Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Betty is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $51 for the meal, plus $2 per pound for the lobster she picks. At the second restaurant, Betty would pay $3 per pound for the lobster, in addition to $15 for the meal. Betty realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Betty pay for her dinner? What is the weight?


Dinner would cost $ __ at either restaurant if Betty's lobster weighed __ pounds.

The average speed of Paul Revere's horse, assuming he rode straight to Lexington without stopping, would have been approximately 25.4 miles per hour.

To find the average speed of Paul Revere's horse, we can use the formula:

average speed = total distance / total time

In this case, the total distance is 11 miles, and the total time is 26 minutes, or 0.4333 hours (since there are 60 minutes in an hour).

So, the average speed of Paul Revere's horse would be:

average speed = 11 miles / 0.4333 hours

average speed ≈ 25.4 miles per hour

Therefore, the average speed of Paul Revere's horse, to the nearest tenth of a mile per hour, would have been 25.4 miles per hour.

Using the formula for average speed, we can calculate that Paul Revere's horse would have had to travel at an average speed of approximately 25.4 miles per hour to cover the 11-mile distance in 26 minutes. This assumes that he rode straight through without stopping.

Learn more about average speed here:

https://brainly.com/question/25005020

#SPJ4

The complete question is:

On April 18, 1775, Paul Revere set off on his midnight ride from Charlestown to Lexington. If he had ridden straight to Lexington without stopping, he would have traveled 11 miles in 26 minutes. In such a ride, what would the average speed of his horse have been, to the nearest tenth of a mile per hour?

Answer:

Step-by-step explanation:

The correct answer is C. Shading will be above the y=-2x+1 line but below the y= 3x-1 line.

The line y=-2x+1 is a line with a slope of -2 and a y-intercept of 1. It represents the solutions that are greater than -2x+1.

The line y=3x-1 is a line with a slope of 3 and a y-intercept of -1. It represents the solutions that are less than 3x-1.

So, when you graph both of these lines on the same coordinate plane, the solutions that satisfy both inequalities will be the region that is above the line y=-2x+1 but below the line y=3x-1, and this is the region that will be shaded.

The approximate length of arc CB is given as follows:

14.17 cm.

The circumference of a circle of radius r is given by the multiplication of 2 by the number π = 3.14 and the radius r, as follows, hence the equation is given as follows:

C = 6.28r.

The radius for this problem is given as follows:

r = 7 cm.

The angle relative to arc CB is given as follows:

2 x 58º = 116º.

As an entire circumference has an angle of 360º, the approximate length of arc CB is obtained as follows:

116/360 x 6.28 x 7 = 14.17 cm.

More can be learned about the radius of a circle at brainly.com/question/24375372

#SPJ1

The value of x that makes the shape a parallelogram is 2/3

A quadrilateral is a polygon that has four sides and four angles. Types of quadrilaterals are kite, square, rectangle, parallelogram and so on.

A parallelogram is a quadrilateral with two pairs of parallel sides. Each parallel sides are equal. Also, the diagonals of a parallelogram bisect each other.

From the diagram, the diagonals bisect each other in other to be a parallelogram, hence:

6x = 3x + 2

3x = 2

x = 2/3

The value of x is 2/3

Find out more on parallelogram at: https://brainly.com/question/970600

#SPJ1

The population of the city has decreased by 15%.

Percentage refers to a way of expressing a number as a fraction of 100, and is often represented by the symbol (%).

To find the percent decrease, we need to determine the difference between the original population and the new population. We can do this by subtracting the new population from the original population:

322,000 - 273,700 = 48,300

This means that the population has decreased by 48,300. To find the percentage decrease, we need to express this as a percentage of the original population. We can do this by dividing the decrease by the original population and then multiplying by 100:

(48,300 / 322,000) x 100 = 15%

To know more about percentage here.

https://brainly.com/question/13729841

#SPJ4

The solution is Option A.

The conversion factor should have gallons in the denominator and the equation will be 350 gallons = 92.3 L

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the amount of gallons of water be = 350 gallons

And , 1 gallon = 3.79 liters

So , the amount of 350 gallons = ( 350 ) x ( 1/3.79 ) L

Substituting the values in the equation , we get

The amount of 350 gallons = ( 350 / 3.79 ) L

On simplifying the equation , we get

The amount of 350 gallons = 92.3 L

Therefore , while converting the gallons to liters , the factor of gallons should be in the denominator

Hence , the equation is 350 gallons = 92.3 L

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

Answer:

304

Step-by-step explanation

it was on my quiz

Answer:

The number 304 is exactly halfway between 61 and 547.

Step-by-step explanation:

To find the halfway point between two given numbers we can simply add them together then divide them by 2.

Note:

let [tex]N[/tex] be the number that is halfway

[tex]N=\frac{547+61}{2}[/tex]

[tex]N=\frac{608}{2}[/tex]

[tex]N=304[/tex]

Answer:

firstly, I would fill up the 10-oz glass with juice and use it to fill the 6-oz glass. This would leave me with 4 oz left in the 10-oz glass

Step-by-step explanation:

Equating the mathematical expressions, for the total costs of both companies to be the same, Jayden and Ramon must buy about 7 shirts.

A mathematical expression consists of the combination of variables, values, constants, and numbers using mathematical operands.

A mathematical expression is not the same as an equation, which states that two mathematical expressions are equal.

                              Designs n More   Custom Creations

Design Fee                       $10                        $0

Variable cost per shirt    $7.50                   $9.00

Let the number of shirts = x

Designs n More's total costs = 10 + 7.5x ... Expression 1

Custom Creations' total costs = 9x ... Expression 2

For the total costs of both companies to be the same, the two expressions for their total costs will be equal:

10 + 7.5x = 9x

10 = 1.5x

x ≈ 7

Thus, approximately, 7 shirts need to be bought for the total costs to be the same.

Learn more about mathematical expressions at https://brainly.com/question/1859113.

#SPJ1

How many shirts will make the two companies' total costs the same?

Answer:

3x² + 9x + 1

Step-by-step explanation:

5x - 2 + 3x² + 4x + 3

= 9x - 2 + 3x² + 3

= 9x + 1 + 3x²

= 3x² + 9x + 1

68.5% of Colton's gross pay is take-home pay. To find the percentage of Colton's gross pay that is take-home pay, we need to divide his net pay by his gross pay and then multiply by 100 to convert the resulting decimal to a percentage.

To find the percentage of Colton's gross pay that is take-home pay, we need to divide his net pay by his gross pay and multiply the resulting decimal by 100 to express it as a percentage. Colton's gross pay is $1421.50 and his net pay is $973.48. Dividing the net pay by the gross pay gives a result of 0.685, or 68.5% when converted to a percentage. This means that 68.5% of Colton's gross pay is take-home pay, or the amount of money that he receives after deductions are made. Therefore, Colton's take-home pay is $973.48, which is 68.5% of his gross pay.

Learn more about percentages here: brainly.com/question/16797504

#SPJ4

Answer: 27

Step-by-step explanation:

8^x+1 = 64

8^x+1 = 8²

x+1 =2

x = 2 - 1

x = 1

To Find :

3^2x +1

Substitute the value of x :

3^2(1)+ 1

3^2+1

3^3

27

The steps to set up the study and the limitations that would be faced are explained below .

The Steps to setup the study are  :

(i) Recruit a large and diverse group of participants who are willing to stick to the prescribed diets for the duration of the study.

(ii) Divide the participants randomly into two or more groups. One group would be given a diet high in trans fats, and the other group(s) would be given a diet low in trans fats.

(iii) Monitor the health status of the participants closely throughout the study .

(iv) At the end of the study, compare the health outcomes of the different groups of participants to determine whether there is a significant difference in health outcomes .

The Limitations of this type of study include :

⇒ the difficulty of controlling all aspects of participants' diets, since participants may consume other foods outside of what is provided to them.

⇒ the study may not be long enough to detect long-term effects of trans fats on health.

Learn more about Feeding Trial here

https://brainly.com/question/5249450

#SPJ4

The given question is incomplete , the complete question is

One way that researchers study the effects of trans fats on people's health is by setting up controlled experiments. For example, in an experimental feeding trial, participants agree to stick to specific diets that the researchers prescribe. In this case, the researchers might vary the proportions of saturated, unsaturated, and trans fats in the diet of each participant. Throughout the study, the health status of the participants is monitored closely.

Suppose that you are a researcher designing an experimental feeding trial. How would you set up your study and what limitations would you face ?

The speed of both the trains would be 400 mph and 450 mph respectively.

The formula to calculate the distance travelled is -

Distance = Speed x Time

Given is that two cities are 1020 miles apart. Two trains simultaneously left these cities heading toward one another. The speed of one train was 10 mph greater than the speed of the other one. In 5 hours, the trains had not met yet and were 170 miles apart.

Let the speed of one train be {x} mph. Then, the speed of the other train would be {x + 10} mph.

Distance covered by both the trains would be -

train { 1 } = 5x                             ... { 1 }

train { 2 } = 5(x + 10)                          ... { 2 }

Now, we can write -

1020 - {5x + 5(x + 10)} = 170

1020 - 170 = 10x + 50

10x = 800

x = 80

Speed of train { 1 } = 400 mph

Speed of train { 2 } = 450 mph

Therefore, the speed of both the trains would be 400 mph and 450 mph respectively.

To solve more questions on kinematics, visit the link below

https://brainly.com/question/30344224

#SPJ9

The depth of an Olympic pool that goes to 50 ft. deep can be expressed as:

d = 50 ft.

Olympic pool is a type of swimming pool that is used for competitive swimming and diving events. These pools typically have a uniform depth, a smooth and flat bottom and multiple lanes for swimmers to compete in.

The depth of an Olympic pool that goes to 50 ft. deep can be expressed as:

d = 50 ft.

Where d is the depth of the pool. This expression simply states that the depth of the pool is equal to 50 ft.

Learn more about Olympic pool here : brainly.com/question/30052350

#SPJ1

Answer:

1020 handshakes including the bride and the groom. 980 excluding the groom and the bride.

Step-by-step explanation:

(20*19) twenty people on the brides side shake hands with the other 19 people (19 because you can't really shake your own hand).

+(20*30) twenty people on the brides side shake hand with 30 people on the grooms side.

+(20*2) twenty people on the brides side shake hands with the bride and the groom.

this equalssss......

1020!!!!

Since the grooms family does hugs instead of handshakes, you'd only calculate how many the brides side does.

Using unit conversions the total height change from the top of mount Everest to the bottom of the Mariana trench is 12.3 miles

We know that 1 km = 0.62136 miles and 1 foot = 0.000189 miles

Depth of Mariana Trench (d) = 11 km = 11 × 0.62136

                                                          = 6.835 miles

Height of Mount Everest (h) = 29000 ft = 29000 × 0.000189

                                                              = 5.492 miles

Therefore the total height difference top of Mount Everest and to bottom of the Mariana Trench is given by

H = Depth of Mariana Trench + Height of Mount Everest

H = d + h

H = 6.835 miles + 5.492 miles

H = 12.327 miles

H = 12.3 miles

To learn more about unit conversions here:

brainly.com/question/19420601

#SPJ4

Answer: 5 Months

Step-by-step explanation:

Alright, we know he will make $120 a month (since 50 + 70 = 120)

(Let's have months=m)

So now we need to figure out for how many months (m) will he need to get to $600.

We know 120 a month so we can get the equation: 120m=600

Now all we have to do is solve for m

Divide both sides by two to get m=5

Checking Answers

70(5)=350

50(5)=250

250+350=600

So this solution works.

Answer: 5 months

Step-by-step explanation: so, what you have to do is add up 120 5 times so in total you will have 600 so the answer is 5 months.

Answer:

p + (m × 1) = t

If a plant is already ___cm tall and it will grow one cm every month, an equation to find out how much the plant grew in __ months is this:

(Let t = total number of centimeters, m = number of months, and p = the length of the plant already.)

Therefore, the equation you can use is p + (m × 1) = t.

On solving the provided question, we cans ay that  in this triangle by Pythagorean theorem [tex]A^2 = B^2 + C^2[/tex] => AC = [tex]\sqrt{115}[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here, in this triangle by Pythagorean theorem

[tex]A^2 = B^2 + C^2[/tex]

AC = [tex]\sqrt{14^2 - 9^2}[/tex]

AC  = [tex]\sqrt{196 - 81}[/tex]

AC = [tex]\sqrt{115}[/tex]

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Step-by-step explanation:

Use PEMDAS (Order of operations).

Simplify exponents

33554432 - 1048576 + 54288

Add and subtract (left to right)

33030144

63 goes into 33030144 524288 times.

Answer:

2^19(63)

Step-by-step explanation:

(2^5)^5-(2^4)^5+2^19

2^25-2^20+2^19

2^19(2^6-2+1)

2^19(64-2+1)

2^19(63)

well, since we know that one root is 5, that is a factor of it is (x-5), so hmmm by the remainder theorem we also know that if we plug "5" as our argument in our f(x), that is, if we do f(5), it must result to 0. so f(5) = 0, if that's so then

[tex]2x^2+bx-10=f(x)\implies 2(5)^2+b(5)-10=f(5) \\\\\\ 2(5)^2+b(5)-10=0\implies 50+5b-10=0\implies 5b=-40 \\\\\\ b=\cfrac{-40}{5}\implies \boxed{b=-8} \\\\[-0.35em] ~\dotfill\\\\ 2x^2-8x-10=0\implies 2(x^2-4x-5)=0\implies 2\stackrel{ {\Large \begin{array}{llll} x=-1 \end{array}} }{(x+1)}(x-5)=0[/tex]

Answer: about 1587 cm^2

Step-by-step explanation: The equation for area of circle is A= πr^2 OR A= (pi/4)d^2

Given the diameter is 46.7, the radius would be half of that which is 23.35.

Simply plug it into the equation

A =  π23.35^2

OR

A= (π/4)46.7^2

Since you are using 3 in place of pie, it would be 3(23.35)^2  OR (3/4)46.7^2

the answer i got was 1,635 cm^2 so your closest choice to that is 4

Answer:

x = 4

Step-by-step explanation:

2x - 3 = 5   Add 3 to each side

2x - 3 + 3 = 5 + 3

2x = 8  Divide both sides by 2

[tex]\frac{2x}{2}[/tex] = [tex]\frac{8}{2}[/tex]

x = 4

Answer:

123.88 square units

Step-by-step explanation:

r = radius of circle

  = radius of sector

 = Length of LM

 = Length of MN

 = 13 units

When the angle is measured in degrees:
Area of a sector: [tex]\frac{Angle OfSector}{360^{o}}[/tex]× [tex]\pi r^{2}[/tex]

                = [tex]\frac{84}{360}[/tex]×[tex][\pi (13)^{2}][/tex]

                = 123.883 [tex]units^{2}[/tex]

                = 123.88 square units (Rounded to the nearest hundredth)

Answer: 6 containers

Step-by-step explanation:

Fraction division.

2/3 divided by 1/8.

Keep-change-flip. (or a similar method for dividing fractions)

2/3 times 8/1 is 16/3.

He will fill 5 and 1/3 containers, so 6 containers will have paint in them.

(っ◔◡◔)っ ♥

Hope this helps.

MM4343

Using the unitary method, we find that the store created approximately 37 bags with 15 random cards in each bag.

This problem can be solved using the unitary method. It is given that the

number of Anniversary cards is 163,

number of Birthday cards is 258,

number of Get Well cards is 98

and the number of Thank you cards is 47

So, the total number of cards will be equal to the sum of all these cards, that is,

163+258+98+47

= 566 cards

To create bags of 15 random cards, we have to divide the total number of cards by 15  which gives,

566/15 = 37.734

Thereby, we can say that the store created approximately 37 bags with 15 random cards in each bag.

Learn more about the unitary method on

https://brainly.com/question/23423168?referrer=searchResults

#SPJ4