Answer:
Quantity of fuel is 24 L, based on the model S=2400/Q when S=100
Step-by-step explanation:
If the output power of the car remains constant, the speed would reduce as the masses increase, which is the shown in the observed data.
Hence S does NOT vary directly with the mass and quantity, but varies INVERSELY with the mass and fuel (which has a mass).
Many models are possible to fit the results. Product models with a single constant k
S(m,q) = kmq and S(m,q) = k/mq
do not fit both observation, hence rejected.
A possible model with two constants is shown below
S(m,q) = k1/m + k2/q..................(1)
1. m=220, q=30 => 80 = k1/220 + k2/30 ..........(2)
2. m=300, q=40 => 60 = k1/300 + k2/40 ..........(3)
Solve system (2) and (3) gives k1=0, k2 = 2400.
So it appears that the speed is independent of the mass (m) [unlikely], but inversely proportional to the quantity (q) of fuel, giving
S(q) = 2400/q
When speed = 100 km/h, and mass = 250 kg, substitute
100 = 2400/q => q=2400/100 = 24
Please answer this question now
Answer:
y = 9.1
Step-by-step explanation:
By applying Sine rule in the given triangle WXY,
[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinY}}{\text{WX}}=\frac{\text{SinX}}{\text{WY}}[/tex]
[tex]\frac{\text{SinW}}{\text{w}}=\frac{\text{SinY}}{\text{y}}=\frac{\text{SinX}}{\text{x}}[/tex]
Since m∠W + m∠X + m∠Y = 180°
m∠W + 58° + 106° = 180°
m∠W = 180° - 164°
m∠W = 16°
[tex]\frac{\text{Sin16}}{\text{w}}=\frac{\text{Sin106}}{\text{y}}=\frac{\text{Sin58}}{\text{8}}[/tex]
[tex]\frac{\text{Sin106}}{\text{y}}=\frac{\text{Sin58}}{\text{8}}[/tex]
y = [tex]\frac{8\times (\text{Sin106})}{\text{SIn58}}[/tex]
y = 9.068
y ≈ 9.1
An investment counselor calls with a hot stock tip. He believes that if the economy remain strong the investment rules will result In a profit of $30,000. If the economy grows at a moderate pace the investment will result in a profit of $10,000 however if the economy goes into recession the investment will result in a loss of $30,000. You contact and economics who believes there is a 20% probability the economy will remain strong a 70% probability the economy will grow at a moderate pace in a 10% probability the economy will slip into recession. What is the expected profit from this investment?
Answer: $10,000
Step-by-step explanation:
Given the following :
Profit if economy remains strong = $30,000
Profit if economy grows at moderate pace = $10, 000
Loss if economy goes into recession = $30,000
Probability that economy will remain strong = 20% = 0.2
probability the economy will grow at a moderate pace = 70% = 0.7
probability the economy will slip into recession = 10% = 0.1
Expected value = sum of (x * p(x))
Here expected value equals;
Strong economy profit = $30,000 * 0.2 = $6000
Moderate economy profit = $10,000 * 0.7 = $7000
Loss on Recession = $30,000 * 0.1 = $3000
Expected profit = $(6000 + 7000 - 3000)
Expected profit = $10,000
In how many ways can you put seven marbles in different colors into four jars? Note that the jars may be empty.
Answer: 16,384
Step-by-step explanation:
The seven marbles have different colours, so we can differentiate them.
Now, suppose that for each marble we have a selection, where the selection is in which jar we put it.
For the first marble, we have 4 options ( we have 4 jars)
For the second marble, we have 4 options.
Same for the third, for the fourth, etc.
Now, the total number of combinations is equal to the product of the number of options for each selection.
We have 7 selections and 4 options for each selection, then the total number of combinations is:
C = 4^7 = 16,384
Answer:
the answer is 16384
Step-by-step explanation:
have a nice day.
What is the diameter of the circle whose center is at (6, 0) and that passes through the point (2, -3)?
Answer:
10
Step-by-step explanation:
[tex]\left(x-h\right)^{2}+\left(y-k\right)^{2}=r^2[/tex]
[tex]\left(x-6\right)^{2}+\left(y-0\right)^{2}=r^2\\[/tex]
We used (2,-3)
[tex]\left(2-6\right)^{2}+\left(-3-0\right)^{2}=25[/tex]
[tex]r^2=25\\[/tex] , so [tex]r = 5[/tex]
But this one is asking for the diameter, and to find it. It's simply 2r.
2*5 = 10
Please help I don't understand this at all
Answer:
Since ΔABC is equilateral, ∠ACB = 60°. Since ΔCED is isosceles (we know this because CE = ED from the graph), ∠ECD = ∠EDC from Base Angles Theorem, and since the sum of angles in a triangle is 180°, they measure (180 - 32) / 2 = 74° each. Since BCD is a straight line, it measures 180° so we can write:
60 + x + 74 = 180
134 + x = 180
x = 46°
Answer:
46 degrees
Step-by-step explanation:
Since triangle ABC is equilateral that means each angle in that triangle is 60 degrees.
We also know that for triangle ECD angle C and angle D have to be 74 degrees, because a triangle has 180 degrees in total and the only unique angle is at the top which is 32. So it is 180-32=148, than 148/2=74.
We than know that a half circle is 180 degrees aswell, so we do 180-60=120
120-74=46
What is the apothem of a equilateral triangle with radius 9cm
Answer:
4.5 cm
Step-by-step explanation:
apothem=R/2=9/2=4.5 cm
Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, 0), B(6, 0), C(6, 7), D(2, 7). What is the area of rectangle A, B, C, D? square units NEED ASAP 40 POINTS LIGIT
Answer:
[tex]\boxed{\sf \ \ 28 \ \ }[/tex]
Step-by-step explanation:
Hello,
Please find attached the graph
AB = 6-2 = 4
DA = 7-0 = 7
So the area of the rectangle is AB * DA = 4 * 7 = 28
Hope this helps
Examine the diagram of circle C. Points A, B, and Q are on circle C. Given that m∠ACB=52∘, what is the arc length of AQB⌢?
Hey there! :)
Answer:
Third choice: 13π/15 in.
Step-by-step explanation:
Begin by finding the circumference of the entire circle. Use the formula
C = 2rπ to solve:
C = 2(3)π
C = 6π.
Next, we can set up a proportion to find the arc length of AQB:
[tex]\frac{6\pi }{360}= \frac{x}{52}[/tex]
Cross multiply:
52 · 6π = 360 · x
312π = 360x
Divide both sides by 360:
312π/360 = 360x/360
x = 13π/15 in.
Answer:
The answer is 77n/15 inches :)
Step-by-step explanation:
Pam works as an office administrator. She spends $7500 of her income on personal expenses each year. If this represents 18% of her salary, how much money does Pam earn in one year?
Answer: Pam's total salary is $41666.666
Step-by-step explanation:
Assume her total earning or salary per year = y
Personal expenses spent yearly = $7500
Personal expenses yearly ($7500) = 18% of y
100%y =
18% of y = 7500
(18/100)y = $7500
100% y = Total salary
0.18y = $7500 - - - - - - - (1)
1y = Total salary
(Total salary * 0.18y) = (7500 * y)
Total salary = 7500y / 0.18y
Total salary = 7500/0.18
Total salary = $41666.666
j is 7 times as large as 6. Solve for j. j=
Answer:
42
Step-by-step explanation:
7 times as large as 6 = 7 * 6
7 * 6 = 42
Hope this helps
Answer:
42
Step-by-step explanation:
Answer this in two minutes
Answer:
900
Step-by-step explanation:
a heptagon has 7 sides, so we take the hexagon's sum of interior angles an and add 180 to it's getting us, 720 + 180 = 900 degrees
74 divided by 3 times 7 equals what?
Answer:
518 / 3.
Step-by-step explanation:
(74 / 3) * 7 = (74 * 7) / 3 = 518 / 3 = 172 and 2/3 = 172.6666666667.
Hope this helps!
What is the approximate length of arc s on the circle below? Use 3.14 for Pi. Round your answer to the nearest tenth. A circle is shown. 2 rays form an angle of 45 degrees. The length of the rays is 8 inches. Arc s contains the angle measuring 45 degrees.
The length of the arc s is 6.283 inches.
Length of an ArcThe length of an arc is given by the formula,
[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360}[/tex]
where
θ is the angle, which arc creates at the center of the circle in degrees.
Given to us,Radius, r = 8 in.
Angle, θ = 45°,
Length of the Arc[tex]\rm{ Length\ of\ an\ Arc = 2\times \pi \times(radius)\times\dfrac{\theta}{360}[/tex]
[tex]\rm{ Length\ of\ the\ Arc\ s = 2\times \pi \times(8)\times\dfrac{45}{360}[/tex]
[tex]\rm{ Length\ of\ the\ Arc\ s =6.283\ inches.[/tex]
Hence, the length of the arc s is 6.283 inches.
Learn more about Length of an Arc:
https://brainly.com/question/1577784
The approximate length of arc s on the given circle is; 6.28inches
Length of an arc.The length of an arc is given by the formula;
L = (a/360) ×2πr.where, a = angle subtended by the arcr = radius of the circle.Therefore,
Length, L = (45/360) × 2 × 3.14 × 8
L = 50.24/8L = 6.28 inchesRead more on length of an arc;
https://brainly.com/question/2005046
What the answer now fast correct
Answer:
12.6 units.
Step-by-step explanation:
According to cosine formula:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]
Using cosine formula in triangle STU, we get
[tex](SU)^2=(ST)^2+(TU)^2-2(ST)(TU)\cos T[/tex]
[tex]t^2=(5)^2+(15)^2-2(5)(15)\cos (53^{\circ})[/tex]
[tex]t^2=25+225-150(0.60)[/tex]
[tex]t^2=160[/tex]
Taking square root on both sides.
[tex]t=\sqrt{160}[/tex]
[tex]t\approx 12.6[/tex]
Therefore, the value of t is 12.6 units.
Examine the system of equations. –2x + 3y = 6 –4x + 6y = 12 Answer the questions to determine the number of solutions to the system of equations. What is the slope of the first line? What is the slope of the second line? What is the y-intercept of the first line? What is the y-intercept of the second line? How many solutions does the system have?
Answer:
Examine the system of equations.
–2x + 3y = 6
–4x + 6y = 12
Answer the questions to determine the number of solutions to the system of equations.
What is the slope of the first line?
✔ 2/3
What is the slope of the second line?
✔ 2/3
What is the y-intercept of the first line?
✔ 2
What is the y-intercept of the second line?
✔ 2
How many solutions does the system have?
✔ infinitely many
The equations are a multiple of the other, therefore, by the multiplicative
property of equality, the equations are equivalent.
Response:
The slope and y-intercept of the first equation are [tex]\underline{\dfrac{2}{3} \ and \ 2}[/tex] respectivelyThe slope and y-intercept of the second equation are [tex]\underline{\dfrac{2}{3} \, and \, 2}[/tex]The system of equations have infinitely many solutions.Methods used to obtain the above response.The given system of equations are;
-2·x + 3·y = 6
-4·x + 6·y = 12
Required:
The slope of the first line.
Solution:
The slope of the first line is given by the coefficient of x when the equation is expressed in the form; y = m·x + c.
Therefore, from -2·x + 3·y = 6, we have;
3·y = 2·x + 6
[tex]y = \dfrac{2}{3} \cdot x + \dfrac{6}{3} = \dfrac{2}{3} \cdot x + 2[/tex]
[tex]y =\dfrac{2}{3} \cdot x + 2[/tex]
[tex]\underline{The \ slope \ of \ the \ first \ equation \ is \ \dfrac{2}{3}}[/tex]
Required:
The slope of the second line;
Solution:
The equation of the second line, -4·x + 6·y = 12, can be expressed in the form;
[tex]y =\dfrac{4}{6} \cdot x + \dfrac{12}{6} = \dfrac{2}{3} \cdot x + 2[/tex]
[tex]y = \mathbf{\dfrac{2}{3} \cdot x + 2}[/tex]
[tex]\underline{The \ slope \ of \ the \ second \ equation \ is \ therefore \ \dfrac{2}{3}}[/tex]
The y-intercept of the first line = 2The y-intercept of the second line = 2Given that the equation have the same slope and the same y-intercept, the equations are equations of the same line, therefore;
The equations have an infinite number of solutionsLearn more about the solutions of a system of equations here:
https://brainly.com/question/15356519
x =
117
124
107
102
145
Hint: Sum = (n-2)180
Enter
Answer:
x = 125°
Step-by-step explanation:
The given polygon is a hexagon with 6 sides.
The sum of the interior angles for any given polygon = (n - 2)180, where n is the number of sides of the polygon.
Therefore:
[tex] x + 117 + 124 + 102 + 145 + 107 = (6 - 2)180 [/tex]
[tex] x + 595 = (4)180 [/tex]
[tex] x + 595 = 720 [/tex]
Subtract both sides by 595 to solve for x:
[tex] x + 595 - 595 = 720 - 595 [/tex]
[tex] x = 125 [/tex]
x = 125°
Find the missing lengths of the sides.
Based on your work in Question 1 through 3, what is the relationship between the radius, AB , and the tangent line, BC ? What can you conclude about any tangent line to a circle and the radius of the circle? Explain.
Without further context I can't say much other than the radius is perpendicular to the tangent. In other words, the radius and tangent line form a 90 degree angle. This is one particular radius and its not just any radius. The radius in question must have the point of tangency as its endpoint.
The radius, AB is perpendicular to the tangent line, BC so their slopes are negative reciprocals of one another. Because I generated a circle at random for this activity, this conclusion likely applies to any tangent line to a circle. In other words, the tangent line to any circle is perpendicular to the radius at their point of intersection.
3) In a paddling pool there are 30 floating ducks. Each duck is marked with a number on the underside. 15 are marked with the number 1, 9 are marked with the number 2 and 6 are marked with number 3. There are prizes for those who pick a duck with the number 3 on it. What is the probability of Molly picking a duck with the number 3 on it? Give your answer as a fraction in its lowest terms.
Answer: 1/5
Step-by-step explanation:
Given the following :
Total number of ducks in pool = 30
Mark 1 = 15 ducks
Mark 2 = 9 ducks
Mark 3 = 6 ducks
Probability of picking a duck with Mark 3:
Probability = (number of required outcomes / total possible outcomes)
Number of required outcomes = number of ducks with mark 3 = 6 ducks
P(picking a duck with Mark 3) = 6/30
6/30 = 1/5
= 1/5
A King wanted to replace his Prime-Minister but didn't want to upset him too much. So he called the Prime-Minister to his chamber and put two pieces of paper in his briefcase. He told the Prime-Minister that "On one piece of paper it says 'leave' and on the second piece of paper it says 'stay'". The piece of paper that you pull out of the briefcase will decide your fate." The Prime-Minister realized that both pieces of paper say 'leave'. What should the Prime-Minister do to be able to keep his position?
Answer: Ask the king to draw first and read it. Explain that if the king selects "leave" the PM's choice could only be "stay". It is then unnecessary for the PM to draw. It avoids embarrassing the king in his lie, demonstrates the PM's intelligence, and keeps his job.
Step-by-step explanation:
PLEASE PLEASE HELP ME A pinecone drops from a tree branch that is 36 feet above the ground. The function h = -16t2 + 36 is used. If the height h of the pinecone is in feet after t seconds, at about what time does the pinecone hit the ground? Could 2 seconds be a reasonable answer to this model?
Answer:
T = 1.5s
Step-by-step explanation:
Hello,
To find the time the pincone hits the ground, we need to use the equation given.
Note that h = 0 when the pinecones hits the ground.
This question relates to motion under gravity.
h = -16t² + 36
0 = -16t² + 36
Make t² the subject of formula
16t² = 36
t² = 36 / 16
t² = 2.25
Take the square root of both sides
t = √(2.25)
t = 1.5s
The time it takes the pinecone to hit the ground is 1.5s.
Ahmed earns $1.50 for every video game he sells. When he sells one carton of 30 video game, he earns an additional $10. What is the minimum number of video games he has to sell in order to earn $450?
Answer:
Step-by-step explanation:
1.50x + 10[x/30] >= 450
x >= 246.3
check:
1.50*246 + 10*8 = 449
$450
find the value of x and explain
Answer:
D
Step-by-step explanation:
The chord- chord angle 105° is half the sum of the arcs intercepted by the angle and its vertical angle, thus
[tex]\frac{1}{2}[/tex](120 + x) = 105 ( multiply both sides by 2 )
120 + x = 210 ( subtract 120 from both sides )
x = 90 → D
PLSSSS HELP The area of a cylinder varies jointly with the radius and the height. When the radius is 3 and the height is 6 the area is 36π. Find the are when the radius is 4 and the height is 5
Answer:
167.55
Step-by-step explanation:
so it varies jointly so
A-area if cylinder
so
[tex]a \: \alpha \: \pi \: r \: ^{2} h[/tex]
so
[tex]a = k\pi \: r^{2}h[/tex]
where k is the constant
so apply the first set of values to get k=2/3
then substitute the k with the second set of values
Please answer this fast in two minutes now
Answer:
18.3Step-by-step explanation:
from cosines theorem:
t² = 11² + 14² - 2•11•14•cos87°
t² = 121 + 196 + 308•0.05236
t² = 333.12688
t = √333.12688
t = 18.2517... ≈ 18.3
Ou are taking a multiple-choice test that has 4 questions. Each of the questions has 3 answer choices, with one correct answer per question. If you select one of these choices for each question and leave nothing blank, in how many ways can you answer the questions?
Answer:
In 256 ways
Step-by-step explanation:
The number of answer choices will be; 4 * 3 = 12 answer choices
Okay, so per question we have 4 choices
The number of ways we can answer the first question is 4 ways since there are 4 choices
For the second question, 4 ways also
For the third 4 ways
And for the last question, four ways too
So the number of ways to correctly answer the question will be ;
4 * 4 * 4 * 4 = 256 ways
In the right triangle shown, DF=EF=3DF=EF=3D, F, equals, E, F, equals, 3.
How long is DEDED, E?
Choose 1 answer:
Answer:
DE = 4.24
Step-by-step explanation:
The diagram is not shown; However, the question can still be solved without the diagram.
Having said that,.
Given that
DF = EF = 3
This implies that DE is the hypothenus and will be solved using Pythagoras theorem.
DE² = EF² + DF²
Substitute 3 for EF and DF
DE² = 3² + 3²
DE² = 9 + 9
DE² = 18
Take Square Root of both sides
DE = √18
DE = 4.242640687119285
DE = 4.24 (Approximated)
Select the sequences that are geometric.
18, 36, 54, 72, …
4.1, 8.2, 16.4, 32.8, …
–7, 14, –28, 56, …
980, 784, 627.2, 501.76, …
5, 2, –1, –4, …
Answer:
BCD
Step-by-step explanation:
Answer: B,C & D
Step-by-step explanation:
Exactamente a las 6:45 am mi reloj se daño y comenzo a caminar en sentido contrario a la velocidad correcta, ahora son las 9:30 am que hora esta marcando mi reloj? ayuda :(
Answer:
El reloj está marcando:
las 4:00 horas
Step-by-step explanation:
El reloj avanzó a su mismo ritmo pero en sentido contrario a partir de las 6:45
si ahora son las 9:30 el reloj marca:
9:30 = 9horas 30minutos = 9h 30'
6:45 = 6horas 45minutos = 6h 45´
1 hora = 60'
9h 30' = 8h + 60' + 30' = 8h + 90' = 8h 90'
entonces:
8h 90'
- 6h 45'
= 2h 45
entonces el reloj está marcando 2h 45' menos que la hora en que se dañó.
por tanto:
6h 45'
- 2h 45'
= 4h 00'
El reloj ahora está marcando las
4 horas en punto.
Will there be more than one relay exchange between 2 consecutive tenths of a mile?
Answer:
No
Step-by-step explanation:
data provided in the question
Long = 2 miles
distance = [tex]\frac{2}{11}[/tex]
based on the above information,
We can conclude that
there is not more than one relay as if we divide the 2 by 11 so it comes 0.18 which is greater than 0.1
i.e
0.18 > 0.1
So there is no need for more than one relay i.e to be exchanged between two consecutive mile