Determine the mode of the set of data in the stem and Leaf plot below.

Answer: 3/2 + i/2

Step-by-step explanation: Simplify and write eht enaswer in standard form, a + bi.

Hope this helps! :) ~Zane

Given,

f(x)=4x^2-9

g(x)=2x+3

1.

(f+g)(x)=f(x) + g(x)

=4x^2-9+2x+3

=4x^2+2x-6

2.

(f-g)(x)=f(x)-g(x)

4x^2-9-2x-3

=4x^2-2x-12

when x=3, then,

f(3)=4×(3)^2-9=27

g(3)=2×3+3=9

5.

f(g(3))=f(9)=4×(9)^2-9

=312

5.

g(f(3))=g(27)=2×27+3=57

Answer:

listen to romap they are correct

Step-by-step explanation:

Answer:

 - The scientist can use these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.

- The scientist can substitute these measurements into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] and solve for the distance between the Sun and the shooting star (which would be the hypotenuse of the righ triangle).

Step-by-step explanation:

 You can observe in the figure attached that  "AC" is the distance between the Sun and the shooting star.

Knowing the distance between the Earth and the Sun "y" and the angle x°,  the scientist can use only these two measurements to calculate the distance between the Sun and the shooting star by applying one of the trigonometric functions: Cosine of an angle.

 This is:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

In this case:

[tex]\alpha=x\°\\\\adjacent=BC=y\\\\hypotenuse=AC[/tex]

Therefore, the scientist can substitute these measurements into [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex] , and solve for the distance between the Sun and the shooting star "AC":

[tex]cos(x\°)=\frac{y}{AC}[/tex]

[tex]AC=\frac{y}{cos(x\°)}[/tex]

The scientist can use the two measurements by applying the knowledge of trigonometry, particularly Cosine (cos).

[tex]cos x = \frac{adjacent (y)}{hypotenuse (AC)}[/tex]

AC = [tex]\frac{y}{cos x}[/tex]

where the distance between the shooting star and the sun is AC

and the distance between Earth and Sun is BC = y

the right angled triangle has three sides

cosine (θ) = [tex]\frac{adj}{hyp}[/tex]

sine (θ) = [tex]\frac{opp}{hyp}[/tex]

tan (θ) = [tex]\frac{opp}{adj}[/tex]

where (θ) =  angle of interest

This is the branch of mathematics that is concerned with angles of triangles as well as the length of it's sides.

Read more on trigonometry: https://brainly.com/question/24349828

Answer:

x-y-3=0

Step-by-step explanation:

The slope of the line that passes through the points (0,-3) and (3,0) is

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\ \\=\dfrac{0-(-3)}{3-0}\\ \\=\dfrac{3}{3}\\ \\=1[/tex]

The equation of the line is

[tex]y=m(x-x_1)+y_1\\ \\y=1\cdot (x-0)+(-3)\\ \\y=x-3\\ \\x-y-3=0[/tex]

Answer:

yes

Step-by-step explanation:

A rational number can be expressed in the form

[tex]\frac{a}{b}[/tex], where a, b are integers

6.610 can be expressed as

6 [tex]\frac{610}{1000}[/tex] = [tex]\frac{6610}{1000}[/tex] ← a rational number

6.610 is a rational number.

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Or in other words, any number that can be written as a ratio (or fraction) of two integers is a rational number.

Thus 6.610 is definitely a rational number as it satisfies the definition of a rational number.

We have, 6.610 = 661/100 which is expressed as the ratio of two integers.

Therefore, 6.610 is a rational number.

To learn more about rational number, refer -

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Answer:

$14,236

Step-by-step explanation:

25000 x 0.92 = 23000 = 1 Year

23000 x 0.92 = 21600 = 2 Years

19872

18282.24

16819.66

15474.09

14236 = 7 Years

The answer would be 14000

Answer:

5/36 (I won't repeat it 3 times :-) )

Step-by-step explanation:

We just have to calculate the ratio of times an action movie played in the las year, that should be a good indication of the chances for an action movie to be played next, since the reference data is quite large.  We're talking about a full year, no just a week or a month.

So, 15 action movies out of 108 movies...

The probability that next movie is an action movie is: 15 / 108 , or 5/36

That's roughly 1/7.

Answer:

15/108

Step-by-step explanation:

I did it and got it right.

Hope this helps:)

The correct answer is C. 49.

Remember that there are 100 students divided into 7-12 and 13-18 age group. So there should be 50 for each. The table should go like this:

7-12 age group

23 adventure or biography

27 - detective 

so you just have to subtract 50 from 23, which makes it 27. The remaining belongs to the 13-18 age group.

13-18 age group

1 - detective 

49 - adventure or biography.

Answer:

49

Step-by-step explanation:

Total number of students =100

Out of the 50 students in the age group 7−12 years who participated in the survey, 23 liked adventure or biography.

So, 50-23 = 27 Out of the 50 students in the age group 7−12 years who participated in the survey liked detective

Now we are given that The total number of students of both age groups who liked detective books was 28.

No. of students of age group 13-17 who like detective books = Students of both age group like detective - No.of students of 7−12 years who liked detective = 28-27 =1

So ,The total number of students of both age groups who liked adventure or biography was 100-28 = 72

Since the age group 7−12 years who participated in the survey, 23 liked adventure or biography.

So,  the age group 13-17 years who participated in the survey liked adventure or biography = 72-23=49

Age group          Adventure or Biography       Detective     Total

 7-12                              23                                    27               50  

 13-18                            49                                     1                  50

Total                             72                                    28               100

So, Option C is true.

The total number of students in the age group 13−18 years who liked adventure or biography. is 49

Answer:

The value is 13

Step-by-step explanation:

You can notice that 48/12 is 4 and 20/5 is 4. Therefore, divide 52 by 4

The value of x is 13.

Two triangles are said to be similar when corresponding angles of both triangles are congruent and ratio of corresponding sides are in equal proportion.

Given that, sides of one triangle are 48, 52, and 20.

Sides of other triangle are,  12, x and 5

Since, corresponding sides are in the proportion.

                   [tex]\frac{48}{12}=\frac{20}{5}=\frac{52}{x} \\\\x=\frac{52}{4}=13[/tex]

Learn more about the Similarity of triangle here:

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Answer:

Step-by-step explanation:

D is correct.  The area of the whole circle is (360/360)πr^2.  That of the unshaded sector is (theta/360)πr^2.

The expression which can be used to find the area of the shaded sector when the angle is measured in radians, is (θ/2)×r². Option A is correct.

Area of the circular sector is the space occupied by it. The area of the circular sector is the half of the product of angle of the sector and the radius of the circle.

When the angle is measured in degree it be given as,

Area of sector=(θπr²)/360

Here, r is the radius of the circle and θ is the angle of the sector.

When the angle is measured in radian it be given as,

Area of sector=(θ/2)×r²

Here, r is the radius of the circle and θ is the angle of the sector.

Hence, the expression which can be used to find the area of the shaded sector when the angle is measured in radians, is (θ/2)×r². Option A is correct.

Learn more about the area of a circular sector here;

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the approximate height

Answer:b

Step-by-step explanation: I took the test

After 2 months, the gym memberships at Gym A and Gym B will cost the same amount, based on the membership cost equations of each gym.

We need to determine after how many months the total costs of gym memberships at Gym A and Gym B will be the same. The cost of a gym membership at Gym A is described by the equation C = 12m + 36, where C represents the total cost and m represents the number of months. For Gym B, the cost is given by the equation C = 20m + 20.

To find the number of months where the costs are equal, we set the two equations equal to each other:

12m + 36 = 20m + 20

Subtracting 12m from both sides gives us:

36 = 8m + 20

Subtracting 20 from both sides gives us:

16 = 8m

Dividing both sides by 8 gives us:

m = 2

Therefore, after 2 months, the total costs for gym memberships at both Gym A and Gym B will be the same.

Answer: 162

Step-by-step explanation:

3(2+4(5+2^3)]

3(2+4(5+8)

3(2+(4)(13))

3(2+52)

(3)(54)

=162

Answer:

0.75 I think

Step-by-step explanation:

The correct trigonometry formula  [tex]tan^{-1}[/tex] (71°) . Therefore ,  [tex]tan^{-1}[/tex](71°) is correct .

The correct trigonometry formula to use to solve for the given angle is the tangent formula.

This is because you are given the side opposite to the angle (48) and the side adjacent to the angle (34), and you need to solve for the angle itself (71°).

The tangent formula is:

tan(angle) = opposite / adjacent

In this case, you would have:

[tex]tan^-1[/tex] = 48 / 34

[tex]tan^-1[/tex] = 0. 708333  degree

[tex]tan^-1[/tex] = 0.71 degree

[tex]tan^-1[/tex]  (0.71)      

= 35.3112 degree.

Therefore, the correct answer is tan(71°).

Thank you this is right

Answer:

B) x+y=120; 12x+20y=1720

Step-by-step explanation:

If variables are defined as ...

x = number of student tickets sold

y = number of adult tickets sold

then the problem statement can be modeled by ...

x + y = 120 . . . . . . the total number of tickets sold is 120

12x + 20y = 1720 . . . . . the total collected from ticket sales was $1720

___

Total revenue is the sum of the revenues from sales of each ticket type. The revenue from a given ticket type is the product of that ticket price and the number sold.

Answer:

10

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

I hope this helped it took so long to find.

Answer:

simple random sampling

Step-by-step explanation:

Simple random sampling is the fundamental sampling technique in which a group of subjects is selected for a particular study from a larger group, the population. Each subject is chosen purely by chance and each individual of the larger group (population) has an equal probability of being included in our sample.

Answer:

  (-5, -8)

Step-by-step explanation:

The expression can be divided by 2 to give ...

  x² +13x +40

The solutions to this will have a product of 40 and a sum of -13, the opposite of the x-coefficient. All of the offered choices have a product of 40, but only (-5, -8) has a sum of -13.

By setting up and solving a system of equations based on the total costs and number of animals, it is determined that there were 21 birds at the shelter on Wednesday.

To solve how many birds were at the shelter on Wednesday, we can set up a system of equations based on the costs and the total number of animals. Let the number of birds be b and the number of cats be c.

The total cost for birds and cats is $161.50, and there are 43 birds and cats together. This gives us two equations:

$3.50b + $4.00c = $161.50

b + c = 43

We can solve this system of equations by first expressing c in terms of b from the second equation:

c = 43 - b

Now we can substitute c into the first equation:

$3.50b + $4.00(43 - b) = $161.50

After simplifying:

$3.50b + $172.00 - $4.00b = $161.50

Combining like terms:

-$0.50b = -$10.50

Dividing by -0.50:

b = 21

So, there were 21 birds at the shelter on Wednesday.

$10.50 a $1.25 is $9.75 then you do $800 / $9.75 which is 82.05 so we round up with any decimal and he would need to sell 83 pies to start making a profit.

Answer:

[tex]-\frac{3\sqrt{58} i}{{58}}-\frac{7\sqrt{58}j}{{58}}[/tex]

Step-by-step explanation:

The given vector is:

v = -3i-7j

The unit vector is found by dividing the vector by its magnitude

[tex]Unit\ vector\ of\ v=\frac{v}{||v||}[/tex]

We have to find the magnitude first

So,

[tex]||v||=\sqrt{(-3)^{2} +(-7)^{2}}\\ =\sqrt{9+49}\\ =\sqrt{58}[/tex]

The unit vector is:

[tex]\frac{-3i-7j}{\sqrt{58} } \\=>-\frac{3i}{\sqrt{58}}-\frac{7j}{\sqrt{58}}\\=>(-\frac{3i}{\sqrt{58}}*\frac{\sqrt{58}}{\sqrt{58}}) -(\frac{7j}{\sqrt{58}}*\frac{\sqrt{58}}{\sqrt{58}})\\=>-\frac{3\sqrt{58} i}{{58}}-\frac{7\sqrt{58}j}{{58}}[/tex]

Therefor the last option is the correct answer ..

The unit vector in the same direction as v = -3i-7j is found by calculating the magnitude of v and then dividing v by its magnitude. The result is (-3/sqrt(58))i + (-7/sqrt(58))j.

To find the unit vector in the same direction as v = -3i-7j, we first need to calculate the magnitude (length) of v. The magnitude of a vector can be calculated using the Pythagorean theorem as applied to vector components, so for our vector v, the magnitude |v| would be sqrt((-3)^2 + (-7)^2) = sqrt(9 + 49) = sqrt(58).

Next, we find the unit vector by dividing the vector by its magnitude. This gives us: (-3/sqrt(58))i + (-7/sqrt(58))j.

Therefore, the unit vector in the same direction as v is (-3/sqrt(58))i + (-7/sqrt(58))j.

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Answer:

a° = 118° , b° = 49° , c° = 144° , d° = 98°

Step-by-step explanation:

* Lets study the figure and take the information to solve the question

- There is a circle

- There is an inscribed triangle in the circle

- Each vertex of the triangle is an inscribed angle in the circle

- Each vertex subtended by an arc

- The measure of any inscribed angle is half the measure of its

  subtended arc

* Now lets solve the question

- The sum of the measures of the interior angles of a triangle is 180°

∵ The triangle has angle of measure 59° and another angle of

   measure 72°

∴ The measure of the third angle = 180° - (59° + 72°) = 49°

∵ b° is the measure of the third angle in the triangle

∴ b° = 49°

- The arc of measure a° is intercept the angle of measure 59°

∵ The measure of the angle is half the measure of the arc

∴ 1/2 a° = 59° ⇒ multiply both sides by 2

∴ a° = 118°

- The arc of measure c° is intercept the angle of measure 72°

∵ The measure of the angle is half the measure of the arc

∴ 1/2 c° = 72° ⇒ multiply both sides by 2

∴ c° = 144°

- The arc of measure d° is intercept the angle of measure 49°

∵ The measure of the angle is half the measure of the arc

∴ 1/2 d° = 49° ⇒ multiply both sides by 2

∴ d° = 98°

Answer:

None will be left.

Step-by-step explanation:

John needed 1000 Muffins a week for his party

Each person ate 100 Muffins

So there were [tex]\frac{1000}{100}[/tex] = 10 people in the party and they ate all the Muffins.

No Muffins were left over.

[tex]\frac{-5}{8} * \frac{2}{3}[/tex]

Multiply the top with the top and the bottom with the bottom:

[tex]\frac{(-5)*2}{8*3}[/tex]

[tex]\frac{-10}{24}[/tex]

Then you can simplify:

[tex]\frac{-5}{12}[/tex]

Hope this helped!

Answer:

-5/12

Step-by-step explanation:

Multiply the top of both fractions and the bottom of both fractions, -5*2=-10,8*3=24

so -10/24 can be simplified to -5/12

Answer:

Step-by-step explanation:

[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================[/tex]

[tex]\text{We have the equation}\ y=\dfrac{1}{3}x+6\to m_1=\dfrac{1}{3}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{3}}=-3.\\\\\text{We have the equation}\ y=-3x+b.\\\\\text{Put the coordinates of the point}\ (2,\ -3):\\\\-3=-3(2)+b\\-3=-6+b\qquad\text{add 6 to both sides}\\3=b\to b=3\\\\\text{Finally:}\\\\y=-3x+3[/tex]

Answer:

20.9, rounded answer: 21 miles

Step-by-step explanation:

x= distance between the airport and Ann's home.

since Ann is paying $2.10 per mile let 2.10 be the coefficient

our equation:

5 is our constant since that's how much Ann trips the driver

since the total is equal to 49.10, that's what our equation will be equal to

2.10x+5=49.10

sub "5"

2.10x+5-5=49.10-5

2.10x=44

divide both sides by "2.10"

2.10/2.10x=44/2.10

x=20.9

we can round 20.9 to 21

I don’t know what the answer is I wish I could help

Answer:

Simplify 23x

.

Tap for more steps...

2x3−12=13+56x

Simplify 56x

Step-by-step explanation:

For this case we must solve the following equation:

[tex]\frac {2} {3} x- \frac {1} {2} = \frac {1} {3} + \frac {5} {6} x[/tex]

Subtract [tex]\frac {5} {6} x[/tex] on both sides of the equation:

[tex]\frac {2} {3} x- \frac {5} {6} x- \frac {1} {2} = \frac {1} {3}[/tex]

We add [tex]\frac {1} {2}[/tex] to both sides of the equation:

[tex]\frac {2} {3} x- \frac {5} {6} x = \frac {1} {3} + \frac {1} {2}\\\frac {12-15} {18} x = \frac {2 + 3} {6}\\\frac {-3} {18} x = \frac {5} {6}\\- \frac {1} {6} x = \frac {5} {6}\\[/tex]

We multiply by 6 on both sides of the equation:

[tex]-x = 5[/tex]

We multiply by -1 on both sides of the equation:

[tex]x = -5[/tex]

Answer:

[tex]x = -5[/tex]

given,

height of triangle(h)=3.5 in.

base of triangle (b)=4 in.

length of side of triangle(s)= 4 in.

length of prism(l)=9 in.

we have,

surface area of traingular prism( A)=bh+2ls+lb

=4×3.5+2×9×4+9×4

=14+72+36

=122 square inches

Answer:

They're right

Step-by-step explanation: