the ratio of diners to waiters is 1:8 respectively. If the total number of people in the restrant is 36, how many waiters are there

Answer:

Step-by-step explanation:

i do 6th grade aleks too!

The length of side p of the triangle rounded to the nearest tenth is 7.5.

The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

It is expressed as;

p = √( n² + m² - ( 2nm × cosθ ) )

Given the figure in the diagram;

Plug the values into the above formula and simplify.

p = √( n² + m² - ( 2nm × cosθ ) )

p = √( (11)² + (13)² - ( 2 × 11 × 13 × cos( 35 ) ) )

p = √( 121 + 169 - ( 286 × cos( 35 ) ) )

p = √( 290 - ( 286 × cos( 35 ) ) )

p = √( 290 - 234.27748  )

p = √( 290 - 234.27748  )

p = √55.72252

p = 7.5

Therefore, the value of p is 7.5.

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Answer:

Option B) A and C

Step-by-step explanation:

C: Yes the area can be found by multiplying the 4 and 7 and then dividing the product by two.

The size of the angle between EM and the base of the prism is equal to 28.5°.

First of all, we would determine side length MA based on the ratio between side lengths DM and MA as follows;

DM : MA = 3 : 4

Total side parts = 14 cm

(3 + 4) parts = 14 cm

7 parts = 14 cm

1 part = 2 cm

Therefore, side length MA = 2 × 4 = 8 cm.

By applying Pythagorean's theorem to right triangle MAB, we have the following:

c² = a² + b²

Where:

a, b, and c represents the side lengths of a right triangle.

c² = 8² + 14²

c² = 260

c = √260

c = 16.1245 cm.

By applying tan trigonometry to right triangle AEB, we have:

tanθ = opposite/adjacent

opposite = tan32° × 14

opposite = 8.7482 cm.

By applying tan trigonometry to right triangle EMB, we have:

tanθ = opposite/adjacent

θ = tan⁻¹(opposite/adjacent)

θ = tan⁻¹(8.7482/16.1245)

θ = tan⁻¹(0.5425)

θ = 28.5°.

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Answer:

MN = 7x + 3

Step-by-step explanation:

Because MN connects the midpoints M and N  of AD and BC respectively

MN is the midsegment of trapezoid ABCD , then

MN = [tex]\frac{AB+DC}{2}[/tex]

AB + DC = 6x + 7 + 8x - 1 = 14x + 6

MN = [tex]\frac{14x+6}{2}[/tex] = [tex]\frac{14x}{2}[/tex] + [tex]\frac{6}{2}[/tex] = 7x + 3

To evaluate [tex]f(g(3))[/tex], we need to first evaluate g(3), then evaluate f(g(3)).

[tex]$$g(3)=7 \cdot 3^2+6 \cdot 3+2=65$$[/tex]

A relationship between a number of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs that are individually connected to exactly one output. There are two domains or scopes for each function. f is typically used to represent functions (x). The input is x. Y = f is a common way to represent the function (x).

To evaluate [tex]f(g(3))[/tex], we need to first evaluate g(3), then evaluate f(g(3)).

[tex]$$g(3)=7 \cdot 3^2+6 \cdot 3+2=65$$[/tex]

So

[tex]f(g(3))=f(65)=\frac{1}{2} \cdot 65-4=\frac{1}{2} \cdot 65-4=28[/tex]

To evaluate [tex]g(f(8))[/tex], we need to first evaluate [tex]f(8)[/tex], then evaluate [tex]f(8)[/tex].

[tex]f(8)=\frac{1}{2} \cdot 8-4=2\\\\g(f(8))=g(2)=7 \cdot 2^2+6 \cdot 2+2=46\\g(f(8))=46[/tex]

[tex]g\left(\frac{1}{8}\right)=7\left(\frac{1}{8}\right)^2+6 \cdot \frac{1}{8}+2=\frac{121}{8}+\frac{3}{2}+2=\frac{135}{8}[/tex]

[tex]f\left(g\left(\frac{1}{8}\right)\right)=f\left(\frac{135}{8}\right)=\frac{1}{2} \cdot \frac{135}{8}-4=\frac{135}{16}-4=\frac{135-64}{16}=\frac{71}{16}\\f\left(\frac{1}{2}\right)=\frac{1}{2} \cdot \frac{1}{2}-4=-4[/tex]

So,

[tex]$$f\left(f\left(\frac{1}{2}\right)\right)=f(-4)=\frac{1}{2} \cdot-4-4=-8-4=-12$$[/tex]

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Answer: [tex]230[/tex]

Step-by-step explanation:

To find coterminal angles, add/subtract integer multiples of [tex]360^{\circ}[/tex].

[tex]-490^{\circ}+360^{\circ}=-130^{\circ}\\\\-130^{\circ}+360^{\circ}=230^{\circ}[/tex]

An angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘ is 130∘.

To find an angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘, we can use the concept of coterminal angles.

Coterminal angles are angles that have the same initial and terminal sides when drawn in standard position. To find a positive coterminal angle with a negative angle, we can add 360 degrees to the negative angle until we get an angle within the desired range (0∘ to 360∘).

Let's find the positive coterminal angle:

θ = -490∘ + 360∘

θ = -130∘

So, an angle θ that is coterminal with −490∘ and lies between 0∘ and 360∘ is 130∘.

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Answer:Commutative property of multiplication

Step-by-step explanation:

Commutative property of multiplication

Answer:

0 + 11i

Step-by-step explanation:

A complex number is a number in the form a + bi, where a is the real part and b is the imaginary part. In this case, the real part is given as 0 and the imaginary part is given as 11. Therefore, the complex number is:

0 + 11i

where 0 is the real part and 11i is the imaginary part.

Some of the common forms of help include:

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To solve the equation, you can use the following steps:

Start by isolating the absolute value expression on one side of the equation:

-5|x+3| = 18

Now, since the absolute value is positive, it has two solutions:

x + 3 = -18 or x + 3 = 18

Solving for x in each case:

x = -21 (if x + 3 = -18) or x = 15 (if x + 3 = 18)

So the two solutions to the equation are x = -21 and x = 15.

Answer:

36 m

Step-by-step explanation:

It says to use a graph so here is one with the height shown as  36 m

Answer:

y=3x+5

Step-by-step explanation:

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Answer:

y=mx+c

Step-by-step explanation:

-5/y=3x meaning that y=mx+c, hope this helps :)

The shaded area is 157.1 square cm

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

Diameter = 10 cm

So, the area of the small semicircles is

Area = 1/2π(d/2)²

This gives

Area = 1/2π(10/2)²

Evaluate

Area = 25/2π

For the big semicircle, we have

Area = 1/2π(D/2)²

Area = 1/2π(20/2)²

So, we have

Area = 50π

i.e.

Area =50 * 3.142 = 157.1

This represents the shaded area because the small semicircles cancel out

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Answer:

Initial value=50

Rate of change=12.5

Step-by-step explanation:

The rate of change is just the slope.

Initial value is y-intercept.

The system of equations is solved and the value of x = 5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

3x + y = 13   be equation (1)

Let the second equation be represented as B

Now , the value of B is

2x - 4y = 18   be equation (2)

Multiply equation (1) by 4 , we get

12x + 4y = 52   be equation (3)

Adding equation (2) and equation (3) , we get

14x = 70

Divide by 14 on both sides of the equation , we get

x = 70/14

x = 5

Substitute the value of x in equation (1) , we get

15 + y = 13

Subtracting 15 on both sides of the equation , we get

y = -2

Hence , the value of x and y is 5 and -2 respectively

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The function g(x) is equal to g(x) = 3x².

Given is functions f(x) and g(x) are shown on the graph and f(x) = x².

The function g(x) is equivalent to 3 times function f(x) for every value of {x}. So, we can write - g(x) = 3x²

Therefore, the function g(x) is equal to g(x) = 3x².

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Answer:

The function f(x) to model U. S. cell phone usage over the time period of 2010 to 2016 can be expressed as f(x) = 43 * (1.23^x), where x is the number of years since 2010. Part b: The estimated cell phone usage in 2013 can be calculated by substituting x = 3 into the function f(x) = 43 * (1.23^x). This yields an estimated cell phone usage of 68.4 million in 2013, which can be rounded to the nearest ten thousand to 68 million.

Step-by-step explanation:

The greatest number of boxes is 4

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

88 books and 76 DVDs

To do this, we simply calculate the GCF

So, we have the following representation

88 = 2^2 * 11

76 = 2^2 * 19

This gives

GCF = 2^2

GCF = 4

The greatest number of boxes he could have used is 4 boxes.

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Answer:

2418

Step-by-step explanation:

Step 1: Setup

Set up your multiplication problem like this:

             9 3

     x       2 6

Step 2: Multiply

3 x 6 = 18. Put 8 below the line and 1 as a reminder on top:

             1  

             9 3

     x       2 6

               8

Step 3: Multiply

6 x 9 = 54. Take 54 and add 1 from the previous step to get 55. Enter 55 at the bottom:

             9 3

     x       2 6

           5 5 8

Step 4: Add 0

Enter a 0 at the bottom right as a place holder, because you now move over one digit:

             9 3

     x       2 6

           5 5 8

     +         0

Step 5: Multiply

2 x 3 = 6. Put 6 below the line and 0 as a reminder on top:

             0  

             9 3

     x       2 6

           5 5 8

     +       6 0

Step 6: Multiply

2 x 9 = 18. Take 18 and add 0 from the previous step to get 18. Enter 18 at the bottom:

             9 3

     x       2 6

           5 5 8

     +   1 8 6 0

Step 7: Add to get an answer

Add up the bottom two numbers (558 + 1860 = 2418) to get the answer:

             9 3

     x       2 6

           5 5 8

     +   1 8 6 0

     =   2 4 1 8

The bottom line is the answer. Therefore, 93 times 26 equals:

2418

The rate of change of the volume is 871.2 ft³/sec

Rate of change of volume is the change in volume with time.

The rate of change of radius is 6 feet per second.

rate of change in volume = dv/dt

rate of change in radius = dr/dt

to find radius of the sphere;

V = 4/3 πr³

163 = 4/3 x3.14r³

r³ = 163× 3)/4×3.14

r³ = 488/12.56

r³ = 38.85

r = 3.4 feet

therefore

dr/dt = 1/4πr² × dv/dt

= 6 = 1/4×3.14× 3.4² × dv/dt

dv/dt = 6×4× 3.14× 3.4²

dv/dt = 871.2 feet³ per second

therefore the rate of change of the volume is 871.2 feet³ per second

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Answer:

25 min

Step-by-step explanation:

60-50=10

10+15=25

Step-by-step explanation:

Answer: -42

Step-by-step explanation:

61.025 meters is the maximum height obtained by the baseball

A relation is a function if it has only One y-value for each x-value.

The length of time and the maximum height can be found by finding the vertex of the parabola.

h(t) = -4.9t² + 34.3t + 1

x = -b/2a

t = -34.3/-9.8

t=3.5

Now plug in t value in the function

h(3.5)= -4.9(3.5)² + 34.3(3.5)+ 1

=-4.9(12.25)+120.05+1

=-60.025+120.05+1

=61.025 meters

Hence, 61.025 meters is the maximum height obtained by the baseball

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The  two different subtraction that each have a different of 1 are 1/2 and 1/2

A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25.

To solve the problem we must know about fractions.

The number should be odd, therefore, the number should be 1, 3, 5, 7, etc.

1          9/8 - 5/8 = 4/8 = 1/2

2          7/8 -5/4 = 2/4 = 1/2

These for the two different subtraction that each have a different of 1

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The negation of the given statement

In Mathematics, the negation of a statement is the opposite of the given mathematical statement.

Given:

Statement: None of the members of the club can vote.

We have to focus on the word  "None" and the negation of word None is Some or at least.

So, Every member of the club can vote is not negation of the statement.

and, At least one member of the club cannot vote is not negation of the statement.

and, Some members of the club can vote is negation of the statement.

and, At least one member of the club can vote is negation of the statement.

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The number of degrees moved by the minute hand of a clock in 2/3hours is 240°

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360 °.

The hand of minute will move 360° to complete an hour.

If a full round will make angle at a point. Which is 360°

Therefore 2/3 of an hour will give an angle of 2/3 of 360°

= 2/3 × 360

= 240°

therefore the number of degrees moved by the minute hand in 2/3 hour is 240°

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