Han and Priya want to know the mean height of the 30 students in their dance class. • The mean height for Han’s sample is 59 inches. • The mean height for Priya’s sample is 61 inches.

Answer:

angle HMS = 62 degrees

x = 13 degrees

AT = 28

Step-by-step explanation:

angle SHM and angle HMS are both inside the triangle SMH.

We want to find the angle of HMS. We know that the sum of the angles in the triangle adds up to 180 degrees. There are two angles that we already know.

Angle SHM = 28 (given)

Angle HSM = 90 (because it is a right angle which is always 90 degrees, right angles are formed at two perpendicular lines)

Angle HMS = x (we let angle HMS be a variable as we don't know the value for it)

x + 90 + 28 = 180

x = 62 ddegrees

HMS is 62 degrees

TSA is a right angle in triangle AST because it is formed by two perpendicular lines. Right angles always equal 90 degrees.

10x - 40 = 90

10x = 130

x = 13 degrees

AT and HT are both congruent sides. We know this because the figure we are given is a kite. In a kite, we have two pairs of sides that are congruent to each other.  HT is congruent to AT while HM is congruent to AM.

So,

8x - 4 = 2x + 20

Subtraact 2 x from both sides

6x - 4 = 20

Add 4 to both sides

6x = 24

Divide 6 on both sides.

x = 4

Plug x back to AT.

AT = 2(4) + 20 = 28

Answer:

See below ~

Step-by-step explanation:

The function can be written as :

Answer:

Step-by-step explanation:

First you take your smallest number, which in this case is 4 - then you find your maximum number which is 14. Then we can list these numbers on a piece of paper and cross a number out from each side until you reach the middle number which would be 8. Then you go from the min to the middle number which would be 5. Then you repeat between the max number and the middle number which is 11. So your minumum would be 4, max would be 14, Q1 would be 5 Median would be 8 and Q3 would be 11. Let me know if I got it right! I haven't done it for a while, but I am pretty sure this is correct..

The missing values are:

Minimum value = 4 ,

Q₁ = 5 ,

Median = 6,

Q₃ = 11

Maximum value = 14.

The set of values known as quartiles divides a batch of data into four equal portions.

We have,

Minimum value = 4

Now, arrange the data in ascending order

4,4,5,5, 6, 6, 8, 10, 11, 11, 12, 14

Then, Quartiles

Q₁ = [ (n+1)/4]th term

   = (12+1) / 4

  = 3.25th term

  = 3rd term + 0.25 ( 4th term - 3th term)

  = 5 + 0.25 (5 -5)

   = 5

Now, Median = (N/2)th term

           = 12 /2

           = 6th term

          = 6

and, Q₃ = [3(n+1)/4]th term

   = 3 × 3.25

   = 9.75

   = 9th term + 0.75( 10th term - 9th term)

   = 11 + 0.75 (10 -10)

   = 11

and, Maximum value = 14

Learn more about Quartiles here:

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#SPJ2

Answer:

2 and 3

Step-by-step explanation:

So, 24=2x2x2x3

42=2x3x7

3 and 2

Answer:

2 and 3

Step-by-step explanation:

prime factors for 42: 2, 3, and 7

prime factors for 24: 2,2,2 and 3

Answer:

2

Step-by-step explanation:

Following the substitution rules:

O becomes P and

E becomes F

because they are vowels(a,e,i,o,u) change to next letter.

C becomes A

L becomes J

G becomes E

because constants change to the letter two before the given letter.

So COLLEGE becomes APJJFEF

so it now has 2 vowels.

1. Convert 8cm³ into m³

= 8.0E-6 m³

(divide the volume value by 1e+6)

2. Convert 0.7m³ into cm³

= 700000 cm³

(multiply the volume value by 1e+6)

3. Convert 4000000cm³ into m³

= 4 m³

(divide the volume value by 1e+6)

Answer:

They are the same.

Step-by-step explanation:

1.1 and 1.10 are both the same, actually. There is just an extra 0 at the end. For example, 2 and 2.0 are the same, because 0 is 0, and it doesn't change your answer. The 0 could go on as in 1.100000000 but it will still equal 1.1 .

Hope this helped :)

Answer:

x = 10.76 cm

Step-by-step explanation:

[tex]\frac{7}{sin(40^{o} )} =\frac{x}{sin(81^{o} )}[/tex]

[tex]x=\frac{7sin(81^{0}) }{sin(40^{o} )} =10.76cm[/tex]

Hope this helps

Answer:

yes

Step-by-step explanation:

yes

#1

#2

#3

Answer:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

[tex]\implies \sf \cos(28^{\circ})=\dfrac{x}{25}[/tex]

[tex]\implies \sf x=25cos(28^{\circ})[/tex]

[tex]\implies \sf x=22.1\:(nearest\:tenth)[/tex]

Given:

[tex]\implies \sf \cos(26^{\circ})=\dfrac{15}{x}[/tex]

[tex]\implies \sf x=\dfrac{15}{\cos(26^{\circ})}[/tex]

[tex]\implies \sf x=16.7\:(nearest\:tenth)[/tex]

Given:

[tex]\implies \sf \tan(41^{\circ})=\dfrac{x}{16}[/tex]

[tex]\implies \sf x=16\tan(41^{\circ})[/tex]

[tex]\implies \sf x=13.9\:(nearest\:tenth)[/tex]

Answer:

A guideline is a statement by which to determine a course of action. A guideline aims to streamline particular processes according to a set routine or sound practice. 

Answer:

x=-2

Step-by-step explanation:

Hey there!

In order to solve this equation, you need to combine like terms

The equation after combining the x terms and the contants will look like this

10x+3=12x+7

Now you have to take 10x away from both sides

3=2x+7

Now bring all the constants to the left side

3-7=2x

Simplify

-4=2x

divide 2 on both sides to get x by itself

x=-2

So, the answer is x=-2

Answer:

76.6%

Step-by-step explanation:

345/450 * 100%

I hope it helps and sorry if I'm wrong

Answer:

The ratio of the new distance to the old distance is  (11/2) .

The intensity is inversely proportional to the square of the distance,

so the new intensity will be  (2/11)²  times the old intensity.

Intensity =                 8,000 (2/11)² =

                              32,000 / 121  =  262.463  units

  Rounded to the nearest whole unit:  262 units

Step-by-step explanation:

264 units of intensity came from a distance of 11 miles option (c) 264 units is correct.

It is given that the intensity is 8000 units at a distance of 2 miles.

It is required to find the intensity at a distance of 2 miles.

Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station.

Suppose the Intensity of the signal is I and the distance is d, then:

[tex]\rm I \propto\frac{1}{d^2}[/tex]

Intensity from the station [tex]\rm I_1=8000 \ units[/tex]

[tex]\rm I_1[/tex] intensity at distance [tex]\rm d_1=2 \ miles[/tex]

Intensity from the station [tex]=\rm I_2[/tex]

[tex]\rm I_1[/tex] intensity at distance [tex]\rm d_2=11 \ miles[/tex]

[tex]\rm \frac{I_2}{I_1} = \frac{d_1^2}{d_2^2}[/tex]       (From the proportional relation)

[tex]\rm \frac{I_2}{8000} = \frac{2^2}{11^2}[/tex]

[tex]\rm I_2 =8000\times\frac{4}{121} \\\\\rm I_2 = 264.46 \ units[/tex] ≈ 264 units

Thus, the 264 units of intensity came from a distance of 11 miles.

Learn more about the fraction here:

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Answer:

[tex]x2 - 9x + 14 = 0[/tex]

Step-by-step explanation:

x2 - 9x + 14 = 0

Answer:

4 dollars, a dime, a nickel, and a penny

Answer:

4 dollars

1 dime

1 nickel

1 penny

Step-by-step explanation:

Answer:

9 3/8 as a fraction or 9.375 as a decimal

Step-by-step explanation:

4/8 + 8 7/8 = 75/8= 9 3/8= 9.375

Answer:

83.6

Step-by-step explanation:

just use your calculator

Answer:

83.6

Step-by-step explanation:

It's simple, just type it in the calculator and you'll get the answer

3x+y=5 & 5x-4y=-3

3x+5x=8x+y-4y=-3

           8x+y-4y=-3

     8x+3y=-3

         -3     -3

8x=-6

x = 1 and y = 2.

Step-by-step explanation:

to do this, i changed the form of one of the equations so it was in the y= form then plugged it into the pther equation to solve for x. once i had x i plugged it into one of the equation to get y! hope this helps

Answer:

5.5

Step-by-step explanation:

6 x 5.5 = 33

The solution for r is 5.5

Answer:

r = 5.5

Step-by-step explanation:

6r=33

1. divide both sides by 6

6/6=1

33/6= 5.5

2. r=5.5

Answer:The penguin will walk 75.15 feet in 45 seconds.

It will take the penguin 26.95 seconds to walk 45 feet.

Through cross multiplication we can determine the unknown quantity we need

Step-by-step explanation:

1. - 3p^3 + 7p^2 - 3

2. 5a^3 - 5a^2

3. 6 + 7n^3

4. - 6n^3

5. a^2 + 2r^4

6. 9r^3 + 2r^4

7. 1

8. 6x^4 - 6x

9. - 7k^4 - 11k^2 + 6

10. 2n^5 - 2n^4 + 3n + 3

11. 14a^5 + 14a^4 - 10a^3 - 16a

12. - 14n^4 - 7n^2 + 8n + 7

13. 18x^5 + 6x^4 + 12x^3

14. 7r^3 - 3r^2 + 20r

15. 8n - 8n^4

16. - 2x^5 + 10x^4 + 5x + 14

17. 4x^5 - 15x^3 - 11x - 1

18. 5a^5 + 23a^2 - 11a

19. 15v^5 + 4v^3 - 24v^2

20. 2b^4 + 15b^3 - 3

Answer:

(4,-8) is the only correct solution because it is the only one to have a Y value of -8

The standard deviation of the dataset is the square root of the variance

The mean and the standard deviation of the dataset are 24.6 and  5.70, respectively

The dataset is given as;

25, 24, 32, 16, 22, 34. 19. 27, 18, 29

Calculate the mean using:

μ = Sum/Count

So, we have:

μ = (25+ 24+ 32+ 16+ 22+ 34+ 19+ 27+ 18+ 29)/10

Evaluate

μ = 24.6

The standard deviation is then calculated using:

[tex]\sigma =\sqrt{ \frac{\sum(x - \mu)^2}{n}[/tex]

So, we have:

[tex]\sigma = \sqrt{\frac{(25 - 24.6)^2 + .................. + (27- 24.6)^2 + (18- 24.6)^2 + (29- 24.6)^2}{10}}[/tex]

Evaluate

[tex]\sigma = \sqrt{32.44}[/tex]

Evaluate the square root

[tex]\sigma = 5.70[/tex]

Hence, the mean and the standard deviation of the dataset are 24.6 and  5.70, respectively

Read more about variance at:

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Answer:

please where's the diagram

Answer:

To represent all the possible amounts that Samantha can pay, you will write that x is less than or equal to 15.

This means that any amount up to and including 15 is a possibility.

Step-by-step explanation:

Answer:

x≤15

Step-by-step explanation:

x means how much samantha is able to spend on lunch each week. she can spend only 15 dollars or less. -Crispin