Answer:the cost of one child's ticket is $6
the cost of one adult ticket is $9
Step-by-step explanation:
Let x represent the cost of one child's ticket
Let y represent the cost of one adult ticket.
Tickets for a minor league baseball game for an adult and two children cost a total of $21. This means that
2x + y = 21 - - - - - - - - - - 1
The adult ticket is three dollars more than a child's ticket. This means that
y = x + 3
Substituting y = x + 3 into equation 1, it becomes
2x + x + 3 = 21
3x + 3 = 21
3x = 21 - 3 = 18
x = 18/3 = 6
y = x + 3 = 6 + 3
y = 9
The radius of a spherical balloon being filled with air expands at 4 cm^3 per minute. Assuming the balloon fills in spherical shape, how fast is the radius of the spherical balloon increasing in cm per minute after 2.25 minutes?
Answer: dr/dt = 0.042 cm/minute
Step-by-step explanation:
Given;
dV/dt = 4cm^3/minute
t = 2.25minutes
Volume of a sphere is given as;
V = (4/3)πr^3
Change in Volume ∆V can be derived by differentiating the function.
dV/dt= 4πr^2 . dr/dt
dV/dt = 4πr^2dr/dt ....1
dV/dt is given as 4 cm^3/min
radius after 2.25 minutes can be gotten from the the volume.
Volume after 2.25mins = 4×2.25 = 9cm^3
9cm^3 = V = 4/3πr^3
r^3 = 27/4π
r = (27/4π)^1/3
From equation 1.
dr/dt = (dV/dt)/4πr^2 = 4/(4πr^2) = 1/(πr^2)
dr/dt = 1/(π(27/4π)^2/3)
dr/dt = 0.042cm/minute.
Joe baked 16 apple pies and 6 blueberry pies. Whitney bakes 19 apple pies and 12 blueberry pies . Who baked a higher ratio of apple pies to blueberry pies
Answer:
Joe baked a high ratio. Hope this helps :)
Answer:
Joe
Step-by-step explanation:
Joe baked more than twice as many apple pies as blueberry. (16 > 12)
Whitney baked less than twice as many apple pies as blueberry. (19 < 24)
Joe baked a higher proportion of apple pies.
Weinstein, McDermott, and Roediger (2010) con- ducted an experiment to evaluate the effectiveness of different study strategies. One part of the study asked students to prepare for a test by reading a passage. In one condition, students generated and answered questions after reading the passage. In a se tion, students simply read the passage a second time. All students were then given a test on the passage material and the researchers recorded the number of correct answers.
a. Identify the dependent variable for this study.
b. Is the dependent variable discrete or continuous?
c. What scale of measurement (nominal, ordinal, interval, or ratio) is used to measure the dependent variable?
Answer:
a) The number of correct answers
b) Discrete
c) Ratio
Step-by-step explanation:
We are given the following in the question:
Experiment:
Evaluate the effectiveness of different study strategies. All students were then given a test on the passage material and the researchers recorded the number of correct answers.
a) The dependent Variable
The number of correct answers given is the dependent variable because it depends on the number of times the passage is read.
b) Nature of dependent variable.
It is a discrete variable.Since, the number of questions will always be expressed in whole numbers and cannot be expressed as decimals. They are always counted and not measured.c) Scale of measurement
Ratio is used to measure the dependent variable because true zero for the number of correct questions answered exist.If the measure is zero that means truly no questions were answered correctly.The correct answers are as follows: a: number of correct answers on the test, b: discrete, and c: ratio scale.
a. The dependent variable for this study is the number of correct answers on the test.
b. The dependent variable is discrete because it consists of countable values, specifically the number of questions answered correctly, which can only be whole numbers.
c. The scale of measurement used to measure the dependent variable is the ratio scale. This is because the number of correct answers has a true zero point (it is possible to have zero correct answers), and the differences between the numbers of correct answers are meaningful and consistent. Additionally, the ratio scale allows for the comparison of ratios, such as one student answering twice as many questions correctly as another.
To elaborate, in experimental design, the dependent variable is the variable that is measured to assess the effect of the independent variable (in this case, the study strategy). The dependent variable is what changes as a result of manipulating the independent variable. In this study, the researchers are interested in how different study strategies affect test performance, so they measure test performance by counting the number of correct answers each student provides.
The nature of the dependent variable as discrete or continuous depends on whether the data can take on any value within a range (continuous) or only specific values (discrete). Since the number of correct answers can only be whole numbers (e.g., 5 correct answers, not 5.5), it is discrete.
Finally, the scale of measurement indicates the level of precision with which the variable is measured. The nominal scale is used for categorical data without any order (e.g., gender, race). The ordinal scale is used for data that can be ranked but without equal intervals between ranks (e.g., socioeconomic status). The interval scale is used for data with equal intervals between values but no true zero (e.g., temperature in Celsius or Fahrenheit). The ratio scale is used for data with a true zero and equal intervals between values, allowing for the comparison of ratios (e.g., height, weight, and in this case, the number of correct answers). Since the number of correct answers can be zero (indicating no correct answers) and the differences between scores are meaningful, the dependent variable in this study is measured on a ratio scale.
Find the angle measure to the nearest degree.
cos A = 0.7431
How do I do this?
Answer:
Step-by-step explanation:
If you are looking for a missing angle measure, you use the 2nd button and the cos button. Make sure, first off, that your calculator is in "degree" mode by hitting the "mode" button and making sure that the "degree" is highlighed and not the "radian". Then hit "clear". Once you know that you are in the correct mode, hit "2nd" then "cos" and you will see this on your screen:
[tex]cos^{-1}([/tex]
Inside the parenthesis you will enter your decimal, so it looks like this now:
[tex]cos^{-1}(.7431[/tex]
You do NOT have to close the parenthesis, but you can if you want to. Then hit "enter" to get that the angle that has a cosine of .7431 is 42.0038314 or, to the nearest degree, 42
The inverse cosine function is used to find the angle from the cosine value. In this case, angle A is approximately 42 degrees.
Explanation:To find the angle measure when given the cosine value, you use the inverse cosine function, sometimes written as cos-1 or arccos. The inverse cosine of a given number tells you what angle has that given cosine value.
So for cos A = 0.7431, we need to find the inverse of cosine of 0.7431. Use your calculator's inverse cosine function (often labeled as cos-1 or arccos) with the input 0.7431. Ensure your calculator is in degree mode if the answer needs to be in degrees, which seems to be your case.
Using this process, you should find that angle A is approximately 42 degrees (42.006 to be exact).
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In a recent year, Washington State public school students taking a mathematics assessment test had a mean score of 276.1 and a standard deviation of 34.4. A random sample of 64 students is drawn form this population.(A) Identifying the mean and standard error of the sample mean score ¯X (x bar).(B) What is the distribution of ¯ X? and Why?(C) Find the probability that the sample mean score ¯X(x bar) is at least 285.
Answer:
a) [tex] \mu_{\bar x} =\mu = 276.1[/tex]
[tex]\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3[/tex]
b) From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)[/tex]
c) [tex]P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)[/tex]
[tex]P(Z\geq2.070)=1-P(Z<2.070)=1-0.981=0.019[/tex]
Step-by-step explanation:
Let X the random variable the represent the scores for the test analyzed. We know that:
[tex] \mu=E(X) = 276.1 , \sigma=Sd(X) = 34.4[/tex]
And we select a sample size of 64.
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Part a
For this case the mean and standard error for the sample mean would be given by:
[tex] \mu_{\bar x} =\mu = 276.1[/tex]
[tex]\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3[/tex]
Part b
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)[/tex]
Part c
For this case we want this probability:
[tex] P(\bar X \geq 285)[/tex]
And we can use the z score defined as:
[tex] z=\frac{\bar x -\mu}{\sigma_{\bar x}}[/tex]
And using this we got:
[tex]P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)[/tex]
And using a calculator, excel or the normal standard table we have that:
[tex]P(Z\geq2.070)=1-P(Z<2.070)=1-0.981=0.019[/tex]
the price of a car was $20,000 in 2014, $16,000 in 2015 and $12,800 in 2016. what is the rate of the depreciation of the price of car per year?
a. 15%
b. 20%
c. 25%
d. 30%
Answer:
b. 20%
Step-by-step explanation:
2014
Car price = 20000
2015
Car price = 16000
Depreciation = 20000 - 16000 = 4000
Depreciation % = (4000/20000)*100 = 20%
2016
Car price = 12800
Depreciation = 16000 -12800 = 3200
Depreciation % = (3200/16000)*100 = 20%
There were 166 paid admissions to a game. The price was $2 for adults and $.75 for children. The amount of data taken in was $293.25 how many adults and how many children attended.
Answer:the number of adults that attended the game is 135.
the number of children that attended the game is 31
Step-by-step explanation:
Let x represent the number of adults that attended the game.
Let y represent the number of children that attended the game.
There were 166 paid admissions to a game. This means that
x + y = 166
The price was $2 for adults and $.75 for children. The amount of data taken in was $293.25. This means that
2x + 0.75y = 293.25 - - - - - - - - - - 1
Substituting x = 166 - y into equation 1, it becomes
2(166 - y) + 0.75y = 293.25
332 - 2y + 0.75y = 293.25
- 2y + 0.75y = 293.25 - 332
- 1.25y = - 38.75
y = - 38.75/- 1.25
y = 31
x = 166 - y = x = 166 - 31
x = 135
What is the percent increase between getting a high school scholarship and bachelors degree when high school scholarship is $421 and bachelors degree is $670
Answer:
The percent increase between getting a high school scholarship and bachelor's degree is 59.14%.
Step-by-step explanation:
Given:
High school scholarship is $421.
Bachelor's degree is $670.
Now, to find the percent increase between a high school scholarship and bachelor's degree.
So, we get the amount of increase between a high school scholarship and bachelor's degree.
[tex]670-421=249.[/tex]
Thus, the amount of increase = $249.
Now, to get the percent increase between a high school scholarship and bachelor's degree:
[tex]\frac{249}{421}\times 100[/tex]
[tex]=\frac{24900}{421}[/tex]
[tex]=59.14\%.[/tex]
Therefore, the percent increase between getting a high school scholarship and bachelor's degree is 59.14%.
The percent increase from a high school scholarship ($421) to a bachelor's degree ($670) is calculated to be roughly 59.1%. The overall value of a bachelor's degree over a lifetime typically exceeds this amount, with degree holders potentially earning millions more than their counterparts with only a high school diploma.
Explanation:The subject of this question is a mathematical one, dealing with percentage increase. To find the percent increase between getting a high school scholarship and a bachelor's degree, we first subtract the smaller value (high school scholarship) from the larger value (bachelor's degree). We then divide the result by the starting value (high school scholarship). Thus, the formula is: [(670 - 421)/421] * 100%.
A simplified calculation gives us: [(249)/421] * 100% = 59.1%.
Therefore, there is a 59.1% increase in the value from a high school scholarship to a bachelor's degree based on the given figures.
It's also worth noting that over the course of a career, according to a 2021 report from the Georgetown University Center on Education and the Workforce, adults with a bachelor's degree earn an average of $2.8 million during their careers, $1.2 million more than the median for workers with a high school diploma.
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The Department of Education wishes to estimate the proportion of all college students who have a job off-campus. It surveyed 1600 randomly selected students, 451 had such jobs. The population of interest to the Department of education is: 1. All 1600 students surveyed 2. All college students o some of college students who have off-campus jobs 3. All college students who have off-campus jobs 4. The 451 students in the survey who had off-campus jobs
Answer: 2. All college students
Step-by-step explanation:
A population is a large group of individuals that have some common feature by the researcher's point of interest.
Herero , the Department of Education wishes to estimate the proportion of all college students who have a job off-campus.
So , he need data of all students to compute the exact proportion.
But instead of that he surveyed 1600 randomly selected students which determine the sample.
Sample just gives the estimate of the parameter.
Hence, the population of interest to the Department of education is " All college students" .
The population of interest to the Department of Education, which wants to estimate the proportion of all college students who have a job off-campus, is all college students, not just the ones surveyed or who have off-campus jobs.
Explanation:In the context of this question asked by the Department of Education, the population of interest refers to the group about which the Department wants to draw conclusions. The Department is looking for a proportion, specifically the proportion of all college students who have a job off-campus. Therefore, the population of interest to the Department of Education is option 2: all college students. This is because the Department wants to estimate a characteristic (having a job off-campus) of this entire group, not just of the students in the sample or of students who have off-campus jobs.
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John wants to find the width of a canyon. He walks along the side for 75 ft and marks a point and then walks 16.5 ft and marks another point. Then he turns at a right angle away from the canyon and walks to a point that is in line with the first point marked and another point perpendicular across the canyon from the starting point.
A) Can he conclude the two triangles are similar? Why or why not?
B) if it was 24 ft that he walked for AB, can the canyon width be found? If so, find it and show all work.
Answer:
A) Yes , the triangles are similar as indicated and shown from the analysis of the diagram.
B) Yes, the canyon width AE can be found and it is calculated and gotten as 109.09ft
Step-by-step explanation:
Attached below is the step by step calculations and explanation of both answers.
According to postal regulations, the girth plus the length of a parcel sent by fourth-class mail may not exceed 108 in. What is the largest possible volume of a rectangular parcel with two square sides that can be sent by fourth-class mail?
Answer:
11,664 in³
Step-by-step explanation:
For a square side length of x, the girth is 4x and the length of the parcel is then allowed to be up to 108-4x.
The total volume is the product of the edge lengths, so is ...
V = (108 -4x)(x²) = -4x³ +108x²
This will be a maximum where its derivative is zero:
dV/dx = -12x² +216x = 0 = -12x(x -18)
This is zero for x=0 and for x=18.
The maximum volume parcel is 18 in by 18 in by 36 in, and has a volume of ...
(18 in)(18 in)(36 in) = 11,664 in³
To find the largest possible volume of a rectangular parcel with two square sides adhering to postal regulations, we use a derived formula V = x²(108 - 4x) and apply optimization to find the maximum volume.
To answer the question about the largest possible volume of a rectangular parcel with two square sides that can be sent by fourth-class mail, we use the given postal regulation that states the girth plus the length of a parcel may not exceed 108 inches. Assuming we have a box with dimensions x (for the length and width of the square sides) and y (for the length), the girth is calculated as 4x (since we have two square sides) and the total allowed measurement is 4x + y <= 108 inches. The volume V of the parcel is x²y.
First, we express y in terms of x: y = 108 - 4x. We can then rewrite the volume formula in terms of x: V = x²(108 - 4x). To maximize the volume, we take the derivative of V with respect to x and set it to zero: dV/dx = 2x(108 - 4x) - 4x². Solving for x, we find the critical points which will give us the value of x that maximizes the volume. Plugging this x value back into V or y = 108 - 4x, we can find the maximum volume and the dimensions of the parcel. Without explicitly solving the calculus problem, the general approach is to use optimization via calculus or other mathematical techniques to maximize the volume function.
When Quentin ordered a tennis racquet recently, he agreed to pay a 7% shipping and handling charge. If Quentin paid 9.45 in shipping and handling, how much must the racquet have cost?
Answer:
Racket must have cost 135.
Step-by-step explanation:
Given:
Percentile amount of shipping and handling charge = 7%
Actual amount of shipping and handling charge= 9.45
we need to find the Cost of racket.
Solution:
Let the cost of racket be 'x'.
Now we can say that:
Percentile amount of shipping and handling charge multiplied by cost of racket and then divided by 100 is equal to actual amount of shipping and handling charge.
framing in equation form we get;
[tex]\frac{7}{100}x=9.45[/tex]
Multiplying both side by [tex]\frac{100}{7}[/tex] we get;
[tex]\frac{7}{100}x\times \frac{100}{7}=9.45\times \frac{100}{7}\\\\x=135[/tex]
hence Racket must have cost 135.
If a rectangle has an area of 2x^2+7x+3 find the perimeter
Answer:
Perimeter of the rectangle=6x+8 square units
Step-by-step explanation:
Given that area of rectangle is [tex]2x^2+7x+3[/tex]
Area of rectangle=lw square units
[tex]2x^2+7x+3=2x^2+x+6x+3[/tex]
[tex]=x(2x+1)+3(2x+1)[/tex]
[tex]=(x+3)(2x+1)[/tex]
[tex]2x^2+7x+3=(x+3)(2x+1)[/tex]
Comparing the above equation with the given area we get
lw=(x+3)(2x+1)
Therefore length=x+3 and width=2x+1
To find the perimeter :
Perimeter of the rectangle=2(l+w) square units
[tex]=2((x+3)+(2x+1))[/tex]
[tex]=2(x+3+2x+1)[/tex]
[tex]=2(3x+4)[/tex]
[tex]=6x+8[/tex]
Therefore perimeter of the rectangle=6x+8 square units
A homeowner wants to insulate the new recreation room in her basement. She has been told that 3' of insulation would do the job. The walls are all 9' high and respectively measure 13', 13', 18', and 18' in length. How many rolls will she need if each roll measures 3' x 2' x 50'?
Answer:
6 rolls
Step-by-step explanation:
Data provided in the question:
Height of wall = 9'
Width of walls = 13', 13', 18' and 18'
Dimension of roll = 3' x 2' x 50'
Now,
Total area of the walls = 9' × 13' + 9' × 13' + 9' × 18' + 9' × 18'
= 117 + 117 + 162 + 162
= 558 ft²
Area of each roll = 2' × 50'
= 100 ft²
Thus,
Number of rolls required = [ Total area of the walls ] ÷ [ Area of each roll ]
= 558 ft² ÷ 100 ft²
= 5.58 ≈ 6 rolls
Final answer:
To insulate the recreation room, the homeowner needs to calculate the total area of the walls and then divide it by the area covered by one roll of insulation. After calculating the areas and factoring in the size of the rolls, it is determined that the homeowner needs to purchase 4 rolls of insulation.
Explanation:
The homeowner needs to calculate the amount of insulation needed for a new recreation room. To determine the number of rolls required, we first need to calculate the total area to cover by adding the areas of all four walls. The walls are 9’ high with two of them measuring 13’ in length and the other two are 18’ in length.
The total area These areas can be calculated using the formula Area = Height × Length for each wall. For the 13’ walls: Area = 9’ × 13’ = 117 sq ft (per wall). So, for both, it would be 117 sq ft × 2 = 234 sq ft. And for the 18’ walls: Area = 9’ × 18’ = 162 sq ft (per wall), which is 162 sq ft × 2 = 324 sq ft in total. Now, let's add these together to get the total area of all walls that need insulation: 234 sq ft + 324 sq ft = 558 sq ft.
Next, we calculate how many square feet are in each roll. Since each roll measures 3’ x 50’, the area per roll is 3’ x 50’ = 150 sq ft.
Finally, by dividing the total area needed by the area one roll covers, we can determine the number of rolls:
Number of rolls needed = Total area ÷ Area per roll = 558 sq ft ÷ 150 sq ft/roll ≈ 3.72 rolls.
Since we cannot purchase a fraction of a roll, the homeowner will need to purchase 4 rolls of insulation.
A quadrilateral has no pairs of parallel sides. Which name best describes the figure?
rectangle
trapezoid
parallelogram
kite
Answer:
Therefore,
A quadrilateral that has no pairs of parallel sides is
KITE.
Step-by-step explanation:
A quadrilateral that has no pairs of parallel sides is
KITE.
In Kite there are no pairs of Parallel sides.
The Figure for Kite ABCD is below (not to the scale).
Rectangle and Parallelogram:
Opposite sides are Parallel .
Hence they have pairs of parallel sides,
Trapezoid:
Trapezoid has one pair of parallel side.
Hence it has a pair of parallel sides,
Therefore,
A quadrilateral that has no pairs of parallel sides is
KITE.
Answer:
Kite
Step-by-step explanation:
Find the standard deviation of the following data. Answers are rounded to the nearest tenth. 5, 5, 6, 12, 13, 26, 37, 49, 51, 56, 56, 84
Answer:
24.2(to the nearest tenth)
Step-by-step explanation:
The question is ungrouped data type
standard deviation =√ [∑ (x-μ)² / n]
mean (μ)=∑x/n
= [tex]\frac{5+5+6+12+13+26+37+49+51+56+56+84}{12}[/tex]
=33.3
x-μ for data 5, 5, 6, 12, 13, 26, 37, 49, 51, 56, 56, 84 will be
-28.3, -28.3, -27.3, -21.3, -7.3, 3.7, 15.7,17.7, 22.7,22.7,50.7
(x-μ)² will be 800.89, 800.89,745.29,453.69,53.29,13.69,246.49,313.29,515.29,515.29,2570.49
∑ (x-μ)² will be = 7028.59
standard deviation = √(7028.59 / 12)
=24.2
The side of a cube is 9 cm long.What is the cube's surface area? ____ cm2A) 27B) 729 C) 486What is the cube's volume?Lol 729 ____ cm3A) 27B) 729C) 486
Answer:C, B
Step-by-step explanation:
A volleyball reaches its maximum of 13 feet, 3 seconds after it is served. What quadratic formula could model the height of the volleyball over time after it is served.
Answer:
[tex]H=-(t-3)^2+13[/tex]
Step-by-step explanation:
The path covered by the volleyball will be a downward parabola with the vertex being the highest point of the ball.
A general form of a downward parabola is given as:
[tex]y=-a(x-h)^2+k[/tex]
Where [tex](h,k)[/tex] is the vertex of the parabola and 'a' is a constant.
Now, let 'h' be the vertical height and 't' be the time taken.
So, the equation would be of the form:
[tex]H=-a(t-h)^2+k[/tex]
Now, as per question:
h = 2 seconds, k = 13 feet.
[tex]H=-a(t-3)^2+13[/tex]
Now, taking a = 1. So, the formula that can be used is:
[tex]H=-(t-3)^2+13[/tex]
This month kami sold 70 figurines in 2 sizes. The large figurines sold for $12 each and the small figurines sold for $8 each. The amount of money he received from the sales of the large figurines was equal to the amount of money he received from the sales of the small figurines. How many large figurines did Kami sell?
Answer:Kami sold 28 large figurines.
Step-by-step explanation:
Let x represent the number of large figurines that Kami sold.
Let y represent the number of small figurines that Kami sold.
This month kami sold 70 figurines in 2 sizes. This means that
x + y = 70 - - - - - - - - - - 1
The large figurines sold for $12 each and the small figurines sold for $8 each. The amount of money he received from the sales of the large figurines was equal to the amount of money he received from the sales of the small figurines. This means that
12x = 8y
y = 12x/8
y = 1.5x
Substituting y = 1.5x into equation 1, it becomes
x + 1.5x = 70
2.5x = 70
x = 70/2.5 = 28
y = 1.5x = 1.5 × 28 = 42
Which statement is correct using "is not equal to'' (≠)? A) 70 pieces of candy divided equally between 5 friends _____ 14 pieces each. B) 95 pieces of candy divided equally between 5 friends _____ 19 pieces each. C) 115 pieces of candy divided equally between 5 friends _____ 21 pieces each. D) 145 pieces of candy divided equally between 5 friends _____ 29 pieces each. Eliminate
Answer: C. 115 pieces of candies divided equally between 5 friends is not equal to 21 each
Step-by-step explanation: 115 divided by 5 is 23 each and not 21.
HELP! What does X equal? WILL GIVE BRAINLIEST!
If A = {x | x is an even integer}, B = {x | x is an odd integer}, C = {2, 3, 4, 5}, and D = {9, 10, 11, 12}, list the element(s) of the following set.
C ∪ D = _________.
Final answer:
To find the union of sets C and D, you combine the elements of both sets without repeating any elements. The union, C ∪ D, is therefore {2, 3, 4, 5, 9, 10, 11, 12}.
Explanation:
The question asks to list the elements of the set that is the union of two sets C and D. The union of two sets contains all the elements that are in either set. Therefore, C ∪ D is the set that includes all the elements from both sets C and D without duplication.
Set C contains the integers {2, 3, 4, 5} and set D contains the integers {9, 10, 11, 12}. Hence, the union of sets C and D, denoted C ∪ D, would be {2, 3, 4, 5, 9, 10, 11, 12}. This combines all the unique elements from both sets.
For a boat to float in a tidal bay, the water must be at least 2.5 meters deep. The depth of water around the boat, ????(????), in meters, where ???? is measured in hours since midnight, is____________.
Final answer:
The depth of water around the boat, d(t), varies based on the tidal patterns. Tides are influenced by various factors including the moon's gravity, ocean depth, and local geography. Accurate prediction requires tidal charts and local data.
Explanation:
The depth of water around the boat, represented as d(t), varies based on time due to the tidal patterns. The tides are influenced by numerous factors such as the alignment and gravitational pull of the moon and sun, the depth of the ocean, and local geographical features like bays and estuaries. In the case of the Bay of Fundy, the tides can have an exceptionally large range due to its shape and the resonance of the tidal forces.
The frequency and height of tides will determine how often and to what extent the water level rises and falls, thus affecting the depth at any given hour. To forecast these tidal levels and ensure safe boating conditions, experts create tidal charts with high accuracy, taking into account local bathymetry and global tidal patterns. However, the actual mathematical representation of d(t) would require access to these local tidal patterns and data from the mentioned charts or measurement systems to create a function that accurately represents the changing water depth around the boat.
A simple reflex requires the nervous system to perform three functions. Two of these functions are to collect and distribute information. What is the third function?
Answer:
Integrate information
Step-by-step explanation:
Jonas is jogging from the Park to the school. He has jogged 0.424 miles so far. He has 0.384 mile left to jog. How far is the park located away from the school?
Answer:the park is located 0.808 miles away from the school
Step-by-step explanation:
Jonas is jogging from the Park to the school. The total number of miles that Jonas has jogged so far is 0.424.
He has 0.384 mile left to jog. This means that the distance of the park from the school would be the sum of the distance that he has jogged so far and the distance that he has left to jog. It becomes
0.424 + 0.384 = 0.808 miles
The demand function for a product is given by p = −0.05x2− 0.3x + 8 where p is the unit price in dollars and x is the weekly demand for the product each week, measured in thousands of units. Find the consumer’s surplus if the market price for the product is $5.
Answer:
The answer is 5300 units.
Step-by-step explanation:
The equation will be exactly lie below if the price is 5$:
[tex]5=-0.05x^2-0.3x + 8\\0=-0.05x^2-0.3x+3[/tex]
Roots of the parabol will be:
[tex]x_{1}=-11.3\\x_{2}=5.3[/tex]
In fact that there will be no negative production, The consumer surplus will be 5300 units
Over the interval from 4 seconds to 10 seconds, the object's speed was calculated to be 3 m/s. What is the object's position after 8 seconds have elapsed.
Answer:
1 meter farther
Step-by-step explanation:
The difference in time from 4 seconds to 10 seconds is 6 seconds.
The speed is half of the difference of time.
That is why the speed is 3 m/s.
The difference in time from 10 to 18 is 8 seconds.
Take the time and divide it by 2 to get the speed.
The speed is 4 m/s.
The object's position is 1 more meter.
4 m/s - 3 m/s = 1 m/s
The object's position after 8 seconds is 24 m to have elapsed.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Over the interval from 4 seconds to 10 seconds, the object's speed was calculated to be 3 m/s.
Now,
Since, Over the interval from 4 seconds to 10 seconds, the object's speed was calculated to be 3 m/s.
That is,
The speed = 3 m/s
Time = 10 - 4 = 6 seconds
So, The distance cover by object's in 6 seconds = 3 x 6
= 18 m
Hence, The object cover the distance in 8 seconds = 18 x 8 / 6
= 24 m
So, The object's position after 8 seconds is 24 m to have elapsed.
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Find an equation of the circle with center at ( 5 , 1 ) that is tangent to the y-axis in the form of ( x − A ) 2 + ( y − B ) 2 = C where A , B , C are constant
Answer:
(x -5)² +(y -1)² = 25
Step-by-step explanation:
The equation for a circle centered at (h, k) with radius r is ...
(x -h)² +(y -k)² = r²
Here, the radius is equal to the x-coordinate of the center, since you want the circle tangent to the y-axis. That means (h, k) = (5, 1) and r = 5. The equation you want is ...
(x -5)² +(y -1)² = 25
The equation of the circle with center at (5,1) and tangent to the y-axis is (x - 5)² + (y - 1)² = 25.
To find this equation, we can use the general form of a circle's equation, which is:
(x - A)² + (y - B)² = C
Where A and B are the x and y coordinates of the center of the circle, respectively, and C is the square of the radius of the circle. Since the circle is tangent to the y-axis and its center is at (5,1), the radius of the circle must be 5 units because this is the horizontal distance from the center to the y-axis. Therefore, C will be 5², which is 25. The complete equation of the circle is:
(x - 5)² + (y - 1)² = 25
A food truck operator is parked in a lot at the corner of two streets. She wants to be equidistant from both streets. Should she park her truck on a perpendicular bisector, an angle bisector, a median, or an altitude?a) perpendicular bisectorb) angle bisectorc) mediand) altitude
Answer:
Angle bisector
Step-by-step explanation:
median isn't applicable in this case as the roads from the streets are inclined at an angle.
altitude refers to height which is also not applicable
The perpendicular bisector is the locust of points equidistant from two points,
in this question the street are not seen as points but as lines which forms an angle and the bisection of this angle forms a locus where she can park her car. If she parks her car anywhere on the angular bisector of the two streets, she would be at equal distance from both streets.
The spherical balloon is inflated at the rate of 10 m³/sec. Find the rate at which the surface area is increasing when the radius of the sphere is 3m?
The rate at which the surface area of the sphere is increasing can be found using related rates in calculus. By differentiating the volume formula with respect to time, we relate the rates of change for the radius and surface area, and then plug in the given volume increase rate when the radius is 3m.
Explanation:The problem requires the application of related rates in calculus to find the rate at which the surface area of a sphere is increasing. To calculate this, we can use the formula for the volume of a sphere, which is V = \frac{4}{3}\pi r^3, and the formula for the surface area, which is S = 4\pi r^2. Given a rate of volume increase, \frac{dV}{dt} = 10 m^3/sec, we can differentiate the volume with respect to time to find the relationship between the rates of change of the radius and volume. Then we use the rate of change of the radius to find the rate of change of the surface area.
Step 1: Differentiate the volume with respect to time.
\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}
Step 2: Solve for \frac{dr}{dt} when the radius is 3m.
Step 3: Use the value of \frac{dr}{dt} to find \frac{dS}{dt} (the rate of surface area increase).
Step 4: \frac{dS}{dt} = 8\pi r \frac{dr}{dt}