Answer:
a [tex]\mathbf{P(X=3)=0.1406}[/tex]
b [tex]\mathbf{\[P\left( {X = 3 \ or \ 4 } \right) = 0.1025}[/tex]
c [tex]\mathbf{\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = 0.1035}[/tex]
Step-by-step explanation:
Given that:
In a multiple choice quiz:
there are 5 questions
and 4 choices for each question (a, b, c, d)
let X be the correctly answered question = 1 answer only
and Y be the choices for each question = 4 choices
The probability that Robin guessed the correct answer is:
Probability = n(X)/n(Y)
Probability = 1//4
Probability = 0.25
The probability mass function is :
[tex]P(X=x)=0.25 (1-0.25)^{x-1}[/tex]
We are to find the required probability that the first question she gets right is the 3rd question.
i.e when x = 3
[tex]P(X=3)=0.25 (1-0.25)^{3-1}[/tex]
[tex]P(X=3)=0.25 (0.75)^{2}[/tex]
[tex]\mathbf{P(X=3)=0.1406}[/tex]
b) Find the probability that She gets exactly 3 or exactly 4 questions right
we know that :
n = 5 questions
Probability P =0.25
Let represent X to be the number of questions guessed correctly i,e 3 or 4
Then; the probability mass function can be written as:
[tex]\[P\left( {X = x} \right) = \left( {\begin{array}{*{20}{c}}\\5\\\\x\\\end{array}} \right){\left( {0.25} \right)^x}{\left( {1 - 0.25} \right)^{5 - x}}\][/tex]
[tex]P(X = 3 \ or \ 4)= P(X =3) +P(X =4)[/tex]
[tex]\[P\left( {X = 3 \ or \ 4 } \right) = \left( {\begin{array}{*{20}{c}}\\5\\\\3\\\end{array}} \right){\left( {0.25} \right)^3}{\left( {1 - 0.25} \right)^{5 - 3}}\] + \left( {\begin{array}{*{20}{c}}\\5\\\\4\\\end{array}} \right){\left( {0.25} \right)^4}{\left( {1 - 0.25} \right)^{5 - 4}}\][/tex]
[tex]\[P\left( {X = 3 \ or \ 4 } \right) = \dfrac{5!}{3!(5-3)!}\right){\left( {0.25} \right)^3}{\left( {1 - 0.25} \right)^{5 - 3}}\] + \dfrac{5!}{4!(5-4)!} \right){\left( {0.25} \right)^4}{\left( {1 - 0.25} \right)^{5 - 4}}\][/tex]
[tex]\[P\left( {X = 3 \ or \ 4 } \right) = \dfrac{5!}{3!(2)!}\right){\left( {0.25} \right)^3}{\left( {0.75} \right)^{2}}\] + \dfrac{5!}{4!(1)!} \right){\left( {0.25} \right)^4}{\left( {0.75} \right)^{1}}\][/tex]
[tex]\[P\left( {X = 3 \ or \ 4 } \right) = 0.0879+0.0146[/tex]
[tex]\mathbf{\[P\left( {X = 3 \ or \ 4 } \right) = 0.1025}[/tex]
c) Find the probability if She gets the majority of the questions right.
We know that the probability mass function is :
[tex]\[P\left( {X = x} \right) = \left( {\begin{array}{*{20}{c}}\\5\\\\x\\\end{array}} \right){\left( {0.25} \right)^x}{\left( {1 - 0.25} \right)^{5 - x}}\][/tex]
So; of She gets majority of her answers right ; we have:
The required probability is,
[tex]P(X>2) = P(X=3) +P(X=4) + P(X=5)[/tex]
∴
[tex]\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = \left( {\begin{array}{*{20}{c}}\\5\\\\3\\\end{array}} \right){\left( {0.25} \right)^3}{\left( {1 - 0.25} \right)^{5 - 3}}\] + \left( {\begin{array}{*{20}{c}}\\5\\\\4\\\end{array}} \right){\left( {0.25} \right)^4}{\left( {1 - 0.25} \right)^{5 - 4}}\]+ \left( {\begin{array}{*{20}{c}}\\5\\\\5\\\end{array}} \right){\left( {0.25} \right)^5}{\left( {1 - 0.25} \right)^{5 - 5}}\][/tex]
[tex]\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = \dfrac{5!}{3!(5-3)!}\right){\left( {0.25} \right)^3}{\left( {1 - 0.25} \right)^{5 - 3}}\] + \dfrac{5!}{4!(5-4)!} \right){\left( {0.25} \right)^4}{\left( {1 - 0.25} \right)^{5 - 4}}\] + \dfrac{5!}{5!(5-5)!} \right){\left( {0.25} \right)^5}{\left( {1 - 0.25} \right)^{5 - 5}}\][/tex]
[tex]\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = \dfrac{5!}{3!(5-3)!}\right){\left( {0.25} \right)^3}{\left( {1 - 0.75} \right)^{2}}\] + \dfrac{5!}{4!(5-4)!} \right){\left( {0.25} \right)^4}{\left( {0.75} \right)^{1}}\] + \dfrac{5!}{5!(5-5)!} \right){\left( {0.25} \right)^5}{\left( {0.75} \right)^{0}}\][/tex]
[tex]\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = 0.0879 + 0.0146 + 0.001[/tex]
[tex]\mathbf{\[P\left( {X = 3 \ or \ 4 \ or \ 5 } \right) = 0.1035}[/tex]
Applying the Segment Addition Postulate
Point B lies between points A and C on AC. Let x
represent the length of segment AB in inches.
A
B
3x
Use the segment to complete the statements.
The value of x is v.
The length of AR in inches is
✓x
C
The length of BC in inches is
20 inches
Intro
Answer:
x = 5, AB=5, BC = 15
Step-by-step explanation:
AC = AB + BC (Segment Addition)
AC= 20, AB =x Bc = 3x,
20= x+3x 20=4x
x=5
AB=x, AB =5
BC=3x BC= 15
The segment addition postulate states gives the value of x as 5, given
that the sum of x and 3·x is 20.
Responses:
The value of x is 5The length of [tex]\overline{AB}[/tex] is 5 inchesThe length of [tex]\overline{BC}[/tex] is 15 inchesHow does segment addition postulate give the value of x?From the given diagram, we have;
[tex]\overline{AB}[/tex] = x
[tex]\overline{BC}[/tex] = 3·x
According to segment addition postulate we have;
[tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] = [tex]\overline{AC}[/tex] = 20 inches
Which gives;
x + 3·x = 20
Therefore;
4·x = 20
[tex]x = \dfrac{20}{4} = 5[/tex]
The value of x is 5The length of [tex]\overline{AB}[/tex] is 5 inches[tex]\mathbf{\overline{BC}}[/tex] = 3·x
[tex]\mathbf{\overline{BC}}[/tex] = 3 × 5 = 15
The length of [tex]\overline{BC}[/tex] is 15 inchesLearn more about segment addition postulate here:
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246,000 in scientific notation
Answer:
246000 in scientific notation is 2.46e5, or 2.46 x 10^5
Step-by-step explanation:
246000, move the decimal place 5 places to the left.
2.4x10^5
Answer:
2.46 × 10⁵
Step-by-step explanation:
The decimal point is after the first non-zero digit.
⇒ 2.46
Multiply the number with base 10 and an exponent which will equal to 246,000.
⇒ 10⁵
Question 21 of 39
Which of the following situations may be modeled by the equation y = 2x+20
?
A. Carlos has written 18 pages of his article. He plans to write an
additional 2 pages per day
B. Don has already sold 22 vehicles. He plans to sell 2 vehicles per
week
C. Martin has saved $2. He plans to save $20 per month
D. Eleanor has collected 20 action figures. She plans to collect 2
additional figures per month
SI
The correct answer is D. Eleanor has collected 20 action figures. She plans to collect 2 additional figures per month
Explanation:
The purpose of using an equation is to express mathematically a situation or relation. This involves understanding accurately how factors or numbers relate. According to this, the equation y = 2x + 20 fits with the situation described in D because this equation can be used to calculate the number of books Eleanor has as y is the total; 2 is the number of new books per month; x the number of months; and 20 books Eleanor already has.
Also, the number of months is multiplied by 2, and this is added to 20 which equals the total number of books. For example, after three months the total of books would be 26 considering y (total of books) = 2 x 3 (months) + 20 ⇒ 26 books.
What is the value of the 7 in the number 0.873?
Write your answer as a fraction.
Answer: 7/100
Step-by-step explanation:
In this question, ignore the 8 and the 3 and focus on the 7. Isolate it and you will get 0.07. 0.07 in fraction from is 7/100.
The place value of 7 in the decimal number 0.873 is in the hundredth place thus it will be 7/100 or 0.07.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
Given the decimal,
0.873
8 → Tenth place (Fraction value 8/10)
7 → Hundredth place(Fraction value 7/100)
3 → Thousandth place (Fraction value 3/1000)
Since 7 is at hundredth place thus it will be 7/100.
Hence "The place value of 7 in the decimal number 0.873 is in the hundredth place thus it will be 7/100 or 0.07".
For more about the number system,
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What are the solutions to the system of equations graphed below?
Answer:
Hey there!
The solutions to a system are where the lines, or graphs intersect each other.
We see that the graphs intersect at (0, -4) and (2, 0).
Thus, the solutions are (0, -4) and (2, 0).
Hope this helps :)
Compute the determinants using a cofactor expansion across the first row. Also compute the determinant by a cofactor expansion down the second column.
[ 0 4 1
5 −3 0
2 3 1 ]
Answer:
The determinant is 1Step-by-step explanation:
Given the 3* 3 matrices [tex]\left[\begin{array}{ccc}0&4&1\\5&-3&0\\2&3&1\end{array}\right][/tex], to compute the determinant using the first row means using the row values [0 4 1 ] to compute the determinant. Note that the signs on the values on the first row are +0, -4 and +1
Calculating the determinant;
[tex]= +0\left[\begin{array}{cc}-3&0\\3&1\\\end{array}\right] -4\left[\begin{array}{cc}5&0\\2&1\\\end{array}\right] +1\left[\begin{array}{cc}5&-3\\2&3\\\end{array}\right] \\\\= 0 - 4[5(1)-2(0)] +1[5(3)-2(-3)]\\= 0 -4[5-0]+1[15+6]\\= 0-20+21\\= 1[/tex]
The determinant is 1 using the first row as co-factor
Similarly, using the second column [tex]\left[\begin{array}{c}4\\-3\\3\end{array}\right][/tex] as the cofactor, the determinant will be expressed as shown;
Note that the signs on the values are -4, +(-3) and -3.
Calculating the determinant;
[tex]= -4\left[\begin{array}{cc}5&0\\2&1\\\end{array}\right] -3\left[\begin{array}{cc}0&1\\2&1\\\end{array}\right] -3\left[\begin{array}{cc}0&1\\5&0\\\end{array}\right] \\\\= -4[5(1)-2(0)] - 3[0(1)-2(1)] -3[(0)-5(1)]\\= -4[5-0] -3[0-2]-3[0-5]\\= -20+6+15\\= -20+21\\= 1[/tex]
The determinant is also 1 using the second column as co factor.
It can be concluded that the same value of the determinant will be arrived at no matter the cofactor we choose to use.
Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1m to catch rainwater off his roof. He has a full 2 liter tin of paint in his store and decides to paint the tank (not the base). If he uses 250ml to cover 1m^2, will he have enough paint to cover the tank with one layer of paint? ( Take π = 3.142)
Answer:
There is enough paint to cover the tank with one layer of paint.
Step-by-step explanation:
Given the cilindrical configuration of the tank and supposing that only external face must be painted, the surface area of the section (lateral wall + lid) can be calculated by the following expression:
[tex]A_{s} = 2\pi\cdot r\cdot h + \pi\cdot r^{2}[/tex]
Where [tex]r[/tex] and [tex]h[/tex] represent the radius and the height of the cube, respectively.
If [tex]r = 0.55\,m[/tex] (a diameter is two times the length of radius) and [tex]h = 1.4\,m[/tex], the intended surface area is:
[tex]A_{s} = 2\pi\cdot (0.55\,m)\cdot (1.1\,m)+\pi\cdot (0.55\,m)^{2}[/tex]
[tex]A_{s} \approx 4.751\,m^{2}[/tex]
It is known that 250 mL of paint are needed to cover a square meter of the surface area, the needed amount of paint to cover the required area is estimated by simple rule of three:
[tex]Q = \frac{4.751\,m^{2}}{1\,m^{2}}\times (250\,mL)[/tex]
[tex]Q = 1187.75\,mL\,(1.188\,L)[/tex]
In consequence, there is enough paint to cover the tank with one layer of paint.
Please help ?!!! Solve the three equations in the table using any method of your choice. List the method you used.
Equation
x^2-4=-12
-9x^2+4x-10=0
x^2+8x=-17
With solutions and method
Step-by-step explanation:
[tex]x = \frac{ - b \frac{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
The quadratic formula is honestly the most straightforward way of solving here.
Your other options are completing the square (which is the same thing as the quadratic formula but it's good to know that method if you have to take Integral Calculus at some point) or maybe factoring by grouping if it's appropriate. But the quadratic formula will work for you in all three equations:
1) a=1, b=0, c=8
This reduces pretty quickly into x=8i,-8i due to the negative under the radical. (Actually we didn't even really need the formula here.)
2) a=-9, b=4, c=-10
This reduces into x=(-4+i√(344))/-18, (-4-i√(344))/-18 and doesn't go any further because 344 isn't a perfect square.
3) a=1, b=8, c=17
This reduces to x=(-4+i), (-4-i)
So those are the answers for each.
Please Refer to the screenshot. Hope this helps!
How do you find the surface area of a triangle? A square?
Answer:
The area formula of a triangle is (base * height) / 2 and the area of a square is s² where s is the length of one side.
When graphing the inequality y ≤ 2x − 4, the boundary line needs to be graphed first. Which graph correctly shows the boundary line? A.) Picture 1 B.) Picture 2 C.) Picture 3 D.) Picture 4
Option A.) Picture 1 is correct
in the problem inequality y ≤ 2x − 4 is given
Right graph for boundary line has been asked.
Inequality can be defined as the relation of the equation contains the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
For the boundary line
y ≤ 2x − 4 this equation transform into
y= 2x-4
above equation is the boundary condition for the given inequality
so in picture one the the dotted line shows the information of equation
y= 2x-4.
Thus, the boundary condition for inequality y ≤ 2x − 4 is in picture 1
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Of 380 randomly selected medical students, 21 said that they planned to work in a rural community. Find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community.
Answer:
[tex]0.0553 - 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0323[/tex]
[tex]0.0553 + 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0783[/tex]
Step-by-step explanation:
The info given is:
[tex] X= 21[/tex] number of students who said that they planned to work in a rural community
[tex] n= 380[/tex] represent the sample size selected
[tex]\hat p =\frac{21}{380}= 0.0553[/tex] the estimated proportion of students who said that they planned to work in a rural community
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
Replpacing we got:
[tex]0.0553 - 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0323[/tex]
[tex]0.0553 + 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0783[/tex]
A mean for estimation is the minimum-maximum variation estimate's C.I. The % of pupils planning to work in a rural community alters between 0.0323 and 0.0783.
Confidence interval:
Let's [tex]p^{}[/tex] represent the sampling fraction of the people who promised to work in a rural area.
Sample size:
[tex]n = 380[/tex]
x: the large number the pupils expected to work in a rural setting
[tex]p^{} = \frac{x}{n} \\\\p^{} = \frac{21}{ 380} = 0.0553\\\\(1- \alpha)\ \ 100\%[/tex]confidence for true proportion:
[tex]( p^{}\ \pm Z_{\frac{\alpha}{2}} \times \sqrt{p^{} \times \frac{(1-p^{})}{n}} ) \\\\[/tex]
For [tex]95\%[/tex]confidence interval:
[tex]\to 1 - \alpha = 0.95[/tex]
When:
[tex]\to \alpha = 0.05[/tex]
Calculating the value of Z by using the table:
[tex]\to Z_{0.025} = 1.96[/tex]
When the [tex]95\%[/tex] of the confidence interval:
[tex]\to (0.0553 \pm Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380}})\\\\\to (0.0553 - Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380})},0.0553 + Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380}))}\\\\[/tex]
by solving the value we get:
[tex]\to ( 0.0323 , 0.0783 )[/tex]
We are [tex]95\%[/tex] sure that the true proportion of students planning to work in a rural community is between [tex]0.0323[/tex] and [tex]0.0783[/tex]. That is we are [tex]95\%[/tex] sure that the percentage of students planning to work in a rural community is between [tex]3.23\%[/tex] and [tex]7.83\%[/tex].Find out more about the Confidence interval here:
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WILL MARK BRAINIEST IF CORRECT!!!! Select the correct answer. This table represents a function. Is this statement true or false?
Answer:
true
Step-by-step explanation:
doesn't over lap each other
The accompanying data represent the total travel tax (in dollars) for a 3-day business trip in 8 randomly selected cities. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers.
67.85 78.62 70.28 84.03 79.28 87.72 101.54 97.28
1. Determine a point estimate for the population mean travel tax.
2. Construct and interpret a 95% confidence interval for the mean tax paid for a three-day business trip.
Filling the missing boxes.
The lower bound is $_______and the upper bound is $_______. One can be______% confident that all cities have a travel tax between these values.
The lower bound is $______and the upper bound is $______. The travel tax is between these values for______% of all cities.
The lower bound is $_____and the upper bound is $______. There is a_______% probability that the mean travel tax for all cities is between these values.
The lower bound is $_______and the upper bound is______. One can be______% confident that the mean travel tax for all cities is between these values.
3. What would you recommend to a researcher who wants to increase the precision of the interval, but does not have access to additional data?
A. The researcher could decrease the level of confidence.
B. The researcher could decrease the sample standard deviation.
C. The researcher could increase the level of confidence.
D. The researcher could increase the sample mean.
Answer:
1. Point estimate M (sample mean): 83.33
2. The lower bound is $73.36 and the upper bound is $93.30. One can be______% confident that the mean travel tax for all cities is between these values.
3. A. The researcher could decrease the level of confidence.
Step-by-step explanation:
A point esimate for the population mean travel tax can be done with the sample mean.
We can calculate the sample mean as:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{8}(67.85+78.62+70.28+84.03+79.28+87.72+101.54+97.28)\\\\\\M=\dfrac{666.6}{8}\\\\\\M=83.33\\\\\\[/tex]
2. We have to calculate a 95% confidence interval for the mean.
The sample mean is M=83.33.
The sample size is N=8.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
We calculate the sample standard deviation as:
[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{7}((67.85-83.33)^2+(78.62-83.33)^2+(70.28-83.33)^2+. . . +(97.28-83.33)^2)}\\\\\\s=\sqrt{\dfrac{994.49}{7}}\\\\\\s=\sqrt{142.07}=11.92\\\\\\[/tex]
The standard error is:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{11.92}{\sqrt{8}}=\dfrac{11.92}{2.828}=4.214[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=8-1=7[/tex]
The t-value for a 95% confidence interval and 7 degrees of freedom is t=2.36.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.36 \cdot 4.214=9.97[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 83.33-9.97=73.36\\\\UL=M+t \cdot s_M = 83.33+9.97=93.30[/tex]
The 95% confidence interval for the mean travel tax is (73.36, 93.30).
We can be 95% confident that the true mean travel tax is within this interval.
3.. If we have no access to additional data, we can not decrease the standard deviation or increase the sample size.
The only way to have a narrower confidence interval is decreasing its level of confidence. With the same sample information, the lower the confidence, the narrower is the interval.
Will give brainliest, someone please help
━━━━━━━☆☆━━━━━━━
▹ Answer
Area = 9
▹ Step-by-Step Explanation
A = b * h ÷ 2
A = 9 * 2 ÷ 2
A = 9
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 290 babies were born, and 261 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?
Answer:
The 99% confidence interval estimate of the percentage of girls born is between 85.46% and 94.54%.
Usually, babies are equally as likely to be boys or girls. Here, it is desired to increase the probability of conceiving a girl, which is achieved, considering the lower bound of the confidence interval is considerably above 50%.
Step-by-step explanation:
Confidence interval for the proportion:
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 = 290, \pi = \frac{261}{290} = 0.9[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 - 2.575\sqrt{\frac{0.9*0.1}{290}} = 0.8546[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 + 2.575\sqrt{\frac{0.9*0.1}{290}} = 0.9454[/tex]
Percentage:
Proportion multplied by 100.
0.8546*100 = 85.46%
0.9454*100 = 94.54%
The 99% confidence interval estimate of the percentage of girls born is between 85.46% and 94.54%.
Based on the result, does the method appear to be effective?
Usually, babies are equally as likely to be boys or girls. Here, it is desired to increase the probability of conceiving a girl, which is achieved, considering the lower bound of the confidence interval is considerably above 50%.
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) −3, 2, − 4 3 , 8 9 , − 16 27 , ...
Answer:
The general term is
Sn = -(-2)ⁿ.3¹⁻ⁿ
step by step Explanation:
we were told to find a general term of the above sequence, what should come to mind is that the terms will follow an order....
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
PLSS I NEED HELP I NEED HELP SOMEONE SAVE ME
Answer:
sorry but are you dyin why do u need help why do you need someone to save you just say i need answers to this equation pls
Shaun's tent (shown below) is a triangular prism. Find the surface area, including the floor, of his tent.
Answer: 52.8
Step-by-step explanation: it’s on khan ,
Yesterday in Juneau, Alaska it was -20 degrees and in San Diego, California it was 75 degrees. What was the difference in temperature between these two cities?
Select one:
a. -20 degrees
b. 55 degrees
c. 75 degrees
d. 95 degrees
Answer: d) 95 degrees
Step-by-step explanation:
To find this solution, simply subtract -20 from 75, to get 95. In reality, you would take the absolute value of one temperature - another, but all you need to remember is to always subtract the smaller temperature from the larger.
Answer:
95 degrees(answer d)
Step-by-step explanation:
when you have a negative temp. and a positive temp., you add the two numbers to find the difference.
that means, 20+75=95 degrees(take away the negative sign when adding only.)
That means the difference between the two temperatures is 95 degrees.
What is the discrimination of this function !! Please help
Answer:
Option C is correct.
The discriminant of the function is negative since the function doesn't have real roots as evident from the graph.
Step-by-step explanation:
The discriminant of a quadratic equation is the part of the quadratic formula underneath the square root symbol, that is, (b² - 4ac).
The discriminant tells us whether there are two solutions, one solution, or no solutions.
- When the discriminant is positive or greater than zero, that is, (b² - 4ac) > 0, the quadratic function has 2 real distinct roots.
- When the discriminant is equal to zero, that is, (b² - 4ac) = 0, the quadratic function has 1 repeated root.
- When the discriminant is negative or lesser than zero, that is, (b² - 4ac) < 0, the quadratic function has no real roots.
For this question, the graph of the quadratic function shows that it doesn't have real roots (this is evident because the graph doesn't cross the x-axis), hence, the duscriminant of this quadratic function has to bee negative.
Hope this Helps!!!
Suppose that the function g is defined, for all real numbers, as follows.
A human resources representative claims that the proportion of employees earning more than $50,000 is less than 40%. To test this claim, a random sample of 700 employees is taken and 305 employees are determined to earn more than $50,000.The following is the setup for this hypothesis test:{H0:p=0.40Ha:p<0.40Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.
Answer:
The statistic for this case would be:
[tex] z=\frac{\hat p -p_o}{\sqrt{\frac{\hat p(1-\hat p)}{n}}}[/tex]
And replacing we got:
[tex] z= \frac{0.436-0.4}{\sqrt{\frac{0.436*(1-0.436)}{700}}}= 1.92[/tex]
Step-by-step explanation:
For this case we have the following info:
[tex] n =700[/tex] represent the sample size
[tex] X= 305[/tex] represent the number of employees that earn more than 50000
[tex]\hat p=\frac{305}{700}= 0.436[/tex]
We want to test the following hypothesis:
Nul hyp. [tex] p \leq 0.4[/tex]
Alternative hyp : [tex] p>0.4[/tex]
The statistic for this case would be:
[tex] z=\frac{\hat p -p_o}{\sqrt{\frac{\hat p(1-\hat p)}{n}}}[/tex]
And replacing we got:
[tex] z= \frac{0.436-0.4}{\sqrt{\frac{0.436*(1-0.436)}{700}}}= 1.92[/tex]
And the p value would be given by:
[tex] p_v = P(z>1.922)= 0.0274[/tex]
Maurice shot 2 under par, or -2, on each of the first 4 holes of golf. What is his score with respect to par after the fourth hole?
Answer: -8
Step-by-step explanation: If he scored -2 four times then his score would be -8 (-2×4).
Find the expression for h (x)
Answer:
We have this original function given:
[tex] g(x) =-x^2 +5[/tex]
And we want to transtale vertically downward 4 units this function and we will get the new fnction h(x) and on this case we have to do this transformation:
[tex] h(x)= g(x) -4[/tex]
And replacing we got:
[tex] h(x) = -x^2 +5 -4 =-x^2 +1[/tex]
Step-by-step explanation:
We have this original function given:
[tex] g(x) =-x^2 +5[/tex]
And we want to transtale vertically downward 4 units this function and we will get the new fnction h(x) and on this case we have to do this transformation:
[tex] h(x)= g(x) -4[/tex]
And replacing we got:
[tex] h(x) = -x^2 +5 -4 =-x^2 +1[/tex]
Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following equation. y = x squared + x + 6 a. (0.5, -5.75) c. (-0.5, 6) b. (-0.5, 5.75) d. (0.5, 5.75) Please select the best answer from the choices provided A B C D
Answer:
B. (-0.5, 5.75)
Step-by-step explanation:
Use a graphing calc and analyze the graph for the minimum value (vertex).
Sandy evaluated the expression below. (negative 2) cubed (6 minus 3) minus 5 (2 + 3) = (negative 2) cubed (3) minus 5 (5) = 8 (3) minus 25 = 24 minus 25 = negative 1 What was Sandy’s error?
Answer:
should be - 8
Step-by-step explanation:
-2*-2=4 4*-2=-8
Answer:
Sandy should have evaluated (negative 2) cubed as –8.
Step-by-step explanation:
Got it right on the test
In which function is x = 2 mapped to 32?
f (x) = Negative 3 x squared minus 4
g (x) = 4 (x + 3) squared minus 68
h (x) = 3 x
j (x) = 2x minus 62
Answer:
B
Step-by-step explanation:
Took the test edge2021
The function g(x) = 4(x + 3)² - 68 is the function which is mapped to 32 at x = 2 option (B) g(x) = 4(x + 3)² - 68 is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
A function which is at x = 2 mapped to 32
The above statement means that at x = 2
The value of the function will be 32
The given functions:
f(x) = -3x² - 4
Plug x = 2
f(2) = -3(2)² - 4
f(2) = -16
g(x) = 4(x + 3)² - 68
Plug x =2
g(2) = 4(2 + 3)² - 68
g(2) = 100 - 68
g(2) = 32
Thus, the function g(x) = 4(x + 3)² - 68 is the function which is mapped to 32 at x = 2 option (B) g(x) = 4(x + 3)² - 68 is correct.
Learn more about the function here:
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What is the value of x?
45
m
(2x-5)
Answer:
if m is supposed to be the equals (=) sign then x = 25
Step-by-step explanation:
45 = (2x-5)
+5 +5
50 = (2x)
÷2 ÷2
25 = x
Answer: 70
Step-by-step explanation:
Find the slope of the line on the graph. Write your answer as a fraction or a whole number, not a mixed number or decimal.
Answer:
-4/8
Step-by-step explanation:
Using rise over run would give you -4/8. Since the rise is going downward four times the number would be negative. Since the run is going to the right 8 times it would be positive.
Answer: the slope is -1/2
Step-by-step explanation: The rise is -4. Easy to see from the y-intercept, 4 below the origin. The run is 8, again easy to see from the distance between the x-intercept at -8, 8 unite away from the origin.
So slope = rise/run -4/8 simplify (by LCM, 4) So you get slope = -1/2
Kimberly is a program director for the channel KID. She tracked the cartoons shown on the channel for a week. The probability that the show had animals in it was 0.7. The probability that the show aired more than 10 times was 0.4. The probability that the show had animals in it and aired more than 10 times was 0.2. Which equation shows the correct use of the addition rule to determine the probability that a randomly selected show had animals in it or aired more than 10 times?
Options
0.7+0.2−0.4=0.5 0.7+0.2=0.9 0.7+0.4=1.1 0.4+0.2=0.6 0.7+0.4−0.2=0.9Answer:
[tex](E)0.7+0.4-0.2=0.9[/tex]
Step-by-step explanation:
In probability theory
[tex]P$(A or B)=P(A)+P(B)$-$P(A and B)[/tex]
Let the event that the show had animals in it = A
P(A)=0.7
Let the event that the show aired more than 10 times =B
P(B)=0.4
P(A and B)= 0.2
[tex]P$(A or B)$=0.7+0.4-0.2=0.9[/tex]
Therefore, the equation which shows the correct use of the addition rule to determine the probability that a randomly selected show had animals in it or aired more than 10 times is:
[tex]0.7+0.4-0.2=0.9[/tex]
The correct option is E.