Answers
You want to end up with [tex]A\sin(\omega t+\phi)[/tex]. Expand this using the angle sum identity for sine:
[tex]A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi[/tex]
We want this to line up with [tex]2\sin(4\pi t)+5\cos(4\pi t)[/tex]. Right away, we know [tex]\omega=4\pi[/tex].
We also need to have
[tex]\begin{cases}A\cos\phi=2\\A\sin\phi=5\end{cases}[/tex]
Recall that [tex]\sin^2x+\cos^2x=1[/tex] for all [tex]x[/tex]; this means
[tex](A\cos\phi)^2+(A\sin\phi)^2=2^2+5^2\implies A^2=29\implies A=\sqrt{29}[/tex]
Then
[tex]\begin{cases}\cos\phi=\frac2{\sqrt{29}}\\\sin\phi=\frac5{\sqrt{29}}\end{cases}\implies\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)[/tex]
So we end up with
[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]
Answer:
y(t) = √29·sin(4πt +1.1903)amplitude: √29angular frequency: 4πphase shift: 1.1903 radiansStep-by-step explanation:
In the form ...
y(t) = Asin(ωt +φ)
you have ...
Amplitude = Aangular frequency = ωphase shift = φThe translation from ...
y(t) = 2sin(4πt) +5cos(4πt)
is ...
A = √(2² +5²) = √29 . . . . the amplitude
ω = 4π . . . . the angular frequency in radians per second
φ = arctan(5/2) ≈ 1.1903 . . . . radians phase shift
Then, ...
y(t) = √29·sin(4πt +1.1903)
_____
Comment on the conversion
You will notice we used "2" and "5" to find the amplitude and phase shift. In the generic case, these are "coefficient of sin( )" and "coefficient of cos( )". When determining phase shift, pay attention to whether your calculator is giving you degrees or radians. (Set the mode to what you want.)
If you have a negative coefficient for sin( ), you will need to add 180° (π radians) to the phase shift value given by the arctan( ) function.
Related Questions
What is the range of the function F(x) graphed below?F(x)= -(x+2)^2+3
Answers
Answer:
range of the function F(x) is (-infinity, 3)
Step-by-step explanation:
I do not see the graph function F(x), so will assume that it is a graph of the function F(x) over the complete domain (-inf,inf).
As you can see from the attached graph, the function reaches a maximum at y=+3, and extends all the way to -infinity.
So the range of the function F(x) is (-infinity, 3)
a lottery game has balls numbered 1 through 19. what is the probability selected ball is an even numbered ball or a 4 g
Answers
Answer:
Probability ball is an even numbered ball or a 4 [P(A or B)] = 9 / 19
Step-by-step explanation:
Given:
Number of balls = 1 to 19
Find:
Probability ball is an even numbered ball or a 4
Computation:
Total even number = 2, 4, 6, 8, 10, 12, 14, 16, 18
Probability to get even number P(A) = 9 / 19
Probability to get 4 number P(B) = 1 / 19
P(A and B) = 1 / 19 (4 common)
Probability ball is an even numbered ball or a 4 [P(A or B)]
P(A or B) = P(A) + P(B) -P(A and B)
P(A or B) = [9 / 19] + [1 / 19] - [1 / 19]
Probability ball is an even numbered ball or a 4 [P(A or B)] = 9 / 19
A line with a slope of 5 passes through the point (2,10). What is its equation in slope intercept form
Answers
Answer:
The answer is
y = 5xStep-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question
Slope / m = 5
Equation of the line passing through point (2 , 10) is
y - 10 = 5(x - 2)
y - 10 = 5x - 10
y = 5x - 10 + 10
y = 5xHope this helps you
Which is the recommended method for reading your math textbook most effectively? a. read, question, summarize, practice b. highlight, skim, ask, and review c. preview, read, summarize, and review
Answers
Answer: a. read, question, summarize, practice
Step-by-step explanation:
This may be subjective, but the most efficient method usually is:
> Read:
Obviously the first step is read, if there is something that you do not understand, keep reading (but take note of all the things that you don't understand), is important that you have a complete overview on the topic that you are studying
> Question:
Now is time to ask about the things that you did not understand in the first read, always when you do not fully understand something, is a good habit to ask about it, this is the best and easiest way to learn.
> Summarize:
Now that you understand all the text (or at least most of it) is the moment to summarize your new knowledge: Write all the new equations that you learned, also write for what they are for, when they can be useful, etc.
This is what you will use to solve exercises, so you should be clear when writing.
> Practice:
This is one of the most important parts, here is where you put in practice your new knowledge. Here you may find some problematic situations where you need to be inventive with your equations, which will allow you to learn new ways to use your equations, so this is a really important step.
So the correct option is A.
Eight women and six men apply for a job at Google. Four of the applicants are selected for interviews. Let X denote the number of women in the interview pool. a) Give (explicitly) the probability mass function for X. Also describe a plot of F(x). b) Give (explicitly) the cdf, F(x), for X. Also show a plot of it. c) Determine the probability that more women are interviewed than men.
Answers
Answer:
See below
Step-by-step explanation:
images attached showing all working
a) The possible values of X are as follows
X = {0,1,2,3,4}
P(x) = P(X=x)
b) The cdf in this case, as in the F(x), comes out to be a step function graph on the basis of values obtained from the probability mass function.
c) To find out the probability when more women are interviewed than me, add together the matrices from when value of X is equal to 2, 3 and 4 (from part a).
Which correlation coefficient could represent the relationship in the scatterpot. Beach visitors
Answers
Answer:
A. 0.89.
Step-by-step explanation:
The value of correlation coefficient ranges from -1 to 1. Any value outside this range cannot possibly be correlation coefficient of a scatter plot representing relationship between two variables.
The scatter plot given shows a positive correlation between average daily temperatures and number of visitors, as the trend shows the two variables are moving in the same direction. As daily temperature increases, visitors also increases.
From the options given, the only plausible correlation that can represent this positive relationship is A. 0.89.
The height of an object dropped from the top of a 144-foot building is given by . How long will it take the object to hit the ground?
Answers
They left off the equation but we can know it's
y(t) = h₀ - g t² / 2
That's
y(t) = 144 - 16 t²
It hits the ground when
0 = 144 - 16 t²
16 t² = 144
t² = 144 / 16 = 9
t = 3 seconds
Answer: 3 seconds
Solve log x = 3. (2 points)
Answers
Answer:
x=1000
Step-by-step explanation:
log x = 3
log10 ( x) = 3
Raise each side to the power of 10
10^( log10 ( x)) =10 ^3
x = 10 ^3
x = 1000
Answer:
[tex]\boxed{x=1000}[/tex]
Step-by-step explanation:
[tex]log (x)= 3[/tex]
[tex]log_{10} (x)= 3[/tex]
Use logarithmetic definition:
[tex]log_a(b)=c[/tex]
[tex]b=a^c[/tex]
[tex]a=10\\b=x\\c=3[/tex]
Plug in the values.
[tex]x=10^3[/tex]
[tex]x=1000[/tex]
DIRECTIONS: Road the question and select the best respons
A right prism of height 15 cm has bases that are right triangles with legs 5 cm and 12 cm. Find the total
surface area of the prism,
OA 315 cm square
OB, 480 cm square
Oc. 510 cm square
OD. 570 cm square
Please explain how to get the answer
Answers
Answer:
C. 510 cm^2
Step-by-step explanation:
Well to find TSA or Total Surface Area,
We need to find the area of al the triangles and rectangles.
Let's start with the 2 rectangles facing forwards.
They both have dimensions of 5*15 and 12*15,
75 + 180
= 255 cm ^2
Now let's do the back rectangle which has dimensions of 15 and 13.
15*13 = 195 cm^2
Now we can do the top and bottom triangles,
Since we don't have height we can use the following formula,
[tex]A = \sqrt{S(S-a)(S-b)(S-c)}[/tex]
S is [tex]S = \frac{1}{2} (A+B+C)[/tex]
S= 15
Now with s we can plug that in,
[tex]A = \sqrt{15(15-5)(15-13)(15-12)}[/tex]
The a b and c are the sides of the triangle.
So let's solve,
15 - 5 = 10
15 - 13 = 2
15 - 12 = 3
10*2*3 = 60
60*15 = 900
[tex]\sqrt{900}[/tex] = 30 cm^2
Since there is 2 triangles with the same dimensions their areas combined is 60 cm^2
60 + 255 + 195 = 510 cm^2
Thus,
the TSA of the right triangular prism is C. 510 cm^2.
Hope this helps :)
Answer:
C) 510 square centimetres
Step-by-step explanation:
The surface area of a prism is given as:
A = bh * pL
where b = base length of the prism = 12 cm
h = base width = 5 cm
p = b + h + c
where c = slant height = 13 cm
L = height of the prism = 15 cm
Therefore, the surface area of the prism is:
A = (12 * 5) + (12 + 5 + 13) * 15
A = 60 + (30 * 15)
A = 60 + 450
A = 510 square centimetres
That is the surface area of the prism.
Efficiency is the ratio of output work to input work, expressed as a percentage. Light bulbs put out less light energy than the amount of electrical energy that is put into the bulb. An illustration of a wide arrow with a light bulb at the tail of it labeled electrical energy 100 J, breaks into a small arrow going forward labeled light 10 J and a larger curling away labeled heat 90 J. The goal of the bulb is to produce light. What is the efficiency of this bulb as it works to put out light? 10% 80% 90% 100%
Answers
Answer:
10%
Step-by-step explanation:
Using the given formula with the given data, we have ...
efficiency = output work / input work
= (10 J)/(100 J) = 0.10 = 10%
Answer:
A) 10%
Step-by-step explanation:
10/100=10
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice
the reciprocal of the larger is 11/15,
then find the two integers.
Answers
Answer:
Step-by-step explanation:
Let x represent the smaller integer.
Let y represent the larger integer.
A positive integer is 2 less than another. It means that
y = x + 2
If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 11/15, it means that
1/x + 2/y = 11/15- - - - - - - - - - 1
Substituting y = x + 2 into equation 1, it becomes
1/x + 2/(x + 2) = 11/15
Considering the left hand side of the equation, it becomes
(x + 2 + 2x)/x(x + 2)
Therefore,
(3x + 2)/(x² + 2x) = 11/15
Cross multiplying, it becomes
15(3x + 2) = 11(x² + 2x)
45x + 30 = 11x² + 22x
11x² + 22x - 45x - 30 = 0
11x² - 23x - 30 = 0
11x² + 10x - 33x - 30 = 0
x(11x + 10) - 3(11 + 10) =℅0
(x - 3)(11x + 10) = 0
x - 3 = 0 or 11x + 10 = 0
x = 3 or x = - 10/11
Since it us a positive integer, the smaller integer is 3 and the larger integer is 3 + 2 = 5
Answer: Let x represent the smaller integer.Let y represent the larger integer.A positive integer is 2 less than another. It means that y = x + 2 If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 11/15, it means that 1/x + 2/y = 11/15- - - - - - - - - - 1Substituting y = x + 2 into equation 1, it becomes 1/x + 2/(x + 2) = 11/15Considering the left hand side of the equation, it becomes(x + 2 + 2x)/x(x + 2) Therefore,(3x + 2)/(x² + 2x) = 11/15Cross multiplying, it becomes15(3x + 2) = 11(x² + 2x)45x + 30 = 11x² + 22x11x² + 22x - 45x - 30 = 011x² - 23x - 30 = 011x² + 10x - 33x - 30 = 0x(11x + 10) - 3(11 + 10) =℅0(x - 3)(11x + 10) = 0x - 3 = 0 or 11x + 10 = 0x = 3 or x = - 10/11Since it us a positive integer, the smaller integer is 3 and the larger integer is 3 + 2 = 5
Step-by-step explanation:
Click on the solution set below until the correct one is displayed.
Answers
Answer:
{ } or empty set.
Step-by-step explanation:
The solutions should be where the two lines intersect, but in this case, the parallel lines never intersect. That means that they have no solutions.
Hope this helps!
Answer:
{ } or empty set
Step-by-step explanation:
It's because these lines are parallel so they don't intersect to give you a coordinate.
is any answers loading for you guys or is it just me
Answers
Answer:
not just you
Step-by-step explanation:
Applications of exponential functions need help ASAP PlZ
Answers
Answer:
Second choice is correct.
Step-by-step explanation:
Simple interest = $12600
Compounded interest = $14656
Best Regards!
Antisocial personality disorder (ASPD) is characterized by deceitfulness, reckless disregard for the well-being of others, a diminished capacity for remorse, superficial charm, thrill seeking, and poor behavioral control. ASPD is not normally diagnosed in children or adolescents, but antisocial tendencies can sometimes be recognized in childhood or early adolescence. James Blair and his colleagues have studied the ability of children with antisocial tendencies to recognize facial expressions that depict sadness, happiness, anger, disgust, fear, and surprise. They have found that children with antisocial tendencies have selective impairments, with significantly more difficulty recognizing fearful and sad expressions.
Suppose you have a sample of 40 14-year-old children with antisocial tendencies and you are particularly interested in the emotion of surprise. The average 14-year-old has a score on the emotion recognition scale of 11.80. (The higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion). Assume that scores on the emotion recognition scale are normally distributed.
You believe that children with antisocial tendencies will have a harder time recognizing the emotion of surprise (in other words, they will have higher scores on the emotion recognition test).
What is your null hypothesis stated using symbols? ________
What is your alternative hypothesis stated using symbols? _________
This is a ____ tailed test. Given what you know, you will evaluate this hypothesis using a _______ statistic.
Using the Distributions tool, locate the critical region for a = 0.05.
Answers
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 11.80
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 11.80
Step-by-step explanation:
We are given that you have a sample of 40 14-year-old children with antisocial tendencies and you are particularly interested in the emotion of surprise. The average 14-year-old has a score on the emotion recognition scale of 11.80.
Assume that scores on the emotion recognition scale are normally distributed.
Let [tex]\mu[/tex] = true average score on the emotion recognition scale
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 11.80
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 11.80
This a right-tailed test because the higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion.
We can evaluate this hypothesis using One-sample t-test statistics or One-sample z-test statistics depends on the information given in the question.
If the z-test statistic is used, then the critical region at 0.05 level of significance will be an area more than the critical value of 1.645.
And if the t-test statistic is used, then the critical region at 0.05 level of significance with 39 degrees of freedom will be an area more than the critical value of 1.685.
The null hypothesis should be considered as the [tex]H_0: \mu = 11.80[/tex]
The alternative hypothesis should be considered as the [tex]H_A: \mu > 11.80[/tex]
It is the right-tailed test.
Calculation of the null hypothesis & alternative hypothesis:Since The average 14-year-old has a score on the emotion recognition scale of 11.80.
So here the null hypothesis should be [tex]H_0: \mu = 11.80[/tex]
And, here it is the right-tailed test since there should be higher the score on the given scale, due to this it should strongly an emotion that represent for rightly identified. Also high scores represent the high difficults for recording the emotion.
Learn more about hypothesis here: https://brainly.com/question/18831983
Find the vertical and horizontal asymptotes, domain, range, and roots of f (x) = -1 / x-3 +2.
Answers
Answer:
Vertical asymptote: [tex]x=3[/tex]
Horizontal asymptote: [tex]f(x) =2[/tex]
Domain of f(x) is all real numbers except 3.
Range of f(x) is all real numbers except 2.
Step-by-step explanation:
Given:
Function:
[tex]f (x) = -\dfrac{1 }{ x-3} +2[/tex]
One root, [tex]x = 3.5[/tex]
To find:
Vertical and horizontal asymptote, domain, range and roots of f(x).
Solution:
First of all, let us find the roots of f(x).
Roots of f(x) means the value of x where f(x) = 0
[tex]0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5[/tex]
One root, [tex]x = 3.5[/tex]
Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.
For x = 3, the value of f(x) [tex]\rightarrow \infty[/tex]
For all, other values of [tex]x[/tex] , [tex]f(x)[/tex] is defined.
Hence, Domain of f(x) is all real numbers except 3.
Range of f(x) i.e. the values that are possible output of the function.
f(x) = 2 is not possible in this case because something is subtracted from 2. That something is [tex]\frac{1}{x-3}[/tex].
Hence, Range of f(x) is all real numbers except 2.
Vertical Asymptote is the value of x, where value of f(x) [tex]\rightarrow \infty[/tex].
[tex]-\dfrac{1 }{ x-3} +2 \rightarrow \infty[/tex]
It is possible only when
[tex]x-3=0\\\Rightarrow x=3[/tex]
[tex]\therefore[/tex] vertical asymptote: [tex]x=3[/tex]
Horizontal Asymptote is the value of f(x) , where value of x [tex]\rightarrow \infty[/tex].
[tex]x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2[/tex]
[tex]\therefore[/tex] Horizontal asymptote: [tex]f(x) =2[/tex]
Please refer to the graph of given function as shown in the attached image.
A snake tank measures 1.8 m x 0.5 m x 0.5 m. What is the surface area of the tank including the top? Use the formula: SA = 2hl+2hw+2lw
Answers
Answer:
4.1
Step-by-step explanation:
1.8 x 0.5 = 0.9
0.5 x 0.5 = 0.25
2(0.9 + 0.9 + 0.25) = 2(1.8 + 0.25) = 2(2.05)
2 x 2.05 = 4.1
Therefore the answer is 4.1
I hope that was helpful!
what other numbers can you square that result in 9 ?
Answers
Step-by-step explanation:
I'm not sure what your answers are, but you can only square 3 and -3 to get 9.
Answer:
3, -3
Step-by-step explanation:
3*3 = 9
-3 * -3 = 9
These are the only two numbers that square to 9
A group of patients select from among 38 numbers, with 18 odd numbers (black) and 18 even
numbers (red), as well as 0 and 00 (which are green). If a doctor pays $7 that the outcome is an odd
number, the probability of losing the $7 is 20/38 and the probability of winning $14 (for a net gain of
only $7, given you already paid $7) is 18/38
If a doctor pays $7 that the outcome is an odd number, how would you figure out what is the doctors
expected value is?
Answers
Answer: $2.95
Step-by-step explanation:
Given: Probability of losing the $7 = [tex]\dfrac{20}{38}[/tex]
Probability of winning $14 = [tex]\dfrac{18}{38}[/tex]
Then, the expected value = (- $7) x ( Probability of losing the $7) + $14 x(Probability of winning $14)
= [tex](-\$ 7)\times\dfrac{20}{38}+(\$14)\times\dfrac{18}{38}[/tex]
= [tex]-\dfrac{70}{19}+\dfrac{126}{19}[/tex]
= [tex]\dfrac{56}{19}\times\approx\$2.95[/tex]
∴ If a doctor pays $7 that the outcome is an odd number, the doctor's
expected value is $2.95.
Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts.
Diet Regular
μ μ1 μ2
n 20 20
x 0.78062lb 0.81645 lb
s 0.00444 lb 0.00745 lb
A. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.
What are the null and alternative and hypotheses?
B. What is the test statistic? (Round to two decimal places as needed.)
C. What is the P-value? (Round to three decimal places as needed.)
State the conclusion for the test.
A. Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.
B. Fail to reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.
C. Fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.
D. Reject the null hypothesis. There is not sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.
b. Construct a confidence interval appropriate for the hypothesis test in part (a).
___lb < u1 - u2 < ___lb (Round to three decimal places as needed.)
Does the confidence interval support the conclusion found with the hypothesis test?
(No/Yes) because the confidence interval contains (zero/only positives values/ only negative values)
Answers
Answer:
(A) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1 \geq \mu_2[/tex]
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1<\mu_2[/tex]
(B) The value of t-test statistics is -18.48.
(C) The P-value is Less than 0.005%.
(D) Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.
Step-by-step explanation:
We are given that the Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right;
Diet Regular
μ μ1 μ2
n 20 20
x 0.78062lb 0.81645 lb
s 0.00444 lb 0.00745 lb
Let [tex]\mu_1[/tex] = mean weight of contents of cans of diet soda.
[tex]\mu_2[/tex] = mean weight of contents of cans of regular soda.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1 \geq \mu_2[/tex] {means that the contents of cans of diet soda have weights with a mean that is more than or equal to the mean for the regular soda}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1<\mu_2[/tex] {means that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda}
The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;
T.S. = [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1- \mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean weight of cans of diet soda = 0.78062 lb
[tex]\bar X_2[/tex] = sample mean weight of cans of regular soda = 0.81645 lb
[tex]s_1[/tex] = sample standard deviation of cans of diet soda = 0.00444 lb
[tex]s_2[/tex] = sample standard deviation of cans of regular soda = 0.00745 lb
[tex]n_1[/tex] = sample of cans of diet soda = 20
[tex]n_2[/tex] = sample of cans of diet soda = 20
Also, [tex]s_p =\sqrt{\frac{(n_1-1)s_1^{2}+ (n_2-1)s_2^{2}}{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(20-1)\times 0.00444^{2}+ (20-1)\times 0.00745^{2}}{20+20-2} }[/tex] = 0.00613
So, the test statistics = [tex]\frac{(0.78062-0.81645)-(0)}{0.00613 \times \sqrt{\frac{1}{20}+\frac{1}{20} } }[/tex] ~ [tex]t_3_8[/tex]
= -18.48
The value of t-test statistics is -18.48.
Also, the P-value of the test statistics is given by;
P-value = P( [tex]t_3_8[/tex] < -18.48) = Less than 0.005%
Now, at a 0.01 level of significance, the t table gives a critical value of -2.429 at 38 degrees of freedom for the left-tailed test.
Since the value of our test statistics is less than the critical value of t as -18.48 < -2.429, so we have sufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.
omplete)
HWS
X 3.3.13-BE
The manufacturer's suggested retail price (MSRP) for a particular car is $25,495, and it is expected to be worth $20,081 in 2 years.
(a) Find a linear depreciation function for this car.
(b) Estimate the value of the car 4 years from now.
(c) At what rate is the car depreciating?
(a) What is the linear depreciation function for this car?
f(x) =
(Simplify your answer. Do not include the $ symbol in your answer.)
Answers
Answer:
a) y = 25495 - 2707x
b) y = 25495 - 2707(4) = 14,667
c) $2,707 per year
Step-by-step explanation:
Value now: $25,495
Value in 2 years: $20,081
Loss of value in 2 years: $25,495 - $20,081 = $5,414
Loss of value per year: $5,414/2 = $2,707
a) y = 25495 - 2707x
b) y = 25495 - 2707(4) = 14,667
c) $2,707 per year
3x²-9x+1+0 Find the discriminant
Answers
Answer:
[tex]\boxed{D = 69}[/tex]
Step-by-step explanation:
The given quadratic equation is:
[tex]3x^2-9x+1 = 0[/tex]
Comparing it with the standard form of Quadratic Equation [tex]ax^2+bx+c = 0[/tex] , we get:
a = 3, b = -9 and c = 1
Discriminant = b² - 4ac
D = (-9)²-4(3)(1)
D = 81 - 12
D = 69
Please explain this to me If f(x)=4x-2 than f(x-1)= A. 4x^2-6x+2 B. 4x^2+2x+2 C. 4x+2 D. 4x-6 E. 4x-1
Answers
Answer:
D. 4x − 6
Step-by-step explanation:
f(x) = 4x − 2
f(x−1) = 4(x−1) − 2
f(x−1) = 4x − 4 − 2
f(x−1) = 4x − 6
Owen has enough materials to build up to 10 birdhouses in shop class. Each birdhouse needs 12 square feet of wood. The function W(b) = 12b represents the total amount of wood that Owen would need to build b birdhouses. What domain and range are reasonable for the function? A. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120 B. D: 0 ≤ b ≤ 120 R: 0 ≤ W(b) ≤ 10 C. D: 0 ≤ b ≤ 10 R: 12 ≤ W(b) ≤ 120 D. D: 10 ≤ b ≤ 12 R: 0 ≤ W(b) ≤ 120
Answers
Answer:
A. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120
Step-by-step explanation:
Since b represents the number of birdhouses, it is reasonable for that to have non-negative values. The maximum material availability means that b > 10 is not of practical use. This eliminates choices B and D.
Since W represents the amount of wood required for b birdhouses, it is reasonable for the range of it to match 12 times the domain: 12·0 = 0 to 12·10 = 120. This eliminates choice C.
The appropriate choice is ...
A. D: 0 ≤ b ≤ 10 R: 0 ≤ W(b) ≤ 120
PLEASE HELP Two prisms are composed to form a V shape. The thickness of each prism is 1 unit, and width of each prism is 2 units. If the length of one prism is greater than the length of the other prism by 1 unit and the total volume of the figure is 30 cubic units, what are the lengths of the prisms?
Answers
Answer:
7 units, 8 units
Step-by-step explanation:
Apparently, the cross section of each prism is a rectangle 1 unit by 2 units. Hence the total length will be ...
(30 units³)/((1 unit)(2 units)) = 15 units
Two numbers that differ by 1 and have a sum of 15 are 7 and 8.
The lengths of the prisms are 7 units and 8 units.
The ratio of boys to girls in Jamal's class is 3:2. If four more girls join the class, there will be the same number of boys and girls. What is the number of boys in the class?
Answers
Answer:
4 boys
Step-by-step explanation:
Let x represent boys and y represent girls
Hence, x : y = 3 : 2
x/y = 3/2
2x = 3y ------ (1)
x/y + 4 = 3/3
3x = 3(y + 4)
3x = 3y + 12 --------- (2)
From (1): x = 3y/2
Substitute x into (2) we have:
9y/2 = 3y + 12
9y = 6y + 24
9y - 6y = 24
3y = 24
∴ y = 8
From (2) : 3x = 24 - 12 = 12
∴ x = 4
Hence there Four boys
The length of a rectangle is 4yd longer than its width. If the perimeter of the rectangle is 36yd, find its area
Answers
Answer:
[tex] \boxed{\sf Area \ of \ the \ rectangle = 91 \ yd^{2}} [/tex]
Given:
Length of the rectangle = 4 yd longer than its width
Perimeter of the rectangle = 36 yd
To Find:
Area of the rectangle
Step-by-step explanation:
Let the width of the rectangle be 'w' yd
So,
Length of the rectangle = (w + 4) yd
[tex] \therefore \\ \sf \implies Perimeter \: of \: the \: rectangle = 2(Length + Width) \\ \\ \sf \implies 36 = 2((4 + w) + w) \\ \\ \sf \implies 36 = 2(4 + w + w) \\ \\ \sf \implies 36 = 2(4 + 2w) \\ \\ \sf 36 =2(2w+4) \: is \: equivalent \: to \: 2(2w + 4) = 36: \\ \sf \implies 2(2w + 4) = 36 \\ \\ \sf Divide \: both \: sides \: of \: 2 (2w + 4) = 36 \: by \: 2: \\ \sf \implies 2w + 4 = 18 \\ \\ \sf Subtract \: 4 \: from \: both \: sides: \\ \sf \implies 2w = 14 \\ \\ \sf Divide \: both \: sides \: of \: 2w = 14 \: by \: 2: \\ \sf \implies w = 7[/tex]
So,
Width of the rectangle = 7 yd
Length of the rectangle = (7 + 4) yd
= 13 yd
[tex] \therefore \\ \sf Area \ of \ the \ rectangle = Length \times Width \\ \\ \sf = 7 \times 13 \\ \\ \sf = 91 \: {yd}^{2} [/tex]
Construct the cumulative frequency distribution for the given data.
Age (years) of Best Actress when award was won Frequency
20-29 28
30-39 37
40-49 14
50-59 3
60-69 4
70-79 1
80-89 1
Age (years) of Best Actress when award was won Cumulative Frequency
Less than 30
Less than 40
Less than 50
Less than 60
Less than 70
Less than 80
Less than 90
Answers
Answer:
Age Frequency Cumulative Frequency
Less than 30 28 28
Less than 40 37 28 + 37 = 65
Less than 50 1 4 65 + 14 = 79
Less than 60 3 79 + 3 = 82
Less than 70 4 82 + 4 = 86
Less than 80 1 86 + 1 = 87
Less than 90 1 87 + 1 = 88
Step-by-step explanation:
Given:
The Frequency Distribution table of ages of best actresses when award was won
To find:
Construct the cumulative frequency distribution
Solution:
In order to construct cumulative frequency distribution for the given data, each frequency from above table is added to the sum of the previous frequencies. For example, frequency for Less than 40 is 37 and the previous frequency (less than 30) is 28 so in order to calculate cumulative frequency 28 i.e. previous frequency is added to 37 (frequency of less than 30) and the cumulative frequency is 65. The complete table is given above.
Please help! I got 14 but it says it's incorrect! Find the maximum number of real zeros of the polynomial. f(x)=2x^(6)-3x^(3)+1-2x^(5)
Answers
Answer:
There are two or zero positive solutions and zero negative roots (zeros).
Step-by-step explanation:
Use Descartes' Rule of Signs to determine the number of real zeros of [tex]f(x)=2x^6-3x^3+1-2x^5[/tex]
[tex]f(x)=2x^6-2x^5-3x^3+1\\[/tex]
Can you figure out the missing number in this sequence? Type your answer below!
88511,16351,?,10251
Answers
Answer:
731`55
Step-by-step explanation:
*Step-by-step explanation:*
The given sequence:
88511, 16351, ?, 10251
To find, the missing number (?) = ?
The pattern follow:
1. To Add the first 2 digits in the number .
2. Subtract digit 3 from Digit 2 .
3. The multiply digit 3 and 4 .
4. To divide digit 4 by 3.
16351 ⇒ 8 + 8 = 16, 8 - 5 = 3, 5 × 1 = 5 and \dfrac{1}{1} =111=1
= 16351
? ⇒ 1 + 6 = 7, 6 - 3 = 3, 3 × 5 = 15 and \dfrac{5}{1}15 = 5
= 73155
10251 ⇒ 7 + 3 = 10, 3 - 1 = 2, 1 × 5 = 5 and \dfrac{5}{5}55 = 1
= 10251
∴ The missing number of the given sequence = 73155
Thus, the missing number of the given sequence is 73155.
The third number in the sequence is : 73155
The given sequence is:
88511, 16351, ?, 10251
Now the pattern to find the missing value is:
Add, subtract, multiply and then divide.
These patterns are applied on the previous number's double digits to get the next number of the sequence.
Example:
Take 88511.
First pair (8,8): Add them: 16
Second pair (8,5): Subtract them: 8-5 = 3
Third pair: (5,1): Multiply them: 5
Fourth pair(1,1): Divide them: 1/1 = 1
Thus the next number of the sequence we get is 16351.
Similarly, doing it on 2nd term (16351) to find the missing third term:
Add (1,6): 7
Subtract (6,3): 3
Multiply (3,5): 15
Divide (5,1): 5
Thus the third number in the sequence is : 73155
Learn more here:
https://brainly.com/question/3000144