By definition, two vector are equivalent when they have the same length, and they point in the same direction. Any two or more vectors will be equal if they are collinear, codirected, and have the same magnitude.
Given f(x)= 1/x+6, find the average rate of change of f(x) on the interval [8,8+h]. Your answer will be an expression involving h
Function:
[tex]f(x)=\frac{1}{x+6}[/tex]Interval: [ 8, 8+h ]
Average rate of change:
[tex]A(x)=\frac{f(b)-f(a)}{b-a}[/tex]where a = 8 and b = 8 + h...
[tex]\begin{gathered} f(b)=\frac{1}{b+6} \\ f(8+h)=\frac{1}{8+h+6}=\frac{1}{h+14} \\ f(8+h)=\frac{1}{h+14} \end{gathered}[/tex][tex]\begin{gathered} f(a)=\frac{1}{a+6} \\ f(8)=\frac{1}{8+6}=\frac{1}{14} \end{gathered}[/tex]Then:
[tex]\begin{gathered} A(x)=\frac{\frac{1}{h+14}-\frac{1}{14}}{8+h-8}=\frac{\frac{1}{h+14}-\frac{1}{14}}{h}=-\frac{1}{14\cdot(h+14)} \\ A(x)=-\frac{1}{14h+196} \end{gathered}[/tex]A storage container is 3 feet long, 5 feet wide, and 6 feet tall. if the diameter of a baseball is about 1.43 inches, approximately how many basketballs fit in the container? ( volume of a sphere is V = 4/3pi^3)
First, let's find the volume of the storage container:
Vs = 3*5*6 = 90 ft³
Now, let's do a conversion:
1.43 in * 1ft/12in = 0.119 ft
The radius is the diameter divide by 2:
r = 0.119/2 = 0.059583 ft
Let's find the volume of the baseball:
V = 4/3 π r³ = 4/3 π (0.059583)³ = 0.000886 ft³
Now divide the volume of the storage container by the volume of the baseball:
90/0.000886 ≈ 101573
Approximately 101573 balls fit in the container
2) A scuba diver descends to a location that is -12 1/3 m relative to sea level. He then descends another 8 1/4 M. What is the scuba divers final location relative to sea level.
NUMBERS ONLY
Answer:
-26 m
Step-by-step explanation:
you take away 8 1/4 from original
a bowling alley charges its customers an hourly rate to bowl plus shoe rental. The hourly rates are per Lane. a linear model of this situation contains the values (2,39) and (3, 56.25), where x represents the number of hours bowled on one lane, and why represents the total cost for bowling.
Answer:
[tex]\$17.25[/tex]Explanation: We have to find the hourly rate to bowl, provided the following information:
[tex]\begin{gathered} (x_1,y_1)=(2,39) \\ (x_2,y_2)=(3,56.25) \end{gathered}[/tex]Where x is the number of hours and y is the total cost.
[tex]\begin{gathered} y(x)=mx \\ m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{56.25-39}{3-2} \\ m=\frac{56.25-39}{3-2}=\frac{\$17.25}{1hr} \\ m=\frac{\operatorname{\$}\times17.25}{1hr} \\ \therefore\rightarrow \\ y(x)=17.25x \end{gathered}[/tex]Therefore it costs $17.25 for an hour to bowl.
Convert the Cartesian equation x^2 + y^2 + 3y = 0 to a polar equation.r^2 = -3 sin θr = √3 sin θr = -3 sin θ
SOLUTION
From the question
[tex]x^2+y^2+3y=0[/tex]This becomes
[tex](x^2+y^2)+3y=0[/tex]In polar,
[tex]\begin{gathered} x^2+y^2=r^2 \\ \\ \text{and } \\ \\ y=r\sin \theta \end{gathered}[/tex]So, this becomes
[tex]\begin{gathered} r^2+3r\sin \theta=0 \\ \\ \frac{r^2}{r}=\frac{-3r\sin \theta}{r} \\ \\ r=-3\sin \theta \end{gathered}[/tex]a laptop has listed of a price of 548.98 before tax. If the sales tax rate is 8.75%, find the total cost of the laptop with sales taxes included round to nearest cent
we have to add to the original price the tax part. So we get
[tex]548.98+548.98\cdot0.0875=597.01575\approx597.02[/tex]If a population isa sample of the population could be
REQUIRED;
To identify which of the statements given properly depicts the population and the sample.
Explanation:
In statistics and research processes, a population ideally refers to the entire group that we want to study and reach conclusions about. It can best be described as all-inclusive.
On the other hand, a sample is a portion taken out of an entire population for the purpose of studies or research and the appropriate data is collected from these.
We shall now examine the options given one after the other.
(A) Registered state voters randomly collected for a poll; all citizens of the state. This represents SAMPLE and POPULATION
(B) All professional football players; all professional athletes. This represents POPULATION and POPULATION
(C) All customers at a shopping mall; people who purchased shoes. This represents POPULATION and SAMPLE.
(D) Passengers with window seats; all passengers on an airplane. This represents SAMPLE and POPULATION.
ANSWER:
Therefore, the correct answer is OPTION C.
"If a population is all customers at a shopping mall, a sample of the population could be peole who purchased shoes.
Which lists all of the x-intercepts of the graphed function? A. (0,6)B. (1,0) and (2,0)C. (1,0), (2, 0), and (-3,0)D. (1,0), (2,0), (-3, 0), and (0, 6)
From the graph, the points at which the curve touch the x-axis is the intercepts on x
looking at the graph, the curve cut through the x axis at points -3, 1 and 2
hence the points will be
(-3, 0), (1, 0) and (2, 0)
Thus, the correct option is C;
(1, 0), (2, 0) and (-3, 0)
Triangle JKL is rotated 270° counterclockwise about the origin to form triangle J'K'L'. What is the y-coordinate of point J'? y 6 5 4 K 3 2. 1 -6 -5 -4 -3 -2 1 2 3 4 0 -1 6 Jo -2 3 4 -5 L -6 Type the answer in the box.
Rotation of 270° ,counterclockwise
Find center point of triangle
JK = √ 9^2 +5^2
. = √ 106
JL = √9^2 + 3^2
. = √90
KL = 8
Then now find point J'
Distance from J to origin = JO = √4^2+2^2 =√20
Angle is arctan (2/4) = 26.56°
Then new coordinates J' are
Angle 270+26.56 = 296.56°
From origin trace a line perpendicular to JO
then
y = √20• Cos 26°
y = 4
Answer:
-4
Step-by-step explanation:
good luck kiddos :)
any letters or words in your answer! Ciera works at a day care center. Her job is to make sure there are always enough adult workers. Last month, there were 7 adults for 56 children, which is the minimum ratio allowed under state law. This month, 74 children are expected to enroll. How many adults will there need to be at the center? Your answer
10 adults
Explanation
Step 1
find the unit rate
[tex]\text{unit rate=}\frac{Number\text{ of Children}}{\text{Number of adults}}[/tex]Let
number of children=56
number of adults=7
replace,
[tex]\begin{gathered} \text{unit rate=}\frac{Number\text{ of Children}}{\text{Number of adults}}= \\ \text{unit rate=}\frac{56\text{ Children}}{7\text{ adults}} \\ \text{unit rate= 8 Children per adult} \end{gathered}[/tex]Step 2
Let x represents the adults needed for 74 children
find the unit rate:
[tex]\begin{gathered} \text{unit rate=}\frac{Number\text{ of Children}}{\text{Number of adults}} \\ \text{unit rate=}\frac{74}{x} \end{gathered}[/tex]as the unit rate must be the same
[tex]\begin{gathered} 8\frac{Children}{\text{adult}}=\frac{74}{x} \\ 8=\frac{74}{x} \\ cross\text{ multiply} \\ 8x=74\cdot1 \\ 8x=74 \\ \text{divide both sides by 8} \\ \frac{8x}{8}=\frac{74}{8} \\ x=9.25 \\ \text{hence, we n}eed\text{ 10 adults at the center} \end{gathered}[/tex]Write an inequality to match the statement.The difference of a number x and 7 is less than or equal to the sum of the same number x and 5
The difference of a number x and 7 is less than or equal to the sum of the same number x and 5
The difference means subtraction.
A number is x
Less than or equal is represented with the symbol ≤
So:
The difference of a number x and 7
x-7
is less than or equal to the sum of the same number x and 5
≤ x+5
Altogether:
x-7≤ x+5
Is the ordered pair (3,-4) a solution to : 5x-2y=17
Given
[tex]5x-2y=17[/tex]Set x=3 and solve for y, as shown below
[tex]\begin{gathered} x=3 \\ \Rightarrow5*3-2y=17 \\ \Rightarrow15-2y=17 \\ \Rightarrow-2y=2 \\ \Rightarrow y=-1 \end{gathered}[/tex]Therefore, a solution to the equation is the ordered pair (3,-1).
(3,-4) cannot be a solution to the equation.the hikers received more fruit then they brought on the hike?
When the fruit in question was shared. They each got 14/4 = 3 and half ( 3.5 )
Those who brought less than 3 and half are those who we need to find
Baxter brought 3, Hendrick = 2, Mary = 4, Kendra = 5.
So those who brought less than they got ( 3 and half ) are Baxter and Hendrick
divide 406 by -14 A) -29B) -34C) 34D) 44
The correct answer is -29 (option A)
find the volume for the spear shown to The Right. Use 3.14 for pi sphere is 5.8
Semicircle perimeter is 5.8 m
THEN
2π • R + 2R = 5.8
R = 5.8/(2π + 2) = 0.7 meters
Now find Volume
Volume V = (4/3)•π•R^3
V= (4/3)•π•(0.7^3) = 1.438 cubic meters
V=. 1.438 m^3
determine whether the triangle with the given side lengths is a right triangle4 ,7, 11
For the a triangle to be a right angle triangle, the length of the three sides must form a pythagorean triple. This means that if we apply pythagoras theorem, the square of the length of the longest side must equal the sum of the squares of the length of the other sides. This means that
11^2 must be equal to 4^2 + 7^2
11^ = 121
4^2 + 7^2 = 16 + 49 = 65
Since they are not equal, then the triangle with the given sides, 4, 7, 11 cannot form a right angle triangle.
What is the missing step in this proof?A.Statement: 24 25, and 21 23.Reason: Alternate Interior Angles TheoremB.Statement: DÈ is parallel to AC.Reason: AB is a transversal cutting De and AC.C.Statement: 2124, and 23 25.Reason: Alternate Interior Angles TheoremD.Statement: 2124, and 23 25.Reason: 21 and 24, and 23 and 25 are pairs of supplementary angles.
Answer
Option C is correct.
Explanation
The alternate interior angles theorem explains that when two parallel lines are cut by a transversal, the alternate interior angles are congruent.
Hope this Helps!!!
Which expression is a factor of 9r2 – 4r + 1? F3r-1 Gr 1 H 9741 3 There are no real factors.
There are no real factors
Here, we want to factorize the given expression
To check if there are real factors, we will need to get the determinant
mathematically, we have this as;
[tex]D=b^2-4ac[/tex]where a is 9, b is -4 and c is 1
Substituting these values;
[tex]D=(-4)^2-4(9)(1)\text{ = 16-36 = -20}[/tex]As we can see, the value of the determinant is negative
Whenever the determinant value is negative, there are no real roots
17) Determine if the number is rational (R) or irrational (I)
Given the number:
[tex]71.\bar{5186}[/tex]You can identify that there is a line about the first four decimal digits. That indicates that is a Repeating Decimal or Recurring Decimals.
Repeating Decimals are defined as those numbers whose decimal part becomes periodic.
By definition, Rational Numbers are those numbers that can be written as a simple fraction whose numerator and denominator are both integers.
By definition, Repeating Decimals are Rational Numbers.
Hence, the answer is: It is a Rational Number.
N5 pointsSketch the graph of the piecewise function below. Make sure your graph is cle-4,4% -3f(x) = -x + 3, - 3 341 Dra5
We are asked to plot the piecewise function given by:
SO we notice two points where the function graph is going to change:
x = -3 , and x = 3
We plot it in pieces :
Notice the endpoints of the different segments as "solid dots" or "empty dots" depending on the retrictions of the domain as given in the instructions.
1Convert without rounding:8into a decimal (no need to show work)Τ Τ Τ ΤParagraphVArialV3 (12pt)V
Given: the fraction 1/8.
Objective is to convert this fraction in to decimal.
[tex]\frac{1}{8}=0.125[/tex]Answer: 0.125
PLS HELP DUE TODAY!Find the mean, median, mode, and range of each set of data round answers to the nearest hundredth 0,3,2,1,7,4,3,2,1,1,1,0,2,3,0,2,6,2Second question:Find the mean, median, mode, and range of each set of data round answers to the nearest hundredth 3,2,2,1,0,0,5,3,1,0,1,0,2,6,3,2,3
To answer this question, we (first) need to order the data from the least to the greatest element of this set:
[tex]l=\mleft\lbrace0,3,2,1,7,4,3,2,1,1,1,0,2,3,0,2,6,2\mright\rbrace[/tex]If we order in that mentioned way, we have (this is done, mostly to find the median):
[tex]l=\mleft\lbrace0,0,0,1,1,1,1,2,2,2,2,2,3,3,3,4,6,7\mright\rbrace[/tex]MedianTo find the median of this data, we need to find the value for which 50% of the data are below this value, and above this value - it is a central value. We have 18 elements:
0,0,0,1,1,1,1,2,2,2,2,2,3,3,3,4,6,7
Since we have an even number of elements, we need to find the "average" of both central numbers:
[tex]Median=\frac{2+2}{2}\Rightarrow Median=2[/tex]Therefore, the median is equal to 2.
ModeThe mode is the element that is more founded into the set of numbers. In this case, if we look carefully at the data, we have that this value is 2 because we have 5 cases in which 2 appears in that set of data.
MeanTo find the mean, we need to sum each of the elements in the set of data, and then divide that result by the number of data - in this case, we have 18 elements. Then, we have:
[tex]Mean=\frac{(0+0+_{}0+1+1+1+1+2+2+2+2+2+3+3+3+4+6+7)}{18}[/tex][tex]\text{Mean}=\frac{40}{18}\Rightarrow Mean=2.22222222222\ldots[/tex]If we round the mean to the nearest hundredth, we have that the mean = 2.22.
RangeThe range is the difference between the maximum value and minimum value of the set of data, and we have:
Minimum = 0
Maximum = 7
Therefore, the range is equal to R = (7 - 0) ---> Range = 7.
In summary, for this set of data, we have that:
• Mean = 2.22 (rounded to the nearest hundredth)
,• Median = 2 (2.00 rounded to the nearest hundredth)
,• Mode = 2 (2.00 rounded to the nearest hundredth)
,• Range = 7 (7.00 rounded to the nearest hundredth)
What are the new coordinates of the point (-2,1) after undergoing the transformation?
Given the following rule of a transformation:
[tex]P(x,y)\rightarrow P^{\prime}(x+2,2y)[/tex]We will find the new coordinates of the point (-2,1) after undergoing the transformation.
[tex](-2,1)\rightarrow(-2+2,2(1)=(0,2)[/tex]So, the answer will be the last option (0, 2)
Find a standard deviation of the binomial for which N = 420 and P = 0.90. Answer choices 37.86.153786.2
The standard deviation σ is given by:
[tex]\begin{gathered} \sigma=\sqrt{np(1-p)} \\ \text{ Where} \\ p=\text{ the probability of success} \\ n=\text{ number of trials} \end{gathered}[/tex]Substitute n = 420 and p = 0.90 into the formula:
[tex]\sigma=\sqrt{420\cdot0.90(0.10)}\approx6.15[/tex]Hence the correct answer is 6.15
Second Choice
Eli and her sister are buying a present for their father. They want to buy him a tie that sings jingle bells. The Thai which is regularly $35 is on sale for 40% off because it is after the winter holidays. The girls will split the cost evenly and their mother gave them $15 to help with the cost of the tie. If the tax is 8%, how much will Eli and her sister each have to spend on their father's tie?
Answer:
Explanation:
The regular cost of the tie = $35
There is a sale for 40% off.
[tex]\text{Discount}=40\%\text{ of \$35}=\frac{40}{100}\times35=14[/tex]Thus, the price after the discount will be:
[tex]35-14=\$21[/tex]Next, the tax is 8%.
[tex]\text{Tax}=8\%\text{ of 21=}\frac{8}{100}\times21=\$1.68[/tex]Therefore, the total price at which the tie is purchased will be:
[tex]21+1.68=\$22.68[/tex]Since their mother gave them $15 to help with the cost of the tie, subtract 15.
[tex]22.68-15=\$7.68[/tex]This amount, $7.68 is the split between Eli and her sister.
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A floor tile is 2 feet wide. Convert the width to inches.
Solution
- The conversion from feet to inches is given below:
[tex]1ft\to12inches[/tex]- We are told that the tile is 2ft wide. Thus, we can convert the width to inches using the above conversion as follows:
[tex]\begin{gathered} \frac{12\text{ in}}{1\text{ ft}}=\frac{x\text{ in}}{2\text{ ft}} \\ \\ \text{ Multiply both sides by 2} \\ x=\frac{12\times2}{1} \\ \\ \therefore x=24inches \end{gathered}[/tex]Final Answer
The answer is 24 inches
Coordinate R (1,5) S (6,-1) and T (1,-4) are connected to form ∆ RST if ∆ RST is congruent to ∆ RWT what are the coordinates of W
The triangles are similar, then ratio of corresponding sides of triangle are equal. The ratio of corresponding sides of two triangle RST and triangle RWT is,
[tex]\begin{gathered} \frac{RS}{RW}=\frac{RT}{RT} \\ \frac{RS}{RW}=1 \\ RS=RW \end{gathered}[/tex]Determine the length of side RS.
[tex]\begin{gathered} RS=\sqrt[]{(1-6)^2+(5+1)^2} \\ =\sqrt[]{25+36} \\ =\sqrt[]{61} \end{gathered}[/tex]So the distance between point RW is also equal to square root 61.
For option (-4,2),
[tex]\begin{gathered} RW=\sqrt[]{(-4-1)^2+(5-2)} \\ =\sqrt[]{25+9} \\ =\sqrt[]{36} \end{gathered}[/tex]For o(-6,-1),
[tex]\begin{gathered} RW=\sqrt[]{(-6-1)^2+(5+1)^2} \\ =\sqrt[]{49+36} \\ =\sqrt[]{85} \end{gathered}[/tex]For (-4,-1),
[tex]\begin{gathered} RW=\sqrt[]{(1+4)^2+(5+1)^2} \\ =\sqrt[]{25+36} \\ =\sqrt[]{61} \end{gathered}[/tex]So coordinate of point W is (-4,-1) as it give same distance of RS and RW.
Answer: (-4,-1)
Solve the quadratic equation by completing the square.4a²- 48a +52 = 0a= _,_
Given
[tex]4a^2-48a+52=0[/tex]Solution
[tex]\begin{gathered} 4a^2-48a+52=0 \\ So\text{ divide both sides by 4} \\ \frac{4a^2}{4}-\frac{48a}{4}+\frac{52}{4}=0 \\ which\text{ gives } \\ a^2-12a+13=0 \\ Keep\text{ a on LHS} \\ a^2-12a=-13 \\ Take\text{ the half of coefficient of a and square it} \\ (-\frac{12}{2})^2=36 \\ \\ rewrite\text{ as perfect square} \\ \\ (a-6)^2=-13+36 \\ (a-6)^2=23 \\ \end{gathered}[/tex][tex]\begin{gathered} a-6=\pm\sqrt{23} \\ a=6\pm\sqrt{23} \end{gathered}[/tex][tex]\begin{gathered} a=10.79583\text{ ,}a=1.20416 \\ or \\ a=6+\sqrt{23},\:a=6-\sqrt{23}\quad \\ \\ \end{gathered}[/tex]Keico is selling rattle tickets to raise money for the sancol band. The odds againet winning a prize in the raffleare 121. What is the probability of winning a prize? Express your anewer as a decimal. if necessary, round youranower to the nearest thousandth.0 130 0.923O 0.083O 0.0777
Given:
The odds against winning a prize in the raffle are 12:1
[tex]\begin{gathered} \text{Probability of winning a prize=}\frac{1}{13} \\ \text{Probability of winning a prize=}0.077 \end{gathered}[/tex]0.077 is the probability of winning a prize.
Mixture of 40 liters of paint is 25% red tint, 30% yellow tint and 45% water. Five liters of red tint and five liters of yellow tint are added to the original mixture. What is the percent of water in this new mixture?
Step 1
25% of 40 litres is;
[tex]\frac{25}{100}\times40=10\text{ litres of red tint}[/tex]Step 2
30% of 40 litres;
[tex]\frac{30}{100}\times40=\text{ 12 litres of yellow tint}[/tex]Step 3
45% of 40 litres;
[tex]\frac{45}{100}\times40=18\text{ litres}[/tex]Step 4
5 liters of red tint are added and 5 liters of yellow tint are added to the original mixtures
[tex]\begin{gathered} 10\text{ +5=15 litres of red tint} \\ 12+5=17\text{ liters of yellow tint} \\ 18\text{ liters of water} \end{gathered}[/tex]Answer; What is the percent of water in this new mixture?
[tex]\begin{gathered} Total=15+17+18=50\text{ liters} \\ \frac{18}{50}\times100=36\text{\%} \end{gathered}[/tex]