Answer:
The answer to your question is x = 0 and x = 1
Step-by-step explanation:
Equation
[tex]\frac{x}{x - 2} + \frac{x - 1}{x + 1} = -1[/tex]
1)
[tex]\frac{x(x + 1) + (x - 2)(x - 1)}{(x - 2)(x + 1)} = - 1[/tex]
Expand
2) x² + x + x² - x - 2x + 2 = -1(x - 2)(x + 1)
Simplify
3) 2x² -2x + 2 = -1(x² + x - 2x - 2)
4) 2x² - 2x + 2 = -x² + x + 2
Equal to zero
5) 2x² - 2x + 2 + x² - x - 2 = 0
6) 3x² - 3x = 0
Factor
7) 3x(x - 1) = 0
8) 3x₁ = 0 x₂ - 1 = 0
9) x₁ = 0/3 x₂ = 1
10) x₁ = 0 x₂ = 1
John drove to Daytona Beach, Florida, in hours. When he returned, there was less traffic, and the trip took only hours. If John averaged mph faster on the return trip, how fast did he drive each way?
Question: John drove to a distant city in 5 hours.
When he returned, there was less traffic and the trip took only 3 hours.
If John averaged 26 mph faster on the return trip, how fast did he drive each way
Answer:
For the first trip he drove at a speed of 39 mph
For the second trip he drove at a speed of 65 mph
Step-by-step explanation:
Let the distance for both journey be Z because they are equal.
Let the speed for the first journey be X
Let the speed of the second journey be Y
Formula for speed = distance ÷ time
For the first journey the speed X = Z ÷ 5
For the second journey the speed Y = Z ÷ 3
Since John averaged 26 mph faster in the second trip than the first trip due to traffic, it means that the difference in speed between the first & second trip is 26 mph
Difference in speed = (Z÷3) - (Z÷5) = 26
subtracting both results to (5Z-3Z) ÷ 15 = 26
Upon cross multiplication
2Z = 390
Z = 390÷2 = 195 miles
Therefore speed for first journey = 195 ÷ 5 = 39 mph
Speed for second journey = 195 ÷ 3 = 65 mph
To verify, 65 - 39 = 26 mph
A company produces three combinations of mixed vegetables that sell in 1-kg packages. Italian style combines 0.4 kg of zucchini, 0.3 kg of broccoli, and 0.3 kg of carrots. French style combines 0.5 kg of broccoli and 0.5 kg of carrots. Oriental style combines 0.2 kg of zucchini, 0.3 kg of broccoli, and 0.5 kg of carrots. The company has a stock of 18 comma 200 kg of zucchini, 28 comma 100 kg of broccoli, and 38 comma 700 kg of carrots. How many packages of each style should it prepare to use up existing supplies?
Answer:
Italian style = 19,000 packages
French style = 13,000 packages
Oriental style = 53,000 packages
Step-by-step explanation:
let the number of packages of Italian style = x
let the number of packages of French style = y
let the number of packages of Oriental style = z
See the attached table which summarize the problem
Using the table we can get the following system of equations:
0.4x + 0 * y + 0.2z = 18,200
0.3x + 0.5y + 0.3z = 28,100
0.3x + 0.5y + 0.5z = 38,700
Solving the 3 equations together to find x , y and z
Using the calculator
x = 19,000
y = 13,000
z = 53,000
Car A travels 702 miles on 12 gallons of gasoline car b travels 873 miles and 15 gallons of gasoline David wants to buy a car with the lowest fuel canister find out the distance traveled by each car per gallon of gasoline then tell which of the two cars AorB David should by
David should buy Car A because it covers more miles in one gallon than Car B
Step-by-step explanation:
Given
Distance traveled by Car A = [tex]d_A = 702\ miles[/tex]
Gallons used by Car A = [tex]g_A = 12[/tex]
Distance traveled by Car B = [tex]d_B = 873\ miles[/tex]
Gallons used by Car B = [tex]g_B = 15[/tex]
In order to find the distance traveled on one gallon, we will divide the total distance by number of gallons
So,
Distance traveled by Car A in one gallon = [tex]\frac{702}{12} =58.5\ miles\ per\ gallon[/tex]
Distance traveled by Car B in one gallon = [tex]\frac{873}{15} = 58.2\ miles\ per\ gallon[/tex]
We can see that Car A travels more distance in one gallon that is 58.5 miles per gallon
So,
David should buy Car A because it covers more miles in one gallon than Car B
Keywords: Fractions, Unit rate
Learn more about unit rate at:
brainly.com/question/9527422brainly.com/question/9381523#LearnwithBrainly
Car A gets 58.5 miles per gallon, Car B gets 58.2 miles per gallon. David should buy Car A.
Car A: Travels 702 miles on 12 gallons = 702 miles/12 gallons = 58.5 miles per gallon
Car B: Travels 873 miles on 15 gallons = 873 miles/15 gallons = 58.2 miles per gallon
David should buy Car A as it has a slightly higher fuel efficiency of 58.5 miles per gallon compared to 58.2 miles per gallon for Car B.
Terry's essay has 9 more pages than stacey's essay. If s represents the number of pages in stacey's essay, write an expression for the number of pages in terry's essay
t = 9 + s is the expression for number of pages in terry's essay
Solution:
Given that, Terry's essay has 9 more pages than stacey's essay
Let "s" be the number of pages in Stacey essay
Let "t" be the number of pages in terry essay
To find: Expression for the number of pages in terry's essay
From given statement,
Terry's essay has 9 more pages than stacey's essay
Which means, number of pages in terry essay is 9 more than number of pages in Stacey essay
Therefore,
Number of pages in terry essay = 9 + number of pages in Stacey essay
[tex]t = 9 + s[/tex]
Thus the expression for number of pages in terry's essay is found
Suppose m is a positive integer. Is the set consisting of 0 and all polynomials with coefficients in F and with degree equal to m a subspace ofP(F)?
Answer:
For this case we don't have any problems for the conditions 1) and 3), but we have a problem with condition 2) since is not satisfied.
We just need to find a counterexample to show that the statement is False. If we find two elements in the subset provided S, and we show that the sum is not in S, then we have the counter example.
Let's say that we have two elements [tex] a^m +1 , -a^m +1 \in S[/tex] so both elements are in S, and if we apply the condition for the addition closed we got:
[tex] (a^m +1) +(-a^m +1) = a^m -a^m +1+1 = 2[/tex]
And by definition of S, 2 is not in S so then since we can't satisfy the closed addition property then S can't be a subsapce
Step-by-step explanation:
For this case the answer would be no.
It can't be a subspace because we not satisfy the condition of closed under addition.
We need to remember that a subset U of V is a subspace of V if and only if U satisfies the following 3 conditions
1) Additive identity [tex] 0 \in U[/tex]
2) Closed under addition [tex] u,v \in U \Rightarrow u+x \in U[/tex]
3) Cloases under scalar multiplication [tex] a \in F, u \in U \Rightarrow au \in U[/tex]
Proof
For this case we don't have any problems for the conditions 1) and 3), but we have a problem with condition 2) since is not satisfied.
We just need to find a counterexample to show that the statement is False. If we find two elements in the subset provided S, and we show that the sum is not in S, then we have the counter example.
Let's say that we have two elements [tex] a^m +1 , -a^m +1 \in S[/tex] so both elements are in S, and if we apply the condition for the addition closed we got:
[tex] (a^m +1) +(-a^m +1) = a^m -a^m +1+1 = 2[/tex]
And by definition of S, 2 is not in S so then since we can't satisfy the closed addition property then S can't be a subsapce
Solve for x. Show all work
3(x + 5) = x - 7
The answer is x equal -11
Answer: x = -11
Step-by-step explanation: First distribute or multiply through the parentheses on the left side of the equation.
When we do this, we get 3x + 15 = x - 7.
Then subtract x to get 2x + 15 = -7.
Then subtract 15 to get 2x = -22.
Then divide both sides of the equation by 2 and we find that x = -11.
The full fare is $100, the discounted fare is $70. In the next period (the last one before departure) there will be a request for the discounted fare with probability 0.5, and a full fare request with probability 0.4; probability of no request is 0.1.
Answer:$78
Step-by-step explanation:
The two events,i.e request for full fare and the request for discounted fare ar mutually exclusive ,i.e if one happens the other cannot and vice versa .
The representation via set diagram will show a disjointed subset while P(AnB)^° is 1- (P(A)+P(B))=0.1.
Where A is the probability of full fare request while B is the probability of discounted request.
Probability (AUB)=P(A)+ P(B)=0.5×100+0.4×70=78.
Find the equation for the line that passes through (-1, -2) and (4, 3). Is the
point (3, 1) on this line?
Answer:
The answer to your question is a) y = x - 1 b) the point is not on the line
Step-by-step explanation:
Data
A ( -1, -2)
B (4, 3)
C ( 3, 1)
Process
1.- Find the slope of the line (m)
Formula
m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Substitution
m = [tex]\frac{3 + 2}{4 + 1} = \frac{5}{5} = 1[/tex]
2.- Find the equation of the line
Formula
y - y1 = m(x - x1)
Substitution
y + 2 = 1(x + 1)
Solve for y
y = x + 1 - 2
y = x - 1
- Prove that the point (3, 1) is on the line
1 = 3 - 1
1 = 2
The point is not on the line because 1 ≠ 2
A manufacture inspects 800 light bulbs and finds that 796 of them have no defects. What is the experimental probability that a light build chosen at random has no defects
Answer:
The experimental probability that a light build chosen at random has no defects is 99.5 % or P(A)=0.995.
Step-by-step explanation:
let S be the sample space for the inspection of the light bulbs.
Therefore, n(s) = 800
let ' A ' be the event of no defects bulbs.
Therefore, n(A) = 796
Now the Experiment probability for a light bulb chosen has no defects will be given by,
[tex]P(A)=\dfrac{n(A)}{n(S)}[/tex]
Substituting the values we get
[tex]P(A)=\dfrac{796}{800}=0.995[/tex]
The experimental probability that a light build chosen at random has no defects is 99.5 % or P(A)=0.995.
Russia's sister gives him two packs of baseball cards per month each pack has 11 card she gave him three extra packs for his birthday how many cards does Richard get in a year
Answer:
Russia gets 267 baseball cards in a year.
Step-by-step explanation:
Given:
Number of packs given per month = 2
Number of cards in each pack = 11
Number of cards given on his birthday = 3
Now, we know that, there are 12 months in a year.
Using unitary method, the total number of packs given in year and total cards can be calculated. So,
Packs given in 1 month = 2
∴ Packs given in 12 months = 2 × 12 = 24
Number of cards in 1 pack = 11
∴ Number of cards in 24 packs = 11 × 24 = 264
Now, his birthday will come once in a year. So, additional cards received by him will be 3 only. So,
Total number of cards = Number of cards in 24 packs + Additional cards
Total number of cards = 264 + 3 = 267
Therefore, Russia gets 267 baseball cards in a year.
A least squares regression line was created to predict the Exam 3 score of STA 2023 students based on their Exam 1 score. The study found that the value of R-squared was 28.8% and the least squares regression line was yhat=50.57+0.4845x. What is the correlation coefficient, r?a. 0.54b. -0.54c. 5.37d. -5.37e. 0.08f. -0.08
Answer:
a) 0.54
Step-by-step explanation:
The correlation coefficient can be found by taking square root of R-squared value and the sign of correlation coefficient can be assessed by considering the sign of slope value. So,
r²=28.8%=28.8/100=0.288
r=[tex]\sqrt{r^{2} }[/tex]=[tex]\sqrt{0.288}[/tex]=0.5367
By rounding to two decimal places the correlation coefficient
r=0.54
We can see that slope=0.4845 has positive sign so, the correlation coefficient contains the positive sign.
Hence the correlation coefficient r=0.54.
Jamie bought a load of gravel to cover her driveway. Her brother works for the gravel company and got her a 28% discount. If Jamie paid $357.83 for the gravel (without tax), what would it have cost her without the discount?
Answer:without the discount, it would have cost her $497
Step-by-step explanation:
Let x represent the amount that the gravel would have cost her without the discount.
Her brother works for the gravel company and got her a 28% discount. The value of the discount would be
28/100 × x = 0.28 × x = 0.28x
It mans that the amount that she paid for the gravel is
x - 0.28x = 0.72x
If Jamie paid $357.83 for the gravel (without tax), it means that
0.72x = 357.83
x = 357.83/0.72
x = 496.99
Approximately $497
You are visiting baltimore, MD and a taxi company charges a flat fee of 3.00 for using the taxi and 0.75 per mile. How much woks a taxi ride for 8 miles cost
Answer: the cost of riding the taxi for 8 miles is $9
Step-by-step explanation:
The taxi company charges a flat fee of 3.00 for using the taxi and 0.75 per mile. This means that the total cost of using the taxi and travelling x miles would be
3 + 0.75x
This is the equation representing the situation.
To find the cost of riding the taxi for 8 miles, we would substitute x = 8 in our equation. It becomes
Therefore, the total cost of riding the taxi for 8 miles would be
3 + 0.75 × 8
= 3 + 6 = $9
Apertures for the diffraction studied in this chapter are __________. A. a single slit.
B. a circle.
C. a square.
D. both A and B.
E. both A and C.
Answer: the correct option is D
Step-by-step explanation:
Note: the chapter summary can be found in chapter 22 of the Pearson Education,Inc. (PDF format).
In the chapter, a single slit aperture diffraction and a circle aperture diffraction was discussed.
A circle aperture diffraction occurs when light pass through a tiny hole or aperture to produce a circular disc image. This disc is called Airy's disc.
To calculate the aperture diameter,d we can use the formula below;
d= m× λ/ sin θ. ------------------------------------------------------------------------------(1).
The single slit aperture diffraction is when light pass through a single slit to produce. The wavelength, λ is greater than the width of the aperture.
Suppose you buy a car with a value of $8,500. Each year the value of your car will depreciate by 4.7%. How much will your car be worth in 6 years?
A) $11,196.93
B) $6,779.17
C) $7,488.42
D) $6,367.61
Answer:
D
Step-by-step explanation:
y=a(1-r)^n
a is the initial cost of the vehicle
r is the percentage decrease in decimal
n is the number of years.
so y as the final cost is computed as:
8500(1-0.047)^6
we get $6367.61
A researcher wants to determine if preschool attendance is associated with high school graduation for low-income students. She randomly assigns low-income children to two groups; one group will attend preschool program, the second group will not attend preschool. The researcher plans to follow the children in the study for 20 years and observe whether or not they graduate from high school. Which of the following is the response variable in this study?
A) Whether or not a subject graduates high school
B) The length of time it takes a subject to graduate high school
C) Whether or not a subject attends preschool
D) The income status of the children
Answer:
Option A) Whether or not a subject graduates high school
Step-by-step explanation:
We are given the following experiment in the question:
Experiment: if preschool attendance is associated with high school graduation for low-income students.
Independent variable: preschool attendance
The children were divided into two groups, one group will attend preschool program, the second group will not attend preschool.
The response variable is another term for dependent variable.
Here,
Dependent variable: whether or not children will graduate from high school.
Because this is dependent on the variable whether the child attends the preschool or not.
Option A) Whether or not a subject graduates high school
Final answer:
The response variable in the study is A) Whether or not a subject graduates high school. This measures the outcome of the treatment, which is preschool attendance for low-income children.
Explanation:
In this study, the response variable is the outcome that the researcher is trying to measure as a result of manipulating the experimental conditions. The experimental condition in this case is whether the child attends preschool or not. Hence, the response variable would be A) Whether or not a subject graduates high school. The preschool attendance (C) is the independent variable or treatment variable, as it is what the researcher manipulates and controls. The variables of the length of time it takes to graduate (B), and the income status of the children (D) are not the focus of the measurement for the direct effect of preschool attendance.
Low-income children have been observed to have various educational disadvantages compared to their wealthier peers, such as lower standardized test scores, lower graduation rates, and higher dropout rates. The study aims to investigate if attending preschool can help bridge the educational achievement gap that starts before children even enter formal schooling. By assigning low-income children randomly to either attend preschool or not, the researcher can control for other variables and focus on the impact of preschool attendance on high school graduation.
When there is a _____ relationship, as values of variable X (e.g., income) increase, values of variable Y (e.g., education level) also increase.
Answer:
When there is a positive relationship, as values of variable X (e.g., income) increase, values of variable Y (e.g., education level) also increase.
Step-by-step explanation:
Consider the provided information.
It is given that the value of variable x increase, and value of variable y also increase.
A positive relationship is when the values increase together or we can say that the value both variable tends to move in same direction. If the value of x increase then the value of y is also increase.
A Negative relationship is when one value decreases as the other increases. Or we can say that the value of x increase the value of y decrease.
Hence, the provided relationship is positive as both values moves in same direction.
When there is a positive relationship, as values of variable X (e.g., income) increase, values of variable Y (e.g., education level) also increase.
At least ____ % of healthy adults have body temperatures within 22 standard deviations of 98.32degrees°F. (Round to the nearest percent as needed.)
Answer:
95%
Step-by-step explanation:
We are asked to find the percentage of healthy adults have body temperatures within 2 standard deviations of 98.32 degrees°F.
We will use Empirical rule of normal distribution to answer our given problem.
Empirical rule of normal distribution states that 68% of data falls within the first standard deviation from the mean. 95% of data fall within two standard deviations. 99.7% of data fall within three standard deviations.
Therefore, 95% of healthy adults have body temperatures within 2 standard deviations of 98.32 degrees°F.
A college bookstore marks up the price that it pays the publisher for a book by 35 %. If the selling price of a book is $ 87.00 comma how much did the bookstore pay for this book?
Answer:the amount that the bookstore pay the publisher for the book is $64.4
Step-by-step explanation:
Let x represent the amount that the bookstore pay the publisher for the book.
The college bookstore marks up the price that it pays the publisher for a book by 35%. This means that the value of the mark up would be
35/100 × x = 0.35 × x = 0.35x
Therefore, the amount that the bookstore is selling the book would be
x + 0.35x = 1.35x
If the selling price of a book is $ 87.00, then it means that
1.35x = 87
x = 87/1.35 = 64.4
A rectangular painting measures 15 inches by 18 inches and contains a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and its frame is 90 inches. Determine the width of the frame.
To determine the width of the frame, subtract twice the frame width from the length and width of the outer rectangle and set up an equation based on the perimeter.
Explanation:To determine the width of the frame, we need to first find the dimensions of the inner rectangle formed by the painting. If we subtract twice the frame width from the length and width of the outer rectangle, we get the length and width of the inner rectangle. Let's call the width of the frame 'x'.
The length of the inner rectangle is 15 inches - 2 inches, and the width of the inner rectangle is 18 inches - 2 inches. The perimeter of the inner rectangle is the sum of its four sides, which can be calculated using the
formula P = 2l + 2w. We know that the perimeter of the inner rectangle is 90 inches, so we can set up the equation:
90 = 2(15 - 2x) + 2(18 - 2x)
Solving this equation will give us the value of 'x', which represents the width of the frame.
Learn more about the Dimensions of a rectangular frame here:https://brainly.com/question/32613996
#SPJ3
The school that Emily goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold24 adult tickets and 3 student tickets for a total of $223.00. The school took in $152 on the second day by selling 7 adult tickets and 6 student tickets. What is the price each of one adult ticket and one student ticket?
Answer:
Step-by-step explanation:
Let x represent the price of one adult ticket.
Let y represent the price of one student ticket.
On the first day of ticket sales the school sold 24 adult tickets and 3 student tickets for a total of $223.00. This means that
24x + 3y = 223 - - - - - - - - - - - -1
The school took in $152 on the second day by selling 7 adult tickets and 6 student tickets. This means that
7x + 6y = 152 - - - - - - - - - - - - - -2
Multiplying equation 1 by 6 and equation 2 by 3, it becomes
144x + 18y = 1338
21x + 18y = 456
Subtracting, it becomes
123x = 882
x = 882/123
x = 7.17
Substituting x = 7.17 into equation 2, it becomes
7 × 7.17 + 6y = 152
50.19 + 6y = 152
6y = 152 - 50.19 = 101.81
y = 101.81/6 = 16.97
An excercise machine with an original price of %850 is on sale at 12% off.
What is the the discount amount?
What is the exercise machine's sale price
The discount amount of exercise machine is $ 102
The sales price of machine is $ 748
Solution:
Given that,
Original price of machine is $ 850
Discount rate = 12 %
To find: discount amount and sales price of machine
Find the discount amount:Given that discount rate is 12 % , which means 12 % of original price of machine
Discount amount = 12 % of original price of machine
Discount amount = 12 % of 850
[tex]Discount\ Amount = 12 \% \times 850\\\\Discount\ Amount = \frac{12}{100} \times 850\\\\Discount\ Amount = 0.12 \times 850 = 102[/tex]
Thus the discount amount is $ 102
Find the sales price of machineSales price = Original price - Discount amount
[tex]Sales\ Price = 850 - 102\\\\Sales\ Price = 748[/tex]
Thus the sales price of machine is $ 748
Five pounds of candy that is 20% chocolate is combined with a candy that is 40% chocolate. How many pounds of the candy that is 40% chocolate should be used to get a candy that is 25% chocolate?
Answer:
5/3 pounds
Step-by-step explanation:
Five pounds of candy that is 20% chocolate is combined with a candy that is 40% chocolate
Let x be the pounds of candy that is added with 40% of chocolate
5 pounds that is 20%. 20% = 0.2
x pounds that is 40%. 40% = 0.4
mixture is x+5 pounds that is 25%. 25%= 0.25
[tex]0.2(5)+0.4x=0.25(x+5)[/tex]
[tex]1+0.4x=0.25x+1.25[/tex]
Subtract .25x from both sides
[tex]1+0.15x=+1.25[/tex]
Subtract 1 from both sides
[tex]0.15x=0.25[/tex]
divide both sides byu 0.15
x=5/3 pounds
Popcorn is now available in two different cups at a theater; a square pyramid or a cone. They have the same height of 20 cm. The price of each cup is the same. Which cup is the better deal?
Answer:
Square pyramid cup is better deal then Cone cup.
Step-by-step explanation:
Diagram is missing in the question we have attached diagram for your reference.
Given:
height of square pyramid = 20 cm
height of cone = 20 cm
Base of square pyramid = 12 cm
diameter of cone = 12 cm
radius of cone is half of diameter.
radius of cone = [tex]\frac{diameter}{2}=\frac{12}{2} = 6\ cm[/tex]
We need to find the which cup is the better deal.
Solution:
We will first find the volume of both cups and then we can say the the one which has greater volume is the better deal in buying.
Volume of square pyramid is calculated by one third times square of the base times height.
framing in equation form we get;
Volume of square pyramid = [tex]\frac{1}{3}\times 12^2\times20= 960\ cm^3[/tex]
Now we know that;
Volume of cone is calculated by one third times square of the radius times height times π.
framing in equation form we get;
Volume of cone = [tex]\frac{1}{3}\pi r^2h= \frac{1}{3}\pi\times 6^2\times 20 \approx 754cm^3[/tex]
Now we can see that;
Volume of square pyramid cup which [tex]960\ cm^3[/tex] is greater than Volume of cone cup [tex]754\ cm^3[/tex]
Hence Amount of popcorn will be more in square pyramid cup then in cone cup.
Hence Square pyramid cup is better deal then Cone cup.
i need help plz
Choose the word or phrase that best completes each sentence.
1. George Washington when he went to fight the French in the Ohio River Valley.
2. The British then sent a to attack the French Fort Duquesne.
3. The British in the first battle of the French Indian War.
Answer:
heres your answers
Step-by-step explanation:
George Washington was defeated when he went to fight the French in the Ohio River Valley.
The British then sent a trained army to attack the French Fort Duquesne.
The British suffered a defeat in the first battle of the French Indian War.
For triangle JKL, angle JKL measures 90 degrees, and side JL has a length of 260 centimeters. If side JK > side KL, which of the following could be a combination of the lengths of sides JK and KL50 / 100 / 120 / 200 / 240.
Answer:
100/240/260 will be the combination.
Step-by-step explanation:
In a right angle triangle JKL,
∠JKL = 90° and side JL is the hypotenuse of the triangle.
By Pythagoras theorem,
JK² + KL² = JL²
Since JL = 260
Therefore, (JK)² + (KL)²= (260)² = 67600
In the given options, square of two numbers total becomes 67600.
And the possible numbers will be 100 and 240.
(100)² + (240)² = 10000 + 57600 = 67600
Since side JK > side KL
Therefore, measure of JK = 240 cm, KL = 100 cm and JL = 240 cm could be the combination among all values.
Nolan has some nickels and some dimes. He has no more than 19 coins worth no less than $1.30 combined. If Nolan has 5 nickels, determine all possible values for the number of dimes that he could have. Your answer should be a comma separated list of values.
Answer:
Step-by-step explanation:
A nickel is worth 5 cents. Converting to dollars, it becomes
5/100 = $0.05
A dime is worth 10 cents. Converting to dollars, it becomes
10/100 = $0.1
Let x represent the number if nickels.
Let y represent the number of dimes.
He has no more than 19 coins. This means that
x + y ≤ 19
He has no less than $1.30 combined. This means that
0.05x + 0.1y ≥ 1.3
If Nolan has 5 nickels, then, substituting x = 5 into x + y ≤ 19, it becomes
5 + y ≤ 19
y ≤ 19 - 5
y ≤ 14
substituting x = 5 into 0.05x + 0.1y ≥ 1.3, it becomes
0.05 × 5 + 0.1y ≥ 1.3
0.25 + 0.1y ≥ 1.3
0.1y ≥ 1.3 - 0.25
0.1y ≥ 1.05
y ≥ 1.05/0.1
y ≥ 10.5
Therefore, all possible values for the number of dimes that he could have would be
10.5 ≤ y ≤ 14
Out of 229 racers who started the Eugene marathon, 208 completed the race, 17 gave up, and 4 were disqualified. What percentage of racers did not complete the marathon?
Answer:
9.17% of racers did not complete the marathon.
Step-by-step explanation:
Consider the provided information.
Out of 229 racers who started the Eugene marathon.
208 completed the race, 17 gave up 4 disqualified .
Then total racers who could not complete the marathon is
229-208=21
Now calculate the percentage:
[tex]Percentage=\frac{21}{229}\times 100\\\\Percentage=\frac{2100}{229}\\\\Percentage\approx9.17[/tex]
Hence, 9.17% of racers did not complete the marathon.
The science club is raising money for a trip to the museum. Tickets to the museum cost $8. Five students already have a membership to the museum, so they will get in for free. The club raised the $296 needed to take all students in the club to the museum.
Answer:there are 42 students in the club.
Step-by-step explanation:
Let s represent the number of students in the club.
Tickets to the museum cost $8. Five students already have a membership to the museum, so they will get in for free. The club raised the $296 needed to take all students in the club to the museum. This means that
8(s - 5) = 296
8s - 40 = 296
8s = 296 + 40 = 336
s = 336/8
s = 42
Brittany picked 5 oranges. She shared them equally between her 7 brothers. What fraction of an orange did each brother receive? A. 1/7 B. 7/5 C. 5/7 D. 1/5
Answer:
C 5/7
Step-by-step explanation:
you have to split the 5 oranges between the 7 brothers, so you would do 5/7
5 split between 7 is the same as 5/7
Answer:5/7
Step-by-step explanation:
If you take each orange and cut them into 7 pieces then you could pass out one piece of each 1/7 of the oranges to each brother. You would do this 5 times until each brother had 5/7 and all the oranges would be passed out to the brothers.