Certain drugs are eliminated from the bloodstream at an exponential rate (for example, 10% of a drug eliminatesfrom the blood per hour). Write an exponential model for the following situation. The drug dosage is 600 mg, Thedrug is eliminated at a rate of 5.3% per hour. Use D as the amount of the drug in milligrams and t as the time inhours.D=________ (type an expression using t as the variable.)How much of the drug is left after 4 hours?
Answers
Explanation:
If the dug dosage is 600 mg and 5.3% is eliminated per hour, we have:
\(\begin{gathered} D(t)=600\cdot(1-\frac{5.3}{100})^t \\ D(t)=600\cdot(\frac{94.7}{100})^t \\ D(t)=600\cdot(0.947)^t \end{gathered}\)Because for each hour the drug is eliminated at a rate of 5.3%, so the 94.7% of the previous amount remains.
Answer:
\(D(t)=600\cdot(0.947)^t\)How much of the drug is left after 4 hours?
\(\begin{gathered} D(4)=600\cdot(0.947)^4 \\ D(4)\approx4.82.5598\text{ mg} \\ \end{gathered}\)Related Questions
A fish tank is in the shape of a rectangular prism. What is the volume of the fish tank? Round to the nearest tenth if necessary.
Answers
Answer:
The volume is 10 × 20 × 12 = 2,400 square inches.
write an equation in slope intercept form that passes through the given point and is perpendicular to the graph of given equation (1,-2) y=5x+4
Answers
The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.
To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.
The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.
To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.
The negative reciprocal of 5 is -1/5.
Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Substituting the values:
y - (-2) = (-1/5)(x - 1)
Simplifying:
y + 2 = (-1/5)(x - 1)
To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:
y + 2 = (-1/5)x + 1/5
Subtracting 2 from both sides:
y = (-1/5)x + 1/5 - 2
Combining the constants:
y = (-1/5)x - 9/5
Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.
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4.
fourteen hundredths + eighty and seventy-nine thousandths =
Answers
Deandre's chocolate bar is 53% cocoa. If the weight of the chocolate bar is 69 grams, how many grams of cocoa does it contain? Round your answer to the nearest tenth.
Answers
The grams of cocoa does it contains is 36.57 grams
How many grams of cocoa does it contains?From the question, we have the following parameters that can be used in our computation:
Weight of the chocolate bar = 69
Proportion = 53%
This implies that
Grams of cocoa = weight of the chocolate bar * Proportion
Substitute the known values in the above equation, so, we have the following representation
Grams of cocoa = 53% * 69
Evaluate the products
Grams of cocoa = 36.57
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45. A 5-foot log leans against a wall and inclines at a 45° angle from the ground. What expression will
solve the distance between the base of the log to the base of the wall?
A. sin 45
B. cos 45
C. tan 45
D. csc 45
46. What trigonometric ratio can we use to solve for the height of a building given the distance between
the observer and the base of the building and its angle of elevation?
A. Sine
B. Cosine
C. Tangent
D. Secant
47. With the sun, a girl 1.4 m tall casts a 3.6 m shadow. Find the angle of elevation from the tip of
the shadow to the sun.
A. 18°
B. 19°
C. 20°
D. 21°
48. What formula is used to solve the problem: "Find zB in an oblique triangle ABC with the
following measures: A = 50°, a = 15 and b = 10."
A. Sine Law
B. Cosine Law
C. Tangent Law
D. Cosecant Law
49. In an oblique triangle XYZ, ZX = 63°, x = 139 and y = 140. Find
A: 100°
B. 64°
C. 60°
D. 45°
50. What formula will solve: "Jackie and Peter skate apart with an angle of 15° between them.
Jackie skates for 5 meters and Peter skates for 7 meters. How far apart are the skaters?
A. d² = 52+72-2(5)(7) cos 15
C. 7² = 52+d²-2(5)(d) cos 15
B. 52= d²+72-2(d)(7) cos 15
D. 152=52+72-2(5)(7) cos
Answers
Answer: it was be cos4
Step-by-step explanation: 1/2 divided by 3/4 = cos4
Given m = 7 and the point (3, -1), which of the following is the point-slope form of the equation
Answers
Answer:
y = 7x - 22
Step-by-step explanation:
We know that point-slope form is y = mx + b (b is y-intercept, m is slope, and the y and x is of any point on the line)
We can plug in m as 7, y as -1, and x as 3 to get:
-1 = 21 + b
You can subtract 21 on both side to get b = -22.
Then, we plug in m = 7 and b = -22 to y = mx+b to get y = 7x + (-22) which simplifies to:
y = 7x - 22
Let h(x) = (fog)(x) = (x - 2)^4. Find f(x) given g(x) = x - 2.
f(x) =
Answers
Answer:
f(x) = x^4
Step-by-step explanation:
h(x) = f(g(x)) = (x - 2)^4
g(x) = x - 2
h(x) = f(g(x)) = (g(x))^4
f(x) = x^4
if a flight to europe takes about 13 hours and you make one round trip flight per month how many total days do you travel in a year
Answers
Answer:
13 days
Step-by-step explanation:
Given that a one-way flight to europe will take 13 hours
A round trip will take = 13 hrs x 2 = 26 hours
Also given that we make one round trip per months for 12 months (1 year)
We will take a total of 12 round trips per year
Number of hours taken for 12 round trips
= 26 hours per round trip x 12 round trips
= 26 x 12
= 312 hours
Recall that there are 24 hours in a day, hence to convert 312 hours into days, we have to divide this by 24.
Number of days = number of hours ÷ 24
= 312 ÷ 24
= 13 days
Which of the following situations can be best represented by the inequality 6X + 15 < 100 ?
Answers
Answer:
6x<100-15
6x<85
x<85/6
x<14.17
Step-by-step explanation:
Consider a rectangle with width of x units and an area of 10 square units. The length l of the rectangle can be modeled by the function f (x) = 10\x. Suppose the width of the rectangle increases 1 unit, while the area remains constant. Which graph models the length of the new rectangle?
please explain the answer step by step and explain why you chose the option you chose.
Answers
In linear equation, The graph in option 3 models the length of the new rectangle.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
According to the problem,
width of the rectangle is x units
Area of the rectangle is 10 square units
Length of the rectangle is given by f(x) = 10/x
Now if width becomes (x+1) units
∴ Length will be represented as 10/(x+1)
Now from the given options we need to find the exact graph of f(x) = 10/(x +1)
Here if x = 4 , y =2
So the point (4 , 2) is satisfied which is only happening in the graph of option 3
Option 3 represents the correct graph.
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Which of the following python methods can be used to perform simple...
Which of the following python methods can be used to perform simple linear regression on a data set? Select all that apply.
Question 3 options:
A. linregress method from scipy module
B. simplelinearregression from scipy module
C. ols method from statsmodels module
Answers
The python methods that can be used to perform simple linear regression on a data set are -
A. linregress method from scipy module
C. ols method from statsmodels module
The linregress method from the module is the most simplest and effortless method for performing simple linear on the data set. It consists of two arrays one represents the independent variables and the second represents the dependent variables.
The relationship between two variables can be modeled using simple linear regression, where the first variable is treated as the independent variable and the other as the dependent variable. Finding the line of best fit that lowers the squared sum of the residuals is the goal.
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3. Vocabulary Suppose △MNP ∼△RST. How can you identify corresponding parts?
4. Reasoning Suppose △ABC ∼△TUV. Determine whether each pair of measures is equal.
a. the measures of ∠A and ∠T
b. the perimeters of the two triangles
c. the ratios of the sides BC/UV and AC/TV
5. Reasoning e scale of a map is 1 in. : 100 mi. Is the actual distance between two towns 100 times the map distance between the two towns? Explain.
Answers
Similar triangles may or may not have congruent sides, but the ratio of the corresponding sides will always be congruent.
(3) Corresponding sides of △MNP and △RST
Given that △MNP ∼△RST.
This means that, the corresponding sides are:
MN and RSMP and RTNP and ST(4) The equal measures
Given that △ABC ∼△TUV
This means that, the corresponding angles are equal, but corresponding sides are not.
So, the equal measures are:
(a). the measures of ∠A and ∠T (c). the ratios of the sides BC/UV and AC/TVThe unequal measure is:
(b). the perimeters of the two triangles(c) Scale mapping
The scale mapping is given as:
\(Ratio = 1\ in : 100\ mi\)
The above scale means that 1 inches on the scale represents 100 miles of the actual distance.
Take for instance, 5 inches would represent 500 miles.
500 is 5 times 100
Hence, the actual distance between two towns 100 times the map distance between the two towns
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ILL GIVE BRAINLY What is the surface area of the cube?
Drag and drop the correct surface area to match the cube.
Answers
Answer:
Below
Step-by-step explanation:
A cube has SIX sides of equal area
each side has area = L x W and L and W are the same = 4.5 m
so: Area = six X ( 4.5 X 4.5) = 6 * 4.5 * 4.5 = 121.5 m^2
Answer:
Hope the picture will help you...
The GCF of 12 and 28 is _____.
Answers
greatest common factor 12 and 28 is 4
The greatest common factor (GCF) of 12 and 28 is 4.
To find the GCF, you can determine the factors of both numbers and identify the greatest common factor they share.
As we know that a factor is a number that entirely divides another number.
To put it another way, any two integers that multiply to generate a result are factors of the result.
For 12, the factors are 1, 2, 3, 4, 6, and 12.
For 28, the factors are 1, 2, 4, 7, 14, and 28.
The common factors of 12 and 28 are 1, 2, and 4.
Among them, the greatest common factor is 4.
Therefore, the GCF of 12 and 28 is 4.
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I need help please
Answers
Determine if the equation given in slope-intercept form represents the graph. If the equation is correct support your reasoning with why it is correct. If the equation is incorrect, give the correct slope-intercept form equation explaining how you determined it.
Answers
The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.
The graph is given in the question.
As per the given line, we take two points (0, 4) and (5, 8)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 0, y₁ = 4
x₂ = 5, y₂ = 8
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 4 = (8 - 4)/(5-0 )[x -0]
⇒ y - 4 = (4/5)x
⇒ y = (4/5)x + 4
The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.
So, the equation of the line would be y = (4/5)x + 4.
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Please help and Please write real equation for the answer thank you
Answers
Answer:
f(x) = (3x -12)/(x² -7x +12)
Step-by-step explanation:
The equation for a rational function can be written from the clues offered by the horizontal and vertical asymptotes, the y-intercept, and any "holes" in the function graph. Here, those clues are ...
horizontal asymptote: y = 0vertical asymptote: x = 3hole: (x, y) = (4, 3)y-intercept: (0, -1)__
The horizontal asymptote at y=0 tells you the denominator is of higher degree than the numerator. The vertical asymptote at x=3 tells you (x-3) is a factor of the denominator. The hole at x=4 tells you there is a factor of (x-4) in both numerator and denominator.
At this point, the function is tentatively ...
\(f(x)=a\dfrac{x-4}{(x-3)(x-4)}\)
Evaluating this at the y-intercept, x=0, gives ...
f(0) = -1 = a/(0 -3) = -a/3
a = 3 . . . . . multiply by -3
Then our rational function, consistent with all of the features of the graph, is ...
\(f(x)=\dfrac{3(x -4)}{(x -3)(x -4)}\\\\\boxed{f(x)=\dfrac{3x-12}{x^2-7x+12}}\)
A dilation is a transformation in which the _____, but not the shape, of a geometric figure is changed.
Answers
no explanation really
like dilation 2x, 2y makes the size bigger but the shapes rhe same
Guys please help me I don’t understand and my test is due at 12 I only have 40min HELP GREATLY APPRECIATED!!!
Answers
Answer:
{9} Slope: -1
Y-intercept = 0
Step-by-step explanation:
Slope-----
Recall slope-intercept form
y=mx+b, with slope m and a y-intercept of b. With this in mind, we can rewrite our equation as y=−x+0
We see that our slope, or coefficient on x, is −1.
Y-intercept-----
We can rewrite this equation as:y=1x+0
The slope-intercept form of a linear equation is: y=mx+b
Where m is the slope and b is the y-intercept value.
For this equation:y=1x+0
Therefore:
The slope is m=1
The y-intercept is b=0 or (0,0)
Hope this helps!
Please answer this correctly without making mistakes
Answers
Answer:
\( \boxed{\sf 319:3388} \)
Step-by-step explanation:
Total number of tickets sold = 3388
Total number of coach tickets = 3069
Total number of first-class tickets = Total number of tickets sold - Total number of coach tickets
= 3388 - 3069
= 319
\( \therefore\)
Ratio of the number of first-class tickets to the total number of tickets = 319:3388
Answer:
\( \boxed{ 319 : 3388}\)Step-by-step explanation:
Given, Total no. of tickets sold = 3388
Total no. of coach tickets = 3069
Then, No. of first class ticket:
= 3388 - 3069
= 319
We need to find the ratio of first-class tickets to the total number of tickets: 319 : 3388
HELP ME PLS I LITERATELY CANT
Answers
Let's start by finding out how many minutes Jonathan practices per day. Since there are 14 days in 2 weeks, we can divide the total practice time by 14 to get the average daily practice time:
658 minutes ÷ 14 days = 47 minutes per day
Now we can write a proportional equation in terms of d, the number of days Jonathan practices:
t = 47d
This equation tells us that Jonathan's total practice time (t) is proportional to the number of days (d) he practices, with a constant rate of 47 minutes per day. As he practices more days, his total practice time will increase in a linear fashion.
To evaluate whether customers enjoy the barista’s new smoothie, a restaurant manager surveys every other customer who orders the new smoothie. The manager determines that customers enjoy the new smoothie. Select all the statements that are true about the sampling method.
Answers
The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.
Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:
1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.
2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.
3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.
4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.
5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.
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3. My divisor is 8.
I am less than 30.
I am greater than 3 X 8.
My remainder is 5.
What dividend am I?
Answers
Answer: 29
Step-by-step explanation:
29 ÷ 8 = 3 remainder: 5
I solved using long division.
Answer:
29
Step-by-step explanation:
30
24
5
8x3=24
24+5= 29
Beacuase it had to be smaller than 30
What are the zeros of the function below? Check all that apply.A.-5B.2C.-3D.3E.-2F.0
Answers
Given
\(f(x)=\frac{x(x-2)}{(x+3)(x-5)}\)Solution
Set f(x) = 0
\(\begin{gathered} 0=\frac{x(x-2)}{(x+3)(x-5)} \\ Rewrite \\ \frac{x(x-2)}{(x+3)(x-5)}=0 \\ cross\text{ multiply} \\ We\text{ have} \\ x(x-2)=0 \\ x=0 \\ x=2 \end{gathered}\)The final answer
The population growth of a certain city is given by the function P(t) = 0.9(1.5)^t, where t is time in years. Estimate lim P(t), if it exists.
Answers
Answer:
Infinity (∞)
Step-by-step explanation:
Graph the function and observe that the function P(t) increases without bound as x increases.
complete the equation 5/4= ×1/4
Answers
Answer:
X = 5
Step-by-step explanation:
XYZ are referred to as the area number. The number is associated with where you registered for your social security card. X is a number 1 – 7. Y and Z can be any number 0 – 9. How many area code numbers are possible?
Answers
9514 1404 393
Answer:
700
Step-by-step explanation:
The numbers can range from 100 to 799. There are 700 possible numbers.
What is the volume of the triangular prism?
please help!! quickly its a test a look at the picture
7th grade math
Answers
The area of the triangle is:
A = (base•height) : 2 = (3•2) : 2 = 3 m2
So the volume is:
V = 3 • 8 = 24 m3
In a brochure about an outdoor wilderness camp, the yearly attendance is rounded to 28,000 students.
Which could be the number of students who attended the camp if the attendance was rounded to the
nearest thousand?
Choose all answers that apply:
А
28,620
B
27.500
28.350
Answers
Answer:
B) 27,500
Looks like the decimal points in your question are a typo and should be commas... ;) If so, the answer is B
Question 2
5 pts
You deposit $5000 in an account earning 7% interest compounded
monthly. How much will you have in the account in 10 years?
5 nts
Answers
\(s = 5000(1.07) {}^{t} \)
\(s = 5000(1.07) {}^{10} \)
\(s = 5000(1.96715)\)
\(s = 9835.756 \: dollars\)