Recall that
[tex]\text{spead}=\frac{\text{distance }}{\text{time}}[/tex][tex]\text{time}=\frac{dis\tan ce}{\text{speed}}[/tex]Substitute speed=3mph and distance =2mile, we get
Time taken by James to clime mountain is
[tex]=\frac{2}{3}\text{ hours}[/tex]Substitute speed=4mph and distance =2mile, we get
Time taken by James to run back is
[tex]=\frac{2}{4}=\frac{1}{2}\text{hours}[/tex][tex]\text{Total time is taken by James =}\frac{2}{3}+\frac{1}{2}=\frac{2\times2}{3\times2}+\frac{1\times3}{2\times3}=\frac{4+3}{6}=\frac{7}{6}=1.17\text{ hour}[/tex]Substitute speed=2mph and distance =2mile, we get
Time taken by Lucas to clime mountain is
[tex]=\frac{2}{2}=1\text{ hour}[/tex]Substitute speed=5mph and distance =2mile, we get
Time taken by Lucas to run back is
[tex]=\frac{2}{5}\text{ hours}[/tex][tex]\text{Total time taken by lucas =1+}\frac{2}{5}=\frac{5}{5}+\frac{2}{5}=\frac{7}{5}=1.4hours_{}[/tex]James takes 1.17 hours to finish the race and Lucas takes 1.4 hours to finish the race.
James is faster than Lucas.
Express the following in expone(-13) X ... X (-13).35 times
Answer
Explanation
We are asked to express this in expo
Find outside surface area and volume of the solid object assume that the base is regular
The solid object shown is the frustum of a square based pyramid..
To calculate the total surface area, we shall follow the procedure below;
[tex]\begin{gathered} \text{Total Surface Area}=TSA \\ \text{TSA}=\lbrack\frac{1}{2}(P_1+P_2)L\rbrack+B_1+B_2 \\ \text{Where the variables are;} \\ P_1=Perimeter\text{ of base 1} \\ P_2=\text{Perimeter of base 2} \\ L=Slant\text{ height} \\ B_1=\text{Area of base 1} \\ B_2=\text{Area of base 2} \end{gathered}[/tex]We shall now solve as follows;
[tex]\begin{gathered} P_1=2(l+w) \\ P_1=2(14+14) \\ P_1=2(28) \\ P_1=56in \end{gathered}[/tex][tex]\begin{gathered} P_2=2(l+w) \\ P_2=2(24+24) \\ P_2=2(48) \\ P_2=96in \end{gathered}[/tex][tex]\begin{gathered} B_1=l\times w \\ B_1=14\times14 \\ B_1=196in^2 \end{gathered}[/tex][tex]\begin{gathered} B_2=l\times w \\ B_2=24\times24 \\ B_2=576in^2 \end{gathered}[/tex]The total surface area would now be;
[tex]\begin{gathered} \text{TSA}=\lbrack\frac{1}{2}(P_1+P_2)L\rbrack+B_1+B_2 \\ \text{TSA}=\lbrack\frac{1}{2}(56+96)19\rbrack+196+576 \\ \text{TSA}=\lbrack\frac{1}{2}(152)19\rbrack+772 \\ \text{TSA}=\lbrack76\times19\rbrack+772 \\ \text{TSA}=1444+772 \\ \text{TSA}=2216in^2 \end{gathered}[/tex]The volume of a frustum of a square based pyramid is given as;
[tex]\begin{gathered} Vol=\frac{1}{3}h(B_1+B_2+\sqrt[]{B_1B_2}) \\ \text{Where;} \\ h=vertical\text{ height (altitude)} \end{gathered}[/tex]The volume would now be;
[tex]\begin{gathered} \text{Vol}=\frac{1}{3}\times15(196+576+\sqrt[]{196\times576}) \\ \text{Vol}=5(772+\sqrt[]{112896}) \\ \text{Vol}=5(772+336) \\ \text{Vol}=5(1108) \\ \text{Vol}=5540in^3 \end{gathered}[/tex]ANSWER:
Therefore, we have
Total surface area = 2,216 inches squared
Volume = 5,540 inches cubed
you want to buy some noodles A 6 ounce package costs $1.92 A 16 ounce package costs $5.28 A 22 ounce package costs $6.82 which package is the best buy
Given that a 6 ounce package costs $1.92,
the cost per ounce is
= $1.92/6
= $0.32
If a 16 ounce package costs $5.28 ,
the cost per ounce will be
= $5.28/16
= $0.33
Given that aA 22 ounce package costs $6.82
i really need help pleaseThe floor plan of a school auditorium is shown. What is the area of the auditorium?
The area of the auditorium is given by:
Will be the area of the blue rectangle minus the area of the red triangles, so:
The area of the rectangle is:
[tex]\begin{gathered} Ar=w\cdot l \\ where\colon \\ w=32 \\ l=13+3=16 \\ Ar=512ft^2 \end{gathered}[/tex]The area of each triangle is:
[tex]\begin{gathered} At=\frac{b\cdot h}{2} \\ where\colon \\ b=\frac{32-20}{2}=6 \\ h=3 \\ so\colon \\ At=\frac{6\cdot3}{2} \\ At=\frac{18}{2} \\ At=9ft^2 \end{gathered}[/tex]Therefore, the area of the auditorium:
[tex]\begin{gathered} A=Ar-2At \\ A=512-2(9) \\ A=512-18 \\ A=494ft^2 \end{gathered}[/tex]List the sale price of the item. Round to two decimal places when necessary. Original price: $16.45; Markdown: 33%.*
On a number line, where would 3/10 be located? Choose all answers that makea true statement.A. To the right of 1/10B. In the same place as 6/10C. To the left of 8/10D. To the left of 2/10
Consider the number line drawn below
Statement A is correct since 3/10 is located to the right of 1/10.
Statement B is false because 6/10 is located to the right 3/10.
Statement C is correct because 3/10 is placed to the left of 8/10.
Statement D is false because 2/10 is located to the right of 3/10.
Answers: A and C
please help me work through this thank you! read the question carefully since it can be confusing
ANSWER
636,255 cubic centimeters
EXPLANATION
Given:
Thickness = 0.02 cm
Diameter = 45m = 4500cm
Recall, Volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]Determine change in V by differentiating the Volume:
[tex]\begin{gathered} \Delta V=dV=3\times\frac{4}{3}\pi r^{3-1}dr \\ dV=4\pi r^2dr \end{gathered}[/tex]Note: from the given question
dr = 0.02cm
r = 4500/2 = 2250 cm
Recall: for Hemisphere
[tex]\begin{gathered} dV=\frac{1}{2}\times4\pi r^2dr \\ dV=2\pi r^2dr \end{gathered}[/tex]Substitute the values:
[tex]\begin{gathered} dV=2\times3.142\times(2250)^2\times0.02 \\ dV=6.284\times5062500\times0.02 \\ dV=636255cm^3 \end{gathered}[/tex]Hence, the amount of paint needed is 636,255 cubic centimeters.
Given: JIKL is a quadrilateral with angle measures as shown.KDi120"60"Which is true about quadrilateral JIKL?Quadrilateral JIKL is a parallelogram.If mZK = 120, then Quadrilateral JIKL is a parallelogram.O if IK || JL, then quadrilateral JIKL is a parallelogram.O If IJ || KL, then quadrilateral JIKL is a parallelogram.
one of the coditions for a quadrilateral to be a patrallelogram is if and only if two paira of oppositw sied are parallel (by definition),the two pairs of opposite sides are equal in length. Two pairs of opposite angles are equal in measure.
so,
with all this said,
since IJ is parallel to KL, then the quadrilateral is a parallelogram
so the last option is correct
3. Select all the possible input-output pairs for the function y=x".a. (-1,-1)b. (-2,8)c. (3,9)d. (12,7%)e. (4,64)f. (1,-1)
Since the function is y = x, the valuse of x must be equal to the value of y.
Therefore, of the options the only on that complies with this is option a. (-1, -1)
y=hx+d Solve the equation for h.
h = ?
Solve for x
h = ( y - d)/x
Now cancel parenthesis
Then ANSWER IS
h = y/x - d/x
Write point or center in each blank to complete the definitions.
By definition:
- A circle is a round-shaped 2-dimensional figure that consists of a series of points located at the same distance from a point located in the middle of the circle called "Center".
- Therefore, the center of a circle is that point located in the middle of the circle.
- The radius of a circle is half its diameter. It is a segment that goes from the center of the circle to any point on the circumference of the circle.
Hence, the answers are:
1. Center.
2. Point.
3. Point.
Solve the system of equations: 3x + 4y = 33 y = 2 - 4 11 Fill in the coordinates of the ordered pair:(
The system of equations we have is:
[tex]\begin{gathered} \\ \mleft\{\begin{aligned}3x+4y=33 \\ y=x-4\end{aligned}\mright. \end{gathered}[/tex]To solve it, we need to have the variables of both equations on the same side.
Step 1: Substract x from both sides of the second equation
[tex]\begin{gathered} y-x=x-x-4 \\ y-x=-4 \\ -x+y=-4 \end{gathered}[/tex]And now the system is:
[tex]\{\begin{aligned}3x+4y=33 \\ -x+y=-4\end{aligned}[/tex]Step 2: We need to eliminate one variable to solve, for this reason now we multiply the second equation by 3
[tex]\begin{gathered} 3(-x+y=-4) \\ -3x+3y=-12 \end{gathered}[/tex]And we add this with the first equation of the system
[tex]\begin{gathered} 3x+4y=33 \\ -3x+3y=-12 \\ ----------- \\ 0x+7y=21 \end{gathered}[/tex]which is the same as:
[tex]7y=21[/tex]Step 3: solve this previous equation for y, by dividing both sides by 7
[tex]\begin{gathered} \frac{7y}{7}=\frac{21}{7} \\ y=3 \end{gathered}[/tex]Step 4: with the value for y, we find the value of x.
Substituting y=3 in the second equation of the original system of equations:
[tex]y=x-4[/tex][tex]3=x-4[/tex]We add 4 to both sides:
[tex]\begin{gathered} 3+4=x \\ 7=x \end{gathered}[/tex]Answer: y=3 and x=7, representing the result as an ordered pair: (7, 3)
The rectangular gate has diagonal braces. Find HK. H 33.3 in. G in.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
GK = 45 in
JL = 33.3 in
HK = ?
Step 02:
HK = 2*JL
= 2 * 33.3 in
= 66.6 in
The answer is:
HK = 66.6 in
In a class of 26 students, 17 have a brother and 12 have a sister. There are 5 students who do not have any siblings. What is the probability that a student has a brother given that they have a sister?
The number of students have a brother is 17.
The number of students have a sister is 12.
The number of students who donot have any siblings are 5.
The total students are 26.
Let there are x students who have both brother and sister. So number of students with only brother s (17 - x), number of students with sister only is (12 - x).
Determine the number of students have both brother and sister.
[tex]\begin{gathered} 17-x+12-x+x+5=26 \\ -x=26-17-12-5 \\ x=8 \end{gathered}[/tex]So probability for students with both brother and sister is,
[tex]P(\text{ Brother and sister)=}\frac{8}{26}[/tex]Probability for student have sister is,
[tex]P(\text{ sister)=}\frac{12}{26}[/tex]Determine the probability that a student has a brother given that they have a sister.
[tex]\begin{gathered} P\text{ (Brother and sister|sister)=}\frac{P\text{ (Brother and sister)}}{P\text{ (Sister)}} \\ =\frac{\frac{8}{26}}{\frac{12}{26}} \\ =\frac{8}{26}\cdot\frac{26}{12} \\ =\frac{8}{12} \\ =\frac{2}{3} \end{gathered}[/tex]Answer: 2/3
Llamar borrowed $8000 at a rate of 12%, compounded semi annually. Assuming he makes no payments, how much will he go after six years? Do not round any intermediate computations, and round your answer to the nearest cent.
$16097.57
Explanation:Amount borrowed = P = $8000
rate = r = 12% = 0.12
n = number of times compounded = semi-annually
n = 2
time = t = 6 years
Let the amount he owes after 6 years = FV
Using compound interest formula:
[tex]FV\text{ = P(1 +}\frac{r}{n})^{nt}[/tex][tex]\begin{gathered} FV\text{ = 8000(1 + }\frac{0.12}{2})^{2\times6} \\ FV\text{ = 8000(1 + }0.06)^{12} \\ FV\text{ = 8000(1}.06)^{12} \\ FV\text{ = 8000(}2.01219647184) \\ FV\text{ = }16097.5718 \end{gathered}[/tex]To the nearest cent, the amount owed is $16097.57
find all values of x that make 0.1x+ 0.25(102-x) <17.10.true
find all values of x that make 0.1x+ 0.25(102-x) <17.10.true
we have the expression
[tex]0.1x+0.25(102-x)\text{ < 17.10}[/tex]solve the expression for x
apply distributive property left side
0.1x+0.25*102-0.25x < 17.10
0.1x+25.5-0.25x < 17.10
combine like terms left side
-0.15x-25.5< 17.10
Adds 25
4. Write 1 quadratic equation that forms a graph through the points (-4, 0) and (1,0) and has a minimum value at the vertex.
ANSWER
[tex]x^2+\text{ 3x - 4 = 0}[/tex]EXPLANATION
We have that the graphs passes through the points (-4, 0) and (1, 0).
If you notice the value of y in the two points is 0. This means that those two points are the roots of the equation of the graph.
They lie on the x axis.
So, we can write that:
x = -4 and x = 1
=> x + 4 = 0 and x - 1 = 0
=> (x + 4)(x - 1) = 0
[tex]\begin{gathered} \Rightarrow x^2\text{ + 4x - x - 4 = 0} \\ x^2\text{ + 3x - 4 = 0} \end{gathered}[/tex]The fact that the equation has a minimum value at its vertex confirms that the coefficient of x^2 is positive.
Ethan's income is 4500 per month a list of some of his expenses appear below what percent of Ethan's expenses is utilities
Ethan expenses on utilities,
[tex]\begin{gathered} =\frac{160}{2300}\times100 \\ =6.96\text{ \%} \end{gathered}[/tex]so the answer is 6.96 %
Brian decides to mix grades of gasoline in his truck. He puts in7 gallons of regular and5 gallons of premium for a total cost of$45.14. If premium gasoline costs$0.22 more per gallon than regular, what was the price of each grade of gasoline?
In this problem we have two variables, so we need two equation to solve the system.
The first equation comes from the gasoline he puts in his truck so: (R mean the regular gasoline, and P means the premium gasoline)
[tex]7R+5P=45.14[/tex]And the secon equation comes from the value of a individual gallon:
[tex]P=R+0.22[/tex]Now to find the value of the regular gasoline we can replace the second equation into the first equation:
[tex]\begin{gathered} 7R+5(R+0.22)=45.14 \\ 7R+5R+1.1=45.14 \\ 12R=44.04 \\ R=\frac{44.04}{12} \\ R=3.67 \end{gathered}[/tex]Now with the value of R we can rplace that into the second equation:
[tex]\begin{gathered} P=3.67+0.22 \\ P=3.89 \end{gathered}[/tex]the graph of a function f(x) passes through the following points: (0, 0), (1, -2), (2, 0) which of the following could be f(x) f(x)= 2x^2-4x f(x)= -2x^2f(x)= -2x f(x)= 2 √x-4x
Recall that the x-intercepts of a graph are of the form:
[tex](x,0)\text{.}[/tex]Since the graph of f(x) passes through (0,0), (1, -2), and (2,0), then its x-intercepts are (0,0) and (2,0).
Therefore f(x) must be as follows:
[tex]\begin{gathered} f(x)=k(x-0)(x-2) \\ =kx(x-2)\text{.} \end{gathered}[/tex]Where k is a constant.
Since f(x) passes through (1,-2), then:
[tex]-2=f(1)\text{.}[/tex]Then:
[tex]-2=k\cdot1(1-2)\text{.}[/tex]Simplifying the above equation we get:
[tex]\begin{gathered} -2=k(-1), \\ -2=-k\text{.} \end{gathered}[/tex]Therefore:
[tex]k=2.[/tex]Therefore f(x) could be as follows:
[tex]\begin{gathered} f(x)=2x(x-2) \\ =2x^2-4x\text{.} \end{gathered}[/tex]Answer: First option.
11) Which object has a liquid volume that is best measured in milliliters?
Given that mililiters is used to measure little amount of liquids, the object that has a liquid volume that is best measured in mililiters is the bowl of soup
What is the correct answer to this question A 40B 44 C24D 52
Given:
The parallelogram PQRS is a square.
The length of PQ = 2x+8
Perimeter = 96
Required:
Find the length of the side PQ.
Explanation:
Given that perimeter = 96
[tex]\begin{gathered} 4(2x+8)=96 \\ 8x+32=96 \\ 8x=96-32 \\ 8x=64 \\ x=\frac{64}{8} \\ x=8 \end{gathered}[/tex]The value of x is 8.
The length of the side PQ
[tex]\begin{gathered} =2(8)+8 \\ =16+8 \\ =24 \end{gathered}[/tex]Final Answer:
Hey I need a tutor the lines across the other answer choice does not mean it is wrong it is glitched out and I can’t change it back please help thank you
Explanation
In order to answer the question, we will have to get the mode, median, and range of both stores
mode: The mode is the value that appears most frequently in a data set.
Range: The Range is the difference between the lowest and highest values.
median: The Median is the "middle" of a sorted list of numbers.
For store 1
[tex]\begin{gathered} mode:2 \\ range=\text{ 6- 0=6} \\ median\text{ =2} \end{gathered}[/tex]For store 2
[tex]\begin{gathered} mode:1 \\ range=6-0=6 \\ median=\frac{1+2}{2}=1.5 \end{gathered}[/tex]The mode of store 1 is greater than store 2: TRUE
The range of store 1 is greater than store 2: FALSE
The range of store 1 and store 2 is the same: TRUE
The median of data store 2 is greater than data store 1: FALSE
Please helppp!!!!!sasha is mailing her friend a poster.she has a box that measures 13 inches by 6 inches by 4 inches. what is the maximum length in whole inches , the poster can be to still fit in the box
Step 1: Measures of the box:
13 inches by 6 inches by 4 inches
Step 2: The maximum length of the poster should be the maximum length of one of the sides of the box
Therefore, as you can see, ariiwiddagloxcc, the maximum lenght is 13 inches
Unit 1: Lesson 1 - 5 Homework1. Select all the statistical questions.A What is the typical amount of rainfall for the month of June in the GalapagosIslands?B. How much did it rain yesterday at the Mexico City International Airport?C. Why do you like to listen to music?D How many songs does the class usually listen to each day?E How many songs did you listen to today?F. What is the capital of Canada?G. How long does it typically take for 2nd graders to walk a lap around the track?
EXPLANATION :
From the problem, we need to select statistical questions.
Statistical questions are answered by the collection of data and there is always variability in the data.
It means that the answer must NOT have only one answer.
A. Typical amount of rainfall for the month of June, you are estimating the amount of rainfall which has many data to consider.
YES.
B. Amount of rain yesterday, since we are talking about yesterday, there's only one answer.
NO.
C. Reason why you like to listen to music. It is not answered by the data.
NO.
D. Number of songs usually the class listens to each day, we will have different answers here from day to day.
YES.
E. Number of songs did you listen to today, we are talking about today and it will have one answer only.
NO.
F. Capital of Canada, there's only one answer and it will not vary.
NO.
G. How long does it typically take for 2nd graders to walk around the track, we will have data for this since there are different rates for each 2nd grader.
YES.
ANSWER :
The statistical questions are A, D, and G
A boat can travel 357 miles on 119 gallons ofgas, How much gasoline will it need to go 450 miles?
Answer:
It will need 150 gallons of gasoline to go 450 miles
Explanation:
Given that a boat can travel 357 miles on 119 gallons of gas
This means
357 miles = 119 gallons
Let us determine how much gasoline is needed for only one mile by dividing 119 by 357
1 mile = 119/357 gallons
= 1/3 gallons.
To know how much gasaoline it will need to go 450 miles, we multiply 450 by 1/3
450 miles = 450 * 1/3 gallons
= 150 gallons
11.) f(x) = 2 |x + 2| + 8 Transformation 1: Transformation 2: Transformation 3: 13.) f(x) = -|x |- 5 Transformation 1: Transformation 2:
f(x) = 2 (x + 2)^2 + 8
Transformation 1: If we start with y = x^2 and replace x by x + 2, it has the effect of shifting the graph 2 units to the left.
Transformation 2: Then if we multiply the right side by 2, it turns the parabola upside down and gives a vertical expansion by a factor of 2.
Transformation 3: Finally, if we add 8 to the right side, it shifts the graph to 8 units up.
0 to 1, or Never to AlwaysFor each probability given below, think up two situations that havethat probability.In one of those two situations, the probability should be based on atheoretical model. In the other situation, the probability should bebased on observed results. Be imaginative!1. Probability = 02. Probability = 13. Probability = 75%4. Probability = 15. Probability = 2.36. Probability = .01
The probability or likelihood of an event happening or not is usually based on a percentage expressed as 1.0 for "DEFINITELY GOING TO HAPPEN" and 0 for "DEFINITELY CANNOT HAPPEN" and then some in between measuring from 0.1 to 0.9
[tex]undefined[/tex]the cost to rent a car is $45 per day plus $0.22 per mile which is the constant value in this situation?
The cost per miles is $0.22 it depends on the number of miles, then it is not constant
But $45 is a fixed amount every day
So it is a constant value
The constant value is $45
The sum of two numbers is 60. The larger number is 6 more than the smaller number. What are the numbers.Larger number:Smaller numbers:
Let the smaller number be 'x' and the larger number be 'y'.
Given that the sum of the numbers is 60,
[tex]\begin{gathered} x+y=60 \\ y=60-x \end{gathered}[/tex]Also, given that the larger number is 6 more than the smaller number,
[tex]y=x+6[/tex]Substitute the value,
[tex]x+6=60-x[/tex]Taking the variables and constants on either side,
[tex]\begin{gathered} x+x=60-6 \\ 2x=54 \end{gathered}[/tex]Divide both sides by 2,
[tex]\begin{gathered} \frac{2x}{2}=\frac{54}{2} \\ x=27 \end{gathered}[/tex]Substitute this value and obtain the other variable,
[tex]\begin{gathered} y=60-27 \\ y=33 \end{gathered}[/tex]Thus, the larger number is 33 and the smaller number is 27.