Using the binomial distribution, it is found that there is a 0.7873= 78.73% probability that at least 2 of them say job applicants should follow up within two weeks.
For each manager, there are only two possible outcomes. Either they say job applicants should follow up within two weeks, or they do not say it. The opinion of a manager is independent of any other manager, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
P(X = x) = Cₙ,ₓ.pˣ.(1-p)ⁿ⁻ˣ
Cₙ,ₓ = n!/x!
The parameters are:
n is the number of trials.
x is the number of successes.
p is the probability of a success on a single trial.
In this problem:
43% say job applicants should follow up within two weeks. If 7 human resource managers are randomly selected, n = 8
The probability that at least 2 of them say job applicants should follow up within two weeks is P(X≥2), which is given by,
P(X≥2) = 1 - P(X < 2)
In which:
P(X<2)=P(X=0)+P(X=1)
Then,
P(X=x) = Cₙ,ₓ.pˣ.(1-p)ⁿ⁻ˣ
P(X=0) = C₇,₀.(0.43)°.(0.57)⁷ = 0.0195
P(X=1) = C₇,₁.(0.43)¹.(0.57)⁶ = 0.1032
P(X<2) = P(X=0)+P(X=1)
= 0.0195+0.1032
= 0.2127
P(X≥2) = 1-P(X<2)
= 1 - 0.2127
= 0.7873
0.7873 = 78.73% probability that at least 2 of them say job applicants should follow up within two weeks.
Hence we get the probability as 78.73%.
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If ZY = 26, what is the length of the diameter of circle X?
Given ZY = 26
To find the length of the diameter of circle X.
From the figure shown, it can be observed that ZY is the radius of circle Y.
If ZY is the radius of circle Y, the diameter of circle Y is ZX, which is twice the radius of circle Y.
[tex]\begin{gathered} ZX=2\times ZY \\ ZY=26 \\ ZX=2\times26 \\ ZX=52 \end{gathered}[/tex]ZX is the radius of the circle X.
If ZX is the radius of circle X, the diameter of circle X would be twice the radius of circle X.
[tex]\begin{gathered} D_{\text{circel X}}=2\times ZX \\ ZX=52 \\ D_{\text{circle X}}=2\times52 \\ D_{\text{circle X}}=104 \end{gathered}[/tex]Hence, the length of the diameter of circle X is 104 units
write log_4 10 as a quotient of natural logarithms.ln__ln__
We have to use the change-of-base formula of logarithms to simply write this log.
The logarithm to convert is:
[tex]\log _410[/tex]The change of base formula (using natural logarithms) is:
[tex]\log _ab=\frac{\ln b}{\ln a}[/tex]Matching this with the logarithm, we can write it as:
[tex]\log _410=\frac{\ln 10}{\ln 4}[/tex]How can I draw a frequency table to represent the information given? how can I calculate the realtive frequency of a size 6 shoe? How can I calculate the probability that if a pupil is chosen at random, that he/she wears a size 7 shoe?
SOLUTION
The relative frequency of size 6 shoe is given as
[tex]\frac{3}{30}=\frac{1}{10}=10\%[/tex]The probability of picking a shoe size of 7 is
[tex]\frac{6}{30}=\frac{1}{5}[/tex]The mean phone bill is $______The median phone bill is $______Determine the mode phone bill. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Given: $36.52,$42.30.$39.78. $38.26. $44.39, $49.55
to find: Mean , Median and mode
soluiton:
Since, formula for mean
[tex]=\frac{su\text{m of all terms}}{nu\text{mber of terms}}[/tex]Here, sum of all terms = 36.52 + 42.30 + 39.78 + 38.26 + 44.39 + 49.55 = 250.8
number of terms = 6
Thus,
[tex]\operatorname{mean}=\frac{250.8}{6}=41.8[/tex]Hence, mean of phone bill is $41.8
Since, number of terms = 6 which is even
so, median
[tex]=\mleft\lbrace\frac{\frac{n}{2}+(\frac{n}{2}+1)th\text{ term}}{2}\mright\rbrace[/tex]arranging the terms in ascending order: 36.52 , 38.26, 39.78, 42.30, 44.39, 49.55
Now, median
[tex]\begin{gathered} =\mleft\lbrace\frac{3rd+4th\text{ term}}{2}\mright\rbrace \\ =\frac{39.78+42.30}{2} \\ =41.04 \end{gathered}[/tex]Hence, median of the phone bill is $41.04
Mode:
Given terms are 36.52 , 38.26, 39.78, 42.30, 44.39, 49.55
If no value or number in the data set appears more than once, then it has no mode
Hence, the phone bill has no mode
12. Find the weighted average of the student's grades listed below, using the given percentage value for each category.AssignmentScore (%)WeightTest 18330%Test 29430%Homework8410%Quizzes8710%Final Exam7920% %
To find the weighted average we just need to sum all the scores multiplied by their respective weight.
To find 30% of a value, is the same as multiplying by 30 and dividing by 100. As a decimal, this can be represented as 0.3.
[tex]\frac{30}{100}=0.3[/tex]Now, doing the sum multiplying the scores by their respective weights, we have:
[tex]\begin{gathered} \bar{x}=83\times0.3+94\times0.3+84\times0.1+87\times0.1+79\times0.2 \\ \bar{x}=24.9+28.2+8.4+8.7+15.8 \\ \bar{x}=86 \end{gathered}[/tex]The weighted average of this student is 86.
Out of 167 randomly selected adults in the United States who were surveyed, 70 exercise on a regular basis. Construct a 90% confidence interval for the proportion of all adults in the United States who exercise on a regular basis. Round to three decimal places
ANSWER:
(0.356, 0.482)
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the proportion with the data of the statement:
[tex]\begin{gathered} p=\frac{x}{n}=\frac{70}{167} \\ \\ p=0.4192 \end{gathered}[/tex]For a 90% confidence interval, we have that the value of Z is the following:
[tex]\begin{gathered} \alpha=1-90\% \\ \\ \alpha=1-0.9=0.1 \\ \\ \alpha\text{/2}=\frac{0.1}{2}=0.05 \\ \text{ } \\ \text{The corresponding value of Z would be:} \\ \\ Z_{\alpha\text{/2}}=1.645 \end{gathered}[/tex]We calculate the interval as follows:
[tex]\begin{gathered} \text{ Upper limit }=p+Z_{\alpha\text{/2}}\cdot\sqrt{\frac{p\cdot(1-p)}{n}}=0.4192+1.645\cdot\sqrt{\frac{0.4192\cdot\left(1-0.4192\right)}{167}}\:=0.482 \\ \\ \text{ Lower limit}=p-Z_{\alpha\text{/2}}\cdot\sqrt{\frac{p\cdot(1-p)}{n}}=0.4192-1.645\cdot\sqrt{\frac{0.4192\cdot\left(1-0.4192\right)}{167}}\:=0.356 \end{gathered}[/tex]The 90% confidence interval for the proportion of all adults in the United States is (0.356, 0.482)
The graph of the function F is shown above. What is limF(x)?
Answer:
4
Explanation:
To evaluate a limit, we look at both right and left limi s. If the left and right limits both approach the ssme value, then the limit exists. t
As can be observed from the graph, as we reach x = 2 from the right, the functionseems to reach y = 4. In other other words,
[tex]\lim_{x\to2^+}f(x)=4[/tex]Note the tiny plus sig in the limit . This tells us that we are approaching the limit from the right.
Now let us take a look atthe rleft-hand limit.
Now as we approach x = 2 from the left we see that the function seems to take the value y =4. In other words,
[tex]\lim_{x\to2^-}^f(x)=4.[/tex]Note also the tiny negative sign in the limit. This tells us that we are approaching the limit from the left.
Now both the left and the right-hand limits approach the same value; therefore, the limit exists and its value is the following.
[tex]\boxed{\lim_{x\to2}f(x)=4.}[/tex]A rectangular piece of metal has an area of 112 square centimeters. Its perimeter is 46 centimeters. What are the dimensions of the piece?
Let the length of rectabgle be l and width of rectangle be b.
The equation for the area of rectangle is,
[tex]l\cdot b=112[/tex]The equation for perimeter of rectangle is,
[tex]\begin{gathered} 2(l+b)=46 \\ l+b=23 \\ l=23-b \end{gathered}[/tex]Substitute 23 - b for l in the equation lb
can you please help me this is my last one!
281 is the same (equal) as the total (sum) of f and 270
281 = f +270
Find the surface area of the cylinder below. Use 3.14 for l~l. round your answer to the nearest tenth.
what is the slope and the y-intetercept of each problemy= -2x - 3y= -2x + 2
Answer:
• m=-2, b=-3
,• m=-2, b=2
Explanation:
The slope-intercept form of the equation of a line is:
[tex]y=mx+b\text{ where }\begin{cases}m=\text{slope} \\ b=y-\text{intercept}\end{cases}[/tex]Part A
Given the equation:
[tex]y=-2x-3[/tex]• The slope, m = -2
,• The y-intercept, b=-3
Part B
Given the equation:
[tex]y=-2x+2[/tex]• The slope, m = -2
,• The y-intercept, b=2
Consider this system of linear equations:y = 4/5x - 3y = 4/5x + 1Try solving the system of equations algebraically and describe the result you get.
the system has not solution
Explanation
[tex]\begin{gathered} y=\frac{4}{5}x-3 \\ y=\frac{4}{5}x+1 \end{gathered}[/tex]Step 1
to solve this we can use, Equalization, It consists in isolating from both equations the same unknown factor to be able to equal both expressions, obtaining one equation with one unknown factor.
[tex]\begin{gathered} \text{set y=y} \\ so \\ \frac{4}{5}x-3=\frac{4}{5}x+1 \\ \text{subtract 4/5 of x in both sides} \\ \frac{4}{5}x-3-\frac{4}{5}x=\frac{4}{5}x+1-\frac{4}{5}x \\ -3=1 \end{gathered}[/tex]we got that
-3=1, it is false, which means there are no values that satisfy the equation, I n other words
the system has no solution
I hope this helps you
Which expression best completes the following definition of a complexnumber?where a and bare real numbers and iThe set of all numbers in the formequals -1.
we are given that a and b are real numbers . and that i is a square root of -1
so we expect a and be to be real numbers , this can be expressed as
a + b (i)
so option B is correct .
a. Determine whether the equation x/4-x/3=1 is a linear equation. If yes, identify the equation in standard form.
The given equation is a linear equation and its standard form is [tex]3x-4y=12[/tex].
The given equation is -
[tex]\frac{x}{4}-\frac{y}{3}=1[/tex] ---- (1)
We have to determine if the given equation is a linear equation. If it is a linear equation, then we have to write it in standard form.
A linear equation is referred to as the equation of a straight line.
A linear equation with two variables can be written in the standard form as
[tex]ax+by=c[/tex]
where a, b, c are constants
and, x, y are variables
So, from equation (1), we can say that -
The equation [tex]\frac{x}{4}-\frac{y}{3}=1[/tex] is a linear equation.
Identifying the equation in standard form, we have
[tex]\frac{x}{4}-\frac{y}{3}=1\\= > \frac{3x-4y}{12}=1\\ = > 3x-4y=12[/tex]
Hence, the standard form of the given linear equation is [tex]3x-4y=12[/tex].
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If AC=20, AE = 25, and AB= 5, what is the length of AD?
Answer:
it is 5 because if ab=5 and ac=20
please help with this i will attach photo of figure
The variable I=f(w) represents the number of individuals (in thousands) infected w weeks after the epidemic begins.
The value of I=f(2) represents the number of individuals in thousandas infected 2 weeks after the beginning of the epidemic.
From the graph, where I=8, we can conclude that there are 8,000 infected people after 2 weeks of the beginning of the epidemic.
Answer:
f(2) = 8
Means 8,000 people are infected after 2 weeks of the beginning of the epidemic.
The graph below shows the solution to which system of inequalities?A. x< 1 and y2 xB. ys 1 and y>xC. x≤ 1 and y> xD. y< 1 and y2
To answer this question let's look at each line first.
The slant line can be express by the equation:
[tex]y=x[/tex]We notice that the shaded part is above this line, then we have that that inequality is written as:
[tex]y\ge x[/tex]Now, the horizontal line is express as:
[tex]y=1[/tex]since the shaded region is below that line and the line is dashed the inequality is:
[tex]y<1[/tex]Therefore, the system of inequalities is:
[tex]\begin{gathered} y\ge x \\ y<1 \end{gathered}[/tex]Factor the trinomial100y^2 - 52y +1
Solution
- The question tells us to factor the following trinomial:
[tex]100x^2-52x+1[/tex]- We simply need to rewrite the x-term and factorize the result
- This is done below:
[tex]\begin{gathered} 100x^2-52x+1 \\ 100x^2-50x-2x+1 \\ \text{Factorize} \\ 50x(2x-1)-1(2x-1) \\ \\ (2x-1)\text{ is co}mmon\text{ so we factorize it out} \\ \\ (2x-1)(50x-1) \end{gathered}[/tex]Final Answer
The factored trinomial is
[tex](2x-1)(50x-1)[/tex]changing the value of b in f(x)=mx+b results in a translation or reflection?
8. The chart below shows the student lunch menu at a school. A lunch consists of onesandwich, one snack, and one drink.Lunch MenuSandwichSnack Drinkturkey apple juicebologna bananamilkpeanut buttercookieshamyogurtHow many different lunch choices does a student have?hirtants and subite or
We have to find all the different lunch choices that a student have, where one lunch consists of one sandwich, one snack, and one drink.
For doing so, we remember the multiplication principle. As for each option of sandwich, we have _ options for the snacks, and for each snack we have _ options of drinks, we just have to multiply each one of the values. In this case,
Help n k oh hi k. Hi hold kb b g g I
SOLUTION:
[tex]v(n)=(14)\cdot b^n[/tex]The correct answer is;
If b = 1.06, the weekly growth rate of the share's value is 6%
Please answer all questions. Please show your work in the answers.I skated 3 miles in 5 minutes.a. How many miles per minute is that?b. I skated 3 miles in 5 minutes. How many minutes per mile is that?c. If I skated 3 miles in 5 minutes, how far will I skate in an hour?ML and MC live 37 miles apart from each other. ML drives at a speed of 8 miles per hour, and MC drives at a speed of 4 miles per hour. How long does it take until ML and MC meet?Protein bar A has 15 grams of protein in a 40 gram bar. Protein bar B has 20 grams of protein in a 60 gram bar. Which bar has more protein per gram?
1)
a) In order to find the value of miles per minute, we just need to divide the number of miles by the number of minutes:
[tex]\frac{3\text{ miles}}{5\text{ minutes}}=\frac{3}{5}\text{ miles/minute}[/tex]So the result is 3/5 miles per minute.
b) In order to find the number of minutes per mile, since we have the value of miles per minutes, we just need to invert the fraction:
[tex]\frac{3\text{ miles}}{5\text{ minutes}}=\frac{5\text{ minutes}}{3\text{ miles}}=\frac{5}{3}\text{ minutes/mile}[/tex]So the result is 5/3 minutes per mile
c)
In order to calculate the distance after 1 hour (60 minutes), we can use a rule of three:
[tex]\begin{gathered} 5\text{ minutes}\to3\text{ miles} \\ 60\text{ minutes }\to x \\ \\ \frac{5}{60}=\frac{3}{x} \\ \frac{1}{12}=\frac{3}{x} \\ x=3\cdot12=36\text{ miles} \end{gathered}[/tex]So the result is 36 miles.
2)
Since they are going towards each other, the relative speed is the sum of their speeds:
[tex]V=8+4=12\text{ mph}[/tex]Now, to find the time, we just need to divide the distance by the speed:
[tex]t=\frac{37}{12}=3.083=3\text{ hours 5 minutes}[/tex]So the amount of time is 3 hours and 5 minutes.
3)
In order to find which bar has more protein, let's compare the fractions that represents the amount of protein in each bar:
[tex]\begin{gathered} \text{bar A: 15/40 of protein} \\ \text{bar B: 20/60 of protein} \\ \\ \frac{15}{40}=\frac{45}{120} \\ \frac{20}{60}=\frac{40}{120} \\ \frac{45}{120}>\frac{40}{120} \end{gathered}[/tex]So protein bar A has more protein per gram.
Write the equation of an absolute value function that has been stretched by a factor of 2, reflected across x axis, and shifted 6 units to the right
The absolute value function is the function;
[tex]y=|x|[/tex]STEP 1: To stretch this function vertically by a factor of 2 would mean multiplying the function by 2, we have as a result;
[tex]y=2|x|[/tex]STEP 2: To reflect the function over the x-axis, this means that the entire function is multiplied by a negative sign, we have as a result;
[tex]y=-2|x|[/tex]STEP 3: To shift a function horizontally by 6 units to the right means subtracting 6 from every x- value. we have as a final result;
[tex]y=-2|x-6|[/tex]Therefore, the equation of an absolute value function that has been stretched by a factor of 2, reflected across x-axis, and shifted 6 units to the right is;
[tex]y=-2|x-6|[/tex]laws of exponent : multiplication and power to a powerquestion 2)))-2r⁵ • 6r ⁻⁸
You need to remember the following:
- The Product of powers property states that:
[tex]b^m\cdot b^n=b^{(m+n)}[/tex]- According to the Negative exponent rule:
[tex]b^{-m}=\frac{1}{b^m}[/tex]Given the following expression:
[tex](2r^{5})(6r^{-}^{8})[/tex]You can simplify it as following:
1. Multiply the coefficients.
2. Apply the Product of powers property.
3. Apply the Negative exponent rule.
Then, you get:
[tex](2r^{5})(6r^{-}^{8})=12r^{(5-8)}=12r^{-3}=\frac{12}{r^3}[/tex]The answer is:
[tex]\frac{12}{r^3}[/tex]Because there are 3 feet in every yard, the formula F = 3 ⋅ Y will convert Y yards into F feet. Find F ifY = 5 yards5 yards converts to ? feet.
The problem says that
[tex]\text{feet}=3\cdot\text{yards}[/tex]Then, if we want to convert yards to feet, we got to multiply it by three. The question is, how many feet is 5 yards? let's use the formula:
[tex]\begin{gathered} \text{feet}=3\cdot5 \\ \\ \text{feet}=15 \end{gathered}[/tex]Therefore, 5 yards is 15 feet
{(-2, 5), (-1, 2), (0, 1), (2,5)}
Which points are on the graph of the inverse?
Select each correct answer.
(5,2)
(2, 1)
-
(-5, 2)
let's recall that the domain of a function is the range of its inverse function, namely, the inverse has a pair that's just the same but flipped sideways, Check the picture below.
6000 divided by 80 (explain and do work)
we can cancel a zero, because it is a common number
we take 60 because 6 is less than 8, 7x8 is very close to 60 obtain the result and substract from 60
go down the zero and look for a number that multiplied by 8 make 40
so,8x5=40
the solution of the division is 75
Answer:
75
Step-by-step explanation:
6 / 8 = 7.5
so 6000/80 = 75
Hello! I'm a little stumped on this one I think it should be scatter plot
We have a data set that includes the test scores of a class.
We can represent this data, as it is univariate, with a box-and-whisker plot. This will let us graph the distribution of the scores.
A circle graph is only applicable if we group the data in classes. The same for the histogram.
They are not suitable for individual data points that are not grouped.
A scatter plot is also not suitable, as it needs ordered pairs. It will show the relation between two variables, and in this case we have only one variable in the data set.
Answer: box-and-whisker plot.
A circle with a radius of 3.9 cm is centered at the vertex of an angle.Suppose the angle has a measure of 175 ____degrees.What is the radian measure of this angle?____ radians What is the length (in cm) of the arc subtended by the angle's rays along the circle?_____ cm Suppose θ represents the varying degree measure of the angle. Write an expression that represents the length (in cm) of the arc subtended by the angle's rays along the circle. (Enter "theta" for θ.) ______cm
We can draw the following picture:
From the angle-arc relationships, since the vertex is at the center of the circle, then the arc is equal to 175 degrees.
In radians, 175 degrees is equivalent to
[tex]175=175\cdot(\frac{\pi}{180})\text{rad}[/tex]that is
[tex]175=3.054\text{ rad}[/tex]What is the radian measure of this angle? 3.054 radians
The arc-lengh S is given by
[tex]s=r\cdot\theta[/tex]where, r=3.9cm and theta is equal to 3.054 rad (which is 175 degrees but in this formula the number must be written in radians). By sustituting these value, we have
[tex]\begin{gathered} s=(3.9)(3.054) \\ s=11.91\text{ cm} \end{gathered}[/tex]What is the length (in cm) of the arc subtended by the angle's rays along the circle? 11.91 cm
Suppose θ represents the varying degree measure of the angle. Write an expression that represents the length (in cm) of the arc subtended by the angle's rays along the circle.
We wrote the formula above:
[tex]s=r\cdot\theta[/tex]where s is the arc-lenght, r is the radius and theta is the angle (in radians).
The students in a first-grade class were all asked to time how long (in seconds) they could hold their breath. The resultswere tallied and are presented in the following histogram.How many of those students held their breath greater than 12.5 and less than 15.5 seconds?
ANSWER:
13 students
STEP-BY-STEP EXPLANATION:
To find the answer we must add the number of students between the values 12.5 and 15.5, just like this:
[tex]\begin{gathered} 12.5-13.5=2\text{ students} \\ 13.5-14.5=5\text{ students} \\ 15.5-15.5=6\text{ students} \\ \text{Total}=\text{ }12.5-15.5=2+5+6=\text{ 13 students} \end{gathered}[/tex]