The table shows the volume of water released by a dam over a certain period of time. Graph a line representing the data in the table, and find the slope and y-intercept of the line from the graph. Then enter the equation for the graph in slope-intercept form.

If the unknown number is an integer between 280 and 349;

When rounded to the nearest hundred, the unknown number is 300.

If the unknown number is an integer from 350-380;

When rounded to the nearest hundred, the unknown number is 400.

If the approximation is 45 less than the original number, thus it cant be in the range of 350-380.

But;

When 345 is rounded to the nearest hundred, it is 300.

And the difference between the approximated value and the original value is 45.

Hence, 345 is the original number.

CORRECT ANSWER: 345

From the sample space, there are 2 results equal to 3, and there are 36 total results. Then the probability that she rolls a sum equal to 3 is: 2/36 or 1/18

The triangle ΔDEF has the following coordinates

To find the area of a triangle in coordinate geometry, we have a formula. Given 3 vertices A(x1, y1), B(x2,y2) and C(x3,y3), the area of this triangle is given by

Using this formula for our problem, we have

Solving this equation, we have

And this is our answer Area(ΔDEF) = 40.5

The given expression is

We just have to multiply.

Initial value= $600

new value = $ 480

25% decrease is the answer

The total points that the four students score in round 1 is 75 points.

Based on the information given, it's important to convert the numbers to while numbers and then add.

John has 19.5. This will be 20.

Adam had 21.2. This will be 21.

Peter has 23.8. This will be 24.

Grace has 10.2. This will be 10.

The total points will be:

= 20 + 21 + 24 + 10

= 75

The complete question is given below.

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The points of four students are:

John 19.5

Adam 21.2

Peter 23.8

Grace 10.2

About how many points did the four students score in round 1. Estimate by rounding each point total to the nearest whole number

Answer:

Step-by-step explanation:

I would recommend looking up the magic trig hexagon, it has all of these identities and more within it.

1 - this corresponds with C as sin^2(x)+cos^2(x)=1

1-cos^2(x) - this corresponds with A, using the identity from number 1, we can rewrite it in the form sin^2(x)=1-cos^2(x)

cot(x) - for this it is important to know that cotangent is the inverse of tangent. Since tan(x)=sin(x)/cos(x), cot=cos(x)/sin(x) which is B.

sec^2(x) - much like the cos and sin pythagorean identity, sec and tan are related. sec^2(x)=tan^2(x)+1 which is answer choice E.

tan(x) - this is sin(x)/cos(x), choice D.

Answer:

Question 1: 3

Question 2: $120

Step-by-step explanation:

Set up a proportion

[tex]\frac{inches}{miles}[/tex] = [tex]\frac{inches}{miles}[/tex]  fill in the numbers that you know and solve for the unknow.

[tex]\frac{5}{2}[/tex] =[tex]\frac{7.5}{m}[/tex]  Cross multiply

5x =7.5(2)

5x = 15  Divide both sides by 5

x = 3

If we take 40% off that means that we leave 60% on

Percent means per hundred

[tex]\frac{60}{100}[/tex]  When you divide by hundred, you move the decimal two places to the left.

200(.6)

$120.00

Answer:

a) 6

b) 6

-6

c) 6

6

Explanation:

a) For the number line, the distance will be the difference between the endpoint and the initial point as shown;

Distance = -3 - (-9)

Distance = -3 + 9

Distance = 6units

b) -3 - (-9)

= -3 + 9

= 6

c) -9 - (-3)

= -9 + 3

= -6

d) For the modulus

|-3 - (-9)|

= |-3 + 9|

= |6|

Since the modulus of a value returns a positive value, |6| = 6

e) |-9-(-3)|

= |-9+3)|

= |-6|

Since the modulus of a negative value gives a positive value, hence;

|-6| = 6

Answer:

a) 6

b) 6

-6

c) 6

6

Explanation:

a) For the number line, the distance will be the difference between the endpoint and the initial point as shown;

Distance = -3 - (-9)

Distance = -3 + 9

Distance = 6units

b) -3 - (-9)

= -3 + 9

= 6

c) -9 - (-3)

= -9 + 3

= -6

d) For the modulus

|-3 - (-9)|

= |-3 + 9|

= |6|

Since the modulus of a value returns a positive value, |6| = 6

e) |-9-(-3)|

= |-9+3)|

= |-6|

Since the modulus of a negative value gives a positive value, hence;

|-6| = 6

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

436.8m -------------------> 62.08s

xm -------------------------->1s

Using cross multiplication:

Since each of the data value is multiplied by 5, the new mean will be 5 times the original mean.

To get the original mean, we need to divide by 5.

Therefore the original mean is given by:

Answer: 8

In graph A, you can see that:

• The height of Frozen Field is 50 meters

• The height of Winter Hill is 15 meters

• The height of Blizzard Run is 35 meters

Now, we can write the equation that describes the height difference between Winter Hill and Frozen Field.

In graph B, you can see that:

• The height of Frozen Field is 45 meters

• The height of Winter Hill is 10 meters

• The height of Blizzard Run is 55 meters

Now, we can write the equation that describes the height difference between Winter Hill and Frozen Field.

Therefore, the graph where the height difference between Winter Hill and Frozen Field is equal to the height of Blizzard Run is graph A.

x = 8

From the line geometry shown, the line a and b are parallel lines while line "t" is the transversal.

Since the horizontal lines are parallel, hence;

Given the following parameters

Equate both expressions to have:

Hence the value of x is 8

The given equation is

To solve this equation we have to isolate x on one side and put the numbers on the other side

To do that we will add 3 to each side to move 3 from the left side to the right side

Simplify it

Now we need to move 2 from the left side to the right side, then

Divide both sides by 2

Then the solution of the equation is

x = 6

The price/volume option that will allow the firm to avoid losing money on this project is C. 2,300 units at $34.00 each.

To determine the correct option, we use the cost-volume-profit analysis tool.

The cost-volume-profit (CVP) analysis involves determining how the volume of sales drives profitability.

The CVP technique classifies costs into their variable and fixed cost elements for the purpose of this analysis.

Variable cost per unit = $16

Fixed cost = $40,000

                        Option A    Option B   Option C  Option D   Option E

Sales units        3,000         1,900        2,300        2,500        1,700

Unit selling price $29       $36.50        $34          $31.50        $39

Sales revenue $87,000   $69,350   $78,200    $78,750    $66,300

Variable costs   48,000     30,400     36,800      40,000      27,200

Fixed cost         40,000     40,000     40,000      40,000     40,000

Total costs        88,000     70,400     76,800      80,000     67,200

Thus, the price/volume option that meets the firm's goal is Option C because the sales revenue exceeds the total costs.

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A. 3,000 units at $29.00 each.

B. 1,900 units at $36.50 each.

C. 2,300 units at $34.00 each.

D. 2,500 units at $31.50 each.

E. 1,700 units at $39.00 each.

since n, mand r are the constants for a, b,c n=6

A parallelogram is a 4 sided figures that has the opposite sides parallel.

Figure A has right angles so the opposite sides are parallel

Figure B has the opposite sides of equal length, so the opposite sides are parallel

Figure C has right angles so the opposite sides are parallel

For Question A, Figure A, B C are parallelograms

Squares have opposites sides parallel and all 4 sides of equal length and all angles right angles

The only figure with all 4 sides of equal length, all 4 angles right angles is Figure C ( opposites sides are parallel because 4 sides are equal length and all 4 angles are right angles)

The figure that is a square is Figure C

Rectangles are shapes that have opposite sides parallel and all 4 angles are right angles. Squares are special rectangles

Figure A has opposite sides parallel and all 4 angles equal length. Figure C is a square, which is a special rectangle

The rectangles are figures A and C

a) The yield to maturity of the IOU Corporation's bond is -0.39%.

b) The current yield of the IOU Corporation's bond is 5.58%.

The bond's yield to maturity (YTM) is the total rate of return earned by a bondholder with all interest payments and the original principal repaid.

We can compute the yield to maturity using the following YTM formula:

Yield to Maturity = [Annual Interest + {(FV-Price)/Maturity}] / [(FV+Price)/2]

Where:

FV = Face Value of the Bond

Price = Current Market Price

Maturity = Maturity Period.

Bond's face value = $2,000

Current date = April 19, 2021.

Company (Ticker)  Coupon  Maturity  Last Price  Last Yield  EST volume

                                                                                                      (000s)

IOU            (IOU)       6.3    April 19, 2037  112.97         ??            1,857

Annual interest = $126 ($2,000 x 6.3%)

Maturity period = 16 (2037 - 2021)

Price = $2,259.4 ($2,000 x 112.97/100)

Yield to Maturity = [Annual Interest + {(FV-Price)/Maturity}] / [(FV+Price)/2]

= [$126 + {($2,000 - $2,259.4)/16}] / [($2,000 + 2,259.4)/2]

=  [$126 -$259.4)/16] / [($4,259.4)/2]

= -8.3375/2,129.7

= -0.39%

Current yield = Annual Coupon/Current Price

= 5.58% ($126/$2,259.4 x 100)

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Given:

An algebraic expression we can use to compare the price of IBM shares as being $74.50 more than AT&T shares is x + 74.50, where x is the value of AT&T shares.

An algebraic expression consists of variables, terms, constants, and mathematical operations, including addition, subtraction, multiplication, division, and others.

The five algebraic expressions include monomial, polynomial, binomial, trinomial, multinomial.

We can also describe algebraic expressions as falling under the following categories:

An example of an algebraic expression is 2x + 3y.

Let the value of AT&T share = x

Let the value of IBM share = x + 74.50

Thus, we can, algebraically, conclude that AT&T's share price is x while the price of IBM's share is x + 74.50 on that particular day.

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The simplest form of the given division is,[tex][tex]\frac{550}{13}[/tex][/tex].

What is division?
The opposite of multiplication is division. Dividing a sum of numbers into equal pieces. A number is divided in division, which is a straightforward procedure.

Given that: (55/7)/(13/5)/(42/3)

First to simplify:

[tex](13/5)/(42/3)[tex]\frac{(\frac{13}{5}) }{(\frac{42}{3}) } = \frac{(\frac{13}{5}) }{14} \\[/tex] [tex]= \frac{13}{(5)(14)} \\= \frac{13}{70}[/tex][/tex]

So, expression becomes,

[tex][tex]\frac{(\frac{55}{7} )}{(\frac{13}{70} )}[/tex][/tex]

Now to simplify this expression.

Using:[tex][tex]\frac{(\frac{a}{b} )}{(\frac{c}{d} )} = \frac{ad}{bc}[/tex][/tex]

Then,[tex][tex]\frac{(\frac{55}{7} )}{(\frac{13}{70} )} = \frac{(55)(70)}{(7)(13)} = \frac{3850}{91} = \frac{550}{13}[/tex][/tex]

Therefore, [tex][tex]\frac{550}{13}[/tex][/tex] is the simplest form of the given division.

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Assuming these are volume percentages and the volumes don't change when you mix them, we can calculate this using a system of equations.

But first we need to identify each equation and variable.

let x be the volume of 7% vinegar used and y be the volume of 12% vinegar used.

The total volume is the sum of those and it must be equal to 370 mL, so:

The amount of vinegar in the x volume of 7% vinegar can be calculated by multiplying x by the 7%, that is, by 0.07:

Similarly, the amount of vinegar in y is:

So, the total amount of vinegar after the mixture is:

Since the percentage of the final mixture is 8%, the amount after the mixture can also be calculated by taking 8% of the final volume of 370mL, that is:

The two ways of calculating the amount of vinegar in the mixture must be the same, so we have got our second equation:

So, the system of equations is:

We can solve this by substitution:

Thus:

And, going back to the first equation:

Complementary angles - The smaller angle is 24 degrees in size.

what are complementary angles?

Angles that add up to a precise 90 degree angle are said to be complementary. For instance, 30 degrees and 60 degrees are complementary angles.

Let x equal the first angle's measurement for the sake of explanation.

Let y be the size of the first angle's complement.

One angle, which we'll refer to as y, is 18 more than twice as large as another, x.

y = 18 + 2x

Complementary angles add up to 90 degrees.

x + 18 + 2x = 90

By substituting for y,

we get x + 18 + 2 x = 90.

Putting like phrases together and taking 18 off on both sides...

3x + 18 = 90

     - 18    -18

3x = 72

By dividing both sides by 3, you get

3x/3 = 72/3

24 degrees is the angle between the two that is smaller. and the other angle would be,

y= 18+2x

=18+2(24)= 66 degrees.

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Net worth is equal to total assets minus total liabilities (debt).

So,

Total Assets = 253000

Total Liabilities = 216345

Hence,

Net Worth = 253000 - 216345 = $36,655

The total minutes in the game is 48. The total playing game for Jason is 32. The ratio is

Simplifying it, we have

So, the playing ratio is 2 to 3 for Jason.

From the problem, we have an inequality of :

Subtract 9 to both sides of the inequality :

Divide both sides by 5 :

The answer is x ≤ 3

We must find the equation that models the amount of medication in the bloodstream as a function of the days passed from the initial dose. The initial dose is a and we are going to use x for the number of days and M for the amount of mediaction in the bloodstream. We are going to model this using an exponential function which means that the variable x must be in the exponent of a power:

We are told that the half-life of the medication is 6 hours. This means that after 6 hours the amount of medication in the bloodstream is reduced to a half. If the initial dose was a then the amount after 6 hours has to be a/2. We are going to use this to find the parameter b but first we must convert 6 hours into days since our equation works with days.

Remember that a day is composed of 24 hours so 6 hours is equivalent to 6/24=1/4 day. This means that the amount of medication after 1/4 days is the half of the initial dose. In mathematical terms this means M(1/4)=M(0)/2:

We can divide both sides of this equation by a:

Now let's raised both sides of this equation to 4:

Which can also be written as:

Then the equation that models how much medication will be in the bloodstream after x days is:

Using this we must find how much medication will be in the bloodstream after 4 days for an initial dose of 500mg. This basically means that a=500mg, x=4 and we have to find M(4):

So after 4 days there are 0.00763 mg of medication in the bloodstream.

Now we have to indicate how much more medication will be if the initial dose is 750mg instead of 500mg. So we take a=750mg and x=4:

If we substract the first value we found from this one we obtained the required difference:

So the answer to the third question is 0.00381mg.

The area of a parallelogram is computed using the formula base x height.

Here we have a parallelogram with an area of 72 square meters and a height of 9 meters. Using the formula, we can solve for the base.

The base is 8 meters long.

The average of a set is computed as follows:

In this case,