Answer: 13
Step-by-step explanation: first we have to know what an integer, which is a single whole number without fractions or decimal numbers e.g. 1,2,3,4,5,6,7,8,9
So now we are to find the least possible positive difference between two digit integers with combination of 2,4,6,9
So first, since it has to be the lowest difference, we have to look between these numbers for the lowest difference between the given integers, 6-4 = 2, 4-2 = 2, now the rest of the combination will give numbers higher that 2, e.g. 9-6 = 3, 6-2 = 4, 9-4 = 5, 9-2 = 7, so we can say our two digit integers can start with either 4 and 2, or 6 and 4, which is the tens in the two digit integers, so to get the least difference in this values, the units number of the bigger two digit integer will be smaller than the units number of the smaller two digit integers
So let's take the number 2, and 4
The bigger two digit integer will obviously start will 4, and since it's supposed to have the smaller units number, the two digit integer will be 46, and the second two digit integer will be 29, the finding the difference
We have 46-29=17
The taking the other combination of integer to give the smallest value, which was 2, (6 and 4) then giving the units number of the bigger integer which will be the smaller units number value (2), that two digit integer will be 62, and the other 49, finding the difference
62-49= 13
So therefore the least possible positive difference = 13
Shane spends $2,000 each week for supplies and labor to run his car detailing business. He charges $30 for each car and $45 for each truck. Which inequality could Shane use to calculate the number of cars, , and trucks, , he needs to detail in order to make a profit?
Answer:
Step-by-step explanation:
Shane spends $2,000 each week for supplies and labor to run his car detailing business. This means that his total cost of running his car detailing business is $2000
Let x represent the number of cars that he would need. If he charges $30 for each car, the total amount charged for x cars would be 30×x = $30x
Let y represent the number of trucks that he would need. If he charges $45 for each car, the total amount charged for y trucks would be 45×y = $45y
In order to make profit, the inequality would be
30x + 45y greater than 2000
Final answer:
Shane can use the inequality 30c + 45t > 2000 to calculate the combination of cars (c) and trucks (t) he needs to detail in order to make a profit, where the costs are $2,000 weekly and charges are $30 and $45 respectively.
Explanation:
To calculate the number of cars (c) and trucks (t) Shane needs to detail in order to make a profit, we can set up an inequality based on his weekly costs and his charges for detailing cars and trucks.
With $2,000 for supplies and labor as his weekly expenses and charging $30 for each car and $45 for each truck, Shane's profit inequality would look like:
30c + 45t > 2000
This inequality states that the total revenue from detailing c cars and t trucks must be greater than his weekly expenses of $2,000 to make a profit.
I need some help with these 2 questions.
Answer:
see attached
Step-by-step explanation:
For the figure A, the figure is symmetrical about a vertical line through its center. It has line symmetry.
__
For the figure O, it is symmetrical about both vertical and horizontal lines, as well as being symmetrical about its center point. It has line and point symmetry.
The half-life of a substance is how long it takes for half of the substance to decay or become harmless (for certain radioactive materials). The half-life of a substance is 37 years and there is an amount equal to 202 grams now. What is the expression for the amount A(t) that remains after t years, and what is the amount of the substance remaining (rounded to the nearest tenth) after 100 years?
Answer:
31.0 grams.
Step-by-step explanation:
According to the given information
Half-life of a substance = 37 years
Initial amount = 202 gram
The exponential function for half-life of a substance is
[tex]A(t)=A_0(0.5)^{\frac{t}{h}}[/tex]
where, A₀ is initial amount, t is time and h is half life.
Substitute A₀=202 and h=37 in the above function.
[tex]A(t)=202(0.5)^{\frac{t}{37}}[/tex]
We need to find the amount of the substance remaining after 100 years.
Substitute t=100 in the above function.
[tex]A(100)=202(0.5)^{\frac{100}{37}}[/tex]
[tex]A(100)=31.0282146[/tex]
Round the answer to the nearest tenth.
[tex]A(100)\approx 31.0[/tex]
Therefore, the amount of the substance remaining after 100 years is 31.0 grams.
The population of geckos in a reptile habitat can be represented by the expression s(1.35)t, where s is the initial number of geckos and t is the time, in years. What is the approximate equivalent quarterly growth rate of the geckos?
A.
8.75%
B.
7.79%
C.
2.53%
D.
33.75%
Answer:
D i guess
Step-by-step explanation:
quarterly means 1/4
so 1.35*1/4
=0.3375
this number is changed to decimal from percentage so change it to percentage which is 33.75%
solve 5(x-y)+2y=5 step by step
Answer:
y = -5/3 + 5/3x
Step-by-step explanation:
Solve for y. View image.
The low temperature on Monday was 6 degrees warmer than Sunday's low of -9°F.The low temperature on Tuesday was 3 degrees warmer than Monday's low.What was the low temperature on Tuesday.
Answer: the low temperature on Tuesday is 0 degree Fahrenheit
Step-by-step explanation:
The low temperature on Monday was 6 degrees warmer than Sunday's low of -9°F. This means that the temperature on Monday would be
- 9 + 6 = - 3 degrees Fahrenheit
The low temperature on Tuesday was 3 degrees warmer than Monday's low temperature. This means that the low temperature on Tuesday would be
- 3 + 3 = 0 degree Fahrenheit
Final answer:
By sequentially adding the temperature differences to each day's low, we find that Sunday's low was -9°F, Monday's was -3°F, and Tuesday's was 0°F. So the low temperature on Tuesday was 0°F.
Explanation:
The student's question involves calculating temperature changes over consecutive days. Here's the step-by-step explanation:
The low temperature on Sunday was -9°F.
Monday's low was 6 degrees warmer than Sunday's, so we add 6 to -9°F, resulting in -3°F for Monday's low.
Tuesday's low was 3 degrees warmer than Monday's, so we add 3 to -3°F, which is 0°F.
Therefore, the low temperature on Tuesday was 0°F.
The solar eclipse travels 2300 miles in 1 hour. In the first 20 minutes it travels 766 2/3 miles. How long does it take for the solar eclipse to travel 1150 miles?
Answer:
Solar Eclipse will required 30 mins to travel Distance of 1150 miles.
Step-by-step explanation:
Given:
Total Distance = 2300 miles
Time required = 1 hr
we will convert hour in minutes.
1 hr = 60 mins
hence Time = 60 mins
We need to find the time required to travel 1150 miles.
We will first find the speed at which solar eclipse travels.
Speed can be calculated by dividing Distance with time.
Speed = [tex]\frac{Distance}{time}[/tex]
Substituting the values we get;
Speed = [tex]\frac{2300}{60}=38.33\ mi/hr[/tex]
Now to find Time required to travel 1150 miles we will divide 1150 miles with Speed.
Time required to travel 1150 miles = [tex]\frac{1150}{38.33}= 30\ mins[/tex]
Hence Solar Eclipse will required 30 mins to travel Distance of 1150 miles.
Boxes that are 18 inches tall are being stacked next to boxes that are 24 inches tall.What is the shortest height at which the two stack will be the same height
Final answer:
The common multiple of the heights of the two stacks is 72 inches which will also be the same height of stack
Explanation:
The boxes that are being stacked have different heights - 18 inches and 24 inches. To find the shortest height at which the two stacks will be the same height, we need to determine the common multiple of 18 and 24.
18 and 24 have a common multiple of 72. Therefore, the two stacks will be the same height when they reach 72 inches.
Answer: The shortest height at which the two stacks will be the same height is 72 inches.
In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct ________ and ________. blind sampling; random group assignment blind group assignment; random sampling random sampling; random group assignment blind group assignment; blind sampling
In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling and random group assignment
Explanation:
The terms Random sampling and Random group assignment are greatly different in process of the sample selection. The study related to the determination of how sample participants can be drawn from the population refers to the process of Random sampling. The sample participants are subjected to a treatment by the usage of a random procedure comprises the Random group assignment.
When a researcher wants validate externally then random selection can be used. When a researcher wants to determine the effects of treatment within that group which is known as determination of internal validity then he can opt for Random group assignment.
Answer:
In order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling/random group assignment.
Explanation:
Random selection is a representation of the sample of people for your research from a community. Random assignment is the assigning of the sample that describes various groups or operations in the study.
Reasons:
Random sampling enables us to get a sample representative of the community.Random assignment enables us to make positive that the only distinction among the various treatment combinations is what needs to study.Random assignment is crucial for sound empirical design. With adequately large representations, random assignment performs it unlikely that there are methodical variations among the groups.Thus we can say in order to maximize the chances that experimental groups represent the population of interest, researchers should conduct random sampling/random group assignment.
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https://brainly.com/question/9423006A restaurant is making hamburgers. The cooks use 2/3 pound of beef hamburger if the cooks have 48 2/3 pounds of beef how many hamburgers can they make
Answer:
The number of hamburger does the cook make is 73 hamburger .
Step-by-step explanation:
Given as :
The quantity of beef use by cook to make hamburger= [tex]\dfrac{2}{3}[/tex] pound
The total quantity of beef does the cook have = 48 [tex]\dfrac{2}{3}[/tex] pound
I.e The total quantity of beef does the cook have = [tex]\dfrac{146}{3}[/tex] pound
Let The number of hamburger does the cook make = n hamburger
Now, According to question
The number of hamburger does the cook make = [tex]\dfrac{\textrm total quantity of beef does cook have}{\textrm total quantity of beef required for hamburger}[/tex]
Or, n = [tex]\frac{\frac{146}{3}}{\frac{2}{3}}[/tex]
Or, n = [tex]\frac{146\times 3}{2\times 3}[/tex]
∴ n = 73
So,The number of hamburger does the cook make = n = 73 hamburger
Hence,The number of hamburger does the cook make is 73 hamburger . Answer
Let d(t) be the total number of miles Joanna has cycled, and let t represent the number of hours after stopping for a break during her ride.
d(t)=12t+20
So,_______ d(4) = . This means that after _____________, Joanna __________.
At t = 4, the distance traveled is 68 miles. This means that after the break, Joanna traveled 48 miles.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The linear function is given below.
d(t) = 12t + 20
The distance traveled when t = 4 is calculated as,
d(4) = 12 x 4 + 20
d(4) = 48 + 20
d(4) = 68 miles
So, at t = 4, the distance traveled is 68 miles. This means that after the break, Joanna traveled 48 miles.
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3(8-3t)=5(2+t)(if there is no solution,type in ''no solution'') t= Answer
Answer:
t = 1
Step-by-step explanation:
3 (8 - 3t) = 5 (2 + t)
24 - 9t = 10 + 5t
- 9t - 5t = 10 - 24
- 14t = - 14
- t = - 14/14
- t = - 1
t = 1
Before being put out of service, the supersonic jet Concorde made a trip averaging 120 mi/h less than the speed of sound for 0.1 h and 410 mi/h more than the speed of sound for 3.0 h. If the trip covered 3,990 mi, what is the speed of sound?
Answer:
894.19 mi/hr
Step-by-step explanation:
Total distance of the trip = 3990 mi
Let the speed of the sound be 'x' miles per hour
Now,
Total distance = Speed × Time
Therefore,
According to the question
3,990 mi = [ ( x - 120 ) × 0.1 ] + [ ( x + 410 ) × 3.0 ]
or
3,990 mi = 0.1x - 12 + 3x + 1230
or
0.1x + 3x = 2772
or
3.1x = 2772
or
x = 894.19 mi/hr
Elenas anut bought her a 150$ saving bond when she was born. When elena is 18 years old, the bond will have earned a 106% in interest. How much will the bond be worth when elena is 18 years old
Answer:
The Amount after 18 years is $66,942,391.5
Step-by-step explanation:
Given as :
The principal invested in saving bond = p = $150
The Time period for the bond = t = 18 years
The rate of interest applied on bond = 106%
Let The Amount after 18 years = $A
Now, From compound interest
Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, A = $150 × [tex](1+\dfrac{\textrm 106}{100})^{\textrm 18}[/tex]
Or, A = $150 × [tex](2.06)^{\textrm 18}[/tex]
Or, A = $150 × 446,282.61
∴ A = $66,942,391.5
So,The Amount after 18 years = A = $66,942,391.5
Hence,The Amount after 18 years is $66,942,391.5 Answer
The length of a rectangle Is twice the width of the rectangle the length of a diagonal of the rectangle is 25cm work out the ares of the rectangle give your answer as an integer
Answer:Area is 50 cm^2
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The formula for determining the area of a rectangle is expressed as
Area = LW
The length of a rectangle Is twice the width of the rectangle. This means that
L = 2W
The length of a diagonal of the rectangle is 25cm. This is the hypotenuse of the right angle triangle that is formed. Applying Pythagoras theorem,
25^2 = L^2 + W^2 - - - - - - - 1
Substituting L = 2W into equation 1, it becomes
25^2 = (2W)^2 + W^2
25^2 = 4W^2 + W^2 = 5W^2
Taking square of both sides,
W = √25 = 5
L = 2W = 3×5 = 10
Area = LW = 10×5 = 50 cm^2
The length of a rectangle is twice the width. Using the Pythagorean Theorem, we can find the dimensions of the rectangle and calculate its area. Hence the final answer is 248 cm².
Explanation:To find the area of a rectangle, we need to know both the length and the width of the rectangle.
Let's assume the width of the rectangle is 'w'.
According to the question, the length of the rectangle is twice the width, so the length of the rectangle is '2w'.
We can use the Pythagorean Theorem to find the length of the diagonal:
Using the formula a^2 + b^2 = c^2, where 'a' and 'b' are the length and width of the rectangle, and 'c' is the length of the diagonal, we can set up the equation:
w^2 + (2w)^2 = 25^2.
Simplifying the equation, we get: 5w^2 = 625
Dividing both sides of the equation by 5, we get: w^2 = 125
Taking the square root of both sides, we get: w = 11.18
The area of the rectangle is length times width, so the area is: 2w * w = 2 * 11.18 * 11.18 = 248.27
Rounding to the nearest integer, the area of the rectangle is approximately 248 cm².
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Jakubowski Farms Gourmet Bread Base is the brand name for a mix designed for use in bread making machines. The mixes are sold in 2-pound canisters for $14.99 plus shipping. People learn about the product through word-of-mouth and bread machine demonstrations the company's founder gives to groups in Wisconsin, where she lives. The products are only available through the mail. This is a description of the company's?
Answer:
The description of the company's is marketing mix.
Step-by-step explanation:
Consider the provided information.
Jakubowski Farms Gourmet Bread Base is the brand name for a mix designed for use in bread making machines which is the product.
We have given that the price is $14.99 plus shipping.
The promotion is word of mouth and public demonstrations.
The place is mail.
The marketing mix is defined as the set of actions or tactics that a company uses to market its brand or product. The 4Ps constitute a standard marketing mix-price, product, promotion and venue.
These four elements are the marketing mix—product, price, promotion, and place.
Hence, the description of the company's is marketing mix.
.
Which of the following ordered pair could NOT be included in this set if it is a function? { (-4, 2), (3, 6), (4, 3), (x, y) }
A) (x, y) = (4, -3)
B) (x, y) = (3, 6)
C) (x, y) = (1, 2)
D) (x, y) = (-3, 6)
Answer:
Option A) (x, y) = (4, -3)
Step-by-step explanation:
we know that
A function is a relation from a set of inputs (independent variable) to a set of possible outputs (dependent variable) where each input is related to exactly one output
we know that
The set of the function is { (-4, 2), (3, 6), (4, 3), (x, y) }
The ordered pair (x, y) = (4, -3)
could not be included, because for the input value of x=4, the function would have two output values (y=-3,y=3) and remember that each input is related to exactly one output
Michael and Ashley each buy x pounds of turkey and y pounds of ham. Turkey cost $3 per pound at store A and $4.50 per pound at store B. Ham cost $4 per pound at store A and $6 per pound at store B. Micheal spends $18 at store A, and Ashley spends $27 at store b could Micheal and Ashley bought the same amount of turkey?Explain.
Yes. Micheal and Ashley bought same amount of turkey which is 6 pounds.
Step-by-step explanation:
The question requires to you to form simultaneous equations and solve them.
Take the number of pounds for turkey to be x and that for ham to be y
For store A where michael spent $18
turkey cost $3 per pound ---- 3x
ham cost $4 per pound------4x
The equation for cost will be ; 3x+4y =18
For store B where Ashley spent $27
turkey cost $4.5 per pound
ham cost $6 per pound
The equation for cost is : 4.5x +6y=27
The two equations are;
3x+4y=18
4.5x+6y=27
Solving the equations by graph you get ;
x=6 and y=4.5 for both linear graphs. This means both equations produce similar amounts of turkey and ham . Micheal and Ashley bought same amount of turkey which is 6 pounds.
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There were 60 people on a bus. After 3 stops, the number of people decreased to 48. What was the percent of decrease in the number of people on the bus?
Answer:
80% People Decreased after 3 Stops.
Step-by-step explanation:
Given:
Total Number of People on the bus =60
Number of people decreased = 48
We need to find the the percent of decrease in the number of people on the bus.
The percent of decrease in the number of people on the bus can be calculated by dividing Number of people decreased on the bus with Total Number of people on the bus and then multiplied with 100.
Framing in equation form we get;
percent of decrease in the number of people on the bus = [tex]\frac{\textrm{Number of people decreased on the bus}}{\textrm{Total Number of people on the bus}}\times100[/tex]
Substituting the values we get;
percent of decrease in the number of people on the bus = [tex]\frac{48}{60}\times100 = 80\%[/tex]
Hence 80% People Decreased after 3 Stops.
A 500-foot wear tower used to measure wind speed has a guy wire attached to it 200 feet above the ground. The angle between the wire and the vertical tower is 47 degrees. Approximate the length of the guy wire to the nearest foot.
Answer:
293 feet
Step-by-step explanation:
The distance the wire is attached in the tower is 200 feet
the angle between the wire and the tower is 47 degrees
The length of the wire (x) is the hypotenuse of the triangles formed
The formed triangle is a right angle triangle
For 47 degree angle the adjacent side is 200 feet and hypotenuse is x
[tex]cos(theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]cos(47)=\frac{200}{x}[/tex]
Cross multiply it
[tex]xcos(47)= 200[/tex]
divide by cos on both sides
[tex]x=\frac{200}{cos(47)}[/tex]
x=293.25 feet
Solve
3x + 4y = 8
-2X + 5y = 3
Answer: x = 28/33, y = 25/23
( 28/23, 25/23)
Step-by-step explanation:
3x + 4y = 8 ----------------------(1)
-2x + 5y = 3 ---------------------(2)
Using elimination method
Consider the coefficient of y in equation 1 and 2
Therefore multiply as follows
(1) x 5 -------- 15x + 20y = 40.
(2) x 4 -------- -8x + 20y = 12
Therefore carry out subtraction on the two equations
23x + 0y = 28
23x = 28
x = 28/23.
Now substitute for x in any of the equations above to get y
3(28/23) +4y = 8
84/23 +4y = 8
Multiply through by 23 to have s simple linear equation
84 + 92y = 184
Collect like terms
92y = 184 - 84
92y = 100
y = 100/92
Reduce to lowest term by dividing by 4
y = 25/33.
(28/23, 25/23)------ solution
Check
Substitute for x and y values in any equations above.
3(28/23) + 4(25/23)
84/23 + 100/23
Resolved into fraction with 23 as the common LCM
184/23
= 8
The third term in a geometric sequence is -81. The common ratio is 1/3
Write a exponential equation for this sequence.
Answer:
Step-by-step explanation:
A geometric sequence is a sequence in which the successive terms increase or decrease by a common ratio. The formula for the nth term of a geometric sequence is expressed as follows
Tn = ar^(n - 1)
Where
Tn represents the value of the nth term of the sequence
a represents the first term of the sequence.
n represents the number of terms.
From the information given,
r = 1/3
T3 = - 81
n = 3
Therefore,
- 81 = a× 1/3^(3 - 1)
-81 = a × (1/3)^2
-81 = a/9
a = -81 × 9 = - 729
The exponential equation for this sequence is written as
Tn = - 729 * (1/3)^(n-1)
Answer:
[tex]t(n)=-729(\frac{1}{3}) ^{n-1}[/tex]
Step-by-step explanation:
Given:
A geometric sequence with third term = -81
Common ratio = [tex]\frac{1}{3}[/tex]
General term of a geometric sequence is given by the formula:
[tex]t(n)=ar^{n-1}[/tex]
where :
t(n) is nth term
a is the first term
r is the common ratio
n=1,2,3,4...
Here r=1/3 and t(3)=-81
[tex]ar^{2}=-81\\a\times\frac{1}{3}^{2}=-81\\a=-729[/tex]
General equation becomes:
[tex]t(n)=-729(\frac{1}{3}) ^{n-1}[/tex]
Find the radius of the circle with an area of 153.9 in? Use 3.14 for T.
A. 3.5 in.
B. 7 in.
D. 14 in.
C. 7.9 in.
Answer:
B. 7 in.
Step-by-step explanation:
Area = A =pi r^2
r^2 = A / pi
r = √(A / 3.14)
= √(153.9 / 3.14)
= 7 in.
You are going to play a game where you bet a dollar and get to flip a coin ten (10) times. If you get four (4) heads in a row, you win. If you make the tenth flip without getting four heads in a row, you lose. Run this game ten thousand times (10,000). Approximately what is the probability that you will win? (choose the proper range)
Must be answered in Excel with formula.
Answer:
Approximately 4,000 times
Step-by-step explanation:
If you're flipping a coin to get 4 heads out of 10 and you times it by 10,000 then you would have a probable win rate of 4,000.
150 parents were surveyed. 26% said that the kids were noddy and 70% said their kids were nice. How many parents didn't answer with either naughty and nice?
Answer:
The parents who didn't answer with either naughty and nice are 6.
Step-by-step explanation:
Given:
150 parents were surveyed. 26% said that the kids were naughty and 70% said their kids were nice.
Now, to find parents who didn't answer with either naughty and nice.
So, as given in question:
70% said that their kids are naughty.
26% said that their kids are nice.
So, to get the percentage of parents who didn't answer we subtract.
Thus, the percentage of parents who didn't answer with either naughty and nice:
100% - (70% + 26%)
100% - 96% = 4%.
Hence, 4% of parents didn't answer.
Now, to get how many parents didn't answer we calculate the percentage of the total who didn't answer:
Total parents surveyed = 150.
Parents who didn't answer = 4% of the total parents surveyed.
[tex]Parents\ who\ didn't\ answer = 4\% of 150.[/tex]
[tex]Parents\ who\ didn't\ answer = \frac{4}{100}\times 150.[/tex]
[tex]Parents\ who\ didn't\ answer = \frac{600}{100}.[/tex]
[tex]Parents\ who\ didn't\ answer = 6.[/tex]
Therefore, the parents who didn't answer with either naughty and nice are 6.
Determine the equivalent system for the given system of equations:
2x + 3y = 7
4x − 2y = 4
(A) 2x + 3y = 7
8x − 4y = 4
(B) 2x + 3y = 7
6x + y = 11
(C) −2x − 3y = 7
4x − 2y = 4
(D) 2x + 3y = 7
6x + y = 4
No options given in the question are equivalent to the original system of equations because none of them retain the same solutions as the original system.
Explanation:The equivalent system for the given system of equations can be found by manipulating the original system of equations. The original system of equations is:
2x + 3y = 7
4x − 2y = 4.
Equations are equivalent if one is a multiple of the other. We can see that if the second equation is multiplied by 2, it will become:
8x - 4y = 8,
which is not an option given in your question. Therefore, none of the presented options (A-D) are equivalent to the initial system of equations. Always remember that an equivalent system retains the same solutions as the original system.
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If you invest a one-time lump sum of $28,000 into a mutual fund that will average 12% compounded monthly, how much will you have in 35 years? Pick the closest value.
Answer:
$1,828,669
Step-by-step explanation:
For the original lump sum of $28,000 is our principal, P, the annual interest rate r, compounded monthly for n=12 months throughout a period of 35 years (t) will have a final Accrued Amount of investment A given by the formula:
A= (Principal + Interest) = P(1 + r/n)^nt =28000(1+0.12/12)^35*12
=28000(1.01)^420=
28000*65.3096= $1828669
If 4 more than 4 times a certain number is the same as 4 more than the product of 3 and 4, what is that number?
A. 3
B. 4
C. 5
D. 8
E. 12
Answer: the number is 3
Step-by-step explanation:
Let the number be represented by x.
If 4 more than 4 times a certain number is the same as 4 more than the product of 3 and 4, it means that
4x + 4 = 4 + 3×4
4x + 4 = 4 + 12
4x + 4 = 16
Subtracting 4 from the left hand side and the right hand side of the equation, it becomes
4x + 4 - 4 = 16 - 4
4x = 12
Dividing the left hand side and the right hand side of the equation by 4, it becomes
x = 12/4 = 3
im taking my final right now and don't want to fail please help.
Answer:
3n+2
Step-by-step explanation:
they informed that it is a linear function. so, let the required linear function be ax+b.[where, a and b are some constants and x is a variable ( input values)]
when x=1, the output is 5so, if x=1, ax+b=5so, a+b=5
if x=2, ax+b=8so,2a+b=8
solving the above 2 equations,subtract the first equation from second:
2a+b-a-b=8-5
a=3.
by substituting the value of a in one of the above equations,
you will get b as 2
so, when the input is n, output will be : 3n+2
Find the following limit. ModifyingBelow lim With x right arrow minus infinity (StartFraction 1 minus x Superscript 4 Over x squared plus 4 x EndFraction )Superscript 5
The limit of the given expression as x approaches negative infinity is 1. This is computed by simplifying and rationalizing the expression, then applying the limit, which leads to a result of 1.
Explanation:To solve the given limit problem, we will first rationalize the expression. Given the expression as: (1-x⁴) / (x²+4x), we can simplify this by factoring out an x² from both the numerator and the denominator. The expression then becomes: (1/x²- 1) / (1+ 4/x). Taking the limit as x approaches negative infinity, we will have: lim (1/x² - 1)⁵/ (1+4/x)⁵. Factoring out x² from the numerator and x from the denominator, we have: lim (1 - 1/x^2)⁵/ (1+ 4/x)⁵ As x approaches negative infinity, the terms 1/x²and 4/x approaches 0, hence the limit becomes (1⁵)/(1⁵) = 1.
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The limit as x approaches -∞ of [(1 - x^4) / (x^2 + 4x)]^5 is -1. This is calculated by dividing each term in the fraction by x^2, and observing the resulting behaviours of the terms as x approaches -∞.
Explanation:Finding the limit of a function as x approaches -∞ is a fundamental concept in Calculus. In order to find the limit of (1 - x^4) / (x^2 + 4x) all raised to the power of 5 as x approaches -∞, divide each term in the fraction by x^2. This results in Limit x → -∞ (1/x^2 - 1)((1 + 4/x)^-5). We then can observe that as x approaches -∞, the expression 1/x^2 and 4/x will become zero.
Consequently, the limit of the fraction is (-1)^5, which equals -1. As a result, the limit as x approaches -∞ of [(1 - x^4) / (x^2 + 4x)]^5 is -1. This limit-finding process works because of the application of laws of limits and the behaviour of polynomials, particularly their asymptotic behaviours as demonstrated in concepts like infinite limit and powers.
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