If there are 15 packets each contaning 20 toys in a box and another box has 20 packets with 15 toys in each packets which box has more number of toys?(use property of whole number)

Answer:

B)1-x≤-1 OR 1-x≥1

[tex]S=\{x\in\mathbb{R}| x\le 0\quad \text{or}\quad x\ge 2 \}[/tex]

Step-by-step explanation:

[tex]2|1-x|+1\geq 3[/tex]

[tex]2|1-x|\geq 2[/tex]

[tex]|1-x|\geq 1[/tex]

Once we have an absolute value inequality, remember that:

For a > 0

[tex]\boxed{\text{If } |x|\leq a \Longleftrightarrow -a\leq x \leq a}[/tex]

[tex]\boxed{\text{If } |x|\geq a \Longleftrightarrow x\leq -a \text{ or } x\geq a }[/tex]

Therefore,

[tex]1-x\le -1\quad \text{or}\quad 1-x\ge 1[/tex]

Solving

[tex]1-x\le -1 \Longleftrightarrow x\geq 2[/tex]

[tex]1-x\ge 1 \Longleftrightarrow x\leq 0[/tex]

We have

[tex]x\geq 2 \quad \cup \quad x \leq 0[/tex]

[tex](-\infty, 0] \cup [2, \infty)[/tex]

[tex]S=\{x\in\mathbb{R}| x\le 0\quad \text{or}\quad x\ge 2 \}[/tex]

Step-by-step explanation: lol like a dozen

Answer: (0.8115, 0.8645)

Step-by-step explanation:

Let p be the proportion of people who leave one space after a period.

Given:  Sample size : n= 525

Number of people responded that they leave one space. =440

i.e. sample proportion: [tex]\hat{p}=\dfrac{440}{525}\approx0.838[/tex]

z-score for 90% confidence level : 1.645

Formula to find the confidence interval :

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]0.838\pm (1.645)\sqrt{\dfrac{0.838(1-0.838)}{525}}\\\\=0.838\pm (1.645)\sqrt{0.00025858285}\\\\=0.838\pm (1.645)(0.01608)\\\\= 0.838\pm0.0265\\\\=(0.838-0.0265,\ 0.838+0.0265)\\\\=(0.8115,\ 0.8645)[/tex]

Hence, a 90% confidence interval for the proportion of people who leave one space after a period: (0.8115, 0.8645)

Answer:

2+2y

Step-by-step explanation:

20=2(y-6)+10

20= (2×y-2×6)+10

20= (2y-12)+10

Open the bracket

20=2y-12+10

Collect liked terms

20=12+10+2y

20=22+2y

=22-20+2y

2+2y

Hope this helps

Comment for more explanation

Answer:

x=2

Step-by-step explanation:

1+4x=7+x

↦4x-x=7-1

↦3x=6

↦x=6/3

↦x=2

.°. x=2

Hope you understand it

Answer:

x = 2

Step-by-step explanation:

For this equation, we simply need to solve for x.

1 + 4x = 7 + x

1 + -1 + 4x = 7 + -1 + x

4x = 6 + x

4x + -x = 6 + x + -x

3x = 6

3x * (1/3) = 6 * (1/3)

x = 2

So the solution to this equation is x = 2.

Cheers.

Answer:

89 , 91

Step-by-step explanation:

let one be x and the other be x+2

Supplementary angles are those angles that sum up to [tex]180^{o}[/tex]

equating both sides

x+x+2 = 180

2x+2 = 180

2x = 180-2

2x = 178

x = 89

x+2 = 89+2 = 91

Answer:

its a.

Step-by-step explanation:

Answer:

D is correct.

Step-by-step explanation:

2x ≤ 14

x  ≤ 7

Answer:

D) x ≤ 7

Step-by-step explanation:

2x + 1 ≤ 15

2x ≤ 15 - 1

2x ≤ 14

x ≤ 14 : 2

x ≤ 7

Answer:

Option two and three for the domain and range question

Answer:

E. - 7

Step-by-step explanation:

2x2-X2+5X-10-4=0

X2+5X-14=0

X2-2X+7X-14.=0

X(X-2). 7(X-2)=0

(X+7). (X-2)

X=-7, X=2

Answer:

the answer is -7 and 2

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

3x -5 =2.5x + 3 - (x-4)

3x - 5 = 2.5x + 3 -x+4

3x - 5 = 1.5x +7

1.5x = 12

x =8

The solution to the linear equation 3x - 5 = 2.5x + 3 - (x-4) is x = 8.

The given expression is,

x-5=2.5x+3-(x-4)

Simplify the equation by combining like terms.

Start with the terms on the right-hand side of the equation:

2.5x+3-(x-4)

= 2.5x + 3 - x + 4 (distributing the negative sign)

= 1.5x + 7

Now let's combine the terms on the left-hand side of the equation:

3x - 5

Now the reduced equation be,

3x - 5 = 1.5x + 7

Isolate the variable (x) on one side of the equation.

Subtracting 1.5x from both sides:

3x - 1.5x - 5 = 1.5x - 1.5x + 7

1.5x - 5 = 7

Add 5 to both sides:

1.5x - 5 + 5 = 7 + 5

1.5x = 12

Solve for x by dividing both sides by 1.5:

1.5x/1.5 = 12/1.5

x = 8

So the solution to the linear equation 3x - 5 = 2.5x + 3 - (x-4) is x = 8.

To learn more about equations visit:

https://brainly.com/question/29174899

#SPJ6

Answer:

4

Step-by-step explanation:

- and - become +

so, -12 + 8 = -4

but we remove the minus and make it a positive 4

Answer:

7√2

Step-by-step explanation:

Knowing that the angle is 45° (or π/4 radians) and the opposite leg has a length of 7,  you can find the length of b with:

7 / b = sin(π / 4)

7 / (sin(π / 4)) = b

b = 7 / (1 / √2)

b =7√2

A simpler way to get the answer is to note that a right triangle with one 45° angle must be an isoceles right triangle, so both legs are the same length. Using the Pythagorean Theorem:

a² + 7² = b²

Since we know a = 7,

7² + 7² = b²

b = √(2 * 49)

b = 7√2

Answer:

Step-by-step explanation:

-5+1

-4

Answer:ok

Step-by-step explanation:wow

Answer:

y = ½x + ¾

slope (m) = ½

y-intercept(b) = ¾

Step-by-step explanation:

4y - 2x = 3

4y = 2x + 3

y = (2x + 3) ÷ 4

y = 2/4x + 3/4

y = ½x + ¾

slope (m) = ½

y-intercept(b) = ¾

Answer:

24

Step-by-step explanation:

Answer:

B. No solutions

Step-by-step explanation:

8x+2y=14

8x+2y=4

These linear equations are in standard form, and the Ax values are the same (8x) and the By values are the same (2y).  The only value that is the different is the C values (14 and 4), which will be the cause of a no solution for this system of equations.

Answer:

b

..........

Step-by-step explanation:

0≠14-4

...

The answer to the question is 46

Answer:

Domain= possible x values

Range= possible y values.

Domain= all real numbers

Range= all numbers greater than -2.

Let me know if this helps :)

Domain = all real numbers and Range = ( -2 , ∞) of the given exponential graph

" Domain of exponential function y = aˣ is all the values of x and range is the all calculated values of 'y' after substituting value of x."

General exponential function

y = aˣ

According to the graph,

Given exponential function,

y = 3ˣ - 2

x represents the domain of the function.

y represents the range of the function

compare with exponential equation

a= 3 >1

As the value of 'x' increases value of 'y' moves to infinity.

Therefore, value of y defined for all the values of 'x'.

Therefore,

Domain is set of all real numbers.

Function y is transformed by -2.

Substitute x=0 in y = 3ˣ-2 we get,

y = -2

Therefore,

Range = (-2 , ∞)

Hence, Domain = all real numbers and Range = ( -2 , ∞) of the given exponential graph.

Learn more about domain and range here

https://brainly.com/question/1632425

#SPJ2

☆ The relation between x and y is y = a cos x° +b

Taking 1st condition from the table .

→ x = 0 and y = 9

→ y = a + cos 0° + b

→ 9 = a + cos 0° + b

☆ We know that cos 0° = 1

→ 9 = a(1) + b

Now taking other condition

→ x = 90° and y = 1

→ y = a cos 90° + b

→ 1 = a cos 90° + b

☆ We know that cos 90° is 0

→ 1 = a(0) + b

Putting the value of b in equation 1st .

→ 9 = a + 1

→ a = 8 .

Now taking the value of x according to the question .

☆ x = 45 °

→ y = 8 ( cos 45°) + 1

☆ We know that cos 45° is 1/√2

→ y = 8(1/√2) + 1

→ 8 = 4×√2×√2

So the answer is 4√2+1

Answer:

4/6 and 8/12 and 16/24

Step-by-step explanation:

well because it is math and math works like this basically all of theese are equal to 2/3

Data:

age of Dollah = x (unknown element)

age of Fatimeh = x + 5 (age of Dollah + 5)

the product is 234

Equation:

x * (x + 5) = 234

x² + 5x = 234

x² + 5x - 234 = 0

Δ = b² - 4 a c = 5² - 4 (1 * -234) = 25 - 4 (-234) = 25 - (-936)

= 25 + 936 = 961

x₁,₂=[tex]\frac{b^{2} ± \sqrt{delta} }{2a}[/tex] = [tex]\frac{5^2 +/- \sqrt{961} }{2}[/tex] = [tex]\frac{25 +/- 31}{2}[/tex]

x1 = (25+31)/2 =  56 / 2 = 28

x2 = (25 -31)/2 = -6 / 2 = -3 [age can't be negative, so the first one is accettable]

So:

Dollah's age (x) = 28 years old

Fatima's age (x + 5) = 28 + 5 = 32 years old

Answer:

28

Step-by-step explanation:

The first five prime numbers are = 2,3,5,7,11

Addition of the prime nos. = 2+3+5+7+11=28

The first prime numbers are: 2, 3, 5, 7, 11.

The sum is 2 + 3 + 5 + 7 + 11 = 28, so option 4

The U shape is called a parabola

If the "a" is positive, then the parabola opens upward as shown in the graph on the left.

If "a" is negative, then the parabola opens downward. This is the parabola on the right.

The way I remember is that "a" being positive means it puts a smile on, which is what the parabola on the left resembles. The parabola on the right is a frowny face so "a" is negative.

A parabola is vertically cut in half by the axis of symmetry. One half mirrors over this vertical line to get the other half. The axis of symmetry passes through the vertex. The vertex is either the highest point or the lowest point depending on whether 'a' is negative or positive.

Answer:  see proof below

Step-by-step explanation:

Use the following Product to Sum Identities:

2 sin A sin B = cos (A - B) - cos (A + B)

2 sin A cos B = sin (A + B) + sin (A - B)

Use the Unit Circle to evaluate: cos 120 = -1/2    &      sin 60 = √3/2

Proof LHS → RHS

LHS:                                            sin 20 · sin 40 · sin 80

Regroup:                              (1/2) sin 20 · 2 sin 40 · sin 80

Product to Sum Identity:     (1/2) sin 20 [cos(80-40) - cos (80+40)]

Simplify:                                (1/2) sin 20 [cos 40 - cos 120]

Unit Circle:                            (1/2) sin 20 [cos 40 + (1/2)]

Distribute:                             (1/2) sin 20 cos 40 + (1/4) sin 20

Product to Sum Identity:       (1/4)[sin(20 + 40) + sin (20 - 40)] + (1/4) sin 20

Simplify:                                 (1/4)[sin 60 + sin (-20)] + (1/4) sin 20

                                           = (1/4)[sin 60 - sin 20] + (1/4) sin 20

Unit Circle:                             (1/4)[(√3/2) - sin 20] + (1/4) sin 20

Distribute:                              (√3/8) -  (1/4) sin 20 + (1/4) sin 20

Simplify:                                  √3/8

LHS = RHS:   √3/8 = √3/8  [tex]\checkmark[/tex]

We are given the equation cos(20°)(cos(40°)(cos(60°)(cos(80°) = √3 / 8. Let's once again start by applying the identity 'sin(s)sin(t) = - cos(s + t) + cos(s - t) / 2. In this case if we focus on the expression 'cos(20°)(cos(40°),' s would be = 20°, and t = 40°.

[tex]\mathrm{Use\:the\:following\:identity}:\quad \sin \left(s\right)\sin \left(t\right)=\frac{-\cos \left(s+t\right)+\cos \left(s-t\right)}{2}[/tex]

[tex]\sin \left(20^{\circ \:}\right)\sin \left(40^{\circ \:}\right)=\frac{-\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}[/tex]

[tex]\mathrm{Substitute}:\frac{-\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\sin \left(80^{\circ \:}\right)[/tex]

[tex]\mathrm{Multiply\:fractions}:\frac{\sin \left(80^{\circ \:}\right)\left(-\cos \left(60^{\circ \:}\right)+\cos \left(-20^{\circ \:}\right)\right)}{2}[/tex]

Remember that cos(- x) = cos(x). Respectively cos(- 20°) = cos(20°). Let's substitute and afterwards apply the identity 'cos(60°) = 1 / 2.'

[tex]\frac{\sin \left(80^{\circ \:}\right)\left(-\cos \left(60^{\circ \:}\right)+\cos \left(20^{\circ \:}\right)\right)}{2} = \frac{\sin \left(80^{\circ \:}\right)\left(-\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]

And if we further simplify the expression, we should receive the following...

[tex]\frac{\sin \left(80^{\circ \:}\right)\left(-1+2\cos \left(20^{\circ \:}\right)\right)}{4}[/tex]

Now we want to prove that this expression = √3 / 8. The denominator here is 4 so we can multiply the whole thing by 2 to have a denominator of 8. 2((sin(80°)(- 1 + 2cos(20°)) when simplified = √3. Therefore the expression is true.

Answer:

x = 1

y = 5

Step-by-step explanation:

5x - 2y = -5

5x + 6y = 35

=> 5x + 6y = 35

=> 5x - 5x + 6y = 35 - 5x

=> 6y = 35 - 5x

=> 6y/6 = 35/6 - 5/6x

=> y = 35/6 - 5/6x

=> 5x - 2 (35/6 - 5/6x) = -5

=> 5x - 35/3 + 5/3x = -5

=> 15/3x -35/3 + 5/3 = -15/3

=> 20/3x -35/3 = -15/3

=> 20/3x -35/3 + 35/3 = -15/3 + 35/3

=> 20/3x = 20/3

=> 20/3x * 3 = 20/3 * 3

=> 20x = 20

=> 20x/20 = 20/20

=> x = 1

=> 5x + 6y = 35

=> 5(1) + 6y = 35

=> 5 + 6y = 35

=> 5 -5 + 6y = 35 -5

=> 6y = 30

=> 6y/6 = 30/6

=> y = 5

So, x = 1

     y = 5

Answer:

DIVISION PROPERTY OF EQUALITY

Step-by-step explanation:

Given the equation r4 = 16,wm we can rewrite the equation as 4r = 16

The coefficient at the left hand side of the equation that we are to move to rge right is 4 (the number attached to the r variable). To do this we are going to apply the Division property of equality. This property is a property where both sides of an equation is divided through by the same constant without affecting the equality sign or by still keeping the equation.

To move the coefficient of r to the other side, we will divide both sides of the equation by 4 as shown;

4r/4 = 16/4

r = 4×4/4

r = 4

Hence the property that is used to move the coefficient (4) to the other side of the equation is the DIVISION PROPERTY OF EQUALITY.

it is a number less then zero

Answer:

a negative number is when a number exceeds below zero

for example 7 --8 would be -1

Answer:

Step-by-step explanation:

That will be 3a + 3b + 3c pounds of mortar.

as there will be 3a pounds of water and 3c pounds of cement.