Graph the system of inequalities presented here then use your graph to answer the following questions:

y > 5x + 5
y is greater than negative 1 over 2 times x plus 1

Part A: Graph both equations and use 2 different colors to shade. Use a 3rd color to show the solution area. Describe the graph of the system, including shading and the types of lines graphed (dotted or solid lines). Provide a description of the solution area.

Part B: Is the point (-2, 5) included in the solution area for the system? Justify your answer mathematically.

Please help. I'm so sick today that I can't think and just need to finish my homework

Answer:

Step-by-step explanation:

I'm going to paint you a picture in words of what this looks like on paper.  We have a train leaving from a point on your paper heading straight west.  We have another train leaving from the same point on your paper heading straight east.  This is the "opposite directions" that your problem gives you.  

Now let's make a table:

                 distance       =        rate      *       time

Train 1

Train 2

We will fill in this table from the info in the problem then refer back to our drawing.  It says that one train is traveling 12 mph faster than the other train.  We don't know how fast "the other train" is going, so let's call that rate r.  If the first train is travelin 12 mph faster, that rate is r + 12.  Let's put that into the table

               distance        =        rate        *        time

Train 1                                        r

Train 2                                    (r + 12)

Then it says "after 2 hours", so the time for both trains is 2 hours:

               distance        =        rate        *        time

Train 1                                        r           *          2

Train 2                                  (r + 12)       *          2

Since distance = rate * time, the distance (or length of the arrow pointing straight west) for Train 1 is 2r.  The distance (or length of the arrow pointing straight east) for Train 2 is 2(r + 12) which is 2r + 24.  The distance between them (which is also the length of the whole entire arrow) is 232.  Thus:

2r + 2r + 24 = 232 and

4r = 208 so

r = 52

This means that Train 1 is traveling 52 mph and Train 2 is traveling 12 miles per hour faster than that at 64 mph

Answer: its A    ^3^❤

Step-by-step explanation:

that guy above me probably got yall confused

Answer:

The three questions about the given triangle has been answered below.

Step-by-step explanation:

We are given a right angled triangle whose sides are of length 20, 21 and 29.

(1) sin(B) = [tex]\frac{side opposite to B}{hypotenuse}[/tex]

              = [tex]\frac{21}{29}[/tex]

              = 0.72

(2) sin(A) = [tex]\frac{20}{29}[/tex]

     sin(A)  = 0.689

     ∠CAB = [tex]sin^{-1}(0.689)[/tex]

     ∠CAB = 43.551°

(3) We suppose that cosA < sinA and we haveto find which all angles will satisfy this condition.For this the angle A should be greater than 45°.

From the given options the angles that satisfy this are 55 , 66 and 75.

45 is not included as then sinA = cosA and that condition is not there.

We can use sine and cosine trigonometric ratios to calculate the ratio and measures of angles.

A: The ratio equivalent to sin(B) is  [tex]\dfrac{21}{29}[/tex]

B: The measure of angle  ∠CAB is  [tex]43.6^\circ[/tex]

C: The possible measures of angle A can be: 55, 66 or 75

A: The ratio equivalent to sin(B) is:

[tex]sin(B) = \dfrac{CA}{AB} = \dfrac{21}{29}\\[/tex]

B: The measure of angle ∠CAB is calculated as:

[tex]sin(A) = \dfrac{CB}{BA} = \dfrac{20}{29} = 0.69\\\\A = arcsin(0.69) = 43.6^{\circ}\\\\\angle CAB = 43.6^{\circ}[/tex]

C: When sin A > cos A, the measures of angle A from 25,35,45,55,66,75 are:

55, 65 and 75:

The reason for the angles possible are 55, 66 ,75 is that:

[tex]\theta \leq 45\\sin(\theta) \leq cos(\theta)[/tex]

Thus, we have:

A: The ratio equivalent to sin(B) is  [tex]\dfrac{21}{29}[/tex]

B: The measure of angle  ∠CAB is  [tex]43.6^\circ[/tex]

C: The possible measures of angle A can be: 55, 66 or 75

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Answer:

Option C.

Step-by-step explanation:

The vertices of triangle PQR are P(3, −6), Q(6, −9), and R(−15, 3).

It is given that triangle PQR dilated by a scale factor of 3 to obtain triangle P′Q′R′.

We know that a figure and its image after dilation are similar. It means triangle PQR and triangle P′Q′R′

If a figure dilated by factor k about the origin then

[tex](x,y)\rightarrow (kx,ky)[/tex]

PQR dilated by a scale factor of 3, so

[tex](x,y)\rightarrow (3x,3y)[/tex]

Using this rule we get

[tex]P(3,-6)\rightarrow P'(3(3),3(-6))=P'(9,-18)[/tex]

[tex]Q(6,-9)\rightarrow Q'(3(6),3(-9))=Q'(18,-27)[/tex]

[tex]R(-15,3)\rightarrow R'(3(-15),3(3))=R'(-45,9)[/tex]

The vertices of image are P'(9,-18), Q'(18,-27) and R'(-45,9).

Therefore, the correct option is C.

Answer:

C

Step-by-step explanation:

Answer:

Option (b) is correct.

The correlation between age and weight  shown in the table is positive.

Step-by-step explanation:

According to the given values, it is found that there is a positive correlation between age and weight.

In this problem, when the age increases, so does the weight, hence they have positive correlation.

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Answer:

  0.5

Step-by-step explanation:

We assume your function is

  [tex]f(x)=\sqrt{4-x}[/tex]

The distance formula can be used to find the distance from the point on the curve (x, f(x)) to the origin:

  d^2 = (x)^2 + (f(x))^2 = x^2 + (4 -x)

Written in vertex form, this is ...

  d^2 = (x -1/2) + 3.75

This has a minimum at x=1/2, so that is the x-coordinate of the point closest to the origin.

In the function f(x) = √(4-x), the x-coordinate of the point on the graph that is closest to the origin is x=0 because the function exists in the first quadrant, meaning the shortest distance to the origin is along the y-axis.

The function described is f(x) = √(4-x). We're looking for the x-coordinate of the point on the graph of this function that is closest to the origin. The distance from any point (x, y) to the origin (0, 0) is given by D=√(x²+y²). For this function, y=f(x) = √(4-x), so the distance can be written as D=√(x²+(4-x)²). To find the minimum distance, we take the derivative of this distance function with respect to x, set it equal to zero and solve for x. However, because this function lives in the first quadrant (y is always equal to or greater than 0), the shortest distance to the origin would be along the y-axis. Thus, the solution is x=0, and that is the x-coordinate of the point on the function's graph that is closest to the origin.

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Final answer:

To represent the total amount Abigail's parents will pay both Abigail and her sister for working the same number of hours, you could use the algebraic expressions 5h + 3h or (5 + 3)h, where h is the number of hours worked.

Explanation:

Abigail's parents pay her for weeding the yard and pay her little sister for raking leaves. If both of them work for the same amount of hours, we can represent the total amount their parents will pay using algebraic expressions. Let h be the number of hours they work.

One way to write the expression is: 5h + 3h, where 5 represents the dollars per hour for Abigail and 3 represents the dollars per hour for her sister.

Another way to represent this is: (5 + 3)h, which simplifies the expression by adding the hourly wages first and then multiplying by the number of hours worked, h.

Both expressions will give us the total amount paid to Abigail and her sister for the same number of hours worked, h.

Jose will spend 18 minutes on his science homework.

Step-by-step explanation:

Given,

Time Jose have to spend on homework = 5/6 hour

We know that 1 hour = 60 minutes

Therefore;

[tex]\frac{5}{6}\ hour = \frac{5}{6}*60\ minutes\\\\\frac{5}{6}\ hour = 50\ minutes[/tex]

Time Jose have to spend on homework = 50 minutes

Time spent on math home work = [tex]\frac{1}{3}\ of\ his\ time[/tex]

Time spent on math home work = [tex]\frac{1}{3}*50=16.66\ minutes[/tex]

Rounding off to nearest whole minute;

Time spent on math homework = 17 minutes

Time spent on reading homework = 15 minutes

Total time spent = Mathematics + Reading + Science

50 = 17+15+Science

50 = 32 + Science

Science = 50-32 = 18 minutes

Jose will spend 18 minutes on his science homework.

Keywords: addition, fraction

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Answer:

The arithmetic average return would be 3.96%

Step-by-step explanation:

Given,

The returns in 5 years are,

-​9.7%, -​8.1%, ​15%, 7.2%, and​ 15.4%

We know that,

[tex]\text{Arithmetic average}=\frac{\text{Sum of all observations}}{\text{Number of observations}}[/tex]

Hence,

The arithmetic average return of the investment = [tex]\frac{-9.7-8.1+15+7.2+15.4}{5}[/tex]

[tex]=\frac{19.8}{5}[/tex]

= 3.96%

Answer:

It will cost him $616 for 160 gallons of gas.

Step-by-step EXPLANATION FIRST YOU HAVE TO MULTIPLY 3.25 BY 160 TO GET $520, THEN JUST ADD IT BY $96 TO GET $616.

It will cost Lee $520 to purchase 160 gallons of gas.

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division. The priority of these opeartors in a given expression can be determined by PEDMAS. Each letter represents one operation as P for Parenthesis, E for exponential, D for division, M for Multiplication, A for Addition and S for Subtraction.

The price of gas per gallon is $3,25.

The cost of 160 gallons can be calculated as follows,

Number of gallons × Price per gallon

⇒ 160 × 3.25

⇒ 520

Hence, the price of 160 gallons is given as $520.

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Kendal bought 7 boxes of cookies, kept 2 boxes for herself and brought 60 cookies to the party.

Let x represent the number of boxes of cookies bought by Kendal.

Each box has 12 cookies, hence:

number of cookies = 12x

Kendal brings 60 cookies to the party. She keeps 2 boxes for herself. To find the number of boxes we use:

12x = 60 + 12(2)

12x = 84

x = 7

Therefore Kendal bought 7 boxes of cookies, kept 2 boxes for herself and brought 60 cookies to the party.

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Final answer:

To find the number of boxes, x, Kendal bought, we can set up an equation based on the information given. The equation (x - 2) * 12 = 60 can be used to find the number of boxes Kendal bought.

Explanation:

To find the number of boxes, x, Kendal bought, we can set up an equation based on the information given. Kendal initially buys x boxes of cookies. Each box contains 12 cookies. She decides to keep two boxes for herself and brings 60 cookies to the party.

The number of cookies Kendal brings to the party can be calculated by multiplying the number of boxes she bought minus the number of boxes she kept for herself by the number of cookies in each box. So, the equation to find x would be:

(x - 2) * 12 = 60

Solving this equation will give us the value of x, which represents the number of boxes Kendal bought.

Answer:

Eugene friend will have more pie than Eugene.

Eugene friend has [tex]\frac{3}{5}[/tex] more pie than Eugene.

Step-by-step explanation:

Given:

Amount of pie Eugene has = 3

Amount of Pie given to friend  = [tex]1\frac{4}{5}[/tex]

[tex]1\frac{4}{5}[/tex] can be Rewritten as [tex]\frac{9}{5}[/tex]

We need to find who has pie and how much more.

We will first find the amount of pie Eugene is left with.

The amount of pie Eugene is left with is equal to Amount of pie Eugene had minus Amount of pie given to friend.

Framing the equation we get;

The amount of pie Eugene is left = [tex]3-\frac{9}{5}[/tex]

We will take LCM to solve the same.

The amount of pie Eugene is left = [tex]3-\frac{9}{5} = \frac{3\times5}{5}-\frac{9}{5} =\frac{15}{5}-\frac{9}{5} = \frac{15-9}{5} =\frac{6}{5}[/tex]

Now  [tex]\frac{9}{5} = 1.8[/tex] and  [tex]\frac{6}{5} = 1.2[/tex]

Hence  [tex]\frac{9}{5}[/tex] is greater than  [tex]\frac{6}{5}[/tex]

Hence Eugene friend will have more pie than Eugene.

Now we will find amount more pie Eugene friend has.

Amount More Eugene friend has can be calculate by Subtracting Amount of of Eugene has with Amount of pie his friend has.

Amount More Eugene friend has =[tex]\frac{9}{5} - \frac{6}{5} =\frac{9-6}{5}= \frac{3}{5}[/tex]

Hence Eugene friend has [tex]\frac{3}{5}[/tex] more pie than Eugene.

Answer:

The answer is True.

Step-by-step explanation:

Sales variance is computed in same manner as cost variance that is computing both price and volume variance. However interpretation of end result will not be same. For example in material price variance if

A = actual purchase price = $ 4, B = standard purchase price= $ 5 and Qt= quantity purchased = 500 units then

Material price varaince = 500 (5-4) = 500,

This gives us favourable price variance of 500 dollars. However in sales price variance if

A = actual sales price = $ 4, B = standard sale price= $ 5 and Qt= quantity sold = 500 units then

Sale price varaince = 500 (5-4) = (500)

This gives us unfavourable sales price variance of 500 dollars.

This show that formulas to compute variances are same but sale price decrease give us un favorable variance and cost price decrease gives us favorable price variance and vice versa.

Answer:angle DAB will be equal to angle CAB

Step-by-step explanation:

AC is a straight line and forms one of the sides of triangle ABC. If point D is placed on line AC, angle DAB would remain equal to angle CAB since they are on the same line the angle formed with line AB remains the same.

The measure of angle DAB will be congruent to angle CAB if AB and CD are parallel and right angles to AC and AD. The relationship changes as point D moves along AC, with angle DAB diminishing if DE remains parallel to AB.

If point D is placed on AC, the measure of ∠DAB will relate to the measure of ∠CAB based on several geometric principles. If AB is parallel to CD and D moves along AC, with DE remaining constantly parallel to AB, the angle at D (∠DAB) will diminish as D moves away from A. If AB and CD maintain parallels and AC makes equal angles with them, then accordingly ∠DAB will also equal ∠CAB at the point where the two angles are bisected by AC.

Moreover, if AB and CD are right angles to AC and AD, as described by the circle theorem stating that angles inscribed in the same arc are congruent, then ∠DAB will be congruent to ∠CAB.

i got 1.0436 on my calculation hope this helps...

Answer:

H(160)=150  means that  Kana's height is 150 cm when she is 160 months old

Step-by-step explanation:

According to the model described in the question:

H(t)=X where

Thus H(160)=150 states

Answer:

When Kana was 160 months old, her height was equal to 150 centimeters.

Step-by-step explanation:

Answer:

Expected net gain is -$0.75. Not a fair game. Appropriate price is $2.25.

Step-by-step explanation:

There is 1 in 600 chance to win the grand price (1/600)

There are 2 in 600 chance to win the 2nd price (2/600 = 1/300)

There are 5 in 600 chance to win the 3rd price (5/600 = 1/120)

We can use these probability to calculate the expected gain from this game

[tex]E_g = 700\frac{1}{600} + 200*\frac{1}{300} + 50*\frac{1}{120} = \$2.25[/tex]

Since the cost to play is $3, the expected net gain from this game is

$2.25 - $3 = -$0.75

So this game is not fair as the player is losing money. The appropriate price should instead be $2.25

The expected value of $1.91 is less than the cost of $3 per ticket, indicating it is not a fair game. To make it fair, the price per ticket should be set at $1.91.

Determining Fairness:

The expected value of $1.91 is less than the cost of $3 per ticket, indicating it is not a fair game. To make it fair, the price per ticket should be set at $1.91.

Answer:

The number of Senators are 120 and number of Representatives are 440.

Step-by-step explanation:

Given,

Total number of members = 560

Solution,

Let the number of Senators be 'x'.

Since, the number of representatives is 160 less than five times the number of senators.

Framing the above sentence in equation form,we get the number of Representative.

So, number of Representative = [tex]5x-160[/tex]

Now, Total number of members is the sum of total number of Senators and total number of representative.

Total number of members = Total number of Senators + Total number of representative

On substituting the values, we get;

[tex]x+5x-160=560\\\\6x=560+160\\\\6x=720\\\\x=\frac{720}{6}\\\\x=120[/tex]

Total number of Senators = 120

So, number of Representative = [tex]5\times120-160=600-160=440[/tex]

Thus the number of Senators are 120 and number of Representatives are 440.

Answer:

A) quantitative

Step-by-step explanation:

A data that can be counted or expressed numerically constitute quantitative data. Quantitative data collection method is capturing statistical data in numbers, figures, or values. Quantitative data collection usually answered the questions of “how many?”, "how much?" and “how often?” are the occurrence of a particular data. These questions are quantitative data collection methods based on numbers and mathematical calculations. Quantitative data collection methods are based on random sampling and structured data collection. Some of the quantitative data collection methods are surveys, questionnaires, quizzes, interviews and direct observation.

Answer:

answer is the first option

Step-by-step explanation:

Answer:

A) 14 cm² per sec

B) 0 cm per sec

C) -28 cm per sec

Step-by-step explanation:

We know that,

If l = length of a rectangle and w = width of the rectangle

A) Area of a rectangle,

[tex]A=l\times w[/tex]

Differentiating with respect to t ( time )

[tex]\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}[/tex]

We have,

[tex]l=12\text{ cm}, w=5\text{ cm}, \frac{dw}{dt}=2\text{ cm per sec}, \frac{dl}{dt}=-2\text{ cm per sec}[/tex]

[tex]\frac{dA}{dt}=12\times 2+5\times -2[/tex]

[tex]\frac{dA}{dt}=24-10[/tex]

[tex]\frac{dA}{dt}=14\text{ square cm per sec}[/tex]

B) Perimeter of the rectangle,

[tex]P=2(l+w)[/tex]

Differentiating with respect to t ( time ),

[tex]\frac{dP}{dt}=2(\frac{dl}{dt}+\frac{dw}{dt})=2(-2+2)=0[/tex]

C) Length of the diagonal,

[tex]D=\sqrt{l^2+w^2}[/tex]

[tex]D^2 = l^2 + w^2[/tex]

Differentiating with respect to t ( time ),

[tex]2D\frac{dD}{dt}=2l\frac{dl}{dt}+2w\frac{dw}{dt}[/tex]

Since, if l = 12 cm, w = 5 cm,

[tex]D=\sqrt{12^2+5^2}=\sqrt{144+25}=\sqrt{169}=13\text{ cm}[/tex]

[tex]\implies 2\times 13 \frac{dD}{dt}=2(12)(-2)+2(5)(2)[/tex]

[tex]26\frac{dD}{dt}=-48+20=-28\text{ cm per sec}[/tex]

Using implicit differentiation, it is found that:

a) The rate of change of the area of the rectangle is: 14 cm²/sec.

b) The rate of change of the perimeter of the rectangle is: 0 cm/sec.

c) The rate of change of the lengths of the diagonal of the rectangle is: [tex]\mathbf{-\frac{14}{13}}[/tex] cm/sec.

Item a:

The area of a rectangle of length l and width w is given by:

[tex]A = lw[/tex]

Applying implicit differentiation, the rate of change is of:

[tex]\frac{dA}{dt} = w\frac{dl}{dt} + l\frac{dw}{dt}[/tex]

For this problem, the values are:

[tex]w = 5, \frac{dl}{dt} = -2, l = 12, \frac{dw}{dt} = 2[/tex]

Then:

[tex]\frac{dA}{dt} = 5(-2) + 12(2)[/tex]

[tex]\frac{dA}{dt} = 14[/tex]

The rate of change of the area is of 14 cm²/sec.

Item b:

The perimeter is given by:

[tex]P = 2l + 2w[/tex]

Applying implicit differentiation, the rate of change is of:

[tex]\frac{dP}{dt} = 2\frac{dl}{dt} + 2\frac{dw}{dt}[/tex]

Then

[tex]\frac{dP}{dt} = 2(-2) + 2(2) = 0[/tex]

The rate of change of the perimeter is of 0 cm/sec.

Item c:

The diagonal is the hypotenuse of a right triangle in which the sides are the length and the width, then, applying the Pythagorean Theorem:

[tex]d^2 = l^2 + w^2[/tex]

The value of the diagonal is:

[tex]d^2 = 5^2 + 12^2[/tex]

[tex]d^2 = 169[/tex]

[tex]d = \sqrt{169}[/tex]

[tex]d = 13[/tex]

The rate of change is:

[tex]2d\frac{dd}{dt} = 2l\frac{dl}{dt} + 2w\frac{dw}{dt}[/tex]

Then

[tex]26\frac{dd}{dt} = -48 + 20[/tex]

[tex]26\frac{dd}{dt} = -28[/tex]

[tex]\frac{dd}{dt} = -\frac{14}{13}[/tex]

The rate of change of the lengths of the diagonals of the rectangle  is of [tex]\mathbf{-\frac{14}{13}}[/tex] cm/sec.

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Answer:

floor

Step-by-step explanation:

price floor is a situation when the price changed is greater or leave than the equilibrium price determined by the force of demand and supply. For a price floor to be effective, the minimum price has to be higher than the equilibrium price. It must be set above the equilibrium price. The opposite of price floor is price ceiling.

Answer:

The expression representing the Total Cost of the item is  [tex]P + 0.07P[/tex].

Step-by-step explanation:

Given:

Price of Certain item = 'P' dollars

Sales tax =7%

We need to find the expression for Total Cost of the item when tax is applied.

we will first find the Amount deducted in tax;

Amount deducted in Tax is equal to Percentage of sales tax multiplied by Price of Certain item and then divide by 100

Framing in equation form we get;

Amount Deducted in Tax  = [tex]\frac{7}{100}\times P = 0.07P[/tex]

Now Total Cost of the item is equal to sum of Price of Certain item and Amount deducted in tax.

Expressing in expression form we get;

Total Cost of item = [tex]P + 0.07P[/tex]

Hence The expression representing the Total Cost of the item is  [tex]P + 0.07P[/tex].

Answer:

Step-by-step explanation:

Given

Circle has radius [tex]r=5 in.[/tex]

Area of the sector is given by

[tex]A_s=\frac{\theta }{2\pi }\times \pi r^2[/tex]

if [tex]A_s[/tex] is one-sixth  of area of circle then

[tex]A_s=\frac{\pi r^2}{6}[/tex]

[tex]\frac{\pi r^2}{6}=\frac{\theta }{2\pi }\times \pi r^2[/tex]

[tex]\theta =\frac{2\pi }{6}=\frac{\pi }{3}\ radian[/tex]

If [tex]A_s[/tex] is one-fourth of area of circle then

[tex]A_s=\frac{\pi r^2}{4}[/tex]

[tex]\theta =\frac{2\pi }{4}[/tex]

[tex]\theta =\frac{\pi }{2}[/tex]

The cost will be the same when 1 shirt is ordered.

Cost Comparison

Option 1: Cost = $41 (setup fee) + $10 (shirt price)

Option 2: Cost = $36 (setup fee) + $15 (shirt price)

Let's assume the number of shirts is 'x'.

Equating the costs of both options:

$41 + $10x = $36 + $15x

$5x = $5

x = 1

Therefore, the cost will be the same for 1 shirt.

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Answer: there are 10 multiple choice questions and 15 short-answer questions

Step-by-step explanation:

Let x represent the number of multiple choice questions in the test.

Let y represent the number of short-answer questions in the test.

If the test has 25 questions, it means that

x + y = 25

Multiple-choice questions are worth 2 points, and short-answer questions are worth 4 points. The test is worth a total of 80 points. It means that

2x + 4y = 80 - - - - - - - -1

Substituting x = 25 - y into equation 1, it becomes

2(25 - y) + 4y = 80

50 - 2y + 4y = 80

- 2y + 4y = 80 - 50

2y = 30

y = 30/2 = 15

x = 25 - y = 25 - 15 = 10

A. The number of multiple-choice questions plus the number of short-answer questions is 25.

Answer:

A makes the most sense

Step-by-step explanation:

as if you don't get tricked and notice that C and D are not true but between A and B are two answers but B isn't correct if you go over what it means without getting tricked and A is to be the right answer

Answer:

h=12, w=24, t=8

Step-by-step explanation:

System of Linear Equations

We have 3 unknown variables and 3 conditions between them. They form a set of 3 equations with 3 variables.

We have the following data, being  

w = price of a sweatshirt

t = price of a T-shirt

h = price of a pair of shorts

19.

The first condition states the price of a sweatshirt is twice the price of a pair of shorts. We can write it as

[tex]\displaystyle w=2h[/tex]

The second condition states the price of a T-shirt is $4 less than the price of a pair of shorts. We can write it as

[tex]\displaystyle t=h-4[/tex]

The final condition states Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for $136, thus

[tex]\displaystyle 3w+2h+5t=136[/tex]

This is the system of equations we need to solve for w,t,h

20.

To solve the system, we replace w in terms of h and t in terms of h. Those relations have been already written, so

[tex]\displaystyle 3(2h)+2h+5(h-4)=136[/tex]

Operating

[tex]\displaystyle 6h+2h+5h-20=136[/tex]

[tex]\displaystyle 13h=156[/tex]

Solving for h

[tex]\displaystyle h=12[/tex]

The other two variables are

[tex]\displaystyle w=2h=24[/tex]

[tex]\displaystyle t=12-4=8[/tex]

Answer:

[tex]H_{0}: \mu \leq 600\text{ dollars}\\H_A: \mu > 600\text{ dollars}[/tex]

Step-by-step explanation:

We are given the following in the question:

Manager's claim: The mean guest bill for a weekend is $600 or less.

A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months.

A sample of weekend guest bills were collected to test the manager’s claim.

We design the null and alternate hypothesis in the following manner:

[tex]H_{0}: \mu \leq 600\text{ dollars}\\H_A: \mu > 600\text{ dollars}[/tex]

Conclusion when null hypothesis cannot be rejected:

When we fail to reject the null hypothesis and accept the null hypothesis, thus, we have enough evidence to support the manager's claim that the mean guest bill for a weekend is $600 or less.

Conclusion when null hypothesis can be rejected:

When the null hypothesis is rejected, we accept the alternate hypothesis.

Thus, there are not sufficient evidence to support the manager's claim  that the mean guest bill for a weekend is $600 or less.

Answer:

C. There were 6,27 times as many people who visited the aquarium on the seventh day as on the first day.

Explanation:

[tex]\displaystyle 1,3^7 = 6,2748517 ≈ 6,27[/tex]

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Answer:

5.5 years old.

Step-by-step explanation:

Let D represent present age of Robert's dog and C represent present age of Karen's cat.

We have been given that Robert's dog is 4 years older than Karen's cat. We can represent this information in an equation as:

[tex]D=C+4...(1)[/tex]

We are also told that in 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. After 3 years age of dog and cat would be [tex]D+3[/tex] and [tex]C+3[/tex] respectively.

We can represent this information in an equation as:

[tex]D+3+C+3=13...(2)[/tex]

From equation (1), we will get:

[tex]C=D-4[/tex]

Upon substituting this value in equation (2), we will get:

[tex]D+3+D-4+3=13[/tex]

Combine like terms:

[tex]2D+2=13[/tex]

[tex]2D+2-2=13-2[/tex]

[tex]2D=11[/tex]

[tex]\frac{2D}{2}=\frac{11}{2}[/tex]

[tex]D=5.5[/tex]

Therefore, Robert's dog is 5.5 years old right now.

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