Consider the relationship chart for the a fast-food restaurant,
Assume that the areas required for each department are:
Department Area Required (Square feet)
(CB) 300
(CF) 200
(PS) 200
(DD) 200
(CS) 300
Assume facility dimension of 6 (horizontal) by 8 (vertical) squares, where each square is 5 feet on a side. As a result, for example the CB department requires 12 squares. Develop a layout for the fast-food restaurant.

Answer:

2 and 3 and y

Step-by-step explanation:

2x2x4x y x 1x2x3x3x3

-2x7x y x 2x3x z x3x3

Answers:  

2.857142 mph

4.190476 ft per second

Both values are approximate

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

Work Shown:

21 min = 21/60 = 0.35 hrs which is exact

distance = rate*time

rate = distance/time

rate = (1 mile)/(0.35 hrs)

rate = (1/0.35) mph

rate = 2.857142 mph which is approximate

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

21 min = 21*60 = 1260 seconds

1 mile = 5280 ft

rate = distance/time

rate = (5280 ft)/(1260 seconds)

rate = (5280/1260) ft per second

rate = 4.190476 ft per second approximately

Answer: 2.857 miles/hr

4.19 ft/sec

Step-by-step explanation:

60 min=1 hr.

1 mi/21 min*60 min=

60 min*1 mi/21 min=2.857 miles/hr

60 sec=1 min

60*60 sec=1 hr

1 hr=3600 sec

2.857 miles/hr=

2.857/3600 miles/sec=0.00079 miles/sec

1 mile=5280 ft

0.00079 miles/sec=

0.00079*5280 ft/sec=4.19 ft/sec

Taking into account the definition of a system of linear equations, 178 children, 62 students and 89 adults attended to the movie theater.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be found, with which when are replaced in the equations, they must give the solution proposed.

In this case, a system of linear equations must be proposed taking into account that:

On the other hand, you know:

So, the system of equations to be solved consists of the following equations:

Equation 1: C + S + A= 329

Equation 2: 5C + 7S + 12A= 2392

Equation 3: A= C÷2= 1/2C

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

Replacing equation 3 in equation 1 and isolating the variable S you get:

C + S + 1/2C= 329

3/2C + S= 329

S= 329 - 3/2C

Replacing this expression and equation 3 in equation 2 you get:

5C + 7(329 - 3/2C) + 12×1/2C= 2392

Solving:

5C + 7×329 - 7×3/2C + 12×1/2C= 2392

5C + 2303 - 21/2C + 6C= 2392

5C - 21/2C + 6C= 2392 -2303

1/2C= 89

C= 89÷ 1/2

C= 178

Remembering that S= 329 - 3/2C, you get S= 329 - 3/2×178 → S= 62

Finally, substituting the value of C in Equation 3: A= 1/2C= 1/2×178 → A=89

In summary, 178 children, 62 students and 89 adults attended to the movie theater.

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Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 4.

A bisector divides an angle or segment into two equal halves.

Given the data in the question;

Since XZ is a  perpendicular bisector of segment WY,

Segment WX is equal to Segment XY

Segment WX = Segment XY

Plug in the given values and solve for k.

6k + 8 = 11k - 12

Collect like terms

6k - 11k = -12 - 8

-5k = -20

Divide both sides by the coefficient of k

-5k/-5 = -20/-5

k = 4

Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 4.

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The banker should invest $ 30,000 at 6 % interest rate to earn an interest of 3800 per year from both the investments.

Principal 1 = $ 50,000

Rate 1 = 4 %

Let principal 2 be x

Rate = 6 %

Time = 1 year

Interest = 3800

Using simple interest, we get that:

SI = p × r × t

3800 = ( 50,000 × 0.04 × 1) + ( x × 0.06 × 1)

3800 = 2000 + 0.06 x

0.06 x = 3800 - 2000

0.06 x = 1800

6 x = 180000

x = 180000 / 6

x = 30,000

Therefore, we get that, the banker should invest $ 30,000 at 6 % interest rate to earn an interest of 3800 per year from both the investments.

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Answer:

n(AuB)=15

n(AnB)=8 is the answer!

Answer:

  6.1 cm

Step-by-step explanation:

You want to know the remaining side of the irregular figure such that the perimeter is 110 cm.

The perimeter of a plane figure is the sum of the lengths of the sides. Working clockwise from the upper left corner, we have ...

  34.6 +8.6 +17.3 +11.6 +? +11.6 +11.6 +8.6 = 110

  103.9 +? = 110 . . . . collect terms

  ? = 6.1 . . . . . . . . . subtract 103.9

The length of the missing side is 6.1 cm.

__

Additional comment

If the angles that appear to be right angles actually were right angles, the perimeter would be 109.6 cm. The perimeter is longer than this, so at least three of the angles are not right angles.

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Hello! In this question, we were given an expression and would have to express it without the use of exponents.

__________________________________________________________

Explanation:

In the question, we were given:

(3a³)²

In order to express the expression without the exponents, we would have to first simplify it and then expand the expression.

__________________________________________________________

Solve:

[tex](3a^3)^2[/tex]

Simplify by "squaring" the variable inside the parenthesis, in which in this case we would multiply the "2" to the "3".

[tex]3a^6[/tex]

Now in this step, we would have to expand the expression in a different form to get rid of the exponent.

To get rid of the exponent, we would expand the " [tex]a^6[/tex] " term.

Note that the term [tex]a^6[/tex] is the same thing as a · a · a · a · a · a, it is just the expanded version of the exponent.

This means that our expressed expression without exponents, including our constant "3" would be:

3 · a · a · a · a · a · a

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Answer:

3 · a · a · a · a · a · a

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Answer:

b=–2

Step-by-step explanation:

we've got:

(3+bx)⁵===> b⁵x⁵+15b⁴x⁴+90b³x³+720b²x²+405bx+243

and we've also got the coefficient of x³ as –720

90b³=–720===> b³=–8===> b=–2

Number 50 in the Jack's equation represents the rate of change in the oven's temperature over time (per minute) or with respect to time by using the slope form concept.

As per the question statement, Jack is preheating his oven before using it to bake. He wants to predict the final temperature after [tex]x[/tex] minutes.

He wrote the equation [tex]y =50x+78[/tex] , where [tex]y[/tex]  represents the final temperature in [tex]fahrenheit[/tex]. We are supposed to tell the significance of number 50 in the given equation.

As we know that the equation which is in the form of [tex]y=mx+c[/tex], or the slop form equation, m is called the slope or the rate of change of value of [tex]y[/tex] with respect to value of [tex]x[/tex].

And the given equation [tex]y =50x+78[/tex] is also of the form of [tex]y=mx+c[/tex] hence we conclude that 50 is the slope or the  rate of change of value of [tex]y[/tex] with respect to value of [tex]x[/tex].

As y is the temperature in Fahrenheit therefore x is the time hence "50 Degrees Fahrenheit change of temperature per unit minute" is the significance of 50.

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Given that the triangle is a right triangle, the value of sin (n) is √5/5.

Hence, option D)√5/5 is the correct answer.

Trigonometry is simply a branch in mathematics that looks into the relationships between angles and side lengths of a triangle.

Given the data in the question;

To determine the value of sine n, we will use one of six functions of an angle commonly used in trigonometry.

Sine of angle n = Opposite of angle n / Hypotenuse

sin(n) = Opposite / Hypotenuse

Plug in the given values and simplify

sin(n) = Opposite / Hypotenuse

sin (n) = 2 / 2√5

Next, rationalize the denominator.

Cancel out the common factor 2.

sin (n) = 2 / 2√5

sin (n) = 1 /√5

Multiply both the numerator and the denominator by √5.

sin (n)  = (1×√5) / (√5 × √5)

sin (n)  = √5/5

Given that the triangle is a right triangle, the value of sin (n) is √5/5.

Hence, option D)√5/5 is the correct answer.

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[tex] \sqrt{12.25 } = 3.5[/tex]

Answer:

False

Step-by-step explanation:

3 x 1/3

3/1 x 1/3 = 1

Answer:false

Step-by-step explanation: i did the test

The lateral area of the cone is 394 square inches

The formula for lateral area of a cone is expressed as;

Lateral area = πr √h² + r²

Given that;

Substitute the values into the formula

Lateral area = 3. 142(6) √20² + 6²

Lateral area = 18. 85 √436

Lateral area = 18. 85 × 20. 8

Lateral area = 394 square inches

Thus, the lateral area of the cone is 394 square inches

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If Wilson produces only one 1 bag, then his profit starts decreasing

Given the function;

Let  f ( x ) = [tex]2x^4 - 4x^3 + 7[/tex]

Where;

x is  the number of bags of cereal produced

[tex]f'x = 2x^4 - 4x^3 + 7[/tex]

[tex]f'(x) = 8x^3 - 12x^2[/tex]

Factorize the expression

[tex]f'(x) = 4x^2(2x - 3)[/tex]

If the value of x is decreasing, we have;

f ′ ( x ) ≤ 0

4x² (2x - 3) ≤ 0

If x² ≥ 0, then;

2x - 3  ≤ 0

x ≤ 3/ 2

With x as the number of bags

x ∈ N

x = 1 is the only possibility

Thus, if Wilson produces only one 1 bag, then his profit starts decreasing

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The complete question:

Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: pi = 2x ^ 4 - 4x ^ 3 + 7,  where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing

Based on the results of the physical fitness test, the reason why we are unable to calculate the mean number of pull-us done by the students in each class is that we don't have the exact number of pull-ups done by each student.

To calculate the simple mean of a distribution of numbers, we would need the value of all the numbers to be known. These numbers will then be summed up and divided by the number of the distribution.

In this case of the physical fitness test, the number of pull-ups is not known for all the students as there are some that either did below 5 or above 10 and we don't know the exact number of pull-ups done.

As a result, we are unable to calculate the mean.

Question is:
Explain why we are unable to calculate the mean number of pull-ups done by the students in each class.

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The inequality graph of the system of inequalities is graph (a)

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The system of inequalities is given as

-2x + 3y < 9

x^2 - y <= 10

4x + y > 3

In the above system of inequalities, there are two linear inequalities and a parabola inequality

The inequality symbols in the linear inequalities are opposite

This means that the region between both lines would be shaded

Also, for the parabola; the upper part would be shaded.

This is so because when y is made the subject of the formula, the symbol  becomes >=

Using the above as a guide, the inequality graph of the system of inequalities is graph (a)

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Answer:
The cost that Kaleb would spend at McDonalds if he ordered 3 McGriddles would be 11.50.

Step-by-step explanation:

We know this is the answer because, when solving for c(3), we would get c(3)=2.3(3)+2.50=11.50.

Answer: 3√6

Step-by-step explanation:

√54​=

√(9*6)=3√6

Answer: -4

Step-by-step explanation:

it is -4 because we are looking for like the opposite so the opposite of 4 is -4

Answer:

Absolute value of |4| = 4

Step-by-step explanation:

The absolute value of a number is always positive

Using the Empirical Rule, it is found that 16% of men over 20 have upper arm lengths greater than 44.2 cm.

It states that, for a normally distributed random variable:

For the distribution in this problem, we have that:

Hence, 44.2 is one standard deviation above the mean, as 44.2 = 39.1 + 1 x 5.1.

The normal distribution is symmetric, meaning that 50% of the measures are above the mean and 50% are below. Of those measures above the mean, 68% are less than 44.2 and 32% are more than 44.2 cm, hence:

0.5 x 32 = 16%.

16% of men over 20 have upper arm lengths greater than 44.2 cm.

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In the given situation (A) the median is a good measure regardless of whether the outlier is included.

To find the median:

Therefore, in the given situation (A) the median is a good measure regardless of whether the outlier is included.

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The correct question is given below:

The following dataset represents the dollar amounts of donations collected at the entrance to a free museum for one hour.

(Refer to the table given below)

Is the median a reasonably good measure of central tendency for this dataset? What if the outlier were removed from consideration?

Select the correct answer below:

(A) The median is a good measure regardless of whether the outlier is included.

(B) The median is a very poor measure regardless of whether the outlier is included.

(C) The median is a good measure when the outlier is included, but it would be a very poor measure if the outlier were removed from consideration.

(D) The median is a very poor measure when the outlier is included, but it would be a good measure if the outlier were removed from consideration.

The two fractions are equivalent.

When two fractions have the same value, they are said to be equivalent, meaning that even though the numbers in the two fractions are different, their overall value is the same.

Fractions that are not equal to one another are referred to as nonequivalent fractions. The same cross multiplication procedure must be used to determine whether two fractions are comparable or not.

Consider these two fractions,

x = ( m / 4n ) and y = ( 2m / 8n )

Now when the fraction x is multiplying and dividing by 2.

We get,

x = ( m / 4n ) × ( 2 / 2 )

x = 2m / 8n

Therefore, x = y

Hence, the fractions are equivalent.

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Answer:

146 centimeters or 1.46 meters.

Step-by-step explanation:

1m = 100cm

2m = 200cm

200 - 54 =146

Hope this helps!

The probability that the first student chosen will be a boy and the second will be a girl is 0.28.

Probability is also called the chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

Total students = 9

Number of girls = 4

Number of boys = 5

Probability of choosing first boy = Number of boys / total students

⇒ 5/9

Now since 1 boy extract so remaining students = 9 - 1 = 8

Probability of choosing second girl = Number of girls / Total students

⇒ 4//8

Probability of A and B = P(A) × P(B)

Therefore,

The probability that the first student chosen will be a boy and the second will be a girl = (5/9) × (4/8) = 0.28

Hence "The probability that the first student chosen will be a boy and the second will be a girl is 0.28".

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Answer:

0.0058543

Step-by-step explanation:

58.543/10,000 = 58.543 divide 10,000