Answer:
0.0475
Step-by-step explanation:
We use the binomial approximation to the normal to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In a large company, the proportion of employees who were promoted during the last year was 0.10.
This means that [tex]p = 0.1[/tex]
100 employees
This means that [tex]n = 100[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 100*0.1 = 10[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.1*0.9} = 3[/tex]
What is the probability that at least 15 of them were promoted during the last year?
This is [tex]P(X \geq 15)[/tex], which is 1 subtracted by the pvalue of Z when X = 15. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15 - 10}{3}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a pvalue of 0.9525
1 - 0.9525 = 0.0475.
0.0475 is the answer.
please help with this problem
Answer:
choice 1) 0, -4/5
Step-by-step explanation:
1/(t² + t) = 1/t - 5
multiply both sides of the equation by (t² + t):
1 = (t² + t)/t - 5t² - 5t
1 = t + 1 - 5t² -5t
-5t² - 4t = 0
t(-5t - 4) = 0
t = 0
-5t = 4
divide both sides by -5:
t = -4/5
Express f(x) in the form f(x) = (x - k)q(x) +r for the given value of k.
f(x) = 4x^3+ x² + x-8, k= -1
Answer:
f(x) = (x + 1)*(4*x² - 3*x + 4) - 12
Step-by-step explanation:
We have:
f(x) = 4*x³ + x² + x - 8
We want to write this in:
f(x) = (x - k)*q(x) + r.
with k = -1
Then we want to write:
4*x³ + x² + x - 8 = (x - (-1))*q(x) + r
4*x³ + x² + x - 8 = (x + 1)*q(x) + r
Because f(x) is polynomial of degree 3, we know that q(x) must be a polynomial of degree 2.
then:
q(x) = a*x² + b*x + c
Then:
4*x³ + x² + x - 8 = (x + 1)*(a*x² + b*x + c) + r
4*x³ + x² + x - 8 = a*x³ + b*x² + c*x + a*x² + b*x + c + r
if we take common factors in the right side we get:
4*x³ + x² + x - 8 = a*x³ + (b + a)*x² + (c + b)*x + (c + r)
Now, we must have:
4*x³ = a*x³
then:
4 = a
We also must have:
x² = (b + a)*x²
1 = (b + 4)
1 - 4 = b
-3 = b
We also must have:
x = (c + b)*x
1 = (c + (-3))
1 + 3 = c
4 = c
And finally:
- 8 = (c + r)
-8 = 4 + r
-8 - 4 = r
-12 = r
Then:
f(x) = (x + 1)*(4*x² - 3*x + 4) - 12
If $42.60 is in the tip jar and you share equally with 2 other people what is my share
Answer:
$14.20
Step-by-step explanation:
$42.60 ÷ 3
$14.20
The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 325 grams and a standard deviation of
10 grams. Find the weight that corresponds to each event. (Use Excel or Appendix C to calculate the z-value. Round your final
answers to 2 decimal places.)
3378
318.26
to
33174
a. Highest 10 percent
b. Middle 50 percent
c. Highest 80 percent
d. Lowest 10 percent
Answer:
a. Above 337.8 grams.
b. Between 318.25 grams and 331.75 grams.
c. Above 316.59 grams.
d. Below 312.2 grams
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 325 grams and a standard deviation of 10 grams.
This means that [tex]\mu = 325, \sigma = 10[/tex]
a. Highest 10 percent
This is X when Z has a pvalue of 1 - 0.1 = 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 325}{10}[/tex]
[tex]X - 325 = 10*1.28[/tex]
[tex]X = 337.8[/tex]
So 337.8 grams.
b. Middle 50 percent
Between the 50 - (50/2) = 25th percentile and the 50 + (50/2) = 75th percentile.
25th percentile:
X when Z has a pvalue of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 325}{10}[/tex]
[tex]X - 325 = -0.675*10[/tex]
[tex]X = 318.25[/tex]
75th percentile:
X when Z has a pvalue of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 325}{10}[/tex]
[tex]X - 325 = 0.675*10[/tex]
[tex]X = 331.75[/tex]
Between 318.25 grams and 331.75 grams.
c. Highest 80 percent
Above the 100 - 80 = 20th percentile, which is X when Z has a pvalue of 0.2. So X when Z = -0.841.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.841 = \frac{X - 325}{10}[/tex]
[tex]X - 325 = -0.841*10[/tex]
[tex]X = 316.59[/tex]
Above 316.59 grams.
d. Lowest 10 percent
Below the 10th percentile, which is X when Z has a pvalue of 0.1, so X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 325}{10}[/tex]
[tex]X - 325 = -1.28*10[/tex]
[tex]X = 312.2[/tex]
Below 312.2 grams
For what values of b will F(x) = logbx be a decreasing function?
Answer:
It is a decreasing function for 0 < b < 1.
Step-by-step explanation:
Logarithm function:
The logarithm function is given by:
[tex]F(x) = \log_{b}{(x)}[/tex]
The base b determines if the function increases or decreases.
For 0 < b < 1, the function decreases.
For b > 1, the function increases.
In this question:
By the definition above, it is a decreasing function for 0 < b < 1.
Solve for
3+4 |x/2 + 3| = -11
9514 1404 393
Answer:
no solution
Step-by-step explanation:
The absolute value cannot be negative. Here, the absolute value expression must be -3.5 in order to satisfy the equation. It cannot have that value.
there is no solution
from 2005 to 2015, a population of lions decreased by 2% annualy. there were 1500 of this population of likns in 2005. how many lions wew left by 2015
Answer:
30
Step-by-step explanation:
I think that's the answer but if I'm wrong tell me right away I'll try another method.
Chuck put new wallpaper in his bathroom. The pattern of the wallpaper
used 3 triangles to make a straight angle. The measures of the angles
are (9x - 72). (73x + ) and 11) What is the measure of the
obtuse angle? 7.3.5
ext
Tota
Answer:
x = 2.93
Step-by-step explanation:
The sum of angles of the triangle is 180degrees, hence;
9x - 72 + 73x + 11 = 180
82x - 61 = 180
82x = 180 + 61
82x = 241
Divide both sides by 82
82x/82 = 241/82
x = 2.93
Note that the functions might not be accurate but the same methos should be employed for any function given
What are the outliers???
solve (x – 5)^2 = 17
Answer:
x = 5 ± √17
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsMultiple RootsStep-by-step explanation:
Step 1: Define
(x - 5)² = 17
Step 2: Solve for x
[Equality Property] Square root both sides: x - 5 = ±√17[Addition Property of Equality] Add 5 on both sides: x = 5 ± √17a publisher for a promising new novel figures fixed costs overhead, advances, promotion, copy editing, type setting and so on at $57,000 and variable costs printing, paper, binding, shipping at $2.90 for each book produced. If the book is sold to distributors for $10 each, how many must be sold to break even?
Answer:
$2.90 for each book produced. If the book is sold to distributors for $10 each, how many must be sold to break even?
Step-by-step explanation:
. citizen of the represented state
no links please or you will be reported .
Answer:
Step-by-step explanation:
2 should be 50 degrees as well. 1 should be 130 (to get the needed 180) 3 should be 130 degrees. Hopefully this is correct
Find the conjugate and product of
i2 + 9
Answer:
i2 - 9
-85
Step-by-step explanation:
Conjugate of an expression is gotten by simply changing the sign to the opposite sign. For example, the conjugate of 5 is -5, the conjugate of x+2 is x-2. Given the complex value 2i+9, the conjugate will be -85
Taking their product
(2i+9)(2i-9)
Expand
2i(2i)-9(2i)+9(2i)+9(-9)
= 4i²-18-+18i-81
= 4i² - 81
Since i² = -1
= 4(-1) - 81
= -4-81
= -85
Hence the product will give -85
The double box plot shows the cost of the top-selling lunch menu items at two local restaurants. Determine which inference is true about the two populations.
Answer:
The spread of the data for The Red Brick Grill is greater than that for Sophie's Cafe.
Step-by-step explanation:
In the picture
how to get the answer.
how to get the 1.2762815625?
I know it says to multiple, but how to multiple to get that number?
thanks
9514 1404 393
Answer:
1.05 × 1.05 × 1.05 × 1.05 × 1.05 = 1.2762815625
Step-by-step explanation:
An exponent indicates how many times the base is a factor in the product. That is, 1.05 to the 5th power means ...
1.05⁵ = 1.05 × 1.05 × 1.05 × 1.05 × 1.05
This multiplication expression is evaluated in the usual way.
= 1.1025 × 1.05 × 1.05 × 1.05
= 1.157625 × 1.05 × 1.05
= 1.21550625 × 1.05
= 1.2762815625
__
All scientific and graphing calculators have a button for computing the power of a number. On my calculator its label is [tex]\displaystyle \boxed{y^x}[/tex]. The particulars of the function of this button can be found in the manual for your calculator.
For on-line calculators, such as the go.ogle calculator, or the Desmos graphing calculator, the caret (^) is used to signify an exponent. (See the input line in the first attachment for an example.)
A plumber charges a customer a one-time service fee of $79, $62 per hour for labor, and a surcharge of $15 per hour due to the call being an emergency.
Write an expression to represent the total charges for the plumber in two different ways. Let h represent the number of hours the job takes.
Answer:
As a plumber charges a customer a one-time service fee of $ 79, $ 62 per hour for labor, and a surcharge of $ 15 per hour due to the call being an emergency, to write an expression to represent the total charges for the plumber in two different ways, with H representing the number of hours the job takes, the following equations should be formulated:
Option 1:
Fixed amount + amount per hour multiplied by the number of hours + emergency amount multiplied by the number of hours = X
79 + 62H + 15H = X
Option 2:
Fixed amount + sum of emergency amount and the amount per hour multiplied by the number of hours = X
79 + ((62 + 15) x H) = X
1. Kathy is building a bed for her dollhouse. She used her real bed as a guide for how to
create the dollhouse bed. Her bed is 36 inches wide and 60 inches long. If she wants
to scale this down by 1/10, what would be the dimensions of the dollhouse bed?
Explain how you got your answer.
*Use the term SCALE FACTOR in your explanation.
PLS ANSWER QUICKLY !!!
solve 7!!!!!!!!!!!!!!!!!!!!!!!
Answer:
?
Step-by-step explanation:
The number of microscopic organisms in a petri dish grows exponentially with time. The function P below models the number of organisms after growing t days in the petri dish. Based on the function, which of the following statements is true?
P(t) = 60(3)^t/2
A. the predicted number of organisms in the dish triples every two days
B. The predicted number of organisms in the dish doubles every three days
C. The predicted number of organisms in the dish triples every day
D. The predicted number of organisms in the dish doubles every day
Answer:
A
Step-by-step explanation:
Given
P(t) = 60 [tex](3)^{\frac{t}{2} }[/tex]
Then
P(1) = 60 × [tex]3^{\frac{1}{2} }[/tex] = 60[tex]\sqrt{3}[/tex]
P(2) = 60 × 3 = 180
P(3) = 60 × [tex]3^{\frac{3}{2} }[/tex] = 60 ×[tex]\sqrt{3^{3} }[/tex] = 60 × 3[tex]\sqrt{3}[/tex] = 180[tex]\sqrt{3}[/tex]
P(4) = 60 × 3² = 60 × 9 = 540
P(5) = 60 × [tex]3^{\frac{5}{2} }[/tex] = 60 × [tex]\sqrt{3^{5} }[/tex] = 60 × 9[tex]\sqrt{3}[/tex] = 540[tex]\sqrt{3}[/tex]
P(6) = 60 × 3³ = 60 × 27 = 1620
From these 6 results we see that
P(3) = 3 × P(1)
P(4) = 3 × P(2)
P(5) = 3 × P(3)
P(6) = 3 × P(4)
The predicted number of organisms triples every 2 days → A
What is the slope of the line?
Answer:
1
Step-by-step explanation:
SOMEONE HELP ME PLS ASAP I WILL GIVE BRAINLIEST PROVE ABCD IS A PARALLELOGRAM
Answer:
It's a parallelogram because it has two parallel side (a,d)+(b,c) or (a,b)+(d,c). The shape is connected by the line "a,d"
Step-by-step explanation:
Use the remainder theorem and synthetic division to find f(k) for the given value of k.
Answer:
3
Step-by-step explanation:
Given that,
[tex]f(x) =-x^3-8x^2-15x+3[/tex]
We need to find the value of f(x) when k = -5
Put x = -5 in th given function.
So,
[tex]f(-5) =-(-5)^3-8(-5)^2-15(-5)+3\\\\=3[/tex]
Hence, the value of the given function is equal to 3.
ayme built a box in the shape of a rectangular prism with the dimensions shown. What is the volume of the box, in cubic inches? A rectangular prism has a length of 8 inches, a width of 2 inches, and a height of 4 inches. Use the formula V = l w h, where V represents the volume, l represents the length, w represents the width, and h represents the height. Inches cubed
Answer:
[tex]64(in)^{3} [/tex]
Step-by-step explanation:
The volume of a box is equal to the length l times the width w times the height h.
[tex](lenght) \times (width) \times (height)[/tex]
Substitute the values of the length l=8, the width w=2, and the height h=4 into the formula.
[tex]8 \times 2 \times 4[/tex]
Multiply 8 by 2.
[tex]16 \times 4[/tex]
Multiply 16 by 4.
[tex]64 {in}^{3} [/tex]
Hence, the volume of the rectangle prism is 64(in)³.
Answer:
64 in³Step-by-step explanation:
Given dimensions:
l = 8 inw = 2 inh = 4 inVolume of the prism is:
V = lwhV = 8*2*4 = 64 in³If the domain of f(n) = -4n - 3 is (-1, 1/4, 4), what is the range?
{-1, 2, -19)
{-7.-4.-13)
{1, -4, -19)
Create an inequality, 5 less than a number is less than -2
Answer:
x - 5 < -2
Answer is there
help screenshot below
show work , I’ll vote you brainliest if it is correct . Thank you
Answer:
Whats the question to this problem? Do you want to know if it's correct?
i can help! Just show your work? 1/2 times whatever X is + X+1 over whatever X is = 1/2 i can get the answer if you need it unless what i said helped! :) Your welcome!
Step-by-step explanation:
Have a great week! Hope i helped! Plz dont delete answer i promise i will help and it will be correct!
A CD cost a music store $5.75 to make. If the markup is 125%, what is going to be the cost of the CD in the store?
Answer:
12.94
Step-by-step explanation:
5.75x125%=7.19
7.19+5.75=12.94
Question 11. What is the product of 1.6 x 10- and 3.2 x 10' A. 5.12 x 10-4 B. 5.12 x 10 C.5.12 x 10 D. 5.12 x 104 please help will mark as brallinat
Answer:
A- [tex]5.12*10^{-4}[/tex]
Step-by-step explanation:
1.6* 3.2
add the exponents so 10 to the -4
What does please put it in simplest radical form and rationalize the denominators
N=
M=
Answer:
n = 6
m = 6√3
Step-by-step explanation:
Reference angle = 30°
Opposite = n
Adjacent = m
Hypotenuse = 12
✔️To find n, apply the trigonometric ratio, SOH:
Sin 30° = Opp/Hyp
Sin 30° = n/12
n = Sin 30° × 12
n = ½ × 12 = 6
✔️To find m, apply the trigonometric ratio, CAH:
Cos 30° = Adj/Hyp
Cos 30° = m/12
m = Cos 30° × 12
m = √3/2 × 12 (cos 30 = √3/2)
m = √3 × 6
m = 6√3