Final answer:
The value of 'a' is found to be approximately 328.33 when b = 3 and c = 3, using the constant of proportionality obtained from the given values a = 197 when b = 5 and c = 5.
Explanation:
When a quantity varies directly as another quantity and inversely as the square of a third quantity, we can express this relationship with the following equation:
a = k x (b / c2)
where k is the constant of proportionality. Given that a = 197 when b = 5 and c = 5, we can solve for k:
197 = k x (5 / 52)
197 = k x (5 / 25)
197 = k / 5
k = 197 x 5
k = 985
Now we can use this value for k to find a when b = 3 and c = 3:
a = 985 x (3 / 32)
a = 985 x (3 / 9)
a = 985 x (1/3)
a = 328.333...
Hence, the value of a, when b = 3 and c = 3, is approximately 328.33.
A set of cards contains the numbers 1 through 20. Mathieu chooses a card a random, records the number of the card, and then returns the card to the set. He conducts 200 trials of this event. Based on the theoretical probability, how many times can Mathieu expect to choose a multiple of 5?
Answer: There are 40 times that Mathieu can expect to choose a multiple of 5.
Step-by-step explanation:
Since we have given that
Numbers between 1 to 20 = 20
Numbers which are divisible by 5 = 4
i.e. {5,10,15,20}
So, Probability that getting a number divisible by 5 is given by
[tex]\dfrac{4}{20}=\dfrac{1}{5}[/tex]
If the number of trials = 200
Then, Number of times Mathieu expect to choose a multiple of 5 is given by
[tex]\dfrac{1}{5}\times 200\\\\=40[/tex]
Hence, there are 40 times that Mathieu can expect to choose a multiple of 5.
Choose all the answers that apply.
The greenhouse effect is:
a) slowly increasing global temperature
b) caused when atmospheric gases trap heat
c) melting the polar ice caps
d) slowly increasing sea levels
e) increasing because of carbon dioxide emissions
Answer:
The greenhouse effect is the process by which radiation from a planet's atmosphere warms the planet's surface to a temperature above what it would be without this atmosphere.So following options are correct options
slowly increasing global temperaturecaused when atmospheric gases trap heatincreasing because of carbon dioxide emissionsAnswer:
A - slowly increasing global temperature
B - caused when atmospheric gases trap heat
E - increasing because of carbon dioxide emissions
Step-by-step explanation:
<1 and <2 are complementary angles. m <1=52 what is the measurement id <2?
I need answer ASAP!
If a company's revenue is 50 billion USD a year, how much money does it make per hour?
What is the value of x?
please help fast!! what is the surface area??
A person who weighs 240 pounds burns 180 calories per mile of running. If a person burns thirty-six calories by running one mile, how much does the person weigh?
Answer: 48 pounds
Step-by-step explanation:
Given: A person who weighs 240 pounds burns 180 calories per mile of running.
There is a direct relation ship between the weight of the person and the calories burn.
If a person burns thirty-six calories by running one mile.
Let x be the weight of the person then
[tex]\frac{x}{36}=\frac{240}{180}\\\Rightarrow\ x=\frac{240\times36}{180}\\\Rightarrow\ x=48[/tex]
The weight of the person is 48 pounds.
(-3,2) 90 degrees about the origin clockwise
i also need help with this question
What percent of the people chose turkey or ham as their favorite sandwich? A. 6% B. 50% C. 28% D. 62%
If the dimensions of the rectangle are doubled what is the area of the new rectangle.
double x + 3= 2x + 6. double four is 8. 8 * 2x + 6 = 16x + 48
What is the area of the composite figure? (6π + 4) cm2 (6π + 16) cm2 (12π + 4) cm2 (12π + 16) cm2
The angle of elevation from a sailboat to the top of a 121-foot lighthouse on the shore measures 16 degree. How far is the sailboat from the lighthouse to the nearest foot?
Answer:
Step-by-step explanation:
can someone help me solve this
Mr Nickelson tells the class that they double the least common denominator for 1/2 3/5 and 9/15 to find the number of the day what number is the number of the day
Given fractions are [tex] \frac{1}{2} ,\frac{3}{5} ,\frac{9}{15} [/tex]
To find the least common denominators of the given fractions, we need to find the least common multiple (L.C.M.) of the numbers given in denominators i.e. 2, 5, and 15.
Finding the LCM of 2, 5, and 15 :-
2 = 1 x 2
5 = 1 x 5
15 = 3 x 5
So least common multiple of 2, 5, and 15 would be (1 x 2 x 3 x 5) = 30.
Hence, common denominator would be 30.
The teacher tells us to double the common denominator to find the answer that is the number of the day.
So we need to double the value of common denominator i.e. 2 x 30 = 60.
It means that 60 is the number of the day.
Hence, 60 is the final answer.
The number of the day is 4.
Explanation:Least common denominator for 1/2 3/5 and 9/15
To find the least common denominator (LCD) for fractions, we need to find the smallest multiple that is common to all the denominators.
For 1/2, 3/5, and 9/15, the denominators are 2, 5, and 15 respectively.
To find the LCD, we need to double the smallest denominator, which is 2, resulting in an LCD of 4.
Therefore, the number of the day is 4.
Learn more about Least Common Denominator here:https://brainly.com/question/12127721
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ASAP
The Choir Booster Club had a budget of $1,300.00 at the start of the school year. They spend $225.30 on t-shirts, $482.25 on lost uniforms, and $135.68 on a holiday party. How much does the booster club have left in their budget?
A. $1,543.23
B. $1,074.70
C. $543.27
D. $456.77
Final answer:
After calculating the expenses, the Choir Booster Club has D. $456.77 left in their budget. This is determined by subtracting the costs of t-shirts, lost uniforms, and the holiday party from their starting budget of $1,300.00.
Explanation:
The Choir Booster Club started the year with a budget of $1,300.00 and spent money on various items. To calculate how much of the budget remains, we need to subtract the costs of the t-shirts, lost uniforms, and the holiday party from the starting budget:
Starting budget: $1,300.00Cost of t-shirts: $225.30Cost of lost uniforms: $482.25Cost of holiday party: $135.68Now, subtract the total expenditures from the starting budget:
$1,300.00 - $225.30 - $482.25 - $135.68 = $456.77 remaining
Therefore, the correct answer is: D. $456.77
You are working as an apprentice for the bksb Newcastle Arena.
An indoor sport exhibition is coming to the arena. Your supervisor has asked you to help set up a handball pitch and seating area as shown in the plan view below..
Use the following formulae:
Perimeter of a rectangle = 2l + 2w
Circumference of a circle = πd
π = 3.14
Area of a rectangle = lw
Area of a circle = πr²
What is the total perimeter of the pitch and seating area?
m
What is the total area of the pitch and seating area?
m2
1. (08.02)A pair of equations is shown below.
x + y = 5
y = one halfx + 2
If the two equations are graphed, at what point do the lines representing the two equations intersect?
A. (2,5)
B. (5, 2)
C. (2, 3)
D. (3, 2)
Answer:
(2,3)
Step-by-step explanation:
Given : [tex]x + y = 5[/tex]
[tex]y=\frac{x}{2}+2[/tex]
To find: what point do the lines representing the two equations intersect
Solution:
[tex]x + y = 5[/tex]
[tex]y=\frac{x}{2}+2[/tex]
Plot the lines on the graph
Green line denotes [tex]x + y = 5[/tex]
Purple line denotes [tex]y=\frac{x}{2}+2[/tex]
So, Intersection point = (2,3)
Refer the attached figure
So, option C is true
Hence Intersection point is (2,3)
A field has a length of 50.5 meters, and a width of 9.2 meters. What is the perimeter and the area of the field?
round 1.496 to the place value of the underlined digit (in this case, 9)
a. 1.4
b. 1.49
c. 1.5
d. 1.497
Arnold has been given a 6 foot by 6 foot sheet of cardboard to make an open box by cutting an equal size square from each corner, folding up the resulting flaps, and taping at the corners. Your task is to label dimensions on a sketch with same size variable cut from each corner.
Part II: How does each variable expression relate to the length, width, and height of the box when folded?
A six sides dice rolls twice. What is the probability that the first roll is a even number and the second roll is a number greater than 4?
Choose the best description for the real number 34 over 3.
Irrational, because it is a fraction
Irrational, because it is a repeating decimal
Rational, because it is a fraction
Rational, because it is a terminating decimal
Answer: The correct option is
(C) Rational, because it is a fraction.
Step-by-step explanation: We are given to choose the best description for the real number 34 over 3.
The given real number can be written as :
[tex]f=\dfrac{34}{3}.[/tex]
We know that
a number of the form [tex]\dfrac{p}{q},~q\neq 0[/tex] is a rational number. That is, a fraction with non zero denominator is a rational number.
Since the given number can be written as a fraction, so it is a rational number.
Thus, option (C) is CORRECT.
Answer:
c
Step-by-step explanation:
Dakota’s dance troupe sold T-shirts as a fundraiser so that they could go to summer camp. When the girls began their fundraiser, 600 people wanted their T-shirts. They were actually short by 210 T-shirts, so the troupe ordered more. They raised the price in hopes of earning more profit, but when the price increased, the demand went down. Use the given information to analyze what happened with the fundraiser.
What happens when the quantity is above the equilibrium point?
Answer:
If the quantity is above the equilibrium point, there is an oversupply.
Step-by-step explanation:
The demand and supply curves intersect at a point called the equilibrium point. At this point, the price and quantity of equilibrium are determined. If we increase the price of the products, there is a decrease in the quantity demanded.
If demand and supply are perfectly elastic, when the price increases, the quantity demanded decreases proportionally. Given this, we can deduce that the collection of funds did not vary from what they would have obtained by selling the rest of the t-shirts at the same price.
If the quantity is above the equilibrium point, there is an oversupply.
Have a nice day!
Factor completely.
40t−16
Enter your answer in the boxes.
The expression 40t - 16 is factored completely by first identifying the greatest common factor, which is 8, then factoring it out to get the result 8(5t - 2).
To factor the expression 40t - 16 completely, we need to find the greatest common factor (GCF) of the terms. The GCF of 40t and 16 is 8. Therefore, we can factor out 8 from both terms:
40t - 16 = 8(5t) - 8(2) = 8(5t - 2)
So, the completely factored form of the expression 40t - 16 is 8(5t - 2).
HELLLLLLPPPPPPPPPP.......... i asked some friends for help and they didn't really understand it.... And my teachers are confusing me as well...
Eder needs 6 cookies and 2 brownies for every 4 plates he makes for a bake sale. Drag cookies and brownies into the box to show how many Eder needs for 10 plates.
Answer:
Eder needs 15 cookies and 5 brownies for every 10 plates he makes.
Step-by-step explanation:
In order to know hoy many cookies and brownies Eder needs for 10 plates, given the fact that he needs 6 cookies and 2 brownies for every 4 plates, we need to perform the following calculation:
6C + 2B = 4X (plates)
6/4C + 2/4B = X
1.5C + 0.5 B = X
So, as we can see, 1.5 cookies and 0.5 brownies are needed for every plate. To know how many of those are needed for ten plates, we ned to multiply those numbers by 10.
1.5 x 10 = 15
0.5 x 10 = 5
Eder needs 15 cookies and 5 brownies for every 10 plates he makes.
During the month of June, Ava kept track of the number of days she saw birds in her garden.she saw birds on 18 days of the month. what is the experimental probability that she will see birds in her garden on july 1?
A highway speed monitor is located on the side of the road that has a speed limit of 45 mph. The system records the speeds of passing vehicles. The data below shows the speeds of the first 9 cars that pass. 46 56 45 44 45 61 55 53 39 What is the standard deviation, to the nearest tenth, based on the posted speed limit, 45 mph? a0 The tenth car traveling on this road breaks down and is being pushed by its owners as it passes the speed monitor. A speed of 1.5 mph is recorded. The measure of central tendency most affected by this tenth speed is the a1 What is the new standard deviation, to the nearest tenth, after the tenth speed is recorded? a2
Answer:
a0 - 8.0
a1 - mean
a2 - 15.7
if 2x+5= 12 for some value of x, then what does 6x+20 equal???