Answer:
A) 0.3
B) 0.2
Step-by-step explanation:
We are given the following in the question:
P(Industry in Shanghai) = P(A) = 0.7
P(Industry in Beijing) = P(B) = 0.4
P(Industry in Shanghai or Beijing) = P(A∪B) = 0.8
a)We need to find the probability that the industry is located in both Shanghai and Beijing that is we need to find P(A∩B)
Formula:
P(A∪B) = P(A) + P(B) - P(A∩B)
Putting the values we get,
0.8 = 0.7 + 0.4 - P(A∩B)
P(A∩B) = 0.3
Thus, the probability that the industry is located in both Shanghai and Beijing is 0.3.
b)Now, we need to find the probability that it is not in either cities
Probability = 1 - Probability(Industry in Shanghai or in Beijing)
= 1 - P(A∪B)
= 1 - 0.8
= 0.2
The probability that the industry will locate in both Shanghai and Beijing is 0.3, while the probability that it will locate in neither of the cities is 0.2.
Explanation:This problem is solved using the concept of probability in Mathematics. Let's denote A as the event that an industry with locate in Shanghai and B is the event that it will locate in Beijing.
The probability of A, P(A), is given as 0.7 and the probability of B, P(B), is given as 0.4. The probability it will locate in either of the cities, P(A U B), is given as 0.8.
We know, P(A U B) = P(A) + P(B) - P(A ∩ B), where P(A ∩ B) represents the probability the industry will locate in both cities. Using the given probabilities:
0.8 = 0.7 + 0.4 - P(A ∩ B), so P(A ∩ B), the probability the industry will locate in both cities, is equal to 0.3. (a)
The probability the industry will not locate in either of the cities, denoted as P'(A U B), is equal to 1 - P(A U B) = 1 - 0.8 = 0.2. (b).
This means there is a 30% chance the industry will locate in both Shanghai and Beijing, and a 20% chance it will locate in neither city.
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A 27-foot pole casts a 25-foot shadow. At the same time, a nearby tower casts a 45-foot shadow. How tall is the tower?
Answer:
The answer to your question is: 48.6 ft
Step-by-step explanation:
See the picture below
Use the Thales's theorem to solve this exercise
x / 27 = 45 / 25
x = 45(27) / 25
x = 1215 / 25
x = 48.6 ft
Answer: 48.6
Step-by-step explanation:
((:
The perimeter of a rectangle is 66 inches. If the length is 3 less than five times the width, find the length and width.
Answer:
length: 27 incheswidth: 6 inchesStep-by-step explanation:
Let w represent the width of the rectangle. The perimeter is twice the sum of length and width so is ...
P = 2(L + w) . . . . . . equation for perimeter
66 = 2((5w-3) +w) . . . substitute the given values
33 = 6w -3 . . . . . . . divide by 2 and collect terms
36 = 6w . . . . . . . . . add 3
6 = w . . . . . . . . . . . .divide by 6
L = 33-6 = 27
The length is 27 inches; the width is 6 inches.
Do more than 50 percent of the children in a certain group have brown hair?
(1) 70 percent of the boys in the group have brown hair.
(2) 30 percent of the children in the group are girls with brown hair.
Answer:
What we know is that 30% of the group have brown hair and are girls. It means that in the other 70% we have the boys with brown hair, the other boys and the other girls.
In the case all the girls have brown hair, the 70% remaining would be boys. So 70% of then would have brown hair. (0.7*0.7=0.49 -> 49% of the children would be brown hair) so 49% (boys) and 30% (girls) are more than 50%..
Now, let's suppouse that 90% of the group are girls. It means 10% are boys and 70% of that 10% (=7%) are the boys in the group that have brown hair. Now 7% + 30% of the children have brown hair, wich isn't more than the half.
We have explained with two extreme cases that the information is not enough for making a precise answer
Marcus purchased 80 shares of stock in a computer company at $74.19 per share and Taylor purchased 65 shares of stock in a different computer company for $85.21 per share. After holding the stock for two years, Marcus sold his for a total of $6,404.57, and Taylor sold hers for a total of $6,192.83. Which person had a higher ROI and by how much?
Answer: Taylor, by 3.9 pp ($184.81)
Step-by-step explanation:
Marcus: Invested 80 x 74.19 = 5935.20
Taylor: Invested 65 x 85.21 = 5538.65
After 2 y
Marcus: Sold for 6404.57
Taylor: Sold for 6192.83
Net profit
Marcus: 6404.57 - 5935.20 = 469.37
Taylor: 6192.83 - 5538.65 = 654.18
ROI
Marcus: 469.37/5935.20 * 100 = 7.91%
Taylor: 654.18/5538.65 * 100 = 11.81%
Taylor had a higher ROI by 3.9 percentage points (11.81 - 7.91)
George picked flowers every day for three days. On the first day George picked 2 flowers. On the second day George picked 6 flowers, and on the third day he picked 10. A function can model George's sequence. What is the slope of that function? A) 2 B) 3 C) 4 D) 5
Answer:
The answer to your question is: 4
Step-by-step explanation:
first day second day third day
2 6 10
represent them considering number two
2 2 + 4 2 + 8
Here, we can notice that the increase
from day 1 to day 2 was 4 and the
increase from day 2 to three was also 4
then the slope will be 4.
On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
A. 0.027
B. 0.090
C. 0.417
D. 0.657
E. 0.900
Answer: The answer is d.
Step-by-step explanation: Ok, so, we know that we have 3 radio stations, each one has a 30% chance of broadcasting a song that leo likes.
Lets see the cases:
Station A has a probability of 0.30 to broadcast a song, but let's suppose that it doesn't, then we go to station B, who has te same probability, 0.30, but for this to happen, we first must have the 0.70 prob of A to broadcasting another song, so here we have a probability of (0.30)*(0.70).
Now with a similar way of thinking, if Station B also fails, we will have a probability of 0.70*0.70*0.30 for Station C succes.
Also, there is the case were station A broadcast the nice song, which we already know that is with probability of 30%.
So, the total probability will be the sum of the 3 cases: 0.30 + 0.30*0.70 + 0.30*0.70*0.70 = 0.657.
The blue line arrives every 10 minutes the red line arrives every 8 minutes and the yellow line arrives every 12 minutes, how long until they arrive at the station at the same time
Answer:
They all arrive at the station at the same time after 120 minutes.
Step-by-step explanation:
For solving these types of question we use Least Common Multiples (L.C.M.).
Since for getting a common time they will meet, we interested in a multiplier.
Now, We will take L.C.M. of all the numbers:
10 = 2 × 5
8 = 2 × 2 × 2
12 = 2 × 2 × 3
∴ L.C.M. = 2 × 2 × 2 × 3 × 5 = 120 {taking smallest common multiples)
Thus, they all lines will meet after 120 minutes.
Plzzzz help quickly!!! Worth 20 points will mark brainliest! The data below shows cell phone bills for various numbers of minutes used.
What does the slope of the line of best fit represent?
A. There is a charge of $0.15 for each minute of use.
B. There is a charge of $0.45 for each minute of use.
C. There is a monthly fee of $15.00
D. There is a monthly fee of $45.00
Answer:
A
Step-by-step explanation:
Option: A is the correct answer.
A. There is a charge of $0.15 for each minute of use.
Step-by-step explanation:We know that the slope of the line of best fit represents the ratio of change in the dependent variable to the change in the independent variable.
Here the dependent variable is: Phone bill
and the independent variable is the number of minutes used.
Let the line of best fit passes through (100,60) and (300,90).
This means that the slope of the line of best fit is:
[tex]Slope=\dfrac{90-60}{300-100}\\\\Slope=\dfrac{30}{200}\\\\Slope=0.15[/tex]
Hence, the answer is: Option: A
Explain why each function is continuous or discontinuous. (a) The temperature at a specific location as a function of time (b) The temperature at a specific time as a function of the distance due west from New York City (c) The altitude above sea level as a function of the distance due west from New York City (d) The cost of a taxi ride as a function of the distance traveled (e) The current in the circuit for the lights in a room as a function of time
Answer:
(a) The temperature at a specific location as a function of time.
This is a continuous function as the temperature cannot increase in an instant like time.
(b) The temperature at a specific time as a function of the distance due west from New York City.
This is a continuous function as the temperature in one location is affected by its neighboring places.
(c) The altitude above sea level as a function of the distance due west from New York City.
The altitude above sea level can be discontinuous at a cliff, or continuous at very deep hole.
(d) The cost of a taxi ride as a function of the distance traveled.
This is a discontinuous function as the cost still raises if you make a stop.
(e) The current in the circuit for the lights in a room as a function of time.
This is a discontinuous function as the function takes the value of 0 when the switch is off and 1 when the switch is on.
The electron traveling speed makes this discontinuous.
Final answer:
a) Continuous
b) Continuous
c) Continuous
d) Discontinuous
e) Continuous
Explanation:
In examining whether a function is continuous or discontinuous, we consider if there are any interruptions in the value of the function as the input changes. Here's an analysis for each given scenario:
The temperature at a specific location as a function of time tends to be continuous because temperature normally changes gradually over time without abrupt jumps.The temperature at a specific time as a function of the distance due west from New York City could be continuous, assuming that there are no abrupt changes in the geographical factors that influence temperature.The altitude above sea level as a function of the distance due west from New York City is typically continuous, generally changing smoothly as one moves across the landscape.The cost of a taxi ride as a function of the distance traveled is often a piecewise function, with portions being continuous within certain distance intervals, but possibly discontinuous at specific points where the rate changes (e.g., base fare to metered fare).The current in the circuit for the lights in a room as a function of time is generally continuous when the lights are on, but if the light switch is flipped, this creates a discontinuity at the moment the lights turn on or off.A continuous probability function has been defined such that probability equals area under the curve of the function over an interval. For real-world phenomena like temperature and altitude, these functions tend to be continuous as they reflect gradual changes over time or distance.
A dealer bought 50 caps for Rs 1500. He sold 15 for Rs. 35 each and 15 for Rs. 40 each. At what price per cap should he sell the remainder to gain 15% on his outlay?
Answer:
₹30/cap
Step-by-step explanation:
To gain 15%, the dealer must have total revenue of ...
₹1500 × 1.15 = ₹1725
His revenue so far is ...
15 × ₹35 +15 × ₹40 = ₹1125
There are 50 -15 -15 = 20 caps remaining, and the dealer wants additional revenue of ₹1725 -1125 = ₹600. He must sell them at a price of ...
₹600/(20 caps) = ₹30/cap
The area of a certain rectangle is 288 yd2. The perimeter is 68 yd. What are the dimensions of the rectangle?
A) 24 yd by 10 yd
B) 18 yd by 16 yd
C) 22 yd by 12 yd
D) 36 yd by 8 yd
Please show work-THX
Answer:
The rectangle is 16*18
Step-by-step explanation:
The area of a rectangle is length * width and the perimeter is 2 times length * width
A = l*w
P = 2(l+w)
Replacing A and P
288 = l*w
68 = 2(l+w) => 34 = l+w => 34 - w = l
replacing l in the area
288 = (34 - w) w
w^2 - 34w + 288 = 0
(w - 16)(w - 18)
w = 16
w = 18
replacing in 34 - w = l
you get that when w = 16, l = 18 and when w = 18, l = 16
You received a discount on each book you buy . The original price of each book is x dollars You buy 5 books for a total of (5x - 15 dollars factor the expression using GCF
Answer:
5(x -3)
Step-by-step explanation:
The GCF of 5 and 15 is 5, since 5 is a factor of 15. Factoring that out gives ...
5x -15 = 5(x -3)
Can someone please help me with this problem? Thank you.
Answer:
HOPE IT HELPS YOU
THANKYOU
PLEASE THANK ME
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If this is calculus AP the answer will be right
=73
you add both angles 56 and 51 then you compare it with the high of the rectangle 7.9 ft to get the answer.
find and simplify the difference quotients f(6+h) – f(6)
f(x) = 15x² + 6
Answer:
180h + 15h²
Step-by-step explanation:
Since both have same function i.e. function of f, so we simply put 6 + h and 6 in place of x in f(x)
Here,
f(x) = 15x² + 6
Then, f(6+h) - f(6)
= [15(6 + h )² + 6] - [15(6 )² + 6]
⇒ [15 (36 + 12h + h²) + 6] - [15 × 36 + 6]
⇒ [ 15 × 36 + 15 × 12h + 15h² + 6 - 15 × 36 - 6 ]
⇒ 15 × 12h + 15h²
⇒ 180h + 15h²
Find the break-even point for the given cost and revenue equations. Round to the nearest whole unit.
C = 15n + 269,000
R = 95n
Answer:
[tex]n=3,587\ units[/tex]
Step-by-step explanation:
we know that
The term Break even is when the Revenue is equal to the Cost (the profit is equal to zero)
so
we have
[tex]C=15n+269,000[/tex]
[tex]R=95n[/tex]
Equate the equations
[tex]95n=15n+269,000[/tex]
Solve for n
[tex]95n-15n=269,000[/tex]
[tex]75n=269,000[/tex]
[tex]n=3,587\ units[/tex]
Answer:
It’s C, 3363
Step-by-step explanation:
Mary has a third of the money that Erin has. Erin has $8 less than John. Together they have $267. How much money does each of them have?
Mary has $37, Erin has $111, and John has $119 and together they have $267 .
1. Mary has a third of the money that Erin has. Let's represent the amount of money Mary has as "m" and the amount Erin has as "e."
Based on the information given, we can write the equation:
m = (1/3)e
2. Erin has $8 less than John. Let's represent the amount Erin has as "e" and the amount John has as "j."
Based on the information given, we can write the equation:
e = j - 8
3. Together they have $267. This means the total amount of money they have is the sum of what Mary, Erin, and John have:
m + e + j = 267
Now, let's substitute the values we know into the equations to solve for the unknowns.
From equation 1, we have m = (1/3)e. Substituting this into equation 3, we get:
(1/3)e + e + j = 267
To simplify the equation, let's multiply all terms by 3 to eliminate the fraction:
e + 3e + 3j = 801
4e + 3j = 801
From equation 2, we have e = j - 8. Substituting this into the above equation, we get:
4(j - 8) + 3j = 801
Simplify and solve for j:
4j - 32 + 3j = 801
7j - 32 = 801
7j = 801 + 32
7j = 833
j = 833 / 7
j = 119
Now that we know the value of j (which represents the amount John has), we can substitute it back into equation 2 to find the value of e (the amount Erin has):
e = j - 8
e = 119 - 8
e = 111
Finally, we can substitute the values of e and j into equation 1 to find the value of m (the amount Mary has):
m = (1/3)e
m = (1/3)111
m = 37
So, Mary has $37, Erin has $111, and John has $119.
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An insurance company has hired a sales representative, and has agreed to pay him a fixed salary of $2,000 per month, along with a commission of 2% on every sale made by him in a month. For the month of March, 20X1, the sales representative made a total sales of $15,000. Calculate the cost of the sales representative for the month.
Answer:
$2300
Step-by-step explanation:
The commission earned by the representative is ...
commission = 0.02 × $15,000 = $300
so the total to be paid to the sales representative is ...
salary + commission
= $2000 +300 = $2300
Adam bought a $1,670 custom video game/sound system on a special no interest plan. He made
$100 down payment and agreed to pay the entire purchase off in 1 and half years. The minimum monthly
payment is $10. If he makes the minimum monthly payment up until the last payment, what will be
the amount of his last payment?
Hello!
if he bought it with no interest applied, then the last payment will be $1400
1670 - 100 = 1570
if he has to pay it off in 18 months (1 and a half years), and only pays $10 per month, that means he will pay off $170 before the last payment is due.
1570 - 170 = 1400
so his last payment will have to be $1400 to pay it off completely
I hope this helps, and have a nice day!
$1,400 is the amount of his last payment.
1. First, determine the total amount Adam needs to pay after the down payment. Adam made a $100 down payment on the $1,670 system, so the remaining amount to be paid is:
[tex]\[ \text{Remaining amount} = \$1,670 - \$100 = \$1,570 \][/tex]
2. Next, calculate the total number of monthly payments Adam will make. Since he agreed to pay off the purchase in 1 and a half years, and there are 12 months in a year, the total number of payments is:
[tex]\[ \text{Total payments} = 1.5 \times 12 = 18 \text{ payments} \][/tex]
3. The minimum monthly payment is $10. To find out how much Adam will have paid after 17 payments (one less than the total number of payments), we multiply the monthly payment by the number of payments:
[tex]\[ \text{Amount paid after 17 payments} = 17 \times \$10 = \$170 \][/tex]
4. Now, subtract the amount paid after 17 payments from the remaining amount to find the last payment:
[tex]\[ \text{Last payment} = \$1,570 - \$170 = \$1,400 \][/tex]
Therefore, the amount of Adam's last payment will be $1,400.
A manufacturer of tennis rackets finds that the total cost of manufacturing x rackets/day is given by 0.0003x2 + 4x + 500 dollars. Each racket can be sold at a price of p dollars, where p = −0.0002x + 9 Find an expression giving the daily profit P for the manufacturer, assuming that all the rackets manufactured can be sold. Hint: The total revenue is given by the total number of rackets sold multiplied by the price of each racket. The profit is given by revenue minus cost. (Simplify your answer completely.)
Answer:
[tex]PT =-0.0005^2 +5x - 500[/tex]
Step-by-step explanation:
We have price (P) = [tex]-0.0002x + 9[/tex]
to calculate Total revenue (TR) we have to multiply Price by Production quantity.
[tex]TR=P * X[/tex] , we denote production quantity with the letter X.
[tex] TR=(-0.0002x + 9)*x[/tex]
We apply distributive law and then we have:
[tex] TR=-0.0002x^2 + 9x[/tex] , this is the Total revenue (TR) of selling X amount of production at a P price.
Now we only have to find the Profit (PT) using the formula:
[tex]PT=TR - TC[/tex] , TR is total revenue and TC is total cost
The expression of the daily profit (PT) for the manufacturer is:
[tex] PT=-0.0002x^2 + 9x - (0.0003x^2 + 4x + 500)[/tex]
[tex] PT= - 0.0002^2 + 9x -0.0003^2 -4x -500[/tex]
[tex]PT =-0.0005^2 +5x - 500[/tex]
The daily profit for the manufacturer, given by P, is equal to -0.0005x^2 + 5x - 500, where x represents the number of rackets manufactured and sold each day.
Explanation:In this example, the manufacturer's daily profit, P, is given by the difference between the total revenue and the total cost. The total revenue is found by multiplying the price of each racket, p , by the number of rackets sold daily, x. i.e, px. The total cost is given by the equation 0.0003x^2 + 4x + 500. Thus, the daily profit is P = (px) - (0.0003x^2 + 4x + 500). Substituting the expression for p gives P = [(−0.0002x + 9)x] - (0.0003x^2 + 4x + 500), which simplifies to P = - 0.0002x^2 + 9x - 0.0003x^2 - 4x - 500. Further simplification leads to P = -0.0005x^2 + 5x - 500. Therefore, the daily profit for the manufacturer is given by P = -0.0005x^2 + 5x - 500.
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The population of a community is known to increase at a rate proportional to the number of people present at time t. The initial population P0 has doubled in 5 years. Suppose it is known that the population is 12,000 after 3 years. What was the initial population P0? (Round your answer to one decimal place.)
Answer:
The initial population P0 is 7500
Step-by-step explanation:
First of all, we are told that the population is proportional to time. This means that as time goes by, the population will increase. This type of relationship between two variables has the form of a linear equation expressed as:
y = mx + b,
where m is the slope of the curve and b is the intercept of it.
In this case we can state the following equation:
P = mt + P0
Where P is the population at a certain time "t", "m" is the slope of the curve, "t" is the time (this is the independent variable) and P0 is the intercept of the curve and represents the initial population.
Once we state the equation, let's see what we know:
If t = 0, then P = P0
If t = 3, then P = 12000 just as we are told
and if t = 5, then P = 2 P0 because after five years the population has doubled compared to the initial population (P0).
From the definition of the slope of the curve:
(Y2 - Y1)/(X2-X1) = m
and using the data described before we can formulate the slope value:
m = (2P0 - P0)/(5-0)
m = (2P0 - P0)/5
m = P0/5
Then, let's replace the value of m in the following equation:
P = mt + P0
12000 = (P0/5) × 3 + P0 → This is the equation presented when 3 years has gone by and we now have a population of 12000.
12000 = (3/5) P0 + P0
12000 = (8/5) P0
12000×5/8 = P0 = 7500
Then we can calculate the value of the slope m:
m = P0/5
m = 7500/5 = 1500
Now, knowing the value of m and the initial population P0 we are able to calculate the population at any value of "t".
The line segment EF has a midpoint with coordinates M (-2,2). Use the formula to find the coordinates of the other endpoint given that E is located at coordinates (2,8).
Answer:
The answer to your question is: F = (-6, -4)
Step-by-step explanation:
Segment = EF
mpM = (-2, 2)
first point = E = (2, 8)
second point = F = (x, y)
Formula
Xmp = (x1 + x2) / 2 Ymp = (y1 + y2) / 2
x2 = 2xmp - x1 y2 = 2ymp - y1
Process
x2 = 2(-2) - 2 y2 = 2(2) - 8
x2 = -4 - 2 y2 = 4 - 8
x2 = -6 y2 = -4
F = (-6, -4)
The coordinates of the other endpoint of the line segment EF, given that the midpoint M is (-2,2) and the endpoint E is (2,8), are (-6,-4). This is determined by using the midpoint formula and solving for the remaining variables.
Explanation:To find the coordinates of the other endpoint F, we apply the midpoint formula which is M ( (x₁ + x₂) / 2, (y₁ + y₂) / 2 ). Here, we have the midpoint M(-2,2) and one endpoint E(2,8).
It's like saying: (-2,2) = ( (2 + x₂) / 2, (8 + y₂) / 2 ).
To solve for x₂ (the x-coordinate of point F) and y₂ (the y-coordinate of point F), we will set up two separate equations based on the x and y coordinates.
For the x-coordinate, (-2) = (2 + x₂) / 2. Solve for x₂ gives x₂ = -2*2 - 2 = -6.
For the y-coordinate, 2 = (8 + y₂) / 2. Solve for y₂ gives y₂ = 2*2 - 8 = -4.
So, point F, the other endpoint of the line segment EF, has the coordinates (-6,-4).
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What is the circumference of a circle with a diameter of 5.8 inches? Use 3.14 for π and round the answer to the nearest tenth. A) 9.1 inches B) 18.2 inches C) 36.4 inches D) 105.6 inches
Answer: B) 18.2 inches
Step-by-step explanation:
We know that the circumference of a circle is given by :-
[tex]\text{Circumference}=\pi d[/tex]
Given : Diameter of a circle = 5.8 inches
Then, the circumference of the circle will be :-
[tex]\text{Circumference}=(3.14)\times5.8=18.212\approx18.2\text{inches}[/tex]
Hence, the circumference of the circle = 18.2 inches
Answer:
Option B.
Step-by-step explanation:
It is given that diameter of the circle is 5.8 inches.
[tex]d=5.8[/tex]
Radius of the circle is
[tex]r=\dfrac{d}{2}=\dfrac{5.8}{2}=2.9[/tex]
We need to find the circumference of the circle.
Circumference of a circle is
[tex]C=2\pi r[/tex]
Substitute π= 3.14 and r=2.9 in the above formula, to find the circumference of the circle.
[tex]C=2(3.14)(2.9)[/tex]
[tex]C=18.212[/tex]
Round the answer to the nearest tenth.
[tex]C=18.2[/tex]
The circumference of the circle is 18.2 inches. Therefore, the correct option is B.
Find the measures of the unknown angles in degrees.
Blank #1: value for c
Blank #2: value for w
Blank # 1
Blank # 2
Answer:
c = 63
w = 85
Step-by-step explanation:
Since the 2 lines are parallels c is the same angle as 63 and w is the supplementary angle of 95
Ten times the sum of half a number x and 9 is 13.
10(x/2 + 9) = 13
5x + 90 = 13
5x = 13 - 90
Can you do the rest?
The common denominator of
5/6-2/7
The common denominator is 42
Given,
5/6-2/7
Now,
Take LCM of 6 and 7 for obtaining the common denominator,
LCM of 6,7
As 7 is a prime number and 6 is non prime number than there LCM is obtained by multiplying the two numbers .
Hence LCM is 6* 7
LCM = 42
Now
Multiply the denominators 6 and 7
Hence the result will be,
35 - 12 /42
23/42 .
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Final answer:
To find the common denominator of 5/6 and 2/7, multiply each fraction by a factor that will give the least common denominator of 42, then subtract the resulting fractions with the same denominator.
Explanation:
To find the common denominator for the fractions 5/6 and 2/7, we need to determine a shared denominator that both original denominators can be multiplied into without changing the value of the fractions. Multiplication is the key technique to creating a common denominator. In this case, the least common denominator (LCD) is 42 because 6 and 7 have no common factors other than 1, and 6 times 7 equals 42. To transform these fractions, we multiply the numerator and denominator of each fraction by the number that will give us our LCD as the new denominator.
To calculate the difference using the LCD:
Multiply 5/6 by 7/7 to get 35/42.
Multiply 2/7 by 6/6 to get 12/42.
Now, subtract the two new fractions: 35/42 - 12/42 = 23/42.
It is essential to remember that we never add or subtract the denominators when combining fractions; we only combine the numerators after establishing a common denominator.
Estimate the time juanita will arive at her aount's home 320 miles away if she leaves at 9:00 am.,drives about 60 miles per hour, and stops for a 40 minute break halfway
Final answer:
Juanita will arrive at her aunt's home around 3:00 pm after accounting for 5 hours and 20 minutes of driving time and a 40-minute break to her journey that began at 9:00 am.
Explanation:
The question is asking us to estimate the arrival time for Juanita who is traveling to her aunt's home 320 miles away. Juanita leaves at 9:00 am, drives at an average speed of 60 miles per hour, and plans to take a 40-minute break halfway through her trip.
To estimate the time it will take Juanita to reach her aunt's house, we need to calculate the driving time and add the time for the break.
The driving time is calculated by dividing the total distance by the average speed. The total driving time is 320 miles \'d'vided by' 60 miles per hour, which equals approximately 5.33 hours or 5 hours and 20 minutes of driving time.
Next, we add the 40-minute break to the driving time. Convert 40 minutes to hours by dividing by 60, which is approximately 0.67 hours or 40 minutes. Now, we sum the hours: 5 hours and 20 minutes driving + 40 minutes break = 6 hours total time spent.
Juanita left at 9:00 am, so we add the 6 hours to this time. Therefore, Juanita should arrive at her aunt's home around 3:00 pm.
Please help me out!!!!!!!!!!!!!!!!
Answer:
y = 0.5x
Step-by-step explanation:
Given that x and y vary directly then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition x = 1, y = 0.5, then
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{0.5}{1}[/tex] = 0.5, hence
y = 0.5x ← equation of variation
IF A SUBSCRIPTION IS $499 PLUS 8% TAX FOR 30 DAYS, BUT IS BEING PRORATED FOR 7 DAYS, PLUS THERE IS A $10 OFF COUPON, WHAT'S THE FINAL COST?
Answer:
$528.12
Step-by-step explanation:
499-10
489×1.08= 528.12
Answer:
The final cost is $115.74.
Step-by-step explanation:
Total amount of 30 days with tax = [tex]499+(0.08\times499)[/tex] = 538.92 dollars
This value is for 30 days, and its prorated for 7 days, so value for 7 days is =
[tex]\frac{538.92}{30}\times7[/tex] = 125.74 dollars
And $10 is off, so final cost is [tex]125.74-10=115.74[/tex] dollars
(Suppose the discount coupon is applied at the end of billing)
The final cost is $115.74.
You travel from point A to point B in a car moving at a constant speed of 70 km/h. Then you travel the same distance from point B to another point C, moving at a constant speed of 90 km/h. Is your average speed for the entire trip from A to C equal to 80 km/h? Explain why or why not.
Yes, the average speed for the entire trip from A to C is equal to 80 km/h.
Given
You travel from point A to point B in a car moving at a constant speed of 70 km/h.
You travel the same distance from point B to another point C, moving at a constant speed of 90 km/h.
What is the average speed?The average speed is defined as the change in displacement and change in a time interval.
The formula is used to calculate average speed;
[tex]\rm Average \ speed= \dfrac{V_1+V_2}{2}[/tex]
Where [tex]\rm V_1[/tex] is 70 and [tex]\rm V_2[/tex] is 90.
Substitute all the values in the formula
[tex]\rm Average \ speed= \dfrac{V_1+V_2}{2}\\\\\rm Average \ speed= \dfrac{70+90}{2}\\\\\rm Average \ speed= \dfrac{160}{2}\\\\\rm Average \ speed= 80[/tex]
Hence, the average speed for the entire trip from A to C is equal to 80 km/h.
To know more about Average speed click the link given below.
https://brainly.com/question/13569465
Write the first five terms of the geometric sequence if the nth term is given by 36(1/3)^n-1
Answer:
G1=36,G2=12,G3=4,G4=4/3,G5=4/9
Step-by-step explanation:
Since the nth term is given by;
Gn= 36(1/3)^n-1, then, substitute the values of n as 1,2,3,4 and 5 to get the values of G1,G2,G3,G4 and G5 respectively.
G1=36(1/3)^1-1 = 36
G2= 36(1/3)^2-1= 12
G3= 36(1/3)^3-1 = 4
G4= 36(1/3)^4-1 = 4/3
G5= 36(1/3)^5-1=4/9
Answer:
36, 12, 4, 4/3, 4/9.
Step-by-step explanation:
We find each term by substituting the sequence number.
So the first term (where n = 1)
= 36(1/3)^(1-1)
= 36(1/3)^0
= 36 * 1
= 36.
The second term is 36(1/3)^(2-1) = 36 * 1/3
= 12.
We can find subsequent terms by just multiplying the previous term by 1/3 so the third term = 12 * 1/3 = 4.
So the first 5 terms are 36, 12, 4, 4/3, 4/9.