MODELING REAL LIFE You collect S234 selling small and large smoothies. You sell a total of 46 smoothies. How many of each size did you sell?
20 small smoothies
26 large smoothies

If in an analysis of variance problem involving 3 treatments and 10 observations per treatment, S S E = 399.6. The M S E for this situation is  C. 14.8.

We would be making use of this formula to find or determine the MSE which is the variance within the sample.

MSE = S S E / r (c-1)

Where:

MSE represent variance within the sample = ?

SSE represent sum of the squares of error = 399.6

r represent 3 treatment

c represent observation per treatment = 10

Let plug in the formula so as to know the variance within the sample (MSE )

Sample variance ( MSE ) = 399.6 /3 (10 - 1 )

Sample variance ( MSE ) = 399.6 / 3 (9)

Sample variance ( MSE ) = 399.6 / 27

Sample variance ( MSE ) = 14.8

Therefore  we can conclude that the correct option is C which is 14.8.

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Answer:

Step-by-step explanation:

12.5663706144

Answer:

A line is defined by two points, and any other point that lies on the same line as those two points will also be on the same line. Therefore, to find the points that lie on the same line as (– 7,– 2) and (– 14,– 7), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

The slope of a line is calculated as the change in y-values divided by the change in x-values between two points on the line. In this case, the slope is (–7 – (–2))/(–14 – (–7)) = –5/–7 = 5/7.

The y-intercept is the point where the line crosses the y-axis, so we can plug in the value of x as 0 to find the y-intercept. Plugging in the values from one of the given points, we get y = (5/7) * (–7) + b = –5 + b, so b = –2.

Therefore, the equation of the line is y = (5/7)x – 2. Any point that satisfies this equation will lie on the same line as (– 7,– 2) and (– 14,– 7).

Some examples of points that lie on this line include (0, –2), (–7, –2), and (–14, –7).

The parametric equations for the tangent line to the given curve is x = 1-7t , y = 6t and z = 1-7t  .

In the question ,

it is given that ,

x = [tex]e^{-7t}[/tex]cos(6t), y = [tex]e^{-7t}[/tex]sin(6t), z = [tex]e^{-7t}[/tex] ,

So , the parametric equation of the curve will be ,

r(t) = [  [tex]e^{-7t}[/tex]cos(6t), [tex]e^{-7t}[/tex]sin(6t), [tex]e^{-7t}[/tex] ]

the point given as (1,0,1) implies that ,

[tex]e^{-7t}[/tex]cos(6t) = 1 , [tex]e^{-7t}[/tex] = 0 , sin(6t), [tex]e^{-7t}[/tex] = 1 which implies that ⇒ t = 0 .

So , the point (1,0,1) is the point r(0) .

Now , differentiating x , y and z with respect to t ,

we get ,

r'(t) = [  [tex]-e^{-7t}[/tex][7cos(6t) + 6sin(6t)], [tex]e^{-7t}[/tex][6cos(6t) - 7sin(6t)], [tex]-7e^{-7t}[/tex] ]

substituting , t = 0,

we get ,

r'(0) = [-7 , 6 , -7]

the equation of the tangent line passing through the point (1,0,1) and parallel to the tangent vector r'(0) is

r(t) = r(0) + tr'(0) = (1,0,1) + t(-7,6,-7)

So , r(t) = [ 1 - 7t , 6t , 1 - 7t ]

So , x = 1 - 7t   , y = 6t and  z = 1 - 7t  .

Therefore , the required parametric equations are x = 1 - 7t   , y = 6t and  z = 1 - 7t  .

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By using algebraic expression, the proof of

(a + b)(a - b) = a² - b² has been shown below-

What is algebraic expression?

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

Algebraic expressions are of different types based on number of terms.

They are monomial, binomial, trinomial and so on

Algebraic expression with one term is called monomial

Algebraic expression with two terms is called binomial

Algebraic expression with three terms is called trinomial

The given algebraic expression is

(a + b)(a - b)

a² - ab + ba - b²

a² - ab + ab - b² [Commutative law of addition]

a² - b²

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$50,700 he make in commission in​ 2011.

%Earns= 13% commission/week

Last week sold = $7,500

In order to obtain the last week earns in commission we need to multiply % rate of commission by the last week sold as shown as follows:

$Earns = 0.13 (decimal form)*$7,500

Earns = $975

Last week, he made $975 in commission.

If he averages that same amount each week, he should make $975* 52(number of weeks per year) = $50,700/year

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Answer:

The answer is 256

Step-by-step explanation:

Answer:

256

Step-by-step explanation:

4 · 4 · 8 · 2 = 256

The required answer for the given system of linear equations is No solution.

What is a system of linear equation?

A system of linear equations comprises two or more linear equations made up of two or more variables so that all equations in the system are considered simultaneously. In this case, linear equations are first-order equations, where the maximum power of the variable is 1. One, two, or three variables may be present in a linear equation. As a result, we are able to formulate linear equations with n variables.

Solve for the first variable in one of the equations, then substitute the result into the other equation, we will get

No solution

The graph of the given system of linear equations is given below

Hence, the required answer for the given system of linear equations is No solution.

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The freezing point of the 2.75 m solution of octane in benzene is -8.56 °C.

The freezing point of a solution is the temperature at which the solution becomes a solid. The freezing point of a solution is lower than the freezing point of the pure solvent because the solute particles interfere with the movement of the solvent molecules, which slows down the freezing process.

To determine the freezing point of a solution, we can use the freezing point depression equation:

ΔTf = Kf x molality

where ΔTf is the change in freezing point, Kf is the freezing point depression constant for the solvent, and molality is the concentration of the solute in the solution expressed in moles of solute per kilogram of solvent.

To find the freezing point of a 2.75 m solution of C8H18 (octane) in benzene, we need to know the freezing point depression constant for benzene, which is 5.12 °C/m. We can then use the equation above to calculate the change in freezing point:

ΔTf = 5.12 °C/m x 2.75 m = 14.06 °C

To find the freezing point of the solution, we need to subtract the change in freezing point from the freezing point of the pure solvent. The freezing point of pure benzene is 5.5 °C, so the freezing point of the 2.75 m solution of octane in benzene is:

5.5 °C - 14.06 °C = -8.56 °C

This means that the freezing point of the 2.75 m solution of octane in benzene is -8.56 °C. At this temperature, the solution will become a solid.

the triangle could represent in a relation as x = 60 - 2(y + z)  and x = 2z + 20.

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The following linear equation accurately describes the circumstance where "The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles":

x = 60 - 2(y + z) —- (1)

The following linear equation sums up the statement, "The largest angle is twice the smallest angle plus 20 degrees," as it applies to angles:

x = 2z + 20 —- (2)

Hence the triangle could represent in relation as x = 60 - 2(y + z)  and x = 2z + 20.

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120 many combinations are possible.

The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.

Consider a collection of three integers P, Q, and R. The number of ways that we may choose two numbers from each group is thus determined by combination.

It is represented as: [tex]^nC_r[/tex]

where, n = total number of objects in the set

r = number of choosing objects from the set

Given that,

Cell Phone Models A particular cell phone company offers:

4 models of phones

each in 6 different colors

each available with any one of 5 calling plans

Thus, possible combination numbers are:

= (No. of models) × (No. of colors) × (No. of calling plans)

= (4)× (6)× (5)

= 120 possibilities

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A solution to an equation is a value that, when substituted for the variable, makes the equation true. In the equation x+2=7, the solution is x=5.

This is because if we substitute 5 for x, the equation becomes 5+2=7, which is a true statement. To find this solution, we need to solve the equation by subtracting 2 from both sides, leaving us with x=5. This solution works because it satisfies the equation; when we substitute 5 for x, the equation is true.

In equations, solutions are important because they are the values that make the equation true. Without solutions, equations would remain unsolved and incomplete, which is why it is important to find the solution to an equation.

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The median is defined as the midpoint of the values after they have been arranged in rank. Option B

Median is simply defined as the middle value of a given sorted list of numbers or data set.

It is seen as the value that separates the higher half from the lower half of a  given data sample,  a probability distribution or a population.

For a data set, it is also called "the middle" value.

It also involves ordering the data set or a group of numbers in an ascending order, that is, from least to greater number.

The media is selected from picking the number in the midpoint for an even set of data which does not always occur.

In an odd group of data, after ordering the number from the least to the greatest, the two mid-numbers are taken, added and divided by half to determine the median.

Hence, the median is the midpoint of a set of ordered data.

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(A)  If f(t) is increasing, it's not  true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.

(B) f(t) is concave up, its' not true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.

Left-Hand Sums and Right-Hand Sums give us different approximations of the area under a curve. If one sum gives us an overestimate and the other an underestimate, then we can hone in on what the actual area under the curve might be. Any left-hand sum will be an under-estimate of the area of R. Since f is increasing, a left-hand sum will use the smallest value of f on each sub-interval. This means any left-hand sum will fail to cover all of R and any right-hand sum will be an over-estimate of the area of R. Since f is increasing, a right-hand sum will use the largest value of f on each sub-interval. This means any right-hand sum will cover R and then some.

A) If f(t) is increasing then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt, if the graph is increasing then the left-hand sum gives an overestimated value of the actual value.

B) If f(t) is concave up, then the left-hand sum gives an overestimate of the integral from a to b of f(t)dt, if the graph is concave up then the trapezoid approximation is an overestimate, and the midpoint is underestimated.

So,  If f(t) is increasing, it's not  true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt. and if f(t) is concave up, its' not true that the left-hand sum gives an overestimate of the integral from a to b of f(t)dt.

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Answer:

Below

Step-by-step explanation:

To add or subtract fractions ( or numbers with fractions in them) you HAVE to put the fractions into a common denominator form .....

Common denominator for 5 and 7 is 35

3 3/7 = 120/35

2  1/5 = 77/35

120/35  -  77/35  =  ( 120 - 77) / 35 =  43/35 = 1  8/35

The equation of the line that passes through the point (0, 3) & (0, 4) and the slope of the equation is undefined.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).

To find the slope of the line, we can use the slope formula:

m = (y2 - y1)/(x2 - x1)

The line on the graph passes through points (0, 3) & (0, 4).

m = (4-3)/(0-0)

m = 1/0

m = ∞

so, the slope is undefined.

Therefore, the equation of the line that passes through the point (0, 3) & (0, 4) and the slope of the equation is undefined.

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The terminal point on the unit circle use exact values are,

( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )

Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point. For example, 12.5 is a decimal number.

According to the question, it is provided that,

θ =  11π/6 radians

Now,

x = 1.cos(11π/6)

x = cos(11π/6)

x = cos(330°)

x = [tex]\sqrt{\frac{3}{2} }[/tex]

y = 1.sin(11π/6)

y = sin(11π/6)

y = -0.5

y = - [tex]\frac{1}{2}[/tex]

Then,

( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )

These two represents the terminal points

To find the terminal positions, we merely used the aforementioned equations, equated these two equations, and concluded that the same should be taken into consideration.

It could be figure out by using the x and y points

Therefore

The terminal point on the unit circle use exact values are,

( x , y ) = ( [tex]\sqrt{\frac{3}{2} }[/tex] , - [tex]\frac{1}{2}[/tex] )

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Answer:

5/12

Step-by-step explanation:

Total 12 flowers

5 are white

12-5=7

red + yellow = 7

x+2x+1 = 7

3x+1=7

3x=6

x=2

white : 5

red : 2

yellow : 5

12 flowers in total, 5 yellow flowers, probability that yellow is picked is 5/12

Whole milk has 3.25 % milk fat in it. That means 100 grams has 3.25 % of milk fat. so,10 grams of milk has 0.325 milk fat in it.

What is milk fat?

The percentage of butterfat in milk, as measured by weight, is known as the fat content of milk. To create a range of goods, the fat content, notably of cow's milk, is altered. In order to facilitate instant identification, the milk container is typically marked with the amount of fat present.

Milk is important for the growth of the body. It plays for the growth and development of the body. 100 grams of milk fat has 3.25 % milk fat in it.

100 grams = 3.25 % of milk fat.

10 grams = x

x = 10 * 3.25 / 100

=0.325  %

Milk contains lots of proteins and minerals. It is essential for the growth of the body. It also contains important minerals such as calcium and proteins.

Therefore, Whole milk has 3.25 % milk fat in it. That means 100 grams has 3.25 % of milk fat. so,10 grams of milk has 0.325 milk fat in it.

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Answer: the thing is I don’t know

Step-by-step explanation:

Answer:

-12 _ -|12|

(-12) = (-12)

Thus, Both are equal

A power series representation for the function the interval of convergence is x > -14 .

Given :

a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = 1273 Determine the interval of convergence.

f ( x ) = 3 / 17 + x

Interval of convergence :

The interval of convergence can be calculated once you know the radius of convergence. First you solve the inequality |x − a| < R for x and then you check each endpoint individually.

3 / 17 + x < 1

3 < 1 * ( 17 + x )

3 < 17 + x

-14 < x

x > -14

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The value of algebraic multiplicity will be 1 and geometric multiplicity will be 1

[tex]$$\begin{aligned}& A=\left[\begin{array}{ccc}3 & -2 & 0 \\-2 & 4 & 4 \\1 & 0 & 2\end{array}\right] \\& \Rightarrow A=\left[\begin{array}{ccc}-1 & 1 & 0 \\0 & 0 & 0 \\1 & 1 & -2\end{array}\right]\end{aligned}$$[/tex]

[tex]$$Det(A-\lambda I) = Det A=\left[\begin{array}{ccc}(-1-\lambda) & 1 & 0 \\0 & -\lambda & 0 \\1 & 1 & (-2-\lambda)\end{array}\right]$$[/tex]

[tex]$$-(1+\lambda)\left|\begin{array}{cc}-\lambda & 0 \\1 & -2-\lambda\end{array}\right|-1\left|\begin{array}{cc}0 & 0 \\1 & -2-\lambda\end{array}\right|$$[/tex]

[tex]$$\begin{aligned}& =-(1+\lambda)\left(\lambda^2+2 \lambda\right) . \\& =-\lambda(1+\lambda)(\lambda+2) .\end{aligned}$$[/tex]

So, for [tex]\lambda=-1[/tex], eigen values are [tex]\lambda[/tex]=0,-1,-2.

Hence, the value of algebraic multiplicity=1

[tex]AV=\lambda v \\& \Rightarrow A V=-V\\ \Rightarrow-V_1+V_2=-V_1\\ \Rightarrow V_2=0 \\& v_1+v_2-2 v_3=-v_3\\ \Rightarrow v_1+v_2-v_3=0\\ \Rightarrow v_1=v_3 \\[/tex]

[tex]$$\begin{aligned}& \Rightarrow \quad\left[\begin{array}{l}v_1 \\0 \\v_1\end{array}\right] \\& =v_1\left[\begin{array}{l}1 \\0 \\1\end{array}\right]\end{aligned}$$[/tex]

So, the value of eigen vectors are: [tex]& =\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right] \\[/tex]

And the value of geometric multiplicity =1

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The equation of the graph is [tex]-\frac{3x^{2} }{2x +6}[/tex]

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Answer: C

Step-by-step explanation:

due to the slope

O (x) = [tex]3x^{3} + 12x^{2}[/tex] is  a polynomial function ox in standard form for the volume of the rectangular prism formed by the outer surfaces of the box

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable)

calculation

outside length are height = x

width = x +4 , length = 3x

volume = l *b * h

o(x) = 3x ( x+ 4 )x

= 3[tex]x^{2}[/tex](x+4 )

= O (x) = [tex]3x^{3} + 12x^{2}[/tex]

there is 1 inch of wood , so lengths of inner sides 2 inch less than outer sides as 1 inch from reduced

length = 3x-2

width = x +4-2 = x+2

height = x -2

volume = l*b*h

=[tex]3x^{3} - 2x^{2} - 12x + 8[/tex]

w(x) = [tex]14(6^{2}) + 12(6) -8\\ 504 + 72 -8 \\568inch^{3}[/tex]

so volume of wood = [tex]568inch^{3}[/tex] for x =6

O (x) = [tex]3x^{3} + 12x^{2}[/tex] is  a polynomial function ox in standard form for the volume of the rectangular prism formed by the outer surfaces of the box.

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Answer: 20 units

Step-by-step explanation:

Since the rectangle is on the graph, we can directly count the units.

Perimeter is the sum of all sides.

4+4+6+6=20

start by plugging values for x into the function

a) f(1) = 4 (1/2)^1

f(1) = 2

the first coordinate point is (1,2)

b) f(0) = 4(1/2)^0

f(0) = 4

(0,4)

this method will help you find the coordinate points and where to plot.

Answer:

Last option:

[tex]\dfrac{4x^4y^2}{z}[/tex]

Step-by-step explanation:

Original expression is

[tex]\dfrac{12x^6y^{-4}z^2}{3x^2y^{-6}z^3}\\\\[/tex]

Let us eliminate the obvious wrong answers

[tex]\dfrac{12}{3} = 4\\\\[/tex]

so the coefficient in the answer should be 4.

We can eliminate first and third choices

Now for each term with the same variable, compute the division
[tex]\dfrac{x^6}{x^2} = x^{6-2} = x^4\\\\[/tex]

Second choice is out so the last choice is the correct one.

We can go further with the other terms

[tex]\dfrac{y^{-4}}{y^{-6}} = y^{-4 - (-6)} = y ^{-4+6} = y^2[/tex]

[tex]\dfrac{z^2}{z^3} = z^{2-3} = z^{-1} = \dfrac{1}{z}[/tex]

Multiplying all these individual terms gives
[tex]4 \cdot x^4 \cdot y^2 \cdot \dfrac{1}{z}\\\\= \dfrac{4x^4y^2}{z}[/tex]

The total amount that will be paid will be $89.70.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, Adryanna got a manicure for $35 and a pedicure for $43 and she plans on leaving a 15% tip

The total amount that will be paid will be:

= ($35 + $43) + (15% × $78)

= $78 + $11.7

= $89.7

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Benjamin's employer will withhold $42.05 in Additional Medicare Tax for this period.

To calculate the amount withheld by Benjamin's employer in Medicare tax, we apply the proportion of the Medicare tax to his total earnings.

The parameters for this problem are given as follows:

Then the amount withheld by the employee for the Medicare Tax is calculated with the multiplication of the decimal equivalent of 1.45%, which is of 0.0145, by Benjamin's gross earnings of $2,900 as follows:

Amount = 0.0145 x 2900 = $42.05.

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