Chef should prepare 4 cakes and 5 batches of pastry in order to achieve maximum profits and his maximum profit or revenue by solving through inequality is $260.
Given Chef uses 5 cups of cake batter for 1 cake and 4 cups of batter for 1 batch of cupcakes. Chef wants to make at least 4 cakes. Profit on 1 cake is $35 and $30 for 1 batch of cupcake.
let the number of cakes be x and the number of batches of cupcakes be y such that
5x+4y<=40--------1
x>=4---------------2
Maximize Profit=35x+30y
Inequalities contains different signs so we have to change one inequality.
5x+4y<=40
-x<=-4
Now assume them equalities
5x+4y=40-------3
-x=-4
multiply second equations by 5
-5x=-20-----------4
now add 3 and 4
5x+4y-5x=40-20
4y=20
y=5
now put the value of y in 5x+4y=40
5x+4*5=40
5x+20=40
5x=20
x=4.
Maximum Profit=35x+30y
=35*4+30*5
=$260
Hence chef should make 4 cakes and 5 batches of pastry and maximum profit of $260.
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[tex]3x+9+2x=x-2x-3[/tex]
Answer:
Step-by-step explanation:
Equation
3x + 9 + 2x = x - 2x - 3
Solution
Combine all the like terms.
3x+2x+9 = x - 2x - 3
5x + 9 = -x - 3 Add x to both sides of the equation
5x+x +9 = -x+x -3 Combine
6x + 9 = - 3 Subtract 9 from both sides of the equation
6x+9-9 = - 3-9 Combine
6x = -12 Divide both sides by 6
6x/6 = -12/6
x = - 2
Answer x = - 2
is 6x^5 + 3x^4 + 1^3
a fifth-degree polynomial with three terms in standard form
The statement is true, it is a polynomial of degree 5 with 3 terms.
Is the statement true?
A polynomial is of the form:
[tex]p(x) = a_n*x^n + ... + a_0[/tex]
Where the degree is the maximum exponent of the polynomial, in this case, is n.
The given polynomial is:
[tex]p(x) = 6x^5 + 3x^4 + x^3[/tex]
So, the maximum exponent is 5, which means that the degree of the polynomial is 5.
And it has 3 terms, so the statement is true.
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What is the approximate value of x in the diagram below? (Hint: You will need
to use one of the trigonometric ratios given in the table.)
Answer:
B. 39.59
Step-by-step explanation:
So 43 degrees, you know the length of the opposite side (27) and the angle (43 degrees), the only unknown is the hypotenuse. So you're looking for a trigonometric ratio that uses the angle (all of them do, except technically the inverse don't), the opposite side, and the hypotenuse. Sine is defined as [tex]\frac{opposite}{hypotenuse}[/tex]. So let's plug in known values:
[tex]sin(43) = \frac{27}{x}[/tex]
Multiply both sides by x
[tex]sin(43) * x = 27[/tex]
divide both sides by sin(43)
[tex]x=\frac{27}{sin(43)}[/tex]
Normally I would use a calculator, but in this case I'll use the approximation given in the problem of 0.682
[tex]x=\frac{27}{0.682}[/tex]
simplify the fraction
[tex]x\approx39.59[/tex]
Adam put $100 in a savings account. After 10 years, he had $1649 in the account. What rate of interest did he earn? Use the formula A = Pert, where A is the ending amount, P is the principal (initial amount), r is the interest rate, and t is time.
A.20%
B.5%
C.28%
D.3%
Answer:
Step-by-step explanation: C. 28%
[tex]A = Pe^{rt}[/tex]
[tex]1649 = 100 \cdot e^{10r}\\16.49 = e^{10r}\\\ln{16.49} = 10r\\r = \frac{\ln{16.49}}{10} = 0.28\\[/tex]
Construct a confidence interval for p1-p2 at the given level of confidence.
x1=30, n1=235, x2=39, n2=294, 90 % confidence
Using the z-distribution, the 90% confidence interval for the difference of proportions is given by: (-0.0534, 0.0434).
What is the mean and the standard error for the distribution of differences?For each sample, the mean and the standard error are given as follows:
[tex]p_1 = \frac{30}{235} = 0.1277, s_1 = \sqrt{\frac{0.1277(0.8723)}{235}} = 0.0218[/tex].[tex]p_2 = \frac{39}{294} = 0.1327, s_1 = \sqrt{\frac{0.1327(0.8673)}{294}} = 0.0198[/tex].For the distribution of differences, they are given by:
[tex]\overline{p} = p_1 - p_2 = 0.1277 - 0.1327 = -0.005[/tex].[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0218^2 + 0.0198^2} = 0.0294[/tex]What is the confidence interval?The interval is given by:
[tex]\overline{p} \pm zs[/tex]
In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
Hence the bounds of the interval are:
[tex]\overline{p} - zs = -0.005 - 1.645(0.0294) = -0.0534[/tex]
[tex]\overline{p} + zs = -0.005 + 1.645(0.0294) = 0.0434[/tex]
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What should be subtracted from 5/8 to make it -1
Answer:
13/8
Step-by-step explanation:
let the number be x
5/8 - x = -1
-x = -1 - 5/8
-x = - 13/8
x = 13/8
5/8- 13/8 = -1
Answer:
13/8
Step-by-step explanation:
5/8 - x = -1 where x is the number to be found.
- x = -1 - 5/8
x = 5/8 + 1
= 13/8.
Which term describes the line segment that connects a vertex of a triangle to a point on the line containing the oppostie side, so that the line segment is perpendicular to that line?
Answer:
90 degree and the angle sides
There are 8 flavors of cupcakes on the dessert menu. You are asked to choose 3 flavors of cupcakes out of the 10 on the menu. How many differnet combinations of 3 cupcakes are there if order does not matter
There are 80 different combinations of 3 cupcakes are there if order does not matter
How to determine the combination?The given parameters are:
Flavors = 10
Flavors to choose = 3
The number of combination is calculated using:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
This gives
[tex]^{10}C_3 = \frac{10!}{7!3!}[/tex]
Expand
[tex]^{10}C_3 = \frac{10 * 9 * 8 * 7!}{7!3 * 2 * 1}[/tex]
Evaluate quotient
[tex]^{10}C_3 = 80[/tex]
Hence, there are 80 different combinations of 3 cupcakes are there if order does not matter
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a) If x and 125° are adjacent angles in linear pair, find xº [with proper process]
Answer:
x=55°
Step-by-step explanation:
x=180°-125°
x=55°
Can't seem to solve this one
Answer:
.88
Step-by-step explanation:
[tex] \sqrt{.7775} = .88[/tex]
The standard deviation is the square root of the variance.
Name the marked angle in 2 different ways
The 2 different angles you can name are <UVT and <VST. Hope this helps and please mark brainlist
Population dynamics must consider the number of individuals that are lost per unit of time, also called the
Population dynamics must consider the number of individuals that are lost per unit of time, also called the mortality rate.
Mortality, or mortality, is a measure of the number of deaths (generally or due to a particular cause) in a particular population, scaled to the size of that population per unit of time.
The relative incidence of deaths in a particular population over a particular time period. Often expressed as the rate of human deaths or wildlife deaths from environmental hazards during a public health crisis. The highest mortality rate for patients over the age of 80 was during the last flu season.
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On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The number b varies directly with the number a. For example b = 2a equals negative 2 and StartFraction 3 Over 4 EndFraction. when a = –2a equals negative 2 and StartFraction 3 Over 4 EndFraction.. Which equation represents this direct variation between a and b?
b = –a
–b = –a
b – a = 0
b(–a) = 0
Option 1. The equation that represents the direct variation that exists between a and b is b = –a.
How to find the direct variation hereThe direct variation is of this form y ∝ x
This gives the equation
y = kx
The constant is k
From our question we have
b ∝ a so b = ka
b = [tex]2\frac{3}{4}[/tex]
a = [tex]-2\frac{3}{4}[/tex]
Remember that b = ka
[tex]2\frac{3}{4} = -2\frac{3}{4} k[/tex]
This would cancel out to
1 = -k
or k = -1
Hence the equation would be written as
b = -a
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If quadrilateral JKLM had a translation where all the vertices were in the second quadrant, what would be the vertices?
HELP HELP HELP
Just a quick question for 100 points! :)
Answer:
see attached graphs
Step-by-step explanation:
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Parent function: [tex]f(x) = x[/tex]
Each transformation is a transformation of the parent function only:
Translation of 4 units down
[tex]\implies f(x)-4=x-4[/tex]
[tex]\implies y=x-4[/tex]
A stretch by a factor of 3
[tex]\implies 3f(x)=3x[/tex]
[tex]\implies y=3x[/tex]
A reflection and a translation 1 unit up
[tex]\implies f(-x)+1=-x+1[/tex]
[tex]\implies y=-x+1[/tex]
The mean number of words per minute (WPM) read by sixth graders is 86 with a variance of 225. If 44 sixth graders are randomly selected, what is the probability that the sample mean would differ from the population mean by less than 3.71 WPM
p = 6.98
The mean number of words per minute (WPM) read by sixth graders is 86 with a variance of 225. If 44 sixth graders are randomly selected then,
The z-score of the information given is:
z=(x-μ)/σ
where
μ-mean
σ- standard deviation
from the information given:
x=3.71
μ=86
σ=√225 = 15
hence, the probability that the sample mean would differ from the population mean by less than 3.71 WPM is
z = (3.71 + 86)/15
z = 5.98
thus,
p = 1 + 5.98 = 6.98
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Triangle A C B is cut by bisector C D. The lengths of sides A C and C B are congruent.
CD bisects ∠ACB. Which statements must be true? Check all that apply.
AD = BD
AC = CD
m∠ACD = m∠BCD
m∠CDA = m∠CDB
m∠DCA = m∠DAC
The statements that are true are AD = BD , m∠ACD = m∠BCD , m∠CDA = m∠CDB , Option A , C and D
What is a Triangle ?A triangle is a polygon with three sides , angles and vertices.
It is given a Δ ACB
CD is the angle bisector of ∠ACB
AC ≅ CB
To determine which statement are true
First it has to be proved that Δ DCB is congruent to Δ ACD
In the triangles
AC = CB (Given )
∠ACD = ∠DCB (CD is the angle bisector of ∠ACB)
DC = DC ( Common side )
thus Δ DCB is congruent to Δ ACD
Therefore the following statements are true
AD = BD (CPCTC)
m∠ACD = m∠BCD (CPCTC)
m∠CDA = m∠CDB (CPCTC)
Therefore Option A , C and D are the statements that are true .
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Answer:
Step-by-step explanation:
a,c,d
i need help with this ASAP i've been stuck on this question for a while
Answer:
B. 8
Step-by-step explanation:
Triangle's weight is equal to the sphere's weight.
Total of 16 blocks. Since the triangle's weight is equal to the sphere's, the weight will be half of the blocks.
Divide 2 from 16.
16/2=8
The triangle's weight is equal to 8 blocks.
Hope this helps!
If not, I am sorry.
During the two hours of the morning rush from 8 a.m. to 10 a.m., 100 customers per hour arrive at the coffee shop. The coffee shop has a capacity of 0.8 minutes per customers. What is the number of customers waiting at 10 a.m.
So, 40 Customers are waiting at 10 A.M.
According to statement
Number of customers arrives at coffee shop per hour = 100
Capacity of shop for per minute per customer = 0.8 minute
Capacity of shop for customers per hour = 80
Find number of customers are by
Queue growth rate = Demand - Capacity
Put the values in the formula and find the growth rate
So,
Queue growth rate= 100 - 80 = 20.
Length of queue at 10 a.m. = 2 × 20 = 40.
So, 40 Customers are waiting at 10 A.M.
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(2 StartRoot 7 EndRoot + 3 StartRoot 6 EndRoot) (5 StartRoot 2 EndRoot + 4 StartRoot 3 EndRoot)
CAN ANYONE HELP! PLSS
Answer:
x = 8
Step-by-step explanation:
An Equilateral triangle is a triangle in which all three sides and angles are equal. The value of each angle of an equilateral triangle is 60 degrees therefore we get the equation 9x - 12 = 60
Add 12 from both sides to isolate the 9x leaving us with:
9x = 72
Divide both sides by 9 to give us x, which is
x = 8
A shop sold white, pink and red T-shirts. 24% of the T-shirts were white. There were 198 more pink than white T-shirts. The remaining 114 T-shirts were red. How many pink T-shirts were there
Number of pink T-shirts was 342
How to solve it?Given: 24% of the T-shirts were white
Let, total number of T-shirts be x
According to question,
Total number of white T-shirts = 24x/100
Total number of pink T-shirt = 24x/100+ 198
Total number of red T-shirts = 114
According to the question:
24x/100+24x/100+ 198 + 114 = x
312 = x - 48x/100
312 = 52x/100
x = (312*100)/52
x = 600
so Number of pink T-shirts :
=(24*600)/100+198
= 144 + 198
= 342
Hence total Number of pink T-shirts was 342.
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What reason represents the same ratio as for every 12 apples, 9 of them are green?
4: 3
6: 8
9:16
3: 4
Answer:
4:3
Step-by-step explanation:
If you divide both 12 and 9 by 3 (the smallest number they can both be divided by), you get 4 and 3. the ratio is for every 4 apples, 3 would be green. So 4:3
The triangles are congruent by SSS or HL.
Triangles P Q R and S T U are shown. Triangle P Q R is reflected across Q R and then is shifted up and to the right to form triangle S T U.
Which transformation(s) can map TrianglePQR onto TriangleSTU?
translation only
rotation only
rotation, then reflection
reflection, then translation
From the information given about the triangle, the transformation that can map Triangle PQR onto Triangle STU is D. reflection, then translation.
What is a congruent triangle?Congruent triangles are known as triangles that have the same size, shape and angles.
It is also important to note that the transformation that can map Triangle PQR onto Triangle STU is reflection, then translation. This is so because it is a vital to form of congruent triangles.
There, the transformation that can map triangle PQR onto triangle STU is reflection, then translation. Option D
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Answer:
reflection, then translation
Step-by-step explanation:
The answer above is correct.
You are trying to help esteban understand the concept of a 5% slack in the line. you explain that having 5% slack means that the length is 5% longer than it would be
The correct answer is 5.25%.
What is slack length?These include the optimal muscle fibre length, the length at which the muscle can generate maximum force, and the tendon slack length, the length at which the tendon starts to generate a resistive force to stretch.
Given,
two figure
To find, slack length (l)
AB = √4² + 3² ⇒ 5
l = [tex]5 + \frac{5}{100} * 5[/tex]
l = 5.25
Hence slack length is 5.25
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If it were completely straight. You compare ΔABC to Fiqure DEF where curve DE is 5% longer than line segment AB . t Right Triangle without Slack Figure with Slack Brake :cord Enter the length of curve DE given that the curve is 5% longer than line segment AB.
Quick algebra 1 question for 50 points!
Only answer if you know the answer, Tysm!
[tex]revenue = selling \: price \times quantity \: sold[/tex]
[tex]m(t) = 3t[/tex]
B)Since we only have 75 tickets to sell, the domain is:t ε [ 0 , 75 ]Range: (extra)m ε [ 0 , 225 ]#1
M(t)=3tBecause
revenue=sold price×no of items
#2
The restriction is of 75tickets and the tickets can't be negative
so
0≤t≤75Domain
[0,75]how many Jamaican dollars are equivalent to US $135 , if US =$1 - JA $87.50
11812.5 Jamaican dollars is equivalent to $135
How to determine the amount?The conversion rate is given as:
$1 = JA 87.50
Multiply both sides of the conversion rate by 135
135 * $1 = JA 87.50 * 135
Evaluate the product
$135 = JA 11812.5
Hence, 11812.5 Jamaican dollars is equivalent to $135
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Find arc AB.
A. 54°
B. 108°
C. 72°
D. 126°
A triangle is a three-edged polygon with three vertices. The measure of arc AB is 72°. Thus, the correct option is C.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
Since in the ΔAOB, the length of the side OA and OB are,
OA = OB = radius
Therefore, the triangle is an isosceles triangle. Thus, we can write,
∠OAB = ∠OBA = 54°
Now, the sum of all the angles of ΔAOB is,
∠AOB + ∠OAB + ∠OBA = 180°
∠AOB + 54° + 54° = 180°
∠AOB = 72°
Hence, the measure of arc AB is 72°. Thus, the correct option is C.
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Please help me( ´人` )
The following diagram shows a quadrant OPQ in the sector ORST with centre O and a radius of 21 cm.
Given Q is the midpoint of OR, calculate the area, in cm², of the shaded region.
A 285.025
B 308.045
C 365.075
D 410.025
Answer:
D
Step-by-step explanation:
First let's list down the formulas we will be using.
Area of Quadrant = 1/4 x Area of Circle
= [tex]\frac{1}{4} \pi r^{2}[/tex]
Area of Part of a circle = (θ/360)[tex]\pi r^{2}[/tex]
First, we will find Angle QOT.
Angle QOT = 360 - 231 = 129
Area of ORST = [tex]\frac{129}{360} \pi (21)^{2} \\=\frac{6321}{40} \pi cm^{2}[/tex]
Next we know that, Q is midpoint of OR, therefore OQ = QR
and OQ = 0.5 * OR
OQ = 0.5 * 21 = 10.5cm = radius of Quadrant QOP
Area of Quadrant QOP = [tex]\frac{1}{4} \pi (10.5)^{2} \\=\frac{441}{16} \pi cm^{2}[/tex]
Lastly,
Area of Shaded Region = Area of ORST - Area of Quadrant QOP
= [tex]\frac{6321}{40} \pi -\frac{441}{16} \pi \\= 409.86cm^{2}[/tex]
Similar to the other question you asked, choose the closes answer as there might be some rounding differences. I kept it in fractions as it will ensure maximum precision.
WILL GIVE BRAINLIEST
I NEED TO FIND X AND Y
Answer:
x = 3
y = 2
Step-by-step explanation:
Equations
7x - 7y = 7
-4x - 7y = - 26 Multiply both sides of the equation by - 1
-1(-4x - 7y = - 26)
4x + 7y = 26
Solution
Add the two equations together
7x - 7y = 7
4x + 7y = 26
11x = 33 Divide by 11
11x/11 = 33/11
x = 3
4x + 7y= 26 Use this equation to solve for y. Use x = 3
4*3 + 7y = 26 Combine the left
12 + 7y = 26 Subtract 12 from both sides
12 - 12 + 7y = 26 - 12 Combine
7y = 14 Divide by 7
7y/7 = 14/7
y = 2