The adult male foot length of 30.8 cm is significantly low.
What is Range Rule of Thumb?According to the Range Rule of Thumb, the range is approximately four times the standard deviation. In statistics, another measure of spread is the standard deviation. It explains how your data is grouped around the mean.
According to the range rule, the standard deviation of a sample is approximately equal to one-fourth of the data range. To put it another way, s = (Maximum - Minimum)/4. This is a simple formula to use, but it should only be used as a rough estimate of the standard deviation.
The value will then be:
= (30.8 - 27.27) / 4.
= 3.53 / 4
= 0.8825
The number is less than the standard deviation of 1.46.
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find the measurement indicated in each trapezoid
Answer:
∠ R = 115°
Step-by-step explanation:
• each lower base angle is supplementary to the upper base angle on the same side, that is
∠ R + ∠ S = 180°
∠ R + 65° = 180° ( subtract 65° from both sides )
∠ R = 115°
The total monthly charges, $C, for a mobile plan consist of a fixed amount of $ 120 and a variable amount which depends on the usage. For every minute used, $0.20 is charged. If the duration of usage is 120 minutes, calculate the total monthly charges for the mobile plan
The total monthly charges for the mobile plan if the usage is 120 minutes is $480.
Given that,
A mobile plan's total monthly costs, $C, are made up of a fixed fee of $ 20 and a variable fee that is based on usage. The cost is $0.20 per minute used.
We have to calculate the total monthly charges for the mobile plan if the usage is 120 minutes.
We know that,
A mobile plan fee is $20
For 1 min $0.20 for mobile plan
For 120 minutes
=120×0.2
=24
=24×20
=480
Therefore, the total monthly charges for the mobile plan if the usage is 120 minutes is $480.
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A rectangular yard measuring 35 ft by 55 ft is bordered (and surrounded) by a fence. Inside, a walk that is 3 ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.
The area of walk is 504 square feet
Area of rectangleThe area of rectangle is define as a product of length L and width w
calculate the area of rectangle yard
Area = L x W,
where A equal the Area, L equals the length and W equal width.
A = 35 x 55
A= 1925 square feet
Area of the rectangular yard is 1925 square feet
From the question, we have 3ft wide goes all the way along the fence inside.
Therefore, we subtract six feet from each of the value of length ( 35) and width (55) because each side has 3feet .
Area = L x W
A = 29 x 49
A = 1421 square feet
Area of new rectangle formed by allowing for three foot walk is 1421 square feet
Area of Walk
To get the area walk; we subtract area of new rectangular formed from area of rectangular yard
Area of Walk = Area of Rectangular yard - Area of new rectangle
Area of Walk = 1925 - 1421
Area of Walk = 504 square feet.
Therefore, the area of walk is 504 square feet.
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Need help pls on maths question
Answer please anyone help same doubht
Step-by-step explanation:
Answer:
Refer to the photos taken.
Step-by-step explanation:
A small toy rocket is launched from a 18-foot pad. The height (h, in feet) of the rocket t seconds after
taking off is given by the formula h = - 3t^2 + 3t+18. How long will it take the rocket to hit the
ground?
The time it would take the rocket to hit the ground upon launch is; 3 seconds.
At what time does the rocket hit the ground?It follows from the task content that the time taken for the rocket in discuss to hit the ground upon launch is to be determined.
Since the given formula for the height in terms of time, t is;
h = - 3t² + 3t + 18
It follows that ; when the rocket hits the ground; the height; h = 0.
Therefore;
0 = - 3t² + 3t + 18
0 = -3t² + 9t - 6t + 18
0 = -3t ( t - 3 ) - 6 ( t - 3)
-3t - 6 = 0 OR. t - 3 = 0.
t = -2. OR. t = 3.
Therefore, since the time after launch can only be positive; the time taken for the rocket to hit the ground is; 3 seconds.
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We couldn't find any school results for There were X quarts of liquid in a
con-tainer. First, 3/4 of the liquid in the container was removed. Then
another 1/2 quart was poured into the container. Write an expression in
terms of X for the number of quarts of liquid in the container at the end.
Then write another equivalent expres-sion. Explain.
Initial liquid volume is x.
3/4 of the liquid was removed:
[tex]x - \cfrac{3}{4} x[/tex]Then 1/2 quarts added, the expression including the addition is:
[tex]x - \cfrac{3}{4} x + \cfrac{1}{2}[/tex]Simplify to get equivalent expression:
[tex]\cfrac{1}{4} x + \cfrac{1}{2}[/tex]Question 1: Multiply: 12.10²
A 120
B 12000
c 1200
D 1.2
Am pula mare!
Da aaaaaaaaaaa????
Which of the following statements are true for triangle A B C ? Select all that apply.
Triangle DEF is congruent to triangle GHI is correct.
What is triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. A triangle having vertices A, B, and C is known as triangle ABC. Any three points in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.
A triangle is a polygon with three edges and three vertices. A triangle's total number of angles equals 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
The sum of two sides of a triangle is greater then the third side. Mathematically -
a + b > c
There are different types of triangles such as -
Equilateral, scalene, isosceles, and other triangles are used.
Given are three triangles ΔABC, ΔDEF, ΔIHG.
ΔDEF is congruent to ΔGHI as -
EF = IH (given)
∠E = ∠H (right angle)
FD = IG (given)
Using SAS congruent rule, ΔDEF ≅ ΔGHI
Therefore, triangle DEF is congruent to triangle GHI is correct.
The complete question is : Which of the following statements are correct?
Select all that apply.
Triangle ABC is congruent to triangle DEF.
Triangle DEF is congruent to triangle GHI.
All three triangles are congruent.
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You recently joined a gym. You had to pay a joining fee of $40, and you will pay $20 per month to maintain the membership. Part A (6 points) Write an equation in slope-intercept form that represents the cost of the membership in relation to time.
The cost of the membership is the initial joining fee plus the cost per month multiplied by the number of months.
If the cost after [tex]m[/tex] months is [tex]c[/tex] dollars, then [tex]c=20m+40[/tex].
Dolphins and other sea creatures can leap to great heights by swimming straight up and exiting the water at a high speed. A 230kg dolphin leaps straight up to a height of 6.4 m When the dolphin reenters the water, drag from the water brings it to a stop in 1.5 m
The motion of the dolphin, evaluated using the kinematic equations and Newton's second law of motion are;
The time it takes the dolphin to stop is about 0.268 secondsThe force of the water on the dolphin is about 9626.88 NWhat is the Newton's second law of motion?Mathematically, Newton's second law of motion states that force is the product of mass and acceleration.
The mass of the dolphin = 230 kg
Height to which the dolphin leaps = 6.4 m
The distance the drag brings the dolphin to a stop = 6.4 meters
First part;
The time it takes the dolphin to stop can be found from the equation;
At the water surface;
m·g·h = 0.5·m·v² (conservation of energy)
g·h = 0.5·v²
v² = 2·g·h
Therefore;
v² = 2 × 9.81 × 6.4 = 125.568
In the water, the initial velocity is v, the velocity at 1.5 meters depth is u, we get;
u² = v² - 2·a·s
Therefore;
v² = 2·a·s
a = v²/(2·s)
a = 125.568/(2 × 1.5) = 41.856
a = 41.856 m/s²
v = u - a·t
t = (u - v)/a
Therefore;
t = (√(125.568))/41.856 ≈ 0.268
The time it takes the dolphin to stop is about 0.268 seconds
Second part
Newton's second law of motion states that force is directly proportional to the rate of change of momentum produced
Mathematically
Force = Mass × Acceleration
Force on the dolphin, F = 230 kg × 41.856 m/s²= 9626.88 N
The possible parts of the question, obtained from a similar question are;
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What are the steps in solving rational expressions?
The steps in solving two rational numbers is using the cross multiplication method and then do the arithmetic operation on the numerator
The rational expression is defined as the expression with both numerator and denominator has polynomials.
Consider two rational expressions
Add two expression using cross multiplication
a/b + c/d
Cross multiply the expression
a/b + c/d = (ad + cb) / bd
Subtract two expression using cross multiplication
a/b - c/d
Cross multiply the expression
a/b + c/d = (ad - cb) / bd
Therefore, the two rational expression can be solved by using the cross multiplication method and do the arithmetic operation
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list all of the mutipes of 5 less than or equal to 50
Answer: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Step-by-step explanation: Add 5 until you get to 50.
Find the amount Erica owes at the end of 6 years if $ 5300 is loaned to her at a rate of 8 % compounded monthly. use A=P(1+r÷n)ⁿt
The amount owed is $
(Do not round until the final answer. Then round to the nearest cent as needed.)
The final amount compounded monthly at a rate of 8% over 6 years on a principal of $5300 is $8551.56
Compound InterestCompound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.
The formula of compound interest as given in the questions is
A = Final amount P = principalr = ratet = timen = number of times compoundedA = P[(1 + r/n)^nt
Substituting the values into the formula
A = 5300(1 + 0.08/6)^12 * 6
A = 8,551.56
Erica will owe $8551.56
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y.y^3.y^2 pleas help me and spread the gospel of God
Answer:
[tex]y^6[/tex]
Step-by-step explanation:
1) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].
[tex]y^{1+3+2[/tex]
2) Simplify 1 + 3 to 4.
[tex]y^{4+2}[/tex]
3) Simplify 4 + 2 to 6.
[tex]y^6[/tex]
Thank you,
Eddie
Tom's growth chart
categorical
discrete
continuous
Tom's growth chart is a continuous graph.
What is a continuous graph ?Continuous graphs are those in which every single value of x has a corresponding value of y, and the line of the graph is always uninterrupted.This is because every point is situated adjacent to the one on either side of it. The graph is continuous if the line is continuous, in other words. If a function's graph is a continuous curve with no breaks, holes, or gaps, then the function is considered continuous.One with dispersed points is a discrete graph and a direction or trend for it could be present or not. Categorical data is visualized using bar charts and pie charts. According to the visual, both sorts of graphs have variances.To learn more about continuous graph , refer:
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In ΔSTU, s = 250 inches, ∠U=17° and ∠S=52°. Find the length of t, to the nearest 10th of an inch.
The length of t will be;
⇒ t = 294.30 inches.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
In ΔSTU, s = 250 inches, ∠U=17° and ∠S=52°.
Now,
Since, In ΔSTU, s = 250 inches, ∠U=17° and ∠S=52°.
Hence, ∠ T = 180 - (17 + 52)
∠ T = 180 - 69
∠ T = 111°
Now, We use the sin rule as;
⇒ t / sint = s / sin s
⇒ t / sin 111° = 250 / sin 52
⇒ t = sin 111° × 250 / sin 52
⇒ t = 0.93 × 250 / 0.79
⇒ t = 294.30 inches.
Thus, The length of t will be;
⇒ t = 294.30 inches.
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Answer: 296.2
Step-by-step explanation:
t/sin111 = 250/sin52
t=250 sin111/52 = 296.1826 = 296.2
The table shows Tonya's homework assignment. Tonya's teacher instructed the class to simplify each expression by dividing the numerator and denominator by the GCF.
Complete the table by simplifying each expression and then finding the value.
Divide the numerator and denominator by the GCF to reduce a fraction. (This is also referred to as "writing a fraction in the simplest terms.") The common factors are sometimes shown to be "cancelled." It is worth noting that the result is an equivalent fraction in its simplest form.
How do you divide the numerator to the denominator by GCF?To put it simply, we must divide the numerator (x) by the denominator (y) to simplify it. For example, after simplifying 3 6, represent it as a fraction and identify the numerator and denominator. 3 6 can be written as 3/6. Further simplification yields 1/2.
Let's pretend the fraction is a proper fraction. The denominator is the numerator. We want to reduce the fraction to its simplest form.
a) Use Numerator =Remainder* as the denominator.
Now Numerator >Remainder* b)Numerator Remainder*=Remainder** c) ••• (keep going until Remainder =0)
d) When the Remainder equals zero, the Divisor is the GCD (or GCF, as you say). GCF is a misnomer because it only deals with numbers. Only the term GCF applies to variables (with numerical values, as in algebraic expression).
Let us look at an example.
407/3367 is the fraction.
As evident, the numbers407 ,3367 does not appear to have share Divisors 2 or 3 or 5 or 7 or 11 from prima facie considerations. So we may take recourse of successive division method.
3367 ÷407 =Remainder 111 (quotient 8)
407 ÷ 111 =Remainder 74 (quotient 3)
111 ÷74=Remainder 37 (quotient 1)
74 ÷37 =Remainder 0 (ZERO )
Here 37 divides leaving Remainder zero. Therefore the GCD is 37
Fraction 407 /3367 =(407 ÷37)/(3367÷37)=11/91
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The half-life of nitrogen-16 is approximately 7.13 seconds.
Step 3 of 3 : How much of a 3 gram sample of nitrogen-16 would remain after 4 seconds? Round to three decimal places.
Using half-life and disintegration constant, the sample that will remain 4 seconds 2.03g
RadioactivityThis is the spontaneous decay of an active radioactive sample. The decay curve is exponential and it slope is constantly changing.
The half-life of this sample given can be used to find the disintegration constant of the sample.
The formula of half - life is given as
T₁/₂ = ln2 / λ
T₁/₂ = Half-Life λ = disintegration constantSubstitute the values into the equation;
7.13 = 0.693 / λ
λ = 0.693 / 7.13
λ = 0.0972
The amount of sample left after 4 seconds will be
A = Ne⁻(λt)
A = 3e⁻(0.0972 * 4)
A = 2.03g
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In which quadrant is the number 5i located on the complex plane?
The number 5i located on the complex plane in I Quadrant.
What is Complex Plane?
The real axis and the imaginary axis are the graph's horizontal and vertical axes, which are orthogonal (or perpendicular). The labels Re and Im are typically present. The complex plane is the plane defined by these coordinates.
We are aware that in a two-dimensional plane, an ordered pair's x- and y-coordinates are treated as the real and imaginary parts of the complex number, respectively.
i.e., a+bi=(a,b) -- Quadrant I,
-a+bi=(-a,b) -- Quadrant II,
a-bi=(a,-b) -- Quadrant III
and
-a-bi=(-a,-b) -- Quadrant IV
The complex number that is being presented is 5i, aland it is located in quadrant I.
As a result, the complex number in question belongs in Quadrant I.
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Help Please!
3. An exercise equipment company is producing 45 lb. weights. To ensure the quality of their weights, they randomly select 60 weights and find that the mean weight of their sample is 45.07 lbs. with a standard deviation of 0.09 lbs. Create a 95% confidence interval and interpret the answer in context.
A. (45.0509, 45.0891); The exercise equipment company can be 95% confident the population mean of their 45 lb. weights lies between 45.0509 and 45.0891 lbs.
B. (44.8423, 45.2977); The exercise equipment company can be 95% confident the population mean of their 45 lb. weights lies between 44.8423 and 45.2977 lbs.
C. (44.9772, 45.0228); The exercise equipment company can be 95% confident the population mean of their 45 lb. weights lies between 44.9772 and 45.0228 lbs.
D. (45.0472, 45.0928); The exercise equipment company can be 95% confident the population mean of their 45 lb. weights lies between 45.0472 and 45.0928 lbs.
4. Raul is analyzing a set of data he collected and creating a confidence interval. If he chose to reduce the size of the sample and increase the level of confidence, how would that affect the confidence interval? Explain.
A. The size of the confidence interval would decrease because Raul would be dividing by a larger z-score and multiplying by a smaller sample size.
B. The size of the confidence interval would increase because Raul would be dividing by a smaller z-score and multiplying a larger sample size.
C. The size of the confidence interval would increase because Raul would be multiplying by a larger z-score and dividing by a smaller sample size.
D. The size of the confidence interval would decrease because Raul would be multiplying by a smaller z-score and dividing by a smaller sample size
The responses for the confidence intervals of the 45 lbs weight and the set of data are;
3. D. (45.0472, 45.0928); The exercise equipment company can be 95% confident the population mean of their 45 lb weights lies between 45.0472 and 45.0928
4. C. The size of the confidence interval would increase because Raul would be multiplying by a larger z-score and dividing by a smaller sample size.
What is a confidence interval?The confidence interval is the likelihood of a parameter of a population can be found within a range of values during a specified percentage or proportion of the time.
3. The confidence interval can be found using the formula;
[tex]CI = \overline x \pm z\cdot \dfrac{s}{\sqrt{n} }[/tex]
Where;
[tex]\overline x[/tex] = The mean of the sample = 45.07 lbs
s = The standard deviation of the sample = 0.09 lbs
n = The sample size
z = The confidence level = 1.96 at 95% confidence level
Therefore;
[tex]CI = 45.07 \pm 1.96\times \dfrac{0.09}{\sqrt{60} }[/tex]
45.0472 < μ < 45.0928
The correct option is therefore, option D
Therefore;
The company can be 95% sure that the mean of the population of the 45 lb weights are between 45.0472 and 45.0928 lbs4. Decreasing the sample size, n, will decrease the value by which the term on the right of the ± is being divided, increasing the confidence interval.
Increasing the level of confidence will increase z, thereby also increasing the confidence interval.
The correct option is therefore, option C.
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Cindy is attempting to calculate how much her car payment would be for a car that costs $27,000 to be repaid with monthly payments in 4 years at 4% APR.
Cindy's monthly payment of $609.63 will cost her $29,262.24 in 4 years at a 4% APR.
How is the total cost determined?The total cost that Cindy will spend on the car which costs $27,000 is computed by multiplying the monthly payment by 48 months (the payment period).
The monthly payment can be determined using an online finance calculator that compounds the interest rate monthly for four years.
Cost of car = $27,000
Annual Percentage Rate (APR) = 4%
Payment period = 4 years (monthly)
N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 4%
PV (Present Value) = $27,000
FV (Future Value) = $0
Results:
PMT = $609.63
Sum of all periodic payments = $29,262.24
Total Interest = $2,262.45
Thus, Cindy will spend $29,262.24 for a car that costs $27,000, if she repays monthly for 4 years.
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On Tuesday, the Soto Salad restaurant served 6 ½ cups of Italian salad dressing. If the restaurant serves ¼ cup of dressing with each salad, how many salads were ordered with Italian dressing?
Group of answer choices
26
22
24
28
Answer:
26
Answer choice 1.
Step-by-step explanation:
6 1/2 ÷ 1/4 is our equation.
6 1/2 as an improper fraction is 13/2
Our new equation is 13/2÷1/4
flip the divisor into a reciprocal and multiply:
13/2×4/1
simplify:
13/1×2/1
26/1
=26
PLEASE MARK BRAINLIESTAnswer: The answer is A or 26
Step-by-step explanation: I have my ways ;>
Please help will mark Brainly
Answer:
neither narrower or broader
Step-by-step explanation:
if you look at your problem it says identical so that means exactly the same so it would be the second choice neither narrower or broader
What is 4x + 2 < 5x?
Step-by-step explanation:
4x +2 <5x4x <5x-24x-5x<-2-x<-2x<2please I need help on question 5
The value of x is 19 and the measure of angles in triangle ABC are 75°, 75° and 30° respectively.
What is a triangle?triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.
If ABC is a triangle, then it is denoted as ∆ABC, where A, B and C are the vertices of the triangle. A triangle is a two-dimensional shape, in Euclidean geometry, which is seen as three non-collinear points in a unique plane.
The sum of ∠A + ∠B + ∠C = 180°( sum of angles in a triangle )
3x + 18 + 7x - 58 + 2x - 8 = 180°
12x -48° = 180°
12x = 228
x = 228/12
x = 19
but ∠A = 3x + 18, but x = 19
∠A = 3(19) + 18 which is 75°
Also ∠B = 7x -58
∠B = 7(19) - 58 which is 75°
∠C = 2x -8
∠C = 2(19) - 8 which is 30°
In conclusion, the value of x = 19, ∠A = 75°, ∠B = 75° ∠C = 30°
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Determine the solution to the system of equations
x - 6y + 4z = -12
x + y = 0
2x + 2y = 0
Answer:
x = 0 , y = 0 , z = -3
Step-by-step explanation:
Solve the following system:
{x - 6 y + 4 z = -12 | (equation 1)
x + y - 4 z = 12 | (equation 2)
2 x + 2 y + 5 z = -15 | (equation 3)
Swap equation 1 with equation 3:
{2 x + 2 y + 5 z = -15 | (equation 1)
x + y - 4 z = 12 | (equation 2)
x - 6 y + 4 z = -12 | (equation 3)
Subtract 1/2 × (equation 1) from equation 2:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - (13 z)/2 = 39/2 | (equation 2)
x - 6 y + 4 z = -12 | (equation 3)
Multiply equation 2 by 2/13:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - z = 3 | (equation 2)
x - 6 y + 4 z = -12 | (equation 3)
Subtract 1/2 × (equation 1) from equation 3:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - z = 3 | (equation 2)
0 x - 7 y + (3 z)/2 = -9/2 | (equation 3)
Multiply equation 3 by 2:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - z = 3 | (equation 2)
0 x - 14 y + 3 z = -9 | (equation 3)
Swap equation 2 with equation 3:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x - 14 y + 3 z = -9 | (equation 2)
0 x+0 y - z = 3 | (equation 3)
Multiply equation 3 by -1:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x - 14 y + 3 z = -9 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 3 × (equation 3) from equation 2:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x - 14 y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Divide equation 2 by -14:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 2 × (equation 2) from equation 1:
{2 x + 0 y+5 z = -15 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 5 × (equation 3) from equation 1:
{2 x+0 y+0 z = 0 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Divide equation 1 by 2:
{x+0 y+0 z = 0 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Collect results:
Answer: {x = 0 , y = 0 , z = -3
Step-by-step explanation:
How do you define a function?
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
This means that a function f will map an object x to exactly one object f(x) in the set of potential outputs if the object x is in the set of inputs (referred to as the domain) (called the codomain).
The metaphor of a function machine, which accepts an object as its input and produces another object as its output based on that input, makes the concept of a function simple to understand.
Given a collection of possible outputs Y (codomain) and a set of inputs X (domain), a function is more precisely defined as f: X→Y which shows that f is a function from X to Y using this notation.
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Tony bought a shirt for a friend's birthday for $27.00. He liked the shirt so much that he returned to the store a week later to buy a shirt for himself. Tony found the price of the shirt had changed to $32.13. Rounded to the nearest whole percent, what is the percent increase in the price of the shirt?
You have to divide 27 by 100 and that gives you .27.
If you multiply until you reach 32.13 with different numbers you get 19. It is a 19% increase.
How do you find equivalent in math?
To find equivalent expression in math is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
In mathematics, equivalent fractions are those with the same denominator and differing numerators.
The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.
It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.
This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.
For instance, if we simplify 5/15, we get a fraction that is equal to 1/3, which is equal to 5/15.
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Describe the function‘s end behavior. f(x)=−10+2x^5−9x^3
as x→∞,f(x)→
as x→−∞,f(x)→
The function‘s end behavior is falls to the left and rises to the right.
The given function is [tex]f(x)=-10+2x^5-9x^3[/tex].
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Use the degree and the leading coefficient to determine the behavior.
Falls to the left and rises to the right.
Find where the first derivative is equal to 0 to find the local maxima and minima.
x =−3√30/10 is a local maximum
x = 3√30/10 is a local minimum
Therefore, the function‘s end behavior is falls to the left and rises to the right.
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