Zach tried to solve an equation step by step. 34=z−1234+12=z−12+12Step 154=zStep 2\begin{aligned} \dfrac34&=z-\dfrac12\\\\ \dfrac34+\dfrac12&=z-\dfrac12+\dfrac12&\green{\text{Step } 1}\\\\ \dfrac54&=z&\blue{\text{Step } 2} \end{aligned} 4 3 ​ 4 3 ​ + 2 1 ​ 4 5 ​ ​ =z− 2 1 ​ =z− 2 1 ​ + 2 1 ​ =z ​ Step 1 Step 2 ​ Find Zach's mistake. Choose 1 answer: Choose 1 answer:

Answer:

y = 250

Step 1:

To solve, we plug in 50x for y.

[tex]50x=200+10x[/tex]

Then, we subtract the 10x from the right side. Our goal is to get the x by itself first.

[tex]40x=200[/tex]

Then, we divide both sides by 40, since we have to get the x by itself.

[tex]\frac{40x}{40}=x\\\\\frac{200}{40} =5[/tex]

x = 5

Step 2:

Now that we found x, we plug in 5 to the original equation and solve from there.

[tex]y=200+10(5)\\y=200+50\\y=250[/tex]

y = 250

Answer:

1

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

3 cubed=3✖️3✖️3=27

Answer:

3³ = 3 × 3 × 3 = 9 × 3 = 27

Hope this helps you

Answer:

Does this sample provide convincing evidence that the machine is working properly?

Yes.

Step-by-step explanation:

Normal distribution test:

[tex]$z=\frac{x- \mu }{ \frac{\sigma}{\sqrt{n}} }=\frac{ (x-\mu)\sqrt{n}}{\sigma} $[/tex]

Where,

[tex]x: \text{ sample mean}[/tex]

[tex]\sigma: \text{ standard deviation}[/tex]

[tex]n: \text{ sample size determination}[/tex]

[tex]\mu: \text{ hypothesized size of the screw}[/tex]

[tex]$z=\frac{(1.476-1.5)\sqrt{200} }{0.203 } $[/tex]

[tex]$z=\frac{(-0.024)10\sqrt{2} }{0.203 } $[/tex]

[tex]z \approx -1.672[/tex]

Once the significance level was not given, It is usually taken an assumption of a 5% significance level.

Taking the significance level of 5%, which means a confidence level of 95%, we have a z-value of [tex]\pm 1.96[/tex]

Therefore, we fail to reject the null. It means that the hypothesis test is not statistically significant: the average length is not different from 1.5!

Answer:

I hope it helps you......

Answer:

work is shown and pictured

Answer:

The answer is C

Step-by-step explanation:

Answer: X

Step-by-step explanation:

Step-by-step explanation:

Answer:

The answer is C.) (2, -5)

Answer:

4 litres of 12% solution

2 litre of 24% solution

Step-by-step explanation:

Let the 12% solution = l

Let the 24% solution = h

Dimitri needs a total of 6 litres of both :

l + h = 6 - - - - - - - - (1)

He needs a mixture of both volumes of both to give a 16% volume

12%l + 24%h = 16% * 6

0.12l + 0.24h = 0.96 ----(2)

From (1)

l + h = 6;

l = 6 - h

Substitute l =6-h into (2)

0.12(6 - h) + 0.24h = 0.96

0.72 - 0.12h + 0.24h = 0.96

0.72 + 0.12h = 0.96

0.12h = 0.96 - 0.72

0.12h = 0.24

h = 0.24 / 0.12

h = 2

From ;

l = 6 - h

l = 6 - 2

l = 4

Answer:

1.road 1

2. scooter

3. walk

Answer:

1. road 1

2. scooter

3. walk

Step-by-step explanation:

1. in the corresponding point on the tree, you have road 2. therefore, the most logical answer would be road 1.

2. you are given three options of travel. as "walk" and "bike" are already provided, they cannot be the answer to fill in for box 2. therefore, you are left with "scooter."

3. similarly, you are given three options of travel. as "bike" and "scooter" are already provided, they cannot be the answer to fill in for box 3. therefore, you are left with "walk."

Answer:

44 units²

Step-by-step explanation:

For triangles: (bases and heights of both triangles are equal)

Base = 4 units, height = 3 units

For trapezoid:

Base 1 = 5 units, base 2 = 3 units, height = 8 units

Area of figure = Area of two triangles + Area of trapezoid

= 2 *1/2 * base * height + 1/2(base 1+ base 2) *height

=4*3 + 1/2(5+3)*8

= 12 + 8*4

= 12 + 32

= 44 units²

The required area of the figure shown in the graph is given as 44 square units.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

here,
The area of the given figure  is given as,
Area = Area of 1 + Area of 2 + Area  3 + Area 4
Area = length × width + [1/2× base × height] + [1/2× base × height] + [1/2× base × height]

Area = 8 × 3 + 1/2 × 4 × 3 + 1/2 × 4 × 3 + 1/2 × 8 × 2
Area = 44 square units.

Thus, the required area of the figure shown in the graph is given as 44 square units.

Learn more about the surface area here: https://brainly.com/question/2835293

#SPJ6

Answer:

Hey there!

He can create 7 plates at most, with one carrot cake and one marble cake on each plate.

Hope this helps :)

Answer:

Step-by-step explanation:

Since the sequence is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

d = 6

a = 2

n = 12

So the 12th term of the sequence is

A(12) = 2 + (12-1)6

= 2 + 11(6)

= 2 + 66

Hope this helps you

Answer:

x=3.00 or x= 8.00

Explanation:

Let us denote side of the cut-out square as x inches

Then base of box = 16-2x by 6-2x

The volume = V = (16-2x)(6-2x)

= 96-3x-12x+4x

dV/dx = 96-44x+4x^2

= 0 for a max V

divide by 4

X^2 -11x +24=0

Using quadratic formula to solve the equation

X= (11± √11^2-(4×1×24)/2

(11± √25)/2

x= 3 or 8inches

From the equation of volume = V = x(16-2x)(6-2x)

Substitute

let x = 3 , V = 3(16-6)(6-6) = 0

let x = 8 , V = 8(16-16)(6-16) = 0

Therefore, the maximum volume exist at both point x=3 or x= 8

Answer:

2(cos30°+isin30°)

Step-by-step explanation:

Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.

On converting the rectangluar to polar form of the complex number;

x = rcosθ and y = rsinθ

Substituting in the rectangular form of the comlex number above;

z = rcosθ + irsinθ

z = r(cosθ+isinθ)

r is the modulus of the complex number and θ is the argument

r =√x²+y² and θ = tan⁻¹y/x

Given the complex number in rectangular form z = -(3)^1/2 - i

z = -√3 - i

x = -√3 and y = -1

r = √(-√3)²+(-1)²

r = √3+1

r = √4

r = 2

θ = tan⁻¹ (-1/-√3)

θ = tan⁻¹ (1/√3)

θ = 30°

Hence the complex number in polar form will be z = 2(cos30°+isin30°)

Answer:

-7/8

Step-by-step explanation:

Step-by-step explanation:

We need to find the value of k so that the triangle with vertices (1, -1), (-4,2k) and (-k, – 5) is 24 sq. units.

The area of triangle is given by :

[tex]A=\dfrac{1}{2}\times [x_1(y_2-y_3)-x_2(y_3-y_1)+x_3(y_1-y_2)][/tex]

Here,

x₁ = 1, y₁ = -1, x₂ = -4, y₂ = 2k, x₃ = -k and y₃ = -5

So,

[tex]24=\dfrac{1}{2}\times [1(2k-(-5))-(-4)((-5)-(-1))+(-k)((-1)-(2k))][/tex]

We need to solve the above equation,

[tex]48=[1(2k-(-5))-(-4)((-5)-(-1))+(-k)((-1)-(2k))][/tex]

On solving the above equation we get the value of k as :

k = 4.7

Answer:

4.25%

Step-by-step explanation:

Commision =  441.30 - 375 = 66.30

Commision is based on  = 6560-5000 = 1560

Rate of Commision = (in decimal) 66.30/1560 = 0.0425  

Rate of Commision = 0.0425  * 100 =   4.25 %

Answer:

1.25

Step-by-step explanation:

8x² -38x + 35 = 0

8x² - 10x - 28x + 35 = 0

2x(4x - 5)-7(4x - 5) = 0

(4x−5)(2x−7) = 0

4x - 5 = 0 or 2x - 7 = 0

x = 5/4 or x = 7/2

x = 1.25 or 3.5

Smallest value being = 1.25

Answer:

See below.

Step-by-step explanation:

SQUARE:

The area of the square is:

[tex]9x^2-12x+4[/tex]

Factor it:

[tex]=9x^2-6x-6x+4\\=3x(3x-2)-2(3x-2)\\=(3x-2)(3x-2)\\=(3x-2)^2[/tex]

Remember that all four sides of a square is equal. The area is simply the side squared. Therefore, all four sides of the square measure (3x-2).

RECTANGLE:

[tex]25x^2-16y^2\\[/tex]

Factor it. This resembles the difference of two squares, where:

[tex](x-a)(x+a)=x^2-a^2[/tex]

[tex]25x^2-16y^2\\=(5x)^2-(4y)^2\\=(5x-4y)(5x+4y)[/tex]

This cannot be simplified further. Note that the sides of rectangles doesn't necessarily have to be the same.

The dimensions of the rectangle is:

(5x-4y) by (5x+4y)

Answer:

Step-by-step explanation:

1. the area of square is 9x^2-12x+4 square units

shortcut: (a-b)^2= a^2-2ab+b^2

then simplify 9x^2-12x+4 to (3x-2)^2

area of square = s^2

then side equals sqrt((3x-2)^2)

s = (3x-2) units

2. the area of rectangle is (25x^2-16y^2) square units

shortcut: (a^2-b^2) = (a-b)(a+b)

then simplify (25x^2-16y^2) to (5x-4y)(5x+4y) square units

one side is: (5x-4y) units

one side is (5x+4y) units

Answer:

3,500 tons

Step-by-step explanation:

We know that 1,400 tons is 2/5 of the Consolidated Brick Company's output.

This means that 1/5 must be equal to 700 tons if 2/5 is 1,400.

So, we can find the total output by multiplying 700 by 5, since 700 is 1/5 of the total.

700(5) = 3,500 tons

Answer:

[tex] f = 12.7 [/tex]

Step-by-step explanation:

Given:

<H = 94°

FG = h = 15

<F = 58°

GH = f = ?

Use the law of sines to find f:

[tex] \frac{f}{sin(F)} = \frac{h}{sin(H)} [/tex]

[tex] \frac{f}{sin(58)} = \frac{15}{sin(94)} [/tex]

[tex] \frac{f}{0.848} = \frac{15}{0.998} [/tex]

[tex] \frac{f}{0.848} = 15.03 [/tex]

Multiply both sides by 0.848

[tex] \frac{f}{0.848}*0.848 = 15.03*0.848 [/tex]

[tex] f = 15.03*0.848 [/tex]

[tex] f = 12.74544[/tex]

[tex] f = 12.7 [/tex] (nearest tenth)

Step-by-step explanation:

Given:

Successful outcome

Red=3

Blue=2

Possible outcome

Total=5 balls

Required:

The probability of drawing red ball

Formula:

Probability= Successful outcome ÷ Possible outcome

Solution:

Probability= Successful outcome ÷ Possible outcome

Probability=3÷5

Probability=3/5 or 0.6

Hope this helps ;) ❤❤❤

Answer:

n = 4

Step-by-step explanation:

4(2n + 3) = 44

Expand the brackets.

4(2n) + 4(3) = 44

8n + 12 = 44

Subtract 12 on both sides.

8n + 12 - 12 = 44 - 12

8n = 32

Divide both sides by 8.

(8n)/8 = 32/8

n = 4

Answer:

740 m^2

Step-by-step explanation:

Answer:

2/13

Step-by-step explanation:

In a standard deck of cards, there are 52 cards total, 4 kings, and 4 queens.

Probability is calculated by (number of favorable outcomes)/(number of possible outcomes), so our probability would be 8/52, which can be simplified to 2/13.

Hope this helps!

Answer:

Surface area of the roof of the kennel, including the bottom face is 58.96 ft^2

Step-by-step explanation:

The image is attached below

For the triangular sides of the roof, area is

A = [tex]\frac{1}{2}bh[/tex]

where b is the base = 4 ft

h is the vertical height = 2.24 ft

A =  [tex]\frac{1}{2}*4*2.24 =[/tex] 4.48 ft^2

for the two faces we have 2 x 4.48 ft^2 = 8.96 ft^2

For the rectangular sections of the roof, area is

A = [tex]lh[/tex]

where [tex]l[/tex] is the length of the rectangle = 5 ft

h is the height of the rectangle = 3 ft

A = 5 x 3 = 15 ft^2

For the two rectangular faces, we have 2 x 15 ft^2 = 30 ft^2

For the bottom face, area is

A = [tex]lw[/tex]

where [tex]l[/tex] is the length of the house = 5 ft

w is the width of the house = 4 ft

A = 5 x 4 = 20 ft^2

Surface area of the roof of the dog kennel is

8.96 ft^2 + 30 ft^2 + 20 ft^2 = 58.96 ft^2

Answer:

hello :

Step-by-step explanation:

x(x+3)(x+3)=0  means : x=0 or x+3=0 or x+3=0

x=0 or x=-3 or x=3

Answer:

r=2

Step-by-step explanation:

y = k x^r  is the formula for a direct variation

y = k x^ -r is the formula for a indirect variation

20= 5 (1/2)^ -r

Divide each side by 5

4 = (1/2) ^ -r

Rewriting

2^2 = 2^ -1 ^ -r

2^2 = 2 ^ r

The bases are the same so

2 =r

Answer:

r=-2

Step-by-step explanation:

because i had this questiion and i got it right