Find the value of:
\( \rm \: \frac{2}{7} \: of \: 1 \: week\)
​

Answer:

the minimum work he can do to complete it in 3 days is 1/3.

So he should do at least 1/3 of the work each day to complete it on time.

Answer = 1/3

Step-by-step explanation:

Answer:

x = 30

y = 68

z = 82

Step-by-step explanation:

Let the first angle be X, the second angle be Y, and the third angle be Z.

You can write these 3 equations to represent the relationships between the angles:

\(x+y+z=180\\y+z=5x\\z=y+14\)

Step 1. Z is already isolated in the 3rd equation, so the first thing I would do is use that to eliminate the Z in the 1st and 2nd equations.

\(z=y+14\\\\x+y+z=180\\x+y+(y+14)=180\\\\y+z=5x\\y+(y+14)=5x\)

Step 2. Now, simplify both of those and treat them like a system of 2 equations. I'll simplify the top equation first and solve for x:

\(x+y+(y+14)=180\\x+y+y+14=180\\x+2y+14=180\\x+2y=166\\x=166-2y\)

Plug that into the other equation:

\(y+(y+14)=5x\\y+y+14=5(166-2y)\\2y+14=830-10y\\12y+14=830\\12y=816\\y=68\)

Step 3. Now we have the value of one variable. Use that to solve for x in the previous equation:

\(x=166-2y\\x=166-2(68)\\x=166-136\\x=30\)

Step 4. Now we have two variables. Pick any of the original 3 equations you want to solve for z:

\(x+y+z=180\\30+68+z=180\\98+z=180\\z=82\)

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

Finally, you can confirm that by plugging these into all of the original equations to make sure they meet the conditions.

\(30+68+82=180\\180=180\\\\68+82=5(30)\\150=150\\\\82=68+14\\82=82\)

Answer:

-x=50

Step-by-step explanation:

answer

The ratios are;

Sin θ =  5/6

Cos θ = √11/6

Tan θ =  5√11/11

Sec  θ =  6√11/11

Cosec  θ = 6/5

Cot θ =  √11/5

These trigonometric ratios are used to relate the angles of a right triangle to the lengths of its sides

We can see that the hypotenuse is obtained from;

x =√\((10)^2 + (2\sqrt{} 11)^2\)

x = √100 + 44

x = 12

Then;

Sin θ = 10/12 = 5/6

Cos θ =  2√11/12

= √11/6

Tan θ = 10/2√11

= 20√11/44

= 5√11/11

Sec  θ =  1/Cos  θ

=  6/√11

= 6√11/11

Cosec  θ = 1/Sin

 θ = 6/5

Cot θ = 1/tan θ

= 11/ 5√11

= 55√11/275

= √11/5

Sinβ = 2√11/12

= √11/6

Cos β = 10/12

= 5/6

Tan β = 2√11/10

= √11/5

Sec β = 6/5

Cosec β = 6√11/11

Cot β = 5√11/11

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Answer:

Step-by-step explanation:

Given that;

the following procedure for accomplishing our task are:

1. Flip the coin.

2. Flip the coin again.

From here will know that the coin is first flipped twice

3. If both flips land on heads or both land on tails, it implies that we return to step 1 to start again. this makes the flip to be insignificant since both flips land on heads or both land on tails

But if the outcomes of the two flip are different i.e they did not land on both heads or both did not land on tails , then we will consider such an outcome.

Let the probability of head = p

so P(head) = p

the probability of tail be = (1 - p)

This kind of probability follows a conditional distribution and the probability  of getting heads is :

\(P( \{Tails, Heads\})|\{Tails, Heads,( Heads ,Tails)\})\)

\(= \dfrac{P( \{Tails, Heads\}) \cap \{Tails, Heads,( Heads ,Tails)\})}{ {P( \{Tails, Heads,( Heads ,Tails)\}}}\)

\(= \dfrac{P( \{Tails, Heads\}) }{ {P( \{Tails, Heads,( Heads ,Tails)\}}}\)

\(= \dfrac{P( \{Tails, Heads\}) } { {P( Tails, Heads) +P( Heads ,Tails)}}\)

\(=\dfrac{(1-p)*p}{(1-p)*p+p*(1-p)}\)

\(=\dfrac{(1-p)*p}{2(1-p)*p}\)

\(=\dfrac{1}{2}\)

Thus; the probability of getting heads is \(\dfrac{1}{2}\) which typically implies that the coin is fair

(b) Could we use a simpler procedure that continues to flip the coin until the last two flips are different and then lets the result be the outcome of the final flip?

For a fair coin (0<p<1) , it's certain that both heads and tails at the end of the flip.

The procedure that is talked about in (b) illustrates that the procedure gives head if and only if the first flip comes out tail with probability 1 - p.

Likewise , the procedure gives tail if and and only if the first flip comes out head with probability of  p.

In essence, NO, procedure (b) does not give a fair coin flip outcome.

Answer:

x=10, z=97

Step-by-step explanation:
For X:

Since 83 and (13x-47) are vertically opposite they are equal:

13x-47=83

Add 47 to both sides:

13x-47+47=83+47

Simplify:

13x=130

Divide both sides by 13:

13x÷13=130÷13

Simplify:

x=10

For Z:
The angles (13x-47) and z are on a straight line so we can equate the sum of these 2 to 180:

(13x-47)+z=180

Substitute value of x worked out from previous working out:

13(10)-47+z=180

Simplify:

130-47+z=180

83+z=180

Subtract 83 from both sides:

83+z-83=180-83

Simplify:

z=97

Answer: x=1+1/3

Step-by-step explanation: -(3x-12)=9x-4

We move all terms to the left:

-(3x-12)-(9x-4)=0

We get rid of parentheses

-3x-9x+12+4=0

We add all the numbers together, and all the variables

-12x+16=0

We move all terms containing x to the left, all other terms to the right

-12x=-16

x=-16/-12

x=1+1/3

The point charges placed 0.500 m apart are 10.4 nC and 43.9 nC. Then, the electric field halfway between these charges will be -4824 N/C.

The physical field that surrounds particles with an electrical charge is called an electric field. All other charged particles in the field are affected by it, either being attracted to it or being repelled by it.

The electric field because of a point charge q is written as \(E=\frac{kq}{r^2}\)

Positive point charges cause the electric field to point away from the point, whereas negative point charges cause the electric field to point in the direction of the point. Then, the electric field of the midpoint p in the diagram is written as,

\(\begin{aligned}E_p&=\mathrm{\frac{k(10.4\;nC)}{(0.25\;m)^2}-\frac{k(43.9\;nC)}{(0.25\;m)^2}}\\&=\mathrm{\frac{k(10.4-43.9)\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{\frac{9\times 10^9\;Nm^2/C^2\times 33.5\times10^{-9}\;C}{(0.25\;m)^2}}\\&=-\mathrm{4824\;N/C}\end{aligned}\)

The required answer is -4824 N/C.

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Answer:

answer is 1,080

Step-by-step explanation:

45×24=1,080

Answer:

a=65, m=−1

a=65, m=1

Step-by-step explanation:

Answer:

-1 is the answer to A, hope this helps

Answer:

6/4 or 1 1/4

Step-by-step explanation:

1/4 times 6 because the question is asking for the recipe to be made 6 times. So 1/4 times 6 or 1/4 time 6/1 is 6/4 or 1 1/4.

Answer:

2/3 cups

Step-by-step explanation:

if we put all ingredients toghether will have

1/4+2/3+1 and 1/3=1/4+1 and 2/3+1/3=1/4+ 2= 2cups and 1/4 or 2.25 cups

So 2.25 cups is 1 batch of dressing

          6 cups is x batches of dressing

cross multiply x=6*1/2.25= 6/2.25

so insted of 1/4 vineger will need (1/4)(6/2.25)=6/9=2/3 cups of vinegar

Answer:

c) 113°

Step-by-step explanation:

Exterior angle is equal to the sum or the "remote" interior angles, that is the two angles that are not just next to the exterior angle. See image.

So the answer, quickly:

exterior angle

= 65° + 48°

= 113°

This is why:

(skip if you don't care)

The three angles in a triangle add up to 180° But also, a linear pair of angles also add up to 180°

So

x + 65° + 48° = 180°

x + y = 180°

y = 65° + 48°

See image.

The values of tht missing part of the triangle are;

A= 20.9°

a = 13.06

c = 33.6

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find side c

sinB/b = sinC/c

sin45.9/26.30 = sin113.2/c

csin 45.9 = 26.30 × sin113.2

0.718c = 23.90

c = 23.90/0.718

c = 33.6

Angle A = 180-(113.2+ 45.9)

angle A = 20.9°

sinA/a = sinB/b

sin20.9/a = 0.718/26.30

0.357 × 26.30 = 0.718a

a = 9.389/0.718

a = 13.06

Therefore A = 20.9°

a = 13.06

c = 33.6

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Answer:

I think it's A.

Step-by-step explanation:

I hope it is helpful to you

By definition of proportion, the value of x is,

⇒ x = 80

We have to given that;

In a triangle,

Perpendicular = 60

Now, By Pythagoras theorem we get;

60² = 36² + y²

3600 = 1296 + y²

y² = 3600 - 1296

y² = 2304

y = 48

Hence, By definition of proportion;

⇒ x / 48 = 60 / 36

⇒ x = 80

Thus, By definition of proportion, the value of x is,

⇒ x = 80

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Answer:

$15798.4

Step-by-step explanation:

We will have to use this formula A = Peᵃᵇ

A = Final amount

P = Initial amount (12,000)

e = Mathematical constant: 2.7183

a = Interest rate (5.5% or 0.055)

b = Years

So our equation will look like this

A = 12,000e⁵ ⁰·⁵⁵

A = 12,000(2.7183)·²⁷⁵

A = 12,000(1.316533)

A = 15798.396

Answer:

the expression is invented

Answer:

AB is not a tangent. The lengths 4, 12, and 13 do not form a right triangle.

√(4^2 + 12^2) = √160, which is not equal to 13.

Answer:

No

Step-by-step explanation:

if AB is a tangent the the angle BAC = 90°

using Pythagoras' theorem

then square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

BC² = 13² = 169

AB² + AC² = 12² + 4² = 144 + 16 = 160

since BC²≠ AB² + AC²

then Δ ABC is not a right triangle so AB is not a tangent

Answer:

Step-by-step explanation:

Remember PEMDAS

7+(2x4)-8÷(12-6)x(6÷2)​

7 + 8 - 8 : 6 × 3 =

7 + 8 - 8/6 × 3 =

7 + 8 - 4 =

11

The number of points to be removed from the graph is 2

from the question, we have the following parameters that can be used in our computation:

The graph

From the graph, we can see that

2 points have the same y coordinates

Another 2 points have the same y coordinates

For it to be a function, one of the 2 points must be removed each

So, we have the number of points to be removed from the graph is 2

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37.5w + 155.95 = 455.95; where w = 8; signifies the number of weeks required to babysit the business in order to purchase the gaming chair.

A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality.

Equations can be categorized as identities or conditional equations.

w = (455.95-155.95)/(37.50)

=300/37.50

=8

So, number of weeks = 8

As a result, w = 8 and 37.5w + 155.95 = 455.95 is the solution.

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Let us see how we can solve this step by step each :

6417 ÷ 31 , we divide 64 by 31 and get the resulting quotient as 2 .

Then we bring down 1 . So , the number below is 21 , which cannot be divided by 31 .

So , we will have to bring down 7 for which we have to add a 0 to the quotient . Then the quotient will become 20 as of now .

As 217 is divisible by 3 , I put seven near 21 , making the quotient as 217 and get the remainder 0 .

Hence in the correct solution the correct quotient = 207 .

But the same thing has not been done in Xavier's solution as he has put a 0 after 7 instead of putting it before 7 . Hence , Xavier's mistake is that he put the 0 after 7 instead of putting it before 7 .

In Xavier's solution the quotient is = 270

Therefore , Xavier's mistake is that he put the 0 after 7 instead of putting it before 7 .

Answer: The two numbers are $x = 5$ and $y = 7.5$.

Step-by-step explanation:

Let the two numbers be $x$ and $y$, where $x < y$. We can write the two given statements as the following two equations:

$$2y = 3x + 15$$

$$\frac{1}{5}x + \frac{1}{9}y = 10$$

We can solve this system of equations using elimination. Multiplying the first equation by 5 and the second equation by 9, we get

$$10y = 15x + 75$$

$$9x + y = 90$$

Subtracting these equations, we get

$$8y - 9x = 15$$

Multiplying this equation by 8, we get

$$64y - 72x = 120$$

Adding this equation to 5 times the first equation, we get

$$69y - 72x = 120 + 75$$

$$69y - 72x = 195$$

Dividing both sides by 3, we get

$$23y - 24x = 65$$

Subtracting this equation from 4 times the second equation, we get

$$96y - 36x = 360 - 260$$

$$96y - 36x = 100$$

Dividing both sides by 60, we get

$$\frac{16}{3}y - \frac{6}{5}x = \frac{5}{3}$$

Substituting the expression for $y$ from the first equation, we get

$$\frac{16}{3}(3x + 15) - \frac{6}{5}x = \frac{5}{3}$$

This simplifies to

$$\frac{16}{5}x + \frac{64}{5} = \frac{5}{3}$$

Solving for $x$, we find that $x = 5$. Substituting this value into the first equation, we find that $y = 15/2 = 7.5$. Therefore, the two numbers are $x = 5$ and $y = 7.5$.

Answer:

me

Step-by-step explanation:

becaus im the bes guy

The maximum revenue possible in this situation is 15625/A dollars, where A is the coefficient in the quadratic equation.

To find the maximum revenue possible in this situation, we can use the concept of vertex or the vertex form of a quadratic equation.

The revenue equation is given by R = -Ax^2 + 250x, where A is a constant coefficient.

The maximum revenue occurs at the vertex of the parabolic curve represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, a = -A and b = 250. Plugging in these values, we get:

x = -250 / (2 * (-A))

= 125 / A

To find the maximum revenue, we substitute this value of x into the revenue equation:

R = -A * (125 / A)^2 + 250 * (125 / A)

= -A * (15625 / A^2) + (31250 / A)

= -15625 / A + 31250 / A

= 15625 / A

The maximum revenue is given by 15625 / A. The value of A is not specified in the question, so we cannot determine the exact maximum revenue without knowing the value of A. However, we can say that the maximum revenue increases as A decreases.

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Answer:

specific line

Step-by-step explanation:

An ordered pair satisfies the equation is the point lies on the specific line​