The number of cases per batch that the manufacturer should produce to minimize cost is 462 cases per batch.
How can inventory costs be minimized?To minimize inventory costs, especially setup and holding costs, the economic order quantity (EOQ) technique is deployed.
The EOQ model refers to the ideal order or batch quantity a company should purchase per order or produce per batch to minimize its inventory costs.
Some of a company's inventory costs include holding costs, shortage costs, setup, and ordering costs.
Using the EOQ model shows the ideal minimum units that the manufacturer should produce per batch to minimize costs.
The EOQ formula is square root of: [2(setup costs)(demand rate)] / holding costs.
Data and Calculations:Annual demand = 22,638 cases
Storage cost per case = $7
Setup cost per batch = $33
Product unit cost = $15 per case
EOQ = square root of: [2(setup costs)(demand rate)] / holding costs.
= square root of 2 x $33 x 22,638/$7
= square root of 213,444
= 462
Number of batches = 49 (22,638/462)
Thus, the number of cases per batch that the manufacturer should produce to minimize cost is 462 cases per batch.
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I have 3 more then twice as many socks then keith she has 19 pairs of socks how many do keith have using algebra to solve this what is one step to take?
Answer:
40
Step-by-step explanation:
19*2 = 38 + 2 = 40
Answer:
Step-by-step explanation:
we have to get k by itself on one side of the equal sign. To do that we have to get rid of 3. To get rid of 3 we have to do the opposite. The opposite of +3 is -3 so we -3 on both sides. 19 - 3 = 16. So k = 16
k+3=19
-3 -3
k=16
On Wednesday, the temperature changes -3
∘
each hour for 10 hours. If the temperature was 12
∘
to begin with on Wednesday, what was the temperature after the 10 hours.
Answer:
-24 would be the temperature
Answer:
-24 BECAUSE I did all the math.
When a lilac bush is planted, it is 24 inches tall. Each month, it grows 6 inches taller. How tall will It get over time?
Dependent variable: ______
Independent variable: ______
Equation: ______
Answer:
Dependent variable: time(months) or [tex]t[/tex]
Independent variable: 6
Step-by-step explanation:
[tex]h=24+6t[/tex]
(h=height)
Find the solution of the differential equation that satisfies the given initial condition. dy/dx=x/y , y(0)=-1
Separating variables, we have
[tex]\dfrac{dy}{dx} = \dfrac xy \implies y\,dy = x\,dx[/tex]
Integrate both sides.
[tex]\displaystyle \int y\,dy = \int x\,dx[/tex]
[tex]\dfrac12 y^2 = \dfrac12 x^2 + C[/tex]
Given that [tex]y(0)=-1[/tex], we find
[tex]\dfrac12 (-1)^2 = \dfrac12 0^2 + C \implies C = \dfrac12[/tex]
Then the particular solution is
[tex]\dfrac12 y^2 = \dfrac12 x^2 + \dfrac12[/tex]
[tex]y^2 = x^2 + 1[/tex]
[tex]y = \pm\sqrt{x^2 + 1}[/tex]
and because [tex]y(0)=-1[/tex], we take the negative solution to accommodate this initial value.
[tex]\boxed{y(x) = -\sqrt{x^2+1}}[/tex]
Which pair of words describe this system of equations
3y=9x-6
2y-6x=4
The pair of words that describe the given system of equations is: consistent and dependent.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
It demonstrates the equality of the relationship between the expressions written on the left and the right.
Given equations:
3y=9x-6
2y-6x=4
The first equation can be simplified and written as: y=3x-2
Similarly, the second equation can be written as: y-3x=2
It can be seen that the two equations are the same. Thus, the given system of equations is consistent and dependent.
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NO LINKS!! Please help me with this problem
Information : The given hyperbola is a horizontal hylerbola with its centre (3 , -5) and one of its focus at (9 , -5) and vertex at (7 , -5) and as we can see that the focus and vertex have same y - coordinates, it must have its Transverse axis on line y = - 5.
Now,
it's vertex is given, I.e (7 , -5)
so, length of semi transverse axis will be equal to distance of vertex from centre, i.e
a = 7 - 3 = 4 unitsNow, it's focus can be represented as ;
[tex]\qquad \sf \dashrightarrow \: (3 + ae, - 5 )[/tex]
so,
ae + 3 = 9and we know, a = 4
[tex]\qquad \sf \dashrightarrow \: 4e + 3 = 9[/tex]
[tex]\qquad \sf \dashrightarrow \: 4e = 6[/tex]
[tex]\qquad \sf \dashrightarrow \: e = \cfrac{3}{2} [/tex]
Now, let's find the measure of semi - conjugate axis (b)
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = {a}^{2} ( {e}^{2} - 1)[/tex]
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = 16( \frac{9}{4} - 1)[/tex]
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = 16( \frac{9 - 4}{4} )[/tex]
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = 16( \frac{5}{4} )[/tex]
[tex]\qquad \sf \dashrightarrow \: {b}^{2} = 20[/tex]
[tex]\qquad \sf \dashrightarrow \: b = \sqrt{20} [/tex]
So, it's time to write the equation of hyperbola, as we already have the values of a and b ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {(x - h)}^{2} }{ {a}^{2} } - \cfrac{( {y - k)}^{2} }{ {b}^{2} } = 1[/tex]
[ plug in the values, and h = x - coordinate of centre, and k = y - coordinate of centre ]
[tex]\qquad \sf \dashrightarrow \: \cfrac{ ({x-3)}^{2} }{ {16}^{} } - \dfrac{ {(y+5)}^{2} }{ { {20} }^{} } = 1[/tex]
Hello and Good Morning/Afternoon:
Let's solve this problem step-by-step:
Let's find the format of the standard form of hyperbole:
[tex]\hookrightarrow \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2} =1[/tex]
(h,k): hyperbole center ⇒(3,-5)Let's find the value of a, b:
value of a: distance between vertex (7, -5) and center (3, -5)[tex]a = \sqrt{(7-3)^2+(-5--5)^2} =\sqrt{16} =4[/tex]
value of b: [tex]\sqrt{c^2-a^2}[/tex]⇒value of c: distance between focus (9, -5) and center (3, -5)
[tex]c = \sqrt{(3-9)^2+(-5--5)^2}=\sqrt{36} =6[/tex]
⇒ therefore:
[tex]b = \sqrt{c^2-a^2} =\sqrt{6^2-4^2}=\sqrt{20}[/tex]
Let's plug everything into our standard form of the equation:
[tex]\frac{(x-3)^2}{4^2} -\frac{(y--5)^2}{(\sqrt{20})^2 } =1\\\frac{(x-3)^2}{16} -\frac{(y+5)^2}{20 } =1[/tex] <== Answer
Hope that helps!
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About 5% of the population has a particular genetic mutation. 300 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 300. Round your answer to two decimal places.
The standard deviation for the number of people with the genetic mutation is 3.77
How to determine the standard deviation?The given parameters are:
Sample size, n = 300
Proportion that has the particular genetic mutation, p = 5%
The standard deviation for the number of people with the genetic mutation is calculated as:
Standard deviation = √np(1 - p)
Substitute the known values in the above equation
Standard deviation = √300 * 5% * (1 - 5%)
Evaluate the product
Standard deviation = √14.25
Evaluate the exponent
Standard deviation = 3.77
Hence, the standard deviation for the number of people with the genetic mutation is 3.77
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A cannonball is shot straight upward with a velocity of 80 ft/sec. Its height after t seconds is given by f (t) = 80t - 16 t to the second power. Round your answers to 1 decimal place if necessary.
How high will the cannon ball go?
How many seconds will it take to reach this maximum height?
Check the picture below, so the ball's path is pretty much like so, and it reaches its hightest at its vertex, so
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&80\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&0\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ f(t)=80t-16t^2\implies f(t)=-16t^2+80t+0 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+80}x\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 80}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (80)^2}{4(-16)}\right) \implies \left( - \cfrac{ 80 }{ -32 }~~,~~0 - \cfrac{ 6400 }{ -64 } \right) \\\\\\ \left( \cfrac{5}{2}~~,~~100 \right)\implies \underset{~\hfill feet ~~ }{\stackrel{seconds\qquad }{\left( 2\frac{1}{2}~~,~~100 \right)}}[/tex]
(x^2-y^2)dx+2xydy=0
so this is a problem of a differential equation I've been trying so hard to match with the given answer but failed every time I tried. So, is there anyone who can really can help me out to catch the mistakes that I'm making?
* The last line of my workout is just a dump guess.
The pictures are my workouts also the answer to this question is attached. Please read my solutions by this order : pic-1, pic-3 & pic-2, if necessary.
[tex](x^2 - y^2) \, dx + 2xy \, dy = 0[/tex]
Multiply both sides by [tex]\frac1{x^2}[/tex].
[tex]\left(1 - \dfrac{y^2}{x^2}\right) \, dx + \dfrac{2y}x \, dy = 0[/tex]
Substitute [tex]y=vx[/tex], so [tex]v=\frac yx[/tex] and [tex]dy=x\,dv+v\,dx[/tex].
[tex](1-v^2) \, dx + 2v (x\,dv + v\,dx) = 0[/tex]
[tex](1 + v^2) \, dx + 2xv \, dv = 0[/tex]
Separate the variables.
[tex]2xv\,dv = -(1 + v^2) \, dx[/tex]
[tex]\dfrac{v}{1+v^2}\,dv = -\dfrac{dx}{2x}[/tex]
Integrate both sides
[tex]\displaystyle \int \frac{v}{1+v^2}\,dv = -\frac12 \int \frac{dx}x[/tex]
On the left side, substitute [tex]w=1+v^2[/tex] and [tex]dw=2v\,dv[/tex].
[tex]\displaystyle \frac12 \int \frac{dw}w = -\frac12 \int\frac{dx}x[/tex]
[tex]\displaystyle \ln|w| = -\ln|x| + C[/tex]
Solve for [tex]w[/tex], then [tex]v[/tex], then [tex]y[/tex].
[tex]e^{\ln|w|} = e^{-\ln|x| + C}[/tex]
[tex]w = e^C e^{\ln|x^{-1}|}[/tex]
[tex]w = Cx^{-1}[/tex]
[tex]1 + v^2 = Cx^{-1}[/tex]
[tex]1 + \dfrac{y^2}{x^2} = Cx^{-1}[/tex]
[tex]\implies \boxed{x^2 + y^2 = Cx}[/tex]
Your mistake is in the first image, between third and second lines from the bottom. (It may not be the only one, it's the first one that matters.)
You incorrectly combine the fractions on the left side.
[tex]\dfrac1{-2v} -\dfrac v{-2} = \dfrac1{-2v} - \dfrac{v^2}{-2v} = \dfrac{1-v^2}{-2v} = \dfrac{v^2-1}{2v}[/tex]
1+1-1(2)+1=?
A,0
B,1
C,2
D,3
Answer:
B. 1
Step-by-step explanation:
-1*2 = -2
-2+1 = -1
-1+1 = 0
0+1 = 1
A four-person committee is chosen from a group of eight boys and six girls.
If students are chosen at random, what is the probability that the committee consists of all boys?
Answer:
7.....gggggggggggggggh
The Red Label Scotch Company is planning to produce 600 litres of Scotch Whisky. Three components A, B & C are mixed to form the final product. Component A, B and C cost Rs.10, Rs.15 and Rs.20 per litre respectively. In the final product, the amount of A component to be 2½ times the amount of component C. The total cost of the components should be Rs.8250. Determine the quantity of each components which should be included in the final product. (Use inverse of matrix Method).
Answer:
c
Step-by-step explanation:
In 5-card poker, the number of outcomes favorable to an event E is given in the table. Find the
probability of being dealt four of a kind or a a straight.
The probability of being dealt four of a kind or a straight is
(Round to 6 decimal places.)
Event E
Royal flush
Straight flush
Four of a kind
Full house
Flush
Straight
Three of a kind
Two pairs
One pair
No pair
Total
# of Outcomes Favorable to E
4
36
624
3744
5108
10,200
54,912
123,552
1,098,240
1,302,540
2,598,960
The probability of being dealt four of a kind or a straight is 0.00416 or 0.416%.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
In 5-card poker, find the probability of being dealt the following hand. Refer to the table.
From the table:
Total number of outcomes = 2598960
Total number of favorable outcomes = 624 + 10200 = 10824
The probability of being dealt four of a kind or a straight
P = 10824/2598960
P = 0.00416
In percentage:
P = 0.416%
Thus, the probability of being dealt four of a kind or a straight is 0.00416 or 0.416%.
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How do I graph the following set {x is an even number, -1≤x<12}
Step-by-step explanation:
Use this sort of layout, but where x will be an odd number, do not shade it. there should be a pattern of shaded segments followed by unshaded segments repeating
ill give you brainliest :)
Following the instructions for the inequalities gives the following results:
1. 4<7, both sides multiplied by 7
= 28<49, both sides multiplied by 6
= 168<294, both sides multiplied by 3
= 504<882, both sides multiplied by 10
= 5,040<8,820
2. 11>2, add 5 to both sides
= 16>3, add 3 to both sides
= 19>9, add -4
= 15>5
3. -4<-2, subtract 6
= -10<-8, subtract 8
= -18<-16, subtract 2
= -20<-18
4. -8<8, divide by -4
= 2>-2, divide by -2
= -1<1
5. The inequalities remain correct at the end because the same mathematical operations are performed on both sides simultaneously.
What are inequalities?Inequality is a relationship of a non-equal comparison between two numbers or algebraic expressions.
Inequality can be represented as greater than, greater than or equal to, less than, or less than or equal to.
Thus, the rules for inequalities show that if one adds to, subtracts from, multiplies by, or divides by the same number on both sides of an inequality, the inequality remains true.
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A bagel factory produced 300 bags of bagels. There were 7 bagels in each bag. How many
bagels did the factory produce?
bagels
Si al invertir $60.000 se pierde un 8% ¿A cuánto asciende la pérdida?
Trabajando con porcentajes, concluimos que la pérdida es de $4800.
¿A cuánto asciende la pérdida?
Sabemos que la inversión inicial es de $60000, y de esta cantidad, se pierde un 8%.
Entonces la pérdida va a ser el 8% de $60000.
Podemos escribir las relaciones:
$60000 = 100%
x = 8%
Queremos resolver esto para x, tomando el cociente entre esas relaciones y resolviendo para x obtenemos:
x = $60000*(8%/100%) = $60000*0.08 = $4800
Así, concluimos que la pérdida es de $4800.
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ASAP HELP ME WITH THIS QUESTIONN
Answer:
inductive reasoning
Step-by-step explanation:
(sin alpha +cos alpha )2
Step-by-step explanation:
sin alpha^2 + 2sin alpha* cos alpha + cos alpha^2
sin alpha^2 + cos alpha^2 +2sin alpha* cos alpha
1+ 2sin alpha* cos alpha
1+sin2 alpha
Jocelyn has a ladder that is 15 ft long. She wants to lean the ladder against a vertical wall so that the top of the ladder is 13.5 ft above the ground. For safety reasons, she wants the angle the ladder makes with the ground to be less than 75°. Will the ladder be safe at this height? Show your work and equation to support your answer
By using trigonometric relations, we will see that the angle that the ladder makes with the ground is 64.2°, so we conclude that the ladder is safe.
Will the ladder be safe at this height?Notice that the ladder makes a right triangle with the wall.
Such that the hypotenuse (the ladder itself) measures 15 ft, and one of the catheti (distance between the ground and top of the ladder) measures 13.5ft
If we considerate the angle that the ladder makes with the ground, the known cathetus is the opposite cathetus.
Then we can use the relation:
sin(x) = (opposite cathetus)/(hypotenuse)
Then:
sin(x) = (13.5ft)/(15ft)
If we use the inverse sine function on both sides, we get:
Asin(sin(x)) = Asin( 13.5ft/15ft)
x = Asin(13.5/15) = 64.2°
So the angle is less than 75°, which means that in fact, the ladder is safe.
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The volume of a rectangular prism is given by the following function:
V(x) = 2x³ + x² - 16 - 15
The length of the rectangular prism is (x − 3) and the width is (2x + 5). What is the height?
[tex]v(x) = wlh \\ 2x {}^{3} + {x}^{2} - 16 x- 15 =(2x + 5)(x - 3)h \\ h = \frac{2x {}^{3} + x {}^{2} - 16x - 15 }{2x {}^{2} - x - 15 } \\ using \: long \: divison \\ h = x + 1[/tex]
help! giving brainlest to best answer!
Answer:
C...........................
i need help w this pls
Answer: C
Step-by-step explanation: The y-intercept is 1/5 since the point on the y-axis is (0, 1/5). The slope is 2/3 because the other coordinate is up 2 and right 3 from (0, 1/5) *remember rise over run*. The shading means that the answer (y) must be less than or equal to 2/3x + 1/5, hence it being underneath the line.
Evaluate the function f(x) = –2x2 – 3x + 5 for the input value –3.
−22
–4
2
32
Hi there,
please see below for solution steps :
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
Evaluate by substituting :
[tex]\begin{gathered} \boldsymbol{f(x)=-2x^2-3x+5; \ evaluate \ when \ x=-3} \\\boldsymbol{Write \ -3 \ everywhere \ you \ see \ and \ x :}\\\boldsymbol{f(-3)=-2(-3)^2-3(-3)+5}\\\boldsymbol{Evaluate \ using \ Order \ of \ Operations :}\\\boldsymbol{f(-3)=-2(9)+9+5= > -18+9+5= > -18+14= > -4}\end{gathered}[/tex]
Therefore, the answer is [tex]\LARGE\textbf{-4}[/tex].
I hope the answer - and steps - made sense to you !!
Happy Learning !!
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
Find the value of b.
Step-by-step explanation:
The value of b will be 43° as it is vertically opposite angle.. !!
6. Find the values of x and y. 30° 17
Answer:
X = 17√3
Y = 34
Step-by-step explanation:
TO calculate the values of X and y we use SOHCAHTOA.
Calculating for Xtan 30 = opposite/adjacent
tan30 = 17/X
Cross multiply
tan30 ×X = 17
Divide bothsides by tan30
Note: tan30= 1/√3X = 17/1/√3
X=17√3
X= 29.4X = 29 ( approximately)
Calculating for y[tex]sin30 = \frac{Opposite}{Hypothenus} \\ \\ sin30 = \frac{17}{y} [/tex]
Cross multiply[tex]sin30 \times y = 17[/tex]
Divide bothsides by sin30[tex] \frac{sin30 \times y}{sin30} = \frac{17}{sin30} \\ \\ y = \frac{17}{0.5} = 34 \\ y = 34[/tex]
Given: m space measured angle space C space equals space 76, a = 20, and b = 13. What is the length of c to the nearest tenth?
Based on the given parameters, the length of c is 8.0 units
How to determine the side length of c?The given parameters are
Angle c = 76 degrees
Side a = 20
Side b = 13
The length of c is then calculated using the following law of sines
c^2 = a^2 + b^2 - 2absin(C)
Substitute the known values in the above equation
So, we have
c^2 = 20^2 + 13^2 - 2 * 20 * 13 * sin(76)
Express 20^2 as 400
c^2 = 400 + 13^2 - 2 * 20 * 13 * sin(76)
Express 13^2 as 169
c^2 = 400 + 169 - 2 * 20 * 13 * sin(76)
Evaluate the product and sin(76)
c^2 = 400 + 169 - 520 * 0.9703
Evaluate the product
c^2 = 400 + 169 - 504.55
Evaluate the exponents
c^2 = 400 + 169 - 504.55
So, we have
c^2 = 64.45
Evaluate the square root
c = 8.0
Hence, the length of c is 8.0 units
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The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1. x –2 0 1 2 3 h(x) 0 –12 0 8 0 If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function?
Using the Factor Theorem, the equation of h(x) is given as follows:
h(x) = -2(x³ - 2x² - 5x + 6)
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
Looking at the table, considering the values of x when h(x) = 0, the roots of h(x) are given as follows:
[tex]x_1 = -2, x_2 = 1, x_3 = 3[/tex]
Then the rule is:
h(x) = a(x + 2)(x - 1)(x - 3)
h(x) = a(x² + x - 2)(x - 3)
h(x) = a(x³ - 2x² - 5x + 6)
The h-intercept is of -12, as when x = 0, h = -12, hence this is used to find a as follows:
6a = -12
a = -12/6
a = -2.
Hence the function is given by:
h(x) = -2(x³ - 2x² - 5x + 6)
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Calculate the volume of a sphere that has a radius of 4 meters
Answer:
268.08
Step-by-step explanation:
use the formula 4/3πr^3Answer:
803.84 m³
Step-by-step explanation:
The formula to find the volume of a sphere is:
V = 4 π r³
Given that,
radius ⇒ 4m
Let us find the volume now.
V = 4 π r³
V = 4 π × ( 4 )³
V = 4 π × 64
V = 4 π × 64
V = 12.56 × 64
V = 803.84 m³
Simplify the expression cos (tan-1(x/2)).
\cos (\tan \left( -1\right) (\frac{x}{2}))
c
o
s
(
t
a
n
(
−
1
)
(
2
)
)
Simplify
1
Combine multiplied terms into a single fraction
\cos (\tan \left( -1\right) \cdot \frac{x}{2})
c
o
s
(
t
a
n
(
−
1
)
⋅
2
)
\cos (\frac{\tan \left( -1\right) x}{2})
c
o
s
(
t
a
n
(
−
1
)
2
)
Solution
\cos \left( \frac{\tan \left( -1\right) x}{2}\right)
c
o
s
(
t
a
n
(
−
1
)
2
)
Answer:
Step-by-step explanation:
[tex]cos(tan^{-1}(\frac{x}{2} ))\\put~tan^{-1}(\frac{x}{2} )=t\\\frac{x}{2} =tan~t\\sec^2t-tan^2t=1\\sec^2t=1+tan^2t=1+(\frac{x}{2} )^2=\frac{x^2+4}{4} \\sec~t=\pm\frac{\sqrt{x^2+4}}{2} \\cos ~t=\pm\frac{2}{\sqrt{x^2+4}} \\hence~cos(tan^{-1}(\frac{x}{2} ))=cos~t=\pm\frac{2}{\sqrt{x^2+4}}[/tex]