Answer:
109
7²=49 (7×7=49)
10×5=50
Therefore,
49+50+10= 109
In a mathematical competition, there are 2021 participants. Gold, silver, and bronze medals are awarded to the winners as follows: the number of silver medals is at least twice the number of gold medals: i the number of bronze medals is at least twice the number of silver medals: ii) the number of all medals is not more than 40% of the number of participants. The competition director wants to maximize the number of gold medals to be awarded based on the given conditions. In this case what is the maximum number of bronze medals that can be awarded?
Here we have some given restrictions that affect the number of medals, using these, we want to find the maximum number of bronze medals that can be awarded.
We will find that:
The maximum number of bronze medals that can be awarded is 535
Now let's see how we can get that.
Let's define the variables:
G = number of gold medals.
S = number of silver medals.
B = number of bronze medals.
Now we can see what information we have.
There are 2021 participants.
The number of silver medals is at least twice the number of gold medals.
S ≥ 2*G
The number of bronze medals is at least twice the number of silver medals:
B ≥ 2*S.
The number of all medals is not more than 40% of the number of participants.
The total number of medals is (G + S + B)
40% of the total number of participants is:
(40%/100%)*2021 = 0.4*2021 = 808.4
Then we have:
G + S + B ≤ 808.4
We can rewrite the above inequality as:
G + S + B ≤ 808.
Then we have 3 inequalities:
S ≥ 2*G
B ≥ 2*S
G + S + B ≤ 808
Now we want to maximize the number of gold medals.
This means that the total number of medals should be exactly 808 (the maximum number of total medals) so we have:
G + S + B = 808.
Also, if we want to maximize the number of gold medals, then we need to minimize the number of silver medals and the number of bronze medals, such that we get:
S = 2*G
B = 2*S
Now we have 3 equations:
G + S + B = 808
S = 2*G
B = 2*S
Replacing the third equation in the first one, we get:
G + S + 2*S = 808
G + 3*S = 808
Now we can replace:
S = 2*G
in the above equation to get:
G + 3*(2*G) = 808
G + 6*G = 808
7*G = 808 =
G = 808/7 = 115.43
But we can have 0.43 of a gold medal, so we need to round down to the next whole number:
G = 115
Now, with this restriction, we want to find the maximum number of bronze medals.
This means that we need to minimize the number of silver medals, so we use:
S = 2*G = 2*115 = 230
And the number of bronze medals will be such that:
B + G + S = 880
B + 115 + 230 = 880
B = 880 - 115 - 230 = 535
The maximum number of bronze medals that can be awarded is 535
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I got he first day and can’t remember how to do this??
Answer:
area= 9 pi km²
circumference= 6 pi km
Step-by-step explanation:
area = pi r ²
so pi × 3²
area = 9 pi km²
circumference = d × pi
so 6 pi km
It costs $7 for a ticket to the Pike
football game and $2.50 per
snack. Write a function rule in
function notation for this
situation.
Answer:
let the number of snacks bought be x
f(x) = 7 +2.5(x)
=> f(x) is the amount you spend in total
.
Which of the following is
an irrational Number?
Answer:
C
Step-by-step explanation:
Because it has no pattern, isnt repeating, and isnt a whole number.
Pencils cost at school $0.07 each A box holds 12 pencils how much does 2 boxes cost the school
Answer:
Below.
Step-by-step explanation:
0.07x12=0.84 x 2=1.68.
write down the degree of given polynomial 5x⁴+4x²+2x+1
Answer:
4
Step-by-step explanation:
To find the degree of a polynomial, identify the term with the greatest exponent. The exponent of that term is the degree of the polynomial.
In the given polynomial 5x⁴+4x²+2x+1, the term with the greatest exponent is 5x⁴. This term has an exponent of 4, so therefore, the degree of the polynomial is 4.
I hope this helps!
What is the Answer of this simplified? 2a+4b-11ab-6b
Answer:
2a - 2b - 11ab
Step-by-step explanation:
2a + 4b - 11ab- 6b
subtracting:
4b - 6b(4 - 6)b-2bsimplify like terms by subtracting or adding.
➡️ 2a - 2b - 11ab
"LiFe Is LiKe A bOx Of ChOcOlAtEs YoU nEvEr KnOw WhAt YoUr GoInG tO gEt" Forest Gump
Answer:
yes this quote isabsolutely right as
life is very innocent , we can make our life whatever we like
How can I solve this problem?
Answer:
It just had relocation 4 in direction of positive and in term of x so
find f(x-5)
GL HF
each day for several days, the charge in the price of a share of socks was -3$. The total charge in price during those days was -36$. Over how many days did the price decline
Answer: 12 days
Step-by-step explanation:
if the price is declining by -3$ then you just divide -36$by the -3$ and you get the amount of days it declined
The ratio of the areas of two right isosceles triangles are in the 16.25
Calculate the ratio of their corresponding heights.
Answer:
Ratio of area = 16:25
Step-by-step explanation:
ar(ABC)/ar(DEF) = side²/side'²
16/25 = s²/s'²
√(16/25) = s/s'
4/5 = s/s'
Ratio of side are 4:5
Z= 1+2x,for x
Immediate help pls
Answer:
Z/2-1/2=x
Step-by-step explanation:
Z=1+2x
subtract 1 from both sides
Z-1=2x
divide both sides by 2
Z/2-1/2=x
Answer:
x= z-1/2 is the solution. thank you
Is -15/2 a rational number or integer or whole number or all of them??
Answer: Rational number
It is a rational number because it is a fraction of two integers. Those two integers being -15 and 2.
In general, any rational number is of the form P/Q where P and Q are integers. The Q cannot be zero. Another example of a rational number is 2/3. In this example, P = 2 and Q = 3.
Going back to -15/2, we would have P = -15 and Q = 2.
The fraction -15/2 is not a whole number nor is it an integer. This is because -15/2 = -7.5 and this is sufficient to see we don't have an integer result. We would need to have nothing after the decimal point to get a whole number.
Answer:
I don't really know
Step-by-step explanation:
Err.. sorry but i am in grade 6
Use the following terms in the same sentence: hypothesis, controlled experiment, and variable
Answer:
The scientist stated her hypothesis, set up a controlled experiment, and isolated the variable that could affect her work.
Find the equation of the line passing through the point (-4, 4) and is perpendicular to the line y = 2x - 5.
Answer: y = (-1/2)x + 2
Concept:
When two lines are perpendicular to each other, their slopes are negative reciprocals.
The reciprocal of a number is 1 divided by the number.
In other words, it is the image opposite of a term.
Solve:
Given information
Given line = y = 2x - 5
Point = (-4, 4)
Find the slope of the line
Given the line is perpendicular to the line y = 2x - 5, the slope of the line would be negative reciprocal of the line y = 2x - 5.
Slope of line [y = 2x - 5] = 2
Slope of new line = (-1/2)
Find the y-intercept by substituting the given point
Equation of the new line: y = (-1/2)x + b
b = y-intercepty = (-1/2)x + b
4 = (-1/2) (-4) + b
4 = 2 + b
4 - 2 = 2 + b - 2
b = 2
Finalize the equation of the line
Slope = -1/2
Y-intercept = 2
[tex]\boxed{y=-\frac{1}{2}x+2 }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
find an equation for the line below
Answer:
[tex]y=\displaystyle -\frac{1}{4}x+\displaystyle \frac{15}{4}[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.
1) Determine the slope (m)
[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
In the graph, two points are indicated: (-5,5) and (3,3). Plug these into the equation:
[tex]m=\displaystyle \frac{3-5}{3-(-5)}\\\\m=\displaystyle \frac{3-5}{3+5}\\\\m=\displaystyle \frac{-2}{8}\\\\m=\displaystyle \frac{-1}{4}[/tex]
Therefore, the slope of the line is [tex]\displaystyle -\frac{1}{4}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\displaystyle -\frac{1}{4}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\displaystyle -\frac{1}{4}x+b[/tex]
Plug in one of the points we used earlier and solve for b:
[tex]3=\displaystyle -\frac{1}{4}(3)+b\\\\3=\displaystyle -\frac{3}{4}+b\\\\3+\displaystyle \frac{3}{4}=b\\\\\frac{15}{4} =b[/tex]
Therefore, [tex]\displaystyle \frac{15}{4}[/tex] is the y-intercept. Plug this back into [tex]y=\displaystyle -\frac{1}{4}x+b[/tex]:
[tex]y=\displaystyle -\frac{1}{4}x+\displaystyle \frac{15}{4}[/tex]
I hope this helps!
If F(x) = 4x - 1 and G(x) = x2 + 7, what is G(Fx))?
Step-by-step explanation:
gof(x)= g(f(x))
gof(x)= g(4x-1)
gof(x)= (4x-1)²+7
gof(x)=16x²-8x+1+7
gof(x)=16x²-8x+8
Which number is irrational? explain why?
a) -(9) b) 4.0005
c)2.17 d) (40)
Answer:
√40 is an irrational number
Step-by-step explanation:
"An irrational number is a real number that cannot be expressed as a ratio of integers, for example, √ 2 is an irrational number."
Alex said 20
2° = 1 and 5^1= 5.
True
False
Answer:
True
Step-by-step explanation:
Every number to the power of 0 is equal to one, so 2⁰ = 1 it's true
and every number to the power of 1 is equal to itself, so
5¹ = 5, also true
A rock climber is descending down a 500-foot tall cliff. After 8 minutes, the rock climber
has descended to a height of 280 feet. Find the height as a linear function of time
We have that The height as a linear function of time is
[tex]x=-27.5T+500[/tex]
From the Question we are told that
Time t=8 minutes
Height h=500
Descended height h_d= 280 feet.
Generally the equation for the linear function is mathematically given as
Let
Height as a linear function =x
[tex]x=\frac{h_d-h}{t}*T+h[/tex]
[tex]x=\frac{280-500}{8}*T+500[/tex]
[tex]x=-27.5T+500[/tex]
In conclusion
The height as a linear function of time is
[tex]x=-27.5T+500[/tex]
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Bert is on a Ferris wheel. The radius of the Ferris wheel is 6 metres. Its axle is 7 metres above the ground. It takes 100 seconds to complete one full revolution. Bert enters the Ferris wheel at its lowest height. The ride starts at 0 seconds.
Work or explanation must be provided for full marks. Answers involving radians will result in a mark of zero.
a) Sketch a height vs time graph of ONE cycle of Bert’s motion on the ride. Show at least 5 KEY POINTS and label them on your graph.
b) Determine an equation of the sinusoidal function h(t) to represent Bert’s journey, where h represents the height of the Ferris Wheel and t represents the time in seconds.
Choose the MOST appropriate sinusoidal function based on the information provided.
The motion of a Ferris wheel, spinning about a fixed axis is rotational motion
a) Please find attached the height vs time graph of ONE cycle of Bert's motion on the ride, showing 5 Key points, including; The period, amplitude, the vertical shift, horizontal shift, the neutral axis
b) The equation to represent Bert's journey is h(t) = 6·sin(3.6·(t - 25)) + 7
The reason the above equation are correct are:
The given parameters of the Ferris wheel are;
Radius, r = 6 meters
The height of the axle above the ground, h = 7 metres
The time it takes to complete one revolution, T = 100 seconds
The level at which Bert enters the Ferris wheel = The lowest level
The time at which the ride starts = 0 seconds
a) The graph of a Ferris wheel is a graph sinusoidal function with the following details
The general form of the sinusoidal function is, y = a·sin(b·(t - h)) + D
Amplitude = The radius = 6 meters
The vertical shift, D = The elevation of the axle above the ground = 7 meters
The period, T = 360/b
∴ b = 360/T = 360/100 = 3.6
At t = 0, sin(b·(t - h)) = -1
Given that sin(-90) = -1
Therefore; (3.6·(0 - h)) = -90
π/50 = -π/2
-h = -25
∴ The horizontal shift, h = 25
The function of the Ferris wheel is y = 6·sin(3.6·(t - 25)) + 7
The graph of the function is created on MS Excel, using the above sinusoidal equation of the Ferris wheel
The 5 key points included in the graph are;
The period, THorizontal shift, hAmplitude, aNeutral axisVertical shift, Db) The appropriate equation of the sinusoidal function of the Ferris wheel is determined from the general sinusoidal function equation, y = a·sin(b·(t - h)) + D, as follows;
From part (a);
a = 6, b = 3.6, h = 25, and D = 7
The equation of the sinusoidal function h(t) to represent Bert's journey, is h(t) = a·sin(b·(t - h)) + D
Where;
h = The height of the Ferris Wheel
t = The time in seconds
a = The amplitude = 7
b = The 360/(The period) = 3.6
h = The horizontal shift = 25°
D = The vertical shift = 7 meters
The MOST appropriate equation of the sinusoidal function h(t) is therefore;
h(t) = 6·sin(3.6·(t - 25)) + 7
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1) Alice is a truck driver who drives the same route every day for 5 days. On the
last day she takes a detour that adds 17.3 miles to her daily mileage. At the end
of the 5 days, Alice has driven 927.8 miles. How many miles does Alice drive on
her regular route when there is no detour?
Answer:
Alice drives 168.26 miles daily and 841.3 miles per 5 days on her regular route when there is no detour.
Step-by-step explanation:
First, we need to divide 927.8 miles by 5.
927.8 ÷ 5 = 185.56 is her daily mileage, including the detour.
Since her detour added 17.3 miles to her daily mileage, we need to subtract this from her current daily mileage.
185.56 - 17.3 = 168.26 is her daily mileage when there is no detour.
Now, in order to find her mileage for 5 days, we need to multiply this number by 5.
168.26 x 5 = 841.3
Therefore, Alice drives 168.26 miles daily and 841.3 miles per 5 days on her regular route when there is no detour.
Comprueba que la ecuación 3x + 3 = 9 tiene por solución x = 2; para ello sustituye
en la ecuación la incógnita x por 2:
3 • ___ + 3 = 9
2 es __________________ de la ecuación 3x + 3 = 9
AYUDAAAAAAAAA
Answer:
3 x 2 + 3 = 9 ✔️
2 es x de la ecuación 3x + 3 = 9
Si esto es correcto, por favor dígame Brainliest.
Solve the inequality.
3x + 10 < 3 or 2x – 5 > 5
Answer:
3x + 10 < 3
=> 3x < -7
=> x < -7/3
2x - 5 ≥ 5
=> 2x ≥ 10
=> x ≥ 5
Answer:
x < -7/3 or x > 5
Find the least common multiple of 4 and 20
Answer:
Heya mate....
Step-by-step explanation:
This is ur answer.....
LCM of 4 and 20 is 20.Hope it helps!
Brainliest pls!
Follow me :)
Answer:
Technically, it could be one. since one goes into everything but I'm not sure if you're teacher accepts that answer. So 2. 2 goes into 4 two times and 2 goes into 20 ten times
Step-by-step explanation:
Convert 12.12 to a fraction
Answer:
303/25 is an equivalent fraction form for decimal 12.12.
Simplify the following expression
by combining like terms.
-2a+2+a+6=[?]a+[ ]
Answer:
-a + 8.
Step-by-step explanation:
-2a + 2 + a + 6
= -2a + a + 2 + 6
= -a + 8.
Answer:
-2a + a + 2 + 6 = [ a + 8]a + [ ]
= [ a+ 8 ]a +[ ]
= 2a + 8a
= 10a
3 points
Below are dot plots for three different data sets. The standard deviation for
these three data sets are given in the following table.
Standard deviation
Data Set
59
Looking at the dot plots and without calculating the
standard deviations, match the data sets to the
standard deviations.
Standard deviation of 5.9
Da Sot
Data Set
Standard deviation of 3.3
Data Set
10
15
20
Standard deviation of 23
Answer:
I don't understand this
please solve these please
Answer:
A no. ans is 17a/20
B no. ans is 10c-7d/35
C no. ans is +1/−1⋅2/2⋅−1⋅3/2⋅−1⋅4
I only know this much answer.Sorry. but hope this is helpfull.true or false, in deductive thinking, you start with a given set of rules and conditions and determine what must be true as a consequence.