The rate of change in blood pressure at 3 seconds is approximately -11.7558 mm Hg per second.
What is differentiation?A function's derivative with respect to an independent variable can be used to define differentiation. Calculus differentiates to measure the function per unit change in the independent variable. A function of x is y = f(x).
To find the rate of change in blood pressure at 3 seconds, we need to differentiate the function P(t) with respect to t and evaluate it at t = 3.
P(t) = -20 cos(300°) + 100
Taking the derivative with respect to t, we have:
P'(t) = -20 (-sin(300°)) = 20 sin(300°)
Now we need to evaluate P'(t) at t = 3:
P'(3) = 20 sin(300°)
To calculate this value, we need to convert 300 degrees to radians since the sine function expects angles in radians. Recall that 360 degrees is equal to 2π radians.
300 degrees = (300/360) * 2π radians = (5/6) * 2π radians = (5/3)π radians
Now we can substitute this value into the equation:
P'(3) = 20 sin((5/3)π)
Using the approximate value of π as 3.14159, we can calculate:
P'(3) ≈ 20 sin((5/3) * 3.14159) ≈ 20 sin(5.23599) ≈ 20 * (-0.58779) ≈ -11.7558
Therefore, the rate of change in blood pressure at 3 seconds is approximately -11.7558 mm Hg per second.
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Solve the following system using substitution. y + 17 = 2x
what time does a 12-hour clock read a) 80 hours after it reads 11:00? b) 40 hours before it reads 12:00? c) 100 hours after it reads 6:00?
a) 80 hours after 11:00 on a 12-hour clock would be 7:00.
b) 40 hours before 12:00 on a 12-hour clock would be 4:00.
c) 100 hours after 6:00 on a 12-hour clock would be 10:00.
a, To find this, we need to divide 80 by 12 (the number of hours on the clock), which gives us a quotient of 6 and a remainder of 8. We then add the remainder to the starting time of 11:00, giving us 7:00.
b, To find this, we need to subtract 40 from 12 (the number of hours on the clock), which gives us 8. We then subtract 8 from the starting time of 12:00, giving us 4:00.
c, To find this, we need to divide 100 by 12 (the number of hours on the clock), which gives us a quotient of 8 and a remainder of 4. We then add the quotient (which represents a full cycle of 12 hours) to the starting time of 6:00, giving us 6+8=14:00, which is equivalent to 2:00 on a 12-hour clock. Finally, we add the remainder of 4 to 2:00, giving us 10:00.
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Doreen walks 3.46 kilometers on the treadmill. How many meters does Doreen walk?
Answer:
3460 m
Step-by-step explanation:
There are 1000 meters in a kilometer and since Doreen walks 3.46 km, she must walk 3460 m.
3.46 x 1000 = 3460
Answer:
3.46 km = 3.46*1000m = 3460 m
The table shows elevations at various locations.
A 3-column table with 4 rows. Column 1 is labeled Location with entries Death Valley, Lake Eyre, Western Sahara, Salton Sea. Column 2 is labeled Country with entries United States, Australia, Egypt, United States. Column 3 is labeled Elevation (meters) with entries negative 86, negative 15, negative 55, negative 69.
If you plotted the elevations on a vertical number line, which elevation would be farthest from 0?
Death Valley
Lake Eyre
Western Sahara
Salton Sea
Answer:
The answer is A.
Answer: Death Valley
Step-by-step explanation: :D
A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches. Which equation can be used to solve for x, the increase in side length of the square in inches? x2 + 4x – 81 = 0 x2 + 4x – 65 = 0 x2 + 8x – 65 = 0 x2 + 8x – 81 = 0
Answer:
C) x2 + 8x – 65 = 0
Step-by-step explanation:
just took it :)
Answer:
c
Step-by-step explanation:
What is the value of x + y? I've tried to figure out how to solve this, but I'm not very good at it, any help would be amazing!!
9514 1404 393
Answer:
x + y = 60
Step-by-step explanation:
Vertical angles are congruent.
Equation/Solution for x:
85 = 3x +55
30 = 3x . . . . . . subtract 55 from both sides
10 = x . . . . . . . divide both sides by 3
Equation/Solution for y:
95 = 2y -5
100 = 2y . . . . add 5 to both sides
50 = y . . . . . . divide both sides by 2
The objective:
x + y = 10 + 50
x + y = 60
Simplify the polynomial. Then find its value for the given value of the variable.
(full question attached as image)
Answer:
simplified: xy²value: 4Step-by-step explanation:
The polynomial is simplified by combining like terms. Like terms are identified more easily if the variables in each term are written in the same order. We usually like to use alphabetical order. Two of the like terms have opposite coefficients, so they cancel. The result is ...
(3 1/2 -2 1/2)xy² +(-2 4/5 +2 4/5)x²y
= xy² . . . . simplified expression
__
For x = 1, y = -2, the value of the expression is ...
(1)(-2)² = 4
What is the equation of a line that passes through the given point and is parallel to the given line. (-3, 2) and y = -4
Answer:
its A y = 3
Step-by-step explanation:
Use the equation xy= 12.6. Find the value of y when x=7
Answer: y = 1.8
Step-by-step explanation:
xy = 12.6 If x is 7 but 7 in the equation for x
7y = 12.6 Divide both sides by 7
y = 1.8
what is 100 * 100 the anser is 1000
Answer:
yes
Step-by-step explanation:
Answer:
No it is 10,000
Step-by-step explanation:
100*100 is like adding 2 zeros to 100. so 1 zero would make it 1000, and 2 zeros would make it 10,000
A survey was conducted about real estate prices. Data collected is 181386,243922,355008,406791,542820,648303,782200 , 845053,924494,1089774,1175704,1274928,1308954 . What is the median price
The median price from the given data is 648,303.
To find the median price from the given data, we need to arrange the prices in ascending order and then locate the middle value. If there is an odd number of data points, the median will be the middle value. If there is an even number of data points, the median will be the average of the two middle values.
Let's arrange the data in ascending order:
181,386,243,922,355,008,406,791,542,820,648,303,782,200,845,053,924,494,1,089,774,1,175,704,1,274,928,1,308,954
There are a total of 13 data points, which is an odd number. So, the median price is the middle value.
The middle value is the 7th value:
Median Price = 648,303
Therefore, the median price from the given data is 648,303.
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Question 10(Multiple Choice Worth 5 points)
(Identifying Functions LC)
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma 3, at negative 1 comma negative 2, at 0 comma 2, and at 5 comma 1
Is the relation a function? Explain.
No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.
Is the relation a function:
No, because for each input there is not exactly one output.How to know if the relation is a functionTo determine if the relation is a function, we need to check if there is exactly one output for each input.
Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).
This means that there are two outputs for the same input, so the relation is not a function.
Therefore, the correct answer is: "No, because for each input there is not exactly one output."
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Which of the following has eight faces?ООO A. octahedronO B. tetrahedronO C. icosahedronO D. dodecahedron
Given:
The number of faces =8.
Required:
We need to find the polyhedron with 8 faces.
Explanation:
Recall that the tetrahedron is a polyhedron composed of four triangular faces
The number of faces in tetrahedron =4.
Recall that the octahedron is a polyhedron with 8 faces.
The number of faces in the octahedron= 8.
Recall that the dodecahedron is a polyhedron with 12 faces.
The number of faces in the dodecahedron = 12.
Recall that the icosahedron is a polyhedron with 20 faces.
The number of faces in icosahedron =20.
Final answer:
octahedron
7. how many different license plates are possible if state uses a. two letters followed by a four-digit integer (leading zeros are permissible and the letters and digits can be repeated)? b. three letters followed by a three-digit integer (leading zeros are permissible and the letters and digits can not be repeated)?
Number of of difference license plate are possible, when two letters followed by four digit integer is 6760000 and when three letters followed by three digit number is 17576000
Here two letters are followed by a four digit integer
There are 26 letters available
Number of possible combinations = 26 × 26
= 676 pair of numbers
In each digits of a four digit numbers 10 numbers are possible
Total number of combinations = 10 × 10 × 10 × 10
= 10000
Number of different license plate = 676 × 10000
= 6760000
Part b
Number of three letters combination = 26 × 26 × 26
= 17576
Number of three digit integer combination = 10 × 10 × 10
= 1000
Number of different licence plate = 17576 × 1000
= 17576000
Therefore, three are 6760000 combinations if it is a two letter followed by four digit integer and 17576000 combination if it is a three letters followed by three digit numbers
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1. If cosA=21/29, what is the perimeter of the triangle?
2. If sinA=10/26, what is the perimeter of the triangle?
3. If tanA=15/8, what is the perimeter of the triangle?
4. If cosA-12/37, what is the perimeter of the triangle?
5. If tanA-12/16, what is the perimeter of the triangle?
Answer:
Step-by-step explanation:
For each one, solve for the missing side, x, then add all sides together to get the perimeter, P.
1) x = √(29² - 21²) = 20
P = 21+29+20 = 70
2) x = √(12² - 10²) = 6.63
P = 10+26+6.63 = 42.63
3) x = √(8² + 15²) = 17
P = 8+15+17 = 40
4) x = √(37² - 12²) = 35
P = 12+35+37 = 84
5) x = √(12² + 16²) = 20
P = 12+16+20 = 48
consider two large independent samples from two populations. the difference in the two sample means has which kind of distribution?
When we have two large independent samples from two populations, the difference in the two sample means will follow an approximate normal distribution.
This is due to the central limit theorem, which states that when we have a large enough sample size (typically, greater than 30), the distribution of the sample means will be normal regardless of the underlying distribution of the populations. As the two samples are independent, the difference in means will also be independent. Therefore, we can use the normal distribution to estimate the probability of observing a certain difference in means. It is important to note that this approximation may not hold for small sample sizes, and the underlying distributions of the populations can also impact the shape of the distribution. We can say that the normal distribution approximation is widely used in statistics and hypothesis testing, making it an essential concept for understanding and interpreting data.
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would the following method produce a random sample of a school population of 1000 students? answer yes or no. all students with last names beginning with the letter m.
Selecting all students with last names beginning with the letter M would not produce a random sample of a school population of 1000 students. Hence the answer is no.
A random sample is obtained by selecting individuals from a population in a way that ensures every member of the population has an equal chance of being included in the sample.
By choosing only students with last names beginning with the letter M, you are introducing a bias and not providing an equal chance for all students to be selected.
To obtain a random sample of 1000 students from a school population, you would need to use a random selection method that ensures each student has an equal probability of being chosen.
This could be achieved through techniques such as random number generators, random sampling software, or random sampling techniques like stratified or cluster sampling.
Selecting all students with last names beginning with the letter M would not meet the requirements of a random sample, as it would not provide an equal chance for all students in the population to be included.
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Lines a and b are perpendicular. The equation of line a is y= 1/3+ 3. What is the
equation of line b?
Answer: y= -3x -4
Step-by-step explanation: the lines are perpendicular, so
the slope of line b is the negative reciprocal of the slope of line a. So -3x
From the graph you see that the y-intercept is -4
In slope intercept form the equation is y= -3x -4
1.) do you have a 5‘ x 7‘ rectangular rug in your classroom. You also have a bunch of square foot tiles and some tape measures. a.) what is the most primitive way to determine the area of the rug? b.) what is a less primitive way to determine the area of the rug, and why does this method work?
See explanation below
Explanation:
a) The first thing we will do is draw the rectangular rug with the measuremnet 5 foot by 7 foot:
We will assume each 1 cm of the represent 1 foot, if we are using a ruler with cm as measurement to draw the diagram.
Then, we draw a box with measurement of 1foot by 1 foot
The most primitive way to determine the area of the rug is to count each of the boxes. The amount you get is the area of the rug.
When you count, the number of boxes = 35
Since the each box is 1 foot by 1 foot:
\(\begin{gathered} \text{Area = 35}\times1foot\times1\text{ foot} \\ \text{Area of the rug = 35ft}^2 \end{gathered}\)b) A less primitive way to determine the area of the rug, is to multiply the length by the width.
the length (longer side) = 7ft, the width (shorter side) = 5ft
\(\begin{gathered} \text{Area = 5foot}\times7foot\text{ } \\ \text{Area = 35 foot}^2 \\ \end{gathered}\)This method works because we have 5 columns and 7 rows. When we multiply the two, it gives an area since each box represent 1 foot by 1 foot.
PLEASE HELP ME THIS IS DUE IN TWO HOURS! :(
The length of Rectangle 1 is 3.2 x 10^5 m. The width of Rectangle 1 is 1.6 x 10^4 m. What is the area of Rectangle 1? Write the answer in Scientific Notation.
Find the area of Rectangle 2 if its length is 1.28 x 10^7 m and its width is 8 x 10^3 m. Write the answer in Scientific Notation.
Answer:224 squared
Step-by-step explanation:
H
GIVING AWAY BRAINLY!!
choose the linear expression 4(10x - 4).
Answer Choices:
A.) 10x - 16
B.) 40x - 16
C.) 40x + 16
D.) 40x - 4
how do you solve this 1 1/4 + 1 1/2
Answer:
your answer for 11/4+11/2 would be 8.25
Step-by-step explanation:
Answer:
1 1/4 + 1 1/2 = 2 3/4
Step-by-step explanation:
first do 1/4 plus 1/2 to solve that you need the same denominator. To get the same denominator you have to see which number they both go into equally, 4 goes into 4 once and 2 goes into 4 twice, meaning you can make both denominators 4. 2 * 2 = 4 and if you do something to the denominator you have to do it to the numerator, so 1/2 would become 2/4. 1/4 plus 2/4 is 3/4. now move onto the whole numbers 1+1=2. so, the answer must be
2 3/4. hope this helps
how many samples of size n=2 can be drawn from this population
The samples of size n = 2 that can be drawn from this population is 28
How many samples of size n=2 can be drawn from this populationFrom the question, we have the following parameters that can be used in our computation:
Population, N = 8
Sample, n = 2
The samples of size n = 2 that can be drawn from this population is calculated as
Sample = N!/(n! * (N - n)!)
substitute the known values in the above equation, so, we have the following representation
Sample = 8!/(2! * 6!)
Evaluate
Sample = 28
Hence, the number of samples is 28
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Complete question
A finite population consists of 8 elements.
10,10,10,10,10,12,18,40
How many samples of size n = 2 can be drawn this population?
2. What is the name of the ray that is opposite RP?
Answer:
its pr
Step-by-step explanation:
because im smart
Dan measured the number of gallons of paint his paint sprayer uses in 4 hours, the sprayer uses 42 gallons. Can a constant rate be used to describe the relationship between the number of hours and the gallons of paint used? Explain.
Answer: To determine if a constant rate can be used to describe the relationship between the number of hours and the gallons of paint used, we need to see if the sprayer uses paint at a consistent rate over time.
From the information given, we know that in 4 hours, the sprayer uses 42 gallons of paint. This means that the rate of paint usage is 42/4 = 10.5 gallons per hour.
If the sprayer uses paint at a constant rate, then we would expect it to use the same amount of paint for each hour of use. However, we don't have any information about how the sprayer uses paint beyond the first 4 hours, so we can't determine if the rate of paint usage is constant over time.
Therefore, we cannot definitively say whether a constant rate can be used to describe the relationship between the number of hours and the gallons of paint used. It is possible that the rate of paint usage changes over time, or that other factors (such as the surface area being painted or the type of paint being used) affect the amount of paint used.
Step-by-step explanation:
9/63 (equal to less than or greater than) 1/7 please help i only have 3 minutes
Answer:
9/63 equal to 1/7
9/63
=(9/9)*(1/7)
=1*(1/7)
=1/7
Can anyone help me with this math equation?
Answer:
if the X is a multiplication then 1.8 would be the answer
Step-by-step explanation:
Before the beginning of the school year, a fourth-grade teacher obtains assessment results from the previous year for students who will be in his class. The teacher can most appropriately use this information to
Obtaining assessment results from the previous year for students entering the fourth-grade class allows the teacher to gain valuable insights into their academic strengths and weaknesses.
By reviewing the assessment results from the previous year, the fourth-grade teacher can obtain a clear understanding of each student's individual academic performance. This information helps the teacher tailor their instructional strategies to meet the specific needs of each student. For students who excelled in certain areas, the teacher can provide enrichment activities or more challenging assignments to keep them engaged and motivated. On the other hand, for students who struggled in certain subjects, the teacher can offer targeted interventions and additional support to help them catch up.
Furthermore, the assessment results can guide the teacher in identifying any learning gaps or misconceptions that need to be addressed early on in the school year. Overall, utilizing the previous year's assessment results allows the teacher to create a more personalized and effective learning experience for their fourth-grade students, fostering growth and academic success.
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Unite rates explanations
Answer:
A unit rate is ratio where the denominator is usually 1. We can calculate unit rate as a division of two quatities. For example, the price of 10 apples is $20, then the unit rate is the division of $20 by the number of apples
$20/10 = $2 per apple
So, the unit rate is the price per apple.
Pleaseee helppp me question 2 !!!
Answer:
2.is a function
Domain:(0,1,2,3)
Range: (0,-1,-2,-3)
3. Not a function
4. Is a function
D:(0,1,2,3)
R:(1,2,3,4,)