The estimated error in the calculated area is approximately 3.2ft²
How did we estimate the error?To estimate the error in the calculated area of a square, use linear approximation or differentials.
The area of a square is given by the formula A = s², where s represents the length of a side.
Calculate the area of the square using the given side length of 16 ft:
A = (16 ft)²
A = 256 ft²
Now, let's consider the possible error in the side length, which is ±0.1 ft. Treat this error as a change in the side length (Δs) and use linear approximation or differentials to estimate the corresponding change in the area (ΔA).
Using linear approximation, express the change in the area as:
ΔA ≈ 2s Δs
Substituting the values:
ΔA ≈ 2(16 ft)(0.1 ft)
ΔA ≈ 3.2 ft²
Therefore, the estimated error in the calculated area is approximately 3.2ft².
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$274 for 40 hours of work as a unit rate
Answer:
6.85 units per hourStep-by-step explanation:
$274 for 40 hours of work as a unit rate
in practice you look for the hourly wage, you find it by dividing the wages divided by the working hours
274 : 40 = 6.85 units per hour
Solve for x.
A) 6
B) 4
C) 5
D) 7
Answer:
c
Step-by-step explanation:
Aight, let's hop to it:
So we got
[tex] \frac{5x}{45} = \frac{20}{36} = = > \\ \frac{x}{9} = \frac{5}{9} = = > \\ x = 5[/tex]
and boom
Question about a rational expression
The equation is -9=6/v
In the explanation, it tells me to multiply v on both sides. My question is why do you multiply v on both sides and not 6?
When I did the problem I multiplied 6 on both sides and got -54=v, but apparently the answer is -2/3 so I’m confused as to why you multiply v on both sides and not 6.
Preeta’s book has 300 pages. Each day she reads 10 more pages than the day before. She finishes her book in 6 days. How many pages does she read?
Step-by-step explanation:
1. if the number of pages in the 1st day is 'x', then the 2d day - 'x+10', the 3d day - 'x+20', the 4th day - 'x+30', the 5th day - 'x+40' and the last day - 'x+50' pages;
2. if the sum of all the pages is 300, then it is possible to make up the equation:
x+x+10+x+20+x+30+x+40+x+50=300;
3. x=25, it means:
1st day - 25;
2d day - 35;
3d day - 45;
4th day - 55;
5th day - 65;
6th day - 75 pages.
What is the length of BC?
Answer:
75/4
Step-by-step explanation:
Assuming BA and ED are parallel, we know thay the two triangles are similar.
So,
[tex]\frac{25-x}{x}=\frac{36}{12} \\ \\ \frac{25-x}{x}=3 \\ \\ 25-x=3x \\ \\ 4x=25 \\ \\ x=\frac{25}{4} \\ \\ BD=25-\frac{25}{4}=\frac{75}{4}[/tex]
Solve the following systems of inequalities and select the correct graph: 2x − y > 4 x + y < −1 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.
The solution to the system of inequalities is given as Graph II.
A group of two or more inequalities in one or more variables is referred to as a system of inequalities.
When a problem demands a variety of solutions and those solutions must satisfy many constraints, systems of inequalities are utilized.
What is the calculation leading to the above solution?The system of inequality,
2x - y < 4
x + y < -1
First we draw the graph of both line. So make table of each line
For line 2x - y < 4
x : -1 0 1
y : -6 -4 -2
Test point (0,0)
0 - 0 < 4
0 < 4
True (Shade towards origin)
For line x + y < -1
x : -1 0 1
y : 0 -1 -2
Test point (0,0)
0 + 0 < -1
0 < -1
False (Shade away from origin)
Plot the points graph.
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Full Question:
The graphs associated with the question are attached.
If two numbers are selected at random ,one after the other with replacement from the set A=(5,6,7,8,9) find the probability of selecting at least one prime number
Answer:
16/25
Step-by-step explanation:
(at least 1 prime selected)=1−(no primes selected)
There are 3 numbers in the set that are not prime (6,8,9)
(no primes selected)=(35)2=925
(at least 1 prime selected)=1−925
=1625
18. Find the value of 3x² x 2(x-3y) divide by 6 when x is 6 and y is 1
Answer:
11664
Step by Step:
Evaluate for x=6,y=1
3(6^2)(6^2)(6−(3)(1))
3(6^2)(6^2)(6−(3)(1))
=11664
Show the calculation to find the μ and σ of a binomial variable whose probability of success if 0.3 with a total number of attempts of 20.
Using the binomial distribution, we have that:
The mean is of [tex]\mu = 6[/tex].The standard deviation is of [tex]\sigma = 2.05[/tex].What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
[tex]\mu = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
For this problem, the parameters are:
n = 20, p = 0.3.
Hence:
[tex]\mu = np = 20 \times 0.3 = 6[/tex][tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20 \times 0.3 \times 0.7} = 2.05[/tex]More can be learned about the binomial distribution at https://brainly.com/question/24863377
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Please Evaluate C(6,3)
The value of the expression C(6,3) is 20
How to evaluate the expression?The expression is given as:
C(6, 3)
This means 6 combination 3.
And it can be written as:
[tex]^6C_3[/tex]
Apply the combination formula
[tex]^6C_3 = \frac{6!}{3!3!}[/tex]
Evaluate the expression
[tex]^6C_3 = 20[/tex]
Hence, the value of the expression C(6,3) is 20
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You are training to compete in a 10-kilometer race, and you know the circular running trail at your park is one mile long. How many times will you need to run this trail in order to run 10 kilometers?
So to run 10km, you need to run 6.25 times the trail. (Or 7 if you only accept whole numbers as answers, we need to round up).
How many times will you need to run this trail in order to run 10 kilometers?If you run the trail x times, then you will run:
y = x*1mi
Now remember that:
1 mi = 1.6 km
Replacing that, we get the linear equation:
y = x*1.6km
Now we want to find the value of x such that:
x*1.6km = 10km
Dividing both sides by 1.6km
x = 10km/1.6km = 6.25
So to run 10km, you need to run 6.25 times the trail. (Or 7 if you only accept whole numbers as answers, we need to round up).
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While traveling in Europe, you notice that the price of gas is $1.12 per liter. What is the price per gallon?
Select the statement that best describes √ 1 5
Marco has joined a bowling league, and is trying to raise his average to 130. On his last four games he scored 128, 127, 123, and 122. How much will he need to score on the next game to raise his mean to 130?
The score Macro needs in his next game to have a mean of 130 is 150.
What should be the next score?Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
130 = (128 + 127 + 123 + 122 + x) / 5
Where x represents the fifth score
130 = (500 + x) / 5
130 x 5 = 500 + x
650 = 500 + x
650 - 500 = x
x = 150
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F(x)=x^3*125 complex zeros
Answer: 0
Step-by-step explanation:
[tex]125x^3 =0\\\\x^3 =0\\\\x=0[/tex]
Find the angle between the vectors.
U=< -4,-3>
V = < -1,5>
Step-by-step explanation:
The formula for the angle between vectors
[tex] \alpha = \cos {}^{ - 1} ( \frac{uv}{ |u| |v| } ) [/tex]
To multiply vectors, multiply the first component and multiply the second component and add them.
(-4*-1) + (-3*5)= 4-15=-11.
To find magnitude of vectors, use the Pythagorean theorem
[tex]u = \sqrt{ { - 4}^{2} + { - 3}^{2} } = 5[/tex]
[tex]v = \sqrt{ - 1 {}^{2} + 5 {}^{2} } = \sqrt{26} [/tex]
so
[tex] |u| |v| = 5 \sqrt{26} [/tex]
Know we have,
[tex] \alpha = \cos {}^{ - 1} ( \frac{7}{5 \sqrt{26} } ) [/tex]
[tex] \alpha = 105.94[/tex]
in degrees,
[tex] \alpha = 1.849[/tex]
in radians
Answer:
115.6° (1 d.p.)
Step-by-step explanation:
To find the angle between two vectors:
Create a triangle with the vectors as two sides and the included angle θ between them.Find the magnitude of each vector (the length of each side of the triangle).Use the cosine rule to find the angle θ.**Please see attached for the triangle diagram**
Given vectors:
[tex]\textbf{u}=-4\textbf{i}-3\textbf{j}[/tex]
[tex]\textbf{v}=-\textbf{i}+5\textbf{j}[/tex]
Use Pythagoras Theorem to find the magnitude of each vector:
[tex]\implies |\textbf{u}|=\sqrt{(-4)^2+(-3)^2}=5[/tex]
[tex]\implies |\textbf{v}|=\sqrt{(-1)^2+5^2}=\sqrt{26}[/tex]
[tex]\overrightarrow{\text{UV}}=\textbf{v}-\textbf{u}=(-\textbf{i}+5\textbf{j})-(-4\textbf{i}-3\textbf{j})=3\textbf{i}+8\textbf{j}[/tex]
[tex]|\overrightarrow{\text{UV}}|=\sqrt{3^2+8^2}=\sqrt{73}[/tex]
Cosine Rule (for finding angles)
[tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
where:
C = anglea and b = sides adjacent the anglec = side opposite the angleFind angle θ using the cosine rule:
[tex]\implies \cos(\theta)=\dfrac{|\textbf{u}|^2+|\textbf{v}|^2-|\overrightarrow{\text{UV}}|^2}{2|\textbf{u}||\textbf{v}|}[/tex]
[tex]\implies \cos(\theta)=\dfrac{5^2+\left(\sqrt{26}\right)^2-\left(\sqrt{73}\right)^2}{2(5)\left(\sqrt{26}\right)}[/tex]
[tex]\implies \cos(\theta)=\dfrac{-22}{10\sqrt{26}}[/tex]
[tex]\implies \theta=\cos^{-1}\left(\dfrac{-22}{10\sqrt{26}}\right)[/tex]
[tex]\implies \theta=115.5599652...^{\circ}[/tex]
Therefore, the angle between the vectors is 115.6° (1 d.p.).
Melissa is driving at a constant speed. She catches up to a minivan half a mile ahead of her that is
moving at 50 miles per hour in 50 seconds. How many miles per hour is the speed of the sports
car?
The speed of the sports car is 53.6 miles per hour
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time
Distance covered by Melissa = 0.5 miles + Distance covered by minivan
Let speed of Melissa be x miles per second
x. 50 = 0.5 + 50x50/3600
x .50 = 0.5 + 25/36
x = 1/100 + 1/72
x = 0.001 + 0.013
x = 0.014 miles per second
x = 3600 x 0.014 = 53.6 miles per hour
Thus the speed of the sports car is 53.6 miles per hour
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Express the following function, F(x), as a composition of two functions, f and g:
Answer:
There are many different answers to this question but here is one that I thought of.
g(x)=x^2
f(x)=x/(x+4)
f(g(x))=F(x): plug in x^2 into each of the x in f(x) and and answer should equal F(x)
Step-by-step explanation:
since the function F(x) had 2 x^2 in it, I thought that g(x) could easily be x^2 that way u can subsitute the x in f(x) later to x^2 and get the right answer.
The measure of dispersion that measures how much the data differ from the mean is called the.
The measure of dispersion that measures how much the data differ from the mean is called the standard deviation.
What is standard deviation?Standard deviation is a statistical measure of dispersion as opposed to the measure of central tendency like mean, median and mode.
The standard deviation is a measure of how spread out data values are around the mean.
It is defined as the square root of the variance and represented with the Greek letter σ.
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Q.3. Set up the equations and solve them to find the unknown numbers in the cases given below:
1) If you add 6 to five times a number, it gives 46.
2) Two-third of a number minus 5 gives 11.
3) If you take onethird of a number and add 4 to it, gives 45.
4) When person X subtracts 12 from thrice of a number, it gives 18.
5) When Jenny subtracts twice the number of pens, she has from 40, she gets 16.
6) Virat guesses a number. If he adds 18 to that number and then divides the sum by 6, he gets answer 7.
7) Ami guesses anumber. If she subtracts 8 from two third of a number, she gets 6
I want Answer quickly
The following expressions set up as an equation to solve for the unknown numbers in the cases given below:
Algebraic equationlet
The unknown number = x5x + 6 = 46
5x = 46 - 6
5x = 40
x = 40/5
x = 8
2/3x - 5 = 11
2/3x = 11 + 5
2/3x = 16
x = 16 ÷ 2/3
x = 16 × 3/2
x = 48/2
x = 24
1/3x + 4 = 45
1/3x = 45 - 4
1/3x = 41
x = 41 ÷ 1/3
x = 41 × 3/1
x = 123
3x - 12 = 18
3x = 18 + 12
3x = 30
x = 30/3
x = 10
40 - 2x = 16
-2x = 16 - 40
-2x = -24
x = -24/-2
x = 12
(x + 18) / 6 = 7
(x + 18) = 7 × 6
x + 18 = 42
x = 42 - 18
x = 24
2/3x - 8 = 6
2/3x = 6 + 8
2/3x = 14
x = 14 ÷ 2/3
x = 14 × 3/2
= 42/2
x = 21
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Which inequality in standard form represents the
shaded region?
The figure is represented by the inequality y ≥ 5 · x² - 40 · x - 45. (Correct choice: C)
What inequality represents the figure
In accordance with the figure, we have an inequation of the form y ≥ f(x). Now we proceed to find the quadratic equation of the parabola:
f(x) = a · (x + 1) · (x - 9)
- 125 = a · (4 + 1) · (4 - 9)
- 125 = a · 5 · (- 5)
- 125 = - 25 · a
a = - 5
f(x) = 5 · (x + 1) · (x - 9)
f(x) = 5 · (x² - 8 · x - 9)
f(x) = 5 · x² - 40 · x - 45
The figure is represented by the inequality y ≥ 5 · x² - 40 · x - 45. (Correct choice: C)
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The function f(x) = 300(0.5)x/100 models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after Round to the nearest whole number.
The amount of the radioactive material in the vault after 140 years is 210 pounds
How to determine the amountWe have that the function is given as a model;
f(x) = 300(0.5)x/100
Where
x = number of years of the vault = 140 yearsf(x) is the amount in poundsLet's substitute the value of 'x' in the model
f(x) = 300(0.5)x/100
[tex]f(x) = \frac{300(0.5) * 140}{100}[/tex]
[tex]f(x) =\frac{21000}{100}[/tex]
f(140) = 210 pounds
This mean that the function of 149 years would give an amount of 210 pounds rounded up to the nearest whole number.
Thus, the amount of the radioactive material in the vault after 140 years is 210 pounds
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Hurry please help!!!!
Determine which statement is true about the zeros of the function graphed below.
An upward parabola f on a coordinate plane vertex at (1, 4) and intercepts the y-axis at 5 units.
A.
Function f has exactly two complex solutions.
B.
Function f has exactly one real solution and no complex solutions.
C.
Function f has exactly two real solutions.
D.
Function f has one real solution and one complex solution.
Answer:
A. Function f has exactly two complex solutions.
Step-by-step explanation:
The function will have real solutions where the graph crosses the x-axis. It will always have a total number of solutions equal to its degree. The ones that are not real are complex.
ApplicationThe graph has its vertex above the x-axis and extends upward from there. It never crosses the x-axis, so there are no real solutions. That means both solutions are complex.
what are the restricted values for??
Considering the domain of the function, it is restricted for:
B. [tex]x \neq -3, x \neq -2, x \neq 0[/tex].
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function.
A fraction cannot have a denominator of zero, hence:
[tex]4x^2 - 12x \neq 0[/tex].[tex]-x^2 + 5x - 6 \neq 0[/tex].We solve these two inequalities to find the restrictions, hence:
[tex]4x^2 - 12x \neq 0[/tex]
[tex]4x(x - 3) \neq 0[/tex]
[tex]4x \neq 0 \rightarrow x \neq 0[/tex]
[tex]x - 3 \neq 0 \rightarrow x \neq 3[/tex].
[tex]-x^2 + 5x - 6 \neq 0[/tex].
[tex]x^2 - 5x + 6 \neq 0[/tex]
[tex](x - 3)(x - 2) \neq 0[/tex]
[tex]x - 2 \neq 0 \rightarrow x \neq 2[/tex].
[tex]x - 3 \neq 0 \rightarrow x \neq 3[/tex].
Hence the correct option is:
B. [tex]x \neq -3, x \neq -2, x \neq 0[/tex].
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Which table shows a linear function?
The first table with the following values of x and y, shows a linear function.
x = -4, y = 8
x = -1, y = 2
x = 1, y = 2
x = 2, y = 4
x = 3, y = 6
Definition of a Linear Function:
A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
For the above chosen option, the value of y corresponding to a value of x is twice that of its x value. This linear function can be represented as follows,
y = | 2x | .......... (1)
In this linear function, mod represents, that y is always maintained positive. Besides, the value of y is always twice that of the x. Hence, the linear function can also be written as, y ± 2x = 0.
Since, equation (1) is of the form, y = mx + c, it produces a straight line. Here, m = 2 and c = 0. Thus, it is a linear function.
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if x+y=7/10 and x-y=5/14 then x^2-y^2=?
Add both
2x=1x=1/2=0.5Put in first one
y=0.7-0.5y=0.2Find
x²+y²(0.5)²+(0.2)²0.25+0.040.29Triangle ABC is translated 3 units to the left and downward 10 units to form triangle A'B'C', then dilated by a factor of 2 to form triangle A''B''C''. Which of the following statements is true for ΔABC and ΔA''B''C''?
Triangle A"B"C" are similar triangles to triangle ABC and all corresponding angles are congruent. Also, triangle A"B"C" is twice the size of triangle ABC.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Translation is the movement of a point either up, left, right or down in the coordinate plane.
Triangle ABC is translated 3 units to the left and downward 10 units to form triangle A'B'C', then dilated by a factor of 2 to form triangle A''B''C''.
Hence:
Triangle A"B"C" are similar triangles to triangle ABC and all corresponding angles are congruent. Also, triangle A"B"C" is twice the size of triangle ABC.
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Does this table represent a function? Why or why not
Answer:
No
Step-by-step explanation:
This table does not represent a function. The domain(x) can have only one range(y) in order for a set of data to represent a function. However, the domain value 2 has the range of both 1 and 4. Therefore, the table does not represent a function.
Has a base of 3, is reflected over the y-axis, has a horizontal shift right by 5 and an asymptote of y=-3
The equation of the exponential function is [tex]y = 3^{-x -5} - 3[/tex]
How to determine the equation?An exponential equation is represented as:
y = b^x
Where b represents the base.
The base is 3.
So, we have:
[tex]y = 3^x[/tex]
When reflected over the y-axis, we have:
[tex]y = 3^{-x[/tex]
When shifted right by 5 units, we have:
[tex]y = 3^{-x -5[/tex]
Lastly, the function has an asymptote of y=-3
So, we have:
[tex]y = 3^{-x -5} - 3[/tex]
Hence, the equation of the exponential function is [tex]y = 3^{-x -5} - 3[/tex]
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Tornadoes Use the frequency distribution from Exercise 12 in Section on page 49 to construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how?
The distribution is skewed because it's on the right side of the polygon and this illustrates that's it's positively skewed.
How to illustrate the information?It should be noted that the polygon can be gotten by plotting the data.
After the analysis of the distribution, the distribution is skewed to the right.
This illustrates that it is skewed.
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