Which soap deal has the lowest price per ounce?


$5.50 for 13.0 oz

$5.75 for 14.0 oz

$3.45 for 3.5 oz

$5.25 for 12.0 oz

The equation of the tangent line at (1,1) is given as follows:

y - 1 = -0.25(x - 1).

The curve for this problem is given as follows:

x² - y² = 2x + y + xy - 4.

Applying implicit differentiation, we obtain the slope of the tangent line, as follows:

2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y

(dy/dx)(1 + x + 2y) = 2x - 2 - y

m = (2x - 2 - y)/(1 + x + 2y).

At x = 1 and y = 1, the slope is given as follows:

m = (2 - 2 - 1)/(1 + 1 + 2)

m = -0.25.

Hence the point-slope equation is given as follows:

y - 1 = -0.25(x - 1).

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The least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

The equation in this problem is given as follows:

1/x + 2/(x - 3) = 5.

The denominators of each expression are given as follows:

x and x - 3 are not factors of each other, hence we multiply them and the least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

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The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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A third variable associated with two variables under study that results in a correlation between the two variables, falsely implying a causal relationship between the pair, is a) a lurking variable.

A lurking variable is an uncontrolled and unknown variable but significant effect on both independent and dependent variables.

A lurking variable creates a correlation between the independent and dependent variables without being intended by the researcher.

We can differentiate a lurking variable from a confounding variable.

A confounding variable is taken into account in research and can also influence the variables of interest but it is not credited with any relationship between the independent and dependent (response) variables.

Thus, the existence of a third variable resulting in a correlation between the independent and dependent variables is called a lurking variable.

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y = 5x (option B)

We need to find the constant of proportion for the table.

For proportional relationship:

y = kx

k = constant of proportionality

k = y/x

k = 30/6 = 5

k = 35/7 = 5

k = 40/8 = 5

k = 45/9 = 5

Since k is constant, the relationship between y and x:

5 = y/x

y = 5(x)

y = 5x (option B)

Answer:

12.3455882353

Step-by-step explanation:

(103/8) = 12.875

(9/14) = 0.64285714285

0.64285714285 x 14 = 9

(9/17) = 0.5294117647

12.875 - 0.5294117647 = 12.3455882353

Required solution of the given equation 3.1 = -0.5 + 0.3x is x = 12.

What is equation?

A mathematical statement that asserts that two expressions are equal is called equation

. It is consist of variables, constants, and mathematical operations such as , subtraction, addition, division, multiplication . We can use equations in mathematics to model real-world situations or to solve problems. It can also be used to express relationships between quantities, to find unknown values, and to test hypotheses. Equations can be written in various forms, such as linear, exponential, trigonometric ,quadratic. Equation depends on the type of relationship being modeled.

Here given equation is 3.1 = -0.5 + 0.3x.

We are Simplifying it,

\(3.1 + 0.5 = 0.3x \\ 0.3x = 3.6 \\ x = \frac{3.6}{0.3} \\ x = 12\)

So, required solution of the given equation is 12.

Therefore, option C is the correct answer.

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Correct question is "What is the solution to this equation? 3.1 = -0.5 + 0.3x A:x=6 B:x=3 C:x=12 D:x=0.8".

Answer:

it should be 14,580 m^2

(the ^2 means squared btw)

The relationship between M and C can be given by the equation C= 6M + 12

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: A movie rental company charges a monthly fixed membership fee of $12 plus $6 per movie that the user rents in that month.

Now M represents the number of movies and C represents the user's total charge for the month

Thus C= 6M + 12

where 6M is the total cost due to renting some number of movies M

Hence, The relationship between M and C can be given by the equation C= 6M + 12

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The expression which shows how many grams of raisins are in the bowl will be

(0.01x) * 150 + (0.01y) * 250

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The expression which shows how many grams of raisins are in the bowl will be:

= (x% × 150) + (y% × 250)

= (0.01x) * 150 + (0.01y) * 250

This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.

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Answer:

93

Step-by-step explanation:

All the angles in a triangle add up to 180 degrees.

52 + 35 + x = 180

87 + x = 180

x = 93 degrees

Answer:

min: 56

lower quartile: 70

median: 74

upper quartile: 80

max: 86

Answer:

-22

Step-by-step explanation:

h(5)=-5•5+3

h(5)=-25+3

h(5)=-22

Answer:

-22

Step-by-step explanation:

Replace x with 5 and multiply tge -5 by 5 wich equals -25 and add 3 which would make -22

Answer:

25

Step-by-step explanation:

19 *100/76

Number into 100 by percentage

Answer: Rs. 100

Step-by-step explanation:

Given the following :

Total expenditure for dance show = Rs. 25000

Profit made except expenditure = Rs. 12,000

Number of people who observed and paid for the show = 370

Amount paid per person will be :

(Total amount or revenue realized / number of observers who paid)

Total revenue realized = (total expenditure + profit made)

Total Revenue realized = Rs.(25,000 + 12,000) = Rs. 37,000

Amount paid per observer = (Rs. 37,000 / 370)

= Rs. 100

Answer:

Step-by-step explanation:

The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000,  3,983 rounded to the nearest thousand is 4,000,  13,560 rounded is 14,000.

7,000 + 4,000+ 14,000 = 25,000

The length of each piece lies between 4 and 5 inches.

What is the whole number?

A whole number is a number that does not have any fractional or decimal part. It is a non-negative integer, which means it can be zero or any positive integer. In other words, a whole number is any of the numbers 0, 1, 2, 3, 4, 5, 6, and so on.

If the candy maker chops a 17-inch taffy into 4 equal-length pieces, he is dividing the original length by 4.

To find the length of each piece, we need to perform the division:

17 / 4 = 4.25

Each piece would be 4.25 inches long.

To find the two whole numbers between which the answer lies, we can round 4.25 to the nearest whole numbers:

Rounded down: 4

Rounded up: 5

Therefore, the length of each piece lies between 4 and 5 inches.

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Answer:

the answer is monkey epaulets monkey

Step-by-step explanation:

123

Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

The others operate in a similar manner. The following must be done, however, in order to determine the probability of anything NOT occurring, such as drawing a sweet that is NOT a kit-kat:  1 - P(kit-kat)

You only need to multiply the quantity of the selected candy by the total number of candies if you choose to put each piece of candy back after choosing it.

In this case, the desired confectionery is P(snickers). 12 in number.

In total, the bag contains 20 sweets.

P(snickers) = 12/20 = 3/5

The others function in the same way. The following must be done, however, in order to determine the likelihood of anything NOT occurring, such as drawing a sweet that is NOT a kit-kat:

1 - P(kit-kat)

The complete question is:

Suppose a bag of candy contains 12 Snickers, 5 Kit-Kats, and 3 Three Musketeers. Find each probability if you choose one piece of candy at random.

a) P(Snickers) b) P(Kit-Kat) c)P(Three Musketeers) d) P(not Kit-Kat)

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The sum of the square of the ages is 405.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

The Ages of seven children are listed: x = 5, 5, 11, 9, 8, 5, 8.

The squared of the ages:

= 25, 25, 121, 81, 64, 25, 64

The sum of the square of the ages:

= 25 + 25 + 121 + 81 + 64 + 25 + 64

= 405

Therefore, the result is 405.

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- - - - - - - - - - - - - - - -

There is some unnecessary information in the problem, first, it should be removed.

"The dosage of cough medicine for a child 4 to 6..."

"2 days"

Listing the age and days don't matter here, it's the rest of the problem that matters!

- - - - - - - - - - - - - - - -

"1/2(a teaspoon) every 4 hours,"  This is one dose. Multiply 1/2 by five to see how many teaspoons are consumed.

1/2 x 5 = 2 1/2 (teaspoons)

- - - - - - - - - - - - - - - -

Good luck! :)

~pinetree

Answer: x = 138

Step-by-step explanation:

\(108+117+x=3 * 121\\3 * 121 = 363\\Rearrange unknown terms to the left side of the equation\\x=(363-108)-117\\\\255-117=138\\x=138\)

Answer:

Step-by-step explanation:

Set up an equation:

7x + 10x + 13x = 100000 and solve for x:

30x = 100000 so

x = 3333.33

Anna gets 7(3333.33) = 23333.31

Louise gets 10(3333.33) = 33333.33

Lacey gets 13(3333.33) = 43333.29

The solution to the system, as an ordered triple is: (3, -4, 6).

To solve the following given system of equations:

2x + y + 3z = 20 --> eqn. 1

x + 2y - z = -11 --> eqn. 2

3x - 2z = -3 --> eqn. 3

Multiply equation 1 by 2 to get eqn. 4:

4x + 2y + 6z = 40 --> eqn. 4

Subtract eqn. 4 from eqn. 2:

x + 2y - z = -11 --> eqn. 2

4x + 2y + 6z = 40 --> eqn. 4

-3x - 7z = -51 --> eqn. 5

Add equations 3 and 5 together:

3x - 2z = -3 --> eqn. 3

-3x - 7z = -51 --> eqn. 5

-9z = -54

z = -54/-9

z = 6

Substitute the value of z into equation 5:

-3x - 7(6) = -51 --> eqn. 5

-3x - 42 = -51

-3x = -51 + 42

-3x = -9

-3x/-3 = -9/-3

x = 3

Find the value of y by substituting the values of x and z into equation 1:

2(3) + y + 3(6) = 20 --> eqn. 1

6 + y + 18 = 20

24 + y = 20

y = 20 - 24

y = -4

The solution as an ordered triple is: (3, -4, 6).

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Check the picture below.

so hmm we have a 6x6 square atop and a triangle with base of 6 and a height of "h", let's get "h".

\(\sin( 42^o )=\cfrac{\stackrel{opposite}{h}}{\underset{hypotenuse}{2}} \implies 2\sin(42^o)=h \implies 1.34\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{6})(\underset{h}{1.34})}~~ + ~~\stackrel{ square }{(6)(6)}} ~~ \approx ~~ 4.02+36~~ \approx ~~ \text{\LARGE 40.0}\)

Answer:168 inches

Step-by-step explanation:

the answer is 168 inches because 28 times 6 is equivalent to 168 and then u have to put the inches on the end.