Answer:
6
Step-by-step explanation:
We can establish 6 as an upper bound, since 1*2*3 = 6, and 6 is clearly the greatest number that is a divisor of itself.
We can show that the product of any three consecutive numbers is divisible by 6, because out of any three consecutive integers, at least one must be divisible by 3, and at least one must be divisible by 2. Since the product must have factors of 2 and 3, it must also have 6 as a factor.
What is the answer for x? (3x-3)° [6(x-10)]
Answer:
x = 19
Step-by-step explanation:
The angles are vertical angles which means they are equal
3x-3 = 6(x-10)
Distribute
3x-3 = 6x-60
Subtract 3x from each side
3x-3 -3x = 6x-60-3x
-3 =3x-60
Add 60 to each side
-3+60 =3x-60+60
57 = 3x
Divide by 3
57/3 = 3x/3
19 =x
someone could help me?
Answer:
[tex]B= 3.14 * 4^4 = 50.24cm^2\\h = 16cm\\V=B*h=50.24*16=803.84cm^3[/tex]
Step-by-step explanation:
The area of the base is the area of a circle with a radius equal to 4 cm. It means that the area can be calculated as:
[tex]B = 3.14 * r^2\\B= 3.14 * 4^4 = 50.24cm^2[/tex]
The height of the cylinder is shown in the picture, it is equal to 16 cm.
Finally, the volume of the cylinder can be calculated as:
[tex]V = B*h=50.24*16 = 803.84cm^3[/tex]
Where B is the base and h is the height of the cylinder.
BRAINLIEST ANSWER GIVEN Without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions. The length of a rectangle is 2 feet longer than the width. The perimeter is 20 feet. Find the dimensions of the rectangle. Length= ?; width=?
Answer:
length = 6 feetwidth = 4 feetStep-by-step explanation:
Perimeter of a rectangle = 2l + 2w
where l is the length
w is the width
The length of the rectangle is 2 feet longer than the width is written as
l = 2 + w
Perimeter = 20feet
So we have
20 = 2( 2 + w ) + 2w
20 = 4 + 2w + 2w
4w = 16
Divide both sides by 4
w = 4
Substitute w = 4 into l = 2 + w
That's
l = 2 + 4
l = 6
length = 6 feetwidth = 4 feetHope this helps you
Answer:
w = 4 and L = 10
Step-by-step explanation:
perimeter of a rectangle = 2(l+w)
p = 20
L = 2 + w
w = ?
20 = 2(2 + w + w)
20 = 2(2 + 2w)
20/2 = 2 + 2w
10 = 2 + 2w
10 - 2 = 2w
8 = 2w
w = 8/2 = 4
L = w + 2
L = 4 +2 = 6
w = 4 and L = 10
You are given the following information obtained from a random sample of 5 observations. 20 18 17 22 18 At 90% confidence, you want to determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.) a) State the null and the alternative hypotheses. b) Compute the standard error of the mean. c) Determine the test statistic. d) Test to determine whether or not the mean of the population is significantly less than 21.
Answer:
a
The null hypothesis is
[tex]H_o : \mu = 21[/tex]
The Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
b
[tex]\sigma_{\= x} = 0.8944[/tex]
c
[tex]t = -2.236[/tex]
d
Yes the mean population is significantly less than 21.
Step-by-step explanation:
From the question we are given
a set of data
20 18 17 22 18
The confidence level is 90%
The sample size is n = 5
Generally the mean of the sample is mathematically evaluated as
[tex]\= x = \frac{20 + 18 + 17 + 22 + 18}{5}[/tex]
[tex]\= x = 19[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }[/tex]
[tex]\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }[/tex]
[tex]\sigma = 2[/tex]
Now the confidence level is given as 90 % hence the level of significance can be evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10[/tex]%
[tex]\alpha =0.10[/tex]
Now the null hypothesis is
[tex]H_o : \mu = 21[/tex]
the Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
The standard error of mean is mathematically evaluated as
[tex]\sigma_{\= x} = \frac{\sigma}{ \sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x} = \frac{2}{ \sqrt{5 } }[/tex]
[tex]\sigma_{\= x} = 0.8944[/tex]
The test statistic is evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 19 - 21 }{ 0.8944 }[/tex]
[tex]t = -2.236[/tex]
The critical value of the level of significance is obtained from the critical value table for z values as
[tex]z_{0.10} = 1.28[/tex]
Looking at the obtained value we see that [tex]z_{0.10}[/tex] is greater than the test statistics value so the null hypothesis is rejected
what other numbers can you square that result in 9 ?
Step-by-step explanation:
I'm not sure what your answers are, but you can only square 3 and -3 to get 9.
Answer:
3, -3
Step-by-step explanation:
3*3 = 9
-3 * -3 = 9
These are the only two numbers that square to 9
Which group of plants were the first to adapt to life on land? flowering pine mosses conifers
Answer:
mosses
Step-by-step explanation:
use socratic
Mosses are also known as the amphibian of the plant kingdom. The mosses were the first plant that can even survive on the land.
Bryophytes:It is the group of small plants that complete its life cycle in both land and water. They were the first plants to adapt to live on the land.For example- mosses.Conifers, pines, and flowering plants developed much later after the evolution of bryophytes.
Therefore, the mosses were the first plant that can even survive on the land.
Learn more about Bryophytes:
https://brainly.com/question/841138
Transformations of exponential functions
Answer:
Since the transformation is made by shifting the function right, it is a horizontal transformation.
A lottery ticket has a grand prize of $31 million. The probability of winning the grand prize is .000000018. Determine the expected value of the lottery ticket.
Answer:
$0.558
Step-by-step explanation:
The expected value is the sum of the value of each outcome times the chance that it happens. In this case, there are two outcomes:
Win $31 millionWin $0Then our expected value can be calculated as:
[tex]EV=(31,000,000)(0.000000018)+(0)(1-0.000000018)=0.558[/tex]
pleassssssssssssssssssssssssseeeeeeeeeeeeeeeeeeeeeeee helpppppppppppppp meeeeeeeee i giveeeee you bralienstttttt
Answer:
487 divide by 14
Step-by-step explanation:
have a nice day
How can I factor these complex conjuages? a^2 + b^2 and a^2 - b
Answer:
1) [tex](a+ib)(a-ib)[/tex]
2) [tex]a^2+i^2b[/tex]
Step-by-step explanation:
1) [tex]a^2+b^2[/tex]
=> [tex]a^2 - (-1)b^2[/tex] (We know that -1 = [tex]i^2[/tex] )
=> [tex]a^2-i^2b^2[/tex]
=> [tex](a)^2-(ib)^2[/tex]
Using Formula [tex]a^2 -b^2 = (a+b)(a-b)[/tex]
=> [tex](a+ib)(a-ib)[/tex]
2) [tex]a^2-b[/tex]
=> [tex]a^2+(-1)b[/tex] (We know that -1 = [tex]i^2[/tex] )
=> [tex]a^2+i^2b[/tex] (It cannot be simplified further)
Answer:
[tex]\boxed{(a+ib)(a-ib)}[/tex]
[tex]\boxed{a^2+i^2b}[/tex]
Step-by-step explanation:
[tex]a^2 + b^2[/tex]
Rewrite expression.
[tex]a^2- (-1)b^2[/tex]
Use identity : [tex]-1=i^2[/tex]
[tex]a^2- i^2 b^2[/tex]
Factor out square.
[tex]a^2-(ib)^2[/tex]
Apply difference of two squares formula : [tex]a^2-b^2 =(a+b)(a-b)[/tex]
[tex](a+ib)(a-ib)[/tex]
[tex]a^2-b[/tex]
Rewrite expression.
[tex]a^2+(-1)b[/tex]
Use identity : [tex]-1=i^2[/tex]
[tex]a^2+i^2b[/tex]
Use z scores to compare the given values. The tallest living man at one time had a height of 249 cm. The shortest living man at that time had a height of 120.2 cm. Heights of men at that time had a mean of 176.55 cm and a standard deviation of 7.23 cm. Which of these two men had the height that was more extreme?
Answer:
Step-by-step explanation:
Average height = 176.55 cm
Height of tallest man = 249 cm
Standard deviation = 7.23
z score of tallest man
= (249 - 176.55) / 7.23
= 10.02
Average height = 176.55 cm
Height of shortest man = 120.2 cm
Standard deviation = 7.23
z score of smallest man
= ( 176.55 - 120.2 ) / 7.23
= 7.79
Since Z - score of tallest man is more , his height was more extreme .
(25 points) PLEASE HELP, I gotta get this done or my mom will beat the hell out of me
Solve
x + y = 2
4y = -4x + 8
by elimination (not Gaussian!)
Thanks!
(also, please show work!)
Answer:
x=1
y=1
Step-by-step explanation:
Please look at the image below for solutions⬇️
Answer:
Step-by-step explanation:
Add the equations in order to solve for the first variable . Plug this value into the equations in order to solve for the remaining variables.
Point form
(x, 2-x)
Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far (in miles) is it from Jeremy's home to school?
Answer:
9 miles
Step-by-step explanation:
Let's say that the speed that Jeremy's father drives Jeremy through traffic is x. When there is no traffic, Jeremy's father drives 18 miles per hour faster than his speed in traffic, x. This would make the speed that Jeremy's father drives Jeremy to school without traffic, 18 / 60 + x. This is as it is 18 miles per hour faster, not 18 miles per minute faster.
Now recall the formula Speed = Distance / Time, or S = D / T. We want the distance here ( How far (in miles) from Jeremy's home to school ) so let's isolate D here in this formula,
S = D / T ⇒ D = S [tex]*[/tex] T - and as you know, the distance from Jeremy's home to school is the same, with or without traffic. So, we can consider case 1 : Jeremy's " distance traveled " in traffic, and case 2 : Jeremy's " distance traveled " without traffic, and make them equal to one another.
20 [tex]*[/tex] x = 12 [tex]*[/tex] ( 18 / 60 + x ),
20x = 3.6 + 12x,
8x = 3.6,
x = 0.45 - Now the distance is 20 [tex]*[/tex] x, and hence 20 [tex]*[/tex] 0.45 = 9 miles
Which equation shows y-5=x converted to slope intercept form.
Answer:
C) y = x + 5
Step-by-step explanation
Add 5 to both sides
Six years ago, an investor purchased a downtown apartment complex and an adjacent piece of land. The current value of the property is $850,000. Of the total, the current value of the apartment complex is $710,000 and the current value of the land is $140,000. Using the straight-line method, assuming an average appreciation of 6% on the land and an average depreciation of 3% on the apartment complex, what was the original value of the property? Round your answer to the nearest dollar.
Answer: $951,064.06 would be your answer.
Step-by-step explanation: Hope that helped!
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps
Answer:
123 domestic stamps
89 foreign stamps
Step-by-step explanation:
Answer:
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
Which equation represents the total number of stamps Malik collected?
✔ x + y = 212
Which equation represents the difference in the number of foreign and domestic stamps Malik collected?
✔ x – y = 34
Which system of linear equations represents the situation?
✔ x – y = 34 and x + y = 212
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
This system of equations models the given information for both stamp types.
x – y = 34
x + y = 212
Solve the system of equations.
How many foreign stamps does Malik have?
✔ 89 foreign stamps
How many domestic stamps does Malik have?
✔ 123 domestic stamps
Step-by-step explanation:
its right on 2021 edge! :) hope this helps
Hey, the question is with the image. Pls help
Answer:
8
Step-by-step explanation:
Line segment TS is tangent to circle O at point N.
Circle O is shown. Line segment Q N goes from one side of the circle to the other side. Tangent T S intersects the circle at point N. Point P is on the circle between points Q and N. Point R is on the circle between points Q and N. Angle Q N T is 74 degrees.
If the measure of Angle Q N T is 74°, what is the measure of Arc Q P N?
37°
74°
148°
212°\
Answer:
148°
Step-by-step explanation:
The measure of the intercepted arc QN is twice the measure of inscribed angle QNT.
arc QN = 2(74°) = 148°
_____
Comment on the question and answer
Your description "on the circle between points Q and N" is ambiguous. You used the same description for both points P and R. The interpretation we used is shown in the attachment. If point P is on the long arc NQ, then the measure of arc QPN will be the difference between 148° and 360°, hence 212°. You need to choose the answer that matches the diagram you have.
__
We call angle QNT an "inscribed angle" because it is a degenerate case of an inscribed angle. The usual case has the vertex of the angle separate from the ends of the arc it intercepts. In the case of a tangent meeting a chord, the vertex is coincident with one of the ends of the intercepted arc. The relation between angle measure and arc measure remains the same: 1 : 2.
Answer:
148
Step-by-step explanation:
Edge 2020
Olivia, a golfer, claims that her drive distance is more than 174 meters, on average. Several of her friends do not believe her, so she decides to do a hypothesis test, at a 10% significance level, to persuade them. She hits 15 drives. The mean distance of the sample drives is 188 meters. Olivia knows from experience that the standard deviation for her drive distance is 14 meters. H0: μ=174; Ha: μ>174 α=0.1 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?
Answer:
3.87
Step-by-step explanation:
The computation is shown below:
Data provided in the question
mean distance = [tex]\bar x[/tex] = 188 meters
Standard deviaton = [tex]\sigma = 14[/tex]
Hits drivers = 15
The distance = 174 meters
H_0: μ≤174;
H_a: μ>174
Based on the above information, the test statistic z-score is
[tex]z = \frac{\bar x - \mu }{\sigma / \sqrt{n} } \\\\ = \frac{188 - 174}{\ 14 / \sqrt{15} }[/tex]
= 3.87
Hence, the test statistic is 3.87
Note:
We take the μ≤174 instead of μ=174;
Find the sum of 1342, -295, -456,89.
Answer:
680
Step-by-step explanation:
add 1342+89 to get 1431
then add -295+-456 to get -751
then subtract 751 from 1431 to get 680
Step-by-step explanation:
Hope this is correct and helpful
HAVE A GOOD DAY!
Of the cartons produced by a company, % have a puncture, % have a smashed corner, and % have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner nothing%. (Type an integer or a decimal. Do not round.)
Full Question
Of the cartons produced by a company, 10% have a puncture, 6% have a smashed corner, and 0.4% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner nothing ____%. (Type an integer or a decimal. Do not round.)
Answer:
[tex]P(Punctured\ or\ Smashed\ Corner) = 0.156[/tex]
Step-by-step explanation:
Given
[tex]Puncture\ Corner = 10\%[/tex]
[tex]Smashed\ Corner = 6\%[/tex]
[tex]Punctured\ and\ Smashed\ Corner = 0.4\%[/tex]
Required
[tex]P(Punctured\ or\ Smashed\ Corner)[/tex]
For non-mutually exclusive event described above, P(Punctured or Smashed Corner) can be calculated as thus;
[tex]P(Punctured\ or\ Smashed\ Corner) = P(Punctured\ Corner) + P(Smashed\ Corner) - P(Punctured\ and\ Smashed\ Corner)[/tex]
Substitute:
10% for P(Puncture Corner),
6% for P(Smashed Corner) and
0.4% for P(Punctured and Smashed Corner)
[tex]P(Punctured\ or\ Smashed\ Corner) = 10\% + 6\% - 0.4\%[/tex]
[tex]P(Punctured\ or\ Smashed\ Corner) = 15.6\%[/tex]
Convert % to fraction
[tex]P(Punctured\ or\ Smashed\ Corner) = \frac{15.6}{100}[/tex]
Convert to decimal
[tex]P(Punctured\ or\ Smashed\ Corner) = 0.156[/tex]
Using Venn probabilities, it is found that:
The probability that a randomly selected carton has a puncture or a smashed corner is 15.6%.In this problem, the events are:
Event A: Puncture.Event B: Smashed corner.The "or" probability is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
10% have a puncture, hence [tex]P(A) = 0.1[/tex]6% have a smashed corner, hence [tex]P(B) = 0.06[/tex].0.4% have both a puncture and a smashed corner, hence [tex]P(A \cup B) = 0.004[/tex].Then:
[tex]P(A \cup B) = 0.1 + 0.06 - 0.004 = 0.156[/tex]
The probability that a randomly selected carton has a puncture or a smashed corner is 15.6%.
To learn more about Venn probabilities, you can check https://brainly.com/question/25698611
Marie is saving money for home repairs. So far, she has saved $1,558. She needs at least $2,158 for the repairs. She plans to
add $60 per week to her current savings until she can afford the repairs.
In this activity, you will algebraically model and solve an inequality based on this situation and interpret the solutions within
realistic guidelines
Part A
Question
Given the situation, which inequality models the number of additional weeks Marie needs to continue saving to afford the
home repairs?
Select the correct answer.
1,558 + 60x 22,158
60x + 1,558 5 2,158
1,558 - 60x s 2,158
2,158 - 60x 2 1,558
Answer:
Inequality: [tex]1558 + 60 x \geq 2158[/tex]
Number of Weeks: [tex]x \geq 10[/tex]
Step-by-step explanation:
Given
[tex]Initial\ Savings = \$1558[/tex]
[tex]Amount\ Needed = \$2158[/tex]
[tex]Additional\ Savings = \$60\ weekly[/tex]
Required
Represent this using an inequality
Represent the number of weeks as x;
This implies that, She'll save $60 * x in x weeks
Her total savings after x weeks would be
[tex]Initial\ Savings + 60 * x[/tex]
From the question, we understand that she needs at least 2158;
Mathematically, this can be represented as (greater than or equal to 2158)
[tex]\geq 2158[/tex]
Bringing the two expressions together;
[tex]Initial\ Savings + 60 * x \geq 2158[/tex]
Substitute 1558 for Initial Savings
[tex]1558 + 60 * x \geq 2158[/tex]
[tex]1558 + 60 x \geq 2158[/tex]
Hence, the inequality that represents the situation is [tex]1558 + 60 x \geq 2158[/tex]
Solving further for x (number of weeks)
[tex]1558 + 60 x \geq 2158[/tex]
Subtract 1558 from both sides
[tex]1558- 1558 + 60 x \geq 2158 - 1558[/tex]
[tex]60x \geq 600[/tex]
Divide both sides by 60
[tex]\frac{60x}{60} \geq \frac{600}{60}[/tex]
[tex]x \geq 10[/tex]
This means that she needs to save $60 for at least 10 weeks
Answer:
Its the first one
Step-by-step explanation:
I just did it lol
The linear combination method is applied to a system of equations as shown. 4(.25x + .5y = 3.75) → x + 2y = 15 (4x – 8y = 12) → x – 2y = 3 2x = 18
Answer:
x+2y=12-------(1)
x-2y=3---------(2)
Adding equations 1 and 2
we get
2x=18
x=9
Equation 1
9+2y=15
2y=15-9
2y=6
y=3
The solution of the given system is x=9, y=3
Step-by-step explanation
Is this equation linear or nonlinear?
y =x/2
Answer:
linear
Step-by-step explanation:
6th grade math , help me please :)
Answer:
a= 7/20
b=35
Step-by-step explanation:
A was simple because 7 people with blue eyes for every 20 people written in fraction form. For b they say what if it was 100 total people so 20 x 5 = 100 so 7 x 5= 35 so your answer to b is 35
What is the image of (-8, 10) when reflected in the y-axis?
Answer:
if you're just reflecting the point over the y-axis it just becomes (8,10)
Answer: (8, 10)
Explanation and Example:
I have a trick that I use. I'm not sure if it will make sense to you but I'll explain it. When the question asks you to reflect over the x-axis, then keep the x in (x,y) the same and just flip the sign for the y. If the question asks you to reflect over the y-axis, then keep y the same and flip the sign for x.
Reflect over x-axis:
(-2, 6) -----> (-2, -6)
Reflect over y-axis:
(-4, -8) -----> (4, -8)
Winston and Alice are taking a trip. Winston left at 8 am and traveled an average of 50 miles per hour. Alice left at 10 am and traveled an average of 70 miles per hour. At what time are they at the same place at the same time? Write a system of equation to represent this situation. Then use the substitution method with that system to determine at the time they will be in the same location. How many miles away from home will they be at that time?
Answer:
3 PM
350 miles
Step-by-step explanation:
Let's say t is the number of hours since 8 AM.
The distance traveled by Winston is:
w = 50t
The distance traveled by Alice is:
a = 70(t−2)
When w = a:
50t = 70(t−2)
50t = 70t − 140
140 = 20t
t = 7
Winston and Alice will be at the same place 7 hours after 8 AM, or 3 PM.
The distance they travel is 350 miles.
NEED HELP THANKLSSSS
Answer:
Side length: 3 cm.
Surface area: 54 cm squared.
Step-by-step explanation:
The formula for a cube is the side length cubed, since the formula for a rectangular prism is length times width times height. Those three measurements are the same for a cube.
So, since the volume is 27 cm cubed, we can say that the side length of the cube is the cube root of 27 cm cubed, or 3 cm.
There are 6 sides on a cube, and every cube has the same area. Since the side length of the cube is 3 cm, the area of one side of the cube is 3 * 3 = 9 cm squared. 9 * 6 = 54 cm squared.
Hope this helps!
The Orchard Cafe has found that about 15% of the diners who make reservations don't show up. If 77 reservations have been made, how many diners can be expected to show up? Find the standard deviation of this distribution
Answer:
65 dinners are expected to show up
The standard deviation of the distribution is 3.13
Step-by-step explanation:
Given
Proportion = 15%
Population = 77
Required
Expected Number that'll show up
Standard Deviation
If 15% won't show up; then
100% - 15% = 85% will show up
Expected Number, E(x) of Dinner is calculated as thus;
[tex]E(x) = np[/tex]
Where [tex]p = 85\%[/tex] (calculated above)
and [tex]n = 77[/tex]
Convert p to decimal
[tex]p = 0.85[/tex]
So;
[tex]E(x) = 0.85 * 77[/tex]
[tex]E(x) = 65.45[/tex]
[tex]E(x) = 65[/tex]
65 dinners are expected to show up
Calculating Standard Deviation, SD
Standard Deviation is calculated as;
[tex]SD = \sqrt{np(1-p)}[/tex]
Substitute 0.85 for p and 77 for n
[tex]SD = \sqrt{77 * 0.85 * (1-0.85)}[/tex]
[tex]SD = \sqrt{77 * 0.85 * 0.15}[/tex]
[tex]SD = \sqrt{9.8175}[/tex]
[tex]SD = 3.13328900678[/tex]
[tex]SD = 3.13[/tex] (Approximated)
The standard deviation of the distribution is 3.13
A manager receives 8 applications for a specific position. She wants to narrow it down to 5. In how many ways can she rank 5 applications?
Answer:
56 number of ways
Step-by-step explanation:
This question is a combination question since it involves selection.
Generally, if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
If a manager receives 8 applications for a specific position and wants to narrow it down to 5, the number of ways he can do this is 8C5
8C5 = 8!/(8-5)!5!
= 8!/3!5!
= 8*7*6*5!/3*2*5!
= 8*7*6/3*2
= 8*7
= 56 number of ways.
This means that the manager can rank 5 applications in 56 number of ways
The number of ways that can she rank 5 applications should be 6720.
Calculation of the number of ways:Since A manager receives 8 applications for a specific position. She wants to narrow it down to 5.
So here we do apply the permutation here:
[tex]= 8!\div 5!3! \times 5!\div 0!\\\\= 8\times 7\times 6\times 5\times 4[/tex]
= 6720
Hence, The number of ways that can she rank 5 applications should be 6720.
Learn more about ways here: https://brainly.com/question/18988173