What are the solutions for the given equation?

x2+4x+16=0


x=−2±4i3‾√


x=−2±23‾√


x=−2±2i3‾√


x=−2±43‾√

Answer:

$74,750

Step-by-step explanation:

Given that,

The cost of a computer = $65,000 + value added tax at 15%

We need to find the amount the computer actually cost the customer.

Total cost = Cost of computer + VAT at 15%

\(=65000+65000\times \dfrac{15}{100}\\\\=\$74,750\)

So, the computer actually cost the customer is $74,750.

Based on the fact that this is an equilateral triangle, the value of y can be found to be 5.

The figure given is an equilateral triangle which means that the lengths of all the sides are equal.

As DC is equal to 20, it means that all the other sides should be 20 as well.

This means that the value of y is:

20 = 15 + y

y = 20 - 15

y = 5

In conclusion, y is 5.

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Answer:

there will be 7 roses as I thought

Answer:

The tip will be $6.30

A quadratic polynomial can be written using the sum and product of its zeroes as: x² + (α+β) + αβ = 0 Where α and β are the roots of the equation. ☛ x² + ( 0+√5)x + 0 = 0 .

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Answer: B or D

Step-by-step explanation:

Karens ration is 5:15 whilst chens is 6:19

1/3 of 15 is gonna be 5, while 19 is gonna be around 6.3

I got 1/3 cause there is 3 colors, and red is one of them, since the question is asking about the total. I would be leaning more towards B though.

Answer:

Chen: 6/19

Step-by-step explanation:

Anne: 2/14 = 0.142

Karen: 5/15 = 0.133

Janice: 4/14 = 0.285

Chen: 6/19 = 0.316

Answer:

5,000,000,000+200,000,000+40,000,000+8,000,000+600,000+60,000+3,000+700+10+1

Step-by-step explanation:

5,000,000,000 + 200,000,000+ 40,000,000+ 8,000,000+ 600,000+ 60,000+ 3,000

+ 700 + 10 + 1

To show that `(n + 3)7 ∈ Θ(n7)`, we need to prove that `(n + 3)7 = Θ(n7)`.This can be done by showing that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)` .Now, let's prove the two parts separately:

Proof for `(n + 3)7 = O(n7)`.

We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≤ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≤ n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + n7
≤ 2n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6
≤ 2n7 + 84n6 + 441n5 + 2205n4 + 10395n3 + 45045n2 + 153609n + 729
```Thus, we can take `c = 153610` and `k = 1` to satisfy the definition of big-Oh notation. Hence, `(n + 3)7 = O(n7)`.Proof for `(n + 3)7 = Ω(n7)`We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≥ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≥ n7
```Thus, we can take `c = 1` and `k = 1` to satisfy the definition of big-Omega notation. Hence, `(n + 3)7 = Ω(n7)`.

As we have proved that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)`, therefore `(n + 3)7 = Θ(n7)`.Thus, we have shown that `(n + 3)7 ∈ Θ(n7)`.From the proof, we can see that we used the Binomial theorem to expand `(n + 3)7` and used algebraic manipulation to bound it from above and below with suitable constants. This technique can be used to prove the time complexity of various algorithms, where we have to find the tightest possible upper and lower bounds on the number of operations performed by the algorithm.

Hence, we have shown that `(n + 3)7 ∈ Θ(n7)` for non-negative integer n.

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Answer:

Step-by-step explanation:

You want the amounts invested in each of three accounts, earning 6%, 7%, and 8%. Given is the total interest for one year ($260), the total amount invested ($3600), and the fact that twice as much was invested at 8% as at 6%.

Let x represent the amount invested at 6%. Then 2x is the amount invested at 8%, and (3600 -x -2x) is the amount invested at 7%. The total interest earned is ...

  0.06x +0.07(3600 -3x) +0.08(2x) = 260

Simplifying the equation, we find ...

  0.01x +252 = 260

  x = (260 -252)/0.01 = 800 . . . . . . subtract 252 and divide by 0.01

The amounts invested in the various accounts are ...

6%: $800

7%: $1200

8%: $1600

There are two events, one for person is positive tested and another one for person is negative tested. These events are mutually exclusive. So, these are not independent events.

We have to consider a person is drawing at random from the residents of berkeley and then giving them a test for covid-19. Let us consider two events

We have to check event 'a' and 'b' are independent or mutually exclusive. As we know, Mutually exclusive events are those which cannot happen at same time. Hence a person being positive and negative at same time is not possible. Hence events are mutually exclusive and not independent.

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The equivalent fractions here are: 14/18 ,  21/27 , 28/36 , 35/45 , 42/54.

Given, the number 7/9

7/9 = (7/9 × 2/2) = 14/18

7/9 = (7/9 × 3/3) = 21/27

7/9 = (7/9 × 4/4) = 28/36

7/9 = (7/9 × 5/5) = 35/45

7/9 = (7/9 × 6/6) = 42/54

hence the equivalent fractions here are:

14/18 , 21/27 , 28/36 , 35/45 , 42/54

Equivalent fractions are those fractions that reflect the same value even if they may have distinct numerators and denominators. For instance, the fractions 9/12 and 6/8 are comparable as both, when simplified, equal 3/4.

When reduced to their most basic form, all equivalent fractions become the same fraction.

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Answer:

B: shift vertically up by 3

Step-by-step explanation:

I suggest using desmos graphing for future questions like these

Hope this helps :)

Using proportions, it is found that they traveled a total of 3066 miles around the lake.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships.

One example of application of proportions is for unit rate problems, in which we find the unit rate for a single person, and then the total amount for a number n of people is given by n multiplied by the unit rate.

For this problem, we have that:

Hence the total distance traveled by all these people is given as follows:

200 x 15.33 = 3066 miles.

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Answer:

550.5323531336038

Step-by-step explanation:

I have a hint: if you ever need help with triangle trigonometry questions go to carbside depot trigonometry calculator it is a literal life savor

We have a variable x that is normally distributed with:

A. Using the data above we must find the 56th-percentile for the random variable x.

First, we need to find the z-score associated with this percentile. How we do that? We must find the value of z that solves the following equation:

Based on this, we find that the solution is z = 0.151 because from the normal table we see that:

Therefore, the percentile we are looking for is computed using the following formula:

B. We must find the proportion of the values for the random variable x between 82 and 89.

In mathematical terms, in this case, we must compute the following probability:

Again, we must obtain the z-scores to solve this. The corresponding z-values needed to be computed are:

Now, because the variable x is a normal distribution, then the variables Zlow and Zup have a normal distribution. Therefore, the probability is computed in the following way:

C. Finally, we must compute the following probability:

The corresponding z-value needed to be computed is:

Again, because x follows a normal distribution, then the variable Zlow has a normal distribution and the probability is computed as:

Summary

The results are:

A. 76.208

B. 0.1507

C. 0.0168

Answer:

d. 135

Step-by-step explanation:

\( {m}^{2} = 3...(given) \\ \therefore \: {( {m}^{2} )}^{3} = {3}^{3} \\ \therefore \: m^{6} = 27 \\ \therefore \: 5m^{6} = 27 \times 5 \\ \therefore \: 5m^{6} = 135\)

The number of bracelets and the number of necklaces will be 10 and 5, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

A gem dealer had a proper measure of gold to make wristbands and pieces of jewelry. The amount of gold in every armband is 5 grams and the amount of gold in every accessory is 16 grams. A goldsmith utilized 130 grams.

Let 'x' be the number of Bracelets and 'y' be the number of Necklaces. Then the equation is given as,

5x + 16y = 130

The term 16y in the equation should be a multiple of 5 to get the whole value.

If the value of y is 5. Then the number of bracelets is given as,

5x + 16(5) = 130

5x + 80 = 130

5x = 50

x = 10

The number of bracelets and the number of necklaces will be 10 and 5, respectively.

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The table has a greater rate of change.

The rates of change are equal.

In the given problem, we have a table showing the relationship between x and y values. By comparing the change in y with the change in x, we can determine the rate of change. Looking at the table, we observe that for every increase of 1 in x, there is a corresponding increase of 1 in y. Therefore, the rate of change for this table is 1.

The slopes are equal.

The equation has a greater slope.

In problem 2, we are given a linear equation in the form y = mx + b, where m represents the slope. The given equation is y = 2x + 7, which means the slope is 2. To compare the rates of change, we compare the slopes. If the slopes are equal, the rates of change are equal. In this case, the slopes are equal to 2, so the rates of change are the same.

The function rule has a greater slope.

The slopes are equal.

In problem 3, we are told that as x increases by 1, y increases by 3. This information gives us the rate of change between x and y. The slope of a function represents the rate of change, and in this case, the slope is 3. Comparing the slopes, we find that they are equal, as both have a value of 3. Therefore, the rates of change are the same.

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Given data:

The total numbers of factories are n=9.

The numbers of fctories selected are r=5.

The expression for selecting 5 factories is,

Thus, there are 126 ways of selecting 5 factories.

Answer:

\(( - ) \times ( - ) = ( + )\)

Negative × Negative = positive

Example;

\( (- 1) \times (- 1 )=( + 1)\)

I hope I helped you^_^

Answer:

  5541.77 cm^3

I don't see this exact answer, but 5538.96 comes closest.  (Did someone change pi last night?)

Step-by-step explanation:

Volume of a cone is V = (1/3)\(\pi\)\(r^{2}\)h, where h is the height of the cone (27 cm) and r is the radius (14 cm).

V = (1/3)(3.14)(14)^2(27)

V = 5541.77 cm^3

Comparing the slopes of both lines, we can conclude that they are neither perpendicular nor parallel lines.

Find the slope of line 1 given the points (-3, 1) and (-7, -2):

Slope (m) = change in y / change in x = (-2 - 1)/(-7 -(-3))

Slope (m) = -3/-4

Slope (m) = 3/4.

Find the slope of line 2 given the points (2, -1) and (8, 4):

Slope (m) = change in y / change in x = (4 - (-1))/(8 - 2)

m = 5/6

The slope of both lines are different and their product is not equal to -1, therefore, they are neither parallel nor perpendicular lines.

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Maintain the 95% level of confidence but report a confidence interval with a smaller margin of error, the medical researcher should increase the sample size.

This will provide a more precise estimate of the mean birth weight of babies born to women over the age of 40.

Maintain the 95% level of confidence but report a confidence interval with a smaller margin of error, the researcher should increase the sample size.

The larger the sample size, the smaller the margin of error, which means that the estimated mean birth weight of all babies born to women over the age of 40 will be more precise.
Redoing the study and choosing a different sample of size 100 will not necessarily reduce the margin of error, as the variability in the sample may be the same.

To achieve a smaller margin of error, the researcher needs to increase the sample size.
With a larger sample size, the researcher will have a more representative sample of the population, which will lead to a more accurate estimate of the mean birth weight of all babies born to women over the age of 40.

However, the larger sample size may require more resources and time to collect the data.

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The inequality that represents the amounts in dollars that could be deposited in a new checking account is a ≥ 75.

This inequality states that "a" must be greater than or equal to 75 dollars, which is the minimum deposit required for opening a new checking account.

the inequality "a ≥ 75" represents the amounts in dollars that could be deposited in a new checking account, where "a" is the amount being deposited and must be greater than or equal to $75.

To represent this mathematically, we can use an inequality. An inequality is a statement that compares two values using symbols like "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "! =" (not equal to).

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Answer: 378

Step-by-step explanation:

439 minus 78 equals 378.

Answer:

190

Step-by-step explanation:

10x5x2=100

5x3x2=30

3x10x2=60

100+30+60=190

answer. B hope this helps

The length of BC is 18.2 units.

The correct answer is option b) BC = 18.2.

Since AD is the perpendicular bisector of BC, it divides BC into two equal segments. Let's call the point of intersection between AD and BC as M. Therefore, BM = MC.

According to the given information,

AB = AC = 21.3. Since AD is the perpendicular bisector of BC, it implies that AM is equal to MC.

Therefore, AM = MC = BC/2.

We are also given that DC = 9.1. Since MC = DC, we can conclude that BC/2 = 9.1.

To find BC, we can multiply both sides of the equation by 2:

BC = 2 x 9.1

BC = 18.2.

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