Answer:
16.3 hours.
Step-by-step explanation:
"Decays exponentially at a rate of 11% per hour" translates into
(1 - 0.11)^h, where h is the number of hours during which the drug decays.
The negative sign comes from "decay."
The complete formula applicable here is
d(h) = (100 mg)(1 - 0.11)^h, where h is the number of hours.
We want to know how many hours it will be until all but 15 mg remain. The appropriate formula for this is
15 mg = (100 mg)()^h. Dividing both sides by 100 mg, we get:
15 mg
------------- = 0.89^h, or 0.15 = 1.11^h
100 mg
Apply properties of logs to solve this. Take the natural log of both sides of the above equation. We get:
ln 0.15 = h(ln 0.89). Dividing both sides by ln 0.89, we get:
h = 16.3
The original 100 mg dosage would decay to 15 mg after 16.3 hours.
Tyler baked 702 cookies. He sold them in boxes of 18. After selling all of the boxes of cookies for the same amount each, he earned $136.50. How many boxes of cookies did Tyler sell
Answer:
I'm not quite sure but I believe he sold 39 Boxes for $3.50 a box.
Step-by-step explanation:
-You would divide 702 by 18 Since he puts them in boxes of 18.
702/18= 39
-Then you would divide $136.50 by 39
136.5/39= 3.5
Which means each box was $3.50 a piece
Tyler sold 39 boxes of cookies, with the price of each box is $3.5
Further explanation
Given:
Tyler baked 702 cookies
He sold them in boxes of 18 cookies
Tyler earned $136.50
Question:
How many boxes of cookies did Tyler sell?
to find out how many boxes of cookies he sold we are going to divide the total cookies he made with the number of cookies in each box
[tex]\boxed {= \frac{702}{18} = 39 }[/tex]
so there were 39 boxes of cookies. He sold all of them and earned $136.50. Price per box would be:
[tex]\boxed {\frac{136.50}{39} = 3.5 }[/tex]
With total earned $136.50, Tyler sold 39 boxes of cookies at $3.5/box
Learn MoreMixed fraction brainly.com/question/213168
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Keywords: mixed fraction, fraction, division, division big numbers, math word problem, multiplication
Which expression is equivalent to 5x - 5x + 3x - 3x?
A) -16x
B) -4x
C) 4x
D) 0
what the answer
Solve the system of equations using elimination.
-7x + 5y = 24
–9x + 5y = 18
A)
(9, 3)
B)
(3, 9)
C)
(
4
5
, 3)
D)
(3,
4
5
)
Answer: B. (3,9)
Step-by-step explanation:
7x -5y = -24(times by -1)
–9x + 5y = 18
-2x=-6
X= 3
(Substitute 3 in)
-9(3)+5y=18
-27+5y=18
5y=45
Y=9
A forest covers 43,000 acres. A survey finds that 0.2% of the forest is old-growth trees. How many acres of old-growth trees are there?
Answer:
8,600 acres are old-growth trees.
Step-by-step explanation:
You can find this by multiplying the percentage by the overall number of acres
20% * 43,000 = 8,600
Answer:
There are 86 acres of old-growth trees.
Step-by-step explanation:
In order to answer the question, we need to calculate the 0.2% of 43,000.
We can calculate this stating that exists a linear relationship between the percentage and the amount of acres. We also need to state that 43,000 acres are the 100% of the acres.
Therefore, we can write the following equation to calculate the percentage :
[tex]\frac{43,000}{100}=\frac{x}{0.2}[/tex]
If we solve the equation in terms of ''x'' :
[tex]x=(\frac{43,000}{100}).(0.2)=86[/tex]
[tex]x=86[/tex]
We find that if 43,000 acres are the 100% of the acres ⇒ The 0.2% of the acres are 86 acres (in which there are old-growth trees).
Use the picture below to find the length of x. Round your answer to the nearest hundredth.
Answer: 6.71
=======================================
Work Shown:
The longest horizontal portion of length 6 breaks up into two equal pieces of length 3 each. Focus on the smaller right triangle on the right hand side. This right triangle has legs of 3 and 6. The hypotenuse is x.
Use the pythagorean theorem with a = 3, b = 6, c = x to find the value of x
a^2 + b^2 = c^2
3^2 + 6^2 = x^2
9 + 36 = x^2
45 = x^2
x^2 = 45
x = sqrt(45)
x = 6.7082039
x = 6.71
An open box is made from a rectangular piece of cardboard measuring 12 inches by 16 inches by cutting identical squares from the corners and turning up the sides. What are the lengths of the sides of the removed squares if the area of the bottom of the open box is 60 in square inches?
show work please.
Answer: 12 inches
Step-by-step explanation: First you add multiply then subctrtrac.t
The size of the squares cut from each corner of the cardboard is 3 inches to create an open box with a bottom area of 60 square inches.
We need to compute the size of the squares cut from each corner of the cardboard to create an open box with a bottom area of 60 square inches. We begin with a rectangular piece of cardboard measuring 12 inches by 16 inches.
Let x be the length of the sides of the squares that are removed. When the squares are cut out and the sides are folded up, the new dimensions of the bottom of the box will be (12 - 2x) inches by (16 - 2x) inches. Thus the area of the bottom will be:
(12 - 2x)(16 - 2x) = 60Expanding the left side of the equation:
[tex]192 - 24x - 32x + 4x^2 = 60[/tex]Combine like terms and set the equation equal to zero:
[tex]4x^2 - 56x + 132 = 0[/tex]Divide all terms by 4 to simplify:
[tex]x^2 - 14x + 33 = 0[/tex]Factor the quadratic equation:
(x - 11)(x - 3) = 0Setting each factor equal to zero gives us the possible values for x:
x = 11 or x = 3Since the cardboard's dimensions are only 12 inches by 16 inches, x cannot be 11, because it would not leave any base for the box. Therefore, x must be 3 inches.
Hence, the lengths of the sides of the squares removed from each corner are 3 inches.
Sal recorded the number of crackers in each snack-sized package he opened. Which statement must be true according to the box plot? The data is symmetric, and the lowest number of crackers in a package was 7. The data is symmetric, and the lowest number of crackers in a package was 8. The data is skewed, and the lowest number of crackers in a package was 7. The data is skewed, and the lowest number of crackers in a package was 8.
Answer:
The data is skewed, and the lowest number of crackers in a package was 7
Step-by-step explanation:
Hi,
First of all, since the question was incomplete due to the missing capture of the range shown on the box plot. I attached it for you so I could answer your question as well.
Taking into consideration the attached image's information, symmetric would be right down the middle, but it is not.
The image shows that it is positively skewed with the lowest number being 7.
Answer:
c
Step-by-step explanation:
did it on edge
The width of Florida is 4/5 of its length if the length of Florida is about 450 miles what is the approximate width
2 Math Questions about coordinates
Answer:
y = -3
x = -2
Step-by-step explanation:
2x - y = 17
y = x - 10
Adding these 2 equations:-
2x + y - y = 17 + x - 10
2x = x + 7
x = 7
Now substitute for x in the first equation:-
2(7) - y = 17
14 - 17 = y
y = -3 (answer)
Last equation:-
x + 3y = 16
4x - 5y = -38
Now multiply first equation by 5 and the second by 3:-
5x + 15y = 80
12x - 15y = -114 Adding:-
17x = -34
x = -2 (answer)
The population of a pack of wolves is 88. The population is expected to grow at a rate of 2.5% each year.
Which function equation represents the population of the pack of wolves after t years?
f(t)=88(0.025)^t
f(t)=88(1.025)^t
f(t)=88(1.25)^t
f(t)=88(2.5)^t
Answer:
Option B is correct.
[tex]f(t) = 88(1.025)^t[/tex] represents the population of the pack of wolves after t years
Step-by-step explanation:
The exponential growth function is given by;
[tex]f(t) = a(1+r)^t[/tex] ......[1]
where
a represented the initial value
r represents the rate(in decimal)
t represents the time in years
As per the given statement: The population of a pack of wolves is 88. Also, the population is expected to grow at a rate of 2.5% each year.
⇒ a = 88 and r =2.5% = 0.025.
Substituting these values in equation [1], we have;
[tex]f(t) = 88(1+0.025)^t[/tex]
or
[tex]f(t) = 88(1.025)^t[/tex]
Therefore, the population model of the pack of wolves after t years is given by: [tex]f(t) = 88(1.025)^t[/tex]
Final answer:
The correct function equation that represents the population of the pack of wolves after t years is f(t) =[tex]88(1.025)^t[/tex]
Explanation:
The population of a pack of wolves can be represented by an exponential function equation. In this case, the population is expected to grow at a rate of 2.5% each year.
The correct function equation that represents the population of the pack of wolves after t years is f(t) = [tex]88(1.025)^t[/tex]
This equation takes the initial population of 88 and multiplies it by 1.025 raised to the power of t, which represents the number of years.
PLEASE HELP!!!!!!!!
WILL MARK BRAINLEST
What is the justification for each step in solving the inequality?
2x+ 2/3 ≤3x− 5/6
Select from the drop-down menus to correctly justify each step.
2x+ 2/3 ≤3x− 5/6 Given
2x≤3x− 3/2
−x≤− 3/2
−x/−1 ≤ − 3/2 −1
x≥ 3/2
First is "given", but we don't have to worry about that
Second is "subtraction property" because we subtract 2/3 from both sides
Third is "subtraction property" for similar reasons as before, but we subtract 3x from both sides
Fourth is "division property" because we divide both sides by -1. Note how the inequality sign flips. This is because we divide both sides by a negative number.
The last would be something along the lines of "simplify" or "reduce"
An individual borrowed ?$89000 at an APR of 6?%, which will be paid off with monthly payments of ?$638 for 20 years. The number of payments per year
Answer: Total payments = $153,120
Interest paid = $64,120
Step-by-step explanation:
$638 x 12 months x 20 years = $152,120
Paid: $152,120
Borrowed: $89,000
Difference: $64,120
Kris has a box of 8 crayons. Silvia, s box has 6 times of many crayons as Kris box . How many crayons are in sylvia box
The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 189. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 15. Thirty more restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of restaurant-purchased meals eaten in a restaurant, the number eaten in a car, and the number eaten at home.
Answer:
87 people in the restaurant, 45 people eat in the car and 57 people eat at home.
Step-by-step explanation:
Let x be 'restaurant-purchased meals eaten in a restaurant', y be the 'restaurant-purchased meals eaten in a car' and z be the 'restaurant-purchased meals eaten at home'.
We can use the given information "the total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 189" to write an equation [tex]x+y+z=189[/tex].
We can use the information "the total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 15" to write another equation [tex]y+z=x+15[/tex].
We can use the information "thirty more restaurant-purchased meals will be eaten in a restaurant than at home" to write the third equation as x=z+30
Now we need to solve this system of three equations to get the values of x, y and z.
We can solve for x directly from the first two equations.
[tex]x+x+15=189\\2x=174\\x=87[/tex]
Substituting this value of x in the third equation we can get the value of z.
[tex]87=z+30\\z=57[/tex]
Finally, we can substitute the values of x and z in the first (or second) equation to get the value of y.
[tex]87+y+57=189\\y+144=189\\y=45[/tex]
Therefore, 87 people in the restaurant, 45 people eat in the car and 57 people eat at home.
An insurance policy pays 80% of the first $20,000 of a patient's medical expenses, and 60% of the remainder. If the patient's total medical bill is $72,000, how much will the policy pay?
In the described insurance policy, 80% of the first $20,000 is covered, which is $16,000. The remaining amount from the total cost of $72,000 is $52,000, of which 60%, or $31,200, is covered. Therefore, the total amount paid by the insurance policy is $47,200.
Explanation:The subject is dealing with a situation of an insurance coverage. The insurance policy pays 80% from the first $20,000 and 60% from the remaining amount of the medical bill. If the total amount of the medical bill is $72,000, we have to find out how much would the policy pay.
First, calculate 80% of the first $20,000: (80/100) * 20,000 = $16,000. The remainder of the medical bill above $20,000 would be $72,000 - $20,000 = $52,000. Then, calculate 60% of this remaining $52,000: (60/100) * 52,000 = $31,200. Finallly, add the two amounts, $16,000 + $31,200 = $47,200.
So, the insurance policy will pay $47,200 towards a total medical bill cost of $72,000.
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50 POINTS + BRAINLIEST:
Are the two triangles below similar?
Triangles GHI and JKL are shown. Angle G equals 46 degrees, Angle I equals 27 degrees, Angle K equals 108 degrees, Angle L equals 27 degrees, side GH equals 4, side HI equals 5, side KJ equals 2, side JL equals 4.
Yes; they have congruent corresponding angles.
No; they do not have congruent corresponding angles.
Yes; they have proportional corresponding sides.
No; they do not have proportional corresponding sides.
Answer: No; they do not have congruent corresponding angles.
helpp please
Which equation could be solved to find y, the measure of adc?
Answer:
C
Step-by-step explanation:
We can use the formula for chords ,and tangents
< ABC = 1/2 (ADYC - AC)
61 = 1/2(y - 119)
Answer:
Option C. [tex]\frac{1}{2}[/tex] ( y-119 ) = 61
Step-by-step explanation:
In the given diagram AB and AC are tangents to circle O.
Length of arc AC = 119°
Inscribed angle between tangents AB and BC is 61°
We have to find the measure 'y' of arc ADC.
As we know the formula
m∠A = [tex]\frac{1}{2}[/tex] [m( arc ADC ) -m(arc AC)]
Now we put the values in this equation
61 = [tex]\frac{1}{2}[/tex] ( y-119 )
So Option C 61 = [tex]\frac{1}{2}[/tex] ( y-119 ) is the answer.
Math question for 10 points and brainliest! See picture
[tex]y=\dfrac{1}{2}x+2\\\\for\ x=0\to y=\dfrac{1}{2}(0)+2=0+2=2\to(0;\ 2)\\\\for\ x=2\to y=\dfrac{1}{2}(2)+2=1+2=3\to(2;\ 3)\\\\y=2x-1\\\\for\ x=0\to y=2(0)-1=0-1=-1\to(0;\ -1)\\\\for\ x=2\to y=2(2)-1=4-1=3\to(2;\ 3)\\\\Look\ at\ the\ picture.\\\\Answer:\ (2;\ 3)\to x=2;\ y=3.[/tex]
Draw the lewis structure for so2. how many single bonds, double bonds, triple bonds, and unshared pairs of electrons are on the central atom, in that order? 1. 2, 1, 0, 0 2. 0, 1, 1, 0 3. 3, 0, 0, 1 4. 0, 2, 0, 0
According to its Lewis structure, the sulfur dioxide (SO2) molecule forms 0 single bonds, 2 double bonds, has 0 triple bonds, and 1 lone pair of electrons on the central (sulfur) atom.
Explanation:The Lewis structure of sulfur dioxide (SO2) can be represented as :
:O=S=O:
Here, sulfur is the central atom. It forms one double bond with each oxygen atom. There are no single or triple bonds present, and the sulfur atom has one lone pair of electrons.
Therefore, the correct count of single bonds, double bonds, triple bonds and unshared pairs of electrons on the central atom, in that order, is - 0, 2, 0, 1
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In the Lewis structure for SO2, or sulfur dioxide, there are zero single bonds, two double bonds, zero triple bonds, and one unshared pair of electrons on the central sulfur atom. The correct sequence for SO2 is therefore 0, 2, 0, 1.
Explanation:SO2, or sulfur dioxide, consists of a central sulfur atom with oxygen atoms on both sides. The Lewis structure for SO2 includes one lone electron pair and double bonds with the two oxygen atoms. To calculate this, we first count the valence electrons from the atoms: sulfur has 6 valence electrons and each oxygen atom has 6 as well, for a total of 18 valence electrons.
To start the Lewis structure, we place the least electronegative atom - sulfur - in the center and the two oxygen atoms on each side. We then place a single bond between the sulfur and each oxygen. This accounts for four valence electrons (2 from each bond), leaving us with 14 more. Next, we distribute the remaining electrons to the oxygen atoms as lone pairs, as necessary, to satisfy the octet rule. If there are still electrons left over, we create double bonds until we have used all of the electrons. Here, it results in double bonds between sulfur and each oxygen atom with one lone pair on the sulfur.
Given these steps, for SO2, we have 0 single bonds, 2 double bonds, 0 triple bonds, and 1 unshared pair of electrons on the central atom, sulphur. So the correct option would be 0, 2, 0, 1.
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Pants $80 buy one at regular pric. Get a second one for half price. (How much for 2 pair?)
Answer:
$200 will be price of 2 pairs
Step-by-step explanation:
It is given that the price of one pant is $80
The second is given at half price which is $40
but in the case of pants buying or anything buying when we are given an off then after buying an item the same discount is given for all
so as he bought one pant then the other pant will be given at half price
now the third pant will also be given at half price i.e: $40
fourth price will also be given at $40
so four pants will become 2 pairs
price of 2 pairs = $80+$40+$40+$40
=$200
Please help! Need answered! Please and thank you.
Answer:
1. lim x→0 7e^x =7
2. lim f(x) does not exist
f(3) = 5
3. 1/12
Step-by-step explanation:
f(x) = 7e^x
lim x→0 7e^x =7
AS we can see from the graph it is around 7
We know that e^0 =1 so 7*1 =7
2. The limit does not exists, because approaching the limit from the left f(3-) is 3. Approaching the limit from the right f(3+) is 5. f(3) = 5 since there is a closed circle at 3 with a value of 5.
3. f(x) = x^ 1/2
We take the derivative
f'(x) = 1/2 x^ (-1/2)
= 1/2 1/( x^.5)
To find it at x=36
= 1/2 * 1/( 36^.5)
= 1/2 * 1/6
= 1/12
Since they are not equal, the limit does not exist.
Which of the following mappings is not a function?
A function in mathematics is a mapping where each input has exactly one output. A mapping is not a function if any input in the mapping maps to multiple outputs.
Explanation:In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. So a mapping is not a function if any input maps to multiple outputs.
For instance, if we have a mapping {a -> 1, b -> 2, c -> 1}, it is a function because even if 'a' and 'c' have the same output '1', it's okay because each individual input ('a', 'b', 'c') relates to exactly one output. But if we have a mapping {a -> 1, a -> 2}, this is not a function because 'a' maps to two different outputs ('1' and '2').
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Which equation shows a line that is parallel to the line
In January the price of a kilogram of brand X rice was $7.60.In May the price of a kilogram of Brand X rice became $8.80.Find the percent increase in price.
Answer:
15.79% is the percent increase in price
Step-by-step explanation:
As per the given statement: In January the price of a kilogram of brand X rice was $7.60.
⇒ Price of brand X in January = $7.60
Also, it is given that in May the price of a kilogram of Brand X rice became $8.80.
⇒ Price of brand X in May = $8.80
Increase in price = $8.80 - $7.60 = $1.20
To find the percent increase in price;
[tex]Percent increase in price =\frac{Increase in price}{Price of X in January} \times 100[/tex]
= [tex]\frac{1.20}{7.60} \times 100 = 15.79\%[/tex]
Therefore, the percent increase in price approx. is, 15.79%
The price of a kilogram of brand X rice increased by approximately 15.79% from January ($7.60) to May ($8.80).
To find the percent increase in price of the brand X rice from January to May, we first calculate the difference in price and then divide it by the original price.
After that, we multiply the result by 100 to get the percentage.
The original price in January was $7.60, and the new price in May was $8.80.
The difference in price is $8.80 - $7.60 = $1.20.
Now we divide the difference by the original price: $1.20 / $7.60 = 0.1579.
To find the percent increase, we multiply this number by 100: 0.1579 x 100 = 15.79%.
So, the price of a kilogram of brand X rice increased by approximately 15.79% from January to May.
Please answer this question! Thirty points and brainliest!
Answer:
choice A
Step-by-step explanation:
Closed circles on the end of the number line means we include it in our inequality (has an equals)
-3 <= x <= 1
Answer:
The answer is A.
Step-by-step explanation:
paris run 3 1/2 laps around the circular track in the school gym. The track has a diameter of 1/2 mile. About how far does paris run?
Answer:
5.497787144 miles
Step-by-step explanation:
Remember that circumference of a circle can be calculated with:
[tex]2\pi r[/tex]
r=radius
We also know that the radius is just a half of the diameter.
So, the radius of the track is (1/2)/2=1/4 miles
Now, use the circumference of a circle formula to find how much she runs in 1 lap.
[tex]2\pi (\frac{1}{4} )[/tex]
Simplify
[tex]\frac{\pi }{2}[/tex]
This is how much she runs in 1 lap.
Multiply by 3.5 for 3 and a half laps.
[tex]\frac{\pi }{2}*3.5[/tex]
The answer is around 5.497787144 miles.
Kevin is riding his bike to work. He can bike 6 1/2 kilometers in 3/5 of an hour. How many kilometers can Kevin bike in one hour?
Answer:
If Kevin can ride 13/2 kilometers in 3/5 of an hour then he can ride 13/6 in 1/5 of an hour. If you multiply 1/5 of an hour by 5 you would get an hour which would also be 5x the distance as 13/6. Kevin can bike 65/6 or 10 and 5/6 kilometers in an hour.
Will give brainliest!!
Answer:
continuous.
Step-by-step explanation:
Given function is [tex]f(x)=5x^4-9x^3+x-7[/tex].
and value of a = 7.
Now we need to find if the given function [tex]f(x)=5x^4-9x^3+x-7[/tex] is continuous or not.
By definition of continuity, we know that a function is continuous at a given point if both left and right hand limits are equal.
Left Hand Limit = LHL
[tex]LHL=\lim_{x\rightarrow 7^-}f(x)=5(7)^4-9(7)^3+(7)-7=8918[/tex]
Right Hand Limit = RHL
[tex]RHL=\lim_{x\rightarrow 7^+}f(x)=5(7)^4-9(7)^3+(7)-7=8918[/tex]
Since both limits are equal at a=7 so we can say that given function is continuous at a=7
Juan's cell phone company charges $35 a month for phone service plus $0.50 for each text message.How many text messages does Juan send in a month if his bill was $52?
The number of text messages sent by Juan in a month is 34.
What is the process of division?Multiplication is the inverse of division. If three parties of 4 add up to 12, 12 split into three equal groups adds up to 4 in each collective in division. The main goal of separating is to determine how many equal categories form or how many people are in each collective when sharing fairly.For the given question;
Total bill charged to Juan's cell by phone company is $52.
phone service = $35.
text message charge = $0.50 each.
The total cost for message is 52 - 35 = $17.
The number of messages = total message cost/ charge of each message
The number of messages = 17 / 0.5
The number of messages = 34
Thus, the number of text messages sent by Juan in a month is 34.
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Write a function rule for the table.
X f(x)
0 3
1 4
2 5
3 6
A. f(x) = x + 3
B. f(x) = –3 – x
C. f(x) = x – 3
D. f(x) = 3x
Answer:
the linear function is y = x +3
A is correct option.
Step-by-step explanation:
The slope intercept form of a line is given by y = mx +b, where b is the y-intercept and m is the slope.
For y-intercept, x =0
From the given table, at x = 0, f(x)=3
Therefore, y-intercept, b= 3
Hence, the equation is in the form y = mx+3
Now, use the point (1,4) to find m
4 = m(1)+3
4 = m +3
m = 1
Therefore, the linear function is y = x +3
A is correct option.