QUESTION 8
Find the smallest positive integer that is a multiple of 4 and 5.

The point B lies on 2.7

\(2 \frac{3}{4} \) is the only fraction that gives us 2.7

Let's see ~

\(2 \frac{3}{4} \\ \\ \frac{11}{4} \\ \\ = 2.7\)

Answer:

c

Step-by-step explanation:

in order for it to be a triangle the smaller sides have to add up to be greater than the longest side

for a 5+14=19 so that is not a triangle because the  side dont add up to be greater than 19

for b 14+8=22 so that is also not a triangle because the sides dont add up to be greater than 24

for c 5+15=20 so that is a triangle because to 2 shorter sides added are greater than the longest side

for d 14+9=23 so that is not a triangle because the two smaller sides dont add up to be greater than 24

Light bulbs is normally distributed with a variance of 625 and a mean lifetime of 520 hours, we need to calculate the cumulative probability up to 549 hours. The answer will be rounded to four decimal places.

Given a normally distributed lifetime with a mean of 520 hours and a variance of 625, we can determine the standard deviation (σ) by taking the square root of the variance, which gives us σ = √625 = 25.

To find the probability of a bulb lasting for at most 549 hours, we need to calculate the area under the normal distribution curve up to 549 hours. This can be done by evaluating the cumulative distribution function (CDF) of the normal distribution at the value 549, using the mean (520) and standard deviation (25).

The CDF will give us the probability that a bulb lasts up to a certain point. Rounding the result to four decimal places will provide the desired precision.

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The problem involves using normal distribution to find the probability of a given outcome. Using the Z-score, we can determine that the probability of a light bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%

Given the mean (µ) of the lifetime of a bulb is 520 hours. Also, the variance (σ²) is given as 625. Thus, the standard deviation (σ) is the square root of the variance, which is 25.

To find the probability of a bulb lasting for at most 549 hours, we first calculate the Z score. The Z-score formula is given as follows: Z = (X - µ) / σ, where X is the number of hours, which is 549. So substitute the given values into the formula. Z = (549 - 520) / 25, the Z value is 1.16.

We then look up the Z-table to find the probability associated with this Z-score (1.16), which is approximately 0.8770. Therefore, the probability of a bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%.

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Answer: D. W

Step-by-step explanation:

The angles make a straight line.

Answer:

11 is the answer.

Process :-

AB = AM + MB

or, AB = 5.5 + 5.5 ( AM = MB = 5.5)

so, AB = 11

Main Answer:The upper bound is the maximum radius among the Gershgorin discs, and the lower bound is the minimum radius.

Supporting Question and Answer:

How can companion matrices and Gershgorin's theorem be used to find upper and lower bounds on the moduli of the zeros of a given polynomial?

Companion matrices are constructed from the coefficients of a polynomial and can help determine the eigenvalues, which represent the roots of the polynomial. Gershgorin's theorem provides a method to estimate the location of eigenvalues by analyzing the Gershgorin discs centered at the diagonal entries of the companion matrix. By finding the maximum and minimum radii among these discs, we can establish upper and lower bounds on the moduli of the polynomial's zeros.

Body of the Solution:To find upper and lower bounds on the moduli of the zeros of the given polynomial using companion matrices and Gershgorin's theorem, we can follow these steps:

1.Arrange the polynomial in descending order of the exponent of z:

2z^8 + 2z^7i + z^6 − 20iz^4 + 2iz − i^3

2.Create the companion matrix A associated with the polynomial. The companion matrix is a square matrix of size (n-1), where n is the degree of the polynomial. The matrix is formed as follows:

A =\(\left[\begin{array}{ccccccccc}0&0&0&0&0&0&0&0&i\\1&0&0&0&0&0&0&0&0\\0&1&0&0&0&0&0&0&0\\0&0&1&0&0&0&0&0&0\\0&0&0&1&0&0&0&0&0\\0&0&0&0&1&0&0&0&0\\0&0&0&0&0&1&0&0&0\\0&0&0&0&0&0&1&0&0\\0&0&0&0&0&0&0&1&0\end{array}\right]\)

3.Find the eigenvalues of the companion matrix A. The eigenvalues represent the roots of the polynomial.

4.Apply Gershgorin's theorem to find upper and lower bounds on the moduli of the roots. According to Gershgorin's theorem, each eigenvalue of the matrix A lies within at least  one of its Gershgorin discs. A Gershgorin disc is a disc in the complex plane centered at the diagonal entry of a matrix, with a radius equal to the sum of the absolute values of the remaining entries in that row.

For each eigenvalue λ, determine the Gershgorin discs centered at the diagonal entries of the companion matrix and find the maximum and minimum radii.

5.The upper bound is the maximum radius among the Gershgorin discs, and the lower bound is the minimum radius.

These bounds provide an estimate of the maximum and minimum moduli of the zeros of the polynomial.

Final Answer: Therefore,the upper bound is the maximum radius among the Gershgorin discs, and the lower bound is the minimum radius.

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The U.S. Constitution is a document that is revered by Americans, as it embodies the country's founding principles. However, the people who wrote it were not without flaws. They were a product of their time, and some held beliefs that are now widely considered to be racist and unacceptable.

The best way to remember the people who wrote the Constitution is to acknowledge their contributions to American society and their flaws. We should not forget the past, as it shapes who we are as a nation today. However, we must also recognize the problematic aspects of our history and strive to learn from them.Most of the Founding Fathers were slaveholders, and their belief in the superiority of white people is evident in their writings. Thomas Jefferson, who is credited with writing the Declaration of Independence, owned over 600 slaves during his lifetime and believed that black people were inferior to white people. James Madison, who was the chief architect of the Constitution, was also a slaveholder. While these facts cannot be denied, it is also true that these men were instrumental in creating a document that has been the foundation of American society for over 200 years.The best way to acknowledge the contributions and flaws of the Founding Fathers is to teach the history of the Constitution in a balanced and nuanced way. Students should learn about the historical context in which the Constitution was written, including the fact that many of the Founding Fathers were slaveholders. They should also learn about the ways in which the Constitution has been amended to protect the rights of all Americans, including women, minorities, and LGBTQ+ people. By doing so, we can honor the legacy of the Founding Fathers while also recognizing their shortcomings. In conclusion, the best way to remember the people who wrote the Constitution is to acknowledge their contributions to America as well as their flaws. We must teach the history of the Constitution in a balanced and nuanced way, recognizing the historical context in which it was written and the ways in which it has been amended to protect the rights of all Americans.

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After Composite the given function  If \(f(x) = x^2\) and \(g(x) = x^2-7x+12\), \(g(f(x))\) is \(x^{4}\) - 7\(x^{2}\) + 12

What is a function?

A functiοn in mathematics is a cοnnectiοn between twο sets οf elements, the dοmain and the range, where each element in the dοmain is related tο a particular element in the range. An οutput value that cοrrespοnds tο an input value is prοduced by a set οf rules knοwn as a functiοn.

To find g(f(x)), we need to first compute f(x), which is \(x^{2}\). Then we plug that value into g(x) in place of x.

So, g(f(x)) = g(\(x^{2}\))

Now, we need to compute g(\(x^{2}\)).

g(\(x^{2}\)) is given by:

g(\(x^{2}\)) = \((x^2)^{2}\) - 7(\(x^{2}\)) + 12

Simplifying this expression, we get:

g(\(x^{2}\)) = \(x^{4}\) - 7\(x^{2}\) + 12

So the final answer is option C: \(x^{4}\)-7\(x^{2}\)+12.

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Answer:x − x^{2} − 1.

Step-by-step explanation:

.

Answer:

3k-30

Step-by-step explanation:

3(k-10) = 3k-30

hope this help

Double-check the input and review the solution provided by the matrix calculator to ensure accuracy.

The matrix calculator is a useful tool for solving equations involving matrices. To find the values of the variables in the matrix calculator, follow these steps:

1. Enter the coefficients of the variables and the constant terms into the calculator. For example, if you have the equation 2x + 3y = 10, enter the coefficients 2 and 3, and the constant term 10.

2. Select the appropriate operations for solving the equation. The calculator will provide options such as Gaussian elimination, inverse matrix, or Cramer's rule. Choose the method that suits your equation.

3. Perform the selected operation to solve the equation. The calculator will display the values of the variables based on the solution method. For instance, Gaussian elimination will show the values of x and y.

4. Check the solution for consistency. Substitute the obtained values back into the original equation to ensure they satisfy the equation. If they do, you have found the correct values of the variables.Remember to double-check the input and review the solution provided by the matrix calculator to ensure accuracy.

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The probability that the counter removed is red is given as follows:

18/55.

A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.

The probabilities of a red counter being removed from Bag B is obtained considering these following scenarios:

Hence the probability that the counter removed is red is calculated as follows:

p = 4/11 x 6/10 + 3/11 x 4/10 = 36/110 = 18/55.

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Answer:

C

Step-by-step explanation:

Hopefully

C

I did it on edge hopefully this helps you and don't think i copied the other person

The radical expression \(\frac{\sqrt{200} }{28}\) can be simplified to \(\frac{\sqrt{25} }{7}\) or \(5*\frac{\sqrt{14} }{7}\)

To simplify the given radical expression, we can simplify the numerator and denominator separately. The square root of 200 can be simplified as follows: √200 = √(2 * 100) = √2 * √100 = 10√2.

Similarly, the square root of 28 can be simplified as follows: √28 = √(4 * 7) = √4 * √7 = 2√7.

Now, substituting these simplified values into the original expression, we have \(\frac{\sqrt{200} }{28}\) = \(\frac{10\sqrt{2} }{2\sqrt{7} }\)

To further simplify the expression, we can divide the common factor of 2 from both the numerator and denominator: \(\frac{10}{2}\) * \(\frac{\sqrt{2} }{\sqrt{7} }\) = 5 * \(\frac{\sqrt{2} }{\sqrt{7} }\)

Finally, we rationalize the denominator by multiplying the expression by (√7/√7): \(5*\frac{\sqrt{2} }{\sqrt{7} } *\frac{\sqrt{7} }{\sqrt{7} } =5\frac{\sqrt{14} }{7}\)

Therefore, the simplified form of the radical expression \(\frac{\sqrt{200} }{28}\) is \(\frac{\sqrt{25} }{7}\) or \(5*\frac{\sqrt{14} }{7}\)

The radical expression \(\frac{\sqrt{200} }{28}\) can be simplified to \(\frac{\sqrt{25} }{7}\) or \(5*\frac{\sqrt{14} }{7}\)

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Step-by-step explanation:

when counting the events we see, he did

22+19+20+18+21 = 100 experiments.

and he got in 20 cases out of the possible 100 a purple marble.

that means the observed probability to pull a purple marble is 20/100 = 1/5.

now he does 25 more pulls.

each with the probity of 1/5 to pull a purple marble.

so, he should expect to pull a purple marble 25×1/5 = 5 times.

Solution:

Perimeter of square = 40cm

But perimeter of square = 4 × side

Therefore, 4 × side = 40 cm

Therefore, side= 40/4 cm = 10cm

Now, the area of the square = (side × side)

Therefore, area of the square = 10 × 10 cm² =

100 cm².

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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Solution:

Given:

Let's represent the number of oranges and grapefruits by the letters o and g.

This means that...

Now, let's solve the expression to find out how much does Dion has to pay.

Substituting o and g with the given values:

We also know that Dion gave a $20. To find the change, subtract the money Dion gave with the money required to pay for the fruits.

Thus, Dion got $13.85 as change.

The compound propositions ¬(p↔q) and p↔¬q are logically equivalent. This means that they have the same truth values for all possible combinations of truth values of the propositional variables p and q.

To show the logical equivalence between ¬(p↔q) and p↔¬q, we can construct a truth table and compare the truth values of both propositions for all possible combinations of truth values for p and q.

For ¬(p↔q), the expression ¬(p↔q) means "not (p if and only if q)" or "the negation of (p↔q)". In a truth table, we evaluate the truth values of p↔q and then negate the result.

For p↔¬q, the expression p↔¬q means "p if and only if not q". In a truth table, we evaluate the truth values of ¬q and then check if it is equivalent to p.

By comparing the truth values in the truth table, we can observe that ¬(p↔q) and p↔¬q have the same truth values for all possible combinations of truth values of p and q. Therefore, we can conclude that ¬(p↔q) and p↔¬q are logically equivalent.

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Step-by-step explanation:

let the unknown be x

24 - x^2 = 5x

-x^2 - 5x + 24 = 0

(x - 3)(x + 8) =0

x = 3 (or) x = -8

if u wanna check

if you wanna check

24 - (-8)^2 =5(-8)

24 - 64 = -40

-40 = -40

since you ask for negative solution

x= -8 is a NUMBER

the solution is 5times of a NUMBER = -8 × 5 = -40

hope I got it right^^,good luck!

In order to prove the triangles are similar, you have to use SAS, SSS and AA rule.

In triangle, the similarity theorem states that if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Here we have to find the 3 shortcuts to prove the triangles are similar.

According to the similarity theorem, here we have triangle that is similar to other if two pairs of angles are congruent (AA) or if two pairs of sides are proportional and the included angles are congruent whereas if three pairs of sides are proportional (SSS).

Here we must know that the term similarity and congruent are similar terms.

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Answer:

12.8 ft or exactly sqrt 164

Step-by-step explanation:

Pythagoreans is a^2+b^2=c^2

10^2+8^2=164

sqrt 164 = 12.8 ft

Answer:

MO, NO, MN

Step-by-step explanation:

First, we can identify this triangle as a right triangle, as given by the square next to the O. Next, we know that a right angle is equal to 90 degrees, and the sum of the angles of a triangle is equal to 180 degrees.

Therefore,

∠M + ∠O + ∠N (the angles of the triangle) = 180

49 + 90 + ∠N = 180

139 + ∠N = 180

subtract both sides by 139 to isolate the variable

∠N = 41

Therefore, ∠N is 41 degrees.

In a triangle, given the angles, we know that the side opposite the smallest angle is the side with the smallest length and so on.

Our angle lengths are

41, 49, and 90 degrees in order.

Therefore, the side opposite the largest angle (90 degrees, or ∠O) is the longest side. This is MN. Similarly, ∠N is the smallest angle, and the side opposite of that (MO) is the shortest side. This leaves NO to be in the middle

Answer:

12:15

16:20

20:25

Step-by-step explanation:

4 Nike : 5 Adidas

times 3 = 12:15

times 4 = 16:20

times 5 = 20:25

In this movie, the ratio of children to adults suggests that there are 27 children in attendance.

We have to give that,

There are 9 children for every 4 adults.

This means that if there were 13 people, 9 of them would be children and 4 would be adults.

Children would therefore be:

= 9 / 13

If there were 39 people, the number of children would be:

= 9/13 x 39

= 27 children

In conclusion, there are 27 children.

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The complete question is,

In the newest animated movie, for every 9 children, there are 4 adults. There are a total of 39 children and adults in the movie.

How many children are in the movie?

Answer:

y > 1/3x -3

Step-by-step explanation:

Just find the equation of the line, which is y = 1/3x -3, and then determine what the symbol is going to be. Since the line is dotted, it will either be < or >. When the shaded area is on top of the line, it's >. Remember that by saying left on the bottom or right on top.

Answer:

No

Step-by-step explanation:

Answer:

0 cannot go into 4

4 can go into 8

8 cannot go into 12

Answer:

The expression (8-i)/(2+i) in standard form is, 3 - 2i

Step-by-step explanation:

The expression is,

(8-i)/(2+i)

writing in standard form,

\((8-i)/(2+i)\\\)

Multiplying and dividing by 2+i,

\(((8-i)/(2+i))(2-i)/(2-i)\\(8-i)(2-i)/((2+i)(2-i))\\(16-8i-2i-1)/(4-2i+2i+1)\\(15-10i)/5\\5(3-2i)/5\\=3-2i\)

Hence we get, in standard form, 3 - 2i

The expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

To write the expression (8-i)/(2+i) in standard form a+bi, we need to eliminate the imaginary denominator. We can do this by multiplying the numerator and denominator by the conjugate of the denominator.

The conjugate of 2+i is 2-i. So, we multiply the numerator and denominator by 2-i:

(8-i)/(2+i) * (2-i)/(2-i)

Using the distributive property, we can expand the numerator and denominator:

(8(2) + 8(-i) - i(2) - i(-i)) / (2(2) + 2(i) + i(2) + i(i))

Simplifying further:

(16 - 8i - 2i + i^2) / (4 + 2i + 2i + i^2)

Since i^2 is equal to -1, we can substitute -1 for i^2:

(16 - 8i - 2i + (-1)) / (4 + 2i + 2i + (-1))

Combining like terms:

(15 - 10i) / (3 + 4i)

Therefore, the expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

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Answer:

(0,0), (8,0), (2,-4)

you just multiply x and y coordinates by 2