By setting up and solving a system of two equations based on the problem, we find that the larger country is 86,673 square kilometers in area and the smaller is 86,300 square kilometers.
Explanation:This problem can be solved by using a system of two equations in two variables. Let's denote areas of two countries as x (for the bigger country) and y (for the smaller country).
The information from the problem provides us with two equations:
1) x + y = 172,973 (since combined area of two countries is 172,973 square kilometers),
2) x - y = 373 (since Country A is larger by 373 square kilometers).
Solving these equations will give the areas of the individual countries. Countries' areas can be found by adding the two equations together to eliminate y, you get 2x = 173,346, so x = 86,673 square kilometers.
Then, you can substitute x into the first equation: 86,673 + y = 172,973, from which y = 172,973 - 86,673 = 86,300 square kilometers.
So, the larger country's area is 86,673 square kilometers and the smaller country's area is 86,300 square kilometers.
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Esteban poured himself a hot beverage that had a temperature of 195 degrees then set it on the kitchen table to cool. The temperature of the kitchen was a constant 68 degrees. If the drink cooled to 185 degrees in 3 minutes, how long will it take for the drink to cool to 102 degees
Please help ASAP
Find how long it takes $1500 to double if it is invested at 7% interest compound semiannually. Use the formula A=P (1+r/n)^nt to solve the compound interest problem.
It will take approximately ? Years .
Round to the nearest tenth as needed.
Leila went to a basketball games. The game started at 2:38 pm and it was 3 hour 40 minutes long. When did the game end
Leila's basketball game started at 2:38 pm and after adding the duration of 3 hours and 40 minutes, the game ended at 6:18 pm.
Leila went to a basketball game that started at 2:38 pm and lasted for 3 hours and 40 minutes. To find out when the game ended, we need to add the duration of the game to the starting time.
First, let's add the hours:
2:38 pm + 3 hours = 5:38 pm
Next, let's add the minutes:
5:38 pm + 40 minutes = 6:18 pm
Therefore, the basketball game ended at 6:18 pm.
translate into algebraic expression. use the veritable j to rep. janelles score.
8 more than twice janelles score.
Find the ratio of the length of this basketball court to it width as a fraction is simplest form. Width=37ft length=80ft
How many hundredths are in 401.308
combine like terms to simplify 2xy-xy-y+7y-xy
kock's kinky curve is created by starting with a straight line segment and replacing it with a four segments, each 1/3 as long as the original segment. So, at the second stage the curve has three bends, At the next stage, each segment is replaced by four segments, and so on. How many bends does this curve have at the third stage? the fourth stage? The nth stage?
Answer:
thats disturbing
Step-by-step explanation:
. Holly is flipping a coin and pulling a marble from a bag. There are 4 white marbles, 2 blue marbles, and 5 green marbles, all of the same size, in the bag. What is the probability that the coin lands on heads and she pulls a green marble from the bag?
The probability that the coin lands on heads and a green marble is pulled from the bag is 5/22. This is calculated by multiplying the individual probabilities of landing heads on the coin flip (0.5) and pulling a green marble from the bag (5/11).
Explanation:To solve this, we need to first consider the probability of each independent event and then multiply them together to find the total probability of both events happening simultaneously.
Flipping a coin has a theoretical probability of landing on heads as 0.5, since there are two possible outcomes: heads or tails.
For the marble pull, there are 4 white marbles, 2 blue marbles, and 5 green marbles in the bag, making a total of 11 marbles.
The probability of pulling out one green marble is the number of green marbles over the total number of marbles, which is 5/11.
To find the combined probability, we multiply the individual probabilities:
0.5 (probability of heads) × 5/11 (probability of a green marble) = 5/22.
Therefore, the probability that the coin lands on heads and Holly pulls out a green marble is 5/22.
Final answer:
To find the probability of Holly landing heads on a coin toss and pulling a green marble, multiply the probability of each independent event: the probability of getting heads (0.5) and the probability of choosing a green marble (5/11), resulting in 5/22.
Explanation:
The question involves calculating the probability of two independent events occurring together. The first event is flipping a coin and getting heads, which has a probability of 0.5 (assuming the coin is fair). The second event involves pulling a green marble from a bag containing 4 white marbles, 2 blue marbles, and 5 green marbles. The probability of pulling out a green marble is the number of green marbles over the total number of marbles, which is 5/11. Since these are independent events, their joint probability is the product of their individual probabilities: 0.5 * (5/11). This results in an overall probability of 5/22.
Margaret is saving $20 every week so that she can have enough money to buy a bracelet she wants. The bracelet costs $525. What is the minimum number of weeks she will have to save to be able to buy the bracelet.?
Sarah's investment in jet blue stock grew 28% to $448 how much did she originally invest?
Final answer:
Sarah's original investment was calculated by dividing the final amount of $448 by 1 plus the percentage increase in decimal form, which gives us $350 as the original investment before a 28% growth.
Explanation:
The student is asking to calculate the original investment amount before a 28% increase resulted in a final amount of $448. To find the original investment, we divide the final amount by 1 plus the percentage increase in decimal form. In this case, the percentage increase is 28%, which is 0.28 in decimal form.
The formula to find the original investment (O) is:
O = Final Amount / (1 + Percentage Increase)
So, the original investment would be calculated as follows:
O = $448 / (1 + 0.28) = $448 / 1.28
After performing the division, we find the original investment is:
O = $350
Therefore, Sarah originally invested $350 in JetBlue stock.
what decimal is equivalent to 8%
(a). 8.0
(b). 0.8
(c). 0.08
Skate land charges $50 flat fee for a birthday party rental and $4 for each person. Joanne has no more than $100 to budget for her party. Right and inequality that models for situation and display it on a graph. How many people can attend Joeys party?
The amount of jen's monthly phone bill is normally distributed with a mean of $65 and a standard deviation of 11. what percentage of her phone bills are between 32 and 98
The percentage of her phone bills are between 32 and 98 will be 99.73%.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x – μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
The amount of Jen's monthly phone bill is normally distributed with a mean of $65 and a standard deviation of 11.
Then the percentage of her phone bills are between 32 and 98 will be
The value of z-score for x = 32, we have
z = (32 – 65) / 11
z = –3
The value of z-score for x = 98, we have
z = (98 – 65) / 11
z = 3
Then the percentage will be
P(32 < x < 98) = P(-3 < z < 3) × 100
P(32 < x < 98) = 0.9973 × 100
P(32 < x < 98) = 99.73%
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How to estimate 51% of 62
what is 1.3% of 5000 what is 1/3 of $5,000
The value of 1.3% of 5000 is 65 and 1/3 of $5,000 is 1650.
What is the fundamental principle of multiplication?If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
WE know that percentage is a minimum number or ratio that is measured by a fraction of 100.
We need ot find the 1.3% of 5000 and 1/3 of $5,000.
So first 1.3% of 5000 ,
1.3% x 5000
1.3 / 100 x 5000
1.3 x 50
65
Second 1/3 of $5,000,
1/3 x $5,000
0.33 x 5,000
1650
Therefore, the value of 1.3% of 5000 is 65 and 1/3 of $5,000 is 1650.
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Answer in factored form x^2-2x-35
In a bag, a child has 325 coins worth $19.50. There were three types of coins: pennies, nickels, and dimes. If the bag contained the same number of nickels as dimes, how many of each type of coin was in the bag?
for today only I am authorizing you to offer a free insurance plan for one year to customers who sign up for our regularly costs 6.99 a month. that will save the customer almost how much a year
A customer would save nearly $83.88 in a year if they were offered a free insurance plan which usually costs $6.99 per month.
Explanation:The question pertains to how much a customer would save in a year if they were offered a free insurance plan for one year which normally costs $6.99 a month. To calculate the annual savings, multiply the monthly cost by 12 (the number of months in a year). Therefore, $6.99 x 12 = $83.88. That is nearly how much a customer would save in insurance premiums over the course of a year.
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Please help ASAP
Find how long it takes $1500 to double if it is invested at 7% interest compound semiannually. Use the formula A=P (1+r/n)^nt to solve the compound interest problem.
It will take approximately how many Years ?
Round to the nearest tenth as needed.
when table sugar is burned in air, carbon dioxide and water vapor are products, as shown by the following unbalaned chemical equation: C12H22O11(s)+O2(g) =CO2(g)+H2O(g)
The balaned chemical equation of C₁₂H₂₂O₁₁(s)+ 12 O₂(g) = 12 CO₂(g)+ 11 H₂O(g).
What is a balanced chemical equation?A chemical equation is a representation of elements taking part in chemical reactions.In a chemical reaction, all elements are written with their physical state.Law of a chemical equation
The mass of the reactant side is always equal to the mass of the reactant side.To balance the chemical equation coefficient is added to make the number of atoms equal on both sides.Reactant side = product side
C₁₂H₂₂O₁₁(s)+O₂(g)⇒ CO₂(g)+H₂O(g) (unbalanced)
C₁₂H₂₂O₁₁(s)+ 12 O₂(g) ⇒12 CO₂(g)+ 11 H₂O(g) (balanced)
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The graph y=ln(x) is translated 7 units to the left and 4 units upward. The transformed equation is ____.
what is the mean of 23,25,24,26,23,25,22,22,23,40
Please help
If f(x)=x^3+x-7 and g(x)=-5x, find (fog)(x) and (gof)(x)
(fog)(x)=?
Pool is 25ft long and 15 ft wide and the width of the walkway is to be the same all around the pool. How wide do I make the walkway?
express as the sum or difference of logarithms .simplify answer
[tex]log_6(17w)[/tex] can be expressed as [tex]log_6(17) + log_6(w)[/tex] using the sum of logarithms property.
To express log base 6 of 17w as the sum of logarithms, you can use the properties of logarithms, specifically the product rule for logarithms:
[tex]log_b(xy) = log_b(x) + log_b(y)[/tex]
In this case, you have log base 6 of 17w, and you want to express it as the sum of logarithms. You can do this as follows:
[tex]log_6(17w) = log_6(17) + log_6(w)[/tex]
So, log base 6 of 17w can be expressed as the sum of log base 6 of 17 and log base 6 of w.
This is a straightforward application of the product rule for logarithms, where you split the logarithm of a product into the sum of the logarithms of the individual factors.
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In 1992, George Brown started the Old Oregon Wood Store to manufacture Old Oregon tables. Each table is carefully constructed by hand using the highest-quality oak. Old Oregon tables can support more than 500 pounds, and since the start of the Old Oregon Wood Store, not one table has been returned because of faulty workmanship or structural problems. In addition to being rugged, each table is beautifully finished using a urethane varnish that George developed over 20 years of working with wood-finishing materials. The manufacturing process consists of four steps: preparation, assembly, finishing, and packaging. Each step is performed by one person. In addition to overseeing the entire operation, George does all of the finishing. Tom Surowski performs the preparation step, which involves cutting and forming the basic components of the tables. Leon Davis is in charge of the assembly, and Cathy Stark performs the packaging.
1. What is the fastest way to manufacture Old Oregon tables using the original crew? How many could be made per day?
2. Would production rates and quantities change significantly if George would allow Randy to perform one of the four functions and make one of the original crew the backup person?
3. What is the fastest time to manufacture a table with the original crew if Cathy is moved to either preparation or finishing?
4. Whoever performs the packaging function is severely underutilized. Can you find a better way of utilizing the four-or five-person crew than either giving each a single job or allowing each to manufacture an entire table? How many tables could be manufactured per day with this scheme?
Final answer:
The fastest way to manufacture Old Oregon tables using the original crew is by task specialization, with each person performing a specific step in the manufacturing process. Production rates and quantities would not change significantly if Randy joined the crew and one of the original members became the backup. Cathy's movement to a different step would not affect the fastest time to manufacture a table. Utilizing the crew through task specialization could increase the number of tables manufactured per day.
Explanation:
1. The fastest way to manufacture Old Oregon tables using the original crew is by having each person perform a specific step in the manufacturing process. This means George does the finishing, Tom performs the preparation, Leon handles the assembly, and Cathy takes care of the packaging. Assuming each step takes the same amount of time, and all crew members work efficiently, they would be able to manufacture one table per day.
2. If Randy were to perform one of the four functions and one of the original crew members became the backup person, the production rates and quantities would not change significantly. The crew would still be able to manufacture one table per day.
3. If Cathy were moved to either the preparation or finishing step, the fastest time to manufacture a table with the original crew would not change. They would still be able to manufacture one table per day.
4. To better utilize the crew, they could adopt a task specialization approach. Instead of giving each person a single job or allowing each to manufacture an entire table, they could divide the manufacturing process into smaller tasks and assign each person to specialize in a specific task. For example, one person could cut and form the components, another could assemble the table, another could handle the finishing, and another could take care of the packaging. With this scheme, they could potentially manufacture more than one table per day, depending on the efficiency of the specialized tasks.
Streamlining or reassigning workers can significantly increase the production rate of Old Oregon tables. By adjusting tasks and implementing rotational systems, the original crew can produce significantly more tables per day.
1. The fastest way to manufacture Old Oregon tables with the original crew is to streamline each step to ensure minimal transition time between phases.
Assuming each step takes a consistent amount of time, if we estimate each step (preparation, assembly, finishing, packaging) takes 2 hours, each worker can complete their specific task within that period per table. Therefore, the maximum output with a 10-hour workday would be about 2.5 tables per day without considering any overlap in work shifts.2. If George allows Randy to perform one of the functions and assigns one of the original crew members as a backup, the production rate can potentially increase.
Assuming that placing Randy reduces the total time per table to 6 hours (instead of 8 hours), the efficiency gain could allow the crew to produce approximately 3.33 tables per day.This is a significant improvement, though the exact rate would depend on the efficiency of the backup system.
3. The fastest time to manufacture a table with the original crew if Cathy is moved to either preparation or finishing can vary.
If Cathy moves to preparation, Tom might need to adjust to overlapping shifts.If preparation and finishing each take 2.5 hours respectively, the bottleneck (assembly and packaging) would then shift to around 3 hours each. This would result in a total time of 5.5 hours per table, allowing around 1.8 tables to be produced per day.4. For better utilization of the crew and increasing overall production, a possible approach is to implement a rotational system where each worker is proficient in multiple stages.
This way, during less-demanding steps such as packaging, the underutilized worker can assist in preparation or assembly. By doing so, if the average time per table is reduced to 5 hours, the team could potentially produce up to 4 tables in a 10-hour workday.Simplified ratio 0.4
without a calculator work out 0.5 multiplied by 0.8
Determine the unit price to the nearest tenth of a cent, and then determine the better buy. Option A: 12 eggs for $2:30 or Option B: 18 eggs for $3.25
Answer:
Since the option B has the lower unit price, it is the better buy.
Step-by-step explanation:
The better buy is the one with the lowest unit price.
For each of the Options, we can find the unit price by a rule of three problem.
Rule of three problem
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.
In this problem, the measures are:
- The number of units
- The total price
As the number of units increases, so will the total price, which means that the relationship between the measures is direct and we have the following rule of three:
Option A:
12 units - $2.30
1 unit - $x
12x = 2.30
[tex]x = \frac{2.30}{12}[/tex]
x = $0.20.
In option A, the unit price is $0.20
Option B
18 units - $3.25
1 unit - $x
18x = 3.25
[tex]x = \frac{3.25}{18}[/tex]
x = $0.18.
In option B, the unit price is $0.18.
Since the option B has the lower unit price, it is the better buy.