Answer: Polaris would appear at [tex]26\°[/tex] latitude
Step-by-step explanation:
Let's begin by explaining that Latitude is the angular distance between the Earth's equator, and a specific point on the planet. It is measured in degrees and is represented according to the hemisphere in which the point is located, which can be north or south latitude.
In this sense, latitude [tex]0\°[/tex] refers to the equatorial line that divides the Earth in two hemispheres (North and South), and Miami's latitude [tex]26\°[/tex] refers to the Northern hemisphere.
On the other hand, talking about the North Star (also known as Polaris); if we were just in the North Pole (latitude [tex]90\°[/tex]), Polaris would by exactly over our heads or the zenith ([tex]90\°[/tex] over the horizon), but as we go until latitude [tex]26\°[/tex], Polaris altitude will be approximately at that same angle over the horizon.
Hence, from an observer located in Miami, Polaris would appear at [tex]26\°[/tex] N.
In Miami, with a latitude of 26° N, the North Star appears at an altitude of 26° above the horizon. As you move southward, it appears lower; when you travel north, it appears higher. Precise navigation also considers the slight angular difference between Polaris and the true celestial pole.
In Miami, Florida, which has a latitude of 26° N, the North Star, or north celestial pole, would appear at an altitude of 26° above the northern horizon. This is because the altitude of the North Star above the horizon is roughly equivalent to the latitude of the observer's location in the Northern Hemisphere. Therefore, as one drives southward from Miami to a city at a lower latitude, the North Star would appear lower in the sky. Conversely, driving northward would make the North Star appear higher.
It's important to note that due to the Earth's curvature, as you move southward from Miami, both the North Star and the southern sky would appear to sink, while the opposite would occur as you move northward. If you were to reach the equator, the North Star would align with the northern horizon, and it would not be visible from latitudes south of the equator. For precision in navigation or astronomy, one must also account for the small angular distance between Polaris and the true north celestial pole.
A manufacturer finds it costs him x + 5x + 7 dollars to produce x tons of an item. At 2 production levels above 3 tons, he must hire additional workers, and his costs increase by 3(x - 3) dollars on his total production. If the price he receives is $13 per ton regardless of how much he manufactures and if he has a plant capacity of 10 tons, what level of output maximizes his profits?
Answer: The maximum = 3 tons
Step-by-step explanation:
The cost function C(x) = x + 5x + 7
P(×) = 13x - x^2 - 5x -7
If x <3
P= x^2 +8x -7
Differentiating to get x
dp/dx = -2x + 8
X= 8/2
C=4
Maximum will be 3 tons
When x=3
P= 13x - x^2 -5x +7 -3x + 9
When x>3
dp/dx = x^2+5x +2
X = 5/2 = 2.5
HELP PLEASEEE
What are the exact and approximate circumference of a circle whose diameter is 2 1 over 3 km ?
Use 3.14 for π when finding the approximate circumference. Round your answer to the nearest hundreth
Enter your answers in the boxes
Answer:
Exact circumference is [tex]7\frac{49}{150}km[/tex]
Approximate circumference is [tex]7.33 km[/tex]
Step-by-step explanation:
We are given;
The diameter of a circle as [tex]2\frac{1}{3} km[/tex]We are required to determine the exact and approximate circumference of the circle.
We know that the circumference of the circle is given by;Circumference = πD, where D is the diameterTaking π as 3.14
[tex]Circumference=3.14 (2\frac{1}{3}km)[/tex]
[tex]=7\frac{49}{150}km[/tex]
The exact circumference of the circle is [tex]7\frac{49}{150}km[/tex]
[tex]7\frac{49}{150}km=7.327 km\\ = 7.33 km (nearest hundredth)[/tex]
Thus, the approximate circumference of the circle is [tex]7.33 km[/tex]
Ben decided to volunteer forty hours to community service projects. The garden project took 2/3 of the time. How many hours did the garden project take?
Answer:
26.67 hours
Step-by-step explanation:
Given:
Number of hours of service projects (N) = 40 hours
Time taken to complete the garden project is two-third of the total time.
Therefore, the time taken to complete the garden project can be obtained by multiplying the part to the total time taken.
So, the hours taken for garden project is given as:
[tex]x=\frac{2}{3}\times N\\\\x=\frac{2}{3}\times 40\\\\x=\frac{80}{3}\\\\x=26.67\ hours[/tex]
Therefore, it took 26.67 hours to complete the garden project.
Jacob brought some tickets to see his favorite singer. He brought some adult tickets and some children tickets for a total of 9 tickets. The adult tickets cost $10 per ticket and the children tickets cost $8 per ticket if he spent a total of $76 then how much are adult and children tickets. Did he buy?
Answer: he bought 2 adult tickets and 7 children tickets.
Step-by-step explanation:
Let x represent the number of adult tickets that he bought.
Let y represent the number of children tickets that he bought.
He brought some adult tickets and some children tickets for a total of 9 tickets. This means that
x + y = 9
The adult tickets cost $10 per ticket and the children tickets cost $8 per ticket if he spent a total of $76, it means that
10x + 8y = 76 - - - - - - - - - - - -1
Substituting x = 9 - y into equation 1, it becomes
10(9 - y) + 8y = 76
90 - 10y + 8y = 76
- 10y + 8y = 76 - 90
- 2y = - 14
y = - 14/ -2
y = 7
x = 9 - y = 9 - 7
x = 2
Assuming A = dominant allele that produces red-eye, a = recessive allele that produces sepia eye, B = dominant allele that produces longwing, b = recessive allele that produces apterous wing. When crossing Aabb x AaBB, what is the probability of producing offspring with the sepia eye?
Answer:
25% of probabilities
Step-by-step explanation:
A= red eye
a=sepia eye
B=longwing
b=apterous
AB aB
Ab AABb AaBb
ab AaBb aaBb
AABb=25%
AaBb=25%
Ab= 25%
aaBb=25%
aaBb= sepia eye with longwig
The percentage of Male workers who prefer a female boss over a male boss increased approximately linearly from 5% in 1974 to 9% in 1998. Predict when 9% of male workers will prefer a female boss.
The percentage of male workers who preferred a female boss increased at a rate of 0.1667% per year from 1974 to 1998. Using this information, we can predict that 9% of male workers would prefer a female boss in the year 1998.
Explanation:This question involves linear relationships and prediction in mathematics. In this case, we're looking at an increase from 5% to 9% in male workers who preferred a female boss--this increase occurred over a period of 24 years (from 1974 to 1998). So, the rate of increase in male workers who preferred a female boss over those years was (9% - 5%) / 24 years = 0.1667% per year. Since the percentage was 5% in the beginning year 1974, we need to find the year when this percentage will become 9%. So, 9% = 5% + 0.1667% * (number of years from 1974). Solving this for the number of years gives approximately 24 years. Therefore, the year when 9% of male workers will prefer a female boss would be 1974+24 = 1998
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The table below show the total amount How did your predictions compare to your actual findings of mean and mean absolute deviation? Explain
Mean and Mean Absolute Deviation
Step-by-step explanation:
The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.
Here's how to calculate the mean absolute deviation.
Step 1: Calculate the mean.
Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.
Step 3: Add those deviations together.
Step 4: Divide the sum by the number of data points.
Talia wants to play a basketball game at a carnival. the game cost the player $5 to play, and the player gets to take too long distance shots. if they missed both shots, they get nothing. if they make one shot, they get their $5 back. Thalia has a 40% chance of making this type of shot.
here is the probability distribution of x= the amount of money Talia gains from playing the game.
x= money gain -$5 $0 $5
P(x) 0.36 0.48 0.16
Given that μx = -$1, calculate Θ x.
round your answer to two decimal places
Θx = _______ dollars
Answer:3.46$
Step-by-step explanation:
Probability distribution:
[tex]\to x \ \ \ \ \ \ \ -\$5 \ \ \ \ \ \ \ \$0 \ \ \ \ \ \ \ \$5\\\\\to P(x) \ \ \ \ \ \ \ 0.36 \ \ \ \ \ \ \ 0.48 \ \ \ \ \ \ \ 0.16\\\\[/tex]
[tex]\to \mu_{x}= Mean\ (X)= E(X) \ = - \$ 1\\\\\to \sigma^{2}_{x}= \Sigma_{x} x^2 p(x)- (\mu_{x})^2\\\\[/tex]
[tex]=(-5)^2 \times 0.36 + 0+ (5)^2 \times 0.16 - (-1)^2\\\\=25 \times 0.36 + 0+ 25 \times 0.16 - 1\\\\=9 + 0+ 4 - 1\\\\= 13-1\\\\=12\\\\[/tex]
Therefore,
[tex]\to \sigma_{x}=\sqrt{12}= \$ 3.464[/tex]
Therefore, the final answer is "3.464".
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The following function represents an arithmetic sequence.
f(1)=−1.5
f(n+1)=f(n)+0.5
What is f(10)?
Answer:
3
Step-by-step explanation:
Each term of the sequence has 0.5 added to the one before. The first 10 terms are ...
-1.5, -1.0, -0.5, 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0
f(10) = 3.0
_____
If you like, you can use the given information about the first term (-1.5) and the common difference (0.5) to write an explicit formula:
f(n) = f(1) +d(n -1)
f(n) = -1.5 +0.5(n -1)
Then the 10th term is ...
f(10) = -1.5 +0.5(10 -1) = -1.5 +4.5 = 3
Find the value of x. Show all your work for full credit.
Can anyone help me!!!
Answer:
Therefore the value of x is
[tex]x=5[/tex]
Step-by-step explanation:
Given:
Consider the figure such that
PQ || BC
AP = 20 , AB = 36
AQ = 5x , AC = 45
To Find:
x = ?
Solution:
In Δ APQ and Δ ABC
∠APQ ≅ ∠ACB {Corresponding angles are equal since PQ is parallel to BC}
∠A≅ ∠A ……….....{Reflexive Property}
Δ APQ~ Δ ABC….{Angle-Angle Similarity test}
If two triangles are similar then their sides are in proportion.
[tex]\dfrac{AP}{AB} =\dfrac{AQ}{AC}=\dfrac{PQ}{BC} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
Substituting the values we get
[tex]\dfrac{AP}{AB} =\dfrac{AQ}{AC}\\\\\dfrac{20}{36} =\dfrac{5x}{45}\\\\x=\dfrac{20\times 45}{36\times 5}=5\\\\x=5[/tex]
Therefore the value of x is
[tex]x=5[/tex]
Cecilia bought a new car the total amount she needs to borrow is 29542 she plans to take out 4 years loan at an APR of 6.3/ what is the monthly payment?
Answer:
697.87
Step-by-step explanation:
You are looking for the monthly payment (PMT) on a loan (borrow = loan).
This is the formula you would use for installment loans (loan payment)
PVA = PMT [(1 - (1+APR/n)^-nY)/APR/n]
NOTE:
PMT = regular payment amount = ?
PVA = starting loan principal (amount borrowed) = 29542
APR = annual percentage rate (as a decimal) = 0.063
n = number of payment periods per year (they told you that it is monthly, so n =12)
Y = loan term in years (can be a fraction) = 4
NOTE: a helpful tip is so start with the original formula and rearrange it to make what you are looking for the subject of the formula.
We're solving for the monthly payment. So rearrange the formula:
PVA = PMT [(1 - (1+APR/n)^-nY)/APR/n]
PMT = [PVA (APR/n)]/(1 - (1+APR/n)^-nY)
PMT = [29542 (0.063/12)] / (1 - (1+ 0.063/12)^-12x4)
∴ PMT = 697.8653...
Round off the answer to as many decimal places as instructed by your lecturer/teacher.
Here we have rounded off to 2 decimal places:
∴ PMT = 697.87
Based on the information given the monthly payment is $697.87 .
Given:
PMT = ?
PVA =29542
APR = 6.3% or 0.063
n =12×4=48
Hence:
PMT = [29542 (0.063/12)] / (1 - (1+ 0.063/12)^-12x4)
PMT = [29542 (0.063/12)] / (1 - (1+ 0.00525)^-12x4)
PMT = [29542 (0.00525)] / (1 - (1.00525)^-48)
PMT = [29542 (0.00525)] / (1-0.777757)
PMT = 155.0955/0.22224274
PMT = 697.865316
PMT= 697.87 (Approximately)
Inconclusion the monthly payment is $697.87 .
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You are adding an addition to your patio. The area ( in square feet) of the addition can be represented by k² - 3k - 10.
a) The area of the patio before the addition was 50 square feet. Find it.
b) Find the area of the addition and the area of the entire patio after the addition.
Answer:
[tex]k^{2}-3k+40[/tex]
Step-by-step explanation:
We suppose;
A= area before addition
B= Area of addition [tex]k^{2}-3k-10[/tex]
a) As area of pation before addition is 50 - it means A= 50
b) Area of addition and the area of entire pation after addition = A+B
= 50 + [tex]k^{2}-3k-10[/tex]
=[tex]k^{2}-3k+40[/tex]
Answer:We suppose;
A= area before addition
B= Area of addition
a) As area of pation before addition is 50 - it means A= 50
b) Area of addition and the area of entire pation after addition = A+B
= 50 +
=
Evan cut a triangular piece of cloth to use in a quilt. The perimeter of the cloth is 934 cm. The base of the triangular cloth is 214cm. The remaining two sides are the same length.Choose Yes or No to tell if each expression models how to find the length of the other two sides of Evan's cloth.934−2s=214 114+2s=934 2s=934−214 2s−214=934
Answer:
934−2s=214; Yes
114+2s=934; No
2s=934−214; Yes
2s−214=934; No
Step-by-step explanation:
The base of the triangular cloth is 214cm. The remaining two sides are the same length.
Let s be the length of other sides.
Perimeter = Sum of all sides of a triangle.
[tex]Perimeter = s+s+214[/tex]
[tex]Perimeter =2s+214[/tex]
It is given that the perimeter of the triangular cloth is 934 cm.
[tex]2s+214=934[/tex] .... (1)
Equation (1) can be rewritten as
[tex]2s=934-214[/tex] and [tex]214=934-2s[/tex]
On solving we get
[tex]2s=720[/tex]
Divide both sides by 2.
[tex]s=360[/tex]
Therefore, the length of the other two sides of Evan's cloth is 360 cm.
Chen has 17CDs. She gives 2 to her brother and buys 4 more. Her brother gives her 1 and she gives 3 to her best friend. How many CDs does Chen have now?
Answer: she has 17 CDs now.
Step-by-step explanation:
The total number of CDs that Chen had initially is 17.
She gives 2 to her brother. This means that she would be having
17 - 2 = 15
She buys 4 more. It means that she would be having
15 + 4 = 19
Her brother gives her 1. So the number that she has is
19 + 1 = 20
she gives 3 to her best friend. Therefore, the number of CDs that Chen has now is
20 - 3 = 17
SHOW YOUR WORK!! Identify the simplest polynomial function having integer coefficients with the given zeros: 3i, −1, 2
Answer:
[tex]p(x)=x^4-x^3+7x^2-9x-18[/tex]
Step-by-step explanation:
The given polynomial has roots 3i, −1, 2
Since [tex]3i[/tex] is a root [tex]-3i[/tex] is also a root.
The factored form of this polynomial is [tex]P(x)=(x-3i)(x+3i)(x+1)(x-2)[/tex]
We need to expand to get:
[tex]p(x)=(x^2-(3i)^2)(x^2-x-2)[/tex]
This becomes [tex]p(x)=(x^2+9)(x^2-x-2)[/tex]
We expand further to get:
[tex]p(x)=x^4-x^3+7x^2-9x-18[/tex]
The polynomial function is [tex]p (x) = x^4 - x^3 + 7x ^2 - 9x - 18[/tex]
The calculation is as follows;The factored form of the given polynomial should be
[tex]P(x) = (x - 3i) (x + 3i) (x + 1) (x - 2)[/tex]
Now we have to expand it
[tex]p(x) = (x^2 - (3i)^2) (x^2 - x - 2)\\\\= (x^2 + 9) (x^2 - x - 2)[/tex]
[tex]p (x) = x^4 - x^3 + 7x ^2 - 9x - 18[/tex]
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A game stop membership cost $20 and includes one game A month for five dollars. Nonmembers can get one more game a month for seven dollars. What a system of a simulation in linear equations to use this information to decide whether to become a
Answer:
C(x) = 5x + 20 (for members)
C(x) = 3.5x (for non-members)
Step-by-step explanation:
Cost of membership = $20
Price of a game per month = $5
So, the linear equation to compute the total cost for a member can be computed by:
C(x) = 5x + 20
where x is the number of games per month
On the other hand, non-members can get one more game per month for $7 which means they get 2 games for $7. The price for a single game is $7/2 = $3.5 a month.
The linear equation to compute the total cost for a non-member is:
C(x) = 3.5x
where x is the number of games per month.
The following system of equations can be used to decide whether to become a member or not, by substituting the number of games in place of x and finding out the total cost.
C(x) = 5x + 20 (for members)
C(x) = 3.5x (for non-members)
Marilyn Mallinson invested $30000, part at 6% annual interest and the rest at 7.5% annual interest. Last year she earned $1995 in interest. How much money did she invest at each rate?
Answer: she invested $17000 in the account earning 6% annual interest.
she invested $13000 in the account earning 7.5% annual interest.
Step-by-step explanation:
Let x represent the amount that she invested in the account earning 6% annual interest.
Let y represent the amount that she invested in the account earning 7.5% annual interest.
Marilyn Mallinson invested $30000, part at 6% annual interest and the rest at 7.5% annual interest. This means that
x + y = 30000
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
Considering the account earning 6% annual interest.
P = x
R = 6%
T = 1 year
I = (x × 6 × 1)/100 = 0.06x
Considering the account earning 7.5% annual interest,
P = y
R = 7.5
T = 1
I = (y × 7.5 × 1)/100 = 0.075y
Last year she earned $1995 in interest. This means that
0.06x + 0.075y = 1995 - - - - - - - -
Substituting x = 30000 - y into equation 1, it becomes
0.06(30000 - y) + 0.075y = 1995
1800 - 0.06y + 0.075y = 1995
- 0.06y + 0.075y = 1995 - 1800
0.015y = 195
y = 195/0.015 = 13000
x = 30000 - y = 30000 - 13000
x = 17000
Finally, the arena decides to offer advertising space on the jerseys of the arena’s own amateur volley ball team. The arena wants the probability of being shortlisted to be 0.14. What is this as a percentage and a fraction? What is the probability of not being shortlisted?
Give your answer as a decimal. Those shortlisted are entered into a final game of chance. There are six balls in a bag (2 blue balls, 2 green balls and 2 golden balls). To win, a company needs to take out two golden balls. The first ball is not replaced.
What is the probability of any company winning advertising space on their volley ball team jerseys?
Answer: 7/50
14%
1/30
Step-by-step explanation:0.14 to fraction =0.14/100=14/100=7/50
0.14 to %= 0.14 ×100=14%
Total number of balls=6
Blue balls=2
Golden balls=2
Green balls=2
Probability of picking the first ball=1/6
Probability of picking the second ball= 1/5
P(winning wit 2 golden balls)=1/6×1/5=1/30
The probability of any company winning advertising space on their volleyball team jerseys is approximately 0.0093, or 0.93%.
Probability of Being Shortlisted
The probability of being shortlisted is given as 0.14.
As a Percentage:[tex]\[ 0.14 \times 100 = 14\% \][/tex]
As a Fraction:[tex]\[ 0.14 = \frac{14}{100} = \frac{7}{50} \][/tex]
Probability of Not Being Shortlisted:The probability of not being shortlisted is:
[tex]\[ 1 - 0.14 = 0.86 \][/tex]
Probability of Winning Advertising Space
To win the advertising space, a company needs to draw two golden balls consecutively without replacement from a bag containing 6 balls (2 blue, 2 green, and 2 golden).
Total Balls:There are 6 balls in total.
First Draw:The probability of drawing a golden ball first:
[tex]\[ \frac{2}{6} = \frac{1}{3} \][/tex]
Second Draw:After drawing one golden ball, there are 5 balls left, including 1 golden ball:
The probability of drawing a golden ball second:
[tex]\[ \frac{1}{5} \][/tex]
Combined Probability:The probability of drawing two golden balls consecutively is the product of the individual probabilities:
[tex]\[ \frac{1}{3} \times \frac{1}{5} = \frac{1}{15} \][/tex]
Final Probability of Winning Advertising Space
Since the company needs to be shortlisted first and then draw the two golden balls to win the advertising space, the combined probability is:[tex]\[0.14 \times \frac{1}{15}\][/tex]
Convert 0.14 to a fraction:[tex]\[0.14 = \frac{7}{50}\][/tex]
Multiply the probabilities:[tex]\[\frac{7}{50} \times \frac{1}{15} = \frac{7}{750}\][/tex]
Convert to a decimal:[tex]\[\frac{7}{750} \approx 0.0093\][/tex]
A proton initially has and then 8.00 s later has (in meters per second). (a) For that 8.00 s, what is the proton's average acceleration in unit vector notation, (b) in magnitude, and (c) the angle between and the positive direction of the x axis
Answer:
Some details are missing in the question, here are the details ; A proton initially has v = -6.5i + 17j + 13k and then 8.00s later has v = -2.8i + 17j - 9.3k (in meters per seconds).
a) proton's average acceleration in unit vector notation = 0.46i - 2.78k
b) Magnitude = 2.85m/s2
c) angle between and the positive direction of the x axis = 279.39 degree (counter clockwise)
Step-by-step explanation:
The detailed and step by step explanation is as shown in the attachment
Lake Michigan's volume is approximately 1,180 cubic miles and its surface area is approximately 14,332,090 acres. The 2015 water level was 11 inches above the 2014 level. What is the percentage change in the lake volume over that year? Hint: Find and use the answers to these questions: • What is the average depth of the lake in feet? Hint: Consider the depth of a box with the volume and surface area of the lake. • Approximately how much water in cubic feet has the lake gained?
Answer:
a.) depth of the lake = (volume of the lake) / area of lake
= 173,693,585,360,000 / 624,305,840,400 = 278.22 feet
b.) 11 inches = 0.9167 feet
Water gained in cubic feet gained by the lake
= 624,305,840,400 [tex]\times[/tex] 0.9167
= 572,282,434,719.5 cubic feet
c.) the percentage change in the lake volume over that year
= 572,282,434,719.5 cubic feet / 173,693,585,360,000 cubic feet
= 0.0033
= 0.33%
Step-by-step explanation:
i) acres to square feet : 1 acre = 43560 square feet
therefore 14,332,090 acres = 624,305,840,400 square feet
ii) 1 mile = 5280 feet
1 cubic mile = 5280 [tex]\times[/tex] 5280 [tex]\times[/tex] 5280 = 147,197,952,000 cubic feet
therefore 1180 cubic miles = 173,693,585,360,000 cubic feet
a.) depth of the lake = (volume of the lake) / area of lake
= 173,693,585,360,000 / 624,305,840,400 = 278.22 feet
b.) 11 inches = 0.9167 feet
Water gained in cubic feet gained by the lake
= 624,305,840,400 [tex]\times[/tex] 0.9167 = 572,282,434,719.5 cubic feet
c.) the percentage change in the lake volume over that year
= 572,282,434,719.5 cubic feet / 173,693,585,360,000 cubic feet
= 0.0033
= 0.33%
the sum of three consecutive number is 114. what is the smallest of the three numbers?
Answer:
37
Step-by-step explanation:
37+38+39
Answer: the smallest of the three numbers is 37
Step-by-step explanation:
Let x represent the smallest number.
Since the three numbers are consecutive, it means that the next number would be x + 1
Also, the last and also the largest number would be x + 2
If the sum of the three consecutive numbers is 114, it means that
x + x + 1 + x + 2 = 114
3x + 3 = 114
Subtracting 3 from the Left hand side and the right hand side of the equation, it becomes
3x + 3 - 3 = 114 - 3
3x = 111
Dividing the Left hand side and the right hand side of the equation by 3, it becomes
3x/3 = 111/3
x = 37
For the staff breakfast on Friday Mr. Taylor purchased 5 cartons of eggs (a carton contains a dozen eggs). Je used 2 and 11/12 cartons for scrambled eggs and 1 and 1 and a 3rd cartons for breakfast burritos. How many eggs did he have left?
Answer: he has 9 eggs left.
Step-by-step explanation:
Mr. Taylor purchased 5 cartons of eggs and a carton contains a dozen eggs. A dozen of eggs is 12 eggs. It means that 5 cartons of eggs would contain
5 × 12 = 60 eggs
He used 2 and 11/12 cartons for scrambled eggs. Converting 2 11/12 into improper fraction, it becomes
35/12 cartons .
He used 1 and 1 and a 3rd cartons for breakfast burritos. Converting
1 1/3 into improper fraction, it becomes 4/3 cartons
Total number of cartons that he used would be
35/12 + 4/3 = (35 + 16)/12 = 51/12
The number of cartons left would be
5 - 51/12 = (60 - 51)/12 = 9/12
Since a carton has 12 eggs,
9/12 carton will have 9/12 × 12 = 9 eggs
What is the value of t=1 ∑³ (4 x 1/2^t-1)
Answer:
7
Step-by-step explanation:
[tex]\sum\limits_{t=1}^{3}(4\cdot(\frac{1}{2})^{t-1})[/tex]
This is the sum of the first three terms of a geometric sequence, where the first term is 4 and the common ratio is ½.
We can use a formula to find the sum, or, since there's only three terms, we can find the value of each term then add up the results.
4 · (½)¹⁻¹ = 4
4 · (½)²⁻¹ = 2
4 · (½)³⁻¹ = 1
4 + 2 + 1 = 7
Clovis is standing at the edge of a cliff, which slopes 4 feet downward from him for every 1 horizontal foot. He launches a small model rocket from where he is standing. With the origin of the coordinate system located where he is standing, and the x-axis extending horizontally, the path of the rocket is described by the formula y = −2x² + 160x.
(a) Give a function h = f(x) relating the height h of the rocket above the sloping ground to its x-coordinate.
(b) Find the maximum height of the rocket above the sloping ground. What is its x-coordinate when it is at its maximum height?
(c) Clovis measures its height h of the rocket above the sloping ground while it is going up. Give a function x = g(h) relating the x-coordinate of the rocket to h.
(d) Does this function still work when the rocket is going down? Explain.
Answer:
a) -2x^2 + 164x
b) 3362 feet
c) (82 , -328)
d) yes
Step-by-step explanation:
y = -2x^2 + 160x
Slope = 4 feet downward for every 1 horizontal foot.
a) h(x) = -2x^2 + 160x - (-4x)
= -2x^2 + 160x + 4x
= -2x^2 + 164x
b) The highest point occurs at the vertex of the parabolic equation. x is the same as the number of the axis of symmetry.
x = -b/2a
From the equation, a = -2 , b= 164
x = -164/ 2(-2)
x = -164/-4
x = 41
Put x = 41 into the value of h(x)
h(x) = -2x^2 + 164x
= -2(41^2) + 164(41)
= -2(1681) + 6724
= -3362 + 6724
= 3362 feet.
The maximum height occurs at 41 feet out from the top of the sloping ground at a height of 3362ft about the top edge of the cliff.
c) h(x) = -2x^2 + 164x
2x^2 - 164x + h = 0 when 0 ≤ x ≤ 41
Solve the equation using the formula (-b+/-√b^2 - 4ac) / 2a
a = 2, b= -164 , c = h
= [-(-164) +/- √(-164)^2 - 4(2)(h) ] / 2(2)
= (164 +/- √26896 - 8h)/ 4
This gives the value of -328 ≤ h ≤ 3362 is used because the rocket hits the sloping ground of (82 , -328)
d) the function still works when it is going down
We first find the function h=f(x) for the rocket's height above the ground. The maximum height is found using the vertex formula with x=(-b)/(2a). We can also determine the function x=g(h) for when the rocket is going up, but this does not work for when the rocket is going down due to needing negative roots.
Explanation:(a) Because the ground slopes 4 feet downward for every 1 horizontal foot, the ground line equation is y=-4x. So, to find the height of the rocket 'h' above the ground, we subtract the equation of the rocket's path from this equation for height of the ground, which gives h=f(x)=y-(-4x)=-2x²+160x+4x=-2x²+164x.
(b) To find the maximum height (vertex) of the parabolic path the rocket takes, we use x=(-b)/(2a) from the standard quadratic equation format (ax²+bx+c=0). Here, a=-2 and b=164. So, x=(-164)/(2*-2)=41. Therefore, the maximum height is when x=41, and we substitute x=41 into the equation h=f(x) to find the maximum height.
(c) To obtain x as a function of h, we can rearrange our equation for h=f(x) to make x=g(h). This will be a square root function because of the x² in the equation. However, since we only want the going up part, we just consider the positive root.
(d) This function doesn't work for when the rocket is going down as it would require considering the negative root, which isn't included in our function g(h) as it involves square roots.
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PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!! I NEED TO FINISH THESE QUESTIONS BEFORE MIDNIGHT TONIGHT.
Find CD.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
CD =
Answer:
Step-by-step explanation:
This is classic right triangle trig. We have the reference angle of 59 degrees, we have the side adjacent to that angle of 4 units, and we are looking for CD which is the hypotenuse of the triangle. That is the cosine ratio:
[tex]cos\theta=\frac{adj}{hyp}[/tex]
Filling in:
[tex]cos(59)=\frac{4}{hyp}[/tex]
Doing some algebraic acrobats there to solve for the hypotenuse gives you:
[tex]hyp=\frac{4}{cos(59)}[/tex]
Use your calculator to solve this in degree mode:
hyp = 7.8 units
Kindle Fire Prevention Corp. has a profit margin of 6.2 percent, total asset turnover of 2.1, and ROE of 18.34 percent. What is this firm’s debt–equity ratio? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Answer: Debt- Equity ratio is 0.41
Step-by-step explanation: Debt- Equity ratio is calculated by subtracting one from the equity multiplier.
To solve this problem the du pont analysis is used which is Return on equity = Profit margin * Total Asset turnover * equity multiplier
0.1834 = 0.062 × 2.10 * Equity multiplier (EM)
0.1834 = 0.1302
EM = 1.41
Therefore debt-equity ratio = EM - 1
= 1.41 - 1 = 0.41
Final answer:
The Debt-Equity Ratio of Kindle Fire Prevention Corp. is calculated using the Dupont Identity formula, which links ROE to profit margin, asset turnover, and the equity multiplier. Using the provided financial ratios, the calculated Debt-Equity Ratio is 139.86 after rounding to two decimal places.
Explanation:
The student has asked to calculate the debt–equity ratio for Kindle Fire Prevention Corp. using given financial ratios. To find the debt–equity ratio, we use the Dupont Identity which links the Return on Equity (ROE) to profit margin, asset turnover, and the equity multiplier (which is inversely related to the debt-equity ratio).
First, we express ROE as the product of profit margin, asset turnover, and equity multiplier:
ROE = Profit Margin × Total Asset Turnover × Equity Multiplier
Given: ROE = 18.34%, Profit Margin = 6.2%, Asset Turnover = 2.1
We rearrange the formula to solve for Equity Multiplier:
Equity Multiplier = ROE / (Profit Margin × Total Asset Turnover)
Substitute the given values:
Equity Multiplier = 18.34% / (6.2% × 2.1) = 18.34 / (0.062 × 2.1)
Equity Multiplier = 18.34 / 0.1302 = 140.862
Since Equity Multiplier = 1 + Debt-Equity Ratio, we can find the Debt-Equity Ratio by subtracting 1 from Equity Multiplier:
Debt-Equity Ratio = Equity Multiplier - 1 = 140.862 - 1 = 139.862
Therefore, the Debt-Equity Ratio of Kindle Fire Prevention Corp. is 139.86 (rounded to two decimal places).
To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (4, 2), we know that (4, 2) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x = a can be found using the formula
Answer:
[tex]x-4y+4=0[/tex]
[tex]f(x)=\sqrt x[/tex] and x=4
Step-by-step explanation:
We are given that a curve
[tex]y=\sqrt x[/tex]
We have to find the equation of tangent at point (4,2) on the given curve.
Let y=f(x)
Differentiate w.r.t x
[tex]f'(x)=\frac{dy}{dx}=\frac{1}{2\sqrt x}[/tex]
By using the formula [tex]\frac{d(\sqrt x)}{dx}=\frac{1}{2\sqrt x}[/tex]
Substitute x=4
Slope of tangent
[tex]m=f'(x)=\frac{1}{2\sqrt 4}=\frac{1}{2\times 2}=\frac{1}{4}[/tex]
In given question
[tex]m=\lim_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}[/tex]
[tex]\frac{1}{4}=\lim_{x\rightarrow 4}\frac{f(x)-f(4)}{x-4}[/tex]
By comparing we get a=4
Point-slope form
[tex]y-y_1=m(x-x_1)[/tex]
Using the formula
The equation of tangent at point (4,2)
[tex]y-2=\frac{1}{4}(x-4)[/tex]
[tex]4y-8=x-4[/tex]
[tex]x-4y-4+8=0[/tex]
[tex]x-4y+4=0[/tex]
The equation of the tangent line of a function at a particular point can be found by using the formula y - y1 = m(x - x1), where the slope m is the derivative of the function at the specific point. In this case, find the derivative at x = 4 and substitute into the formula along with the point (4,2).
Explanation:To find the equation of the tangent line of a function at a particular point, we can indeed utilise the slope-point form of a straight line equation, which is y - y1 = m (x - x1). In this case the point on the line is (4,2).
However regarding the slope, it is calculated as the derivative of the function f(x) at the point x = a.
Let us assume the function f(x). The derivative f '(x), also known as the slope of the tangent line at any point x, is found by taking the derivative of f(x). So to find the slope at x = 4, you would calculate f '(4).
Substitute the value of the derivative at the point (4,2) which represents our m(slope), x1=4 and y1=2 into the linear equation y - y1 = m(x - x1) to generate the equation of the tangent line.
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Melanie is baking breakfast rolls for a band camp fundraiser. She bakes 15 dozen breakfast rolls in 3 hours. After 8 hours, she has baked 40 dozen breakfast rolls. At what rate does Melanie bake breakfast rolls each hour?
Answer:
She bakes rolls at a rate of 60 rolls per hour!
Answer: The rate is 60 per hour
Step-by-step explanation:
The pairs of polygons below are similar. Give the sale factor of figure A to figure B
Yo sup??
Since the two figures are similar therefore their sides are in proportion.
for the first one
factor=2/8=1/4
for the second
factor=10/4=5/2
Hope this helps.
Answer: 7
Step-by-step explanation:
The first four terms of an arithmetic sequence are given.
27, 32, 37, 42, ...
What is the 60th term of the sequence?
Answer:
[tex]a_6_0=322[/tex]
Step-by-step explanation:
we know that
The rule to calculate the an term in an arithmetic sequence is
[tex]a_n=a_1+d(n-1)[/tex]
where
d is the common difference
a_1 is the first term
we have that
[tex]a_1=27\\a_2=32\\a_3=37\\a_4=42[/tex]
[tex]a_2-a_1=32-27=5[/tex]
[tex]a_3-a_2=37-32=5[/tex]
so
The common difference is d=5
[tex]a_4-a_3=42-37=5[/tex]
Find 60th term of the sequence
[tex]a_n=a_1+d(n-1)[/tex]
we have
[tex]a_1=27\\d=5\\n=60[/tex]
substitute
[tex]a_6_0=27+5(60-1)[/tex]
[tex]a_6_0=27+5(59)[/tex]
[tex]a_6_0=322[/tex]
The 60th term of the sequence should be 322 when the first four terms should be given.
Calculation of the 60th term of the sequence:Since
a1 = 27
a2 = 32
a3 = 37
And, a4 = 42
So,
= 27 + 5(60 - 1)
= 27 + 5(59)
= 322
hence, The 60th term of the sequence should be 322 when the first four terms should be given.
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