MathMaster logo

MathMaster

  1. Home
  2. general
  3. lorena s garden is surrounded by a corridor of uniform width the garden and the hallway together cover an area of 320 squa
Question

Lorena's garden is surrounded by a corridor of uniform width. The garden and the hallway together cover an area of 320 square meters. If the garden measures 12 meters by 16 meters. determines the width of the hallway

215

likes
1074 views

Answer to a math question Lorena's garden is surrounded by a corridor of uniform width. The garden and the hallway together cover an area of 320 square meters. If the garden measures 12 meters by 16 meters. determines the width of the hallway

Expert avatar
Eliseo
4.6
110 Answers
A continuación se explica cómo resolver el problema: **1. Encuentra el área del jardín:** * Área del jardín = largo * ancho * Área de jardín = 12 metros * 16 metros = 192 metros cuadrados **2. Encuentra el área total del jardín y el pasillo:** * El jardín y el pasillo combinados tienen una superficie de 320 metros cuadrados. **3. Encuentra el área del pasillo:** * Área del pasillo = Área total - Área del jardín * Área del pasillo = 320 metros cuadrados - 192 metros cuadrados = 128 metros cuadrados **4. Modela el pasillo:** * Imagine el pasillo como un marco alrededor del jardín. Llamemos al ancho del pasillo "x". * El largo del jardín más el doble del ancho del pasillo sería 12 + 2x. * El ancho del jardín más el doble del ancho del pasillo sería 16 + 2x. **5. Establecer una ecuación** * El área del pasillo es igual al área total menos el área del jardín: (12 + 2x)(16 + 2x) - 192 = 128 **6. Resuelve la ecuación:** * Ampliar la ecuación: 192 + 56x + 4x^2 - 192 = 128 * Simplificar: 4x^2 + 56x - 128 = 0 *Dividir ambos lados entre 4: x^2 + 14x - 32 = 0 * Factorizar: (x + 16)(x - 2) = 0 *Resolver para x: x = -16 o x = 2 **7. Elija la solución positiva:** *El ancho del pasillo no puede ser negativo, por lo que el ancho del pasillo es de 2 metros. **Respuesta:** El pasillo tiene un ancho de 2 metros.

Frequently asked questions (FAQs)
What is the circumference of a circle with a radius of 5cm?
+
What is the time taken to cover a distance of 150 km when moving at a constant speed of 50 km/h?
+
What is the measure of the third angle in an isosceles triangle if one angle is 65°?
+
New questions in Mathematics
Let f(x)=||x|−6|+|15−|x|| . Then f(6)+f(15) is equal to:
One contestant on a game show has 1,500 points and another contestant has -250 points. What is the difference between the scores of the contestants?
A person who weighs 200 pounds on earth would weigh about 32 pounds on the moon. Find the weight of a person on earth who would weigh 15 pounds on the moon.
Imagine that you are in an electronics store and you want to calculate the final price of a product after applying a discount. The product you are interested in has an original price of $1000 MN, but, for today, the store offers a 25% discount on all its products. Develop an algorithm that allows you to calculate the final price you will pay, but first point out the elements.
The random variable Y is defined as the sum between two different integers selected at random between -4 and 2 (both included). What are the possible values of the random variable Y? What is the value of P(Y=-3)? And whether it is less than or equal to -5?
For a temperature range between -3 degrees Celsius to 5 degrees Celsius, what is the temperature range in degrees Farenheight
Express the following numbers in decimal system, where the subscript indicates the base: 110101 (SUBINDEX=2)
Analyze the following situation Juan is starting a new business, he indicates that the price of his product corresponds to p=6000−4x , where x represent the number of tons produced and sold and p It is given in dollars. According to the previous information, what is the maximum income that Juan can obtain with his new product?
A mutual fund manager has a $350 million portfolio with a beta of 1.10. The risk-free rate is 3.5%, and the market risk premium is 6.00%. The manager expects to receive an additional $150 million which she plans to invest in several different stocks. After investing the additional funds, she wants to reduce the portfolio’s risk level so that once the additional funds are invested the portfolio’s required return will be 9.20%. What must the average beta of the new stocks added to the portfolio be (not the new portfolio’s beta) to achieve the desired required rate of return?
The Humane Society has asked for our help again this week. Currently they are charging $50 for an adoption fee. Unfortunately they just pulled this number out of the air and do not know why they are charging this amount. They would like to charge an amount that covers all the adoption costs – both the variable costs for adoptions as well as the fixed cost for the kennel portion of the Humane Shelter operations. We can help them by doing a breakeven analysis. During a client meeting we gathered these facts. There are 2 part-time employees that each earn $1000 per month. The utilities for the kennel area (water, electricity) are $200 per month. The average food cost for animals in the kennel is $800 per month. In addition, each animal that is adopted receives a rabies vaccination that costs $4 and is micro-chipped that costs $6. At the current cost of $50, how many animals must be adopted to break-even? What would break-even be at a $60 adoption fee? What would break-even be if the fee were lowered to $40? The newspaper has suggested that the Humane Society advertise to increase pet adoptions. The package that they have recommended costs $1000 for a very small ad run every day for a month. If the Humane Society does this extra advertising, how will it affect breakeven? Based on what you have learned about elasticity, what price do you recommend for the adoption fee?
DuocUC 2) The cost C, in pesos, for the production of x meters of a certain fabric can be calculated through the function: (x+185) C(x)=81300-6x+ 20000 a) It is known that C(90) 5.344. Interpret this result. (2 points) b) Calculate C'(x) (2 points) 3 x²+111x-0.87 20000 2000 c) Function C calculates the cost while producing a maximum of 500 meters of fabric. Determine the values of x at which the cost of production is increasing and the values of x at which the cost is decreasing. (3 points) d) If a maximum of 500 meters of fabric are produced, what is the minimum production cost? (
9/14 x 7/27 carry out indicated operation
Calculate the area of the parallelogram with adjacent vertices (1,4, −2), (−3,1,6) 𝑦 (1, −2,3)
A 20-year old hopes to retire by age 65. To help with future expenses, they invest $6 500 today at an interest rate of 6.4% compounded annually. At age 65, what is the difference between the exact accumulated value and the approximate accumulated value (using the Rule of 72)?
2x-4=8
Solve the following 9x - 9 - 6x = 5 + 8x - 9
Sodium 38.15 38.78 38.5 38.65 38.79 38.89 38.57 38.59 38.59 38.8 38.63 38.43 38.56 38.46 38.79 38.42 38.74 39.12 38.5 38.42 38.57 38.37 38.71 38.71 38.4 38.56 38.39 38.34 39.04 38.8 A supplier of bottled mineral water claims that his supply of water has an average sodium content of 36.6 mg/L. The boxplot below is of the sodium contents levels taken from a random sample of 30 bottles. With this data investigate the claim using SPSS to apply the appropriate test. Download the data and transfer it into SPSS. Check that your data transfer has been successful by obtaining the Std. Error of the mean for your data which should appear in SPSS output as 0.03900.. If you do not have this exact value, then you may have not transferred your data from the Excel file to SPSS correctly. Do not continue with the test until your value agrees as otherwise you may not have correct answers. Unless otherwise directed you should report all numeric values to the accuracy displayed in the SPSS output that is supplied when your data has been transferred correctly. In the following questions, all statistical tests should be carried out at the 0.05 significance level. Sample mean and median Complete the following concerning the mean and median of the data. mean =  mg/L 95% CI:  to  mg/L Based upon the 95% confidence interval, is it plausible that the average sodium content is 36.9 mg/L?      median:  mg/L The median value is      36.9 mg/L. Skewness Complete the following concerning the skewness of the data. Skewness statistic =        Std. Error =  The absolute value of the skewness statistic     less than 2 x Std. Error Therefore the data can be considered to come from a population that is      . Normality test Complete the following summary concerning the formal testing of the normality of the data. H0: The data come from a population that     normal H1: The data come from a population that     normal Application of the Shapiro-Wilk test indicated that the normality assumption     reasonable for sodium content (S-W(  )=  , p=   ). Main test Using the guidelines you have been taught that consider sample size, skewness and normality, choose and report the appropriate main test from the following ( Appropriate ONE ) You have selected that you wish to report the one-sample t-test. H0: The mean sodium content     equal to 36.9 mg/L H1: The mean sodium content     equal to 36.9 mg/L Application of the one-sample t-test indicated that the mean is      36.9 mg/L (t(  ) =  , p =   ). You have selected that you wish to report the Wilcoxon signed rank test. H0: The median sodium content     equal to 36.9 mg/L H1: The median sodium content     equal to 36.9 mg/L Application of the Wilcoxon signed rank test indicated that the median is      36.9 mg/L (z =  , N =  , p =   ).
Let I be an interval and let f : I → R be a continuous function such that f(I) ⊂ Q. Show (in symbols) that f is constant.
6(k-7) -2=5
Solve the system of equations by the addition method. 0.01x-0.08y=-0.1 0.2x+0.6y=0.2

You might be interested in