Answers
The amount of people infected after t weeks is modeled by the function presented as follows:
[tex]f(t) = \frac{675000}{1 + 4000e^{-t}}[/tex]
When the epidemic began, we have that t = 0, hence the number of people is given as follows:
f(0) = 675,000/(1 + 4000)
f(0) = 169 people.
Six weeks after the epidemic began, we have that t = 6, hence the number of people is given as follows:
f(6) = 675,000/(1 + 4000 x e^(-6))
f(6) = 61,841 people.
The limiting size of the infected population is the numerator of the fraction, which is 675,000, as the denominator goes to zero when t goes to infinity.
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Related Questions
Which of the numbers listed below are solutions to the equation? Check all
that apply.
x = 49
A. 9
B. 7
C. -7
D. -49
E. 49
F. None of these
Answers
The only solution for the equation is the one in option E, 49
Which numbers are solution for the equation?Here we have the equation:
x = 49
A value of x is a solution only if the equation is true, this means, we have the same number in both sides.
Here obviously there exist only one solution, and it is when x takes the value 49.
49 = 49
So the only correct option is E.
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Women's style of communication has often involved
a.
b.
C.
d.
telling others what to do
thinking only about themselves
understanding others' emotions
trying not to get involved with others
Please select the best answer from the choices provided
O A
Answers
The best answer is (c) understanding others' emotions.
Women tend to have a more empathetic communication style compared to men, and they tend to prioritize relationships and emotions in their interactions. This communication style involves actively listening to others, being supportive, and expressing empathy towards their feelings. Women often seek to connect with others on an emotional level and understand their perspective, rather than simply giving orders or being self-centered.
Research has shown that women's communication style can be more effective in building and maintaining relationships, as it fosters trust, mutual respect, and understanding. This style also creates a supportive environment where individuals can express their emotions freely and receive validation for their feelings.
In conclusion, women's communication style involves understanding others' emotions, listening actively, and showing empathy towards their feelings.
This approach promotes positive relationships and creates an environment of mutual respect and trust.
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please help me with this
Answers
The point (1,2) is the point of intersection of the two lines.
How to verify the pointIt should be noted that to verify if the point (1,2) is a solution to the system of linear equations, we need to substitute x=1 and y=2 into both equations and check if they are true.
The equation is true, so (1,2) is a solution to the first equation.
Substituting x=1 and y=2 into the second equation also makes the equation true.
Therefore, the point (1,2) is the point of intersection of the two lines.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answers
The two options that represent circles with diameter 12 units and center on the y-axis are:
x² + (y - 6)² = 36
x² + (y + 6)² = 36
What is circles diameter?The diameter of a circle is a straight line segment that passes through the center of the circle and connects two points on its circumference. It is twice the length of the circle's radius.
The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:
x² + (y - 6)² = 36
x² + (y + 6)² = 36
Explanation:
For a circle with diameter 12 units, the radius is half of the diameter, which is 6 units.
Since the center of the circle lies on the y-axis, the x-coordinate of the center is 0.
The general equation for a circle with center (h, k) and radius r is (x - h)² + (y - k)² = r².
Using the given information, we substitute h = 0, k = ±6, and r = 6 to get the two equations:
(x - 0)² + (y - 6)² = 6² => x² + (y - 6)² = 36
(x - 0)² + (y + 6)² = 6² => x² + (y + 6)² = 36
Therefore, the two options that represent circles with diameter 12 units and center on the y-axis are:
x² + (y - 6)² = 36
x² + (y + 6)² = 36
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what are the first four terms if a1=5 and an=3an-1?
Answers
a1 = 5
a2 = 3a1 = 3(5) = 15
a3 = 3a2 = 3(15) = 45
a4 = 3a3 = 3(45) = 135
Therefore, the first four terms of the sequence are:
5, 15, 45, 135.
A sprinkler can water a region with an 8 foot radius. A plant is 4 feet east and 6 feet north of the sprinkler. Is the plant in the sprinkler’s range? Why or why not?
Answers
The plant is not in the sprinkler's range since the distance between the sprinkler and the plant is greater than the radius of the sprinkler's range.
The distance between the sprinkler and the plant can be calculated using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the distance between the sprinkler and the plant is the hypotenuse of a right triangle with legs of length 4 feet and 6 feet:
distance = sqrt(4^2 + 6^2)
distance = sqrt(16 + 36)
distance = sqrt(52)
distance ≈ 7.21 feet
Since the distance between the sprinkler and the plant is greater than the radius of the sprinkler's range (8 feet), the plant is not in the sprinkler's range. Therefore, the plant will not receive water from the sprinkler.
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Complex numbers [tex]z[/tex] and [tex]w[/tex] satisfy [tex]|z|=|w|=1, |z+w|=\sqrt{2}[/tex].
What is the minimum value of [tex]P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|[/tex]?
Answers
Okay, here are the steps to find the minimum value of P:
1) Given: |z|=|w|=1 (z and w are complex numbers with unit modulus)
|z+w|=sqrt(2)
Find z and w such that these conditions are satisfied.
Possible solutions:
z = 1, w = i (or vice versa)
z = i, w = 1 (or vice versa)
2) Substitute into P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|
For the cases:
z = 1, w = i: P = |-1-4+2(1+i)i| = |-5+2i| = sqrt(25+4) = 5
z = i, w = 1: P = |1-\frac{4}{i}+2(1+\frac{1}{i})i| = |-3+2i| = sqrt(9+4) = 5
3) The minimum value of P is 5.
So in summary, the minimum value of
P = |w-\frac{4}{z}+2(1+\frac{w}{z})i|
is 5.
Let me know if you have any other questions!
Hello solve this, what is 9 x 5/7
Answers
Answer: 6 3/7
Step-by-step explanation:
9/1 x 5/7
If we multiply the numerators and denominators, we get 45/7 or 6 3/7 as a mixed number.
Answer:
[tex]\frac{45}{7}[/tex] or 6.4285
Step-by-step explanation:
First, multiply 9 and 5, which gives you 45.
9(5)=45
Then, divide 45 by 7.
45/7=6.4285
That gives you [tex]\frac{45}{7}[/tex] or 6.4285
Hope this helps!
In a race, 14 out of the 25 swimmers finished in less than 47 minutes. What percent of swimmers finished the race in less than 47 minutes? Write an equivalent fraction to find the percent.
Answers
We must first convert the given information into an equivalent fraction. The answer is 56%.
What is equivalent fraction?Equivalent fractions have the same value or represent the same portion of a whole even though they may have different numerators and denominators.
To do this, we must multiply both the numerator (14) and denominator (25) by the same number so that the denominator equals 100.
To do this, we must multiply both 14 and 25 by 4.
This gives us 14*4/25*4 = 56/100.
To convert this fraction to a percent, we can simply divide the numerator by the denominator and multiply the result by 100.
Therefore, 56/100 * 100 = 56%.
This result can also be found by setting up a proportion. We can set up the proportion as follows:
14/25 = x/100.
To solve for x, we must multiply both sides by 100. This gives us 14*100/25 = x.
Hence, x = 56. Therefore, 56% of swimmers finished the race in less than 47 minutes.
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In circle S with � ∠ � � � = 60 m∠RST=60 and � � = 4 RS=4 units find area of sector RST. Round to the nearest hundredth
Answers
If the measure of angle RST is 60°, and RS=4 units, then the area of sector RST is 8.374 square units.
In geometry, a "Sector" of a circle is defined as the portion of circle enclosed by two radii and the arc between them. It can be thought of as a slice or a wedge cut out of a circle.
To find the area of the "sector-RST" in circle centered at "S", we use the formula for area of a sector of a circle, which is :
⇒ Area of sector = (θ/360) × π × r²,
where θ = central angle of sector in degrees, π = 3.14159, and r = radius of circle,
In this case, we are given that m∠RST = 60 degrees and RS = 4 units. Since RS is the radius of the circle centered at "S", we use RS = r,
Substituting the values, θ = 60 degrees, r = RS = 4 units,
We get,
⇒ Area of sector RST = (60/360) × 3.14 × (4)²,
= (1/6) × 3.14 × 16,
= 8.374 square units,
Therefore, the required area of sector is 8.374 square units.
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The given question is incomplete, the complete question is
In circle centered at "S", R and T are the points on the circumference with m∠RST = 60 and RS=4 units .Find area of sector RST.
sharon is a good student who enjoys statistics. she sets a goal for herself to do well enough compared to her peers so that her standardized score on her statistics final is equal to her percentile rank (written as a decimal) among her classmates. scores on the statistics final are normally distributed. what goal did she set for herself?
Answers
Sharon's desired percentile rank of 0.78.
To determine the goal Sharon set for herself, we need to understand the relationship between standardized scores and percentile ranks.
In a standardized test, such as Sharon's Statistics final, the standardized score represents how well a student performed relative to the average score of the test-takers.
The percentile rank, on the other hand, indicates the percentage of test-takers that scored below a particular student.
In Sharon's case, she wants her standardized score to be equal to her percentile rank.
Therefore, her goal is to achieve a standardized score of 0.78 (written as a decimal) on her Statistics final.
This means she aims to score better than approximately 78% of her classmates, as indicated by her desired percentile rank of 0.78.
Hence her desired percentile rank of 0.78.
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Why is brainly taking centuries for searches? This is a real pain, each one I have to wait a minimum of 3 minutes for answers to show.
Answers
High Traffic, Large Database, Internet Connectivity are the reason for taking centuries for searches.
What is the centuries for searches?High Traffic: If there are many users accessing the site simultaneously, the servers might get overloaded, leading to slow searches.
Large Database: Brainly has a vast database of questions and answers, which could slow down searches if the search algorithm isn't optimized.
Internet Connectivity: Slow internet connection on your side could result in slow searches
If you're experiencing slow searches, you can try the following: Check your internet connection and make sure it's stable and fast. Try clearing your browser cache and cookies and restart your browser.
If you're using an outdated browser, try updating it to the latest version. Consider reaching out to Brainly's customer support team to report the issue and seek assistance.
Therefore, High Traffic, Large Database, Internet Connectivity are the reason for taking centuries for searches.
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How do you interpret two-way tables?
Answers
Overall, interpreting a two-way table requires careful attention to detail and the ability to think critically about the data. It is important to look beyond the numbers themselves and try to understand what they are telling you about the relationship between the variables.
What are the Two-way tables?
Two-way tables, also known as contingency tables, are a way to display the frequency distribution of two categorical variables. The variables are usually listed as rows and columns, with the frequency of each combination of values shown in the cells of the table.
Interpreting a two-way table involves looking at the relationships between the variables and identifying patterns in the data. Here are some steps you can follow to interpret a two-way table:
Look at the marginal frequencies: These are the totals for each row and column. They give you an idea of the distribution of each variable individually.
Look at the conditional frequencies: These are the frequencies of each combination of values, divided by the marginal frequency of one of the variables.
They tell you the proportion of one variable that has a certain value, given that the other variable has a certain value.
Look for patterns: Look for rows or columns with high or low frequencies, and try to identify any trends or patterns in the data.
Are there any combinations of values that are more or less common than others? Are there any values that seem to be associated with each other?
Draw conclusions: Based on the patterns you observe, draw conclusions about the relationship between the two variables. Do they appear to be independent, or is there evidence of a causal relationship?
hence, Overall, interpreting a two-way table requires careful attention to detail and the ability to think critically about the data. It is important to look beyond the numbers themselves and try to understand what they are telling you about the relationship between the variables.
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An angle measures 3. 4° less than the measure of its complementary angle. What is the measure of each angle?
Answers
Answer:
Let x be the measure of the angle we are trying to find, in degrees.
The complementary angle to x is 90° - x, since the sum of complementary angles is 90 degrees.
The problem tells us that x is 3.4 degrees less than its complementary angle, so we can set up the following equation:
x = (90 - x) - 3.4
Simplifying and solving for x, we get:
x = 86.6/2
x = 43.3
Therefore, the angle we are trying to find has a measure of 43.3 degrees, and its complementary angle has a measure of 90 - 43.3 = 46.7 degrees.
HELP!! VIEW PHOTO THANKS!!
Answers
Step-by-step explanation:
Total people surveyed = 246
total female = 122
divorced = 15 + 13 BUT the 13 was already counted in 'female'
soooo
female OR divorced = 122 + 15 out of 246 = 137/246 = .5569
what is the surface are of a cylender when the radius is 6in and the height is 9 in
Answers
Answer:
565.486677646 inches squared
Step-by-step explanation:
Let's recall the formula for the surface area of a cylinder:
[tex]A=2\pi rh+2\pi r^2[/tex]
Where r is the radius and h is the height.
We are given that the radius is 6 inches and the height is 9 inches.
Substitute the values and solve the equation, like so:
[tex]A=2\pi (6)(9)+2\pi (6)^2=\\A=2\pi (54) +2\pi(36)=\\A=108\pi +72\pi =\\A=180\pi[/tex]
Thus, in terms of pi, the surface area is equal to [tex]180\pi[/tex].
180 times pi is equal to approximately 565.486677646 inches squared.
is this correct 2(n + 6) + (n + 6)
2n + 2 + n + 4
Answers
Answer: False
Step-by-step explanation:
If the question is relating to equality, your answer currently is incorrect.
If we solve both sides of the ( + ) we have :
2(n + 6) = 2n + 12
2n + 12 + n + 6 = 3n + 18
Therefore, the two that are equal are 2(n + 6) + (n + 6) and 3n + 18.
There is also another set of expressions that are equal:
2n + 2 + n + 4 = 3n + 6
Mr. Lewis and Ms. Yonkers are grading 87 papers for a math class. Mr. Lewis has already grade 32, but Ms. Yonkers has only graded 16. Write an equation with the variable (p) and show your work to determine how many papers they have left to grade.
Answers
The number of papers they have left to grade is 39.
What is Subtraction?
Subtraction is a mathematical operation that involves taking away or removing a certain number of items or quantity from a larger group. It is the inverse of addition and is denoted by the minus sign (-).
Let p be the number of papers they have left to grade.
The total number of papers is 87, and Mr. Lewis has already graded 32 and Ms. Yonkers has graded 16, so the number of papers they have left to grade is:
p = 87 - 32 - 16
p = 39
Therefore, they have 39 papers left to grade.
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g a generic drug is being tested to test its efficacy (effectiveness) at reducing blood pressure in patients with hypertension (a.k.a. high blood pressure). in a randomized, double-blind experiment with 200 patients, 100 are given the name-brand drug (control group) and 100 are given a generic version of the drug (treatment group). in the control group, the average reduction in blood pressure is 15.2 mmhg with a standard deviation of 11.5 mmhg. in the treatment group, there is an average reduction of 14.6 mmhg and a standard deviation of 12.5 mmhg. neither group has any outliers. a researcher claims that this study shows the generic drug is not as effective as the name-brand drug. what would be the reply of a statistician? you have two attempts for this problem so choose wisely. if you do not receive 5 points in the gradebook after submitting this assignment then you have answered incorrectly. make sure to try it again before the deadline.
Answers
A statistician would reply that in order to determine if the generic drug is less effective than the name-brand drug, a hypothesis test needs to be conducted.
The null hypothesis (H0) would be that there is no difference in the average blood pressure reduction between the two drugs, while the alternative hypothesis (H1) would be that the name-brand drug has a higher average reduction in blood pressure than the generic drug.
To test these hypotheses, a t-test would be appropriate since we have two independent samples (control and treatment groups) with known means, standard deviations, and sample sizes. The t-test will provide a p-value, which can be compared to a chosen significance level (e.g., α = 0.05).
If the p-value is less than the significance level, we reject the null hypothesis and conclude that there is a significant difference in the average blood pressure reduction between the two drugs. If the p-value is greater than the significance level, we fail to reject the null hypothesis, meaning we do not have enough evidence to claim that the name-brand drug is more effective than the generic drug.
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Complete the inequality.
1/4 ___ 3/16
>
=
Answers
Answer:
1/4 > 3/16
Step-by-step explanation:
1/4 = 4/16
4/16 > 3/16
1/4 > 3/16
hope this helps:)
~~~Wdfads~~~
which vaule of y makes the equation true 13 - y = 17 true?
pls help
Answers
Answer:
y = -4
Step-by-step explanation:
13 - y = 17
y = 13 - 17 = -4
Answer:
y = -4
Step-by-step explanation:
Alright so you shift the y to the other side:
13 = 17 + y
Now you shift the 17 to the other side,
y = 13 - 17 = -4
Hence, y = -4
Hope this helps and be sure to mark this as brainliest! :)
need answer by 11:45am
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Question 3
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20
A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.
Question 4
The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.
Question 5
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
Question 6
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
Question 7
At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer mustard on a hot dog?
900
2,000
2,100
4,000
Answers
The drive-thru with typically more wait time is Burger Quick, because it has a larger median. The Option A.
Why does Burger Quick have a larger median for wait time?The median is a measure of central tendency that represents the middle value of a set of data. In this case, the median wait time at Burger Quick is 15.5 minutes, while the median wait time at Super Fast Food is 12 minutes.
This indicates that, on average, customers at Burger Quick experience a longer wait time compared to customers at Super Fast Food. The larger median at Burger Quick suggests that there may be some longer wait times skewing the data towards the higher end which could be due to various factors such as slower service, or other operational issues at Burger Quick resulting in a longer wait time for customers at their drive-thru.
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Can someone help me ASAP? It’s due today
Answers
The only option that represents an independent event is: Option C: "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".
How to Identify Independent Events?Independent events are defined as those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.
Looking at the given options, the only one that represents an independent event is "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".
This is because each event does not depend on another one of the events being described.
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PLEASE ANSWER ASAP
1. How many atoms are present in 8.500 mole of chlorine atoms?
2. Determine the mass (g) of 15.50 mole of oxygen.
3. Determine the number of moles of helium in 1.953 x 108 g of helium.
4. Calculate the number of atoms in 147.82 g of sulfur.
5. Determine the molar mass of Co.
6. Determine the formula mass of Ca3(PO4)2.
IT WOULD BE HELPFUL
Answers
The number of atoms in 8.500 moles of chlorine atoms can be calculated using Avogadro's number, which is approximately 6.022 × 10²³ atoms/mole.
So, the number of atoms in 8.500 moles of chlorine atoms would be:
8.500 moles × 6.022 × 10²³ atoms/mole = 5.12 × 10²⁴ atoms of chlorine.
The molar mass of oxygen is approximately 16.00 g/mol. Therefore, the mass of 15.50 moles of oxygen would be:
15.50 moles × 16.00 g/mol = 248 g of oxygen.
The molar mass of helium is approximately 4.00 g/mol. Therefore, the number of moles of helium in 1.953 x 10^8 g of helium would be:
1.953 x 10^8 g / 4.00 g/mol = 4.88 x 10⁷ moles of helium.
The molar mass of sulfur is approximately 32.06 g/mol. Therefore, the number of moles of sulfur in 147.82 g of sulfur would be:
147.82 g / 32.06 g/mol ≈ 4.61 moles of sulfur.
The molar mass of cobalt (Co) is approximately 58.93 g/mol.
The formula mass of Ca₃(PO₄)₂ can be calculated by adding the molar masses of all the individual atoms in the formula.
The molar mass of calcium (Ca) is approximately 40.08 g/mol, the molar mass of phosphorus (P) is approximately 30.97 g/mol, and the molar mass of oxygen (O) is approximately 16.00 g/mol.
Therefore, the formula mass of Ca₃(PO₄)₂ would be:
3 × 40.08 g/mol (for Ca) + 2 × (2 × 30.97 g/mol + 4 × 16.00 g/mol) (for P and O) = 310.17 g/mol.
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Which situation can be represented by the equation 2x + 150 = 5x
Mary has 5 stamps and buys 150 stamps each week. Nick has no stamps and buys 2 stamps each week. When will Marty have
more stamps than Mary?
Mary has 2 stamps and buys 150 stamps each week. Nick has no stamps and buys 5 stamps each week. When will they have
the same number of stamps?
Mary has 150 stamps and buys 5 stamps each week. Nick has no stamps and buys 2 stamps each week. When will Marty have
more stamps than Mary?
Mary has 150 stamps and buys 2 stamps each week. Nick has no stamps and buys 5 stamps each week. When will they have
the same number of stamps?
Answers
The situation can be represented by the equation 2x + 150 = 5x is"Mary has 2 stamps and buys 150 stamps each week. Nick has no stamps and buys 5 stamps each week. When will they have the same number of stamps?" (option b)
The equation 2x + 150 = 5x means that two expressions, 2x + 150 and 5x, are equal. In other words, whatever value we substitute for x, these two expressions will always have the same value. We can use this equation to solve different situations by finding the value of x that satisfies the equation.
Mary starts with 2 stamps and buys 150 stamps each week, while Nick starts with no stamps and buys 5 stamps each week. To determine when they will have the same number of stamps, we need to use the equation 2x + 150 = 5x. We can rewrite the equation as 150 = 3x, and solve for x by dividing both sides by 3. This gives us x = 50, which means that it will take Mary 50 weeks to have the same number of stamps as Nick.
Hence the correct option is (b).
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veterinary science: colts the body weight of a healthy 3-month-old colt should be about m 5 60 kg (source: the merck veterinary manual, a standard reference manual used in most veterinary colleges). (a) if you want to set up a statistical test to challenge the claim that m 5 60 kg, what would you use for the null hypothesis h0 ? (b) in nevada, there are many herds of wild horses. suppose you want to test the claim that the average weight of a wild nevada colt (3 months old) is less than 60 kg. what would you use for the alternate hypothesis h1 ? (c) suppose you want to test the claim that the average weight of such a wild colt is greater than 60 kg. what would you use for the alternate hypothesis? (d) suppose you want to test the claim that the average weight of such a wild colt is different from 60 kg. what would you use for the alternate hypothesis? (e) for each of the tests in parts (b), (c), and (d), would the area corresponding to the p-value be on the left, on the right, or on both sides of the mean? explain your answer in each case
Answers
(a) For the null hypothesis, we would use the claim that the average weight of a healthy 3-month-old colt is equal to 60 kg, that is,
H0 : μ = 60 kg.
(b) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is less than 60 kg, that is,
H1: μ < 60 kg.
(c) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is greater than 60 kg, that is, H1: μ > 60 kg.
(d) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is different from 60 kg, that is, H1: μ ≠ 60 kg.
(e) For the test in part (b), the area corresponding to the p-value would be on the left of the mean because the alternate hypothesis is one-tailed and represents a left-tailed test.
For the test in part (c), the area corresponding to the p-value would be on the right of the mean because the alternate hypothesis is one-tailed and represents a right-tailed test.
For the test in part (d), the area corresponding to the p-value would be on both sides of the mean because the alternate hypothesis is two-tailed and represents a two-tailed test.
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1. Find the height of the parabolic balloon arch for the prom when the position of the bottom anchors are at x = 3 feet and x = 7 feet.
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The height of the parabolic balloon arch for the prom is 12.25 feet.
Using these assumptions, we can find the equation of the parabola that the arch follows as x = a(y-k)² + h, where (h,k) is the vertex and a is a constant that determines the shape of the parabola. We can find the value of a by using one of the points that the arch passes through, say (3,0):
3 = a(0-k)² + h h = 3 - a(k²)
Similarly, using the other point that the arch passes through, say (7,0):
7 = a(0-k)² + h h = 7 - a(k²)
Equating the expressions for h, we get:
3 - a(k²) = 7 - a(k²) a = -1/4
Substituting this value of a into one of the equations for h, say h = 7 - a(k²), we get:
h = 7 + 1/4(k²)
So the vertex of the parabola is at (h,k) = (7,0), and the equation of the parabola is x = -1/4(y² - 28y + 49).
To find the height of the arch, we need to find the y-coordinate of the vertex, which is k = 0. So the height of the arch is given by the distance between the vertex and the lowest point of the arch, which is the x-intercept of the parabola. To find the x-intercept, we set y = 0 in the equation of the parabola:
x = -1/4(0² - 28(0) + 49)
x = -1/4(49) = -12.25
However, since we are dealing with a physical object, the height cannot be negative. Therefore, we take the absolute value of the x-intercept, which gives us:
| -12.25 | = 12.25 feet
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Topic 7: Tangents
For questions 19-20, determine if AB is tangent to circle C.
Answers
Based on the definition of the tangent of a circle and the Pythagorean triple of a right triangle, AB is not tangent to circle C in both question 19 and 20.
What is the Tangent of a Circle?In geometry, the tangent of a circle is a line that intersects the circle at exactly one point, which is called the point of tangency. This line is perpendicular to the radius of the circle at that point. This means that it forms a right angle at that point.
19. If AB is tangent to circle C, the lengths of the triangle ABC will form a Pythagorean triple. Let's check:
4.8² + 7.2² = 12²
74.88 = 144 [not true} Therefore, AB is not tangent to circle C.
20. Also, we will have the following:
15² + 11.2² = 6.8²
350.44 = 46.24 [not true].
AB is not tangent to circle C.
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Jane takes her turn on the vine to practice her swing. As she swings, she goes back and forth across the river bank alternately over land and water. She has spent some time thinking about her motion and tells Tarzan to set the stopwatch to take measurements. Assume that her distance varies sinusoidally with the time of her swing. Tarzan finds that when time is 2 seconds, she is -30 feet over land. At time equals 6 seconds, she has crossed 20 feet of water.
Answers
The equation for the sinusoidal function that represents Jane's motion would be d(t) = 25 x sin(π/4 x (t + 4)) - 5
How to find the sinusoidal function ?Let d(t) be the distance Jane is from the bank (in feet) at time t (in seconds). Since Jane's motion is sinusoidal, we can express it as:
d(t) = A x sin(B x (t - C)) + D
We need to find the values of A, B, C, and D that satisfy these conditions.
Since the amplitude is half the peak-to-peak amplitude, we have:
A = 50 / 2 = 25
The vertical shift (D) is the average of the maximum and minimum distances:
D = (20 + (-30)) / 2 = -10 / 2 = -5
Since the sine function is -1 at 3π/2 (270 degrees), we have:
π/4 x (2 - C) = 3π/2
2 - C = 6
C = -4
So, the equation of the sinusoidal function representing Jane's motion is:
d(t) = 25 x sin(π/4 x (t + 4)) - 5
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The question is:
Find the sinusoidal function that represents Jane's motion.
PLEASE ANSWER DUE TODAY!!!!
Answers
Answer:
below
Step-by-step explanation:
26. yes because a straight line is formed
27. domain - -2 to 2
range -2 to 1
Answer:
Yes, the graph is a linear function.
Domain: x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]
Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]
Step-by-step explanation:
A linear function is an expression that will form a straight line when graphed (or a graph that forms a straight line). These points form a straight line, so the function is linear.
The domain of the function is everything that x can be equal to. We can see here that the ordered points are:
(-2, -1.5), (-1.5, -1), (-1, -0.5), (-0.5, 0), (0, 0.5), (0.5, 1), (1, 1.5), (1.5, 2)
So, the domain of the function is all of the x values of the ordered pairs, or:
x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]
(the symbol next to the x means "belongs to.")
As for the range, it is everything that y can be equal to. Let us look once again at the ordered pairs. The range of the function is equal to the y coordinates of these ordered pairs, or:
Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]
Keep in mind that if the function contains more than one value for x or y, it is listed ONLY ONCE in the domain/range.