Expand. Your answer should be a polynomial in standard form. -p^2(p^2-p-1) =​

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!

By using the quadratic formula, the roots of the quadratic equation 2 · x² - 7 · x + 1 are represented by the irrational number x = (7 ± √41) / 4.

For polynomials of the form a · x² + b · x + c = 0, the two roots can be found analytically by quadratic formula, whose expression is described below:

[tex]x = \frac{-b \pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]    

If we know that a = 2, b = - 7 and c = 1, then the roots of the polynomial are:

x = 7/4 ± (1/4) · √41

x = (7 ± √41) / 4

By using the quadratic formula, the roots of the quadratic equation 2 · x² - 7 · x + 1 are represented by the irrational number x = (7 ± √41) / 4.

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The form of the partial fraction decomposition is [tex]\frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]

The fraction is given as:

[tex]\frac{t^4 + t^2 + 1}{(t^2 + 4)(t^2 + 2)^2}[/tex]

To decompose the above, we make use of the following rule:

[tex]\frac{px^n + qx^m +....+ r}{(x^2 + a)(x^2 + b)^2} = \frac{Ax + B}{(x^2 + a)} + \frac{Cx + D}{(x^2 + b)} + \frac{Ex + F}{(x^2 + b)^2}[/tex]

So, we have:

[tex]\frac{t^4 + t^2 + 1}{(t^2 + 4)(t^2 + 2)^2} = \frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]

Hence, the form of the partial fraction decomposition is [tex]\frac{At + B}{(t^2 + 4)} + \frac{Ct + D}{(t^2 + 2)} + \frac{Et + F}{(t^2 + 2)^2}[/tex]

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The truth table for implication of the equations is F F ⇒ T

A truth table is a mathematical logic table that shows the truth values of different logic statements combined by a given logic rule.

Analysis:

P: 7 +1 is not equal to 0 making P to be false(F)

q: 2+2  is not equal to 5 making q to be false(F)

so for conditional or implication, F F⇒ T

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Answer:

Step-by-step explanation:

The sequence of required answers provides a step-by-step solution to the problem.

In the given trinomial, we identify the coefficients as ...

  ax² +bx +c = 25x² -20x -12   ⇒   a=25; b=-20; c=-12

Then the ac product is ...

  ac = (25)(-12) = -300

The factor pairs that make this product can be listed as ...

  -300 = (-300)(1) = (-150)(2) = (-100)(3) = (-75)(4) = (-60)(5) = (-50)(6) = (-30)(10) = (-25)(12) = (-20)(15) . . . . (only pairs with a negative sum are listed)

The sums of these pairs are -299, -148, -97, -71, -55, -44, -20, -13, -5.

The factors of the ac product that add to -20 are -30 and 10.

These factors are used to rewrite the -20x term as a sum.

  25x² -20x -12 = 25x² -30x +10x -12

Grouping these terms in pairs, we can identify common factors:

  = (25x² -30x) +(10x -12)

  = 5x(5x -6) +2(5x -6)

  = (5x +2)(5x +(-6))

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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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]

Answer: 5

5yards = 5napkins

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 resistance measured in ohms according to the given task is; 3.75 ohms.

Since it follows that the three quantities are related by the formula; V = √P. R can be used to estimate the required resistance.

Hence, when V = 130 and P = 1200; we have;

130 = √1200 × R

R = 3.75 ohm

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Answer:

The answer would be A: -15

The probability he will get at least 2 hits in the game is 0.470

The batting average is 0.229

In one game he gets 5 at bat

To find the probability he will get at least 2 hits we use binomial distribution.

The binomial distribution is also a Frequency distribution used for the possible no. of successful outcomes in a given no. of trials in each of which there is the same probability of success.

So we have

n = 5

p = 0.299

q = 1 - p

   = 0.701

[tex]P(X) = nC_{x} p^x q^(n-x)[/tex]

P(at least 2 hits in the game) = 1 - P(less than 2 hits)

= 1 - P(0) - P(1)

[tex]= 1 - 0.701^5 - 5C1 x 0.299 x 0.701^4[/tex]

= 1 - 0.169 - 0.361

= 0.470

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Answer: Option (2)

Step-by-step explanation:

[tex]|3k-2| > 7[/tex] means [tex]3k-2 < -7[/tex] or [tex]3k-2 > 7[/tex].

Solving each of these cases gives [tex]k < -\frac{5}{3}[/tex] or [tex]k > 3[/tex].

So, the answer is Option (2).

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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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

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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TheThe smallest diameter of wrapper that will fit the candy bar is 5cm.

Given:

AD = DC

AC = AD + DC

Segment AD = 2.5cm

Hence:

AC = AD + AD (AD = DC)

AC = 2AD

Where:

AD=2.5

So,

AC = 2(2.5cm)

AC = 5cm

Therefore the smallest diameter of wrapper that will fit the candy bar is 5cm.

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Answer: 5cm.

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{What is addition \& subtraction?}[/tex]

[tex]\huge\textbf{What is addition?}[/tex]

[tex]\bullet\large\textbf{ Well, \underline{addition} simply means when you're ADDING}\\\large\textbf{2 or more numbers from each other to get the result of}\\\large\textbf{a number.}[/tex]

[tex]\huge\textbf{Random notes}[/tex]

[tex]\star\large\textbf{ Usually, you start working with addition when you're in}\\\large\textbf{pre-kindergarten (pre-k also known as head-start)}\\\\\star\large\textbf{ When, you're adding you are going upward.}\\\\\star\large\textbf{ Addition sometimes come after you learn how to count}\\\large\textbf{the basic numbers and so forth because adding never}\\\large\textbf{ends if you really think about.}[/tex]

[tex]\huge\textbf{Example:}[/tex]

[tex]\heartsuit\large\textbf{ 2 \boxed{\bf +} 5 = 7}\\\\\\\heartsuit\large\textbf{ You got the result of 7 because you started at 2 \& went}\\\larg\textbf{up 5 spaces to your right on your number and you landed}\\\large\textbf{on 7.}[/tex]

[tex]\huge\textbf{What is subtraction?}[/tex]

[tex]\bullet\large\textbf{ Well, subtraction simply means you're taking away. Often}\\\large\textbf{people call it take aways.}[/tex]

[tex]\huge\textbf{Random notes:}[/tex]

[tex]\star\large\textbf{ Usually, you start working with subtraction when you're}\\\large\textbf{in pre-kindergarten (pre-k also known as headstart)}\\\\\star\large\textbf{When you're subtracting you are doing downward.}\\\\\star\large\textbf{You focus more on subtraction when you're counting}\\\large\textbf{backwards.}[/tex]

[tex]\huge\textbf{Example:}[/tex]

[tex]\heartsuit\large\textbf{ 7 \boxed{\bf -} 5 = 2 }\\\\\\\heartsuit\large\textbf{ 7 \boxed{\bf -} 2 = 5}\\\\\\\heartsuit\large\textbf{ For equation \#1. you begin at 7 and go BACK 5 spaces}\\\large\textbf{and you should have landed on 2.}\\\\\\\heartsuit\large\textbf{ For equation \#2. you begin at 7 \& go BACK 2 spaces}\\\large\textbf{and you should have landed on 5.}[/tex]

[tex]\huge\textsf{KEEP IN MIND:}[/tex]

[tex]\circ\large\textsf{ Addition OPPOSITE is subtraction \& subtraction OPPOSITE is}\\\large\textsf{addition.}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitirite1040:)}[/tex]

Answer:

x < -4

Step-by-step explanation:

add 8 to both sides

Simplify

Subtract 3x from both sides

Simplify, again

Multiply both sides by -1 ( reverse inequality)

Simplify, again

Divide both sides by 5

And vwola x < -4

HOPE THAT 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

Answer:

a

Step-by-step explanation:

The midline is at y=2.

Eliminate c, d, e

Also, since there is no horizontal shift amongst the remaining options, we know that since y=2 when x=0, this means it must be a sine curve.

This means the answer is a.

Answer:

no solution

Step-by-step explanation:

use grouping method:

f(x) = x^2 - 4x + 2

factor it:

when we try to factor the above equation, we see that there is no ordered pair in which the numbers multiple to -4 and add to 2, so there is no solution

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

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!!

The solution using correct step of substitution in the equation y=2x-1 4x+y=2 is x = 1/2 and y = 0

y = 2x - 1

4x + y = 2

4x + y = 2

4x + (2x - 1) = 2

4x + 2x - 1 = 2

6x - 1 = 2

6x = 2 + 1

6x = 3

x = 3/6

x = 1/2

y = 2x - 1

y = 2(1/2) - 1

= 2/2 - 1

= 1 - 1

y = 0

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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:

67.5

Step-by-step explanation:

I'm assuming this is simple interest.

1500x0.03x1.5=67.5

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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