A colony of bacteria is growing exponentially according to the function below, where t is in hours. What will the approximate number of bacteria be after 7 hours?A.270B.1082C.635,818D.45,674
Answers
we have the exponential function
[tex]B(t)=4e^{0.8t}[/tex]For t=7 hours
substitute
[tex]\begin{gathered} B(t)=4e^{0.8*7} \\ \\ B(t)=1,082\text{ bacteria} \end{gathered}[/tex]The answer is option BRelated Questions
Given the matrices A and B shown below, find – B – 1/3A[ -18 3]. [ -4 12][ -15 -6] [ 8 -12]
Answers
Answer:
[10 -13]
[-3 14]
Explanation:
First, we will calculate 1/3A, so:
[tex]\frac{1}{3}A=\frac{1}{3}\begin{bmatrix}{-18} & 3 & \\ {-15} & -6 & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{\frac{1}{3}(-18)} & {\frac{1}{3}(3)} & \\ {\frac{1}{3}(-15)} & {\frac{1}{3}(-6)} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-6} & {1} \\ {-5} & {-2} \\ & {}\end{bmatrix}[/tex]Because 1/3 multiply each value in the matrix. Now, adding the respective values in the same position, we can calculate -B - 1/3A as:
[tex]\begin{gathered} -B-\frac{1}{3}A=-\begin{bmatrix}{-4} & {12} & \\ {8} & {-12} & {}{}\end{bmatrix}-\begin{bmatrix}{-6} & {1} \\ {-5} & {-2}\end{bmatrix} \\ -B-\frac{1}{3}A=\begin{bmatrix}{4} & {-12} & \\ {-8} & {12} & {}{}\end{bmatrix}-\begin{bmatrix}{-6} & {1} \\ {-5} & {-2}\end{bmatrix} \\ -B-\frac{1}{3}A=\begin{bmatrix}{4-(-6)} & {-12-1} & \\ {-8-(-5)} & {12-(-2)} & {}{}\end{bmatrix} \\ -B-\frac{1}{3}A=\begin{bmatrix}{4+6} & {-12-1} & \\ {-8+5} & {12+2} & {}{}\end{bmatrix} \\ -B-\frac{1}{3}A=\begin{bmatrix}{10} & {-13} & \\ {-3} & {14} & {}{}\end{bmatrix} \end{gathered}[/tex]Therefore, the answer is:
[tex]-B-\frac{1}{3}A=\begin{bmatrix}{10} & {-13} & \\ {-3} & {14} & {}\end{bmatrix}[/tex]f(x) = |×| g(x) = |×+9| – 5 We can think of g as a translated (shifted) version of f. Complete the description of the transformation. Use nonnegative numbers. To get the function g. shift f up/down by units and to the right/left v by units.
Answers
First we can check the value 9 that is added inside the absolute module operator.
This value is together with the variable x inside the operator, that is, from f(x) we can replace x by 'x + 9' in order to get the first part of g(x)
This addition of 9 to the value of x represents a horizontal translation of 9 units to the left.
Then, the subtraction of 5 units outside the absolute module operator is a addition/subtraction to the function, that is, we can subtract 5 units from f(x) in order to get this second part of f(x).
This subtraction of 5 units to the value of f(x) represents a vertical translation of 5 units down.
So the answer is:
To get the function g(x), shift f down by 5 units and to the left by 9 units.
Drag numbers in the box to make each comparison true
Answers
1) Let's find the results of each inequality/equality so that we write out the right choices.
2) Let's begin with the equation. We're going to resort to Algebra:
[tex]\begin{gathered} 12\times\frac{4}{x}=8 \\ 12\times4=8x \\ 48=8x \\ 8x=48 \\ \frac{8x}{8}=\frac{48}{8} \\ x=6 \\ 12\times\frac{4}{6}=8{\color{DarkBlue} } \end{gathered}[/tex]Based on that, we can tell that and filling in the gap with other whole numbers the following:
[tex]\begin{gathered} 12\times\frac{4}{8}<8 \\ 6<8 \\ 12\times\frac{4}{6}=8 \\ 12\times\frac{4}{3}>8 \\ 16>8 \end{gathered}[/tex]Note that we picked whole numbers and it is clear that the greater the denominator the lesser the value.
what is the value of x in the equation 2.5 - 0.25x - -3
Answers
The given equation is expressed as
2.5 - 0.25x = -3
Subtracting 2.5 from both sides of the equation, we have
2.5 - 2.5 - 0.25x = -3 - 2.5
- 0.25x = - 5.5
Dividing both sides of the equation by - 0.25, we have
- 0.25x/- 0.25 = - 5.5/- 0.25
x = 22
there are 4 sets of balls numbered 1 through 12 placed in a bowl. if 4 balls are randomly chosen without replacement, find the probability that the balls have the same number. express your answer as a fraction
Answers
The probability is 12/194580
Explanation:The balls numbered 1 through 12 are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
If 4 balls have the same number, then there are 12 types of this arrangement:
1, 1, 1, 1
2, 2, 2, 2
3, 3, 3, 3
and so on.
There is also 4 * 12 = 48 total number of balls.
We have a permutation:
[tex]\begin{gathered} 48C4=\frac{48!}{(48-4)!4!} \\ \\ =\frac{48!}{44!4!}=194580 \end{gathered}[/tex]Finally, we
[tex]\frac{12}{194580}[/tex]This is the required probability.
9. In April, Community Hospital reported 923 discharge days for adults and children and 107 discharge daysfor newborns. During the month, 192 adults and children and 37 newborns were discharged. Calculate theALOS for adults and children for the month of April. Round to one decimal place.
Answers
Solution:
Average Length of Stay(ALOS) is calculated by summing the number of days for all stays (where partial days, including non-overnight stays, are rounded up to the next full day) and dividing by the number of patients.
[tex]\text{alos}=\frac{total\text{ number of days}}{\text{totl number of patients}}[/tex]The total number of days is
[tex]\begin{gathered} =923+107 \\ =1030 \end{gathered}[/tex]The total number of patients is
[tex]\begin{gathered} =192+37 \\ =229 \end{gathered}[/tex]By applying the formula above, we will have
[tex]\begin{gathered} \text{alos}=\frac{total\text{ number of days}}{\text{total number of patients}} \\ \text{alos}=\frac{1030}{229} \\ \text{alos}=4.4978 \\ \text{alos}\approx4.5 \end{gathered}[/tex]Hence,
The final answer is =4.5
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC = 15 and DC = 6, what is the length of BC in simplest radical form? (Note: the figure is not drawn to scale.) B х A D 6 C с 15 Submit Answer Answer: I
Answers
Answer
BC = x = 3√10
Explanation
To answer this question, we will use the concept of similar triangles.
We know that the two triangles ABC and BDC are similar because they are right angle triangles with one common non-right angle angle too, Angle C.
Using angle C as a reference point, we can write the corresponding sides.
And we know that corresponding sides for similar triangles have the same ratio.
∆ABC = ∆BDC
AB is corresponding to BD
BC is corresponding to DC
CA is corresponding to CB
So,
(AB/BD) = (BC/DC) = (CA/CB)
The sides that we need include
BC, DC, CA and CB
BC = x
DC = 6
CA = 15
CB = x
(BC/DC) = (CA/CB)
(x/6) = (15/x)
Cross multiply
x² = (6)(15)
x² = 90
Take the square root of both sides
√(x²) = √(90)
x = √90
x = √[(9)(10)]
x = (√9) (√10)
x = 3√10
Hope this Helps!!!
Problems 20 - 23. Analytically determine what type(s) of symmetry, if any, the graph of the equation would possess. Show your work.21) y^2 - xy = 6
Answers
Because of gthe graph I conclude that the graph is simmetric about the origin.
Lana owns an office supply shop. At the beginning of each school year, she chooses two or three products to donate to the local middle school.
The table shows the school supplies that Lana has in her shop and how many of each kind she has in stock. Lana is considering different options of supplies to donate. For each option, determine the greatest number of identical boxes she could pack and the number of each supply item she could put in the boxes.
school supplies stock:
pencils-78
markers-110
notebooks-195
erasers-143
folders-330
A option 1: pencils and erasers: ____boxes with ____ pencils and ____ erasers
B option 2: notebooks and folders: ____ boxes with ____notebooks and ____ folders in each box.
C option 3: erasers, markers, and folders: ____ boxes with ____ erasers ____ markers and ____ folders in each box.
Answers
Answer: Step-by-step explanation: Lana needs to order supplies for the upcoming month. Her supplier sells pencils in boxes of 12, markers in boxes of 10, notebooks in boxes of 4, erasers in boxes of 6, and folders in boxes of 15. What is the least number of boxes of each supply item that Lana could order to have the same number of each item delivered? How many of each item will she get? E 3-2
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 4 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 22 feet high?
Answers
[tex]h^{\prime}=\frac{4}{1089\pi}ft\text{ /min}[/tex]
STEP - BY - STEP EXPLANATION
What to find?
dh/dt
Given that;
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 4 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude.
Since we have that the rate is 4 cubic per minute, then dv/dt = 4 (since v is the volume of the cone at time t.)
The formula for the volume of a cone is
[tex]V=\frac{1}{3}\pi r^2h---------------(1)[/tex]Where r is the radius and h is the height.
We have that, the diameter of the cone is approximately three times the altitude.
That is;
diameter = 3h
But, d = 2r
⇒2r = 3h
⇒ r = 3h/2
Now, we substitute r=3h/2 into equation (1).
[tex]V=\frac{1}{3}\pi(\frac{3h}{2})^2h[/tex][tex]=\frac{1}{3}\pi(\frac{9h^2}{4})h[/tex][tex]V=\frac{3}{4}\pi h^3[/tex]Now, differentiate the above with respect to t.
[tex]\frac{dv}{dt}=\frac{3}{4}\pi3h^2\frac{dh}{dt}[/tex]Simplify .
[tex]\frac{dv}{dt}=\frac{9}{4}\pi h^2\frac{dh}{dt}[/tex]Make dh/dt subject of formula.
[tex]\frac{dh}{dt}=\frac{dv}{dt}\times\frac{4}{9\pi h^2}----------(2)[/tex]Recall that, dv/dt = 4 and h=22
Substituting the values into equation (2), we have;
[tex]\frac{dh}{dt}=4\times\frac{4}{9\pi(22)^2}[/tex][tex]=\frac{16}{9\pi\text{ (484)}}[/tex][tex]=\frac{4}{9\pi\text{ (121)}}[/tex][tex]=\frac{4}{1089\pi}[/tex]Therefore, h' = dh/dt = 4/1089π ft/min.
Solve the equation using the Complete The Square Methodx^2+12x=13Do your work on paper. Take a picture, and upload it here. Show all your work/steps.
Answers
Given the quadratic equation:
[tex]x^2+12x=13[/tex]We can rewrite the equation as follows:
[tex]\begin{gathered} x^2+12x-13=0 \\ x^2+2\cdot6\cdot x-13=0 \\ x^2+2\cdot6\cdot x+6^2-6^2-13=0 \\ (x^2+2\cdot6\cdot x+6^2)-36-13=0 \end{gathered}[/tex]We see that the term inside the parenthesis is a perfect square polynomial. Then:
[tex](x+6)^2-49=0[/tex]Solving for x:
[tex](x+6)^2=49[/tex]Taking the square on both sides:
[tex]\begin{gathered} \sqrt{(x+6)^2}=\sqrt{49} \\ \\ |x+6|=7 \end{gathered}[/tex]This equation can turn into two equations:
[tex]\begin{gathered} x+6=7...(1) \\ x+6=-7...(2) \end{gathered}[/tex]Solving (1):
[tex]\begin{gathered} x=7-6 \\ \\ \Rightarrow x=1 \end{gathered}[/tex]Solving (2):
[tex]\begin{gathered} x=-7-6 \\ \\ \Rightarrow x=-13 \end{gathered}[/tex]Finally, the solutions to the equation are:
[tex]\begin{gathered} x_1=1 \\ \\ x_2=-13 \end{gathered}[/tex]Write 16 2/3% a as a decimal and b as a reduced fraction
Answers
Given the following percentage:
[tex]16\frac{2}{3}[/tex]Convert into a decimal and into a reduced fraction
16 + 2/3 =
16 + 2/3 = 0.166666 percent or 0.16 as a repeating decimal
To convert the decimal into a fraction:
[tex]\frac{(0.16\times10^2)-0}{10^2-1}=\frac{16}{99}[/tex]Fraction already reduced no need to simplify it further so....
= 16 / 99
What is the lateral surface area of the of the following figure? A. 982.36B. 851.76C. 785.34D. 709.8
Answers
Given : a triangular prism
The lateral surface area is the sum of the rectangular sides
So, the lateral surface area =
[tex]\begin{gathered} 18.2\cdot13+18.2\cdot13+18.2\cdot20.8 \\ =851.76\operatorname{cm} \end{gathered}[/tex]Another method : Find the perimeter of the triangle then multiply by 18.2
[tex]\begin{gathered} 18.2\cdot(13+13+20.8)_{} \\ =18.2\cdot46.8 \\ =851.76\operatorname{cm} \end{gathered}[/tex]so, the answer is option B. 851.76
The seventh decile is the ___ percentile in terms of the data set.
Answers
The statement is given as
The seventh decile is the ___ percentile in terms of the data set.
ExplanationThe seventh decile is the 70-th percentile in terms of the data set.
AnswerHence the answer is 70th percentile in terms of data set.
Calculator B В What is the measure of D? 25 ft Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. © 45 ft D mD =
Answers
Given data:
The given right angle triangle.
The expression for tan(D) is,
[tex]\tan (D)=\frac{BC}{DC}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} \tan (D)=\frac{25\text{ ft}}{45\text{ ft}} \\ D=\tan ^{-1}(\frac{25}{45})^{} \\ =29.05^{\circ} \end{gathered}[/tex]Thus, the value of angle D is 29.05 degrees.
Find the product of these complex numbers.(8 + 6i)(-5 + 7i) =A.-82 - 86iB.-82 + 26iC.2 + 26iD.2 - 86i
Answers
Solution
Step 1:
Write the expression:
(8 + 6i)(-5 + 7i)
Step 2:
[tex]\begin{gathered} \left(8+6i\right)\left(-5+7i\right) \\ \\ 8\times(-5)\text{ + 8 }\times7i\text{ + 6i }\times(-5)\text{ + 6i }\times\text{ 7i} \\ \\ =\text{ -40 + 56i - 30i + 42i}^2 \\ \\ =\text{ -40 + 26i - 42} \\ \\ =\text{ - 82 + 26i} \end{gathered}[/tex]Final answer
B.
-82 + 26i
Polygon ABCD with A (2,4), B (-4,-8), C (0,4), and D (12,-2), is dilated are the new coordinates? Is this a reduction or enlargement?
Answers
For this exercise it is important to know that, in Dilations:
1. When the scale factor is greater than 1, the Image (the figure obtained after the transformation) is an enlargement.
2. When the scale factor is greater than 0 but less than 1, the Image is a reduction:
[tex]0You know that the coordinates of the vertices of the polygon ABCD are:[tex]\begin{gathered} A(2,4) \\ B(-4,-8) \\ C(0,4) \\ D(12,-2) \end{gathered}[/tex]And the scale factor is:
[tex]k=\frac{1}{2}[/tex]Since:
[tex]0<\frac{1}{2}<1[/tex]It is a reduction.
You can identify that the rule of this transformation is:
[tex]undefined[/tex]The value of a ratio is 4/3. The second quantity in the ratio is how many times the first quantity in the ratio?
Answers
The second quantity in the ratio is 3/4 times the first quantity in the ratio.
How many times in the second quantity in the ratio more than the first quantity?Ratio is the number of times that one value is contained within other value(s). This ratio is expressed as an improper fraction. A fraction is a non-integer that is made up of a numerator and a denominator. An improper fraction is a fraction in which the numerator is larger than the denominator.
In order to determine the number of times the second quantity is greater than the first quantity, determine the inverse of the given fraction.
The inverse of 4 /3 is 3/4.
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The value of y is directly proportional to the value of x. If y = 3 whenx = 7, what is the value of x when y= 10.5? *Hint: Now you are looking for the "X". (show work)
Answers
we have that y=k*x, therefore we can say that k=y/x
[tex]k=\frac{3}{7}[/tex]so, if we have y= 10.5 we get that
[tex]x=\frac{y}{k}=\frac{10.5}{\frac{3}{7}}=24.5[/tex]x=24.5
What is the sum of the rational expressions below?3xХ+X+9 X-4O A.4x2-3xx2 +5X-36O B. 4x2-3x2x+5C.4x2x+5hosD.4xx2 +5x - 36
Answers
Given
[tex]\frac{3x}{x+9}+\frac{x}{x-4}[/tex]To find the sum of the rational expressions.
Explanation:
It is given that,
[tex]\frac{3x}{x+9}+\frac{x}{x-4}[/tex]Then,
[tex]\begin{gathered} \frac{3x}{x+9}+\frac{x}{x-4}=\frac{3x(x-4)+x(x+9)}{(x+9)(x-4)} \\ =\frac{3x^2-12x+x^2+9x}{x^2+9x-4x-36} \\ =\frac{4x^2-3x}{x^2+5x-36} \end{gathered}[/tex]Hence, the answer is option A).
f(x)=(0.13x⁴+0.22x³)-0.88x²-0.25x-0.09for this polynomial use a graph and find the minimum and maximum values written as coordinates
Answers
The given function is:
[tex]f(x)=0.13x^4+0.22x^3_{}-0.88x^2-0.25x-0.09[/tex]The graph for the polynomial f(x) is shown below:
Rewrite x^2+9 in factored form
Answers
The factored form is, x =3i and x = -3i
Given:
The objective is to write x^2+9 in factored form.
The factored form can be written as,
[tex]\begin{gathered} x^2+9=0 \\ x^2=-9 \\ x=\sqrt[]{-9} \\ x=\pm3i \end{gathered}[/tex]Here, i stands for imaginary term due the square root of (-1).
Hence, the factored form is, x =3i and x = -3i.
Calculate the simple interest due on a 54-day loan of $3600 if the interest rate is 3%. (Round your answer to the nearest cent.)
Answers
Answer:
$5832.00cents
Step-by-step explanation:
PRT÷100
$3600 ×54 ×3 /100
= $5832.00cents.
Find the equation of a line passing through the points (3,-4) and (1,2)
Answers
Explanation:
The equation of a line in slope-intercept form is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
The formula for the slope of a line with points (x1, y1) and (x2, y2) is:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]In this case the slope is:
[tex]m=\frac{-4-2}{3-1}=\frac{-6}{2}=-3[/tex]For now we have:
[tex]y=-3x+b[/tex]To find the y-intercept b, we have to replace (x,y) for one of the given points and solve for b. If we use point (1,2):
[tex]\begin{gathered} y=-3x+b \\ \text{ replacing x = 1 and y = 2} \\ 2=-3\cdot1+b \\ 2=-3+b \\ b=2+3=5 \end{gathered}[/tex]Answer:
The equation of the line is: y = -3x + 5
Answer:
y=\neg;[3]x+5
Step-by-step explanation:
Ted and his classmates started watering flowers at 11:36 andfinished watering all the flowers at 13:25. If they wateredflowers at a constant rate, at what time did they finish watering4/7 of the flowers? Give your answer in a 24-hour clock format,such as 19:00.Enter the answer
Answers
SOLUTION
The duration for watering the whole flower is
[tex]\begin{gathered} \text{ finishing time- starting time } \\ 13\colon25-11\colon36 \\ \end{gathered}[/tex]Which is
[tex]1\text{hours 49minutes or 109 minutes }[/tex]This means it takes 109minutes for watering the whole flowers.
The time taken for 4/7 of the flowers is
[tex]\begin{gathered} \frac{4}{7}0f\text{ 109} \\ \\ \frac{4}{7}\times109=\frac{436}{7}=62.29 \\ \\ \end{gathered}[/tex]Then it takes 62minutes 29seconds to wet 4/7 of the flowers
[tex]\begin{gathered} 62\text{minutes 29 seconds will be } \\ 1\text{hours 0.5minutes } \end{gathered}[/tex]The time they will finish watering 4/7 of the flowers will be
[tex]\begin{gathered} \text{starting time +Duration for 4/7 of the flowers } \\ 11\colon36+1;05 \\ 12\colon41 \end{gathered}[/tex]x2 - 4x + 4 = 0 following quadratic equations graphically
Answers
Since we have to solve it graphically, we need to plot the function:
Here, we can see that the point where the graph touches the y axis is when x = 2
The solution to the equation is x = 2
a blueprint for a house has a scale factor of 1 inch 3 ft. a wall in the blueprint is 5 in what is the length of the actual wall in feet
Answers
15 ft
Explanation
you can easily solve this by using a rule of three
Step 1
Let x represents the actual length of the wall in feet
is
[tex]1\text{ inc}\rightarrow3\text{ ft}[/tex]then
[tex]5\text{ in}\rightarrow x[/tex]as the proportion is the same
[tex]\begin{gathered} \frac{1}{3}=\frac{5}{x} \\ \text{cross multiply} \\ x\cdot1=5\cdot3 \\ x=15\text{ ft} \end{gathered}[/tex]so, the answer is 15 ft
I hope this helps you
2. The following triangle is an isosceles triangle. What is the length of the missing side? ? 11 in. 37 ? 4 in. 11 in 37° 4 in 530
Answers
An ISOSCELES triangle has two sides equal, and two base angles are also equal.
The two sides on the left and the right are equal. The right side measures 11 inches, therefore the left side also measures 11 inches.
The correct answer option is 11 inches
Kris and Pat were born on the exact same day but not in the same year their ages are shown in the table When Pat was 30 how old was Chris
Answers
A ) 18 years old
B) 19 years old
C) 27 years old
add three to kris' age to find Pat's age
Explanation
Step 1
when Kris was 15 .how old was pat
find the rule
a) check if the difference between the ages is constant
[tex]\begin{gathered} \text{Pat's age - Kris' Age=} \\ 7-4=3 \\ 10-7=3 \\ 15-12=3 \\ y_4\text{-}15= \\ 22-x_5= \\ 26-23=3 \end{gathered}[/tex]it means Pat is 3 years older than Kriss
then
when Kris was .how old was pat
[tex]\begin{gathered} y_4\text{-}15=3 \\ y_4-15=3 \\ \text{add 15 in both sides} \\ y_4-15+15=3+15 \\ y_4=18 \end{gathered}[/tex]Step 2
when Pat was 22, How old was Kris
the difference between the ages is the same, 3
so
[tex]\begin{gathered} 22-x_1=3 \\ \text{subtract 22 in both sides} \\ 22-x_5-22=3-22 \\ -x_5=-19 \\ x_5=19 \end{gathered}[/tex]Step 3
when Pat was 30, How old was kris
replace
[tex]\begin{gathered} \text{Pat's age -Kris' age=3} \\ 30-\text{Kri's age=3} \\ \text{subtract 30 in both sides} \\ 30-\text{Kri's age-30=3-}30 \\ -\text{Kris'age =-27} \\ \text{Kris'age }=27 \end{gathered}[/tex]Step 4
wich choice best represents the rule
as we saw before,
add three to kris' age to find Pat's age
[tex]\text{Kris' age+3}=\text{Pat's age}[/tex]The probability is
(Round to four decimal places as needed.)
Points: 0 of 1
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Assume that when human resource managers are randomly selected, 43% say job applicants should follow up within
two weeks. If 7 human resource managers are randomly selected, find the probability that at least 2 of them say job
applicants should follow up within two weels.
Answers
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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