8 (y - 7) = - 16
Divide by 8 on both sides
y - 7 = - 2
Add 7 to both sides
y = 5
Answer:
y = 5
Step-by-step explanation:
8(y-7) = -16
Divide each side by 8
8(y-7)/8 = -16/8
y-7 = -2
Add 7 to each side
y -7+7 = -2+7
y = 5
Find the product of 0.032 and -1.9
Answer:
i think it's -0.0608
Step-by-step explanation:
is 4.1 or 4.009 greater
Answer:
Among 4.1 and 4.009 The greater one is 4.1
Hope it will help.
Dakota earned $4.50 in interest in Account A and $15 in interest in Account B after 18 months. If the simple interest rate is 3% for Account A and 4% for Account B, which account has the greater principal? Explain.
this is probably easy for most people but i need help ASAP
Answer:
Account B
Step-by-step explanation:
Hotel Rooms and Beyond: Error-and-erasure correction leveraging the CRT (58 pts) Note: for this entire problem, you can use properties of the Chinese Remainder Theorem that we discussed in lecture, notes, homework, and discussion without proof and without having to specify all the details. Alice is staying at a hotel and she wants to share her room number with Bob by leaving a sequence of notes in a list of pre-arranged locations.
i) There are only 100 possible hotel rooms, labeled 0 to 99.
ii) Alice takes her room number p and computes the remainders y; = p mod pi. The specific p; that she uses are pı = 3, p2 = 5,23 = 7,24 = 11, and ps = 13.
iii) She writes y, on the i-th note and places the note in location i. (Both Alice and Bob know which location corresponds to which numbers i and p.) This sequence of notes can be viewed as a codeword y(p). For example, if Alice is in room 51, she sends the codeword y(51)=(0,1,2,7,12) since 51 mod 3=0, 51 mod 5= 1, 51 mod 7=2, 51 mod 11 = 7, 51 mod 13= 12.
(a) Unfortunately, there is a chance that some of Alice's notes get blown away by the wind. Those missing notes will be treated as erasures and denoted by X It turns out that Alice is in room 51 as above, so she sends the codeword (0,1,2,7,12). Bob gets the received symbols (0,1,2,X,X). Explain how Bob can leverage the CRT to identify Alice's room number. (Alt + A)
(b) Generalizing the previous part, prove that in the case of up to two erasures anywhere, your scheme will always correctly identify the room number. For this part, feel free to just use the properties of the CRT along with the following facts. • Pi
Answer:
Step-by-step explanation:
From the information given we know that
[tex]p \equiv 0 \,\,\,\, \text{mod(3)}\\p \equiv 1 \,\,\,\, \text{mod(5)}\\p \equiv 2 \,\,\,\, \text{mod(7)}\\[/tex]
And we know as well that
[tex]p \equiv x \,\,\,\, \text{mod(11)}\\p \equiv x \,\,\,\, \text{mod(13)}[/tex]
Remember what that the Chinese reminder theorem states.
Theorem:
Let p,q be coprimes, then the system of equations
[tex]x \equiv a \,\,\,\, mod(p)\\x \equiv b \,\,\,\, mod(q)[/tex]
has a unique solution [tex]mod(pq)[/tex].
Now, if you read the proof of the theorem you will notice that if
[tex]q_1 = q^{-1} \,\, mod(p) , p_1 = p^{-1} \,\,mod(q)[/tex]
the the solution looks like this.
[tex]x = aqq_1 + bpp_1[/tex]
Now. you can easily generalize what I just stated for multiple equations and you will see that if you apply the theorem for this case it is straightforward that
[tex]p \equiv 0*35*[35^{-1}]_3+1*21*[21^{-1}]_5+2*15[15^{-1}]_7 \,\,\,\,\,\,\,\, mod(3*5*7)\\p \equiv 1*21*1+2*15*1 \,\,\,\,\,\,\,\,mod(105) \\p \equiv 1*21*1+2*15*1 \,\,\,\,\,\,\,\, \\p \equiv 51[/tex]
Therefore, Alice is in room 51.
(b)
Using the Chinese reminder theorem you need less than 2 erasures. The process is very similar.
Answer:
Step-by-step explanation:
From the information given we know that
And we know as well that
Remember what that the Chinese reminder theorem states.
Theorem:
Let p,q be coprimes, then the system of equations
has a unique solution .
Now, if you read the proof of the theorem you will notice that if
the the solution looks like this.
Now. you can easily generalize what I just stated for multiple equations and you will see that if you apply the theorem for this case it is straightforward that
Therefore, Alice is in room 51.
(b)
Using the Chinese reminder theorem you need less than 2 erasures. The process is very similar.
Step-by-step explanation:
An item originally priced at $55 is marked 25% off. What is the sale price?
Answer:
41.25$
Step-by-step explanation:
Answer:
41.25
Step-by-step explanation:
55/4=13.75
So 13.75 is 25% of 55
So then you would do 55-13.75
Because that is 25% off
The final answer would be $41.25 for the sale price.
You are the engineer in charge of evaluating a new product for potential use in a hydraulic system. The manufacturer has sent 100 randomly chosen samples for you to test. You plan to go through with the deal as long as you can prove that less than 8% of the products you subsequently purchase will be defective. The engineering and business teams at your company believe a 90% confidence level is appropriate for the test.
(a) Specify the null and alternative hypotheses for your test.
(b) Describe (in words) a Type I error for this deal.
(c) Out of the 100 samples provided by the manufacturer, at most how many can be defective for you to agree to use the new product?
(d) For better or worse, your boss convinces you to go through with the deal. Turns out the minimum order is 5000 pieces. Assuming you purchase that many pieces of the new product, and that you found 6 defective pieces out of the 100, generate a 90% two-sided confidence interval for the number of pieces that will be flawed.
Answer:
a) The null hypothesis is represented as
H₀: p ≥ 0.08
The alternative hypothesis is represented as
Hₐ: p < 0.08
b) A type I error for this question would be that
we conclude that the proportion of defective products is less than 8% when in reality, the proportion of defective products, is more than or equal to 8%.
c) At most, the number of defective products in the sample for you to agree to use the new product = 7
d) If minimum of 5000 pieces are purchased, 90% confidence interval for minimum number of flawed pieces will be (103, 497)
Step-by-step explanation:
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and is usually stating the opposite of the theory is being tested. It usually maintains that random chance is responsible for the outcome or results of any experimental study/hypothesis testing. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis takes the other side of the hypothesis; that there is indeed a significant difference between two proportions being compared. It usually confirms the the theory being tested by the experimental setup. It usually maintains that other than random chance, there are significant factors affecting the outcome or results of the experimental study/hypothesis testing. It usually contains the signs ≠, < and > depending on the directions of the test
For this question, we want to prove that less than 8% of the products we subsequently purchase will be defective.
So, the null hypothesis will be that there is not enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective. That is, the proportion of the sample that are defective is more than or equal to 8%.
And the alternative hypothesis is that there is enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective.
Mathematically,
The null hypothesis is represented as
H₀: p ≥ 0.08
The alternative hypothesis is represented as
Hₐ: p < 0.08
b) A type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true. It involves saying that there is enough evidence in the sample to say that less than 8% of the products we subsequently purchase will be defective when in reality, there isn't enough evidence to arrive at this conclusion.
That is, the proportion of defective products in reality, is more than or equal to 8% and we have concluded that the proportion is less than 8%.
c) Out of the 100 samples provided by the manufacturer, at most how many can be defective for you to agree to use the new product?
The engineer agrees to use the new product when less than 8% of the products we subsequently purchase will be defective.
8% of the product = 0.08 × 100 = 8.
Meaning that the engineer agrees to subsequently purchase the product if less than 8 out of 100 are defective.
So, the maximum number of defective product in the sample that will still let the engineer purchase the products will be 7.
(d) For better or worse, your boss convinces you to go through with the deal. Turns out the minimum order is 5000 pieces. Assuming you purchase that many pieces of the new product, and that you found 6 defective pieces out of the 100, generate a 90% two-sided confidence interval for the number of pieces that will be flawed.
Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample proportion) ± (Margin of error)
Sample proportion = 0.495
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error)
Critical value at 90% confidence interval for sample size of 100 using the t-tables since information on the population standard deviation.
Degree of freedom = n - 1 = 100 - 1 = 99
Significance level = (100-90)/2 = 5% = 0.05
Critical value = t(0.05, 99) = 1.660
Standard error of the mean = σₓ = √[p(1-p)/n]
p = 0.06
n = sample size = 100
σₓ = (0.06/√100) = 0.006
σₓ = √[0.06(0.94)/100] = 0.0237486842 = 0.02375
90% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]
CI = 0.06 ± (1.660 × 0.02375)
CI = 0.06 ± 0.039425
90% CI = (0.020575, 0.099425)
90% Confidence interval = (0.0206, 0.0994)
If minimum of 5000 pieces are purchased, 90% confidence interval for minimum number of flawed pieces will be
5000 × (0.0206, 0.0994) = (103, 497)
Hope this Helps!!!
(a) The null hypothesis [tex]\(H_0\)[/tex] is that the proportion of defective products is 8% or less (b) A Type I error occurs when the null hypothesis is true (the actual proportion of defective products is 8% or less), but we incorrectly reject it (c) at most 12 defective products can be found in the sample for the deal to proceed. (d) the 90% two-sided confidence interval for the number of defective pieces in the order of 5000 is from 105 to 496.
(a) The null hypothesis [tex]\(H_0\)[/tex] is that the proportion of defective products is 8% or less. The alternative hypothesis [tex]\(H_1\)[/tex] is that the proportion of defective products is greater than 8%. Mathematically, this can be expressed as:
[tex]\(H_0: p \leq 0.08\) \(H_1: p > 0.08\)[/tex]
(b) A Type I error occurs when the null hypothesis is true (the actual proportion of defective products is 8% or less), but we incorrectly reject it, concluding that the proportion of defective products is greater than 8%. This would mean unnecessarily turning down a good deal and potentially incurring additional costs to find another supplier.
(c) To ensure a 90% confidence level with a maximum defective rate of 8%, we can use the binomial distribution to find the maximum number of defective products allowed in the sample of 100. The formula for a binomial confidence interval is given by:
[tex]\(n \cdot p \pm Z_{\alpha/2} \sqrt{n \cdot p \cdot (1 - p)}\)[/tex]
where [tex]\(n\)[/tex] is the sample size, [tex]\(p\)[/tex] is the defect rate, and [tex]\(Z_{\alpha/2}\)[/tex] is the Z-score corresponding to the desired confidence level. For a 90% confidence level, [tex]\(Z_{\alpha/2} = 1.645\)[/tex]. Plugging in the values:
[tex]\(100 \cdot 0.08 \pm 1.645 \sqrt{100 \cdot 0.08 \cdot (1 - 0.08)}\)[/tex]
[tex]\(8 \pm 1.645 \sqrt{100 \cdot 0.08 \cdot 0.92}\)[/tex]
[tex]\(8 \pm 1.645 \sqrt{7.36}\)[/tex]
[tex]\(8 \pm 1.645 \cdot 2.713\)[/tex]
[tex]\(8 \pm 4.46\)[/tex]
The interval is from [tex]\(8 - 4.46\) to \(8 + 4.46\)[/tex], which gives us a range from approximately 3.54 to 12.46. Since we cannot have a fraction of a defective product, we round down to 3. Therefore, at most 12 defective products can be found in the sample for the deal to proceed.
(d) To generate a 90% two-sided confidence interval for the number of defective pieces out of 5000, given that 6 defective pieces were found out of 100, we first calculate the sample proportion of defective products:
[tex]\(\hat{p} = \frac{6}{100} = 0.06\)[/tex]
The formula for the confidence interval is:
[tex]\(\hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}\)[/tex]
where [tex]\(n\)[/tex] is the sample size (100 in this case), and [tex]\(Z_{\alpha/2}\)[/tex] is the Z-score for a 90% confidence level (1.645). Plugging in the values:
[tex]\(0.06 \pm 1.645 \sqrt{\frac{0.06(1 - 0.06)}{100}}\)[/tex]
[tex]\(0.06 \pm 1.645 \sqrt{\frac{0.06 \cdot 0.94}{100}}\)[/tex]
[tex]\(0.06 \pm 1.645 \sqrt{\frac{0.0564}{100}}\)[/tex]
[tex]\(0.06 \pm 1.645 \cdot \sqrt{0.000564}\)[/tex]
[tex]\(0.06 \pm 1.645 \cdot 0.0237\)[/tex]
[tex]\(0.06 \pm 0.0391\)[/tex]
The interval is from [tex]\(0.06 - 0.0391\) to \(0.06 + 0.0391\)[/tex], which gives us a range from approximately 0.0209 to 0.0991. To find the number of defective pieces in the order of 5000, we multiply these proportions by 5000:
Lower bound: [tex]\(0.0209 \cdot 5000 = 104.5\)[/tex](round to 105)
Upper bound: [tex]\(0.0991 \cdot 5000 = 495.5\)[/tex] (round to 496)
Therefore, the 90% two-sided confidence interval for the number of defective pieces in the order of 5000 is from 105 to 496.
how much water does it take to completely fill a pool that is 50m long 25m wide and 2.5m deep
Answer:
[tex]3,125[/tex]
Step-by-step explanation:
If you want to fill a pool, you will use the formula for finding the volume:
[tex]v=l*w*h[/tex]
In this case, height being depth:
[tex]v=l*w*d[/tex]
Insert values
[tex]v=50*25*2.5[/tex]
Simplify
[tex]v=1,250*2.5\\v=3,125[/tex]
You would need a lot of water.
Answer:
3125000 liter
Step-by-step explanation:
hope i helped
if i can be brainliest that would be great
1/4 divided by 7/16 give an example of real world situation that might involve this expression
Answer:
Step-by-step explanation:
if you have 1/4 of a rope and you need to give 7/16 to your friend how much rope did you give to your friend?
Final answer:
Divide 1/4 by the reciprocal of 7/16 to get 4/7. A real-world example is when needing ¼ cup of sugar with only a 7/16 cup measure, fill it approximately 4/7 full to obtain the needed amount of sugar.
Explanation:
To calculate 1/4 divided by 7/16, you would multiply 1/4 by the reciprocal of 7/16, which is 16/7. This would give you (1/4) * (16/7) = 16/28, which can be simplified to 4/7 after dividing both numerator and denominator by 4. A real-world situation involving this expression could be as follows: Imagine you have a recipe that requires 1/4 of a cup of sugar, but you only have a measuring cup that measures 7/16 of a cup.
To find out how many times you need to fill the 7/16 cup to get the 1/4 cup needed, you would calculate 1/4 divided by 7/16, which will give you 4/7. So, you would fill the 7/16 measuring cup approximately 4/7 of the way full to have 1/4 cup of sugar for your recipe.
The face of a clock is divided into 12 equal parts. The radius of the clock face is 6 inches. Assume the hands of the clock will form a central angle. Which statements about the clock are accurate? Check all that apply.
Step-by-step explanation:
Given, the face of a clock is divided into 12 equal parts.
Angle of each part = [tex]\frac{360}{12}[/tex] = 30°
(i) When one hand points at 2 and the other points at 4, this is can be divided into two parts, 2 to 3 and 3 to 4.
The angle formed = 2 (30) = 60°
Option (i) is correct
(ii) The circumference of the clock is ,
Circumference of circle = 2πr,
where r is the radius = 6 and π = 3.14.
Substituting the values in the formula, we get
Circumference of circle = 37.68.
Option (ii) is wrong.
(iii) With one hand at 5 and the other at 10, this is 5 parts
The angle formed= 30(5) = 150°.
The arc length =[tex]\frac{150}{360}[/tex](37.68) = 15.7
Option (iii) is correct
(iv) When one hand points at 1 and the other points at 9, this is 4 parts,
30(4) = 120°. T
Option (iv) is wrong
(v) The length of the minor arc from 11 to 2, this is 3 parts
3(30) = 90°
minor arc from 7 to 10 is 3(30) = 90°
Option (v) is correct
Answer: options 1,3,5
Consider the polynomial p(s) = s2 + bs + c where b and c are real numbers. Show that all the roots of p(s) are both contained in the open left half plane {s : s < 0} if and only if b > 0 and c > 0. Hint: use the quadratic formula.
Answer:
It is shown in the explanation
Step-by-step explanation:
p(s) = s² + bs + c
a = 1
b = b
c = c
We get Δ as follows
Δ = (b²-4*a*c) = b² - 4*1*c = b² - 4c > 0 ⇒ b² > 4c ⇔ c > 0
s = (-b + √(b² - 4c))/2(1)
⇒ s₁ = (-b + √(b² - 4c))/2
s₂ = (-b - √(b² - 4c))/2(1)
⇒ s₂ = (-b - √(b² - 4c))/2
We have that -b < 0 ⇔ b > 0
then s₁ < 0 and s₂ < 0 ⇔ c > 0 and b > 0
Answer:
For roots to lie on the left half plane, b ⊃ 0 and c ⊃0
Step-by-step explanation:
From quadratic formula, we have;
x = -b±√(b²-4ac)/2a
From the given expression p(s) = s² + bs + c,
x = s
a = 1
b = b
c = c
The quadratic formula can then be written as;
s = -b±√(b²-4*1*c)/2*1
= -b±√(b²-4c)/2
s₁ = -b+√(b²-4c)/2
s₂ = -b±√(b²-4c)/2
From the equation above,
Sum of root = -b
Product of root = c
If both the root lie on left side of the s-plane, then sum of roots will be negative. Hence, -b ∠0. That is, b ⊃0
Also, the product root will be positive, c ⊃ 0
Hence, for roots to lie on the left half plane, b ⊃ 0 and c ⊃0
Solve the system of linear equations by graphing.
y=−2x+2
y=−x−1
Answer:
(3; - 4)
Step-by-step explanation:
Blue: y = -x - 1
Red: y = -2x + 2
The given system of linear equations have solution as x = 3 and y = -4.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
The system of equations are given as,
y =−2x + 2 (1)
y = −x − 1 (2)
The above equations are linear equation in two variables.
Their graph are straight lines which shows their intersection at point (3, -4).
Hence, the solution of the given system of linear equations is x = 3 and y = -4.
To know more about straight line equation click on,
brainly.com/question/21627259
#SPJ2
Convert 4π/3 radians to degrees.
135°
180°
60°
240°
Answer:
240°
Step-by-step explanation:
[tex] \frac{4\pi^{c} }{3} = \frac{4 \times 180 \degree}{3} = 4 \times 60 \degree = 240 \degree \\ [/tex]
3=9-y solve for variable
Answer:
y=6
Step-by-step explanation:
3=9-y
y+3=9
y=6
Answer:
y=6
Step-by-step explanation:
3=9-y
3-9 = -y
-6 = -y
y=6
The area of a rectangle is 100cm2. After a dilation, the area is 25cm2. What is the scale factor?
Answer:
The scale factor is 1/2
Step-by-step explanation:
we know that
A dilation is a non rigid transformation that produces similar figures
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ---> the scale factor
x ---> the area after dilation
y ---> the original area
[tex]z^2=\frac{x}{y}[/tex]
we have
[tex]x=25\ cm^2\\y=100\ cm^2[/tex]
substitute
[tex]z^2=\frac{25}{100}[/tex]
[tex]z^2=\frac{1}{4}[/tex]
[tex]z=\frac{1}{2}[/tex]
Triangle PQR is reflected over the line y = x.
What is the coordinate of the image point R'?
R (2,4)
R (2, -4)
R(-2,4)
Answer:
-2,4
Step-by-step explanation:
i just did it
Answer:
-2,4
Step-by-step explanation:
i just did it on ed 2020
The maintenance department at the main campus of a large state university receives daily requests to replace fluorecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 63 and a standard deviation of 10. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 63 and 83
Answer:
47.5% of lightbulb replacement requests numbering between 63 and 83
Step-by-step explanation:
The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 63
Standard deviation = 10
What is the approximate percentage of lightbulb replacement requests numbering between 63 and 83
63 is the mean
83 = 63 + 2*20
So 83 is two standard deviations above the mean.
The normal distribution is symmetric, so 50% of the measures are above the mean and 50% below the mean.
Of those above the mean, 95% are within 2 standard deviations of the mean.
So
0.5*95% = 47.5%
47.5% of lightbulb replacement requests numbering between 63 and 83
Three forces act on a hook. Determine the magnitude of the resultant of the force.
Use Hooke's law... (just kidding)
Break down each force vector into horizontal and vertical components.
[tex]\vec F_1=(1000\,\mathrm N)(\cos30^\circ\,\vec x+\sin30^\circ\,\vec y)\approx(866.025\,\mathrm N)\,\vec x+(500\,\mathrm N)\,\vec y[/tex]
[tex]\vec F_2=(1500\,\mathrm N)(\cos160^\circ\,\vec x+\sin160^\circ\,\vec y)\approx(-1409.54\,\mathrm N)\,\vec x+(513.03\,\mathrm N)\,\vec y[/tex]
[tex]\vec F_3=(750\,\mathrm N)(\cos195^\circ\,\vec x+\sin195^\circ\,\vec y)\approx(-724.444\,\mathrm N)\,\vec x+(-194.114\,\mathrm N)\,\vec y[/tex]
The resultant force is the sum of these vectors,
[tex]\vec F=\displaystyle\sum_{i=1}^3\vec F_i\approx(-1267.96\,\mathrm N)\,\vec x+(818.916\,\mathrm N)\,\vec y[/tex]
and has magnitude
[tex]|\vec F|\approx\sqrt{(-1267.96\,\mathrm N)^2+(818.916\,\mathrm N)^2}\approx1509.42\,\mathrm N[/tex]
The closest answer is D.
To determine the magnitude of the resultant force acting on a hook when three forces are applied, you can use vector addition. If you have the information of the forces and the angles between them, you can calculate the resultant force using trigonometric functions.
Explanation:To determine the magnitude of the resultant force when three forces act on a hook, you must realize that forces are vector quantities. This means that they have both a magnitude (how much force is being applied) and a direction (the direction the force is being applied in).
If the forces are concurrent (i.e., they act at the same point), one usually uses the parallelogram law or the triangle rule to find the resultant force. You can add two forces to create a resultant, then add the third force to that resultant to find the total resultant. If the forces and the angles between them are known, you can use trigonometric functions to calculate the resultant force.
For instance, if the three forces are F1, F2, and F3, and the angles between them are θ1, θ2, and θ3, the resultant force R can be found using the following equation:
R = √[ (F1 + F2cosθ2 + F3cosθ3)^2 + (F2sinθ2 + F3sinθ3)^2 ]
This equation will give the magnitude of the resultant force. Please note that to use this equation, you must have enough information about the forces and the angles between them.
Learn more about Resultant Force here:https://brainly.com/question/37085280
#SPJ3
What is your favorite color? A larger survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color. Suppose a random sample of n = 75 college students were surveyed and x = 19 of them said that blue is their favorite color. Does this information imply that the proportion of college students who prefer blue differs from that of the general population? Use ???? = 0.05.
Answer:
[tex]z=\frac{0.253 -0.24}{\sqrt{\frac{0.24(1-0.24)}{75}}}=0.264[/tex]
[tex]p_v =2*P(z>0.264)=0.792[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of students said that blue is their favorite color is not different from 0.24
Step-by-step explanation:
Data given and notation
n=75 represent the random sample taken
X=19 represent the students said that blue is their favorite color
[tex]\hat p=\frac{19}{75}=0.253[/tex] estimated proportion of students said that blue is their favorite color
[tex]p_o=0.24[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is different from 0.24.:
Null hypothesis:[tex]p=0.24[/tex]
Alternative hypothesis:[tex]p \neq 0.24[/tex]
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.253 -0.24}{\sqrt{\frac{0.24(1-0.24)}{75}}}=0.264[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z>0.264)=0.792[/tex]
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of students said that blue is their favorite color is not different from 0.24
Answer:
0.792
Step-by-step explanation:
Function g can be thought of as a translated (shifted) version of f(x) = x2.
܂
ܗ ܕ
ܛ ܚ
. ܝ
-7 -6 -5 -4 -4 -2
+
1
2 3
4
5
6
7
+
ܟ ܟ
ܟ ܟ
+
ܕ ܬ
+
ܞ ܕ
+
܂
Write the equation for g(2).
Given:
The given parent function is [tex]f(x)=x^2[/tex]
We need to determine the equation of the new translated (shifted) function g(x).
Vertical stretch:
The general rule to shift the graph f(x), to shift c units upward is [tex]g(x)=f(x)+c[/tex]
From the graph, it is obvious that the graph f(x) is shifted 1 unit upwards.
Thus, applying the above rule, we get;
[tex]g(x)=x^2+1[/tex]
Horizontal stretch:
The general rule to shift the graph f(x) to shift c units to the left is [tex]g(x)=f(x+c)[/tex]
From, the graph, it is obvious that the graph f(x) is shifted 2 units to the left.
Thus, applying the above rule, we have;
[tex]g(x)=(x+2)^2[/tex]
Equation of the new function g(x):
From the figure, it is obvious that the graph g(x) is shifted 1 unit upwards and 2 units to the left.
Thus, we have;
[tex]g(x)=(x+2)^2+1[/tex]
Therefore, the equation of the new function g(x) is [tex]g(x)=(x+2)^2+1[/tex]
Jennifer ran 356 m more than Tyler. Tyler ran a distance of 2 km 30 m how many total meters did Tyler and Jennifer Run
Answer:
Tyler ran 2030 meters. Jennifer ran 2386. Together they ran 4416 meters.
Step-by-step explanation:
Turn the km to m then add them together to get Tyler's distance. From Tyler's distance add what Jennifer ran more of to Tyler's to get Jennifer's distance. Then add together what they ran to get the total amount of meters they ran.
Answer:586
Step-by-step explanation:
What is the relationship between x and y
Given:
Given that the table with values of x and y.
We need to determine the relationship between x and y.
Slope:
The slope of the relation can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the points (2,11) and (4,9), we get;
[tex]m=\frac{9-11}{4-2}[/tex]
[tex]m=\frac{-2}{2}[/tex]
[tex]m=-1[/tex]
Thus, the slope of the relation is m = -1.
y - intercept:
The y - intercept of the relation is the value of y when x = 0.
Hence, from the table, it is obvious that when x = 0, the value of y is 13.
Thus, the y - intercept of the relation is b = 13.
Relationship between x and y:
The relationship between x and y can be determined using the formula,
[tex]y=mx+b[/tex]
Substituting m = -1 and y =13, we get;
[tex]y=-x+13[/tex]
Thus, the relationship between x and y is [tex]y=-x+13[/tex]
An exponential distribution is formed by the time it takes for a person to choose a birthday gift. The average time it takes for a person to choose a birthday gift is 41 minutes. Given that it has already taken 24 minutes for a person to choose a birthday gift,what is the probability that it will take more than an additional 34 minutes
Answer:
43.62% probability that it will take more than an additional 34 minutes
Step-by-step explanation:
To solve this question, we need to understand the exponential distribution and the conditional probability formula.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Conditional probability formula:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Taking more than 24 minutes.
Event B: Taking ore than 24+34 = 58 minutes.
P(A)
More than 24, use the exponential distribution.
Mean of 41, so [tex]m = 41, \mu = \frac{1}{41} = 0.0244[/tex]
[tex]P(A) = P(X > 24) = e^{-0.0244*24} = 0.5568[/tex]
Intersection:
More than 24 and more than 58, the intersection is more than 58. So
[tex]P(A \cap B) = P(X > 58) = e^{-0.0244*58} = 0.2429[/tex]
Then:
[tex]P(B|A) = \frac{0.2429}{0.5568} = 0.4362[/tex]
43.62% probability that it will take more than an additional 34 minutes
The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function
f(x)= -3.357x4 + 35.171x3 - 99.868x2 + 41.098x + 177.252
where x is the number of years since 1996. Find the number of bald eagles in the state in the winter of 2001,
Answer:
f(2x+1)sin(9[tex]F(2x+1)sin(90.9292)\pi[/tex]- 4.3784)
Step-by-step explanation:
The number of bald eagles is 26.
12x+7<-11 and 5x-8>= 40
Answer:
no solution
Step-by-step explanation:
First inequality:
12x < -18 . . . . subtract 7
x < -18/12 . . . divide by 12
x < -1.5 . . . . . . write as decimal
__
Second inequality:
5x -8 ≥ 40
5x ≥ 48 . . . . . . add 8
x ≥ 9.6 . . . . . . . divide by 5
__
There are no solutions to this pair of inequalities. No value of x can be both less than -1.5 and greater than 9.6.
Leo's family keeps recyclables in a cylindrical trash can. Today Leo bought a larger can with a radius and height that are twice the radius and
height of the old can. Leo claims the new and old cans are geometrically similar figures.
Which statement is true?
A. The two cans are similar figures, and the volume of the new can is 2 times the volume of the old can.
B. The two cans are similar figures, and the volume of the new can is 8 times the volume of the old can.
C. The two cans are not similar figures, and the volume of the new can is 2 times the volume of the old can.
D. The two cans are not similar figures, and the volume of the new can is 8 times the volume of the old can.
E. The two cans are similar figures, and the volume of the new can is 4 times the volume of the old can.
Answer:
The answer is B
Step-by-step explanation:
the question states that they are similar, so B is automatically an option. It's 8 times because the radius and height are being doubled. Logically there are more factors to be A and E.
B. The two cans are similar figures, and the volume of the new can is 8 times the volume of the old can.
16 < b - 8, if b = 22
Answer:
False
Step-by-step explanation:
Substitute 22 in for b
16 < b - 8
16 < 22 - 8
16 < 14
False, 14 is not greater than 16
The solution:
16 < b - 8
Add 8 to both sides
24 < b
"Tongue Piercing May Speed Tooth Loss, Researchers Say" is the headline of an article. The article describes a study of 51 young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 19 of the participants. (a) Construct a 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums. (Round your answers to three decimal places.) ( .138 Incorrect: Your answer is incorrect. , .503 Incorrect: Your answer is incorrect. )
Answer:
The 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums is (0.24, 0.506).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 51, \pi = \frac{19}{51} = 0.373[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.373 - 1.96\sqrt{\frac{0.373*0.627}{51}} = 0.24[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.373 + 1.96\sqrt{\frac{0.373*0.627}{51}} = 0.506[/tex]
The 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums is (0.24, 0.506).
If m∠A = 87° and m∠B = 32°, find m∠1.
Answer:
61 degrees
Step-by-step explanation:
87+32=119
180 (total degrees for triangle)-119=67 degrees
HELPPP ASAPP PLZZ:) Question and answers are in the image.
Answer:
C. all real numbers except 3/4
Step-by-step explanation:
f(x) and g(x) are both defined for all real numbers. However, the ratio f/g will be undefined where g(x) = 0. That occurs when ...
4x -3 = 0
4x = 3 . . . . . add 3
x = 3/4 . . . . . divide by 4
The value of x = 3/4 makes f/g undefined, so must be excluded from the domain.
The following gambling game has been proposed, which a player must pay to play. First, a value U is chosen uniformly from the set [0, 10]. Next, a number is chosen according to a Poisson random variable with a parameter U. Letting X be the number chosen, the player receives $X. Find E[X], which is the amount a player should pay to make this a fair game HINT: Use the Law of Total Probability for Expectations, E[X]
Answer:
The player should be required to pay $5 to make this a fair game.
Step-by-step explanation:
U ~ Uniform(0, 10)
E[U] = (0 + 10)/2
= 5
X | U ~ Poisson(U)
E[X | U] = U
By law of total probability for expectations,
E[X] = E[E[X|U]] = E[U] = $5
Therefore the player should be required to pay $5 to make this a fair game.