1) To find out we need to calculate the dot product of those two vectors
[tex]\begin{gathered} m\cdot n=\mleft\langle1,5\mright\rangle\cdot\mleft\langle3,15\mright\rangle=1\cdot3+5\cdot15=3+75=78 \\ \end{gathered}[/tex]Since these vectors have a dot product different than zero, then they are not Orthogonal.
2) Let's now check if they are perpendicular, calculating the norm of each one and the angle between them:
[tex]\begin{gathered} \mleft\|m\mright\|=\sqrt[]{1^2+5^2}=\sqrt[]{26} \\ \|n\|=\sqrt[]{3^2+15^2}=\sqrt[]{9+225}=\sqrt[]{234} \end{gathered}[/tex]And finally the angle theta between them:
[tex]\begin{gathered} \theta=\cos ^{-1}(\frac{u\cdot v}{\|m\|\cdot\|n\|}) \\ \theta=\cos ^{-1}(\frac{78}{\sqrt[]{26}\cdot\sqrt[]{234}}) \\ \theta=0 \end{gathered}[/tex]3) Since the angle is 0, these vectors are parallel since parallel vectors for 0º or 180º
solving the formula for the indicated variable-s = lw + wh + lh, for whow do i start this problem?
The first step we need to take in order to solve the formula for w is changing the side of all the terms that have a w in it to the left side.
[tex]\begin{gathered} s=lw+wh+lh \\ s-lw-wh=lh \end{gathered}[/tex]Then we change switch all the terms that don't have w from the left to the right.
[tex]-lw-wh=lh-s[/tex]Since we have two terms on the left with a "w" we can factor then using the common term:
[tex]w(-l-h)=lh-s[/tex]Now we divide both sides by (-l-h).
[tex]\begin{gathered} w=\frac{lh-s}{-l-h} \\ w=\frac{-lh+s}{l+h} \end{gathered}[/tex]Question 22 ptsYou pay $5 to play a game. To play the game you spin a spinner with 3 colors. If the spinnerlands on blue you earn $20. If the spinner lands on green, you get your $5 back. If the spinnerlands on red, you loose your money. The probabilities of the spinner landing on each color isgiven in the chart below.What is the expected value of this game, given to the nearest penny?Spinner ColorProbabilityBlue0.19Green0.14Red?
GIVEN:
You pay $5 to play a game. To play the game you spin a spinner with 3 colors.
If the spinner lands on blue you earn $20. If the spinner lands on green, you get your $5 back. If the spinner lands on red, you loose your money.
The probabilities of the spinner landing on each color is given in the chart below.
[tex]\begin{gathered} Color----------Probabilities \\ \\ Blue-----------0.19 \\ \\ Green-----------0.14 \\ \\ Red------------0.67 \end{gathered}[/tex]Required;
What is the expected value of this game, given to the nearest penny?
Step-by-step solution;
To solve the question, note that the probability distribution has a blank space. We have the probabilities of landing on a blue color and on a green color. The probability of an event is usually between 0 and 1.00. Therefore, for an experiment with 3 outcomes, the probabilities would all be equal to 1 (regardless of the value given to each outcome). Hence, we are able to calculate the probability of landing on a red color as;
[tex]\begin{gathered} Red=1-(0.19+0.14) \\ \\ Red=0.67 \end{gathered}[/tex]To solve for the expected value of this event, we now have to multiply each probability distribution by the reward attached to each outcome/probability.
For landing on a blue;
[tex]\begin{gathered} Expected\text{ }value=P(x)\times x \\ \\ Expected\text{ }value=0.19\times(\text{\$}20-\text{\$}5) \\ \\ Expected\text{ }value=0.19\times15 \\ \\ EV=2.85 \end{gathered}[/tex]For landing on a green;
[tex]\begin{gathered} EV=0.14\times(\text{\$5}-\text{\$5\rparen} \\ \\ EV=0.14\times0 \\ \\ EV=0 \end{gathered}[/tex]For landing red;
[tex]\begin{gathered} EV=0.67\times(\text{\$0}-\text{\$}5) \\ \\ EV=0.67\times(-5) \\ \\ EV=−3.35 \end{gathered}[/tex]Now we can calculate the expected earnings from playing this game.
We sum up the individual expected earnings as follows;
[tex]\begin{gathered} Expected\text{ }earnings=\Sigma[xP(x)] \\ \\ Expected\text{ }earnings=2.85+0+(-3.35) \\ \\ Expected\text{ }earnings=−0.5 \end{gathered}[/tex]We now have a negative value which means based on the conditions given, the expected earnings from playing this game is a loss of $0.50
ANSWER:
Expected value
[tex]Expecetd\text{ }value=\text{\$}-0.50[/tex]x = Round to the nearest hundredth or keep as a s
x=6.67
1) Examining that figure, we can state that we have two similar triangles with proportional sides and congruent angles.
2) So let's write a proportion so that we can find the measure of x
[tex]\begin{gathered} \frac{hipotenuse}{hipotenuse\text{ 2}}=\frac{\text{Leg}}{\text{leg 2}} \\ \frac{18}{10}=\frac{12}{x} \\ 18x=120 \\ x=\frac{120}{18} \\ x=\frac{20}{3}\text{ }\cong6.66667 \end{gathered}[/tex]3) Since the answer must be rounded to the nearest hundredth we have
the answer as x=6.67
Math Literacy measurements G11 only do 5 and 6 both question are similar
Question 5:
If we divide the total length of the trip by the rate of consumption of the vehicle, we're going to find the amount of liters needed for the trip.
[tex]\frac{250}{9.4}=26.5957447...[/tex]This is the amount of liters needed.
Question 6:
Just as we did in the previous question, first we need to find the amount of liters needed for the trip.
[tex]\frac{2500}{33}=75.7575758...[/tex]Then, using the cost per liter, we can find the total cost of the trip:
[tex]\frac{2500}{33}\times20.20=1530.30303...[/tex]The trip is going to cost R1530.30.
A shipping container will be used to transport several 40-kilogram crated across the country by rail. The greatest weight that can be loaded into the container is 24500 kg.other shipments waiting 11300 kilograms have already been loaded into the container. right and solved an inequality which can be used to determine x, the number of 40 kg crates that can be loaded into the shipping container.
The greatest load that fits in the container is 24500kg
There are already 11300Kg loaded
Let x indicate the number of 40Kg crates, then 40x symbolized the total weight of the crates loaded.
You can express the inequality as
[tex]11300+40x\leq24500[/tex]From this expression we can calculate the number of crates that can be loaded as follows:
[tex]\begin{gathered} 11300+40x\leq24500 \\ 40x\leq24500-11300 \\ 40x\leq=13200 \\ \frac{40x}{40}\leq\frac{13200}{40} \\ x\leq330 \end{gathered}[/tex]You can load up to 330 crates into the container.
f(x) = -4x – 7 find the equation for the inverse function
Answer:
[tex]f^{-1}(x)=-\frac{1}{4}(x+7)[/tex]
Step-by-step explanation:
[tex]f(x)=-4x-7 \implies x=-4f^{-1}(x)-7 \\ \\ x+7=-4f^{-1}(x) \\ \\ f^{-1}(x)=-\frac{1}{4}(x+7)[/tex]
Every month Pablo earns $40 for walking his neighbors dog after school how much does he earn from his job in one year?
We know that Pablo earns $40 every month.
Then, to calculate how much he makes in a year, we use the fact that a year has 12 months.
Then, we can write:
[tex]40\frac{\$}{\text{month}}\cdot12\text{ }\frac{months}{year}=480\frac{\$}{\text{year}}[/tex]Answer: he earns $480 per year.
A garden that is 10/3 of an acre is to be divided into 5 equal-size areas. What is the size of each area?
Answer:
2/3 of an acre
Explanation:
To find the size of each area, we divide the area of the garden by 5. This gives
[tex]\frac{10}{3}\div5[/tex]Now at this point we remind ourselves that if we are dividing a fraction by a number, then we can turn the division into multiplication by taking the reciprocal of the number.
The number we are dividing our fraction by in this case is 5. Now, the reciprocal of 5 is 1/5 and so we can write the above as
[tex]\frac{10}{3}\div5\Rightarrow\frac{10}{3}\times\frac{1}{5}[/tex]Multiplying the denominators together gives
[tex]\frac{10}{3}\times\frac{1}{5}=\frac{10}{3\times5}=\frac{10}{15}[/tex]Now dividing both the numerator and the denominator by 5 gives
[tex]\frac{10\div5}{15\div5}=\frac{2}{3}[/tex]Hence,
[tex]\frac{10}{3}\div5=\frac{2}{3}[/tex]Therefore, the size of each area is 2/3 of an acre.
Write 11/80 as decimal Round to four decimal places as needed
The fraction is given
[tex]\frac{11}{80}[/tex]ExplanationTo determine the decimal form .
[tex]\frac{11}{80}=0.1375[/tex]AnswerHence the answer in decimal form is 0.1375.
A dairy farmer wants to mix a 75% protein supplement and a standard 25% protein ration to make 1500 pounds of a high grade 45%protein ration. How manypounds of each should be use!
Okay, here we have this:
Protein Supplement=75%--------->x pounds
Standard Protein= 25% ---------->(1500-x) pounds
Mixture 45% ----------------> 1500
75%x+25%(1500-x)=45%*1500
75x+25(1500-x)=67500
75x+37500-25x=67500
50x=30000
x=30000/50
x=600 pounds Protein Supplement
900 pounds standar Protein
#13 how many seconds will it take for a ball dropped from a window 144 feet high to hit the ground below?
Question 13.
Given:
Height = 144 feet.
Let's determine how many seconds it will take for a ball dropped from a window of the given height to hit the ground.
Here, we have the equation:
[tex]y=-16x^2+144[/tex]Where:
y represents the height of the ball after x seconds.
Now, when the ball hits the ground, the height will be 0 ft.
Thus, to find the time at 0 ft, substitute 0 for y and solve for x:
[tex]\begin{gathered} 0=-16x^2+144 \\ \\ 16x^2=144 \end{gathered}[/tex]Divide both sides by 16:
[tex]\begin{gathered} \frac{16x^2}{16}=\frac{144}{16} \\ \\ x^2=9 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt{x^2}=\sqrt{9} \\ \\ x=3 \end{gathered}[/tex]Therefore, it will take the ball 3 seconds to hit the ground.
ANSWER:
• (a). y = -16t² + 144
• (b). 3 seconds
-15-3r=6r+3c Solve for r.
Answer:
[tex]r=\frac{-c-5}{3}[/tex]Explanation:
We want to solve for r in the equation below;
[tex]-15-3r=6r+3c[/tex]We need to move all terms of r to one side and divide both sides by the coefficient of r.
firstly subtract 6r from both sides;
[tex]\begin{gathered} -15-3r-6r=6r-6r+3c \\ -15-9r=3c \end{gathered}[/tex]then add 15 to both sides;
[tex]\begin{gathered} -15+15-9r=3c+15 \\ -9r=3(c+5) \end{gathered}[/tex]divide both sides by -9;
[tex]\begin{gathered} \frac{-9r}{-9}=\frac{3(c+5)}{-9} \\ r=\frac{-(c+5)}{3} \\ r=\frac{-c-5}{3} \end{gathered}[/tex]Therefore;
[tex]r=\frac{-c-5}{3}[/tex]Does the coordinate (-2,5) land on the linear equation y = 2x + 9 ?yesnomaybe
Answer:
Yes
Explanation:
The coordinate (-2,5) corresponds to the point (x, y).
This means that:
x= -2 and y=5
To check if the coordinate land on the equation y=2x+9, calculate the value of y when x= -2
[tex]\begin{gathered} \text{When x=-2} \\ y=2(-2)+9 \\ =-4+9 \\ =5 \end{gathered}[/tex]Therefore, the coordinate (-2,5) land on the linear equation y = 2x + 9.
If ∆RST ~ ∆YSZ, find the value of x.
Answer:
x = 48
Step-by-step explanation:
The table gives the temperature in degrees Fahrenheit in five cities at 6 AM on the same day used to table to answer the questions.
Looking at the table, the temperature in Boston at 6 AM is -8°F.
(a)
If the temperature had risen by 17°F at noon, then the new temperature is:
[tex]-8\degree F+17\degree F=9\degree F[/tex](b)
The 6 AM temperature in Toronto was -16°F, and -25°F in Fairbanks. The difference is:
[tex]-16\degree F-(-25\degree F)=-16\degree F+25\degree F=9\degree F[/tex]Which of the following mathematical properties is described by the statement, “whatever is done on one side of the equation must also be done on the other side of the equation”? Identity Property of AdditionAssociative PropertyCommunitive PropertyProperty of Equalitytoday guys please
Given the statement 'whatever is done on one side of the equation must also be done on the other side of the equation”, the mathematical properties that described this statement is Property of equality.
For any equality operation, whatever is done on one sides must be carried out on the other side. For example, given the equation;
3x + 3 = 5
We can subtract 3 from both sides to have;
3x+3 - 3 = 5-3
3x = 2
Then we can divide both sides by 3;
3x/3 = 2/3
From the illustration above, you can see that what we did to the left hand side of the equation, we also did for the right. Hence the correct answer is Property of Equality
The function of a circle is ysquared +x?=r? where r is the radius (any number). Make a circle with a radius of 16. Where does the circle intersect the X and Y axis? What is the relationship between where the circle intersects the axes and the radius (16)? IThe function of a circle is y?+x?=r? where r is the radius (any number). Make a circle with a radius of 16. Where does the circle intersect the X and Y axis? What is the relationship between where the circle intersects the axes and the radius (16)?
112 the circle of the radius
Step-by-step explanation:
3122
Refer to the line for Exercises 17-22.SU17. If RS 19 and RV = 71, find SV.18. If UV = 17 and SU17 and SUI = 38, find SV.13 and SX 30, find SV.19. If VX =20. If TW81 and VW = 35, find TV.21. If SW = 44.5 and SV44.5 and SV 37.1, find VW.22. If TU 15.9 and UW = 28.3, find TW.R====TVWX
Given:
RS=19 and RV=71
Find: SV
Explanation: SV= RV-RS
=71-19
=52
Final answer: the required value of SV is 52.
( pleassee help asap ! ) what is the solution (11.4 - 10) ÷2 ?
what is the solution (11.4 - 10) ÷2 ?
[tex]\begin{gathered} \frac{11.4-10}{2} \\ \frac{1.4}{2} \\ 0.7 \end{gathered}[/tex]The answer would be 0.7
Is 2/9 equal to a terminating decimal or a repeating decimal?
Since the denominator of 2/9 is 9, 2/9 is equal to a repeating decimal.
[tex]\frac{2}{9}=0.222222\ldots=0.\bar{2}[/tex]Answer: repeating decimal
Joanie believes that you cannot use cross products to solve the proportion 50 / 3 equals 75 over x 4x she says that if you multiply both sides of the equation by X you get 50 x / 3 equals 75 then if you multiply both sides of the equation by 3 you get 50 x equals 75 which is a different equation then you would get if you cross multiply what mistake did Yuri make in her reasoning?
The proportion is shown below and we cross multiply, do algebra, to solve it.
[tex]\begin{gathered} \frac{50}{3}=\frac{75}{x} \\ 50x=3\cdot75 \\ 50x=225 \\ x=\frac{225}{50} \\ x=\frac{9}{2} \end{gathered}[/tex]If you read the question, so will see this part:
if you multiply both sides of the equation by 3 you get 50 x equals 75
This is the part where there is a problem. You did say to multiply by 3 (both sides). But don't multiply the right hand side of "75" mistakenly.
The last part of this line should be "equals 75 times 3"
This is the mistake.
help me with this question please
Part a
the given polygon has 8 sides
so
Is a octagon
Part b
The given polygon is not a regular polygon, because all their sides don't have equal lengths and their interior angles are not equals
Select the correct choice below and, if necessary, fill in the answer box to complete your choiceO A. The function is continuous on(Type your answer in interval notation.)0 B. The function is not continuous
From the given image, we can affirm that the function is continuous in all its domain. That's the interval:
[tex]\lbrack4,\infty)[/tex]a circle has a diameter of 10 feet what is the circumference in square feet 28.2 31.4 36.8 40.5
Given a circle has a diameter = 10 feet
The circumference of the
3.5% of 300 is what number
To find 3.5% of 300, we have to multiply 0.035 by 300.
[tex]0.035\times300=10.5[/tex]Hence, the answer is 10.5.Answer:10.5
Step-by-step
1. The price p (in dollars) and the quantity x sold of a certain product obey the demand equation p = -8x + 600. What quantity x maximizes revenue (R= xp)? What is the maximum revenue? What price should the company charge to maximize revenue?2. Jeff invested some money at 7% simple interest and $5000 more than that amount at 15% simple interest. After 1 year, his total interest from the two accounts was $1300. How much did he invest at each rate?
1.The quantity x maximizes revenue is 80 , the price should be company charge to maximize revenue is 9 or 11.
2. $11875 he invest at each rate.
Given that,
In the question there are 2 question.
1.The market equation p = -8x + 600.
We have to determines how much a specific product costs in dollars and how many units are sold. What value of x optimizes profit (R=xp)?
We know,
R = px
R = p(-8p+160)
R= -8p² +160p
R(16) = -8(16)² +160(16)
R(16) = -2048 + 2560
R(16) = 512
R'= -16p + 160 = 0
Revenue maximizing price p= 160/16 = 20/2 = 10
Maximum revenue R(10) = -8(10)² + 160(10) = -800 + 1600 = 800
x=-8p+160
x =-8(10)+160
x = -80 + 160
x = 80
We get,
792 = -8p² +160p
8p² -160p + 792 = 0
2p² - 40p + 198 = 0
p² -20p + 99 = 0
(p-9)(p-11) = 0
p = 9 or 11 as the prices that give at least 792 in revenue
Therefore, The quantity x maximizes revenue is 80 , the price should be company charge to maximize revenue is 9 or 11.
2. Jeff put some money into investments at 7% simple interest and another $5,000 at 15% simple interest. His combined interest from the two accounts after a year was $1300.
We have to find at which rate did he invest how much.
Let C represent the sum Bryan invested in the CD. Then he made a savings account deposit of $5,000 C. Add the interest amounts to reach $1300.00: 15% of the amount in the certificate of deposit is 0.15C, and 7% of the amount in the savings account is 0.07(5,000-C). As a result, we can construct and settle the equation:
0.15C+0.07(5000-C)=1300
0.15C+350-0.07C=1300
0.08C+350=1300
0.08C=1300-350
0.08C=950
C=950/0.08
C=11875.
Therefore, $11875 he invest at each rate.
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Hello, how do I factorize this expression 1-36x^ { 2 } +y ^ { 2 } . Thanks :3
Solution:
Given the expression:
[tex]1-36x^2+y^2[/tex]To obtain the result of the factoring of the above expression, we factor out the common factor.\
In the above expression, there is no common factor.
Hence, the expression cannot be factored.
If Charlie’s Chocolate Fudge costs $1.95 perpound, how many pounds can you buy for $10.00?Set up a proportion.Make sure that the units match going across.Cross multiply to solve,X =_____ pounds for $10.
Let's use a rule of three:
This way,
[tex]x=\frac{10\cdot1}{1.95}\Rightarrow x=5.13lbs[/tex]We could buy 5.13 pounds
Perform the following division and write the quotient in trigonometric form. Write the magnitude inround it to two decimal places if necessary.- 8i4 + 5i
Solution
Given
[tex]\begin{gathered} \frac{-8i}{4+5i} \\ \\ \Rightarrow\frac{-8\imaginaryI}{4+5\imaginaryI}\times\frac{4-5i}{4-5i}=\frac{-32i-40}{16+25}=-\frac{40}{41}-\frac{32}{41}i \end{gathered}[/tex][tex]\begin{gathered} \text{ Let }Z=\frac{-40}{41}-\frac{32}{41}i \\ \\ \text{ Magnitude of }Z=|Z|=\sqrt{(-\frac{40}{41})^2+(-\frac{32}{41})^2} \\ \\ \Rightarrow|Z|=\frac{8\sqrt{41}}{41} \end{gathered}[/tex]In a box there a total of four prizes: Two of them are worth $4, a single prize worth $26, and a single prize worth $241. A player will reach into the box and draw one of the prizes at random. What is the fair price for this game?
So,
First of all, the player has a 1/4 chance of drawing any of the 4 prizes.
This means that the probability of drawing a prize of $4 is 1/2 because there are 2 prizes worth of $4. The probability of drawing a prize of $26 is 1/4 and the probability of drawing a prize of $241 is also 1/4.
To find the fair price, we need to find the expected value of this problem:
This can be obtained by multiplying any possible value of a price for the probability of drawing a prize of that value and adding all these Hvalues together.
This is:
[tex]\begin{gathered} 4\cdot\frac{1}{2}+26\cdot\frac{1}{4}+241\cdot\frac{1}{4} \\ \\ =\frac{275}{4}=68.75 \end{gathered}[/tex]Therefore, the fair price of this game is $68.75.