The function W defined by W(alpha)=1.9alpha + 2.3 models the weight of a kitten, in ounces, that is a weeks old for 0 <= alpha <= 6. According to this model, what is the weight, in ounces, of a kitten that is 3 weeks old?

The function W defined by W(alpha)=1.9alpha + 2.3 models the weight of a kitten, in ounces, that is a weeks old for 0 <= alpha <= 6. According to this model, what is the weight, in ounces, of a kitten that is 3 weeks old?

Question
Upper Level Math
asked 2021-01-31
The function W defined by \(\displaystyle{W}{\left(\alpha\right)}={1.9}\alpha+{2.3}\) models the weight of a kitten, in ounces, that is a weeks old for \(\displaystyle{0}\le\alpha\le{6}\). According to this model, what is the weight, in ounces, of a kitten that is 3 weeks old?

Answers (1)

2021-02-01
Step 1
Given, the function W that models the weight of a kitten, in ounces, that is alpha weeks old for \(\displaystyle{0}\le{a}\le{6}\) is defined as
\(\displaystyle{W}{\left(\alpha\right)}={1.9}\alpha+{2.3}\)
Step 2
We need to find the weight of a kitten that is 3 weeks old,i.e.we need to compute the value of W(3).
According to the given model,
W(3) = 1.9(3)+2.3=5.7+2.3=8 ounces
Result: The weight of a 3 weeks old kitten is 8 ounces.
0

Relevant Questions

asked 2021-05-05
The bulk density of soil is defined as the mass of dry solidsper unit bulk volume. A high bulk density implies a compact soilwith few pores. Bulk density is an important factor in influencing root development, seedling emergence, and aeration. Let X denotethe bulk density of Pima clay loam. Studies show that X is normally distributed with \(\displaystyle\mu={1.5}\) and \(\displaystyle\sigma={0.2}\frac{{g}}{{c}}{m}^{{3}}\).
(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.
(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than \(\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}\).
(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of \(\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}\)? Explain, based on theprobability of this occurring.
(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?
(e) What is the moment generating function for X?
asked 2021-05-05

A random sample of \( n_1 = 14 \) winter days in Denver gave a sample mean pollution index \( x_1 = 43 \).
Previous studies show that \( \sigma_1 = 19 \).
For Englewood (a suburb of Denver), a random sample of \( n_2 = 12 \) winter days gave a sample mean pollution index of \( x_2 = 37 \).
Previous studies show that \( \sigma_2 = 13 \).
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
\( H_0:\mu_1=\mu_2.\mu_1>\mu_2 \)
\( H_0:\mu_1<\mu_2.\mu_1=\mu_2 \)
\( H_0:\mu_1=\mu_2.\mu_1<\mu_2 \)
\( H_0:\mu_1=\mu_2.\mu_1\neq\mu_2 \)
(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference \( \mu_1 - \mu_2 \). Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?
At the \( \alpha = 0.01 \) level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the \( \alpha = 0.01 \) level, we reject the null hypothesis and conclude the data are statistically significant.
At the \( \alpha = 0.01 \) level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the \( \alpha = 0.01 \) level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for
\( \mu_1 - \mu_2 \).
(Round your answers to two decimal places.)
lower limit
upper limit
(h) Explain the meaning of the confidence interval in the context of the problem.
Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.
asked 2021-02-27
An alpha particle (a He nucleus, containing two protons and two neutrons and having a mass of \(\displaystyle{6.64}\cdot{10}^{{-{27}}}\) kg) traveling horizontally at 35.6 km/s enters a uniform, vertical, 1.10 T magnetic field.
A) What is the diameter of the path followed by this alpha particle?
B) What effect does the magnetic field have on the speed of the particle?
C) What are the magnitude of the acceleration of the alpha particle while it is in the magnetic field?
D) What are the direction of the acceleration of the alpha particle while it is in the magnetic field?
asked 2021-04-25
The unstable nucleus uranium-236 can be regarded as auniformly charged sphere of charge Q=+92e and radius \(\displaystyle{R}={7.4}\times{10}^{{-{15}}}\) m. In nuclear fission, this can divide into twosmaller nuclei, each of 1/2 the charge and 1/2 the voume of theoriginal uranium-236 nucleus. This is one of the reactionsthat occurred n the nuclear weapon that exploded over Hiroshima, Japan in August 1945.
A. Find the radii of the two "daughter" nuclei of charge+46e.
B. In a simple model for the fission process, immediatelyafter the uranium-236 nucleus has undergone fission the "daughter"nuclei are at rest and just touching. Calculate the kineticenergy that each of the "daughter" nuclei will have when they arevery far apart.
C. In this model the sum of the kinetic energies of the two"daughter" nuclei is the energy released by the fission of oneuranium-236 nucleus. Calculate the energy released by thefission of 10.0 kg of uranium-236. The atomic mass ofuranium-236 is 236 u, where 1 u = 1 atomic mass unit \(\displaystyle={1.66}\times{10}^{{-{27}}}\) kg. Express your answer both in joules and in kilotonsof TNT (1 kiloton of TNT releases 4.18 x 10^12 J when itexplodes).
asked 2021-05-04

When a gas is taken from a to c along the curved path in the figure (Figure 1) , the work done by the gas is W = -40 J and the heat added to the gas is Q = -140 J . Along path abc, the work done by the gas is W = -50 J . (That is, 50 J of work is done on the gas.)
I keep on missing Part D. The answer for part D is not -150,150,-155,108,105( was close but it said not quite check calculations)
Part A
What is Q for path abc?
Express your answer to two significant figures and include the appropriate units.
Part B
f Pc=1/2Pb, what is W for path cda?
Express your answer to two significant figures and include the appropriate units.
Part C
What is Q for path cda?
Express your answer to two significant figures and include the appropriate units.
Part D
What is Ua?Uc?
Express your answer to two significant figures and include the appropriate units.
Part E
If Ud?Uc=42J, what is Q for path da?
Express your answer to two significant figures and include the appropriate units.
asked 2021-04-19
For the cellar of a new house a hole is dug in the ground, withvertical sides going down 2.40m. A concrete foundation wallis built all the way across the 9.6m width of the excavation. This foundation wall is 0.183m away from the front of the cellarhole. During a rainstorm, drainage from the streetfills up the space in front of the concrete wall, but not thecellar behind the wall. The water does not soak into the clays oil. Find the force the water causes on the foundation wall. For comparison, the weight of the water is given by:
\(\displaystyle{2.40}{m}\cdot{9.60}{m}\cdot{0.183}{m}\cdot{1000}{k}\frac{{g}}{{m}^{{3}}}\cdot{9.8}\frac{{m}}{{s}^{{2}}}={41.3}{k}{N}\)
asked 2021-06-06
Let X and Y be independent, continuous random variables with the same maginal probability density function, defined as
\(f_{X}(t)=f_{Y}(t)=\begin{cases}\frac{2}{t^{2}},\ t>2\\0,\ otherwise \end{cases}\)
(a)What is the joint probability density function f(x,y)?
(b)Find the probability density of W=XY. Hind: Determine the cdf of Z.
asked 2021-03-31
A paraglider is flying horizontally at a constant speed.Assume that only two forces act on it in the vertical direction,its weight and a vertical lift force exerted on its wings by theair. The lift force has a magnitude of 1800 N.
(a) What is the magnitude and direction of the force that theparaglider exerts on the earth ?
(b)If the lift force should suddenly decrease to 1200 N, whatwould be the vertical acceleration of the glider ? For bothquestions, take the upward direction to be the + y direction.
asked 2021-04-24
Problem: From what maximum height can a 75 kg person jump w/obreaking the lower leg bone on either leg? Ignore air resistance and assume the CM of the person moves a distance of 0.60m from the standing to the seat position (that is, in breaking the fall). Assume the breaking strength (force per unit area) of bone is \(\displaystyle{170}\times{10}^{{6}}\ \frac{{N}}{{m}^{{2}}}\) and its smallest cross sectional areais \(\displaystyle{2.5}\times{10}^{{-{4}}}\)
asked 2021-03-12
A 75.0-kg man steps off a platform 3.10 m above the ground. Hekeeps his legs straight as he falls, but at the moment his feettouch the ground his knees begin to bend, and, treated as aparticle, he moves an additional 0.60 m before coming torest.
a) what is the speed at the instant his feet touch theground?
b) treating him as a particle, what is his acceleration(magnitude and direction) as he slows down, if the acceleration isassumed to be constant?
c) draw his free-body diagram (see section 4.6). in termsof forces on the diagram, what is the net force on him? usenewton's laws and the results of part (b) to calculate the averageforce his feet exert on the ground while he slows down. expressthis force in newtons and also as a multiple of his weight.
...