Using the binomial distribution, it is found that there is a 0.4295 = 42.95% probability that at least 4 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
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
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:
41% say job applicants should follow up within two weeks, thus [tex]p = 0.41[/tex]8 managers are selected, thus [tex]n = 8[/tex].The probability that at least 4 of them say job applicants should follow up within two weeks is [tex]P(X \geq 4)[/tex], which is given by:
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.41)^{0}.(0.59)^{8} = 0.0147[/tex]
[tex]P(X = 1) = C_{8,1}.(0.41)^{1}.(0.59)^{7} = 0.0816[/tex]
[tex]P(X = 2) = C_{8,2}.(0.41)^{2}.(0.59)^{6} = 0.1985[/tex]
[tex]P(X = 3) = C_{8,3}.(0.41)^{3}.(0.59)^{5} = 0.2759[/tex]
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0147 + 0.0816 + 0.1985 + 0.2759 = 0.5707[/tex]
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.5705 = 0.4295[/tex]
0.4295 = 42.95% probability that at least 4 of them say job applicants should follow up within two weeks.
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Student Council sells bottled water at the cheerleading completion. At this rate, how many cases of bottled water would they sell in 3 hours? ________________________
Cases Sold: 3 and 6
Time (minutes): 20 and 40
Answer:
27
Step-by-step explanation:
Lets find the rate of selling:
Let v= the rate of selling, b = number of bottles of water, and t = time:
b over t gives us the [tex]v=\frac{b}{t}=\frac{3}{20}=\frac{6}{40}=0.15[/tex] rate of selling:
3 hours is 60min * 3 = 180 mins, and since v=b/t, vt=b:
(0.15) * 180 = 27 bottles of water
The equation x^2+ (k - 3)x + (3 - 2k) = 0, where k is a constant, has two distinct real roots.
(a) Show that k satisfies k^2+2k-3>0
Step-by-step explanation:
For quadratic equation ax^2 + bx + c = 0 to have two distinct real roots,
b^2 - 4ac must be positive.
b^2 - 4ac > 0
(k - 3)^2 - 4(3 - 2k) > 0
k^2 - 6k + 9 - 12 + 8k > 0
k^2 + 2k - 3 > 0
To show that k satisfies k² + 2k - 3 > 0 ,the discriminant is given as Δ [tex]= (k - 3)^2 - 4(1)(3 - 2k) = k^2 + 2k - 3.[/tex]
How to prove the expressionTo have two distinct real roots, the discriminant of the quadratic equation must be positive. The discriminant is given by;
Δ [tex]= (k - 3)^2 - 4(1)(3 - 2k) = k^2 + 2k - 3.[/tex]
For two distinct real roots, Δ > 0. So, we have k² + 2k - 3 > 0. Thus, k satisfies the inequality k² + 2k - 3 > 0.
In summary, for the quadratic equation x² + (k - 3)x + (3 - 2k) = 0 to have two distinct real roots, the value of k must satisfy the inequality k² + 2k - 3 > 0
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The weight of two fish tighter is 16 kg. If one fish weight is 10.5 kg, find the ratio of
the weight of the smaller fish to that of the bigger fish.
HELP!! Will give brainliest
Answer:
my brother said it was
Step-by-step explanation:
1400.053...
By which rule are these triangles congruent?
Answer:
S, S, S
Step-by-step explanation:
what is the cost of insurance for a female at 50 as a percentage of the same insurance for a male in his 30s female cost $819.73 the male's rate would be $1,192.64?
what is the midpoint of-2,2 4,-1
Solve for the values of x for each of the following exponential equations and inequalities.
1. 82− = 2
3. 5 = 25−2
4. 3+2 ≥ 27
5. 43 = 8−1
Answer:
8
2−x
=2
8^{2-x}=8^{1/3}8
2−x
=8
1/3
2-x=\dfrac{1}{3}2−x=
3
1
x=\dfrac{5}{3}x=
3
5
2.
(\dfrac{1}{2})^{x}<\dfrac{1}{8}(
2
1
)
x
<
8
1
(\dfrac{1}{2})^{x}<(\dfrac{1}{2})^{3}(
2
1
)
x
<(
2
1
)
3
x>3x>3
3.
5^x=25^{x-2}5
x
=25
x−2
25^{x/2}=25^{x-2}25
x/2
=25
x−2
\dfrac{x}{2}=x-2
2
x
=x−2
\dfrac{x}{2}=2
2
x
=2
x=4x=4
4.
3^{x+2}\geq273
x+2
≥27
3^{x+2}\geq3^33
x+2
≥3
3
x+2\geq3x+2≥3
x\geq1x≥1
5.
4^{3x}=8^{x-1}4
3x
=8
x−1
2^{6x}=2^{3x-3}2
6x
=2
3x−3
6x=3x-36x=3x−3
3x=-33x=−3
x=-1x=−1
Step-by-step explanation:
Can somebody help me as soon as possible?
Answer:
2400
Step-by-step explanation:
y= -300x + 2400
-300 equals the slope
2400 is the y-intercept
Equation: y = mx + b
help pls don't get it wrong I have an election tmr to see if I have good grades pls help
BTW,,
[tex]join \: bunny \: squad[/tex]
[tex]just \: comment \: if \: you \: want[/tex]
#bunnysquad
#bunnysquadinbrainly
Answer:
pls mark my brainliest because you didn't wriitten coorect question
Step-by-step explanation:
The picture shows a sandwich box:
A sandwich box is shown with a right triangle side. The right triangle has hypotenuse 14 cm and base 12 cm.
What is the approximate minimum height of a shelf in which this box can fit in the position shown in the pi
Answer:
the answer is 7.2 cm
Step-by-step explanation:
14^2 is 196
12^2 is 144
196 - 144 = 52
square root of 52 = 7.2
also i did FLVS & got it right lol
Show your work. -2.5(4x -4) = -6
Answer:
x = 1 3/5
Step-by-step explanation:
distribute.
-2.5*4x + (-2.5*-4) = -6
-10x +10 = -6
subtract 10 on both sides
-10x = -6 -10
divide by -10
x = -16/-10
x = 1 3/5
PLEASE HELP!!! ASAP: Decide whether there is enough information to prove that m || n. If so, state the theorem you would use.
Answer:
Alternative Interior Angles Converse
Step-by-step explanation:
The two angles shown in the figure above are alternate interior angles. Each is located within the two parallel lines intersected by the transversal, and they also lie on opposite side of the transversal.
The pair of angles are Alternate exterior Angle.
What are Parallel lines?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
From the Figure we can see that m is parallel to n.
and, from the property of parallel line we get the following equal angles
Vertical AnglesCorresponding AngleAlternate Interior Angle.Alternate exterior Angle.As, from the figure the pair of angles are Alternate exterior Angle.
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prove that 4^2n + 10n − 1 is divisible by 25. [hint: binomial theorem]
Answer:
0
Step-by-step explanation:
4^2 + 10-1
16 + 10 - 1
26 - 1
25
25 divided by 25 = 0
please help me !!! and thank youu !
Answer:
a=-3
b=-63
c= 2
d=8
e=9
f=128
h=-21
i=24
Step-by-step explanation:
Diane took a loan out for $3000 for 11 months and was charged a simple interest. The total interest she paid was $253. What’s her interest rate
Answer:
$300
Step-by-step explanation:
Diane's interest rate on the loan is approximately 8.43%.
Let's determine Diane's interest rate step by step.
1. First, we need to understand the formula for simple interest:
Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)
where:
P = Principal amount (initial loan amount)
R = Interest rate (unknown, what we want to find)
T = Time period in years
2. We have the following information from the problem:
P = $3000 (Principal amount)
SI = $253 (Total interest paid)
T = 11 months
3. However, to use the formula, we need to convert the time from months to years. Since 1 year has 12 months, we can write:
T = 11 months ÷ 12 months/year
≈ 0.917 years
4. Now, let's rearrange the formula to solve for the interest rate (R):
R = SI / (P × T)
Substituting the given values:
R = $253 / ($3000 × 0.917) ≈ 0.0925
5. Finally, we need to convert the interest rate from a decimal to a percentage:
R = 0.0925 × 100 ≈ 8.43%
So, Diane's interest rate on the loan is approximately 8.43%.
In summary, to find the interest rate, we used the simple interest formula and rearranged it to solve for the rate. We converted the time from months to years before calculating the interest rate. The result is approximately 8.43% interest rate, indicating the percentage of the principal that Diane had to pay as interest over 11 months.
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5551-525152+62626626×552526
solve it.
Answer:
=34602838637675
Step-by-step explanation:
=−519601+(62626626)(552526)
=−519601+34602839157276
=34602838637675
please help me with this sum
Answer:
Step-by-step explanation:
2. 3 × 12 = 3 × 2 × 6 = 3 × 2 × 2 × 3
3. 4 × 9 = 2 × 2 × 3 × 3
4. 6 × 6 = 2 × 3 × 2 × 3
please give me a brainliest answer
Step-by-step explanation:
2. 36 = 3 × 12 = 3 × 2 × 6 = 3 × 2 × 2 × 3
3. 36 = 4 × 9 = 2 × 2 × 3 × 3
4. 36 = 6 × 6 = 2 × 3 × 2 × 3
ABC has side lengths 5 inches, 7 inches, and 10 inches.
JKL has side lengths 12
inches, 35 inches, and 37 inches. PQR has side lengths 13 inches, 10 inches, and 16
inches.
Answer: Obtuse, Right, Acute
Step-by-step explanation:
ABC: 5²+ 7² = 10²
25 + 49 = 100
c is greater so it is obtuse.
JKL: 12² + 35² = 37²
144 + 1225 = 1369
1369 = 1369
legs are equal to c so it is right.
PQR: 13² + 10² = 16²
169 + 100 + 256
269 = 256
c is less so it is acute.
Please help I’ll give brainliest
Answer:
ITS D GOOD LUCK WITH YOUR HMK
What is an acute- angled triangle?
A.) Has 3 acute angles
B.) Has 1 right angle
C.) Has one acute angle
D.) Has 1 obtuse angle
Answer:
c
Step-by-step explanation:
Will mark as brainlist
The title of the poem, "Poetry and Prose, 'is an example of antonyms. Poetry and prose are "opposite' ways of writing.
Search the poem to find the other antonym pairs. Ust the words in the order that they appear in the poem. There are
seven more pairs. Separate each word with a comma. For example: poetry, prose.
If it isn't a poem. It's prose:
And friends cannot be foes.
A package not heavy is light.
And after the day comes night.
if it's ap. it can't be down:
The country is never a town.
When asleep we aren't awake:
To give is never to take
ah, yes, college mathematics. how riveting
poem, prose
friends, foes
heavy, light
day, night
up, down
country, town
asleep, awake
give, take
I truly commend you on your pursuit of such higher level mathematics studies. Good luck!
HELP POINTS FOR Each answEr quantity 4 times x plus 3 end quantity divided by 5 equals quantity 8 times x minus 1 end quantity divided by 9.
[tex]\displaystyle \frac{4x+3}{5} ^{/9}=\frac{8x-1}{9} ^{/5} \\\\\\ 36x+27=40x-5 \\\\ 40x-36x=27+5\\\\ 4x=32 \\\\ \boxed{x=8 }[/tex]
Step-by-step explanation:
Given fractional expression:
(4x+3)/5 = (8x-1)/9
By doing cross multiplication, we get
⇛4x(9) + 3(9) = 8x(5) - 1(5)
⇛36x + 27 = 40x - 5
Now, combine the like terms in one side.
⇛27x - 40x = -5 + 36
⇛-13x = 31
⇛x = 31/-13 Ans.
Write 1000 as a power of 10
a) The simplest form of 20
100
is _____________.
b) The mixed fraction of 80
9
is _____________.
c) When we convert 13 5
7
to an improper fraction, we get __________.
d) In a basket of 27 mangoes, 6 are rotten. This statement can be written as a fraction
as (give the answer in the simplest form) ___________.
Si el punto (5,0) está en una gráfica, żes (5,0)
la intersección con el eje y de la gráfica? Explica
Answer:
Can you put it in English pls..
Step-by-step explanation:
36. The girls' gym teacher needs to purchase
15 softballs, 5 packages of tennis balls,
and 2 soccer balls. She plans to collect
$1 from each of her 15 students to help
pay for the balls. Write and evaluate an
expression to show how much more the
teacher will have to pay.
Help
Answer:Message me for full answer
Step-by-step explanation:
Please I need help I wasn’t at school today
choose the equation of the graphed function
Helpppppppp meeeeeeee
Answer:
Step-by-step explanation:
solution 1:
570 not man = 15% (cause 100% - 85%)
15% = 570
100% = w (for "whole package")
15w = 100 * 570
15w = 57000
w = 57000 / 15
w = 3800
solution 2:
15% = 570
85 = m (for "men)
15m = 570 * 85
15m = 48450
m = 48450 / 15
m = 3230
100% = 85% + 15%
100% = b (for "buch of people")
b = 3230 + 570
b = 3800