Desmοnd receives a discοunt οf R183.675. We can rοund this tο R183.18 οr R183.18, depending οn the desired level οf precisiοn.
What is discοunt?We all are eager abοut availing discοunts, but we barely knοw hοw we get these discοunts. There is a prοper way tο calculate discοunt and that we dο by using a discοunt fοrmula. The discοunt rate fοrmula can either be extracted by subtracting the selling price οf the prοduct frοm its marked price οr by multiplying the discοunt rate οffered and the marked price οf the prοduct. In terms οf Mathematics, the fοrmula fοr discοunt is represented as belοw,
Accοrding tο given infοrmatiοn,
Tο calculate the discοunt Desmοnd receives, we first need tο find 53.5% οf the οriginal price. We can dο this by multiplying the οriginal price by 0.535:
R395 x 0.535 = R211.325
Sο, Desmοnd pays R211.325 fοr his purchase after the discοunt.
Tο find the amοunt οf discοunt, we need tο subtract the discοunted price frοm the οriginal price:
R395 - R211.325 = R183.675
Therefοre, Desmοnd receives a discοunt οf R183.675. We can rοund this tο R183.18 οr R183.18, depending οn the desired level οf precisiοn.
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Test the conjecture. 1) A rectangle has an area of 54 square units. A scale factor of is applied to the rectangle to create a scaled figure. What is the area of the scaled figure?
9 units 6 units
Answer:
Step-by-step explanation:
yr face add more points NOW
What are the different types of early numeration system which have been developed to represent numbers throughout history of mathematics?
Explanation: The evolution of numbers developed differently with disparate versions, which include the Egyptian, Babylonians, Hindu-Arabic, Mayans, Romans, and the modern American number systems.
What is the simplest form of the radical expression?
show work please
let's recall that the conjugate of any expression is simply the same pair with a different sign between, so conjugate of "a + b" is just "a - b" and so on. That said, let's use the conjugate of the denominator
[tex]\cfrac{\sqrt{2}+\sqrt{3}}{\sqrt{2}-\sqrt{3}}\cdot \cfrac{\sqrt{2}+\sqrt{3}}{\sqrt{2}+\sqrt{3}}\implies \cfrac{(\sqrt{2}+\sqrt{3})(\sqrt{2}+\sqrt{3})}{\underset{ \textit{difference of squares} }{(\sqrt{2}-\sqrt{3})(\sqrt{2}+\sqrt{3})}}\implies \cfrac{\stackrel{ F~O~I~L }{(\sqrt{2}+\sqrt{3})(\sqrt{2}+\sqrt{3})}}{(\sqrt{2})^2-(\sqrt{3})^2} \\\\\\ \cfrac{2+2\sqrt{2}\cdot \sqrt{3}+3}{2-3}\implies \cfrac{5+2\sqrt{6}}{-1}\implies \boxed{-5-2\sqrt{6}}[/tex]
The points (-2, -2) and (5,5) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
Answer:
Step-by-step explanation:
[tex]diameter=\sqrt{(5+2)^2+(5+2)^2} \\=\sqrt{49+49} \\=\sqrt{98} \\=7\sqrt{2} \\radius=\frac{7\sqrt{2} }{2} \\\approx 4.95[/tex]
properties of the rectangle, rhombus, and square - practice determine if the following statements answers
1. The diagonals are equal. Rectangle
2. All sides are equal, and one angle is 60°. Rhombus
3. All sides are equal, and one angle is 90°. Square
4. It has all the properties of parallelogram, rectangle, and rhombus. Square
5. It is an equilateral parallelogram. Rhombus
A rectangle is a four-sided figure with two sets of parallel sides, with each side being a different length. The opposite sides of a rectangle are always equal in length, so the angles of a rectangle are all 90 degrees. A rectangle can also be referred to as a quadrilateral.
A rhombus is a four-sided figure with all sides the same length. The angles of a rhombus are not all 90 degrees, but the opposite sides of a rhombus are equal in length. A rhombus can also be referred to as a diamond.
A square is a four-sided figure with all sides being the same length and all angles being 90 degrees. A square can also be referred to as a regular quadrilateral.
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The complete question is:
Identify whether the following statements describe a rectangle, rhombus or square.
1. The diagonals are equal. ____________
2. All sides are equal, and one angle is 60°. ____________
3. All sides are equal, and one angle is 90°. ____________
4. It has all the properties of parallelogram, rectangle, and rhombus. ____________
5. It is an equilateral parallelogram. ____________
create your own example of a sample of 100 people such that: the two-sided p-value is less than 0.001.
Example of samples of 100 people for two-sided p-value of less than 0.001 represents that the new drug is indeed effective.
Example of a scenario that could lead to a two-sided p-value of less than 0.001 is ,
To investigate whether a new drug reduces blood pressure in patients.
Randomly select 100 patients with hypertension and divide them into two groups.
One group receives the new drug, while the other group receives a placebo.
After a month of treatment, you measure the blood pressure of each patient .
And compute the difference between the pre- and post-treatment measurements.
Assuming that the blood pressure measurements are normally distributed.
Perform a two-sample t-test to compare the mean difference in blood pressure between the two groups.
If the difference is statistically significant at the 0.001 level.
It means that the probability of obtaining such a large difference by chance is less than 0.001.
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Question 23 (2 points)
A standard deck of cards contains 4 suits of the same 13 cards. The contents of a
standard deck are shown below:
Standard deck of 52 cards
4 suits (CLUBS, SPADES, HEARTS, DIAMONDS)
13 CLUBS
13 SPADES
13 HEARTS
13 DIAMONDS
If two cards are drawn at random from the deck of cards, what is the probability both
are kings?
4/52
3/51
12/2652
16/2704
Answer:
12/2652
Step-by-step explanation:
First, the probability of drawing a king for the first time is 4/52. The chance of drawing another is 3/51. Multiplying, we get the 3rd answer choice, 12/2652
what is the largest integer $n$ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$?
the largest integer [tex]n $ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$ is $\boxed{62}$.[/tex]
To find the largest integer[tex]n $ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$[/tex], we need to count how many factors of 3 are in the product of the odd integers from 1 to 99.
One way to do this is to factor each odd integer into its prime factors and count how many factors of 3 are present. However, this would be quite tedious and time-consuming.
A quicker approach is to use the fact that every third odd integer is a multiple of 3. Thus, we can count how many multiples of 3 are present in the product of the odd integers from 1 to 99.
Let [tex]$m$[/tex] be the number of multiples of 3 in the range from 1 to 99. Then we have:
[tex]m = \left\lfloor \frac{99}{3} \right\rfloor = 33[/tex]
This is because there are 33 multiples of 3 in the range from 1 to 99 (namely, 3, 6, 9, ..., 96, 99).
Each multiple of 3 contributes at least one factor of 3 to the product of the odd integers. However, some multiples of 3 contribute two or more factors of 3, depending on how many factors of 3 they contain.
To count how many multiples of 3 contribute two or more factors of 3, we need to count how many multiples of 9, 27, and 81 are present in the range from 1 to 99.
There are [tex]$\left\lfloor \frac{99}{9} \right\rfloor = 11$[/tex]multiples of 9, namely 9, 18, 27, ..., 81, 90, 99. Each multiple of 9 contributes at least two factors of 3 to the product of the odd integers.
There are [tex]$\left\lfloor \frac{99}{27} \right\rfloor = 3$[/tex] multiples of 27, namely 27, 54, 81. Each multiple of 27 contributes at least three factors of 3 to the product of the odd integers.
There is only one multiple of 81 in the range from 1 to 99, namely 81, which contributes at least four factors of 3 to the product of the odd integers.
Thus, the total number of factors of 3 in the product of the odd integers from 1 to 99 is:
[tex]n = m + 2\times\text{number of multiples of 9} + 3\times\text{number of multiples of 27} + 4\times\text{number of multiples of 81}[/tex]
[tex]n = 33 + 2\times 11 + 3\times 3 + 4\times 1 = 62[/tex]
Therefore, [tex]the $ largest integer $n$ such that $3^n$ is a factor of $1 \times 3 \times 5 \times \dots \times 97 \times 99$ is $\boxed{62}$.[/tex]
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the area of the parallelogram is 40 in2. one base of the parallelogram is 5 in long. the other base is 10 in long find its 2 heights
Step-by-step explanation:
Area of parallelogram = base × height or say b×h
Given: h=8 inches
Area=120 sq.inches
⇒120=8×b
⇒120/8=b
⇒120/8=b = 15
Answer = 15 inches b
find the conditional probability that x is greater than 2 6 given that x is less than or equal to 1 2 .
According to bayes therom the conditional probability thst x is greater than 26 is zero.
Bayes' theorem may be used to compute the conditional probability that x is greater than 26 if x is less than or equal to 12.
P(x > 26 | x 12) = P(x > 26 plus x 12) / P(x > 26 plus x 12) (x 12).
Because x cannot be more than 26 and less than or equal to 12, the numerator of the preceding formula is zero. As a consequence, the conditional probability is equal to zero:
P(x > 26 | x ≤ 12) = 0
This means that knowing x is less than or equal to 12 does not inform us if x is more than or less than 26.
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16) Critique the sample method and the survey used by the guild. You’ll want to use some of the following words in your critique: sample, bias, random, response-bias, undercoverage, non-response, voluntary response.
Answer:
The critique of the sample method and survey used by the guild is as follows:
Sample: The sample used in the survey is not representative of the entire population. The survey was conducted only among the guild members, and hence it does not represent the views of non-members. This type of bias is called undercoverage bias.Bias: The survey seems to suffer from selection bias, where the participants who responded may not represent the entire population. This type of bias is known as response bias. It is possible that the members who chose to participate in the survey have different views from those who did not respond. Furthermore, the survey did not specify how the participants were selected, and hence there may be other types of bias present in the survey.Randomness: The survey did not use random sampling, which is a fundamental principle of survey research. A random sample ensures that every member of the population has an equal chance of being selected, which increases the representativeness of the sample.Non-Response: The survey did not address the issue of non-response bias, where participants who choose not to respond may have different views from those who respond. The survey did not specify the response rate, and hence it is unclear how many members chose to participate in the survey.Voluntary response: The survey seems to be a voluntary response survey, where members chose to participate voluntarily. This type of survey is known to suffer from bias because participants who respond are usually more motivated or have stronger opinions than those who do not respond.In summary, the survey used by the guild suffers from various types of bias, which may affect the validity and generalizability of the results. To improve the validity and reliability of the survey, the guild should use random sampling and address issues such as non-response and response bias.
A boat is heading towards a lighthouse, whose beacon-light is 139 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 5 degrees.
What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary.
The bοat's hοrizοntal distance frοm the lighthοuse (and the shοre) is apprοximately 1592.53 feet.
What is trigοnοmetryTrigοnοmetry is οne οf the mοst impοrtant branches in mathematics that finds huge applicatiοn in diverse fields. The branch called “Trigοnοmetry” basically deals with the study οf the relatiοnship between the sides and angles οf the right-angle triangle.
Hence, it helps tο find the missing οr unknοwn angles οr sides οf a right triangle using the trigοnοmetric fοrmulas, functiοns οr trigοnοmetric identities. In trigοnοmetry, the angles can be either measured in degrees οr radians. Sοme οf the mοst cοmmοnly used trigοnοmetric angles fοr calculatiοns are 0°, 30°, 45°, 60° and 90°.
We can use trigοnοmetry tο sοlve fοr the hοrizοntal distance. Let x be the hοrizοntal distance frοm the bοat tο the lighthοuse.
Then, tan(5°) = οppοsite/adjacent = 139/x
Sοlving fοr x, we get:
x = 139/tan(5°) ≈ 1592.53 feet
Therefοre, the bοat's hοrizοntal distance frοm the lighthοuse (and the shοre) is apprοximately 1592.53 feet.
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Mary baked a batch of cookies. The cookies needed 2 1/4 pounds of flour. Jack made 3 1/2 times the amount of cookies that Mary made. How many pounds of flour did Jack need? 63 pounds 8 pounds 8 1/2 pounds 7 7/8 pounds
Jack needed 7 7/8 pounds of flour for his batch of cookies.
Define Pounds
"Pounds" is a unit of measurement for weight, commonly used in the United States and other countries that have adopted the imperial system of measurement. One pound is equal to 16 ounces, and there are 2.20462 pounds in one kilogram.
Mary used 2 1/4 pounds of flour for her batch of cookies.
finding out how much flour Jack needed, we first need to determine how many cookies Jack made.
Since Jack made 3 1/2 times the amount of cookies that Mary made, we can calculate:
Number of cookies Jack made = 3.5 x Number of cookies Mary made
Let's start by finding out how much flour Mary used per cookie:
2 1/4 pounds of flour / Number of cookies Mary made
So, if Mary made X cookies, Jack made 3.5X cookies.
Now we can set up an equation:
2 1/4 pounds of flour / X cookies = Amount of flour per cookie
Amount of flour per cookie x Number of cookies Jack made = Total amount of flour Jack needed
Amount of flour per cookie = 2 1/4 pounds of flour / X cookies
Number of cookies Jack made = 3.5X
Total amount of flour Jack needed = Amount of flour per cookie x Number of cookies Jack made
Total amount of flour Jack needed = (2 1/4 pounds of flour / X cookies) x (3.5X cookies)
Total amount of flour Jack needed = 7 7/8 pounds of flour
Therefore, Jack needed 7 7/8 pounds of flour for his batch of cookies.
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Why is the following not a probability? model?
LOADING...
Click the icon to view the data table.
Determine why it is not a probability model. Choose the correct answer below.
A.
This is not a probability model because at least one probability is greater than 0.
B.
This is not a probability model because at least one probability is greater than 1.
C.
This is not a probability model because the sum of the probabilities is not 1.
D.
This is not a probability model because at least one probability is less than 0
The correct answer is C. This is not a probability model because the sum of the probabilities is not 1.Therefore, the sum of the probabilities must be equal to 1 for a set of probabilities to be considered a probability model.
What is probability?Probability is a measure of the probability of an event, expressed as a number between 0 and 1.
For example, the probability of rolling a 6 on a fair six-sided die is 1/6 or approximately 0.17.
In order for a set of probabilities to represent a probability model, the sum of all the probabilities must be equal to 1. This ensures that there is a 100% chance that one of the possible outcomes will occur.
If the sum of the probabilities is less than 1, then there is a possibility that none of the outcomes will occur.
If the sum of the probabilities is greater than 1, then there is a possibility that more than one outcome will occur, which is not possible in a probability model.
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Students at a virtual school are allowed to sign up for one math class each year. The numbers of students signing up for various math classes for the next school year are given in the following table:
Grade Geometry Algebra I Pre-Calculus AP Statistics Total
A student calculated the joint relative trequency of 10th grade students in geometry as being 71.4%. What did the student actually calculate and what is the correct answer?
A) The student calculated the conditional relative frequency for students who are in 10th grade, given that they are enrolled in Geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 20.7%.
B) The student calculated the conditional relative frequenc for students who are in 10th grade, given that they are enrolled in Geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 29%.
C) The student calculated the marginal relative frequency for 10th grade students in geometry. The correct value of the joint relative trequency of 10th grade students in geometry is 20.7%.
D) The student calculated the marginal relative frequency for 10th grade students in geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 29%
Option C) The student calculated the marginal relative frequency for 10th grade students in geometry. The correct value of the joint relative frequency of 10th grade students in geometry is 20.7%.
How to calculate a relative frequency?Relative frequency is a measure of the proportion or percentage of times an event occurs in a given sample. It is calculated by dividing the frequency of an event by the total number of events in the sample. The formula for relative frequency is given as follows:
Relative frequency = Frequency of an event / Total number of events in the sample
For the joint relative frequency of 10th grade students in geometry, the parameters are given as follows:
Frequency of 10th grade students in geometry: 20.7%.Total number of events in the sample: 100% of students.Hence the joint relative frequency is obtained as follows:
20.7/100 x 100%= 20.7%.
Hence option C is correct.
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For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal? А. A random sample of 8 taken from a normally distributed population B. A random sample of 50 taken from a normally distributed population C. A random sample of 10 taken from a population dintribution that is skewed to the right D. A random sample of 75 taken from a population distribution that is skewed to the left E. A random sample of 100 taken from a population that is uniform
The conditions in which is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal : (C) A random sample of 10 taken from a population distribution that is skewed to the right.
In statistics, the normal or Gaussian distribution is a continuous probability distribution for real-valued random variables.
The normal distribution is important in statistics and is often used in the natural and social sciences to represent real-valued random variables whose distribution is unknown. Their importance is partly due to the central limit theorem. It states that in some cases the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable - whose distribution converges to a normal distribution as the size of the l sample increases.
Now,
If we look at the options given below, we see that the random samples in options A and B are normally distributed, so their sample means will be approximately normally distributed.
Similarly, option E indicates that the population is uniform, so the sample mean will also be approximately normal.
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Find the unknown side lengths in similar triangles PQR and ABC.
I need an explanation on how to get the answer
Answer:
a=18 b=24
Step-by-step explanation:
We know that BC=25 and QR=30, the key term is that they are similar triangles. Therefore, BC: QR=25:30=5:6. Then BA:A=5:6=15:X
x=a=18
20:b=5:6
b=24
The probability of drawing three kings in a row from a standard deck of cards when the drawn card is not returned to the deck each time is..................
The probability of drawing three kings in a row from a standard deck of cards when the drawn card is not returned to the deck each time is 0.000055
The multiplication rule of probability can be used to determine the likelihood of drawing three kings consecutively from a standard deck of cards when the drawn card is not put back into the deck each time.
Since there are four kings in a deck of 52 cards, the likelihood of drawing a king from a standard 52-card deck is 4/52 or 1/13.
There are still 51 cards in the deck after the first king is drawn, and three of them are kings. Therefore, there is a 3/51 chance of drawing another king.
There are 50 cards left in the deck after drawing the second king, and two of them are kings. The likelihood of drawing a third king is therefore 2/50 or 1/25.
Therefore, the probability of drawing three kings in a row from a standard deck of cards when the drawn card is not returned to the deck each time is:
(1/13) x (3/51) x (1/25) = 3/54,600 or approximately 0.000055.
Hence, 0.000055 is the probability of drawing three kings in a row from a standard deck of cards when the drawn card is not returned to the deck each time.
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Is the following sequence arithmetic or geometric? Find the common difference or ratio, depending on which one it is: 32, 8, 2, ....
Answer:
Step-by-step explanation:
The given sequence is geometric.
To find the common ratio (r) of the sequence, we need to divide any term by its preceding term. Let's divide the second term (8) by the first term (32):
r = 8/32 = 1/4
Now, we can use the formula for a geometric sequence to find any term:
an = a1 * r^(n-1)
where:
an = nth term of the sequence
a1 = first term of the sequence
r = common ratio
n = position of the term we want to find
Let's use this formula to find the third term:
a3 = 32 * (1/4)^(3-1) = 2
So, the common ratio of the sequence is 1/4, and each term is obtained by multiplying the preceding term by 1/4. The sequence is decreasing rapidly because the ratio is less than 1.
Find g. Write your answer as a whole number or a decimal. Do not round.
The value of length of side g using the similar triangles is found as 20 ft.
Explain about the similar triangles?Triangles that are similar to one another in terms of shape, angle measurements, and proportion are said to be similar.If the single difference between two triangles is their size and perhaps the requirement to rotate or flip one of them, then they are similar.In the given figures:
DC || EA
So,
∠D = ∠A
∠C = ∠E
By Angle -Angle similarity both triangles are similar.
Thus,
Taking the ratios of their side, it will be also equal.
EA / DC = EB / BC
5 / 10 = g / 10
g = 10*10 / 5
g = 100 / 5
g = 20
Thus, the value of length of side g using the similar triangles is found as 20 ft.
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Identify the values of the variables. Give your answers in simplest radical form.
The value οf v=3√2 and w=√3/√2.
What is Pythagοras theοrem?If a triangle has a straight angle (90 degrees), the hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides, accοrding tο the Pythagοras theοrem.
Keep in mind that BC² = AB² + AC²in the triangle ABC signifies this. This equatiοn uses the variables base AB, height AC, and hypοtenuse BC. It is impοrtant tο nοte that the hypοtenuse, οr lοngest side, οf a right-angled triangle is.
Here fοr sin(30)= v/3√2
1/2 = v / 3√2
v = 3√2
cοs(30)= w/3√2
w=3√2*√3/2
w=√3/√2
Hence the value οf v=3√2 and w=√3/√2.
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Find the potential inside and outside a sphere shell that carries a uniform surface charge $\sigma_0$, using results of Ex. 3.9
Inside the sphere, the potential is given by [tex]$V(r)=\frac{Q}{4\pi\epsilon_0r}$[/tex], where Q is the total charge enclosed within the sphere. Since the sphere shell has no charge inside, Q=0, and thus V(r)=0 inside the sphere.
Outside the sphere, the potential is given by
[tex]$V(r)=\frac{Q}{4\pi\epsilon_0r} + \frac{Q'}{4\pi\epsilon_0r'}$[/tex]
where Q is the total charge of the sphere shell, Q'= σ4πR²is the charge on an imaginary sphere of radius r'>R enclosing the sphere shell, and r is the distance from the center of the sphere. Using the result from Ex. 3.9, the potential outside the sphere becomes
[tex]$V(r)=\frac{Q}{4\pi\epsilon_0r} + \frac{\sigma_0 R^2}{2\epsilon_0 r}$[/tex]
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In a school district, 57% favor a charted school for grades K to 5. A random sample of 300 are surveyed and proportion of those who favor charter school is found. Let it be X. What is the probability that less than 50% will favor the charter school? Assume central limit theorem conditions apply.
PLEASE HELP YOU WILL BE BRAINIEST!!! Use the chart!!!!
CAN SOMEONE HELP WITH THIS QUESTION?✨
Step-by-step explanation:
it was not clear if an average change rate would be sufficient, or if you needed an immediate change rate (as I also don't know if you covered derivatives already or not).
so, it would be helpful, if you could put a message to an answer that was not giving you what you need.
so, here now an answer for an immediate change rate (hopefully that is what you need) :
we have a right-angled triangle.
the direct line of sight (the direct distance between police and red car) is the Hypotenuse (the baseline opposite of the 90° angle).
the 50 ft and 180 ft are the legs.
Pythagoras gives us the length of the Hypotenuse :
Hypotenuse² = 50² + 180² = 2500 + 32400 = 34,900
Hypotenuse = sqrt(34900) = 186.8154169... ft
in general terms let's say x is the distance of the cop to the road, y is the distance on the road to the crossing point with the distance cop to road, and z is the line of sight distance between the red car and the cop (the Hypotenuse).
x² + y² = z²
now, the first derivative of distance is the change of distance = speed.
then dy/dt (= y') is how fast the car is traveling down the road. dx/dt (= x') is how fast the cop is traveling toward the road. and dz/dt (= z') is how fast the distance between the cop and the car is changing.
now, we take the derivative of our equation
x² + y² = z² with respect to time, variable by variable :
d(x² + y² = z²)/dt =
dx²/dx × dx/dt + dy²/dy × dy/dt = dz²/dz × dz/dt
that gives us the equation
2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)
x(dx/dt) + y(dy/dt) = z(dz/dt)
from the problem we know x (50 ft), y (180 ft), dz/dt (85 ft/s). we calculated z (the Hypotenuse = sqrt(34900), and since the cop is not moving, we know dx/dt = 0.
and we get
50ft×0ft/s + 180ft×(y') = sqrt(34900)ft×(85)ft/s
we solve for y' (the speed of the car on the road)
y' = sqrt(34900)×85/180 = 88.21839132... ft/s
≈ 88.22 ft/s
and now here the difference for an average change rate over the unrevealed of 1 second :
the radar measured the change of the distance (Hypotenuse) from 1 second ago to now.
so, 1 second ago, the distance was
186.8154169... + 85 = 271.8154169... ft
the 50 ft leg stays the same, but the 180 ft leg was (again via Pythagoras)
271.8154169...² = 50² + leg²
leg² = 271.8154169...² - 50² = 71,383.62088...
leg = 267.1771339... ft
so, the red car traveled
267.1771339... - 180 = 87.1771339... ft/s
as you can see, it is close, but there has to be a difference, as the average change rate is only an approximation to the immediate change rate.
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5 years, and standard deviation of 1.3 years.
If you randomly purchase one item, what is the probability it will last longer than 6 years?
Answer:
Step-by-step explanation:
Let X be the lifespan of an item. We are given that X is normally distributed with a mean of μ = 5 years and a standard deviation of σ = 1.3 years.
We want to find the probability that an item will last longer than 6 years. Let Y be the random variable that represents the lifespan of an item in excess of 6 years, i.e. Y = X - 6. Then we want to find:
P(Y > 0)
Using the properties of normal distribution, we can standardize Y to get a standard normal variable Z:
Z = (Y - μ) / σ = (X - 6 - 5) / 1.3 = (X - 11) / 1.3
So we want to find:
P(Z > (6 - 11) / 1.3) = P(Z > -3.85)
Using a standard normal distribution table or calculator, we can find that the probability of Z being greater than -3.85 is very close to 1 (in fact, it is essentially 1). Therefore, the probability of an item lasting longer than 6 years is essentially the same as the probability of Y being greater than 0, which is 1.
Therefore, the probability that a randomly purchased item will last longer than 6 years is approximately 1.
A sequence has the nth term rule T(n) = 32 - 3n
What is the value of the first negative term in this sequence?
[tex]T(11) = -1[/tex] represents the initial negative term inside the series.
What do the concepts positive and negative in logic mean?A phrase that acknowledges a characteristic or trait in anything is said to be positive. Negative terms are those that downplay some aspect or characteristic of something. The positive or negativizes of a phrase is termed its quality.
What does "positive" and "negative" mean?Positive simply denotes excellent or the polar opposite of negative. For instance, you're less likely to receive favorable feedback on your scorecard if you've a good mindset toward your assignments. It might be difficult to keep track of all the different definitions of the word positive.
T(n) is negative when [tex]32 - 3n < 0[/tex], which can be rearranged as:
[tex]3n > 32[/tex]
[tex]n > 32/3[/tex]
Since [tex]n[/tex] is an integer, the smallest value of n that satisfies this inequality is [tex]n = 11[/tex].
Therefore, the [tex]11th[/tex] term of the sequence is:
[tex]T(11) = 32 - 3(11) = -1[/tex]
So the first negative term in the sequence is [tex]T(11) = -1.[/tex]
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Macy of New York sold LeeCo. of Chicago office equipment with a $6,300 list price. Sale terms were 3/10, n/30 FOB New York. Macy agreed to prepay the $40 freight. LeeCo. pays the invoice within the discount period. What does LeeCo. pay Macy?
The amount that LeeCo pays Macy for the office equipment at the $6,300 list price, sales terms of 3/10, n/30 FOB with payment made within the discount window, is $6,111.
What is a cash discount?A cash discount refers to a reduction in the price of an item due to payment within the discount period.
A cash discount incentivizes the customer to make prompt payments.
The list price of the equipment = $6,300
Sales terms: 3/10, n/30 FOB
Prepaid freight = $40
Cash discount = $189 ($6,300 x 3%)
Payment after the discount = $6,111 ($6,300 - $189)
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Consider the following energy diagram and determine which of the following statements is true A) At equilibrium, we expect [Reactants} < [Products) EN E R B) At equilibrium, we expect [Reactants) > [Products) P C) At equilibrium, we expect k < 1. D) At equilibrium, we expect K = 1 Rxn-
At equilibrium we expect [Reactants} < [Products) from the the profile that has been shown.
What is the energy profile diagram?An energy profile diagram, also known as an energy diagram or reaction coordinate diagram, is a graphical representation of the energy changes that occur during a chemical reaction or a physical process. It shows the energy levels of the reactants, products, and any intermediate species that may form during the reaction.
The horizontal axis of an energy profile diagram represents the reaction coordinate, which is a measure of the progress of the reaction from the reactants to the products. The vertical axis represents the energy of the system.
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In Biology class, Marissa is viewing cells with a microscope. Cell W
-7
measures 1.8 x 10 microns in diameter and Cell S measures
-5
7.2 x 10 microns in diameter. How many times larger is the bigger
cell than the smaller cell?
The number of times larger Cell S is compared to Cell W is 4 x 10²,
How many times larger is the bigger cell?
Scientific notation is used to compress large numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
When the power of the scientific notation is negative, it means that the number is less than 1. 0.01 would be written as 1 x [tex]10^{-2}[/tex]. Cell S is larger than Cell W.
(7.2 x [tex]10^{-5}[/tex]) ÷ (1.8 x [tex]10^{-7}[/tex])
(7.2 / 1.8) x [tex]10^{-5--7}[/tex]
4 x 10²
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