from 24 teachers to 30 teachers

Step-by-step explanation:

5x+2y=29

5x-2y=41

add the equations

10x=70

divide both sides by ten

x=7

substitute 7 in the first equation

5(7)+2y=29

simplify

35+2y=29

subtract 35 from both sides

2y=-6

simplify

y=-3 x=7

3x+2y=9

5x+2y=12

subtract the equations

-2x=-3

simplify

x=1.5

substitute

3(1.5)+2y=9

simplify

4.5+2y=9

subtract 4.5 from both sides

2y=4.5

simplify

y=2.25 x=1.5

5x+2y=-9

2x-3y=4

multiply first equation by three and second by two

15x+6y=-27

4x-6y=8

add equations

19x=-19

simplify

x=-1

substitute

15(-1)+6y=-27

simplify

-15+6y=-27

add 15 to both sides

6y=-12

simplify

y=-2 x=-1

Answer:

1) The mean = 41

The standard deviation = 13.379

2) The mean = 40.67

The standard deviation = 12.365

3) The mean and standard deviation will remain the same

4) The new mean = 44.5  

The new standard deviation = 13.58

5) The mean = 42.25

The standard deviation = 13.83

Step-by-step explanation:

The combines mean is given by the formula;

[tex]\overline {x_{12}} = \dfrac{n_1 \bar x + n_2 \bar x}{n_1 + n_2}[/tex]

The combined standard deviation is given as follows;

[tex]\sigma_{12} = \sqrt{\dfrac{n_1 \times \left (\sigma^2_{1} + d^2_1 \right) + n_2 \times \left (\sigma^2_{2} + d^2_2 \right)}{n_1 + n_2} }[/tex]

d₁ = [tex]\overline{x_{12}}[/tex] - [tex]\overline {x_1}[/tex]

d₂ = [tex]\overline{x_{12}}[/tex] - [tex]\overline {x_2}[/tex]

Substituting the known values, we have;

[tex]\overline {x_{12}} = \dfrac{ 42 + 40}{2}=41[/tex]

d₁ = 41 - 42 = -1

d₂ = 41 - 40 = 1

[tex]\sigma_{12} = \sqrt{\dfrac{ \left (16^2 + 1 \right) + \left (10^2 +1 \right)}{2} } = 13.379[/tex]

2) When n₁ = 1, n₂ = 2, we have;

[tex]\overline {x_{12}} = \dfrac{ 2 \times 42 + 4 \times 40}{6} \approx 40.67[/tex]

d₁ = 40.67 - 42 = -1.33

d₂ = 40.67 - 40 = 0.67

[tex]\sigma_{12} = \sqrt{\dfrac{ 2 \times \left (16^2 + 1.33^2 \right) + 4 \times \left (10^2 +0.67^2 \right)}{6} } \approx 12.365[/tex]

3) The mean and standard deviation will remain the same

4) The new mean = (42 + 47)/2 = 44.5  

The new standard deviation [tex]\sigma_{12} = \sqrt{\dfrac{ \left (16^2 + 2.5^2\right) + \left (10^2 +2.5^2\right)}{2} } \approx 13.58[/tex]

5) [tex]\overline {x_{12}} = \dfrac{ 44.5 + 40}{2}=42.25[/tex]

[tex]\sigma_{12} = \sqrt{\dfrac{ \left (16^2 + 2.5^2\right) + \left (10^2 +4.5^2\right)}{2} } \approx 13.83[/tex]

Answer:

let the number be x

thrice of the number=3x

one-half of the number=(1/2)x

so from the expression we:

3x-x/2=2500

(6x-x)/2=2500

6x-x=2*2500

5x=5000

x=5000/5

x=1000

Answer:

what does lmno means

Step-by-step explanation:

Answer:

absolute value of 8.7 is 8.7

Answer:

Axis is a vertical line at x = 2

Vertex is (2, -1)

y-intercept is (0, 3)

Solutions are x = 1 and x = 3

Step-by-step explanation:

To draw the graph of the quadratic equation you must find at least 5 points lie on the graph by choose values of x and find their values of y

Let us do that

Use x = -1, 0, 1, 2, 3, 4, 5

∵ y = x² - 4x + 3

∵ x = -1

∴ y = (-1)² - 4(-1) + 3 = 1 + 4 + 3 = 8

→ Plot point (-1, 8)

∵ x = 0

∴ y = (0)² - 4(0) + 3 = 0 + 0 + 3 = 3

→ Plot point (0, 3)

∵ x = 1

∴ y = (1)² - 4(1) + 3 = 1 - 4 + 3 = 0

→ Plot point (1, 0)

∵ x = 2

∴ y = (2)² - 4(2) + 3 = 4 - 8 + 3 = -1

→ Plot point (2, -1)

∵ x = 3

∴ y = (3)² - 4(3) + 3 = 9 - 12 + 3 = 0

→ Plot point (3, 0)

∵ x = 4

∴ y = (4)² - 4(4) + 3 = 16 - 16 + 3 = 3

→ Plot point (4, 3)

∵ x = 5

∴ y = (5)² - 4(5) + 3 = 25 - 20 + 3 = 8

→ Plot point (5, 8)

→ Join all the points to form the parabola

From the graph

∵ The axis of symmetry is the vertical line passes through the vertex point

∵ x-coordinate of the vertex point is 2

∴ Axis is a vertical line at x = 2

∵ The coordinates of the vertex point of the parabola are (2, -1)

∴ Vertex is (2, -1)

∵ The parabola intersects the y-axis at point (0, 3)

∴ y-intercept is (0, 3)

∵ x² - 4x + 3 = 0

∵ The solutions of the equation are the values of x at y = 0

→ That means the intersection points of the parabola and the x-axis

∵ The parabola intersects the x-axis at points (1, 0) and (3, 0)

∴ Solutions are x = 1 and x = 3

Answer:

235

Step-by-step explanation:

Answer:

235

20 percent (calculated percentage %) of what number equals 47? Answer: 235.

Step-by-step explanation:

I hope this Helps c:

Answer:12

Step-by-step explanation:

it’s 12 because 4 x 3 = 12

Answer:

48π units³

Step-by-step explanation:

The volume (V) of a cylinder is calculated as

V = πr²h ( r is the radius of the base and h the height )

Here r = 4 and h = 3 , thus

V = π × 4² × 3

   = π × 16 × 3

    = 48π units³ ← exact answer

Step-by-step explanation:

2 /4

3. 5

doing reciprocal

2× 5

3. 4

= 8×15

12

= 120

12

=10 ans

hope it help u..

Answer:

234500000020000000000000000

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

-2(9)+4= -14  and -14 is equal to -14.

Answer:

-30x3 because you are subtracting 30 3 times

Step-by-step explanation:

Answer:

13/16 is the answer. Bad handwriting but try to understand .

Answer:

Company B is offering the lowest price/lb at $12.72/lb.

Step-by-step explanation:

Answer:

use desmos.

Step-by-step explanation:

demos. All you have to do is out the equation into Desmos and it will graph it for you. You can look and learn.

Answer:

sin^2α

Step-by-step explanation:

I will just  pose  x instead  of alpha  here to make things simpler

[tex]\tan ^2\left(x\right)\left(2\cos ^2\left(x\right)+\sin ^2\left(x\right)-1\right)\\\\[/tex]

we know that sin^2x = 1 -  cos^2x so...

[tex]=\left(-1+1-\cos ^2\left(x\right)+2\cos ^2\left(x\right)\right)\tan ^2\left(x\right)[/tex]

[tex]=\cos ^2\left(x\right)\tan ^2\left(x\right)[/tex]

we can rewrite using trigonometric identities (tan = sin/cos)...

[tex]=\left(\frac{\sin \left(x\right)}{\cos \left(x\right)}\right)^2\cos ^2\left(x\right)\\= \sin ^2\left(x\right)[/tex]

Answer:

Fourth option is correct. The length of B'C' is 1 unit.

Step-by-step explanation:

The vertices of triangle ABC are A = (2, 2), B = (4, 3), and C = (6, 3).

Distance formula:

The length of BC is 2 units.

It is given that ΔABC is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image ΔA′B′C′.

It means the ΔABC and ΔA′B′C′ are similar and corresponding sides of ΔA′B′C′ and ΔABC are proportional.

The scale factor is 0.5.

Therefore the length of B'C' is 1 unit and fourth option is correct

Answer:

D= 1 unit

Step-by-step explanation:

Answer: 35

Step-by-step explanation: 85% of 40 basically you multiply 0.85 by 40 :)

Answer:

b = 8.5

Step-by-step explanation:

hope this halps ya!

Step-by-step explanation:

2/3 x 2/2 = 4/6

2/3 x 3/3 = 6/9

2/3 x 4/4 = 8/12

Answer:

f(x)=20+4x = -5

Step-by-step ;

answer is -5 .

Answer:

The value of n is -6

Step-by-step explanation:

∵ k(x) = x²

→ Its graph is a parabola with vertex (0, 0)

∴ The vertex of the prabola which represents it is (0, 0)

∵ The given graph is the graph of p(x)

∵ Its vertex is (0, -6)

∴ h = 0 and k = -6

∵ a = 1

→ Substitute them in the form above

∴ p(x) = 1(x - 0)² + -6

∴ p(x) = x² - 6

→ Substitute x² by k(x)

∴ p(x) = k(x) - 6

∵ p(x) = k(x) + n

→ By comparing the two right sides

∴ n = -6

∴ The value of n is -6

Look at the attached figure for more understanding

The red parabola represents k(x)

The blue parabola represents p(x)

The value of the n is -6.

y = a(x-h)2 + k

where,

(h, k) are the coordinates of the vertex of the parabola in form (x, y);

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

k(x) = x^2

p(x) = k(x) + n

p(x) = k(x)+n

p(x) = x² + n

Comparing with the Equation of a parabola,

y = a(x-h)2 + k

p(x) = x² + n

Therefore, the value of n is k which is the y coordinate of the vertex of the parabola.

Looking at the coordinates of the vertex of the parabola,

(h, n) = (0, -6)

Hence, the value of the n is -6.

Learn more about Parabola:

https://brainly.com/question/4443998

Answer: 24

Step-by-step explanation:

i did the problem and got it right

Answer:

B

Step-by-step explanation:

I am sorry if this is wrong