What is the "least common denominator" of the following two fractions:

1/6 and 1/2

The area of the square field is 67600 m² and the side is 260 m long.

A quadrilateral with all sides equal and all angles are right angles.

Given that, a person takes 40 paces to cover 20 m of a square field according to him the field has a side that is 520 paces long, we need to find the measure of the side and the area,

Since,

40 paces = 20 m

1 pace = 1/2 m

Therefore,

520 paces = 0.5 x 520 m

= 260 m

Therefore, the square field is 260 m long,

Area of the square field = side² = 260²

= 67600 m²

Hence, the area of the square field is 67600 m² and the side is 260 m long.

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The unit rate will be "23.5 miles/gallon". In the below segment, a further solution to the given question is provided.

Given values in the question are:

Total distance,

= 188 miles

Total gas used,

= 8

Now,

⇒ The rate of gas consumption will be:

= [tex]\frac{Total \ distance}{Total \ gas \ used}[/tex]

By putting the given values in the above formula, we get

= [tex]\frac{188}{8}[/tex]

= [tex]23.5 \ miles/gallon[/tex]

Thus the above is the appropriate solution.

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Answer:

m = [tex]\frac{2q}{3y}[/tex]

Step-by-step explanation:

Given

q = [tex]\frac{3ym}{2}[/tex] ( multiply both sides by 2 to clear the fraction )

2q = 3ym ( isolate m by dividing both sides by 3y )

[tex]\frac{2q}{3y}[/tex] = m

Answer:

[tex]- \frac{\pi}{3}[/tex]

Step-by-step explanation:

Given

[tex]y = -3\cos(3x - \pi) + 5[/tex]

Required

The phase

We have:

[tex]y = -3\cos(3x - \pi) + 5[/tex]

Rewrite as:

[tex]y = -3\cos(3(x - \frac{\pi}{3})) + 5[/tex]

A cosine function is represented as:

[tex]y = A\cos(B(x + C)) + D[/tex]

Where:

[tex]C \to[/tex] Phase

By comparison:

[tex]C = - \frac{\pi}{3}[/tex]

Hence, the phase is: [tex]- \frac{\pi}{3}[/tex]

Answer:

144 = c - 379

Step-by-step explanation:

"144 is the same as 379 less than c"

144 = c - 379

Answer and Step-by-step explanation:

This can be written in an equation like this:

144 = c - 379

The question is saying that 144 is the same answer as the result of 379 less than c (or c minus 379). This is why we equal 144 to the result of c minus 379.

#teamtrees #PAW (Plant And Water)

Answer:

x=-6

Step-by-step explanation:

For the rational expression, 6x/(x+6) to be undefined, the denominator need to be 0, so x=-6 is the point at which the function is undefined.

The rational expression 6x / (x + 6) is undefined when x equals -6, and it is defined for all other real numbers.

To find the real numbers for which the rational expression 6x / (x + 6) is undefined, we need to identify the values of x that would make the denominator equal to zero. When the denominator is zero, the expression becomes undefined.

In this case, the denominator is (x + 6). Setting the denominator equal to zero, we have:

x + 6 = 0

Solving for x, we subtract 6 from both sides:

x = -6

Therefore, the rational expression 6x / (x + 6) is undefined when x = -6.

When x is equal to -6, the denominator becomes zero, which causes division by zero. Division by zero is undefined in mathematics. Hence, for x = -6, the rational expression is not defined.

For any other real numbers other than x = -6, the expression is defined and can be simplified or evaluated.

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Answer:

I have no clue my bad bro.

Answer:

Mathematical induction can be used to prove that an identity is valid for all integers n≥1. Here is a typical example of such an identity: 1+2+3+⋯+n=n(n+1)2. More generally, we can use mathematical induction to prove that a propositional function P(n) is true for all integers n≥1.

Step-by-step explanation:

I'd really appreciate a brainleast please:)

Answer:

Add 81/4 to both sides.

Step-by-step explanation:

x^2 − 9x − 8 = 0

x^2 - 9x = 8

Take the coefficient of the x term: -9

Divide by 2: -9/2

Square it: 81/4

Add 81/4 to both sides.

Problem 4a

The instructions are incomplete. You set up the recursive formula, but didn't ask any question about said formula.

I'll assume that your teacher wants you to list out a few terms. I'll list out the first five terms.

The notation a_1 = 4 is the same as writing [tex]a_1 = 4[/tex] where the '1' is a subscript. It tells us that the first term is 4.

The nth term a_n or [tex]a_n[/tex] is defined as such

[tex]a_n = 2*(1/3 + a_{n-1})\\\\[/tex]

Notice how if we replaced n with 2, then we get

[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_2 = 2*(1/3 + a_{2-1})\\\\a_2 = 2*(1/3 + a_1)\\\\[/tex]

So the second term is directly tied to the first term, or it is dependent on it.

We'll replace a_1 with 4 to get the following

[tex]a_2 = 2*(1/3 + a_1)\\\\a_2 = 2*(1/3 + 4)\\\\a_2 = 2*(1/3 + 12/3)\\\\a_2 = 2*(13/3)\\\\a_2 = 26/3\\\\[/tex]

So the second term is 26/3.

As you can guess, the third term is going to be found in a similar fashion

[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_3 = 2*(1/3 + a_{3-1})\\\\a_3 = 2*(1/3 + a_2)\\\\a_3 = 2*(1/3 + 26/3)\\\\a_3 = 2*(27/3)\\\\a_3 = 2*(9)\\\\a_3 = 18\\\\[/tex]

So 18 is the third term.

We'll repeat for n = 4 to get the fourth term.

[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_4 = 2*(1/3 + a_{4-1})\\\\a_4 = 2*(1/3 + a_3)\\\\a_4 = 2*(1/3 + 18)\\\\a_4 = 2*(1/3 + 54/3)\\\\a_4 = 2*(55/3)\\\\a_4 = 110/3\\\\[/tex]

The fourth term is 110/3.

Lastly, we'll plug in n = 5

[tex]a_n = 2*(1/3 + a_{n-1})\\\\a_5 = 2*(1/3 + a_{5-1})\\\\a_5 = 2*(1/3 + a_4)\\\\a_5 = 2*(1/3 + 110/3)\\\\a_5 = 2*(111/3)\\\\a_5 = 2*(37)\\\\a_5 = 74\\\\[/tex]

The fifth term is 74.

==============================================================

Problem 4b

Again, the instructions are missing. I'll assume the same thing as problem 4a.

[tex]a_1 = 6[/tex] is the first term

Plug n = 2 into the first equation to get

[tex]a_n = \frac{n}{a_{n-1}}\\\\a_2 = \frac{2}{a_{2-1}}\\\\a_2 = \frac{2}{a_{1}}\\\\a_2 = \frac{2}{6}\\\\a_2 = \frac{1}{3}\\\\[/tex]

The second term is 1/3.

Repeat for n = 3

[tex]a_n = \frac{n}{a_{n-1}}\\\\a_3 = \frac{3}{a_{3-1}}\\\\a_3 = \frac{3}{a_{2}}\\\\a_3 = \frac{3}{1/3}\\\\a_3 = 3\div\frac{1}{3}\\\\a_3 = 3\times\frac{3}{1}\\\\a_3 = 9\\\\[/tex]

The third term is 9

Repeat for n = 4.

[tex]a_n = \frac{n}{a_{n-1}}\\\\a_4 = \frac{4}{a_{4-1}}\\\\a_4 = \frac{4}{a_{3}}\\\\a_4 = \frac{4}{9}\\\\[/tex]

The fourth term is 4/9

Repeat for n = 5

[tex]a_n = \frac{n}{a_{n-1}}\\\\a_5 = \frac{5}{a_{5-1}}\\\\a_5 = \frac{5}{a_{4}}\\\\a_5 = 5 \div a_{4}\\\\a_5 = 5 \div \frac{4}{9}\\\\a_5 = 5 \times \frac{9}{4}\\\\a_5 = \frac{5}{1} \times \frac{9}{4}\\\\a_5 = \frac{5*9}{1*4}\\\\a_5 = \frac{45}{4}\\\\[/tex]

==============================================================

Problem 4c

I'm not much help here for this problem. Not only are the instructions missing, but it's not clear how this sequence is set up. If I had to guess, it's somehow recursively defined. How exactly, I'm not sure. I would ask your teacher for any clarification.

Answer:

75

Step-by-step explanation:

All of the angles within the triangle must add up to 180 degrees. So, angle 2 =50

The angles 4,2,5 also equal 180 because they are on the blue line. Since angle 2=50 and angle 5= 55 angle 4 must be 75 which is needed to add up to 180.

Answer:

Angle 4 is 75°

b represent angle 2

d represent angle 4

70+60+b=180

130+b=180

b=50

55+50+d=180

105+d=180

d=75

Answer:

It will be irrational

Step-by-step explanation:

irrational+rational=irrational

Answer:

616.2442

area to the nearest whole number=616

Step-by-step explanation:

using formula 1/2absinx

where a =44,b=29 ,x=105

1/2x44x29xsin105

44x29=1276

1276÷2=638

638 x sin 105

the sin of 105 is 0.9659

if u are using a four figure table where u can't find 105 under sin of angle

u simply subtract 105 from 180=75

638 x 0.9659 =616.2442

approx.616

Answer: 1 day

Step-by-step explanation:

i took the test lol...

Answer:

the scale factor is 3/4

x = 16×3/4 = 12

Step-by-step explanation:

the only side length we have for both triangles is the short left side.

we see that we get ED from SR and need to transform 4 into 3. how do we do that ?

well,

4×f = 3

f = 3/4

that is the scaling factor, as all side lengths in EDF are created by multiplying the corresponding side in SRT by the same scaling factor (3/4).

therefore,

x = EF = ST×f = 16×3/4 = 4×3 = 12

Answer:

The scale factor is 4/3 and x is 12

Step-by-step explanation:

→ Divide RS by DE

4 ÷ 3 = 4/3

→ Divide the answer by 16

16 ÷ 4/3 = 12

Answer:

Step-by-step explanation:

favorable events for a sum of 3 are 12,21

P(sum 3)=2/36=1/18

favorable events for a sum of 9 are 36,63,45,54

P(sum of 9)=9/36=1/4

9514 1404 393

Answer:

  B)  40

Step-by-step explanation:

Vertical angle XZU has the same measure as the given angle, 130°. It is equal to the sum of right angle XZV and unknown angle UZV. So, ...

  ∠UZV +90° = 130°

  ∠UZV = 40° . . . . . . . . . subtract 90°

Option 4

Verification:-

[tex]\\ \sf\longmapsto x-7y=-49[/tex]

[tex]\\ \sf\longmapsto 7-7(8)=-49[/tex]

[tex]\\ \sf\longmapsto 7-56=-49[/tex]

[tex]\\ \sf\longmapsto -49=-49[/tex]

And

[tex]\\ \sf\longmapsto 10x+9y=142[/tex]

[tex]\\ \sf\longmapsto 10(7)+9(8)=142[/tex]

[tex]\\ \sf\longmapsto 70+72=142[/tex]

[tex]\\ \sf\longmapsto 142+142[/tex]

Hence verified

Answer:

4.

Step-by-step explanation:

1. 8x - y = 48

9x + 10y = 142

8(7) - 8 = 48

9(7) + 10(8) = 143

No

2. 9x - y = 55

8x + 10y = 140

9(7) - 8 = 55

9(7) - 10(7) = -24

No

3. x-6y=-41

8x + 9y = 127

7 - 6(8) = -41

8(7) + 9(8) = 128

No

4. x-7y=-49

10x + 9y = 142

7 - 7(8) = 49

10(7) + 9(8) = 142

Yes

Answer:

177.3 feet

This is a classic find the vertex of a parabola question.

if this was a calculus class the solution would be to take the derivative and set it equal to zero... -32t+ 105 = 0

BUT i assume that you are not in a calculus class..

so we try plan "B" the  highest (or lowest) point of parabola is it's vertex

the vertex formula is [-b/2a,f(-b/2a)]

in your problem a = -16, b=105, c= 5

so the "X" (TIME) is located at -(105)/(2*-16) = 3.28

plug in 3.28 into -16(3.28)^2 + 105(3.28) + 5 = 177.27

and you will get

Step-by-step explanation:

Answer:

The standard deviation for the number of defective parts in the sample is 1.88.

Step-by-step explanation:

The sample is with replacement, which means that the trials are independent, and thus, the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.  

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

68 defective out of 400:

This means that [tex]p = \frac{68}{400} = 0.17[/tex]

From the shipment you take a random sample of 25.

This means that [tex]n = 25[/tex]

Standard deviation for the number of defective parts in the sample:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{25*0.17*0.83} = 1.88[/tex]

The standard deviation for the number of defective parts in the sample is 1.88.

The standard deviation of the situation is 1.88

The proportion of success is calculated as:

[tex]p = \frac xn[/tex]

So, we have:

[tex]p = \frac {68}{68 + 332}[/tex]

[tex]p = 0.17[/tex]

The standard deviation is then calculated as:

[tex]\sigma= \sqrt{np(1-p)}[/tex]

For a shipment of a random sample of 25, we have:

[tex]\sigma= \sqrt{25 * 0.17 * (1-0.17)}[/tex]

Evaluate the product

[tex]\sigma= \sqrt{3.5275}[/tex]

Evaluate the root

[tex]\sigma= 1.88[/tex]

Hence, the standard deviation of the situation is 1.88

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Answer:

point E

Step-by-step explanation:

it lies after 1 and before two and 1.6 bar is after 1 and before 2

30,20 and 10

30 + 20 + 1/3×30 = 60

50 + 10 = 60

60 = 60

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Answer:

Step-by-step explanation:

Answer:

128/3

Step-by-step explanation:

The sequence follow the rule (1/6)*(4)^(n-1). The 5th term will be (1/6)*(4)^4=128/3

Answer:

128/3

Step-by-step explanation:

1/6, 2/3, 8/3, . . .

1/6, 4/6, 16/6

We are multiplying by 4 each time

1/6 *4 = 4/6

4/6 * 4 = 16/6

This is a geometric sequence with the common ratio of 4

an = a1 (r)^(n-1)

an = 1/6 (4) ^(n-1)

Let n = 5

a5 = 1/6 (4)^(5-1)

a5 = 1/6 (4)^4

a5 = 1/6 * 256

a5 =128/3

X1=-2 and x2=1

You would just need to plug the first y equation value into the 2nd equation to get what I got in the photo. Then solve for the x’s to get the coordinates.

Answer:

b = h*D +hg^3

Step-by-step explanation:

b/h = D +g^3

Multiply each side by h

h* b/h = h*D +hg^3

b = h*D +hg^3

Answer:

60.5/25

2 21/50

Step-by-step explanation:

60.5/25

Equals

2 21/50

Answer:

-64

Step-by-step explanation:

-8^2

-8( -8)

=-64

The solutions are where the two lines cross over each other.

(0,3) and (4,-5)