Answer:
The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.
Step-by-step explanation:
After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.
This means that the amount of caffeine after t hours is given by:
[tex]A(t) = A(0)e^{-kt}[/tex]
In which A(0) is the initial amount and k is the decay rate, as a decimal.
The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.
1 - 0.2722 = 0.7278, thus, [tex]A(10) = 0.7278A(0)[/tex]. We use this to find k.
[tex]A(t) = A(0)e^{-kt}[/tex]
[tex]0.7278A(0) = A(0)e^{-10k}[/tex]
[tex]e^{-10k} = 0.7278[/tex]
[tex]\ln{e^{-10k}} = \ln{0.7278}[/tex]
[tex]-10k = \ln{0.7278}[/tex]
[tex]k = -\frac{\ln{0.7278}}{10}[/tex]
[tex]k = 0.03177289938 [/tex]
Then
[tex]A(t) = A(0)e^{-0.03177289938t}[/tex]
What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body?
We have to find find A(5), as a function of A(0). So
[tex]A(5) = A(0)e^{-0.03177289938*5}[/tex]
[tex]A(5) = 0.8531[/tex]
The decay factor is:
1 - 0.8531 = 0.1469
The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.
-2(4x-6)=6-6x help me
Answer:
x=3
Step-by-step explanation:
you have to move the terms collect like terms and divide both sides and down load photo math that helps alot with giving answersName a pair of overlapping congruent triangles. (PST and QTU, STR and UTR, or RPU and RQS)
Then state whether they are congruent by SSS, SAS, ASA, AAS, or HL.
Answer:
ΔRUP ≅ ΔRSQ by ASA
Step-by-step explanation:
Angle SRQ is congruent to angle URP by the reflexive property of congruence. The angles at U and S are already marked congruent, as are sides UR and SR. That means we have two angles and the side between them congruent for the two triangles:
ΔRUP ≅ ΔRSQ by ASA
Write the ratio 4 1/5 to 5 2/5 as a simplified fraction
Answer:
[tex]\huge\boxed{4\dfrac{1}{2}:5\dfrac{2}{5}=5:6}[/tex]
Step-by-step explanation:
[tex]4\dfrac{1}{2}:5\dfrac{2}{5}[/tex]
we convert a mixed number to an improper fraction
[tex]4\dfrac{1}{2}=\dfrac{4\cdot2+1}{2}=\dfrac{9}{2}\\\\5\dfrac{2}{5}=\dfrac{5\cdot5+2}{5}=\dfrac{27}{5}[/tex]
Therefore
[tex]4\dfrac{1}{2}:5\dfrac{2}{5}=\dfrac{9}{2}:\dfrac{27}{5}=\dfrac{9\!\!\!\!\diagup^1}{2}\cdot\dfrac{5}{27\!\!\!\!\!\diagup_3}=\dfrac{1}{2}\cdot\dfrac{5}{3}=\dfrac{1\cdot5}{2\cdot3}=\dfrac{5}{6}=5:6[/tex]
The ratio 4 1/5 to 5 2/5 is equivalent to the simplified fraction 7/9.
How to write the simplified factionTo write the ratio 4 1/5 to 5 2/5 as a simplified fraction, we need to convert both mixed numbers to improper fractions and then find their ratio.
Step 1: Convert the mixed numbers to improper fractions:
4 1/5 = (4 * 5 + 1) / 5 = 21 / 5
5 2/5 = (5 * 5 + 2) / 5 = 27 / 5
Step 2: Find the ratio by dividing the first fraction by the second fraction:
Ratio = (21 / 5) / (27 / 5)
Step 3: To divide by a fraction, multiply by its reciprocal:
Ratio = (21 / 5) * (5 / 27)
Step 4: Simplify the fraction:
Ratio = (21 * 5) / (5 * 27)
Ratio = 105 / 135
Step 5: Simplify the fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 15:
Ratio = (105 / 15) / (135 / 15)
Ratio = 7 / 9
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Which ordered pair is in the solution set of 3x − 2y ≥ -1?
F.(-2, -2.5)
G.(-1, 1)
H.(2, 4)
J.(1, 2.5)
Answer:
G
Step-by-step explanation:
Therefore, the option [tex]G(-1,1)[/tex] is correct.
What is the inequality?
An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Here given inequality equation
[tex]3x- 2y \geq -1[/tex]
When the points [tex](-1,1)[/tex] so it would be
[tex]3(-1)-2(1)\geq -1\\\\-3-2\geq -1\\\\-5\geq -1[/tex]
Hence, the option [tex]G(-1,1)[/tex] is correct.
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b. What is the area of the surface of Crater Lake?
Give a step by step explanation
Answer: 23.76 miles
Step-by-step explanation:
You are basically finding the perimeter for question a
given that perimeter is [tex]\pi[/tex]d
Subsitute the values
So perimeter = [tex]\pi[/tex] x 5.5 = 5.5 [tex]\pi[/tex] miles = 17.28 miles (2.d.p)
For question b, the area of the surface of Crater lake is finding its area
Given that area of a circle is [tex]\pi r^{2}[/tex]
Substitute the values
Because 5.5 is the diameter, to find the radius, divide by 2 to get 2.75
Area = 2.75^2 x [tex]\pi[/tex] = 7.5625[tex]\pi[/tex] = 23.76 miles^2 (2.d.p)
Find the slope of the line that passes through (6, 8) and (2, 17).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer:
-9/4
Step-by-step explanation:
Slope is equal to the change in y, over the change in x, or rise over run.
x, is the run
y, is the rise
You can substitute the coordinate numbers on the equation to find the slope. which is y2-y1/x2-x1
m= 17-(8)
——
2-(6)
Your answer will be -9/4 (it doesn’t matter where the negative goes, and there’s a negative because 2-6= -4)
Hope this helps.
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 4 < x < 7.
f(x)
3
5
4.
9
5
15
6
23
7
33
Answer:
Submit Answer
attempt 2 out of 2
Answer:
8
Step-by-step explanation:
It appears your table includes points (4, 9) and (7, 33). The average rate of change on the interval is the slope of the line between these two points:
m = (y2 -y1)/(x2 -x1)
m = (33 -9)/(7 -4) = 24/3 = 8
The average rate of change is 8.
(Brainliest question) Which type of study best describes the following research most likely to be done? A researcher is trying to determine the effects of animal habitats and animal populations after forest fires. So she visits places that have had a naturally occurring Forest fire to study the area.
Experimental study
Observational study
Simulation study
Double blind study
Answer:
Observational study
Step-by-step explanation:
See the researcher visits the forest.She want to experience or observe the forest fire.She want to observe how it affects the animals.Hence it's observational studyMaxden wanted to measure the length of the objects below.
For each one circle which unit of measurement he should use.
A. His puppy
Inches or Yards
B. A toy car
Yards or Centimeters
C. Width of his desk
Yards or Feet
D. His foot
Inches or Yards
Francis owns a cake shop. She is currently preparing cupcakes (x) and cookies (y) for two birthday
parties. The first birthday party ordered 20 cupcakes and 40 cookies and their total cost was $61. The second birthday party ordered 30 cupcakes and 30 cookies. Their total cost was $64.50.
Answer:
Step-by-step explanation:
20x + 40y = 61 this is the equation for the first party
30x + 30y = 64.50 this is the equation for the second party.
write an equation in slope-intercept form for the line with y-intercept −8 and slope 1/3.
Answer:
y = x/3 - 6
Step-by-step explanation:
yeah-ya......... right?
van is watching the birds in his backyard, of the birds he watched 9 of them or 45% are sparrows, how many birds are in his backyard
Help a bro outttttttt
Answer:
15Step-by-step explanation:
pick any 2 sides
3x+6=6x-3
+3
3x+9=6x
-3x
9=3x
/3
x=3
3*9x=27
27-12=15
I need help with pre calculus.
Question 1
Answer: Choice A) -7-----------------
Explanation:
To compute f(g(2)), we'll first need to find g(2).
Locate 2 in the x row. Then read straight down until you get to the g(x) row. You should find that g(2) = 4
This means f(g(2)) becomes f(4). We then repeat the same process as before. Locate 4 in the x row, read straight down til you get to the f(x) row to find that f(4) = -9
Overall, we can say f(g(2)) = -9
We do the same set of steps to compute g(f(-1)). You should find that f(-1) = -1 and g(f(-1)) = g(-1) = -2
Lastly, we subtract the results we got:
f(g(2)) - g(f(-1)) = -9 - (-2) = -9+2 = -7
==============================================
Question 2
Answer: Choice B) 0-----------------
Explanation:
If you were to graph each equation, you should get what you see below.
The red and blue curves do not intersect in any way. We need an intersection point to have a solution. Because there are no intersections, we don't have any solutions. The system is considered inconsistent.
==============================================
Question 3
Answer: Choice B[tex]-2x^2+250x-2000[/tex]-----------------
Explanation:
x = number of scooters made and sold
Each scooter costs $150 to make. If you made x of them, then it costs 150x dollars. Then tack on the fixed cost of $2000 to get the expression [tex]150x+2000[/tex]
The cost function is [tex]C(x) = 150x+2000[/tex]. We'll subtract this from the revenue function R(x) to get the profit P(x)
[tex]\text{Profit} = \text{Revenue} - \text{Cost}\\\\P(x) = R(x) - C(x)\\\\P(x) = (400x-2x^2) - (150x+2000)\\\\P(x) = 400x-2x^2-150x-2000\\\\P(x) = -2x^2+250x-2000\\\\[/tex]
==============================================
Question 4
Answer: Choice B[tex]\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}[/tex]
-----------------
Explanation:
[tex]g(x) = \frac{1}{x+1}\\\\g(f(x)) = \frac{1}{f(x)+1}\\\\g(f(x)) = \frac{1}{x^2+x-3+1}\\\\g(f(x)) = \frac{1}{x^2+x-2}\\\\g(f(x)) = \frac{1}{(x+2)(x-1)}\\\\(g\circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\[/tex]
I started with the outer function g(x) and replaced each x with f(x) in the second step. Then I plugged in f(x) = x^2+x-3 and simplified. Factoring the denominator is helpful to determine where the denominator becomes zero. Specifically, it happens when x = -2 and x = 1. These x values must be kicked out of the domain to avoid a division by zero error.
So we start off with the real number line, and poke holes at x = -2 and x = 1.
The notation [tex]x \in \mathbb{R}[/tex] means x is a real number. Then we tack on [tex]x \ne -2, x \ne 1[/tex]
Overall, the domain is [tex]\left\{x\in \mathbb{R} \big| \ x \ne -2, x \ne 1\right\}[/tex]
Let's see what happens if we tried plugging x = -1 into this composite function:
[tex](g \circ f)(x) = \frac{1}{(x+2)(x-1)}\\\\(g \circ f)(-1) = \frac{1}{(-1+2)(-1-1)}\\\\(g \circ f)(-1) = \frac{1}{(1)(-2)}\\\\(g \circ f)(-1) = \frac{1}{-2}\\\\(g \circ f)(-1) = -0.5\\\\[/tex]
We don't get a division by zero error, so x = -1 is allowed. The same can be said about any other x value as long as it's not -2 and not 1 either.
Write a number using the following clues:
a multiple of 6
greater than 40, but less than 90
Answer:
48
Step-by-step explanation:
There are various multiples of 6 that are greater than 40, but less than 90. Including 42, 48, 54, 60, 66, 72, 78, and 84. :)
Mary works at a local Burger King restaurant. Her regular hourly wage is $14.70. If she works overtime, she
receives an hourly rate of 14 times her regular hourly rate. If she regularly works 40 hours per week with no
overtime, what is her regular weekly pay?
$882
$2.94
$588
$294
Answer:
I’m pretty sure it’s 588
Step-by-step explanation:
14.70 * 40 = 588
What is the constant of proportionality in xy-11=5?
Answer:
xy-11=5
ANSWER:
=16
Step-by-step explanation:
hope it helps to you
mark me as a brainlest please
What is the value -3/5 + (-0.75) +4 7/10
Enter your answer in the box.
Answer:
67/20 as an improper fraction, 3 7/20 as a mixed number and, 3.35 as a decimal
Hope this helped :)
Step-by-step explanation:
What is the equation for the line in slope-intercept form?
Enter your answer in the box.
Answer:1+1
Step-by-step explanation:
1+1=2
solve the system using substitution 5x+3y=-4 y-2x=6
Solving steps:-
5x+3y=−4
y−2x=6
-->To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
5x+3y=−4,−2x+y=6
-->Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.
5x+3y=−4
-->Subtract 3y from both sides of the equation.
5x=−3y−4
--> Divide both sides by 5.
x = 1/5(-3y - 4)
--> Multiply 1/5 −3y−4.
x = -3/5y - 4/5
--> Substitute -3y - 4/ 5 for x n the other equation, −2x+y=6.
-2 (-3/5y - 4/5) + y = 6
--> Multiply −2 times -3y - 4/ 5
6/5y + 8/5 + y = 6
--> Add 6y/5 to y
11/5y + 8/5 = 6
--> Subtract 8/5 from both sides of the equation.
11/5y = 22/5
--> Divide both sides of the equation by 11/5, which is the same as multiplying both sides by the reciprocal of the fraction.
y = 2
--> Substitute 2 for y in x= -3/5y - 4/5. Because the resulting equation contains only one variable, you can solve for x directly.
x = -3/5 x 2 - 4/5
--> Multiply -3/5 times 2.
x = -6 - 4/ 5
--> Add -4/5 to -6/5 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
x = -2
--> The equation is now solved.
Answer : x = -2, y = 2
Explanation : If you think this answer is good, please give "Brainliest" or rate/heart my answer. Hope this helps you.
Select all that apply.
Zack is taking a test in which he answers questions at a rate of question per minute. If Q represents questions and
M represents minutes, which of the following equations describe this rate relationship?
M= 20 x Q
Q = 2 x M
M=1/2 x Q
Q=1/2 x M
The equation Q = 2 x M represents the relationship between question and time.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Given that,
Zack takes a test, in which he answers at rate of 2 question per minute.
Also, Q represents questions
And M represents minutes.
According to given condition,
In 1 minute, Zack answers 2 question,
In M minutes, Zack answers 2 x M question,
Total questions presented by Q,
Q = 2 x M.
The required relationship for M and Q is Q = 2 x M.
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What is the value of X
The answer would be 6 I belive make sure to double check it
How do you use observed data to predict unobserved
what is the explanation
Answer:
the explanation of wot
Step-by-step explanation:
If you give an explanation of something, you give details about it or describe it so that it can be understood.
2+2 (I have been having a lot of trouble on this
Answer:
it's 4
Step-by-step explanation:
I hope it helps .....
Answer:
4
Step-by-step explanation:
2+2=4
I'll give a real world problem to help you understand. So pretend that you have 2 cookies on your plate and your sibling has 2 cookies on their plate too. If your siblings gives you their 2 cookies and you add them to your plate, how many cookies are on your plate now? There should now be 4 of them!
Does this help?
Can someone solve this question ~
[tex] - 6 \: log_{3}(x - 2) = - 24[/tex]
[tex]ɴᵉᵉᵈ \: ɢᵉⁿᵘⁱⁿᵉ \: ᴀⁿˢʷᵉʳ[/tex]
[tex]\huge \sf༆ Answer ༄[/tex]
The value of x is ~
[tex] \sf \: 83[/tex][tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
Let's solve ~
[tex] \sf \: - 6 log_{3}(x - 2) = - 24[/tex][tex] \sf \: log_{3}(x - 2) = \dfrac{ - 24}{ - 6} [/tex][tex] \sf \: log_{3}(x - 2) = 4[/tex][tex]x - 2 = {(3)}^{4} [/tex][tex]x - 2= 81[/tex][tex]x = 81 + 2[/tex][tex]x = 83[/tex]You're welcome spammy ~
The value of x from the given expression is 5
Laws of logarithmGiven the logarithm expression
[tex]-6log_3(x-2)=-24[/tex]According to the law of logarithm, if [tex]log_ab=c, \ hence \ b= a^c[/tex]
Applying this law to the given question, we can see that:
[tex](x-2)^{-6}=3^{-24}\\(x-2)^6=3^{24}\\(x-2)^6=3^6\\[/tex]
Cancel out the exponents to have:
x - 2 = 3
x = 2 + 3
x = 5
Hence the value of x is 5
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A principle at a certain high school claims that the students in her school are above average in SAT. She collects a random sample of 50 students and given an SAT test that provided with a mean score of 541. Is there sufficient evidence statistically to support the principal’s claim? The mean population SAT score is 500 with a standard deviation of 100. SAT scores are normally distributed. Please show all the steps involved in a hypothesis testing including proper statistical symbols, formula used, and report/interpret results in complete sentences.
Using the z-distribution, it is found that since the value of the test statistic is greater than the critical value for the right-tailed test, there is sufficient evidence to support the principal’s claim.
At the null hypothesis, it is tested if they are not above average, that is, their mean is of 500 or below, hence:
[tex]H_0: \mu \leq 500[/tex]
At the alternative hypothesis, it is tested if they are above average, that is, their mean is of more than 500, hence:
[tex]H_1: \mu > 500[/tex]
We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are: [tex]\overline{x} = 541, \mu = 500, \sigma = 100, n = 50[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{541 - 500}{\frac{100}{\sqrt{50}}}[/tex]
[tex]z = 2.9[/tex]
The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with the standard 0.05 significance level, is of [tex]z^{\ast} = 1.645[/tex].
Since the value of the test statistic is greater than the critical value for the right-tailed test, there is sufficient evidence to support the principal’s claim.
A similar problem is given at https://brainly.com/question/25728144
Evaluate the given expression for x = 4.
x? + 5x - 8
Answer:
16
Step-by-step explanation:
[tex]x = 4 \\ 4 + 5(4) - 8 = 16[/tex]
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8593 g and a standard deviation of 0.0511 g. A sample of these candies came from a package containing 464 candies, and the package label stated that the net weight is 396.1 g. (If every package has 464 candies, the mean weight of the candies must exceed 396.1 464=0.8537 g for the net contents to weigh at least 396.1 g.)
Answer:
The package label stated that the net weight is 381.8g If every package has ... brand of candies have a mean weight of 0.8616g and a standard deviation of ...
$5.15 per 5-pound bag
Answer: 1 pound = 1.03
Step-by-step explanation:
not sure what you wanted from this but here are possible answer
Hey there!
When you hear or see the word “per” in math, think of the question/word problem telling you to find the “for each”. This basically mean you’re dividing. So, let’s divide your numbers from each other.
$5.15/5 lb
= 5.15 ÷ 5 lb
= 5.15 ÷ 5 lb
= $1.03
Therefore, your answer SHOULD be: $1.03
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
