Answer:
5 days
Step-by-step explanation:
75 = 10d +25
-25 -25
50 = 10d
/ /
10 10
5 = d
please calculate this limit
please help me
Answer:
We want to find:
[tex]\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n}[/tex]
Here we can use Stirling's approximation, which says that for large values of n, we get:
[tex]n! = \sqrt{2*\pi*n} *(\frac{n}{e} )^n[/tex]
Because here we are taking the limit when n tends to infinity, we can use this approximation.
Then we get.
[tex]\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n} = \lim_{n \to \infty} \frac{\sqrt[n]{\sqrt{2*\pi*n} *(\frac{n}{e} )^n} }{n} = \lim_{n \to \infty} \frac{n}{e*n} *\sqrt[2*n]{2*\pi*n}[/tex]
Now we can just simplify this, so we get:
[tex]\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\[/tex]
And we can rewrite it as:
[tex]\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n}[/tex]
The important part here is the exponent, as n tends to infinite, the exponent tends to zero.
Thus:
[tex]\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n} = \frac{1}{e}*1 = \frac{1}{e}[/tex]
Kevin paid $2.52 for 6 juice boxes. How much should Kevin expect to pay for 18 juice boxes?
Answer:
7.56
Step-by-step explanation:
Kevin should expect to pay approximately $7.56 for 18 juice boxes based on the given information.
To find out how much Kevin should expect to pay for 18 juice boxes based on the given information, we can set up a proportion using the number of juice boxes and the cost:
In general, an expression refers to a combination of symbols, numbers, variables, and operators that represent a specific computation or value. Expressions are a fundamental concept in mathematics, programming, and logic.
Let "x" be the cost of 18 juice boxes.
We have the proportion:
6 juice boxes / $2.52 = 18 juice boxes / x
To solve for "x," we can cross-multiply:
6x = 18 x $2.52
6x = $45.36
Now, divide both sides by 6 to isolate "x":
x = $45.36 / 6
x ≈ $7.56
Therefore, According to the data provided, Kevin should budget about $7.56 for 18 juice cartons.
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Daryl invested $2,200 for 3 years. He received interest of $264. What was the interest rate?
Answer:
4%
Step-by-step explanation:
264 interest/3 years=88 interest/year
principal x interest rate =interest/year
2200 x interest rate =88
interest rate =88/2200
interest rate =.04 or 4%
Find the volume of the solid. PLEASE HURRY ASAP
You decide to make a side business of selling face mask. The marginal cost for making a mask is $0.50 per mask. The total cost to to make 100 mask is hours is $62. You decide to sell the mask for $3 a mask.
Required:
a. Find the linear cost function C(x).
b. Find the revenue function R(x).
c. How many mask must be made to break even. State in a complete sentence using the context of the problem.
d. Determine the interval of profit and loss. State in a complete sentence using the context of the problem
Given:
Marginal cost for making 1 mask = $0.50
Total cost to make 100 masks = $62
Revenue per mask = $3
To find:
(a) Linear cost function C(x)
(b) Revenue function R(x)
(c) Break even point
(d) Interval of profit & loss
Solution:
(a) We know that linear cost function is given by,
Total cost = Fixed cost per unit + (Marginal cost per unit)*(Number of units)
Let 'x' denote the number of units
[tex]\Rightarrow[/tex] C(x) = b + mx
It is given that, m = $0.50
[tex]\Rightarrow[/tex] C(x) = b + 0.5x
It is also given that the total cost of making 100 masks is $62
[tex]\Rightarrow[/tex] C(100) = $62
[tex]\Rightarrow[/tex] b +0.5(100) = 62
[tex]\Rightarrow[/tex] b + 50 =62
[tex]\Rightarrow[/tex] b = 62 - 50
[tex]\Rightarrow[/tex] b = 12
[tex]\Rightarrow[/tex] C(x) = 12 + 0.5x
This is the linear cost function, C(x)
(b) We know that,
Total Revenue = Revenue per unit * Number of units
It is given that a mask is sold for $3, i.e., revenue per mask is $3
Let 'x' denote the number of units
Then the revenue function is given by,
R(x) = 3x
This is the revenue function, R(x)
(c) We know that, break even point refers to the point where total cost is equal to the total revenue. Thus, at break even point, we have,
C(x) = R(x)
[tex]\Rightarrow[/tex] 12 + 0.5x = 3x
[tex]\Rightarrow[/tex] 3x - 0.5x = 12
[tex]\Rightarrow[/tex] 2.5x = 12
[tex]\Rightarrow x=\frac{12}{2.5}[/tex]
[tex]\Rightarrow[/tex] x = 4.8
Since, 'x' denotes the number of masks, it must be a whole number and not a fraction. Thus, we will round off our value to get the break even point as 5 masks.
That is, 5 masks must be made to break even.
(d) We know that the profit function is given as the difference of revenue function and cost function. That is, we have,
P(x) = R(x) - C(x)
[tex]\Rightarrow[/tex] P(x) = 3x - (12 + 0.5x)
[tex]\Rightarrow[/tex] P(x) = 3x - 12 - 0.5x
[tex]\Rightarrow[/tex] P(x) = 2.5x -12
Now, we know that there is profit when the value of the profit function is positive & there is loss when the value of profit function is negative. Thus, we can calculate the intervals of profit and loss by finding the intervals where the profit function is positive & negative respectively. Alternatively, since the break even point denotes the point where the value of the profit function is 0, we can find the intervals of profit and loss as the intervals greater than and lesser than the break even point respectively.
That is, since the break even point is x = 4.8, the interval of profit is given as x > 4.8 & the interval of loss is given as x < 4.8
Taking into account that 'x' denotes the number of masks and thus must be a whole number, we have the intervals of profit and loss as,
Loss:= [tex]x \in [0,4][/tex]
Profit:= [tex]x \in [5, \infty)[/tex]
Final answer:
(a) Linear Cost function: C(x) = 12 + 0.5x
(b) Revenue function: R(x) = 3x
(c) 5 masks must be made to break even
(d) Interval of profit: [tex]x \in [5, \infty)[/tex], Interval of loss: [tex]x \in [0,4][/tex]
1. Of the three angles in a right-angled triangle, one angle has a measure
of 60 degrees. What is the measure of the third angle, Angle X? *
al 60
Answer:
30. A right triangle has one angle that is 90°
All angles add to 180°
180 - 90 - 60 = 30
Step-by-step explanation:
Bạn phương có 1.2tỷ đồng đang cân nhắc đầu tư vào các dự án sau
Kinh doanh cà phê với chi phí đầu tư là 300tr tổng số tiền thu đc 3 năm là400tr
Đầu tư của hàng kinh phí với kinh phí ban đầu là 200tr tổng số tiền thu đc 1năm là 217 tr
Biết rằng lãi suất ngân hàng là 8% năm hãy tính NPV giá trị hiện tại ròng cuat các dự án
Bạn phương nên đầu tư cái nào
Answer:
sssssssss
Step-by-step explanation:
ssssssss
A fast-food chain claims one medium order of its onion rings weighs 114 grams. Patrice thinks she is getting less than what the restaurant advertises. She weighs the next 16 random orders of onion rings before she eats them and finds the sample mean is 112.4 grams and the standard deviation is 7.63 grams. What conclusion can be drawn α = 0.10?
Answer:
Patrice does not have sufficient evidence to reject the fast-food chain's claim.
Step-by-step explanation:
unless she already ate some fries, not enough evidence
Use the piecewise function below to evaluate the points f(–3), f(0), and f(–1).
{9x,x−4,x<−1x≥−1
Question 17 options:
f(–3) = –7, f(0) = –0, and f(–1) = 5
f(–3) = –27, f(0) = –4, and f(–1) = 5
f(–3) = –7, f(0) = –4, and f(–1) = –1
f(–3) = –27, f(0) = –4, and f(–1) = –5
Given:
The piecewise function is:
[tex]f(x)=\begin{cases}9x & \text{ if } x<-1 \\ x-4 & \text{ if } x\geq -1 \end{cases}[/tex]
To find:
The values of [tex]f(-3),f(0), f(-1)[/tex].
Solution:
In the given piecewise function,
[tex]f(x)=9x[/tex] for [tex]x<-1[/tex] and [tex]f(x)=x-4[/tex] for [tex]x\geq -1[/tex].
Putting [tex]x=-3[/tex] in [tex]f(x)=9x[/tex], we get
[tex]f(-3)=9(-3)[/tex]
[tex]f(-3)=27[/tex]
Putting [tex]x=0[/tex] in [tex]f(x)=x-4[/tex], we get
[tex]f(0)=0-4[/tex]
[tex]f(0)=-4[/tex]
Putting [tex]x=-1[/tex] in [tex]f(x)=x-4[/tex], we get
[tex]f(-1)=-1-4[/tex]
[tex]f(-1)=-5[/tex]
The required values are [tex]f(-3)=27,f(0)=-4,f(-1)=-5[/tex].
Therefore, the correct option is D.
Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $10,000 and $50,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. Determine the planning value for the population standard deviation.
1. Determine how large a sample should be taken if the desired margin of error is:
a. $500
b. $200
c. $100
2. Would you recommend trying to obtain the $100 margin of error? Explain
Answer:
1) the planning value for the population standard deviation is 10,000
2)
a) Margin of error E = 500, n = 1536.64 ≈ 1537
b) Margin of error E = 200, n = 9604
c) Margin of error E = 100, n = 38416
3)
As we can see, sample size corresponding to margin of error of $100 is too large and may not be feasible.
Hence, I will not recommend trying to obtain the $100 margin of error in the present case.
Step-by-step explanation:
Given the data in the question;
1) Planning Value for the population standard deviation will be;
⇒ ( 50,000 - 10,000 ) / 4
= 40,000 / 4
σ = 10,000
Hence, the planning value for the population standard deviation is 10,000
2) how large a sample should be taken if the desired margin of error is;
we know that, n = [ ([tex]z_{\alpha /2[/tex] × σ ) / E ]²
given that confidence level = 95%, so [tex]z_{\alpha /2[/tex] = 1.96
Now,
a) Margin of error E = 500
n = [ ([tex]z_{\alpha /2[/tex] × σ ) / E ]²
n = [ ( 1.96 × 10000 ) / 500 ]²
n = [ 19600 / 500 ]²
n = 1536.64 ≈ 1537
b) Margin of error E = 200
n = [ ([tex]z_{\alpha /2[/tex] × σ ) / E ]²
n = [ ( 1.96 × 10000 ) / 200 ]²
n = [ 19600 / 200 ]²
n = 9604
c) Margin of error E = 100
n = [ ([tex]z_{\alpha /2[/tex] × σ ) / E ]²
n = [ ( 1.96 × 10000 ) / 100 ]²
n = [ 19600 / 100 ]²
n = 38416
3) Would you recommend trying to obtain the $100 margin of error?
As we can see, sample size corresponding to margin of error of $100 is too large and may not be feasible.
Hence, I will not recommend trying to obtain the $100 margin of error in the present case.
a) The hypotenuse of a right angled triangle is 15 cm. Taking the
perpendicular sides as x , y write the relation connecting the sides ?
b) If the area is 30 cm² find the length of its perpendicular sides ?
a) By Pythagoras theorem , h^2 is = a^2 + b^2 where a is the hypotenuse and a and b are the legs.
=) 15^2 = x^2 + y^2
That is the relation
b) area of triangle = 1/2 x height x base
=) 1/2 * x * y = 30
=) xy = 15cm
What single transformation maps AABConto AABC?
Answer:B
Step-by-step explanation: There is a mathematical way to do this , but the simplest way is just to imagine all of the transformations and choose the most reasonable one. All of the other answers are ridiculous.
A data related to air pollution in 10 U.S. cities. The dependent variable Y is the annual mean concentration of sulfur dioxide, in micrograms per cubic meter. The explanatory variable X records the number of manufacturing enterprises employing 20 or more workers. Below is Routput of the relationship between X and Y.
Coefficients: Estimate Std. Error t value Pro> tl) (Intercept) 9.4764 9.6266 0.98 0.354 2.0315 0.0070 4.51 0.CO2 ** X Signif. codes: 9 ****' 0.001 ***' 0.01 **' 0.05, 0.1' '1 Residual standard error: 17.9 on 8 degrees of freedom Multiple R-squared: 0.717, Adjusted R-squared: 0.682 F-statistic: 20.3 on 1 and 8 DF, p-value: 0.00198
a) Write the regression equation with parameters from the R output.b) Suppose that the number of manufacturing enterprises employing 20 or more workers in Irvine is 250, could you predict that the annual mean concentration of sulfur dioxide in Irvine?c) What is the residual if in Irvine the annual mean concentration of sulfur dioxide is 15 micrograms per cubic meter.d) What is the value of the correlation coefficient?e) Calculate a 95% confidence interval for the slope of the model.f) Based on the confidence interval, is there a linear relationship between X and Y?
Answer:
Y = 0.0315x + 9.4764
Residual = 2.35
Correlation Coefficient = 0.847
Step-by-step explanation:
From the R output given :
Intercept = 9.4764
Slope = 0.0315
x = number of manufacturing enterprise employing 20 or more workers
y = annual mean concentration of Sulphur dioxide
The regression equation :
y = bx + c
b = slope ; c = intercept
y = 0.0315x + 9.4764
Prediction using the regression equation :
The predicted y value, when x = 250
y = 0.0315(250) + 9.4764
y = 17.3514
The residual, if actual annual concentration = 15
Y residual = 17.35 - 15 = 2.35
The correlation Coefficient value, R
R = √R²
R = √0.717
R = 0.847
Points O and N are midpoints of the sides of triangle DEF.
Triangle D E F is cut by line segment O N. Point O is the midpoint of side E D and point N is the midpoint of side E F. The lengths of E O and O D are 22 centimeters. The lengths of E N and N F are 30 centimeters. The length of O N is 38 centimeters. Line segments D M and M F are congruent.
What is DM?
22 cm
30 cm
38 cm
76 cm
Answer:
DM=38\ cmDM=38 cm
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
Triangles DEF and OEN are similar by AA Similarity Postulate
Remember that if two triangles are similar, then the ratio of its corresponding sides is proportional
In this problem
\frac{DE}{OE}=\frac{DF}{ON}
OE
DE
=
ON
DF
substitute the given values
\frac{44}{22}=\frac{DF}{38}
22
44
=
38
DF
2=\frac{DF}{38}2=
38
DF
DF=2(38)=76\ cmDF=2(38)=76 cm
\begin{gathered}DF=2DM\\76=2DM\\DM=38\ cm\end{gathered}
DF=2DM
76=2DM
DM=38 cm
ur welcomeee♥️♥️♥️
Answer:
C
Step-by-step explanation:
Express the given situation as a linear inequality. needs at least units of a nutritional supplement per day. Red pills provide units and blue pills provide. Let x be the number of red pills and y be the number of blue pills.
A. 6x+ 5y ≥ 32
B. 11(x + y) ≥ 32
C. 320X+ y) ≥ 11
D. x+y≥32
The base of a triangle is 6 meters longer than the height of the triangle. If the area of the triangle is 108 square meters, what are the base and height of the triangle?
Answer:
36 meters
Step-by-step explanation:
A=1/2b×h
108sq. m=1/2.6m×h
both side canceling meter
h=2×108m/6
h=36m. answer
The height of the triangle is 12 meters, and the base of the triangle is 18 meters.
Let's denote the height of the triangle as "h" meters. According to the given information, the base of the triangle is 6 meters longer than the height, so the base can be represented as "(h + 6)" meters.
The area of a triangle is given by the formula: Area = (1/2) * base * height
We are given that the area of the triangle is 108 square meters, so we can write the equation as:
108 = (1/2) * (h + 6) * h
Now, let's solve for "h":
108 = (1/2) * (h² + 6h)
Multiply both sides by 2 to eliminate the fraction:
216 = h² + 6h
Rearrange the equation in standard quadratic form:
h² + 6h - 216 = 0
Now, let's solve this quadratic equation for "h." We can factor it or use the quadratic formula. Factoring, we get:
(h + 18)(h - 12) = 0
Setting each factor to zero:
h + 18 = 0 or h - 12 = 0
Solving for "h" in each case:
h = -18 (discard this negative value as height cannot be negative) or h = 12
Since height cannot be negative, we take the positive value of "h," which is 12 meters.
Now, we can find the base by using the given relationship: base = height + 6
base = 12 + 6 = 18 meters
So, the height of the triangle is 12 meters, and the base of the triangle is 18 meters.
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p(d + x) = 2x + 3
Which equation is correctly rewritten to solve for d?
Answer:
d = [tex]\frac{2x + 3}{p}[/tex] - x
Step-by-step explanation:
First divide both sides by p.
then subtract x from both sides
Answer:
[tex]\displaystyle d = \frac{2x + 3}{d} - x[/tex]
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/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle p(d + x) = 2x + 3[/tex]
Step 2: Solve for d
[Division Property of Equality] Divide p on both sides: [tex]\displaystyle d + x = \frac{2x + 3}{d}[/tex][Subtraction Property of Equality] Subtract x on both sides: [tex]\displaystyle d = \frac{2x + 3}{d} - x[/tex]please help me to do I want primeter and area of this
What is the value of x?
A triangle is given and a line is drawn from the vertex on the opposite side such that 2 triangles are formed. 1st triangle has 2 equal sides and vertex angle as 64 degrees and 2nd triangle has 2 equal sides and vertex angle as x degrees is given.
Answer:
116 degrees
Explanation:
If we divide the triangle from the vertex of the triangle, the vertex angle of each triangle would lie on a straight line in the triangle. Angle on a straight line is 180 degrees.
If the vertex angle of one triangle is 64 degrees then the vertex angle x of the other triangle is 180 degrees - 64 degrees = 116 degrees.
Stephen has some money in a box ,if 3/8 of the money is #4.80,how much does he have in the box?
SOMONE HELP WITH MATH
Answer:
x = 28
Step-by-step explanation:
HFG = EFI
6x - 4 = 164
6x = 164 + 4
6x = 168
x = 168/6
x = 28
Solve for y.
r/3-2/y=s/5
Answer:
y = 2 / (r/3 - s/5)
Step-by-step explanation:
r/3 - 2/y = s/5
add 2/y to both sides
r/3 = s/5 + 2/y
Subtract s/5 from both sides
r/3 - s/5 = 2/y
multiply both sides by y
y(r/3 - s/5) = 2
Divide both sides by r/3 - s/5
y = 2 / (r/3 - s/5)
8 ? i need answers asap
Answer: SInce this is multiple choice I won't provide an explanation. The answers are B) (-1, -4) and E) (4, 6)
Below is a data set containing six observations in ascending order
33 44 51 62 71 X
Find the value of missing data value X, if the range of data is 58
========================================================
Explanation:
The observations are in ascending order, which means the set is sorted from smallest to largest.
The X is at the right-most endpoint, so X is the largest value (aka the max).
The min is 33, so,
max - min = range
X - 33 = 58
X = 58+33
X = 91 is the max
Answer:
Step-by-step explanation:
The range of the data is the highest value - the lowest value.
The lowest in the list is 33 so the highest must be 33 + 58
= 91.
If the base ten blocks shown are to be divided into 6 equal groups, what should be done first?
Find the first three terms of the Maclaurin series for f(x) =
[tex]{e}^{ \frac{x}{2} } [/tex]
Step-by-step explanation:
Starting out with the Taylor series,
[tex]\displaystyle f(x) = \sum_{n=0}^{\infty} \dfrac{f^{(n)}(a)}{n!}(x-a)^n[/tex]
where [tex]f^{(n)}[/tex] is the nth derivative of f(x) and if we set a = 0, we get the special case of the Taylor series called the Maclaurin series:
[tex]\displaystyle f(x) = \sum_{n=0}^{\infty} \dfrac{f^{(n)}(0)}{n!}x^n[/tex]
Expanding this series up to the 1st 3 terms at a = 0,
[tex]f(x) = f(0) + \dfrac{f'(0)}{1!}x + \dfrac{f''(0)}{2!}x^2[/tex]
Let's find the derivatives of [tex]e^{\frac{x}{2}}[/tex]:
[tex]f'(x) = \frac{d}{dx} (e^{\frac{x}{2}}) = \frac{1}{2}e^{\frac{x}{2}} \Rightarrow f'(0) = \frac{1}{2}[/tex]
[tex]f''(x) = \frac{1}{4}e^{\frac{x}{2}} \Rightarrow f''(0) = \frac{1}{4}[/tex]
We can now write the Maclaurin series for [tex]e^{\frac{x}{2}}[/tex]as
[tex]e^{\frac{x}{2}} = 1 + \frac{1}{2} x + \frac{1}{8} x^2[/tex]
draw the graph of each line y=2x-3
Step-by-step explanation:
Here is the answer for your question
i think hhjs is how it goes
answer please..
help me to solve this..
Answer:
16
Step-by-step explanation:
a = 5
b = 3
a - b = 2
▪︎5 - 3 = 2
ab = 15
▪︎5(3) = 15
a^2 - b^2 = ?
5^2 = 25
3^2 = 9
25 - 9 = 16.
a^2 - b^2 = 16.
The exact area of a hub cap on a tire is
[tex]625\pi[/tex]
cm². What is the hub cap's radius?
17
18
19
29:52
Dao receives an employee discount on the purchase of a new automobile. The automobile that he is interested in has
a sticker price of $18,560. If his discount is 18 percent, what is the price that Dao will pay?
Answer: $15219.20
Step-by-step explanation:
Based on the information given, firstly we need to calculate the discount which will be:
= 18% × $18560
= 0.18 × $18560
= $3340.80
Then, the amount that Dao will pay will be:
= Sticker price - Discount
= $18560 - $3340.80
= $15219.20
Therefore, Dao will pay $15219.20