Answers
Applying the tangent ratio, the value of x in the given image is calculated as B. x = 15.92
How to find x using the tangent ratio?The tangent ratio is a trigonometric ratio that represents the ratio of the length of the side opposite a given angle to the length of the side adjacent to that angle in a right-angled triangle. It is denoted as tan(θ), where θ is the angle. Mathematically, tan(θ) = opposite/adjacent.
Thus, using the tangent ratio, we have:
tan 53 = x/12
x = tan 53 * 12
x ≈ 15.92
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Related Questions
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?
Answers
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.
The first four terms of an arithmetic sequence are given.
27, 32, 37, 42, ...
What is the 60th term of the sequence?
Answers
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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The 68-95-99.7 rule tells us how to find the middle 68%, 95% or 99.7% of a normal distribution. suppose we wanted to find numbers a and b so that the middle 80% of a standard normal distribution lies between a and b where a is less than
b. one of the answers below are not true of a and
b. mark the answer that is not true.
Answers
Answer:
The values of a and b are -1.28 and 1.28 respectively.
Step-by-step explanation:
It is provided that the area of the standard normal distribution between a and b is 80%.
Also it is provided that a < b.
Let us suppose that a = -z and b = z.
Then the probability statement is
[tex]P (a<Z<b)=0.80\\P(-z<Z<z)=0.80[/tex]
Simplify the probability statement as follows:
[tex]P(-z<Z<z)=0.80\\P(Z<z)-P(Z<-z)=0.80\\P(Z<z)-[1-P(Z<z)]=0.80\\2P(Z<z)-1=0.80\\P(Z<z) = \frac{1.80}{2}\\P(Z<z) =0.90[/tex]
Use the standard normal distribution table to determine the value of z.
Then the value of z for probability 0.90 is 1.28.
Thus, the value of a and b are:
[tex]a = -z = - 1.28\\b = z = 1.28[/tex]
Thus, [tex]P(-1.28<Z<1.28)=0.80[/tex].
SHOW YOUR WORK!! Identify the simplest polynomial function having integer coefficients with the given zeros: 3i, −1, 2
Answers
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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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?
Answers
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
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?
Answers
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
Phoebe runs at 12km/h and walks at 5km/h. One afternoon she ran and walked a total of 17km. If she ran for the same length of time as she walked for how long did she run
Answers
If correct, it should be one hour. Maybe try and solve it yourself to see if this makes sense
Step-by-step explanation:
Assume the total trip that afternoon took t hours
12(t/2) + 5(t/2) = 17 => t = 2
So she ran for 1 hour.
Factor the expression. x2 – x – 42 (x – 7)(x – 6) (x – 7)(x + 6) (x + 7)(x – 6) (x + 7)(x + 6)
Answers
Answer:
(x - 7)x + 6).
Step-by-step explanation:
x^2 – x – 42
6 * -7 = 42 and 6 - 7 = -1 so the factors are:
(x - 7)x + 6).
The factor form of the expression x² - x - 42 is (x - 7)(x + 6).
To factor the expression x² - x - 42, we need to find two binomial factors that, when multiplied together, give us the original expression.
We can start by looking for two numbers that multiply to -42 and add up to -1, which is the coefficient of the x term in the expression.
The pair of numbers that satisfy these conditions are -7 and 6.
If we multiply these two numbers, we get -42, and if we add them, we get -1.
Therefore, we can write the expression as:
x² - x - 42
= (x - 7)(x + 6)
This means that the original expression can be factored as the product of two binomials: (x - 7) and (x + 6).
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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.
Answers
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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the sum of three consecutive number is 114. what is the smallest of the three numbers?
Answers
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
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
Answers
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)
The following function represents an arithmetic sequence.
f(1)=−1.5
f(n+1)=f(n)+0.5
What is f(10)?
Answers
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
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?
Answers
Answer:
She bakes rolls at a rate of 60 rolls per hour!
Answer: The rate is 60 per hour
Step-by-step explanation:
The table below show the total amount How did your predictions compare to your actual findings of mean and mean absolute deviation? Explain
Answers
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.
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?
Answers
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
Rewrite as a combination of multiple logarithms:
log_8 (10xy^3)
Answers
Answer:
The answer to your question is letter B. log₈10 + log₈x + 3log₈y
Step-by-step explanation:
Just remember the properties of logarithms
- The logarithm of a product is the sum of logarithms.
- The logarithm of a power is equal to the power times the log.
Then
log₈(10xy³) = log₈ 10 + log₈x + log₈y³
and finally
log₈10 + log₈x + 3log₈y
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?
Answers
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]
Follow the steps above, and find c, the total of the payments related to financing, and the monthly payment. A customer buys an automobile from you, the salesman. The price of the car, which includes taxes and license, amounts to $5,955.00. The customer wants to finance the car over 48 months after making a $500 down payment. You inform him that the true annual interest rate is 18%.
Answers
the monthly payment is approximately $163.06 and the total payments related to financing are approximately $7834.88.
To find the monthly payment and the total payments related to financing, we need to follow these steps:
1. Calculate the total amount financed.
2. Use the total amount financed to calculate the monthly payment using the formula for monthly payments on a fixed-rate loan.
3. Multiply the monthly payment by the number of months to find the total payments related to financing.
Given:
- Price of the car = $5955.00
- Down payment = $500.00
- Finance period = 48 months
- Annual interest rate [tex]\(= 18\%\)[/tex]
Step 1: Calculate the total amount financed.
The total amount financed is the difference between the price of the car and the down payment.
[tex]\[ \text{Total amount financed} = \text{Price of the car} - \text{Down payment} \][/tex]
[tex]\[ \text{Total amount financed} = \$5955.00 - \$500.00 \][/tex]
[tex]\[ \text{Total amount financed} = \$5455.00 \][/tex]
Step 2: Calculate the monthly payment.
To calculate the monthly payment, we use the formula for the monthly payment on a fixed-rate loan:
[tex]\[ M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1} \][/tex]
Where:
- M is the monthly payment
- P is the principal amount (total amount financed)
- r is the monthly interest rate (annual interest rate divided by 12)
- n is the number of payments (finance period in months)
First, we need to convert the annual interest rate to a monthly interest rate:
[tex]\[ r = \frac{18\%}{12} = 0.18 \times \frac{1}{12} = 0.015 \][/tex]
Now, we plug in the values:
[tex]\[ M = \frac{5455 \times 0.015 \times (1 + 0.015)^{48}}{(1 + 0.015)^{48} - 1} \][/tex]
[tex]\[ M ≈ \frac{5455 \times 0.015 \times (1.015)^{48}}{(1.015)^{48} - 1} \][/tex]
Using a calculator, we find that the monthly payment M is approximately $163.06.
Step 3: Calculate the total payments related to financing.
[tex]\[ \text{Total payments} = \text{Monthly payment} \times \text{Number of months} \][/tex]
[tex]\[ \text{Total payments} = \$163.06 \times 48 \][/tex]
[tex]\[ \text{Total payments} ≈ \$7834.88 \][/tex]
So, the monthly payment is approximately $163.06 and the total payments related to financing are approximately $7834.88.
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?
Answers
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%
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
Answers
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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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?
Answers
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
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 =
Answers
Add those and you get 149. Subtract 180 from 149 and get 31. D is 31, c is 59, so cd is 90.
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
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.
Answers
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
Answers
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.
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?
Answers
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
What is the slope intercept form of the equation y+18=2(x-1)
Answers
Step-by-step explanation:
Given,
The equation y + 18 = 2( x - 1)
To write the given equation in the slope intercept form = ?
∴ The equation y + 18 = 2( x - 1)
⇒ y + 18 = 2x - 2
⇒ y = 2x - 2 - 18
⇒ y = 2x - 20
⇒ y = 2x + ( - 20) ..... (1)
We know that,
The equation of slope intercept form,
y = mx + c
Where, m is the sope and c is the y-intercept
∴ The slope intercept form of the given equation is: y = 2x + ( - 20)
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))
Answers
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).
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?
Answers
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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Determine the models that could represent a compound interest account that is growing exponentially.
Select all the correct answers.
A(t) = 2,675(1.003)12t
A(t) = 4,170(1.04)t
A(t) = 3,500(0.997)4t
A(t) = 5,750(1.0024)2t
A(t) = 1,500(0.998)12t
A(t) = 2,950(0.999)t
Answers
Answer:A(t)= 2,675(1.003)12t
A(t)=4170(1.04)t
A(t)=5750(1.0024)2t
Step-by-step explanation:Exponential growth is also called growth percentage.
It is calculated using 100% of the original amount plus the growth rate . Example if the amount grows by 5% yearly.5%=0.05
It is written thus(1+0.005)=1.05.
It is usually written in decimal.
The formular for compound interest that is growing exponentially is written as
A=P (1 + i)^N
Looking at the 5 A(t) equations,only 3 of it are growing exponentially.
At a corner gas station, the revenue R varies directly with the number g of gallons of gasoline sold. If the revenue is $56.40 when the number of gallons sold is 12, find a linear equation that relates revenue R to the number g of gallons of gasoline. Then find the revenue R when the number of gallons of gasoline sold is 7.5.
Answers
Answer:
(i) R = 4.70g
(ii) R = $35.25
Step-by-step explanation:
(i) R ∞ g
Removing the proportionality symbol, we have
R = kg, where k is the constant of proportion
56.40 = k(12)
Divide both sides by 12
56.40/12 = k(12)/12
$4.70 = k
k = $4.70
So, R = 4.70g (which is the linear equation relating Revenue, R to number of gallons, g)
(ii) When g = 7.5,
R = 4.70 * 7.5 = 35.25
R = $35.25
The revenue R at a gas station varies directly with the number of gallons of gasoline sold g. The linear equation relating R to g is R = 4.7g. The revenue when the number of gallons sold is 7.5 is $35.25.
Explanation:
In this particular scenario, we're dealing with a problem of direct variation. In a direct variation, as one quantity increases, the other increases proportionally. This can be represented by a linear equation of the form y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of variation (the ratio of y to x).
Here, the Revenue (R) varies directly with the number of gallons of gasoline sold (g). We can calculate the constant of variation (k) by dividing the given Revenue (R) by the given number of gallons (g): k = 56.4 ÷ 12 = 4.7. So, the linear equation relating R to g is: R = 4.7g.
To find the revenue R when the number of gallons of gasoline sold is 7.5, substitute g = 7.5 into the equation: R = 4.7 * 7.5 = $35.25
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