whats the puzzle answer? i need help on this

The term, [tex]\frac{1}{49}[/tex] is simplified form of the expression [tex]7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}[/tex].

The top and bottom of a fraction are said to be in its simplest form if they only share the number one. For the top & bottom to remain whole numbers, you cannot divide them further.

Additionally, lowest terms, or simple form, may be used.

The simplest form of a fraction, for instance, is 4/5. Apart from 1, there isn't a number that divides both 4 and 5. Not in its simplest form is the fraction 3/6. Numerator & denominator can both be divided by 3.

Given to simplify the expression

[tex]7^{-\dfrac{5}{6}} \ \cdot\ 7^{-\dfrac{7}{6}}[/tex]

[tex]7^{(-\dfrac{5}{6}-\dfrac{7}{6})}[/tex]

[tex]7^{(\dfrac{-5-7}{6})}[/tex]

[tex]7^{(\dfrac{-12}{6})}[/tex]

[tex]7^{(-2)}[/tex]

[tex]\dfrac{1}{7} \times \dfrac{1}{7}[/tex]

[tex]\dfrac{1}{49}[/tex]

Thus, [tex]\frac{1}{49}[/tex] is simplified form of the expression [tex]7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}[/tex].

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You will need 280 cups of cranberry juice and 56 cups of Sprite to make 56 cups of the famous punch.

What is the ratio definition?

A ratio is a mathematical comparison of two or more values or quantities. It is usually written as a fraction, with the first value or quantity being the numerator and the second value or quantity being the denominator.

To make 56 cups of famous punch using the ratio of 5 cups of cranberry juice to 2 cups of Sprite, you can use the following method:

Write the ratio of cranberry juice to Sprite as a fraction: 5 cups cranberry juice / 2 cups sprite

Multiply the fraction by the desired number of cups of punch: (5 cups cranberry juice / 2 cups sprite) x 56 cups punch

Simplify the equation by cross-multiplying: 5 cups cranberry juice x 56 cups punch = 2 cups sprite x 56 cups punch

Solve for the number of cups of cranberry juice: 5 cups cranberry juice x 56 cups punch = 280 cups of cranberry juice

To find the amount of Sprite use the ratio 5:2, meaning you have to use 2 cups of sprite for every 5 cups of cranberry juice. So use 280/5*2 = 56 cups of sprite

Hence, you will need 280 cups of cranberry juice and 56 cups of Sprite to make 56 cups of the famous punch.

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The expansion of 1/4(x - 12) is x/4 - 3

In order to expand and simplify an expression, we need to multiply out the parentheses and then simplify the resulting expression by collecting the like terms. Expanding brackets (or multiplying out) is the process by which we remove parentheses. It is the reverse process of factorisation.

For example 4(3-y) can be expanded by multiplying the factor 4 by 3 and y = 12- 4y

Similarly the expression 1/4(x - 12) can be expanded by firstly multiply the factor ¼ by x and 12

therefore 1/4(x - 12) = 1/4×x -12×1/4

= x/4 - 3

Therefore the expansion of 1/4(x - 12) is x/4 -3

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The option that will cost less money from Regina is $8 a class.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Since the cost for the classes at the community center is $72, plus an additional one-time fee of $12 to rent

the yoga equipment used in class. The amount will be:

= $72 + $12

= $84

The other cost at $8 a class for 2 weeks will be:

= $8 × 10 days

= $80

The second option is cheaper.

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Yoga classes are offered 2 days a week for 6 weeks

at both the community center and the local gym.

The cost for the classes at the community center is

$72, plus an additional one-time fee of $12 to rent

the yoga equipment used in class. The cost at the

local gym is $8 a class. Regina wants to know which

class she can take for less money.

The first lefty is the fifth person chosen is7.45%

There are some lefties among the 5 people is, 50.16%

The first lefty is the fifth person chosen is

[tex](.87)^4(.13)=.07447=7.45 \%[/tex]

There are some lefties among the 5 people is,

[tex]$$1-(.87)^5=.50157=50.16 \%$$[/tex]

The first lefty is the second or third person.

[tex]$(.87)(.13)+(.87)^2(.13)=.211497=21.15 \%_0$[/tex]

There are exactly 3 lefties in the group.

[tex]$(5, .13,3)=.0166=1.66 \%$[/tex]

There are at least 3 lefties in the group,

[tex]1 \text { - binomadf }(5, .13,2)=.0179=1.79 \%[/tex]

There are no more than 3 lefties in the group

[tex]\text { binomcdf }(5, .13,3)=.9987=99.87 \%[/tex]

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[tex]44+\cfrac{7}{8}r\implies 44+\cfrac{7}{8}\left( -\cfrac{1}{2} \right)\implies 44-\cfrac{7}{16}\implies \cfrac{(16)44~~ - ~~(1)7}{\underset{\textit{we'll use this LCD}}{16}} \\\\\\ \cfrac{704~~ - ~~7}{16}\implies \cfrac{697}{16}\implies 43\frac{9}{16}[/tex]

Answer: C. 25%

Step-by-step explanation: This is a basic probability problem. First, you must find the total which is in question. 400 grams is the total in this case. The Cs make up 100 grams of this. Next, you put the part over the whole, and divide. 100/400= 0.25. When you want to find the probability with the probability sign, you move the decimal place two points to the right and then add the sign. Hence, 25%.

[tex]f(x)=5x^2-3x+3\implies \left. \cfrac{df}{dx}=10x-3 \right|_{x=1}\implies 10(1)-3\implies 7[/tex]

Answer: 30%

Step-by-step explanation:

because e9 people are chosen and 9 divided by 3 is 3 and 3 x 10 =30

The rule demonstrating the logical equality of the two claims. -((w V p) ^(-91q1w)) DeMorgan's law has the form -(w V p) v-(-91qAw).

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The value of the variable x for the given f(x) = 2 by simplifying the antiderivative of  the given function is given by x = 0.4865.

As given in the question,

Given anti derivative of f(x)  :

For the limit 0 to x for the integration of e^4t with respect t

= [tex]\int\limits^x_0 {e^{4t} } \, dt[/tex]

= ( 1/4) e^4x  + ( 1/4 )

Value of the function f (x)  = 2

Now f(x) = 2

Substitute the value of the function f(x) we get,

( 1/4) e^4x  + ( 1/4 ) = 2

⇒ e^4x + 1 = 8

⇒ e^4x = 7

⇒x = log7 / 4

⇒ x= 0.4865

Therefore, the value of the x by simplifying the antiderivative function f(x) for the given f(x) = 2 is equal to 0.4865.

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The equation for the circle is (x-h)^2 + (y-k)^2 = r^2. Substituting the values, we get (x-0)^2 + (y-5)^2 = 25.

Substituting y=1.5x+5 into the equation, we get (x-0)^2 + (1.5x+5-5)^2 = 25

Simplifying, we get 1.5x^2 +15x+25=25

Solving, we get x=1.

Therefore, the point of intersection is (1,1.5).

The line y=1.5x+5 intersects the circle with radius 5 and centre (0,5) at the point (1,1.5) in the first quadrant.

The equation for a circle with centre (0,5) and radius 5 is (x-0)^2 + (y-5)^2 = 25. When this equation is combined with the line equation y=1.5x+5, it can be solved to find that the line intersects the circle at the point (1,1.5), which is located in the first quadrant.

The equation for the circle is (x-h)^2 + (y-k)^2 = r^2. Substituting the values, we get (x-0)^2 + (y-5)^2 = 25.

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Answer:

36 members paid the total money that would be made would be $180

Step-by-step explanation:

48*75%=36

36*5=180

Answer:

v = 113.04 [tex]units^{3}[/tex]

Step-by-step explanation:

v = 4/3[tex]\pi r^{3}[/tex]

v = 4/3[tex]\pi 3^{3}[/tex]

v = 113.04 [tex]units^{3}[/tex]

The chef needed a) 3¾ cups of lemon juice and b) 20 pints olive oil for the larger batch.

A mixed fraction is one that has both its quotient and remainder represented. A mixed fraction like 2 1/3 is one where the remainder is 1 and the quotient is 2. Therefore, a mixed fraction is made up of both a whole number and a correct fraction.

The recipe was for 4 person, but now here are 40

The scale multiple is = 40/4

                                   = 10

a) As 1 cup = 16 tablespoon

The number of tablespoon of lemon required for 40 men = 6 × 10

                                                                                                 = 60

Converting to cup = 60/16

                              = 3¾ cups

b) As 1 cup = 0.5 pints

The number of cups of olive oil required for 40 men = 1 × 10

                                                                                        = 10

Converting to pints = 10/0.5

                              = 20 pints

Thus, The chef needed 3¾ cups of lemon juice and 20 pints olive oil for the larger batch.

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1. 80 people attended only the FSU-Butler game.

2. 165. Since it's not possible to have negative number of people, the answer is 0.

3. 210 people attended at least two of these games.

4. 340 people attended the Marist and Butler games, but not the North Carolina State game.

5. 365 people attended the North Carolina State or the Butler game

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Answer:

42 is the answer

Step-by-step explanation:

for distributive property of multiplication you could use...

2 x 3 x 7

as 3 x 7 is 21

Using the Empirical Rule, it is discovered that the proportion of people in a population with IQs ranging from 80 to 120 is 0.95 = 95%.

It specifies the following for a normally distributed random variable:

68% of the measurements are within one standard deviation of the mean.

95% of the measurements are within 2 standard deviations of the mean.

99.7% of the measurements are within 3 standard deviations of the mean.

Given a mean of 100 and a standard deviation of 20, we can calculate:

80 = 100 - 2 x 20.

120 = 100 + 2 x 20.

Because these are both the most extreme values within two standard deviations of the mean, then the proportion of people in a population with IQ scores between 80 and 120 is 0.95 = 95%.

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Answer:

4w - 20

Step-by-step explanation:

hope this help i guess

The number of large box is 12 and small box is 8.

What is cube?

The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.

Given :

The volume of small box is 9 cubic feet

The volume of the large box is 12 cubic feet

The volume of all box is 216 cubic feet

There are 20 boxes of paper shipped.

Total Volume covered by small box will be  9x

Total Volume covered by large box will be 24x

Total volume shipped = 216

9x + 24x  = 216

33x = 216

x = 6

So The number of large box is 12 and small box is 8.

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The distance of the fire from each tower is:

i. From Pine Knob: 41 kilometers

ii. From Colt Station: 15 kilometers

Bearing as a topic in mathematics can be used to determine the exact position or location of an object considering its angle of position and distance to a reference point.

Considering the given question; let the distance of the fire (F) from Pine knob (PK) be represented by x, and that from Colt Station (CS) be represented by y.

Angle at PK = 80 - 65

                    = 15^o

Angle at CS = 65 + 70

                    = 135^o

Angle at F can be determined as;

15 + 135 + F = 180   (sum of angle in a triangle)

150 + F = 180

F = 30^o

So that applying the Sine rule to determine the distances of the fire from PK and CS, we have;

a/Sin A = b/Sin B = c/Sin C

29/Sin 30 = y/Sin 15 = x/ Sin 135

29/Sin 30 = y/Sin 15

y = (29*Sin 15)/ Sin 30

  = 7.5052/ 0.5

  = 15.0104

y = 15 kilometers

29/Sin 30 = x/Sin 135

x = (29*Sin 135)/ Sin 30

  = 20.5059/ 0.5

  = 41.0118

x = 41 kilometers

Therefore, the distance from Pine Knob to the fire is 41 kilometers. While the distance from Colt Station to the fire is 15 kilometers.

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Answer:

x = 25 cm

Step-by-step explanation:

20% =

20/100 = 0.20

20% longer =

20% + 100% =

120% =

120/100 = 1.20

Hence, x+5 is 1.20 times that of x:

x * 1.20 = x + 5

1.2x = x + 5

1.2x - x = 5  ==> subtract x on both sides to move x to one side of the

                      equation

1.2x - 1x = 5  ==> 1x = x

(1.2 - 1)x = 5  ==> distribution property

0.2x = 5

x = 25  ==> multiply both sides by 5 ( 0.2 * 5 = 1 )

The total profit of F_1 in the week was $25920 and the total profit of F_2 in the week was $0.

The profit vector can be expressed as p = [35 62 30]. The total profit of F_1 and F_2 can be calculated by multiplying the matrix A by the vector p. The result, Ap, is a vector whose components give the total profits of the two stores in the week.

For example, the total profit of F_1 can be calculated as Ap_1 = [35 62 30] * [400 60 240] = [14000 3720 7200] = 25920.

Similarly, the total profit of F_2 can be calculated as Ap_2 = [35 62 30] * [0 0 0] = [0 0 0] = 0.

Therefore, the total profit of F_1 in the week was $25920 and the total profit of F_2 in the week was $0.

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Answer:

0

Step-by-step explanation:

I believe this is correct. Since they don't have the same sign then you will just have to subtract them.

Answer: 6

Step-by-step explanation:

The solution to the differential equation with the initial condition given is y(x)= (x² + 1)⁴.

Step 1: The given differential equation is dy/dx = 2xy/(x² + 1). Rearranging the equation, we get dy = 2xy dx/(x² + 1).

Step 2: Integrating both sides, we get ∫dy = ∫2xy dx/(x² + 1). On the left side, we have ∫dy = y + C, where C is the constant of integration. On the right side, we have ∫2xy dx/(x² + 1) = x² y + C.

Step 3: Substituting the initial condition y(3) = 6 in the solution, we get 6 = 3² y + C. Solving for C, we get C = 6 - 9y.

Step 4: Substituting C = 6 - 9y in the solution, we get y(x) = (x² + 1)⁴

The solution to the differential equation with the initial condition given is y(x)= (x² + 1)⁴.

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Relative to the mean, there are some school districts where many students are using ipads.

What is called the mean?

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. It is sometimes referred to as the "average" and is the most widely used central tendency metric.

Simply dividing the total number of values in a data set by the sum of all of the values yields it. The calculation can be performed on unprocessed data or data that has been combined into a frequency table.

By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.

Mean: The "average" number; found by adding all data points and dividing by the number of data points. Example: The mean of 4, 1, and 7 is ( 4 + 1 + 7 ) / 3 = 12 / 3 = 4 (4+1+7)/3 = 12/3 = 4 (4+1+7)/3=12/3=4left parenthesis, 4, plus, 1, plus, 7, right parenthesis, slash, 3, equals, 12, slash, 3, equals, 4.

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Answer:

Step-by-step explanation:
Let's represent the missing number with "---" -- so we have so far:

--- --- --- 30 --- --- 128 --- ---  ?
Now, let's say 5th position number is x and 6th position number is y
So, we have 30 + x = y and x+ y = 128
Combining these 2 equation, we get: x + 30 + x = 128 or x = 49, so y = 79

thus from 4th position, the series can be written as
30, 49, 79, 128, 207, 335, 542....
Thus, at 10th position we will have 542 !!!

Answer: 50

Step-by-step explanation:

You can plug in 4 for any of the equations given.

y = 10 + 10(4)

y = 10 + 40

y = 50

OR

y = 30 + 5(4)

y = 30 + 20

y = 50

Answer:

y = 50

Step-by-step explanation:

Since x = 4, plug the value into either equation.

[tex]y =10+10x\\y = 10 + 10(4)\\y=10+40\\y=50[/tex]

Therefore, y equals 50.

When opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram. (PA = RT and PT = AR)

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

A quadrilateral is a specific type of polygon known as a parallelogram if it contains two parallel opposed sides. A parallelogram has the following qualities:

Each coordinate of the Parallelogram :

P (-3, 0) , A(3, -1) , R ( 2, -5) and T(-4, -4)

Length of PA = √((3 + 3)² + (-1 - 0)²) = √(36 + 1) = √37

Lenght of TR = √((-4 - 2)² + (-4 + 5)²) = √(36 + 1) = √37

Length of PT = √((-3 + 4)² + (0 + 4)²) = √(16 + 1) = √17

Length of AR = √((3-2)² + (-1 + 5)²) = √(16 + 1) = √17

Here, PA = RT and PT = AR ,

so when opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram.

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