Problem
(a) Expand and simplify [tex](x^2+2)^2[/tex]
(b) Hence fully factorise [tex]x^4+4x+3[/tex]

Please do not give me irrelevant answers.

The proportion in the tail with regards to the z scores will be:

a. z= 1.00

P(z > 1.00) = 1 - P(Z < 1.00)

= 1 - 0.8413

= 0.1587

The tail will be on the right side.

The proportion of the tail will be 0.1587.

b. z = 0.50

P(z > 0.50) = 1 - P(Z < 0.50)

= 1 - 0.6915

= 0.3085

The tail will be on the right side.

The proportion of the tail will be 0.3085

c. z= -1.25

P(z < -1.25)

= 0.1056

The tail will be on the left side.

The proportion of the tail will be 0.1056.

d. z= -0.40

P(z < -0.40)

= 0.3446

The tail will be on the left side.

The proportion of the tail will be 0.3446.

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The theoretical probability of an event​ computed as

Theoretical Probability = [tex]\frac{ Number of desired outcomes}{ Number of possible outcomes.}[/tex] This is further explained below.

Generally, The theoretical probability formula is the ratio of the number of successful outcomes to the total number of possible possibilities. We may write this formula out as follows:

In conclusion, the theoretical probability is mathematically given as

Theoretical Probability = [tex]\frac{ Number of desired outcomes}{ Number of possible outcomes.}[/tex]

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The best estimate of the sum of the expression given is [tex]\rm 13 \dfrac {31}{26}[/tex]

What is a Fraction ?

A fraction is written as p/q , where q [tex]\rm \ne[/tex] 0

It is asked to determine the sum of the fraction

31/4 + 17/3 + 8/18

Taking the LCM of 4 , 3 , 18

LCM of 4 , 3 ,18 is 36

Therefore

[tex]\rm \dfrac{ 31 *9 + 17 *12 + 8 *2}{36 }[/tex]

(279+204+16) /36

499 / 36

[tex]\rm 13 \dfrac {31}{26}[/tex]

Therefore the best estimate of the sum of the expression given is [tex]\rm 13 \dfrac {31}{26}[/tex].

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Answer:x=4

Step-by-step explanation:

tendrías que poner términos similares juntos, asegurándote de cambiar el signo de cualquier figura que cruce el igual al signo. luego restarías o sumarías, resolverías las ecuaciones de cada lado, ya que ahora están agrupadas. luego dividirás tu respuesta por el coeficiente que es 2 (2x). esto te dejaría con 4

4x - 2x = 1+7

4x-2x= 8

2x =8

divisir

x=8

The compound amount and the interest earned are $13,222.17 and $2,222.17 respectively.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

We know the formula for continuous compounding:

[tex]\rm A = P(e)^{rt}[/tex]

[tex]\rm A = 11000(e)^{0.023\times8}[/tex]

A = $13,222.17

I = A - P = 13,222.17 - 11000

I  = $2,222.17

Thus, the compound amount and the interest earned are $13,222.17 and $2,222.17 respectively.

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The probability that a randomly selected x-value from the distribution will be in the interval:

The probability of a normal distribution can be determined from the symmetrical curve between 1 to 100%.

From the information given:

To determine the probability that a randomly selected x-value is in the given interval:

[tex]P(35 < x < 45) = P(\dfrac{35-40}{5} < Z < \dfrac{45-40}{5})[/tex]

[tex]P(35 < x < 45) = P(\dfrac{-5}{5} < Z < \dfrac{5}{5})[/tex]

[tex]P(35 < x < 45) = P(-1 < Z < 1)[/tex]

[tex]\mathbf{P(35 < x < 45) = P[Z\le 1] -P[Z\le -1]}[/tex]

Using normal distribution table:

P(35 < x < 45) = 0.8414 - 0.1587

P(35 < x < 45) = 0.6827

[tex]P(30 < x < 40) = P(\dfrac{30-40}{5} < Z < \dfrac{40-40}{5})[/tex]

[tex]P(30 < x < 40) = P(\dfrac{-10}{5} < Z < \dfrac{0}{5})[/tex]

[tex]P(30 < x < 40) = P(-2 < Z < 0)[/tex]

[tex]\mathbf{P(30 < x < 40) = P[Z\le0]-P[Z\le -2]}[/tex]

Using normal distribution table:

P(30 < x < 40) = 0.5 - 0.02275

P(30 < x < 40) = 0.47725

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The total weight of cabbage is 14 1/4

An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

Given:

Yasmin purchased 6 heads of cabbage that each weighed 2 and  3/8 pounds.

So,

2 and 3/8 = 19/8

1 cabbage = 19/8 pounds

6 cabbages = x pounds

1 * x = 6 * 19/8

x = 114/8

x = 14 2/8

x = 14 1/4

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Answer:

0

Step-by-step explanation:

same numerator for that it is zero

Answer: A

Step-by-step explanation:

Answer: 5

5yards = 5napkins

The total surface area of the tomato ketchup given in the diagram can be determined as follows:

The total surface area of a shape is the addition of the areas of its individual surface.

So that the questions can be answered as thus:

A. To find the area of the given circle;

i. Area of a circle = [tex]\pi r^{2}[/tex]

where r is the radius of the circle.

area of the circle = π[tex](2.5)^{2}[/tex]

                            = 6.25[tex]\pi[/tex]

ii. There are two identical circles in the cylinder.

iii. The total area of all circles = 2(6.25[tex]\pi[/tex])

                                                 = 12.5[tex]\pi[/tex] square inches

B. To find the area of the rectangle;

i. one side of the rectangle is 5 inches.

ii. The other side of the rectangle = 2[tex]\pi[/tex]r

                                     = 2(2.5)[tex]\pi[/tex]

                                     = 5[tex]\pi[/tex] inches

iii. The area of the rectangle = l x b

                             = 5[tex]\pi[/tex] x 5

                             = 25[tex]\pi[/tex] square inches

C. Total surfce area of the cylinder = 5[tex]\pi[/tex] + 25[tex]\pi[/tex]

                                         = 30[tex]\pi[/tex] square inches

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Answer:

Step-by-step explanation:

First box

6.25

2

12.5

------

Second box

------

5

5

25

------

Last box

------

37.5

Answer:

See below

Step-by-step explanation:

(6x+14)(x-8)   =           Expand

   6x^2 - 48x + 14x - 112 =

     6x^2 - 34x-112        A = 6  B = -34

Answer:

Step-by-step explanation:

[tex]x(6x+14)-8(6x+14)\\6x^2+14x-48x-112\\[/tex]

Rest, you have to substitute the value. Such as A= -112

The weight of each pie will be 6 and 8 pounds respectively if the ratio of the seeds in these piles 3:4

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We have:

A greedy hamster hoarded 2 piles of sunflower seeds. Yesterday the ratio of the seeds in these piles was 3:4

Let 3x and 4x are the seeds from the smaller and bigger pile.

= 4x + 2  (greedy hamster placed another 2 pounds of seeds in the bigger pile)

= 3x - 1/4 (ate 1/4 pound from the smaller pile)

4x + 2 = 5x

Because the quantities of seeds in those piles is in the ratio of 5:16

After solving:

x = 2

Smaller pile weight = 3x = 3(2) = 6

Bigger pile wieght = 4x = 4(2) = 8

Thus, the weight of each pie will be 6 and 8 pounds respectively if the ratio of the seeds in these piles 3:4

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Answer:

if we plus 12 and 10the answer is 22 feet

Answer: 1

Step-by-step explanation:

If [tex]x > -7[/tex], then [tex]x+7 > 0 \implies |x+7|=x+7[/tex]

So, we have the original fraction is equal to

[tex]\frac{x+7}{x+7}=\boxed{1}[/tex]

Hello,

    3y + 4 < 16

⇔ 3y < 16 - 4

⇔ 3y < 12

⇔ y < 12/3

⇔ y < 4

⇒ S = ] - ∞ ; 4 [

Answer:

$4.48

Step-by-step explanation:

It takes $1.12 to feed one kid, to find the cost of all four kids we multiply 1.12 by 4

1.12*4 = $4.48

Answer:

A

Step-by-step explanation:

You are given one angle and one side are similar

 for  Angle-Side-Angle     you obviously need one more angle attached to the given side

A  angle r = ~ angle c

Answer: no they are not similar

Step-by-step explanation: if you find the ratio of sides 85:17, it is 5

The ratio of sides 30 to 6 is also 5

However, the ratio of sides 54 to 9 is 6 so it is not similar

The ratio has to be the same for all sides to be similar

Answer: x < 3

Step-by-step explanation:

      To solve this inequality, we will simplify and isolate the x variable.

   Given:

5x - 4 < 2x + 5

   Add 4 to both sides:

5x < 2x + 9

   Subtract 2x from both sides:

3x< + 9

   Divide both sides by 3:

x < 3

Answer:

x < 3

Step-by-step explanation:

Well you want to isolate x so start by subtracting 2x from both equations that way you remove it from the right side and it's only on the left side.

subtract 2x from both equations

[tex]3x-4 < 5[/tex]

add 4 to both equations

[tex]3x < 9[/tex]

divide both sides by 3

[tex]x < 3[/tex]

The final displacement is 2cm in the right.

Given that the object begins from 0 and moves 3 cm towards the left side and then, 5 cm towards the right side.

The displacement is known as shortest distance between the initial and final positions.

Let the x-axis be the positive, +ve, and on the right side and negative -ve on the left side.

Thus, displacement would be:

D= 0 -3 +5

D= 2 cm

This implies that the object displaces 2cm towards the right side

Hence, the final displacement when object moves from 0 and 3 cm to the left and then 5 cm to the right is 2cm in the right side.

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Answer:

2cm to the right

Step-by-step explanation:

i got this right hope it helps :)

Answer:

90 ft³

Step-by-step explanation:

V = LWH

V = (2 ft)(3 ft)(1 ft)

V = 6 ft³

Each planter has a volume of 6 ft³.

total volume = 15 × 6 ft³ = 90 ft³

Matching each equation of the plecewise function represented in the graph will be:

It should be noted that a domain simply means the set of inputs that are accepted by the function.

In this case, the equation of the piecewise function represented is given.

The graph is attached.

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Answer:

endpoint or straight lines

Step-by-step explanation:

same

The slope and the y-intercept of the function are: A. Slope = -2/5; y-intercept = -1/3.

Slope (m) = change in y / change in x.

Using two pairs of points form the table value, (1/4, -13/30) and (2/3, -3/5)"

Slope (m) = (-13/30 - (-3/5))/(1/4 - 2/3)

Slope (m) = (-13/30 + 3/5))/(1/4 - 2/3)

Slope (m) = (1/6)/(-5/12)

Slope (m) = (1/6)(12/-5) = 12/-30

Slope (m) = -2/5

Plug in m = -2/5 and (x, y) = (2/3, -3/5) into y = mx + b to find the y-intercept (b).

-3/5 = -2/5(2/3) + b

-3/5 = -4/15 + b

-3/5 + 4/15 = b

-1/3 = b

b = -1/3

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Answer:

A. Slope = -2/5; y-intercept = -1/3.

Step-by-step explanation:

Hope this helps!!

Answer:

1. Colouring Pencil 2. Notebook 3. Pencil Case

Step-by-step explanation:

Answer:

d) -8 × 3 = -24

Step-by-step explanation:

a) -18 ÷ 6 = -3

b) 30 ÷ 3 = 10

c) -7 × -7 = 49

d) -8 × 3 = -24

Above from all, option d is done correctly.

Note: when negatives are multiplied together or divided they cancel out to being positive. For example: -1 × -1 = 1

Hello!

Let's solve to verify whether the equations are true.

⇒ -18 ÷ 6 = -3

⇒ Given answer : 3

⇒ Incorrect

⇒ 30 ÷ 3 = 10

⇒ Given answer : -10

⇒ Incorrect

⇒ -7 × -7 = 49

⇒ Given answer = -49

⇒ Incorrect

⇒ -8 × 3 = -24

⇒ Given answer = 24

⇒ Correct

∴ The equation which is correctly calculated is -8 × 3 = -24.

a. The exact value of cosθ = -5/√74

b. The exact value of secθ = -√74/5

c. The exact value of cotθ = 5/7

Since the terminal side of the θ is the point, (-5, -7), we need to find the length of the terminal side.

So, r = √(x² + y²) where

So, r = √(x² + y²)

r = √((-5)² + (-7)²)

r = √(25 + 49)

r = √74

Since the trigonometric ratio cosθ = x/r

Substituting the values of x and r into the equation, we have

cosθ = x/r

cosθ = -5/√74

So, the exact value of cosθ = -5/√74

Since the trigonometric ratio, secθ = r/x

Substituting the values of x and r into the equation, we have

secθ = r/x

secθ = √74/-5

secθ = -√74/5

So,  the exact value of secθ = -√74/5

Since the trigonometric ratio cotθ = x/y

Substituting the values of x and y into the equation, we have

cotθ = x/y

cotθ = -5/-7

cotθ = 5/7

So,  the exact value of cotθ = 5/7

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The total amount of the drink is 2L. Strawberry concentrate will be X amount, and lemon concentrate will be the other part which is 2 - X.

---Note that we can only use one variable because there is only one equation to be set up here. That's why "the other part" is simply the total amount minus the strawberry amount.

0.4(2) = 0.3(x) + 0.55(2 - x)

---0.4, 0.3 and 0.55 are the decimal equivalents of 40%, 30% and 55%

0.8 = 0.3x + 1.1 - 0.55x

0.8 = -0.25x + 1.1

-0.3 = -0.25x

x = 1.2

Therefore, Chris should use 1.2L of strawberry concentrate and 0.8L of lemon concentrate to get 2L of a 40% concentrate mixture.

Hope this helps!