Susie has a part-time job at the video store. She makes between $32.43 and $38.86 a day. Which is a reasonable amount of money that Susie makes for working 6 days?

A.
$126.00
B.
$246.00
C.
$186.00
D.
$306.00

We know that,

In a right-angled triangle,

Hypotenuse ² = Base ² + Height ²

1 – 10 ² = 6 ² + X ²

Or, X ² = 10 ² – 6 ²

Or, X ² = 100 – 36

Or, X ² = 64

Or, X = √ 64

Or, X = 8 Units

2– X² = 7² + 3²

Or, X² = 49 + 9

Or, X² = 58

Or, X = √58

Or, X = 7.61 Units ( Approx )

3 – 15 ² = EF ² + 9

Or, EF² = 15 ² – 9 ²

Or, EF ² = 225 – 91

Or, EF ² = 134

Or, EF = √ 134

Or, EF = 11.6 Inches ( Approx)

.II} 1 – Here the length of the ladder will be the hypotenuse.

Hence, Hypotenuse = 13 Metre

.Now, The vertical wall will be the height.

Hence, Height = 12 Metre

Distance of the foot of the ladder to the wall will be the base.

Let base be B.

Now, Hypotenuse ² = Base ² + Height ²

Or, 13² = B² + 12²

Or, B² = 13² – 12²

Or, B² = 169 – 144

Or, B² = 25

Or, B = √25

Or, B = 5 Metre

Hence, the distance of the foot of the ladder from the wall is 5 metre apart.

⇒Vertical angles are equal .

This means that ∠1=∠2

⇒The trick is to first find the value of the unknown variable x then substitute it in the expression of ∠1 to get the exact magnitude of the angle.

\(5x+12=6x-11\\5x-6x=-11-12\\-x=-23\\\frac{-x}{-1} =\frac{-23}{-1} \\x=23\)

x=23°

To get the exact value of ∠1 Plug in 23° in the place of x in the expression of ∠1:

\(< 1=5x+12\\=5(23)+12\\=127\)

∠1=127°

4x - 26y - 8z = -148 is the equation of the plane that contains the given lines.

To find the equation of the plane that contains the given lines, we need to first check if they are parallel. Two lines are parallel if and only if their direction vectors are parallel.

For the first line, the direction vector is given by the coefficients of t:

v1 = <4, -2, 6>

For the second line, the direction vector is given by the coefficients of s:

v2 = <4, -2, 5>

To check if these vectors are parallel, we can take their cross product:

v1 x v2 = <4, -26, -8>

Since the cross product is not the zero vector, we can conclude that the lines are not parallel, and therefore lie on a plane.

Now, we need to find a point on this plane. Since the two lines intersect at some point, we can choose any point that lies on both lines. One way to do this is to set the two parametric equations equal to each other and solve for t and s:

6 + 4t = 1 + 4s

8 - 2t = 3 - 2s

2 + 6t = 4 + 5s

Solving this system of equations gives t = 3 and s = 2. Substituting these values into either line equations gives the point (18, 2, 20), which lies on both lines and hence on the plane.

Finally, we can use the point we found and the cross product of the direction vectors to write the equation of the plane in standard form, which is:

ax + by + cz = d where a, b, and c are the coefficients of the normal vector, and d is the distance from the plane to the origin.

The normal vector can be found by taking the cross product of the direction vectors:

n = v1 x v2 = <4, -26, -8>

To find the distance from the plane to the origin, we can use the point-normal form of the equation:

n · (p - p0) = 0 where p is any point on the plane, p0 is the given point, and · denotes the dot product. Substituting the values, we get:

4x - 26y - 8z = -148

This is the equation of the plane that contains the given lines.

In summary, to find the equation of a plane that contains two non-parallel lines, we can first check that they are not parallel by taking their cross product. Then, we can find a point on the plane by setting the line equations equal to each other and solving for t and s. Finally, we can use the point we found and the cross product of the direction vectors to write the equation of the plane in standard form.

For more such questions on Equation of plane.

https://brainly.com/question/27190150#

#SPJ11

Answer:

a. 6 + y

b. 3 × x

c. (10 × c) - 5

d. (6 × t) + 14

e. x + y = 18

f. x - 12 = 7

The reason for each step to justify it is:

Division Property of Equality: This step involves dividing both sides of the equation by 4 to isolate the variable term on one side of the equation.

The step involved here is: (w+25)/4

Multiplication Property of Equality: This step involves multiplying both sides of the equation by 4 to simplify the equation and cancel out the denominator.
The step involved here is: 4*(w+25)

Addition Property of Equality: This step involves subtracting 25 from both sides of the equation to isolate the variable term on one side of the equation.

The step involved here is: w+25

Simplifying: This step involves simplifying the expression by combining like terms and performing arithmetic operations to simplify the equation.

The step involved here is: w+25-25=12-25

Subtraction Property of Equality: This step involves subtracting 25 from both sides of the equation to isolate the variable term and solve for the variable.

The step involved here is: w=-13

What is meant by division?

Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is represented by the symbol ÷ or / and is the inverse operation of multiplication. Division can be used to solve problems related to sharing, fractions, and ratios.

What is meant by multiplication?

Multiplication is a mathematical operation that involves adding a number to itself a certain number of times. It is represented by the symbol × or * and is the inverse operation of division. Multiplication can be used to solve problems related to scaling, area, volume, and rates.

To know more about division visit

brainly.com/question/21416852

#SPJ1

well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

The probability of rolling exactly a 1 when a dice is picked randomly from two 4-sided dice and three 6-sided dice is 0.4 or 40%.

To calculate the probability of rolling exactly a 1 when a dice is picked randomly from two 4-sided dice and three 6-sided dice, we need to determine the total number of dice and the number of dice that have a 1 as a possible outcome.

There are two 4-sided dice and three 6-sided dice, so the total number of dice is 2 + 3 = 5.

Out of these five dice, we need to determine how many have a 1 as a possible outcome.

Among the two 4-sided dice, there is only one die (out of two) that has a 1 as a possible outcome.

Among the three 6-sided dice, there is also one die (out of three) that has a 1 as a possible outcome.

Therefore, there are a total of two dice that have a 1 as a possible outcome.

The probability of rolling exactly a 1 when a dice is picked randomly is calculated by dividing the number of favorable outcomes (two dice) by the total number of possible outcomes (five dice):

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 2 / 5

Probability = 0.4

To know more about probability refer here:

https://brainly.com/question/32560116#

#SPJ11

The length of the rivet should be 3/8 inch to pass through the two sheets of metal.

We must take into account the shank length as well as the thickness of the two metal sheets.

Assumed:

The thickness of the two metal sheets and the shank length must be added to determine the overall length of the rivet:

Total length = 2 * (Thickness of sheet metal) + Shank length

Substituting the values:

Total length = 2 * (1/16 inch) + 1/4 inch

Calculating the values:

Total length = 1/8 inch + 1/4 inch

Total length = 1/8 inch + 2/8 inch

Total length = 3/8 inch

So, the length of the rivet should be 3/8 inch to pass through the two sheets of metal.

Learn more about Substituting here : brainly.com/question/26094713

#SPJ4

Answer:

33.333% chance of it being greater than 6

Step-by-step explanation:

7,8, and 9 are the only ones that are greater than 6. So out of 10 possible numbers (0,1,2,3,4,5,6,7,8,9) that means there is a 33.333% chance because 10÷3=3.333 then move the decimal 1 place to the right, and that gives you 33.333%.

There are 3 numbers on the cube greater than 3 ( 4, 5, & 6)

This means he has a 3/6 = 1/2 chance of doing that.

He has a 1/2 chance of getting tails on the coin.

The probability of doing both would be the probability of the cube roll x the probability of the coin toss:

1/2 x 1/2= 1/4

The answer is 1/4

Answer:

see explanation

Step-by-step explanation:

look at the photo

Answer:

m= -3

Step-by-step explanation:

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(3,\:4\right),\:\\\left(x_2,\:y_2\right)=\left(4,\:1\right)\\\\m=\frac{1-4}{4-3}\\\\m = \frac{-3}{1} \\\\Simplify\\m=-3\)

let the price of pizza and soda( per 2 litre bottle) be x and y

from 1st condition

12x+2y=137.6.....(1)

from 2nd condition

x+y =11.95.......(2)

multiply eq. (2) by 2

2x+2y=23.9.....(3)

subtracting (1) and (3)

12x+2y=137.6

2x+2y= 23.9

10x = 113.7

x=113.7/10

x=11.37

2(11.37)+2y=23.9

22.74+2y=23.9

2y=23.9-22.7

2y=1.2

y=0.6

So the prices of  the pizza and soda are 11.37 and 0.6 dollars.

Each pizza costs approximately $10.99, and each 2-liter of soda costs approximately $0.96.

Let x be the cost of one pizza, and y be the cost of one 2-liter of soda.

According to the information given, we can write the following two equations:

1. For the pizza and soda purchased for the theater party:

12x + 6y = 137.64

2. For the pizza and soda purchased for Katya's family:

1x + 1y = 11.95

Now, we have a system of two equations with two variables. We can solve it to find the values of x and y.

First, let's solve the second equation for y:

y = 11.95 - x

Next, substitute this value of y into the first equation:

12x + 6(11.95 - x) = 137.64

Now, simplify and solve for x:

12x + 71.7 - 6x = 137.64

Combine like terms:

6x + 71.7 = 137.64

Subtract 71.7 from both sides:

6x = 65.94

Finally, divide by 6:

x = 65.94 / 6

x ≈ 10.99

Now that we have the value of x, which is the cost of one pizza, we can find the cost of one 2-liter of soda using the second equation:

y = 11.95 - x

y ≈ 11.95 - 10.99

y ≈ 0.96

So, each pizza costs approximately $10.99, and each 2-liter of soda costs approximately $0.96.

To know more about pizza:

https://brainly.com/question/29011903

#SPJ2

It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

To learn more on rate of change click:

https://brainly.com/question/32765463

#SPJ4

simplification :

therefore, correct option is B

The answer is B. 11i. You move 11 to the left of i because of I · 11 and so you switch it.

°.✩┈┈┈┈∘*┈┈୨♡୧┈┈*∘┈┈┈┈✩.°

Hope this helps .+(´^ω^`)+.

The volume of the tank is given by option E, which is 27π\(r^3\).

The volume of a right circular cylinder is calculated using the formula V = π\(r^2\)h, where r is the radius and h is the height. In this case, it is given that the height of the tank is 3 times the diameter, which means h = 3d. The diameter is twice the radius, so d = 2r. Substituting these values into the formula, we have V = π\(r^2\)(3d) = π\(r^2\)3*2r) = 6π\(r^3\). However, the options provided are in terms of \(r^3\), not 6\(r^3\). Comparing the given options, the only one that matches is option E, which is 27π\(r^3\). Therefore, the volume of the tank is 27π\(r^3\).

Learn more about volume here:

https://brainly.com/question/27971379

#SPJ11

Yes, even if you don't know how many handshakes there were overall, you can be sure that there were at least two guests who had the same number.

Assume that the gathering will have n visitors. With the exception of oneself, each person may shake hands with n-1 additional individuals. For each guest, this means that there could be 0, 1, 2,..., or n-1 handshakes.

There will be the following number of handshakes if each guest shakes hands with a distinct number of persons (i.e., no two guests will have the same number of handshakes):

0 + 1 + 2 + ... + (n-1) = n*(n-1) divide by 2

The well known formula for the sum of the first n natural numbers . The paradox arises if n*(n-1)/2 is not an integer since we know that the actual number of handshakes must be an integer. The identical number of handshakes must thus have been shared by at least two other visitors.

Learn more about arithmetic progressions at brainly.com/question/24592110

#SPJ4        

Answer:

B.   y = 10(2)^x

Step-by-step explanation:

y = ab^x

to find "b" divide the function at x = 3 by the function at x = 2

80 = ab^3

——————

40 = ab^2

This results in

2 = b

to find "a" plug pickany value of x

using x = 2

40 = a(2²)

40 = a(4)

a = 10

With a = 10 and b = 2 the exponential function y = ab^x is

y = 10(2)^x

Answer:

A: irrational

B: whole number

C: rational

D: irrational

E: natural

F: irrational

G: integer

H: irrational

I: rational

J: irrational

K: rational

Richard's net pay for the week, considering Social Security, Medicare, and FIT deductions, can be calculated by subtracting the total deductions from his gross earnings.

First, let's determine the amount deducted for Social Security. The Social Security rate is 6.2%, and the maximum earnings subject to this deduction are $118,500. Since Richard is $1,000 below the maximum level, the amount subject to Social Security deduction is $1,000. Therefore, the Social Security deduction is 6.2% of $1,000.

Next, we calculate the Medicare deduction. The Medicare rate is 1.45%, and it is applied to the entire earnings of $1,700.

To calculate the FIT deduction, we need additional information about Richard's taxable income, tax brackets, and exemptions. Without this information, we cannot provide an accurate calculation for the FIT deduction.

Finally, we subtract the total deductions (Social Security, Medicare, and FIT) from Richard's gross earnings of $1,700 to obtain his net pay for the week.

Learn more about subtract here: brainly.com/question/28008319

#SPJ11

To answer this question we will use the following formula to compute the nth term of an arithmetic sequence with a common difference of d and first term a₁:

Substituting n=18, a₁=25, and d=-5 in the above equation we get:

Simplifying the above result we get:

Answer:

Okay, here we have this:

Considering the provided equation, we are going to rewriting it into slope-intercept form. So we obtain the following:

6x+2y=6

2y=-6x+6

y=(-6x+6)/2

y=-3x+3

Finally we obtain that the equation of the line is slope-intercept form is y=-3x+3. Then replacing in y=mx+b, we have:

y=-3x+3

y=mx+b

Then, m=-3 and b=3.

As angle OAB =40-degree, angle AOB is 100 degrees according to the properties of circle and triangle.

Some Properties of circle are distance from center of the circle to each point on the circumstances are equal. hence, OA=OB

Diameter is twice of radius.

The triangle having two equal side length is called isosceles triangle. In the figure, triangle OAB is an isosceles as OA=OB=radius

According to the criteria of isosceles triangle angle OAB =OBA =40°

hence, angle AOB= 180 degrees - (40°+40°) [angle sum of triangle =180°]

                  angle AOB= 100 degrees.

We get, AOB = 100 degrees

to know more about types of triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer:

Number of box seats = 1000

Number of lower deck seats = 5000

Number of upper deck seats = 4000

Step-by-step explanation:

Let number of box seats = \(x\)

Let number of lower deck seats = \(y\)

Let number of upper deck seats = \(z\)

As per question statement:

\(x+y+z=10000\) ...... (1)

Cost for box seat = $10

Cost for \(x\) box seats = 10\(x\)

Cost for lower deck seat = $8

Cost for \(y\) lower deck seats = 8\(y\)

Cost for lower deck seat = $5

Cost for \(z\) lower deck seats = 5\(z\)

As per question statement:

\(10x+8y+5z=70000\) ..... (2)

\(z = 4x\) ..... (3)

Putting value of \(y\) in (1) and (2):

\(x+y+4x=10000\\\Rightarrow 5x+y=10000\) ....... (4)

\(10x+8 y+5\times 4x=70000\\\Rightarrow 30x+8y=70000 ..... (5)\)

8 \(\times\) (4) - (5):

\(10x =\)10000

\(\Rightarrow x = 1000\)

By (3):

\(z = 4000\)

Now, by equation (1):

\(y\) = 5000

Number of box seats = 1000

Number of lower deck seats = 5000

Number of upper deck seats = 4000

The number of accessories that yields the same profit as producing 2 million accessories is 40 million.

The profit of the company is calculated by subtracting the cost from the revenue. The revenue is determined by multiplying the price per accessory by the number of accessories produced. Given that the price is 100 - 10x^2 and the cost is $10 per accessory, the profit can be expressed as:

Profit = (100 - 10x^2) * x - (10 * x)

Since we know that the company currently produces 2 million accessories and makes a profit of 100 million dollars, we can substitute these values into the profit equation and solve for x:

100 million = (100 - 10(2^2)) * 2 - (10 * 2)

100 million = (100 - 40) * 2 - 20

100 million = 60 * 2 - 20

100 million = 120 - 20

100 million = 100 million

From this equation, we see that the profit is equal to 100 million regardless of the number of accessories produced. Therefore, any of the given options (1 million, 3 million, 40 million, 48 million) will yield the same profit. However, the specific number of accessories that yields the same profit as producing 2 million accessories is 40 million.

Learn more about solving equations here: brainly.com/question/14410653

#SPJ11

The statement is false. The existence of a scalar α such that αv is an eigenvector of a does not imply that v itself is an eigenvector of a.

A group of numbers built up in a rectangular array with rows and columns. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

The statement is false. An eigenvector is a non-zero vector that, when multiplied by a matrix, produces a scalar multiple of itself. In other words, if v is an eigenvector of a matrix A, then Av = λv, where λ is the corresponding eigenvalue.

The statement suggests that if a is an nn matrix (presumably an n x n matrix), and a scalar α exists such that αv is an eigenvector of a, then v must also be an eigenvector of a. However, this is not necessarily true.

Let's consider a counterexample to demonstrate this. Suppose we have the 2x2 identity matrix I:

I = [[1, 0],

    [0, 1]]

In this case, any non-zero vector v will satisfy the condition αv = v for α = 1. However, not all non-zero vectors v are eigenvectors of I. In fact, the only eigenvectors of I are [1, 0] and [0, 1] with corresponding eigenvalues of 1.

Therefore, the statement is false. The existence of a scalar α such that αv is an eigenvector of a does not imply that v itself is an eigenvector of a.

Learn more about matrix on:

https://brainly.com/question/30715889

#SPJ4

The value of x in the triangles in diagram A and B is 9.28 respectively.

Triangle is a plane shape that has three sides.

(A) To solve for x in the triangle in diagram A, we use the formula below

Formula:

Where:

Substitute these values into equation 1 and solve for x

(B) Similarly, to solve for x in the triangle in diagram B, we use the formula below

Formula:

Where:

Substitute these values into equation 2 and solve for x

Hence, the values of x in A and B is 9.28 respectively.

Learn more about triangles here: https://brainly.com/question/28470545

#SPJ1

The ratio by mass of copper to zinc in the alloy is 3:1.

To find the ratio by mass of copper to zinc in the alloy, we need to first calculate the total mass of the alloy. We can do this by adding the mass of copper and zinc:

Total mass of alloy = 13.5 g + 4.5 g = 18 g

Now we can find the ratio of copper to zinc by dividing the mass of copper by the mass of zinc:

Ratio of copper to zinc = 13.5 g / 4.5 g = 3:1

Therefore, the ratio by mass of copper to zinc in the alloy is 3:1.

Learn more about mass here

https://brainly.com/question/86444

#SPJ11

Answer:

solve the following questions 2x+3=24