Answer:
a) [tex] P(t) =1600 +50t[/tex]
b) [tex] P(t) = 1600 (1.05)^t[/tex]
Step-by-step explanation:
Assuming the complete question : "A town has a population of 1000 people at time t = 0. In each of the following cases, write a formula for the population, P, of the town as a function of year t. (a) The population increases by 50 people a year. (b) The population increases by 5% a year."
Part a
For this case we can use a linear model in order to estimate the population size since we have a fixed increase each year. So our model would be given by:
[tex] P(t) = P_o + b t[/tex]
Where [tex] b =50[/tex] on this case since represent the increase per year of the slope for the linear model. And the initial amount is [tex] P_o = 1600[/tex], so then the model is:
[tex] P(t) =1600 +50t[/tex]
Part b
For this case we have a rate of increase and when we have this the lineal model is not the most appropiate. So then we can use an exponential model given by:
[tex] P(t) =P_o b^{t}[/tex]
Where [tex] P_o = 1600[/tex] represent the initial population and for this case b is the rate of increase [tex] b = 1+0.05 = 1.05[/tex] since each year we have an increase of 5% and t is the time. So then the model is given by:
[tex] P(t) = 1600 (1.05)^t[/tex]
The population of a town can be calculated through formulas for linear growth (P = P0 + rt) and exponential growth (P = P0 * e^(rt)), depending on whether the population grows by a fixed amount or percentage each year. To use these formulas, the specific growth rate of the town is needed.
Explanation:The subject of the question is about writing formulas for population growth. Let's denote the initial population as P0, the rate of growth as r and the time in years as t. Here are two common formulas:
Linear growth: P = P0 + rt. If the population grows by a fixed amount each year, you can use this formula where r is the number of people the population grows by each year.Exponential growth: P = P0 * e^(rt). If the population grows by a fixed percentage each year, you can use this formula where r is the growth rate expressed as a decimal.To use these formulas, you'd need to know the specific growth rate of the town. It's also important to remember that actual population changes can be more complex and may not follow these exact formulas.
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Construct a dotplot for the following data. 4.85 4.94 5.12 5.14 4.80 4.99 5.19 4.94 4.85 5.12 5.04 4.96 5.28 5.05 4.83 5.27 5.12 5.19 4.89 5.15 5.04 5.17 5.24 5.04 4.91 5.26
Answer:
x frequency
4.8 1
4.83 1
4.85 2
4.89 1
4.91 1
4.94 2
4.96 1
4.99 1
5.04 3
5.05 1
5.12 3
5.14 1
5.15 1
5.17 1
5.19 2
5.24 1
5.26 1
5.27 1
5.28 1
find the dot plot as attached below
Step-by-step explanation:
Construct a dotplot for the following data. 4.85 4.94 5.12 5.14 4.80 4.99 5.19 4.94 4.85 5.12 5.04 4.96 5.28 5.05 4.83 5.27 5.12 5.19 4.89 5.15 5.04 5.17 5.24 5.04 4.91 5.26
Rearranging the data into frequency table
x frequency
4.8 1
4.83 1
4.85 2
4.89 1
4.91 1
4.94 2
4.96 1
4.99 1
5.04 3
5.05 1
5.12 3
5.14 1
5.15 1
5.17 1
5.19 2
5.24 1
5.26 1
5.27 1
5.28 1
The recommended angle for a wheel chair ramp is 5 degrees. If the rise of the ramp to go up the steps is 2 feet, find the horizantal run length that the ramp must start. (Round to one decimal place)
wheel chair ramp
Answer:
22.9 feet
Step-by-step explanation:
You are using Tangent because you have the opposite and adjacent sides
Tan 5 = 2/x
x Tan 5= 2
x= 2/Tan5
= 22.860
To find the horizontal run length of a wheelchair ramp with a 5-degree angle and a 2-foot rise, use the tangent function of trigonometry. Plug the given values into the tangent formula, rearrange to solve for 'Run', and calculate to get a run length of approximately 22.8 feet.
Explanation:The question is referring to the use of trigonometry to solve real-life problems. Here, we are going to use the tangent of the angle, which is defined as the ratio of the opposite side (the rise) to the adjacent side (the run). In this case, we know that the angle is 5 degrees and the rise is 2 feet.
In mathematical terms, this can be written as:
Tan(ρ) = Rise/Run
Substituting the values into the equation, we get:
Tan(5°) = 2/Run
Solving for Run, we get:
Run = 2/Tan(5°)
You can find this value using a calculator, rounding to the nearest tenth, to get the run as approximately 22.8 feet.
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In May, the school store sells 80 erasers. In June, the store sells only 16 erasers. What is the percent of change in erasers sold from May to June?A) 80% B) 20% C) 64% D) 80%
Answer: 80%
Step-by-step explanation:
Since we have given that
Number of erasers sold in May = 80
Number of erasers sold in June = 16
Decrement in 1 month gap is given by
16-80=-64
So, Percentage of change in erasers sold from May to June is given by
[tex]\frac{-64}{80}[/tex] × 100
= -80% (Decreased 80%)
Answer:
80%
Step-by-step explanation:
I took a test with this question on it
A 25-foot ladder rests against a building. The base of the ladder is 15 feet away from the base
of the building. At what height does the ladder rest on the building?
Answer: the top of the ladder is 20ft below the ground.
Step-by-step explanation:
The ladder makes an angle, θ with the ground thus forming a right angle triangle with the wall of the house.
The length of the ladder represents the hypotenuse of the right angle triangle.
The ground distance between the base of the house and the base of the ladder represents the adjacent side of the right angle triangle.
Therefore, to determine the height at which the ladder rest on the building, x, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
25² = x² + 15²
625 = x² + 225
x² = 625 - 225 = 400
x = √400 = 20 ft
To receive a grade of A on 80 question test 90% of the questions must be answered correctly what is the maximum number of questions that can't be missed to still receive an A
Answer:
Step-by-step explanation:
Total number of questions in the test is 80.
To receive a grade of A on the 80 question test, 90% of the questions must be answered correctly. It means that the number if questions that must be answered correctly would be
90/100 × 80 = 0.9 × 80 = 72.
Therefore, the maximum number of questions that can't be missed to still receive an A is 72
A 76.00 pound flask of mercury costs $162.50. The density of mercury is 13.534g/cm 3.
A. Find the price of one cubic inch of mercury by calculating intermediate values.
B. What is the price of one pound of mercury?
C. What is the price of one gram of mercury?
D. What is the price of one cubic centimeter of mercury?
E. What is the price of one cubic inch of mercury?
Answer:
a) 1805.55$
b) 2.14$
c)0.005$
d)0.064$
e)1805.55$
Step-by-step explanation:
Density of mercury is 844.9 lb/ft3.
a) 76 pound flask of mercury is 76/844.9=0.09 ft^3. 0.09 ft^3 mercury cost 162.5$, then 1 ft^3 mercury is
[tex]p=(162.5/0.09)=1805.55[/tex]
1805.55$
b) One pound of mercury is 2.14$
[tex]p=162.5/76=2.14[/tex]
c)76 pound equals 34473 grams. It makes:
[tex]p=162.5/34473=0.005[/tex]
0.005$ is the price of one gram mercury.
d)Total amount of mercury is 34473 grams. Then total volume of mercury is:
[tex]V=34473/13.534=2547.14[/tex]
2547.14 cm3. And the unit price is:
[tex]p=162.5/2547.14=0.064[/tex]
e) 1805.55$. It is found already.
Find the distance between the pair of points given on the graph
Answer: distance = 5
Step-by-step explanation:
The formula for determining the distance between two points on a straight line is expressed as
Distance = √(x2 - x1)² + (y2 - y1)²
Where
x2 represents final value of x on the horizontal axis
x1 represents initial value of x on the horizontal axis.
y2 represents final value of y on the vertical axis.
y1 represents initial value of y on the vertical axis.
From the graph given,
x2 = 1
x1 = - 2
y2 = 0
y1 = - 4
Therefore,
Distance = √(1 - - 2)² + (0 - - 4)²
Distance = √3² + 4² = √9 + 16 = √25
Distance = 5
A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election.
Which of the following statements is true about the percentages?
a. 72% is a sample; 56% is a population.
b. 72% and 56% are both statistics.
c. 72% is a statistic and 56% is a parameter.
d. 72% is a parameter and 56% is a statistic.
e. 72% and 56% are both parameters.
Answer: c. 72% is a statistic and 56% is a parameter.
Step-by-step explanation:
A population is a large group of all possible observations required for a study by the researcher's point of view.A Sample is a finite subset of population that is used by researcher to represent the entire population in an analysis.A parameter is a number that measure a characteristic for the entire population.A statistic is a number that measure a characteristic for the sample.A statistics given an estimate to the population parameter.Given : A study of voting chose 663 registered voters at random shortly after an election.
Population of interest : "registered voters"
Sample : " 663 registered voters "
72% of 663 registered voters said they had voted in the election.
⇒ Statistic = sample proportion registered voters voted in the election.= 72%
Election records show that only 56% of registered voters voted in the election.
⇒ Parameter = Population proportion of registered voters voted in the election = 56%
Hence, the correct answer is "c. 72% is a statistic and 56% is a parameter."
Find f(-1) when f(x)=x^2-3x+6
Answer:
f(-1) = 10
Step-by-step explanation:
f(x)=x² - 3x + 6
when x = -1, substitute x=-1 into the equation above
f(-1) = (-1)² - 3(-1) + 6
= 1 + 3+6
= 10
x2 - 2x - 24 = 0
Solve for X
Answer:
x = 6 or x = -4
Step-by-step explanation:
x^2 - 2x - 24 = 0
(x - 6)(x + 4) = 0
x - 6 =0 or x + 4 = 0
x = 6 or x = -4
Mattie is making a collar for her dog. She needs to buy some chain,a clasp, and a name tag. She wants the chain to be 40 centimeters long. One meter of chain costs $9.75. The clasp is $1.29 and the name tag is$3.43. How much will it cost to make a collar?
Answer:the total cost of the collar is $5.11
Step-by-step explanation:
To make a collar for her dog, she needs to buy some chain,a clasp, and a name tag.
The length of the chain that she wants to buy is 40 centimeters.
1000 centimeters = 1 meter
40 centimeters = 40/1000 = 0.04 meters.
One meter of chain costs $9.75. Therefore, 0.04 meters of chain would cost
0.04 × 9.75 = $0.39
The clasp is $1.29 and the name tag is $3.43. Therefore, the total cost of the collar would be
0.39 + 1.29 + 3.43 = $5.11
The demand d for a companys product cost x is predicted by the function d(x) = 500-2x. The price p in dollars that the company can charge for the product is given by p(x)=x+5
The student is given two functions, d(x) = 500-2x and p(x) = x+5, which represent the demand and price, respectively, of a company's product. To find the relationship between price and quantity, we can substitute the demand function into the price function.
Explanation:The subject of this question is Mathematics. The student is given two functions, d(x) = 500-2x and p(x) = x+5, which represent the demand and price, respectively, of a company's product. To find the relationship between price and quantity, we can substitute the demand function into the price function:
p(x) = x + 5 = d(x) + 5 = (500 - 2x) + 5 = 505 - 2x
So the price can be represented by the equation p(x) = 505 - 2x.
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Find x.
- show details and examples to show your answer.
Answer: 17.3
Step-by-step explanation:
Since it is a right angled triangle , we will use the application of SOHCAHTOA in solving it ,which means
sine Ф = opposite / hypotenuse
cosine Ф = adjacent / hypotenuse
Tangent Ф = opposite / adjacent
Ф stands for the given angle.
From the diagram , the given angle is 25 ,this means that
opposite = x
hypotenuse = 41
This means that we will use sine Ф = opposite / hypotenuse to find the value of x.
Therefore:
sin 25 = x/41
x = 41 sin 25
x = 41 x 0.4226
x = 17.3273
x ≈ 17.3
Johnny must learn more than 10 New Pl. Before the big game you're already learned for writing and recording that represents how many more players he needs to learn to reach his goal
Question is Incomplete; Complete question is given below;
Johnny must learn more than 10 new plays before the big game. He has already learned 4. Write and solve the inequality that represents how many more plays he needs to learn to reach his goal?
Answer:
The Inequality representing the more plays he needs to learn to reach his goal is [tex]x+4>10[/tex].
Johnny should learn more than 6 games to reach his goals.
Step-by-step explanation:
Given:
Number of plays to be learn [tex]>[/tex] 10
Number of plays already learned = 4
we need to write an inequality that represents how many more plays he needs to learn to reach his goal.
Solution:
Let the number of plays needed to learn more be 'x'.
So we can say that;
Number of plays already learned plus number of plays needed to learn more should be greater than total Number of plays to be learn.
framing in equation form we get;
[tex]x+4>10[/tex]
Hence the Inequality representing the more plays he needs to learn to reach his goal is [tex]x+4>10[/tex].
On solving the equality we get;
Subtracting both side by 4 we get;
[tex]x+4-4>10-4\\\\x>6[/tex]
Hence Johnny should learn more than 6 games to reach his goals.
For a project on Egypt, Nick is building a paper model of a square based pyramid. The square base measures 8 inches by 8 inches. The slant height is 10 inches. Which measurement BEST describes the amount of construction paper needed to make this pyramid? (round to nearest whole number)
Answer:
Step-by-step explanation:
The square base measures 8 inches by 8 inches. The slant height is 10 inches.
The formula for determining the area of the square base of the pyramid is l^2. Therefore,
Area of the base = 8^2 = 64 inches^2
The formula for determining the perimeter of the square base is
4l. It becomes
4 × 8 = 32 inches
The amount of construction paper needed to make this pyramid is the total surface area of the pyramid. Therefore,
Total surface area = (1/2 × 32 × 10) + 64
= 160 + 64 = 224 inches^2
Nick will need approximately 224 square inches of construction paper for his square based pyramid project with a base measuring 8 inches by 8 inches and a slant height of 10 inches.
Explanation:To find the amount of construction paper needed for Nick's square based pyramid project, we need to calculate the surface area of the pyramid. The surface area of a pyramid includes the area of the base plus the area of the four triangular sides.
The area of the base (Abase) is the side length squared:
Abase = side × side = 8 inches × 8 inches = 64 square inches.
The area of one triangular side (Atriangular side) is given by the formula:
Atriangular side = 1/2 × base × slant height.
For Nick's project, the base of a triangular side is equal to the side of the square, so:
Atriangular side = 1/2 × 8 inches × 10 inches = 40 square inches.
Since there are four identical triangular sides:
Total area of triangular sides = 4 × 40 square inches = 160 square inches.
Adding the base and triangular sides areas together gives us the total construction paper needed:
Total construction paper needed = Abase + Total area of triangular sides = 64 square inches + 160 square inches = 224 square inches.
Therefore, Nick will need approximately 224 square inches of construction paper for his project. To get the nearest whole number, we round 224 to 224.
Jaime claimes that when you multiply by 100, the decimal point moves to the right. Salome argue that the decimal point only moves when you multiply a whole number by 100. Salmon says that when you multiply a whole number by 100, product has 2 extra zeros. Which student got it correct? Justify your answer.
Answer:
Step-by-step explanation:
2.75×100=275.00
3=3.00×100=100.00
in either case decimal point moves to the right.
but in whole numbers 3=3
At the end of the season, the coach took ten students to burger box.The coach and three students ordered steak-on-a-bun while the other students ordered queen-size burgers. The total bill was $15.15. If a steak-in-a-bun cost $0.90 more than a queen-size burger, find the cost of one of each.
Answer:
Cost of steak-in-a-bun burger is $1.95 and cost of queen-size burger is $1.05.
Step-by-step explanation:
Let the cost of queen-size burger be 'q'.
Let the cost of steak-in-a-bun be 's'.
Given:
a steak-in-a-bun cost $0.90 more than a queen-size burger.
So we can say that;
[tex]s=0.9+q \ \ \ \ equation\ 1[/tex]
Given:
the coach took ten students to burger box.
Hence Number of person at burger box = 11
The coach and three students ordered steak-on-a-bun while the other students ordered queen-size burgers.
So we can say that;
Number of queen sized burger = 11 - 4 =7
Number of steak on a bun burger = 4
Also Given:
Total bill = $15.11
Now we can say that;
Total bill is equal to sum of Number of queen sized burger multiplied by Cost of queen sized burger and Number of steak on a bun burger multiplied by cost of steak on a bun burger.
framing in equation form we get;
[tex]4s+7q =15.15\ \ \ \ equation\ 2[/tex]
Substituting equation 1 in equation 2 we get;
[tex]4(0.9+q)+7q=15.15[/tex]
Applying distributive property we get;
[tex]3.6+4q+7q=15.15\\\\3.6+11q=15.15[/tex]
Subtracting both side by 3.6 we get;
[tex]3.6+11q-3.6 =15.15-3.6\\\\11q=11.55[/tex]
Dividing both side by 11 we get;
[tex]\frac{11q}{11}=\frac{11.55}{11}\\\\q=\$1.05[/tex]
Substituting the value of q in equation 1 we get;
[tex]s=0.9+q=0.9+1.05=\$1.95[/tex]
Hence Cost of steak-in-a-bun burger is $1.95 and cost of queen-size burger is $1.05.
Final answer:
The cost of one steak-on-a-bun is $2.055, and the cost of one queen-size burger is $1.155.
Explanation:
The student's question involves finding the cost of one steak-on-a-bun and one queen-size burger given that the total bill for a group order at a restaurant was $15.15 and that a steak-on-a-bun costs $0.90 more than a queen-size burger.
Let's define Q as the price of a queen-size burger.
Therefore, the price of a steak-on-a-bun would be Q + $0.90. According to the problem, four people (the coach and three students) ordered steak-on-a-bun, and six students ordered queen-size burgers.
The equation representing the total cost is:
4(Q + $0.90) + 6Q = $15.15
Solving for Q, we first expand the equation:
4Q + $3.60 + 6Q = $15.15
Combining like terms, we get 10Q + $3.60 = $15.15.
Subtracting $3.60 from both sides, we get 10Q = $11.55.
Dividing both sides by 10, we find that Q = $1.155, which is the cost of a queen-size burger.
Finally, the cost of a steak-on-a-bun is Q + $0.90 = $1.155 + $0.90 = $2.055.
The cost of one steak-on-a-bun is $2.055, and the cost of one queen-size burger is $1.155.
Charlie has two dimes for Nichols and some quarters in his pocket if the probability of drawing a quarter out of his pocket is 1/2 how many quarters does he
Answer:
He has 2 quarters in his pocket.
While our weight is typically displayed without decimal places (e.g., 165 lbs), it can be displayed with great decimal precision. Limited only by the precision we place on it, the variable of weight is ______.
Answer:
Continuous observation
Step-by-step explanation:
Generally, the weight of any person is displaced in whole numbers without the inclusion of decimal numbers. The decimal numbers are mostly rounded up to the whole number. Based on the argument made in the given problem, the type of weight variable for this type of analysis is known as continuous observation.
Alison bought jelly beans to share with her friends she bought 1 1/4 pounds of blueberry jelly beans and 2 1/3 pounds of Lemon Jelly Beans if she gave 1 and 2/3 pounds of jelly beans away to a friend how many pounds of jelly beans does she have left
After giving away 1 and 2/3 pounds of jelly beans, Alison has 4/3 pounds left.
Explanation:To find out how many pounds of jelly beans Alison has left after giving away 1 and 2/3 pounds, we need to subtract that amount from the total.
1 1/4 pounds + 2 1/3 pounds - 1 2/3 pounds = 2/4 + 7/3 - 5/3 = 8/12 + 28/12 - 20/12 = 16/12 = 4/3 pounds
Therefore, Alison has 4/3 pounds of jelly beans left.
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The student council memebers are making decorative labels to cover 20 identical empty coffee cans for charity drive. Each label will cover the entire lateral surface area of a can. Which is the closest to the lateral surface coffee can
Answer:
127.48 in²Explanation:
The image attached shows the dimensions of the coffe cans considered for this question.
The figure is a cylinder with dimensions:
[tex]\text {radius }3\frac{1}{16}\text {inches and height }6\frac{5}{8}\text {inches}[/tex]Thus, to find the lateral surface of a coffe can, you use the formula for the lateral area of a cylinder:
[tex]LA=2\pi\times r\times h[/tex]Where, LA is the lateral area, r is the radius, and h is the height.
Substituting the dimensions given in the figure, you get:
[tex]LA=2\pi\times 3\frac{1}{16}\times 6\frac{5}{8}[/tex]To multiply, first convert the mixed numbers into improper fractions:
[tex]3\frac{1}{16}=3+\frac{1}{16}=\frac{3(16)+1}{16}=\frac{48+1}{16}=\frac{49}{16}\\ \\ 6\frac{5}{8}=6+\frac{5}{8}=\frac{6(8)+5}{8}=\frac{48+5}{8}=\frac{53}{8}[/tex]
Now, you can multiply:
[tex]LA=2\pi\times \frac{49}{16}\times \frac{53}{8}[/tex][tex]LA=127.48in^2[/tex]James buys a 3 books from the bookstore for $39.99. He has a coupon for 25% off the original price. He is charged 8.5% sales tax. What is the total cost of his purchase?
Answer:
Step-by-step explanation:
The cost of the three books that James bought from the bookstore.
He has a coupon for 25% off the original price. This means that the amount by which the original price was reduced would be
25/100 × 39.99 = 0.25 × 39.99 = $9.8325
The cost of the books would be
39.99 - 9.8325 = $30.1575
He is charged 8.5% sales tax. This means that the amount paid for tax would be
8.5/100 × 30.1575 = 0.085 × 30.1575 = $2.56
the total cost of his purchase would be
2.56 + 30.1575 = $32.7175
Answer:
$32.7175
Step-by-step explanation:
Susan and Jim each on a lawn care business the amount Susan charges for lawn care by the hour is shown in the table 2 hours $48.03 hours $72.07 hours $168.11 hours
Question is Incomplete;Complete question is given below;
Susan and Jim each own a lawn care business. The amount Susan charges for lawn care is shown in the table. The amount him charges for lawn care is shown in the table.
What is the DIFFERENCE between Susan's and Jim's lawn care business in the amounts they charge for 10 hours at work ?
Susan
2 hrs $48
3 hrs $72
7 hrs $ 168
11 hrs $264
Jim
1 hr $20
2 hrs $40
3 hrs $60
4 hrs $80
5 hrs $100
6 hrs $120
A) $16
B) $20
C) $28
D) $40
Answer:
D) $40
Step-by-step explanation:
We need to find the DIFFERENCE between Susan's and Jim's lawn care business in the amounts they charge for 10 hours at work.
Solution:
First we will find the hourly charges of lawn care for both.
Given:
From the table of Jim we can see that
Charges of Jim for 1 hour = $20
So for 10 hour = Charges of Jim for 10 hour.
By using Unitary method we get;
Charges of Jim for 10 hour = [tex]10\times 20 =\$200[/tex]
Now From table of Susan we can see that;
for 2 hours = $48
So for 1 hour = Charges of Susan for 1 hour.
By Using Unitary method we get;
Charges of Susan for 1 hour = [tex]\frac{48}{2}= \$24[/tex]
Now we know that;
Charges of Susan for 1 hour = $24
So for 10 hour = Charges of Susan for 10 hour
again by using Unitary method we get;
Charges of Susan for 10 hour = [tex]24\times10 =\$240[/tex]
Now we need to find the difference between their charges.
Difference can be calculated by subtracting Charges of Jim for 10 hour from Charges of Susan for 10 hour.
framing in equation form we get;
Difference = [tex]\$240-\$200=\$40[/tex]
Hence The difference in the charges for 10 hour of work is $40.
if 12, 15, 18 and 16, 20, and x are the lengths of the corresponding sides of two similar triangles, what is the value of x?
To find the value of x for the corresponding sides of two similar triangles, we set up a proportion using the given sides.
Upon simplifying the ratio, x is calculated to be 24, which is the side length in the second triangle.
Explanation:To find the value of x in two similar triangles with side lengths 12, 15, 18 and 16, 20, x, we use the concept that corresponding sides in similar triangles have proportional lengths.
We start by setting up a proportion using the corresponding sides:
[tex]\(\frac{12}{16} = \frac{15}{20} = \frac{18}{x}\)[/tex]
We can simplify the first two ratios to find a single scale factor:
[tex]\(\frac{12}{16} = \frac{15}{20} \rightarrow \frac{3}{4} = \frac{3}{4}\)[/tex]
This confirms the triangles are indeed similar since the ratios are equal. We then use the third ratio to solve for x:
[tex]\(\frac{18}{x} = \frac{3}{4} \rightarrow x = \frac{4}{3} \cdot 18 = 24\)[/tex]
Therefore, the value of x is 24, which is the length of the corresponding side in the second triangle.
A truck can be ready for company a 420 dayPlus $.30 per mile can we be charges $50 a day plus $.50 per mile to rent the same truck find the number of miles in a day at which the rental costs for a company a and Company B same
Answer:it will take 1850 miles
Step-by-step explanation:
Let x represent the number of miles in a day at which the rental costs for a company A and Company B same.
Let y represent the total cost of renting the truck for x miles with company A.
Let z represent the total cost of renting the truck for x miles with company A.
Company A charges $420 a day Plus $.30 per mile. This means that
y = 420 + 0.3x
Company B charges $50 a day plus $.50 per mile to rent the same truck. This means that
z = 50 + 0.5x
To determine the number of miles in a day at which the rental costs for a company A and Company B same, we will equate y to z. It becomes
420 + 0.3x = 50 + 0.5x
0.5x - 0.3x = 420 - 50
0.2x = 370
x = 370/0.2 = 1850 miles
hi :) this lesson is about 30-60-90 triangles.
I need a formula to find the long side. I dont need the actual length if the long side, I just need the equation to find it. help would be much appreciated.
Answer:
5 times the square root of 3
Step-by-step explanation:
To get the longest side of a 30-60-90 triangle, you take the shortest side and multiply it by the square root of 3.
5*(square root of 3)
The Cinema Center consists of four theaters: Cinemas I, II, III, and IV. The admission price for one feature at the Center is $5 for children, $7 for students, and $9 for adults. The attendance for the Sunday matinee is given by the matrixChildren - Students - AdultsCinema I - 225 - 110 - 70Cinema II - 95 - 160 - 225Cinema III - 280 - 65 - 110Cinema IV - 0 - 240 - 225a. Write a column vector B representing the admission prices.b. Compute AB, the column vector showing the gross receipts for each theater.c. Find the total revenue collected at the Cinema Center for admission that Sunday afternoon.
Answer:
a) Matrix B = [tex]\left[\begin{array}{c}5\\7\\9\end{array}\right][/tex]
b) Matrix AB = [tex]\left[\begin{array}{c}2525\\3620\\2845\\3705\end{array}\right][/tex]
c) $12,695
Step-by-step explanation:
Matrix A = [tex]\left[\begin{array}{ccc}225&110&70\\95&160&225\\280&65&110\\0&240&225\end{array}\right][/tex]
a) Matrix B = [tex]\left[\begin{array}{c}5\\7\\9\end{array}\right][/tex]
Gross Receipt = AB
[tex]\left[\begin{array}{ccc}225&110&70\\95&160&225\\280&65&110\\0&240&225\end{array}\right][/tex] . [tex]\left[\begin{array}{c}5\\7\\9\end{array}\right][/tex] = [tex]\left[\begin{array}{c}2525\\3620\\2845\\3705\end{array}\right][/tex]
c) Total revenue is the sum of receipts from 4 cinemas given in part b
Hence,
Total revenue = $2525 + $3620 + $2845 + $3705 = $12,695
Two cartons weigh 3x-2 and 2x-3 pounds, respectively. If the average weight of the cartons is 10 pounds, the heavier carton weights how many more pounds than the lighter carton
Final answer:
By setting up an equation using the average weight formula and solving for x, we find that x equals 5. Subsequently, the heavier carton weighs 13 pounds, and the lighter carton weighs 7 pounds, making the heavier carton weigh 6 pounds more than the lighter carton.
Explanation:
The question involves finding out how many more pounds the heavier carton weighs compared to the lighter carton when given their weights in terms of x and the average weight.
Firstly, we are given that the weights of the two cartons are 3x - 2 and 2x - 3 pounds, and their average weight is 10 pounds.
To find the value of x, we need to set up an equation using the average weight formula, which is:
(Weight of Carton 1 + Weight of Carton 2) / 2 = Average Weight
Substituting the given weights and average weight into the formula, we get:
((3x - 2) + (2x - 3)) / 2 = 10
Solving the equation by combining like terms and multiplying both sides by 2 to eliminate the fraction gives:
5x - 5 = 20
Adding 5 to both sides and then dividing by 5:
x = 5
Now, let's find the actual weight of each carton:
Weight of the first carton = 3x - 2 = 3(5) - 2 = 13 pounds
Weight of the second carton = 2x - 3 = 2(5) - 3 = 7 pounds
Lastly, we determine how many more pounds the heavier carton weighs compared to the lighter one:
13 pounds - 7 pounds = 6 pounds
Therefore, the heavier carton weighs 6 pounds more than the lighter carton.
Geno is a running back for the Bayside Barn Owls. During the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice.
Answer:
22 yards
Step-by-step explanation:
Use a (+) sign for yards gained and a (-) sign for yards lost.
Geno gained 4 yards 3 times: (+4) × 3.
Geno lost 1 yard twice: (-1) × 2.
Geno gained 6 yards twice: (+6) × 2.
Net change
in field position
=
(4 × 3) + (-1 × 2) + (6 × 2)
=
12 − 2 + 12
=
10 + 12
=
22.
Geno gained 22 yards.
The net change in the position of Geno if In the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice, is 22 yards.
What is addition?In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.
Given:
In the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice,
Calculate the net change in position as shown below,
The net change = Total gained - Total lost,
Total gained = 4 × 3 + 6 × 2
Total gained = 12 + 12
Total gained = 24
Total lost = 1 × 2
Total lost = 2
The net change = 24 - 2
The net change = 22
Thus, the net change in the Geno position is 22 yards.
To know more about addition:
https://brainly.com/question/28008319
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The complete question is:
Geno is a running back for the Bayside Barn Owls. During the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice. Find the net change in the position of Geno.
To earn an A in an algebra course, a student must have a test average of at least 90. Mary has grades of 95, 82, 88 on her first three algebra tests. What minimum score does Mary need to make on her fourth test to earn an A in her algebra course?
Answer: Mary need to make at-least 95 on her fourth test to earn an A in her algebra course.
Step-by-step explanation:
Let x be the grades scored by Mary in the fourth algebra test.
Mary has grades of 95, 82, 88 on her first three algebra tests.
Then, the combined scores in four test will become = 95+82+88+x = 265+x
Average score = (Sum of all scores) ÷ (Number of tests)
[tex]=\dfrac{265+x}{4}[/tex]
As per given ,
To earn an A in an algebra course, a student must have a test average of at least 90.
i.e. Average score ≥ 90
[tex]\Rightarrow\ \dfrac{265+x}{4}\geq90\\\\\Rightarrow\ 265+x\geq 90\times4=360\\\\\Rightarrow\ x\geq360-265 =95\\\\\Rightarrow\ x\geq90[/tex]
Hence, Mary need to make at-least 95 on her fourth test to earn an A in her algebra course.