Solve for X in the equation, where X = 3A − 2B

Answer:

2√137

Step-by-step explanation:

To find AB, we can use the Pythagorean Theorem (a² + b² = c²). In this case, a = 22, b = 8 and we're solving for c, therefore:

22² + 8² = c²

484 + 64 = c²

548 = c²

c = ± √548 = ± 2√137

c = -2√137 is an extraneous solution because the length of a side of a triangle cannot be negative, therefore, the answer is 2√137.

Answer:

14.6

Step-by-step explanation:

(A). STEP ONE: Calculate the mean

(1). Row one = (10 + 12 + 12 + 14 ) = 48/4 = 12.

(2). Row Two: (12 + 11 + 13 + 16 ) = 52/4 = 13.

(3). Row three : (11 + 13 + 14 + 14)/4 = 13.

(4). Row four: (11 + 10 + 7 + 8)/4 = 36/4 = 9.

(5). Row five: (13 +12 + 14 + 13)/4 = 52/4 = 13.

(B). STEP TWO:

- determine the maximum and minimum value for each row.

- for each row, maximum - minimum.

Maximum values for each row:

Row one = 14, row two= 16, row three = 14, row four = 11 and row five = 14.

Minimum value for each row:

Row one = 10, row two = 11, row three = 11, row four =7 and row five = 12.

DIFFERENCES in each row :

row one = 14 - 10 = 4, row two = 16 - 11 = 5, row three = 14 - 11 = 3, row four = 11 - 7 = 4 and row five = 14 -12 = 2.

(C). STEP THREE: Calculate the mean of all the rows = 60/5 = 12.

(D). STEP FOUR : Calculate the Average Range = 18/5 = 3.6.

(E). STEP FIVE : Calculate the UCL.

A = Average rage × 0.729 = 3.6 × 0.729.

B = overall mean = 12.

UCL = A + B = 14.6.

Answer:

Nx = λx

Nx = 0, with x≠0

if N is nilpotent matrix, then the system Nx = 0 has non-trivial solutions

Step-by-step explanation:

given that

let N be a square matrix in order of n

note: N is nilpotent matrix with [tex]N^{k} = 0[/tex], k ∈ N

let λ be eigenvalue of N and let x be eigenvector corresponding to eigenvalue λ

Nx = λx (x≠0)

N²x =  λNx = λ²x

∴[tex]N^{k}x[/tex] =  (λ^k)x

[tex]N^{k}[/tex] = 0, (λ^k)x = [tex]0_{n}[/tex], where n is dimensional vector

where x = 0, (λ^k) = 0

λ = 0

therefore, Nx = λx

Nx = 0, with x≠0

note: if N is nilpotent matrix, then the system Nx = 0 has non-trivial solution

Answer:

- greater than Upper Q 3 plus 1.5 (IQR)

- less than Upper Q 1 minus 1.5 (IQR)

Step-by-step explanation:

To identify outliers the interquartile range of the dataset can be used

Outliers can be identified as data values that are

- greater than Upper Q 3 plus 1.5 (IQR)

- less than Upper Q 1 minus 1.5 (IQR)

Using the interquartile range concept, it is found that:

The interquartile range​ (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.

----------------------------

[tex]v < Q1 - 1.5IQR[/tex] or [tex]v > Q3 + 1.5IQR[/tex]

Thus:

The interquartile range​ (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.

A similar problem is given at https://brainly.com/question/14683936

Answer:

Number of term N = 9

Value of Sum = 0.186

Step-by-step explanation:

From the given information:

Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}[/tex]

Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}[/tex]

Number of term N = 9

The Value of the sum can be determined by using the expression for geometric series:

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}[/tex]

here;

m = 5

n = 9

r = 0.5

Then:

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}[/tex]

[tex]\sum \limits ^n_{k=m}ar^k =0.186[/tex]

For the given the geometric series, 3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³,

the responses are;

(1) The number of terms are 9

(2) The value of the sum is approximately 0.374

The given geometric series is presented as follows;

3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³

(1) The number of terms in the series = 13 - 4 = 9

Therefore;

(2) The value of the sum can be found as follows;

The common ratio, r = 0.5

The sum of the first n terms of a geometric progression is presented as follows;

[tex]S_n = \mathbf{\dfrac{a \cdot (r^n - 1)}{r - 1}}[/tex]

The sum of the first 4 terms are therefore;

[tex]S_4 = \dfrac{3 \times (0.5^4 - 1)}{0.5 - 1} = \mathbf{ 5.625}[/tex]

The sum of the first 13 terms is found as follows;

[tex]S_{13} = \dfrac{3 \times (0.5^{13} - 1)}{0.5 - 1} = \mathbf{ \dfrac{24573}{4096}}[/tex]

Which gives;

The sum of the 5th to the 13th term = S₁₃ - S₄

Therefore;

[tex]The \ sum \ of \ the \ 5th \ to \ the \ 13th \ term =\dfrac{24573}{4096} - \dfrac{45}{3} = \dfrac{1533}{4096} \approx \mathbf{0.374}[/tex]

Learn more about geometric series here:

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Answer:

variable A and Variable B are more negatively related than variable C and variable D.

Step-by-step explanation:

Variables A and B have a covariance = 45

Variables C and D have a covariance = 627

Comparing the relationship between variable A AND B with the relationship between variable C and D

variable A and Variable B are more negatively related than variable C and variable D. this is because the covariance between variable A and Variable B are less positive

Answer:

Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.

Step-by-step explanation:

(i) probability with 16 success out of 24 = 16/24 = 2/3

(ii) (i) probability with 8 success out of 12 = 8/12 = 2/3

Since the two experiments have the same probability, the observed probabilities are the same.

HOWEVER, since the theoretically probability is 1/2, 16.7% less than the experimental results, the number N of trials comes into play.

Using the binomial distribution,

(i)

p = 1/2

N = 24

x = 16 (number of successes)

P(16,24) = C(24,16) p^16* (1-p)^8

= 735471* (1/65536)*(1/256)

= 0.0438

(ii)

p = 1/2

N = 12

x = 8 (number of successes)

P(8,12) = C(12,8) p^8* (1-p)^4

= 495*1/256*1/16

= 0.1208

Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.

Note: It would help to mention the topic you're on so answers will correspond to what is expected.  Here we cover probability and binomial distribution.

Answer:

x^2 + 2x - 20 = 0

x^2 + 2x - 20 + 20 = 0 + 20  ( add 20 to both sides)

x^2 + 2x = 20

x^2 + 2x + 1^2 = 20 + 1^2 ( add 1^2 to both sides)

( x + 1 )^2 = 21

x = [tex]\sqrt{21}-1[/tex]

x = [tex]-\sqrt{21}-1[/tex]

Answer:

A)  x = –1 ± square root 21

is the answer:)

Answer:

24.5 mpg

Step-by-step explanation:

(23,695 - 23,252) / 14 = 24.5mpg

Answer:

The car averaged a total of 24.5 miles per gallon between the two fillings

Step-by-step explanation:

Firstly, we calculate the difference between the mileages.

This will give us the total distance traveled.

That would be 23,695 - 23,352 = 343 miles

The tank capacity obviously is 14 gallons

So mathematically, miles per gallon averaged between the two fillings = distance traveled by the car/gallon of fuel used = 343/14 = 24.5 miles per gallon

Answer:

your third answer

Step-by-step explanation:

its easy just plug in each domain into your function and the result will be the range

Answer:

Step-by-step explanation:

6x - y = 3

4x + 3y = 1

Solve the equation for y

y = -3 + 6x

4x + 3y = 1

Substitute the given value of y into the equation

4x + 3y = 1

plug the value

[tex]4x + 3( - 3 + 6x) = 1[/tex]

Distribute 3 through the parentheses

[tex]4x - 9 + 18x = 1[/tex]

Collect like terms

[tex]22x - 9 = 1[/tex]

Move constant to R.H.S and change its sign

[tex]22x = 1 + 9[/tex]

Calculate the sum

[tex]22x = 10[/tex]

Divide both sides of the equation by 22

[tex] \frac{22x}{22} = \frac{10}{22} [/tex]

Calculate

[tex]x = \frac{5}{11} [/tex]

Now, substitute the given value of x into the equation

y = -3 + 6x

[tex]y = - 3 + 6 \times \frac{5}{11} [/tex]

Solve the equation for y

[tex]y = - \frac{3}{11} [/tex]

The possible solution of the system is the ordered pair ( x , y )

-----------------------------------------------------------

Check if the given ordered pair is the solution of the system of equations

[tex]6 \times \frac{5}{11} - ( - \frac{3}{11} ) = 3[/tex]

[tex]4 \times \frac{5}{11 } + 3 \times ( - \frac{3}{11} ) = 1[/tex]

Simplify the equalities

[tex] 3 = 3[/tex]

[tex]1 = 1[/tex]

Since all of the equalities are true , the ordered pair is the solution of the system

Hope this helps..

Best regards!!

Work Shown:

[tex]\sin^2 \theta + \cos^2 \theta = 1\\\\\left(\frac{3}{10}\right)^2 + \cos^2 \theta = 1\\\\\frac{9}{100} + \cos^2 \theta = 1\\\\\cos^2 \theta = 1 - \frac{9}{100}\\\\\cos^2 \theta = \frac{100}{100}-\frac{9}{100}\\\\\cos^2 \theta = \frac{91}{100}\\\\\cos \theta = \sqrt{\frac{91}{100}} \ \text{ cosine positive in Q1}\\\\\cos \theta = \frac{\sqrt{91}}{\sqrt{100}}\\\\\cos \theta = \frac{\sqrt{91}}{10}\\\\[/tex]

Answer:

√91/10

Step-by-step explanation:

sin 0.3 is equal to 18(approximate value)

cos18°=0.951

which is √91/10

Answer:

4h - 6 = 70.

Step-by-step explanation:

Jahill's height is 70 inches. That is 6 inches shorter than 4 times his sister's height, h. That is the same thing as 4 times h minus 6.

70 = 4 * h - 6

4 * h - 6 = 70

4h - 6 = 70

4h = 76

h = 19.

His sister is 19 inches tall.

Hope this helps!

Answer:

Hello! The answer will be below! :3

Step-by-step explanation:

Question: Jahlil is 6 inches shorter than 4 times his sister’s height. Jahlil’s height is 70 inches. Which equation represents h, his sister’s height in inches?

Answer:The answer is 4h - 6 =70

(His sister is 19 inches tall)

Steps:

4 * h - 6 = 70

So, 4h - 6 = 70......

And 4h will be 76 which means h will equal to 19

His sisters hight is about 19in. tall.....

Hope this helps! :)

⭐️Have a wonderful day!⭐️

Answer:

[tex]12 {y}^{9} - 6 {y}^{5} + 4 {y}^{2} + 21[/tex]

Step-by-step explanation:

divide each term by 2y^3

Multiply through by the least common denominator.

Answer:

26 × 26 × 10 × 10 × 10 = 676 , 000  possibilities

Step-by-step explanation:

There is nothing stating that the letters and numbers can't be repeated, so all  26  letters of the alphabet and all  10

digits can be used again.

If the first is A, we have  26  possibilities:

AA, AB, AC,AD,AE ...................................... AW, AX, AY, AZ.

If the first is B, we have  26  possibilities:

BA, BB, BC, BD, BE .........................................BW, BX,BY,BZ

And so on for every letter of the alphabet.  There are  26  choices for the  first letter and  26  choices for the second letter. The number of different combinations of  2  letters is: 26 × 26 = 676

The same applies for the three digits. There are  10  choices for the first,  10

for the second and  10  for the third:

10 × 10 × 10 = 1000  

So for a license plate which has  2  letters and  3  digits, there are:  26 × 26 ×  10 × 10 × 10 = 676 , 000  possibilities.

Hope this helps.

Answer:

18.4°

Step-by-step explanation:

Use law of cosine.

a² = b² + c² − 2bc cos A

11² = 20² + 28² − 2(20)(28) cos A

121 = 1184 − 1120 cos A

cos A = 0.949

A = 18.4°

Answer:

As X → - ∞ , y → ∞ and as x→ ∞ , y → ∞

Step-by-step explanation:

let f(x) = y = 3x² - 5x + 2

y = 3x² - 5x + 2

= x ( 3x - 5 ) + 2

y = ∞ ( 3 ( ∞ - 5 ) ) + 2

= ∞ (∞ ) + 2

y = ∞

y → ∞ as x → ∞

Now,

as x → - ∞

y = x ( 3x - 5 ) + 2

= ∞ ( 3 ( - ∞ ) - 5 ) + 2

= - ∞ ( - ∞ ) + 2

∞² + 2 = ∞

Hence , Option C is the correct answer.

Answer:

Mathematically you can use the following V = ⁴⁄₃πr³

π = pi

r = radius

To do this you would need a set of scales, a jug, some water, a pen, a ruler and some paper.

ωα√

Answer:isosceles is the correct

Step-by-step explanation:

According to the given conditions the triangle ABC is an isosceles triangle.

An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.

Given that, BD is median and altitude in the triangle ABC, and we are asked to find that what type of the triangle ABC will be if we prove triangles  ADB and CBD congruent by SAS rule,

So, the proof is as follows,

AD = CD [definition of median]

∠ ADB = ∠ CDB [definition of altitude]

BD = BD [reflexive property]

∴ Δ ADB ≅ Δ CBD by SAS rule

AB = BC by CPCT

According to the definition of an isosceles triangle we can say that, ABC is an isosceles triangle.

Hence, according to the given conditions the triangle ABC is an isosceles triangle.

Learn more about isosceles triangles, click;

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Answer:

Step-by-step explanation:

g(x) = |x – 8| + 6 was transformed from the parent function g(x) = |x|:

8 unit right

6 units up

a parent absolute value function has a vertex at (0,0)

if the function is moved so is the vertex:

(0+8,0+6)

(8,6)

So, the vertex of this function is at (8,6)

Answer:  vertex = (8, 6)

Step-by-step explanation:

The Vertex form of an absolute value function is: y = a|x - h| + k   where

g(x) = |x - 8| + 6 is already in vertex form where

h = 8 and k = 6

so the vertex (h, k) = (8, 6)

Answer:

Option A a right tailed hypothesis test

Step-by-step explanation:

A claim given symbolically is most of the time derived from the alternative hypothesis usually tested against the null hypothesis.

A symbolic claim with the option of a less than indicates a left tailed test, while one with the option of greatest than indicate a right tail test and one with the option of both (not equal to; either less or greater) indicates a two tailed test.

In this case study, the sample proportion for the claim was greater than 0.50 thus, the test is a right tailed hypothesis test

Answer:

(D)R: x+2=7

Step-by-step explanation:

Given the statement P:x=5

An equivalent statement will be a statement whose result is exactly x=5.

From the given options:

R: x+2=7

R: x=7-2

R: x=5

Therefore, R is an equivalent statement.

The correct option is D.

Answer:

[tex]z = \frac{x}{y} [/tex]

Step-by-step explanation:

Let x be the price of carton of ice cream

Let y be the number of grams in carton

Let z be price per gram.

[tex]z = \frac{x}{y} [/tex]

Which means price of carton of ice cream divided by the number of grams in carton equals price per gram.

Hope this helps ;) ❤❤❤

Answer:

C. 5

Step-by-step explanation:

The circle has point in the center from where two line blue and red are stretched to the point on the circle. The blue line is 5 in length and the red line length is not known. The circumference of the circle is equal on all the area around the origin. Therefore the red line must also be 5 in length as of blue line.

Answer:

Step-by-step explanation:

Given the shape of the equation -2(x+3) = -10. Since x is being multiplied by -2, the first step would be to divide by -2, which is equivalent to multiply by (-1/2) on both sides. Hence the answer is B

Answer:

[tex]x \geq -91/2[/tex]

Step-by-step explanation:

[tex]6(x+8) \geq -43 + 4x[/tex]

Resolving Parenthesis

[tex]6x+48 \geq -43 + 4x[/tex]

Collecting like terms

[tex]6x - 4 x \geq -43-48[/tex]

[tex]2x \geq -91[/tex]

Dividing both sides by 2

[tex]x \geq -91/2[/tex]

Answer:

x ≥ - 91 / 2

Step-by-step explanation:

In this sample problem, the first thing we want to do is expand the part in parenthesis through the distributive property. This will make the simplification process easier. Another approach would be to divide either side by x + 8, but let's try the first.

Approach 1 : [tex]6(x+8) = 6x + 6 8 = 6x + 48[/tex]

[tex]6x + 48 \geq - 43+4x[/tex] - so we have this simplified expression. We now want to isolate x, so let's combine common terms here. Start by subtracting 6x from either side,

[tex]48 \geq - 43-2x[/tex] - now add 43 to either side,

[tex]91\geq -2x[/tex] - remember that dividing or multiplying a negative value changed the inequality sign. Dividing - 2 on either side, the sign changes to greater than or equal to, with respect to x,

[tex]- 91 / 2 \leq x[/tex], or in other words [tex]x \geq - 91 / 2[/tex]. This is our solution.

Answer: 32

Step-by-step explanation:

Answer: She can select 7 workshops if more than 4 must be about anthropology in 1716 ways.

Step-by-step explanation:

Given, The organizer of a conference is selecting workshops to include. She will select from 9 workshops about anthropology and 5 workshops about psychology.

If he select 7 workshops if more than 4 must be about anthropology, the possible combinations = (5 anthropology, 2 psychology), (  6 anthropology, 1 psychology), (7 anthropology, 0 psychology)

Number of possible combinations = [tex]^9C_5\times ^5C_2+^9C_6\times ^5C_1+^9C_7\times ^5C_0[/tex]

[tex]=\dfrac{9!}{5!4!}\times\dfrac{5!}{2!3!}+\dfrac{9!}{6!3!}\times(5)+\dfrac{9!}{7!2!}\times (1)\\\\=\dfrac{9\times8\times7\times6}{4\times3\times2\times1}\times\dfrac{5\times4}{2}+\dfrac{9\times8\times7}{3\times2\times1}\times5+\dfrac{9\times8}{2}\\\\=1260+420+36\\\\=1716[/tex]  [using formula for combinations [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]

Hence, she can select 7 workshops if more than 4 must be about anthropology in 1716 ways.

Answer:

A: True

B, C and D: False

Step-by-step explanation:

We have a total sales tax for Alabama that is:

[tex]T_A=4.225+1.375+3=8.6[/tex]

The total sales tax for Florida is:

[tex]T_F=6.5+1+1.625=9.125[/tex]

The total sales tax is greater in Florida than in Alabama.

A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE

The sales tax difference in this purchase can be calculated as:

[tex]1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8[/tex]

B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)

C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)

The amount of sales tax in Alabama is:

[tex]ST_A=1500\cdot T_A=1500\cdot 0.086=129[/tex]

D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).

Answer:

2√2−3

Step-by-step explanation:

Simplify each term.

Since there are no imaginary terms, the complex conjugate is the same as the simplified expression.

Hope this can help