Which of the following gives the correct matrix for this system of equations in reduced row echelon form? x1-3x2-x3 + 3x4 = 2 -xi-2x2-x3 +4x4 = 2 -2x1+4x2 +4x3 +4x4 =-3 12 5 14 100 17 5 18 001 14 1 -3 -1 32 0 -5 -2 74 00ー36-3 b) 1 0 0 -36 9 1 22 010 001_ -_ 1 22 -1 -3 1 3 2 d 0 1 0 0 0 22 -12 -7 1 0 0 0 e) 25 010 -5 0 0 6 -16 f O None of the above

Answer:

what we cookin ma boi

Step-by-step explanation:

The correct answer is $34900.

X : Average amount of loan of student debt by state .

X = N ( μ = $28500 , σ² = ( 3200 )² )

To find : What is the cutoff point that would place a state in top 2.5%

Let it be X

P( X > x ) = 0.025

P(X-μ/σ > X - 28500/3200) = 0.025

P(z >Z ) = 0.025

1 - P(z<Z ) = 0.025

P(z<Z ) = 0.975

φ(z) = 0.975

Z = φ⁻¹(0.975)

X - 28500/3200 = 1.96

X = 34772

i.e; P(X > 34772) = 0.025

Since, it is nearly equal to $34900 option b is correct.

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Answer:

Below

Step-by-step explanation:

The first set of graphs is the correct one....it shows Y = constant 18

and shows Z as starting  at 10 (deposit) THEN INCREASING 2 per hour....

  where they cross is 4 hours and charges are the same

Answer: the thing is I don’t know

Step-by-step explanation:

The monthly salary of an employee that has worked for 48 months at the bank is $1226.04. So the option d is correct.

The given table is:

                          Df          SS                     MS                F

Regression          1          555,420          555,420          7.64

Residual              27       1,962,873         72,699

Total                    28        2,518,293

                    Coefficients         Standard Error         t-stat        p-value

Intercept          784.92                322.25                    2.44           0.02

Service             9.19                     3.20                      2.87           0.01

We have to find the monthly salary of an employee that has worked for 48 months at the bank.

Salary = β(0)+ β(1) Service

y = β(0)+ β(1)x

where, Service = x(in months)

Service = y(in $)

From the table

y = 784.92+9.19x

If x=48 months

Then, y = 784.92+9.19(48)

y = 784.92+441.12

y = 1226.04

Hence, the monthly salary of an employee that has worked for 48 months at the bank is $1226.04. So the option d is correct.

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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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Ans (A)   P(CB/M) is  0.07

Ans (B)   P(CB ∩ M) is 0.0343

Ans (C)   P(CB) is 0.03634

Ans (D)   P(M/CB) is 0.94386

Let the population be 100.

Therefore,

No. of males (M) = 49

No. of females (F) = 51

No. of colourblind males =

[tex]\frac{7}{100} * 49 = \frac{343}{100} = 3.43[/tex]

No. of colourblind females =

[tex]\frac{0.4}{51} * 100 = 0.204[/tex]

Total colourblind people (CB) = 3.43 + 0.204 = 3.634

Ans (A)

P(CB/M) = P(CB ∩ M)/P(M) = 3.43/49 = 0.07

Ans (B)

P (CB ∩ M) = 3.43/100 = 0.0343

Ans (C)

P(CB) = 3.634/100 = 0.03634

Ans (D)

P (M/CB) = P(M ∩ CB)/P(CB) = 3.43/3.634 = 0.94386

These are the answers.

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Answer:

27.29 honestly this is a wild guess

Step-by-step explanation:

7.35% of 147.25 = 10.82

147.25-10.82=136.43

20% of 136.43 = 27.286(27.29)

Answer:

Step-by-step explanation:

12.5663706144

To find the slope of the curve, first differentiate the equation of the curve and substitute the value of x in the result

The slope of the curve is the change in y coordinates with respect to the change in x coordinates of the line

To find the slope of the curve at a given point

First differentiate the given equation of the curve with respect to x

That is dy / dx.

The derivative of the equation of the curve  is the slope of the curve.

In next step substitute the value of x in the slope of the curve

The result will be the slope of the curve at a given point

Therefore, these are the steps to find the slope of the curve

I have answered the question in general, as the given question is incomplete

The complete question is:

How to find the slope of a curve at a given point?

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The data item that corresponds to the z-score of 2.5 is 450.

What is Standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.

A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance. Although less robust in practice, it is algebraically easier than the average absolute deviation. The fact that the standard deviation is expressed in the same unit as the data, as opposed to the variance, makes it a valuable statistic.

As, x = z×s + u, where z=2.5, s=60, u=300

⇒ x = 2.5×60 + 300

⇒ x = 150 + 300

⇒ x = 450

The data item that corresponds to the given z-score is 450.

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Answer:

m∠2 = 110°

m∠4 = 110°

Step-by-step explanation:

Corresponding Angles Postulate

When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Transitive Property of Equality

If any angles are congruent to the same angle, then they are congruent to each other.

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

As line p is parallel to line q, according to the Corresponding Angles Postulate:

⇒ m∠2 = m∠10

According to the Vertical Angles Theorem:

⇒ m∠10 = m∠13

According to the Transitive Property of Equality:

⇒ m∠2 = m∠13

Therefore:

⇒ 8x + 14 = 10x - 10

⇒ 8x + 14 - 8x = 10x - 10 - 8x

⇒ 14 = 2x - 10

⇒ 14 + 10 = 2x - 10 + 10

⇒ 24 = 2x

⇒ 2x = 24

⇒ 2x ÷ 2 = 24 ÷ 2

⇒ x = 12

Substitute the found value of x into the expression for the measure of angle 2:

⇒ m∠2 = 8(12) + 14

⇒ m∠2 = 96 + 14

⇒ m∠2 = 110°

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

As line p is parallel to line q, according to the Corresponding Angles Postulate:

⇒ m∠12 = m∠4

⇒ 15y + 5 = 13y + 19

⇒ 15y + 5 - 13y = 13y + 19 - 13y

⇒ 2y + 5 = 19

⇒ 2y + 5 - 5 = 19 - 5

⇒ 2y = 14

⇒ 2y ÷ 2 = 14 ÷ 2

⇒ y = 7

Substitute the found value of y into the expression for the measure of angle 4:

⇒ m∠4 = 13(7) + 19

⇒ m∠4 = 91 + 19

⇒ m∠4 = 110°

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 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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Answer:   C) 4.123 x 106

Step-by-step explanation:

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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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 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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Answer:

C

Step-by-step explanation:

Answer:

B: It translates the graph 9 units to the right.

Step-by-step explanation:

The value 9 has the effect of translating the graph of function f(x) = |x| 9 units to the right. This is because the transformation g(x) = |x - 9| is obtained from f(x) = |x| by subtracting 9 from the argument of the absolute value function. This has the effect of shifting the graph of f(x) to the right by 9 units.

Therefore, the correct answer is B: It translates the graph 9 units to the right.

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

$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:

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

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 missing angle in the parallel lines is as follows;

When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles etc.

Therefore, let find angle m∠STW .

VX and SU are parallel lines. RY is the transversal line.

Hence,

m∠VWY = 125 degrees

m∠VWY =  m∠STW (corresponding angles)

Corresponding angles are congruent to each other.

Therefore.

m∠STW  = 125 degrees

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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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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 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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​

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.

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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