A Chi square test has been conducted to assess the relationship between marital status and church attendance. The obtained Chi square is 23.45 and the critical Chi square is 9.488. What may be concluded?
a. reject the null hypothesis, church attendance and marital status are dependent
b. reject the null hypothesis, church attendance and marital status are independent
c. fail to reject the null hypothesis, church attendance and marital status are dependent
d. fail to reject the null hypothesis, church attendance and marital status are independent

Answer:

Step-by-step explanation:

3π/2 is equivalent to 270°.  The "opposite side" for this angle is -2; the adjacent side is 0, and the hypotenuse is 2.

Thus, sin 3π/2 = opp/hyp = -2/2 = -1, and

         cos 3π/2 = adj/hyp = 0/2 = 0.

Answer:

[tex]sin\frac{3\pi}{2}=-1[/tex] and [tex]cos\frac{3\pi}{2}=0[/tex]

Step-by-step explanation:

We are given that a unit circle

We have to find the value of [tex]sin\frac{3\pi}{2}[/tex] and [tex]cos\frac{3\pi}{2}[/tex] by using the unit circle

Radius of  circle=r=1 unit

We know that

[tex]x=r cos\theta[/tex] and [tex]y=r sin\theta[/tex]

We [tex]\theta=\frac{3\pi}{2}[/tex]

Then x=[tex]1\cdot cos\frac{3\pi}{2}[/tex]

[tex]x=cos (2\pi-\frac{\pi}{2})[/tex]

[tex]x=cos \frac{\pi}{2}[/tex]  ([tex]cos(2\pi-\theta)=cos\theta[/tex])

[tex]x=0 (cos\frac{\pi}{2}=0)[/tex]

[tex]y=1\cdot sin\frac{3\pi}{2}[/tex]

[tex]y=sin(2\pi-\frac{\pi}{2})[/tex]

[tex]y=-sin\frac{\pi}{2}[/tex]  ([tex]sin(2\pi-\theta)=-sin\theta[/tex])

[tex]y=-1[/tex]   ([tex]sin\frac{\pi}{2}=1[/tex])

Hence, [tex]sin\frac{3\pi}{2}=-1[/tex] and [tex]cos\frac{3\pi}{2}=0[/tex]

Answer: 1.8°

Step-by-step explanation:

To calculate the angle between the vectors u and v we use the formula of the dot product.

The dot product between two vecotores is:

[tex]u\ *\ v = |u||v|*cosx[/tex]

Where x is the angle between the vectors

As we know the components of both vectors, we calculate the dot product by multiplying the components of both vectors

[tex]u=6i + 4j\\v=7i +5j[/tex]

Then:

[tex]u\ *\ v = 6*7 + 4*5[/tex]

[tex]u\ *\ v = 42 + 20[/tex]

[tex]u\ *\ v =62[/tex]

Now we calculate the magnitudes of both vectors

[tex]|u|=\sqrt{6^2 + 4^2}\\\\|u|=2\sqrt{13}[/tex]

[tex]|v|=\sqrt{7^2 +5^2}\\\\|v|=\sqrt{74}[/tex]

Then:

[tex]62 = 2\sqrt{13}*\sqrt{74}*cosx[/tex]

Now we solve the equation for x

[tex]62 = [tex]cosx=\frac{62}{2\sqrt{13}*\sqrt{74}}\\\\x=arcos(\frac{62}{2\sqrt{13}*\sqrt{74}})\\\\x=1.8\°[/tex]

Answer: C. 13,839 (the answer is not among the given options, however the result is near this value)

Step-by-step explanation:

The exponential decay model for Carbon- 14 is given by the followig formula:

[tex]A=A_{o}e^{-0.0001211.t}[/tex]  (1)

Where:

[tex]A[/tex] is the final amount of Carbon- 14  

[tex]A_{o}=[/tex] is the initial amount of Carbon- 14

[tex]t[/tex] is the time elapsed (the value we want to find)

On the other hand, we are told the current amount of Carbon-14 [tex]A[/tex]  is [tex]19\%=0.19[/tex], assuming the initial amount of Carbon-14 [tex]A_{o}=[/tex] is  [tex]100\%[/tex]:

[tex]A=0.19A_{o}[/tex] (2)

This means: [tex]\frac{A}{A_{o}}=0.19[/tex] (2)

Now,finding [tex]t[/tex] from (1):

[tex]\frac{A}{A_{o}}=e^{-0.0001211.t}[/tex]  (3)

Applying natural logarithm on both sides:

[tex]ln(\frac{A}{A_{o}})=ln(e^{-0.0001211.t})[/tex]  (4)

[tex]ln(0.19)=-0.0001211.t[/tex]  (5)

[tex]t=\frac{ln(0.19)}{-0.0001211}[/tex]  (6)

Finally:

[tex]t=13713.717years[/tex]  This is the age of the paintings and the option that is nearest to this value is C. 13839 years

Answer:

Option D

Step-by-step explanation:

The equation of a parabola in vertex form is

[tex]y = a(x - h)^{2} + k[/tex]

Where (h,k) is the vertex.

We were given the vertex as (5,-4). This implies that:

h=5, k=-4, we can see that a=2 is the leading coefficient of all the options.

We substitute the values to get:

[tex]y = 2(x - 5)^{2} + - 4[/tex]

Or

[tex]y =2( {x - 5)}^{2} - 4[/tex]

Answer:

16 inches

Step-by-step explanation:

w = width of the rectangle

l = length of the rectangle

The perimeter of a rectangle is the length around it:

P = 2w + 2l

Given:

P = 92

l = w + 14

Substituting:

92 = 2w + 2(w + 14)

92 = 2w + 2w + 28

64 = 4w

w = 16

The width of the rectangle is 16 inches.

Final answer:

The width of the rectangle is 16 inches, deduced by using the perimeter formula for a rectangle and solving for width with given conditions.

Explanation:

To find the width of the rectangle given its perimeter and the fact that its length is 14 inches longer than its width, we start by listing what we know:

The perimeter of the rectangle is 92 inches.

The length (L) is 14 inches longer than the width (W).

Remember, the perimeter (P) of a rectangle is given by P = 2L + 2W. We can substitute L with W + 14, since the length is 14 inches more than the width. This gives us:

P = 2(W + 14) + 2W

Now we can plug in the value for P:

92 = 2(W + 14) + 2W

Then, distribute:

92 = 2W + 28 + 2W

Combine like terms:

92 = 4W + 28

Now, subtract 28 from both sides:

64 = 4W

Lastly, divide by 4 to solve for W:

16 = W

So, the width of the rectangle is 16 inches.

Answer:

Angles 1 and 3 are verical: Given

Angles 1 and 3 are formed by ntersecting lines:

Definition of vertical angles.

Angles 1 and 2 are a linear pair and angles 2 and 3 are a linear pair:

Definition of linear pair.

1 and 2 are supplementary, and 2 and 3 are supplementary:

Linear Pair Theorem

Angles 1 and 3 are congruent:

Congruent Supplement Theorem

Step-by-step explanation:

The first is given because it tells you it is given.

The second is the definition of vertical angles. Vertical angles are angles formed by two intersecting lines.

The third statement is the definition of linear pair. Linear pair is a pair of adjacent angles formed by two lines that intersect.

The fourth statement comes from the theorem of linear pairs.  Linear pair theorem states that if you have 2 angles that are a linear pair, then they are supplementary.

The fifth statement comes from the congruent supplement theorem. It says if 2 angles are supplementary to the same angle, then they are congruent to each other.

Answer:

  4 killer whales

Step-by-step explanation:

The dimensional analysis is ...

  (whales/ft³)(ft³/tank) = whales/tank

Putting the numbers with the units, we get ...

  (1.1142·10^-5 whales/ft³)(3.5900667·10^5 ft³/tank) = 4.00005... whales/tank

The maximum number of killer whales allowed in the main show tank is 4.

Answer: Second Option

[tex]b > 49[/tex]

Step-by-step explanation:

We have the following expression:

[tex]log_7(b) > 2[/tex]

We have the following expression:

To solve the expression, apply the inverse of [tex]log_7[/tex] on both sides of the equality.

Remember that:[tex]b ^ {log_b (x)} = x[/tex]

So we have to:

[tex]7^{log_7(b)} > 7^2[/tex]

[tex]b > 7^2[/tex]

[tex]b > 49[/tex]

The answer is the second option

Answer:

C. -5.3

Step-by-step explanation:

Simply add the negatives straight across to arrive at your answer.

I am joyous to assist you anytime.

Answer: C.-5.3

Step-by-step explanation: I could be wrong

3/6 and 7/14 can both be reduced to 1/2

Lets start with 3/6

3   divided by 3               1

--                                     ----

6  divided by 3                2

now, 7/14

7  divided by 7           1

--                                ----

14 divided by 7           2

Whatever you do to the numerator (top number) you have to do to the denominator (bottom number)

Answer:

The measure of arc EF = 146°

Step-by-step explanation:

From the figure we can see two circles  with same center.

From the figure itself we get measure of arc AB is same as measure of arc EF, measure of arc Ac is same as measure of arc ED and measure of arc BC is same as arc FD.

The measure of arc AB = 146°

Therefore the measure of arc EF = 146°

Yes, the Pythagorean Theorem only works with right triangles.

You can use it to solve for the hypotenuse, or either one of the sides depending on the information you are provided with.

Answer:

yes

Step-by-step explanation:

Answer:

.43

Step-by-step explanation:

If I see % in a number I like to think of it as times 1/100 or divided by 100 (those are the same thing).

So we are doing 43 divided by 100 (or 43/100) which gives you .43 .

Anytime you divide by 100 you have to move the decimal left twice. (43 is 43. so 43. divided by 100 is .43)

Example

23.5%=.235

Why?

23.5 divided by 100 is .235

Another example

4%=.04

Why?

4. divided by 100 is .04

Answer:

C)

Step-by-step explanation:

We are given with a pair of linear equations,

y=x+12

y=3x+2

Let us solve them for x and y

In order to solve them we subtract first equation from the second ,

0=2x-10

Adding 2x on both sides we get

2x=10

Dividing both sides by 2 we get

x=5

Now replacing this value of x  in first equation

y=5+12=17

Hence the solution of the two equations is (5,12)

And by solution of a linear pair of equations, we mean that both the lines passes through that point.

Answer:

cos(z) = .3846153846 and angle z = 67.38°

Step-by-step explanation:

Side UV is corresponding to side YX.  Side VW is corresponding to side YZ.  Side UW is corresponding to side XZ.

Starting with the first corresponding pair, we are told that side UV is 36, and that side YX is 3/5 of that.  So side YX is

[tex]\frac{3}{5}*36=21.6[/tex]

We are next told that side VW is 39, so side YZ is

[tex]\frac{3}{5}*39=23.4[/tex]

In order to find the cos of angle z, we need the adjacent side, which is side XZ.  Side XZ is 3/5 of side UW.  Right now we don't know the length of side UW, so we find it using Pythagorean's Theorem:

[tex]39^2-36^2=UW^2[/tex] and

[tex]UW^2=225[/tex] so

UW = 15

Now we can say that side XZ is

[tex]\frac{3}{5}*15=9[/tex]

The cos of an angle is the side adjacent to the angle (9) over the hypotenuse of the triangle (23.4) so our ratio is:

[tex]cos(z)=\frac{9}{23.4}[/tex]

which divides to

cos(z) = .3846153846

If you need the value of the angle, use the inverse cosine function on your calculator in degree mode to find that

angle z = 67.38°

Answer:

The approximate number of years is 10

The graph in the attached figure

Step-by-step explanation:

Let

f(x) the value of an antique plate

x is the number of yeras

we know that

The system of equations that represented the problem is equal to

[tex]f(x)=18(1.05)^{x}[/tex] ----> equation A

[tex]f(x)=30[/tex] ----> equation B

Solve the system by graphing

The solution of the system of equations is the intersection point both graphs

using a graphing tool

The solution is the point (10.47,30)

see the attached figure

therefore

The approximate number of years is 10

Answer:

1st graph

Step-by-step explanation:

just did it in edge

Answer:

A composition of transformations is a combination of two or more transformations.A composition of reflections over parallel lines has the same effect as a translation (twice the distance between the parallel lines.

Step-by-step explanation:

For this case we have the following expression:

[tex]\frac {11x-2-3 (1-7x) ^ 2} {(x + 1)}[/tex]

We must indicate the first step that allows to start the simplification of the expression.

It is observed that the first step to follow is to solve the square of the binomial that is in the numerator of the expression.

[tex](1-7x) ^ 2[/tex]

Answer:

Option A

Answer:

0

Step-by-step explanation:

11x-2-3(1-7x)^2/(1x+1)

11x-2-3-21x/1+1

-32x-2-3-1

-32x-1+1

-32=0

/-32 /-32

x=0

Answer:

x+(-2), y+(-3)

Step-by-step explanation:

Trapezoid ABCD has vertices A(-5,2), B(-3,4), C(-2,4) and D(-1,2).

The reflection across the y-axis has the rule

(x,y)→(-x,y),

so

The translation that maps points A', B', C' and D' to E, H, G, F is

and has a rule

(x,y)→(x-2,y-3)

Check the picture below.

where is the -16t² coming from?  that's Earth's gravity pull in feet.

[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{30}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{6}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\\\ h(t)=-16t^2+30t+6 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+30}t\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\bf \left(-\cfrac{30}{2(-16)}~~,~~6-\cfrac{30^2}{4(-16)} \right)\implies \left( \cfrac{30}{32}~,~6+\cfrac{225}{16} \right)\implies \left(\cfrac{15}{16}~,~\cfrac{321}{16} \right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\stackrel{\stackrel{\textit{how many}}{\textit{seconds it took}}}{0.9375}~~,~~\stackrel{\stackrel{\textit{how many feet}}{\textit{up it went}}}{20.0625})~\hfill[/tex]

Answer:

Step-by-step explanation:

I'm not sure if this question is coming from a physics class or an algebra 2 or higher math class, but either way, the behavior of a parabola is the same in both subjects.  If a parabola crosses the x axis, those 2 x values are called zeros of the polynomial.  Those zeros translate to the time an object was initially launched and when it landed.  The midpoint is dead center of where those x values are located.  For example, if an object is launched at 0 seconds and lands on the ground 3 seconds later, it reached its max height at 2 seconds.  So what we need to do is find the zeros of this particular quadratic, and the midpoint of those 2 values is where the object was at a max height of 20.06.

I used the physics equation representing parabolic motion for this, since it has an easier explanation. This equation is

[tex]x-x_{0}=v_{0}+\frac{1}{2}at^2[/tex]

where x is the max height, x₀ is the initial height, v₀ is the initial upwards velocity, t is time (our unknown as of right now), and a is the acceleration due to gravity (here, -32 ft/sec^2).  Filling in our values gives us this quadratic equation:

[tex]20.06-6=30(t)+\frac{1}{2}(-32)t^2[/tex]

Simplifying that a bit gives us

[tex]14.06=30t-16t^2[/tex]

Rearranging into standard form looks like this:

[tex]0=-16t^2+30t-14.06[/tex]

If we factor that using the quadratic formula we find that the 2 times where the ball was launched and then where it came back down are

t = .925 and .95 (the ball wasn't in the air for very long!)

The midpoint occurs between those 2 t values, so we find the midpoint of those 2 values by adding them and dividing the sum in half:

[tex]\frac{.925+.95}{2}=.9375[/tex]

Therefore, the coordinates of the vertex (the max height) of this parabola are (.94, 20.06).  That translates to: at a time of .94 seconds, the ball was at its max height of 20.06 feet

Answer:

$3.45

Step-by-step explanation:

$20.30 / 10  = $2.30 = 10%

$2.30 / 2  = $1.15 = 5%

$2.30 + $1.15 = $3.45 = 15%

Answer:

x=20

Step-by-step explanation:

we know that

Triangles YNF and YUN are congruent by SSS

Because

YN=YF=YU=r -----> the radius of the circle

FN=NU ----> given problem

therefore

∠FYN=∠NYU

and

arc FN=∠FYN -----> by central angle

arc NU=∠NYU -----> by central angle

so

arc FN=arc NU

substitute the given values

5x-10=3x+30

solve for x

5x-3x=30+10

2x=40

x=20

Answer:

6144 clients

Step-by-step explanation:

Number of clients in the beginning = 3

The number of clients doubled each month. This means for every month the number of clients was 2 times the previous month. This can be modeled by a geometric sequence, with first term as 3 and common ratio of 2.

The general formula for the geometric sequence is:

[tex]a_{n}=a_{1}(r)^{n-1}[/tex]

Here,

[tex]a_{1}[/tex] is the first term of the sequence which is 3

r is the common ratio which is 2 and n represents the number of term.

We need to calculate the number of clients after 1 year i.e. after 12 months. So here n will be 12. Using these values, we get:

[tex]a_{12}=3(2)^{12-1}=6144[/tex]

Thus, after 1 year the company started by Nick will have 6144 clients

Answer:

12,288

Step-by-step explanation:

all i did was multiple the previous outputs by 2.

3

6

12

24

48

96

192

384

768

1536

3072

6144

12288

Answer:

45 minutes each

Step-by-step explanation:

Set Plan A clients as x and Plan B clients as y to make a system of equations, the constant is the number of hours worked.

3x+5y=6

9x+7y=12

Now solve using substitution or elimination.  I will use elimination.

-9x-15y=-18 I multiplied the whole first equation by -3 to eliminate x.

9x+7y=12, add the equations

-8y=-6 solve for y

y= 3/4 of an hour or 45 minutes

Next plug y into either equation

3x+5(3/4)=6 Solve for x.

3x+15/4=6

3x=2.25

x=0.75, also 45 minutes

To check plug in each variable value to each equation to see if they work if you need to.

Answer:

D. [tex] x = 3 \pm \sqrt{10} [/tex]

Step-by-step explanation:

[tex] x^2 - 6x - 1 = 0 [/tex]

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

a = 1; b = -6; c = -1

[tex] x = \dfrac{-(-6) \pm \sqrt{(-6)^2 - 4(1)(-1)}}{2(1)} [/tex]

[tex] x = \dfrac{6 \pm \sqrt{36 + 4}}{2} [/tex]

[tex] x = \dfrac{6 \pm \sqrt{40}}{2} [/tex]

[tex] x = \dfrac{6 \pm \sqrt{4 \times 10}}{2} [/tex]

[tex] x = \dfrac{6 \pm 2 \sqrt{10}}{2} [/tex]

[tex] x = 3 \pm \sqrt{10} [/tex]

Answer:

Answer in the picture.

Answer:

[tex](-7)(-1.2)\leftrightarrow 8.4[/tex]

[tex](-2\frac{1}{2})(-2)\leftrightarrow 5[/tex]

[tex](2.5)(-2)\leftrightarrow -5[/tex]

[tex](7)(-1.2)\leftrightarrow -8.4[/tex]

Step-by-step explanation:

Product rule of signs:

(+)(+) = (+)

(+)(-) = (-)

(-)(+) = (-)

(-)(-) = (+)

Using these signs simplify the given expression.

[tex](-7)(-1.2)=8.4[/tex]

It means (-7)(-1.2) is equivalent to 8.4.

[tex](-2\frac{1}{2})(-2)=(-\frac{5}{2})(-2)=5[/tex]

It means [tex](-2\frac{1}{2})(-2)[/tex] is equivalent to 5.

[tex](2.5)(-2)=-5[/tex]

It means (2.5)(-2)- is equivalent to -5.

[tex](7)(-1.2)=-8.4[/tex]

It means (7)(-1.2) is equivalent to -8.4.

If two lines l and m are parallel, then a reflection along line l followed by a reflection along line m is the same as a translation. Therefore, the correct answer is: A. translation.

If two lines l and m are parallel, a reflection along l followed by a reflection along m is equivalent to a translation. This can be understood geometrically: when a figure is reflected across parallel lines, it undergoes a displacement without changing its orientation.

The sequence of two reflections results in the figure being shifted along a path parallel to the original lines, akin to a translation. While reflections change orientation and translations shift position, the combination of two reflections across parallel lines maintains the figure's orientation while relocating it.

Answer:

The correct option is  Y = 1,000(1.15)6 2,313 bacteria

Step-by-step explanation:

According to the given statement a growth medium is  inoculated with 1,000 bacteria.

Bacteria grow at a rate of = 15% = 0.15

Add 1 to make it easier = 0.15+1 = 1.15

We have to find the population of the culture 6 days after inoculation.

= 1000(1.15)^6

=1000(2.313)

= 2313 bacteria

The population of the culture 6 days after inoculation = 2313 bacteria

Therefore the correct option is  Y = 1,000(1.15)6 2,313 bacteria....

Answer:AAAAAAAAAAAAAAAAAAAA

Answer:y = 18(1.15)^x

Step-by-step explanation:

g o o g ; e

Answer:

The required equation is [tex]y = 18(1.15)^x[/tex].

Step-by-step explanation:

Consider the provided information.

The Initial value of poster = $ 18

After 1 year amount of increase = $ 20.70

With the rate of 15% = 0.15

Let future value is y and the number of years be x.

[tex]y = 18(1.15)^x[/tex]

Now verify this by substituting x=1 in above equation.

[tex]y = 18(1.15)^1=20.7[/tex]

Which is true.

Hence, the required equation is [tex]y = 18(1.15)^x[/tex].

Answer:

The measure of angle x is 74°

Step-by-step explanation:

we know that

The inscribed angle measures half of the arc that comprises

so

∠ABC=(1/2)[arc ADC]

substitute the given values

150°=(1/2)[4x+4]

300°=[4x+4]

4x=300-4

4x=296

x=74°