If seven bags of Takis cost $5.95, how much does one bag cost?

Here volume of the cuboid is 6x³ + 32x² + 2x - 40.

A cuboid's volume is calculated by summing its length, width, and height.

The number that is used to calculate how much room there is inside a cuboid is called its volume. A cuboid is a common three-dimensional form that surrounds us. Based on a form's parameters, such as its length, width, and height, the term "volume" is used to describe how much of that shape may be contained.

So Here,

height (h) = 2x - 2

Length (l) = 3x + 4

Breadth (b) = x + 5

Volume = l × b × h

= (3x + 4) × (x + 5) × (2x - 2)

= [(3x + 4)(x + 5)](2x - 2)

= (3x² + 13x + 20] (2x - 2)

Volume = 6x³ - 6x² + 38x² - 38x + 40x - 40

Volume (V) = 6x³ + 32x² + 2x - 40

To learn more about cuboid's volume

https://brainly.com/question/29424737

#SPJ4

Answer:

a) (x+6)(x-1)

b) (x+8)(x-5)

c) (x+3)(x-10)

Step-by-step explanation:

The final answer would always have to be two brackets with x and the relevant variables.

x²: You know the possible factors that can be multiplied together would be x and x. Each factor would have to be in different brackets, so we get (x + smth else)(x +smth else)

When factorising quadratic expressions, you need to find the correct pair of factors, that when multiplied together, becomes the constant of the expression. They also need to become the middle term when they are multiplied with the term in the bracket and then added together.

Possible factors for a):

1. 1 × 6 = 6

2. 2 × 3 = 6

You know 1 - 6 = -5, so we shall use the factors 6 and 1.

(x+6)(x-1) = x² -x + 6x - 6

              = x² + 5x - 6

Thus, (x+6)(x-1) is the answer.

Possible factors for b):

1. 1 × 40 = 40

2. 2 × 20 = 40

3. 4 × 10 = 40

4. 5 × 8 = 40

You know 8 - 5 = 3, so we shall use the factors 8 and 5.

(x+8)(x-5) = x² -5x + 8x - 40

               = x² + 3x - 40

Thus, (x+8)(x-5) is the answer.

Possible factors for c):

1. 1 × 30 = 30

2. 2 × 15 = 30

3. 3 × 10 = 30

4. 5 × 6 = 30

You know 3 - 10 = -7, so we shall use the factors 3 and 10.

(x+3)(x-10) = x² -10x + 3x - 30

               = x² - 7x - 40

Thus, (x+3)(x-10) is the answer.

a)

x² - 5x - 6

= x² + x - 6x - 6

= x(x + 1) -6(x + 1)

= (x - 6) (x + 1)

b)

x² + 3x - 40

= x² + 8x - 5x - 40

= x(x + 8) -5(x + 8)

= (x - 5) (x + 8)

c)

x² - 7x - 30

= x² - 10x + 3x - 30

= x(x - 10) + 3(x - 10)

= (x + 3) (x - 10)

Using the doubling time and exponential growth formulae, the population of annual plants will be 4,000 after 42 years, assuming a constant rate of increase and an initial population size of 500.

To answer your question, we will use the doubling time formula and exponential growth formula. Given that the doubling time of a population of annual plants is 14 years, the initial size is 500, and we want to know the population size after 42 years, we can follow these steps:

1. Determine the number of doubling times within 42 years: Since the doubling time is 14 years, we can calculate the number of doubling times by dividing the total time (42 years) by the doubling time (14 years):
  Number of doubling times = 42 / 14 = 3

2. Calculate the growth factor using the doubling time: In exponential growth, the population size increases by a growth factor. Since the population doubles in 14 years, the growth factor (g) is 2 (doubled).

3. Apply the exponential growth formula: The formula for exponential growth is P(t) = P0 * g^t, where P(t) is the population size at time t, P0 is the initial population size, g is the growth factor, and t is the number of doubling times.

4. Plug in the given values and solve for P(t): We know the initial population size (P0) is 500, the growth factor (g) is 2, and the number of doubling times (t) is 3. So the formula becomes:
  P(t) = 500 * 2^3

5. Calculate the population size after 42 years: P(t) = 500 * 8 = 4000

In conclusion, using the doubling time and exponential growth formulae, the population of annual plants will be 4,000 after 42 years, assuming a constant rate of increase and an initial population size of 500.

To learn more about exponential growth formulae, refer here:

https://brainly.com/question/13877030#

#SPJ11

The answer is 18 ounces of salt in 20% solution should be mixed with 27 ounces of 10% solution to produce 45 ounces of 14% salt solution.

let x and y be the amount of 20% and 10% solutions respectively:

x + y = 45 ____eq.1

20%x + 10%y = 14% (45)

20/100x + 10/100 y = 14/100 (45)

0.2x + 0.1y = 0.14 (45)____eq.2

Rewrite eq.1 to (x=45-y) and plug that value into that of eq.2

0.2(45-y) + 0.1y = 6.3

9 - 0.2y + 0.1y = 6.3

-0.1y = -2.7

y = (-2.7) ÷ (-0.1)

y = 27

put the value of y in eq. 1

x + y = 45

x + 27 = 45

x = 45 - 27

x = 18

Therefore, 18 ounces of salt in 20% solution should be mixed with 27 ounces of 10% solution to produce 45 ounces of 14% salt solution.

Full Question:

How many ounces of a 20% salt solution should be mixed with a 10% salt solution to produce 45 ounces of a 14% salt solution?

To know more about ounces:

brainly.com/question/2853335

#SPJ4

a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).

To solve:

12 - 4x = 15 - 3x

12 = 15 + x

-3 = x

Therefore, x is equal to -3.

b) To find the value of AB, plug in the value of x found in part a).

12 - 4x

12 - 4(-3)

12 - (-12)

12 + 12 = 24

Thus, segment AB is equal to 24.

c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.

15 - 3x

15 - 3(-3)

15 - (-9)

15 + 9 = 24

Thus, segment DE is also equal to 24.

We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.

I hope this helps!

Answer:

848.23

Step-by-step explanation:

hope this got you the right anwser

Answer:

A. 10

Step-by-step explanation:

2/4 = x/20

1/2 = x/20

2x = 20

x = 10

Answer: 10

Answer:

19

Step-by-step explanation:

5x+30=125

125-30=95

isolate the variable 95/5=19

An expression is a set of terms combined using the operations +, -, x or ÷, for example 4 x − 3 or 5 x 2 − 3 x y + 17 . An equation is a statement with an equals sign, which states that two expressions are equal in value, for example 4 b − 2 = 6

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

50

6m-n

Let m = 9 and n = 4

when m = 5 and n = 38

N-6m6*9-4

Multiply first

54-4

Then subtract

50

To learn more about  expression

visit : https://brainly.com/question/23968040

#SPJ9

Answer:

x=17

Step-by-step explanation:

LM=3x+18

LO=2LM=2(3x+18)=6x+36

LO=9x-15

Set them equal to each other.

6x+36=9x-15

-3x+36=15

-3x=-51

x=17

The system that sought to ensure the availability of a subservient agricultural labor supply controlled by white people.

Slavery is the practice of forcing individuals to work without pay or freedom. Historically, it has been used as a means of exploiting people for economic gain, and it has been justified on the basis of race, ethnicity, religion, or social status.

In the transatlantic slave trade, which lasted from the 16th to the 19th century, millions of Africans were captured and forcibly transported across the Atlantic Ocean to the Americas, where they were sold into slavery. Slaves were treated as property and denied basic human rights, such as the right to freedom, education, and family.

The system that sought to ensure the availability of a subservient agricultural labor supply controlled by white people is known as "slavery." Slavery was a brutal and inhumane practice that existed in many parts of the world throughout history. In the United States, slavery was primarily used to support the Southern agricultural economy, with enslaved people being forced to work on plantations producing crops such as cotton, tobacco, and sugar cane. The abolition of slavery in the United States was a long and difficult struggle that culminated in the Civil War and the passage of the 13th Amendment to the US Constitution in 1865.

To know more about war visit:

https://brainly.com/question/11874600

#SPJ1

Answer:

It's 36

Step-by-step explanation:

3 × [1+5]×(4-2)]

3×[6×(2)]

3×[12]

=36

Answer:

a. P(G1 and G2) = (6/11)(6/11) = 36/121

b. P(at least 1 green) = 1 - 36/121 = 85/121

c. P(G1 or G2) =

(6/11)(5/11) + (5/11)(6/11) + (6/11)(6/11) =

30/121 + 30/121 + 36/121 = 96/121

d. Yes, G1 and G2 are independent.

Answer:

\(67.20\%\)

Step-by-step explanation:

Given

\(n =2430\) --- sample

\(r = 16.72\%\) --- degeneration rate

From the findings, we have:

\(p = 377\) --- tested positive

\(t =561\) --- total test

Required

The positive predicted value (PPV)

This is calculated using:

\(PPV=\frac{Positive}{Total}\)

i.e.

\(PPV = \frac{377}{561}\)

\(PPV = 0.6720\)

Express as percentage

\(PPV = 0.6720 * 100\%\)

\(PPV = 67.20\)

1. The stretching technique emphasized in the scenario of a tennis player running up to the net and shuffling back to the baseline is dynamic stretching.

2. The stretching technique emphasized in the scenario of a runner performing various stretches for 30 seconds on each side after a run is static stretching.

1. The stretching technique emphasized in the scenario of a tennis player running up to the net and shuffling back to the baseline five times is dynamic stretching. Dynamic stretching involves performing controlled movements that mimic the motions of the activity or sport being performed. In this case, the tennis player is incorporating dynamic movements to warm up and prepare their muscles for the specific demands of playing tennis.

2. The stretching technique emphasized in the scenario of a runner performing a quadriceps stretch, gastrocnemius stretch, and a runner's stretch for 30 seconds on each side of the body after a run is static stretching. Static stretching involves holding a stretch in a stationary position for a certain period of time. In this case, the runner is holding each stretch for 30 seconds, which is a characteristic of static stretching. Static stretching is commonly used to improve flexibility and promote muscle relaxation after exercise.

To know more about technique:

https://brainly.com/question/32623182

#SPJ4

In the given scenario, the type of stretching technique being emphasized is Dynamic Stretching.

Dynamic stretching is a type of stretching technique that involves active movements to improve flexibility and range of motion. It is typically performed as part of a warm-up routine before engaging in physical activity. Unlike static stretching, which involves holding a stretch for an extended period, dynamic stretching incorporates dynamic movements that mimic the actions performed during the activity. This helps to warm up the muscles, increase blood flow, and prepare the body for the upcoming exercise or sports activity.

In the given scenario, the type of stretching technique being emphasized is Static Stretching.

Static stretching, on the other hand, is a stretching method where a stretch is held in a fixed position for a prolonged period of time, typically ranging from 15 to 60 seconds. This technique is often used to improve flexibility and increase the length of muscles and tendons. Static stretching is commonly performed during the cooldown phase after exercise or physical activity. It helps to relax the muscles, reduce muscle soreness, and improve overall flexibility and joint mobility.

Both dynamic stretching and static stretching have their benefits and serve different purposes in a fitness or sports routine. Dynamic stretching is effective for warming up the body and preparing it for physical activity, while static stretching is useful for improving flexibility and promoting relaxation in the muscles. It's important to choose the appropriate stretching technique based on your specific goals and the context of your exercise or sports regimen.

To know more about Dynamic Stretching.

https://brainly.com/question/14635799

#SPJ11

Answer:

x = 11

Step-by-step explanation:

Steps as below:

The permissible exposure limit (PEL) to MDA (4,4'-Methylenebis(2-chloroaniline)) using an 8-hour time-weighted average varies based on the country and regulatory agency.

In the United States, the Occupational Safety and Health Administration (OSHA) has set a PEL of 5 ppb, while in Canada, the Workplace Hazardous Materials Information System (WHMIS) has set a PEL of 10 ppb. In the European Union, the European Chemicals Agency (ECHA) has set a PEL of 15 ppb. The World Health Organization (WHO) has also established a recommended exposure limit (REL) of 20 ppb for MDA.

It is important to note that exposure to MDA can have harmful effects on human health, including damage to the liver, kidneys, and respiratory system. Therefore, it is essential to follow the established PELs and use proper personal protective equipment when handling MDA.

To know more about Average  visit :

https://brainly.com/question/24057012

#SPJ11

a) X'Y' + X'Y + XY simplifies to X' + Y.

b) A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the functions:

a) Complement is W' + X' + YZ.

b) Complement is (A' + B + C)(A'B' + C' + A'B).

a) To prove X'Y' + X'Y + XY = X' + Y, we can use Boolean algebra identities:

X'Y' + X'Y + XY

= Y'(X' + X) + XY(Distributive Law)

= Y' + XY(X + X' = 1)

= X' + Y(Commutative Law)

Therefore, X'Y' + X'Y + XY simplifies to X' + Y.

b) To prove A'BC' + ABC' + BC'D = BC', we can simplify the expression using Boolean algebra:

A'BC' + ABC' + BC'D

= BC'(A' + A) + BC'D   (Distributive Law)

= BC' + BC'D(A + A' = 1)

= BC'(BC' + BC'D = BC' + BC'(1) = BC')

Hence, A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the given functions:

a) The complement of WX(Y'Z + YZ') + W'X'(Y' + Z)(Y + Z') is W' + X' + YZ.

b) The complement of (A + B' + C')(A'B' + C)(A + B'C') is (A' + B + C)(A'B' + C' + A'B).

Learn more About Distributive Law from the given link

https://brainly.com/question/25224410

#SPJ11

A. The constants A, B, and C for the expression (x-1)(x-2)(x-3) / (3x² - 12x + 11) are A = -1, B = 5, and C = -3.

b. The partial fraction decomposition of (x+1)(x²+1) / -2x is (-1/2)/(x+1) + (3/2)x/(x²+1) + (5/2)/x.

A- To find the constants A, B, and C:

Expand the numerator of the rational function:

(x - 1)(x - 2)(x - 3) = x³ - 6x² + 11x - 6

Set up the equation:

x³ - 6x² + 11x - 6 = A(x - 2)(x - 3) + B(x - 1)(x - 3) + C(x - 1)(x - 2)

Expand the right side:

x³ - 6x² + 11x - 6 = (A(x² - 5x + 6)) + (B(x² - 4x + 3)) + (C(x² - 3x + 2))

Collect like terms:

x³ - 6x² + 11x - 6 = (A + B + C)x² + (-5A - 4B - 3C)x + (6A + 3B + 2C)

By comparing the coefficients of x², x, and the constant term, we get the following system of equations:

A + B + C = -6

-5A - 4B - 3C = 11

6A + 3B + 2C = -6

Solving this system of equations, we find A = -1, B = 5, and C = -3.

B- To express (x+1)(x²+1) / -2x as partial fractions:

Write the rational function as A/(x+1) + (Bx+C)/(x²+1) + D/x, where A, B, C, and D are constants.

Multiply through by -2x to get rid of the denominator:

(x+1)(x²+1) = A(-2x)(x²+1) + (-2x)(Bx+C) + D(x+1)(x²+1)

Expand and collect like terms:

x³ + x² + x + 1 = (-2A)x³ + (-A + -2B)x² + (-2C + D)x + (A + C)

Comparing coefficients, we get the following equations:

-2A = 1

-A - 2B = 1

-2C + D = 1

A + C = 1

Solving these equations, we find A = -1/2, B = 0, C = 3/2, and D = 5/2.

Therefore, (x+1)(x²+1) / -2x can be expressed as (-1/2)/(x+1) + (3/2)x/(x²+1) + (5/2)/x, and we can rewrite (x+1)(x²+1) / x⁴ + x³ + x² - x as (-1/2)/(x+1) + (3/2)x/(x²+1) + (5/2)/x.

learn more about partial fractions here:

https://brainly.com/question/30401719

#SPJ4

Answer:

32

Step-by-step explanation:

Answer:

-19 - (-25) = 6

Step-by-step explanation:

-19 - (-25) =

-19 + 25 = 6

Firstly, let's calculate the molar mass of citric acid. We get that:\($$\begin{aligned}\text{Molar mass of citric acid} &= 3(\text{Molar mass of }\ce{C}) + 4(\text{Molar mass of }\ce{H}) + 3(\text{Molar mass of }\ce{O})\\&=3(12.01)+4(1.01)+3(16.00)\\&=192.13\ \text{g/mol}\end{aligned}$$\)

Now, let's calculate the number of moles of baking soda:\($$\begin{aligned}\text{Number of moles of }\ce{NaHCO3} &= \frac{\text{Mass}}{\text{Molar mass}}\\&= \frac{35}{84.01}\\&=0.4165\ \text{mol}\end{aligned}$$\)The balanced equation for the reaction between citric acid and baking soda is as follows:\($$\ce{3H3C6H5O7(aq) + 2NaHCO3(aq) -> Na3C6H5O7(aq) + 3CO2(g) + 3H2O(l)}$$\)The stoichiometric ratio of citric acid and baking soda is 3:2.

The number of moles of citric acid needed would be:\($$\begin{aligned}\text{Number of moles of citric acid} &= \frac{3}{2}\times\text{Number of moles of }\ce{NaHCO3}\\&=\frac{3}{2}\times0.4165\\&=0.6248\ \text{mol}\end{aligned}$$\)Now, we can use the molarity formula to calculate the volume of 0.5 M citric acid solution required:\($$\begin{aligned}\text{Number of moles} &= \text{Molarity}\times\text{Volume in liters}\\0.6248 &= 0.5\times\text{Volume in liters}\\\text{Volume in liters} &= \frac{0.6248}{0.5}\\&=1.25\ \text{liters}\end{aligned}$$\)Therefore, 1.25 liters of 0.5 M citric acid solution would be needed to react with 35 grams of baking soda.

To know more about molar visit:

https://brainly.com/question/31545539

#SPJ11

The interquartile range is a useful tool for measuring variability in a set of data because it overcomes the difficulty of the range being influenced too much by extreme values

The interquartile range is a measure of variability that is commonly used in statistics to describe the spread of a set of data. It is particularly useful because it overcomes the difficulty of the range being influenced too much by extreme values.

In mathematical terms, the interquartile range is defined as the difference between the upper quartile (Q3) and the lower quartile (Q1).

The upper quartile represents the 75th percentile of the data and the lower quartile represents the 25th percentile of the data.

This means that 25% of the data falls below the lower quartile and 75% of the data falls above the upper quartile.

The interquartile range provides a better representation of the spread of the data because it eliminates the influence of extreme values.

These values, also known as outliers, can have a significant impact on the range and can make it appear as though the data is more spread out than it actually is.

By using the interquartile range, the outliers are excluded and a more accurate representation of the spread of the data is obtained.

Therefore, option (a) is correct.

To know more about interquartile here.

https://brainly.com/question/4135956

#SPJ4

The two posters will cover 776 square inches of Melody's bedroom wall.

To find this, you add the area of the two posters together. Poster A has an area of 450 square inches, and poster B has an area of 326 square inches. By adding these two values together, we get 450 + 326 = 776 square inches. This is the total area that the two posters will cover on Melody's bedroom wall. It is important to note that this is assuming that the posters do not overlap each other and that they are placed next to each other, covering an equal area of the wall.

Learn more about Simple Addition here:

https://brainly.com/question/28954094

#SPJ4

The average book owned by other people is 112 which is greater than Michael's.

What is average?

In standard language, a mean could be a single range taken as representative of a listing of numbers, typically the total of the numbers divided by what numbers are within the list.

Main Body:

Books owned by Michael = 97

Average book owned by people = sum of all books / total people

avg. book owned = (225+142+29+103+61)/5

avg book owned by people = 560/5

                                               = 112

Hence books owned by avg people is 112.

To know more about average click on the link below

https://brainly.com/question/20118982

#SPJ1

Answer:

12, 20

Step-by-step explanation:

Don't worry I just know

No, the statement "In spherical geometry, the sum of the angles in a triangle equals 180 degrees." is not true.

The term triangle in geometry refers the polygon with three vertices, sides and angle.

Here we have given the statement "in Euclidean geometry the sum of the angles in a triangle equals 180 degrees"

And we need to find whether this is this also true in spherical geometry.

Basically, the sum of the angles of a spherical triangle is not equal to 180°. Because, we know that the sphere is a curved surface, where locally the laws of the flat Euclidean geometry are good approximations.

Therefore, here in a small triangle on the face of the earth, then the sum of the angles is only slightly more than 180 degrees.

To know more about Triangle here.

https://brainly.com/question/2773823

#SPJ4

Answer:

Step-by-step explanation:

The compound interest formula is \(P(1+r/n)^{nt}\)

Known information:

Now let's set up the equation:

  Future amount: \(18733 (1+\frac{0.051}{4} )^{4*10}\) \(=31,095.49\)

Thus the future amount is $31.095.49.

Hope that helps!