If two spheres have the same center but different radii, they are called concentric spheres.

True

False

Answer:

7

Step-by-step explanation:

the slope intercept form is y=mx + b

where b is the y intercept,

and your question is y=5x + 7

so the y intercept form would equal to 7

Answer:

y intercept equals 1

Step-by-step explanation:

y= -1/2x+1

the slope is -1/2

the y intercept is 1

Answer:

Option D. Divide 15 by 2

Step-by-step explanation:

we know that

To find the y-coordinate of the midpoint of a vertical line, adds the y-coordinates of the endpoints and divide by two

we have the endpoints

(0,0) and (0,15)

The y-coordinate of the midpoint is (0+15)/2=15/2=7.5

therefore

Divide 15 by 2

Answer:

the answer is to count by hands ( A ) and divide 15 by 2 ( D )

Step-by-step explanation:

Answer with explanation:

To find the common multiple of 45 and 95,we will find HCF of 45 and 95.

45=3 × 3× 5

95=5 × 19

⇒H CF(45,95)

=3 × 3×5×19

=855

→Common multiple of 45 and 95 =855

→There are infinite number of multiple of 855 which are 855, 1710, 2565,.....

You have not written between which two numbers.So, you should write multiple of 855 such that it is smaller than the greater number.

Answer:

C. √13

Step-by-step explanation:

The distance between two points is given by

d =sqrt( (x2-x1)^2 + (y2-y1)^2)

  = sqrt( (3-0)^2 + (-3--1)^2)

  = sqrt( 3^2 + (-3+1)^2)

  = sqrt( 9+(-2)^2)

  = sqrt( 9+4)

  = sqrt(13)

To answer this, you basically use Pythagoras' Theroem, but instead of:

[tex]c = \sqrt{a^{2} + b^{2}}[/tex]

it will be :

[tex]distance = \sqrt{(y - y1)^{2} + (x - x1)^{2}  }[/tex]

So you are finding the squareroot of the (difference in y coordinates)² plus (difference in x coordinates) ²:

x is the x-coordinate of (0, -1)      (so x = 0)

y is the y-coordinte of (0, -1)        ( so y = -1)

x1 is the x coordinate of (3, -3)        ( so x1 = 3)

y1 is the y coordinate of (3, -3)        (so y1 = -3)

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

Now, lets find the distance between the two points, by substituting all of this values into the equation at the top:

[tex]distance = \sqrt{(y - y1)^{2} + (x - x1)^{2}  }[/tex]    (substitute in values)

[tex]distance = \sqrt{( 0 -3)^{2} + (-1 - -3)^{2} }[/tex]   (simplify: note -1 - - 3 = -1 + 3)

[tex]distance = \sqrt{( -3)^{2} + (-1 +3)^{2} }[/tex]     (simplify)

[tex]distance = \sqrt{( -3)^{2} + (2)^{2} }[/tex]           (now square the numbers)

[tex]distance = \sqrt{9 + 4 }[/tex]                   (simplify)

[tex]distance = \sqrt{13 }[/tex]

___________________________________________

C.  [tex]\sqrt{13}[/tex]

Answer:

[tex]\frac{7}{10}[/tex]

Step-by-step explanation:

Fraction of the amount donated to school library = [tex]\frac{2}{10}[/tex]

Fraction of the amount donated to animal shelter = [tex]\frac{1}{10}[/tex]

Fraction of the amount donated to food bank = [tex]\frac{4}{10}[/tex]

The rest of the amount was saved for next project.

Thus, the total fraction of the amount donated will be the sum of fractions of amount donated to school library, animal shelter and food bank.

i.e.

Fraction of the amount donated = [tex]\frac{2}{10}+\frac{1}{10}+\frac{4}{10} = \frac{7}{10}[/tex]

This means, Tyler and Katie donated [tex]\frac{7}{10}[/tex] of their profits.

Answer:−1.825

Step-by-step explanation:

Answer:

[tex]z=0.923[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and z, represent an inverse variation if it can be expressed in the form [tex]z*x=k[/tex] or [tex]z=k/x[/tex]

step 1

Find the value of k

For x=6, z=2

[tex]z*x=k[/tex]

substitute

[tex]2*6=k[/tex]

[tex]k=12[/tex]

therefore

The equation of the inverse variation is equal to

[tex]z*x=12[/tex]

step 2

What is the value of z when x=13

substitute the value of x in the equation and solve for z

[tex]z*(13)=12[/tex]

[tex]z=12/13[/tex]

[tex]z=0.923[/tex]

We have the following expression:

[tex]tan(\theta)cot(\theta)-sin^{2}(\theta)=cos^2(\theta)[/tex]

We know that:

[tex]cot(\theta)=\frac{1}{cot(\theta)}[/tex]

Therefore, by substituting in the original expression:

[tex]tan(\theta)\left(\frac{1}{tan(\theta)}\right)-sin^{2}(\theta)=cos^2(\theta) \\ \\ \\ Simplifying: \\ \\ 1-sin^2(\theta)=cos^2(\theta)[/tex]

We know that the basic relationship between the sine and the cosine determined by the Pythagorean identity, so:

[tex]sin^2(\theta)+cos^2(\theta)=1[/tex]

By subtracting [tex]sin^2(\theta)[/tex] from both sides, we get:

[tex]\boxed{cos^2(\theta)=1-sin^2(\theta)} \ Proved![/tex]

We have the following expression:

[tex]\frac{cos(\alpha)}{cos(\alpha)-sin(\alpha)}=\frac{1}{1-tan(\alpha)}[/tex]

Here, let's multiply each side by [tex]cos(\alpha)-sin(\alpha)[/tex]:

[tex](cos(\alpha)-sin(\alpha))\left(\frac{cos(\alpha)}{cos(\alpha)-sin(\alpha)}\right)=(cos(\alpha)-sin(\alpha))\left(\frac{1}{1-tan(\alpha)}\right) \\ \\ Then: \\ \\ cos(\alpha)=\frac{cos(\alpha)-sin(\alpha)}{1-tan(\alpha)}[/tex]

We also know that:

[tex]tan(\alpha)=\frac{sin(\alpha)}{cos(\alpha)}[/tex]

Then:

[tex]cos(\alpha)=\frac{cos(\alpha)-sin(\alpha)}{1-\frac{sin(\alpha)}{cos(\alpha)}} \\ \\ \\ Simplifying: \\ \\ cos(\alpha)=\frac{cos(\alpha)-sin(\alpha)}{\frac{cos(\alpha)-sin(\alpha)}{cos(\alpha)}} \\ \\ Or: \\ \\ cos(\alpha)=\frac{\frac{cos(\alpha)-sin(\alpha)}{1}}{\frac{cos(\alpha)-sin(\alpha)}{cos(\alpha)}} \\ \\ Then: \\ \\ cos(\alpha)=cos(\alpha).\frac{cos(\alpha)-sin(\alpha)}{cos(\alpha)-sin(\alpha)} \\ \\ \boxed{cos(\alpha)=cos(\alpha)} \ Proved![/tex]

We have the following expression:

[tex]\frac{cos(x+y)}{cosxsiny}=coty-tanx[/tex]

From Angle Sum Property, we know that:

[tex]cos(x+y)=cos(x)cos(y)-sin(x)sin(y)[/tex]

Substituting this in our original expression, we have:

[tex]\frac{cos(x)cos(y)-sin(x)sin(y)}{cosxsiny}=coty-tanx[/tex]

But we can also write this as follows:

[tex]\\ \frac{cosxcosy}{cosxsiny}-\frac{sinxsiny}{cosxsiny}=coty-tanx \\ \\ Simplifying: \\ \\ \frac{cosy}{siny}-\frac{sinx}{cosx} =coty-tanx \\ \\ But: \\ \\ \frac{cosy}{siny}=coty \\ \\ \frac{sinx}{cosx}=tanx \\ \\ Hence: \\ \\ \boxed{coty-tanx=coty-tanx} \ Proved![/tex]

We have the following expression:

[tex]\ln\left|1+cos \theta\right|+\ln\left|1-cos \theta\right|=2\ln\left|sin \theta\right|[/tex]

By Logarithm product rule, we know:

[tex]log_{b}(x.y) = log_{b}(x) + log_{b}(y)[/tex]

So:

[tex]\ln\left|1+cos \theta\right|+\ln\left|1-cos \theta\right|=\ln\left|(1+cos \theta)(1-cos \theta)\right|[/tex]

The Difference of Squares states that:

[tex]a^2-b^2=(a+b)(a-b) \\ \\ So: \\ \\ (1+cos \theta)(1-cos \theta)=1-cos^2 \theta[/tex]

Then:

[tex]\ln\left|(1+cos \theta)(1-cos \theta)\right|=\ln\left|1-cos^{2} \theta\right|[/tex]

By the Pythagorean identity:

[tex]sin^2(\theta)+cos^2(\theta)=1 \\ \\ So: \\ \\ sin^2 \theta = 1-cos^2 \theta[/tex]

Then:

[tex]\ln\left|1-cos^{2} \theta\right|=\ln\left|sin^2 \theta|[/tex]

By Logarithm power rule, we know:

[tex]log_{b}(x.y) = ylog_{b}(x)[/tex]

Then:

[tex]\ln\left|sin^2 \theta|=2\ln\left|sin \theta|[/tex]

In conclusion:

[tex]\boxed{\ln\left|1+cos \theta\right|+\ln\left|1-cos \theta\right|=2\ln\left|sin \theta\right|} \ Proved![/tex]

Answer:

c. the time it takes to run the 100-meter race

Step-by-step explanation:

An independent variable is the variable which is not being controlled and it does not depend on the other variables. This is the variable which is being studied/measured in the experiment.

Option a. The previous running experience is not being considered and is not a variable under study in this case. So this is not the answer.

Option b. The teenagers who are being studied constitute the sample. These are not the variables.

Option c. Time is the independent variable, as it is being measured during the experiment and the conclusion is being drawn based on it.

Option d. Amount of caffeine is being decided by Cosella and is therefore not the independent variable.

Therefore, the correct answer is option c

Answer: The contrapositive statement :"If you do not have a gerbil, then you are not a pet owner.”

It is false.

Counter example : If you have a dog, then you are a pet owner.

Step-by-step explanation:

We know that the contrapositive of a statement of the form " If a then b" is "If not a then not b.

Given: The conditional statement is "If you have a gerbil, then you are a pet owner.”

Then the contrapositive statement will be "If you do not have a gerbil, then you are not a pet owner.”

The contrapositive statement is false.

Counter example : If you have a dog, then you are a pet owner.

Means if you area pet owner then it can be any pet not just gerbil.

Answer:

The contrapositive is false.

Step-by-step explanation:

Given conditional statement is :

If you have a gerbil, then you are a pet owner (conditional statement is in the form of if p, then q)

The contrapositive is represented as (if not q, then not p)

So, the contrapositive sentence will be :

If you are not a pet owner, then you do not have a gebril.

This statement is false as if you are not a pet owner then you will not have any animal with you and not only gebril.

Answer: 0.4758

Step-by-step explanation:

Given : Mean : [tex]\mu=137\text{ lb}[/tex]

Standard deviation : [tex]\sigma =28.9\text{ lb}[/tex]

Also, the new population of pilots has normally distributed .

The formula to calculate the z-score :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x=130 lb .

[tex]z=\dfrac{130-137}{28.9}=-0.2422145\approx-0.24[/tex]

For x=171lb.

[tex]z=\dfrac{171-137}{28.9}=1.1764705\approx1.18[/tex]

The p-value =[tex]P(-0.24<z<1.18)=P(z<1.18)-P(z<-0.24)[/tex]

[tex]=0.8809999-0.4051651=0.4758348\approx0.4758348\approx0.4758[/tex]

Hence, the required probability : 0.4758

[tex]\huge{\boxed{\frac{5}{2}}}[/tex]

Slope-intercept form is [tex]f(x)=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

[tex]\frac{5x}{2}=\frac{5}{2}x[/tex], so change the equation to represent this. [tex]f(x)=\frac{5}{2}x+3[/tex]

Great! Now the function is in slope-intercept form, so we can just see that [tex]m[/tex], or the slope, is equal to [tex]\boxed{\frac{5}{2}}[/tex]

Answer: 0.25

Step-by-step explanation:

Given : The  future lifetime of Gary is uniformly distributed with interval [0 years , 60 years].

Then the probability density function for Gary's future lifetime will be:-

[tex]f(x)=\dfrac{1}{60-0}=\dfrac{1}{60}[/tex]

The future lifetime of Eric is uniformly distributed with interval [0 years , 40 years].

Then the probability density function for Erin's future lifetime will be:-

[tex]f(x)=\dfrac{1}{40-0}=\dfrac{1}{40}[/tex]

Now, the joint density function for Gary and Eric's future lifetime :-

[tex]f(x,y)=f(x)f(y)=\dfrac{1}{40\times60}=\dfrac{1}{2400}[/tex]  [∵Their future lifetimes are independent. ]

Now, the probability that Gary dies first is given by :-

[tex]\int^{60}_{0}\int^{40}_{x}f(x,y)\ dy\ dx\\\\=\int^{60}_{0}\int^{40}_{x}\dfrac{1}{2400}\ dy\ dx\\\\=\int^{60}_{0}\dfrac{40-x}{2400}\ dx\\\\=\dfrac{1}{2400}[40x-\dfrac{x^2}{2}]^{60}_{0}\\\\=\dfrac{1}{2400}(2400-\dfrac{3600}{2})=0.25[/tex]

Hence, the probability that Gary dies first =0.25

Answer:

1st problem:

Converges to 6

2nd problem:

Converges to 504

Step-by-step explanation:

You are comparing to [tex]\sum_{k=1}^{\infty} a_1(r)^{k-1}[/tex]

You want the ratio r to be between -1 and 1.

Both of these problem are so that means they both have a sum and the series converges to that sum.

The formula for computing a geometric series in our form is [tex]\frac{a_1}{1-r}[/tex] where [tex]a_1[/tex] is the first term.

The first term of your first series is 3 so your answer will be given by:

[tex]\frac{a_1}{1-r}=\frac{3}{1-\frac{1}{2}}=\frac{3}{\frac{1}{2}=6[/tex]

The second series has r=1/6 and a_1=420 giving me:

[tex]\frac{420}{1-\frac{1}{6}}=\frac{420}{\frac{5}{6}}=420(\frac{6}{5})=504[/tex].

Answer:

C'(4,4)

Step-by-step explanation:

The dilation of quadrilateral ABCD over the origin by a scale factor of 2 has the rule

(x,y)→(2x,2y)

So,

Hence, the coordinates of the image point C' are (4,4) (see attached diagram for details)

Answer:

The coordinates of C' = (4,4)

Step-by-step explanation:

The coordinates of C can be found by looking at the graph,

Coordinates of C = (2,2)

ABCD is dilated by a factor of 2 to get A'B'C'D'.

So, the coordinates of C' will be found by multiplying the coordinates of C by 2.

C' = (2*2,2*2)

C' = (4,4)

So, The coordinates of C' = (4,4)

Answer:

1. [tex]\dfrac{AD}{DB}+1=\dfrac{CE}{EB}+1[/tex]

2. Addition property of equality

Step-by-step explanation:

In triangle ABC,

[tex]\dfrac{AD}{DB}=\dfrac{CE}{EB}.[/tex]

The addition property of equality states that if the same amount is added to both sides of an equation, then the equality is still true.

Use addition property of equality, add 1 to both sides of previouse equality:

[tex]\dfrac{AD}{DB}=\dfrac{CE}{EB}\\ \\\dfrac{AD}{DB}+1=\dfrac{CE}{EB}+1\\ \\\dfrac{AD+DB}{DB}=\dfrac{CE+EB}{EB}[/tex]

Answer:

(AD/DB) +1 = (CE/EB) +1 -----> Addition Property of Equality

Answer:

  TRUE

Step-by-step explanation:

Changing the mean by adding the same number to every data value does not change the differences those values have from the new mean. Hence the standard deviation remains unchanged. If it was 6, it will be 6.

Answer:

True because standard divination stays the same

Step-by-step explanation:

The complementary event to drawing a blue marble includes any outcome other than drawing a blue marble. Therefore, drawing a red marble, a green marble, a red or green marble, or not drawing a blue marble, all are complementary events.

In probability, the complementary event of an event represents all outcomes not covered by the original event. In this case, the original event is 'drawing a blue marble'. Thus, the complementary event would include any outcome other than drawing a blue marble.

Based on the options given:

All these are complementary events to drawing a blue marble, as they all represent outcomes other than 'drawing a blue marble'.

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Answer:

6 units

Step-by-step explanation:

A rectangle's width is one-fourth of its length.

w = 1/4 l

area is 9 square units

A = l*w = 9

  Replacing w with 1/4l

  l * (1/4l) = 9

1/4 l^2 = 9

Multiply each side by 4 to clear the fraction

4 * 1/4 l^2 = 4*9

l^2 = 36

Take the square root of each side

sqrt (l^2) = sqrt(36)

l =6

Answer:

6 units

Step-by-step explanation:

Let the length = L

Then the width = L/4

area = length * width

area = L * L/4 = 9

L^2/4 = 9

L^2 = 36

L = 6 or L = -6

Since we are dealing with a length, we eliminate the negative answer.

Answer: 6 units

P.S. Your equation is incorrect. L(L) = 9 would work for a square with 4 congruent sides and area 9. Here the sides have different lengths. The equation is L(L/4) = 9.

Answer:

51.496 miles

Step-by-step explanation:

circumference of circle= 2pir

here we will tale radius as 8.2 because 16.4 is diameter of circle.

2*3.14*8.2=

6.28*8.2=51.496 miles

Answer:

  10-2x

Step-by-step explanation:

If x is the length of one side of the square, the total width of the cardboard has two squares cut from it. The amount of width remaining is the width of the box. Since the original width of the cardboard is 10, the width of the box is ...

  10 -2x

Answer:

[tex]m =-\frac{1}{2}[/tex]

Step-by-step explanation:

The equation of a line in the pending intersection form is:

[tex]y = mx + b[/tex]

Where m is the slope of the line and b is the intersection with the y axis.

In this case we have the following equation

[tex]y-3=-\frac{1}{2}(x-2)[/tex]

To find the slope of this line you must rewrite it in the form

[tex]y = mx + b[/tex]

Then we solve the equation for y.

[tex]y-3=-\frac{1}{2}(x-2)[/tex]

[tex]y=-\frac{1}{2}(x-2)+3[/tex]

[tex]y=-\frac{1}{2}x-2*(-\frac{1}{2})+3[/tex]

[tex]y=-\frac{1}{2}x+1+3[/tex]

[tex]y=-\frac{1}{2}x+4[/tex]

Note that [tex]m =-\frac{1}{2}[/tex]

Finally the slope is: [tex]m =-\frac{1}{2}[/tex]

The slope of the line with equation; y-3 = -1/2(x-2) is; slope, m = -1/2.

According to the question, the equation of the line in discuss is; y-3 = -1/2(x-2).

To determine the slope of the line, we need to rearrange the equation such that it resembles the slope-intercept form of the equation of a straight line as follows;

The equation of a straight line; y = mx + c.

Now, we expand the equation of the line and rearrange as follows;

By comparison, the slope of the line given bey the equation, y-3=-1/2(x-2) is; slope, m = -1/2.

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Answer:

21°

Step-by-step explanation:

the angles of triangle abc has to = 180 so subtract the known angles to get 21

angles bca and daf have to be the same so its 21

Answer:

[tex]x=21[/tex]

Step-by-step explanation:

We have been given an image of two parallel lines cut by a transversal. We are asked to find the measure of x.

We know that corresponding angles of two parallel lines are equal. We can see that angle BCA and angle DAF are corresponding angles.

Let us find measure of angle BCA using angle sum property.

[tex]54^{\circ}+105^{\circ}+m\angle BCA=180^{\circ}[/tex]

[tex]159^{\circ}+m\angle BCA=180^{\circ}[/tex]

[tex]159^{\circ}-159^{\circ}+m\angle BCA=180^{\circ}-159^{\circ}[/tex]

[tex]m\angle BCA=21^{\circ}[/tex]

Therefore, the value of x is 21 degrees.

Answer:

  168 km

Step-by-step explanation:

Let x represent the distance Tyler drives at the slower speed, and let y represent the distance at the higher speed. Using time = distance/speed, we can write equations for the total travel time:

  x/42 +y/105 = 2.5

  x/28 +y/60 = 4.0 . . . . . 1.5 hours more than the usual 2.5 hours

Multiplying the first equation by 210, we have ...

  5x +2y = 525

Multiplying the second equation by 420, we get ...

  15x +7y = 1680

Subtracting 3 times the first of these equations from the second, we have ...

  (15x +7y) -3(5x +2y) = (1680) -3(525)

  y = 105

Putting this into the very first equation, we get ...

  x/42 + 105/105 = 2.5

  x/42 = 1.5 . . . . . . subtract 1

  x = 63 . . . . . . . . .multiply by 42.

The total distance to Tyler's parents' house is ...

  63 km + 105 km = 168 km

Tyler's total travel distance is approximately 168 km.

Calculating Total Distance Traveled

To determine the total distance Tyler traveled, let du be the distance through urban areas and dm be the distance on the motorway.

→ The total distance is:

[tex]D = d_u + d_m[/tex]

First, using the normal journey:

→ Urban Area:

Speed = 42 km/h

Time = [tex]t_u[/tex] / 42,

→ Motorway:

Speed = 105 km/h

Time = [tex]t_m[/tex] / 105,

→ Total time for normal journey:

→ [tex]t_u/42 + t_m/105 = 2.5\ hours[/tex]

We have:

→ [tex]d_u[/tex] = 42 * [tex]t_u[/tex]

→ [tex]d_m[/tex] = 105 * [tex]t_m[/tex]

When there is fog:

→ Urban Area:

Speed = 28 km/h

Time = [tex]t__uf}[/tex] / 28

→ Motorway:

Speed = 60 km/h

Time = [tex]t_{um[/tex] / 60

Total time for foggy journey:

→ [tex]t_{uf[/tex] /28 + [tex]t_{mf[/tex] /60

Given that he leaves 1 hour early and arrives 30 minutes late, the total journey time in foggy conditions is:

→ 2.5+1+0.5=4 hours

Thus,

→  [tex]t_{uf[/tex] /28 + [tex]t_{mf[/tex] /60 = 4

Solving the Equations

We now have two equations:

→ [tex]t_u/42 + t_m/105 = 2.5\ hours[/tex]

→ [tex]t_{uf}\ /\ 28\ + t_{mf} \ /\ 60 = 4 hours[/tex]

Let's solve these equations step-by-step.

First, let's multiply the first equation by 210 (the least common multiple of 42 and 105):

→ [tex]210(t_u/42 + t_m/105) = 210*2.5[/tex]

→ [tex]5t_u+2t_m=525[/tex] (eq. 1)

Next, let's multiply the second equation by 420 (the least common multiple of 28 and 60):

→ [tex]420( t_u/28+ t_m /60)=420*4[/tex]

→ [tex]15t_u +7t_m =1680[/tex] (eq. 2)

We now solve these two linear equations:

→ [tex]5t_u+2t_m=525[/tex]

→ [tex]15t_u +7t_m =1680[/tex]

First, let's solve Equation 1 for [tex]t_m[/tex] in terms of  [tex]t_u[/tex]:

→ [tex]d_m=(525-5d_u)/2[/tex]

Substitute this expression into Equation 2:

→ [tex]15t_u+7((525-5d_u)/2)=1680[/tex]

Multiply through by 2 to clear the fraction:

→ [tex]30t_u +7(525-5t_u )=3360[/tex]

→ [tex]30t_u +3675-35t_u =3360[/tex]

→ [tex]-5t_ u +3675=3360[/tex]

→ [tex]-5t_u=3360-3675[/tex]

→ [tex]-5t _u=-315[/tex]

→ [tex]t_u=63[/tex]

Now substitute [tex]t_u=63[/tex] back into Equation 1 to find [tex]t_m[/tex]:

→ [tex]5(63)+2t_m =525[/tex]

→ [tex]315+2t_m =525[/tex]

→ [tex]2t_m =210[/tex]

→ [tex]t_m=105[/tex]

Thus, the total distance Tyler travels is:

[tex]= t _u +t_m[/tex]

[tex]=63+105[/tex]

[tex]=168\ kilometers[/tex]

Answer:

[tex]\large\boxed{\Phi=\dfrac{\pi}{9}+\dfrac{2k\pi}{3}\ or\ \Phi=-\dfrac{\pi}{9}+\dfrac{2k\pi}{3}}[/tex]

Step-by-step explanation:

[tex]\cos3\Phi=\dfrac{1}{2}\qquad\text{substitute}\ 3\Phi=\theta\\\\\cos\theta=\dfrac{1}{2}\iff\theta=\dfrac{\pi}{3}+2k\pi\ or\ \theta=-\dfrac{\pi}{3}+2k\pi\qquad k\in\mathbb{Z}\\\\\text{We're going back to substitution:}\\\\3\Phi=\dfrac{\pi}{3}+2k\pi\ or\ 3\Phi=-\dfrac{\pi}{3}+2k\pi\qquad\text{divide both sides by 3}\\\\\Phi=\dfrac{\pi}{9}+\dfrac{2k\pi}{3}\ or\ \Phi=-\dfrac{\pi}{9}+\dfrac{2k\pi}{3}[/tex]

[tex]6x[/tex]

............................................

Answer:  a. reject the null hypothesis, church attendance and marital status are dependent

Step-by-step explanation:

Given : 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.

Null hypothesis : There is no relationship between the variables.

Alternative hypothesis : There is a relationship between the variables.

Here we can see that the obtained chi-square (23.45) value is greater than the critical chi square value (9.488) , then we have to reject the null hypothesis.

So the correct answer is reject the null hypothesis, church attendance and marital status are dependent.

Given the obtained Chi-square 23.45 is greater than the critical Chi square 9.488, we reject the null hypothesis, implying there is a significant relation or dependence between marital status and church attendance.

In a Chi square test, if the obtained Chi square value is higher than the critical Chi square value, it means that the observed data significantly deviates from what is expected under the null hypothesis. Therefore, in this case, where the obtained Chi square is 23.45 and the critical number is 9.488, we would reject the null hypothesis. Considering that the null hypothesis is generally posed under the assumption of no relation or independence between the variables being tested, rejecting it thus implies that there is a significant relationship or dependence between marital status and church attendance. Therefore, the correct answer to the question is a. reject the null hypothesis, church attendance and marital status are dependent

.

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Answer:

$98.47

Step-by-step explanation:

1. 2(9.5) + 3 (7.95) + 49.95 = $92.80

6% • $92.80 = $5.57

$92.80 + $5.57 = $98.47

Answer:

  (1, π/3 +2kπ), (-1, 4π/3 +2kπ) . . . where k is any integer

Step-by-step explanation:

Adding any multiple of 2π to the angle results in the same point in polar coordinates.

Adding 180° (π radians) to the point effectively negates the magnitude. As above, adding any multiple of 2π to this representation is also the same point in polar coordinates.

There are an infinite number of ways the coordinates can be written.

Answer:

All the polar coordinates of point P are [tex](1,2n\pi+\frac{\pi}{3})[/tex] and [tex](-1,(2n+1)\pi+\frac{\pi}{3})[/tex], where n is an integer.

Step-by-step explanation:

The given point is

[tex]P=(1,\frac{\pi}{3})[/tex]            .... (1)

If a point is defined as

[tex]P=(r,\theta)[/tex]          .... (2)

then the polar coordinates of point P is defined as

[tex](r,\theta)=(r,2n\pi+\theta)[/tex]

[tex](r,\theta)=(-r,(2n+1)\pi+\theta)[/tex]

where, n is an integer and θ is in radian.

From (1) and (2) we get

[tex]r=1, \theta=\frac{\pi}{3}[/tex]

So, the polar coordinates of point P are

[tex](r,\theta)=(1,2n\pi+\frac{\pi}{3})[/tex]

[tex](r,\theta)=(-1,(2n+1)\pi+\frac{\pi}{3})[/tex]

Therefore all the polar coordinates of point P are [tex](1,2n\pi+\frac{\pi}{3})[/tex] and [tex](-1,(2n+1)\pi+\frac{\pi}{3})[/tex], where n is an integer.