Answer:
5kg
Step-by-step explanation:
Step 1.
Write in y=mx+c format
m= $/kg
c=flat fee
x=additional kilograms
FedEx:
y=2x+15
USPS:
y=5x
Step 2.
Keep Changing the x value (the no. of kilograms) in both equations until y is the same number
y=5×5
=25
y=2×5+15
=25
∴It would cost the same for both options at 5kg
Answer:
5kg
Step-by-step explanation:
Step 1.
Write in y=mx+c format
m= $/kg
c=flat fee
x=additional kilograms
FedEx:
y=2x+15
USPS:
y=5x
Step 2.
Keep Changing the x value (the no. of kilograms) in both equations until y is the same number
y=5×5
=25
y=2×5+15
=25
∴It would cost the same for both options at 5kg
yes or no? please help! :(
Answer:
Yes it can.
Step-by-step explanation:
We plot the data given on the graph and see whether there is any correlation.
The data is graphed in the figure attached. Looking at the graph we see that the points do seem to lie on a straight line which I have drawn as a dashed line.
The dashed line represents the function
[tex]f(x)=-2x+40[/tex]
The function tells us that as Khaled gives more homework to his students, less students complete their homework.
4/6 times what equals 1/6
Answer:
Although our example says the correct answer is 2/3 x 1/2, remember, with multiplying ... If we divide both 525 and 700 by 175, we can see that 525/700 is equal to 3/4.
Step-by-step explanation:
Final answer:
To solve '4/6 times what equals 1/6', you need to find the reciprocal of 4/6 and multiply it by 1/6. The reciprocal of 4/6 is 6/4, and when you multiply this by 1/6, you get 1/4. Thus, 4/6 times 1/4 equals 1/6.
Explanation:
The question asks for the unknown value that when multiplied by 4/6 gives the result of 1/6. To find the unknown value, you would set up the equation:
[tex]\(\frac{4}{6} \times x = \frac{1}{6}\)[/tex]
To find the value of x, you can divide both sides of the equation by 4/6. In other words, you are looking for the reciprocal of 4/6 that, when multiplied by 1/6, gives 1. The reciprocal of 4/6 is 6/4. Thus, when you perform the division, you get:
[tex]\(x = \frac{1}{6} \times \frac{6}{4}\)[/tex]
To simplify, you multiply the numerators and the denominators:
[tex]\(x = \frac{1 \times 6}{6 \times 4}\)[/tex]
[tex]\(x = \frac{6}{24}\)[/tex]
Since 6 and 24 have a common factor of 6, you can simplify the fraction:
[tex]\(x = \frac{1}{4}\)[/tex]
Therefore, 4/6 times 1/4 equals 1/6.
Look this is very confusing plz explain
Answer:
Step-by-step explanation:
[tex](\sqrt[3]{2} )^{5}=(2^{\frac{1}{3}})^{5}=2^{\frac{1}{3}*5}=2^{\frac{5}{3}}[/tex]
What is the range of f(x) = 1/x?
Answer: f(x)=1x can have any number as an input except for zero.
Step-by-step explanation:
Domain is all the possible x-values that can be plugged in and range is all the possible y-values that can be outputs. f(x)=1x can have any number as an input except for zero.
what is the answer?
Answer:
when multiplying polynomials you want to times the coefficients but add the exponents
(-7a^4b^1c^3)(5a^1b^4c^2) (if there isn't an exponent then it is 1)
-7*5=-35
a^4*a^1=a^5
b^1*b^4=b^5
c^3*c^2=c^5
Your answer would be
-35a^5b^5c^5
Hope this helps ;)
A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment, and find the probability of the given event. (Enter your answer as a fraction.)
The sum of the numbers is at least 4.
The probability of the sum of the numbers rolled on two dice being at least 4 is 25/36.
Explanation:When rolling two dice, the total number of outcomes is 36 (each die has 6 possible outcomes). To find the probability of the sum being at least 4, we need to determine the number of favorable outcomes. The pairs that satisfy this condition are (1, 3), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6). Therefore, there are 25 favorable outcomes. So, the probability is 25/36.
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Could someone help me understand how to solve this?
Answer:
Amount in 4% account: $550
Step-by-step explanation:
Use simple interest formula [tex]I=P\cdot r\cdot t,[/tex] where
I = interest
P = principal
r = rate (as decimal)
t = time.
4% account:
[tex]P_1=x\\ \\r_1=0.04\\ \\t_1=1,[/tex]
then
[tex]I_1=x\cdot 0.04\cdot 1=0.04x[/tex]
5% account:
[tex]P_2=1,500-x\\ \\r_2=0.05\\ \\t_2=1,[/tex]
then
[tex]I_2=(1,500-x)\cdot 0.05\cdot 1=0.05(1,500-x)[/tex]
You have earned $69.50 in total, so
[tex]I_1+I_2=69.50\\ \\0.04x+0.05(1,500-x)=69.50\\ \\4x+5(1,500-x)=6,950\\ \\4x+7,500-5x=6,950\\ \\4x-5x=6,950-7,500\\ \\-x=-550\\ \\x=550\\ \\1,500-x=1,500-550=950[/tex]
Amount in 4% account: $550
Amount in 5% account: $950
A group of students rolled two number cubes 107 times and recorded a sum of seven 10 times. Find the experimental probability of rolling a sum of seven. Write your answer with a % sign without any spaces rounded to the nearest percent. x
Probability is the calculation of = (desired outcomes/total outcomes)
therefore,10/107).
Walter's steps and reasoning for solving an equation are shown below: Given: three halves times x plus ten equals forty Steps Reasons 1. three halves times x plus ten equals forty 1. Given 2. three halves times x plus ten minus ten equals forty minus ten 2. Addition Property of Equality 3. three halves times x equals thirty 3. Simplify 4. three halves times x times two thirds equals thirty times two thirds 4. Multiplication Property of Equality 5. x = 20 5. Simplify Choose which reason is incorrect. Reason 1 Reason 2 Reason 3 Reason 4
Answer:
From Walter's steps we have that Step2: Reason 2 is incorrect.
The correct reason is Subtraction property of equality (we are using this property only not addition property of equality )
Step-by-step explanation:
Given equation is three halves times x plus ten equals forty
It can be written as below
[tex]\frac{3}{2}x+10=40[/tex]
To solve the given equation :
Step1 Reason1 : [tex]\frac{3}{2}x+10=40[/tex]
Step2 Reason2: Subtracting 10 on both sides of the above equation we get
[tex]\frac{3}{2}x+10-10=40-10[/tex] which is Subtraction property of equality
Step3 Reason3: [tex]\frac{3}{2}x=30[/tex]
Step4 Reason4: Multiply the above equation into [tex]\frac{2}{3}[/tex] on both sides we get
[tex]\frac{3}{2}x\times \frac{2}{3}=30\times \frac{2}{3}[/tex]
which is the Multiplication Property of Equality
Step5 Reason5: Simplify the above equation we get
[tex]x= \frac{60}{3}[/tex]
Therefore x=20
From Walter's steps we have that Step2: Reason 2 is incorrect.
The correct reason is Subtraction property of equality (we are using this property only not addition property of equality )
Answer:
b
Step-by-step explanation:
How to solve y= -3/2 x and then I have to graph It
Answer:
See the explanation.Step-by-step explanation:
Here, an equation of straight line is given.
The equation is [tex]y = -\frac{3x}{2}[/tex].
If you put x = 0, in the above equation, you will get y = 0.
Hence, the equation passes through (0, 0).
Again if we put, x = 1 in the above equation, we will get y = - 1.5.
It means the equation also passes through (1, -1.5).
Joining these two points, you can graph the straight line.
The high school tennis team is selling tennis balls to raise $500 for new equipment.They sell the balls for $2 each.
4).How many cases of tennis balls does the tennis team have to sell in order to raise enough money for new equipment.
5).Write and solve the hidden questions you need to answer before finding the answer to exercise 4
There are 24 tennis case and 3 tennis balls in each
Please help me solve this.
Answer:
84 cases
Step-by-step explanation:
The amount of money need to be raised = $ 500
Selling price of each ball = $2
1 Tennis case = 3 balls.
Earnings = Selling Price of each ball x Number of balls sold
Quantity sold = Earnings / Selling Price of each ball
Quantity sold = $ 500 / $ 2 = 250 balls
Using direct proportions
1 case = 3 balls
? cases = 250 balls
No.cases = 250 balls / 3 balls = 83.333
Note: Minimum number of cases required are 83.3333 to earn $ 500; however, we can not sell 0.3333 number of cases, hence, we will sell atleast 84 cases.
The average value of a certain type of automobile was 14,220 in 1993 and depreciated to 9,780 in 1997.
Let y be the average value of the automobile in the year x, where x=0 represents 1993. Write and graph a linear equation that models the value of the automobile in terms of the year x.
The linear equation that models the value of the automobile in terms of the year x is y = -1,110 x + 14,220
Step-by-step explanation:
The average value of a certain type of automobile was 14,220 in 1993 and depreciated to 9,780 in 1997
y be the average value of the automobile in the year xx = 0 represents 1993We need to write and graph a linear equation that models the value of the automobile in terms of the year x
The form of the linear equation is y = mx + b, where b is the initial value (value y at x = 0), and m is the rate of change
∵ The average value the of automobile was 14,220 in 1993
∵ x = 0 represents 1993
∴ The point which represent the data is (0 , 14,220)
- b is the value of y at x = 0
∴ b = 14,220
∵ The average automobile was 9,780 in 1997
- To find x subtract 1993 from 1997
∵ 1997 - 1993 = 4
∴ x = 4
∴ The point which represent the data is (4 , 9,780)
∵ m = Δy/Δx
∴ [tex]m=\frac{9780-14220}{4-0}[/tex]
∴ m = -1,110
- Substitute the values of m and b in the form of the equation
∴ y = -1,110 x + 14,220
The linear equation that models the value of the automobile in terms of the year x is y = -1,110 x + 14,220
The graph is attached below
Each square unit represents 1000 in the graph
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A linear function is a function that changes at a constant rate.
The equation of the linear function is [tex]y = -1110x + 14220[/tex]
The given parameters are:
x = 0, y = 14220 ---- in 1993x = 4, y = 9780 ---- in 1997Start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
This gives
[tex]m = \frac{9780 - 14220}{4- 0}[/tex]
Simplify
[tex]m = \frac{-4440}{4}[/tex]
This gives
[tex]m = -1110[/tex]
The equation is then calculated as:
[tex]y = m(x -x_1) + y_1[/tex]
This gives
[tex]y = -1110(x -0) + 14220[/tex]
Expand
[tex]y = -1110x + 14220[/tex]
Hence, the equation of the linear relationship is [tex]y = -1110x + 14220[/tex]
See attachment for the graph
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George had 1 sheet of paper. He cuts it into 6 inches by 5 inches, and 3 inches by 6 inches. What were the dimension dimensions and total area of his original sheet of paper? Explain.
Answer:
The dimensions of the original sheet of paper are 8 inches by 6 inches.
The total area of the sheet of paper = 8 inches [tex]\times[/tex] 6 inches = 48 [tex]inches^{2}[/tex]
Step-by-step explanation:
i) the two parts of the sheet of paper are 6 inches by 5 inches and 3 inches by 6 inches.
ii) therefore we see that the both parts have a 6 inch side.
iii) therefore we can say that the width of the sheet of paper is = 6 inches
iv) therefore we can also say that the length of the sheet of paper = 3 + 5 inches = 8 inches.
v) therefore the dimensions of the original sheet of paper are 8 inches by 6 inches.
vi) therefore the total area of the sheet of paper = 8 inches [tex]\times[/tex] 6 inches
= 48 [tex]inches^{2}[/tex]
When constructing a graph that compares the land areas of the five largest countries, you choose to depict the five areas with squares of different
sizes. If the squares are drawn so that the areas are in proportion to the areas of the corresponding countries, is the resulting graph valid? Why or why
not?
The resulting graph is valid as it uses the concept of area scaling, where the area of each square accurately represents the relative land sizes of the different countries.
Explanation:Yes, the resulting graph is valid. This is because a proportional representation by different-sized squares aligns with the principle of area scaling. Area scaling is a mathematical concept where each length is scaled by a particular factor and the area will scale by the square of that factor. If the areas of the countries are correctly scaled to the squares, then the graph accurately represents the relative sizes of the land areas of the five largest countries.
For example, if country A is twice as big as country B, the square representing country A should have an area that is four times (2^2) the area of the square representing country B. Vice versa, if country C is half the size of country D, the square for country C should have an area that is a quarter of the square for country D. Therefore, through area scaling, each country will be proportionately represented on the graph.
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which value of the variable is the solution of the equation a+$5.92=$12.29? a=$5.37,$5.47,$6.37,$6.27
Answer:
Option a=$6.37 is correct
The value of the variable is the solution of the given equation is a=$6.37
Step-by-step explanation:
Given equation is a+$5.92=$12.29
To find the value of the variable is the solution of the given equation :
a+$5.92=$12.29
Subracting the above equation by $12.29 on both sides we get
a+$5.92-$12.29=$12.29-$12.29 ( Subtraction property of equality)
a-$6.37=0
Now add $6.37 on both sides we get
a-$6.37+$6.37=0+$6.37 ( Addition property of equality)
a-0=$6.37
Therefore a=$6.37
Therefore option a=$6.37 is correct
Answer:
3rd answer is correct, $6.37
Step-by-step explanation:
Rewrite m+3n=7 to solve for m
A patient is prescribed 450 mg of penicillin to be taken. The pharmacy has supply the solution that contains 750 mg of penicillin per 5.0 mL solutions how many milliliters of the solution should be given to the patient for each dose
Answer:
The pharmacy should give 3.0 mL solution to the patient
Step-by-step explanation:
Given,
750 mg of penicillin in 5 mL solutions
Hence, amount of penicillin in 1 mL of solution= [tex]\frac{750}{5}[/tex] = 150 mg/ mL
So, amount of solution for 450 mg of penicillin= [tex]\frac{450}{150}[/tex] = 3.0 mL
3x + 2y = A
5x + y = B
Eliminating the variable y from the system of equations results in -7x =
2B - A
A + 2B
A - 2B
Answer:
A - 2B
Step-by-step explanation:
3x + 2y = A
5x + y = B
The first equation has 2y. The second equation has y.
If you multiply the second equation by 2, it will have 2y.
Then you subtract teh second equation from the first equation.
2y - 2y = 0, so you eliminate the y variable.
********
3x + 2y = A
2(5x + y) = 2B
********
3x + 2y = A
10x + 2y = 2B
********
Subtract the second equation from the first equation.
3x + 2y - (10x + 2y) = A - 2B
3x - 10x + 2y - 2y = A - 2B
-7x = A - 2B
Answer: A - 2B
zoe and hannah share tips from the ratio 3:7 last week Hannah got £24
Final answer:
To determine Zoe's share from the 3:7 tip ratio when Hannah received £24, divide £24 by 7 to find the value of one part of the ratio, then multiply by 3 to find Zoe's share, resulting in £10.29.
Explanation:
When Zoe and Hannah share tips at a ratio of 3:7 and it is known that Hannah received £24, we can set up a proportion to find out how much Zoe received. Since Hannah's share of the tips corresponds to the 7 parts of the ratio, each part is worth £24 divided by 7 (which is Hannah's portion of the ratio). To find out Zoe's share, we multiply the value of each part by 3 (which is Zoe's portion of the ratio).
Calculate the value of one part of the ratio: £24 / 7 = £3.43 (rounded to two decimal places).
Calculate Zoe's share: £3.43 * 3 = £10.29 (rounded to two decimal places).
Therefore, Zoe's share of the tips would be £10.29.
An animal shelter spends $4.50 per day to care for each cat and $8.00 per day to care for each dog. Savannah noticed that the shelter spent $123.00 caring for cats and dogs on Tuesday. Savannah found a record showing that there were a total of 25 cats and dogs on Tuesday. How many cats were at the shelter on Tuesday
Answer: There were 22 cats and 3 dogs at the shelter on Tuesday.
Step-by-step explanation:
Let be "c" the number of cats at the shelter on Tuesday and "d" the number of dogs at the shelter on Tuesday.
Set up a System of equations:
[tex]\left \{ {{c+d=25} \atop {4.5c+8d=123}} \right.[/tex]
You can use the Elimination Method to solve the System of equations.
The steps are:
1. Multiply the first equation by -8.
2. Add the equations.
3. Solve for the variable "c".
Then:
[tex]\left \{ {{-8c-8d=-200} \atop {4.5c+8d=123}} \right.\\....................\\-3.5c=-23\\\\c=22[/tex]
4. Substitute the value of "c" into the first original equation.
5. Solve for the variable "d" in order to find its value.
Then, you get:
[tex]22+d=25\\\\d=25-22\\\\d=3[/tex]
Here’s another one thank u all for helping me. I really appreciate it!
Answer:
28.56
Step-by-step explanation:
Find the perimeter of the square:
4s
= 4×4
=16
Find the circumference of the circle and since it's half circle for both side it's going to be 1 circle:
3.14×d
= 3.14×4
=12.56
Add perimeter of square and circumference:
16+12.56
=28.56
It might help to think of this shape as a track for runners to run around, even though the scale is much too small for it.
The two semicircles on each end can be combined to form a full circle. This circle has radius r = 2, which is half of the diameter 4 (square's side length).
C = 2*pi*r
C = 2*pi*2
C = 4pi is the exact circumference
C = 4*3.14
C = 12.56 is the approximate circumference
This represents the distance around the curved portions of the track.
The straight portions are 4 each. We do not include the vertical sides as they are not on the outside, and the runners do not run along those vertical portions (they run around the curved parts instead). So we add on 4+4 = 8 to the previous value 12.56 to get 20.56 as our final answer.
Answer: Choice D) 20.56 cmThe equation d = rt relates distance, rate, and time. A turtle walked 400 feet
in 10 minutes. What was the turtle's speed?
Answer:
Step-by-step explanation:
d = rt....and just so you know, speed is the same as rate
since we are looking for r, I am gonna change the equation
d = rt......r = d / t
d = 400
t = 10
now sub
r = d / t
r = 400/10
r = 40 ft per minute <=====
Answer: 40 per minute
Step-by-step explanation:
On a dell river, a boat will pass the Colby drawbridge and then the wave drawbridge opening times.There are 60 minutes in a hour so use 60 as a common denominator. Then rename each opening time using another common denominator. Explain how you found your answer
45/60 and 10/60 because we know that the common denominator is 60 then 3/4 of an hour is 45mins then 1/6 of an hour is 10
By finding common denominators, we can express the boat drawbridge opening times in terms of a shared timeframe, such as every 60 minutes or 30 minutes. The common denominator is the smallest number that the opening times can be equally divided into.
Explanation:The question relates to the application of common denominators in the context of timekeeping. Without specific times for the opening of Colby and Wave drawbridge, I will give a hypothetical scenario as an example.
Let's say Colby drawbridge opens every 20 minutes and Wave drawbridge opens every 15 minutes. A common denominator of 20 and 15 is 60, as they both divide evenly into 60. So, you could rename the opening times in terms of 60 minutes: Colby drawbridge opens 3 times every 60 minutes (60/20) and Wave drawbridge opens 4 times every 60 minutes (60/15).
If we want to use another common denominator, you could use 30. Then Colby drawbridge opens 1.5 times every 30 minutes (30/20) and Wave drawbridge opens 2 times every 30 minutes (30/15).
The way to find common denominators involves looking for the smallest number that both of the numbers can divide equally into. In this case, 60 was an obvious choice since there are 60 minutes in an hour, but other common denominators like 30 can also be used.
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Find the sum of these polynomials.
(х2 +х+ 9) + (7х2 + 5) =
А. 7х2+x+ 14
7х2+x+4
оооо
Ос. 8х2 +х+4
OD. 8х2+x+ 14
SUBMIT
[tex]\text{The sum of given polynomials is } 8x^2+x+14[/tex]
Solution:
Given given expression to calculate is:
[tex](x^2+x+9) + (7x^2+5)[/tex]
We have to add both the polynomials
Addition of two polynomials involves combining like terms present in the two polynomials
We have to add like terms
Like terms means "the terms having same variable and same exponent"
And we have to add the constants
[tex]\rightarrow (x^2+x+9) + (7x^2+5)\\\\\text{Remove the parenthesis and simplify }\\\\\rightarrow x^2 + x + 9 + 7x^2 + 5\\\\\text{Combine the like terms }\\\\\rightarrow x^2 + 7x^2 + x + 9 + 5\\\\\text{Add the coefficients of like terms }\\\\\rightarrow 8x^2 + x + 9 + 5\\\\\text{Add the constants 9 and 5 }\\\\\rightarrow 8x^2 + x + 14[/tex]
Thus the polynomials are added
Solve each word problem using a system of equations. Use substitution or elimination.
1. One number added to three times another number is 24. Five times the first number added to
three times the other number is 36. Find the numbers.
Answer:
Step-by-step explanation:
x + 3y = 24.....multiply by -1
5x + 3y = 36
------------------
-x - 3y = -24 (result of multiplying by -1)
5x + 3y = 36
------------------add
4x = 12
x = 12/4
x = 3 <=======
x + 3y = 24
3 + 3y = 24
3y = 24 - 3
3y = 21
y = 21/3
y = 7 <========
Final answer:
To solve the system of equations for the given word problem, define two variables and set up two equations. Use the substitution or elimination method to find the solution. The numbers are 3 and 7, and this solution is confirmed by substituting the values back into the original equations.
Explanation:
To solve the given word problem using a system of equations, we can define two variables for the two numbers we are looking for. Let's call the first number x and the second number y. Now we can formulate two equations based on the information provided:
One number added to three times another number is 24: x + 3y = 24
Five times the first number added to three times the other number is 36: 5x + 3y = 36
We can choose substitution or elimination method to solve these simultaneous linear equations. To use the substitution method, we start by solving the first equation for x (x = 24 - 3y) and then substitute this expression into the second equation:
Solve for x in the first equation: x = 24 - 3y
Substitute x into the second equation: 5(24 - 3y) + 3y = 36
Expand and simplify: 120 - 15y + 3y = 36
Solve for y: -12y = -84
Divide by -12: y = 7
Substitute y back into x = 24 - 3y to find x: x = 24 - 3(7)
Calculate x: x = 3
So the two numbers are 3 and 7.
As a check, we can substitute these values back into the original equations to verify that they lead to identities:
3 + 3(7) = 24, which simplifies to 24 = 24
5(3) + 3(7) = 36, which simplifies to 36 = 36
This confirms our solution is correct.
WILL MARK THE CORRECT ANSWER BRAINLIEST!
Select all the correct answers:
Answer:
B, D
Step-by-step explanation:
Solve all equations:
A.
[tex]x-3x=-2x+4\\ \\-2x=-2x+4\\ \\0=4[/tex]
This is false equality, so this equation has no solutions.
B.
[tex]x-\dfrac{1}{3}(3x)=0\\ \\x-x=0\\ \\0=0[/tex]
This equality is true for all values of x, so this equation has infinitely many solutions.
C.
[tex]\dfrac{1}{3}x-3=4+2x\\ \\x-9=12+6x\\ \\x-6x=12+9\\ \\-5x=21\\ \\x=-\dfrac{21}{5}[/tex]
This equation has the unique solution.
D.
[tex]3x+2-\dfrac{1}{3}(3x)=2+2x\\ \\9x+6-3x=6+6x\\ \\6x+6=6+6x\\ \\0=0[/tex]
This equality is true for all values of x, so this equation has infinitely many solutions.
E.
[tex]x-\dfrac{1}{3}x+2=0\\ \\3x-x+6=0\\ \\2x=-6\\ \\x=-3[/tex]
This equation has the unique solution.
CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION???
A typical traffic signal is programmed on a timer so that it is red 50% of the time, green 42% of the time, and yellow 8% of the time. The bulbs for each color are LED and are designed to last 100,000 hours. How many years does each color light last? Give your answer in years and months (rounded to the nearest month). What is the problem asking? What do we know? How did you solve the problem? Explain your steps.
Please answer this question for me
Answer:
The complete answer is explained below.
Step-by-step explanation:
The problem is demanding to simply determine the number of years each color light would last.
We know the following information from the question:
As it is clear that a red light remains TURNED ON 50% of the time.Green remains TURNED ON 42% of the timeYellow remains TURNED ON 8% of the time.Also the bulbs for each color are LED and are designed to last 100,000 hours. So, each light does last 100,000 hours.
lets make conversions
As
[tex]1\:day\:=\:24\:hours[/tex]
[tex]1\:year\:=\:365\:days[/tex]
Dividing [tex]100,000[/tex] hours by [tex]24[/tex] hours would bring [tex]4166.67[/tex] days
Dividing [tex]4166.67[/tex] days by [tex]365[/tex] days would bring [tex]11.4[/tex] years, meaning 11 years and 4 months.
Keywords: light, conversion, day, hours
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10% commission. what is her commission on a house that she sold for $619,100? round your answer to the nearest cent, if necessary
Answer:
$681
Step-by-step explanation:
619.100 * 10% = 61.91
619.100 + 61.91 = 681.01
Rounding it down because it is not over 5. $681
Therefore your answer will be $681
Hope this helps!
How far did you drive if you drove 2 hours at 55 miles per hour and 3 hours at 60 miles per hour?
Answer:
290 miles.
Step-by-step explanation:
To answer this, first multiply the hours by miles. 2 hours at 55 miles per hour means a total of 110 miles. 3 hours at 60 miles per hour means a total of 180 miles. Therefore, 110 + 180 = 290, so you drive 290 miles.
Answer:
Step-by-step explanation:
Ben and Josh went to the roof of their 40-foot tall high school to throw their math books offthe edge.The initial velocity of Ben’s book was 60 feet per second while the initial velocity of Josh’s book was 48feet per second. The equation ℎ=−16(++can be used to represent the situation where ℎis the height of the textbook at time seconds, is the initial upward velocity, and is the starting point.Whose textbook reaches the ground first and by how many seconds?
Answer
Josh's textbook reached the ground first
Josh's textbook reached the ground first by a difference of [tex]t=0.6482[/tex]
Step-by-step explanation:
Before we proceed let us re write correctly the height equation which in correct form reads:
[tex]h(t)=-16t^2 +v_{o}t+s[/tex] Eqn(1).
Where:
[tex]h(t)[/tex] : is the height range as a function of time
[tex]v_{o}[/tex] : is the initial velocity
[tex]s[/tex] : is the initial heightin feet and is given as 40 feet, thus Eqn(1). becomes:
[tex]h(t)=-16t^2 + v_{o}t + 40[/tex] Eqn(2).
Now let us use the given information and set up our equations for Ben and Josh.
Ben:
We know that [tex]v_{o}=60ft/s[/tex]
Thus Eqn. (2) becomes:
[tex]h(t)=-16t^2+60t+40[/tex] Eqn.(3)
Josh:
We know that [tex]v_{o}=48ft/s[/tex]
Thus Eqn. (2) becomes:
[tex]h(t)=-16t^2+48t+40[/tex] Eqn. (4).
Now since we want to find whose textbook reaches the ground first and by how many seconds we need to solve each equation (i.e. Eqns. (3) and (4)) at [tex]h(t)=0[/tex]. Now since both are quadratic equations we will solve one showing the full method which can be repeated for the other one.
Thus we have for Ben, Eqn. (3) gives:
[tex]h(t)=0<=>-16t^2+60t+40=0[/tex]
Using the quadratic expression to find the roots of the quadratic we have:
[tex]t_{1,2}=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\t_{1,2}=\frac{-60+/-\sqrt{60^2-4(-16)(40)} }{2(-16)} \\t_{1,2}=\frac{-60+/-\sqrt{6160} }{-32} \\t_{1,2}=\frac{15+/-\sqrt{385} }{8}\\\\t_{1}=4.3276 sec\\t_{2}=-0.5776 sec[/tex]
Since time can only be positive we reject the [tex]t_{2}[/tex] solution and we keep that Ben's book took [tex]t=4.3276[/tex] seconds to reach the ground.
Similarly solving for Josh we obtain
[tex]t_{1}=3.6794sec\\t_{2}=-0.6794sec[/tex]
Thus again we reject the negative and keep the positive solution, so Josh's book took [tex]t=3.6794[/tex] seconds to reach the ground.
Then we can find the difference between Ben and Josh times as
[tex]t_{Ben}-t_{Josh}= 4.3276 - 3.6794 = 0.6482[/tex]
So to answer the original question:
Whose textbook reaches the ground first and by how many seconds?
Josh's textbook reached the ground firstJosh's textbook reached the ground first by a difference of [tex]t=0.6482[/tex]