The modulated power is 15 kW.
The modulated power is given by the formula P_T= P_C (1+ (m_a^2)/2) and is connected to the total power of the carrier signal and the modulation index.
To obtain the modulated power, substitute the values in the given equation and simplify.
Given,
Power of carrier signal (P_C) = 12 kW
= 12000 W
Modulation index ( m_a) = 1/√2
Consequently, when we change the variables in the equation, we get
P_T= P_C (1+ (m_a^2)/2)
=12000 (1+ (1/√2)^2/2)
= 12000 (1+ 1/4)
= 12000 * 5/4
= 3000*5
= 15000 W
= 15 kW
Hence, modulated power is 15 kW.
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Read the following scenario and develop a method for answering the question posed. Be sure to define all variables used, justify your thinking mathematically, and fully answer the questions posed in complete sentences. Orbital Toys sells two types of sets of magnetic spheres, silver, and brass. The store owner, Lucy Ball, pays $8 and $16 for each one set of silver magnetic spheres and brass magnetic spheres respectively. One set of silver magnetic spheres yields a profit of $5 while a set of brass magnetic spheres yields a profit of $7. Ms. Ball estimates that no more than 2000 sets of magnetic spheres will be sold every month and she does not plan to invest more than $20,000 in the inventory of these sets. How many sets of each type of magnetic spheres should be stocked in order to maximize her total monthly profit? What is her maximum monthly profit?
8 dlls for silver
16 dlls for brass
5 dlls profit silver
7 dlls profit spheres
Then the price is
8+5= 13 dlls for silver
16+7=23 dlls for brass
Let S and B be the amount of magnetic silver and brass sphers that are sold, respectively.
Then, Ms. Ball estimation is that
[tex]S+B\leq2000[/tex]Also, she doesn't want to invest more than 20000, so
[tex]\begin{gathered} 8S+16B\leq20000 \\ S+2B\leq2500 \end{gathered}[/tex]The objective function is
[tex]V=5S+7B[/tex]Subjected to:
[tex]\begin{gathered} S+B\leq2000 \\ S+2B\leq2500 \\ S\ge0,\text{ B}\ge0 \end{gathered}[/tex]GRAPH
The interection is at
[tex]\begin{gathered} S=2000-B \\ S=2500-2B \\ 2000-B=2500-2B \\ B=500 \\ S=2000-500 \\ S=1500 \end{gathered}[/tex]So, the extremes must be at (0,1250), (1500,500), (2000,0) , (0,0).
So, if we replace the points
[tex]\begin{gathered} V(0,1250)=5(0)+7(1250)=8750 \\ V(1500,500)\text{ = 5(1500)+7(500)=}11000 \\ V(2000,0)=5(2000)+7(0)=10000 \end{gathered}[/tex]So, the amount she will need to stock to maximize her profit is 1500 of silver and 500 of brass, and the maximum profit is going to be 11000 dlls.
I need help with the problem!
a)The vertex of the function is (3, -1)
b)The line of symmetry is x= 3
c) The maximum is no maximum and minimum is (3, -1)
a) What is the vertex of the function of the parabola ?
[tex]f(x) = x^{2} -6x+8[/tex]
Transforming the function in the vertex form,
[tex]f(x) = a(x-h)^{2} +k[/tex]
[tex]f(x)=(x-3)^{2} -1[/tex]
The vertex of the function is given by,
(h, k) = (3, -1)
So ,the vertex of the function of the parabola is (3, -1)
b) What is the line of symmetry in the function?
In a parabola , the axis of symmetry is x = h.
Here, x = 3
So, the line of symmetry of the function of the parabola is x= 3
c) What is the maximum and minimum?
There is no maximum for the function because, the parabola opens upward. (Refer image for graph)The minimum for the function is the vertex (h, k) = (3, -1)What is a function of a parabola?
A parabola is the shape of a quadratic function's graph. Although the width or steepness of a parabola can vary as well as its direction of opening, they share the same fundamental U form. Regarding a line known as the axis of symmetry, all parabolas are symmetric. The vertex of a parabola is the location where the axis of symmetry of the curve crosses.To learn more about function of a parabola , refer:
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An inverted pyramid is being filled with water at a constant rate of 30 cubic centimeters per second . The pyramíd , at the top, has the shape of a square with sides of length 7cm and the height is 14 cm.
ANSWER :
The answer is 30 cm/sec
EXPLANATION :
We have an inverted square pyramid with a square side of 7 cm and a height is 14 cm.
We need to find the area of the square at 2 cm from below.
Using similar triangles, we will express the side view as 2D :
We need to find the side of the square at 2 cm level.
The ratio of the sides of the smaller triangle and bigger triangle must be the same :
[tex]\begin{gathered} \frac{\text{ smaller}}{\text{ bigger}}=\frac{x}{7}=\frac{2}{14} \\ \\ \text{ Solve for x :} \\ \text{ Cross multiply :} \\ 14x=7(2) \\ 14x=14 \\ x=\frac{14}{14}=1 \end{gathered}[/tex]So the value of x is 1, then the side of the square at 2 cm level is 1 cm
The area of that square is :
A = 1 x 1 = 1 cm^2
The inverted pyramid is filled with water at a constant rate of Q = 30 cm^3 per second.
And we are asked to find the rate when the water level is 2 cm or when the area of the square is 1 cm^2 from the result we calculated above.
Recall the formula of rate :
[tex]\begin{gathered} Q=AV \\ \text{ where :} \\ Q\text{ = constant rate in }\frac{cm^3}{sec} \\ \\ A\text{ = Area of the section in }cm^2 \\ \\ V\text{ = Velocity or rate in }\frac{cm}{sec} \end{gathered}[/tex]We have the following :
[tex]\begin{gathered} Q=30\text{ }\frac{cm^3}{sec} \\ \\ A=1\text{ }cm^2 \end{gathered}[/tex]Using the formula above, the rate is :
[tex]\begin{gathered} Q=AV \\ V=\frac{Q}{A} \\ \\ V=\frac{30\text{ }\frac{cm^{\cancel{3}}}{sec}}{1\text{ }\cancel{cm^2}} \\ \\ V=30\text{ }\frac{cm}{sec} \end{gathered}[/tex]how do I graph the line with the given slope m and y-intercept b.
m=5/3,b=-4
y=(5/3)x+4
I am aware that the slope is "big," m = - 5 /3, and that the yy-intercept is "left(0, 4), right" (0,4). The final graph of the line should be declining when viewed from left to right because the slope is negative.
y = mx+c
how to draw this graph?
step 1: Plot the given equation's yy-intercept, which is left(0,4right), first (0,4).
On the xy axis, the position (0,4) .
step2: Use the slope largem = -5 /3
m= 5/3
to locate a different point using the y-intercept b as a guide. The slope instructs us to move 3 units to the right after dropping down 5 units.
To find the opposite spot, start at (0,4) and go 5 units down and 3 units to the right.
Step 3: Make a line that goes through all of the points.
Create a line that joins the coordinates (0,4) and (3,5)
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i need help with this asap please check work when done
Given the parent function
[tex]y=\cos x[/tex]From the graph,
The range of the function is best modelled by the interval
Comparing the function with general equation of the cosine function,
[tex]B=1[/tex]The formula for the period is,
[tex]T=\frac{2\pi}{B}[/tex]There
Find the volume of a cone with a height of 8 m and a base diameter of 12 mUse the value 3.14 for it, and do not do any rounding.Be sure to include the correct unit in your answer.
The volume V of a cone with radius r and height h is:
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]And the radius is half the diameter. Since this cone has a diameter of 12 m, the radius is:
[tex]r=\frac{12m}{2}=6m[/tex]And the height is 8m. Thus, the volume V is:
[tex]\begin{gathered} V=\frac{1}{3}\pi(6m)^28m \\ \\ V=\frac{\pi}{3}(36m^2)8m \\ \\ V=\frac{\pi}{3}(288)(m^2\cdot m) \\ \\ V=\pi\cdot\frac{288}{3}m^3 \\ \\ V=96\pi m^{3} \end{gathered}[/tex]Now, using 3.14 for π, we obtain:
[tex]\begin{gathered} V=96\cdot3.14m^3 \\ \\ V=301.44m^{3} \end{gathered}[/tex]Therefore, the volume of that cone is 301.44m³.
Question 11 > Alvin can go upstream at a rate of 25 miles per hour and downstream at a rate of 35 miles per hour. One day while Alvin was on the river, he received a call telling him he needs to turn around and come home. So he turned around and went back to his starting point. If his entire trip took 12 hours, how far did he travel on the river? Alvin traveled miles. (Roundtrip) Question Help: Message instructor Submit Question
Given Data:
The upstream speed is, 25 miles/hr.
The downstream speed is, 35 miles/hr.
The total time is, 12 hr.
Let d be the distance traveled. He can travel 25 miles/ hr in upstream, so the time taken will be,
[tex]t=\frac{d}{25}[/tex]He can travel 35 miles/ hr in upstream, so the time taken will be,
[tex]t^{\prime}=\frac{d}{35}[/tex]Total time is, 12 hr. So we have,
[tex]\begin{gathered} 12=\frac{d}{25}+\frac{d}{35} \\ 12=\frac{d}{5\times5}+\frac{d}{7\times5} \\ 12=\frac{1}{5}(\frac{d}{7}+\frac{d}{5}) \\ 12\times5=\frac{d}{7}+\frac{d}{5} \\ 60\times35=5d+7d \\ 2100=12d \\ d=\frac{2100}{12}=175 \end{gathered}[/tex]Therefore the total distance is, 350 mile
Which vehicle has the smallest total volume?What is the volume?
The formula for the volume is,
[tex]V=\text{length}\cdot\text{ width}\cdot\text{ height}[/tex]Determine the volume of Van.
[tex]\begin{gathered} V=10\cdot6\frac{1}{2}\cdot6 \\ =60\cdot\frac{13}{2} \\ =390 \end{gathered}[/tex]Determine the volume of small truck.
[tex]\begin{gathered} V_1=11.3\cdot7.5\cdot6.75 \\ =572.0625 \end{gathered}[/tex]Determine the volume of 2-bedroom moving truck.
[tex]\begin{gathered} V=14\frac{1}{2}\cdot\frac{77}{12}\cdot7\frac{1}{6} \\ =\frac{29}{2}\cdot\frac{77}{12}\cdot\frac{43}{6} \\ =666.798 \end{gathered}[/tex]Determine the volume of 3 bedroom truck.
[tex]\begin{gathered} V=20.5\cdot7.7\cdot8.5 \\ =1341.725 \end{gathered}[/tex]Determine the mega moving truck.
[tex]\begin{gathered} V=22\frac{1}{4}\cdot7\cdot9\frac{1}{3} \\ =1453.666 \end{gathered}[/tex]The smallest volume is equal to
Use compatible numbers.4,921 ÷ 63
Given:
The objective is to divide the 4921÷ 63 using compatible numbers.
Explanation:
First, the compatible numbers are,
[tex]\begin{gathered} 4921=4920 \\ 63=60 \end{gathered}[/tex]To calculate division:
Now, the division can be performed as,
Hence, the value of the division is 82.
How much of the wall does the mirror cover? Use the π button in your calculations and round your answer to the nearest hundredths. Include units.
Since the diameter of the mirror is given, calculate the area of the mirror using the formula
[tex]A=\frac{1}{4}\pi\cdot(D)^2[/tex]replace with the information given
[tex]\begin{gathered} A=\frac{1}{4}\pi\cdot24^2 \\ A=144\pi\approx452.39in^2 \end{gathered}[/tex]The mirror covers 452.39 square inches.
Which graph represents the function over the interval [−3, 3]?f(x)=⌊x⌋−2
Given:
[tex]f(x)=x-2\text{ ,\lbrack-3,3\rbrack}[/tex]15÷6%=
A. 1004
B. 100
C. 24
D. 24
The perimeter of a rectangular room is 80 feet. Let x be the width of the room (in feet) and let y be the length of the room (in feet). Write the equation that could model this situation.
Answer:
2x+2y=80
Step-by-step explanation:
a rectangles perimeter has the formula of width+width+length+length
we can combine like terms so we get 2x+2y and according to the problem this rectangle has the perimeter of 80
octavius wants to write the equation of a line perpendicular to y=-4x + 5 that passes through the point (8,-3). Describe the mistake octavius made and write the correct equation of the line.
The equation of line perpendicular to 4y = x-8 passing through (4,-1) is:
[tex]y = \frac{1}{4} x-5[/tex].
What is a equation of line?These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.
Given equation of line is:
y=-4x + 5
Let [tex]m_{1}[/tex] be the slope of given line
Then,
[tex]m_{1}[/tex] = -4
Let [tex]m_{2}[/tex] be the slope of line perpendicular to given line
As we know that product of slopes of two perpendicular lines is -1.
[tex]m_{1}*m_{2} = -1\\- 4*m_{2}=-1\\ m_{2} = \frac{1}{4}[/tex]
The slope intercept form of line is given by
[tex]y = m_{2}x+c[/tex]
[tex]y = \frac{1}{4} x+c[/tex]
to find the value of c, putting (4,-1) in equation
[tex]-3= \frac{1}{4} *8+c\\-3-2 = c\\c = -5[/tex]
Putting the value of c in the equation
[tex]y=\frac{1}{4} x-5[/tex]
Hence, The equation of line perpendicular to 4y = x-8 passing through (4,-1) is [tex]y=\frac{1}{4} x-5[/tex].
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Drag the correct algebraic representation of the reflection to the white box
Question 1
When any point (x,y) is reflected over the x-axis, the reflection coordinate is (x,-y).
So, the x coordinate remains the same, and the y coordinate goes negative.
A = ( -6, 6 ) → A' = (-6,-6 )
B = (-2,6 ) → B' = (-2,-6)
C= (-6,1 ) → C' = (-6,- 1)
Algebraic representation: ( x, -y )
Express 80 as the product of its prime factors Write the prime factors in ascending order.
Answer:
2×2×2×2×5
Step-by-step explanation:
Express 80 as the product of its prime factors Write the prime factors in ascending order.
2 × 2 × 2 × 2 × 5
2×2×2×2×5 = 80
solve for x in the parallelogram below
justify proposes each step
the answer is associative property of multiplicaction
because
A*(B*C)=(A*B)*C
Nancy is the proud owner of a new car. She paid $1,500 upfront and took out a loan for the rest of the amount. The interest rate on the loan is 5%. If the total cost of buying the car (including the interest Nancy owes) is more than $16,213.02, how much money did Nancy borrow?.1st Question: Assume that x represents the amount of money Nancy borrowed. Write an expression that represents the amount borrowed (the principal) plus the interest owed on that amount.
1st Question:
Assume that x represents the amount of money Nancy borrowed. The interest rate on the loan is 5%. This means that the amount of interest that on the loan would be
5/100 * x = 0.05x
An expression that represents the amount borrowed (the principal) plus the interest owed on that amount is
x + 0.05x
= 1.05x
Secondly
She paid $1,500 upfront and took out a loan of $x for the rest of the amount. If the total cost of buying the car (including the interest Nancy owes) is more than $16,213.02, it means that
1500 + 1.05x > 16,213.02
Subtracting 1500 from both sides of the equation, we have
1500 - 1500 + 1.05x > 16213.02 - 1500
1.05x > 14713.02
Dividing both sides of the inequality by 1.05, we have
1.05x/1.05 = 14713.02/1.05
x > 14012.4
The amount borrowed is greater than $14012.4
1. Canada has the longest coastline of any country. It is 202,080 km. China has 22,147 km of borders - more than any other countries. What is the difference between the two lengths? Label your answer!!
Canada has a coastline if 202,080km and China has 22,147 of borders, so the difference between them can be writen like this:
[tex]202080-22147[/tex]And we can made this operation so the answer is:
[tex]202080-22147=179,933[/tex]This means that the coastline of canada is 179,933 longer than the border of china
Select the correct location on the image. Click the digit in the hundred millions place. 7,7 7 8,7 6 8,2 4.9 Reset Next
In this case you need to click the 7 which is in the hundred millions place
Log^5(1/25)=-2 in exponential form
We'll use the follwowing property, which comes from the definition of a logarithm:
[tex]\log _ab=c\Leftrightarrow a^c=b[/tex]i.e, The logarithm with base a of b is c if, and only if a to the c power equals b.
Using this to translate
[tex]\log _5(\frac{1}{25})=-2[/tex]Into exponential form, will yield:
[tex]5^{-2}[/tex]Because:
[tex]5^{-2}=\frac{1}{25}[/tex]ANSWER:
[tex]5^{-2}[/tex]A chemist has 30% and 60% solutions of acid available. How many liters of each solution should be mixed to obtain 570 liters of 31% acid solution? Work area number of liters | acid strength | Amount of acid 30% acid solution 60% acid solution 31% acid solution liters of 30% acid liters of 60% acid
Let the amount of 30% acid solution be a
Let the amount of 60% acid solution be b
Given, "a" and "b" mixed together gives 570 liters of 31% acid. We can write:
[tex]0.3a+0.6b=0.31(570)[/tex]Also, we know 30% acid and 60% acid amounts to 570 liters, thus:
[tex]a+b=570[/tex]The first equation becomes:
[tex]0.3a+0.6b=176.7[/tex]We can solve the second equation for a:
[tex]\begin{gathered} a+b=570 \\ a=570-b \end{gathered}[/tex]Putting this into the first equation, we can solve for b. The steps are shown below:
[tex]\begin{gathered} 0.3a+0.6b=176.7 \\ 0.3(570-b)+0.6b=176.7 \\ 171-0.3b+0.6b=176.7 \\ 0.3b=176.7-171 \\ 0.3b=5.7 \\ b=\frac{5.7}{0.3} \\ b=19 \end{gathered}[/tex]So, a will be:
a = 570 - b
a = 570 - 19
a = 551
Thus,
551 Liters of 30% acid solution and 19 Liters of 60% acid solution need to be mixed.
On a 7 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?Give your answer as a fraction
Solution
- This is a Binomial probability question. The formula for Binomial probability is:
[tex]\begin{gathered} P(r)=\sum\text{ }^nC_rp^rq^{n-r} \\ where, \\ n=The\text{ total number of trials} \\ r=\text{ The number of successful trials\lparen where answer is correct\rparen} \\ p=\text{ The probability of success \lparen The probability of getting a question } \\ right) \end{gathered}[/tex]- We have been given:
[tex]\begin{gathered} n=7 \\ \text{ since there can only be two answers, it means that the} \\ \text{ probability of getting a question correct is:} \\ p=\frac{1}{2} \\ q=1-p=\frac{1}{2} \\ \\ \text{ The probability of getting at least 1 question wrong means the } \\ probability\text{ of getting 1, 2, 3, 4, 5, 6, or 7 question wrong.} \\ \\ \text{ Instead of calculating all these probabilities, we can simply say} \\ P(1)+P(2)+P(3)+P(4)+P(5)+P(6)+P(7)=1-P(0) \end{gathered}[/tex]- Thus, we have:
[tex]\begin{gathered} P(0)=^7C_0(\frac{1}{2})^0(\frac{1}{2})^7 \\ P(0)=\frac{1}{128} \\ \\ 1-P(0)=1-\frac{1}{128}=\frac{127}{128} \end{gathered}[/tex]Final Answer
The answer is
[tex]\frac{127}{128}[/tex]the table below shows changes in the population densities of the zebra and you knew I'd muscles from 1991 to 2015, in six-year intervals.1. based on the data shown in the table calculate the percent change in the population density of zebra mussels from 1997 to 2003
The table below shows changes in the population densities of the zebra and you knew I'd muscles from 1991 to 2015, in six-year intervals.
1. Based on the data shown in the table calculate the percent change in the population density of zebra mussels from 1997 to 2003
_____________________
1997 (3 250)
2003 (2 500)
Percentage change= 100 *(new value- old value)/old value
Percentage change = 100 *(2500- 3250)/ 3250 = 100* (-0.2308)
Percentage change = -23.08%
__________________________________
Answer
The percent change in the population density of zebra mussels from 1997 to 2003 is -23.08%
There was a decrease of 23. 08%
find the value of x so that the function has the given value
j(x) = -4/3x + 7; j (x) = -5
Answer:
x = 13 [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
j(x) = [tex]\frac{-4}{3}[/tex] x + 7 Substitute -5 for x
j(-5) = [tex]\frac{-4}{3 }[/tex] ( -5) + 7
or
j(-5) =[tex](\frac{-4}{3})[/tex] [tex](\frac{-5}{1})[/tex] + 7 A negative times a negative is a positive
j(-5) = [tex]\frac{20}{3}[/tex] + 7
j(-5) = [tex]\frac{20}{3}[/tex] + [tex]\frac{21}{3}[/tex] [tex]\frac{21}{3}[/tex] means the same thing as 7
j(-5) = [tex]\frac{41}{3}[/tex] = 13 [tex]\frac{2}{3}[/tex]
Instructions: Find the circumference of the circle and round to the nearest tenth.
The circumference of the circle formula is
[tex]C=2\pi r[/tex][tex]r\rightarrow radius[/tex][tex]\begin{gathered} diameter=7.8yd \\ r=\frac{diameter}{2}=\frac{7.8}{2}=3.9yd \\ \end{gathered}[/tex][tex]\begin{gathered} C=2\pi r \\ C=2\times\pi\times3.9 \\ C=24.5yd \end{gathered}[/tex]Hence, the circumference of the circle is 24,5yd
In a certain chemical, the ratio of zinc to copper is 4 to 11. A jar of the chemical contains 528 grams of copper. How many grams of zinc does it contain.
If the ratio of zinc to copper is 4 to 11. A jar of the chemical contains 528 grams of copper. Then 192 grams of zinc does it contain
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that,
In a certain chemical, the ratio of zinc to copper is 4 to 11.
i.e 4:11 or 4 /11
If A jar of the chemical contains 528 grams of copper
We need to find how many grams of zinc does it contain.
Let us consider it as x.
Form a equation,
4/11=x/528
4×528=11x
2112=11x
Divide both sides by 11
192=x
Hence 192 grams of zinc does it contain.
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which is the BEST first step in order to solve this equation15 + 2/3 a = -5a.subtract 15 from both sides b.subtract 2/3 feom both sides c.add 5 to both sides d.multiply by 3 on both sides
In order to solve this equation, we need to isolate the variable a in one side of the equation.
Since we have the number 15 in the same side of the variable, the best first step would be removing this number 15 from this side, and we do this by subtracting 15 from both sides.
Therefore the answer is a.
I was getting helprd earlier but the last part didn't show up nor did the text messages. heres the question."Frieda Friendly works for a local car dealership. She noticed 3/4 of the cars are sedans and that half are white. What fraction of the dealership's car are white sedans?" *the picture is just the last question*
3/4 of the cars are sedans
Half are white ( 1/2)
Multiply the fraction of cars that are sedans (3/4) by the fraction that are white (1/2)
[tex]\frac{3}{4}\times\frac{1}{2}=\frac{3}{8}[/tex]Just divide the fraction to obtain the decimal:
3/8 = 0.375
Multiply by 100 to obtain the percent:
0.375 x 100 = 37.5%
