Answer:
0.5 L
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
A 25 gram sample of a substance that's used for drug research has a k-value of 0.1205. Find the substance's half life in days, round to the nearest tenth.
Complete Question
Situation: A 25 gram sample of a substance used for drug research has a k-value of 0.1205. [tex]N=N_0e^-kt[/tex]
[tex]N_0[/tex]= initial mass(at time t=0) N= mass at a time t K= a positive constant that depends on the substance itself and on the units used to measure time T=time, in daysFind the substance's half-life in days, round to the nearest tenth.
Answer:
5.8 days
Step-by-step explanation:
The decay model for drugs and radioactive substances is given as
[tex]N=N_0e^{-Kt}[/tex]
The half-life of any substance is the time it takes for the substance to decay to half its initial amount. That is the period it takes for:
[tex]N(t)=\dfrac{N_0}{2}[/tex]
If we substitute this into the model, we obtain:
[tex]\dfrac{N_0}{2}=N_0e^{-Kt}\\$Dividing both sides by N_o\\\dfrac12=e^{-Kt}[/tex]
We can solve for t.
Taking the natural logarithm of both sides
[tex]\ln\dfrac12=\ln e^{-Kt}\\\implies-\ln2=-Kt\\t=\dfrac{\ln2}{k} \\$Since k=0.1205$\\t_{1/2}=\dfrac{\ln2}{0.1205}=5.8$ days (to the nearest tenth)[/tex]
Which lines are perpendicular to the line y-1 = (x+2)? Check all that apply.
y + 2 = -3(x - 4)
y-5= 3(x + 11)
y=-3x - 5
y = -x-2
3x + y = 7
Intro
Answer:
y = -x - 2
Step-by-step explanation:
Simplifying the equation of our line;
y - 1 = (x + 2)
y = x + 3
The slope of our line is 1
The slope of the perpendicular line(s) must be -1 (the product of slopes of two perpendicular lines = -1)
The line whose slope is -1 (from the choices) is the one whose equation is:
y = -x - 2
Solve the equation. Negative StartFraction 9 Over 15 EndFraction y + StartFraction 3 Over 21 EndFraction = StartFraction 5 Over 15 EndFraction y minus StartFraction 14 Over 21 EndFraction What is the solution?
Answer:
Step-by-step explanation:
9/15y + 3/21 = 5/15 y - 14/21. Adding 14/21 to both sides we then get 9/15y + 17/21 = 5/15y. Subtracting 5/15y from both sides, we get 4/15y + 17/21 = 0.
Then we get 4/15y = -17/21. Dividing by 4/15 gets us -17/21 * 4/15 = -68/315 = y.
Answer:
y=85/98
Step-by-step explanation:
Solve the equation.
Negative StartFraction 9 Over 15 EndFraction y + StartFraction 3 Over 21 EndFraction = StartFraction 5 Over 15 EndFraction y minus StartFraction 14 Over 21 EndFraction
What is the solution?
y = StartFraction 68 Over 315 EndFraction
y = StartFraction 31 Over 105 EndFraction
y = StartFraction 85 Over 98 EndFraction
y = StartFraction 85 Over 28 EndFraction
Ms. Harwood drives a minivan that gets an average of 22 1/2 miles per gallon of
gasoline. The tank on the minivan holds 18 gallons. How far can Ms. Harwood drive on 1/2 of a tank of gasoline?
11 1/4 miles
112 1/2 miles.
202 1/2 miles
405 miles
Answer:
405 miles
Step-by-step explanation:
Take the miles per gallon and multiply the gallons to get the miles
22.5 * 18
405 miles
Answer:
202 1/2 miles
Step-by-step explanation:
We want to find how far she can drive on 1/2 a tank of gas.
Her tank can hold 18 gallons. Multiply 18 and 1/2, or divide 18 by 2.
18*1/2=18*0.5=9
or
18/2=9
1/2 a tank of gas is 9 gallons. Now, we need to find how far she can drive. Multiply the number of gallons in 1/2 a tank by the miles per gallon.
gallons in 1/2 tank * miles per gallon
We know she has 9 gallons in 1/2 tank, and she gets 22 1/2, or 22.5 miles per gallon.
9 gallons * 22.5 miles/gallon
9*22.5=202.5= 202 1/2
She can drive 202 1/2 miles on 1/2 a tank of gas.
The dual bar chart shows the hair colour of boys and girls in a year group. What fraction of the students are girls? Give your answer in its simplest form
Answer:
5/11
Step-by-step explanation:
there are 72 boys and 60 girls. that means there are 132 students on total.
60/132 = 5/11
Answer:
5/11
Step-by-step explanation:
Black= 22 b + 17 g
Brown= 4 b + 18 g
Blonde= 25 b + 10 g
Red= 21 b + 15 g
Total number= 22+17+4+18+25+10+21+15= 132Number of girls= 17+18+10+15= 60Girls are 60/132= 2 × 2 × 3 × 5/ 2 × 2 × 3 × 11= 5/11 of all studentsSelect the correct numbers. Identify the numbers that are located below -3.5 on a vertical number line. 3 -0.3 -1.5 -5.3 0.3 5.3 -2.5 -6.5
Answer:
It's -5.3 and -6.5
I got it right on my test
-5.3 and -6.5 are located below -3.5 on the vertical number line and its pretty easy to find that out
The polynomial x^2+3x-1 is a factor of x^4+3x^3-2x^2-3x+1 true or false?
Answer:
Yes, it is true that [tex]x^2+3x-1[/tex] is a factor of [tex]x^4+3x^3-2x^2-3x+1[/tex].
Step-by-step explanation:
Let us try to factorize [tex]x^4+3x^3-2x^2-3x+1[/tex]
[tex]x^4+3x^3-2x^2-3x+1\\\Rightarrow x^4-2x^2+1-3x+3x^3[/tex]
Let us try to make a whole square of the given terms:
[tex]\Rightarrow (x^2)^2-2\times x^2 \times 1+1^2+3x^3-3x\\\Rightarrow (x^2-1)^2+3x^3-3x\\[/tex]
--------------
Formula used above:
[tex]a^{2} -2 \times a \times b +b^{2} = (a-b)^2[/tex]
In the above equation, we had [tex]a = x, b = 1[/tex].
--------------
Further solving the above equation, taking [tex]3x[/tex] common out of [tex]3x^3-3x[/tex]
[tex]\Rightarrow (x^2-1)^2+3x(x^2-1)\\[/tex]
Taking [tex](x^{2} -1)[/tex] common out of the above term:
[tex]\Rightarrow (x^2-1)((x^2-1)+3x)\\\Rightarrow (x^2-1)(x^2+3x-1)[/tex]
So, the two factors are [tex](x^2-1)\ and\ (x^2+3x-1)[/tex].
[tex]\therefore[/tex] The statement that [tex]x^2+3x-1[/tex] is a factor of [tex]x^4+3x^3-2x^2-3x+1[/tex] is True.
Dylan scored a total of 48 points in the first 4 games of the basketball season. Which equation can be used to find g, the average number of points he scores per game?
Answer:
g = 48 divided by 4
Step-by-step explanation:
Answer:
g=48/4
Step-by-step explanation:
this thing / mean divided
An has endpoints located at a and b. It was dilated at a scale factor of 1/2 from center 2,0 which statement describes the pre image
Answer:
The pre image is a factor 2 bigger, and there fore it's endpoints a' and b' must also be a factor 2 further away from the center 2,0.
Step-by-step explanation:
This is a long explanation. I did my best to guide you through all the steps needed to answer the question, because it almost instantly happens in my mind. Writing down these "reasoning steps", hopefully can give you some insight in understanding what I am asking myself to finally solve the problem. I hope it helps you, and that you can learn from it.
The pre image is the original image, which is NOT visible. Because original image is not visible, that makes it a little tricky, because you have to "imagine" an image that is not there...
Please understand what is described:
The original was dilated at a scale factor of 1/2 from center 2,0 and that result is now visible as An, which has endpoints located at a and b.
So, the big "problem" is to understand what effect the dialated scale factor of 1/2 has, when it was applied to the ORIGINAL.
You ask yourself, was the original bigger or was the original smaller? If you CONCLUDE that the scaling factor 1/2 must result in a SMALLER image, then the original, then you can finally conclude that the original image must have been bigger to make that happen.
Ok, so the pre image was bigger...
How much bigger was the pre image, when you know a dialation scale factor of 1/2 was used to form the endpoints a and b...
Well, now you ask yourself, by what amount do you need to multiply the scale factor 1/2 to get to 2/2 (which is 1 by the way). You do this, because you want to know how big the original must have been, and the original can be "reconstructed" by "reversing" the dialation the other way around. In other words by what amount do you need to multiply the scale factor 1/2 to get to 2/2.
Since 2 * 1/2 = 1, then the original image can be formed from the given image by applying a dialation factor of 2.
So now we know that the original must have been BIGGER by a factor 2.
Finally, do not forget to mention that ORRIGINAL endpoints, a' and b', MUST also be a factor 2 further away from the center 2,0.
So now you have your answer. I hope it helps.
Susan is attending a talk at her son's school. There are 8 rows of 10 chairs where 54 parents are sitting.
Susan notices that every parent is either sitting on their own or next to just one other person.
What is the largest possible number of adjacent empty chairs in a single row at that talk?
Answer:
The answer is 3.
Hope it helped!
i believe the answer is 3
[tex]\frac{?}{5} * \frac{10}{8} =1.5\\[/tex] What number would replace the '?'
Answer:
[tex] \boxed{\sf \huge \boxed{ \sf ?} = 6} [/tex]
Step-by-step explanation:
[tex] \sf Solve \: for \: \boxed{ \sf ?} : \\ \sf \implies \frac{\boxed{ \sf ?}}{5} \times \frac{10}{8} = 1.5 \\ \\ \sf \implies \frac{\boxed{ \sf ?} \times 10}{5 \times 8} = 1.5 \\ \\ \sf \frac{10}{5} = \frac{ \cancel{5} \times 2}{ \cancel{5}} = 2 : \\ \sf \implies \frac{ \boxed{ \sf 2} \times \boxed{ \sf ?} }{8} = 1.5 \\ \\ \sf \frac{2}{8} = \frac{ \cancel{2}}{ \cancel{2} \times 4} = \frac{1}{4} : \\ \sf \implies \frac{\boxed{ \sf ?}}{ \boxed{ \sf 4}} = 1.5 \\ \\ \sf Multiply \: both \: sides \: of \: \frac{\boxed{ \sf ?}}{4} = 1.5 \: by \: 4 : \\ \sf \implies \frac{4 \times \boxed{ \sf ?}}{4} = 4 \times 1.5 \\ \\ \sf \frac{4 \times \boxed{ \sf ?}}{4} = \frac{ \cancel{4}}{ \cancel{4}} \times \boxed{ \sf ?} = \boxed{ \sf ?} : \\ \sf \implies \boxed{\boxed{ \sf ?}} = 4 \times 1.5 \\ \\ \sf 4 \times 1.5 = 6 : \\ \sf \implies \boxed{ \sf ?} = 6[/tex]
y=kx and x is doubled what happens to y
Answer:
see explanation
Step-by-step explanation:
Because the quantities are in proportion
When x doubles then y doubles
Find b:
16
А
K
9
В
b
C
Answer:
20
Step-by-step explanation:
We can calculate the value of b using Euclidean theorem
b^2 = 16 × 25 ➡ b^2 = 400 and b = 20
please explain while solving
Answer:
48Step-by-step explanation:
In the picture above
I hope it helps :)
Circle C is shown. Secants U W and Y W intersect at point W outside of the circle. Secant U W intersect the circle at point V and secant Y W intersects the circle at point X.
In the diagram of circle C, m∠VWX is 43°. What is mArc V X?
39°
41°
78°
82°
Answer:
78
Step-by-step explanation:
ur boi got it right
h=-16(t-) + 49,
Does the marshmallow reach its maximum height?
Which of the following quadratic regression equations best fits the data shown below?
Answer:
Step-by-step explanation:
In order to do this, you have to know how to use your calculator's regression equation function.
First enter in the data. Hit "stat" then 1:Edit and enter all the x values into L1. After each value, hit enter. When you're done with the x list, arrow over to L2 and enter in all the y-values. If there are already values there you need to clear, arrow up to highlight L1, hit "clear", then "enter" and the values will disappear. Do that for both lists if you need to.
After the data is listed in L1 and L2, hit "stat" again and arrow over to "Calc". Hit 5:QuadReg. If you have a TI 83, your equation will be there for you. If you have a TI 84, you'll need to arrow down to "calculate" to get the equation. Regardless, the equation is
[tex]y=3.48x^2+1.22x+3.44[/tex], the last choice in your options.
Answer: D
Becasye I got it from him
Which equation has a contant of proportionality equal to 1/2
Answer:
c
Step-by-step explanation:
1 = 3
2 6
Cross multiply:
1 * 6 = 2 * 3
Simplifying
1 * 6 = 2 * 3
Multiply 1 * 6
6 = 2 * 3
Multiply 2 * 3
6 = 6
Add '-6' to each side of the equation.
6 + -6 = 6 + -6
Combine like terms: 6 + -6 = 0
0 = 6 + -6
Combine like terms: 6 + -6 = 0
0 = 0
Solving
0 = 0
Which points are on the perpendicular bisector of the given segment? Check all that apply. (−8, 19) (1, −8) (0, 19) (−5, 10) (2, −7)
Answer:
−8, 19
1, −8
-5, 10
Step-by-step explanation:
The points that are on the perpendicular bisector of the given segment is (-5, 10)
What is the perpendicular bisector?Perpendicular bisector is defined as a line that divide an angle into two equal parts at 90 degrees.
The standard equation of a line in point-slope form is expressed as
y-y₁ = m(x-x₁)
First, we need to get the equation of the line using the coordinates (-20, 0) and (10, 15)
Get the slope of the line
m = 15-0/10-(-20)
m = 15/30
m = 1/2
The slope of the line perpendicular to the line is -2
Using the point (-5, 10) on the line, get the equation in the point-slope form:
y - 10 = -2(x + 5)
y - 10 = -2x - 10
y + 2x = -10 + 10
y + 2x = 0
y = -2x
To check which points are on the perpendicular bisector of the given segment, hence;
For the coordinate (-8, 19)
19 = -2(-8)
19 ≠ 16 (This is not a solution)
For the coordinate (1, -8)
-8 = -2(1)
-8 ≠ -2 (This is not a solution)
For the coordinate (-5, 10)
10 = -2(-5)
10 = 10 (This is a solution)
Hence, the point that is on the perpendicular bisector of the given segment is (-5, 10)
Learn more about perpendicular bisector here:
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Anna created the poster shown below: What would be the dimensions of the poster at fraction 1 over 4 times its current size?
A.) Length = 9 cm, width = 4 cm
B.) Length = 144 cm, width = 64 cm
C.) Length = 32 cm, width = 12 cm
D.) Length = 40 cm, width = 20 cm
Answer:
D
Step-by-step explanation:
.........
In a survey, the ratio of the number of people who preferred tea to those who preferred coffee was 9:5
36 more people preferred tea to coffee.
How many people were in the survey?
Answer:
45 people prefered coffee, 81 people prefered tea. A total of 126 people were surveyed.
Step-by-step explanation:
Let t be the people who prefer tea, and let c be the people who prefer coffee.
The ratio between tea and coffee is 9:5, thus we have t/c=9/5. Cross products give us 5t=9c.
Also, we have 36 more people prefer tea than coffee, so we have c+36=t
Thus we have: 5(c+36)=9c
5c+180=9c
180=4c
c=45
c+36=t
45+36=81
3x > -3 solve the following equation
Answer:
x > -1
Step-by-step explanation:
3x > -3
Divide each side of the inequality by 3
3x/3 > -3/3
x > -1
Answer:
[tex]x > - 1[/tex]
Step-by-step explanation:
[tex]3x > - 3 \\ \frac{3x}{3} > \frac{ - 3}{3} \\ x > - 1[/tex]
hope this helps you
brainliest appreciated
good luck! have a nice day!
If you can, please help answer this algebra question.
Answer:
R: {-7,-2,3,8}
Step-by-step explanation:
The range is the output values of the function
The values or 8,3,-2,-7
We put them in order from smallest to largest
R: {-7,-2,3,8}
Answer:
2nd option would be the answer
B
{y:y=-7,-2,3,8}
Step-by-step explanation:
Brian rolls 2 fair dice and adds the results from each. Work out the probability of getting a total that is prime.
Answer:
p(prime) = 5/12
Step-by-step explanation:
The possible totals from rolling two dice are between 2 and 12, inclusive. The primes in that range are ...
2, 3, 5, 7, 11
ProbabilityWe assume that "fair dice" means the probability of any outcome is the same as any other. The attached table shows (shaded) all of the 36 possible outcomes that result in a prime number total. There are 15 of them.
The probability of getting a prime total is 15/36 = 5/12.
P(prime) = 5/12
(25 POINTS) Write the inequality of the following graph?
Answer:
f(x) > -x + 2
Step-by-step explanation:
First I found the equation of the line.
The y intercept is at 2 so I know to add 2 at the end
The slope is -1 since it is going downwards
Since the top side is shaded, that represents greater than, if it was shaded downwards, it would be less than
Putting all that together, the equation is f(x) > -x + 2
A bag of balls is given to you which has 3 red balls, 4 green balls, 2 orange balls and 6 white balls. What is probability of picking a green ball
Answer:
4/15
Step-by-step explanation:
You add up all the balls for the bottom number(denominator), for the top number you put the amount of green balls (numerator)
in binary system 100 + 101 = 1001. write decimal equivalent of the summand and sum.
Answer:
The summands are 4 and 5. The sum is 9.
Step-by-step explanation:
In the binary system, the digits, starting at the right and moving to the left are:
1's
2's
4's
8's
etc.
100 = 0 units + 0 2's + 1 four = 0 + 0 + 4 = 4
101 = 1 unit + 0 2's + 1 4's = 1 + 0 + 4 = 5
In decimal, the addition is:
4 + 5 = 9
The summands are 4 and 5. The sum is 9.
The decimal equivalent of the sum is 9.
It is required to write decimal equivalent of the summand and sum.
Why is binary system?Positional numeral system employing 2 as the base and so requiring only two different symbols for its digits, 0 and 1.It is used for representing binary quantities which can be represented by any device that has only two operating states or possible conditions.
Given:
In the binary system, the digits, starting at the right and moving to the left.
The binary numeral system or base-2 numeral system which represents numeric values using two different symbols: typically 0 (zero) and 1 (one). The base-2 system is a positional notation with a radix of 2.
1's 2's 4's 8's etc.
[tex]100\\\\0*2^{0} +0*2^{1}+1*2^{2}\\\\=0+0+4\\\\=4[/tex]
[tex]101\\\\=1*2^{0} +0*2^{1} +1*2^{2} \\\\=1+0+4\\\\=5[/tex]
In decimal, the addition is:
4 + 5 = 9
∴The summands are 4 and 5.
Therefore, the decimal equivalent of the sum is 9.
Learn more about binary system here:
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can someone help please
Answer:
11/8 or, 1 and 3/8
Step-by-step explanation:
First, we have to make both the denominators the same. In this case, we can multiply 3/4 by 2, to make 4, the denominator, into 8. What we do to the denominator, we must do to the numerator! So, we multiply 3 by 2, and get 6!
Now we have, 5/8 + 6/8, which equals 11/8! Which can also be simplified to 1 and 3/8 (because the numerator is larger than the denominator)
Hope this helps! :)
Two domestic courier services charge as per the functions y = 4x + 1 and y = 3x + 2, where x represents the weight of the parcel in pounds and y represents the total cost of the parcel. For what weight is the total cost the same in both services?
Answer:
1 pound
Step-by-step explanation:
Given the cost function of two domestic courier services.
y=4x+1y=3x+2We want to determine the weight (x) at which the costs (y) will be the same.
Since y=4x+1 and y=3x+2, then:
4x+1=3x+2
4x-3x=2-1
x=1 pound
When the weight of the parcel is 1 pound, the total cost of the parcel will be the same for the two domestic courier.
How would the fraction 5/1-sort 3. Be written if it’s denominator is rationalized using difference of squares?
Answer:
[tex] - \frac{5 + 5 \sqrt{3} }{2} [/tex]
Option A is the correct option.
Solution,
Multiply and divide by its conjugate.
[tex] \frac{5}{1 - \sqrt{3} } \times \frac{1 + \sqrt{3} }{1 + \sqrt{3} } \\ = \frac{5(1 + \sqrt{3)} }{(1 - \sqrt{3} )(1 + \sqrt{3)} } \\ = \frac{5 + 5 \sqrt{3} }{ {(1)}^{2} - { (\sqrt{3}) }^{2} } \\ = \frac{5 + 5 \sqrt{3} }{1 - 3} \\ = \frac{5 + 5 \sqrt{3} }{ - 2} \\ = - \frac{5 + 5 \sqrt{3} }{2} [/tex]
hope this helps...
Good luck on your assignment..
