Answer:
The slope is 2, while the y-intercept is 4. This equation represents starting with 4 cards and adding 2 cards each week.
Step-by-step explanation:
Given the equation which describes the number of cards, y, you have after x weeks: y=2x+4
Comparing this with the slope intercept form of the equation of the line: y=mx+b, where:
m is the slopeb is the y-intercept.We have that:
Slope
Slope, m=2.
A slope of 2 indicates that you buy 2 cards per week.
The y-intercept
The y-intercept of the line, b=4.
This is the starting value. In this case, it represents the number of cards you were given by your friend.
The slope is 2, while the y-intercept is 4. This equation represents starting with 4 cards and adding 2 cards each week.
An object is launched from the ground. The object’s height, in feet, can be described by the quadratic function h(t) = 80t – 16t2, where t is the time, in seconds, since the object was launched. When will the object hit the ground after it is launched? Explain how you found your answer.
Answer:
The object hits the ground 5 seconds after being launched.
Step-by-step explanation:
The height of the object in t seconds after being launched is given by the following equation:
[tex]h(t) = 80t - 16t^{2}[/tex]
When will the object hit the ground after it is launched?
This is t for which h(t) = 0.
So
[tex]80t - 16t^{2} = 0[/tex]
[tex]16t(5 - t) = 0[/tex]
Then
[tex]16t = 0[/tex]
[tex]t = 0[/tex]
This is the launch point
[tex]5 - t = 0[/tex]
[tex]t = 5[/tex]
So
The object hits the ground 5 seconds after being launched.
Answer:
The object will hit the ground after 5 seconds. You can rewrite the quadratic function as a quadratic equation set equal to zero to find the zeros of the function 0 = –16t2 + 80t + 0. You can factor or use the quadratic formula to get t = 0 and t = 5. Therefore, it is on the ground at t = 0 (time of launch) and then hits the ground at t = 5 seconds.
Step-by-step explanation:
This is the exact answer on edg 2020
1/4 of x is 6 please help solve This
Answer:
x = 24
Step-by-step explanation:
Of means multiply and is means equals
1/4 * x = 6
Multiply each side by 4
1/4*4 x = 6*4
x = 24
Find zw and StartFraction z Over w EndFraction . Leave your answers in polar form. z equals 4 (cosine 150 degrees plus i sine 150 degrees )w equals 2 (cosine 250 degrees plus i sine 250 degrees )
Answer:
a) zw = 8 (Cos 40° + i Sin 40°)
b) (z/w) = 2 (Cos 260° + i Sin 260°)
Step-by-step explanation:
z = 4(Cos 150° + i Sin 150°)
w = 2 (Cos 250° + i Sin 250°)
To first simplify,
Cos 150° = -0.8660
Sin 150° = 0.50
Cos 250° = -0.3420
Sin 250° = -0.9397
z = 4(Cos 150° + i Sin 150°)
z = 4 (-0.866 + 0.5i)
z = (-3.464 + 2i)
w = 2 (Cos 250° + i Sin 250°)
w = 2 (-0.342 -0.9397i)
w = (-0.684 - 1.8794i)
a) zw = (-3.464 + 2i) (-0.684 - 1.8794i)
zw = 2.369376 + 6.5102416i - 1.368i - 3.7588i²
Note that i² = -1
zw = 2.369376 + 5.1422416i + 3.7588
zw = (6.128176 + 5.1422416i)
A general complex number z = x + it has the Polar form = r (cos θ + i sin θ)
r = √(x² + y²)
θ = arctan (y/x)
zw = (6.128176 + 5.1422416i)
x = 6.128176
y = 5.1422416
r = √(6.128176² + 5.1422416²) = 7.99997 = 8
θ = arctan (5.1422416/6.128176) = 40°
zw = 8 (Cos 40° + i Sin 40°)
b) (z/w) = (-3.464 + 2i) / (-0.684 - 1.8794i)
To simplify This, we first rationalize, that is, multiply numerator and denominator by (-0.684 + 1.8794i)
(z/w) = [(-3.464 + 2i)×(-0.684 + 1.8794i)] ÷ [((-0.684 - 1.8794i)×((-0.684 + 1.8794i)
(z/w) = [2.369376 - 6.5102416i - 1.368i + 3.7588i²] ÷ [0.467856 - 3.53214436i²]
Note that i² = -1
(z/w) = [2.369376 - 3.7588 - 7.8782416i] ÷ [0.467856 + 3.53214436]
(z/w) = (-1.389424 - 7.8782416i)/4
(z/w) = (-0.347356 - 1.9695604i)
x = -0.347356
y = -1.9695604
r = √[(-0.347356)² + (-1.9695604)²] = 1.9997 = 2
θ = arctan (-1.9695604)/(-0.347356) = 80° on the first quadrant, but the signs on x and y indicates that this is the third quadrant, hence
θ = 180° + 80° = 260°
(z/w) = 2 (Cos 260° + i Sin 260°)
Hope this Helps!!!
A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x , the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x .] Simplify your formula as much as possible.
Answer:
Base Length of 84cmHeight of 42 cm.Step-by-step explanation:
Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.
Step 1:
Let the side length of the base =x
Let the height of the box =h
Since the box has a square base
Volume, [tex]V=x^2h=296352[/tex]
[tex]h=\dfrac{296352}{x^2}[/tex]
Surface Area of the box = Base Area + Area of 4 sides
[tex]A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}[/tex]
Step 2: Find the derivative of A(x)
[tex]If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}[/tex]
Step 3: Set A'(x)=0 and solve for x
[tex]A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84[/tex]
Step 4: Verify that x=84 is a minimum value
We use the second derivative test
[tex]A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6[/tex]
Since the second derivative is positive at x=84, then it is a minimum point.
Recall:
[tex]h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42[/tex]
Therefore, the dimensions that minimizes the box surface area are:
Base Length of 84cmHeight of 42 cm.If A={3,6,9,12 }and B={0,4,8,12}, then find A∩B. *
Answer:
idk
Step-by-step explanation:
Urn has 5 white and 7 black balls. Urn has 3 white and 12 black balls. We flip a fair coin. If the outcome is heads, then a ball from urn is selected, whereas if the outcome is tails, then a ball from urn is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails?
Answer:
Suppose that a white ball is selected, the probability that the coin landed tails = (12/37) = 0.3243
Step-by-step explanation:
Complete Question
Urn A has 5 white and 7 black balls. Urn B has 3 white and 12 black balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a ball from urn B is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails?
Solution
Let the probability of that a head turns up and urn A is selcted be P(A) = (1/2)
Probability that a tail turns up and urn B is selected = P(B) = (1/2)
Probability that a white ball is picked = P(W)
The probability that a white ball is picked given that the coin toss gives a head and urn A is selected = P(W|A) = (5/12)
The probability that a white ball is picked given that the coin toss gives a tail and urn B is selected = P(W|B) = (3/15) = (1/5)
We now require the probability that the coin lands on a tail and urn B is selected given that a white ball is picked, P(B|W)
Note that the conditional probability P(X|Y) is expressed mathematically as
P(X|Y) = P(X n Y) ÷ P(Y)
And P(X n Y) = P(X|Y) × P(Y)
Hence, the required probability
P(B|W) = P(B n W) ÷ P(W)
Although, we do not have the probabilities P(B n W) and P(W), we can calculate them
P(B n W) = P(W n B) = P(W|B) × P(B) = (1/5) × (1/2) = (1/10)
P(W) = P(W n A) + P(W n B) (Since the events A and B are mutually exclusive)
P(W n A) = P(W|A) × P(A) = (5/12) × (1/2) = (5/24)
P(W n B) = (1/10)
P(W) = (5/24) + (1/10) = (37/120)
P(B|W) = P(B n W) ÷ P(W) = (1/10) ÷ (37/120) = (12/37) = 0.3243
Hope this Helps!!!
What is the value of a share of Henley Inc. to an investor who requires a 11 percent
rate of return if Henley is expected to pay a fixed dividend of $1.10 for the next 3 years and
then the dividends will grow at a constant rate of 5% indefinitely
Answer:
Value of Henley Inc.'s share is $16.76
Step-by-step explanation:
The present value of the dividends over for the three years and the terminal value of the dividends would give us a fair share price that an investor would pay
Year 1 PV of dividends=$1.10/(1+11%)^1=$0.99
Year 2 PV of dividends=$1.10/(1+11%)^2=$0.89
Year 3 PV of dividends=$1.10/(1+11%)^3=$0.80
The terminal value formula=dividend*(1+g)/(r-g)
g is the dividend growth rate of 5%
r is the investor's required rate of return which is 11%
terminal value=$1.10*(1+5%)/(11%-5%)=$19.25
The terminal is discounted to present value using the discount factor of year 3
PV of terminal value =$19.25 /(1+11%)^3=$ 14.08
Total present values=$0.99+$0.89+$0.80+$14.08 =$16.76
A man 1.75 meters tall cast a shadow 5.25 meters long. At the same time, a flagpole casts a shadow 120 meters long. How tall is the flagpole?
Answer:
40m
Step-by-step explanation:
5.25 divided by 1.75=3
120 divided by 3=40
grogg surveyed 135 beasts at his school about thier favorite house pet. the pie chart below summarizes his resuts. if 54 of the students preferred dogs, what is the value of x
Department 1 of a two department production process shows:
Units
Beginning Work in Process 9900
Ending Work in Process 49000
Total units to be accounted for 180200
How many units were transferred out to Department 2?
131200.
180200.
170300.
49000.
Answer:
131,200 units
Step-by-step explanation:
The number of units transferred to Department 2 from Department 1 is the total units to be accounted for which is 180,200 units minus the ending work in process of 49,000 units.
The logic here is that Department 1 is to account for 180,200 units ,part of which is the ending working process while the remainder which was transferred out is the difference between the two figures
units transferred to Department 2=180,200-49,000= 131,200.00 units
State the name of the property illustrated.
V5+(-3) =(-3) + 5
Associative
O Distributive
O Both associative and commutative
>
O Commutative
Answer:
The answer is commutative and associative.
Step-by-step explanation:
According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998). Assume that blood pressure is normally distributed. a.) State the random variable. b.) Find the probability that a person in China has blood pressure of 135 mmHg or more. c.) Find the probability that a person in China has blood pressure of 141 mmHg or less. d.)Find the probability that a person in China has blood pressure between 120 and 125 mmHg. e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not? f.) What blood pressure do 90% of all people in China have less than?
Answer:
a) Mean blood pressure for people in China.
b) 38.21% probability that a person in China has blood pressure of 135 mmHg or more.
c) 71.30% probability that a person in China has blood pressure of 141 mmHg or less.
d) 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.
e) Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg
f) 157.44mmHg
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If X is two standard deviations from the mean or more, it is considered unusual.
In this question:
[tex]\mu = 128, \sigma = 23[/tex]
a.) State the random variable.
Mean blood pressure for people in China.
b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.
This is 1 subtracted by the pvalue of Z when X = 135.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{135 - 128}{23}[/tex]
[tex]Z = 0.3[/tex]
[tex]Z = 0.3[/tex] has a pvalue of 0.6179
1 - 0.6179 = 0.3821
38.21% probability that a person in China has blood pressure of 135 mmHg or more.
c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.
This is the pvalue of Z when X = 141.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{141 - 128}{23}[/tex]
[tex]Z = 0.565[/tex]
[tex]Z = 0.565[/tex] has a pvalue of 0.7140
71.30% probability that a person in China has blood pressure of 141 mmHg or less.
d.)Find the probability that a person in China has blood pressure between 120 and 125 mmHg.
This is the pvalue of Z when X = 125 subtracted by the pvalue of Z when X = 120. So
X = 125
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{125 - 128}{23}[/tex]
[tex]Z = -0.13[/tex]
[tex]Z = -0.13[/tex] has a pvalue of 0.4483
X = 120
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 128}{23}[/tex]
[tex]Z = -0.35[/tex]
[tex]Z = -0.35[/tex] has a pvalue of 0.3632
0.4483 - 0.3632 = 0.0851
8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.
e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?
From b), when X = 135, Z = 0.3
Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg.
f.) What blood pressure do 90% of all people in China have less than?
This is the 90th percentile, which is X when Z has a pvalue of 0.28. So X when Z = 1.28. Then
X = 120
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 128}{23}[/tex]
[tex]X - 128 = 1.28*23[/tex]
[tex]X = 157.44[/tex]
So
157.44mmHg
I am completely stumped...
Answer:
x=25[tex]\sqrt{2}[/tex]
Step-by-step explanation:
the hypotenuse is equal to a leg times the square root of 2. which means to find the leg with the hyp given. you take [tex]\frac{50}{\sqrt{2} }[/tex] which then translates to 50 root 2/2=x therefore 25[tex]\sqrt{2}[/tex]
What is 200÷30=??
Round your answer to the nearest tenths.
Answer: the answer will be 7
Step-by-step explanation:
when i round my answer to the nearest tenths I got 7.
My first answer is 6.66666666667
then I round my answer and got 7 because 6 is bigger than 5 so i can put it as a whole number.
Answer: the answer will be 7
Step-by-step explanation:
when i round my answer to the nearest tenths I got 7.
My first answer is 6.66666666667
then I round my answer and got 7 because 6 is bigger than 5 so i can put it as a whole number.
Find g(1) if g(x) = x 2 + 1
Answer:
2
Step-by-step explanation:
g(1) = 1² + 1 = 2
Step-by-step explanation:
it is 2
On the first day of the trip, he will drive one half of the total distance.On the second day of the trip, he will drive half of the remaining distance.On the third day, he will drive four times the distance of the fourth day.On the fourth day, he will drive 5 miles.How many miles is the total trip?
Answer:
Total distance traveled is 100 miles
Step-by-step explanation:
The man will drive half of the trip on the first day, therefore, distance that will be traveled on the first day = 0.5x
where x is the total distance of the trip.
On the second day, he will drive half of the remaining half of the distance, i.e he will drive 0.5 x 0.5x = 0.25x
This implies that the total distance that will be traveled traveled in the final two days of the journey will also be 0.5 x 0.5x = 0.25x.
0.5x + 0.25x + 0.25x = x, which is the total distance traveled.
on the third day he will drive 4 times the distance of the fourth day, therefore, distance that will be traveled on the third day = 4 x 5 = 20 miles
on the fourth day, he will drive 5 mile.
total of the last two days = 5 + 20 = 25 miles.
this 25 miles is equal to 0.25 of the whole trip. Equating these values, we have
0.25x = 25 miles
x = 25/0.25 = 100 miles
An airplane climbs at an angle of 2.7" from an altitude of 4500 ft to an altitude of 5600 ft. How far does the airplane travel as it climbs as
measured along the horizontal?
Answer:
23,325 ft, about 4.42 miles
Step-by-step explanation:
The geometry of the situation can be modeled by a right triangle, where the side adjacent to the 2.7° angle of climb is the horizontal distance, and the side opposite is the vertical change in altitude. That change is ...
5600 ft -4500 ft = 1100 ft
and the angle relation is ...
tan(2.7°) = opposite/adjacent = (1100 ft)/(horizontal distance)
Multiplying this equation by (horizontal distance)/tan(2.7°) gives ...
horizontal distance = (1100 ft)/tan(2.7°) ≈ 23,325 ft
Dividing this by 5280 ft/mi gives ...
horizontal distance ≈ 4.42 mi
The airplane travels about 23,325 ft, or 4.42 miles, horizontally as it climbs.
Perform the indicated operation and write the answer in the form a + bi.
(1 + i)(-3 - 4i)
Answer:
[tex]1-7i[/tex]
Step-by-step explanation:
[tex]\left(1+i\right)\left(-3-4i\right)[/tex]
[tex]=\left(1\cdot \left(-3\right)-1\cdot \left(-4\right)\right)+\left(1\cdot \left(-4\right)+1\cdot \left(-3\right)\right)i[/tex]
[tex]1\cdot \left(-3\right)-1\cdot \left(-4\right)[/tex]
[tex]=-3+4[/tex]
[tex]=1[/tex]
[tex]1\cdot \left(-4\right)+1\cdot \left(-3\right)[/tex]
[tex]=-4-3[/tex]
[tex]=-7[/tex]
[tex]=1-7i[/tex]
will give brainliest
Answer:
About 8.2 cm
Step-by-step explanation:
Assuming that a is one of the legs of this right triangle, then using the Pythagorean Theorem:
[tex]a=\sqrt{15.3^2-12.9^2}\approx 8.2[/tex]
Hope this helps!
Brittany rents bicycles to tourists. She recorded the height (in cm) of each customer and the frame size (in cm) of the bicycle that customer rented. After plotting her results, Brittany noticed that the relationship between the two variables was fairly linear, so she used the data to calculate the following least squares regression equation for predicting bicycle frame size from the height of the customer: y=x+ What is the residual of a customer with a height of 155 cm who rents a bike with a 51 cm frame?
Answer: -1
Step-by-step explanation:
Here is the complete question:
Brittany rents bicycles to tourists. She recorded the height (in cm) of each customer and the frame size (in cm) of the bicycle that customer rented. After plotting her results, Brittany noticed that the relationship between the two variables was fairly linear, so she used the data to calculate the following least squares regression equation for predicting bicycle frame size from the height of the customer: y'=1/3x + 1/3.
What is the residual of a customer with a height of 155 cm who rents a bike with a 51 cm frame?
The regression equation is given as:
y'=(1/3)x + (1/3)
Since the height is given as 155cm, x=155 cm
The predicted frame size,
y'=(1/3)x + (1/3)
y'=(1/3) × 155+ (1/3)
= 51 2/3 + 1/3
= 52
The observed frame size,
y=51
Residual = Observed y- predicted y
=51-52
= -1
The residual of a customer with a height of 155 cm who rents a bike with a 51 cm frame is -1.
Answer:
-1
Step-by-step explanation:
I NEED HELP ASAP PLSSSSSSSS HELPPPPPP I BEG OF YOU
In 20 minutes, John can wrap____
small boxes and Hank can wrap____
small boxes. So, Hank can wrap_____
more small boxes in 20 minutes than John can.
matatila female drink 1/2 litres of milk every day during this month of September how many litres is this all together
Answer:
15 litres
Step-by-step explanation:
(1/2 litre/day)(30 days) = 15 litres
__
Multiply rate by time to get quantity.
In western Kansas, the summer density of hailstorms is estimated at about 1.5 storms per 5 square miles. In most cases, a hailstorm damages only a relatively small area in a square mile. A crop insurance company has insured a tract of 9 square miles of Kansas wheat land against hail damage. Let r be a random variable that represents the number of hailstorms this summer in the 9-square-mile tract.(a) Explain why a Poisson probability distribution is appropriate for r.Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are dependent.Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are dependent. Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are independent.Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent.What is λ for the 9-square-mile tract of land? Round λ to the nearest tenth (b) If there already have been two hailstorms this summer, what is the probability that there will be a total of four or more hailstorms in this tract of land? Compute P(r≥ 4 | r ≥ 2). (Use 4 decimal places.)(c) If there already have been three hailstorms this summer, what is the probability that there will be a total of fewer than six hailstorms? Compute P(r < 6 | r ≥ 3). (Use 4 decimal places.)
Answer:
Step-by-step explanation:
(a) Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent
(b) The required [tex]\lambda[/tex] = 1.7 * 10/5 = 3.4
(c) P(r ≥ 4 | r ≥ 2)
= P(r ≥ 4)/P(r ≥ 2)
= {1 - P(r < 4)}/{1 - P(r < 2)}
For Poisson distribution, P(X = x)
[tex]= \frac{e^{- \lambda} \lambda ^x}{x !}[/tex]
Thus, P(r < 4) = P(r = 0) + P(r = 1) + P(r = 2) + P(r = 3)
= 0.5584
and P(r < 2) = P(r = 0) + P(r = 1) = 0.1468
Thus, P(r ≥ 4 | r ≥ 2) = (1 - 0.5584)/(1 - 0.1468)
= 0.5177
(d) P(r < 6 | r ≥ 3)
= P(3 ≤ r < 6)/P(r ≥ 3)
P(3 ≤ r < 6) = P(r = 3) + P(r = 4) + P(r = 5) = 0.5308
P(r ≥ 3) = 1 - {P(r = 0) + P(r = 1) + P(r = 2)}
= 0.6603
Thus, P(r < 6 | r ≥ 3) = 0.5308/0.6603 = 0.8309
A company estimates that 1% of their products will fall after the original warranty period but within 2 years of the
purchase, with a replacement cost of $480.
If they want to offer a 2 year extended warranty, what price should they charge so that they'll break even (in other words,
so the expected value will be 0)
(round to the nearest cent)
Answer:
They should charge a price of $4.85 so that they'll break even.
Step-by-step explanation:
The expected value will be the sum of the net values multiplied by it's probabilities.
1% of their products will fall after the original warranty period but within 2 years of the purchase, with a replacement cost of $480.
So in 1% = 0.01 of the cases, the company loses $480. That is, a net value of -480.
In 99% = 0.99 of the cases, the company makes x.
The expected value is 0.
We have to find x.
So
[tex]0.99x - 0.01*480 = 0[/tex]
[tex]0.99x = 0.01*480[/tex]
[tex]x = \frac{0.01*480}{0.99}[/tex]
[tex]x = 4.85[/tex]
They should charge a price of $4.85 so that they'll break even.
The Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers. Management projects that the profit per subscriber would increase by 1¢ for each additional subscriber over the current 3,000. How many subscribers are needed to bring a total profit of $113,100?
Answer:
850
Step-by-step explanation:
Current profit per year = $ 20
Number of subscribers = 3000
For each additional subscriber over 3000, the profit will increase by 1 cent or by $ 0.01. For example, for 3001 (3000 + 1) subscribers, the profit will be $ 20.01 per year. Similarly, for 3002 (3000 + 2) subscribers, the profit will be $20.02 per year and so on.
So, for x additional subscribers over 3000, the profit will increase by 0.01(x). i.e. for (3000 + x) subscribers, the profit will be $(20 + 0.01x)
Since, profit per each subscriber is $(20 + 0.01x), the profit for (3000 + x) subscribers will be:
Total profit = Number of subscribers x Profit per each subscriber
Total profit = (3000 + x)(20 + 0.01x)
We want to calculate how many subscribers will be needed to bring a profit of $109,725. So, we replace Total profit by $109,725. The equation now becomes:
Using quadratic formula, we can solve this equation as:
x = -5850 is not a possible solution as this would make the total number of subscribers to be negative. So we reject this value.
Therefore, the answer to this question is 850. 850 more subscribers are needed to being a total profit of $109,725
Find the sum of the first 20 terms of the sequence -7, -3, 1,…
Answer:
620
Step-by-step explanation:
The formula to find the sum of the first n terms of an arithmetic sequence is n(a1 + aN)/2, where n is the number of terms, aN is the last term and a1 is the first term. We do not know the last term, though, so we must find it. The equation for this is an=a1+(n−1)d, where d is the common difference and a1 is the first term, and n is the number of terms. Therefore, the last term, an is, -7+(19)4 = 69.
Finally, we plug it into the first formula, the formula to find the sum, and we get 20*(-7+69)/2, which gives us 620 as our final answer.
What’s the correct answer for this question?
Answer:
[tex]\frac{2}{13}[/tex]
Step-by-step explanation:
There are 4 suits in a standard deck of cards.
Each suit has a king and a queen.
Thus there are 4 kings and 4 queens
P(king) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]
P(queen) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]
P( king) or P(queen) = [tex]\frac{1}{13}[/tex] + [tex]\frac{1}{13}[/tex] = [tex]\frac{2}{13}[/tex]
A gym initially has 5000 members. Each year, the gym loses 10% of its current members and gains 100 new members. Which recursive rule represents the number an of members at the start of the n th year?
Answer:
An = A0 + 100 * n - (An-1) * 0.10
Step-by-step explanation:
Tenemos una regla recursiva para una secuencia es una fórmula que nos dice cómo avanzar de un término a otro en una secuencia. Por lo tanto debemos buscar a An.
Hay un valor inicial que es 5000, una ganancia y una perdida de clientes, que podemos representar así:
An = 5000 + Ganancia - Perdida
Inicial = A0 = 5000
Ganancia = 100, pero cómo sucede cada año, sería: 100 * n
Perdida = 10% de los miembros actuales, si al principio son 5000 por lo tanto A0 * 0.10, pero en este primer caso es que es A0, pero en general serían An-1
reemplazando:
An = A0 + 100 * n - (An-1) * 0.10
A welder produces 7 welded assemblies during the first day on a new job, and the seventh assembly takes 45 minutes (unit time). The worker produces 10 welded assemblies on the second day, and the 10th assembly on the second day takes 30 minutes. Given this information, (a) what is the percent learning rate and (b) what is the total cumulative time to produce all 17 welded assemblies
Answer:
(a). 72.9%.
(b). 13.6 hr.
Step-by-step explanation:
So, we are given the following data or parameters or information which is going to assist us in solving this question/problem;
=> "A welder produces 7 welded assemblies during the first day on a new job, and the seventh assembly takes 45 minutes (unit time). "
=> The worker produces 10 welded assemblies on the second day, and the 10th assembly on the second day takes 30 minutes"
So, we will be making use of the Crawford learning curve model.
T(7) + 10 = T (17) = 30 min.
T(7) = T1(7)^b = 45.
T(17 ) = T1(17)^b = 30.
(T1) = 45/7^b = 30/17^b.
45/30 = 7^b/17^b = (7/17)^b.
1.5 = (0.41177)^b.
ln 1.5 = b ln 0.41177.
0.40547 = -0.8873 b.
b = - 0.45696.
=> 2^ -0.45696 = 0.7285.
= 72.9%.
(b). T1= 45/7^ - 045696 = 109.5 hr.
V(TT)(17) = 109.5 {(17.51^ - 0.45696 – 0.51^ - 0.45696) / (1 - 0.45696)} .
V(TT) (17) = 109.5 {(4.7317 - 0.6863) / 0.54304} .
= 815.7 min .
= 13.595 hr.
Please answer this correctly
Answer:
[tex]10.71 yd[/tex]
Step-by-step explanation:
First let's find the radius of the quarter circle.
[tex]area =\frac{1}{4} \pi {r}^{2} \\ 7.065 = \frac{1}{4} *3.14 {r}^{2} \\ \frac{7.065}{3.14} = \frac{1}{4} * \frac{3.14 {r}^{2} }{3.14} \\ 9 = {r}^{2} \\ \sqrt{9} = r \\ 3 yd= r[/tex]
Now let's find the arc length of this quarter circle.
[tex] \frac{90}{360} \times 2\pi \: r \\ \frac{1}{4} \times 2 \times 3.14 \times 3 \\ = \frac{9.42}{4} \\ = 4.71yd \\ [/tex]
Now let's find the perimeter[tex]perimeter \\ = arc \: \: length + radius + radius \\ = 4.71 + 3 + 3 \\ = 10.71yd[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Answer:
10.71 ydStep-by-step explanation:
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
The formula of an area of a quarter circle:
[tex]A=\dfrac{1}{4}\pi r^2[/tex]
We have the area of a quarter circle:
[tex]A=7.065\ yd^2[/tex]
Substitute to the formula and solve for r :
[tex]\dfrac{1}{4}\pi r^2=7.065[/tex] multiply both sides by 4
[tex]4\cdot\dfrac{1}{4}\pi r^2=7.065\cdot4\\\\\pi r^2=28.26[/tex]
Use 3.14 for π
[tex]3.14r^2=28.26[/tex] divide both sides by 3.14
[tex]\dfrac{3.14r^2}{3.14}=\dfrac{28.26}{3.14}\\\\r^2=9\to r=\sqrt9\\\\\boxed{r=3\ yd}[/tex]
The circumference of this figure consists of an arc (quarter of a cirumference of a circle) and two radiuses.
The formula of a circumference of a circle:
[tex]C=2\pi r[/tex]
The formula of a quarter of a cicrumference of a circle:
[tex]L=\dfrac{1}{4}\cdot2\pi r[/tex]
Substitute
[tex]L=\dfrac{1}{4}\cdot2\pi\cdot3=1.5\pi[/tex]
Use 3.14 for π
[tex]L=1.5(3.14)=4.71\ yd[/tex]
The perimeter of a quarter circle:
[tex]P=4.71+2(3)=4.71+6=10.71\ yd[/tex]
