Answer:
[tex]m(d)=26\ d[/tex]
where [tex]m[/tex] represents miles driven
and [tex]d[/tex] represents number of days driven.
Step-by-step explanation:
Given:
Total distance driven in miles = 70,000
Average distance driven each day = 26 miles
Taking average as unit rate of miles covered per day.
∴ we can say the car covers 26 miles per day.
Using unitary method to find miles driven in [tex]d[/tex] days.
In 1 day miles driven = 26
In [tex]d[/tex] days miles driven = [tex]26\times d =26\ d[/tex]
So, to find [tex]m[/tex] miles driven the expression can be written as:
[tex]m(d)=26\ d[/tex]
Given that the first term is LaTeX: t_1=5t 1 = 5, and the recursive definition is LaTeX: t_{n+1}=3\cdot t_nt n + 1 = 3 ⋅ t n, what would be the second term (i.e. LaTeX: t_2t 2)
Group of answer choices
3
5
8
15
Answer:
Fourth choice: 15Explanation:
The question is: given that the first term is [tex]t_1=5[/tex] and the recursive definition is [tex]t_{n+1}=3\cdot t_n[/tex] , what would be the second term (i.e. [tex]t_2[/tex] )
A recursive defintion or recursive formula is an equation (a rule) that you apply over a term to find the next term, and so you can use it repeatedly to find the successive terms of a series.
In this case, your rule is that you multiply each term by 3, starting from 5.
Thus:
First term: [tex]t_1=5[/tex]Second term = 3 × first term : [tex]t_2=3\cdot t_1=3\cdot 5=15[/tex]Hence, your answer is 15 (the fourth choice).
Dustin is standing at the edge of a vertical cliff, 40 meters high, which overlooks a clear lake. He spots a fluffy white cloud above the lake, which from his point of view has an angle of elevation of $30^\circ.$ He also sees the reflection of the cloud in the lake, which has an angle of depression of $60^\circ.$ Find the height of the cloud above the lake, in meters.
The height of the cloud above the lake is approximately 86.19 meters, calculated using trigonometry relations of angles of elevation and depression from Dustin's point of view standing on a 40-meter high cliff.
Explanation:To find the height of the cloud above the lake, we use trigonometry. Dustin observes the cloud at an angle of elevation of 30° and the reflection at an angle of depression of 60°. The height of the cliff is 40 meters. Since angles of elevation and depression are measured from the horizontal, the angle between Dustin's line of sight to the cloud and to its reflection is 90° (30° + 60°). The height of the cloud can be found by considering two right-angled triangles that Dustin forms with his line of sight to the cloud and to the reflection.
Step 1:Triangle ADC represents the direct line of sight to the cloud, with angle CAD being 30°, and side AC the height of the cliff (40 meters).
Step 2:Triangle BEC represents the line of sight to the reflection of the cloud, with angle CBE being 60°, and side BC the height of the cliff (40 meters).
Step 3:Using the trigonometric relations:
Tan 30° = opposite/adjacent → CD/AC → CD = AC * Tan 30°Tan 60° = opposite/adjacent → CE/BC → CE = BC * Tan 60°Step 4:Since CE and CD form a straight line, the total height of the cloud above the lake is the sum of CD and CE. Using the trigonometry values (Tan 30° = 1/√3, and Tan 60° = √3):
CD = 40 * 1/√3CE = 40 * √3Step 5:Therefore, the height of the cloud above the lake, DE = CD + CE = 40 * (1/√3 + √3).
After calculation, DE = 40 * (1/√3 + √3) ≈ 40 * 2.1547 ≈ 86.19 meters.
So, the height of the cloud above the lake is approximately 86.19 meters.
The profit earned by a hot dog stand is a linear function of the number of hot dogs sold. It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold. Which equation represents y, the profit earned by the hot dog stand for x hot dogs sold?
A. y=48x−2
B. y=48x+2
C. y=2x−48
D. y=2x+48
Answer:
y = 2X-48
Step-by-step explanation:
Cost to the owner for day's supply of hot dogs,buns and mustard = $48
Profit = $2 profit for each hot dog sold
Let X be the number of hot dogs sold
The profit earned by hot dog stand for X number of hot dogs
y = 2X-48
Beta Electronics earned net income of $20,000. Included in the net income was $2,000 of depreciation expense. Current assets increased by $2,000 and current liabilities increased by 1,000. How much cash is provided by operating activities?
Answer:
$21,000
Step-by-step explanation:
Given,
Net income = $20,000
Depreciation = $2,000
Current assets (increase) = $2,000
Current liabilities (increase) = $1,000
Note: An increase in current assets is a reduction in cash balance while an increase in current liabilities is an increase in cash
Considering the note above,
Cash is provided by operating activities = 20000 + 2000 - 2000 + 1000
= $21,000
Chanelle deposits $7,500 she does not with draw or deposit money for 6 years she ears 6% in interest. How much interest will she have at the end of 6 years
Answer: The interest that she will have at the end of 6 years is $2700
Step-by-step explanation:
Chanelle deposits $7,500 and she does not withdraw or deposit money for 6 years. This means that the initial amount and the interest accrued was not altered in 6 years.
She ears 6% in interest. To determine the amount of interest that she would have at the end of 6 years. We will apply the simple interest formula.
I = PRT/100
Where
I = simple interest
P = principal
R = interest rate
T = number of time in years
From the information given
P= $7,500
R = 6
T = 6
I = (7500 × 6 × 6)/100
I = $2700
A 25-ft ladder leans against a building so that the angle between the ground and the ladder is 51 degrees. How high does the ladder reach up the side of the building? Please round your answer to 2 decimal places.
Answer:
19.43 ft
Step-by-step explanation:
Using SOHCAHTOA,
opposite = x
Hypothenus = 25ft
Sin α = opposite /Hypothenus
Sin 51° = x/25
x = 25(Sin51°)
x = 19.4286
x = 19.43(approximate to 2 d.p)
Mike was selling raffle tickets for the school football game. The raffle tickets were $3 for students and $7 for adults. When Mike looked at how much he collected, he counted $455 and 101 ticket stubs. How many student and adult tickets were sold?
Answer: 63 student tickets and 38 adult tickets were sold
Step-by-step explanation:
Mike sold raffle tickets for adults and students for the school football game.
Let x= number of student tickets sold
Let y= number of adult tickets sold
The raffle tickets were $3 for students and $7 for adults. This means x student tickets cost $3x and y adult tickets cost $7y
When Mike looked at how much he collected, he counted $455 and 101 ticket stubs. This means
3x + 7y = 455 - - - - - -1
x + y = 101
Substituting x = 101 - y into equation 1, it becomes
3(101 - y) + 7y = 455
303 -3y + 7y = 455
-3y +7y = 455 - 303
4y = 152
y = 152/4 = 38 tickets
x = 101 - y
x = 101 - 38
x = 63 tickets
Answer:
Step-by-step explanation:
63 students and 38 adults tickets
Consider a wire of length 12 ft. The wire is to be cut into two pieces of length x and 12−x. Suppose the length x is used to form a circle of radius r and the length 12−x is used to form a square with side of length s. What value of x will minimize the sum of their areas?
Answer:
x = 8
Step-by-step explanation:
When cutting the wire we will get two pieces
x and 12 - x
If we build a circle whith x , the lenght of the circle will be x, and if we look at the equation for a lenght of a cicle 2*π*r = x
then r = x/2π
and consequentely A₁ = area of a circle = πr² A₁ = π*x/2π
A₁ = x/2
With the other piece 12 - x we have to make an square so wehave to divide that piece in four equal length
side of the square = s
s = 1/4 ( 12 - x ) and the area is A₂ = [1/4 ( 12 - x)]²
A₂ = ( 12 - x )²/16
Then A₁ + A₂ = A(t) and this area as fuction of x
A (x) = x/2 + 1/16 ( 144 + x² -24x) A (x) =[ (8x + 144 + x² -24x)]/16
Taken derivatives in both sides
A´(x) = 8 + 2x - 24 = 0
2x -16 = 0 x = 8 and s = 12 - 8 s = 4
To minimize the sum of the areas, we need to find the value of x that minimizes the sum of the area of a circle and a square.
Explanation:To minimize the sum of the areas, we need to find the value of x that minimizes the sum of the area of a circle and a square. The area of a circle is given by the formula A = πr^2, and the area of a square is given by the formula A = s^2. We can set up an equation to represent the sum of the areas: πr^2 + s^2. Since we are given that the wire is cut into two pieces of length x and 12-x, we can substitute the values of r and s in terms of x into the equation. Then we can differentiate the equation with respect to x and set the derivative equal to zero to find the critical points. From there, we can determine which critical point corresponds to the minimum value.
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A container contains 3 yellow, 2 orange, and 4 pink roses. Without looking, if James chooses a rose from the container, what is the probability that James will select an orange rose? A pink rose? A yellow rose?
Answer:
4.5%, 0.44%, 0.33%
Step-by-step explanation:
I'm not really good at math,but I do believe this is the answer
Answer:
Orange rose = 3/9
Pink rose = 4/9
Yellow rose = 2/9
Step-by-step explanation:
In order to find probability of picking one item, you add all the possible things you could choose. So, 3+2+4 equals a total of 9 outcomes, and that would be your denominator for your fraction of probability. From there it's really easy. Just put the amount of things your trying to find the probability for in the numerator spot.
Ex.
There are 9 total roses so that would be the denominator (?/9)
To find out the probability for picking an orange rose, you'd put the 2 in as the numerator because that is the total number of orange roses you have (2/?)
Then just put the two together (2/9).
During a recent football game, 77,000 people were present in a stadium with a capacity of 73,000. The accumulation of that number of people in a relatively small area would be consistent with Stokols's definition of
The accumulation of that number of people in a relatively small area would be consistent with Stokols's definition of density. Option D
Definition of density
Density refers to the number of individuals per unit of space. In this scenario, there were 77,000 people present in a stadium with a capacity of 73,000, indicating a high density of individuals in the given area.
Stokols's definition of density aligns with this situation, as it describes the accumulation of individuals in a relatively small area. Crowding, mob behavior, and learned helplessness are not directly related to the concept of density.
During a recent football game, 77,000 people were present in a stadium with a capacity of 73,000. The accumulation of that number of people in a relatively small area would be consistent with Stokols's definition of
A) crowding.
B) learned helplessness.
C) mob behavior.
D) density.
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A person facing east walks east 20 paces, turns, walks north 10 paces, turns, walks west 25 paces, turns, walks south 10 paces, turns, walks east 15 paces, and then stops. What one transformation could have produced the same final result in terms of the position of the person and the direction the person faces?
a) reflection over the north-south axis
b) rotation
c) translation
d) reflection over the east-west axis
Option a) reflection over the north-south axis is the position of the person and the direction the person faces.
Position of the personIf we only consider the person's movement along the East-West axis, this movement was:
walks east 20 paces, walks west 25 paces, and walks east 15 paces.Taking east as positive and west as negative, this is equivalent to +20 -25 +15 = 10 or walks east 10 paces
Considering the person's movement along the North-South axis, this movement was:
walks north 10 paces and walks south 10 paceswhich cancel out each other.
Hence, The answer is Option a) reflection over the north-south axis is the position of the person and the direction the person faces.
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Suppose that time invest $10,000 in an account that offers are percent annual interest, compounded quarterly if the investment increases to $12,694.34 in five years, find the annual rate of interest
The annual rate of interest is 4.80%
Step-by-step explanation:
The formula for compound interest, including principal sum is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] where:
A is the future value of the investment/loan, including interestP is the principal investment amountr is the annual interest rate (decimal)n is the number of times that interest is compounded per unit tt is the time the money is invested or borrowed forSuppose that time invest $10,000 in an account that offers are percent annual interest, compounded quarterly if the investment increases to $12,694.34 in five years
∵ P = $10,000
∵ A = $12,694.34
∵ n = 4 ⇒ compounded quarterly
∵ t = 5 years
- Substitute all these values in the formula above
∴ [tex]12,694.34=10,000(1+\frac{r}{4})^{4(5)}[/tex]
∴ [tex]12,694.34=10,000(1+\frac{r}{4})^{20}[/tex]
- Divide both sides by 10,000
∴ [tex]1.269434=(1+\frac{r}{4})^{20}[/tex]
- Insert ㏒ to both sides
∴ [tex]log(1.269434)=log(1+\frac{4}{n})^{20}[/tex]
∴ [tex]log(1.269434)=20log(1+\frac{4}{n})[/tex]
- Divide both sides by 20
∴ [tex]0.00518=log(1+\frac{4}{n})[/tex]
- Remember [tex]log_{a}b=c[/tex] can be written as [tex]a^{c}=b[/tex]
∵ The base of the ㏒ is 10
∴ [tex]10^{0.00518}=(1+\frac{r}{4})[/tex]
∴ [tex]1.011998806=1+\frac{r}{4}[/tex]
- Subtract 1 from both sides
∴ [tex]0.011998806=\frac{r}{4}[/tex]
- Multiply both sides by 4
∴ 0.04799522 = r
∵ r is the rate in decimal
- To find the annual rate of interest R% multiply r by 100%
∴ R% = 0.04799522 × 100% = 4.799522%
∴ R% ≅ 4.80%
The annual rate of interest is 4.80%
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Water is flowing into a vertical cylindrical tank of diameter 8 m at the rate of 5 m3/min.
Find the rate at which the depth of the water is rising. (Round your answer to three decimal places.)
m/min
The depth of the water in the cylindrical tank is increasing at a rate of 0.1 m/min. This result is gotten by using the concept of related rates in calculus and differentiating volume with respect to time. The given rate of water inflow and dimensions of the cylindrical tank are substituted into the resultant formula.
Explanation:This question is dealing with rates of change, specifically in the context of volume and height within a cylindrical tank. It's a problem in calculus, more specifically related to related rates.
To start, let's understand that the volume V of a cylinder is given by the formula V = πr²h, where r is the radius, h is the height, and π is a constant (~3.14159). We can substitute r with 4m (half of the diameter of 8m) and differentiate both sides with respect to time. Differentiating both sides of the equation with respect to t (time) gives dV/dt =πr² dh/dt (since r is constant with respect to time, but h changes).
Given that the rate at which water flows into the tank, dV/dt, is 5m³/min we can substitute this into the formula. This gives us 5 = π(4)²dh/dt. Simplifying the equation gives us dh/dt = 5 / (π(4)²), which approximately equals 0.1 m/min when rounded to three decimal places.
So, the depth of the water in the tank is increasing at a rate of 0.1 m/min.
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The rate at which the depth of water is rising in the cylindrical tank with a diameter of 8 m and water flowing in at 5 m^3/min is approximately 0.199 m/min.
To find the rate at which the depth of the water is rising, we can use the formula for the volume of a cylinder:
[tex]\[ V = \pi r^2 h \][/tex]where:
V is the volume of the water in the tank,r is the radius of the tank (half of the diameter),h is the depth of the water.Differentiating both sides of the equation with respect to time \( t \) gives us:
[tex]\[ {dV}/{dt} = \pi (2r)(dh/dt) \][/tex]Given that the diameter is 8 m, the radius \( r \) is 4 m. We are also given that the rate of change of volume dV/dt is 5 m³/min. Plugging in these values, we can solve for \( dh/dt \), the rate at which the depth of the water is rising:
[tex]\[ 5 = \pi (2 \times 4)(dh/dt) \][/tex][tex]\[ 5 = 8\pi (dh/dt) \][/tex][tex]\[ dh/dt = \frac{5}{8\pi} \][/tex]Calculating this gives:
[tex]\[ dh/dt \approx 0.199 \text{ m/min} \][/tex]
So, the rate at which the depth of the water is rising is approximately 0.199 m/min.
Mary's family went to Disneyland. Her mom drove 75 miles an hour and her dad drove 60 miles an hour. If they drove for a total of 1710 miles, how many hours did each one of the drive?
Answer: her mum drove for 12.67 hours and her dad drove for 12.67 hours
Step-by-step explanation:
Her mom drove 75 miles an hour and her dad drove 60 miles an hour.
The ratio of her mum's speed to her dad's speed is 75 : 60
Total ratio = 75 + 60 = 135
Since the speed of her mum and her dad will determine the distance that each of them covered,
Distance covered by mum will be
Speed of mum/ total ratio × total distance covered. It becomes
75/135 × 1710 = 950 miles
Distance covered by dad would be total distance - distance covered by mum. It becomes
1710 - 950 = 760 miles
Time spent by her mum = distance covered by her mum / speed of her mum. This becomes
950/75 = 12.67 hours
Time spent by her dad = distance covered by her dad / speed of her dad. This becomes
760/60 = 12.67 hours
25 gallons of milk for $56 Target sells 15 gallons of milk for 32.05 dollars give the unit rate for both groceries stores and determine which store has the better deal
Answer:
Step-by-step explanation:
25 gallons of milk for $56
We would need to determine the unit rate for a gallon of milk in this particular store.
If 25 gallons of milk for $56
Then 1 gallon of milk would cost
56/25 = 2.24
Target sells 15 gallons of milk for 32.05 dollars
We would also to determine the unit rate for a gallon of milk in this particular store.
If 15 gallons of milk for $32.05
Then 1 gallon of milk would cost
32.05/15 = 2.137
The unit cost of a gallon of milk at target provides a better deal because it has a lower unit cost than the other
Zoe is comparing two local yoga programs. Yo-Yoga charges a $35 registration fee and $90 a month. Essence Yoga charges a registration fee of $75 and $80 per month. After how many months will the 2 programs be the same?
Answer:
After 4 months
Step-by-step explanation:
The cost at both the programs consists of a "fixed cost" (reg fee) & "variable cost" ( per month fee).
Let number of months be "x"
Yo-Yoga:
35 fixed
90 per month
So equation would be: 35 + 90x
Essence Yoga:
75 fixed
80 per month
So equation would be: 75 + 80x
To find number of month when cost would be same, we equate both equations and solve for x:
35 + 90x = 75 + 80x
10x = 40
x = 40/10
x = 4
hence, after 4 months, both cost would be same
How many liters of water containing 7 grams of salt per liter must be combined with x liters of water which contains y grams [y is less than 2] of salt per liter to yield a solution with 2 grams of salt per liter.
Answer:
[tex]\frac{(2-y)x}{5}\text{ litres}[/tex]
Step-by-step explanation:
Let l litre of 7 grams of salt per litre is combined with x litres of water which contains y grams of salt per litre to yield a solution with 2 grams of salt per litre.
Thus,
Salt in l litre + salt in x litre = salt in resultant mixture
7l + xy = 2(l +x)
7l + xy = 2l + 2x
7l - 2l = 2x - xy
5l = x(2-y)
[tex]\implies l =\frac{x(2-y)}{5}[/tex]
Hence, [tex]\frac{x(2-y)}{5}[/tex] litres of 7 gram of salt per litre is mixed.
Find the necessary sample size.
Scores on a certain test are normally distributed with a variance of 68. A researcher wishes to estimate the mean score achieved by all adults on the test. Find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 4 units.
2- A college statistics professor has office hours from 9:00 A.M. to 10:30 A.M. daily.
A sample of waiting times to see the professor (in minutes) is 10, 12, 20, 15, 17, 10, 30, 28, 35, 28, 19, 27, 25, 22, 33, 37, 14, 21, 20, 23.
Assume alpha equals 7.84 find the 95.44% confidence interval for the population mean.
Answer:95.44
Step-by-step explanation:
Sarawongs school is selling tickets to the anual talent show on the first day of ticket sales the school sold 1 adult ticket and 2 student for total of $27 the school took in $36 on the second day by selling 2 adult tickets and 2 student tickets what is the price each of one adult ticket and one student ticket
Price of one adult ticket is $9 and price of one student ticket is also $9.
Step-by-step explanation:
Let,
Adult ticket = x
Student ticket = y
According to given statement;
x+2y=27 Eqn 1
2x+2y=36 Eqn 2
Subtracting Eqn 1 from Eqn 2;
[tex](2x+2y)-(x+2y)=36-27\\2x+2y-x-2y=9\\x=9[/tex]
Putting x=9 in Eqn 1;
[tex]9+2y=27\\2y=27-9\\2y=18[/tex]
Dividing both sides by 2;
[tex]\frac{2y}{2}=\frac{18}{2}\\y=9[/tex]
Price of one adult ticket is $9 and price of one student ticket is also $9.
Keywords: linear equations, subtraction
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4. A bowl contains 10 red balls and 10 blue balls. A woman selects balls at random without looking at them.
a) How many balls must she select to be sure of having at least three balls of the same color?
b) How many balls must she select to be sure of having at least three blue balls?
Answer:
a) 5 balls
b) 13 balls
Step-by-step explanation:
a) by the pigeon holes theorem where the pigeon is the ball and the holes here are the colors. For her to have at least 3 balls of the same colors, we can consider the worst case where she selected 2 balls of each color, that makes it 4 balls. Then by the 5th ball it should match either of the colors, making it 3 balls of same color.
b) Similarly, in the worst case let's say she selects all 10 red balls, then the next 3 balls must be blue. So she needs to select a total of 13 balls to make sure that she has at least 3 blue balls.
Jeffrey is an eight-year-old, who used to believe that his meantime for swimming the 25-yard freestyle was 16.43 seconds. Jeffrey’s dad, Frank, thought that Jeffrey could swim the 25-yard freestyle faster using goggles. Frank bought Jeffrey a new pair of expensive goggles and timed Jeffrey for 15- 25-yard freestyle swims. For the 15 swims, Jeffrey's meantime was 16 seconds. Frank thought that the goggles helped Jeffrey to swim faster than the 16.43 seconds. Conduct a hypothesis test using a preset-0.05.
Answer:
Explanation is given in the following attachments
Step-by-step explanation:
Leilani rides her bike for exercise and drinks 70 ounces of water each day in order to stay hydrated before her morning ride she drinks 14 ounces of water leilani wants to know what percent of her daily amount of water she has before her ride
Answer: 20%
Step-by-step explanation:
The total amount of water that Leilani drinks throughout is 70 ounces each day. This means that before and after the ride, she drinks a total of 70 ounces daily
in order to stay hydrated before her morning ride she drinks 14 ounces of water.
To determine what percent of her daily amount of water she has before her ride, we would divide the amount she takes before ride by the total daily amount of water and multiply by 100. It becomes
14/70 × 100 = 20%
Answer:
20
Step-by-step explanation:
Jenny is comparing the cost of two packages of socks.One package has 8 pairs of socks for $12.Another package has 3 pairs of socks for $6.Are the rates equivalent
Answer:
no
Step-by-step explanation:
The second package costs $2 for each pair of socks. If the first package cost that much, it would be 8×$2 = $16 for 8 pairs of socks. That is not the same as $12 for 8 pairs.
__
Another way to look at it is the first package costs twice as much as the second, but has more than twice as many pairs of socks. That means the rates are not equivalent.
A rando sample of 60 second-graders in a certain school district are given a standardized mathematics skills test. The sample mean score is x bar = 55. Assume the standard deviation of test scores is sigma = 9. Compute the value of the test statistic.
Answer:
Assuming that this is a normal distribution, probably what is need is to compute the value of the P-value result to judge a system of hypothesis. So, first of all, we have to determine the null and alternative hypothesis.
In this problem, we don't have an exact demand about a hypothesis. We can assume that the purpose is to demonstrate is there's enough evidence to say that second-graders students have greater math skills than others.
So, assuming that others students have a mean score of 50, the system of hypothesis could be:
Null hypothesis: [tex]H_{o} : u=50[/tex]; that is, that the sample students have an mean score of 50.
Alternative hypothesis: [tex]H_{a}: u>50[/tex]; that is, that the sample students have a mean score more than 50.
So, to know if there's enough evidence to stay that second-graders have a higher score than other students, we must to work around the null hypothesis, accepted or rejected.
First, we have to calculate the Z-value with this formula: [tex]Z=\frac{x-u}{\frac{o}{\sqrt{n} } }[/tex]; where x = 55; o = 9; n = 60 and u = 50.
Replacing all values we have: [tex]Z=\frac{55-50}{\frac{9}{\sqrt{60} } } =\frac{5}{\frac{9}{7.7} } =\frac{5}{1.2} = 4.2[/tex]
So, the Z-value is 4.2, approximately 4. Then, we use the Z-table attached to know the P-value, using a 0.01 level of significance (we can use other, but this is the usual level), then we look for the value which is in the column 0.01 with -4 (it doesn't matter the negative sign, because it's the same result). We see that the P-value is 0.00003.
According with the theory, if the P-value is higher than the level of significance, the null hypothesis should be accepted, because it means that there is no enough evidence to accept it. Therefore, based on this test, the second-graders students have a better mathematics skills core than the other students, because the P-values is lower than the level of significance. (0.00003 < 0.01)
Following a severe snowstorm, Ken and Bettina Reeves must clear their driveway and sidewalk. Ken can clear the snow by himself in 2 hours, and Bettina can clear the snow by herself in 5 hours. After Bettina has been working for 1-hour, Ken is able to join her. How much longer will it take them working together to remove the rest of the snow?
Answer:
It will take 5.6 hours
Step-by-step explanation:
If Ken (K) can clear in two hours and bettina (B) in five hours then;
5K=2B; If B=1 K=2/5 = 0.4 (2-0.4=1.6) plus 4 from B are 5.6 or also: If B=4 (Bettina started 1 hour later 5-1=4) K=8/5=1.6 then K+B=1.6+4=5.6 h
Final answer:
Ken and Bettina Reeves will take approximately 51.4 minutes to finish clearing snow together after Bettina has already put in 1 hour of work by herself. This is calculated by combining their work rates and determining how much of the job is left after Bettina's initial work.
Explanation:
The question involves determining how much longer it will take Ken and Bettina Reeves to finish clearing snow together after Bettina has already worked for 1 hour by herself. To solve this, we can find out their collective work rate when they work together, and use it to calculate the remaining time required to clear the snow.
Step-by-Step Solution:
Find Bettina's work rate: Bettina can clear snow in 5 hours, which means her work rate is ⅓ (one-fifth) of the driveway per hour.
Calculate how much Bettina has cleared in 1 hour: She has cleared ⅓ of the snow.
Ken's work rate is ½ (one-half) of the driveway per hour since he can clear the snow by himself in 2 hours.
Calculate their combined work rate: ½ (Ken) + ⅓ (Bettina) = ⅗ (seven-tenths) of the driveway per hour when working together.
Subtract the portion Bettina has already cleared: 1 - ⅓ = ⅔ (four-fifths) of the driveway remains.
Divide the remaining work by their combined work rate: ⅔ ÷ ⅗ = ⅖ (6/7) hours.
Convert the time to minutes: ⅖ hours is approximately 51.4 minutes.
Therefore, working together, Ken and Bettina will take approximately 51.4 minutes to remove the rest of the snow.
A North-South road meets an East-West road at an intersection. At a certain moment, a car on the North-South road is 4 miles north of the intersection and is traveling north at 55 miles per hour. At the same moment, a truck on the East-West road is 3 miles east of the intersection and is traveling east at 45 miles per hour. How fast is the distance between the car and the truck increasing at that moment?
Answer:
The distance 5 miles North-East of the intersection between the car and the truck increasing at 71.06 miles per hour at that moment.
Step-by-step explanation:
Looking at the attached figures, Fig 1 shows the diagram of the car and the truck.
Using Pythagoras theorem on Fig 1a,
[tex]l^{2} = \sqrt{3^{2} + 4^{2} }[/tex]
[tex]l = \sqrt{9 +16} \\\\l= \sqrt{25} \\\\l = 5 miles[/tex]
The resultant displacement between the car and the truck at that same moment is 5 miles.
From the velocity vector diagram on Fig 2,
The resultant velocity R is given as
[tex]R = \sqrt{45^{2} + 55^{2} }\\\\R = \sqrt{2025 + 3025 }\\\\R = \sqrt{5050 }\\\\R = 71.06mph[/tex]
Therefore, the distance 5 miles North-East of the intersection between the car and the truck increasing at 71.06 miles per hour at that moment.
the median weekly earnings for american workers in 1990 was $412 and in 1999 it was $549. Calculate the average rate of change between 1990 and 1999.
The rate of change between 1990 and 1999 is 15.22
Step-by-step explanation:
The rate of change in this case is given by change in quantity divided by change in time
So,
[tex]Rate\ of\ change = \frac{Increase\ in\ money}{Increase\ in\ time}\\=\frac{549-412}{1999-1990}\\=\frac{137}{9}\\=15.22[/tex]
Hence,
The rate of change between 1990 and 1999 is 15.22
Keywords: Rate of change, median
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On 1/1/X1, Dolan Corp. pays $100,000 to retire its bonds early. At the time of the retirement, the bonds have a face value of $104,000 and a carrying value of $98,000. Question: What should be the amount of gain or loss, if any, the company will record as a result of the early retirement?
Answer: The company has to record a loss of $2,000
Step-by-step explanation:
The accounting for bonds retired early would require the company to pay out cash to remove the bonds payable from its balance sheet. To determine the gain or loss, if the cash paid is less than the carrying value of the bond, then a gain is determined, if the cash paid is more than the carrying value of the bond, then a loss is determined.
From the question the company pays $100,000 which is more than the carrying value of $98,000. Therefore, the company would record a loss $2,000.
Chance has hired a construction crew to renovate his kitchen. They charge $3.89 per square foot for materials and $121.26 per day of labor. Chance spent $2,982.68 on the renovation. If the number of square feet is 252 more than the number of days it took for the renovation, how long did the renovation take?
A.
19 days
B.
16 days
C.
3 days
D.
14 days
Answer:
The answer to your question is: letter B. 16 days
Step-by-step explanation:
Materials = $3.89 square foot
Day of labor = $121.26
Total $2982.68
Square feet = 252 more than the number of days
Process
materials = days of labor + 252
materials = m
days of labor = d
m = d + 252 (I)
Total Equation
3.89m + 121.26d = 2982.68
3.89(d + 252) + 121.26d = 2982.68
3.89d + 980.28 + 121.26d = 2982.68
3.89d + 121.26d = 2982.68 - 980.28
125.15d = 2002.4
d = 16
Number of days 16.
Find the explicit formula for the general nth term of the arithmetic sequence described below. Simplify your answer.
a1= -3 and a10= 69
[tex]\boxed{a_{n}=-3+8(n-1)}[/tex]
Explanation:The explicit formula for the general nth term of the arithmetic sequence is given by:
[tex]a_{n}=a_{1}+d(n-1) \\ \\ \\ Where: \\ \\ a_{n}:nth \ term \\ \\ n:Number \ of \ terms \\ \\ a_{1}:First \ term \\ \\ d:common \ difference[/tex]
Here we know that:
[tex]a_{1}=-3 \\ \\ a_{10}=69[/tex]
So, our goal is to find the common difference substituting into the formula:
[tex]a_{10}=a_{1}+d(10-1) \\ \\ 69=-3+d(9) \\ \\ Solving \ for \ d: \\ \\ 9d=69+3 \\ \\ 9d=72 \\ \\ d=8[/tex]
Finally, we can write the explicit formula as:
[tex]\boxed{a_{n}=-3+8(n-1)}[/tex]
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The explicit formula for the general nth term of the arithmetic sequence is an = 8n - 11.
To find the explicit formula for the general nth term of the arithmetic sequence with a1 = -3 and a10 = 69, we can use the formula for the nth term of an arithmetic sequence, which is:
an = a1 + (n - 1)d, where a1 is the first term and d is the common difference.
First, we find the common difference by using the 10th term:
69 = -3 + (10 - 1)d
72 = 9d
d = 8
Now we have the common difference, so we can write the formula for the nth term:
an = -3 + (n - 1)(8)
Simplifying:
an = 8n - 11
This is the explicit formula for the general nth term of the given arithmetic sequence.