A scientist is studying the characteristics of butterflies and collects a random sample of butterflies to measure. Information regarding the wingspan of the butterflies is shown in the histogram below.

A histogram titled Butterfly Wingspans has wingspans on the x-axis and frequency on the y-axis. Wingspan of 3 has frequency 6; 3.5, 3; 4, 8; 4.5, 14; 5, 6; 5.5, 3; 6, 5; 6.5, 6.7

Which of the following is a true statement regarding the information shown in the histogram?

Wingspan is a categorical variable.
Wingspan is a discrete quantitative variable.
Wingspan is a continuous quantitative variable.
Frequency is a continuous quantitative variable.

Answer:

Step-by-step explanation:

Given the expression:

x³(x−y)⁷−y³(x−y)⁷

This can also be written as (x³-y³)(x-y)⁷

(x³-y³)(x-y)⁷=  (x-y)⁷ (x³-y³)

Expand  (x³-y³)

x³-y³ = (x-y)(x²+xy+y²)

Substitute back into the original expression:

(x-y)⁷ (x³-y³) = (x-y)⁷(x-y)(x²+xy+y²)

(x-y)⁷ (x³-y³) = (x-y)⁸(x²+xy+y²)

(x-y)⁷ (x³-y³) = (x-y)⁸(x²+y²+xy)

Comparing the result with (x−y)^m(x^2+y^2+nxy).

(x-y)⁸ = (x-y)^m

m = 8

Also:

nxy = xy

n = xy/xy

n = 1

Hence the value of m is 8

The value of m is 8

The expression is given as:

[tex]x^3(x-y)^7-y^3(x-y)^7[/tex]

Factor out (x - y)^7 in the above expression

[tex]x^3(x-y)^7-y^3(x-y)^7 = (x^3 - y^3)(x -y)^7[/tex]

Expand out (x^3 - y^3) as the difference of two cubes

[tex]x^3(x-y)^7-y^3(x-y)^7 = (x-y)(x\²+xy+y\²)(x -y)^7[/tex]

Combine the common factors

[tex]x^3(x-y)^7-y^3(x-y)^7 = (x\²+xy+y\²)(x -y)^8[/tex]

Rewrite the expression as:

[tex]x^3(x-y)^7-y^3(x-y)^7 = (x -y)^8(x\²+xy+y\²)[/tex]

The expression format is given as:

[tex](x-y)^m(x^2+y2^+nxy)[/tex]

So, we have:

[tex](x-y)^m(x^2+y2^+nxy) = (x -y)^8(x\²+xy+y\²)[/tex]

By comparison, we have:

[tex]m = 8[/tex]

Hence, the value of m is 8

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Answer:

10

Step-by-step explanation:13+4>а>13-4

a>9

Answer:

sorry siso don't know the answer sorry ☹☹

Answer:

B = 200

Step-by-step explanation:

Cross multiply

10(20) = 200

We are given:                                                                                                        

Density of glass in g/cm³ = 2.5

Finding the density in kg/m³:                                                                              

In converting 2.5 g/cm³ to kg/m³, we will first convert the g to kg

Converting the g to kg:

2.5 g/cm³ * 1

Since 1kg = 1000g, 1kg/1000g = 1

2.5 g/cm³ * 1kg / 1000g

the g in the numerator and the denominator will cancel out and we will get:

2.5 kg / 1000 cm³

Converting the cm³ to m³:

We know that 1 m³ = 10⁶ cm³

So, 10⁶ cm³ / 1 m³ = 1

Multiplying the density by 1

2.5 kg / 10³ cm³   *   1

2.5 kg / 10³ cm³   *   10⁶ cm³ / 1 m³

the cm³ in the numerator and the denominator will cancel out

2.5 * 10⁶ kg / 10³ m³

2.5 * 10³ * 10³ kg / 10³ m³

2.5 * 10³ kg / m³

2500 kg/m³

Answer:

i think its 2

Step-by-step explanation:

The equation of  x² + 6x + y² - 8y = 19 in standard form is (x + 3)² + ( y - 4)² = 44. Hence, Option A is the correct answer.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We have been given the equation as;

x² + 6x + y² - 8y = 19

We need to find the standard form of the equation.

Thus, we have,

(x²  + 6x )+(y²- 8y) = 19

We shall complete the square for the term;

(x²  + 6x + 9 - 9 ) + (y² +  4y + 16 - 16) = 19

Simplifying, we get,

(x²  + 6x + 9) - 9 + (y²- 8y + 16) - 16 = 19

(x²  + 6x + 9) - 9 + (y²- 8y + 16) - 16 = 19 + 9 + 16

Formula used :

x²+2xy+y² = (x+y)²

x²-2xy+y² = (x-y)²

Simplifying, we get,

(x + 3)² + ( y - 4)² = 44

Thus, the equation of  x² + 6x + y² - 8y = 19 in standard form is (x + 3)² + ( y - 4)² = 44.

Hence, Option A is the correct answer.

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Answer:

7/10

Step-by-step explanation:

Answer:

(-7, -10)

[tex]x=-7\\y=-10[/tex]

Step-by-step explanation:

[tex]4x-4y=12[/tex]

Substitute x for -7.

[tex]4(-7)-4y=12[/tex]

Multiply 4 by -7.

[tex]-28-4y=12[/tex]

Add 28 on both sides.

[tex]-4y=40[/tex]

Divide -4 on both sides.

[tex]y=-10[/tex]

Answer:

The coordinates are: (1,3.8), (2,3.6)

Now, plotting these points on graph as shown in figure.

Step-by-step explanation:

We need to graph the function: [tex]f(x)=-\frac{1}{5}x+4[/tex]

For drawing the graph, we need x and y coordinateness.

The can be found as following:

If we put x =1 in the given function, we will get:

[tex]f(x)=-\frac{1}{5}x+4\\Put\:x=1\\f(x)=-\frac{1}{5}(1)+4\\f(x)=-\frac{1}{5}+4\\f(x)=\frac{-1+4*5}{5}\\f(x)=\frac{-1+20}{5}\\f(x)=\frac{19}{5}\\f(x)=3.8[/tex]

So, we get when x =1 f(x) or y = 3.8

Now for finding second point, we put x =2 in the given function

[tex]f(x)=-\frac{1}{5}x+4\\Put\:x=2\\f(x)=-\frac{1}{5}(2)+4\\f(x)=-\frac{2}{5}+4\\f(x)=\frac{-2+4*5}{5}\\f(x)=\frac{-2+20}{5}\\f(x)=\frac{18}{5}\\f(x)=3.6[/tex]

So,  we get when x =2 f(x) or y = 3.6

The coordinates are: (1,3.8), (2,3.6)

Now, plotting these points on graph as shown in figure.

You find 1 on x-axis and 3.8 on y-axis for first point (1,3.8)

Similarly You find 2 on x-axis and 3.6 on y-axis for second point (2,3.6)

Answer:

D

Step-by-step explanation:

Im almost positive its d because for triangles you multiply by radical two for when its 45 degrees then the side for the one part of the triangle would be 26 radical 2 multiplied by 39 to get 1397.243 then you double that to get d

Answer:

9. 9 1/2

10. 1 1/2

11. 15 3/4

12. 1 1/3

13. 12 stores sell shoes.

14. the area of the floor is 7,606.625 ft²

15. 3 1/3

16. 4 skateboards

hope this helps. have a good day

Answer:

let it be equation 1 and 2

Step-by-step explanation:

-3x -(-3x+3) =-6

-3x +3x -3= -6

0x = -3

x = 0

y = -3(0) +3

y = 3

Answer:

8000

Step-by-step explanation:

Answer:

$28.84

Step-by-step explanation:

That's for the first one that I found, the two other problems I don't know yet.

Answer: = 8.346296 × 106

Step-by-step explanation:

Answer:

95

Step-by-step explanation:

Any vector that points in the same or opposite direction would be parallel. So you can just scale (-2, 3) by any real number t to get the vector (-2t, 3t ).

For example, if t = -1, you get the vector (2, -3); if t = 2, you get (-4, 6).

Answer:

15

Step-by-step explanation:

first you have to subtract 4 from 19 to get what k is. that should be your answer. good luck!

Answer:

6. 225 feet in 3 minutes = 75 feet in 1 minute (slower)

   360 feet in 5 minutes = 72 feet in 1 minute

7. $4 for 5 ounces = $0.80 for 1 ounce (most expensive)

   $14 for 20 ounces = $0.70 for 1 ounce

8. 72 people in 6 hours = 12 people in 1 hour

    117 people in 9 hours = 13 people in 1 hour (greater rate per hour)

Answer:

A = 369 feet in 5 minutes B = $4 for 5 ounces C = 117 people in 9 hours

Answer:

8 miles

Step-by-step explanation:

2 miles= an hour

4 miles= two hours

6 miles= three hours

8 miles = four hours

Answer:

8

Step-by-step explanation:

Use Pete's walking speed: 2 miles per hour × 4 hours = 8 miles.

Answer:

I think it is B (SSS congruence)

Step-by-step explanation:

you are only given the sides of the triangles not any of the angles

Answer:

D

Step-by-step explanation:

This I am pretty sure on.

The only side you can 100% say is similar is DE. since it is the same line.

The angles GDE and FDE are the same since there is a line divivding it in half.

All other answers use two or more sides, unless marked with a little dash, indicating that they are the same size, you really can't use those side.

Answer:

None will .

Step-by-step explanation:

103 × 0.43 = 44.29

101 × 0.43 = 43.43

104 × 0.43 = 44.72

102 × 0.43 = 48.86

Answer:

(2x⁴-18x²+3x-4) = (2x+6)(x³-3x²-2) + (7x+8)  .... remainder  7x+8

Step-by-step explanation:

(2x⁴-18x²+3x-4) = (2x+6)(x³-3x²-2) + (7x+8) .... remainder  7x+8

Use long division method

Answer:

18

Step-by-step explanation:

Answer:

36 miles (b+C) (3)of rate

Answer:

-5

Step-by-step explanation:

-8 - -3 basically forget about the - just do the question 8 - 3 then u get 5 then add the - sign

Answer:

Step-by-step explanation:

-5

-8 -(-3)=

-8+3=

-5

4m + 9 + 5m – 12 = 42. A. m = 5 B. m = 4 C. m = –5 D. m = -4

Answer:

15x+98=105

      -98    -98

15x=7

/15    /15

x=7/15

Step-by-step explanation:

x=7/15

Answer: 7.775 as a decimal, as a fraction, 311/40.

Step-by-step explanation:

Answer:

im 95%ly sure itz just 8

Step-by-step explanation: