[tex]x^2-3x+2=0\\x^2-x-2x+2=0\\x(x-1)-2(x-1)=0\\(x-2)(x-1)=0\\x=2 \vee x=1\\\\x^2=4 \vee x^2=1[/tex]
Answer:
Step-by-step explanation:
First we try to factor x²-3x+2.
We have to look for two numbers that multiply to 2 and add -3.
The two numbers are -1 and -2.
(x-1)(x-2) = 0
x-1 = 0 -> x = 1
x-2 = -> x = 2
Now we find x^2.
(1)^2 = 1
(2)^2 =4
Round 1, 165.492 to the nearest hundredth.
Answer:
1, 165.500
Step-by-step explanation:
1, 165.492 rounded to the nearest hundredth is 1, 165.500 because the hundredth space in the decimal is 5 or above, so the whole decimal gets rounded to the nearest hundred, which in this case, would be .500.
165.492 is the correct answer
For this year's fundraiser, students at a certain school who sell at least 75 magazine subscriptions win a prize. If the fourth grade students at this school sell an average (arithmetic mean) of 47 subscriptions per student, the sales are normally distributed, and have a standard deviation of 14, then approximately what percent of the fourth grade students receive a prize
Answer:
The percentage is k = 2.3%
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 47[/tex]
The standard deviation is [tex]\sigma = 14[/tex]
Given that the sales are normally distributed and that students at a certain school who sell at least 75 magazine subscriptions win a prize then the percent of the fourth grade students receive a prize is mathematically represented as
[tex]P(X > 75) = P(\frac{X - \mu }{\sigma } > \frac{75 - \mu }{\sigma })[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X > 75) = P(Z > \frac{75 - 47 }{14 })[/tex]
[tex]P(X > 75) = P(Z > 2)[/tex]
From the standardized normal distribution table
[tex]P(Z > 2) =0.023[/tex]
=> [tex]P(X > 75) = 0.023[/tex]
The percentage of the fourth grade students receive a prize is
k = 0.023 * 100
k = 2.3%
20,000 is 10 times as much as
Answer:
2000
Step-by-step explanation:
20,000 is 2000 times the number 10.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given numbers are 20000 and 10. The number 20000 is how many times the number 10 will be calculated by dividing the number 20000 by 10.
E = 20000 / 10 = 2000
Therefore, the number 20,000 is 2000 times the number 10.
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A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 80 indicated they like the taste. At 95% confidence, test to determine if at least 22% of the population will like the new soft drink.
Required:
Determine the p-value.
Answer: p-value of the test = 0.167
Step-by-step explanation:
Given that,
sample size n = 400
sample success X = 80
confidence = 95%
significance level = 1 - (95/100) = 0.05
This is the left tailed test .
The null and alternative hypothesis is
H₀ : p = 0.22
Hₐ : p < 0.22
P = x/n = 80/400 = 0.2
Standard deviation of proportion α = √{ (p ( 1 - p ) / n }
α = √ { ( 0.22 ( 1 - 0.22 ) / 400 }
α = √ { 0.1716 / 400 }
α = √0.000429
α = 0.0207
Test statistic
z = (p - p₀) / α
z = ( 0.2 - 0.22 ) / 0.0207
z = - 0.02 / 0.0207
z = - 0.9661
fail to reject null hypothesis.
P-value Approach
P-value = 0.167
As P-value >= 0.05, fail to reject null hypothesis.
Since test is left tailed so p-value of the test is 0.167. Since p-value is greater than 0.05 so we fail to reject the null hypothesis.
Hello there are two questions in the link's if both were solved that would be awesome.
Answer:
[tex]\frac{x^{\frac{5}{6}} }{x^{\frac{1}{6}} } = x^{(\frac{5}{6} -\frac{1}{6}) }= x^{\frac{4}{6} }\\\sqrt{x} . \sqrt[4]{x} = x^{\frac{1}{2} } . x^{\frac{1}{4} } = x^{(\frac{1}{2} +\frac{1}{4}) } = x^{\frac{3}{4}[/tex]
Perimeter =68 Length (L) is 4 less than twice the width (W)
Answer:
Length = 21.3333333333; Width: 12.6666666667
Step-by-step explanation:
Perimeter = 68
Perimeter of a rectangle:
2 (L +W)
Length (L) = 2W - 4
Width = W
2 ( 2W -4 +W) = 68
=> 2 (3W - 4) = 68
=> 6w -8 = 68
=> 6w = 76
=> w = 12.6666666667
Length = (12.6666666667 X 2) - 4
=> 21.3333333333
Write each expression in a simpler form that is equivalent to the given expression. Let g be a nonzero number. 1/g^1 or 1/g-1
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
Apply rule : [tex]a^1 =a[/tex]
[tex]\displaystyle \frac{1}{g^1 } =\frac{1}{g}[/tex]
[tex]\displaystyle \frac{1}{g^{-1}}[/tex]
Apply rule : [tex]\displaystyle a^{-b}=\frac{1}{a^b}[/tex]
[tex]\displaystyle \frac{1}{\frac{1}{g^1 } }[/tex]
Apply rule : [tex]\displaystyle \frac{1}{\frac{1}{a} } =a[/tex]
[tex]\displaystyle \frac{1}{\frac{1}{g^1 } }=g[/tex]
Answer:
[tex]\frac{1}{g^1}[/tex]
= [tex]\frac{1}{g}[/tex]
[tex]\frac{1}{g - 1}[/tex]
= [tex]\frac{g^1}{1}[/tex]
= [tex]\frac{g}{1}[/tex]
= g
Hope this helps!
An amusement park is open 7 days a week. The park has 8 ticket booths, and each booth has a ticket seller from 10am to 6pm. On average, ticket sellers work 30 hours per week. Write and equation that can be used to find "t", the minimum number of ticket sellers the park needs. show work if possible.
Answer:
t = (448 hrs/ week) / (30 hrs / week)
Step-by-step explanation:
Number of times park opens in a week = 7
Number of ticket booth = 8
Opening hours = 10am - 6pm = 8 hours per day
Max working hours per ticket seller per week = 30 hours
Therefore each booth works for 8 hours per day,
Then ( 8 * 7) = 56 hours per week.
All 8 booths work for (56 * 8) = 448 hours per week
If Max working hours per ticket seller per week = 30 hours,
Then muninim number of workers required (t) :
Total working hours of all booth / maximum number of working hours per worker per week
t = (448 hrs/ week) / (30 hrs / week)
How many ways can you arrange your 3 statistics books, 2 math books, and 1 computer science book on your bookshelf if (a) the books can be arranged in any order
Answer:
720 different ways.
Step-by-step explanation:
Permutation has to do with arrangement. For example, in order to arrange 'n' objects in any order, this can only be done in n! ways since there is no condition or restriction on how to arrange the objects.
n! = n(n-1)(n-2)... (n-r)!
If there are 3 statistics books, 2 math books, and 1 computer science book on your bookshelf, the total number of books altogether is 3 + 2 + 1 = 6 books.
The number of ways that 6 books can be arranged in any order is 6!.
6! = 6(6-1)(6-2)(6-3)(6-4)(6-5)
6! = 6*5*4*3*2*1
6! = 120*6
6!= 720 different ways.
Hence, the books on your shelf can be arranged in 720 different ways.
A bag contains five white balls and four black balls. Your goal is to draw two black balls. You draw two balls at random. Once you have drawn two balls, you put back any white balls, and redraw so that you again have two drawn balls. What is the probability that you now have two black balls? (Include the probability that you chose two black balls on the first draw.)
Answer:
Probabilty of both Black
= 1/6
Step-by-step explanation:
A bag contains five white balls and four black balls.
Total number of balls= 5+4
Total number of balls= 9
Probabilty of selecting a black ball first
= 4/9
Black ball remaining= 3
Total ball remaining= 8
Probabilty of selecting another black ball without replacement
= 3/8
Probabilty of both Black
=3/8 *4/9
Probabilty of both Black
= 12/72
Probabilty of both Black
= 1/6
A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with mean 100 lb and 5 lb and standard deviation 1 lb and 0.5 lb, respectively. What percent of filled boxes weighing between 104 lb and 106 lb are to be expected?
a. 67%
b. None
c. 37%
d. 57%
Answer:
Option b. None is the correct option.
The Answer is 63%
Step-by-step explanation:
To solve for this question, we would be using the z score formula
The formula for calculating a z-score is given as:
z = (x-μ)/σ,
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
We have boxes X and Y. So we will be combining both boxes
Mean of X = 100 lb
Mean of Y = 5 lb
Total mean = 100 + 5 = 105lb
Standard deviation for X = 1 lb
Standard deviation for Y = 0.5 lb
Remember Variance = Standard deviation ²
Variance for X = 1lb² = 1
Variance for Y = 0.5² = 0.25
Total variance = 1 + 0.25 = 1.25
Total standard deviation = √Total variance
= √1.25
Solving our question, we were asked to find the percent of filled boxes weighing between 104 lb and 106 lb are to be expected. Hence,
For 104lb
z = (x-μ)/σ,
z = 104 - 105 / √25
z = -0.89443
Using z score table ,
P( x = z)
P ( x = 104) = P( z = -0.89443) = 0.18555
For 1061b
z = (x-μ)/σ,
z = 106 - 105 / √25
z = 0.89443
Using z score table ,
P( x = z)
P ( x = 106) = P( z = 0.89443) = 0.81445
P(104 ≤ Z ≤ 106) = 0.81445 - 0.18555
= 0.6289
Converting to percentage, we have :
0.6289 × 100 = 62.89%
Approximately = 63 %
Therefore, the percent of filled boxes weighing between 104 lb and 106 lb that are to be expected is 63%
Since there is no 63% in the option, the correct answer is Option b. None.
The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be 63%.
What is a normal distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with a mean of 100 lb and 5 lb and standard deviation of 1 lb and 0.5 lb, respectively.
The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be
Then the Variance will be
[tex]Var = \sigma ^2[/tex]
Then for X, we have
[tex]Var (X) = 1^2 = 1[/tex]
Then for Y, we have
[tex]Var (Y) = 0.5^2 = 0.25[/tex]
Then the total variance will be
[tex]Total \ Var (X+Y) = 1 + 0.25 = 1.25[/tex]
The total standard deviation will be
[tex]\sigma _T = \sqrt{Var(X+Y)}\\\\\sigma _T = \sqrt{1.25}[/tex]
For 104 lb, then
[tex]z = \dfrac{104-105}{\sqrt{25}} = -0.89443\\\\P(x = 104) = 0.18555[/tex]
For 106 lb, then
[tex]z = \dfrac{106-105}{\sqrt{25}} = 0.89443\\\\P(x = 106) = 0.81445[/tex]
Then
[tex]P(104 \leq Z \leq 106) = 0.81445 - 0.18555 = 0.6289 \ or \ 62.89\%[/tex]
Approximately, 63%.
More about the normal distribution link is given below.
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In a recent survey of drinking laws, a random sample of 1000 women showed that 65% were in favor of increasing the legal drinking age. In a random sample of 1000 men, 60% favored increasing the legal drinking age. Test the claim that the percentage of men and women favoring a higher legal drinking age is different at (alpha 0.05).
Answer:
Step-by-step explanation:
Given that:
Let sample size of women be [tex]n_1[/tex] = 1000
Let the proportion of the women be [tex]p_1[/tex] = 0.65
Let the sample size of the men be [tex]n_2[/tex] = 1000
Let the proportion of the mem be [tex]p_2[/tex] = 0.60
The null and the alternative hypothesis can be computed as follows:
[tex]H_0: p_1 = p_2[/tex]
[tex]H_0a: p_1 \neq p_2[/tex]
Thus from the alternative hypothesis we can realize that this is a two tailed test.
However, the pooled sample proportion p = [tex]\dfrac{p_1n_1+p_2n_2 } {n_1 +n_2}[/tex]
p =[tex]\dfrac{0.65 * 1000+0.60*1000 } {1000 +1000}[/tex]
p = [tex]\dfrac{650+600 } {2000}[/tex]
p = 0.625
The standard error of the test can be computed as follows:
[tex]SE = \sqrt{p(1-p) ( \dfrac{1} {n_1}+ \dfrac{1}{n_2} )}[/tex]
[tex]SE = \sqrt{0.625(1-0.625) ( \dfrac{1} {1000}+ \dfrac{1}{1000} )}[/tex]
[tex]SE = \sqrt{0.625(0.375) ( 0.001+0.001 )}[/tex]
[tex]SE = \sqrt{0.234375 (0.002)}[/tex]
[tex]SE = \sqrt{4.6875 * 10^{-4}}[/tex]
[tex]SE = 0.02165[/tex]
The test statistics is :
[tex]z =\dfrac{p_1-p_2}{S.E}[/tex]
[tex]z =\dfrac{0.65-0.60}{0.02165}[/tex]
[tex]z =\dfrac{0.05}{0.02165}[/tex]
[tex]z =2.31[/tex]
At level of significance of 0.05 the critical value for the z test will be in the region between - 1.96 and 1.96
Rejection region: To reject the null hypothesis if z < -1.96 or z > 1.96
Conclusion: Since the value of z is greater than 1.96, it lies in the region region. Therefore we reject the null hypothesis and we conclude that the percentage of men and women favoring a higher legal drinking age is different.
Need Assistance
Please Show Work
Answer:
3 years
Step-by-step explanation:
Use the formula I = prt, where I is the interest money made, p is the starting amount of money, r is the interest rate as a decimal, and t is the time the money was borrowed.
Plug in the values and solve for t:
108 = (1200)(0.03)(t)
108 = 36t
3 = t
= 3 years
In an examination, 40% of the candidates failed. The number candidates who failed was 160. How many candidates passed the examination?
Answer:
240 candidates
Step-by-step explanation:
40% candidates failed, i. e. out of every 100 candidates 40 failed.
40 failed ----------------------------- 100 total students
1 failed --------------------------------100/40 total students, given 160 failed therefore
160 failed ----------------------------(100/40) x 160 total students
Total students = (100/40) x 160 = 400
Number of candidates passed = (total candidates) - (total candidates failed)
= 400 - 160 = 240 candidates
find the area of the figure pictured below. 3.8ft 8.3ft 7.4ft 3.9ft
The can be divided into two rectangles, one having length [tex]8.3[/tex] and width $3.8$
Another with, dimensions $7.4-3.8=3.6$ and $3.9$
Area of first rectangle=$3.8\times8.3=31.54$
Area of second rectangle =$3.6\times3.9=14.04$
Total area $=31.54+14.04=45.58$ ft²
Answer:
45.58 ft^2
Step-by-step explanation:
We can split the figure into two pieces
We have a tall rectangle that is 3.8 by 8.3
A = 3.8 * 8.3 =31.54 ft^2
We also have a small rectangle on the right
The dimensions are ( 7.4 - 3.8) by 3.9
A = 3.6*3.9 =14.04 ft^2
Add the areas together
31.54+14.04
45.58 ft^2
3. Simplify the following
a)[(116)3 x 114]x 1212
Answer:
48082464 is the answer
Step-by-step explanation:
=[(116)3×114] × 1212
=[348×114] × 1212
=39672 × 1212
=48082464 is the answer
hope it will help :)
Hey There!!
All you really need To do is: Divide [(116)] 3 x 114] x 1212) ( 20 + 51 + 43) ÷ 7
Hope It Helped!~ ♡
ItsNobody~ ☆
20 POINTS! You are planning to use a ceramic tile design in your new bathroom. The tiles are equilateral triangles. You decide to arrange the tiles in a hexagonal shape as shown. If the side of each tile measures 9 centimeters, what will be the exact area of each hexagonal shape?
Answer:
210.33 cm^2
Step-by-step explanation:
We know that 6 equilateral triangles makes one hexagon.
Also, an equilateral triangle has all its sides equal.
If the tile of each side of the triangular tile measure 9 cm, then the height of the triangular tiles can be gotten using Pythagoras's Theorem.
The triangle formed by each tile can be split along its height, into two right angle triangles with base (adjacent) 4.5 cm and slant side (hypotenuse) of 9 cm. The height (opposite) is calculated as,
From Pythagoras's theorem,
[tex]hyp^{2} = adj^{2} + opp^{2}[/tex]
substituting, we have
[tex]9^{2} = 4.5^{2} + opp^{2}[/tex]
81 = 20.25 + [tex]opp^{2}[/tex]
[tex]opp^{2}[/tex] = 81 - 20.25 = 60.75
opp = [tex]\sqrt{60.75}[/tex] = 7.79 cm this is the height of the right angle triangle, and also the height of the equilateral triangular tiles.
The area of a triangle = [tex]\frac{1}{2} bh[/tex]
where b is the base = 9 cm
h is the height = 7.79 cm
substituting, we have
area = [tex]\frac{1}{2}[/tex] x 9 x 7.79 = 35.055 cm^2
Area of the hexagon that will be formed = 6 x area of the triangular tiles
==> 6 x 35.055 cm^2 = 210.33 cm^2
Select the best answer for the question . 7. At a public swimming pool , the probability that an employee is a lifeguard is P(L) = 0.85 , and the probability that an employee is a teenager is P(T) = 0.58 . What's the probability that an employee is a lifeguard , given that the employee is a teenager ? O A. There isn't enough information given. O B. 1.47 OC. 0.68 O D.0.49
Answer:
D) 0.49
Step-by-step explanation:
0.85 * 0.58 = 0.49
The probability is:
D 0.49
Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0,0):
Answer:
It rotated 180 degrees
Step-by-step explanation:
If you use this image and paste in on to google docs you will be able to rotate the image. Use this tool so that your can identify the amount of degrees.
If the Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0,0) then the angle of rotation is option (c) 180 degrees
What is Quadrilateral?
In geometry a quadrilateral is a four-sided polygon, having four edges and four corners
What is Angle of rotation?The angle of rotation is a measurement of the amount, of namely angle, that a figure is rotated about a fixed point, often the center of a circle.
Given,
Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0,0)
Consider the coordinates of D and D'
D(2,3) and D'(-2,-3)
Connect D and D'
∠D0D' = 180 Degrees
Hence, If the Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about the origin, (0,0) then the angle of rotation is option (c) 180 degrees
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Find the slope of the line that passes through the points (1, -4) and (3,-1)
Hi there! :)
Answer:
[tex]\huge\boxed{m = \frac{3}{2}}[/tex]
Find the slope using the slope formula:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in the coordinates of each point:
[tex]m = \frac{-1 - (-4)}{3 - 1}[/tex]
Simplify:
[tex]m = \frac{3}{2}[/tex]
Therefore, the slope of the line is 3/2.
Answer:
3/2
Step-by-step explanation:
The slope is given by
m = (y2-y1)/(x2-x1)
= ( -1 - -4)/(3-1)
= ( -1+4)/(2)
= ( 3/2)
c. What is f (-5)?
When the function is f(x) =-3x+7
Answer:
f(-5) = 22
Step-by-step explanation:
f(x) =-3x+7
Let x = -5
f(-5) =-3*-5+7
= 15 +7
=22
The function fix) = (x - 4)(x - 2) is shown.
What is the range of the function?
8
all real numbers less than or equal to 3
all real numbers less than or equal to -1
all real numbers greater than or equal to 3
all real numbers greater than or equal to - 1
6
2
16
2
14
COL
40
8
G D
Answer:
The range of the function f(x)= (x-4)(x-2) is all real numbers greater than or equal to -1
Step-by-step explanation:
(a) Use appropriate algebra and Theorem to find the given inverse Laplace transform. (Write your answer as a function of t.)
L−1 {3s − 10/ s2 + 25}
(b) Use the Laplace transform to solve the given initial-value problem.
y' + 3y = e6t, y(0) = 2
(a) Expand the given expression as
[tex]\dfrac{3s-10}{s^2+25}=3\cdot\dfrac s{s^2+25}-2\cdot\dfrac5{s^2+25}[/tex]
You should recognize the Laplace transform of sine and cosine:
[tex]L[\cos(at)]=\dfrac s{s^2+a^2}[/tex]
[tex]L[\sin(at)]=\dfrac a{s^2+a^2}[/tex]
So we have
[tex]L^{-1}\left[\dfrac{3s-10}{s^2+25}\right]=3\cos(5t)-2\sin(5t)[/tex]
(b) Take the Laplace transform of both sides:
[tex]y'(t)+3y(t)=e^{6t}\implies (sY(s)-y(0))+3Y(s)=\dfrac1{s-6}[/tex]
Solve for [tex]Y(s)[/tex]:
[tex](s+3)Y(s)-2=\dfrac1{s-6}\implies Y(s)=\dfrac{2s-11}{(s-6)(s+3)}[/tex]
Decompose the right side into partial fractions:
[tex]\dfrac{2s-11}{(s-6)(s+3)}=\dfrac{\theta_1}{s-6}+\dfrac{\theta_2}{s+3}[/tex]
[tex]2s-11=\theta_1(s+3)+\theta_2(s-6)[/tex]
[tex]2s-11=(\theta_1+\theta_2)s+(3\theta_1-6\theta_2)[/tex]
[tex]\begin{cases}\theta_1+\theta_2=2\\3\theta_1-6\theta_2=-11\end{cases}\implies\theta_1=\dfrac19,\theta_2=\dfrac{17}9[/tex]
So we have
[tex]Y(s)=\dfrac19\cdot\dfrac1{s-6}+\dfrac{17}9\cdot\dfrac1{s+3}[/tex]
and taking the inverse transforms of both sides gives
[tex]y(t)=\dfrac19e^{6t}+\dfrac{17}9e^{-3t}[/tex]
Which expression is equivalent to 2(5)^4
Answer:
2·5·5·5·5
Step-by-step explanation:
2(5)^4 is equivalent to 2·5·5·5·5; 2 is used as a multiplicand just once, but 5 is used four times.
Simplify 3 x times the fraction 1 over x to the power of negative 4 times x to the power of negative 3.
Answer:
3x^2
Step-by-step explanation:
3 x times the fraction 1 over x to the power of negative 4 => 3x * 1/x^-4
= 3x *x^4 = 3x^5
times x to the power of negative 3 => x^-3
3x^5 * x^-3 = 3x^2
Answer:
3x^2
Step-by-step explanation:
i got it right on the test on god!
Point E lies within rectangle ABCD. If AE = 6, BE = 7, and CE = 8, what is the length of DE?
Answer:
[tex]\sqrt{51}[/tex] units.
Step-by-step explanation:
Point E is inside a rectangle ABCD.
Please refer to the attached image for the given statement and dimensions.
Given that:
Sides AE = 6 units
BE = 7 units and
CE = 8 units
To find:
DE = ?
Solution:
For a point E inside the rectangle the following property hold true:
[tex]AE^2+CE^2=BE^2+DE^2[/tex]
Putting the given values to find the value of DE:
[tex]6^2+8^2=7^2+DE^2\\\Rightarrow 26+64=49+DE^2\\\Rightarrow DE^2=100-49\\\Rightarrow DE^2=51\\\Rightarrow \bold{DE = \sqrt{51}\ units}[/tex]
How many months does it take for $700 to double at simple interest of 14%?
• It will take
number.
months to double $700, at simple interest of 14%.
The graph of F(x), shown below in pink, has the same shape as the graph of
G(x) = x3, shown in gray. Which of the following is the equation for F(x)?
Greetings from Brasil...
In this problem we have 2 translations: 4 units horizontal to the left and 3 units vertical to the bottom.
The translations are established as follows:
→ Horizontal
F(X + k) ⇒ k units to the left
F(X - k) ⇒ k units to the right
→ Vertical
F(X) + k ⇒ k units up
F(X) - k ⇒ k units down
In our problem, the function shifted 4 units horizontal to the left and 3 units vertical to the bottom.
F(X) = X³
4 units horizontal to the left: F(X + 4)
3 units vertical to the bottom: F(X + 4) - 3
So,
F(X) = X³
F(X + 4) - 3 = (X + 4)³ - 3The transformed function is f ( x ) = ( x + 4 )³ - 3 and the graph is plotted
What happens when a function is transformed?Every modification may be a part of a function's transformation.
Typically, they can be stretched (by multiplying outputs or inputs) or moved horizontally (by converting inputs) or vertically (by altering output).
If the horizontal axis is the input axis and the vertical is for outputs, if the initial function is y = f(x), then:
Vertical shift, often known as phase shift:
Y=f(x+c) with a left shift of c units (same output, but c units earlier)
Y=f(x-c) with a right shift of c units (same output, but c units late)
Vertical movement:
Y = f(x) + d units higher, up
Y = f(x) - d units lower, d
Stretching:
Stretching vertically by a factor of k: y = k f (x)
Stretching horizontally by a factor of k: y = f(x/k)
Given data ,
Let the function be represented as g ( x )
Now , the value of g ( x ) = x³
And , the transformed function has coordinates as A ( -4 , -3 )
So , when function is shifted 4 units to the left , we get
g' ( x ) = ( x + 4 )³
And , when the function is shifted vertically by 3 units down , we get
f ( x ) = ( x + 4 )³ - 3
Hence , the transformed function is f ( x ) = ( x + 4 )³ - 3
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Compute each matrix sum or product if it is defined. If an expression is undefined. Explain why. Let A = (3 4 0 -4 -1 4), B = (8 1 -4 -5 2 -4), C = (1 -1 3 1) and D = (3 -2 4 5).
- 2A, B - 2A, AC, CD
Compute the matrix product -2A.
A. -2A =
B. The expression-2A is undefined because A is not a square matrix.
C. The expression-2A is undefined because matrices cannot be multiplied by numbers.
D. The expression 2A is undefined because matrices cannot have negative coefficients.
Answer:
-2A = (-6, -8, 0, 8, 2, -8)
B - 2A = (2, -7, -4, 3, 4, -12)
AC is undefined.
CD = (3, 2, 12, 5)
Step-by-step explanation:
Given the matrices:
A = (3 4 0 -4 -1 4)
B = (8 1 -4 -5 2 -4)
C = (1 -1 3 1)
D = (3 -2 4 5)
We are required to compute the following
-2A, B - 2A, AC, CD
For -2A:
-2(3 4 0 -4 -1 4)
= (-6, -8, 0, 8, 2, -8)
For B - 2A:
Because B - 2A = B + (-2A), we have:
(8 1 -4 -5 2 -4) + (-6, -8, 0, 8, 2, -8)
(2, -7, -4, 3, 4, -12)
For AC:
(3 4 0 -4 -1 4)(1 -1 3 1)
This is undefined.
For CD:
(1 -1 3 1)(3 -2 4 5)
= (3, 2, 12, 5)
Find the 50th term in the sequence 16, 7, -2, …
This is an arithmetic sequence because the difference
between the terms in the sequence remain constant.
In other words, we subtract 9 from one term to get the next.
So we start off with the explicit formula, shown below in yellow.
"n" will be the number of terms in the sequence,
a1 will be the first term in the sequence,
and d will be the common difference.
Now substitute these in like I have below.
You will get -425 as an answer.
