^2 + (92 - 65.875)^2)]/8 = 197.859375
σ = √197.859375
σ = 14.1
2 population standard deviations to the left of the mean = 65.875 - 2(14.1) = 37.675
2 population standard deviations to the rig tof the mean = 685875 -+2(14.1) == 94.075
Number of terms between 37.675 and 94.075 = 8
Thus,
the percentage of data within 2 population standard deviations of the mean
= 8/8 x 100 = 100%
») A box has a length of 6 centimeters, a width of 4 centimeters, and a height of 5 centimeters. Jen filled the bottom layer of the box with 24 cubes. What is the volume of the box? 120 cubic centimeters 24 cubic centimeters 5 cm 4 cm 96 cubic centimeters 6 cm = 1 cubic centimeter 144 cubic centimeters
Answers
We can find the volume of the box by multiplying the length, width and heigth.
We can write this as:
[tex]V=l\cdot w\cdot h=(6\operatorname{cm})\cdot(4\operatorname{cm})\cdot(5\operatorname{cm})=(24\operatorname{cm})(5\operatorname{cm})=120\operatorname{cm}^3[/tex]The base layer is 24 cm^3 (24 cubes of 1 cm^3) because its the volume of width 4 cm and length 6 cm, with a height of 1 cm (the height of the cube).
If we multiply the number of cubes, 24 of 1 cm^3, by the real height, that is 5 times 1 cm, we get: 24 cm^3 * 5 = 120 cm^3.
Answer: the box has a volume of 120 cm^3
please finish this super fastWhat is the median travel time, in minutes? 21 24 29 36
Answers
Given:
Required:
We need to find the median.
Explanation:
Recall that the vertical line that split the box in two is the median.
The vertical line that split the box in two is the median at 24 minutes.
The median is 24.
Final answer:
The median is 24.
SIMPLIFIED Uplift Summer Algebra 1 Final Assessment - Copy12 of 2012 of 20 ItemsQuestionColton solves -30=6(x-1) by dividing both sides by 6 first. Kaylee solves the same equation by using the Distributive Property first on the right side of the equation. Who is correct?
Answers
The method use by both students are correct. Hence the right answer to the question is OPTION D
The length of two sides of a triangle are 5 inches and 8 inches. Which of the following lengths could be the length of the third side of the triangle?
Answers
there are 2 possible triangles that can arranged one being the 8 the longest side, and another one being the 5 and 8 the sides of the triangle
use the pythagorean theorem to solve.
for the black triangle.
[tex]\begin{gathered} a^2+b^2=c^2 \\ (8^2+5^2)=c^2 \\ (89)=c^2 \\ \sqrt[]{89}=c \\ c=9.43 \end{gathered}[/tex]for the green triangle.
[tex]\begin{gathered} a^2+b^2=c^2 \\ 5^2+b^2=8^2 \\ b^2=(8^2-5^2) \\ b^2=39 \\ b=\sqrt[]{39} \\ b=6.25 \end{gathered}[/tex]Please help me I don’t know how to do this
Answers
Translations
One point located at (x,y), translated to the point (h,k) has been applied the rule:
T(x,y) -> (h,k)
And the translation changed the coordinates by ( h-x, k-y).
The point (4,-9) is mapped to (9,-14). The change is:
(9 - 4, -14 - (-9 ) = (5 , -5)
The rule of translation is:
T(x,y) -> (x + 5 , y -5)
If we translated the point (-9,-8) under the same rule:
T(-9,-8) -> (-9 + 5 , -8 -5)
T(-9,-8) -> ( -4 , -13)
The image of the point (-9,-8) is ( -4 , -13)
15. WORK REQUIRED: Given : ZA = 2D and BA – ED. What congruent sides would allow us to use SAS to prove Triangle ABC is congruent to Triangle DEF? (write your answer in this form: WX=YZ with no spaces) NN TA Your answer This is a regulired question
Answers
Let's begin by listing out the information given to us:
Both triangles have Line BD equal
[tex]BD=BD[/tex]Line AB equals Line CD
[tex]AB=CD[/tex]Angle A equals Angle C
[tex]m\angle A=m\angle C[/tex]Hence, Triangle ABD is congruent to Triangle CDB
Rational and Irrational Numbers make up the____ system.
Answers
We have the following:
Therefore, the answer is real numbers
Find the vbalie If K, and then write an equation to describee the direct variation.
Answers
Given:
x = 9 and y = 6
Use the equation:
y = kx
Where y varies directly as x
K is the constant of proportionality.
Let's find the value of k:
[tex]\begin{gathered} y\text{ = kx} \\ \\ 6\text{ = 9k} \\ \\ \text{Divide both sides by 9:} \\ \frac{6}{9}=\frac{9k}{9} \\ \\ \frac{2}{3}=k \end{gathered}[/tex]k = ⅔
An equation to describe the direct variation is:
[tex]y\text{ = }\frac{2}{3}x[/tex]ANSWER:
[tex]undefined[/tex]Determine whether each sequence is arithmetic. If so, identify the common difference. -34, -28, -22, -16
Answers
Answer:
Question:
Determine whether each sequence is arithmetic. If so, identify the common difference. -34, -28, -22, -16
The numbers are given below as
[tex]-34,-28,-22,-16[/tex]Concept:
Define an arithmetic sequence
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
The general form of an arithmetic sequence is given below as
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ a_1=first\text{ }term \\ n=number\text{ of terms} \\ d=common\text{ difference} \end{gathered}[/tex]To check if they have a common difference, we will use the formulas below
[tex]\begin{gathered} d=a_2-a_1=-28-(-34)=-28+34=6 \\ d=a_3-a_2=-22-(-28)=-22+28=6 \\ d=a_4-a_3=-16-(-22)=-16+22=6 \end{gathered}[/tex]Hence,
Since the sequence has a common difference,
It is therefore an ARITHMETIC SEQUENCE
Their common difference is
[tex]\Rightarrow6[/tex]