Suppose 2022 balls are randomly distributed into 100 boxes. Let X be the total number of balls in the first 20 boxes. P(X = 90) ≈ 0. VarX = 323.52.
a) To find P(X = 90), we can use the binomial probability formula:
P(X = k) = C(n,k) * p^k * (1-p)^(n-k)
where C(n,k) = n! / (k! * (n-k)!)
In this case, n = 2022, k = 90, p = 20/100 = 0.2
P(X = 90) = C(2022,90) * 0.2^90 * 0.8^(2022-90)
P(X = 90) = 1.19 * 10^(-37)
Therefore, P(X = 90) ≈ 0.
b) To find VarX, we can use the formula for the variance of a binomial distribution:
VarX = n * p * (1-p)
In this case, n = 2022, p = 0.2
VarX = 2022 * 0.2 * 0.8
VarX = 323.52
Therefore, VarX = 323.52.
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solve asap
4- Determine whether the variable is discrete or continuous, and determine its level of measurement.
The number of residents in a city
Discrete, interval level
Continuous, interval level
Discrete, ratio level
Continuous, ratio level
11)A pair of dice are rolled. Identify the pair of mutually exclusive events. Getting an even number on the first die; getting a double 5 Getting an odd number on the first die; getting a 4 on the second die Getting a 2 on the first die; getting a sum of 4 Getting a 3 on the first die; getting a sum more than 8
11)A pair of dice are rolled. Identify the pair of mutually exclusive events.
Getting an even number on the first die; getting a double 5
Getting an odd number on the first die; getting a 4 on the second die
Getting a 2 on the first die; getting a sum of 4
Getting a 3 on the first die; getting a sum more than 8
The number of residents in a city is a discrete variable with ratio level of measurement. Therefore, the correct option is option 3. When a pair of dice are rolled, the pair of mutually exclusive events are getting an odd number on the first die; getting a 4 on the second die. Therefore, the correct option is option 2.
The number of residents in a city is a discrete variable because it can only take on whole number values. The level of measurement for this variable is ratio level because there is a true zero point (a city with zero residents) and the differences between values are meaningful. Therefore, the correct answer is discrete, ratio level which is the third option.
Mutually exclusive events are events that cannot occur at the same time. In the case of rolling a pair of dice, the pair of mutually exclusive events is "Getting an odd number on the first die; getting a 4 on the second die." This is because if the first die is an odd number, the second die cannot be a 4 at the same time.
The other options are not mutually exclusive because they can occur at the same time. For example, it is possible to get an even number on the first die and a double 5 at the same time. Therefore, the correct answer is "Getting an odd number on the first die; getting a 4 on the second die" which is the second option.
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suppose 8x + 16 ice cream cones were sold on saturday and 7x - 9 were sold on sunday. what is the total number of ice cream cones sold?
Answer:
this is right.....
Step-by-step explanation:
15x + 6
Find an equation of the circle that has center(-1,2) and passes through(-6,6).
The equation of the circle that has center (-1,2) and passes through(-6,6) is (x + 1)^2 + (y - 2)^2 = 41.
The equation of a circle with center (h,k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2. In this case, the center of the circle is (-1,2) so h = -1 and k = 2. We can use the given point (-6,6) to find the radius of the circle.
The distance between the center and the given point is the radius of the circle, and we can use the distance formula to find it:
r = √((-6 - (-1))^2 + (6 - 2)^2)
r = √((-5)^2 + (4)^2)
r = √(25 + 16)
r = √41
So the equation of the circle is:
(x - (-1))^2 + (y - 2)^2 = (√41)^2
(x + 1)^2 + (y - 2)^2 = 41
Therefore, the equation of the circle that has center(-1,2) and passes through(-6,6) is (x + 1)^2 + (y - 2)^2 = 41.
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You want to have $5000 in two years so that you can go on a vacation. How much should do you need put into your
account to have enough money if it pays 5.89% interest compounded weekly? Hint: You have A, you need to find P!**
You need to deposit $13 into a account to have amount $5000 in 2 years.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Given that, Amount =$5000, rate of interest =5.89% and time period = 2 year = 104 weeks.
Now, 5000=P(1+5.89/100)¹⁰⁴
5000=P(1+0.0589)¹⁰⁴
5000=P(1.0589)¹⁰⁴
5000=384.5P
P=5000/384.5
P=$13
Therefore, you need to deposit $13 into a account to have amount $5000 in 2 years.
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Hi. _______________________________________________________________________________
Answer:
.
Step-by-step explanation:
Ms.lang borrows $2,300 for 30 months at 13% interest per year. How much interest will ms.lang pay? What is the total amount she will repay?
Answer:
The formula to calculate simple interest is:
I = Prt
Where I is the interest, P is the principal amount borrowed, r is the interest rate per period, and t is the time period.
Using this formula, we can calculate the interest Ms. Lang will pay as follows:
I = Prt
I = 2300 * 0.13 * (30/12)
I = $975
Therefore, Ms. Lang will pay $975 in interest over the 30-month period.
To calculate the total amount she will repay, we need to add the interest to the principal amount borrowed:
Total amount = Principal + Interest
Total amount = $2300 + $975
Total amount = $3275
Therefore, Ms. Lang will repay a total of $3275, which includes the $2300 principal and $975 interest.
now, we're assuming this is on a simple interest rate, so hmm say a year has 12 months, so 30 months will just be 30/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$2300\\ r=rate\to 13\%\to \frac{13}{100}\dotfill &0.13\\ t=years\to \frac{30}{12}\dotfill &\frac{5}{2} \end{cases} \\\\\\ I = (2300)(0.13)(\frac{5}{2}) \implies I = 747.5~\hfill \underset{ \textit{amount to be repaid} }{\stackrel{ 2300~~ + ~~747.5 }{\text{\LARGE 3047.5}}}[/tex]
You are planning to sell children's fairy wings at a craft fair. It costs you $5 in supplies to make each set of fairy wings and you will sell them for double your cost.
You have 100 sets of fairy wings and sell 60 of them by 2pm. The craft fair ends at 4pm and you want to sell the rest of your wings faster so you mark the price down by 30%.
With c = supply cost to make a set of wings, and P(c) = price, the equation for the price you first sell the wings is A) P(c)=2c B) P(c)=.7c C) P(c)=.5c D) P(c)=1.5c
The new equation to sell the wings faster with N(p)=new price is A) N(p)=.3p B) N(p)=p-.3 C) N(p)=.7p D) N(p)=.5p
The composed equation N(P(c) is A) .9c B) 1.4c C) .7c D) 2.7c
and represents A) the markup of the discounted price over your supply cost B) your markup profit on all the wings C) how much money you will lose by selling the wings at a lower price
The domain of all the functions is A) [0, infinity) B) (-infinity, 0] C) (-infinity, infinity)
because A) the prices will always be positive numbers B) the wings make it possible to fly C) you can hace any possible answer in these questions D) anything is possible
Answer: Dragonfly wings for the boys cost $1 while fairy wings for the girls cost $2. Phoebe's mom spent $18 on the gifts. How many dragonfly wings and fairy wings
Step-by-step explanation:
Answer:
The answer to the first question is A) P(c) = 2c, because the wings will be sold for double the cost of supplies.
The answer to the second question is B) N(p) = p - 0.3, because the price will be marked down by 30%.
The answer to the third question is A) 0.9c, which represents the markup of the discounted price over the supply cost.
The domain of all the functions is A) [0, infinity), because prices and costs must be positive numbers. Therefore, options B, C, and D are incorrect.
In the figure, each small cube has edges that are 1/3 yd long. Which expression can you use to find the volume of the rectangular prism is cubic yards?
The expressiοn (B) 2 × 4 × 5 × 1/3 × 1/3 × 1/3 can be used tο find the vοlume οf the rectangular prism is cubic yards.
What is equatiοn?A mathematical equatiοn links twο statements and utilises the equals sign (=) tο indicate equality. In algebra, an equatiοn is a mathematical assertiοn that prοves the equality οf twο mathematical expressiοns. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical fοrmula may be used tο determine hοw the twο sentences οn either side οf a letter relate tο οne anοther. The lοgο and the particular piece οf sοftware are usually identical. like, fοr instance, 2x - 4 = 2.
Vοlume is calculated using the fοrmula LWH
Here each cube has side 1/3 yd
Sο vοlume = (2 × 1/3) × (4 × 1/3) × (5 × 1/3)
It can be written as 2 × 4 × 5 × 1/3 × 1/3 × 1/3
Thus, οptiοn B is cοrrect.
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Complete question:
Find the future value of this loan. $17,592 at 6.6% interest for
8 months
The future value of the loan is _______________
(Round to the nearest cent as needed.)
The future value of the loan is $18,358.16. This means that after 8 months, the loan will have grown to $18,397.54 due to the interest.
To find the future value of this loan, we can use the formula FV = PV(1 + r)^t, where FV is the future value, PV is the present value, r is the interest rate, and t is the time period in years.
In this case, we have PV = $17,592, r = 6.6%, and t = 8 months or 0.667 years (8/12).
Plugging these values into the formula, we get:
FV = $17,592(1 + 0.066)^0.667
FV = $17,592(1.066)^0.667
FV = $18,358.16
Therefore, the future value of the loan is $18,358.16. This means that after 8 months, the loan will have grown to $18,397.54 due to the interest.
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simply the expression (6^2)4
Answer:
144
Step-by-step explanation:
6*6=36
36*4=144
What is the solution of the system? Solve using matrices.
{ x+2y=9
{x+y=1
Answer:
Step-by-step explanation:
// Solve equation [2] for the variable x
[2] x = y + 1
// Plug this in for variable x in equation [1]
[1] (y +1) - 2y = 9
[1] - y = 8
// Solve equation [1] for the variable y
[1] y = - 8
// By now we know this much :
x = y+1
y = -8
// Use the y value to solve for x
x = (-8)+1 = -7
Solution :
{x,y} = {-7,-8}
Which change, if any, is needed to the underlined text?
“Taking up to six months, hikers who plan to complete the entire
journey”
-A journey of up to six months, hikers planning to complete it entirely
-Taking up to six months to complete, hikers who plan the entire journey
-The entire journey takes up to six months to complete, so hikers who plan to
finish it
-No change
No change is needed. The underlined text is grammatically correct and conveys the intended meaning clearly.
What is the meaning of the underlined test?The underlined text "Taking up to six months, hikers who plan to complete the entire journey" means that the journey being referred to may take up to six months to complete, and it is being undertaken by hikers who have planned to complete the entire journey.
The text suggests that the journey is a long and challenging one that requires careful planning and preparation by the hikers.
Therefore, the correct answer is as given above. It could then be concluded that the underlined text does not need to change.
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Suppose you applied for positions at four different companies and let X be the number of offers you received.
a- Find the mean
b- standard deviation
of the number of offers you received. Round your answer to two decimal places
The answer of the number of offers you received are as follow,
1. Mean is equal to 1.96.
2. Standard deviation is equal to 1.17 (rounded to two decimal places) .
1.Mean (or expected value) is represented by E(X)
Formula of the expected value is,
E(X) = ∑xP(x)
Substitute the value from the table we get,
⇒E(X) = (0)(0.19) + (1)(0.12) + (2)(0.38) + (3)(0.16) + (4)(0.15)
⇒E(X) = 0 + 0.12 + 0.76 + 0.48 + 0.6
⇒E(X) = 1.96
2. Standard deviation of the number of offers received ,
⇒ Standard deviation 'σ' = √[ Σ(x - E(X))² P(x) ]
Substitute the values from the table we get,
⇒ Standard deviation 'σ'
= √[ (0 - 1.96)² (0.19) + (1 - 1.96)² (0.12) + (2 - 1.96)² (0.38) + (3 - 1.96)²(0.16) + (4 - 1.96)²(0.15) ]
= √[ 1.3728 ]
≈ 1.171665
≈1.17(rounded to two decimal places)
Therefore, the mean and the standard deviation of the number of offers received is approximately 1.96 and 1.17 (rounded to two decimal places) respectively.
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The above question is incomplete, the complete question is:
Suppose you applied for positions at four different companies and let X be the number of offers you received
X : 0 1 2 3 4
P(x) : 0.19 0.12 0.38 0.16 0.15
1. Find the mean
2. standard deviation
of the number of offers you received. Round your answer to two decimal places
A. Translate the following English/verbal phrases into Mathematical phrases:
1. A certain number j added with four
2. The product of a number c and sixteen
3. The product of three and z more than one
4. Eight is increased by the product of e and f
5. A certain number v is divided by seventeen
B. Solve for the following. (2 points each)
x = -3, b=15, c= -2
1. 4x - 5b + 9c
2. 123c - 3b
3. 78b + 2c x 15b
4. X - b + 15c
5. 85x - 4b x c + 7b
The correct Mathematical phrases of the English phrases would be j+4, 16c, 3(z+1), ef+8, and v/17 respectively and the solution of given linear equations (part B) will be -105, -291, 270, -48, and -30 respectively.
In part A, the translation of mathematical phrases gives rise to certain equations of linear nature. It helps in easy understanding of the relations between variables and numerical values. In part B, the values of x, b and c are already given for the sake of simplicity. Substituting these values in given linear equations gives the following results:
4x - 5b + 9c = 4(-3) - 5(15) + 9(-2) = -105123c - 3b = 123(-2) - 3(15) = -29178b + 2c x 15b = 78(15) + 2(-2)×15(15) = +270x - b + 15c = -3 -(15) + 15(-2) = -4885x - 4b x c + 7b = 85(-3) - 4(15)(-2) + 7(15) = -30Learn more about linear equations at:
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coretta buys a pair of jeans that is on sale for 20% off. the regular price is marked $27.00 find the amount of discount on the jeans
Answer: $21.60
Step-by-step explanation: This is a similar way I solve this problem..
You take 20%, notice is it 20% of 100%, our 100% in this case is $27.00, our 20% is missing.. so.. divide 27.00 by 5, because 5 20%'s is 100%, after you divide by 5 you will end up with $5.40, so we know that 20% of $27.00 is $5.40..
Take $27.00 and take $5.40 away, and you will be left with 21.60
20%x5=100%
27.00/5=5.40
27.00-5.40=21.60
Coretta's pair of jeans is $21.60 when it is on sale for 20% off.
Lube used to 9 cups of milk for a pancake recipe to drink another 394 cups of milk how about about how much milk did Luke is using on
To find the total amount of milk used, we simply add the amount of milk used for the pancake recipe and the amount used for drinking. So we add 9 cups and 394 cups together, giving us a total of 403 cups of milk.
We can calculate the total amount of milk that Luke used for the pancake recipe and the additional amount he used for drinking.
For the pancake recipe, Luke used 9 cups of milk.
For drinking, Luke used an additional 394 cups of milk.
Total amount of milk used = Milk used for pancake recipe + Milk used for drinking
= 9 cups + 394 cups
= 403 cups of milk.
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The complete question is:
Lube used to 9 cups of milk for a pancake recipe to drink another 394 cups of milk how about about how much milk did Luke is using on the recipe?
What the pOH of a solution containing [OH-] = 4.91 x
10-11 mol L-1 ?
Report your answer to at least 1 decimal place
The pOH of a solution containing [OH-] = 4.91 x 10-11 mol L-1 is 10.3. We can round the pOH to 10.3.
The pOH of a solution is the negative logarithm of the concentration of hydroxide ions (OH-) in the solution. It can be calculated using the formula:
pOH = -log[OH-]
In this case, the concentration of hydroxide ions is [OH-] = 4.91 x 10-11 mol L-1. Plugging this value into the formula, we get:
pOH = -log(4.91 x 10-11)
Using a calculator, we can find the pOH to be 10.309.
To report the answer to at least 1 decimal place, we can round the pOH to 10.3.
Therefore, the pOH of a solution containing [OH-] = 4.91 x 10-11 mol L-1 is 10.3.
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What is the answer? Please help!
Answer:
the answer is 88 square inches
Step-by-step explanation:
[tex]2(6 \times 4) + 2(4 \times 2) + 2(6 \times 2) = 88[/tex]
PLEASE HURRY ITS DUE IN 24 MINUTES
A chicken breeder has chickens that are white, black or speckled. Speckled chickens have both black and white feathers. This is a co-dominant trait. The allele for white feathers is A and the allele FB for black feathers is F Determine the genotypes for the rooster and hen that the breeder should cross to produce the greatest percentage of speckled chickens. A. Place the alleles for the rooster and the hen that the breeder should cross in the blank boxes outside the Punnett square. B. Place the number that shows the percentage of speckled offspring that will result from this cross in the blank box. . You may use the allele labels more than once. • There may be more than one correct answer. • Place only one label in each blank box F F 25 50 75 100 2/5- Hen Rooster =% speckled
Since speckled chickens have both b and w feathers, they must inherit one allele for w feathers and one allele for b feathers. Therefore, to produce the greatest percentage of speckled chickens, the breeder should cross a w chicken with a b chicken.
The Punnett square for this cross would be:
| F F
A | A F A F
A | A F A F
This shows that all offspring (100%) will be heterozygous for both white and b feathers (genotype: AFAF), which is the genotype for speckled feathers. Therefore, the percentage of speckled offspring that will result from this cross is 100%.
Putting the alleles for the hen and rooster in the blank boxes outside the Punnett square would look like this:
| F F
A | A F A F
A | A F A F
Hen Rooster
20% of $509 and how to work it out
Answer:
101.80
Step-by-step explanation:
Well this is fairly simple, if you can use a calculator. There not much to it so first you convert 20% to a decimal which is 0.2 or 0.20 either works. Then you multiply 0.2 by 509 to get 101.80. I used a calculator to multiply those two but Im not sure how else to do it without a calculator. Hope this helps.
Find a positive angle and a negative angle that is coterminal to the given angle. 95 A. 495, -305 B. 265 -455 C. 275-85 D. 455, -265
The correct answer is option A. 495, -305.
To find a positive angle that is coterminal to the given angle, we can add 360 degrees to the given angle. This is because coterminal angles are angles that have the same initial side and terminal side, but differ in the number of rotations. Adding 360 degrees to the given angle gives us the same initial side and terminal side, but with one extra rotation.
95 + 360 = 455
To find a negative angle that is coterminal to the given angle, we can subtract 360 degrees from the given angle. This gives us the same initial side and terminal side, but with one less rotation.
95 - 360 = -265
Therefore, the positive angle that is coterminal to the given angle is 455, and the negative angle that is coterminal to the given angle is -265.
Answer: A. 495, -305.
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Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 98 degrees occurs at 6 PM and the average temperature for the day is 85 degrees. Find the temperature, to the nearest degree, at 7 AM. degrees
The temperature at 7 AM is approximately 87 degrees.
The outside temperature over a day can be modeled as a sinusoidal function. In this case, we know that the high temperature of 98 degrees occurs at 6 PM and the average temperature for the day is 85 degrees. To find the temperature at 7 AM, we can use the equation:
T(t) = A sin(B(t - C)) + D
where T(t) is the temperature at time t, A is the amplitude, B is the frequency, C is the horizontal shift, and D is the vertical shift.
We know that the average temperature is 85 degrees, so D = 85. We also know that the high temperature of 98 degrees occurs at 6 PM, so A = (98 - 85)/2 = 6.5 and C = 6.
Now we can plug in the values and solve for the temperature at 7 AM:
T(7) = 6.5 sin(B(7 - 6)) + 85
Since we want to find the temperature to the nearest degree, we can round the answer to the nearest whole number:
T(7) = 6.5 sin(B) + 85 ≈ 87 degrees
Therefore, the temperature at 7 AM is approximately 87 degrees.
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A new movie is coming out that you and your family really want to see. You are going to buy tickets for
opening day as soon as they go on sale and want to get extra tickets so friends could come too. You
have $224.50 and wants to get as many tickets as possible. You want to get at least 5 adult tickets and
4 kids tickets.
Use the ticket prices from your local movie theater or look up the average prices of child and adult
tickets for the movie theater.
In your discussion post, share the equations that you used to model this situation and answer the
following questions:
1. Can you get at least 5 adult tickets and 4 kids tickets?
2. What is the most tickets you could have bought and met the given conditions? What number of
each type of ticket is that?
3. After doing more research, you find out that you can rent out a whole theater for $190. If you rent
the theater out, you can have up to 24 people, regardless of whether they are children or adults. In
what situations would it be a better deal to rent out the theater?
1. The equation for the cost of adult tickets is:
$8.97 x number of adult tickets
The equation for the cost of child tickets is:
$6.79 x number of child tickets
The equation for the cost of renting out the theater is:
$190
2. Yes, you can get at least 5 adult tickets and 4 kids tickets.
3. The most tickets you could have bought and met the given conditions is 9 adult tickets and 8 kids tickets.
4. It would be a better deal to rent out the theater if you had more than 24 people.
You must be aware of the costs of adult and child tickets in order to determine if you can purchase at least 5 adult tickets and 4 child tickets. A cinema ticket for an adult costs $8.97 on average, while a ticket for a child costs $6.79 on average. 4 children's tickets would cost $27.16 and 5 adult tickets would cost $44.85 as a result. You would then have $202.49 remaining, which would be enough to pay for 7 additional child tickets. Thus, you can purchase at least 5 adult and 4 child tickets.
The most tickets you could have purchased while still fulfilling the requirements is nine adult and eight child tickets. The total price would be $135.05. The adult tickets would cost $80.73 and the child tickets would cost $54.32. You would now have $89.45, which is insufficient to purchase any additional tickets.
Renting out the theater might be a great option if you have more than 24 individuals. This is due to the fact that hiring out the theater costs $190 and allows for a maximum of 24 guests, both adults and children. Consequently, renting the theater would be less expensive than purchasing individual tickets if you had more than 24 individuals.
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Let T: VV be a linear operator and let Z: V→V be the zero linear transformation defined by Z(u) = 0 for all u EV. Prove that
Im(T) ker(T) - T.T=Z
The statement Im(T) ker(T) - T.T=Z is not necessarily true for all linear operators T.
To prove that Im(T) ker(T) - T.T=Z, we must first understand the terms "operator," "transformation," and "linear."
An "operator" is a function that maps one vector space to another. A "transformation" is a function that maps one set to another. A "linear" transformation is a transformation that satisfies the properties of linearity, meaning that it preserves addition and scalar multiplication.
Now, let's look at the equation Im(T) ker(T) - T.T=Z. The term "Im(T)" refers to the image of the linear operator T, which is the set of all vectors that can be obtained by applying T to any vector in V. The term "ker(T)" refers to the kernel of the linear operator T, which is the set of all vectors that are mapped to the zero vector by T.
To prove that Im(T) ker(T) - T.T=Z, we must show that the difference between the image of T applied to the kernel of T and the composition of T with itself is equal to the zero linear transformation.
First, let's consider the image of T applied to the kernel of T. Since the kernel of T is the set of all vectors that are mapped to the zero vector by T, applying T to any vector in the kernel of T will result in the zero vector. Therefore, Im(T) ker(T) = 0.
Next, let's consider the composition of T with itself, T.T. Since T is a linear operator, the composition of T with itself will also be a linear operator. However, there is no guarantee that T.T will equal the zero linear transformation.
Therefore, Im(T) ker(T) - T.T=Z can be simplified to 0 - T.T=Z. Since T.T is not necessarily equal to the zero linear transformation, the equation does not hold true for all linear operators T.
In conclusion, the statement Im(T) ker(T) - T.T=Z is not necessarily true for all linear operators T.
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Use the ruler provided to measure the dimensions of the parallelogram shown to the nearest 0.5 centimeter.
Which measurement is closest to the area of the parallelogram in square centimeters?
F.14 cm2
G.16.5 cm2
H. 4114
cm2
J.8.5 cm2
F. 14 [tex]cm^2[/tex] is the measurement that most closely resembles the
the parallelogram's area in square centimeters.
what are parallelograms?A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of a polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees. You must have studied a variety of 2D shapes and sizes in geometry, including circles, squares, rectangles, rhombuses, etc. Each of these forms has a unique set of characteristics.
from the question:
We must multiply the parallelogram's base and height in order to determine its area. We can observe from the photograph that the parallelogram's height is around 3 cm, and its base is about 5 cm. Hence, the parallelogram's area is:
Area = Base x Height
= 5 cm x 3 cm
= 15 [tex]cm^2[/tex]
15 square centimeters is the result of rounding this response to the nearest whole number. F. 14 cm2 is the measurement that most closely approximates the parallelogram's area in square centimeters.
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If the simple interest on $7000 for 7 years is $3430, then what is the interest rate?
The interest rate will be 7%
What is simple interest?A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount.
Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
The formula for simple interest is:
S = p*t*r/100
the simple interest on $7000 for 7 years is $3430
r = S*100/(p*t)
r = (3430*100)/(7000*7)
r = 7%
Hence the interest rate will be 7%
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Lennox Madrid Polynomial Long Division (Level 1) Feb 18, 1:52:23 PM Use the long division method to find the result when 2x^(3)+4x^(2)+7x+5 is divided by x+1.
The result of the given polynomial division (2x^(3)+4x^(2)+7x+5 divided by x+1) using long division method is 2x^(2) + 2x + 5.
To find the result of the given polynomial division using long division method, we need to follow the steps below:
Step 1: Write the dividend and the divisor in long division form.
______________________
x + 1 | 2x^(3) + 4x^(2) + 7x + 5
Step 2: Divide the first term of the dividend by the first term of the divisor. In this case, 2x^(3)/x = 2x^(2). Write the result above the dividend.
2x^(2) _______________
x + 1 | 2x^(3) + 4x^(2) + 7x + 5
Step 3: Multiply the result by the divisor and write the product under the dividend.
2x^(2) _______________
x + 1 | 2x^(3) + 4x^(2) + 7x + 5
- (2x^(3) + 2x^(2))
---------------------
Step 4: Subtract the product from the dividend and bring down the next term.
2x^(2) _______________
x + 1 | 2x^(3) + 4x^(2) + 7x + 5
- (2x^(3) + 2x^(2))
---------------------
2x^(2) + 7x + 5
Step 5: Repeat the process until the degree of the remainder is less than the degree of the divisor.
2x^(2) + 2x + 5 _______________
x + 1 | 2x^(3) + 4x^(2) + 7x + 5
- (2x^(3) + 2x^(2))
---------------------
2x^(2) + 7x + 5
- (2x^(2) + 2x)
---------------------
5x + 5
- (5x + 5)
---------------------
0
Step 6: Write the final result as the quotient plus the remainder over the divisor.
[tex](2x^{3} + 4x^{2} + 7x + 5)/(x + 1) = 2x^{2} + 2x + 5[/tex]
Therefore, the answer is 2x^(2) + 2x + 5
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100 Points. Please Help. Due in Two Hours.
2. The given quadratic equation is in the general form:
ax² + bx + c = 0
therefore:
a = 2
b = -4
c = -3
The quadratic formula is thus:
[tex]x=\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex]
Substituting the values found for a, b, and c:
[tex]x=\frac{-(-4)+\sqrt{(-4)^2-4(2)(-3)} }{2(2)}[/tex] and [tex]x=\frac{-(-4)-\sqrt{(-4)^2-4(2)(-3)} }{2(2)}[/tex]
Therefore x = 2.58, x = -0.58
3. Using the same method as above, first, bring all values to one side, leaving the RHS = 0
a = 1
b = 2
c = -1
The quadratic formula is thus:
[tex]x=\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex]
Substituting the values found for a, b, and c:
[tex]x=\frac{-(2)+\sqrt{(2)^2-4(1)(-1)} }{2(1)}[/tex] and [tex]x=\frac{-(2)-\sqrt{(2)^2-4(1)(-1)} }{2(1)}[/tex]
Therefore, x = 0.41, x = -2.41
[tex]2 {x}^{2} - 4x - 3 = 0[/tex]
A Here ,
[tex]\boxed{a = 2 }\\\boxed{b = - 4} \\ \boxed{c = - 3}[/tex]
B Filling in the values of a , b and c in the Quadratic formula below , we get
[tex]x = \frac{- (b)\pm \sqrt{( {b}^{2}) - 4(a)(c) } }{2(a)} \\ [/tex]
C Simplifying each section , we get
[tex]x = \frac{ - ( - 4) + \sqrt{( { - 4}^{2} ) - 4(2)( - 3)} }{2 \times 2} [/tex]
or
[tex]x = \frac{ - ( - 4) - \sqrt{ {( - 4})^{2} - 4(2)( - 3) } }{2 \times 2} [/tex]
D Simplifying answers from Part C , we get
[tex]\boxed{x = \frac{2 + \sqrt{10} }{2}} \: \: \: \: or \: \: \: \: \boxed{ x = \frac{2 - \sqrt{10} }{2} } \\ [/tex]
Therefore ,
[tex]\boxed{x = 2.58} \: \: \: \: and \: \: \: \: \boxed{x = - 0.58}[/tex]
Thus , option A. is correct!_____________________________________
[tex] {x}^{2} + 2x = 1 \\ \implies \: {x}^{2} + 2x - 1 = 0[/tex]
A Here ,
[tex]\boxed{a = 1} \\ \boxed{b = 2} \\ \boxed{c = - 1}[/tex]
B Filling in the values of a , b and c in the Quadratic formula below , we get
[tex]x = \frac{- (b)\pm \sqrt{( {b}^{2}) - 4(a)(c) } }{2(a)} \\ [/tex]
C Simplifying each section , we get
[tex]x = \frac{ - (2) + \sqrt{ ({2}^{2} ) - 4(1)( - 1)} }{2 \times 1} [/tex]
or
[tex]x = \frac{ - (2) - \sqrt{( {2}^{2}) - 4(1)( - 1) } }{2 \times 1} [/tex]
D Simplifying answers from Part C , we get
[tex]\boxed{x = - 1 + \sqrt{2} } \: \: \: \: or \: \: \: \: \boxed{x = - 1 - \sqrt{2} }[/tex]
Therefore
[tex]\boxed{x = 0.41} \: \: \: \: or \: \: \: \: \boxed{x = -2.41 }[/tex]
Thus , option D is correct.hope helpful! :)
pleaseweeee helppppp
Select the correct answer.
Which expression is equivalent to the given expression? Assume the denominator does not equal zero.
Answer:
A
[tex]2y {}^{4} \div x {}^{4} [/tex]
Step-by-step explanation:
Divide 14 by 7 it will be 2.
Now divide the variables.
X variable will give you X{}^{-4} and y{}^{4}.
So bring X variable in the denominator to make it positive.
So your answer will be option A.
Answer:
A
Step-by-step explanation:
It was right for me
Youve made it to Lookout Point and want to to just a little tarther for the day. Determise the distances ta dedide which is dorer. (Round to one decimal places) Question 3 Woire at Clear Sorhes and you get a call Erom friendi who are at fiogeri valey you decide fo mert ha fwary Using the map for coordinater (where the car. is at io,00 where mould you mect rour friends? Round coced inates to one ded mal olare) Mertat: Question 4 Now wa tore to hin
The midpoint is [(Yx + Fx)/2, (Yy + Fy)/2]
The distance between 2 points in the map is √[(FVx - CSx)^2 + (FVy - CSy)^2]
To determine the distance between two points on a map, we can use the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, we are trying to find the distance between Clear Springs (x1, y1) and Finger Valley (x2, y2). Plug in the coordinates for each point into the formula and solve for d.
d = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(Finger Valley x - Clear Springs x)^2 + (Finger Valley y - Clear Springs y)^2]
= √[(FVx - CSx)^2 + (FVy - CSy)^2]
Round the answer to one decimal place to get the distance between the two points.
To find the coordinates of the meeting point between you and your friends, we can use the midpoint formula:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
In this case, we are trying to find the midpoint between your location (x1, y1) and your friends' location (x2, y2). Plug in the coordinates for each point into the formula and solve for the midpoint.
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
= [(Your x + Friends' x)/2, (Your y + Friends' y)/2]
= [(Yx + Fx)/2, (Yy + Fy)/2]
Round the coordinates to one decimal place to get the midpoint, which is the meeting point between you and your friends.'
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