Answer:
D
Step-by-step explanation:
Plug in the x values to get the y values
Patty needs 3/4 cup of bananas to make a loaf of banana bread.
Patty has 1 1/3 cups of bananas.
Does Patty have enough bananas to make 2 loaves of banana bread?
Answer:
She Does NOT
Step-by-step explanation:
3/4 is .75 1 1/3 is 1.33 3/4*2= 1.5 which is more than 1.33
Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours how far did Simon drive in all
Answer:
415 miles
Step-by-step explanation:
Start with the speed equation:
speed = distance/time
Now solve the speed equation for distance:
distance = speed × time
Apply the speed equation solved for distance to the two parts of the trip.
4 hours at 55 mph:
distance = 55 mph × 4 hours = 220 miles
3 hours at 65 mph:
distance = 65 mph × 3 hours = 195 miles
Add the two distances to find the total distance:
total distance = 220 miles + 195 miles = 415 miles
Answer: 415 miles
Answer:
415 miles
Step-by-step explanation:
Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours.
How far did he drive?
d=rt
For the first part of the trip:
d = 55 * 4 = 220 miles
For the second part of the trip:
d = 65*3 =195 miles
Add the miles together
220+195 = 415 miles
What is the common ratio of the geometric sequence below?
625, 125, 25, 5, 1,
The common ratio is 1/5. By dividing each word by the term before it, we may find the geometric progression's common difference.
How to find common ratio ?The common ratio in geometric progression is the ratio of any term in the sequence to divided by the first term.
The Formula to calculate the common ratio in geometric progression, a, ar, ar2, ar3, ar4, ar5… is,
Common ratio = ar/ a = ar2/ ar = ……. = an/ an-1
As stated in the definition, we can compute the common difference of a geometric progression by dividing any term by its preceding term.
Given, the geometric sequence is 625, 125, 25, 5, 1,....
We have to find the common ratio of the given geometric sequence.
In geometric sequence, a, b, c, d, … the common ratio r is given by
r = b/a = c/b = d/c.
So, r = 125/625 = 25/125 = 5/25 = 1/5;
r = 1/5
Therefore, the common ratio is r = 1/5.
To learn more about common ratio refer :
https://brainly.com/question/26509106
#SPJ1
Answer:
B. 25/125
Step-by-step explanation:
Find the slope of the line y=5x+12.
Write your answer as an integer or as a simplified proper or improper fraction.
Answer:
5
Step-by-step explanation:
The slope or gradient of the line
using this formula as our guide line
y = mx +b
where m = slope
x = x– intercept
b = y– intercept
so
y = 5x + 12
the slope will be 5
i hope i helped pls rate as brainliest
Camilla wants to attach a string of lights to the edges of her patio
for a party She does not want the string to go across the edge with
the steps. White a linear expression that represents the length of
string in feet she will need. Then find the length if x = 3. 7.EE1
4x-2
3r
The length of string in feet she will need for her patio is equal to : L{s} = 2(x + y).
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is Camilla who wants to attach a string of lights to the edges of her patio for a party. She does not want the string to go across the edge with the steps.
Assume the shape of the patio is a rectangle with the dimensions of [x] and [y] units long. The length of string in feet she will need will be equivalent to the perimeter of the rectangle. So, the length of string in feet she will need is equal to L{s} = 2(x + y).
Therefore, the length of string in feet she will need for her patio is equal to : L{s} = 2(x + y).
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ1
What is the slope of (0,0) and (4,12)
[tex] \Large{\boxed{\sf Slope = 3}} [/tex]
[tex] \\ [/tex]
Explanation:The slope of a line passing through two points, also known as its gradient, is calculated using the slope formula.
[tex] \\ [/tex]
[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Slope \ formula \text{:}} \\~ \\ \tt m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1}\end{array} \right] } [/tex]
Where m is the slope of the line.
[tex] \\ [/tex]
First, let's identify our values:
[tex] \sf (\underbrace{\sf 0}_{x_1} \ , \ \overbrace{\sf 0}^{y_1} ) \ \ and \ \ (\underbrace{\sf 4}_{x_2} \ , \ \overbrace{\sf 12}^{y_2} ) [/tex]
[tex] \\ [/tex]
Now, substitute these values into the formula:
[tex] \sf \rightarrow m = \dfrac{12 - 0}{4 - 0} \\ \\ \sf \rightarrow m = \dfrac{12}{4} \\ \\ \\ \rightarrow \boxed{\boxed{\sf m = 3}} [/tex]
[tex] \\ [/tex]
[tex] \hrulefill [/tex]
[tex] \\ [/tex]
▪️Learn more about the slope formula here:
↣https://brainly.com/question/28293929
Answer:
slope = 3
How to Solve:
The question is asking us to find the slope, given two points.
These points are (0,0) and (4,12).
We will use the slope formula:
[tex]\boldsymbol{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
Where:
m = slope(x₁,y₁) and (x₂,y₂) are points that the line passes throughPlug in the data:
[tex]\boldsymbol{m=\dfrac{12-0}{4-0}}[/tex]
[tex]\boldsymbol{m=\dfrac{12}{4}}[/tex]
Simplify the fraction to its lowest terms:
[tex]\boldsymbol{m=3}[/tex]
Therefore, the slope is 3.
6 people equally share 1/2 a pan of mac and cheese write a division expression to represent the situation
Answer:
6/1.5
Step-by-step explanation:
You said equally, so you need to make sure that each person gets an even share. To do this, you can do people/things. Hence why the answer is 6/1.5!
Solve the following
6 2/5 - 4 4/5
[tex]6\frac{2}{5} - 4\frac{4}{5}[/tex] can be solved using subtraction of simple fraction and the final result is 8/5 .
what are simple fraction ?
A fraction in which both the numerator and the denominator consist of whole numbers.
Simplest form of a fraction:
A fraction is said to be in its simplest form if 1 is the only common factor of its numerator and denominator. For example, 8/9 ,because 1 is the only common factor of 8 and 9 in this fraction.
Simplifying proper and improper fraction
Find the highest common factor (HCF) of the numerator and denominator.Divide both the numerator and denominator by HCF.We simplify fractions because it is always to work or calculate when the fractions are in the simplest form.
To solve : [tex]6\frac{2}{5} - 4\frac{4}{5}[/tex]
We know that , in simple fraction [tex]6\frac{2}{5} - 4\frac{4}{5}[/tex] can be written as ,
[tex]6\frac{2}{5} - 4\frac{4}{5} = \frac{32}{5} - \frac{24}{5} = \frac{8}{5}[/tex]
Hence , 8/5 is the final answer .
Learn more about Simple Fractions at:
https://brainly.com/question/28336721
#SPJ1
Graph y +1 = 1/3 (x-3)
The graph of the linear equation, y + 1 = 1/3(x - 3), is given in the attachment below.
How to Graph a Linear Equation?A linear equation is an equation of the form "y = mx + b," where x and y are variables, and m is the slope and b is the y-intercept.
To graph a linear equation, of y + 1 = 1/3(x - 3), you can use the following steps:
Rewrite the equation in slope-intercept form to determine its slope (m) and the y-intercept (b).
y + 1 = 1/3(x - 3)
y + 1 = 1/3x - 1
y = 1/3x - 1 - 1
y = 1/3x - 2
The slope (m) of the line would be 1/3, which is the rise over the run of the line.
The y-intercept (b) of the line would be -2, which means the line will intercept the y-axis at -2.
The graph of y + 1 = 1/3(x - 3) is shown in the image below.
Learn more about the linear equation graph on:
https://brainly.com/question/14323743
#SPJ1
Let K=[tex]20^{20}[/tex].Suppose that [tex]\frac{20^{k} }{k^{20} } =20^{n}[/tex].find the largest power of 20 that divides n?
Answer:
20^2 = 400, the 2nd power of 20
Step-by-step explanation:
Given that k=20^20 and 20^k/k^20 = 20^n, you want the largest power of 20 that divides n.
LogarithmsTaking the base-20 logarithm of both equations, we have ...
[tex]\log_{20}{k}=\log_{20}{20^{20}}\ \Longrightarrow\ \log_{20}{k}=20\\\\\log_{20}{\dfrac{20^k}{k^{20}}}=\log_{20}{20^n}\ \Longrightarrow\ k-20\log_{20}{k}=n[/tex]
Substituting for k and log(k), we get ...
[tex]20^{20} -20\cdot20=n\\\\20^2(20^{18}-1)=n[/tex]
This shows us the largest power of 20 that is a factor of n is 20².
I've been unable to figure this out. Anyone able to assist on which is the correct answer?
The domain and range of the given function are {-2, 0, 1, 2, 3} and {-3, 0, 2, 3, 4} respectively
Domain and Range of a FunctionThe domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The domain of a function can be said as all possible values of x and the range of a function is all possible values of y.
The given function is
f(x) = {(0, -3), (2, 0), (3, 2), (1, 4), (-2, 3)
The domain of the function can be given as;
Domain : {-2, 0, 1, 2, 3}
Range : {-3, 0, 2, 3, 4}
Learn more on domain and range of a function here;
https://brainly.com/question/13146216
#SPJ1
Use the scale to help you solve the equation and find the value of x. Enter the
value of x below.
x + 3 = 9
X=_____
Answer:
x=6
Step-by-step explanation:
9-3=6 or 6+3=9
A pilot flies in a straight path for 130 minutes. She then makes a course correction, heading 10° to the right of her original course, and flies 145minutes in the new direction. If she maintains a constant speed of 600 miles per hour, how far is she from her starting position? Round your answer to the nearest mile. Enter deg after any degree value.
By using properties of triangle, it can be calculated that-
The pilot is 2740 miles from her starting position.
What is a triangle?
A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles.
Here,
The diagram has been attached
Time = 130 minutes = 2 hrs 10 minutes = [tex]2 + \frac{10}{60}[/tex] hours = [tex]\frac{13}{6}[/tex] hours
Speed = 600 miles per hour
Distance = [tex]\frac{13}{6} \times 600[/tex] = 1300 miles
Now,
Time = 145 minutes = 2 hrs 25 minutes = [tex]2 + \frac{25}{60}[/tex] hours = [tex]\frac{29}{12}[/tex] hours
Distance = [tex]\frac{29}{12}\times 600[/tex] = 1450 miles
Angle = [tex]10^{\circ}[/tex]
[tex]c^2 = 1300^2 + 1450^2 - 2\times 1300\times 1450\times cos(180-10)\\c^2 = 1690000 + 2102500 - (-3712725.2)\\c^2= 7505225.2\\c= \sqrt{7505225.2}\\c = 2740[/tex]
The pilot is 2740 miles from her starting position.
To learn more about triangle, refer to the link-
https://brainly.com/question/17335144
#SPJ1
Clare would like to buy a video game that costs at least $130. She has saved $48 so far and plans on saving $5 of her allowance each week. Write an inequality to find out the number of weeks it will take until she has enough money to buy the game.
Answer:
5x+48=130
Step-by-step explanation:
5 is the money she gets each week. X is the number of weeks. X can be found easily but for the sake of this question, It's unknown. so 5x and then add the 48 she's already saved you get 5x+48=130 or 5x+48 is greater than or equal to 130.
[tex]\int\limits^2_076e^4 {x} \, dx[/tex]
if all possible samples of size n are drawn from an infinite population with a mean of 36 and a standard deviation of 22, then the standard error of the sample mean equals 2 for samples of size:
Thus , it is False. As there is confidence level is not given, then cant calculate the sample size.
The standard deviation is what?The standard deviation in statistics is a measure of how widely spread a set of values can be or how much they can vary. A low standard deviation denotes that values are typically close to the mean of the collection, whereas a high standard deviation indicates that values are dispersed across a greater range.
Here,
The standard error of the sample mean is equal to 2 for samples of size n if all conceivable samples of that size are taken from a population with an infinite mean and standard deviation.
In the above statement confidence level is not given.
Thus , it is False. As there is confidence level is not given, then cant calculate the sample size.
To know more about standard deviation , visit
https://brainly.com/question/23907081
#SPJ4
How to find the missing side Using Pythagoras Theorem?
y=x² - 4x³
Find the value of y when x = -1.
Answer:
y = 5
Step-by-step explanation:
[tex]y=x^2-4x^3[/tex] (Given)Plug x = -1 in the above equation, we find:[tex]y=(-1)^2-4(-1)^3[/tex][tex]\rightarrow y=1-4(-1)[/tex][tex]\rightarrow y=1+4[/tex][tex]\rightarrow \red{y=5}[/tex]CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
351.5625
1,440,000
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7 cm}\underline{General form of an Exponential Function}\\\\$y=Ae^{kt}$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $k$ is a constant.\\ \phantom{ww}$\bullet$ $t$ is time.\\\end{minipage}}[/tex]
Given:
Doubling period = 15 minutesAt t = 120 minutes, y = 90,000(Let t = time in minutes).
If the doubling period is 15 minutes, then at t = 135 minutes, y = 180,000:
[tex]\implies 90000=Ae^{120k}[/tex]
[tex]\implies 180000=Ae^{135k}[/tex]
Divide the second equation by the first to eliminate A, and solve for k:
[tex]\implies \dfrac{180000}{90000}=\dfrac{Ae^{135k}}{Ae^{120k}}[/tex]
[tex]\implies 2=\dfrac{e^{135k}}{e^{120k}}[/tex]
[tex]\implies 2=e^{135k} \cdot e^{-120k}[/tex]
[tex]\implies 2=e^{15k}[/tex]
[tex]\implies \ln 2 = \ln e^{15k}[/tex]
[tex]\implies \ln 2 =15k \ln e[/tex]
[tex]\implies \ln 2 =15k[/tex]
[tex]\implies k=\dfrac{1}{15}\ln 2[/tex]
Substitute t = 120, y = 90000 and the found value of k into the formula and solve for A:
[tex]\implies 90000=Ae^{\left(120 \cdot \frac{1}{15}\ln 2\right)}[/tex]
[tex]\implies 90000=Ae^{\left(8\ln 2\right)}[/tex]
[tex]\implies 90000=Ae^{\ln256}[/tex]
[tex]\implies 90000=256A[/tex]
[tex]\implies A=\dfrac{90000}{256}[/tex]
[tex]\implies A=351.5625[/tex]
Therefore, the function that models the scenario is:
[tex]\large\boxed{y=351.5625e^{\left(\frac{1}{15}t \ln 2\right)}}[/tex]
So the initial population at time t = 0 was:
351.5625To find the size of the bacteria population after 3 hours, substitute t = 180 into the found formula:
[tex]\implies y=351.5625e^{\left(\frac{1}{15}(180) \ln 2\right)}[/tex]
[tex]\implies y=351.5625e^{\left(12 \ln 2\right)}[/tex]
[tex]\implies y=351.5625e^{\left(\ln 4096\right)}[/tex]
[tex]\implies y=351.5625 \cdot 4096[/tex]
[tex]\implies y=1440000[/tex]
Therefore, the size of the bacterial population after 3 hours was:
1,440,000The initial population at the time t = 0 is 351.5625. And the size of the bacterial population after 3 hours is 1,440,000.
What is Exponential Growth?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.
If n₀ is the initial size of a population experiencing exponential growth, then the population n(t) at time t is modeled by the function:
n(t) = n₀(e[tex])^{rt}[/tex]
Where r is the relative rate of growth expressed as a fraction of the population.
Given:
Doubling period = 15 minutes
At t = 120 minutes, n(t) = 90,000
If the doubling period is 15 minutes, then at t = 120+15 = 135 minutes,
90000 = n₀(e[tex])^{120r}[/tex]
18000 = n₀(e[tex])^{135r}[/tex]]
To find the r:
Take ratio of both of the equations,
90000 / 18000 = n₀(e[tex])^{120r}[/tex] / n₀(e[tex])^{135r}[/tex]
2 = (e[tex])^{135r}[/tex] . (e[tex])^{-120r}[/tex]
r = 1/15 ln2
Substitute the value of r, t and y.
90000 = n₀(e[tex])^{120r}[/tex]
90000 = 256n₀
n₀ = 351.5652
Now, the function
n(t) = n₀(e[tex])^{rt}[/tex]
n(t) = (351.5652)(e[tex])^{(1/15)(180)(ln2)}[/tex]
n(t) = 1440000
Therefore, the initial population at the time t = 0 is 351.5625. And the size of the bacterial population after 3 hours is 1,440,000.
To learn more about the exponential growth;
https://brainly.com/question/12490064
#SPJ1
for School: Practice & Problem Solving
Amelia needs to buy some cat food. At the nearest store, 3 bags of cat food cost $6.75. How much would Amelia spend on 2 bags of cat food?
Answer:
$4.50
Step-by-step explanation:
Use a proportion:
$6.75 is to 3 bags as x is to 2 bags.
6.75/3 = x/2
3x = 2 × 6.75
x = 4.50
Answer: $4.50
Answer:
$4.50
Step-by-step explanation:
Given 3 bags of cat food cost $6.75, you want the cost of 2 bags.
ProportionUnless there is a volume discount (or surcharge), the price is proportional to the quantity. That means 2 bags will cost 2/3 the amount that 3 bags cost.
cost of 2 bags = 2/3 · $6.75 = $4.50
Amelia would spend $4.50 on 2 bags of cat food.
1/4 + 29/16 - 9735/12
Answer:
Step-by-step explanation:
To solve this problem, we need to add and subtract the fractions given. To do this, we need to find a common denominator for all of the fractions.
The least common multiple of 4, 16, and 12 is 48, so we can rewrite each fraction with a denominator of 48:
1/4 = 3/12
29/16 = 87/48
9735/12 = 4047/48
Then, we can add and subtract the fractions as follows:
3/12 + 87/48 - 4047/48 = (3 - 4047)/48 = -4044/48 = -84/16
Therefore, the final answer is -84/16, or -5 and 1/16 in simplified form.
I need help with these 2 questions.
A) Write and solve a proportion to determine the height of the cell phone tower. Please show your work.
B) What is the height of the tower in meters?
Part (A)
Because the right triangles are similar, we can form two ratios P/Q and R/S that are equal to one another.
P/Q = R/S
where,
P = height of the personQ = horizontal distance person is from the left-most cornerR = height of the towerS = horizontal distance the tower is from the left-most cornerIn this case,
P = 1.8 metersQ = 6 metersR = unknown, we'll use variable hS = 60 metersTherefore, we go from this
P/Q = R/S
to this
(1.8)/6 = h/60
Other equations can be set up. This means there are other possible final answers. The key is to have things be consistent. The equation I've set up has the vertical components as the numerators, while the horizontal components are the denominators.
--------------
Answer: (1.8)/6 = h/60====================================================
Part (B)
Let's cross multiply and solve for h.
(1.8)/6 = h/60
1.8*60 = 6h
108 = 6h
6h = 108
h = 108/6
h = 18
--------------
Answer: 18 metersAnswer:
A). [tex]\frac{1.8}{6} = \frac{height}{60}[/tex]
B). 18 meters tall
Step-by-step explanation:
We see TWO right triangles in this problem:
the one with the man and the 6m and the one with the phone tower and the 60mThese triangles are proportional so we can make a ratio out of them
the height of the man over the side of the triangle (6m)
and the height of the tower over the length of its triangle (60m)
Set these equal to each other to complete part A
[tex]\frac{1.8}{6} = \frac{height}{60}[/tex]
And by using cross multiplication (which is what you do for ratios), solve for h!
For a quick example of cross multiplication, I've attached a picture.
Now let's do it!
1.8 × 60 = 6 × h
108 = 6h
108/6 = h
h = 18
The height of the cell phone tower is 18 meters.
standard position intersects the unit circle at (√30/7,-√19/7). What is cot(θ)?
The cotangent of the angle is -√570/30
How to determine the cotangent of the angle?From the question, we have the following parameters that can be used in our computation:
(√30/7,-√19/7)
This means that
(x, y) = (√30/7,-√19/7)
The cot(θ) is calculated as
cot(θ) = y/x
Substitute the known values in the above equation, so, we have the following representation
cot(θ) = (-√19/7)/(√30/7)
Evaluate
cot(θ) = -√19/√30
Rationalize
cot(θ) = -√570/30
Hence, the value of cot(θ) is -√570/30
Read more about unit circle at
https://brainly.com/question/20691579
#SPJ1
write an integral that expresses the increase in the perimeter p(s) of a square when its side length s increases from 2 units to 5 units
The integral to express the increase in the perimeter p(s) of a square when its side length s increases from 2 units to 5 units is:
p(s) = 4s
Integral = ∫2s5s ds
= ∫2s5s dx
= [s2/2]2s5s
= (25/2) - (4/2)
= 20/2
= 10
Therefore, the increase in the perimeter of the square when its side length s increases from 2 units to 5 units is 10 units.
To calculate this increase, we used the formula for the perimeter of a square, which is 4s, and the integral from 2s to 5s, which gives us the area under the graph and the difference between the two side lengths. We then solved for the integral and multiplied it by 4 to get the increase in the perimeter.
For more questions like Perimeter click the link below:
https://brainly.com/question/21890765
#SPJ4
Find the GCF of each expression.
The GCF of 12y - 3 is_____.
The GFC of 4y + 10 is_____.
The GCF of 28 − 8 is _____.
The GCF of 30 + 18 is _____.
The GCF of each expression that was given above are: 3, 2 , 4 , and 6 which can be written as:
12y-3=34y+10=228y-8=430y+18=6What is greatest common factor?The GCF which isthe “greatest common factor”. can be defined as the largest number that is a factor of two or more numbers.
Intance of this is that the GCF of 24 and 36 is 12, and this is due to the fact that the largest factor that is shared by 24 and 36 is 12.
Option 1:
The GCF of 12y-3=3 because the common factor which is the highest factor of 12 and 3 is 3
Option2
The GCF of 4y+10=2 because the common factor which is the highest factor of 4 and 10 is 2 and so on.
Option 3:
The GCF of 28 − 8= 4 because the common factor which is the highest factor of 28 and 8 is 4
Option 4:
The GCF of 30y+18=6 because the common factor which is the highest factor of 30 and 18 is 6
Learn more about GCF at:
https://brainly.com/question/219464
#SPJ1
NO LINKS!!
A deposit pf $6000 is made in a college savings fund that pays 5.0% interest, compounded continuously. The balance will be given to a student after the money has earned interest for 40 years. How much (in dollars) will the student receive? (Round your answer to the nearest cent.)
Answer:
$44,334.34
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]
Given:
P = $6000r = 5.0% = 0.05t = 40 yearsSubstitute the given values into the continuous compounding formula and solve for A:
[tex]\implies A=6000e^{0.05 \times40}[/tex]
[tex]\implies A=6000e^2[/tex]
[tex]\implies A=6000(7.3890560...)[/tex]
[tex]\implies A=44334.33659...[/tex]
Therefore, the balance of the account after 40 years will be $44,334.34 (nearest cent).
The concentration C(t) of a certain drug in the bloodstream after t minutes is given by the formula C(t)=0.05(1−e^−0.2t). What is the concentration after 12 minutes? Round to three decimal places.
Thus after 12 minutes concentration of drug is 0.045.
The concentration C(t) of a certain drug in the bloodstream after t minutes is given by the formula [tex]c(t) = 0.05(1-e^{-0.2t} )[/tex]
Drug concentration is amongst the most important determinants of clinical response to a drug.
Drug concentration will be seen to increase in biological samples drawn from the systemic circulation when the amount of drug absorbed exceeds the amount of drug that is distributed into the extravascular tissues and the drug that is metabolized and/or excreted during this period.
Thus after 12 minutes concentration of the drug is = C(5).
Now
C(5) = [tex]0.05(1-e^{-0.2t} )[/tex]
= [tex]0.05(1-e^{-2.4} )[/tex]
= 0.05(1-0.0907)
= 0.05×0.9093
= 0.045
The drug concentration is 0.045.
For such more questions about concentration:
https://brainly.com/question/14378082
#SPJ4
Hypothesis 1 H0: Receiving a 20 percent off coupon does not increase the number of customers visiting the Lotions and Potions soap store. Ha: Receiving a 20 percent off coupon increases customers visiting the Lotions and Potions soap store. Data Customers on file who visited the store during coupon promo: 32 percent Customers on file who visit the store during a typical week: 30 percent Sample size: 4,500 Questions Did you use a z-test or t-test? Why? What is the P value? Do you accept or reject the alternative hypothesis? Should Lotions and Potions continue to offer this promotion in order to increase visits? Why or why not?
The data Customers on file who visited the store during coupon promo is 32% .
a) We use Z-test for testing hypothesis in this case because it is single proportion.
b) The P-value is 0.0017.
c) As P value < α = 0.05 , So we reject the null hypothesis.
d) Yes, Lotions and Potions continue to offer this promotion in order to increase visits because null hypothesis is rejected that alternative hypothesis is true which gives the same results.
The Null and Alternative hypothesis related to 20 percent off coupon does not increase the number of customers or increase the number of customers.
Sample size ,n = 4,500
Significance level, 0.05
a) We use z-test, because this is single proportion hypothesis test.
Below are the null and alternative Hypothesis,
Null Hypothesis, H₀ : p = 0.3
Alternative Hypothesis, Hₐ : p > 0.3
b) Test statistic,
z = (p-cap - p)/sqrt(p×(1-p)/n)
z = (0.32 - 0.3)/sqrt(0.3× (1-0.3)/4500)
z = 2.93
Using the Z-table, the P value at significance level 0.05 and z = 2.93 is 0.0017
As we see P-value < α = 0.05, so, reject the null hypothesis.
Yes, Lotions and Potions should continue to offer this promotion in order to increase visits.
To learn more about Hypothesis testing, Refer:
https://brainly.com/question/4232174
#SPJ4
Help please fast!! picture attached below 27 point
What is the mean number of points scored by these players?
A. 7
B. 8
C. 9
D. 10
Option (b) is correct as mean of top five scorers on soccer team is 8 from given bar graph.
What is mean in statistics?In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.
Mean = (Sum of values)/(Total observations)
Using above formula, we get
Calculating mean for given bar graph,
[tex]=\frac{4+6+10+9+11}{5}\\=\frac{40}{5}\\=8[/tex]
So, mean score of five players comes out to be 8.
Learn more about mean here:
https://brainly.com/question/14532771
#SPJ1
This graph best represents the motion of an object that
a
is increasing its' acceleration.
b
first increases acceleration then remains constant.
c
shows no motion.
d
was at rest and is accelerating uniformly.
The motion of the object on the graph, can best be represented as an object that d. was at rest and is accelerating uniformly.
What is the acceleration ?The object on the graph is accelerating such that the acceleration is stable and uniform. This is why the speed - time line is a straight and diagonal line to show that the speed is proportional to time.
We know that the object started from rest because at the point where time was 0, the object was not accelerating and so was not moving. As time moves on, the object increases speed, thereby accelerating.
Find out more on acceleration at https://brainly.com/question/24606066
#SPJ1