Answer:
Average speed during the trip = 24 km/h
Step-by-step explanation:
Given:
Speed of cyclist uphill, [tex]v_1[/tex] = 20 km/hr
Speed of cyclist on flat ground = 24 km/h
Speed of cyclist downhill, [tex]v_2[/tex] = 30 km/h
Cyclist has traveled on the hilly road to Beast Island from Aopslandia and then back to Aopslandia.
That means, one side the cyclist went uphill will the speed of 20 km/h and then came downhill with the speed of 30 km/h
To find:
Average speed during the entire trip = ?
Solution:
Let the distance between Beast Island and Aopslandia = D km
Let the time taken to reach Beast Island from Aopslandia = [tex]T_1\ hours[/tex]
Formula for speed is given as:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
[tex]v_1 = 20 = \dfrac{D}{T_1}[/tex]
[tex]\Rightarrow T_1 = \dfrac{D}{20} ..... (1)[/tex]
Let the time taken to reach Aopslandia back from Beast Island = [tex]T_2\ hours[/tex]
Formula for speed is given as:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
[tex]v_2 = 30 = \dfrac{D}{T_2}[/tex]
[tex]\Rightarrow T_2 = \dfrac{D}{30} ..... (2)[/tex]
Formula for average speed is given as:
[tex]\text{Average Speed} = \dfrac{\text{Total Distance}}{\text{Total Time Taken}}[/tex]
Here total distance = D + D = 2D km
Total Time is [tex]T_1+T_2[/tex] hours.
Putting the values in the formula and using equations (1) and (2):
[tex]\text{Average Speed} = \dfrac{2D}{T_1+T_2}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{D}{20}+\dfrac{D}{30}}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{30D+20D}{20\times 30}}\\\Rightarrow \text{Average Speed} = \dfrac{2D\times 20 \times 30}{{30D+20D}}\\\Rightarrow \text{Average Speed} = \dfrac{1200}{{50}}\\\Rightarrow \bold{\text{Average Speed} = 24\ km/hr}[/tex]
So, Average speed during the trip = 24 km/h
Identify the relation that is not a function. weight of an apple to the apple's cost time of day to the temperature at that time weight of a person to a person's height phone number to a person's name
Let x = weight and y = height. It is possible to have a certain weight correspond to multiple heights. This means the input x has multiple output y values. Therefore, we cannot have a function here. A function is only possible if for any x input, there is exactly one y output. The x value must be in the domain.
Initial Knowledge Check
Question 2
Suppose that $4000 is placed in an account that pays 11% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year
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(b) Find the amount in the account at the end of 2 years.
?
Answer:
Step-by-step explanation:
We first need to figure out what the equation is for this set of circumstances before we can answer any questions. We will use the equation
[tex]A(t)=P(1+r)^t[/tex] which is just another form of an exponential equation where
(1 + r) is the growth rate, P is the initial investment, and t is the time in years. We will fill in the values we know first to create the equation:
[tex]A(t)=4000(1+.11)^t[/tex] which simplifies to
[tex]A(t)=4000(1.11)^t[/tex]
Now we'll just sub in a 1 for t and solve, then a 2 for t and solve.
When t = 1:
A(t) = 4000(1.11) so
A(t) = 4440
When t = 2:
[tex]A(t)=4000(1.11)^2[/tex] which simplifies to
A(t) = 4000(1.2321) so
A(t) = 4928.40
The number of patients treated at Dr. Jason's dentist office each day was recorded for seven days: 3, 8, 11, 22, 17, 5, 4. Using the given data, find the mean, median, and mode for this sample. A. mean: 10, median: 8, mode: none B. mean: none, median: 8, mode: 10 C. mean: 8, median: 10, mode: none D. mean: 14, median: 10, mode: 8
Answer: A. mean: 10, median: 8, mode: none
Step-by-step explanation:
Given : The number of patients treated at Dr. Jason's dentist office each day was recorded for seven days: 3, 8, 11, 22, 17, 5, 4.
First we arrange it order.
3, 4, 5, 8, 11, 17, 22
Mean = (Sum of observations) ÷ (Number of observations)
Number of observations = 7
Sum of observations = 3+4+5+8+11+17+22 =70
Mean = 70 ÷7 = 10
Median = Middle-most value
= 8
Mode = Most repeatted value
= none
Hence, the mean, median, and mode for this sample = A. mean: 10, median: 8, mode: none
Need help please! Oh and the options are
A. 2/3
B. 1/5
C. 4/15
D. 2/7
Answer:
C. 4/15There are 15 spaces in total with 4 shaded columnsStep-by-step explanation:
Answer:
Hey there!
The answer would be C. 4/15.
4/5(1/3)=4/15
Let me know if this helps :)
Find the exact value of cos A in simplest radical form.
Answer:
[tex] \cos(A) = \frac{2 \sqrt{6} }{7} [/tex]Step-by-step explanation:
Since we are finding cos A we have
[tex] \cos(A) = \frac{AC}{AB} [/tex]From the question
AC = √96
AB = 14
Substitute the values into the above formula
That's
[tex] \cos(A) = \frac{ \sqrt{96} }{14} [/tex]We have the final answer as
[tex] \cos(A) = \frac{2 \sqrt{6} }{7} [/tex]Hope this helps you
A certain forest covers an area of 2600 km^2. Suppose that each year this area decreases by 4.75%. What will the area be after 11 years? Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
1522km^2
Step-by-step explanation:
To solve this, first convert the percentage to a decimal. That would be .0475.
Now subtract that from 1.0 to get the factor it decreases by. This would be 1-.0475 = .9525
Multiply 2600 x (.9525)^11 = 1522.258 which rounds to 1522 km^2
Answer:
The area will be 1292.98 km² after 11 years.
Step-by-step explanation:
To find what decreases by 4.57% each year in kilometers:
2600 × 4.57/100 = 26 × 4.57
= 118.82 km²
To find the area after 11 years:
118.82 × 11 = 1307.02
2600 - 1307.02 = 1292.98 km²
1292.98 km² is the answer.
A point is randomly chosen on a map of North America. Describe the probability of the point being in each location: North America: New York City: Europe:
Answer:
We know that the map is of North America:
The probabilities are:
1) North America:
As the map is a map of North America, you can point at any part of the map and you will be pointing at North America, so the probability is p = 1
or 100% in percentage form.
2) New York City.
Here we can think this as:
The map of North America is an extension of area, and New Yorck City has a given area.
As larger is the area of the city, more probable to being randomly choosen, so to find the exact probability we need to find the quotient between the area of New York City and the total area of North America:
New York City = 730km^2
North America = 24,709,000 km^2
So the probability of randomly pointing at New York City is:
P = ( 730km^2)/(24,709,000 km^2) = 3x10^-5 or 0.003%
3) Europe:
As this is a map of Noth America, you can not randomly point at Europe in it (Europe is other continent).
So the probaility is 0 or 0%.
Answer:
North America: certain
New York City: unlikely
Europe: impossible
Step-by-step explanation:
simply
Samantha’s college runs on a trimester schedule so she receives a bill 3 times a year for tuition. Each trimester costs $1,450, and Samantha must complete 2 years of college to receive her degree. The average cost for books each trimester is $350. Approximately what will be the total cost for Samantha to get her degree?
Answer:
10800
Step-by-step explanation:
1 trimesters cost = 1450 + 350 $
2 year -> 6 trimester
1800$ x 6 = 10800 $
Please help me with this
verifying, by putting [tex] \theta=60^{\circ}[/tex]
LHS≠RHS
hence the question is FALSE
The equation of C is (x - 2)^2 + (y - 1)^2 = 25. Of the points P(0,5), Q(2,2) R(5,-2), and S(6,6), which point is located outside the circle?
Answer:
( 6,6) is outside
Step-by-step explanation:
(x - 2)^2 + (y - 1)^2 = 25
This is of the form
(x - h)^2 + (y - k)^2 = r^2
where ( h,k) is the center and r is the radius
(x - 2)^2 + (y - 1)^2 = 5^2
The center is at ( 2,1) and the radius is 5
P(0,5), Q(2,2) R(5,-2), and S(6,6)
Adding the radius to the y coordinate gives us 6 so the only point with a y coordinate on the circle is ( 2,6)
( 6,6) is outside the circle
1 - Os coeficientes numéricos de uma equação do 2º grau (ax² + bx + c = 0), são números reais representados pelas letras “a, b e c”. Para que uma equação do 2º grau possa existir, é necessário que o coeficiente “a” seja DIFERENTE de: * 1 ponto a) -2 b) -1 c) 0 d) 1 2) Usando o método de Tentativa e Erro, visto na aula, qual das alternativas abaixo representa uma raiz da equação: x²-5x+6=0 * 1 ponto a) x = 0 b) x = 1 c) x = 2 c) x = -2
Answer:
1) La opción correcta es;
c) 0
2) La opción correcta es;
c) x = 2
Step-by-step explanation:
1) La forma general de una ecuación cuadrática se puede escribir en la forma;
a · x² + b · x + c = 0
Dónde;
a, y b son los coeficientes de x², x y c es el término constante
Por tanto, para que exista un polinomio de 2º grado es necesario que el coeficiente a sea diferente de 0
De lo que tenemos;
(0) × x² + b · x + c = 0, lo que da;
(0) × x² + b · x + c = b · x + c = 0 que es una ecuación lineal o un polinomio de primer grado
Por tanto, la opción correcta es c) 0
2)
La ecuación dada se presenta como sigue;
f (x) = x² - 5 · x + 6 = 0
Usando el método de prueba y error, tenemos;
Cuando x = 0
f (0) = 0² - 5 · (0) + 6 = 6 que no es igual a 0 y, por lo tanto, no es una solución
Cuando x = 1
f (1) = (1) ² - 5 · (1) + 6 = 1 que no es igual a 0 y por lo tanto, no es una solución
Cuando x = 2
f (2) = (2) ² - 5 · (2) + 6 = 0 que es igual a 0 y por lo tanto, es una solución
Cuando x = -2
f (1) = (-2) ² - 5 × (-2) + 6 = 20 que no es igual a 0 y por lo tanto, no es una solución
Por tanto, la opción correcta es c) x = 2
The product of (4z2 + 7z – 8) and (–z + 3) is –4z3 + z2 + z – 24.
The product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24
How to find product of expressions(4z² + 7z – 8) and (–z + 3)
= -4z³+ 12z² - 7z² + 21z + 8z - 24
collect like terms= -4z³ + 5z² + 29z - 24
Therefore, the product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24
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write 1,245 in word form
Answer:
One thousand two hundred and forty five.
Hope this helps! （づ￣3￣）づ╭❤～
Step-by-step explanation:
Find the term of each sequence.
32, 80, 200, ...5th term
Answer:
t5 = 1250
Step-by-step explanation:
Each term is derived by multiplying the previous term by 2.5
t2 = t1 * 2.5
t2 = 32 * 2.5
t2 = 80
===========
tn = a*b^(n - 1)
t3 = 32*2.5^2
t3 = 200
That's just to test the formula. It does work.
===============
t5 = 32*2.5^(5 -1)
t5 = 32*2.5^4
t5 = 1250
HELP ME PLZZzzzzzzzz
Answer:
5 cm
Step-by-step explanation:
The volume (V) of milk in the container is calculated as
V = 8 × 15 × 12 = 480 cm³
After change of position with depth d then
8 × 15 × d = 480
120d = 480 ( divide both sides by 120 )
d = 4 cm
6 to the third power divided by 4+2 x 9(32x8-17x4)
Answer:
3438.
Step-by-step explanation:
6³ ÷ 4 + 2 × 9 (32 × 8 - 17 × 4)
= 6³ ÷ 4 + 2 × 9 (256 - 68)
= 6³ ÷ 4 + 2 × 9 × 188
= 216 ÷ 4 + 2 × 9 × 188
= 54 + 2 × 9 × 188
= 54 + 3384
= 3438
3438 is the answer.
Show that 12.34343434………………can be expressed in the form p/q
Answer:
1222/99
Step-by-step explanation:
12.343434.. =
= 12.(34)
= 12 34/99
= (12*99+34)/99
= (1188+34)/99
= 1222/99
Calculate the volume and surface area of a cone with the base of 20cm, the vertical hieght of 34cm and 35.6cm leaning height.
Answer:
Step-by-step explanation:
Volume = 1/3πr²h
Surface Area = πr(r+√(h²+r²))
V = 1/3π(10)²(34) = 3560 .5 cm³
SA = π(10)(10 + √(34²+10²)) = 1427.5 cm²
△ABCis reflected to form △A′B′C′. The vertices of △ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of △A′B′C′ are A′(3, −1), B′(4, 2), and C′(6, −5). Which reflection results in the transformation of △ABC to △A′B′C′? Reflection across the x-axis reflection across the y-axis reflection across y = x reflection across y=−x
Answer:
reflection across y = x
Step-by-step explanation:
Transformation is the movement of a point from its initial position to a new position. If a shape is transformed, all its point are also transformed. Types of transformation is reflection, rotation, transformation and dilation.
If a point is reflected across the x axis, the x coordinate is the same but the y coordinates is negated. If X(x, y) is reflected across the x axis the new point is X'(x, -y)
If a point is reflected across the y axis, the y coordinate is the same but the x coordinates is negated. If X(x, y) is reflected across the y axis the new point is X'(-x, y)
If a point is reflected across y = x, the x coordinate and y coordinates are interchanged. If X(x, y) is reflected across the y=x axis the new point is X'(y, x)
If a point is reflected across y = -x, the x coordinate and y coordinates are interchanged and both negated. If X(x, y) is reflected across the y=ix axis the new point is X'(-y, -x)
The vertices of △ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of △A′B′C′ are A′(3, −1), B′(4, 2), and C′(6, −5). The reflection of △ABC to form △A′B′C′ shows a reflection across x axis since the x and y coordinates are interchanged
Answer:
reflection across y = x
Step-by-step explanation:
Given the sequence 4, 8, 16, 32, 64, ..., find the explicit formula. A. an=10(2n−1) B. an=5(2n−1) C. an=4(2n−1) D. an=20(2n−1)
Answer:
. an=4(2n−1)
Step-by-step explanation:
The generic version was basedOn the brand name and was 2/3 the size of the brand name. If the generic television set is 12 inches by 24 inches what are the dimensions of the brand name television
Answer:
18 inches by 36 inches.
Step-by-step explanation:
Since we have given that
The generic version was basedOn the brand name and was 2/3
And given Dimensions of generic version is given by 12inches ×24inches
If we use the first dimensions of 12inches we have
12=2/3 × brand
12×3/2 = brand
=18inches= brand
we use the first dimensions of 24 inches we have
24=2/3 × brand
24×3/2 = brand
=36 inches= brand
brand= 36 inches
Therefore,the dimensions of brand name will be 18 inches by 36 inches.
I need help with 3 and 4
Answer:
Step-by-step explanation:
3) G
Step-by-step explanation:
Q(-1,-1) R(3,1) S(2,-4)
x+2 y+3 translation then rotation 180 (x,y) be (-x,-y)
Q -1+2 -1+3 (1,2) (-1,-2)
R 3+2 1+3 (5,4) (-5,-4)
S 2+2 -4+3 (4,-1)
A shipping company borrows $70 million at 5% p.a. compound interest to build a new cruise ship. If it repays the debt after 3 years, how much interest will the company pay?
Answer:
about 11.03 million
Step-by-step explanation:
Use the equation I = P(1+r/100)^n - P (I is the compound interest, P is the principle, r is the rate percent, and n is the number of years):
Substitute the values given:
I = 70,000,000(1 + 5/100)^3 - 70,000,000
Use a calculator to solve and you will get ~11.03 million.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
The interest the company paid is $11 million.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
P = $70 million
r = 5%
t = 3 years
n = 1
A = 70 ( 1 + 0.05)³
A = 70 ( 1.05)³
A = 70 x 1.05 x 1.05 x 1.05
A = $81 million
The amount of interest.
= A - P
= 81 - 70
= $11 million
Thus,.
The interest the company paid is $11 million.
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Em um posto de combustível, o litro da gasolina estava custando R$2,40.Um cliente gastou R$72,00 para encher o tanque de seu carro. O valor do litro da gasolina sofreu 2 aumentos sucessivos,ambos de 10%. Quando o mesmo cliente gastara para encher o tanque do seu carro, após esees aumentos
Answer:
english i think u need hekp
Solve. 100+[12×{20−(10÷5)}]
Answer:
316
Step-by-step explanation:
A. 115
B. 167
C. 126
D. 96
Answer:
126
Step-by-step explanation:
Let x be the missing length
The triangles are similar:
● UE/140 = 45/x
From the graph we deduce that:
● UE = 140 - 90 = 50
Replace UE by its value
● 50/ 140 = 45/x
Switch x and 50
● x / 140 = 45/50
45/50 is 9/10 wich is 0.9
● x/140 = 0.9
Multiply 0.9 by 140
● x = 140 × 0.9
● x = 126
Answer:
I think its c 126
Step-by-step explanation:
in the equation x=c-b/a, find the value of x when c=10, b=2, and a=2
Answer:
9
Step-by-step explanation:
x = c - b/a
x = 10 - 2/2
x = 10 - 1
x = 9
Answer:
x = c - b (divided by) a
Step-by-step explanation:
x = 10 - 2over2
x = 10 - 1
x = 9
try 18/2 since that part is a fraction.
Maurice needs 45 exam review books for the students in his math class. The local bookseller will sell him the books at $3 each. He can also purchase them over the internet for $2 each plus $35 for postage. How much does he save by accepting the better offer?
Answer: he will save $42.50
Step-by-step explanation:
45÷3=15
45÷2+35=57.50
57.50-15= $42.50
Find the value of x. Your answer must be exact.
X
12.
600
X=
Answer:
x = 6√3Step-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find x
To find x we use sine
sin ∅ = opposite / hypotenuse
From the question
The hypotenuse is 12
The opposite is x
Substitute the values into the above formula and solve for x
That's
[tex] \sin(60) = \frac{x}{12} [/tex]
[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]
[tex]x = \frac{ \sqrt{3} }{2} \times 12[/tex]
We have the final answer as
x = 6√3Hope this helps you
Please please please help
Answer:
[tex]\boxed{s=3}[/tex]
Step-by-step explanation:
Use a proportion to solve for the missing side length - a/c = b/d.
AB = XYBC = YZ4/2 = 6/s cross-multiply
4s = 12 divide by 4
[tex]\boxed{s=3}[/tex]
Answer:
Step-by-step explanation:
Because these triangles are similar, their sides exist in proportion to one another. Their angles are exactly the same. but their sides are proprtionate IF they are similar. We are told they are so setting up the proportion:
[tex]\frac{4}{2}=\frac{6}{s}[/tex] and cross multiply:
4s = 12 so
s = 3
You could also look at the fact that the height of the larger triangle is 4 and the height of the smaller is 2, so the larger is twice as big as the smaller; likewise, the smaller is half the size of the larger (that means the same thing). So if the larger side is 6, half of that is 3.
