Answer:
It would be g(x) = 2^-x
Step-by-step explanation:
Use the formulas to generate a Pythagorean Triple with x = 8 and y = 3.
A squared+b squared=c squared
5 squared+2 squared=c squared
25+4=29
The square root of 29 is C.
The order would be 2, 5, the square root of 29
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Using the given formula, Pythagorean Triple with x = 8 and y = 3 is 5329=5329.
What are Pythagorean triples?Pythagorean triples are a²+b² =c² where a, b and c are the three positive integers. These triples are represented as (a,b,c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.
Given that, x=8 and y=3.
The formula is (x²+ y²)²= (x² - y²)² + (2xy)²
Now, (8²+ 3²)²= (8² - 3²)² + (2×8×3)²
(64+9)²=(64-9)² +(48)²
73²=55²+48²
5329=5329
Therefore, using the given formula, Pythagorean Triple with x = 8 and y = 3 is 5329=5329.
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"Your question is incomplete, probably the complete question/missing part is:"
The identity (x²+ y²)²= (x² - y²)² + (2xy)² can be used to generate Pythagorean triples. What Pythagorean triple could be generated using x = 8 and y = 3?
What is the solution of each equation?
2s = 34
Answer:
17
Step-by-step explanation:
sdfbh
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The calculated scale factor from ABC to A'B'C is 1/3
Calculating the scale factor from ABC to DEF?From the question, we have the following parameters that can be used in our computation:
The triangles
From the triangles, we have the following parameters
A = (0, 3)
A' = (0, 1)
Using the above as a guide, we have the following:
Scale factor of the dilation = A'/A
So, we have
Scale factor of the dilation = (0, 1)/(0, 3)
Evaluate
Scale factor of the dilation = 1/3
Hence, the scale factor of the dilation is 1/3
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Give the equation of the circle centered at the origin and passing through the point (0, 6).
The equation of circle is x² + y² = 36.
We have,
Center= (0, 0)
Passing point = (0, 6)
We know the equation of circle is
(x-h)² + (y-k)² = r²
where (h, k) be the center and r be the radius.
Now, the radius of circle is
= √(6-0)² + (0-0)²
= √36
= 6 unit
So, the equation of circle
(x-0)² + (y-0)² = 6²
x² + y² = 36
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A company that produces cranberries knows that about 7 % 7%7, percent of its cranberries are bruised in the bagging process. They changed their bagging method, and they were curious if the proportion of cranberries bruised was different. They tested H 0 : p = 0.07 H 0 :p=0.07H, start subscript, 0, end subscript, colon, p, equals, 0, point, 07 versus H a : p ≠ 0.07 H a :p =0.07H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 07, where p pp is the proportion of cranberries bruised, with a random sample of 600 600600 cranberries. They found that 10 % 10%10, percent of cranberries in the sample were bruised. Those results yielded a test statistic of z ≈ 2.88 z≈2.88z, approximately equals, 2, point, 88 and a P-value of approximately 0.004 0.0040, point, 004. Assume that the conditions for inference were met. Is there sufficient evidence at the α = 0.01 α=0.01alpha, equals, 0, point, 01 level to conclude that the proportion of cranberries bruised is different than 7 % 7%7, percent? Choose 1 answer:
There is sufficient evidence at α = 0.01 level to conclude that proportion of cranberries is different than 7% because 0.004 < 0.01
What do you mean by proportion?
The main pillars on which proportion is explicated are ratio and fractions. When two ratios are written as a fraction using the formula a/b, ratio a:b, and then a proportion, they are equal. A and b in this situation can be any two integers.
Null hypothesis, H0:p=0.07
Alternative hypothesis, Hα:p≠0.07
Sample size (n)= 600
Sample proportion of cranberries (p') = 0.10
Test statistics z = 2.88
P-value = 0.004
To prove that the percentage of cranberries that have been bruised is different from 7%, we must demonstrate that there is sufficient evidence at the α = 0.01 level of significance.
Therefore, it is clear that P-value = 0.004 is lower than α = 0.01
We come to the conclusion that our null hypothesis is false. (Since p value <alpha, the null hypothesis is rejected.)
Thus the correct answer is Yes, because 0.004 < 0.01
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Show that the path of a moving point parallel to the axes of x and y with velocitiesu +
ey andv + ex is a conic section
We have shown that the path of a moving point with velocities u + ey and v + ex, parallel to the axes of x and y, is either a line (when v - \(e^2\) ≠ 0) or a horizontal line (when v - \(e^2\) = 0), both of which are conic sections.
To show that the path of a moving point parallel to the axes of x and y with velocities u + ey and v + ex is a conic section, we can analyze the motion of the point using the principles of calculus and conic sections.
Let's denote the position of the point at any given time t as (x, y). We are given that the velocities along the x and y axes are u + ey and v + ex, respectively. This means that the derivatives of x and y with respect to time, dx/dt and dy/dt, can be expressed as:
dx/dt = u + ey
dy/dt = v + ex
Now, let's integrate these expressions to obtain x and y as functions of t. Integrating dx/dt with respect to t gives:
x = ut + eyt + C1
Similarly, integrating dy/dt with respect to t gives:
y = vt + ext + C2
Where C1 and C2 are constants of integration.
Now, we can eliminate the parameter t by expressing t in terms of x and y. From the equation y = vt + ext + C2, we can solve for t:
t = (y - ext - C2) / v
Substituting this value of t into the equation for x, we get:
x = u[(y - ext - C2) / v] + ey[(y - ext - C2) / v] + C1
Simplifying this equation, we obtain:
vx - u - evx + ue + vy - \(e^2\)x - eyC2 = C1v
Rearranging the terms, we get:
vx - vy + ue + evx - \(e^2\)x = C1v + eyC2 - u
Let's define new constants A = ue + ev and B = C1v + eyC2 - u. The equation then becomes:
(v - \(e^2\))x + (u + ev)y = A + B
This equation is in the standard form of a conic section, specifically a line. However, we can manipulate this equation further to reveal other possible conic sections.
Let's consider the case when v - \(e^2\) ≠ 0. In this case, we can divide both sides of the equation by v - \(e^2\), yielding:
x + [(u + ev)/(v - \(e^2\))]y = (A + B)/(v - \(e^2\))
Now, let's define another constant C = (u + ev)/(v -\(e^2\)) and rewrite the equation as:
x + Cy = D
Where D = (A + B)/(v - \(e^2\)).
This equation represents a line in the x-y plane.
On the other hand, if v - \(e^2\) = 0, the equation becomes:
0x + (u + ev)y = A + B
This simplifies to:
(u + ev)y = A + B
Which is a horizontal line parallel to the x-axis.
Therefore, we have shown that the path of a moving point with velocities u + ey and v + ex, parallel to the axes of x and y, is either a line (when v - \(e^2\) ≠ 0) or a horizontal line (when v - \(e^2\) = 0), both of which are conic sections.
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Which of the following statements is true?
Answer: The y-intercept is 5
Step-by-step explanation:
PLEASE HURRY AND ANSWER!!!!
The probability that that arrow will land on the part labelled C after the first spin would be = 1/5.
How to calculate the probability of the chosen event?To calculate the probability of the chosen event, the formula for probability should be used which is given as follows:
Probability = possible outcome/ sample space
Where possible outcome = 2
sample space = A,B,B,B,C,C,D,D,D,E = 10
Therefore the probability that the arrow will land on the part labelled C after the first spin = 2/10 = 1/5.
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2, 202, 402, 602 what is the common difference
-2
Step-by-step explanation:
The difference between second term and first term or third term and second term in an AP series is called common difference.
Hence, in the given sequence −2,−4,−6,......, the common difference is −4−(−2)=
What is the value of this expression when X equals 8? 4X -6+ X +3
Answer:
32-6+8+3
37
Step-by-step explanation:
Answer:
32 - 6 + 8 + 3 = 37
Step-by-step explanation:
Since we have the x-value, we can plug it in.
4(8) -6 +(8) +3
32 - 6 + 8 + 3
26 + 11
37
find the real solutions of 9-l2xl=2
Answer
x = -7/2, 7/2
Step-by-step explanation
Given the equation:
\(9-|2x|=2\)Subtracting 9 at both sides of the equation:
\(\begin{gathered} 9-9-\lvert2x\rvert=2-9 \\ -\lvert2x\rvert=-7 \end{gathered}\)Dividing by -1 at both sides of the equation:
\(\begin{gathered} \frac{-\lvert2x\rvert}{-1}=\frac{-7}{-1} \\ |2x|=7 \end{gathered}\)Now we have two options:
\(\begin{gathered} 2x=7 \\ \text{ Or} \\ 2x=-7 \end{gathered}\)Solving the first option:
\(\begin{gathered} 2x_1=7 \\ \frac{2x_1}{2}=\frac{7}{2} \\ x_1=\frac{7}{2} \end{gathered}\)Solving the second option:
\(\begin{gathered} 2x_2=-7 \\ \frac{2x_2}{2}=\frac{-7}{2} \\ x_2=-\frac{7}{2} \end{gathered}\)Helen bought ice cream for her friends after school. she bought 4 single-scoop ice cream cones for a total of $8.25 and 6 sundaes. Each sundae costs the same amount, and Helen paid a total of #33.75 for the ice cream. What was the price per sundae Helen paid?
Answer:
x= $4.25
$4.25 per sundae
Step-by-step explanation:
The equation is 8.25 + 6x = 33.37
subtract 8.25 from both sides
6x=25.5
Divide each side by 6
x=4.25
The distance between two points is 10 units, if the coordinates of one of the endpoints are (4, -7), find x if the coordinates of the other endpoint are (x, 1).
Answer:
10
Step-by-step explanation:
let the distance = d
d² = (x2-x1)² + (y2-y1)²
=>
10²= (x-4)²+(1+7)²
100 = (x-4)²+64
(x-4)²=100-64
= 36
x-4 = √36
x-4=6
x= 6+4
x= 10
Round the weight of one dose to the nearest gram
Answer:
whats the weights?
Step-by-step explanation:
8. The box plots show the heights of a sample of two types
of trees.
The median height of Tree _____ Is greater
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I am not sure how to do this and I don’t have much time before my test solve problem a
Given:
a)
Consider the triangles ABC and ADC.
AB=DC
\(\angle\text{ABC}=\angle\text{ADC}\)The common side is AC.
Using the two-column method.
\(1.AB=DCand\angle ABC=\angle ADC\ldots\ldots\ldots.1.\text{given}\)\(2.AC\cong AC\ldots\ldots.2.\text{Reflexive property }\)\(3.\Delta\text{ABC}\cong\Delta ADC\ldots\ldots.3.\text{SAS potulates}\)b)
Consider the triangle.
\(1.\angle DEF\cong\angle KJLandDE=JL\ldots\ldots1.given\)Using triangle sum property, we get
\(\angle EDF+\angle EFD+\angle DEF=180^o\)\(\angle EDF+70^o+60^o=180^o\)\(\angle E\text{DF}=50^o\)\(2.\angle EDE\cong\angle JLK\ldots\ldots..2.triangel\text{ sum property.}\)\(3.\Delta\text{DEF}\cong\Delta\text{KJL}\ldots\ldots\text{.}\mathrm{}\text{ASA postulates}\)Find the sum of the first 20 arithmetic progression 2, 7, 12, 17, 22
Answer: 5
Step-by-step explanation: 2 + 5 = 7, 7 + 5 = 12, 12 + 5 = 17, 17 + 5 = 22
Elena drank 3 liters of water yesterday. Jada drank 3/4 times as much water as elena. Link drank twice as much as Jada. Did jada drink more or less then elena? Explain how you know
Answer:
Step-by-step explanation:
3\4 bc on a nuberline it would be 3 3\4
I--I----(etc)
so yeah hope i helped
A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 3points with99 % confidence assuming s=14 based on earlier studies? Suppose the doctor would be content with 95 %confidence. How does the decrease in confidence affect the sample size required?
We need a sample size of at least 154 subjects to estimate the mean HDL cholesterol within 3 points with 95% confidence.
Dcreasing the confidence level from 99% to 95% reduces the required sample size. This is because a higher confidence level requires a larger z-value, which increases the sample size needed to achieve the desired margin of error.
What is Standard deviation?The standard deviation is a measure of the amount of variation or dispersion of a set of data values. It is calculated as the square root of the variance, which is the average squared difference between each value and the mean.
What is mean?The mean is a measure of central tendency that represents the average value of a set of data. It is calculated by summing up all the values in the set and dividing by the number of values.
According to the given information:
To estimate the required sample size, we can use the formula:
n = (z-value)² × s² / E²
where:
z-value = the z-score corresponding to the desired level of confidence
s = the population standard deviation (given as 14)
E = the desired margin of error (3 points)
For a 99% confidence level, the z-value is 2.576 (obtained from a standard normal distribution table). Plugging in the given values, we get:
n = (2.576)² × 14² / 3²
n = 267.89
We need a sample size of at least 268 subjects to estimate the mean HDL cholesterol within 3 points with 99% confidence.
For 95% confidence, the z-value is 1.96. Using the same formula, we get:
n = (1.96)² × 14² / 3²
n = 153.44
We need a sample size of at least 154 subjects to estimate the mean HDL cholesterol within 3 points with 95% confidence.
As we can see, decreasing the confidence level from 99% to 95% reduces the required sample size. This is because a higher confidence level requires a larger z-value, which increases the sample size needed to achieve the desired margin of error.
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The length of a rectangle is twice its width. Find its lenght and width, if its perimeter is 7 1/3 cm.
The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.
Let's assume the width of the rectangle is "b" cm.
According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.
The formula for the perimeter of a rectangle is given by:
Perimeter = 2 * (length + width)
Substituting the given perimeter value, we have:
7 1/3 cm = 2 * (2b + b)
To simplify the calculation, let's convert 7 1/3 to an improper fraction:
7 1/3 = (3*7 + 1)/3 = 22/3
Rewriting the equation:
22/3 = 2 * (3b)
Simplifying further:
22/3 = 6b
To solve for "b," we can divide both sides by 6:
b = (22/3) / 6 = 22/18 = 11/9 cm
Therefore, the width of the rectangle is 11/9 cm.
To find the length, we can substitute the width back into the equation:
Length = 2b = 2 * (11/9) = 22/9 cm
So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.
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In the exercise, X is a binomial variable with n = 5 and p = 0.2. Compute the given probability. Check your answer using technology. HINT [See Example 2.] (Round your answer to five decimal places.) P(X = 3)
Answer:
0.0512
Step-by-step explanation:
We are told in the question that X isa Binomial variable. Hence we solve this question, using the formula for Binomial probability.
The formula for Binomial Probability = P(x) = (n!/(n - x) x!) × p^x × q ^n - x
In the above question,
x = 3
n = 5
p = probability for success = 0.2
q = probability for failures = 1 - 0.2 = 0.8
P(x) = (n!/(n - x) x!) × p^x × q ^n - x
P(3) = (5!/(5 - 3) 3!) × 0.2^3 × 0.8^5-3
P(3) =( 5!/2! × 3!) × 0.2³ × 0.8²
P(3) = 10 × 0.008 × 0.64
P(3) = 0.0512
Given the graph of f(x) above, find the following and write your answers using interval notation (Separate multiple intervals with a comma):
(a) Domain: 7
(b) Range:
(c) Interval(s) on which f(x) is increasing:
(d) Interval(s) on which f(x) is decreasing:
(e) Interval(s) on which f(x) is constant:
(f) Local maxima: 3
(g) Local minima: -5
Answer:
a) [-9,8)
b) [-5,5]
c) (-4,0), (1,6)
d) [-9,-4), (6,8)
e) [0,1]
f) just the y-value: 5; as a point: (-8,5)
g) just the y-value: -5; as a point: (-4,-5)
Step-by-step explanation:
a) Domain is all of the x-values that are defined in the function. The smallest x-value in the graph is -9, and the largest is 8. And all values in between are defined (have corresponding y-values). But notice that there's an open dot on (8,0).
b) Range is found the same way as Domain, but with the y-values. The smallest y-value of this function is -5, and the largest is 5.
For c-e, notice where the graph changes direction and draw a vertical line from the x-axis through the turning point. These lines are the boundaries between intervals of increasing/decreasing/constant. You should have vertical lines at x=-4, x=0, x=1, and x=6.
c) Interval(s) on which f(x) is increasing: Reading the graph from Left To Right, between which vertical lines is the graph going up?
d) Interval(s) on which f(x) is decreasing: Reading the graph from Left To Right, between which vertical lines is the graph going down?
e) Interval(s) on which f(x) is constant: Reading the graph from Left To Right, between which vertical lines is the graph staying flat?
f) Look for the highest non-infinity point on the graph
g) Look for the lowest non-infinity point on the graph
Factorizie completely 2ap+aq-bq-2bp
Answer:
2ap + aq - bq -2bp = (a - b)(2p + q)
Step-by-step explanation:
(2ap + aq) - (bq -2bp)
a(2p +q) -b(q + 2p) [ taking a common from the first, and b from the second]
(2p + q) [a - b] [takin (2p + q)]
(2p + q)(a - b)
The completely factored form of the expression 2ap + aq - bq - 2bp is
(a - b)(2p + q).
In order to completely factorize the given expression, we need to look for common factors and apply factorization techniques.
Given expression: 2ap + aq - bq - 2bp
Step 1: Look for common factors.
Notice that 'a' is common in the first two terms, and '-b' is common in the last two terms.
Step 2: Factor out the common terms.
We can factor 'a' from the first two terms: a(2p + q)
And factor '-b' from the last two terms: -b(q + 2p)
Step 3: Rearrange the expression.
Now we have: a(2p + q) - b(q + 2p)
Step 4: Factor by grouping.
We can see that (2p + q) is common in both terms, so we can factor it out: (2p + q)(a - b)
Step 5: Final result.
Thus, the completely factored form of the given expression is
(a - b)(2p + q).
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If f(x)=√x-3, which inequality can be used to find the domain of f(x)?
square root of x - 3 over or equal to zero, x minus three over or equal to zero, square root of x-3 under or equal to zero; x-3 under or equal to 0
The inequality that can be used to find the domain of f(x) is x - 3 ≥ 0.
The correct answer is the second one i.e.x minus three over or equal to zero.
What is the Domain of a Square Root Function?Fundamentally, the square root function has the form f(x) = √x. In other words, f(x) = √x is the parent square root function.A negative number's square root is not a real number. Therefore, negative values cannot be put into the square root function.That is, the set of all real numbers that are not negative constitutes the domain of the square root function, f(x) = √x.Consequently, [0,∞ ) is the square root function domain. It should be noted that the domain also contains 0.Given:
Function f(x) = √x-3
The fact that a negative number cannot be used as the term in the root square, so
x - 3 ≥ 0 which implies that, x ≥ 3.
From the inequality, we can tell that the domain of the function is the interval [3,∞).
Hence the inequality is x - 3 ≥ 0.
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Is the event independent or overlapping:
A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?
Mutually exclusive or independent:
A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5.
Mutually exclusive or overlapping:
A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that is is a milk chocolate or has no peanuts inside?
Mutually exclusive or independent:
You flip a coin and then roll a fair six sided die. What is the probability the coin lands on heads up and the die shows an even number?
The first question:
"A spinner has an equal chance of landing on each of its eight numbered regions. After spinning, what is the probability you land on region three and region six?"
Since the spinner has an equal chance of landing on each of its eight regions, the probability of landing on region three is 1/8, and the probability of landing on region six is also 1/8.
To find the probability of both events occurring (landing on region three and region six), you multiply the probabilities together:
P(landing on region three and region six) = P(landing on region three) * P(landing on region six) = (1/8) * (1/8) = 1/64.
Therefore, the probability of landing on both region three and region six is 1/64.
The events are mutually exclusive because it is not possible for the spinner to land on both region three and region six simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The second question:
"A bag contains six yellow jerseys numbered 1-6. The bag also contains four purple jerseys numbered 1-4. You randomly pick a jersey. What is the probability it is purple or has a number greater than 5?"
To find the probability of either event occurring (purple or number greater than 5), we need to calculate the probabilities separately and then add them.
The probability of picking a purple jersey is 4/10 since there are four purple jerseys out of a total of ten jerseys.
The probability of picking a jersey with a number greater than 5 is 2/10 since there are two jerseys numbered 6 and above out of a total of ten jerseys.
To find the probability of either event occurring, we add the probabilities together:
P(purple or number greater than 5) = P(purple) + P(number greater than 5) = (4/10) + (2/10) = 6/10 = 3/5.
Therefore, the probability of picking a purple jersey or a jersey with a number greater than 5 is 3/5.
The events are overlapping since it is possible for the jersey to be both purple and have a number greater than 5.
--------------------------------------------------------------------------------------------------------------------------
The third question:
"A box of chocolates contains six milk chocolates and four dark chocolates. Two of the milk chocolates and three of the dark chocolates have peanuts inside. You randomly select and eat a chocolate. What is the probability that it is a milk chocolate or has no peanuts inside?"
To find the probability of either event occurring (milk chocolate or no peanuts inside), we need to calculate the probabilities separately and then add them.
The probability of selecting a milk chocolate is 6/10 since there are six milk chocolates out of a total of ten chocolates.
The probability of selecting a chocolate with no peanuts inside is 7/10 since there are seven chocolates without peanuts out of a total of ten chocolates.
To find the probability of either event occurring, we add the probabilities together:
P(milk chocolate or no peanuts inside) = P(milk chocolate) + P(no peanuts inside) = (6/10) + (7/10) = 13/10.
Therefore, the probability of selecting a milk chocolate or a chocolate with no peanuts inside is 13/10.
The events are mutually exclusive since a chocolate cannot be both a milk chocolate and have no peanuts inside simultaneously.
--------------------------------------------------------------------------------------------------------------------------
The fourth question:
"You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows an even number?"
The probability of the coin landing heads up is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely.
The probability of rolling an even number on the die is 3
/6 or 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes.
To find the probability of both events occurring (coin lands heads up and die shows an even number), we multiply the probabilities together:
P(coin lands heads up and die shows an even number) = P(coin lands heads up) * P(die shows an even number) = (1/2) * (1/2) = 1/4.
Therefore, the probability of the coin landing heads up and the die showing an even number is 1/4.
The events are independent since the outcome of flipping the coin does not affect the outcome of rolling the die.
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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
If each collectible coin weighs 2.5 grams, how much do 3 collectible coins weigh all together?
A) 9.5 grams
B) 8.5 grams
7.5 grams
D 6.5 grams
Answer:
Hello! answer: 7.5 grams
Step-by-step explanation:
To find the answer we simply just do 2.5 × 3 so... 2.5 × 3 = 7.5 so 7.5 grams is the answer! Hope that helps!
PLEASE HELP ME ASAP I NEED IT
Answer: t = 12
Step-by-step explanation:
Answer:
t = 12
Step-by-step explanation:
8x12 is 96 = 1 is 97.
Also, they are across from each other meaning it's equal to 97.
Identify all the lines of symmetry of the following rectangle.
Explain, in your own words, how you found the lines
The triangle presented in the image has 2 axes of symmetry because it is only possible to divide it 2 times.
What are axes of symmetry?The axes of symmetry are a concept of geometry that are classified into two groups:
The plane axis of symmetry: This is an imaginary line that divides a figure into two parts, ensuring that the symmetrical points are at the same distance from it.The axis of axial symmetry: This is the symmetry around an axis, it is a point of translation and rotation in which all the semi-planes taken from a certain perpendicular bisector have identical characteristics.According to the above, it can be inferred that the rectangle presented in the image has only two axes of symmetry.
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Answer: the verified answer is wrong
Step-by-step explanation:
it's not a triangle is a rectangle but it still has 2 axes tho
The weight of an organ in adult males has a bell shaped distribution with a mean of 325 grams and a standard deviation of 50 grams. (A) about 99.7% of organs will be between what weights? (B) what percentage of organs weighs between 275 grams and 375? (C) what percentage of organs weighs between 275 grams and 425 grams?
Answer:
A)
The number of weights of an organ in adult males = 374.85
B)
The percentage of organs weighs between 275 grams and 375
P(275≤x≤375) = 0.6826 = 68%
C)
The percentage of organs weighs between 275 grams and 425
P(275≤x≤375) = 0.8185 = 82%
Step-by-step explanation:
A)
Step(i):-
Given mean of the normal distribution = 325 grams
Given standard deviation of the normal distribution = 50 grams
Given Z- score = 99.7% = 0.997
\(Z = \frac{x-mean}{S.D} = \frac{x-325}{50}\)
\(0.997 = \frac{x-325}{50}\)
Cross multiplication , we get
\(0.997 X 50= x-325\)
x - 325 = 49.85
x = 325 + 49.85
x = 374.85
The number of weights of an organ in adult males = 374.85
Step(ii):-
B)
Let X₁ = 275 grams
\(Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{275-325}{50} = -1\)
Let X₂ = 375 grams
\(Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{375-325}{50} = 1\)
The probability of organs weighs between 275 grams and 375
P(275≤x≤375) = P(-1≤Z≤1)
= P(Z≤1)- P(Z≤-1)
= 0.5 + A(1) - ( 0.5 - A(-1))
= A(1) + A(-1)
= 2 A(1)
= 2 × 0.3413
= 0.6826
The percentage of organs weighs between 275 grams and 375
P(275≤x≤375) = 0.6826 = 68%
C)
Let X₁ = 275 grams
\(Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{275-325}{50} = -1\)
Let X₂ = 425 grams
\(Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{425-325}{50} = 2\)
The probability of organs weighs between 275 grams and 425
P(275≤x≤425) = P(-1≤Z≤2)
= P(Z≤2)- P(Z≤-1)
= 0.5 + A(2) - ( 0.5 - A(-1))
= A(2) + A(-1)
= A(2) + A(1) (∵A(-1) =A(1)
= 0.4772 + 0.3413
= 0.8185
The percentage of organs weighs between 275 grams and 425
P(275≤x≤375) = 0.8185 = 82%
will give brainliest
The sum of the two rational equations is equal to (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²).
How to simplify the addition between two rational equations
In this question we must use algebra definitions and theorems to simplify the addition of two rational equations into a single rational equation. Now we proceed to show the procedure of solution in detail:
(n + 5) / (n² + 3 · n - 10) + 5 / (3 · n²) Given(n + 5) / [(n + 5) · (n - 2)] + 5 / (3 · n²) x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)1 / (n - 2) + 5 / (3 · n²) Associative and modulative property / Existence of the multiplicative inverse[3 · n² + 5 · (n - 2)] / [3 · n² · (n - 2)] Addition of fractions with different denominator(3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²) Distributive property / Power properties / ResultTo learn more on rational equations: https://brainly.com/question/20850120
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