[tex] \rm \frac{x}{5} + 2 \leqslant 6[/tex]
[tex] \rm x + 2 \leqslant 6 \times 5[/tex]
[tex] \rm x + 2 \leqslant 30[/tex]
[tex] \rm x \leqslant 30 - 2[/tex]
[tex] \rm x \leqslant 28[/tex]
[tex]\dfrac x5 +2 \leq 6 \\\\\\\implies \dfrac x5 \leq 4 \\\\\\\implies x \leq 20 \\\\\text{Interval,} ~ (-\infty, 20][/tex]
Evaluate the following expression. 12!
Answer:479001600
Step-by-step explanation:
12 factorial is 12 * 11 * 10 ..... all the way to one
A way to do it by hand is
12 * 1
11 * 2
10 * 3
9 * 4
8 * 5
7 * 6
stop here because 6 * 7 and 5 *8 are already listed
This gives you 6 products then multiply those 6 products by pairs which gives you three pairs which gives you three products then compute a pair then multiply by last product.
Easy math but a lot of written work
vertex, maximum height, and axis of symmetry
Answer:
19 height
Step-by-step explanation:
sorry but thats all i know
hope it helps, have a nice day/night! :D
A vehicle purchased for $25000 depreciates at a constant rate of 5% per year. Determine the approximate value of the vehicle 12 years after purchase. Round to the nearest whole number.
Answer:
$13,509.
Step-by-step explanation:
After each year the vehicle is worth 95% of the previous value.
95% = 0.95.
So after 12 years the approximate value
= 25000 * 0.95^12
= $13,509.
find the formula for a function of the form y=ae^(-x)+bx with global minimum at (1,10).
The formula for a function of the form [tex]y = a\cdot e^{-x} + b\cdot x[/tex] with global minimum at [tex](1, 10)[/tex] is [tex]y = 5\cdot e^{1-x}+5\cdot x[/tex].
We can use first and second derivative tests to determine all coefficients of the function described in statement so that the point given is an absolute minimum. The expressions for such tests are introduced below:
FDT
[tex]-a\cdot e^{-x}+b = 0[/tex] (1)
[tex]b = a\cdot e^{-x}[/tex]
SDT
[tex]y''=a\cdot e^{-x}[/tex] (2)
Where [tex]y'' > 0[/tex].
If we know that [tex](x, y) = (1, 10)[/tex], then we have the following system:
[tex]10 = a\cdot e^{-1}+b[/tex] (3)
[tex]b = a\cdot e^{-1}[/tex] (4)
[tex]y'' = a\cdot e^{-1}[/tex] (5)
By (4) in (3):
[tex]10 = 2\cdot a\cdot e^{-1}[/tex]
[tex]a = \frac{10}{2\cdot e^{-1}}[/tex]
[tex]a = 5\cdot e[/tex]
By (5) we prove that [tex]y'' > 0[/tex], and we get the value of [tex]b[/tex] by (4):
[tex]b = 5[/tex]
Thus, the formula for a function of the form [tex]y = a\cdot e^{-x} + b\cdot x[/tex] with global minimum at [tex](1, 10)[/tex] is [tex]y = 5\cdot e^{1-x}+5\cdot x[/tex].
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The probability that a man will be alive in 25 years is 3/5. and the probability that his wife will be alive is 2/3. Determine the probability that in 25 years:
a. both will be alive
b. at least one will be alive
c. only the wife will be alive
Answer:
e
Step-by-step explanation:
chicken nuggets
A) 6/25
B) 13/15
C) 4/15
Explanation:
A) P(both will be alive) = (3/5)(2/5) = 6/25
B) P(at least one will be alive) = 1-P(both die) = 1-(2/5)(1/3) = 13/15
C) P(only the wife will be alive)=(2/5)(2/3) = 4/15
distance from the point to 0, so it can never be
negative.
a. Coordinate plane
b. Opposite
c. Absolute value
d. Quadrant
distance from the point to O, so it can never be negative so answer is
b.oppsite
Find the equation of the line.
Answer:
y= 4/1x +1
Step-by-step explanation:
the number on the y axis is the b and you do rise over run to find m you rise (so you go up or down) 4 times and run( go to the sides) once.
rise 4
-------- = -----
run 1
Answer:
y = 3x + 1
Step-by-step explanation:
Slope: As it rises 3, it runs 1
Slope = Change in y/change in x
Slope = 3/1
y - intercept = 1 ,the point of intersection
Equation : y = mx + b
m = slope
b = y-intercept
Equation : y = 3x + 1
-Chetan K
what is 0.5734 rounded to the nearest thousandth
Answer:
0.573
Hope that helps :)
What is 0.14 as a fraction
Answer:
7/50
Step-by-step explanation:
Here is an easy way of converting a decimal number to fraction.
Step 1:
Write it down as 0.14/1
Step 2:
Multiply bottom and top by 10 for every number after the decimal, since there is 2 numbers after the decimal you do 10*10 = 100
[tex]\frac{0.14(100)}{1(100)}[/tex] = 14/100
Step 3:
You can simplify 14/100 to 7/50 and thats why 7/50 is the answer
Answer:
[tex]\frac{14}{100}[/tex] or [tex]\frac{7}{50}[/tex]
Step-by-step explanation:
To find 0.14 we have to see what place it's in, since it was in the hundredths place, we put 14 over 100, which is 14/100.
To simplify this fraction we have to find the GCM (Greatest Common Factor), the GCM of 14 and 100 is 2. Then we divide both the bottom and the top by 2 (whatever you do to the bottom, you do to the top), which gives us 7/50.
To conclude, 0.14 as a fraction is 14/100 or 7/50.
5(x+6)-8x=3(10-x)n no solution, one solution, or all real numbers are solutions
Answer:
Infinite, any number
Step-by-step explanation:
Simplify
30 - 3x = 30 - 3x
Please helpppp me step my step all the wayyy
Carla and Diane Bought identical suit cases at a different stores. Carla’s suitcase originally cost $75 and was discounted 15% Daniels suitcase originally cost 85$ and was on sale for 20% off the original price which suitcase was a the better deal? What do we know ? List important facts ? What do we want to find out ?? Solve ??? Show ur work? Explain starts ur Asnwer and give details ? And justify your steps ?
SOMEONE PLEASE HELPPPPPP MEEEEE
THIS IS DUEEEE RIGHT NOWWW
WITH ALL THE WORK I TRIED ALL NIGHT PLEASEEEEEEE
Answer:
carlas had the better deal
Step-by-step explanation:
if you buy an suitcase at $85 with 20% discount, you will pay 85 - 17 = 68 dollars.
if you buy an suitcase at $75 with 15% discount, you will pay 75 - 11.25 = 63.75
divide 20% by a 100 =0.2 than times 0.2 by $85 which will equal 17 subtract 17 from $85
do the same for the second one.
Rachel invests $25,000 at age 25. She hopes the investment will be worth $125,000 when she turns 50. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.
The rate of growth will she need to achieve her goal is 2.8%
The formula for finding the compound amount is expressed as:
[tex]A =P(1+\frac{r}{n} )^{nt}[/tex]
P is the amount invested = $25000
t is the time in years = 25 years
A is the amount = $125000
r is the rate in %
Substitute the given parameters into the formula to have:
[tex]125000 =25000(1+r )^{25}\\5 =(1+r)^{25}\\log5=25log(1+r)\\log(1+r)=\frac{log5}{25} \\log(1+r)=0.02796\\1+r = e^{0.02795}\\1+r=1.0283\\r = 1.0283 -1\\r = 0.0283\\[/tex]
Hence the rate of growth will she need to achieve her goal is 2.8%
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Some home computers can do a calculation in 2 x 10 ? seconds. Write this number in standard form.
2 × 10 = 20
see Picture.
If you get this right i'll give u 40 :)
Answer:
1.NO 2. Yes
Step-by-step explanation:
Answer:
The first and second one is no
Step-by-step explanation:
(1/5) to the second power is 1/25 and adding 25/25 gets 26/25 which is not equal to 24/25
1 to the second power is still one and (1/4) to the second power is 1/16. 16/16 plus 1/16 is 17/16 which is not equal to 25/26
Suppose that the price p (in dollars) and the demand x (in thousand of units) of a commodity satisfy the demand equation 6p+x+xp=94
How fast is demand changing when the price is set at $9 and the price is rising at the rate of $2 per week?
dx/dt
=
The demand is decreasing at the rate of _________units per week.
The demand is decreasing at the rate of 2units per week.
Given the price p (in dollars) and the demand x (in thousands of units) of a commodity satisfy the demand equation 6p+x+xp=94
Differentiating the function with respect to time will result in;
[tex]6\frac{dp}{dt}+\frac{dx}{dt} + x \frac{dp}{dt} + p\frac{dx}{dt} = 0[/tex]
Given the following paramters
p = $6
dp/dt = $2/wk
Substitute the given parameters into the formula to have:
[tex]6(2)+\frac{dx}{dt} + 2x + 9\frac{dx}{dt} = 0[/tex]
To get the demand x, we will simply substitute p = 9 into the expression to have:
6(9)+x+9x=94
10x+54 = 94
10x = 94 - 54
10x = 40
x = 4
Substitute x = 4 into the derivative to have:
[tex]6(2)+\frac{dx}{dt} + 2x + 9\frac{dx}{dt} = 0\\6(2)+\frac{dx}{dt} + 2(4) + 9\frac{dx}{dt} = 0\\6(2)+\frac{dx}{dt} + 8 + 9\frac{dx}{dt} = 0\\20 + 10\frac{dx}{dt} =0\\10\frac{dx}{dt} =-20\\\frac{dx}{dt} =\frac{-20}{10}\\\frac{dx}{dt} =-\$2/wk[/tex]
Hence the demand is decreasing at the rate of 2units per week.
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Which statement best describes what the volume of an object represents? Volume is the length of an object. Volume is the amount of matter in an object. Volume is the amount of space taken up by an object. Volume is the ability of an object to floa
Answer:
Volume is the amount of space taken up by an object
Does each function describe exponential growth or decay?
Drag and drop the equations into the boxes to correctly complete the table.
Growth
Decay
y = 250(1 + 0.004)^t
y = 426(0.98)^t
y = 12,000(1/2) ^t
9514 1404 393
Answer:
growthdecaydecayStep-by-step explanation:
An exponential function will describe growth if the base of the (positive) exponent is greater than 1. It will describe decay of the base is less than 1.
y = 250(1 + 0.004)^t . . . . . 1.004 > 1 ⇒ growth
y = 426(0.98)^t . . . . . . . . . 0.98 < 1 ⇒ decay
y = 12,000(1/2) ^t . . . . . . . 1/2 < 1 ⇒ decay
Can you help me with this ?:)
With explanation step-step Thanks
Part A
The given angle is 4pi/3. Multiply it by the factor 180/pi to convert from radians to degree mode.
Note how the given angle has pi in the numerator, while the conversion factor has pi in the denominator. The two pi terms will cancel.
(4pi/3)*(180/pi)
(4/3)*(180/1)
(4*180)/(3*1)
720/3
240
The angle 4pi/3 radians is equivalent to 240 degrees. This 240 degree angle is in quadrant 3. Any angle in this quadrant is between 180 degrees and 270 degrees, excluding both endpoints. This is the bottom left quadrant, aka the southwest quadrant.
Answer: Quadrant 3===========================================================
Part B
To find the reference angle, we'll subtract off pi. This only works for angles in quadrant 3. This is because the first pi radians, aka 180 degrees, is taken up by the first two upper quadrants. The remaining bit in the third quadrant is all we care about to find the reference angle.
reference angle = (given angle in quadrant 3) - pi
reference angle = (4pi/3) - pi
reference angle = (4pi/3) - (3pi/3)
reference angle = (4pi - 3pi)/3
reference angle = pi/3
Answer: pi/3 radians===========================================================
Part C
Use a calculator or a reference table to find that
tan(4pi/3) = tan(pi/3) = sqrt(3)
Alternatively, you can compute the sine and cosine values first
sin(pi/3) = sqrt(3)/2cos(pi/3) = 1/2Dividing the two items in the order mentioned will get us the tangent value
tan = sin/cos
tan(pi/3) = sin(pi/3) divide cos(pi/3)
tan(pi/3) = sqrt(3)/2 divide 1/2
tan(pi/3) = sqrt(3)
In the jump from the second to last step, to the last step, the denominators '2' cancel out when dividing.
Answer: sqrt(3)On a coordinate plane how are the location of points -6,7 and -6,-7 related
Answer:both involving 6 and 7. (-6,-7) would be in quadrant 3 while point (-6,7) would be on top of it in quadrant 2.
Step-by-step explanation:
Explain the differences and similarities of the steps for dividing whole numbers and decimals.
Answer: Comparing a whole numbers and a decimals:
First let’s talk about the similarities of comparing whole numbers and decimals:
=> their place value always matters.
Now, let’s proceed to their differences
=> in comparing whole numbers, we don’t care about the value to the nearest decimal points or the value of ones. We always look at the highest value, not unless the highest values are all the same.
=> In comparing decimals, the value to the nearest decimal points or the tenths place value always matters.
Step-by-step explanation:
Estimate the limit 1/x+2-1/4/x-1
Answer:
Step-by-step explanation:
Begin by finding a common denominator in the numerator of that rational expression. The common denominator is 3(x+2):
[tex]\frac{\frac{(3)1}{(3)x+2} -\frac{(x+2)1}{3(x+2)} }{x-1}[/tex] which simplifies to
[tex]\frac{\frac{3}{3x+6} -\frac{(x+2)}{3x+6} }{x-1}[/tex] which simplifies further to
[tex]\frac{\frac{3-x-2}{3x+6} }{x-1}[/tex] and
[tex]\frac{\frac{1-x}{3x+6} }{x-1}[/tex] Bring up the lower fraction and flip it and multiply:
[tex]\frac{1-x}{3x+6}*\frac{1}{x-1}[/tex] In order to make the 1-x into x-1, multiply the numerator of that fraction on the left by -1 to get:
[tex]-\frac{x-1}{(3x+6)(x-1)}[/tex] and now the x-1 terms cancel out, leaving us with:
[tex]-\frac{1}{3(1)+6}=-\frac{1}{9}=-.1111[/tex]
____________is the exact average deviation of data values from the mean in squared units, and ____________ is the approximate average deviation of data values from the mean in regular units.
Variance is the exact average deviation of data values from the mean in squared units and the Standard deviation of data values from the mean in regular units.
Variance is a statistical measure of the dispersion of numbers in a data collection. Variance estimates how much more each number in the set deviates from the mean, and from each and every other number in the set.
The variance is a measure of the degree of variability. It is determined by averaging the squared deviations out of the mean.
The greater the spread of the data, the greater the variance in proportion to the mean.
The standard deviation is determined as the square root of variance by calculating the departure of each data point from the mean. The standard deviation represents the average level of variation in your dataset. It informs you how far each number deviates from the mean on average.
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what is the probability of a 200 year flood this year
Answer:
0.5 chance
Step-by-step explanation:
Likewise, the term "100-year storm" is used to define a rainfall event that statistically has this same 1-percent chance of occurring.
Answer:
0.5
Step-by-step explanation:
The possibility are very very very low, but never a no
The height of a parallelogram is 6[tex]a^{2}[/tex][tex]b^{5}[/tex] and the base of a parallelogram is 4[tex]a^{3}[/tex][tex]b^{4}[/tex] Find the area of the parallelogram using the formula A = bh
[tex]\text{Area of parallelogram} = \text{Base}~ \times~\text{Height} = (4a^3b^4)(6a^2 b^5)=24a^5 b^9[/tex]
A nutrition company is marketing a low-calorie snack brownie. A serving size of the snack is 3 brownies and has a total of 50 calories. Determine how many calories 14 brownies would have. Round to the nearest calorie
The number of calories in 14 brownies is 233 calories.
The first step is to determine the average calorie in 1 brownie.
Average calorie = 50 calories / 3 = 16.667 calories
In order to determine the number of calories in 14 brownies, multiply the average calorie by 14 brownies.
Total calories = 16.67 x 14 = 233 calories
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what is the amount if local tax withheld on this W-2
A) $2294
B) $2340
C) $256
D) 4599
Step-by-step explanation:
the local tax is B) $2340 thats what i got
See attachment picture please
Answer:
How can we answer it without question?
The letters A, B, and C can be arranged in six ways. Five ways are listed below.
Find the sixth way.
АВС ACB BAC ВСА САВ
Answer:
CBA would be the sixth
Step-by-step explanation:
Nicole drinks 0.25 L of milk every day. How much milk does she drink on 13 days?
Answer:
3.25 L
Step-by-step explanation:
0.25*13=3.25
The following section is a statement from the rental agreement Tim signed when he rented his car this past weekend.
"Upon checkout, the fuel level of the vehicle will be determined by turning the vehicle on and visually inspecting the fuel gauge. The approximate fuel level will be recorded on the Check-Out sheet and verified with initials by the vehicle Renter. One copy of the Check-Out sheet will be given to the customer. Another copy will be kept with the on-site records of the vehicle.
"The rented vehicle must be returned with a minimum fuel level the same as that indicated on the Check-Out sheet. A vehicle returned with a fuel level less than the approximate level indicated on the Check-Out sheet will be completely refueled with on-site pumps. The price of the fuel used to refuel the vehicle will be added to the Renter's total charge at a cost of $4.50 per gallon plus a $5.00 refueling charge."
Tim forgot to refuel the vehicle when he returned it. His Check-Out sheet indicates that the vehicle had about 1/2 of a tank left. The tanks is now nearly empty.
If it takes 11.75 gallons of gas to refuel the car Tim rented, how much extra should he expect to pay because he forgot to get gas?
a.
$26.44
b.
$31.44
c.
$52.88
d.
$57.88
Answer: D
Step-by-step explanation:
Tim should expect to pay an extra $52.88 because he forgot to refuel the car. option D is correct.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The car that Tim rented needed 11.75 gallons of gas to refill to the same fuel level as indicated on the Check-Out sheet.
Since the rental agency charges $4.50 per gallon of gas plus a $5.00 refueling charge, the cost of refueling the car will be:
11.75 gallons x $4.50/gallon + $5.00
= $57.88
Therefore, Tim should expect to pay an extra $57.88 because he forgot to refuel the car. The correct answer is (d).
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