2
Select the correct answer from the drop-down menu.
Which equation satisfies all three pairs of a and b values listed in the table?
a b
0-10
1 -7
2-4
The equation is

The trigonometric equation is tan 2A cot A-1 = sec 2A

We have to prove the trigonometric equation

tan 2A cot A-1 = sec 2A

Now let us take LHS

tan 2A cot A-1  

2tanA/1-tan²A - 1 . cotA - 1

2-1+tan²A/1-tan²A

1+tan²A/1-tan²A

sec2A

Hence, the trigonometric equation is tan 2A cot A-1 = sec 2A

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Answer:

B. 1 tick mark represents 0.2 unit

Step-by-step explanation:

Looking at the axis and going over 2 tick marks is .4

.4 /2 = .2

Each tick mark is .2 units

Answer:

xs7

Step-by-step explanation:

Answer:

x = -5

Step-by-step explanation:

-5 - 15x - 10 = -4x - 8x

-5 - 10 = -4x - 8x + 15x

-15 = -12x + 15x

-15 = 3x

x = -5

Answer:

  y = -10·sin(πt/5) +12

Step-by-step explanation:

You want the equation of the height of a rider of a Ferris wheel that has a radius of 10 and is 2 off the ground, with a period of 10 seconds, moving downward, starting from even with the center.

The general form of the equation will be ...

  y = A·sin(2πt/T) + B

where A is a scale factor that is based on the radius and initial direction, and B is the height of the center of the wheel above the ground.

We assume that 2 [units] off the ground means the low point of the travel is at that height. Then the middle of the wheel is those 2 [units] plus the radius of the wheel:

  B = 2 + 10 = 12

The scale factor A will be the radius of the wheel, made negative because the initial direction is downward from the initial height. That is, ...

  A = 10

The period (T) is given as 10 seconds.

Putting these parameters together gives ...

  y = -10·sin(2πt/10) +12

  y = -10·sin(πt/5) +12

__

Additional comment

We wonder if this wheel is really only 20 inches (20 in) in diameter, as that dimension seems suitable only for a model. We suspect it is probably 20 meters (20 m) in diameter.

Sometimes "m" is confused with "in" when it is written in Roman font and reproduced with poor resolution.

<95141404393>

Answer:

  (x +4)²/25 +(y -3)²/16 = 1

Step-by-step explanation:

You want the equation of the ellipse with center (-4, 3) and semi-axes 5 and 4 in the x- and y-directions, respectively.

The standard form equation for an ellipse with center (h, k) and sem-axes 'a' and 'b' in the x- and y-directions, respectively, is ...

  (x -h)²/a² +(y -k)²/b² = 1

Using the given values, we find the equation to be ...

  (x +4)²/25 +(y -3)²/16 = 1

__

Additional comment

The longer of the two axes is the "major" axis, and its end points are the "vertices". For the purpose of an ellipse with center, vertices, and co-vertices specified, the equation is not affected by which axis is longer.

Effectively, this is the equation of a circle with different scale factors in the x- and y-directions.

<95141404393>

The probability that the sample's mean length is greater than 6.3 inches is0.8446.

Here, we have,

Given mean of 6.5 inches, standard deviation of 0.5 inches and sample size of 46.

We have to calculate the probability that the sample's mean length is greater than 6.3 inches is 0.8446.

Probability is the likeliness of happening an event.

It lies between 0 and 1.

Probability is the number of items divided by the total number of items.

We have to use z statistic in this question because the sample size is greater than 30.

μ=6.5

σ=0.5

n=46

z=X-μ/σ

where μ is mean and

σ is standard deviation.

First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required probability.

z=6.3-6.5/0.5

=-0.2/0.5

=-0.4

p value from z table is 0.3446

Probability that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.

Hence the probability that the mean length is greater than 6.3 inches is 0.8446.

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Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =[tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = [tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = [tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  [tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

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Answer:

3:26

Step-by-step explanation:

.

In order to understand and prioritize the vaccination strategy for the community health clinic, first accurately assess the demographics of the community based on the data provided.

Calculating the absolute numbers of people in each group: over 65 and immunocompromised, and under 65 and immunocompromised. For this, we'll apply the given percentage to the total population of 50,000.

Knowing the total number of people in each category will help us understand the size of each target group and prioritize accordingly. The clinic's current priority is immunocompromised people over 65, so having the exact figure will aid in planning for vaccine supply and outreach strategies.

Furthermore, the analysis of this data can also aid in projecting the needs for future vaccine campaigns for the remaining community members. Finally, this detailed analysis will help in crafting an effective communication plan that emphasizes the clinic's priority of serving the most vulnerable first, while still acknowledging the needs of all community members.

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The estimated population of the town in 2023 is 57,344.

(a) Let P be the population in t years after 2014.

Since the population doubles every year, we can use the formula :

P = P₀(2)ⁿ, where P₀ is the initial population in 2014.

We have P₀= 112, so the equation is P = 112(2)ⁿ.

(b) To find the population in 2023, we need to find t when t + 2014 = 2023.

So t = 2023 - 2014 = 9.

Substituting t = 9 into the equation from part (a), we get:

P = 112(2)⁹

P ≈ 57,344

Therefore, the estimated population of the town in 2023 is 57,344.

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8 people didn't use any of the gym pool or track facilities.

The number of people use any facilities need to subtract the total number of people who used at least one facility from the total number of people in the sport centre.

The total number of people who used at least one facility by adding the number of people who used each facility and subtracting the number of people who used two facilities and three facilities:

Total = Gym + Pool + Track - (Gym and Pool) - (Pool and Track) - (Gym and Track) + (Gym and Pool and Track)

Total = 77 + 62 + 65 - 27 - 23 - 31 + 4

Total = 127

The number of people who didn't use any facilities is:

135 - 127 = 8

8 people didn't use any of the gym, pool or track facilities.

The number of individuals who did not utilise any facilities must be subtracted from the total number of individuals who utilised at least one facility.

The total number of individuals who utilised at least one facility is calculated by adding the individuals who utilised each facility and deducting the individuals who utilised two and three facilities:

Total = Fitness Centre + Pool + Track - Fitness Centre and Pool - Fitness Centre and Track - Fitness Centre and Pool and Track

Total = 77 + 62 + 65 - 27 - 23 - 31 + 4

Total = 134-127

= 8

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On performing , the "row-operation" 2R₁ + R₂ → R₂ on the matrix "M", the resulting new-matrix is [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex] .

The matrix "M" is given as : [tex]\left[\begin{array}{ccc}5&1&-5\\0&-2&2\end{array}\right][/tex],

We have to apply the Row-Operation : 2R₁ + R₂ → R₂, on the matrix "M",

Performing the row-operation "2R₁ + R₂ → R₂" on a matrix "M" means multiplying the first-row of "M" by 2, and then adding the resulting values to the second-row of "M" to produce a new value for each element in the second row.

This operation does not affect the first row of "M" and changes the values in the second row of "M".

⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\2\times5+0&2\times 1-2&2\times(-5)+2\end{array}\right][/tex],

⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\10+0&2-2&-10+2\end{array}\right][/tex],

⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex].

Therefore, the new-matrix is [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex].

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The inverse variation is y = 9/x, using that equation we can see that n = 9.

An inverse variation between two variables x and y can be written as:

y = k/x

Where k is a constant.

We know that this inverse variation contains the point (3, 3), replacing these values we have:

3 = k/3

3*3 = k

9 = k

Then the inverse variation is:

y = 9/x

Now we want to find n such that (1, n) is on the relation above, then we will get:

n = 9/1

n = 9

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Divide the total number of blocks by the total number of storage containers.

5144/8 = 643 blocks in each storage container.

The statements that complete the function transformations are left, up, stretch and stretch

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

f(x) = (x + 94)²

Also, we have

f(x) = x²

This implies that f(x) = (x + 94)² is obtained by shifting f(x) = x² left by 94 units

Next, we have

f(x) = x² + 94

This implies that f(x) = x² + 94² is obtained by shifting f(x) = x² up by 94 units

Next, we have

f(x) = 94√x from f(x) = √x

This implies that f(x) = 94√x can be obtained from vertically stretching f(x) = √x by a factor of 94

Also, the graph of f(x) = √94x can be obtained from horizontally stretching f(x) = √x by a factor of 1/94

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Answer:

Eat that cookie and you will not regret about it

The distance that the plane traveled from point A to point B is given as follows:

10,750 ft.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

The altitude of 5375 feet is the opposite angle, hence the position A is obtained as follows:

tan(15º) = 5375/A

A = 5375/tangent of 15 degrees

A = 20060 ft.

The position B is obtained as follows:

B = 5375/tangent of 30 degrees

B = 9310 ft.

Hence the distance is of:

20060 - 9310 = 10,750 ft.

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The expression that will represent the volume of the identical rectangular base pyramid is: 2[One-third (5) (0.25) (2)] cubic units.

To calculate for the volume of a rectangular base pyramid, we use the formula:

volume = 1/3 × area of base rectangle × height

volume of one identical pyramid = (1/3 × 5 × 0.5 × 2)cubic units

volume of the two identical pyramid = 2(1/3 × 5 × 0.5 × 2)cubic units.

Therefore, the expression that will represent the volume of the identical rectangular base pyramid is: 2[One-third (5) (0.25) (2)] cubic units.

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Answer: x= 10

Step-by-step explanation:

2x+4=24

2x=24-4

2x=20

x=10

Answer:

Step-by-step explanation:

2x+4=4

subtract 4 from both sides

2x=0

divide by 2 on both sides

x=0

Answer:

1 1/6 metre

Step-by-step explanation:

1/3 pink + 5/6 purple

To add, we need to get a common denominator

1/3 *2/2 = 2/6

2/6 + 5/6

7/6

Change from an improper fraction to a mixed number

1 1/6 metre

Answer:

1)  A = 32.6°, C = 111.4°, b = 12.0

2) A = 53.6°, B = 85.7°, C = 40.7°

Step-by-step explanation:

Given values of triangle ABC:

First, find the measure of side b using the Law of Cosines for finding sides.

[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]

As the given angle is B, change C for B in the formula and swap b and c:

[tex]b^2=a^2+c^2-2ac\cos(B)[/tex]

Substitute the given values and solve for b:

[tex]\implies b^2=11^2+19^2-2(11)(19)\cos(36^{\circ})[/tex]

[tex]\implies b^2=482-418\cos(36^{\circ})[/tex]

[tex]\implies b=\sqrt{482-418\cos(36^{\circ})}[/tex]

[tex]\implies b=11.9929519...[/tex]

Now we have the measures of all three sides of the triangle, we can use the Law of Cosines for finding angles to find the measures of angles A and C.

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]

To find the measure of angle A, swap a and c in the formula, and change C for A:

[tex]\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}[/tex]

[tex]\implies \cos(A)=\dfrac{19^2+(11.9929519...)^2-11^2}{2(19)(11.9929519...)}[/tex]

[tex]\implies \cos(A)=0.842229094...[/tex]

[tex]\implies A=\cos^{-1}(0.842229094...)[/tex]

[tex]\implies A=32.6237394...^{\circ}[/tex]

To find the measure of angle C, substitute the values of a, b and c into the formula:

[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

[tex]\implies \cos(C)=\dfrac{11^2+(11.9929519...)^2-19^2}{2(11)(11.9929519...)}[/tex]

[tex]\implies \cos(C)=-0.364490987...[/tex]

[tex]\implies C=\cos^{-1}(-0.364490987...)[/tex]

[tex]\implies C=111.376260...^{\circ}[/tex]

Therefore, the remaining side and angles for triangle ABC are:

[tex]\hrulefill[/tex]

To solve for the remaining angles of the triangle ABC given its side lengths, use the Law of Cosines for finding angles.

[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Cosines (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]

Given sides of triangle ABC:

Substitute the values of a, b and c into the Law of Cosines formula and solve for angle C:

[tex]\implies \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

[tex]\implies \cos(C)=\dfrac{21^2+26^2-17^2}{2(21)(26)}[/tex]

[tex]\implies \cos(C)=\dfrac{828}{1092}[/tex]

[tex]\implies C=\cos^{-1}\left(\dfrac{828}{1092}\right)[/tex]

[tex]\implies C=40.690560...^{\circ}[/tex]

To find the measure of angle B, swap b and c in the formula, and change C for B:

[tex]\implies \cos(B)=\dfrac{a^2+c^2-b^2}{2ac}[/tex]

[tex]\implies \cos(B)=\dfrac{21^2+17^2-26^2}{2(21)(17)}[/tex]

[tex]\implies \cos(B)=\dfrac{54}{714}[/tex]

[tex]\implies B=\cos^{-1}\left(\dfrac{54}{714}\right)[/tex]

[tex]\implies B=85.6625640...^{\circ}[/tex]

To find the measure of angle A, swap a and c in the formula, and change C for A:

[tex]\implies \cos(A)=\dfrac{c^2+b^2-a^2}{2cb}[/tex]

[tex]\implies \cos(A)=\dfrac{17^2+26^2-21^2}{2(17)(26)}[/tex]

[tex]\implies \cos(A)=\dfrac{524}{884}[/tex]

[tex]\implies A=\cos^{-1}\left(\dfrac{524}{884}\right)[/tex]

[tex]\implies A=53.6468753...^{\circ}[/tex]

Therefore, the measures of the angles of triangle ABC with sides a = 21, b = 26 and c = 17 are:

Answer: I believe the answer is Yolanda.

Step-by-step explanation: Because Maurice ran 110 meters in 20.9 seconds, which is slower than Yolanda. Completing the race in 20 seconds is better than 20.9 seconds.

Answer:

6 1/243

Step-by-step explanation:

6 goes into 1459, 243 times

243*6=1458

1459-1458=1

So there is a remainder of 1

So the answer would be 6 1/243

The volume of cylinder which is having radius as 5 units and height as 11 units, is 863.5 cubic units.

A "Cylinder" is a 3-dimensional geometric shape that consists of a circular base and a curved surface which extends up from base to fixed height.

The volume(V) of a cylinder is the amount of space enclosed by the cylinder, and it is given by the formula : V = πr²h;, where π is = 3.14, "r" denotes radius of base; "h" denotes the height;

Given that the radius is 5 units and the height is 11 units,

Substituting the values,

We get,

V = π × (5)² × (11);

V = 275π cubic units;

V = 275×3.14 = 863.5 cubic units;

Therefore, the required volume is = 863.5 cubic units.

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The given question is incomplete, the complete question is

If radius is 5 units, and height is 11 units, Find the Volume of the Cylinder.

Based on the contribution margin and the sales volume, Menu Item D is the most profitable and popular.

The contribution margin is the profitability that is shown in the difference between the selling price and the variable cost per unit of an item.

The contribution margin can be computed per unit or in total.  Using the sales volume to multiply the contribution margin per item gives the total contribution margin in dollars.

 Breakfast     Selling Price    Food Cost       Sales     Contribution Margin

Menu Item               ($)                  ($)           Volume         Unit         Total

А                         $10.00             $3.00           250          $7.00      $1,750

B                         $16.00             $6.00             50        $10.00        $500

C                         $18.45             $8.00             60        $10.45        $627

D                         $14.75             $4.25           300        $10.50      $3,150

E                          $8.75             $2.50             80          $6.25        $500

F                        $12.50              $5.75            180         $6.75       $1,215

G                        $9.00              $2.60           280         $6.40      $1,792

TOTAL                                                          1,200

Thus, we can conclude that Menu Item D enjoys the highest profitability and popularity.

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Mean (Juniors) = Sum / number of data points = 1085 / 12 ≈ 90.42

Median (Juniors) = (95 + 95) / 2 = 95

Mean (Seniors) = Sum / number of data points = 1095 / 12 ≈ 91.25

Median (Seniors) = (80 + 80) / 2 = 80

Juniors: 125, 90, 95, 80, 100, 100, 120, 85, 95, 120, 95, 85

First, sort the data: 80, 85, 85, 90, 95, 95, 95, 100, 100, 120, 120, 125

Sum = 1085

Mean (Juniors) = Sum / number of data points = 1085 / 12 ≈ 90.42

Median (Juniors) = (95 + 95) / 2 = 95

Seniors: 135, 70, 65, 100, 35, 175, 80, 80, 90, 65, 120, 60

First, sort the data: 35, 65, 65, 70, 80, 80, 90, 100, 120, 120, 135, 175

Sum = 1095

Mean (Seniors) = Sum / number of data points = 1095 / 12 ≈ 91.25

Median (Seniors) = (80 + 80) / 2 = 80

Variability

Juniors:

Range = max - min = 125 - 80 = 45

Seniors:

Range = max - min = 175 - 35 = 140

C. Based on the mean and median, it appears that seniors spend slightly more time on homework on average (mean ≈ 91.25) compared to juniors (mean ≈ 90.42).

However, the median time spent for seniors (80 minutes) is less than that of juniors (95 minutes), indicating that the data for seniors might be skewed by some outliers.

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Maria have to spend $ 45.95 less than what she spends now in order to save $ 70 per month.

Hence the correct option is (A).

From the given Maria's Income Statement we can see that,

Her total income from Fast food Restaurant = Gross Pay + Allowance = $ 580 + $ 50 = $ 630.

Total deductions by taxation = Federal Income Tax + State Income Tax + Social Security Tax = $ 58 + $ 16 + $ 24.36 = $ 98.36

So here net income = $ (630 - 98.36) = $ 531.64.

Here total expenses = Auto + Clothing + Food + Entertainment + Other = $ 290.02 + $ 92.29 + $90.28 + $ 32 + $ 3 = $ 507.59

So Her Savings = Net Income - Total Expenses = $ 531.64 - $ 507.59 = $ 24.05.

Now in order to save $ 70 per month Maria has to spend = $ 70 - $ 24.05 = $45.95 less than she spend now.

Hence the correct option will be (A).

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The perimeter of the rectangular polygon is given by P = 20.2 units

Given data ,

Let the perimeter of the polygon be represented as P

Now , the value of P is

Perimeter P of rectangle = 2 ( Length + Width )

Now , width is 3.8 and the length is 6.3

On simplifying , we get

P = 2 ( 3.8 + 6.3 )

P = 20.2 units

Hence , the perimeter is P = 20.2 units

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