Which expression is equivalent to the given expression after using the distributive property?

6 · 13 + 6 · 7


6 · 7(13 + 6 )

6 · 7(13 + 6 )

6 · (13 + 6) · 7

6 · (13 + 6) · 7

6 (13 + 7)

6 (13 + 7)

6(13 + 6) + 7

6(13 + 6) + 7

Answer:

37degrees

Step-by-step explanation:

In order to get the required angle, we will use the SOH, CAH, TOA identity.

Let;

Adjacent = 60m

Opposite = 45m

According to TOA:

tan theta = opp/adj

tan theta = 45/60

tan theta = 0.75

theta = arctan 0.75

theta =  36.86

Hence the  angle, to the  nearest degree, between her path and the longest side of the playground is 37degrees

The optimal solution is Z = -74, X = 4, Y = 2.

Maximize Z = 20X + 3Y

Subject to:

A1: 2X + Y + S1 = 10

R2: 3X + 3Y + S2 = 18

R3: 2X + 4Y + S3 = 20

X = 0, Y ≥ 0

The initial tableau for the simplex method is given below.

The column labels represent the variables, and the row labels represent the equations and slack variables. The bottom row (RHS) represents the right-hand side values of the equations.

To find the optimal solution, we'll perform the simplex method iterations:

Iteration 1:

Pivot column: Y (the most negative coefficient in the Z row)

Pivot row: S2 (smallest positive ratio of RHS to coefficient in the pivot column)

Performing row operations:

Divide row S2 by 3 to make the pivot element (coefficient of Y) equal to 1.

Row S2 = Row S2 / 3

Row S2: 1 | 1 | 0 | 1/3 | 0 | 6

Eliminate other elements in the pivot column:

Row Z = Row Z - (3 * Row S2)

Row S1 = Row S1 - (1 * Row S2)

Row S3 = Row S3 - (0 * Row S2)

Row Z: 20 | 0 | 0 | -3 | 0 | -18

Row S1: 1 | 0 | 1 | -1/3 | 0 | 4

Row S3: 2 | 1 | 0 | -2/3 | 1 | 14

Iteration 2:

Pivot column: X (the most negative coefficient in the Z row)

Pivot row: S1 (smallest positive ratio of RHS to coefficient in the pivot column)

Performing row operations:

Divide row S1 by 1 to make the pivot element (coefficient of X) equal to 1.

Row S1 = Row S1 / 1

Row S1: 1 | 0 | 1 | -1/3 | 0 | 4

Eliminate other elements in the pivot column:

Row Z = Row Z - (20 * Row S1)

Row S2 = Row S2 - (0 * Row S1)

Row S3 = Row S3 - (2 * Row S1)

Row Z: 0 | 0 | -20 | -2/3 | 0 | -74

Row S2: 1 | 1 | 0 | 1/3 | 0 | 6

Row S3: 0 | 1 | -2 | -2/3 | 1 | 6

Since there are no negative coefficients in the Z row, we have reached the optimal solution.

Final Solution:

Z = -74 (maximum value of the objective function)

X = 4

Y = 2

S1 = 0

S2 = 6

S3 = 6

Therefore, the maximum value of Z is -74, and the optimal values for X and Y are 4 and 2, respectively. The slack variables S1, S2, and S3 are all zero, indicating that all the constraints are satisfied as equalities.

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Answer:

The unknown angles are 45 and 63

Step-by-step explanation:

5x + 7x + 72 = 180 (angle sum property)

12x + 72 = 180

12x = 180 - 72

12x = 108

x = 108/12

x = 9

Therefore, 5x = 5*9 = 45

                7x = 7*9 = 63

The measure of the angels are as follows

The angles and sides are worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The directions described on a right triangle is assumed to be

opposite = leg XY = 18 metes

adjacent = leg YZ = 24 meters

hypotenuse = leg XZ = ?

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 18² + 524²

x = √900

x = 30 meters

The angles

let the angle be x

angle YZX

tan x = Opposite / Adjacent

tan x = 18 / 24

tan x = 0.75

x = arc tan 0.75

x = 36.87 degrees

angle YXZ = 90 - 36.87 = 53.13 degrees

The missing side is 30meters while the angles are  YXZ = 53.13 degrees and angle YZX= 36.87 degrees

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Answer: B

Step-by-step explanation:

Process of elimination...

anything positive is automatically greater than any negative, so that rules out A and C.

D is the tricky one. Remember, smaller portions of a whole are greater than larger portions. Think of it this way, if you cut two candy bars into pieces; one into thirds and one into fourths. One third would be greater than one fourth. So, 11 thirds would also be greater than 11 fourths.

Answer:

-1/3, -1/4, -3/10, -1/8, -1/16, 1/3, 1/4, 3/10, 1/8, 2/5.

Step-by-step explanation:

-2/5 is -0.4 and 1/2 is 0.5

Ten rational numbers in between are, -0.33333 (-1/3), -0.25 (-1/4), -0.3 (-3/10), -0.125 (-1/8), -0.0625 (-1/16), 0.33333 (1/3), 0.25 (1/4), 0.3 (3/10), 0.125 (1/8), 0.4 (2/5)

Answer:

\({ \rm{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }} \\ \)

Answer:

y=-2+8

Step-by-step explanation:

The answer is y=-2+8 because of course the slope has to be -2 as you stated in your Question. So all you have to do is change the Y-Intercept until you reach the point. Since the Slope is negative, the Y-Intercept will rise until you reach your point. You may double check my answer to see if it is right, it is up to you. If you find any fault in my answer please let me know. Have a good day!

Answer:

0 because we can't have Repetitious x in function.

The equation of the line tangent  to the curve at the points , y = 8ex cos(x), (0, 8) as calculated is y' = 0.

We will differentiate y = 4ex cos(x) so as to find the required equation.

we get the differential as ,

y' = - 8eˣsin(x)

given the value of x as 0 and y as 8

y' = -8e⁰sin(0)

Now as we know that the value of sin( 0 ) is 0 , therefore the equation becomes,

y'= 0  

Differentiation is a branch of calculus which is used to calculate the rate of change in a given object in a specified time. The other  branch of calculus is integration.

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Answer:

\( \sqrt{9 } = 3 \)

The 1930s was a period of significant change in the U.S. entertainment industry, with the emergence of new technologies and the development of new forms of media. Here are some of the key changes that took place:

Overall, the 1930s was a period of significant change in the U.S. entertainment industry, with the rise of new technologies and the emergence of new forms of media leading to the development of new genres and changing audience preferences.

Yes, infrared spectroscopy would indeed be helpful in determining,

if the dehydration reaction of cyclohexanol to form cyclohexene was successful in an organic chemistry lab.

Infrared spectroscopy (IR spectroscopy) is a widely used analytical technique in organic chemistry,

That provides information about the functional groups present in a compound.

It measures the absorption of infrared radiation by the sample,

Which corresponds to the vibrations of different chemical bonds in the molecule.

In the case of cyclohexanol and cyclohexene, there is a significant difference in their functional groups.

Cyclohexanol contains an -OH group alcohol, whereas cyclohexene contains a carbon-carbon double bond alkene.

These functional groups have characteristic absorption bands in the IR spectrum.

By comparing the IR spectra of the starting material cyclohexanol and the desired product cyclohexene.

One can determine if the dehydration reaction was successful.

The presence or absence of characteristic absorption bands for the alcohol (-OH) and the alkene (C=C).

In the product spectrum can provide evidence of the reaction's success.

If the desired cyclohexene is formed, the absorption band corresponding to the -OH group should disappear,

Indicating the removal of the alcohol functionality.

Additionally, a new absorption band corresponding to the C=C bond should appear in the product spectrum.

Therefore, IR spectroscopy can be a valuable tool in confirming the success of the dehydration reaction and characterizing the functional groups present in the resulting product.

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Answer: 280 squrriels, 488 animals in total

Step-by-step explanation:

If you want to solve the amount of squrriels this is what you would do:

1.Ratio => 3:5=168:x

2. Cross Multiply => 840=3x

3. Simplify => x= 280

280 squrriels

If you want to solve for total:

Add the amount of squrriels and bunnies:

=> 280+168=448

488 animals in total

Have a nice day! :D

Answer:

Squirrels = 280

Total Animals: 448

Step-by-step explanation:

Every 3 bunnies there were 5 squirrels.

So what happens if there are 168 bunnies?

The equation to solve this is  3:5 = 168:x

1. Get a calculator, because with a calculator it's easier to solve.

2.  Convert into fraction form. 3/5 = 168/x

3. Multiply the 2 numbers diagonal from each other.

4. 3x=840

5. Divide both numbers by 3.

6. You get x=280

To get total animals.

1. Get a calculator or a piece of paper. (your choice)

2. Add 168+ 280, because there are 168 bunnies and 280 squirrels.

3. There are 448 animals in the problem.

The number of fourths which we have in 3 1/2, in the simplest form,​ is 14 fourths.

The word fourth means a value coming after the third in order, position, time, etc. Often written as in 4th. To find the answer, we need to convert the mixed number 3 1/2 into an improper fraction.

:. 3 1/2 = (3 x 2 + 1)/2

:. = 7/2

Now, we can divide 7/2 by 1/4 to find out how many fourths are in 3 1/2:

= (7/2) ÷ (1/4)

= (7/2) x (4/1)

= 28/2

= 14

Therefore, there are 14 fourths in 3 1/2.

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The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is  52!/(47! * 5!).

The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is 52 choose 5, which is equal to 52!/(47! * 5!), where the exclamation point indicates the factorial function. This is known as the binomial coefficient, and it represents the number of ways to choose a certain number of items from a larger set. In this case, the binomial coefficient is used to find the number of ways to choose 5 cards from a deck of 52 cards.

The order of the cards is irrelevant in card games like poker. A five-card draw of 1,2,7,9, K is equivalent to a draw of K,7,9,1,2. What counts is the fundamental overall group.

Order is irrelevant, therefore we utilize a combination (instead of a permutation)

We will substitute n = 52 and r = 5 into the nCr combination formula, which is n C r = (n!)/(r!*(n-r)!)

so we obtain:

n C r = r!*(n-r)!/(n!)

52 C 5 = (52!)/(5!*(52-5)!)

52 C 5 = (52!)/((52-5)!*5!)

The complete question is:-

Which expression can you use to find the number of ways to choose 5 cards from a 52-card deck?

a) (52-5)! / 52!5!

b) 52! / (52-5)!

c) 52! / (52-5)!5!

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The period of the function f(x) = sin¹x + cos4x is 2π. Option (3) is the correct answer.

A periodic function is a function whose values repeat at regular intervals or periods. The period of a periodic function is the distance or length of a period in the horizontal direction.In the given function, f(x) = sin¹x + cos4x, the period of sin¹x is π, and the period of cos4x is 2π/4 or π/2.

Therefore, the period of the given function is the least common multiple (LCM) of π and π/2, which is 2π. Hence, option (3) is the correct answer. The period of the function f(x) = sin¹x + cos4x is 2π. The period of a periodic function is the distance or length of a period in the horizontal direction.

In the given function,

f(x) = sin¹x + cos4x, the period of sin¹x is π, and the period of cos4x is 2π/4 or π/2.

Therefore, the period of the given function is the least common multiple (LCM) of π and π/2, which is 2π. Hence, option (3) is the correct answer.

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Answer:

If u r using rise/run, then it is 6/4

Step-by-step explanation:

The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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The integral ∫∫s xyz ds, over the given surface s, is equal to √2 ∫∫r ρ^3cosθsinθ(4-y) dρdθ, where r is the region in the xy-plane bounded by the cylinder x^2+y^2=4.

To evaluate the given integral ∫∫s xyz ds, where s is the part of the plane z=4−y that lies in the cylinder x^2+y^2=4, we can use the method of our choice. Let's use the method of cylindrical coordinates.

1. Set up the surface integral for the given function over the given surface s as a double integral over a region r in the xy-plane.
  ∫∫s xyz ds = ∫∫r xyz √(1 + (∂z/∂x)^2 + (∂z/∂y)^2) dA

2. To find the region r, we need to determine the bounds for the cylindrical coordinates. Since the cylinder has radius 2, we have 0 ≤ ρ ≤ 2. The z-coordinate ranges from the plane z = 4-y to the plane z = 0. Thus, the bounds for z are 0 ≤ z ≤ 4-y.

3. Convert the integral into cylindrical coordinates by substituting x = ρcosθ and y = ρsinθ.
  ∫∫r xyz √(1 + (∂z/∂x)^2 + (∂z/∂y)^2) dA
  = ∫∫r ρ^3cosθsinθ(4-y) √(1 + (-sinθ)^2 + (-cosθ)^2) dρdθ

4. Evaluate the double integral by integrating with respect to ρ first and then θ.
  ∫∫r ρ^3cosθsinθ(4-y) √2 dρdθ
  = √2 ∫∫r ρ^3cosθsinθ(4-y) dρdθ

Therefore, the integral ∫∫s xyz ds, over the given surface s, is equal to √2 ∫∫r ρ^3cosθsinθ(4-y) dρdθ, where r is the region in the xy-plane bounded by the cylinder x^2+y^2=4.

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Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Answer:

Wendy will think cookie club chocolate cookies are not chocolatey enough

Step-by-step explanation:

Wendy thinks the perfect chocolate chip cookie has 35 chocolate chips for every 5 ounces of dough. Cookie Club makes batches of chocolate chips cookies with 100 chocolate chips and 15 ounces of dough. What will Wendy think about Cookie Club's cookies?

Perfect chocolate chip cookie=35 chocolate chips for every 5 ounces of dough

Wendy's perfect chocolate chip cookies = 35 chocolate chips for every 5 ounces of dough

= 35 : 5

=7:1

Cookie club chocolate chips cookies=100 chocolate chips for every 15 ounces of dough

=100 : 15

=20 : 3

Cookie club chocolate cookies have 3 times the amount of dough

Therefore,

Wendy will think cookie club chocolate cookies are not chocolatey enough

Answer:

Not choclatey enough

Step-by-step explanation:

Answer:

133°

Step-by-step explanation:

angles on a straight line = 180°

180 - 144 = 36°

angles in a triangle = 180°

36 + 31 = 67

180 - 67 = 113

answer = 113°

Answer:

Step-by-step explanation:

mid point=((-2+16)/2,(8+4)/2)=(7,6)

The spillage refer to Cyber Awareness Challenge 2022 is explained below.

The Cyber Awareness Challenge 2022 is an important event that focuses on raising awareness about the dangers and risks associated with the use of technology and the internet.

In this context, spillage refers to the accidental or unintentional release of sensitive information. This can be caused by a variety of factors, including human error, technical glitches, and malicious attacks.

In addition, the challenge will explore the consequences of spillage, such as identity theft, financial loss, and reputational damage. This is why it is so important to take the challenge seriously and to understand the importance of cyber awareness and security.

By participating in the Cyber Awareness Challenge 2022, students will gain valuable skills and knowledge that will help them protect themselves and their information in the digital world

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Answer:

24

Step-by-step explanation:

knowing a parallelogram, JK = ML

so,

14 + 2x = 5x – 1

2x – 5x = –14 –1

–3x = –15

3x = 15

x = 5

substitute x=5 into 14 + 2x

14 + 2(5) = 24

Answer: Yes, you will make it on time

Step-by-step explanation:

The distance from San Antonio to Dallas is 274 miles

We take 274 divided by 65 = 4.2 hours or 4 hours and 12 minutes to get there at the speed of 65 mph

We have 4 1/2 hours to get there

4 1/2 hours = 4 hours 30 minutes

So, you will make it on time!