Find a ᵟ > 0 that works with ᵋ= 0.02 such that if |x-2| < ᵟ then |6x-12|< ᵋ
Answers
The required positive value that works with ε = 0.02. Answer: δ = ε/6 = 0.02/6 = 0.0033 (approx).
Given ε = 0.02, finding δ > 0 such that inequality |x - 2| < δ results in inequality |6x - 12| < ε.
Let |x - 2| < δ.Then, |6x - 12| < ε can be written as |6(x - 2)| < ε. Given |x - 2| < δ .Hence, |6(x - 2)| < 6δ. Finding δ such that 6δ < ε or δ < ε/6. Let δ = ε/6. Then, we have |6(x - 2)| < 6δ = 6(ε/6) = ε. Hence, if |x - 2| < ε/6 then |6x - 12| < ε. Thus, taking δ = ε/6 as the required positive value that works with ε = 0.02. Answer: δ = ε/6 = 0.02/6 = 0.0033 (approx).
learn more about inequality
https://brainly.com/question/20383699
#SPJ11
Related Questions
John works a fortnightly wage of $750.00. If his basic week is 40 hours. what is his: Weekly wage basic rate and basic fortnight??
Answers
Answer:
Basic wage rate = $9.375 per hour
Step-by-step explanation:
Given :
Fortnight wage = $750
Basic week, hours worked per week = 40 hours
Weekly basic wage rate :
Fortnight = 2 weeks
Hence, weekly wage = fortnight wage / 2 = 750 /2 = $375
Weekly basic wage rate = $375 / Number of hours worked per week = $375 / 40 = $9.375 per hour
a ratio of angel fish at a store is 5:4. the ratio of angel fish to goldfish is 4:3 . There are 60 clown fish at the pet store
how many angel fish are there?
how many goldfish are there
Answers
Answer:
an i oop
Step-by-step explanation:
Answer:
So if there are 60 clownfish and the ratio from clownfish to angelfish is 5:4, this is the equation you are looking at:
5:4 = 60:?
To find ? you have to do 60 divided by 5 which equals 12 and multiply it times 4 to see how many angelfish there will be if there are 60 clownfish.
12 x 4 = 48
So if there are 60 clownfish there will be 48 angelfish. The ratio is 60:48
For the next one, same thing if there are 48 angelfish, then you are looking at this equation:
4:3 = 48:?
Again, we solve like we did the last one.
48 divided by 4= 12
3 x 12= 36
So, if there are 48 angelfish there will be 36 goldfish. The ratio is 48:36
I hope this helps:)
Step-by-step explanation:
A fundraising event was held by a high school to support a local animal shelter. The following information was recorded: The first-year students raised $562.50 The second-year students raised $136.25 less than the first-year students. The third-year students raised $200.75 more than the second-year students. What was the total amount of money raised by all three groups?
Answers
Answer: $1615.75
Step-by-step explanation:
First Group
$562.50
Second Ground
$562.50 - $136.25 = $426.25
Third Group
$426.25 + $200.75 = $627
Add All Together
$627 + $426.25 + $562.50 = $1615.75
which of the following are characteristics of bar charts? multiple select question. plotted rectangles should be the same height. plotted rectangles should be the same width. bar charts are used for qualitative data. there should be gaps between bars.
Answers
The correct characteristics of bar charts are:Plotted rectangles should be the same height.Plotted rectangles should be the same width.There should be gaps between bars.
Plotted rectangles should be the same height: In a bar chart, each rectangular bar represents a specific category or group, and the height of the bar corresponds to the value or quantity associated with that category. To accurately represent the data, all the bars in a bar chart should have the same height, allowing for easy visual comparison between the different categories.Plotted rectangles should be the same width: The width of the rectangular bars in a bar chart is not significant and can vary.
The emphasis is placed on the height of the bars to represent the data accurately. However, it is common practice to keep the bars in a bar chart equally spaced and of uniform width to maintain consistency and visual appeal.Bar charts are used for qualitative data: This statement is incorrect. Bar charts are primarily used to represent categorical or qualitative data.
The categories or groups are typically displayed along the horizontal axis, while the vertical axis represents the values or frequencies associated with each category.
There should be gaps between bars: In a bar chart, it is standard to have gaps between adjacent bars to visually separate them and avoid the appearance of a continuous bar. These gaps help distinguish individual categories and make it easier for viewers to interpret the chart accurately.So, the correct characteristics of bar charts are that the plotted rectangles should be the same height, the plotted rectangles should be the same width, and there should be gaps between bars.
Learn more about quadratic equation here:
https://brainly.com/question/30164833
#SPJ8
The main characteristics of bar charts are that they should have bars of equal width, use gaps to distinguish different categories, and they can represent both qualitative and quantitative data. The bars could represent various entities like countries, or years, and the size of the bar depicts a numerical or percentage information.
Explanation:The characteristics of bar charts include the following: the plotted rectangles (bars) should be of the same width to ensure uniformity, and they represent quantities, sizes, rates or other numerical values. Bar charts are not only useful for displaying qualitative data, but they can also represent quantitative data. Moreover, there should ideally be gaps between the bars to distinguish between the different categories being compared.
These charts use either horizontal or vertical bars to show comparisons among categories. For instance, bars in a bar chart can represent different countries or years, and the height or length of the bar signifies a numerical or a percentage value. Bar graphs provide a visual perspective that aids in understanding data better and enables easy comparison of data across different categories.
Learn more about Bar Charts here:https://brainly.com/question/32329301
#SPJ6
Rafael and his sister bought snacks for movie night.
Rafael got 3 boxed candies and 1 bag of chips for $6.99.
His sister got 2 bags of chips and 1 boxed candy for $5.98.
Find the cost for 1 of each of these items in dollars.
One boxed candy costs $ ?
and one bag of chips costs $?
Answers
Answer:
Each boxed candies are 5.98, and Each bag of chips are 6.99 Sorry if incorrect
Answer:
bag of chips is 2.19
boxed candy is 1.60
Step-by-step explanation:
Desmos Calculator
Match the graph
with its inequality.
6.677
a. y<-3
b. x > 2
C. 5x+10y > 0
d. y < x
e. 2y – x < 6
f. 6x + 3y >9
g. 3y - 4x > 12
h. y < -2x – 4.
i. 8x – 6y < 10
j. 3x – 1 zy
-10
Answers
The characteristics of the given graph that can be used to find the
inequality are the y-intercept and the shaded region of the inequality.
Correct response:
The inequality of the given graph is \(\underline{j. \hspace{0.3 cm} 3 \cdot x - 1 \geq y}\)Method used to find the inequality of the graphGiven:
From the given diagram, we have that the inequality is a linear inequality,
therefore, the inequality can be expressed as y ≤ m·x + c.
Where:
m = The slope
c = The y-intercept
From the graph, the y-intercept of the graph of the inequality is at the point (0, -1)
Therefore;
At x = 0, y = -1The shaded region which is to the right of the line with a positive slope
(the straight line increasing from left to right) indicates that the value of y is
less than the equation of the line of the inequality.
The solid line in the graph indicates that the inequality relationship is less
than or equal to (≤).
The inequality that has -1 as the y-intercept and a shaded region to the right of the solid line from among the given options is option j. 3·x - 1 ≥ y
The above inequality can be written as follows;
y ≤ 3·x - 1
Therefore;
The inequality of the graph is \(\underline{j. \hspace{0.3 cm} 3 \cdot x - 1 \geq y}\)Learn more about inequalities here:
https://brainly.com/question/11374918
A pilot flew a jet from City A to City B, a distance of 2000 mi. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 6 h 40 min. What was the speed from City A to City B
Answers
The speed from City A to City B is 275 mph.
To find the speed of the jet from City A to City B, we can use the concept of average speed and the given information about the round-trip duration.
Let's assume the outbound speed of the jet is x mph.
Since the return trip is 20% faster, the speed for the return trip would be 1.2x mph.
The total distance for the round-trip is 2000 miles, so the one-way distance is 1000 miles.
Now, let's calculate the time taken for each leg of the trip:
Outbound trip time = Distance / Speed = 1000 / x hours
Return trip time = Distance / Speed = 1000 / (1.2x) hours
According to the given information, the total round-trip duration is 6 hours and 40 minutes, which is equivalent to (6 + 40/60) hours = 6.67 hours.
Using the above information, we can set up an equation:
Outbound trip time + Return trip time = Total round-trip time
1000 / x + 1000 / (1.2x) = 6.67
To simplify the equation, we can multiply through by 1.2x:
(1.2 \(\times\) 1000) + 1000 = 6.67 \(\times\) 1.2x
1200 + 1000 = 8x
2200 = 8x
x = 275
For similar question on speed.
https://brainly.com/question/27888149
#SPJ11
7. Use the table to answer the following question.
8.
free to
Cupcake Topping Total
Chocolate chips 30
Marshmallows
15
M&Ms
10
Chocolate sprinkles 20
Rainbow sprinkles 25
What percent of the cupcake toppings are chocolate
sprinkles?
Answers
Answer:
I THINK I help u after my online class cause my online is 2:00 pm to 12:00 am. it's so hard
A student graphs the function f (x) = 2(4) using a graphing calculator. The student then replaces the 2 in the equation with an 8.
Which best describes the change the student sees when graphing the new function?
O The graph of the new function will be vertically shifted up 4 units when compared to the previously graphed function.
O The graph of the new function will be vertically shifted up 6 units when compared to the previously graphed function.
O The graph of the new function will be vertically stretched by a factor of 4 when compared to the previously graphed function.
O The graph of the new function will be vertically stretched by a factor of 6 when compared to the previously graphed function.
C
Answers
The equation will be changed into = f(x)= 32
What is a "Simple Equation"?
The link between two expressions on either side of the sign is represented by a mathematical equation.
One variable and an equal sign are typically present. Like this: 2x - 4 Equals 2.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
the function f (x) = 2(4)
f(x)= 32
A statement is not an equation if it has no "equal to" sign.
A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.
Hence, The equation will be changed into = f(x)= 32
Learn more about mathematical equation
brainly.com/question/29514785
#SPJ1
From the observation deck of a skyscraper, Brandon measures a 45^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 1140 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
Answers
The horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.
What is trigonometry?Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.
Given that:-
The angle is = 45The height of the skyscraper is 1140 feet.The horizontal distance will be calculated by applying the angle property in the right angle triangle.
tan45 = ( P / B )
B = P / tan45
B = P Since ( tan45 =1 )
B = 1140 feet.
Therefore the horizontal distance from the base of the skyscraper out to the ship will be 1140 feet.
To know more about Trigonometry follow
https://brainly.com/question/24349828
#SPJ1
What is the domain of the function y=2/x-6?
Answers
Step-by-step explanation:
TO FIND THE DOMAIN OF THIS FUCTION AVOID SITUATIONS LIKE Y=2/0 FOR THIS IS UNDEFINED.
TAKING THE DENOMINATOR AND EQUATING IT TO ZERO
=> X – 6 =0
=> X=6
SO AVOID HAVING X = 6 IN THE DENOMINATOR FOR WHICH THE FUNCTION WILL BECOME UNDEFINED
THEREFORE, X ≠6
DOMAIN ={ X£R, x ≠6}
I.e all real numbers except 6
Eric wants to save $75,000 for his child’s college education in 12 years. Find the periodic deposit (payment) of an annuity earning 8% interest, compounded annually, needed to achieve a future balance of $75,000.
Answers
Answer:
Interest = $72,000
Step-by-step explanation:
We know the interest formula is:
Interest = Principal x Rate x Time
First, put in the numbers:
Interest = $75,000 x 8% x 12 years
Then calculate:
Percent means over a hundred, so 8% is 8 over 100:
Interest = $75,000 x \(\frac{8}{100}\) x 12 years
Put $75,000 over 1, so you can multiply it with 8%:
Interest = $6,000 x 12 years
Finally, multiply:
Interest = $72,000
Therefore, to achieve the future balance of $75,000, Eric needs an interest of $72,000.
We can use the formula for the present value of an annuity to find the periodic deposit needed to achieve a future balance of $75,000 in 12 years at an annual interest rate of 8%, compounded annually.
The formula for the present value of an annuity is:
P = (PMT x [1 - (1 + r)^-n]) / r
Where:
PMT = periodic payment
r = interest rate per period
n = number of periods
P = present value
In this case, we want to solve for PMT. We know that the future value (FV) is $75,000, the interest rate (r) is 8%, compounded annually, and the number of periods (n) is 12.
First, we need to find the present value (P) of the annuity using the formula for future value:
FV = P x (1 + r)^n
$75,000 = P x (1 + 0.08)^12
$75,000 = P x 2.51817
P = $75,000 / 2.51817
P = $29,753.08 (rounded to the nearest cent)
Now we can plug in the values we know into the formula for the present value of an annuity and solve for PMT:
$29,753.08 = (PMT x [1 - (1 + 0.08)^-12]) / 0.08
$29,753.08 = (PMT x 6.71008) / 0.08
PMT = ($29,753.08 x 0.08) / 6.71008
PMT = $354.55 (rounded to the nearest cent)
Therefore, Eric needs to make a periodic deposit (payment) of $354.55, invested at an annual interest rate of 8%, compounded annually, to achieve a future balance of $75,000 for his child's college education in 12 years.
Select all expressions that are equal to 3⋅3⋅3⋅3⋅3
a) 3 ⋅ 5
(b) 3^5
(c) 3^4 ⋅ 3
(d) 5 ⋅ 3
(e) 5^3
Answers
because they all add up to 243
but a, d, and e don’t.
Find the composition of
transformations that
map ABCD to EHGF.
Reflect over the [? l-axis,
then translate
(x+[ 1. y+[ l).
Note:
Enter x or y for axis.
Enter
Answers
The composition of transformations that map ABCD to EHGF is: reflect over the x-axis, then translate (x + 3. y + 1).
What is a reflection?In Mathematics and Geometry, a reflection over the x-axis is modeled by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
Since triangle ABCD was reflected over the x-axis, the coordinate A of triangle ABCD can be calculated as follows;
(x, y) → (x, -y)
A (-5, 2) → (-5, -(2)) = (-5, -2)
For the translation, we have:
(x, y) → (x + a, y + b)
A (-5, -2) → E (-2, 1)
-5 + a = -2
a = -2 + 5
a = 3
-2 + b = -1
b = -1 + 2
b = 1
Read more on reflection here: https://brainly.com/question/21671606
#SPJ1
I need help, answering this!
Answers
Answer:
The length is 15.71 feet.
Step-by-step explanation:
help me pls ASAP I need it in 5mins
Answers
Answer:
74 cars
Step-by-step explanation:
14(2) + 4x = 324
28 + 4x = 324
4x = 296
x = 74
What is the simplest form of the radical expression?
√2+√5/√2-√5
Answers
here u go...........
Four fifths of a number equals 11.
Answers
Answer:
13.2
Step-by-step explanation:
hope this helped
Answer:
13 3/4
Step-by-step explanation:
11 x 5/4 = 55/4 = 13 3/4
check:
13 3/4 x 4/5 = 55/4 x 4/5 = 210/20 = 11
In the diagram below, FED ~ ACEG. Find d. 5 m 의 4 m E 10 m Write your answer as a whole number or a decimal. Do not round. meters
Answers
Answer:
Step-by-step explanation:
k
In a certain town there were 483 robberies last year. This year the number of
robberies has gone
down 12%. How many robberies were there this year, to the nearest whole number?
Answers
4.83x12=57.96
483-57.96=425.04
=425 robberies
pls help! will give brainlist!
which equation represents the line the passes through the points (4,7) and (-2,-2)?
Answers
Answer:
Step-by-step explanation:
I would say the answer is 3/2x +1
Someone plz help me I will give brainliest !!
Answers
Answer:
I think its 8
Step-by-step explanation:
what product has 4 zeros after the digit 3
Answers
factor to write an equivalent expression 36x-16
Answers
Answer:
\(36x - 16 = 4(9x - 4)\)
consider the curve defined by the equation y+cosy=x+1
Answers
The equation y + cos(y) = x + 1 defines a curve in the xy-plane. The curve represents the relationship between x and y values that satisfy the given equation.
The equation y + cos(y) = x + 1 is a transcendental equation, which means it does not have a simple algebraic solution. To study the curve defined by this equation, we can analyze it graphically or numerically.
By plotting points that satisfy the equation, we can observe the shape and behavior of the curve. The equation combines both algebraic terms (y and x) and trigonometric functions (cos(y)), resulting in a complex relationship between x and y values.
Therefore, the curve represents all the points (x, y) that satisfy the equation, forming a distinct pattern in the xy-plane.
Learn more about these curves here: brainly.com/question/29736815
#SPJ11
Please help me with this question
Answers
Answer:
1.5 cm
Step-by-step explanation:
Triangles WTY and UTV are similar. Segment WT corresponds to UT and segment YT corresponds to VT. Thus we can create an equation knowing that the ratio of WT to UT must equal to the ratio of YT to VT.
WT = 7.5 cm
UT = ?
YT = 15 cm
VT = 12 cm
WT / UT = YT / VT
7.5 / UT = 15 / 12
UT = 6
WT = WU + UT
7.5 = WU + 6
WU = 1.5
Let
Rwhich is a normal randomly distributed variable with mean 10% and
standard deviation 10% the return on a certain stock i.e R - N(10,
10 ^ 2) What is the probability of losing money
Answers
If R is a normal randomly distributed variable with mean 10% and standard deviation 10%, the return on a certain stock can be represented as R - N(10,10²), then the probability of losing money is 0.1587.
To find the probability of losing money, follow these steps:
Let Z be a standard normal variable such that (R - 10)/10 = Z. So, the z-score can be calculated as Z= 0-10/10= -1Using the standard normal distribution table to look up the probability that Z is less than -1, the probability, P(Z<-1)=0.1587.Hence, the probability of losing money is 0.1587.
Learn more about probability:
brainly.com/question/30390037
#SPJ11
justin went to the track at bobcat stadium and performed the 1.5-mile run test to estimate his vo2max. he completed 1.5 miles in 11 minutes and 25 seconds. what is his estimated vo2max? round your answer to the first decimal place.
Answers
3Justin's estimated Vo2 max is 25.8(mL*kg*min)
What is Vo2 max ?
The amount (volume) of oxygen used by your body while exercising as hard as you can is referred to as VO2 max. It's a common tool for determining your level of fitness. Knowing your VO2 max can assist you in training for sports, tracking fitness progress, and improving your heart health.
Here using vo2 max fomula 1.5 miles ,
=> VO2 max = 3.5+483/Time
Here Time= 11 min 25 sec = 25/60 = 0.41 min
Then time=11.42 mins. Now,
=> VO2 max = 3.5+ 483/11.41
=> VO2 max = 3.5+42.3
=>VO2 max = 25.8(mL*kg*min)
Hence His estimated Vo2 max is 25.8(mL*kg*min)
To learn more about VO2 max refer the below link
https://brainly.com/question/28651863
#SPJ4
if a wave has a wavelength of 25.4 cm and a frequency of 1.63 khz, its speed is closest to
Answers
Its speed is closest to 414m/s
given that
A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is typically defined in wireless systems in metres (m), centimetres (cm), or millimetres (mm) (mm). The wavelength is more frequently described in nanometers (nm), which are units of 10-9 m, or angstroms (), which are units of 10-10 m, for infrared (IR), visible light (UV), and gamma radiation ().
Frequency, which is defined as the quantity of wave cycles per second, and wavelength have an inverse relationship. The wavelength of the signal decreases with increasing signal frequency.
a wave has a wavelength = 25.4cm
a frequency = 1.63khz
now, we need to find speed of the wave
speed = wavelength × frequency
speed = 25.4 × 16.3
= 414m/s
speed = 414m/s
To learn more about wavelength:
https://brainly.com/question/13533093
#SPJ4
a trough is 12 ft long and its ends have the shape of isosceles triangles that are 2 ft across at the top and have a height of 1 ft. if the trough is filled with water at a rate of 11 ft3/min, how fast (in ft/min) is the water level rising when the water is 9 inches deep?
Answers
The rate at which the water level rises when the water is 9 inches deep is 0.61 ft./ min
Let x represents the height in feet and
V = (1/2)(b)(h)(l)
V = (0.5)(2x)(x)(12)
V = 12x^2
dV/dt = 24x dx/dt
dx/dt = (1/24)(1/x) dV/dt
At x = (9/12) ft
dx/dt = (1/24)(1/x) dV/dt
dx/dt = (1/24)( 12/9)(11)
dx/dt = 0.61 ft./min
Hence, the rate at which the water level rises when the water is 9 inches deep is 0.61 ft./ min
To read more about rates, visit https://brainly.com/question/199664
#SPJ4