Tyler and Matt were arguing about which method to solve the following system of equations. (See photo)
Matt Argues that using substitution is the easiest where as Tyler sees elimination as the easiest State which method is the most efficient and why, and then solve the system.

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

Answer:

-12 _ -|12|

(-12) = (-12)

Thus, Both are equal

By solving simultaneous equation conditions, there are 26 small smoothies and 20 large smoothies.

What is the simultaneous equation?

Two or more algebraic equations that share variables, such as x and y, are referred to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations.

Given, total selling = $234

Let, x be the number of small smoothies sold

y be the number of large smoothies sold

Then, from the given condition,

x + y = 46 ⇒ x = 46-y   ........... (i)

4x + 6.5y = 234  ................. (ii)

Now, substituting the value of x from (i) in (ii), then

4(46-y) + 6.5y = 234

or, 184 - 4y + 6.5y = 234

or, 184 + 2.5y = 234

or, 2.5y = 234 - 184 = 50

or, y = 50/2.5 = 20

and, x = 46-20 = 26

Hence, 26 small smoothies and 20 large smoothies.

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Answer:

1200 beats in 3 seconds

or

400 more beats per second

Step-by-step explanation:

as we can see by the graph mosquitos beat their wings 600 times per second

600x3

1800 beats in 3 seconds

honey bees do it 600 times in 3 seconds so we subtract

1800-600

1200

hopes this helps please mark brainliest

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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The final volume of the gas is 2.8 L. The correct option is the second option 2.8 L

From the question, we are to determine the final volume of the gas.

From the general gas equation, we have that

P₁V₁/T₁ = P₂V₂/T₂

Where P₁ is the initial pressure

V₁ is the initial volume

T₁ is the initial temperature

P₂ is the final pressure

V₂ is the final volume

T₂ is the final temperature

From the given information,

P₁ = 1 atm

V₁ = 2.5 L

T₁ = 25 °C = 25 + 273.15 K = 298.15 K

P₂ = 0.85 atm

V₂ = ?

T₂ = 15 °C = 15 + 273.15 K = 288.15 K

Thus,

P₁V₁/T₁ = P₂V₂/T₂

(1 × 2.5)/298.15 = (0.85 × V₂)/288.15

V₂ = (1 × 2.5 × 288.15)/(0.85 × 298.15)

V₂ = 2.8425 L

V₂ ≈ 2.8 L

Hence, the volume is 2.8 L

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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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Answer: the thing is I don’t know

Step-by-step explanation:

$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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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:

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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If you have a z-score of +2.0 on an exam, it means that your grade is 2 standard deviations above the mean for this exam. So the option e is correct.

In the given question, we have to find the one correct inter- pretation if you have a z-score of +2.0 on an exam.

The standard deviation is a measurement of how much a group of values vary or are dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Z-score it's a measure of how many standard deviations below or above the population mean.

If you have a z-score of +2.0 on an exam, it means that your grade is 2 standard deviations above the mean for this exam. So the option e is correct.

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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.

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 probability density function as calculated from the given data is       fₙ (u)=−ln(u).

​

Y1 and Y2 are independent random variables and both have uniform distribution over the interval (0,1)(0,1).

We need to find out the density function of  U = Y1Y2 using the method of transformations.

Density function of Y1

= 0 or 1

Density function of Y2

= 0 or 1

Therefore joint density function is,

( 0 , 1)   where, 0≤y 1 ≤1,0≤y 2 ≤1

There are 3 steps to find joint density function of Y and U using methods of transformations

Hence, the required probability density function is :

fₙ (u)=−ln(u)

An independent random variable is one that has no effect on the other random variables in your experiment. In other words, it has no bearing on the likelihood of another occurrence occurring.

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​

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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(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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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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By observing the figure we can make the pairs as

∠1 ≅ ∠3 ---------(Opposite angles)
∠2 ≅ ∠4 ---------(Opposite angles)
∠5 ≅ ∠7 ---------(Opposite angles)
∠6 ≅ ∠8 ---------(Opposite angles)
∠4 ≅ ∠6 ---------(Alternate angles)
∠3 ≅ ∠5 ---------(Alternate angles)

What are opposite angles and Alternate angles?

Opposite angles are angles that are located opposite each other, with respect to a straight line or a transversal. They are also called vertically opposite angles.

Alternate angles are angles that are located on opposite sides of the transversal and on the same side of the straight line or the transversal. They are also called corresponding angles.

In the given figure,

By observing the opposite angles and alternate angles we can fill the blocks,

∠1 ≅ ∠3 ---------(Opposite angles)

∠2 ≅ ∠4 ---------(Opposite angles)
∠5 ≅ ∠7 ---------(Opposite angles)
∠6 ≅ ∠8 ---------(Opposite angles)

∠4 ≅ ∠6 ---------(Alternate angles)

∠3 ≅ ∠5 ---------(Alternate angles)

Hence, we have found the opposite angles and alternate angles from the figure.

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The following equations is equivalent to y = -5x² + 20x - 6 = > y = -5(x + 10)² + 494.

Factoring 5x2-20x-6

The first term is,  5x2  its coefficient is  5 .

The middle term is,  -20x  its coefficient is  -20 .

The last term, "the constant", is  -6

Step-1 : Multiply the coefficient of the first term by the constant   5 • -6 = -30

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   -20 .

     -30    +    1    =    -29

     -15    +    2    =    -13

     -10    +    3    =    -7

     -6    +    5    =    -1

     -5    +    6    =    1

     -3    +    10    =    7

     -2    +    15    =    13

     -1    +    30    =    29

Equation at the end of step2:   5x2 - 20x - 6  = 0

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 5 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

What is  Parabolas ? Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   2.0000  

Plugging into the parabola formula   2.0000  for  x  we can calculate the  y -coordinate :

 y = 5.0 * 2.00 * 2.00 - 20.0 * 2.00 - 6.0

or   y = -26.000

Root plot for :  y = 5x2-20x-6

Axis of Symmetry (dashed)  {x}={ 2.00}

Vertex at  {x,y} = { 2.00,-26.00}

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-0.28, 0.00}

Root 2 at  {x,y} = { 4.28, 0.00}

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Answer:

Step-by-step explanation:

12.5663706144

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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The fixed cost of the plumber is £30 and the hourly rate for the plumber is  £25.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

Let the fixed cost of a plumber is y.

Let the number of hours of work done be x.

As per the first condition, that one piece of work takes the plumber 5 hours and costs £155.

Then, the equation according to the statement will be,

y + 5x = £155      (i)

In the second condition, another piece of work takes the plumber 8 hours and costs £230.

Then, the equation according to the statement will be,

y + 8x = £230     (ii)

Now, subtract equation (ii) from the equation for the value of x,

y + 5x = £155

y + 8x = £230

-3x = -75

x = £25

Put x = £25 in equation (i)

y + 5x = £155

y + 5(25) = 155

y = 155 - 125

y = £30.

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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 functions that have a vertex at x = 0 are (a) f(x) = |x| and (d) f(x) = |x| - 6

From the question, we have the following parameters that can be used in our computation:

The absolute functions in the options

As a general rule;

A absolute functions can be represented as

f(x) = a|x - h| + k

Where

Vertex = (h, k)

A vertex that has x value of 0 means

(h, k) = (0, k)

So, we have

f(x) = a|x - 0| + k

Evaluate

f(x) = a|x| + k

Looking at the options, we have

f(x) = |x| and f(x) = |x| - 6

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The different ways you could use all 4 measuring cups to measure 2 cups of flour are One 1/2 cup, two 1/4, three 1/6 and one & half 1/6 cup

From the question, we have the following parameters that can be used in our computation:

Flour = 2 cups

Measuring cups = 1/2 cup, 1/4 cup, 1/6 cup & 1/6 cup

Next, we create an expression from the measuring cups that have a value of 2

One instance is:

1 * 1/2 cup + 2 * 1/4 cup + 3 * 1/6 cup + 1/5 * 1/6 cup = 2 cups

Hence, the measurement is One 1/2 cup, two 1/4, three 1/6 and one & half 1/6 cup

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Complete question

A chocolate cake recipe calls for 2 cups of flour. You gather your measuring cups and notice you have these sizes: 1/2 cup, 1/4 cup, 1/6 cup & 1/6 cup.

What are the different ways you could use all 4 measuring cups to measure 2 cups of flour?​

The focal length of the parabola whose coefficient a is equal to 9, is 1/36.

What is focal length?

In a two-dimensional plane, a parabola is a curve that is symmetrical about the axes, passes through the vertex, and is perpendicular to the directrix. In other words, the locus of points that are equally spaced apart from the directrix and the fixed point, let's call it focus, is a parabola. The distance along the axis of symmetry from the vertex to the focus of the parabola is known as its focal length.

The focal length of a parabola is calculated as c' = 1/4a

In the given question, c' is the focal length and the coefficient a is the general quadratic equation and a=9.

Substituting the above values, in the focal length equation, we get,

c' = 1/(4*9)

⇒ c' = 1/36

Hence, the focal length of the parabola whose coefficient a is equal to 9, is 1/36.

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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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An estimate of the error standard deviation sigma in the simple linear regression model is y = -31.8037 + 0.9867x .

Given :

For the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x= cube strength (MPa) based on the following sample data:

The coefficient of determination is the number of the observed samples of axial strength of asphalt that cannot be explained by variation in cube strength.

Using regression calculator :

The regression model is y = -31.8037 + 0.9867x .

A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope.

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