-2x +9y=8
x=y+3
Step by step

Answer: 9 adults 7 children

Step-by-step explanation:

Answer:

Step-by-step explanation:

take theta as reference angle

tan theta=opposite/adjacent

=15/8

Answer:

option B

Step-by-step explanation:

First find opposite side using Pythagoras theorem:

[tex]17^2 = 8^2 + opposite^2 \\\\opposite^2 = 289 - 64 = 225\\\\opposite = 15[/tex]

Therefore,

          [tex]tan \theta = \frac{opposite}{adjacent} = \frac{15}{8}[/tex]

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

Explanation:

I'll be using the formula

[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]

which is the nCr combination formula. We use nCr instead of nPr because the order of coasters doesn't matter. The whole time, the value of n stays fixed at n = 17 which is the total number of coasters to pick from.

While n is constant, the value of r will vary. It ranges from r = 15 to r = 17 inclusive of both endpoints. In other words, r will take on values from the set {15,16,17}. So we have three cases to consider. The r value is how many coasters we select. This is due to the "at least 15" which means "15 or more".

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

If you ride r = 15 coasters, then we have the following number of combinations

[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{17} C _{15} = \frac{17!}{15!*(17-15)!}\\\\_{17} C _{15} = \frac{17!}{15!*2!}\\\\_{17} C _{15} = \frac{17*16*15!}{15!*2!}\\\\_{17} C _{15} = \frac{17*16}{2!}\\\\_{17} C _{15} = \frac{17*16}{2*1}\\\\_{17} C _{15} = \frac{272}{2}\\\\_{17} C _{15} = 136\\\\[/tex]

There are 136 ways to ride exactly 15 coasters (when selecting from a pool of 17 total). The order doesn't matter.

We'll use this result later, so let x = 136.

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

If r = 16, then we follow the same steps as above. You should get 17C16 = 17

There are 17 ways to ride 16 coasters where order doesn't matter. Effectively this is the same as saying "there are 17 ways of picking a coaster that you won't ride"

Let y = 17 so we can use it later

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

Lastly, if r = 17, then nCr = 17C17 = 1 represents one way to ride all 17 coasters where order doesn't matter.

Let z = 1

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

Add up the values of x, y, and z to get the final answer

x+y+z = 136+17+1 = 154

Answer:

2500

Step-by-step explanation:

Answer:

[tex]\frac{dr}{dt}=0.11062ft/sec[/tex]

Step-by-step explanation:

From the question we are told that:

Radius [tex]r=5ft[/tex]

Height [tex]H=15ft[/tex]

Rate [tex]R=15ft/3sec =5ft/s[/tex]

Surface Radius [tex]R_{surf}=2.2ft[/tex]

Generally the equation for Volume is mathematically given by

 [tex]V=\frac{1}{3}\pi*r^2h[/tex]

Since radius to height ratio gives

 [tex]\frac{r}{h}=\frac{5}{15}[/tex]

 [tex]\frac{r}{h}=\frac{1}{3}[/tex]

 [tex]h=3r[/tex]

Therefore

 [tex]V=\frac{1}{3}\pi*r^2(3r)[/tex]

 [tex]V=\pi r^3[/tex]

Generally the equation for Change of Volume is mathematically given by

 [tex]\frac{dv}{dt}=\pi \frac{d}{dt}(r^3)[/tex]

 [tex]\frac{dv}{dt}=\pi 3*r^2 \frac{dr}{dt}[/tex]

 [tex]\frac{dv}{dt}=\pi 3*(2.2)^2 \frac{dr}{dt}[/tex]

 [tex]\frac{dr}{dt}=\frac{5}{45.62}[/tex]

 [tex]\frac{dr}{dt}=0.11062ft/sec[/tex]

No, There is no any sentences are incorrect.

Hence, All sentences are correct.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Consider the following statements about the effect of different values of a on the function,

⇒ y = a bˣ

Now, We know that;

For the value of a such that |a| > 1

The graph of y = bˣ is vertically stretch.

And, For the values of a such that 0 < |a| < 1;

The graph of y = bˣ is vertically compress.

And, When we take negative value of a.

Then, Function reflect y = bˣ across the y-axis.

Thus, There is no any sentences are incorrect.

Hence, All sentences are correct.

Learn more about the function visit:

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Given:

The geometric sequence is:

25.5, 5.1, 1.02, 0.204, ...

To find:

The explicit rule for the given geometric sequence.

Solution:

We have,

25.5, 5.1, 1.02, 0.204, ...

Here, the first term is 25.5 and the common ratio is:

[tex]r=\dfrac{a_2}{a_1}[/tex]

[tex]r=\dfrac{5.1}{25.5}[/tex]

[tex]r=\dfrac{1}{5}[/tex]

The explicit rule for a geometric sequence is:

[tex]a_n=ar^{n-1}[/tex]

Where, a is the first term and r is the common ratio.

Putting [tex]a=25.5,\ r=\dfrac{1}{5}[/tex] in the above formula, we get

[tex]a_n=25.5(\dfrac{1}{5})^{n-1}[/tex]

Therefore, the correct option is B.

Answer:

A 70°

Step-by-step explanation:

Angle of the triangle

=180-60-60

=60°

x= 180-60-50

=120-50

=70°

Answer:

Step-by-step explanation:

$39

The net worth should be considered as the $39.

We know that

Net worth = Total assets - total liabilities

here,

total assets = checking & savings + baseball card + check for work done

= $275 + $210 + $19

= $504

And, the total liabilities = owe + borrowed

= $415 + $50

= $465

So, the net worth be

= $504 - $465

= $39

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Answer:

you add an image

Step-by-step explanation:

Answer:

... if it had the same slope in the y=mx+b equation where m is the slope and x is just x and b is the y-intercept

Step-by-step explanation:

say Car A had the equation y=2x+3- Car B would also have to have be y=2x but the y intercept could be any value

Answer:

(-10, -4)

Step-by-step explanation:

That is the ordered pair

Answer:

Volume: The space which fills up a certain object on the inside.

Answer:

Option A, 1/8 pound would be the correct answer

Step-by-step explanation:

Since mode of the data is the number in the data that occurs the most, if noticed 1/8 occurs 4 times in the data set given and hence is the mode of the data set

Hope this helps!

tan( 20 ) + 4 Sin( 20 ) =

( Sin( 20 ) / Cos( 20 ) ) + 4 Sin( 20 ) =

Sin( 20 ) + 4 Sin( 20 ).Cos( 20 ) / Cos( 20 ) =

Sin( 20 ) + 2 × 2 Sin(20).Cos(20)/ Cos(20) =

Sin( 20 ) + 2 × Sin( 40 ) / Cos( 20 ) =

Sin( 20 ) + 2Sin( 40 ) / Cos( 20 ) =

Sin( 20 ) + 2Cos( 50 ) / Cos ( 20 ) =

Sin( 20 ) + 2Cos( 20 + 30 ) / Cos( 20 ) =

________________________________

2 × Cos( 30 + 20 ) =

2 × [ Cos(30).Cos(20) - Sin(30).Sin(20) ] =

2 × [ √3/2 × Cos(20) - 1/2 × Sin(20) ] =

√3 Cos(20) - Sin(20)

_________________________________

Sin( 20 ) + 2Cos ( 20 + 30 ) / Cos( 20 ) =

Sin( 20 ) + √3 Cos(20) - Sin(20) / Cos(20) =

Sin(20) - Sin(20) + √3 Cos(20) / Cos(20) =

0 + √3 Cos(20) / Cos(20) =

√3 Cos(20) / Cos(20) =

Cos(20) simplifies from the numerator and denominator of fraction

√3 × 1 / 1 =

√3

And we're done ....

Answer:

BD ≈ 2.8 units

Step-by-step explanation:

By angle bisector theorem,

"If a segment bisects an angle of a triangle, then it divides the opposite side  into the segments which are proportional to the other two sides"

Here, AD is the bisector of the ∠BAC,

[tex]\frac{BD}{CD}=\frac{AB}{AC}[/tex]

[tex]\frac{8.1}{5.9}= \frac{BD}{2}[/tex]

BD = [tex]\frac{2\times 8.1}{5.9}[/tex]

BD = 2.75

BD ≈ 2.8 units

Answer:

(95.215 ; 100.785)

(95 ; 101) (nearest whole number)

Step-by-step explanation:

To obtain the confidence interval :

Mean ± margin of error

Mean = 98 hours

Margin of Error = Tcritical * (s/√n)

samole standard deviation, s = 5.6 hours

df = n - 1 = 18 - 1 = 17

Tcritical at (0.05, df = 17) = 2.110

Hence ;

Margin of Error = 2.110 * (5.6/√18) = 2.785

Confidence interval :

98 ± 2.785

Lower boundary = 98 - 2.785 = 95.215

Upper boundary = 98 + 2.785 = 100.785

(95.215 ; 100.785)

Answer:

735 mm³

Step-by-step explanation:

49 x 15 = 735

Answer:

735mm

Step-by-step explanation:

Answer:

3 ft, 3ft, 5ft => 45 cubic feet

6 ft, 2 ft, 4 ft => 48 cubic feet

7 ft, 2 ft, 2 ft => 28 cubic feet

6 ft, 5 ft, 2 ft => 60 cubic feet

Step-by-step explanation:

Recall: formula for volume of a rectangular prism is given as, V = L × W × H

✔️Volume of rectangular prism with the following dimensions:

L = 3 ft

W = 3 ft

H = 5 ft

V = 3 × 3 × 5

V = 45 cubic feet

✔️Volume of rectangular prism with the following dimensions:

L = 6 ft

W = 2 ft

H = 4 ft

V = 6 × 2 × 4

V = 48 cubic feet

✔️Volume of rectangular prism with the following dimensions:

L = 7 ft

W = 2 ft

H = 2 ft

V = 7 × 2 × 2

V = 28 cubic feet

✔️Volume of rectangular prism with the following dimensions:

L = 6 ft

W = 5 ft

H = 2 ft

V = 6 × 5 × 2

V = 60 cubic feet

Answer:

∠BAC = 75°

Step-by-step explanation:

just subtract angle BAD from angle CAD

9514 1404 393

Answer:

  3

Step-by-step explanation:

For x > 0, the function f(x) is ...

  f(x) = 3x -4 . . . . . . . . for x > 0

Translating this down 1 unit makes it ...

  g(x) = f(x) -1 = 3x -5

The rate of change for any interval such that x > 0 in the whole interval is the coefficient of x: 3.

The rate of change on the interval is 3.

__

If you like, you can find the rate of change from ...

  m = (g(5) -g(2))/(5 -2) = (10 -1)/3 = 9/3 = 3

The rate of change is 3.

Answer:

$15,264 cost amount on new advertising.

Shown as new equation that includes (original + new customer base)

n3=15264a

Step-by-step explanation:

First we have to find original amount of customers as 3 represents a multiple of n

n3=13824a

n3 means n x 3 then customer base is one third

= 1/3 x 13,824  = 4608 original customers per year

= 4608 original customers +480 new customers

4608 + 480 = 5088 total orig+initial  customers

5088 x 3 = 15264 cost

= ($)15,264 cost

new equation

n3=15264a

Answer:

take 28 degree as reference angle

using sine angle

sin28=p/h

0.46=10/h

0.46h=10

h=10/0.46

h=21.73

therefore hypotenuse =21.73

again using sine rule

take 25 degree as reference angle

sin 25=p/h

0.42=SR/21.73

0.42*21.73=SR

9.12=SR

9.1=SR

Step-by-step explanation:

Answer:

Step-by-step explanation:

D.all citizens; registered voters

Given :

A function f(x) for different range of x.

To Find :

The value of f( -3 ) .

Solution :

We have to find the value of function at x = -3.

Now, in the given figure -3 lies in range x ≤ -2 and definition of function at that range is :

[tex]f(x) = \dfrac{2}{x}[/tex]

So, putting value of x = -3 in above equation, we get :

[tex]f(-3) = \dfrac{2}{-3} \\\\f(-3) = \dfrac{-2}{3}[/tex]

Hence, this is the required solution.

Answer:

y = mx + b

m =(-2--4)/(-6--7)

m = 2

-2 = 2(-6) +b

b = 10

y= 2x + 10

Answer:

y = 1/3x + 70/3

Step-by-step explanation:

2 points on the graph:

(20, 30) and (50, 40)

Slope:

m=(y2-y1)/(x2-x1)

m=(40 - 30)/(50 - 20)

m= 10/30

m= 1/3

Slope-intercept:

y - y1 = m(x - x1)

y - 30 = 1/3(x - 20)

y - 30 = 1/3x - 20/3

y = 1/3x + 70/3

Answer:

The slope is 3

Step-by-step explanation:

12x−4y=3

Solve for y

Subtract 12x from each side

-12x +12x−4y=-12x+3

-4y = 12x+3

Divide each side by -4

-4y/-4 = -12x / -4 +3/-4

y = 3x -3/4

This is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 3

Answer:

The slope is 3

Step-by-step explanation:

12x−4y=3

Solve for y

Subtract 12x from each side

-12x +12x−4y=-12x+3

-4y = 12x+3

Divide each side by -4

-4y/-4 = -12x / -4 +3/-4

y = 3x -3/4

This is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 3