Why is Mathematics called the queen of science (1 paragraph response please)

1. The maximum and the minimum number of guests that Trevor and Michael should host at the banquet are 18 and 14, respectively.

2. The minimum number of tables that Trevor and Michael will need for the banquet is 2.

We can employ the mathematical operations of addition, multiplication, division, and subtraction to determine the numbers.

Since the budget is limited to $450 or less, we can compute the maximum and the minimum number of guests for the event, using division operation.

Total budget for the banquet = $400 ± $50

Cost per guest = $25

Maximum number of guests to expect = 18 ($450/$25)

Minimum number of guests to expect = 14 ($350/$25)

The number of guests a table can accommodate = 7

The minimum number of tables to use for the banquet = 2 (14/7)

The maximum number of tables to use = 3 (18/7)

Thus, using division operation, Trevor and Michael should expect to host between 14 and 18 guests at the banquet.

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The number of degrees of freedom for the chi-square goodness-of-fit test is of:

2.

The number of degrees of freedom for a chi-square goodness-of-fit test is obtained according to the multiplication presented as follows;

df = (r - 1) x (c - 1).

In which the variables are listed as follows:

The table in this problem has three rows, given as follows:

The table has two columns, which are given as follows:

Hence the number of degrees of freedom of the test is given as follows:

df = (3 - 1) x (2 - 1) = 2 x 1 = 2.

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[tex]\fbox{7.07...}[/tex]

First, we need the square of both numbers (8 and 18)

square of 8:

[tex]\sqrt{8}[/tex]

[tex]=2.828[/tex]

square of 18:

[tex]\sqrt{18}[/tex]

[tex]=4.242[/tex]

Now, let's add both numbers:

[tex]2.828+4.242[/tex]

[tex]=7.07[/tex]

Answer:

-7

Step-by-step explanation:

The sinusoid that models 4° = A cos B(x - C) and 68° = A cos B(x - C) the change in temperature in the house.

The heater turns on when the house is 4° below the set temperature and turns off when the house is 4° above the set temperature. The temperature is set at 68°. At 10:15 am the heater turns on, and at 10:30 am the heater turns off.

Temperature fluctuations can be modeled using the sine and cosine functions throughout the day.

The equations that can be used to model these data is of the form:

At 10:30 am the heater turned off,

⇒ 4° = A cos B(x - C)

At 10:15 am the heater turned on,

⇒68° = A cos B(x - C)

where A, B, and C are constants, y is the temperature in °C and x is the time

Thus, The sinusoid that models 4° = A cos B(x - C) and 68° = A cos B(x - C) is the change in temperature in the house.

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The magnitude is approximately 186 pounds.

A mathematical object's magnitude, often known as its size, is a quality that indicates whether it is bigger or smaller than other things of the same sort. Formally speaking, an object's magnitude represents the ordered (or ranked) outcome of the class of objects it belongs to.

We have to assume that the notation starts South and then moves 76 degrees East.

The 70-pound force is going at an angle down and to the right.

The down one is negative and the right one is positive.

We have to use the vectors as the hypotenuse of a rectangle.

70 cos(76) = vertical = 16.93 down

70 sin(76) = horizontal = 67.92 right

120 cos(80) = vertical = 20.83 up

120 sin(80) = horizontal =118.17 right

We have to add up all the values vertically and horizontally, and we get

-16.93 + 20.83 =3.9 up

67.92 + 118.17= 186.09 right

Here, the magnitude is the hypotenuse.

sqrt(15.21+34629.49) =186.13 pounds.

Direction is cos⁻¹(3.9/186.13) = 88.802  

Remember this is North then 88.802 degrees East

Therefore, the magnitude is approximately 186 pounds.

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Diagonal of rectangle is changing by the rate of 4.373 in. /sec.

Rate of change (ROC) is the rate at which a variable changes over a particular period of time

To find the average rate of change, divide the change in the y-values ​​by the change in the x-values . Finding the average rate of change is especially useful for identifying changes in measurable values ​​such as average speed or average velocity.

A ratio is a special ratio in which the two terms have different units.

the calculation part is shown in the below picture attached .

so after seeing the solution we come to an answer of = 4.373 in./sec

therefore diagonal of rectangle is changing by the rate of 4.373 in. /sec

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The equation of the parabola is f(x) = 7(x-3)^2+5.

Given:

The equation of the parabola that has the same shape has f(x) = 7x^2 but with vertex(3,5) in the form of f(x) = a(x-h)^2 + k.

If the parabola has same shape then its a values are same.

so f(x) = 7x^2

here a = 7

so the equation with vertex (3,5) also has a value is 7.

(h,k) = (3,5)

f(x) = a(x-h)^2+k

= 7(x-3)^2 + 5.

Therefore the equation of the parabola is f(x) = 7(x-3)^2+5.

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The length of rectangle is 1170 ft and width is 770 ft.

The perimeter of a form is the space surrounding its edge. A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. We must sum up the lengths of the rectangle's four sides in order to get its perimeter. Since there are two of each side length, it is easy to accomplish this by simply adding the length and width and multiplying the result by two. The perimeter formula is defined as perimeter=(length + width)2.

Given,

The perimeter of the flag is 2,280 ft .

Length = 400 ft

Let l represent the size of the flag.

and

The width is w.

then in line with the preceding statement

l = w+400

Sphere size is 2280 feet.

The perimeter formula is provided by:

Perimeter = 2(Length + Width)

2280 = 2( w + w+ 400)

2280/2 = 2w - 400

1140 + 400 = 2w

1540 = 2w

width = 770

Length = 770 + 400

Length = 1170

The length of rectangle is 1170 ft and width is 770 ft.

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Answer:

2. 25

max = 88 feet

See the attachment photo!

The number of different ways to arrange 7 video games is  = 7!

The question requests for the number of arrangements; That means we're dealing with permutation

the number of video games is 7;

To arrange 7 games, we make use of the following permutation formula;

[tex]^{n}P_{n} = \frac{n!}{(n-n)!}[/tex]

So, we have

n=7

No. of ways we can arrange is = [tex]\frac{7!}{(7-7)!}[/tex] = 7!

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The expected value of the sum of these events will be 2 / 3.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that the expected value for getting heads, on 30 coin tosses, is 15. The expected value for rolling a 1, after 30 die rolls is 5.

The probability of the sum will be calculated as,

P = ( 15 / 30 ) + ( 5 / 30 )

P =  ( 20 / 30 )

P = 2 / 3

Therefore, the expected value of the sum of these events will be 2 / 3.

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Applying the definition of linear pair angles, the measures are:

y = 10

m∠JKM = 106°

m∠MKL = 74°

A linear pair involves two angles that lie adjacent to each other on a straight line. The sum of their measures is equal to 180 degrees, this is because linear pair angles are supplementary to each other.

Given the following:

Measure of angle JKM = (10y + 6)°

Measure of angle MKL = (8y - 6)°

Therefore:

m∠JKM + m∠MKL = 180 [linear pair angles are supplementary]

Substitute

10y + 6 + 8y - 6 = 180

Combine like terms

18y = 180

18y/18 = 180/18

y = 10

Plug in the value of y to find the measures:

Measure of angle JKM = (10y + 6)° = 10(10) + 6 = 106°

Measure of angle MKL = (8y - 6)° = 8(10) - 6 = 74°

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Recent research has confirmed the Spillover Hypothesis by demonstrating a favourable association between life and job happiness.

According to the spillover hypothesis, behaviour or affect in a family system might flow immediately from one place or connection to another. Transfer takes place in the same valence, which means that one subsystem's negative affect is connected to another's negative affect, or stress at work spills over and intensifies stress at home. The compensatory hypothesis offers a different perspective by arguing that transfer between family subsystems occurs in the opposite valence, leading a person to seek fulfilment in one relationship or environment in order to make up for shortages in another.

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Answer:

Step-by-step explanation:

Ok;

1. Area is base times height.

Here shown, the base is 18cm and the height is 11cm. Don't be fooled by the 14cm for it is just the leg of a triangle not full height!!

18*11=198cm^2

2. Divide by two. We just caculated the area of the rectangle. Now we know a triangle is half of a rectangle's area so divide by 2!

198/2= 98cm^2

Answer:

The picture is not Clear. Please provide a better view of the question.

Step-by-step explanation:

The new function p(x) =  2x³+3x²-23x-12  is the product of expressions x+4, x-3, and 2x+1

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

Given: the expressions x+4, x-3, and 2x+1

The product of the expressions  is:

p(x) = (x+4)(x-3)(2x+1)

      = (x²-3x+4x-12)(2x+1)

     =  (x²+x-12)(2x+1)

    = 2x³+2x²-24x+x²+x-12

   =  2x³+3x²-23x-12

Therefore, the new function is p(x) =  2x³+3x²-23x-12.

Since the new function is a polynomial, it demonstrates the Fundamental Theorem of Algebra which states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers

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The equations using any method for the given situation illustrated that:

Equation for Jordan: 225 + 45w

Equation for RayAnn: 150 + 60w

Let the number of weeks be represented by w.

Jordan saved $225 and continues to save $45 each week. The equation for this will be:

= 225 + (45 × w)

= 225 + 45w

RayAnn saved $150 and continues to save $60 each week. The equation will be:

= 150 + (60 × w)

= 150 + 60w

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Answer:

b = (4/3), with rounding

Step-by-step explanation:

Area = A, in cm^2

n = days

A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]

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

Data:

n = 2, A = 1.8

A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]

1.8 =  [tex]A_{0}[/tex][tex]b^{2}[/tex]

n = 3, A = 2.4

2.4 = [tex]A_{0}[/tex][tex]b^{3}[/tex]

Although we are not given the initial area, we can still make the calculation since we have two data points and each has the same initial area, [tex]A_{0}[/tex].  Lets take the first equation and multiply it by b, in order to bring the [tex]b^{2}[/tex] to [tex]b^{3}[/tex]

1.8 =  [tex]A_{0}[/tex][tex]b^{2}[/tex]

b(1.8 =  [tex]A_{0}[/tex][tex]b^{2}[/tex])

1.8b = [tex]A_{0}[/tex][tex]b^{3}[/tex]

We can know from the second equation that 2.4 = [tex]A_{0}[/tex][tex]b^{3}[/tex] .  We can eliminate this term in the above relationship by substituting 2.4:

1.8b = [tex]A_{0}[/tex][tex]b^{3}[/tex]

1.8b = 2.4

b =  1.3333

       or (4/3)

Check:

Does the value of (4/3) for b work for both data points?  To check this, we do need to assume an initial starting area.  Lets assume the starting area, [tex]A_{0}[/tex] = 1.

n = 2, A = 1.8, b = (4/3)

A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]

1.8 =  1*[tex](4/3)^{n}[/tex]

1.8 =  1.78  Close enough?

n = 3, A = 2.4, b = (4/3)

2.4 = [tex]A_{0}[/tex][tex](4/3)^{n}[/tex]

2.4 = 1*[tex](4/3)^{3}[/tex]

2.4 = 2.37 Close enough?

well, your proportion setup is good, let's simply use that then

[tex]\stackrel{Jaylan}{\cfrac{~~ \frac{ 3}{4 } ~~}{\frac{1}{5}}}\implies \cfrac{3}{4}\cdot \cfrac{5}{1}\implies \cfrac{15}{4}\implies \cfrac{3\frac{3}{4}}{1}~\frac{water}{lime} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Wanchen}{\cfrac{~~ \frac{ 2}{3 } ~~}{\frac{1}{6}}}\implies \cfrac{2}{3}\cdot \cfrac{6}{1}\implies \cfrac{12}{3}\implies \cfrac{4}{1}~\frac{water}{lime}[/tex]

well, the one with the lesser lime flavor will  be the one that put too much water in the drink, the more water the less the fruit mix, the more waterdowned the drink is, well hell who put more water per lime?  well Wanchen, shame on you.

6900 hours, make a list of multiples until lcm is found

Answer:

8

Step-by-step explanation:

4*8=32

6*8=48

9*8=72

They are all multiples of 8

Answer: 8

Step-by-step explanation: You can factor out 32, 48, and 72 by using prime factorization which is listing all of the PRIME factors for each number

32: 2 x 2 x 2 x 2 x 2

48: 3 x 2 x 2 x 2 x 2

72: 3 x 3 x 2 x 2 x 2

If you look at all the prime factors, 2 appears in every number 3 times, so you do 2x2x2 to get the final answer, which is 8.

The statement that would be true concerning the graph would be that the graph will have a slope of -0.5.

A slope is defined as the difference between a chosen point on the vertical and horizontal axis.

The slope of a straight line graph has a constant equation that is used to determine its slope. Thus;

y = mx + b

Where m = the measure of the steepness of the straight line graph.

From the equation of the graph that was given;

y = -0.5x + 12. The slope of the graph which is represented by 'm' would be -0.5.

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Answer:

about 77.2°

Step-by-step explanation:

The figure is omitted--please sketch it.

Make sure your calculator is in degree mode.

[tex] \cos( \alpha ) = \frac{2}{9} [/tex]

[tex] \alpha = {cos}^{ - 1} \frac{2}{9} = 77.2[/tex]

77.2 degrees

The x-intercept is 1 if the function is f(x) =  (x-1)²/x²-1 after plugging f(x) = 0 or y = 0 the answer is 1.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The function is:

f(x) =  (x-1)²/x²-1

To find the x-intercept where y = 0

or f(x) = 0

0 =  (x-1)²/x²-1

x ≠ ±1

x - 1 = 0

x = 1

Thus, the x-intercept is 1 if the function is f(x) =  (x-1)²/x²-1 after plugging f(x) = 0 or y = 0 the answer is 1.

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The equation that passes (6,0) and (3,4) is -3y=4(x-6)

What are the different forms of straight lines ?

The following information about the straight line is required if we wish to obtain the equation for it.

1. The y-intercept and slope

2. Two-point and slope

3. Two things.

4. the intersection of the x- and y-axes

the straight line that passes through (6,0) and (3,4).

The equation can be expressed in a point-slope form which is ,

y/x-6=4/-3

∵ -3y=4(x-6)

Hence,

The equation that passes (6,0) and (3,4) is -3y=4(x-6)

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Yes, the difference in mean mpg between 4 and 8 cylinder cars statistically significant because the calculated value of t statistic is higher than the critical t value.

What is t statistic and critical value of t?

T statistic is ratio of a parameter's estimated value to its standard error when it deviates from its hypothesized value.

Critical t value is a cut-off point in t distribution

In question, the calculated t statistic is 8.1023 and critical t value one tail is 1.7139 and critical t value two tail is 2.0686. So, the value of calculated t statistic is higher than critical t value one tail or two tail. Therefore, we can reject the null hypothesis.

Thus, yes, the difference in mean mpg between 4 and 8 cylinder cars statistically significant because the calculated value of t statistic is higher than the critical t value.

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The order of the rational numbers from the least to greatest is   [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 <  [tex]7\frac{3}{4}[/tex]  .

in the question ,

it is given that the rational numbers are -7.3, [tex]7\frac{3}{4}[/tex], 7.23, [tex]-7\frac{2}{3}[/tex] .

we have to arrange the rational numbers in order from least to greatest .

For arrangement we first convert all the rational numbers in decimal form .

the decimal form of the given rational numbers are as follows .

(i) -7.3 is already given in decimal form .

(ii) [tex]7\frac{3}{4}[/tex] = (7*4+3)/4 = (28+3)/4 = 31/4 = 7.75

(iii) 7.23 is already in decimal form .

(iv) [tex]-7\frac{2}{3}[/tex] = -(7*3+2)/3 = -23/3 = -7.666

the order is -7.666 < -7.3 < 7.23 < 7.75

which is   [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 <  [tex]7\frac{3}{4}[/tex]

Therefore , The order of the rational numbers from the least to greatest is    [tex]-7\frac{2}{3}[/tex] < -7.3 < 7.23 <  [tex]7\frac{3}{4}[/tex] .

The given question is incomplete , the complete question is

Order the following rational numbers from least to greatest.

-7.3, [tex]7\frac{3}{4}[/tex], 7.23, [tex]-7\frac{2}{3}[/tex]   .

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The Sum of 40 terms of the Arithmetic Sequence is 3,420..

Arithmetic Series is defined as a sum of the terms of arithmetic progression or sequence.

An Arithmetic progression is a sequence of terms in which the difference between two consecutive terms is a constant number.

We have following information about series

sum of 12 terms of an arithmetic series (S₁₂) = 186

the 20th term of arithmetic sequence = 83

i.e., a₂₀ = 83

As we know that nth term of arithmetic progression is aₙ= a + (n-1)d

where , a---> first term of sequence

n ----> nth term

d -----> constant difference between two consecutive terms

put n= 20 in above formula we get,

83 = a + (20-1 )d = a+ 19d ----(1)

Now , Using the sum of n arithmetic terms formula, Sₙ = n/2 ( 2a + (n-1)d)

so, for n = 12

186 = 12/2 ( 2a + 11d ) => 2a + 11d = 31 ---(2)

Solving equations (1) and (2) we get,

27d = 135 => d = 5

putting the value of d in equation (1)

83 = a + 19×5 => a = 83 - 95 = -12

thus sequence is like as -12, -7 , -2 , ------

Sum of first 40 terms of arithmetic sequence (S₄₀) = 40/2 ( 2× (-12) + 39d ) = 20 ( -24 + 39×5)

= 20( 171) = 3,420

So, required result is 3,420..

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