Henry wrote 4z2 - 22 as
4. Are 4z2 – 22 and 4 equivalent expressions?
Explain.

Answer:

c) inversely

Step-by-step explanation:

In Mathematics an inverse relationship can be defined as a relationship between two variables, in which an increase in the value of one variable leads to a decrease in the value of the other variable i.e as the value of one variable becomes large, the value of the other variable becomes small.

Mathematically, an inverse relationship is given by the formula;

A = K/B

Where;

A and B are the variables.

K is the constant of proportionality.

Hence, if an increase in one quantity brings about a corresponding decrease in the other and vice versa, then the two quantities vary inversely.

Given:

The probability of landing A is 0.70.

The probability of landing B is 0.60.

The probability of landing both is 0.50.

To find:

The probability of landing A given it lands B.

Solution:

We have,

[tex]P(A) = 0.70[/tex]

[tex]P(B) = 0.60[/tex]

[tex]P(A\cap B) = 0.50[/tex]

The probability of landing A given it lands B is

[tex]P\left(\dfrac{A}{B}\right)=\dfrac{P(A\cap B)}{P(B)}[/tex]

[tex]P\left(\dfrac{A}{B}\right)=\dfrac{0.50}{0.60}[/tex]

[tex]P\left(\dfrac{A}{B}\right)=\dfrac{5}{6}[/tex]

[tex]P\left(\dfrac{A}{B}\right)=0.8333...[/tex]

[tex]P\left(\dfrac{A}{B}\right)\approx 0.83[/tex]

Therefore, the probability of landing A given it lands B is about 0.83.

Answer:

a) P(n) is true for all 'n' in the set ; { 0,2,4,6,8 ….. }

b) P(n) is true for all 'n' in the set ; { 0,1,2,3,4,5 ............ }

Step-by-step explanation:

a) As P(0) is true

we will assume that

this simply means  that ;  P(n) is true for all 'n' in the set

{ 0,2,4,6,8 ….. }

b) since P(0) and P(1) are true

we will assume that

also P(1) and P(2) are true

we will assume that

Also from the previous answers it can be seen that P(2) + P(3) is true

we will assume

This simply means that P(n) is true for all 'n' in the set

{ 0,1,2,3,4,5 ............ }

Answer:

1,737.3 feet

Step-by-step explanation:

Let's assume the length of the bridge consists of 2 right triangles as shown in the diagram. Use pythagorean theorem to find the other missing leg of each right triangle.

Let the missing leg for each triangle be x and y respectively.

Length of bridge = x + y

✔️x = √(1115² - 860²) = √503,625

x ≈ 709.7 (nearest tenth)

✔️y = √(1340² - 860²)

y ≈ 1,027.6 (nearest tenth)

✔️ Length of bridge = 709.7 + 1,027.6 = 1,737.3 ft

Answer:

Let's assume the fraction is 1/1

decreasing 1 by 10% = .9

decreasing 1 by 50% = .5

So the fraction becomes .9/.5 = 1.8

So its value increases by 180%

Step-by-step explanation:

Answer: x(15x)

Step-by-step explanation:

Answer:

8.75

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

15+12=27

27-5=22

Answer:

(20×20)+(2×20×30)

400+1200

1600inches^2

Answer:

1600 in^2

Step-by-step explanation:

We only have to add the areas of one square in the centre and 4 surrounding triangles.

area of the square=20×20=400 in^2

area of one triangle=1/2×20×30=300 in^2

area of four triangles=4×300=1200 in^2

So, total surface area of the square pyramid=400+1200=1600 in^2

*The units given should be in^2.

Answer:   y = 200·1.15^t

Step-by-step explanation:

The ratio from one year to the next is 1.15, so the balance is a geometric sequence. Since t starts at zero, we can write the balance (y) after t years as

 y = initial value · (common ratio)^t

 y = 200·1.15^t

Answer:

x = 25°

Step-by-step explanation:

3x + 30 + 2x + 3x + 30 + 4x = 360° (a full circle contains 360°)

12x + 60° = 360°

12x = 300°

x = 25°

Answer:

d i hope please be d please please

if other experts state the same thing in their own paper or document.

Step-by-step explanation:

D makes the most sense to me hopefully this helps

Answer:

24 cubic in

Step-by-step explanation:

Hope this helps UwU

Answer:

The simple interest is of 526.

The total amount is 3156.

Step-by-step explanation:

Simple Interest

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex]

In this question, we have that:

[tex]P = 2630, I = 0.08, t = 2.5[/tex]

The simple interest is:

[tex]E = P*I*t = 2630*0.08*2.5 = 526[/tex]

The simple interest is of 526.

The total amount is:

[tex]T = E + P = 2630 + 526 = 3156[/tex]

The total amount is 3156.

Answer:

150x=y

Step-by-step explanation:

2x150=300

4x150=600

6x150=900

8x150=1200

Answer:

D. 13.02

Step-by-step explanation:

Apply trigonometric function to find the height (h) of the wall.

Reference angle = 40°

Hypotenuse = 17 ft

Adjacent = h (height of the wall)

Apply CAH:

Cos 40 = Adj/Hyp

Cos 40 = h/17

17*Cos 40 = h

13.0227555 = h

h ≈ 13.02 ft

Answer:

7. A

8. C

Step-by-step explanation:

7. 2(-2)^2 - 3(-2) + 4 = 18 (A.)

8. 2(3a)^2 - 3(3a) + 4 = C

Answer:

(a)

[tex]\%Decrease= 12.5\%[/tex] --- TV

[tex]\%Decrease= 20\%[/tex] --- Laptop

(b) Laptop

Step-by-step explanation:

Given

Normal                       Sales

[tex]TV = 2000[/tex]                  [tex]TV = 1750[/tex]

[tex]Laptop = 1800[/tex]             [tex]Laptop = 1440[/tex]

Solving (a): Percentage increase of decrease for both

Percentage change is calculated as:

[tex]\%Change = \frac{New - Old}{Old} * 100\%[/tex]

For TV

[tex]\%Change = \frac{1750 - 2000}{2000} * 100\%[/tex]

[tex]\%Change = \frac{-250}{2000} * 100\%[/tex]

[tex]\%Change = -0.125* 100\%[/tex]

[tex]\%Change = -12.5\%[/tex]

It is a decrease because it is negative

[tex]\%Decrease= 12.5\%[/tex]

For Laptop

[tex]\%Change = \frac{1440 - 1800}{1800} * 100\%[/tex]

[tex]\%Change = \frac{-360}{1800} * 100\%[/tex]

[tex]\%Change = -0.2* 100\%[/tex]

[tex]\%Change = -20\%[/tex]

It is a decrease because it is negative

[tex]\%Decrease= 20\%[/tex]

Solving (b):

Laptop has the best reduced price  because it has a larger percentage decrease

Answer:

the answer 0.035 g = 35 milligrams

Answer:

Step-by-step explanation:

35miligram in 0.035g

Answer:

1504

Step-by-step explanation:

3472-1968=1504

CHECK

1968+1504=3472

Answer:

Step-by-step explanation:

It's a 30-60-90 triangle. The sides of a 30-60-90 triangle are in the ratio 1:√3:2

The side opposite the 90° angle is 12√3, so the side opposite the 30° is (12√3)/2 = 6√3.

The side opposite the 60° angle is (6√3)√3 = 18

x = 18

y = 6√3

Answer:

x = 18

y = 6√3

Step-by-step explanation:

<3

Answer:

$102

Step-by-step explanation:

2% of $100 = 0.02 * $100 = $2

The increase is $2.

$100 + $2 = $102

Answer: $102

Answer:

100 x 0,2 x 1 year(12/12 months)

=$102 after a year

Answer:

9.5 I think

STEPS-

9+4+11+14=38

38/4=9.5

Answer:

B

Step-by-step explanation:

B is the most likely answer due to

13x.5=6.5

and

53x.25=13.25

13.25+6.5=19.75$

Now stop making a high schooler do your work xD

Answer:B

Step-by-step explanation:

Answer:

its B

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

y= x + 8..... (1)

y= 3x - 11..... (2)

y - x = 8..... (3)

y - 3x = -11..... (4)

eliminating x:

(3) × 3: 3y - 3x = 24 ........ (5)

(4) × 1: y - 3x = -11 ......... (6)

(5) - (6): 2y = 35

Divide both sides by 2, therefore, y = 17.5

substitute the value of y into (3)

y - x = 8

17.5 - x = 8

17.5 - 8 = x

9.5 = x

I hope it'll help

Answer:

1:2

Step-by-step explanation:

18 inches to 1 yard

We need to convert 1 yard to 36 inches

18 inches : 36 inches

Divide each side by 18

18/18 : 36/18

1:2