Answer: 85 i think
Step-by-step explanation:
If the mean age of the managers in company is 52 years with a standard deviation of 2.5 years, what is the probability that a randomly chosen manager will be between 54.5 and 57 years old
Answer:
13.5 %
Step-by-step explanation:
For a normal distribution, the Empirical Rule states that 68% of values lie between 1 standard deviation of the mean, 95% of values lie between 2 standard deviations of the mean, and 99.7% of values lie between 3 standard deviations of the mean. Here, we can see that 54.5 is 1 standard deviation away from the mean and 57 is 2 standard deviations away. This means that we want to find the difference between 1 and 2 standard deviations from the mean (in the positive direction)
To find the difference, we can simply find (percent of values 2 standard deviations of the mean) - (percent of values 1 standard deviation from the mean) = percent of values between 1 and 2 standard deviations from the mean
= 95-68 = 27 %
Finally, this gives us the percent of values between 1 and 2 standard deviations from the mean on both sides. We want to only find the positive aspect of this, as we don't care how many values are between 49.5 and 47 years old. Because normal distributions are symmetric, or equal on both sides of the mean, we can simply divide by 2 to eliminate the half we don't want, resulting in 27/2 = 13.5
The probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.
Given that, average age managers = 52 years standard deviation = 2.5 years.
What is standard deviation?Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.
Considering the equation Z = (X−μ)/σ
Where, X is the lower or higher value, as the case may be μ is the average σ is standard deviation
Now, z1= (54.5 - 52)/2.5
= 1
z2= (57 - 52)/2.5
= 2
Now, z2-z1= 2-1
= 1
P(54.5>Z<57)= 0.8413
Therefore, the probability that a randomly chosen manager will be between 54.5 and 57 years old is 0.8413.
Learn more about the standard deviation visit:
brainly.com/question/13905583.
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Which among the given schemes offers a monthly instalment of less than Rs 5000. ?
a) Scheme A
b) Scheme B
c) Scheme C
d) Both Scheme A and Scheme B
Write the equation in slope-intercept form. y=2(x−8)+4x
Answer:
y=6x-8
Step-by-step explanation:
y=2(x-8)+4x
y=2x+4x-8, y=6x-8
Coronado reported the following information for the current year: Sales (44000 units) $880000, direct materials and direct labor $440000, other variable costs $44000, and fixed costs $360000. What is Coronado’s break-even point in units?
a) 32727.
b) 40000.
c) 60923.
d) 36000.
During a particularly dry growing season in a southern state, farmers noticed that there is a delicate balance between the number of seeds that are planted per square foot and the yield of the crop in pounds per square foot. The yields were the smallest when the number of seeds per square foot was either very small or very large.
What is the explanatory variable for this relationship?
yield of the crop
location of the farm
precipitation for the growing season
number of seeds planted per square foot
I think it's (D).
number of seeds planted per sf
Answer:
The guy above me is correct
Step-by-step explanation:
2022
Answer:
number of seeds planted per square foot
Step-by-step explanation:
response is the yield explained by how many seeds are planted
Mua hàng hóa 10000kg về nhập kho,Đơn giá 200 000đ/kg,thuế gtgt là 10%,trả bằng chuyển khoản 50%,còn nợ người bán.Chi phí vận chuyển 2 100 000 bao gồm thueest gtgt 5% trả tiền mặt
Use the discriminant to determine the number of solutions to the quadratic equation −40m2+10m−1=0
From the analysis of the discriminant, you obtain that the quadratic function has no real solutions.
In first place, you must know that the roots or solutions of a quadratic function are those values of x for which the expression is 0. This is the values of x such that y = 0. That is, f (x) = 0.
Being the quadratic function f (x)=a*x² + b*x + c, then the solution must be when: 0 =a*x² + b*x + c
The solutions of a quadratic equation can be calculated with the quadratic formula:
[tex]Solutions=\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a}[/tex]
The discriminant is the part of the quadratic formula under the square root, that is, b² - 4*a*c
The discriminant can be positive, zero or negative and this determines how many solutions (or roots) there are for the given quadratic equation.
If the discriminant:
is positive: the quadratic function has two different real solutions. equal to zero: the quadratic function has a real solution. is negative: none of the solutions are real numbers. That is, it has no real solutions.In this case, a= -40, b=10 and c= -1. Then, replacing in the discriminant expression:
discriminant= 10² -4*(-40)*(-1)
Solving:
discriminant= 100 - 160
discriminant= -60
The discriminant is negative, so the quadratic function has no real solutions.
A general wishes to draw up his 7500 soldiers in the form of a square. After arranging, he found out that some of them are left out. How many soldiers were left out ?
If you want to form a square of 7500 soldiers, the side of the square must be [tex]\sqrt{7500}\approx86.6[/tex] soliders.
But since you cannot have 0.6 solider, the general needs to find the closest perfect square to the number 7500 which is less than 7500.
That number is 7396 which when square rooted gives 86 soliders on the side.
Subtract 7396 from 7500 and get how many soliders were left out,
[tex]7500-7396=\boxed{104}[/tex]
Hope this helps :)
Which equation does the graph of the systems of equations solve?
two linear functions intersecting at 3, negative 2
−one thirdx + 3 = x − 1
one thirdx − 3 = −x + 1
−one thirdx + 3 = −x − 1
one thirdx + 3 = x − 1
Answer:
-1/3x+3 = x-1
Step-by-step explanation:
The solution is (3,-2)
Check and see if the point solves the equation
-1/3x+3 = x-1
-1/3(3) +3 = 3-1
-1+3 = 3-1
2=2 yes
Answer:
C
Step-by-step explanation:
What is the completely factored form of this polynomial? x3 + 3x2 - 6x – 18
A. (x - 2)(x - 3)(x + 3)
B. (x2 - 6)(x + 3)
C. (x2 + 3)(x-6)
D. (x + 6)(x - 1)(x + 3)
Answer:
(x+3) ( x^2 -6)
Step-by-step explanation:
x^3 + 3x^2 - 6x – 18
Factor by grouping
x^3 + 3x^2 - 6x – 18
Factor x^2 out of the first group and -6 out of the second group
x^2( x+3) -6(x+3)
Factor out x+3
(x+3) ( x^2 -6)
A poll of 2,060 randomly selected adults showed that 89% of them own cell phones. The technology display below results from a test of the claim that 91% of adults own cell phones. Use the normal distribution as an approximation to the binomial distribution, and assume a 0.01 significance level to complete parts (a) through (e).
Test of p=0.91 vs p≠0.91
Sample X N Sample p 95% CI Z-Value p-Value
1 1833
2,060 0.889806 ( 0.872035 , 0.907577 ) ~ 3.20 0.001
a. Is the test two-tailed, left-tailed, or right-tailed?∙
Left-tailed test∙
Two-tailed test∙
Right tailed test
b. What is the test statistic?
The test statistic is _____ (Round to two decimal places as needed.)
c. What is the P-value?
The P-value is _____ (Round to three decimal places as needed.)
d. What is the null hypothesis and what do you conclude about it?
Identify the null hypothesis.
A. H0:p<0.91∙
B. H0:p≠0.91∙
C. H0:p>0.91∙
D. H0:p=0.91.
Answer:
Two tailed test
Test statistic = 3.20
Pvalue = 0.001
H1 : p ≠ 0.91
Step-by-step explanation:
Given :
Test of p=0.91 vs p≠0.91
The use if not equal to ≠ sign in the null means we have a tow tailed test, which means a difference exists in the proportion which could be lesser or greater than the stated population proportion.
The test statistic :
This is the Z value from the table given = 3.20
The Pvalue = 0.001
Since Pvalue < α ;Reject H0
At a time hours after taking a tablet, the rate at which a drug is being eliminated r(t)= 50 (e^-01t - e^-0.20t)is mg/hr. Assuming that all the drug is eventually eliminated, calculate the original dose.
Answer:
2500 mg
Step-by-step explanation:
Since r(t) is the rate at which the drug is being eliminated, we integrate r(t) with t from 0 to ∞ to find the original dose of drug, m. Since all of the drug will be eliminated at time t = ∞.
Since r(t) = 50 (e^-01t - e^-0.20t)
m = ∫₀⁰⁰50 (e^-01t - e^-0.20t)
= 50∫₀⁰⁰(e^-01t - e^-0.20t)
= 50[∫₀⁰⁰e^-01t - ∫₀⁰⁰e^-0.20t]
= 50([e^-01t/-0.01]₀⁰⁰ - [e^-0.20t/-0.02]₀⁰⁰)
= 50(1/-0.01[e^-01(∞) - e^-01(0)] - {1/-0.02[e^-0.02(∞) - e^-0.02(0)]})
= 50(1/-0.01[e^-(∞) - e^-(0)] - {1/-0.02[e^-(∞) - e^-(0)]})
= 50(1/-0.01[0 - 1] - {1/-0.02[0 - 1]})
= 50(1/-0.01[- 1] - {1/-0.02[- 1]})
= 50(1/0.01 - 1/0.02)
= 50(100 - 50)
= 50(50)
= 2500 mg
what is the absolute value of -5/9
Answer:
5/9
Step-by-step explanation:
In short, the absolute value of a number turns that number into a positive value no matter what. Here is a small representation:
Negative -> Positive
Positive -> Positive
Since we are working with a negative value, it will turn positive.
Best of Luck!
I NEED HELP PLEASE !!!
Answer: Because [tex]\frac{\pi }{3} =\frac{180\°}{3} =60\°[/tex], therefore [tex]\frac{\pi }{3} =60\°[/tex].
The difference between two positive integers is 7 and the sum of their squares is 949. What are the numbers?
Answer:
25 and 18
Step-by-step explanation:
Let's say that the first number is x and the second one is y.
First, the difference between them is 7, so x-y=7
Next, the sum of their squares is 949, so x²+y² = 949
We have
x-y=7
x²+y²=949
One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there
Adding y to both sides in the first equation, we have
x = 7 + y
Plugging that into the second equation for x, we have
(7+y)²+ y² = 949
expand
(7+y)(7+y) + y² = 949
49 + y² + 7y + 7y + y² = 949
combine like terms
2y² +14y + 49 = 949
subtract 949 from both sides to put this in the form of a quadratic equation
2y² + 14y - 900 = 0
divide both sides by 2
y² + 7y - 450 = 0
To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.
The factors of 450 are as follows:
1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.
Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have
y² + 25y - 18y - 450 = 0
y(y+25) - 18(y+25) = 0
(y-18)(y+25) = 0
Solving for 0,
y-18 = 0
add 18 to both sides
y=18
y+25 = 0
subtract 25 from both sides
y= -25
As the question states "two positive integers", this means that y must be positive, so y = 18. We know x-y=7, so
x-18 = 7
add 18 to both sides to isolate x
x = 25
reflect the x axis A B C D
Answer:
see explanation
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
A (- 1, - 17 ) → A' (- 1, 17 )
B (0, - 12 ) → B' (0, 12 )
C (- 5, - 11 ) → C' (- 5, 11 )
D (- 6, - 16 ) → D' (- 6, 16 )
I need help answering this ASAP
Answer:
"D"
if you multiply by Conjugate
the denominator would end up A^2 - b^2
the answer has 25 - 10x
that is D
Step-by-step explanation:
QUESTION 5 - 1 POINT
An investment of $32,000 is worth $38,302 after being compounded monthly at 3%. How many years was the investment
for? (Round to the nearest whole year).
9514 1404 393
Answer:
6
Step-by-step explanation:
The compound interest formula tells you the future value of principal P invested at annual rate r compounded n times per year for t years is ...
A = P(1 +r/n)^(nt)
Solving for t, we get ...
t = log(A/P)/(n·log(1 +r/n))
Using the given values, we find t to be ...
t = log(38302/32000)/(12·log(1 +0.03/12)) ≈ 5.9997
The investment was for 6 years.
pLEASE help best and right answer gets brainliest
Step-by-step explanation:
| - 5 | + | - 4 |
5 + 4
= 9
| - 6| - 4
6 - 4
2
I hope this answers your question.
Find the missing side lengths.
Answer:
x is 18, and y is 9 √ 3
Step-by-step explanation:
Since this is a right triangle that contains a 30 degree angle, we know this is a special right triangle, and the missing angle is 60 degrees since a triangle is 180 degrees, and 180 - 90 - 30 = 60.
The relationship is listed below:
The side opposite of the 30 degrees can be represented as a variable, say "p", and the hypotenuse which is x in your question is twice this. The side opposite of the 60 degree angle is x + √3
So x is 18, and y is 9√3
Find f such that f'(x) = 8x – 3. f(4) = 0
Answer: y=29 / (4,29)
Step-by-step explanation:
By graphing [tex]f(x)=8x-3[/tex] and [tex]f(4)=0[/tex] on Desmos. You'll be able to find that when x is 4, y is 29.
Similarly, you can plugin 4 into the original equation ([tex]f(x)=8x-3[/tex]) Which looks like:
[tex]8(4)-3\\32-3=29[/tex]
Additionally, you can change [tex]f(x)=[/tex] to [tex]y=[/tex] as it is the exact same thing. With that in mind, you can do the same with [tex]f(x)=0[/tex] and just change it to x=4. As you're wanting to know what the y-value is when x=4.
Answer:
4x²-3x+c is our original equation
Step-by-step explanation:
we have an independent number I called this number c
put 4 from x and try to find c
f(4)=4*(4²)-3*(4)+c=0
we have to be careful about f(4) is 0
64-12+c=0 and c is -52 so our original equation is 4x²-3x-52
Which expression corresponds to this graph?
Answer:
C
Step-by-step explanation:
The expression is x>55 and 55 isn't included
Answer:
c
Step-by-step explanation:
Need the help thanks guys
Answer:
Option D is the correct answer.
Step-by-step explanation:
The equation of the function is in vertex form. Thus, we can analyze the equation to determine the x and y values of the vertex. We know that the template format of a vertex form equation is as follows:
f(x) = a(x – h)2 + k . The only constants we need are h and k, where 'h' is the x-value of our vertex and 'k' is the y-value of our vertex.
The value of 'k' can be found quite simply by looking at the equation: -9.
The value of 'h' is a little trickier, as we must take into account the 'subtract' sign of the template equation, meaning that the '+7' in the given equation actually means that we are subtracting negative seven. Thus, the value of 'h' is -7.
Thus, the vertex of this graph is (-7,-9).
This means that option D is correct.
Answer:
The vertex is at ( -7, -9)
Step-by-step explanation:
y = (x+7)^2 -9
This is written in vertex form
y = a( x-h)^2 +k where ( h,k) is the vertex
y = ( x - -7)^2 + -9
The vertex is at ( -7, -9)
What is the value of the expression
below?
(7)3
Answer:
21
Step-by-step explanation:
Write the number in standard form as a decimal
Answer:
4.00810.1Step-by-step explanation:
I hope it will help youplease make me brainlestTHANK UPlease help! Question and answers are in the pic
So far she worked 4 days at 5 1/2 hours a day for a total of 22 hours.
22 hours x $8.50 = $187
Subtract that from the cost of the computer:
899-187 = $712
She needs $712 more.
Amount she makes per shift: $8.50 x 5 1/2 hours = $46.75
Divide what she needs by amount per shift:
712 / 46.75 = 15.22 shifts
She needs to work 16 more shifts.
Question 26 of 58
Mr. Nguyen recorded the numbers of students in his homeroom class who
participated in spirit week.
The table shows the number of students who dressed up each day.
Day
Mon Tues. Wed. Thurs. Fri. Total
Number of students 2
2
5
5
6
20
Find the mean and the median of the data set.
Determine which of these values is greater.
O A. The mean, 5, is greater than the median, 4.
OB. The mean, 5, is greater than the median, 2.
O c. The median, 6, is greater than the mean, 2.
O D. The median, 5, is greater than the mean, 4.
Answer:
D
Step-by-step explanation:
The answer is D.
Use the vertex
(h, k)
and a point on the graph
(x, y)
to find the general form of the equation of the quadratic function.
(h, k) = (−4, −1), (x, y) = (−7, 8)
Answer:
Step-by-step explanation:
Let the quadratic function be
y=a(x+4)²-1
∵(-7,8) lies on it.
8=a(-7+4)²-1
8+1=a(-3)²
9a=9
a=9/9=1
so quadratic function is
f(x)=1(x+4)²-1
or
f(x)=x²+8x+16-1
so quadratic function is
f(x)=x²+8x+15
find the sum 38+39+40+41...+114+115
It seems like you want to find the sum of 38 to 115:
[tex] \displaystyle \large{38 + 39 + 40 + 41 + ... + 114 + 115}[/tex]
If we notice, this is arithmetic series or the sum of arithmetic sequences.
To find the sum of the sequences, there are three types of formulas but I will demonstrate only one and the best for this problem.
[tex] \displaystyle \large{S_n = \frac{n(a_1+a_n) }{2} }[/tex]
This formula only applies to the sequences that have the common difference = 1.
Given that a1 = first term of sequence/series, n = number of terms and a_n = last term
We know the first term which is 38 and the last term is 115. The problem here is the number of sequences.
To find the n, you can use the following formula.
[tex] \displaystyle \large{n = (a_n - a_1) + 1}[/tex]
Substitute an = 115 and a1 = 38 in the formula of finding n.
[tex] \displaystyle \large{n = (115 - 38) + 1} \\ \displaystyle \large{n = (77) + 1} \\ \displaystyle \large{n = 78}[/tex]
Therefore the number of sequences is 78.
Then we substitute an = 115, a1 = 38 and n = 78 in the sum formula.
[tex] \displaystyle \large{S_{78} = \frac{78(38+115) }{2} } \\ \displaystyle \large{S_{78} = \frac{39(38+115) }{1} } \\ \displaystyle \large{S_{78} = 39(153) } \\ \displaystyle \large \boxed{S_{78} = 5967}[/tex]
Hence, the sum is 5967.
What is the equation of the line that passes through the point (8,−3) and has an undefined slope?
HELP FAST PLS!!
Answer:
x = 8
Step-by-step explanation:
undefined slope => m = oo
passes (8, -3) => (x1, y1)
the equation is : y-y1 =m(x-x1)
y+3 = oo(x-8)
=> x -8 = (y+3)/oo
x -8 = 0
x = 8
so, the equation is: x = 8
