Answer:
[tex]\frac{dF}{F}=4\frac{dR}{R}[/tex]
So a 5% relative increase in R would mean a 20% relative increase in F
Step-by-step explanation:
First we need to remind the definition of relative increase of a variable.
For a variable A its relative increase is given by [tex]\frac{dA}{A}[/tex].
Using this, the relative increase in F is [tex]\frac{dF}{F}[/tex] and similarly the relative increase in R is given by [tex]\frac{dR}{R}[/tex].
Let's then start by deriving F with respect to R:
[tex]\frac{dF}{dR}=4kR^3[/tex]
thus
[tex]dF=4kR^3dR[/tex]
[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{F}[/tex]
[tex]\implies \frac{dF}{F}=\frac{4kR^3dR}{kR^4}[/tex]
[tex]\implies \frac{dF}{F}=4\frac{dR}{R}[/tex].
If we plug the value 5% [tex]\left( \frac{5}{100}\right)[/tex] in [tex]\frac{dR}{R}[/tex] we get
[tex]\frac{dF}{F}=4\times5\%=20\%[/tex]
According to Poiseuille's Law, the flux of blood through a blood vessel is proportional to the fourth power of the vessel's radius. By differentiating both sides of the equation, it can be shown that a small relative change in radius corresponds to four times that change in flux. Therefore, a 5% increase in radius results in a 20% increase in blood flow.
Explanation:Poiseuille’s Law states that the flux (F), which is the volume of blood flowing per unit time through a given point in a blood vessel, is proportional to the fourth power of the blood vessel's radius, R. In terms of an equation, F = kR4, where k is a constant of proportionality.
To show that the relative change in F is approximately four times the relative change in R, consider a small change in R (expressed as ΔR), and the corresponding change in F (ΔF). The relative change in F is ΔF/F and the relative change in R is ΔR/R.
By differentiating both sides of the equation, you get ΔF/ΔR = 4kR3. Therefore, ΔF/F = 4(ΔR/R), proving the statement. A 5% increase in the radius would therefore result in a 20% increase in the flux, or the blood flow rate.
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A basketball team practices their shooting. The function f(x) represents the number of baskets made during practice, where x is the number of players at the practice. Does a possible solution of (12, 36) make sense for this function? Explain your answer.
Answer:
The answer to your question is below
Step-by-step explanation:
I think it will easy to understand if we graph this information but let's explain it without the graph.
According to the information given, we know that f(x) represents the number of baskets and x the number of players at the practice.
So, if we have the point (12, 36) we can conclude that during practice there were 12 players and there were 36 baskets.
For me, it makes sense.
Answer: Yes. The input and output are both possible
Step-by-step explanation:
The reason why is because f(x) stands for y and in parenthe this is how it looks like(x,y) and if you put the numbers in you have (12,36) 12 stands for the number of players and f(x) or y stands for the number of baskets made.
The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean μ, the actual temperature of the medium, and standard deviation σ. What would the value of σ have to be to ensure that 95% of all readings are within 0.6° of μ?
Answer: 0.3061.
Step-by-step explanation:
Given : The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean [tex]\mu[/tex], the actual temperature of the medium, and standard deviation [tex]\sigma[/tex].
Let X be the random variable that represents the reading of the thermometer.
Confidence level : [tex]=95\%[/tex]
We know that the z-value for 95% confidence interval is 1.96.
Then, we have
[tex]-1.96<\dfrac{X-\mu}{\sigma}<1.96[/tex] [tex]z=\dfrac{X-\mu}{\sigma}[/tex]
[tex]\Rightarrow\ -1.96\sigma<X-\mu<1.96\sigma[/tex]
But all readings are within 0.6° of [tex]\mu[/tex].
So, [tex]1.96\sigma=0.6[/tex]
[tex]\Rightarrow\ \sigma=\dfrac{0.6}{1.96}=0.30612244898\approx0.3061[/tex]
Hence, the required standard deviation will be
The confidence level is 95% in normal distribution then The value of standard deviation is 0.3061.
What is a normal distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
Given
The temperature reading from a thermocouple placed in a constant temperature medium is normally distributed with mean μ, the actual temperature of the medium, and standard deviation σ.
Let x be the random variable that represents the reading of the thermometer.
The confidence level is 95%. Then the z-value for 95% confidence level interval is 1.96.
Then we have
[tex]-\ \ 1.96 \ < \dfrac{x- \mu}{\sigma} < 1.96\\-1.96 \sigma < x- \mu \ < 1.96 \sigma[/tex]
But all the readings are within 0.6° of μ. Then
[tex]1.96 \sigma = 0.6\\[/tex]
On solving
[tex]\sigma = \dfrac{0.6}{1.96}\\\\\sigma = 0.306122 \approx 3061[/tex]
Thus, the standard deviation is 0.3061.
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true or false Linear? y = –5x
True. It is linear because it forms a straight line.
Answer:
TrueStep-by-step explanation:
It is a straight line, which is always linear.
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walt averages 98 miles per hourin 4 races. if each race is 95 miles in lenght, how many miles did walt drive in the race?
Answer: 380
Step-by-step explanation: Did you mean to ask how much time it took him? If he’s doing 4 races each being 95 miles it would simply be 95 x 4 = 380
The total distance driven by Walt is calculated by multiplying the length of each race (95 miles) by the number of races (4), giving a total of 380 miles.
Explanation:Walt averages 98 miles per hour, each race is 95 miles long, and he completed 4 races. To find the total distance driven by Walt, we only need to know how long each race is and how many races Walt completed because the speed at which Walt drives does not affect the total distance he covered in the race. Therefore, to get the total distance, we simply multiply the length of each race by the number of races. In this case, Walt drove 95 miles x 4 = 380 miles in total.
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Find the solution of the following equation whose argument is strictly between 270^\circ270 ∘ 270, degree and 360^\circ360 ∘ 360, degree. Round your answer to the nearest thousandth. z^4=-625z 4 =−625
[tex]\rightarrow z^4=-625\\\\\rightarrow z=(-625+0i)^{\frac{1}{4}}\\\\\rightarrow x+iy=(-625+0i)^{\frac{1}{4}}\\\\ x=r \cos A\\\\y=r \sin A\\\\r \cos A=-625\\\\ r \sin A=0\\\\x^2+y^2=625^{2}\\\\r^2=625^{2}\\\\|r|=625\\\\ \tan A=\frac{0}{-625}\\\\ \tan A=0\\\\ A=\pi\\\\\rightarrow z= [625(\cos (2k \pi+pi) +i \sin (2k\pi+ \pi)]^{\frac{1}{4}}\\\\k=0,1,2,3,4,....\\\\\rightarrow z=(625)^{\frac{1}{4}}[\cos \frac{(2k \pi+pi)}{4} +i \sin \frac{(2k\pi+ \pi)}{4}] [/tex]
[tex]\rightarrow z_{0}=(625)^{\frac{1}{4}}[\cos \frac{pi}{4} +i \sin \frac{\pi)}{4}]\\\\\rightarrow z_{1}=(625)^{\frac{1}{4}}[\cos \frac{3\pi}{4} +i \sin \frac{3\pi}{4}]\\\\ \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]\\\\ \rightarrow z_{3}=(625)^{\frac{1}{4}}[\cos \frac{7\pi}{4} +i \sin \frac{7\pi}{4}][/tex]
Argument of Complex number
Z=x+iy , is given by
If, x>0, y>0, Angle lies in first Quadrant.
If, x<0, y>0, Angle lies in Second Quadrant.
If, x<0, y<0, Angle lies in third Quadrant.
If, x>0, y<0, Angle lies in fourth Quadrant.
We have to find those roots among four roots whose argument is between 270° and 360°.So, that root is
[tex] \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}][/tex]
The solutions are[tex]\( z = 5e^{i(\frac{9\pi}{4})} \), \( z = 5e^{i(\frac{17\pi}{4})} \), \( z = 5e^{i(\frac{25\pi}{4})} \), and \( z = 5e^{i(\frac{33\pi}{4})} \).[/tex]
To find the solutions of the equation [tex]\( z^4 = -625 \) in the given range of argument, we first rewrite the equation in polar form. Let \( z = re^{i\theta} \), where \( r \) is the magnitude of \( z \) and \( \theta \) is its argument.[/tex]
The equation becomes:
[tex]\[ (re^{i\theta})^4 = -625 \]\[ r^4e^{4i\theta} = -625 \]Now, since the right side is a negative real number, we can express it in polar form as \( -625 = 625e^{i\pi} \). So we have:\[ r^4e^{4i\theta} = 625e^{i\pi} \][/tex]
Comparing the magnitudes and arguments on both sides, we get:
[tex]\[ r^4 = 625 \]\[ 4\theta = \pi \]Solving for \( r \) and \( \theta \):\[ r = \sqrt[4]{625} = 5 \]\[ \theta = \frac{\pi}{4} \][/tex]
However, we need solutions in the given range of argument, which is between [tex]\( 270^\circ \) and \( 360^\circ \). Since \( \frac{\pi}{4} \) is approximately \( 45^\circ \) or \( \frac{\pi}{4} \), we need to add multiples of \( 2\pi \) to this angle to get solutions within the desired range.[/tex]
The solutions are:
[tex]\[ z_1 = 5e^{i(\frac{\pi}{4} + 2\pi)} \]\[ z_2 = 5e^{i(\frac{\pi}{4} + 4\pi)} \]\[ z_3 = 5e^{i(\frac{\pi}{4} + 6\pi)} \]\[ z_4 = 5e^{i(\frac{\pi}{4} + 8\pi)} \]Simplifying the angles:\[ z_1 = 5e^{i(\frac{9\pi}{4})} \]\[ z_2 = 5e^{i(\frac{17\pi}{4})} \]\[ z_3 = 5e^{i(\frac{25\pi}{4})} \]\[ z_4 = 5e^{i(\frac{33\pi}{4})} \][/tex]
Finally, we can convert these back to rectangular form if needed:
[tex]\[ z_1 = 5\left(\cos\frac{9\pi}{4} + i\sin\frac{9\pi}{4}\right) \]\[ z_2 = 5\left(\cos\frac{17\pi}{4} + i\sin\frac{17\pi}{4}\right) \]\[ z_3 = 5\left(\cos\frac{25\pi}{4} + i\sin\frac{25\pi}{4}\right) \]\[ z_4 = 5\left(\cos\frac{33\pi}{4} + i\sin\frac{33\pi}{4}\right) \][/tex]
You can compute the approximate values of these complex numbers and round them to the nearest thousandth if necessary.
Complete Question;
Find the solution of the following equation whose argument is strictly between [tex]$270^\circ$[/tex] , degree and [tex]$360^\circ$[/tex] , degree. Round your answer to the nearest thousandth. [tex]\[z^4 = -625z\][/tex]
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Suppose the schools pay $2.00 per bottle for the juice and sell it to community members for $2.50 per bottle. What percent markup are they charging?
- the answer is 25% markup
just exlpain how to get the answer
Answer:
The answer to your question is 25%
Step-by-step explanation:
Data
Initial price = $2.00
Final price = $2.50
First we subtract the final price to the inicial price
increment = 2.50 - 2.00
= $0.50 It's the amount that the school increases to the community members
Now we use a rule of three to find the percent
$2.00 ---------------------- 100%
$0.50 --------------------- x
x = 0.50 x 100/2 = 50/2 = 25%
The minute hand of a clock is 6 inches long and moves from 12 to 4 o'clock. How far does the tip of the minute hand move? Express your answer in terms of pi and then round to 2 decimal places.
Answer: 12.56 inches
Step-by-step explanation: First, when know the following:
A clock is a circle, so the total movement, from 12 to 12 is 360° or 2π.
It is also know that a circle circunference (The total size of the circle on a straight line) is 2π * Radius
The minute hand does a circle on its travel, that circle radius is equal to 6 inches.
The movement from 12 to 4 is a third (4/12 = 1/3). Knowing this:
120° = (1/3) * 360° = (1/3) * 2π = (2/3) * π
So the travel from 12 to 4 is (2/3)π
To know the distance on inches, we multiply the distance on radians per the radius.
Total distance = 6 * (2/3)π
Total distance = 4π inches
Total distance = 12.56 inches
Final Answer:
The tip of the minute hand moves approximately 12.57 inches from 12 o'clock to 4 o'clock.
Explanation:
To solve this problem, we will consider the movement of the minute hand as an arc on a circle. The distance that the tip of the minute hand moves is the length of the arc that it traces as it moves from 12 o'clock to 4 o'clock. Here's how we'll calculate it:
Step 1: Determine the angle of movement in degrees.
The clock is divided into 12 hours, so each hour represents an angle of 360 degrees / 12 = 30 degrees. Since the minute hand moves from 12 o'clock to 4 o'clock, it covers 4 hours. Thus, the angle covered is 4 hours * 30 degrees/hour = 120 degrees.
Step 2: Convert the angle from degrees to radians.
To find the arc length, it is convenient to work with radians rather than degrees. The conversion from degrees to radians is performed using the factor π radians = 180 degrees.
[tex]\( \text{Angle in radians} = \text{Angle in degrees} \times \frac{\pi}{180} \)[/tex]
So, for our angle:
[tex]\( \text{Angle in radians} = 120 \times \frac{\pi}{180} \\\\\( \text{Angle in radians} = \frac{2}{3} \pi \)[/tex]
Step 3: Use the arc length formula.
The arc length (s) on a circle can be calculated using the formula s = r * θ, where r is the radius (length) of the circle (in this case, the length of the minute hand), and θ is the angle in radians.
[tex]\( s = r * \theta \\\\\( s = 6 \text{ inches} * \frac{2}{3} \pi \\\\\( s = 4 \pi \text{ inches} \)[/tex]
So, the distance the tip of the minute hand moves is [tex]\( 4 \pi \)[/tex] inches.
Step 4: Calculate the numerical value of the arc length.
To find the numerical value, we will approximate [tex]\( \pi \)[/tex] to 3.14159.
[tex]\( s \approx 4 * 3.14159 \\\\\( s \approx 12.56636 \text{ inches} \)[/tex]
Step 5: Round the numerical value to two decimal places.
[tex]\( s \approx 12.57 \text{ inches} \)[/tex]
Therefore, the tip of the minute hand moves approximately 12.57 inches from 12 o'clock to 4 o'clock.
A rectangular solar panel has a length that is 12 inches shorter than 3 times its width. If the perimeter of the panel is 160 inches, what are the dimensions of the panel?
Answer:
width = 23 inches
length = 57 inches
Step-by-step explanation:
Let x inches be the width of the rectangular solar panel.
So,
width = x inches
3 times the width = 3x inches
12 inches shorter than 3 times the width = 3x - 12 inches
length = 3x - 12 inches
The perimeter of the rectangle is
[tex]P=2(\text{Width}+\text{Length})[/tex]
Hence,
[tex]160=2(x+3x-12)\\ \\160=2(4x-12)\\ \\80=4x-12\ [\text{Divided by 2}]\\ \\4x=80+12\\ \\4x=92\\ \\x=23\ inches\\ \\3x-12=3\cdot 23-12=69-12=57\ inches[/tex]
Sophie is buying fabric to make items for a craft fair. The table shows some combinations of how much of each color fabric she might buy. Which equations model the total yards of fabric Sophie will buy? Check all that apply.
A. X+Y=28
B. 28+X=Y
C. X-Y=28
D. 28-X=Y
E. 28-Y=X
Answer:
OPTION A.
OPTION D.
OPTION E.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
The Standard form of the equation of the line is:
[tex]Ax + By = C[/tex]
Where "A" is a positive integer, and "B" and "C" are integers.
Choose two points from the table and find the slope with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
Points:
[tex](1,27)\\\\(4,24)[/tex]
So we get that the slope is:
[tex]m=\frac{24-27}{4-1}=-1[/tex]
Let's substitute the slope and the coordinates of the point (1,27) into [tex]y=mx+b[/tex] and then solve for "b":
[tex]27=(-1)(1)+b\\\\27+1=b\\\\b=28[/tex]
Then, we get that the equation of the line in Slope-Intercept form is:
[tex]y=-x+28[/tex] or [tex]28-x=y[/tex]
In order to write it in Standard form, we can add "x" to both sides of the equation:
[tex]y+x=-x+28+x\\\\x+y=28[/tex]
We can solve for "x" by subtracting "y" from both sides of the equation:
[tex]x+y-y=28-y\\x=28-y\\\\28-y=x[/tex]
Answer:
A,D, and E
Step-by-step explanation:
Owens Industries is trying to increase its profile in the community. As part of this effort, Owens sponsors a Little League baseball team. The cost of sponsorship is $850. How should Owens record this transaction in order to maintain a balanced accounting equation (A = L + SE)?
The Owens Industries should credit $850 to their Assets, denoted by A and debit the sum of $850 to the Stockholder's Equity, denoted by SE.
Step-by-step explanation:In the question,
As the Owens industries is trying to increase its profile.
Cost of sponsorship = $850
To maintain the profile he can, by using the transaction accounting balance equation,
A = L + SE
The Owens Industries should credit $850 to their Assets, denoted by A and debit the sum of $850 to the Stockholder's Equity, denoted by SE.
That is,
$850 = L + $850
L = 0
This is how the accounting equation can be balanced.
Solve for n.
1/2n+3/4n=1/2
Answer:
n=2/5 or 0.4
Step-by-step explanation:
thx mate brainliest plzz
Which of the following is equivalent to
Answer:
Step-by-step explanation:
To solve this, we need to remember that when you multiplicate two roots you can multiply the numbers inside the two roots and put them inside just one root.
So in this case we have ∛5ab² ·∛25ab
We are going to multiply the numbers inside the roots and we get
∛5ab²·25ab = ∛75a²b³
But 75 = 5³ so we have
∛75a²b³ = ∛5³a²b³
Since we have powers of 3 inside the root, we can take them outside the root with the exponent divided by 3.
∛5³a²b³ = 5b∛a²
Thus, the correct answer is a) 5b∛a²
show that when the measure of an angle is added to three times the angle's complement, the result is equal to the sum of the anle's complment and the angle's supplement.
Answer with Step-by-step explanation:
Let x be the angle
We have to show that when the measure of an angle is added to three times the angle's complement , the result is equal to the sum of the angle;s complement and the angle' s supplement.
Angle's complement =90-x
(by definition of complementary angles)
Therefore, the angle's supplement=180-x ( By definition of supplement angles )
According to question
[tex]x+3(90-x)=270-2x[/tex]
[tex]90-x+180-x=270-2x[/tex]
Hence, when the measure of an angle is added to three times the angle's complement , the result is equal to the sum of the angle's supplement.
Hence, proved
Write an example of a number with a first non-zero digit six place values away from the decimal point. Then, write this number in scientific notation.
Answer:
The answer to your question is: 7.00 x 10⁶
Step-by-step explanation:
- Write a number with a non-zero digit 7
- Six place values away from the decimal point 7 000 000.00
-Write this number in scientific notation 7.00 x 10⁶
An example of a number with its first non-zero digit six places away from the decimal is 0.000001, which is written in scientific notation as 1 × 10^-6 by moving the decimal six places to the right.
An example of a number with its first non-zero digit six place values away from the decimal point is 0.000001. To write this number in scientific notation, we follow the standard convention: moving the decimal point such that there is only one non-zero digit to the left of the decimal point and counting the number of places the decimal point has moved to determine the power of 10.
In this case, we move the decimal point six places to the right, which gives us 1 × 10^-6. This means that 0.000001 in scientific notation is expressed as 1 × 10^-6 .
In this year, the average cost of a traditional Thanksgiving dinner for 10, featuring turkey, stuffing, cranberries, pumpkin pie, and trimmings, was $48.05, a decrease of 1.76% from the cost in the last year. What was the average cost of a traditional Thanksgiving dinner in the last year?
Answer:
Last year, the average cost of a traditional Thanksgiving dinner was $48.91.
Step-by-step explanation:
If this year the cost of a traditional Thanksgiving dinner was decreased by 1.76% compared to last year, then
last year cosr - 100%
this year cost - 100%-1.76%=98.24%
So,
$x - 100%
$48.05 - 98.24%
Write a proportion:
[tex]\dfrac{x}{48.05}=\dfrac{100}{98.24}[/tex]
Cross multiply:
[tex]98.24x=48.05\cdot 100\\ \\98.24x=4,805\\ \\x\approx 48.91[/tex]
Last year, the average cost of a traditional Thanksgiving dinner was $48.91.
Final answer:
The average cost of a traditional Thanksgiving dinner in the last year was approximately $48.91, calculated by dividing this year's cost of $48.05 by the percentage decrease converted to a decimal (1 - 0.0176).
Explanation:
To calculate the average cost of a traditional Thanksgiving dinner in the last year, given this year's average cost and the percentage decrease, we can use the formula original price = discounted price / (1 - discount rate). The discount rate in this case is the percentage decrease in cost, expressed as a decimal. Given that this year's average cost is $48.05 and the decrease is 1.76%, we first convert the percentage to a decimal by dividing by 100, which gives us 0.0176.
The formula becomes:
original price = $48.05 / (1 - 0.0176)
original price = $48.05 / 0.9824
original price = $48.91 approximately
Therefore, the average cost of a traditional Thanksgiving dinner in the last year was about $48.91.
If each side of a square patio is increased by 4 feet, the area of the patio would be 196 square feet. Solve the equation (s+4)2=196 for s to find the length of a side of the patio.
Answer:
The answer is 10
Step-by-step explanation:
The side length cannot be negative, hence the side length of the patio will be 10 feet
Give the expression that represents the statement given as:
[tex](s+4)^2 = 196[/tex]
We need to get the length of the side of the patio "s"
[tex](s+4)^2 = 196\\s+4 = \pm\sqrt{196}\\s+4=\pm14[/tex]
Subtract 4 from both sides
[tex]s+4-4=14-4\\s=14-4\\s =10ft[/tex]
Since the side length cannot be negative, hence the side length of the patio will be 10 feet
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find the area and circumference.
Answer:
area ≈ 176.7 cm²circumference ≈ 47.1 cmStep-by-step explanation:
The radius is half the diameter, so is ...
r = d/2 = 15 cm/2 = 7.5 cm
The area formula is ...
A = πr²
Filling in the radius, we have ...
A = π·(7.5 cm)² = 56.25π cm² ≈ 176.7 cm² . . . area
__
The circumference formula is ...
C = πd
Filling in the diameter, we have ...
C = π·(15 cm) = 15π cm ≈ 47.1 cm . . . circumference
Fred is 4 times as old as Nathan and is also 27 years older than Nathan. Let f be Fred's age and let n be Nathan's age. Which system of equations represents this situation?
Answer:
The system of equations is
[tex]f=4n[/tex] and [tex]f=n+27[/tex]
Fred's age is 36 years old and Nathan's age is 9 years old
Step-by-step explanation:
Let
f -----> Fred's age
n ----> Nathan's age
we know that
[tex]f=4n[/tex]-----> equation A
[tex]f=n+27[/tex] ----> equation B
equate the equations and solve for n
[tex]4n=n+27\\4n-n=27\\3n=27\\n=9[/tex]
Find the value of f
[tex]f=4(9)=36[/tex]
therefore
Fred's age is 36 years old and Nathan's age is 9 years old
Answer:
The system of equations is f=4n and f=n+27
Step-by-step explanation:
Select the graph that represents the given set. (Click on the graph until the correct one is showing.) B = {(1, 2), (2, 1), (3, 0), (4, -1)}
Answer:
3rd graph
Step-by-step explanation:
Hi, the answer would be the 3rd graph because each given set is shown on that coordinate relation.
Hope this helps, I attached the graph in case my explanation was confusing.
Third graph represents the set B = (1, 2), (2, 1), (3, 0), (4, -1).
Here, Set of points given as,
B = (1, 2), (2, 1), (3, 0), (4, -1).
We have to check the graph which represents the given set.
How to show points on graph?
Points are identified by stating their coordinates in the form of (x, y).
Where x is coordinate of x - axis and y is coordinate of y - axis.
Now,
Set of points given as,
B = (1, 2), (2, 1), (3, 0), (4, -1).
⇒ Third graph represents the set B = (1, 2), (2, 1), (3, 0), (4, -1).
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Explain the distance formula. Then use it to calculate the
distance between A(1, 1) and B(7, −7).
Answer:
[tex]dAB=10\ units[/tex]
Step-by-step explanation:
we know that
The distance formula is derived by creating a triangle and using the Pythagorean theorem to find the length of the hypotenuse. The hypotenuse of the triangle is the distance between the two points
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
A(1, 1) and B(7, −7)
Let
(x1,y1)=A(1, 1)
(x2,y2)=B(7, −7)
substitute the given values in the formula
[tex]dAB=\sqrt{(-7-1)^{2}+(7-1)^{2}}[/tex]
[tex]dAB=\sqrt{(-8)^{2}+(6)^{2}}[/tex]
[tex]dAB=\sqrt{64+36}[/tex]
[tex]dAB=\sqrt{100}[/tex]
[tex]dAB=10\ units[/tex]
Answer: The required distance between the points between A(1, 1) and B(7, −7) is 10 units.
Step-by-step explanation: We are given to explain the distance formula. Also, to calculate the distance between A(1, 1) and B(7, −7).
Distance formula : The distance between any two two points with co-ordinates (a, b) and (c, d) is given by
[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]
Therefore, the distance between the points A(1, 1) and B(7, −7) is given by
[tex]D\\\\=\sqrt{(7-1)^2+(-7-1)^2}\\\\=\sqrt{36+64}\\\\=\sqrt{100}\\\\=10.[/tex]
Thus, the required distance between the points between A(1, 1) and B(7, −7) is 10 units.
Alexandra has 78 emails in her inbox. She deletes 47 emails.How many emails are left in het inbox? Draw jumps and level the number line to show your thinking.
Answer:
31 emails, but I can't do a # number line.
Step-by-step explanation:
Answer: There are 31 emails left in her inbox.
Step-by-step explanation:
Since we have given that
Number of emails in her inbox = 78
Number of emails she deleted = 47
We need to find the number of emails that are left in her inbox.
So, for left we would use "Subtraction operator"
So, Number of emails left in her inbox = Number of emails in her inbox - Number of emails she deleted.
[tex]=78-47\\\\=31[/tex]
Hence, there are 31 emails left in her inbox.
A student is conducting a research project that involves using a survey. The survey asks subjects about their political affiliation and their favorite politicians. No identifiable information will be collected. This study would be categorized as which type of review?
Answer:
This study will be identified as : exempt review
Step-by-step explanation:
A student is conducting a research project that involves using a survey. The survey asks subjects about their political affiliation and their favorite politicians.
No identifiable information will be collected.
This study will be identified as : exempt review
To qualify for a review at the exempt level, the research should be less than the minimal risk defined.
Samantha has cut a pastry into four parts. Suppose PS||RQand T is the midpoint of PR. Determine whether SPT = QRT brainly
Answer:
Here's ur answer
Step-by-step explanation:
A man who has lost $37 playing roulette in Las Vegas wins $43 playing blackjack. He then loses $44 playing wheel of fortune. Write an expression using the numbers -37, 43 and 44 to describe this situation and then simplify it. Write your simplified result below.
_____
Answer:
(-37+43)-44=x
Step-by-step explanation:
i put the parentheses only because of PEMDAS. it's a pretty straightfoward question. To put it in an expression however, I'm not sure. Best of luck!
The register that holds bit values (flags) that describe comparison operation results, control conditional BRANCH execution, or indicate actual or potential error conditions ____.
Answer:
program status word
Step-by-step explanation:
The acronym for PSW is Program Status Word. The Program Status Word or the PSW consists of status bits which shows the present Central Processing Unit state.
The PSW or Program Status Word is IBM System/360 architecture which means it is an independent model architecture for S/360 series of computers developed by IBM.
The status register contains all the information about the processor.
Thus the answer is program status word.
A triangle hss one angle mesuaring 3x degrees. A second angle mesures 2x + 20 degrees and the third angle measures 4x - 20 degrees. What is the value of x
Answer:
Step-by-step explan 3x+2x+20+4x-20=180. 9x=180 X=180÷9. X=20
You are standing 41 meters from the base of a building. You estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82°. If the total height of the building is another 124 meters above the 86th floor, what is the approximate height of the building? (Round your answers to one decimal place.)
Answer:
408.6 meters.
Step-by-step explanation:
Let x be the height from the base of the building to the 86th floor,
∵ the total height of the building is another 124 meters above the 86th floor,
So, the total height of the building = ( x + 124 ) meters,
Now, the angle of elevation from the point on the ground to 86th floor = 82°,
Also, the distance from the point to the base of the building = 41 meters,
Thus, by trigonometric ratio,
[tex]tan 82^{\circ}=\frac{x}{41}[/tex]
[tex]\implies x = 41\times tan 82^{\circ}=284.614788895\approx 284.6\text{ meters}[/tex]
Hence, the height of the building = ( 284.6 + 124 ) = 408.6 meters.
The height of the building in consideration is given approximately as 408.61 meters
What is angle of elevation?You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.
Consider the figure attached for the given situation as described in the problem.
The person watching the building's 86th floor is at A.
The 86th floor is at C, the base of the building is at B.
The total height of the building is at D.
Using the tangent ratio to find the height of the building, we get:
[tex]\tan(82^\circ) = \dfrac{x}{41} \\\\x = \tan(82^\circ) \times 41\\x \approx 284.61 \: \rm meters[/tex] (from calculator).
Thus, the height of the building is length of AD
= |AD| = x + 124 ≈ 284.61 + 124 = 408.61 meters
Thus, the height of the building in consideration is given approximately as 408.61 meters
Learn more about tangent ratio here:
https://brainly.com/question/19594654
Please help!!!step by step
Answer:
slope = -1/3, y-intercept (0, -3), x-intercept (-9 , 0)
Step-by-step explanation:
3 - x = 3(y + 4)
3 - x = 3y + 12
3y = 3 - x - 12
3y = -x -9
y = -1/3 x - 3
slope = -1/3
when x = 0 (y-intercept)
y = -1/3 × 0 - 3
y = -3
y-intercept (0, -3)
when y = 0 (x-intercept)
0 = -1/3 x - 3
1/3 x = -3
x = -9
x-intercept (-9 , 0)
ABC Auto Insurance classifies drivers as good, medium, or poor risks. Drivers who apply to them for insurance fall into these three groups in the proportions 30 percent, 50 percent, and 20 percent, respectively. The probability a "good" driver will have an accident is .01, the probability a "medium" risk driver will have an accident is .03, and the probability a "poor" driver will have an accident is .10. The company sells Mr. Brophy an insurance policy and he has an accident. What is the probability Mr. Brophy is: a. A "good" driver? b. A "medium" risk driver? c. A "poor" driver?
Answer:
a.[tex]P(E_1/A)=0.0789[/tex]
b.[tex]P(E_2/A)=0.395[/tex]\
c.[tex]P(E_3/A)=0.526[/tex]
Step-by-step explanation:
Let [tex]E_1,E_2,E_3[/tex] are the events that denotes the good drive, medium drive and poor risk driver.
[tex]P(E_1)=0.30,P(E_2)=0.50,P(E_3)=0.20[/tex]
Let A be the event that denotes an accident.
[tex]P(A/E_1)=0.01[/tex]
[tex]P(A/E_2=0.03[/tex]
[tex]P(A/E_3)=0.10[/tex]
The company sells Mr. Brophyan insurance policy and he has an accident.
a.We have to find the probability Mr.Brophy is a good driver
Bayes theorem,[tex]P(E_i/A)=\frac{P(A/E_i)\cdot P(E_1)}{\sum_{i=1}^{i=n}P(A/E_i)\cdot P(E_i)}[/tex]
We have to find [tex]P(E_1/A)[/tex]
Using the Bayes theorem
[tex]P(E_1/A)=\frac{P(A/E_1)\cdot P(E_1)}{P(E_1)\cdot P(A/E_1)+P(E_2)P(A/E_2)+P(E_3)P(A/E_3)}[/tex]
Substitute the values then we get
[tex]P(E_1/A)=\frac{0.30\times 0.01}{0.01\times 0.30+0.50\times 0.03+0.20\times 0.10}[/tex]
[tex]P(E_1/A)=0.0789[/tex]
b.We have to find the probability Mr.Brophy is a medium driver
[tex]P(E_2/A)=\frac{0.03\times 0.50}{0.038}=0.395[/tex]
c.We have to find the probability Mr.Brophy is a poor driver
[tex]P(E_3/A)=\frac{0.20\times 0.10}{0.038}=0.526[/tex]
Final answer:
The probability that Mr. Brophy is a good, medium, and poor risk driver given he has had an accident is approximately 0.079, 0.395, and 0.526 respectively, as calculated using Bayes' theorem.
Explanation:
Using Bayes' theorem, we can find out the probability that Mr. Brophy is a good, medium, or poor risk driver given that he has had an accident:
Let's denote A as the event of having an accident and Gi, Mi, Pi as the events of Mr. Brophy being a good, medium, or poor risk driver respectively.
P(Gi) = 0.30, P(Mi) = 0.50, P(Pi) = 0.20P(A|Gi) = 0.01, P(A|Mi) = 0.03, P(A|Pi) = 0.10The total probability of an accident, P(A), is given by:
P(A) = P(A|Gi)P(Gi) + P(A|Mi)P(Mi) + P(A|Pi)P(Pi)
P(A) = (0.01)(0.30) + (0.03)(0.50) + (0.10)(0.20) = 0.003 + 0.015 + 0.02 = 0.038
The probability of Mr. Brophy being a good driver given he had an accident, P(Gi|A), is:
P(Gi|A) = (P(A|Gi)P(Gi)) / P(A) = (0.01)(0.30) / 0.038 ≈ 0.079
The probability of Mr. Brophy being a medium risk driver given he had an accident, P(Mi|A), is:
P(Mi|A) = (P(A|Mi)P(Mi)) / P(A) = (0.03)(0.50) / 0.038 ≈ 0.395
The probability of Mr. Brophy being a poor risk driver given he had an accident, P(Pi|A), is:
P(Pi|A) = (P(A|Pi)P(Pi)) / P(A) = (0.10)(0.20) / 0.038 ≈ 0.526
Which of the following rational functions is graphed below?
Answer:
A
Step-by-step explanation:
from the graph you can tell that there is a vertical asymp. at -3.
In the anwers A is the only one with vertical asymp. at -3.
Answer:
A f(x)=[tex]\frac{x}{x+3}[/tex]
Step-by-step explanation:
To answer this question, to identify which rational function relates to that graph we must at first look for Rational Function in this form:
[tex]P(x)=\frac{Q(x)}{R(x)}[/tex]
Where P(x)= Polynomial Quotient, Q(x)=Quotient, R(x)=Remainder. Q(x) and R(x) are Polynomial Functions.
So exclude B, then C, for they do not fit as Polynomial Functions.
Then rather than setting the graph, the second step would be looking for the vertical asymptote, given by the equation on the denominator. We must detach it from the original function then solve it.
x+3=0 ∴ x=-3