Answer:
The relator recived $8,186.4
Step-by-step explanation:
What you have to do is find the 60% of the commission. Commission is 4% of $341,100 (100%)
First do a cross multiplication to find 4% of $341,100
100% ___ $341,100
4%______x:
[tex]x=(4*341,100)/100=13,644[/tex]
So, the 4% of $341,100 is $13,466
Now you have to find the 60% of $13,466
100% ___ $13,466
60%______x:
[tex]x=(60*13,466)/100=8,186.4[/tex]
The answer is: $8,186.4
13.10. Suppose that a sequence (ao, a1, a2, ) of real numbers satisfies the recurrence relation an -5an-1+6an-20 for all n> 2. (a) What is the order of the linear recurrence relation? (b) Express the generating function of the sequence as a rational function. (c) Find a generic closed form solution for this recurrence relation. (d) Find the terms ao,a1,.. . ,a5 of this sequence when the initial conditions are given by ao 2 and a5 (e) Find the closed form solution when ao 2 and a 5.
a. This recurrence is of order 2.
b. We're looking for a function [tex]A(x)[/tex] such that
[tex]A(x)=\displaystyle\sum_{n=0}^\infty a_nx^n[/tex]
Take the recurrence,
[tex]\begin{cases}a_0=a_0\\a_1=a_1\\a_n-5a_{n-1}+6a_{n-2}=0&\text{for }n\ge2\end{cases}[/tex]
Multiply both sides by [tex]x^{n-2}[/tex] and sum over all integers [tex]n\ge2[/tex]:
[tex]\displaystyle\sum_{n=2}^\infty a_nx^{n-2}-5\sum_{n=2}^\infty a_{n-1}x^{n-2}+6\sum_{n=2}^\infty a_{n-2}x^{n-2}=0[/tex]
Pull out powers of [tex]x[/tex] so that each summand takes the form [tex]a_kx^k[/tex]:
[tex]\displaystyle\frac1{x^2}\sum_{n=2}^\infty a_nx^n-\frac5x\sum_{n=2}^\infty a_{n-1}x^{n-1}+6\sum_{n=2}^\infty a_{n-2}x^{n-2}=0[/tex]
Now shift the indices and add/subtract terms as needed to get everything in terms of [tex]A(x)[/tex]:
[tex]\displaystyle\frac1{x^2}\left(\sum_{n=0}^\infty a_nx^n-a_0-a_1x\right)-\frac5x\left(\sum_{n=0}^\infty a_nx^n-a_0\right)+6\sum_{n=0}^\infty a_nx^n=0[/tex]
[tex]\displaystyle\frac{A(x)-a_0-a_1x}{x^2}-\frac{5(A(x)-a_0)}x+6A(x)=0[/tex]
Solve for [tex]A(x)[/tex]:
[tex]A(x)=\dfrac{a_0+(a_1-5a_0)x}{1-5x+6x^2}\implies\boxed{A(x)=\dfrac{a_0+(a_1-5a_0)x}{(1-3x)(1-2x)}}[/tex]
c. Splitting [tex]A(x)[/tex] into partial fractions gives
[tex]A(x)=\dfrac{2a_0-a_1}{1-3x}+\dfrac{3a_0-a_1}{1-2x}[/tex]
Recall that for [tex]|x|<1[/tex], we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
so that for [tex]|3x|<1[/tex] and [tex]|2x|<1[/tex], or simply [tex]|x|<\dfrac13[/tex], we have
[tex]A(x)=\displaystyle\sum_{n=0}^\infty\bigg((2a_0-a_1)3^n+(3a_0-a_1)2^n\bigg)x^n[/tex]
which means the solution to the recurrence is
[tex]\boxed{a_n=(2a_0-a_1)3^n+(3a_0-a_1)2^n}[/tex]
d. I guess you mean [tex]a_0=2[/tex] and [tex]a_1=5[/tex], in which case
[tex]\boxed{\begin{cases}a_0=2\\a_1=5\\a_2=13\\a_3=35\\a_4=97\\a_5=275\end{cases}}[/tex]
e. We already know the general solution in terms of [tex]a_0[/tex] and [tex]a_1[/tex], so just plug them in:
[tex]\boxed{a_n=2^n+3^n}[/tex]
Select all of the answers below that are equal to B = {John, Paul, George, Ringo, Pete, Stuart}
Question 2 options:
{The Monkees}
{book, door, speakers, soap, toothpaste, pool stick}
{flowers, computer monitor, flag, teddy bear, bread, thermostat}
{Paul, Ringo, Pete, John, George, Stuart}
{bookmark, needle, street lights, sock, greeting card, Ringo}
{scotch tape, iPod, Sharpie, Street Lights, window, clock}
Answer: Option (4) is correct.
Step-by-step explanation:
Given that,
B = {John, Paul, George, Ringo, Pete, Stuart}
Now, we have select the Set that is equal to the Set B.
From all the options given in the question, option (4) is correct.
It contains all the elements of Set B but only the arrangement or sequence of the Set is different.
Correct Set 4 = {Paul, Ringo, Pete, John, George, Stuart} = Set B
The set matching B = {John, Paul, George, Ringo, Pete, Stuart} from the options provided is {Paul, Ringo, Pete, John, George, Stuart}, as it contains all the same members regardless of order and no other elements.
Explanation:The question asks to select all answers that are equal to the set B = {John, Paul, George, Ringo, Pete, Stuart}. A set, in this context, is defined as a collection of distinct objects, considered as an object in its own right. In a set, the order of elements does not matter, but duplication of elements is not allowed. From the provided options, the only answer that matches set B exactly is {Paul, Ringo, Pete, John, George, Stuart}, since it contains all the same elements as set B, regardless of order, and does not include any additional elements.
A slot machine has three slots; each will show a cherry, a lemon, a star, or a bar when spun. The player wins if all three slots show the same three items. If each of the four items is equally likely to appear on a given spin, what is your probability of winning? (Enter your probability as a fraction.)
Answer:
1/16
Step-by-step explanation:
Lets say you are trying to get the cherry when you are spinning. That means that in each slot there is a 1/4 chance of getting the cherry because out of 4 choices only one is the cherry. That is only for one slot and there are 3 slots. That means you take the probability for each slot which is 1/4 and multiply them together. Then you get 1/4*1/4*1/4 since there are 3 slots which is 1/64. However that is only for the cherry and there are 4 different items that you could get. This means there is 1/64 chance for each of the 4 items which is 1/64+1/64+1/64+1/64 which is 4*1/64 which is 1/16.
The probability of winning the slot game is calculated by multiplying the probabilities of each independent event. In this case, the probability of the same item appearing in all three slots is 1 * 1/4 * 1/4, which results in a winning probability of 1/16 or 0.0625.
Explanation:The subject of this question is the probability of winning in the context of a slot machine game. In this scenario, the slot machine has four different items (cherry, lemon, star, bar) and each item is equally likely to appear on a spin. The player wins if all three slots display the same item.
Firstly, for the first slot, any one of the four items could appear, so the odds are simply 1 (it is certain an item will appear). For the first item to then appear in the second and third slots (i.e., for all three slots to show the same item), with each slot being an independent event, the probability is 1/4 for each subsequent slot.
Therefore, the probability of winning is given by the product of probabilities for each independent event, i.e., 1 * 1/4 * 1/4 = 1/16. Hence, the player's probable chance of winning in a single spin is 1 in 16 or 0.0625 in decimal form.
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5. The differential equation y 00 − xy = 0 is called Airy’s equation, and is used in physics to model the refraction of light. (a) Assume a power series solution, and find the recurrence relation of the coefficients. [Hint: When shifting the indices, one way is to let m = n − 3, then factor out x n+1 and find an+3 in terms of an. Alternatively, you can find an+2 in terms of an−1.] (b) Show that a2 = 0. [Hint: the two series for y 00 and xy don’t “start” at the same power of x, but for any solution, each term must be zero. (Why?)] (c) Find the particular solution when y(0) = 1, y 0 (0) = 0, as well as the particular solution when y(0) = 0, y 0 (0) = 1.
Not sure why, but I wasn't able to post my solution as text, so I've written it elsewhere and am posting screenshots of it here.
In the fifth attachment, the first solution is shown above the second one.
What number is needed to complete the pattern below? 36 34 30_24 21 18 15
The mean per capita consumption of milk per year is 140 liters with a standard deviation of 22 liters. If a sample of 233 people is randomly selected, what is the probability that the sample mean would be less than 137.01 liters? Round your answer to four decimal places.
Answer: 0.0192
Step-by-step explanation:
Given : The mean per capita consumption of milk per year : [tex]\mu=140\text{ liters}[/tex]
Standard deviation : [tex]\sigma=22\text{ liters}[/tex]
Sample size : [tex]n=233[/tex]
Let [tex]\overline{x}[/tex] be the sample mean.
The formula for z-score in a normal distribution :
[tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
For [tex]\overline{x}=137.01[/tex]
[tex]z=\dfrac{137.01-140}{\dfrac{22}{\sqrt{233}}}\approx-2.07[/tex]
The P-value = [tex]P(\overline{x}<137.01)=P(z<-2.07)= 0.0192262\approx 0.0192[/tex]
Hence, the probability that the sample mean would be less than 137.01 liters is 0.0192 .
The brain volumes (cm cubed)of 50 brains vary from a low of 904cm cubedto a high of 1490cm cubed.Use the range rule of thumb to estimate the standard deviation s and compare the result to the exact standard deviation of 174.7cm cubed,assuming the estimate is accurate if it is within 15 cm cubed.The estimated standard deviation is 146.5cm cubed.(Type an integer or a decimal. Do not round.)Compare the result to the exact standard deviation.
Answer:
The Range Rule of Thumb says that the range is about four times the standard deviation. So, if you need to calculate it, you need to divide range (Maximum - Minimum) with 4, S=[tex]\frac{R}{4}[/tex].
Step-by-step explanation:
R=1490 - 904
S = 586 / 4 = 149.5
If you compare the exact standard desviation (149.5 cm) with the estimated (146.5 cm), it is a difference of 3 cm, is not neccesary round the result.
Hope my answer has been useful.
Answer:
x_bar = 1197 cm^3 , s.d_e = 146.5 cm^3
Outside the 15 cm^3 tolerance. Not a good estimation.
Step-by-step explanation:
Given:
- Lowest value of brain volume L = 904 cm^3
- Highest value of brain volume H = 1490 cm^3
- Exact standard deviation s.d_a = 174.7 cm^3
Find:
Use the range rule of thumb to estimate the standard deviation s and compare the result to the exact standard deviation of 174.7 cm^3 assuming the estimate is accurate if it is within 15 cm^3.
Solution:
- The rule of thumb states that the max and min limits are +/- 2 standard deviations about the mean x_bar. Hence, we will set up two equations.
L = x_bar - 2*s.d_e
H = x_bar + 2*s.d_e
Where, s.d_e is the estimated standard deviation.
- Solve the two equations simultaneously and you get the following:
x_bar = 1197 cm^3 , s.d_e = 146.5 cm^3
- The exact standard deviation is s.d_a = 174.7 cm^3
So, the estimates differs by:
s.d_a - s.d_e = 174.7 - 146.5 = 28.2 cm^3
Hence, its outside the tolerance of 15 cm^3. Not a good approximation.
Suppose that you wish to cross a river that is 3900 feet wide and flowing at a rate of 5 mph from north to south. Starting on the eastern bank, you wish to go directly across the river to a point on the western bank opposite your current position. You have a boat that travels at a constant rate of 11 mph.
a) In what direction, measured clockwise from north, should you aim your boat? Include appropriate units in your answer.
b) How long will it take you to make the trip? Include appropriate units in your answer.\
Please show your work so I may understand. Thank you so much!
Answer:
a) 297°
b) 4.52 minutes
Step-by-step explanation:
a) Consider the attached figure. The boat's actual path will be the sum of its heading vector BA and that of the current, vector AC. The angle of BA north of west has a sine equal to 5/11. That is, the heading direction measured clockwise from north is ...
270° + arcsin(5/11) = 297°
__
b) The "speed made good" is the boat's speed multiplied by the cosine of the angle between the boat's heading and the boat's actual path. That same value can be computed as the remaining leg of the right triangle with hypotenuse 11 and leg 5.
boat speed = √(11² -5²) = √96 ≈ 9.7980 . . . . miles per hour
Then the travel time will be ...
time = distance/speed
(3900 ft)×(1 mi)/(5280 ft)×(60 min)/(1 h)/(9.7980 mi/h) ≈ 4.523 min
In a study investigating a link between walking and improved health, researchers reported that adults walked an average of 873 minutes in the past month for the purpose of health or recreation. Specify the null and alternative hypotheses for testing whether the true average number of minutes in the past month that adults walked for the purpose of health or recreation is lower than 873 minutes.
Answer:
[tex]H_0:\mu =873\\\\H_a: \mu<873[/tex]
Step-by-step explanation:
Given : In a study investigating a link between walking and improved health, researchers reported that adults walked an average of 873 minutes in the past month for the purpose of health or recreation.
Claim : The true average number of minutes in the past month that adults walked for the purpose of health or recreation is lower than 873 minutes.
i.e. [tex]\mu<873[/tex]
We know that the null hypothesis contains equal sign , then the set of hypothesis for the given situation will be :-
[tex]H_0:\mu =873\\\\H_a: \mu<873[/tex]
The null hypothesis assumes no difference, so it reflects an average walking time of 873 minutes (H0: μ = 873). The alternative hypothesis reflects the research query, suggesting the true average is less than 873 minutes (Ha: μ < 873).
Explanation:In statistics, the null hypothesis and the alternative hypothesis are often used to test claims or assumptions about a population. In this case, the research is about whether the true average number of minutes in the past month that adults walked for the purpose of health or recreation is lower than 873 minutes.
The null hypothesis (H0) is often a statement of 'no effect' or 'no difference'. Here, it would be: H0: μ = 873. This means that the population mean (μ) of walking time is equal to 873 minutes.
The alternative hypothesis (Ha) is what you might believe to be true or hope to prove true. In this study, it would be: Ha: μ < 873. This means that the population mean of walking time is less than 873 minutes.
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Identify the vertex for (x-3)2 – 1.
Question 4 options:
One of the options below is the answer
(-3, -1)
(-3, 1)
(3, 1)
(3, -1)
Answer:
D. (3, -1).
Step-by-step explanation:
The vertex for ( x - a)^2 + b is (a, b).
Comparing (x - 3)^2 - 1 with this we get:
a = 3 and b = -1.
Answer: Last Option
(3, -1)
Step-by-step explanation:
We have the following quadratic function:
[tex]f(x) =(x-3)^2 - 1[/tex]
By definition for a quadratic function in the form:
[tex]f (x) = a (x-h) ^ 2 + k[/tex]
the vertex of the function is always the point (h, k)
Note that for this case the values of h, a, and k are:
[tex]a = 1\\h = 3\\k = -1[/tex]
Therefore the vertex of the function [tex]f(x) =(x-3)^2 - 1[/tex] is the point
(3, -1)
A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the unexplained variation is 2.119. Find the coefficient of determination.
Answer: [tex]R^{2}[/tex] = 0.89
Step-by-step explanation:
Coefficient of determination is represented by [tex]R^{2}[/tex]. This tells us that how much of the variation in the dependent variable is explained by the independent variable.
It is the ratio of explained variation by the independent variables to the total variation in the dependent variable.
Hence,
Coefficient of determination = [tex]\frac{Explained\ Variation}{Total\ Variation}[/tex]
= [tex]\frac{18.592}{20.711}[/tex]
[tex]R^{2}[/tex]= 0.89
∴ 89% of the variation in the dependent variable is explained by the independent variables.
The coefficient of determination is calculated by dividing the explained variation by the total variation. For the student's data, the coefficient of determination is approximately 0.8978, which translates to about 89.78% of the variation in the dependent variable being explained by the regression line.
Explanation:The student is asking about the coefficient of determination, which is a statistical measure in a regression analysis. To find the coefficient of determination, we use the explained variation and the total variation from the regression equation. It is calculated by dividing the explained variation by the total variation and then squaring the result if needed to find r squared.
In this case, the explained variation is 18.592 and the total variation is 20.711. The formula to find the coefficient of determination (r²) is:
r² = Explained Variation / Total Variation
Plugging in the values we have:
r² = 18.592 / 20.711
r² ≈ 0.8978
Expressed as a percentage, the coefficient of determination is approximately 89.78%, which means that about 89.78% of the variation in the dependent variable can be explained by the independent variable using the regression line.
Find the accumulated amount of the annuity. (Round your answer to the nearest cent.) $1000 monthly at 4.6% for 20 years.
Answer:
Accumulated amount will be $2504.90.
Step-by-step explanation:
Formula that represents the accumulated amount after t years is
A = [tex]A_{0}(1+\frac{r}{n})^{nt}[/tex]
Where A = Accumulated amount
[tex]A_{0}[/tex] = Initial amount
r = rate of interest
n = number of times initial amount compounded in a year
t = duration of investment in years
Now the values given in this question are
[tex]A_{0}[/tex] = $1000
n = 12
r = 4.6% = 0.046
t = 20 years
By putting values in the formula
A = [tex]1000(1+\frac{0.046}{12})^{240}[/tex]
= [tex]1000(1+0.003833)^{240}[/tex]
= [tex]1000(1.003833)^{240}[/tex]
= 1000×2.50488
= 2504.88 ≈ $2504.90
Therefore, accumulated amount will be $2504.90.
Question: Assume the bucket in Example 4 is leaking. It starts with 2 gallons of water (16 lb) and leaks at a constant rate. It finishes draining just as it reaches the top. How much work was spent lifting the water alone? (Hint: do not include the rope and bucket, and find the proportion of water left at elevation x ft.)
"Example 4": A 5-lb bucket is lifted from the ground into the air by pulling in 20 ft of rope at a constant speed. the rope weighs 0.08 lb/ft. (intentionally left out initial example question, because already answered and not needed, to avoid confusion. I need the answer from the first paragraph.
To calculate the work done to lift the leaking water, consider the average weight of the water over each part of the journey and calculate force x distance. After doing this, it is found that the total work done is 160 ft-lb.
Explanation:This problem is a example of work done against gravity. Gravity pulls the water downward, whereas the rope lifts it upward. Remember the formula for work is Work = force x distance. In this case, the force is the weight of the water being lifted (decreasing as the water leaks out) and the distance is the height the bucket is raised.
Let's start by assuming that the rate of the water leaking out is linear. This means that if the bucket is lifted halfway up the rope when it's half empty, then its average weight over the first 10 feet is 0.75 * 16 lb (12 lb), and its average weight over the next 10 feet is 0.25 * 16 lb (4 lb).
So the work done is calculated as follows:
First 10 feet: Work1 = 12lb * 10ft = 120 ft-lbNext 10 feet: Work2 = 4lb * 10ft = 40 ft-lbTherefore, the total work done in lifting the water alone is Work1 + Work2 = 160 ft-lb.
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To solve this problem, you can use calculus to determine the work done lifting the water as it leaks out of the bucket. To find the amount of work done to lift the water to the top, you'll need to integrate the varying weight of the water over the distance it's lifted. Since the water leaks out at a constant rate, it will linearly decrease in weight from 16 pounds to 0 pounds over the course of the 20-foot ascent.
You're given that the bucket starts with 16 pounds of water, which is equal to 2 gallons. That's because 1 gallon of water weighs approximately 8 pounds. The water weight decreases to 0 pounds as the height reaches 20 feet.
The weight of the water as a function of height, \( w(x) \), can be modeled as a linear function that starts from 16 lb at the ground (when \( x = 0 \)) and goes to 0 lb at 20 ft (when \( x = 20 \)). Thus, the weight function is:
\[ w(x) = 16 - \frac{16}{20}x \]
This simplifies to:
\[ w(x) = 16 - 0.8x \]
The work done lifting the water from height \( x \) to \( x + dx \) is \( w(x) \cdot dx \).
Work, \( W \), is the integral of this force over the distance it's applied:
\[ W = \int_{0}^{20} w(x) \, dx \]
Substitute \( w(x) \) into the equation:
\[ W = \int_{0}^{20} (16 - 0.8x) \, dx \]
Evaluating this integral involves finding the antiderivative:
\[ W = \left[ 16x - 0.4x^2 \right]_{0}^{20} \]
Apply the bounds of the integration (from 0 to 20):
\[ W = \left( 16(20) - 0.4(20)^2 \right) - \left( 16(0) - 0.4(0)^2 \right) \]
\[ W = (320 - 0.4(400)) - (0 - 0) \]
\[ W = 320 - 160 \]
Therefore, the total work done lifting the water alone is:
\[ W = 160 \text{ foot-pounds} \]
Kayla needs $14,000 worth of new equipment for his shop. He can borrow this money at a discount rate of 10% for a year.
Find the amount of the loan Kayla should ask for so that the proceeds are $14,000.
Maturity = $
Answer:
$15400
Step-by-step explanation:
Principle amount, P = $14000
Time, T = 1 year
Rate of interest, R = 10%
We know that maturity amount,
[tex]A = P\left (1+\frac{R}{100} \right )^{n}[/tex]
where n is number of years
[tex]A = P\left (1+\frac{R}{100} \right )^{n}[/tex]
[tex]A = 14000\left (1+\frac{10}{100}\right )^{1}[/tex]
[tex]A = 14000\left (1+\frac{1}{10}\right )[/tex]
[tex]A = 14000\left (\frac{11}{10}\right )[/tex]
[tex]A = 15400[/tex]
The maturity amount is $15400
Kayla should take out a loan of $12,727.27 to have $14,000 after accounting for a 10% discount rate over one year.
Kayla needs to determine the amount she must borrow so that after accounting for the interest rate of 10%, she will have proceeds of $14,000 to invest in new equipment for her shop. The equation to calculate this is the present value (amount borrowed) equals the future value (amount after interest) divided by one plus the interest rate to the power of the period, which in this case is one year.
Using this formula:
Amount Borrowed = $14,000 / (1 + 0.10)1
Amount Borrowed = $14,000 / 1.10
Amount Borrowed = $12,727.27
Therefore, Kayla should ask for a loan of $12,727.27 to receive $14,000 after one year.
How many milliliters of an injection containg 1 mg of drug per milliliter of injection should be adminstered to a 6-month-old child weighing 16 Ibs. to achieve a subcutaneous dose of 0.01 mg/kg?
Answer:
0.0726mL
Step-by-step explanation:
Let's find the answer by using the following formula:
(subcutaneous dose)=(milliliters of the injection)*(drug concentration)/(child weight)
Using the given data we have:
(0.01mg/kg)=(milliliters of the injection)*(1mg/mL)/(16lbs)
milliliters of the injection=(0.01mg/kg)*(16lbs)/(1mg/mL)
Notice that the data has different units so:
1kg=2.20462lbs then:
16lbs*(1kg/2.20462lbs)=7.25748kg
Using the above relation we have:
milliliters of the injection=(0.01mg/kg)*(7.25748kg)/(1mg/mL)
milliliters of the injection=0.0726mL
Please help me with this
Answer:
The correct answer is last option
Step-by-step explanation:
From the figure we can see two right angled triangle.
Points to remember
If two right angled triangles are congruent then their hypotenuse and one leg are congruent
To find the correct options
From the figure we get all the angles of 2 triangles are congruent.
one angle is right angle. But there is no information about the hypotenuse and legs.
So the correct answer is last option
There is not enough information to determine congruency.
Two people agree to meet for a drink after work but they are impatient and each will wait only 15 minutes for the other person to show up. Suppose that they each arrive at independent random times uniformly distributed between 5 p.m. and 6 p.m. What is the probability they will meet?
Answer: 50% is the probability
Step-by-step explanation:
There are to people showing up at to different times now the probability is out of a 100%.
So 100 divided by 2 will equal to a 50
Find an equation for the line that passes through the points (-4, -1) and (6, 3)
Answer:
y=2/5x+3/5
Step-by-step explanation:
Use the slope formula to get the slope:
m=4/10
m=2/5
The y intercept is 3/5
The equation is y=2/5x+3/5
Answer:
y = (2/5)x + 3/5
Step-by-step explanation:
Points to remember
Equation of the line passing through the poits (x1, y1) and (x2, y2) and slope m is given by
(y - y1)/(x - x1) = m where slope m = (y2 - y1)/(x2 - x1)
To find the slope of line
Here (x1, y1) = (-4, -1) and (x2, y2) = (6, 3)
Slope = (y2 - y1)/(x2 - x1)
= (3 - -1)/(6 - -4)
= 4/10 = 2/5
To find the equation
(y - y1)/(x - x1) = m
(y - -1)/(x - -4) = 2/5
(y + 1)/(x + 4) = 2/5
5(y + 1) = 2(x + 4)
5y + 5 = 2x + 8
5y = 2x + 3
y = (2/5)x + 3/5
Find the value of x.
A) x = 2
B) x = 3
C) x = 33
D) x = 52
Answer:
B) x = 3
Step-by-step explanation:
The given triangle has three angles:
∠R, ∠S and ∠T
The exterior angle theorem says that
∠S+∠T = ∠R
Putting the values of angles
(57+x) + 25x = 45x
57 + x + 25x = 45x
57+26x = 45x
57 = 45x - 26x
57 = 19x
x = 57/19
x = 3
Hence, the correct answer is:
B) x = 3 ..
Answer:
B
Step-by-step explanation:
X = 3
The mean speed of a sample of vehicles along a stretch of highway is 67 miles per hour, with a standard deviation of 3 miles per hour. Estimate the percent of vehicles whose speeds are between 58 miles per hour and 76 miles per hour. (Assume the data set has a bell-shaped distribution.)
Answer:
99.85%
Step-by-step explanation:
Most of today's student calculators have probability distribution functions built in. Here we are to find the area under the standard normal curve between 58 mph and 76 mph, if the mean speed is 67 mph and the std. dev. is 3 mph.
Here's what I'd type into my calculator:
normalcdf(58, 76, 67, 3)
The result obtained in this manner was 0.9985.
This states that 99.85% of the vehicles clocked were traveling at speeds between 58 mph and 76 mph.
Answer: 99.9%
Step-by-step explanation:In a normal distribution (bell-shaped distribution), the percent that is between the mean and the standard deviations are:
between the mean and mean + standard deviation the percentage is = 34.1%
between the mean + standard deviation and mean + 2 times the standard deviation is = 13.6%
between the mean + 2 times the standard deviation and the mean + 3 times the standard deviation is: 2.14%
And is the same if we subtract the standard deviation.
So in the range from 58 to 67, we can find 3 standard deviations, and in the range from 67 to 76, we also can find 3 standard deviations:
58 + 3 + 3 + 3 = 67
67 + 3 + 3 + 3 = 76
So the total probability is equal to the addition of all those ranges:
2.14% + 13.6% + 34.1% + 34.1% + 13.6% + 2.14% = 99.9%
So 99.9% of the cars have velocities in the range between 58 miles per hour and 76 miles per hour
The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 5 cm/s. When the length is 12 cm and the width is 4 cm, how fast is the area of the rectangle increasing?
Answer:
Area of the rectangle is increasing with the rate of 84 cm/s.
Step-by-step explanation:
Let l represents the length, w represents width, t represents time ( in seconds ) and A represents the area of the triangle,
Given,
[tex]\frac{dl}{dt}=6\text{ cm per second}[/tex]
[tex]\frac{dw}{dt}=5\text{ cm per second}[/tex]
Also, l = 12 cm and w = 4 cm,
We know that,
A = l × w,
Differentiating with respect to t,
[tex]\frac{dA}{dt}=\frac{d}{dt}(l\times w)[/tex]
[tex]=l\times \frac{dw}{dt}+w\times \frac{dl}{dt}[/tex]
By substituting the values,
[tex]\frac{dA}{dt}=12\times 5+4\times 6[/tex]
[tex]=60+24[/tex]
[tex]=84[/tex]
Hence, the area of the rectangle is increasing with the rate of 84 cm/s.
Prove that
For all sets A and B, A∩(A∪B)=A.
Answer:
A∩(A∪B)=A
Step-by-step explanation:
Let's find the answer as follows:
Let's consider that 'A' includes all numbers between X1 and X2 (X1≤A≥X2), and let's consider that 'B' includes all numbers between Y1 and Y2 (Y1≤B≥Y2). Now:
A∪B includes all numbers between X1 and X2, as well as the numbers between Y1 and Y2, so:
A∪B= (X1≤A≥X2)∪(Y1≤B≥Y2)
Now, A∩C involves only the numbers that are included in both, A and C. This means that 'x' belongs to A∩C only if 'x' is included in 'A' and also in 'C'.
With this in mind, A∩(A∪B) includes all numbers that belong to 'A' and 'A∪B', which in other words means, all numbers that belong to (X1≤A≥X2) and also (X1≤A≥X2)∪(Y1≤B≥Y2), which are:
A∩(A∪B)=(X1≤A≥X2) which gives:
A∩(A∪B)=A
Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (–5, –5), (4, 6) L2 : (–9, 8), (–18, –3)
Answer: The lines L1 and L2 are parallel.
Step-by-step explanation: We are given to determine whether the following lines L1 and L2 passing through the pair of points are parallel, perpendicular or neither :
L1 : (–5, –5), (4, 6),
L2 : (–9, 8), (–18, –3).
We know that a pair of lines are
(i) PARALLEL if the slopes of both the lines are equal.
(II) PERPENDICULAR if the product of the slopes of the lines is -1.
The SLOPE of a straight line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of line L1 is
[tex]m_1=\dfrac{6-(-5)}{4-(-5)}=\dfrac{6+5}{4+5}=\dfrac{11}{9}[/tex]
and
the slope of line L2 is
[tex]m_2=\dfrac{-3-8}{-18-(-9)}=\dfrac{-11}{-9}=\dfrac{11}{9}.[/tex]
Therefore, we get
[tex]m_1=m_2\\\\\Rightarrow \textup{Slope of line L1}=\textup{Slope of line L2}.[/tex]
Hence, the lines L1 and L2 are parallel.
Answer:
Parallel
Step-by-step explanation:
A standard six-sided die is rolled. What is the probability of rolling a number greater than or equal to 3? Express your answer as a simplified fraction or a decimal rounded to four decimal places.
The numbers on a six sided die are: 1, 2, 3, 4 ,5 ,6
There are 4 numbers that are either equal to 3 or greater than 3: 3, 4, 5 ,6
The probability of getting one is 4 chances out of 6 numbers, which is written as 4/6.
4/6 can be reduced to 2/3 ( simplified fraction)
Final answer:
The probability of rolling a number greater than or equal to 3 on a six-sided die is 2/3 or 0.6667 when rounded to four decimal places.
Explanation:
To find the probability of rolling a number greater than or equal to 3 on a standard six-sided die, we count the favorable outcomes and then divide this number by the total number of possible outcomes. The sample space, S, of a six-sided die is {1, 2, 3, 4, 5, 6}.
Numbers greater than or equal to 3 are 3, 4, 5, and 6. So, there are 4 favorable outcomes. The total number of possible outcomes is 6 (since there are 6 sides on the die).
The probability is thus the number of favorable outcomes (4) divided by the total number of possible outcomes (6), which simplifies to 2/3 or approximately 0.6667 when rounded to four decimal places.
Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables. requals0.952 What is the value of the coefficient of determination?
Answer:
Step-by-step explanation:
Given that [tex]r = 0.952[/tex]
We have coefficient of determination
[tex]r^2 =0.952^2\\=0.906304[/tex]
=90.63%
This implies that nearly 91% of variation in change in dependent variable is due to the change in x.
The coefficient of determination is the square of the correlation (r) between predicted y scores and actual y scores; thus, it ranges from 0 to 1.
An R2 of 0 means that the dependent variable cannot be predicted from the independent variable.
An R2 of 1 means the dependent variable can be predicted without error from the independent variable.
Belle Corp. has a selling price of $50 per unit, variable costs of $40 per unit, and fixed costs of $100,000. What sales revenue is needed to break-even?
I need help working out this problem. I get confused on the process.
Answer:
$500 000
Step-by-step explanation:
Let r = revenue
and c = costs
and n = number of units. Then
r = 50n and
c = 40n + 100 000
At the break-even point,
r = c
50n = 40n + 100 000
10n = 100 000
n = 10 000
The break-even point is reached at 10 000 units. At that point,
r = 50n =50 × 10 000 = 500 000
A sales revenue of $500 000 is needed to break even.
Belle Corp. needs to achieve a sales revenue of $500,000 to cover both its variable and fixed costs and thus reach the break-even point.
Explanation:To calculate the breakeven point of Belle Corp., we need to understand that breakeven is the point where total costs (fixed and variable) equal total sales revenue. The formula for calculating the breakeven point in units is Total Fixed Costs / Contribution Margin per Unit. The contribution margin per unit is the Selling Price per Unit minus the Variable Cost per Unit.
For Belle Corp.,
Selling Price per unit = $50Variable Cost per unit = $40Contribution Margin per unit = Selling Price per unit - Variable Cost per unit = $10Fixed Costs = $100,000Breakeven point in units = Fixed Costs / Contribution Margin per unit = 10,000 units.To calculate sales revenue necessary to breakeven, we multiply the breakeven point in units by the selling price per unit. Therefore, Sales revenue needed to break-even = Breakeven units * Selling Price per unit = 10,000 units × $50 = $500,000.
Learn more about Breakeven analysis here:https://brainly.com/question/34782949
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Prove for every positive integer n that 2! * 4! * 6! ... (2n)! ≥ [(n + 1)]^n.
Answer:Given below
Step-by-step explanation:
Using mathematical induction
For n=1
[tex]2!=2^1[/tex]
True for n=1
Assume it is true for n=k
[tex]2!\cdot 4!\cdot 6!\cdot 8!.......2k!\geq \left ( k+1\right )^{k}[/tex]
For n=k+1
[tex]2!\cdot 4!\cdot 6!\cdot 8!.......2k!2\left ( k+1\right )!\geq \left ( k+1\right )^{k}\dot \left ( 2k+2\right )![/tex]
because value of [tex]2!\cdot 4!\cdot 6!\cdot 8!.......2k!=\left ( k+1\right )^{k}[/tex]
[tex]\geq \left ( k+1\right )^{k}\dot \left ( 2k+2\right )![/tex]
[tex]\geq \left ( k+1\right )^{k}\left [ 2\left ( k+1\right )\right ]![/tex]
[tex]\geq \left ( k+1\right )^{k}\left ( 2k+\right )!\left ( 2k+2\right )[/tex]
[tex]\geq \left ( k+1\right )^{k+1}\left ( 2k+\right )![/tex]
Therefore [tex]2!\cdot 4!\cdot 6!\cdot 8!.......2k!2\left ( k+1\right )! must be greater than \left ( k+1\right )^{k+1}[/tex]
Hence it is true for n=k+1
[tex]2!\cdot 4!\cdot 6!\cdot 8!.......2k!2\left ( k+1\right )!\geq \left ( k+1\right )^{k+1}[/tex]
Hence it is true for n=k
Find the y -intercept and the slope of the line.
Write your answers in simplest form.
-6x - y = 1
Answer:
The slope is -6 and the y intercept is -1
Step-by-step explanation:
Lets put the equation in slope intercept form (y=mx+b) where m is the slope and b is the y intercept
-6x-y =1
Add y to each side
-6x-y+y = 1+y
-6x = 1+y
Subtract 1 from each side
-6x-1 = y+1-1
-6x-1 =y
y = -6x-1
The slope is -6 and the y intercept is -1
Given that for simplicity that the number of children in a family is 1, 2, 3, or 4, with probability 1/4 each. Little Joe (a boy) has no brothers. What is the probability that he is an only child? (Set the problem up carefully. Remember to define the sample space, and any events that you use!)
The probability that Little Joe, who has no brothers, is an only child is calculated using conditional probability and results in a 1/4 chance.
The question asks us to find the probability that Little Joe, who has no brothers, is an only child. The sample space for the number of children in a family can be defined as {1, 2, 3, 4}, since each of these outcomes has an equal probability of 1/4. We will define event A as Little Joe being an only child, and event B as the family having no additional male children. Since Little Joe is a boy and has no brothers, cases with more than one male child should not be a part of our conditional sample space.
To solve this, we are looking at the conditional probability P(A|B). The probability that Little Joe is an only child given he has no brothers is P(A|B) = P(A and B) / P(B). We can determine that P(A and B) is simply the probability that there is one child and that child is a boy (Little Joe), which is 1/4. Event B can happen in three scenarios: Little Joe is an only child, Little Joe has one sister, or Little Joe has two or three sisters, and each scenario has an equal probability. Therefore, P(B) = 1/4 (only child) + 1/4 (one sister) + 1/4 (two sisters) + 1/4 (three sisters), which adds to 1/4 * 4 = 1.
The answer therefore is P(A|B) = (1/4) / 1 = 1/4. There is a 1/4 chance that Little Joe, who has no brothers, is an only child.
The year-end 2013 balance sheet of Brandex Inc. listed common stock and other paid-in capital at $2,600,000 and retained earnings at $4,900,000. The next year, retained earnings were listed at $5,200,000. The firm’s net income in 2014 was $1,050,000. There were no stock repurchases during the year. What were the dividends paid by the firm in 2014?
Answer: Dividend paid = $750,000
Explanation:
In order to compute the dividends paid by the firm in 2014 , we'll use the following formula :
Retained earning at end = Retained earning at beginning +Net income -Dividend paid
$5,200,000 = $4,900,000 + $1,050,000 - Dividend paid
Dividend paid = $4,900,000 + $1,050,000 - $5,200,000
Dividend paid = $750,000