a) The constant k is 5.427 x 10^−12 and its natural logarithm is -26.68.
b) The mean salary of the given model by using the probability density function is approximately $270.86.
a) The cumulative distribution function of the given random variable is provided as follows:
F(x) = {1−kx^−3 if x>44000, and 0 otherwise
The cumulative distribution function is given as
F(x) = 1−kx^−3 if x>44000 and F(x) = 0, if x≤44000i)
We need to check the value of the cumulative distribution function at 44000
We have, F(44000) = 0
0 = 1−k(44000)^−3
⇒ 1 = k(44000)^−3
⇒ k = 1/(44000)^−3
⇒ 5.427 x 10^−12
Taking the natural logarithm of k, we have ln(k) = −28.68 (approx.)
Hence, the constant k is 5.427 x 10^−12 and its natural logarithm to three decimal places is -28.68
b) The probability density function is given as,
f(x) = F'(x) = 3kx^−4, for x>44000 and f(x) = 0, otherwise
The mean or expected value of the random variable is given as
E(X) = ∫[−∞,∞]xf(x)dx
= ∫[44000,∞]x(3kx^−4)dx
= 3k∫[44000,∞]x^−3dx
= 3k[(−1/2)x^−2] [∞,44000]
= (3k/2)(44000)^−2
= 270.86 (approx.)
Therefore, the mean salary given by the model is $270.86 (approx.)
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a survey of 50 people were taken 30 like chocolate 20 like vanilla 10 like both how mnay like choclate
From the survey of 50 people 20 people like chocolate.
A survey was conducted with 50 people, out of which 30 liked chocolate, 20 liked vanilla, and 10 liked both. The question is asking how many people like chocolate.
To determine the number of people who like chocolate only, we subtract the number of people who like both flavors from the total number of people who like chocolate.
The number of people who like chocolate alone = total number of people who like chocolate - the number of people who like both
= 30 - 10= 20
This means that out of the 50 people surveyed, 20 individuals like chocolate, while 10 people enjoy both chocolate and vanilla.
Therefore, 20 people like chocolate.
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i need help with this
Answer:
1) [tex]y\leq 2x-3[/tex]
2)See below photo, or graph it yourself using [tex]y < 2 - \frac{1}{2} x[/tex]. This would look like the line for that equation, but dotted and shaded in below.
3) I disagree with Oscar. Because the equation for the second line is less than, not less than OR equal to, and that point falls right on the line for [tex]y < 2 - \frac{1}{2} x[/tex], it is not a valid solution.
Step-by-step explanation:
1) First, I found the slope. It's rising 2 over 1, so the slope is 2/1 or 2. Then, the y-intercept, which is -3. From there I created the equation.
2) I had to put this into slope-intercept form by subtracting x from both sides to get [tex]2y < 4-x[/tex]. Then I divided both sides by two to get [tex]y < 2 - \frac{1}{2} x[/tex]. Then I put it into an online graphing program (I used desmos's).
3) Explains itself!
Let me know if this helped by hitting thanks or brainliest. If not, please comment and I'll get back to you ASAP!
If 140 men working 10 hours a day can build a house in 16 days, find out how many men will build same kind of house in 12 days by working 13 hours a day?
We need 144 men to build the house in 12 days working 13 hours a day.
Let M be the number of men needed to build the house in 12 days working 13 hours a day.
140 x 10 x 16 = M x 13 x 12
Simplifying the equation, we get:
22400 = 156M
Dividing both sides by 156, we get:
M = 144.1
An equation in mathematics is a statement that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The expressions on either side can be numbers, variables, or combinations of both. The equation expresses that the values of the expressions on both sides are equivalent.
Equations play a fundamental role in many areas of mathematics and are used to model various real-world situations, such as physics, engineering, and finance. They can be solved using various techniques, such as substitution, elimination, or graphing, to find the values of the variables that satisfy the equation.
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7) 99 was divided by some number, then added to 15. Next, this sum was
multiplied by 8, which gave a product of 48. Find this number.
Answer:
-11
Step-by-step explanation:
48 ÷8=6-15=-9
99÷-9=-11
Bernie helped design a magician costume for a school play. He used 5.75 feet of ribbon for the magician's wand. He used 11.75 feet of the same ribbon to decorate the magician's robe. If Bernie used $10.50 of ribbon in all, how much did the ribbon cost per foot?
The best solution gets brainlist
The ribbon cost $0.60 per foot.
Solution:[tex]\text{Total number of ribbon used} = (5.75 + 11.75) = 17.50 \ \text{feet}[/tex]
[tex]\text{17.50 feet of ribbon cost} = \$10.50[/tex]
[tex]\text{1 foot of ribbon cost = x}[/tex]
Cross Multiply[tex]17.50 \times x = 1 \ foot \times \$10.50[/tex]
[tex]x = 1 \ foot \times 10.50\div17.50[/tex]
[tex]x = \$0.60[/tex]
Therefore, The ribbon cost per foot $0.60 per foot.
Which number has a 3 with a value 100 times greater than the three in 62,091.384
Answer:
You didn't give any options, but I'm guessing one of them has a 3 in the tens digits, which should be the right answer
Step-by-step explanation:
300?
Please help me with this question.
A principal gathered data about the distance in miles that his teachers and bus drivers live from the school
A principal gathered data about the distance in miles that his teachers and bus drivers live from the school. then, the interquartile range of the distances for the bus drivers in 5 miles less than the interquartile range of the distance for the teacher.
Interquartile Range:
In descriptive statistics, the interquartile range (IQR) is a measure of the statistical distribution, the distribution of data. IQR can also be referred to as bad reading, 50% mean, fourth distribution, or H-distribution. It is defined as the difference between the 75th and 25th percentile of the data. To calculate the IQR, the data set is divided into quartiles, or four parts of equal rank by linear interpolation. These quartiles are represented by Q1 (also known as the lower quartile), Q2 (the median) and Q3 (also known as the upper quartile).
The lower quartile is the 25th percentile and the upper quartile is the 75th percentile, so IQR = Q3 − Q1
Basically, the interquartile range represents the width or “spread” of the collection. The interquartile range is determined by the difference between the upper quartile (highest 25%) and lower quartile (lowest 25%) points of a data set.
From the figure, we can find:
The interquartile range of the bus driver is: 20 -10 = 10
The interquartile range of the teacher is: 30 -15 = 15
Therefore,
the interval interquartile distance is bus The driver's distance was 5 miles less than the interquartile range of the teacher's distance.
Complete Question:
A principal gathered data about the distance in miles that his teachers and bus drivers live from the school .The box plots below show these data.
(1) The inter Quartile range of the distances for the bus driver is twice the interquartile range of the distances for the teachers.
(2) The range of the distances for the teachers is twice the range of the distances for the bus drivers.
(3) the interquartile range of the distances for the bus drivers in 5 miles less than the interquartile range of the distance for the teacher.
(4) The range of the distances for the teachers is 5 miles less than the range of the distances for the bus driver.
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Answer: C. The interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.
Which graph represents this equation? [tex]y=\frac{3}{2}x^{2}-6x[/tex]
I know the answer is C. What I want to know is WHY.
The x-intercepts are (0, 0) and (4, 0), and the y-intercept is (0, 0).
Why are equatiοns graphed?By graphing linear equatiοns, yοu can explain the relatiοnship between twο variables visually. We can easily see what happens tο οne variable as the οther grοws by using a graph. The value οf the x variable rises as we mοve tο the right οn a graph.
[tex]y = (3/2)x^2 - 6x[/tex] is the given equatiοn.
We can use the fοrmula tο find the x-cοοrdinate(s) οf the vertex οf this parabοla:
x = -b/2a
where a and b are the cοefficients οf the equatiοn's x² and x terms, respectively.
In this case, a = 3/2 and b = -6, resulting in:
x = -(-6)/(2*3/2) = 4
As a result, the vertex's x-cοοrdinate is 4.
Tο find the y-cοοrdinate οf the vertex, enter this value οf x intο the fοllοwing equatiοn:
[tex]y = (3/2)(4)^2 - 6(4) = -12[/tex]
As a result, the parabοla's vertex is at the pοint (4, -12).
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A battery is charged. The percentage of the battery’s capacity that is charged as a function of time (in minutes) is graphed.
Answer:
what
Step-by-step explanation:
what
A machine at a company makes toy cars at a constant rate. The company received an order for toy cars that exceeded the number of toy cars that the company had in stock.
In order to make the additionaI 100 toy cars required to meet demand, the company wiII need to run the machine for 8 hours.
what is unitary method ?To answer mathematics issues invoIving proportionaI reIationships, utiIize the unitary method. It entaiIs determining the vaIue of a singIe unit or item and using that data to determine the vaIue of a specified number of units or items. When tackIing chaIIenges in business, finance, and science that require rates, ratios, and proportions, the unitary technique is very heIpfuI. The unitary technique, for instance, can be used to caIcuIate a singIe item's price given the price of aII the other products combined.
given
The formuIa beIow can be used to determine how Iong it wiII take to generate the requisite number of toy cars if we know the rate at which the machine produces them:
Time is caIcuIated as (Number of toy cars required - Number of toy cars in stock) / Production Rate.
For instance, if the machine can produce 10 toy cars per hour and the business needs to make an additionaI 100 to compIete the order, but they aIready have 20 toy cars on hand, the time needed to make the extra toy cars wiII be:
Time = (100-20) / 10 = 8 hours.
In order to make the additionaI 100 toy cars required to meet demand, the company wiII need to run the machine for 8 hours.
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Complete question:
1. A machine at a cοmpany makes toy cars at a constant rate. The company received an order for toy cars that exceeded the number of toy cars that the company had in stock.
Which three pieces of information are needed to determine the amount of time it will take the machine to make enough additional toy cars to fill the order?
Select the three pieces of information that are needed.
A. the cost to make each toy car
B. the rate that the machine makes toy cars
C. the number of toy cars requested in the order
D. the number of people needed to run the machine
E. the number of toy cars available when the order was received
Amina was given 25% trade discount on an article listed 0.75p she sold it with a cash discount of 5% find Amina's percentage profit
Amina's percentage profit is 25%, as the percentage profit must be rounded down to the nearest whole number.
What is profit?Profit is an important concept in economics and finance, referring to the difference between the cost of production and the revenue generated from the sale of goods and services. It is a measure of success and financial performance and is used to analyze the profitability of a business. Profit is generally expressed as a percentage of revenue or as a dollar amount.
To calculate this, first find the cost of the article after the trade discount:
Article Cost = 0.75p - (0.75p * 0.25) = 0.75p * 0.75 = 0.5625p
Next, find the cost of the article after the cash discount:
Article Cost = 0.5625p - (0.5625p * 0.05) = 0.5625p * 0.95 = 0.5343p
Finally, calculate the percentage profit:
Percentage Profit = (0.75p - 0.5343p) / 0.75p * 100 = 0.2167 / 0.75 * 100 = 28.89%
Amina's percentage profit is 25%, as the percentage profit must be rounded down to the nearest whole number.
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The 1948 and 2018 temperatures at 197 random locations across the globe were compared and the mean difference for the number of days above 90 degrees was found to be 2.9 days with a standard deviation of 17.2 days. The difference in days at each location was found by subtracting 1948 days above 90 degrees from 2018 days above 90 degrees.
What is the lower limit of a 90% confidence interval for the average difference in number of days the temperature was above 90 degrees between 1948 and 2018?
What is the upper limit of a 90% confidence interval for the average difference in number of days the temperature was above 90 degrees between 1948 and 2018?
What is the margin of error for the 90% confidence interval?
Does the 90% confidence interval provide evidence that number of 90 degree days increased globally comparing 1948 to 2018?
Does the 99% confidence interval provide evidence that number of 90 degree days increased globally comparing 1948 to 2018?
If the mean difference and standard deviation stays relatively constant would decreasing the degrees of freedom make it easier or harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
If the mean difference and standard deviation stays relatively constant does lowering the confidence level make it easier or harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
The lower limit of a 90% confidence interval for the average difference in the number of days the temperature was above 90 degrees between 1948 and 2018 is -22.8 days and the upper limit is 28.6 days.
The margin of error for the 90% confidence interval is 25.4 days.
The 90% confidence interval does provide evidence that the number of 90-degree days increased globally comparing 1948 to 2018.
The 99% confidence interval also provides evidence that the number of 90-degree days increased globally comparing 1948 to 2018.
If the mean difference and standard deviation stay relatively constant, decreasing the degrees of freedom would make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
Lowering the confidence level would also make it harder to conclude that there are more days above 90 degrees in 2018 versus 1948 globally.
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If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is A(x) p(x) * (a) Find A'(x). Why does the company want to hire more workers if A'(x) > 0? (b) Show that A'(x) > 0 if p'(x) is greater than the average productivity.
The average productivity of the workforce, A(x), is given by
A(x) = p(x)/x,
where p(x) is the total value of the production when there are x workers in the plant.
A'(x) is the derivative of A(x) with respect to x.
A'(x) = (p(x)/x)' = (p'(x)x - p(x))/x^2.
The company wants to hire more workers if A'(x) > 0 because it means that the average productivity of the workforce is increasing with additional workers.
A'(x) > 0 if p'(x) is greater than the average productivity, which is p(x)/x.
Therefore, A'(x) > 0 if p'(x) > p(x)/x.
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Please help me solve this
The ratio of the deposit to the total of the 12 equal payments is 3 : 5.
How to find the ratio of the deposit to the total of the 12 equal payments?The VAT on the van is calculated as follows:
VAT = 20% * £8500 = £1700
Total cost = £8500 + £1700 = £10200
Total amount paid in the 12 equal payments = 12 * £531.25 = £6375
Deposit = £10200 - £6375 = £3825
Deposit : Total of 12 equal payments = £3825 : £6375 = 3 : 5
Therefore, the ratio of the deposit Raya pays to the total of the 12 equal payments is 3 : 5.
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venus is known as the ''cloudy planet'' because it is covered with thick, yelllow clouds. The gravity of venus is 90% of earths gravity. To calculate your weight on venus, multiply your weight by 0.9
Answer:
Step-by-step explanation:
How does Priestley present the theme of social class in Act 1? 3 paragraphs 80 POINTS!!!
INTRODUCTION: What are Priestley’s overarching ideas about the class system? How are Priestley’s ideas about class seen in Act 1 of the play?
PARAGRAPH 1 -
PARAGRAPH 2-
PARAGRAPH 3-
CONCLUSION: What are Priestley’s overarching ideas about the class system? How are Priestley’s ideas about class seen in Act 1 of the play?
A 17-ft ladder is leaning against the side of a house. The top of the ladder is sliding down the house at rate of 5 ft/sec. a) Determine how fast the bottom of the ladder is sliding away when the top of the ladder is 8 feet from the ground. b) At what rate is the angle o between the ladder and the ground is changing then.
a) d/dt [√(289 - 8²)] = d/dt [√(255)] = d/dt [√(5²*17)] = 5/2√17 m/s.
b) The required value is the rate of change of x when the top of the ladder is 8 feet from the ground, then y = 15 feet.
a) Determine how fast the bottom of the ladder is sliding away when the top of the ladder is 8 feet from the ground. As the ladder leans against the side of the house, it makes a right angle with the ground. Using Pythagorean Theorem, the length of the ladder is given by.
Ladder length = √(hypotenuse)² - (height)²= √(17² - height²) meters. Taking the derivative of both sides of this equation, we get: dL/dt = [d/dt √(289 - h²)] meters/sec. Let h = 8 feet, dL/dt = -5 feet/sec.
Thus, the rate of change of the bottom of the ladder is d/dt [√(289 - h²)] meters/sec when the top of the ladder is 8 feet from the ground, and the bottom of the ladder is sliding away at a rate of 5 feet/sec.
b) At what rate is the angle o between the ladder and the ground changing then. Let y be the height of the ladder and the angle it makes with the ground be x. From the given values, y = 17 cos x.
Taking the derivative of both sides with respect to time: dy/dt = -17 sin x (dx/dt)In the given problem, dx/dt = -5/17sin x. Then, dy/dt = 5 sin x cos x= (5/2) sin 2x.
Solving this value of sin x by Pythagorean Theorem, sin x = 8/17. Substituting the value in the equation for the derivative, we get: dy/dt = (5/2) * sin 2x= (5/2) * sin 2(arc sin(8/17))= (5/2) * (2*8/17 * 15/17)= (600/289) ft/sec.
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Look at photo and let me know the answers to the three blanks ASAP! Thank you!
a) Heating cost for a month with 25°F is $67.10
b) Heating cost for a month with 0°F is $98.60
c) Decrease in the monthly heating cost is $1.26
Define the term graph?The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis.
(a) To find the predicted heating cost for a month with an average temperature of 25°F, we can substitute x = 25 into the equation of the line of best fit:
y = -1.26x + 98.60
y = -1.26(25) + 98.60
y = 67.10
Hence, $67.10 is the estimated monthly heating expense for a month with an average temperature of 25°F.
(b) To find the predicted heating cost for a month with an average temperature of 0°F, we can substitute x = 0 into the equation of the line of best fit:
y = -1.26x + 98.60
y = -1.26(0) + 98.60
y = 98.60
Thus, $98.60 is the estimated monthly heating expense for a month with an average temperature of 0°F.
(c) The slope of the line of best fit is -1.26, which means that for every increase of one degree Fahrenheit in the average monthly temperature, the predicted decrease in the monthly heating cost is $1.26.
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What is the slope of the line passing through the points (4, -6) and (2, 3)?
Answer:
m = -9/2
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (4, -6) (2, 3)
We see the y increase by 9, and the x decrease by 2, so the slope is
m = -9/2
(5 points) For each of the following vector spaces, write down the zero vector. No justification required.a. (1 point) The vector space R 4 with the standard vector addition/scalar multiplication.b. (1 point) The vector space P3 with standard polynomial addition/scalar multiplication.c. (1 points) The vector space M22 with standard matrix addition/scalar multiplication.d. (2 points) The vector space M23 with standard matrix addition/scalar multiplication.
Here are the solutions:
a) R4 = {(a, b, c, d) | a, b, c, d ∈ R}
b) P3 = {a0 + a1x + a2x^2 + a3x^3 | a0, a1, a2, a3 ∈ R}
c) M22 = {(aij) | i, j = 1, 2}
d) M23 = {(aij) | i = 1, 2, j = 1, 2, 3}
For the given vector space R4 with the standard vector addition/scalar multiplication, the zero vector is the following: 0 = [0, 0, 0, 0].b) For the given vector space P3 with standard polynomial addition/scalar multiplication, the zero vector is the following: 0(x) = 0.c) For the given vector space M22 with standard matrix addition/scalar multiplication, the zero vector is the following:[0 0] [0 0]d) For the given vector space M23 with standard matrix addition/scalar multiplication, the zero vector is the following:[0 0 0][0 0 0].
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I need help please i will give you stars and 12 points
Answer:
5:3 = 5/3
Step-by-step explanation:
Given Sin∅ = 3/5
We know sin∅ = Perpendicular/Hypotenuse
And, By inverse relationship, we get
cosec∅ = Hypotenuse/Perpendicular = 1/sin∅
So, csc∅ = 5/3, 5:3
the combined score on this test ranges from 400 to 1600. if you were to randomly draw five numbers from a 400-1600 number set, what is the probability that the medium score of the actual 2022 sat results is contained in between the highest and lowest value of these five random numbers?
The combined score on the 2022 SAT test ranges from 400 to 1600. If you were to randomly draw five numbers from a 400-1600 number set, the probability that the medium score of the actual 2022 SAT results is contained in between the highest and lowest value of these five random numbers is approximately 0.004%
How do we find the probability?To find the probability that the medium score of the actual 2022 SAT results is contained in between the highest and lowest value of these five random numbers, we need to find the probability of the following event: “the three other random numbers drawn lie between the highest and lowest values.
The probability of choosing one of the five numbers that falls within the range is (1600 – 400)/1201 = 1/2.25.
The first number can be any number within the 400-1600 range, so the probability is 1.The second number must lie within the range created by the highest and lowest values of the first number, which has a width of 1201. Thus, the probability is 1201/3201.
The third number must lie within the range created by the highest and lowest values of the first two numbers, which has a width of 801. Thus, the probability is 801/2401.The fourth and fifth numbers must lie within the range created by the highest and lowest values of the first three numbers, which has a width of 401.
Thus, the probability is 401/1601.Therefore, the probability of the medium score of the actual 2022 SAT results being between the highest and lowest values of these five random numbers is (1/2.25) * (1201/3201) * (801/2401) * (401/1601) * 1 = 0.000038 or approximately 0.004%.
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If the volume of a hexagonal prism is 3,660 ft³, what is the volume of a hexagonal pyramid in cubic feet
with the same dimensions?
The volume of a hexagonal pyramid in cubic feet with the same dimensions = 1220 ft³
What is hexagonal pyramid?A hexagοnal pyramid is a three-dimensiοnal geοmetric shape that cοnsists οf a base that is a regular hexagοn (a six-sided pοlygοn with all sides and angles equal) and six triangular faces that meet at a single pοint abοve the base, called the apex. The six triangular faces fοrm a pyramid shape with the base, which is why it's called a hexagοnal pyramid.
This relatiοnship can be derived using the fοrmula fοr the vοlume οf a pyramid V = (1/3)Bh, where B is area οf base and h is height οf pyramid. Since the base οf the pyramid is a hexagοn inscribed within the hexagοnal base οf the prism, the area οf the base is (3√3/2)a², where a is the side length οf the hexagοn. The height οf the pyramid is the same as the height οf the prism, which we can call h.
Thus, the volume of pyramid is
[tex]\rm V_p[/tex] = (1/3)(3√3/2)a²h
= (√3/2)a²h, while the volume of prism is
[tex]\rm V_p[/tex]r = [tex]\rm B_p[/tex]r h = (3√3/2)a²h.
Dividing [tex]\rm V_p[/tex]r by 3 gives [tex]\rm V_p[/tex]
so we have [tex]\rm V_p[/tex] = [tex]\rm V_p[/tex]r/3, as claimed. so
[tex]\rm V_p[/tex] = 3360/3 ft³
[tex]\rm V_p[/tex] = 1220ft³
volume of a hexagonal pyramid in cubic feet 1220ft³
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in fig. 8-25, a block slides along a track that descends through distance h.the track is frictionless except for the lower section. there the block slides to a stop in a certain distance d because of friction. (a) if we decrease h,will the block now slide to a stop in a distance that is greater than, less than, or equal to d? (b) if, instead, we increase the mass of the block, will the stopping distance now be greater than, less than, or equal to d?
a block slides along a track that descends through distance h. The track is frictionless except for the lower section. There the block slides to a stop in a certain distance d because of friction. If we decrease h, will the block now slide to a stop in a distance that is greater than, less than, or equal to d?As per the given information, when a block slides along a track that descends through a distance h, the track is frictionless except for the lower section. There the block slides to a stop in a certain distance d because of friction. Now if we decrease h, then the distance covered by the block before it comes to rest will also decrease. So the block will slide to a stop in a distance that is less than d. Hence the answer is less than d.If we increase the mass of the block, will the stopping distance now be greater than, less than, or equal to d?
As the mass of the block increases, the force of friction acting on the block will also increase. Hence the stopping distance will also increase. So the stopping distance now will be greater than d. Hence the answer is greater than d.In conclusion, the answer to (a) is less than d, and the answer to (b) is greater than d.
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Which two angles in the triangles below are complementary?
I NEED HELPPPPPPPP
Answer:
∠ BAC and ∠ CAD
Step-by-step explanation:
• Complementary angles sum to 90°
∠ BCA and ∠ ACD are a linear pair and sum to 180°
∠ BCA + 110° = 180° ( subtract 110° from both sides )
∠ BCA = 70°
the sum of the 3 angles in a triangle = 180°
in Δ ABC
∠ BAC + 55° + 70° = 180°
∠ BAC + 125° = 180° ( subtract 125° from both sides )
∠ BAC = 55°
in Δ ACD
∠ CAD + 110° + 35° = 180°
∠ CAD + 145° = 180° ( subtract 145° from both sides )
∠ CAD = 35°
then
∠ BAC + ∠ CAD = 55° + 35° = 90°
∠ BAC and ∠ CAD are complementary
Answer:
(a) ∠BAC and ∠CAD
Step-by-step explanation:
You want to know which angles in the figure are complementary.
Complementary anglesTwo angles are complementary when the total of their measures is 90°. In the given figure, triangle ABD is a right triangle with the right angle at vertex A.
The two acute angles at vertices B and D will be complementary:
∠ABC and ∠CDA . . . . . not on the list of choices
Ray AC divides the right angle into two complementary parts:
∠BAC and ∠CAD . . . . . first choice on the list
__
Additional comment
The two smaller triangles are isosceles. Angles CDA and CAD are both 35°, so have a sum of 70°. Likewise, angles ABC and BAC are both 55°, with a sum of 110°.
Angles BCA and ACD are a linear pair, so have a sum of 180°. They are supplementary, not complementary.
Barbara is going to buy a shirt for 15.00$ and a pair of pants for 25.00$. She has to also pay 7% sales tax. If Barbara pays with a 50$ bill, how much change will she get back?
Barbara will get $7.20 back in change.
What exactly is a sales tax?A sales tax that is typically added to the selling price by the seller.
Without tax, the total cost of the shirt and pants is:
$15.00 + $25.00 = $40.00
The sales tax is 7% of $40.00, which is as follows:
0.07 x $40.00 = $2.80
So, with tax, the total cost of the shirt and pants is:
$40.00 + $2.80 = $42.80
If Barbara pays with a $50 bill, she will receive the following change:
$50.00 - $42.80 = $7.20
As a result, Barbara will receive $7.20 in change.
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3) Jiya walks 6 km due east and then 8 km due north. How far is she from her
starting place?
6 km
8 km
Answer:
10km
Step-by-step explanation:
Pythagoras
Formula=[tex]a^2+b^2=c^2[/tex]
[tex]6^{2} +8^{2} =c^2\\c^2=100\\c=\sqrt{100} \\c=10km[/tex]
Use Euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem y' = 4y + 3xy, y(2) = 1. Step 1 Euler's Method says that we can use a given step size h to approximate the solution to the initial-value problem y' = F(x, y), y(x) = yo by using the iterative formula Yn = Yn - 1 + HF(xn - 1. Yn - 1). To estimate y(2.5) for y' = 4y + 3xy, y(2) = 1 with step-size h = 0.1, we need 5 5 iterations.
The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size.
To estimate y(2.5) with step size 0.1 using Euler's Method, we need 5 iterations. The iterative formula is Yn = Yn-1 + hF(xn-1, Yn-1), where F(x, y) = 4y + 3xy. Using this formula and the initial condition Y(2) = 1, the 5 iterations are:
Therefore, the approximation of y(2.5) using Euler's method with step size 0.1 is
.
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60 identical machines in a factory pack 150 crates of limes per day
between them.
a) Write the ratio of the number of machines to the number of crates
packed per day in the form 1: n.
b) How many crates of limes would 70 of these machines pack per day?
Give any decimals in your answers to 1 d.p.
a) To write the ratio of the number of machines to the number of crates packed per day in the form 1: n, we need to find the number of crates packed per day per machine. We can do this by dividing the total number of crates packed per day by the number of machines:
Number of crates packed per day per machine = 150 crates/day ÷ 60 machines = 2.5 crates/machine/day
Therefore, the ratio of the number of machines to the number of crates packed per day in the form 1: n is 1:2.5 or 2:5.
b) To find out how many crates of limes 70 of these machines would pack per day, we can use the ratio from part (a) to set up a proportion:
1 machine : 2.5 crates/day = 70 machines : x crates/day
Solving for x, we get:
x = (70 machines × 2.5 crates/day) / 1 machine = 175 crates/day
Therefore, 70 of these machines would pack 175 crates of limes per day.
Step-by-step explanation:
a) The ratio of the number of machines to the number of crates packed per day can be written as:
60 : 150
To simplify this ratio, we can divide both sides by 10:
6 : 15
Finally, we can divide both sides by 3 to get the ratio in the form 1 : n:
1 : 2.5
Therefore, the ratio of the number of machines to the number of crates packed per day is 1 : 2.5.
b) If 60 machines can pack 150 crates per day, then one machine can pack:
150/60 = 2.5 crates per day
So, 70 machines can pack:
70 × 2.5 = 175 crates per day
Therefore, 70 machines can pack 175 crates of limes per day.
Let A denote the balance at the end of Month n for each month where the balance is positive. To find a formula for An, we can do the following. For Month 1, note that A1 = 4000(1.015) - 100 For Month 2, note that A2 =[4000(1.015 ) – 100] (1.015) – 100
= 4000(1.015)^2 – 100 - 100(1.015) For Month 3, note that A3 = [4000(1.015)^2 - 100 - 100(1.015)] (1.015) - 100 = [4000(1.015)^3 - 100 - 100(1.015)] - 100(1.015)^2
B. (6 pts) (Formulas for An) i. Give a recursive formula for An. Make sure to show that the formula is consistent with the results for n= 1,2,3 on the previous page. ii. Give an explicit formula for An in summation notation that captures the pattern exhibited at the bottom of the previous page. Make sure to show that the formula is consistent with the results for n = 1,2,3 on the previous page.
(a) The recursive formula for An is: An = (1.015)An-1 - 100.
(b) The explicit formula for An in summation notation is: An = 4000(1.015)^n - 100[1 + (1.015) + (1.015)^2 + ... + (1.015)^(n-1)].
(a) This formula says that to find the balance for month n, we take the balance for month n-1, multiply it by 1.015 (to account for the interest rate), and subtract 100 (to account for the withdrawal). This formula is consistent with the results for n=1,2,3 on the previous page.
(b) The explicit formula for An in summation notation is: An = 4000(1.015)^n - 100[1 + (1.015) + (1.015)^2 + ... + (1.015)^(n-1)].
This formula says that to find the balance for month n, we take the starting balance of 4000 multiplied by the interest rate raised to the power of n, and then subtract the sum of 100 multiplied by the geometric series (1 + r + r^2 + ... + r^(n-1)), where r = 1.015. This formula is consistent with the results for n=1,2,3 on the previous page.
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