Answer: 4
Step-by-step explanation:
[tex]1102_{3}=2+0(3)+1(9)+1(27)=38\\\\212_{n}=2+1(n)+2(n^2)=2n^2 + n+2\\\\\implies 2n^2 + n+2=38\\\\2n^2 + n-36=0\\\\(n-4)(2n+9)=0\\\\n=-\frac{9}{2}, 4[/tex]
However, as the base must be positive, n=4.
Consider a message signal m(t) with the spectrum shown in the following Figure. The message signal bandwidth W=1KHz, This signal is applied to a product modulator, together with a carrier Accos(2πfc t)wave producing the DSB-SC modulated wave S(t). This modulated wave is next applied to a coherent detector. Assuming perfect synchronism between the carrier waves in the modulator and detector, determine the spectrum of the detector output when: (a) The carrier frequency fc=1.25 KHz. And (b) The carrier frequency fc=0.75 KHz. What is the lowest carrier frequency for which each component of the modulated wave S(t) is uniquely determined by m(t)?
The lowest carrier frequency at which each modulated wave S(t) component may be uniquely defined by m(t) is
Fc,Fc+w,Fc-w =>1.5k,2.5k,0.5kHz
-Fc,-Fc+w,-Fc-w =>-1.5k,-0.5k,-2.5kHz
"-w,w -1kHz,1kHz" are the frequency components of the detector output in this case.
Fc,Fc+w,fc-w =>0.75k,1.75k,-0.25kHz
-Fc,-Fc+w,-Fc-w =>-0.75k,0.25k,-1.75kHz
This is further explained below.
What is the lowest carrier frequency for which each component of the modulated wave S(t) is uniquely determined by m(t)?For a modulated wave with frequency components, the equation looks like this:
Fc,Fc+w,Fc-w =>1.5k,2.5k,0.5kHz
-Fc,-Fc+w,-Fc-w =>-1.5k,-0.5k,-2.5kHz
"-w,w -1kHz,1kHz" are the frequency components of the detector output in this case.
b)
In conclusion, we may state that the modulated wave has frequency components as well.
Fc,Fc+w,fc-w =>0.75k,1.75k,-0.25kHz
-Fc,-Fc+w,-Fc-w =>-0.75k,0.25k,-1.75kHz
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Find the volume of the triangular prism. 10 cm 8 cm Volume = 12 cm [?] cm³
Answer:
Step-by-step explanation:
volume of the triangular prism height times base times length so 10 times 8 times 12 = 960.
What is the simple interest earned on $ 235 at 4.5 % for 2 years?
Answer:
$21.15
Step-by-step explanation:
(235)(.045)(2)
Suppose we want to choose letters, without replacement, from distinct letters.
(a) If the order of the choices is relevant, how many ways can this be done?
(b) If the order of the choices is not relevant, how many ways can this be done?
The number of ways when the choice is not relevant is 1716
How to determine the number of ways?The number of letters are:
Letter, n = 13
The letter to choose are:
r = 6
Relevant choice
When the choice is relevant, we have:
[tex]Ways = ^nP_r[/tex]
This gives
[tex]Ways = ^{13}P_6[/tex]
Evaluate
Ways = 241235520
Hence, the number of ways when the choice is relevant is 1235520
Not relevant choice
When the choice is not relevant, we have:
[tex]Ways = ^nC_r[/tex]
This gives
[tex]Ways = ^{13}C_6[/tex]
Evaluate
Ways = 1716
Hence, the number of ways when the choice is not relevant is 1716
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The graph shows a system of equations:
What is the solution to the system of equations?
y = -x + 5
y=x-1
(-3,2) (3,-2) (3,2) (-3,-2)
The solution to the system of equations is (3, 2)
System of equationGive the system of equation below
y = -x + 5
y=x-1
Equate both expression
-x+5 =x - 1
Equate
-x - x = -1 - 5
-2x = -6
x = 3
Since y = x - 1
y = 3 - 1
y = 2
Hence the solution to the system of equations is (3, 2)
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NEED FAST AND CORRECT!! Use the box plots comparing the number of males and number
of females attending the latest superhero movie each day for a
month to answer the questions.
Males
10
H
Females
20
30
Part A: Describe the shape of each plot
Part B: What is the best measure of center for Males? Females?
How do you know?
Part C: What is the best measure of spread for Males? Females?
How do you know?
Part D: Provide a possible reason for the outlier in the data set. Table
The description of the box plots are as follows:
The Interquartile Range is given as 23; and the difference between the median values is 14What is the calculation for the above?IQR = 25 - 2
= 23
The difference between the median values
= 20 - 6
= 14
What are the respective best measure of center for males? females?The mean would be a better measure of center for Females because the data has no outliers.The median would be a better measure of center for Males because the data has outliers.What is the reason for the outlier in the data set?That female admires those movie stars and has a large group of pals with whom she goes out on a regular basis to keep them company.
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Solve for X please hurry
Answer: 23.1
Step-by-step explanation:
[tex]\frac{x}{14}=\frac{33}{20}\\\\x=\frac{(33)(14)}{20}\\\\x=23.1[/tex]
Ramon is six years younger than 4 times his brothers age. Oh f his brother is 5 year old, how old is Ramon
Answer:
14
Step-by-step explanation:
The equation would be R = 5(4) - 6. Multiply 5 by 4 to get 20, then subtract 6 to get 14.
1 Austin has found that both(13,17) and (24,61) are solutions to a system of linear equations how are the two lines related? explain
Considering that the graphs have two intersection points, the two lines are equal.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In a graph, the solution of two linear equations is the intersection of the two lines. Hence, if there are two solutions, as is the case in this problem, the two lines are equal.
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(x-1)^2 + (y-2)^2 = 6.25
Answer: The center of the circle will be (1,2) and the radius will be 2.5
Step-by-step explanation: Basically since its (x-1) it would become x=1 so that's ur first value same thign with y but that would be ur second value. And since in your equation it is 6.25 that would be 2.5 because 6.25 is r^2 and you are looking for r.
A smart-phone is thrown upwards from the top of a 384-foot building with an initial velocity of 32 feet per
second. The height h of the smart-phone after t seconds is given by the quadratic equation
h 16t² + 32t + 384. When will the smart-phone hit the ground
Answer:
When t = 4
Step-by-step explanation:
The phone will hit the ground when h = 0.
[tex]16t^2 + 32t + 384 =0 \\ \\ t^2 + 2t + 24=0 \\ \\ (t+6)(t-4)=0 \\ \\ t=-6, 4[/tex]
However, as time cannot be negative, we know the answer is when t = 4.
Simplify the following
Answer:
[tex]6 + ( \frac{4}{3} + ( \frac{5}{6} - \frac{1}{3} ))[/tex]
[tex] = 6 + ( \frac{4}{3} + ( \frac{5 - 2}{6})) [/tex]
[tex] = 6 + ( \frac{4}{3} + \frac{3}{6})[/tex]
[tex] = 6 + ( \frac{8 + 3}{6})[/tex]
[tex] = 6 + \frac{11}{6} [/tex]
[tex] = \frac{6}{1 } + \frac{11}{6} [/tex]
[tex] = \frac{36 + 11}{6} [/tex]
[tex] = \frac{47}{6} [/tex]
[tex] = 7 \frac{5}{6} [/tex]
What is the equation of the line that passes through the point (5,4) and has a slope of 2
Hello,
[tex]y = ax + b[/tex]
We know the slope is 2 so :
[tex]y = 2x + b[/tex]
The equation of the line that passes through the point (5,4) so :
[tex]4 = 2 \times 5 + b[/tex]
[tex]4 = 10 + b[/tex]
[tex]b = 4 - 10[/tex]
[tex]b = - 6[/tex]
The equation of the line that passes through the point (5,4) and has a slope of 2 is :
[tex]y = 2x - 6[/tex]
y = 2x - 6
Step-by-step explanation:Most lines are written in slope-intercept form, but we can use slope-point form in situations like this.
Slope-Point Form
The formula for slope-point form is [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]. So, we can plug in the information we have, the point and slope.
y - 4 = 2(x - 5)This is an equation for the line given to us. However, this form can be simplified further.
Slope-Intercept Form
Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept. To find the most simplified form of the equation we need to use the properties of equality.
First, distribute the 2
y - 4 = 2x - 10Next, add 4 to both sides
y = 2x - 6Now, we have the equation for the line in slope-intercept form. Both of the equations technically meet the requirements for the question, but slope-intercept is more common to use.
Solve the following
8903=e
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{8,903 = e^{5x}}}[/tex]
[tex]\huge\textbf{Simplify:}[/tex]
[tex]\mathsf{8,903 = e^{5x}}}[/tex]
[tex]\mathsf{e^{5x} = 8,903}}[/tex]
[tex]\huge\textbf{Solve for the exponent:}[/tex]
[tex]\large\textsf{We get: }\downarrow\\\\\mathsf{2.718282^{5x}=8903}[/tex]
[tex]\huge\textbf{Take the logarithm from both sides:}[/tex]
[tex]\mathsf{log(2.718282^{5x}) = log(8,903x)}[/tex]
[tex]\large\textsf{We get:}\\\\\mathsf{5x \times log(2.718282)=log(8903)}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{5x = \dfrac{log(8903)}{log(2.718282)}}[/tex]
[tex]\large\textsf{We get: }\\\\\mathsf{5x = 9.094143}[/tex]
[tex]\huge\textbf{Divide 5 to both sides:}[/tex]
[tex]\mathsf{\dfrac{5x}{5} = \dfrac{9.094143}{5}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x= \dfrac{9.094143}{5}}[/tex]
[tex]\mathsf{x = 1.818829}[/tex]
[tex]\mathsf{x \approx 2}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x =}\frak{\ 1.818829}}\huge\checkmark[/tex]
[tex]\large\textbf{Or if you're estimating your answer}\downarrow[/tex]
[tex]\huge\boxed{\mathsf{x \approx }\frak{\ 2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
y − 6 =3/5(x + 5); (0, 8)
The equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40
Equation of a lineThe equation of a line in point-slope form is expressed as;
y - y0 = m(x -x0)
where
m is the slope
(x0, y0) is the point on the line
Given the following parameters
Point (0,8)
Slope from the equation = 3/5
Substitute
y - 8 = 3/5(x - 0)
5(y -8) =3x
5y - 40 = 3x
5y - 3x = 40
Hence the equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40
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In ΔABC, BC = 13, CA = 20 and AB = 19. Which statement about the angles of ΔABC must be true?
m∠B > m∠A > m∠C
m∠C > m∠B > m∠A
m∠A > m∠B > m∠C
m∠C > m∠A > m∠B
m∠B > m∠C > m∠A
m∠A > m∠C > m∠B
Answer:
m∠B > m∠C > m∠A
Step-by-step explanation:
The angle opposite the largest side in a triangle is the largest, and the angle opposite the shortest side is the smallest.
Let f(x) = 3x²+2, g(x) = 3x - 5. Find the following value or expression.
(fog)(x)
Answer:
(f∘g)(x) = 27x² -90x +77
Step-by-step explanation:
The composition of functions (f∘g)(x) is interpreted to mean f(g(x)). The value is found the way any function value is found. The argument is substituted for the variable in the function definition.
SubstitutionAfter substituting g(x) for the argument of f(x), the resulting expression can be simplified.
[tex](f\circ g)(x) =f(g(x))=f(3x-5)\\\\=3(3x-5)^2+2=3(9x^2-30x+25)+2\\\\\boxed{(f\circ g)(x)=27x^2-90x+77}[/tex]
You are buying shoes for an athletic store. They cost $32 per pair of shoes. The company decides Mark Up the shoes by 75%. What is the selling price for shoes in the athletic store?
A. $56.00
B. $40.00
C. $45.00
D. $24.00
E. $8.00
Answer:
A. $56
Step-by-step explanation:
The markup is added to the cost price to find the selling price.
MarkupThe markup is 75% of the cost price:
markup = 75% × $32 = $24
Selling priceThe selling price is the cost price plus the markup:
selling price = cost + markup
selling price = $32 +24 = $56
The selling price of shoes in the athletic store is $56 per pair.
The selling price for shoes in the athletic store with 75% mark up is [tex]\$56[/tex]
Selling price of the item is sum of Markup and cost price.
The cost of shoes is [tex]\$32[/tex]. The company decides Markup by [tex]75\%[/tex] of cost price.
Find Markup value.Markup = [tex]\frac{75}{100}\times 32[/tex]
Markup = [tex]\$24[/tex]
Find selling price.Selling price = Markup + Cost price
Selling price = [tex]24+32[/tex]
Selling price = [tex]\$56[/tex]
The selling price for the shoes in the athletic store is [tex]\$56[/tex].
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Find the vertex of the function h(x) = x2 – 4x – 21
Answer: (2, -25)
Step-by-step explanation:
The x coordinate of the vertex is [tex]x=-\frac{-4}{2(1)}=2[/tex].
When x=2, [tex]h(2)=2^2 - 4(2)-21=-25[/tex].
So, the vertex is (2, -25).
Describe an algorithm for finding the smallest integer in a finite sequence of natural numbers.
Answer:
min = a_1
for i:= 2 to n:
if [tex]a_i[/tex] < min then min = [tex]a_i[/tex]
return min
Step-by-step explanation:
We call the algorithm "minimum" and a list of natural numbers [tex]a_1, a_2, \cdot\cdot\cdot, a_n.[/tex]
So lets first set the minimum to [tex]a_1[/tex]
min = a_1
now we want to check all the other numbers.
We can use a simple for loop, to find the minimum
min = a_1
for i:= 2 to n:
if [tex]a_i[/tex] < min then min = [tex]a_i[/tex]
return min
Answer:
The sequence of natural numbers is a_1, a_2, a_3, ..., a_n.
Use min as the variable that will contain the minimum value.
Set min = a_1
In a loop, compare min to each number from a_2 to an.
If min > a_i, then let min = a_i
min = a_1
for i = 2 to n
if min > a_i, then min = a_i
Based on the length sir the segments in the hyperbola below, how long is the transverse axis?
Answer: The transverse axis of the hyperbola lies on the line y=–3 and has length 6; the conjugate axis lies on the line x=2 and has length 8.
Step-by-step explanation:
A college graduate expects to earn a salary of $55,000 during the first year after graduation and receive a 3% raise every year after that. What is the total income he will have received after ten years?
Answer:
$73915.40
Step-by-step explanation:
→ Find the multiplier
( 3 + 100 ) ÷ 100 = 1.03
→ Multiply by principal amount and raise it to the power of years
55000 × 1.03¹⁰ = 73915.40
Answer: $630,513.36
Step-by-step explanation:
Making a Formula for His Salary on a Given YearLet's make a table of values to see how much he earns every year after graduation.
1 year -> $55,000
2 years -> 55,000 * 103% = $56,650
3 years -> 56,650 * 103% = 55000 * 103% * 103% = $58,349.50
4 years -> 58349.50 * 103% = 55,000 * 103% * 103% * 103% = 55000(1.03)³
Here, we see that every year, he gets 103% of what he got the previous year, which is also 1.03 times his previous salary.
We also see that we multiply 55000 by 1.03 three times in the fourth year, and two times in the third year. This means that we multiply 55000 by 1.03 n-1 times.
Using this, let's generalize this for n.
n years -> [tex]55000(1.03)^{n-1}[/tex]
Finding the Sum after Ten YearsWe are trying to find his total income after ten years, or the sum of his salary from year 1 to year 10. We can represent this in sigma notation like this
[tex]% Adjusted limits of summation$\displaystyle\sum_{n=1} ^{10} 55000(1.03)^{n-1}$[/tex]
This essentially translates to the sum of the first ten terms in the sequence [tex]55000(1.03)^{n-1}[/tex], starting at n=1.
Since this is a geometric sequence, or a sequence where we need to multiply by the same number to get to the next term, we can find the sum using the sum of geometric series formula. This formula is as follows:
[tex]S_n=a_1\frac{1-r^n}{1-r}[/tex]
where [tex]S_n[/tex] is the sum of the first n terms, [tex]a_1[/tex] is the first term, r is the common ratio, and n is the number of terms. In this question, [tex]S_n[/tex] is the total income after n years, [tex]a_1[/tex] is his salary after the first year, r is how much his salary increases by each year, and n is the number of years we are calculating the sum for.
[tex]a_1[/tex] -> 55000
r -> 1.03
n -> 10
Now that we have the values for each variable, let's plug them in and solve
[tex]S_{10}=55000(\frac{1-1.03^{10}}{1-1.03})\\S_{10}=630513.36[/tex]
The total income he will have received after ten years is $630,513.36.
Six men, A, B, C, D, E, and F of negligible honesty, met on a perfectly rough day, each carrying a light inextensible umbrella. Each man brought his own umbrella and took away let us say 'borrowed' _ - another's. The umbrella borrowed by A belonged to borrower of B's umbrella. The owner of the umbrella borrowed by C borrowed the umbrella belonging to the borrower of D's umbrella. If the borrower of E's umbrella was not the owner of that borrowed by F, who borrowed A's umbrella?
Answer:
Six Serving Men is a team exercise that examines an issue from twelve different viewpoints. It is based on the words of the poem by Rudyard Kipling: I keep six honest serving men, they taught me all I knew. Their names are What and Why and When and How and Where and Who. To use this technique in a meeting, provide 12 areas for answering questions related to the central topic
Step-by-step explanation:
Consider the dot plot below. Of the following statements, which two characteristics of this dot plot make the median a better choice than the mean to summarize the center of the distribution?
A dot plot with an axis marked from 0 to 10 at increments of 1 is shown. Plot shows 8 dots at 10, 7 dots at 9, 6 dots at 8, 3 dots at 7, 2 dots at 0 and 6, and 1 dot at 5.
The mean is equal to the median and the data are symmetric.
The peak is equal to the median and the data are skewed.
The data are symmetric and there are outliers.
The data are skewed and there are outliers.
The two characteristics that makes the median a better choice are: A. The data are skewed and there are outliers.
What Characteristics of a Dot Plot Makes Median a Better Choice?In a data distribution, the median is a better choice to use to describe the data over the mean when an outlier exist and the data is skewed.
IN the dot plot given below, the data has an outlier of 10 while the data distribution is also screwed, this makes the median a better choice.
Therefore, the answer is: A. The data are skewed and there are outliers.
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How does doubling the lengths of the sides of a rectangle to form a similar rectangle affect the area
Doubling the lengths of the sides of a rectangle quadruple the area
How to determine the effect?Let the dimension of the rectangle be L and W.
So, the area is
A = LW
When the lengths are doubled, we have:
A2 = 2L * 2W
This gives
A2 = 4LW
This means that the initial area is multiplied by 4
Hence, doubling the lengths of the sides of a rectangle quadruple the area
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4. Kelly has a list of patient temperatures in Fahrenheit, but she needs them converted to Celsius. Help her convert the
temperatures using the formula(°F-32) x = °C. Note: temperatures are listed to the nearest tenth.
Method
Oral
Axillary
Rectal
Temperature °F
98.2 °F
96.6 °F
100.1 °F
Temperature C
°℃
°C
°℃
F
After conversion 98.2 °F=119.2°C
96.6 °F=116.3°C
100.1 °F==122.6°C
How can we convert temperature from Fahrenheit to Celsius?
We will convert using this formula
C= (F-32) *5/9
We will convert temperature from Fahrenheit to Celsius as shown below:
C= (F-32) *5/9
For Oral
Temperature=98.2°F
C= (98.2-32) *5/9
=119.16°C
Rounding to nearest tenth
=119.2°C
For Axillary
Temperature=96.6 °F
C= (96.6-32) *5/9
=116.28°C
Rounding to nearest tenth
=116.3°C
For Rectal
Temperature=100.1 °F
C= (100.1-32) *5/9
=122.58
Rounding to nearest tenth
=122.6°C
Hence, after conversion 98.2 °F=119.2°C
96.6 °F=116.3°C
100.1 °F=122.6°C
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Who knows the answer for this problem please solve asap
The value of x to the nearest hundredth is 4.14
Side-angle-side theoremThe given diagram is a right triangle with the following parameters
Opposite side to 16 degrees = x
Hypotenuse = 15
Using the expression below
sin theta = x/15
sin16 = x/15
x = 15sin16
x = 4.135
Hence the value of x to the nearest hundredth is 4.14
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what is the solutions to the system of equations below? y=3/4x-12 and y= -4x -31
The solution to the system of equations is: x = -4, y = -15.
How to Solve a System of Equations?Given the equations of a system as:
y = 3/4x - 12 --> eqn. 1
y = -4x - 31 --> eqn. 2
Substitute y = (-4x - 31) into eqn. 1 to find x:
-4x - 31 = 3/4x - 12
-4x - 3/4x = 31 - 12
-19/4x = 19
Multiply both sides by -4/19
x = 19(-4/19)
x = -4
Substitute x = -4 into eqn. 2
y = -4(-4) - 31
y = 16 - 31
y = -15
The solution is: x = -4, y = -15.
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Given f(x) =
4x + 2, find f(x + 3).
Answer:
f(x + 3) = 2(x + 7)
Step-by-step explanation:
Now lets find out what does f(x + 3) means.
f(x + 3) means shifting the entire function 3 units to the left. Which also means, all x values will be shifted to the left by that number of units. (Excluding the constant that is multiplied or divided by x, eg. 5x + 6 shifted by 7 units to the left is 5(x + 7) + 6 and not 5x + 7 + 6.)
From the above,
f(x + 3) = 4(x + 3) + 2 = 4x + 12 + 2 = 4x + 14 = 2(x + 7)
19
Select the correct answer.
Which exponential function has the greatest average rate of change over the interval [0, 2]?
OA j(x) = 3(1.6)²
OB. An exponential function, f, with a y-intercept of 1.5 and a common ratio of 2.
OC.
OD.
g(x)
k(x)
The function with the greatest average rate of change is the function k(x)
How to determine the function?The average rate of change is calculated as
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
The interval is [0,2].
So, we have
[tex]m = \frac{y_2 - y_1}{2 -0}[/tex]
[tex]m = \frac{y_2 - y_1}{2}[/tex]
For function j(x), we have
j(2) = 3 * 1.6^2 = 7.68
j(2) = 3 * 1.6^0 = 3
So, we have
[tex]m_j = \frac{7.68 - 3}{2}[/tex]
[tex]m_j = 2.34[/tex]
For function g(x), we have
g(2) = 25/2
g(0) = 8
So, we have
[tex]m_g = \frac{25/2 - 8}{2}[/tex]
[tex]m_g = 2.25[/tex]
For function k(x), we have
k(2) = 9
k(0) = 4
So, we have
[tex]m_k = \frac{9 - 4}{2}[/tex]
[tex]m_k = 2.5[/tex]
For function f(x), we have
f(2) = 1.5 * 2^2 = 6
f(0) = 1.5
So, we have
[tex]m_f = \frac{6 - 1.5}{2}[/tex]
[tex]m_f = 2.25[/tex]
The function with the greatest average rate of change is the function k(x) with a rate of 2.5
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