In this Physics problem, we calculate the horizontal distance a stone travels when thrown horizontally from a cliff to determine the ratio of heights between two buildings.
Explanation:The horizontal distance the stone will travel can be calculated using the formula:
d = v*t
Where d is the distance, v is the initial velocity, and t is the time of flight. Using the information given, we can calculate the distance the stone from block A will travel, and then find the ratio of building A's height to building B's height.
An automobile tire has a radius of 0.315 m, and its center moves forward with a linear speed of v = 19.3 m/s. (a) Determine the angular speed of the wheel. (b) Relative to the axle, what is the tangential speed of a point located 0.193 m from the axle?
Answer:
angular speed: 61.3 radians/stangential speed at .193 m: 11.8 m/sStep-by-step explanation:
The forward speed of the center of the tire with respect to the ground is the same as the tangential speed of the tire at its full radius of 0.315 m, relative to the axle.
The angular speed of the tire is the ratio of tangential speed to radius:
(19.3 m/s)/(0.315 m) ≈ 61.27 radians/s
The tangential speed at any other radius is the product of angular speed and radius. At a radius of 0.193 m, the tangential speed is ...
(0.193 m)×(19.3 m/s)/(0.315 m) ≈ 11.825 m/s ≈ 11.8 m/s
(a) The angular speed of the wheel is approximately 61.27 rad/s.
(b) The tangential speed of a point 0.193 m from the axle is about 11.82 m/s, relative to the axle.
let's break this down step by step.
Given:
Radius of the tire, r = 0.315 m
Linear speed of the center of the tire, v = 19.3 m/s
Distance from the axle to the point, d = 0.193 m
(a) To determine the angular speed of the wheel (ω), we can use the formula relating linear speed (v) and angular speed (ω) for a rotating object:
v = ω * r
where:
v = linear speed
ω = angular speed
r = radius
We can rearrange this equation to solve for ω:
ω = v / r
Now, substitute the given values:
ω = 19.3 m/s / 0.315 m
ω ≈ 61.27 rad/s
So, the angular speed of the wheel is approximately 61.27 rad/s.
(b) To find the tangential speed of a point located 0.193 m from the axle relative to the axle, we'll use the formula:
Tangential speed (vt) = ω x distance from the axle (d)
We already have the value of ω from part (a), which is approximately 61.27 rad/s. Now, let's calculate the tangential speed:
vt = 61.27 rad/s x 0.193 m
vt ≈ 11.82 m/s
So, the tangential speed of a point located 0.193 m from the axle, relative to the axle, is approximately 11.82 m/s.
1. If $18,000 is invested at 6% compounded monthly, what is the amount after 7 years?
Please show me steps to find 1/3 + m = 13/15
Hello!
Answer:
[tex]\boxed{m=\frac{8}{15}}[/tex]
Step-by-step explanation:
First, you switch sides.
[tex]m+\frac{1}{3}=\frac{13}{15}[/tex]
Then, you subtract by 1/3 from both sides.
[tex]m+\frac{1}{3}-\frac{1}{3}=\frac{13}{15}-\frac{1}{3}[/tex]
Simplify and solve.
[tex]\frac{13}{15}=\frac{8}{15}[/tex]
Therefore, [tex]\boxed{\frac{8}{15}}[/tex], which is our final answer.
I hope this helps you!
Have a nice day! :)
A skateboarder went a kilometer in 3 minutes with the wind, and returned in four minutes against the wind.
How fast could he skateboard one kilometer if there was no wind?
Please explain your answer! Please!
Step-by-step answer:
Answer to problems of this kind is the reciprocal of the harmonic mean of the time required.
We need to find the average of the speeds, not the average of the time.
The respective speeds are 1/3 and 1/4.
The average of the speeds is therefore (1/3+1/4)/2 = 7/24 (harmonic mean of the time taken).
The time required is therefore the reciprocal of the unit speed,
T = 1/(7/24) = 24/7 = 3 3/7 minutes, or approximately 3.43 minutes.
Find the area under the curve y =f( x) on [a,b] given f(x)=tan(3x) where a=0 b=pi/12
Answer:
The area under the curve y=f(x) on [a,b] is [tex]\frac{1}{6}\ln(2)[/tex] square units.
Step-by-step explanation:
The given function is
[tex]f(x)=\tan(3x)[/tex]
where a=0 and b=pi/12.
The area under the curve y=f(x) on [a,b] is defined as
[tex]Area=\int_{a}^{b}f(x)dx[/tex]
[tex]Area=\int_{0}^{\frac{\pi}{12}}\tan (3x)dx[/tex]
[tex]Area=\int_{0}^{\frac{\pi}{12}}\frac{\sin (3x)}{\cos (3x)}dx[/tex]
Substitute cos (3x)=t, so
[tex]-3\sin (3x)dx=dt[/tex]
[tex]\sin (3x)dx=-\frac{1}{3}dt[/tex]
[tex]a=\cos (3(0))=1[/tex]
[tex]b=\cos (3(\frac{\pi}{12}))=\frac{1}{\sqrt{2}}[/tex]
[tex]Area=-\frac{1}{3}\int_{1}^{\frac{1}{\sqrt{2}}}\frac{1}{t}dt[/tex]
[tex]Area=-\frac{1}{3}[\ln t]_{1}^{\frac{1}{\sqrt{2}}[/tex]
[tex]Area=-\frac{1}{3}(\ln \frac{1}{\sqrt{2}}-\ln (1))[/tex]
[tex]Area=-\frac{1}{3}(\ln 1-\ln \sqrt{2}-0)[/tex]
[tex]Area=-\frac{1}{3}(-\ln 2^{\frac{1}{2}})[/tex]
[tex]Area=-\frac{1}{3}(-\frac{1}{2}\ln 2)[/tex]
[tex]Area=-\frac{1}{6}\ln 2[/tex]
Therefore the area under the curve y=f(x) on [a,b] is [tex]\frac{1}{6}\ln(2)[/tex] square units.
Choose the equation of the graph shown.
y=-2cosx
y=-2sinx
y=2cosx
y= 2sinx
Answer:
y = -2 sin x
Step-by-step explanation:
As a basic,
y = cos x has a value of 1 at x = 0, and
y = sin x has a value of 0 at x = 0
Note: the value 1 can change to 2, 3, 4, etc. if the amplitude increases
Looking at the graph at x = 0, we see the y-value is 0, so definitely this is a sin graph. We can eliminate the cos choices.
So is it y = 2 sin x or y = -2 sin x??
If the graph goes downward from 0 (at x = 0), it is reflected of original, so that would be y = - sinx.
Since the graph decreases (goes downward) from x = 0, it is definitely the graph of negative sin. So y = - 2 sin x
Help on this ALGEBRA QUESTIONS !!!
Simplify the expression, if possible. 512 ^1/2
A. 32
B. 16√ 2
C. 64
D. It's not a real number.
Note that [tex]x^{\frac{1}{2}}=\sqrt[2]{x}[/tex]
Which means that:
[tex]512^{\frac{1}{2}}=\sqrt[2]{512}=\sqrt[2]{16^2\cdot2}=\boxed{16\sqrt[2]{2}}[/tex]
the answer is B.
Hope this helps.
r3t40
According to an article in Newsweek, the natural ratio of girls to boys is 100:105. In China, the birth ratio is 100: 114 (46.7% girls). Suppose you don’t believe the reported figures of the percent of girls born in China. You conduct a study. In this study, you count the number of girls and boys born in 150 randomly chosen recent births. There are 60 girls and 90 boys born of the 150. Based on your study, do you believe that the percent of girls born in China is 46.7?
Based on the study results, the percentage of girls born in China could range from 32.98% to 47.02%.
Explanation:To determine if the percentage of girls born in China is 46.7%, we can calculate the confidence interval for the proportion of girls in the population using a binomial distribution. Based on the study, out of 150 births, 60 were girls and 90 were boys.
Calculate the sample proportion of girls: p = 60/150 = 0.4Calculate the standard error: SE = sqrt((p*(1-p))/n) = sqrt((0.4*(1-0.4))/150) ≈ 0.0357Calculate the margin of error: ME = z*(SE) = 1.96*(0.0357) ≈ 0.0702Calculate the confidence interval: CI = p ± ME = 0.4 ± 0.0702 = (0.3298, 0.4702)The confidence interval suggests that the true proportion of girls born in China could range from 32.98% to 47.02%. Since the reported figure of 46.7% falls within this interval, it is plausible based on the study results.
In testing whether the means of two normal populations are equal, summary statistics computed for two independent samples are as follows:
Brand X n2=20 xbar 2=6.80 s2=1.15
Brand Y n1=20 xbar1=7.30 s1=1.10
Assume that the population variances are equal. Then, the standard error of the sampling distribution of the sample mean difference xbar1−xbar2 is equal to: Question 2 options: (a) 1.1275 (b) 0.1266 (c) 1.2663 (d) 0.3558.
Answer: (d) 0.3558.
Step-by-step explanation:
We know that the standard error of sample mean difference is given by:-
[tex]S.E.=\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2}}[/tex]
Given : [tex]n_1= 20\ ,\ n_2=20[/tex]
[tex]s_1=1.10\ ,\ \ s_2=1.15[/tex]
Then , the standard error of the sampling distribution of the sample mean difference [tex]\overline{x_1}-\overline{x_2}[/tex] is equal to :-
[tex]S.E.=\sqrt{\dfrac{1.10^2}{20}+\dfrac{1.15^2}{20}}\\\\\Rightarrow\ S.E.=0.355844066973\approx0.3558[/tex]
Hence, the standard error of the sampling distribution of the sample mean difference [tex]\overline{x_1}-\overline{x_2}[/tex] is equal to 0.3558.
Final answer:
The standard error of the sampling distribution of the sample mean difference is calculated using the formula involving standard deviations and sample sizes of the independent samples; the correct answer, after computation, is 0.3558.
Explanation:
The standard error of the sampling distribution of the sample mean difference (ëxbar1 - ëxbar2) when assuming population variances are equal can be computed using the formula for the standard error of the difference of two independent sample means, which is the square root of the sum of their variances divided by their respective sample sizes. The formula is:
SE = √((s1²/n1) + (s2²/n2))
Given the summary statistics:
n1 = n2 = 20 (sample sizes)s1 = 1.10 (standard deviation of sample 1)s2 = 1.15 (standard deviation of sample 2)The calculation of the standard error would be:
SE = √((1.10²/20) + (1.15²/20))
SE = √((1.21/20) + (1.3225/20))
SE = √(0.0605 + 0.066125)
SE = √(0.126625)
SE = 0.3558 (when rounded to four decimal places)
Hence, the correct answer is option (d) 0.3558.
2x + 1 < 5
Solve the following inequality. Then place the correct number in the box provided.
Answer:
[tex]\boxed{x<2}[/tex]
Step-by-step explanation:
You subtract by 1 from both sides of equation.
[tex]2x+1-1<5-1[/tex]
Simplify.
[tex]5-1=4[/tex]
[tex]2x<4[/tex]
Divide by 2 from both sides of equation.
[tex]\frac{2x}{2}<\frac{4}{2}[/tex]
Simplify, to find the answer.
[tex]4\div2=2[/tex]
X<2 is the correct answer.
Answer: [tex]x<2[/tex]
Step-by-step explanation:
Given the inequality [tex]2x + 1 < 5[/tex] you can follow this procedure to solve it:
The first step is to subtract 1 from both sides on the inequaltity.
[tex]2x + 1-(1) < 5-(1)\\\\2x < 4[/tex]
Now, the second and final step is to divide both sides of the inequality by 2. Therefore, you get this result:
[tex]\frac{2x}{2}<\frac{4}{2} \\\\(1)x<2\\\\x<2[/tex]
Lester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the six months following the exercise program. Below are the results. At the .05 significance level, can he conclude that the number of absences has declined? Estimate the p-value.
Final answer:
Lester Hollar can assess the impact of the fitness program on absenteeism by conducting a paired samples t-test at a 0.05 significance level. If the p-value is less than 0.05, the program effectively reduced absences; otherwise, there is insufficient evidence to conclude its effectiveness.
Explanation:
Evaluating the Exercise Program’s Impact on Employee Absenteeism
Lester Hollar wishes to assess if the company’s fitness program led to a decline in employee absences. With a sample of eight participants, he analyzed absenteeism before and after the program’s implementation. To determine if absences have decreased, a hypothesis test at the 0.05 significance level (alpha) is conducted.
To evaluate the change in absences, two sets of absenteeism data are compared using a statistical test, such as the paired samples t-test. This test examines if the mean difference in absences before and after the program is statistically significant. If the p-value obtained from the test is less than the significance level of 0.05, the null hypothesis (no change in absences) would be rejected, suggesting that the exercise program was effective in reducing absences.
If Lester Hollar finds a p-value greater than 0.05, he would not reject the null hypothesis, indicating that there isn’t sufficient evidence to conclude the program's impact. It’s also important to estimate the p-value precisely as it gives a measure of the strength of evidence against the null hypothesis. However, without the specific data, we cannot calculate the p-value or make a definitive conclusion here.
×
_+4=20
6
Solve the following equation. Then place the correct number in the box provided.
Answer:
Step-by-step explanation:
X/6 +4 = 20
X/6 = 20 - 4
X/6 = 16
X = 16/6
(05.05 MC) The area of a triangle is 24 square inches. What is the height of the triangle if the base length is 8 inches?
height: 6
formula: 1/2bh
hope this helps :)
For this case we have that by definition, the area of a triangle is given by:
[tex]A = \frac {1} {2} b * h[/tex]
Where:
b: It's the base
h: It's the height
They tell us as data that:
[tex]A = 24 \ in ^ 2\\b = 8in[/tex]
Substituting the data and clearing the height:
[tex]24 = \frac {1} {2} 8 * h\\24 = 4h\\h = \frac {24} {4}\\h = 6[/tex]
So, the height of the triangle is 6in
Answer:
[tex]h = 6in[/tex]
A composite figure is divided into two congruent trapezoids, each with a height of 4 cm.
What is the area of this composite figure?
Answer:
The area of this composite figure is [tex]64\ cm^{2}[/tex]
Step-by-step explanation:
we know that
If the composite figure is divided into two congruent trapezoids, then the area of the composite figure is equal to the area of one trapezoid multiplied by two
so
The area of the composite figure is
[tex]A=2[\frac{1}{2}(b1+b2)h][/tex]
[tex]A=(b1+b2)h[/tex]
substitute the values
[tex]A=(6+10)4[/tex]
[tex]A=64\ cm^{2}[/tex]
Answer:
64cm
Step-by-step explanation:
I looked at the guy's answer on top of mine and it was correct, go thank him!
The average annual salary for employees in a store is $50,000. It is given that the population standard deviation is $4,000. Suppose that a random sample of 70 employees will be selected from the population.What is the value of the standard error of the average annual salary? Round your answer to the nearest integer.
Answer: 478
Step-by-step explanation:
The formula to calculate the standard error of the population mean is given by :-
[tex]S.E.=\dfrac{\sigma}{\sqrt{n}}[/tex], where [tex]\sigma[/tex] is the standard deviation and 'n' is the sample size.
Given: Mean : [tex]\mu=$\50,000[/tex]
Standard deviation : [tex]\sigma= $\4,000[/tex]
Sample size : [tex]n=70[/tex]
Now, the value of the standard error of the average annual salary is given by :-
[tex]S.E.=\dfrac{50000}{\sqrt{70}}=478.091443734\approx478[/tex]
Hence, the standard error of the average annual salary = 478
The value of the standard error of the average annual salary is calculated using the formula SE = population standard deviation / [tex]\sqrt{sample size}[/tex] ,which for a population standard deviation of $4,000 and a sample size of 70 employees, comes out to approximately $478.
To calculate the standard error of the average annual salary, you'd use the formula for the standard error of the mean when you know the population standard deviation: SE = σ /[tex]\sqrt{n}[/tex], where σ is the population standard deviation and n is the sample size.
In this case, the population standard deviation σ is $4,000, and the sample size n is 70 employees. Using the formula, we get SE = 4000 / [tex]\sqrt{70}[/tex], which will give us the standard error of the average annual salary.
Performing the calculation: SE = 4000 / [tex]\sqrt{70}[/tex] ≈ 4000 / 8.367 = 478.29, which when rounded to the nearest integer is $478. Therefore, the value of the standard error of the average annual salary is approximately $478.
a.
solve
[tex]\frac{1}{n} \pi = \theta - \frac{1}{2}sin(2 \theta)[/tex] for [tex] \theta[/tex] in terms of "n"
(derivation of equation below)
b. Based on your answer in
part a, if [tex] \theta = arccos(1 - \frac{a}{r} ) = {cos}^{ - 1} (1 - \frac{a}{r} )[/tex] or [tex] a = r-2cos( \theta)[/tex]
find "a" as a function of
r & n. (find f(r,n)=a).
alternately, if a+b=r, we can write [tex] \theta = arccos( \frac{b}{r} ) = {cos}^{ - 1} (\frac{b}{r} )[/tex]
then solve for "a" in terms of r and n
show all work and reasoning.
Solve analytically if possible
Answer:
a) There is no algebraic method for finding θ in terms of n
b) should be a = r(1 -cos(θ))
Step-by-step explanation:
Algebraic methods have been developed for solving trig functions and polynomial functions individually, but not in combination. In general, the solution is easily found numerically, but not analytically.
You would be looking for the numerical solution to ...
f(n, θ) = 0
where f(n, θ) can be ...
f(n, θ) = θ - (1/2)sin(2θ) - π/n
___
The attached shows Newton's method iterative solutions for n = 3 through 6:
for n = 3, θ ≈ 1.3026628373
for n = 4, θ ≈ 1.15494073001
...
100 people responded to a survey about their ice cream preferences, and listed below are the results. 55 liked vanilla 30 liked chocolate 40 liked strawberry 10 liked both vanilla and strawberry 10 liked both strawberry and chocolate 15 liked both vanilla and chocolate 5 liked all three flavors How many did not like any of the three flavors?
To find the number of people who did not like any of the three flavors, we need to subtract the number of people who liked at least one flavor from the total number of people.
Explanation:To find the number of people who did not like any of the three flavors, we need to subtract the number of people who liked at least one flavor from the total number of people.
From the given information, we can create a Venn diagram to represent the preferences:
Picking it up from the explanation above, it becomes clear that 10 people liked both vanilla and strawberry, 10 people liked both strawberry and chocolate, and 15 people liked both vanilla and chocolate. We also know that 5 people liked all three flavors. Using this information, we can determine the number of people who liked at least one flavor by adding up the numbers in the overlapping circles: 10 + 10 + 15 + 5 = 40 people.
To find the number of people who did not like any of the three flavors, we subtract 40 from the total number of people who responded to the survey: 100 - 40 = 60 people.
Learn more about Ice cream survey here:https://brainly.com/question/18427332
#SPJ3
To find out how many people did not like any of the three flavors, we use the principle of inclusion-exclusion, resulting in 5 people who did not like vanilla, chocolate, or strawberry.
The student has asked a question related to combinations without repetition and the interpretation of survey results. To determine how many people did not like any of the three flavors (vanilla, chocolate, strawberry), we can use the principle of inclusion-exclusion. Here are the steps to solve this:
First, add the number of people who liked each flavor: 55 (vanilla) + 30 (chocolate) + 40 (strawberry) = 125.Next, subtract the numbers who liked each combination of two flavors: 125 - (10 + 10 + 15) = 125 - 35 = 90.Now, add back those who liked all three flavors because they were subtracted twice: 90 + 5 = 95.Finally, since there were 100 people surveyed, subtract the number who liked at least one flavor from the total: 100 - 95 = 5.Therefore, 5 people did not like any of the three flavors.
Eliminate all exponents by Expanding 6^3 y^4
Answer:
216*y*y*y*y
Step-by-step explanation:
6 cubed is 216, and y^4 expanded is yyyy. So if I'm understanding correctly, you want as your answer:
216*y*y*y*y
Use the Newton-Raphson method to find the root of the equation f(x) = In(3x) + 5x2, using an initial guess of x = 0.5 and a stopping criterion of &= 0.1%. Report your answer to 3 decimal places. What is the estimate for the root? What is the approximate relative error? %
Answer with explanation:
The equation which we have to solve by Newton-Raphson Method is,
f(x)=log (3 x) +5 x²
[tex]f'(x)=\frac{1}{3x}+10 x[/tex]
Initial Guess =0.5
Formula to find Iteration by Newton-Raphson method
[tex]x_{n+1}=x_{n}-\frac{f(x_{n})}{f'(x_{n})}\\\\x_{1}=x_{0}-\frac{f(x_{0})}{f'(x_{0})}\\\\ x_{1}=0.5-\frac{\log(1.5)+1.25}{\frac{1}{1.5}+10 \times 0.5}\\\\x_{1}=0.5- \frac{0.1760+1.25}{0.67+5}\\\\x_{1}=0.5-\frac{1.426}{5.67}\\\\x_{1}=0.5-0.25149\\\\x_{1}=0.248[/tex]
[tex]x_{2}=0.248-\frac{\log(0.744)+0.30752}{\frac{1}{0.744}+10 \times 0.248}\\\\x_{2}=0.248- \frac{-0.128+0.30752}{1.35+2.48}\\\\x_{2}=0.248-\frac{0.17952}{3.83}\\\\x_{2}=0.248-0.0468\\\\x_{2}=0.2012[/tex]
[tex]x_{3}=0.2012-\frac{\log(0.6036)+0.2024072}{\frac{1}{0.6036}+10 \times 0.2012}\\\\x_{3}=0.2012- \frac{-0.2192+0.2025}{1.6567+2.012}\\\\x_{3}=0.2012-\frac{-0.0167}{3.6687}\\\\x_{3}=0.2012+0.0045\\\\x_{3}=0.2057[/tex]
[tex]x_{4}=0.2057-\frac{\log(0.6171)+0.21156}{\frac{1}{0.6171}+10 \times 0.2057}\\\\x_{4}=0.2057- \frac{-0.2096+0.21156}{1.6204+2.057}\\\\x_{4}=0.2057-\frac{0.0019}{3.6774}\\\\x_{4}=0.2057-0.0005\\\\x_{4}=0.2052[/tex]
So, root of the equation =0.205 (Approx)
Approximate relative error
[tex]=\frac{\text{Actual value}}{\text{Given Value}}\\\\=\frac{0.205}{0.5}\\\\=0.41[/tex]
Approximate relative error in terms of Percentage
=0.41 × 100
= 41 %
Write an exponential function y = abx for a graph that includes (–4, 72) and (–2, 18).
Answer:
[tex]y=4.5(0.5)^{x}[/tex]
Step-by-step explanation:
* Lets revise the meaning of exponential function
- The form of the exponential function is [tex]y=ab^{x}[/tex],
where a ≠ 0, b > 0 , b ≠ 1, and x is any real number
- It has a constant base b
- It has a variable exponent x
- To solve an exponential equation, take the log or ln of both sides,
and solve for the variable
* Lets solve the problem
∵ y = a(b)^x is an exponential function
∵ Its graph contains the point (-4 , 72) and (-2 , 18)
- Lets substitute x and y by the coordinates of these points
# Point (-4 , 72)
∵ [tex]y=ab^{x}[/tex]
∵ x = -4 and y = 72
∴ [tex]72=ab^{-4}[/tex]
- The change any power from -ve to +ve reciprocal the base of
the power ([tex]p^{-n}=\frac{1}{p^{n}}[/tex]
∴ [tex]72=\frac{a}{b^{4}}[/tex]
- By using cross multiplication
∴ [tex]a=72b^{4}[/tex] ⇒ (1)
# Point (-2 , 18)
∵ x = -2 and y = 18
∴ [tex]18=ab^{-2}[/tex]
∴ [tex]18=\frac{a}{b^{2}}[/tex]
- By using cross multiplication
∴ a = 18b² ⇒ (2)
- Equate the two equations (1) and (2)
∴ [tex]72b^{4}=18b^{2}[/tex]
- Divide both sides by 18b²
∵ [tex]\frac{72b^{4}}{18b^{2}}=4b^{4-2}=4b^{2}[/tex]
∵ [tex]\frac{18b^{2}}{18b^{2}}=(1)b^{2-2}=(1)b^{0}=(1)(1)=1[/tex]
∴ 4b² = 1 ⇒ divide both sides by 4
∴ [tex]b^{2}=\frac{1}{4}=0.25[/tex] ⇒ take square root for both sides
∴ b = √0.25 = 0.5
- Lets substitute the value ob b in equation (1) or (2) to find a
∵ a = 18b²
∵ b² = 0.25
∴ a = 18(0.25) = 4.5
- Lets substitute the values of a and b in the equation [tex]y=ab^{x}[/tex]
∴ [tex]y=4.5(0.5)^{x}[/tex]
- We can write it using fraction
∴ [tex]y=\frac{9}{2}(\frac{1}{2})^{x}[/tex]
ANSWER
[tex]y = \frac{9}{2} ( { \frac{1}{2} })^{x}[/tex]
EXPLANATION
Let the exponential function be
[tex]y = a {b}^{x} [/tex]
Since the graph includes (–4, 72), it must satisfy this equation.
[tex]72= a { b}^{ - 4}[/tex]
Multiply both sides by b⁴ .
This implies that,
[tex]a = 72 {b}^{4} ...1[/tex]
The graph also includes (-2,18).
We substitute this point also to get:
[tex]18=a {b}^{ - 2} [/tex]
Multiply both sides by b²
[tex]a = 18 {b}^{2} ...(2)[/tex]
We equate (1) and (2) to obtain:
[tex]72 {b}^{4} = 18 {b}^{2} [/tex]
Multiply both sides by
[tex] \frac{72 {b}^{4} }{ {18b}^{4} } = \frac{18 {b}^{2} }{18 {b}^{4} } [/tex]
[tex]4 = \frac{1}{ {b}^{2} } [/tex]
Or
[tex]{2}^{ 2} = ( \frac{1}{b} )^{2} [/tex]
[tex] \frac{1}{b} = 2[/tex]
[tex]b = \frac{1}{2} [/tex]
Put b=½ into equation (2).
[tex]a = 18 {( \frac{1}{2} })^{2} [/tex]
[tex]a = \frac{18}{4} [/tex]
[tex]a = \frac{9}{2} [/tex]
Therefore the equation is
[tex]y = \frac{9}{2} ( { \frac{1}{2} })^{x} [/tex]
what is m angle ABC
Answer:
3rd option: 60 degrees
Step-by-step explanation:
We can see in the diagram that the angle on C is a supplementary angle, which means that the sum of 135 and internal angle will be equal to 180 degrees.
Let x be the internal angle,
Then
x+135 = 180
x = 180-135
x = 45 degrees
So now we know that two interior angles of the triangle.
Also we know that sum of all internal angles of triangle is 180 degrees.
Using the same postulate:
A+B+C = 180
75 + B + 45 = 180
120+B = 180
B = 180 - 120
B = 60 degrees
So,
third option is the correct answer ..
Answer:
It’s 120 I got it right on the test !
Captain Ralph is in trouble near the sunny side of Mercury. The temperature of the ship's hull when he is at location (x, y, z) will be given by T (x, y, z) = e−x2 − 2y2 − 3z2, where x, y, and z are measured in meters. He is currently at (1, 1, 1). (a) In what direction should he proceed in order to decrease the temperature most rapidly?
The maximum rate of change occurs in the direction of the gradient vector at (1, 1, 1).
[tex]T(x,y,z)=e^{-x^2-2y^2-3z^2}\implies\nabla T(x,y,z)=\langle-2x,-4y,-6z\rangle e^{-x^2-2y^2-3z^2}[/tex]
At (1, 1, 1), this has a value of
[tex]\nabla T(1,1,1)=\langle-2,-4,-6\rangle e^{-6}[/tex]
so the captain should move in the direction of the vector [tex]\langle-1, -2, -3\rangle[/tex] (which is a vector pointing in the same direction but scaled down by a factor of [tex]2e^{-6}[/tex]).
The direction Captain Ralph should proceed in order to decrease the temperature most rapidly is towards the direction of the steepest temperature decrease gradient. This direction is given by the negative gradient of the temperature function.
In this case, the negative gradient of T(x, y, z) = e^(-x^2 - 2y^2 - 3z^2) at the point (1, 1, 1) would be (-2e^(-6), -4e^(-6), -6e^(-6)).
Therefore, Captain Ralph should proceed in the direction (-2e^(-6), -4e^(-6), -6e^(-6)) to decrease the temperature most rapidly at his current location.
The inverse function of f(x) = ex has a asymptote at
Answer:
x=0
Step-by-step explanation:
You are given the function [tex]f(x)=e^x.[/tex] To find it inverse function, express x in terms of y:
[tex]y=e^x\\ \\\ln y=x[/tex]
Now change x into y and y into x:
[tex]y=\ln x\\ \\f^{-1}(x)=\ln x[/tex]
The graph of the function [tex]f^{-1}(x)[/tex] has vertical asymptote x=0.
Vertical asymptote at x = 0
A gas storage tank is in the shape of a right circular cylinder that has a radius of the base of 2ft and a height of 3ft. The farmer wants to paint the tank including both bases but only has 1 gallon of paint. If 1 gallon of paint will cover 162 square feet, will the farmer have enough paint to complete the job?
Answer:
Yes, the farmer have enough paint to complete the job.
Step-by-step explanation:
It is given that a gas storage tank is in the shape of a right circular cylinder.
The radius of the base is 2 ft and the height of cylinder is 3 ft.
The total surface area of a cylinder is
[tex]S=2\pi rh+2\pi r^2[/tex]
Total surface area of gas storage tank is
[tex]S=2\pi (2)(3)+2\pi (2)^2[/tex]
[tex]S=12\pi+8\pi[/tex]
[tex]S=20\pi[/tex]
[tex]S=62.8318530718[/tex]
[tex]S\approx 62.83[/tex]
The total surface area of gas storage tank is 62.83 square feet.
The farmer has 1 gallon of paint and 1 gallon of paint will cover 162 square feet.
Since 62.83<162, therefore 1 gallon of paint is enough to paint the gas storage.
Hence the required statement is Yes, the farmer have enough paint to complete the job.
Answer:
Yes, the farmer have enough paint to complete the job.
Step-by-step explanation:
1 gallon is good
A certain group of women has a 0.640.64%
rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
What is the probability that the woman selected does not have red/green color blindness?
nothing
(Type an integer or a decimal. Do not round.)
Answer:
the probability that the woman selected does not have red/green color blindness is 0.9936.
Step-by-step explanation:
Final answer:
The probability that a randomly selected woman does not have red/green color blindness is 99.36%.
Explanation:
If the rate of red/green color blindness among a certain group of women is 0.64%, this means that out of every 100 women, 0.64 women on average would have red/green color blindness.
The complement of a probability event occurring is equal to 1 minus the probability of the event.
Therefore, the probability that a randomly selected woman does not have red/green color blindness is :
1 - 0.0064
which is 0.9936 or 99.36%.
The sum of Eli’s age and Cecil’s age is 60. Six years ago, Eli was three times old as Cecil. Find Eli’s age now
Answer:
Eli's age = 42 years
Step-by-step explanation:
Let x be Eli's age and y be Cecil's age
So,
According to the statement given
x+y=60 eqn 1
Eli's age 6 years ago = x-6
Cecil's age 6 years ago = y-6
So according to the given statement
x-6 = 3(y-6)
x-6 = 3y - 18
x-3y = -18+6
x-3y= -12 eqn 2
Subtracting eqn 2 from eqn 1
x+y - (x-3y) = 60 - (-12)
x+y-x+3y = 60+12
4y = 72
y = 18
Cecil's age = 18 years
Putting y = 18 in eqn 1
x+18=60
x = 60-18
x = 42
Eli's age = 42 years ..
There are ten members of the debate team: Ann, Bill, Carla, Don, Ed, Frank, Gretchen, Harry, Isabel, and Jen. If they randomly choose three co-leaders of the group, what is the probability that Gretchen, Don, and Carla are chosen as the co-leaders?
Answer:
1/120
Step-by-step explanation:
There are 10 members, and three are chose as co-leaders. The number of possible combinations is:
₁₀C₃ = 120
One of those 120 combinations is Gretchen, Don, and Carla. So the probability is 1/120, or approximately 0.83%.
Rhea is solving a math puzzle. To find the solution of the puzzle, she must find the product of two numbers. The first number is the sum of 23 and x, and the second number is 18 less than two times the first number. Which of the following functions represents the product of these two numbers?
Answer:
Function which represents the product of these two numbers is:
(23+x)(28+2x)
Step-by-step explanation:
The first number is the sum of 23 and x
i.e. First number=23+x
The second number is 18 less than two times the first number.
i.e. Second number=2(23+x)-18
= 46+2x-18
= 28+2x
Product of the two numbers=(23+x)(28+2x)
Hence, function which represents the product of these two numbers is:
(23+x)(28+2x)
If records indicate that 15 houses out of 1000 are expected to be damaged by fire in any year, what is the probability that a woman who owns 14 houses will have fire damage in 2 of them in a year? (Round your answer to five decimal places.)
Answer: 0.01708
Step-by-step explanation:
Given : If records indicate that 15 houses out of 1000 are expected to be damaged by fire in any year.
i.e. the probability that house damaged buy fire in a year : [tex]p=\dfrac{15}{1000}=0.015[/tex]
The formula for binomial distribution is given by :-
[tex]^{n}C_xp^x(1-p)^{n-x}[/tex]
Now, the probability that a woman who owns 14 houses will have fire damage in 2 of them in a year (put n=14 and x=2), we get
[tex]^{14}C_2(0.015)^2(1-0.015)^{14-2}\\\\=\dfrac{14!}{2!(14-2)!}(0.015)^2(0.985)^{12}\\\\=0.0170788520518\approx0.01708[/tex]
Hence, the required probability = 0.01708
A quality control inspector has drawn a sample of 1414 light bulbs from a recent production lot. If the number of defective bulbs is 22 or more, the lot fails inspection. Suppose 20%20% of the bulbs in the lot are defective. What is the probability that the lot will fail inspection? Round your answer to four decimal places.
Answer: 0.8021
Step-by-step explanation:
The given problem is a binomial distribution problem, where
[tex]n=14,\ p=0.2, q=1-0.2=0.8[/tex]
The formula of binomial distribution is :-
[tex]P(X=r)=^{n}C_{r}p^{r}q^{n-r}[/tex]
The probability that the lot will fail inspection is given by :_
[tex]P(X\geq2)=1-(P(X\leq1))\\\\=1-(P(0)+P(1))\\\\[/tex]
[tex]=1-(^{14}C_{0}(0.2)^{0}(0.8)^{14-0}+^{14}C_{1}(0.2)^{1}(0.8)^{14-1})\\\\=1-((1)(0.8)^{14}+(14)(0.2)(0.8)^{13})\\\\=0.802087907\approx0.8021[/tex]
Hence, the required probability = 0.4365