Roman earns $8.50 an hour as an intern at law firm. Usually he works 30 hours a week. This week however, there is a big case and he worked 47 hours. What is his gross pay for this week? (Standard overtime rules.)

The wire that Marlee had left is 20.8 inches.

From the information given, it was stated that Marlee is making jewelry for a class craft show and that she began with 115 inches of wire.

Amount used for rings = 25.75 inches..

Amount given to her by the teacher = 30 1/4 inches.

Amount used for bracelets = 38 1/2

inches.

Amount used for necklace = 60.2 inches

It should be noted to know the wire left, we have to subtract the values that were used and then add the value that her teacher gave her from the original value. This will be calculated thus:

This will be:

= 115 - 25.75 + 30.25 - 38.5 - 60.2

= 20.8 inches

Therefore, in conclusion, the wire that Marlee had will be 20.8 inches left.

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Answer:

yes a product of any number to 0 is equal to 1

The cost of one sandwich is $5.7

The given parameters are:

Order = 3

Tax = 8% off

Total cost = $20.66

Tip = $5

The cost of one sandwich is calculated as:

Total cost = Order * Cost of One (x) * (1 - tax) + Tip

This gives

20.66 = 3 * x * (1 - 8%) + 5

Subtract 5 from both sides

15.66 = 3 * x * (1 - 8%)

Make x the subject

x = 15.66/[3 * (1 - 8%)]

Evaluate

x = 5.7

Hence, the cost of one sandwich is $5.7

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Answer:

What you are looking for is the length of the 'solid diagonal'. First we need to find the length of the base diagonal. That can be done easily using Pythagorean theorem.  52+32−−−−−−√=6. Now this diagonal is a leg of the bigger right triangle whose hypotenuse is the required solid diagonal. You can see this from amd's picture. So apply Pythagorean theorem again.  62+(2.5)2−−−−−−−−−√=37.25−−−−√. You can work that out with a calculator.

In general for a cuboid with dimensions a, b and c(order doesn't matter), the solid diagonal is:  a2+b2+c2−−−−−−−−−−√

Step-by-step explanation:

Answer:

√62+(2.5)2=√37.25.

Step-by-step explanation:

What you are looking for is the length of the 'solid diagonal'. First we need to find the length of the base diagonal. That can be done easily using Pythagorean theorem.  52+32=6" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; box-sizing: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;"> 52+32−−−−−−√=6 52+32=6. Now

For the following equation of the line: y = (1/5)x + 1, y = (1/5)x + 5, y = 5x + 1, and y = 5x + 5, the line that is perpendicular to it and has the same y - intercept is: y = -5x + 1, y = -5x + 5, y = (-1/5)x + 1, and y = (-1/5)x + 5, respectively.

If two equations of the line are perpendicular with each other, then their slopes are negative reciprocal of one another.

To generate the equation of the line perpendicular to the given lines, with the same y-intercept,

1. Get the slope of each line and determine its y-intercept

2. Take the negative reciprocal of the slope and use it and the same y-intercept to get the equation.

y = (1/5)x + 1

slope = 1/5

y-intercept = 1

perpendicular line :

slope = -5

y-intercept = 1

equation : y = -5x + 1

y = (1/5)x + 5

slope = 1/5

y-intercept = 5

perpendicular line :

slope = -5

y-intercept = 5

equation : y = -5x + 5

y = 5x + 1

slope = 5

y-intercept = 1

perpendicular line :

slope = -1/5

y-intercept = 1

equation : y = (-1/5)x + 1

y = 5x + 5

slope = 5

y-intercept = 5

perpendicular line :

slope = -1/5

y-intercept = 5

equation : y = (-1/5)x + 5

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Answer:

C     y = 5x + 1

Step-by-step explanation:

Took the test on edu

Answer:

It's the graph with two dots and no area marked, first image (for me).

Step-by-step explanation:

|x| = 1 means "the distance from x to the 0 point on the axis is exactly 1". There's only 2 numbers x that satisfy that condition: -1 and 1

The second and third image both show an area marked, so it cannot be the right answer, while the first image shows precisely two numbers: -1 and 1

Answer: Rotation

Step-by-step explanation:

Answer: the thickness of each sheet of paper is 2in thick.

Step-by-step explanation:

There is none.

If box contains 5 reams of paper, the estimated thickness of 2 sheets of paper is T/1250.

To estimate the thickness of 2 sheets of paper, we can use the given information about the number of reams in the box and the number of sheets in one ream of paper.

First, we know that one ream of paper contains 500 sheets. Since the box contains 5 reams, the total number of sheets in the box is 5 reams × 500 sheets/ream = 2500 sheets.

Next, we can calculate the thickness of one sheet by dividing the total thickness of the reams by the number of sheets. Let's assume the thickness of the 5 reams combined is T.

Thickness of one sheet = T/2500

Now, to estimate the thickness of 2 sheets, we multiply the thickness of one sheet by 2:

Estimated thickness of 2 sheets = (T/2500) × 2 = 2T/2500 = T/1250

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Light is about 874052.5 times faster than sound

From the question, we are to determine the magnitude by which light is faster than sound

From the given information,

The speed of light is about 2.998 x 10⁸ meters per second.

and

The speed of sound is about 343 meters per second.

To determine how many rimes faster the speed of light is than the speed of sound, we will divide the speed of light by the speed of sound

That,

The magnitude by which light is faster than sound = (2.998 x 10⁸) / 343

The magnitude by which light is faster than sound = 874052.5

Hence, light is about 874052.5 times faster than sound

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Answer:

20

Step-by-step explanation:

the 0 is not significant since it is not sandwiched between 2 sigfigs and is not the last digit after a decimal

Domain

[tex]-\infty \: < x < \infty[/tex]

Range

[tex]f\left(x\right)\ge \:-7\:[/tex]

Answer:

40 3/8 bushels of apples

Step-by-step explanation:

13 1/8 bushels and 27 2/8 bushels

13 1/8 + 27 2/8 =

(13 + 27) = 40

(1/8 + 2/8) = 3/8

40 3/8

Definition of Relation:

Let A and B be sets. A relation R from A to B is a subset of Ax B

Definition of Function:

A function f from a set A (domain) to a set B (codomain) is a relation that satisfies the following properties:

1) Every element in A there is an element y in B such that (x,y) F

2) For all elements z in A there exist a unique element y in B.

The cartesian product of the sets A (a, b) and B (r,y) is

A x B {(a,z) (a,y).(b,),(b,s)}

Step 2

1. T ((a,x), (a,y))

Since T-((a,z), (a,y)) is a subset of (a, b) x (x,y).

so T is a relation from (a,b) to (x,y).

But for the element a in domain, there exist two different images x and y in co-domain.

This violates the definition of function.

Therefore, T_{1} = \{(a, x), (a, y)\} is a relation but not a function.

Step 3

2. T_{2} = \{(b, x), (b, y)\}

Since T_{2} - \{(b, x), (b, y)\} is a subset of \{a, b\}\{x, y\} .

so T_{1} is a relation from \{a, b\} to \{x, y\}

But for the element b in domain, there exist two different images x and y in co-domain

This violates the definition of function

Therefore, T_{2} = \{(b, x), (b, y)\} is a relation but not a function.

Step 4

,T 1 =\ (a,z)\

Since 7-((a,z)) is a subset of \{a, b\}\{x, y\}

so Ty is a relation from \{a, b\} * to (x,y\

But the element & in domain does not map with any element in co-domain

This violates the definition of function

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The slope of the line is -10/9 and the value of y-intercept of the line is 50/3.

Slope of the line:

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

Given,

The point (9,10) that cuts off the least area from the first quadrant

Here we need to find the slope and y intercept of the line.

A line is passing through a point (9,10) cuts off least area in first quadrant.

The equation of the line passing through point (9,10) and has slope m can be expressed as,

=> y - 10 = m (x - 9)

=> y = m(x - 9) + 10

=> y - mx = - 9m + 10

Divide the terms by - 9m + 10, then we get,

=> (y/- 9m+10) - (mx/ - 9m+10) = 1

=> (mx/9m+10) - (y/9m+10) = 1

It can be rewritten as,

[tex]\implies\frac{x}{\frac{9m-10}{m}} -\frac{y}{10-9m}[/tex]

We know that,

The equation of straight line in intercept form is

=> x/a + y/b = 1

So, the intercept made by the line on x-axis i.e. a and on y-axis i.e. b are:

a = 9m-10/m

b =  10 - 9m

The area of the triangle made by the line in first quadrant can be expressed as,

=> A = 1/2 x (9m-10/m) x (10 - 9m)

=> A = -1/2 (9m-10)²/m-----------------------(1)

Differentiate the equation (1) with respect to m.

[tex]\frac{dA}{dm}=-\frac{1}{2}[\frac{2m(9m-10).9-(9m-10)^2}{m^2}][/tex]

[tex]\frac{dA}{dm}=-\frac{9m-10}{2m^2}[2m.9-(9m-10)][/tex]

[tex]\frac{dA}{dm}=-\frac{9m-10}{2m^2}[18m-9m-10)][/tex]

when we simplify it,

=> dA/dm = -(9m-10)/2m² [9m-10]

Let dA/dm = 0, then

=> 0 = -1/2m² (9m-10)(9m-10)

=> 0 = 1/m² (10-9m)(9m-10)

=> 0 = (10 - 9m) (9m -10)

Therefore, the value of m is,

=> 10 - 9m = 0

=> -9m = -10

=> m = 10/9

And

=> 9m - 10 =0

=> 9m = 10

=> m = 10/9

The line will be in first quadrant and forms a triangle with axes if the slope is negative.

Substitute m = -10/9

Then, b = 10-9m

Then,

=> y = 10 - 6(-10/9)

=> y = 10 + 20/3

=> y = 50/3

So, the slope of the line is -10/9 and the value of y-intercept of the line is 50/3.

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Satisfactory internal control reduces the probability of errors or frauds in the accounts.

What functions may a strong internal control system perform?

Why are internal controls necessary?

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Speed is the constant of proportionality for the relationship between distance and time.

Relationship between these two values is distance is directly proportional to time .

As given,

Distance =400 kilometers

Time=8 hours

Let s, d, and t represents speed, distance and time.

Speed = d / t

           = 400/8

           = 50 km/ hour

           = constant

Hence ,

d = 50t

⇒ d ∝ t

Therefore, speed is the constant of proportionality for the relationship between distance and time.

Relationship between these two values is distance is directly proportional to time .

The complete question is:

An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. using for distance in kilometers and for number of hours, an equation that represents this situation d=50t.

What are two constants of proportionality for the relationship between distance in kilometers and number of hours? What is the relationship between these two values?

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Answer:

first order

Step-by-step explanation:

they're basically a linear function. to make it easier you could just put the coordinates on the side of the table.

Answer:

Step-by-step explanation:

x = -3 to 3

means that they are asking for the graph from -3 to 3 on the x-axis

gradient is (-1/2) which means rise is -1 when run is 2

y-intercept is 3.

go to 3 on the y axis which means the coordinate (0,3) go downwards by 1 and to the right by 2. This will lead you to coordinate (2,-1). Now connect both points by a straight line.

The value of h(2) for the function h(x) = 18 - 9x + x^4 is 16.

According to the given question.

We have a function h(x) = 18 - 9x + x^4

Here, we have to find the value of h(2). For this we will substiute x = 2 in the function h(x) = 18 - 9x + x^4.

Therefore, the value of h(2) for the function h(x) = 18 - 9x + x^4 is given by

h(x) = 18 - 9x + x^4

h(2) = 18 - 9(2) + 2^4

h(2) = 18 - 18 + 16

h(2) = 16

Hence, the value of h(2) for the function h(x) = 18 - 9x + x^4 is 16.

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Given x is Complimentary angle

Also, line1 is parallel to line2

Thus,
x [tex]+[/tex]  139° [tex]=[/tex] 132° [Alternate angle]

x [tex]=[/tex] 132°[tex]_[/tex][tex]_[/tex]- 139°

x[tex]=[/tex] -7°

What is Complimentary angle?

When two angles are added together, complementary angles are defined. When the total of the two angles is 90 degrees, we get a pair of complimentary angles. In other terms, two angles are said to be complimentary if they combine to make a right angle. In this case, we say that the two angles work well together.

If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complimentary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.

60° + 30° in the illustration below equals 90°. These two angles are therefore complimentary according to the "Definition of Complementary Angles." The term "complement" refers to each angle that is one of the complimentary angles. Here,

The opposite of 30° is 60°.

The opposite of 60° is 30°.

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Applying the triangle proportionality theorem, the length of line EC is: 7.2 units.

Since lines AC and DE are parallel to each other in the triangle, and DE intersects sides AB and AC, then we would have the following proportion based on the triangle proportionality theorem:

BD/DA = CE/EA

BD = 18 units

DA = 15 units

CE = ?

EA = 6 units

Plug in the values

18/15 = CE/6

(18)(6) = (CE)(15)

108 = CE(15)

Divide both sides by 15

108/15 = CE(15)/15

7.2 = CE

EC = 7.2 units

Therefore, applying the triangle proportionality theorem, the length of line EC is: 7.2 units.

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Answer:

130.94

Step-by-step explanation:

'Combine' I assume is to add so here's the answer!

23.8+40+38.94+28.2= 130.94

Angle 5 = 180 - 146 = 34

Angle 6 = 146 since vertical angles are congruent

Angle 7 = 34 since vertical angles are congruent, or you could say 180-146 = 34 again. Any pair of adjacent angles add to 180. All four angles add to 360.

Answer:

Step-by-step explanation:

first we can turn these mixed fractions into normal numbers so

1.42<.336 FALSE

.54>1.357 false

.615>.96 false

1.16>1.83 TRUE

Answer:

$1020.00

Step-by-step explanation:

15% means 15/100 divide by 100 and you get .15

.15 x 1200 gives us the rebate.  The rebate is 180.  We subtract that from 1200. 1200 -180 = 1020

Another way to think about this, is that we are taking 15% off we are leaving on 85%

.85 x 1200 = 1020

Answer: 51.33

Step-by-step explanation:

7+8.75+12.5+15.33+7.75 = 51.33

Step-by-step explanation:

You want to demonstrate the identity ...

  (1-tan⁴(A))·cos⁴(A) = 1 -2·sin²(A)

Working with the left side, we have ...

  [tex](1-\tan^4(A))\cos^4(A)=1-2\sin^2(A)\\\\(1-\dfrac{\sin^4(A)}{\cos^4(A)})\cos^4(A)=1-2\sin^2(A)\qquad\text{use tangent identity}\\\\\cos^4(A)-\sin^4(A)=1-2\sin^2(A)\qquad\text{multiply it out}\\\\(\cos^2(A) +\sin^2(A))(\cos^2(A)-\sin^2(A))=1-2\sin^2(A)\qquad\text{factor}\\\\1((1-\sin^2(A))-\sin^2(A)) = 1-2\sin^2(A)\qquad\text{use $\cos^2$ identity}\\\\1-2\sin^2(A)=1-2\sin^2(A)\qquad\text{Q.E.D.}[/tex]

__

Additional comment

The referenced identities are ...

  tan = sin/cos

  cos² = 1 -sin²

and the factorization of the difference of squares:

  a² -b² = (a +b)(a -b).

A distribution of scores in which almost the entire class scored very high, but a few students scored fairly low would be representing a negatively skewed distribution.

A real-valued random variable's probability distribution's asymmetry can be quantified by looking at how skew it is around its known as skewness.

There are three types of probabilities of a value can be:

Positively skewed

negatively skewed

unskewed

From the given question, the distribution of scores in which almost the entire class scored very high, but a few students scored fairly low would be representing a negatively skewed distribution.

Therefore the correct answer would be an option (D)

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Your question is incomplete, probably the missing part is:

A distribution of scores in which almost the entire class scored very low, but a few students scored fairly high would be ______.

a. normally distributed

b. positively skewed

c. unskewed

d. negatively skewed