Answer:
breadth = 10 cm
length = 13 cm
Step-by-step explanation:
so,
perimeter = 46cm
2(l+b) = 46cm
or, 2(3+b+b) = 46cm ( because l = 3+b)
or, 2(3+2b) = 46cm
or, 6 + 4b = 46cm
or, 4b = 46cm - 6
or, 4b = 40cm
or, b = 40/4 cm
so, b = 10 cm
now,
l = 3cm + b
l = 3 cm + 10cm
= 13cm
Answer:
Let us assume the breadth of the rectangle be 'b' cm.
So length of the rectangle will be b+3 cm.
Now
Perimeter =46
[tex] \large \mid\orange {2(l + b) = 46}[/tex]
[tex] \large \mid\orange {2(b+3+b)=46}[/tex]
[tex] \large\mid \orange {2(2b+3) = 46}[/tex]
[tex] \large\mid \orange {4b + 6 = 46}[/tex]
[tex] \large \mid \orange{4b = 46 - 6}[/tex]
[tex] \large\mid \orange {4b = 40}[/tex]
[tex] \large \mid \orange{b = \frac{40}{4} }[/tex]
[tex] \large\mid \orange {b = 10}[/tex]
[tex] \large \orange{l=b+3= \:10 + 3 = 13 cm }[/tex]
Length = 13cm
Breadth = 10cm
A landscaper buys 1 gallon of plant fertilizer. He uses 1/5 of the fertilizer, and then divides the rest into 3 smaller bottles. How much does he put in each bottle?
Answer:
[tex]\frac{4}{15}[/tex] of a gallon per bottle
Step-by-step explanation:
1 - [tex]\frac{1}{5}[/tex] = [tex]\frac{4}{5}[/tex]
[tex]\frac{4}{5}[/tex] / 3 = [tex]\frac{4}{5}[/tex] x [tex]\frac{1}{3}[/tex] = [tex]\frac{4}{15}[/tex]
this question is much too hard would anyone please help me
Answer:
B and C are the same angles so if B is 60 so is C
Answer:
b= 60
c= 60
Step-by-step explanation:
<b and 120 form a straight line so the add to 180
b+120 =180
b = 180-120
b = 60
angles b and c are alternate interior angles so they are equal
b = c= 60
The ratio of copper to zinc in a certain alloy is 3 to 2. If 30 grams of copper are used, how many grams of zinc are needed to make this alloy?
Answer:
zinc is 20grams
Step-by-step explanation:
Given data
Ratio copper :zinc = 3:2
Copper =30 grams
Applying the ratio
3/2=30/x
Cross multiply
3x=30*2
3x=60
Divide both sides by 3
x=60/3
x=20
Hence zinc is 20grams
The temperature at 2 a.m. was -10°C.
At an earlier time the temperature was
0°C. It changed by -2°C each hour
until 2 a.m. At what earlier time was
the temperature 0°C?
Answer:
-1
Step-by-step explanation:
8. A bag contains 72 toffees. How many toffees can be stored in 122 such bags? Estimate the number of toffees to nearest tens.
9.The working of a metro station is controlled by 28 persons. Estimate the number of persons required to control the working of 88 such stations to the nearest tens.
Answer:
8.) 8,780 toffees can be stored in 122 such bags.
9.) 2,460 people are required to control the working of 88 such stations.
Step-by-step explanation:
QUESTION 8:
We know that there are 72 toffees per bag
So if we want to know how many toffees can be stored in 122 such bags:
72 x 122 = 8,784
ROUND IT TO THE NEAREST TENS:
Look at the digit to the right of the tens place: 8,784–>4. 4 and below means that the digit will be repkaced by 0 and the tens place remains the same.
So 8,784 rounded to tens is 8,780
Tye answer for question 9 is
2,460 (do the same thing)
Which equation is equivalent to 4 x = t + 2
s = t-2
s=4/t+2
s=t+2/4
s=t+6
consider a triangle ABC. Suppose that a=16, b=30, and c=35. Solve the triangle. Carry your intermediate computations to at least four decimal places and round your answers to the nearest tenth
9514 1404 393
Answer:
A = 27.1°B = 58.8°C = 94.1°Step-by-step explanation:
An angle can be found using the Law of Cosines.
c² = a² +b² -2ab·cos(C)
C = arccos((a² +b² -c²)/(2ab)) = arccos((16² +30² -35²)/(2·16·30))
C = arccos(-69/960) ≈ 94.1217°
Then another angle can be found using the Law of Sines:
sin(B)/b = sin(C)/c
B = arcsin(b/c·sin(C)) ≈ 57.7516°
The third angle can be found from the sum of angles of a triangle.
A = 180° -94.1217° -58.7516° = 27.1267°
The angles of the triangle are about (A, B, C) = (27.1°, 57.8°, 94.1°).
Help me with this answer I don’t it
Answer:
f(-2) = g(-2) this is the answer
Please help me with solving these. Thank you very much. Have a great day!
Answer:
Problem 20)
[tex]\displaystyle \frac{dy}{dx}=(\cos x)^x\left(\ln \cos x-x\tan x\right)[/tex]
Problem 21)
A)
The velocity function is:
[tex]\displaystyle v(t) =2\pi(\cos(2\pi t)-\sin(\pi t))[/tex]
The acceleration function is:
[tex]\displaystyle a(t)=-2\pi^2(2\sin(2\pi t)+\cos(\pi t))[/tex]
B)
[tex]s(0)=2\text{, }v(0) = 2\pi \text{ m/s}\text{, and } a(0) = -2\pi^2\text{ m/s$^2$}[/tex]
Step-by-step explanation:
Problem 20)
We want to differentiate the equation:
[tex]\displaystyle y=\left(\cos x\right)^x[/tex]
We can take the natural log of both sides. This yields:
[tex]\displaystyle \ln y = \ln((\cos x)^x)[/tex]
Since ln(aᵇ) = bln(a):
[tex]\displaystyle \ln y =x\ln \cos x[/tex]
Take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{d}{dx}\left[\ln y \right]=\frac{d}{dx}\left[x \ln \cos x\right][/tex]
Implicitly differentiate the left and use the product rule on the right. Therefore:
[tex]\displaystyle \frac{1}{y}\frac{dy}{dx}=\ln \cos x+x\left(\frac{1}{\cos x}\cdot -\sin(x)\right)[/tex]
Simplify:
[tex]\displaystyle \frac{1}{y}\frac{dy}{dx}=\ln \cos x-\frac{x\sin x}{\cos x}[/tex]
Simplify and multiply both sides by y:
[tex]\displaystyle \frac{dy}{dx}=y\left(\ln \cos x-x \tan x\right)[/tex]
Since y = (cos x)ˣ:
[tex]\displaystyle \frac{dy}{dx}=(\cos x)^x\left(\ln \cos x-x\tan x\right)[/tex]
Problem 21)
We are given the position function of a particle:
[tex]\displaystyle s(t)= \sin (2\pi t)+2\cos(\pi t)[/tex]
A)
Recall that the velocity function is the derivative of the position function. Hence:
[tex]\displaystyle v(t)=s'(t)=\frac{d}{dt}[\sin(2\pi t)+2\cos(\pi t)][/tex]
Differentiate:
[tex]\displaystyle \begin{aligned} v(t) &= 2\pi \cos(2\pi t)-2\pi \sin(\pi t)\\&=2\pi(\cos(2\pi t)-\sin(\pi t))\end{aligned}[/tex]
The acceleration function is the derivative of the velocity function. Hence:
[tex]\displaystyle a(t)=v'(t)=\frac{d}{dt}[2\pi(\cos(2\pi t)-\sin(\pi t))][/tex]
Differentiate:
[tex]\displaystyle \begin{aligned} a(t)&=2\pi[-2\pi\sin(2\pi t)-\pi\cos(\pi t)]\\&=-2\pi^2(2\sin(2\pi t)+\cos(\pi t))\end{aligned}[/tex]
B)
The position at t = 0 will be:
[tex]\displaystyle \begin{aligned} s(0)&=\sin(2\pi(0))+2\cos(\pi(0))\\&=\sin(0)+2\cos(0)\\&=(1)+2(1)\\&=2\end{aligned}[/tex]
The velocity at t = 0 will be:
[tex]\displaystyle \begin{aligned} v(0)&=2\pi(\cos(2\pi (0)-\sin(\pi(0))\\&=2\pi(\cos(0)-\sin(0))\\&=2\pi((1)-(0))\\&=2\pi \text{ m/s}\end{aligned}[/tex]
And the acceleration at t = 0 will be:
[tex]\displaystyle \begin{aligned} a(0) &= -2\pi ^2(2\sin(2\pi(0))+\cos(\pi(0)) \\ & = -2\pi ^2(2\sin(0)+\cos(0)) \\ &= -2\pi ^2(2(0)+(1)) \\ &= -2\pi^2(1) \\ &= -2\pi^2\text{ m/s$^2$} \end{aligned}[/tex]
Find the value of k, if (x - 2) is a factor of the polynomial p(x) = 2x2 + 3x - k
Answer:
The value of k is 14.
Step-by-step explanation:
(x - 2) is a factor of the polynomial
[tex]x - 2 = 0 \rightarrow x = 2[/tex]
This means that [tex]p(2) = 0[/tex]
p(x) = 2x² + 3x - k
[tex]p(2) = 2(2)^2 + 3(2) - k[/tex]
[tex]0 = 8 + 6 - k[/tex]
[tex]14 - k = 0[/tex]
[tex]k = 14[/tex]
The value of k is 14.
In how many ways can a committee of 3 men and 2 women be formed from a group of 9 men and 10 women?
Answer:
first you have to find the number of ways 3 men can be chosen, then the number of ways 2 women can be chosen, and then you need to multiply these numbers together to get the number of ways because multiplication will show the total arrangements possibilities. use combination since order does not matter.
number ways for 2 out of 10 women total: 10 choose 2= 45
number of ways for 3 out of 9 men total: 9 choose 3= 84
84x45= 3780
3780 total ways
number of ways
A checker board is a square board that is divided into smaller squares, with eight squares along each side. Describe how to find the number of small squares on a checker board without counting.
Plsssss ans I am suffering
Workers employed in a large service industry have an average wage of $9.00 per hour with a standard deviation of $0.50. The industry has 64 workers of a certain ethnic group. These workers have an average wage of $8.85 per hour. Calculate the probability of obtaining a sample mean less than or equal to $8.85 per hour. (Round your answer to four decimal places.)
Answer:
The probability of obtaining a sample mean less than or equal to $8.85 per hour=0.0082
Step-by-step explanation:
We are given that
Average wage, [tex]\mu=[/tex]$9.00/hour
Standard deviation,[tex]\sigma=[/tex]$0.50
n=64
We have to find the probability of obtaining a sample mean less than or equal to $8.85 per hour.
[tex]P(\bar{x} \leq 8.85)=P(Z\leq \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}})[/tex]
Using the values
[tex]P(\bar{x}\leq 8.85)=P(Z\leq \frac{8.85-9}{\frac{0.50}{\sqrt{64}}})[/tex]
[tex]P(\bar{x}\leq 8.85)=P(Z\leq \frac{-0.15}{\frac{0.50}{8}})[/tex]
[tex]P(\bar{x}\leq 8.85)=P(Z\leq -2.4)[/tex]
[tex]P(\bar{x}\leq 8.85)=0.0082[/tex]
Hence, the probability of obtaining a sample mean less than or equal to $8.85 per hour=0.0082
B
These triangles
are congruent by
the triangle
congruence
postulate [?].
D
E
A. SSS
B. SAS
C. Neither, they are not congruent
Answer:
SAS
Step-by-step explanation:
AC ≅ EC (Given), ∠ACB ≅∠ECD ( Vertical Angles), and BC ≅ DC
What's the surface area of this shape???
Answer:
197 in^2
Step-by-step explanation:
Add the areas of each face:
2 trapezoid faces:
(5+9) ÷ 2 x 5 = 35
2(35) = 70 in^2
2 squares:
5 x 5 = 25
2(25) = 50 in^2
Rectangular base:
5 x 9 = 45 in^2
Area of slanted rectangle:
6.4 x 5 = 32 in^2
Add:
32 + 45 + 50 + 70 = 197
the pizza Question i cant do and need desperate help
Answer:
the answer is c
Step-by-step explanation:
Find the Length of ST
Step-by-step explanation:
Consider Similarity and enlargement
To get the enlargement factor,
Take the ratio result of any two similar sides. i.e
PQ/AB = 3.6/2 = 1.8
The enlargement factor is 1.8
To get ST, consider ED then multiply it by the enlargement factor. i.e
= 5 x 1.8
= 9
Use elimination to solve the system of equations.
10x + 5y = 55
y - 2x = -9
A. (1,1)
B. (1,5)
C. (5, 1)
D. (4,5)
Answer:
C. (5,1)
Step-by-step explanation:
10x+5y=55 equation 1
y-2x=-9 equation 2
y=-9+2x isolate y in equation 2
10x+5(-9+2x)=55 substitute value of y from equation 2 into equation 1
10x-45+10x=55
20x=100
x=5
solve for y by using x value (5) in either equation
y-2x=-9
y-2(5)=-9
y-10=-9
y=1
công thức đạo hàm của ln(u) = ?
Answer:
U'/U
Step-by-step explanation:
Ahmed can 8 1/3 km in one hour. how much distance will he cover in 2 2/5
Answer:
In 2 2/5 hours, he will cover 20 km.
Step-by-step explanation:
Given that,
Ahmed can 8 1/3 km in one hour.
We need to find the distance he cover in 2 2/5 h.
In 1 hour = 8 1/3 km = 25/3 km
2 2/5 hour means 12/5 hour
In 12/5 hour = 12/5 × 25/3 km
= 20 km
So, in 2 2/5 hours, he will cover 20 km.
The square below represents one whole.
What percent is represented by the shaded area?
%
The anwser is 6%
Answer:
the answer is 6%
hdhxbxcbxbxszznzj
a solid wooden cube has 4.35cm long.calculate the volume of the cube
Answer:
82.31
Step-by-step explanation:
I believe this is correct, if it isn't feel free to let me know and I will fix it. I'm sorry in advance if this is incorrect.
Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
y = 5x
20x - 4y = 0
Answer:
Dependent Equations
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/CoefficientsCoordinates (x, y)Solving systems of equations by substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 5x
20x - 4y = 0
Step 2: Solve for x
Substitution
Substitute in y [2nd Equation]: 20x - 4(5x) = 0Multiply: 20x - 20x = 0Combine like terms: 0 = 0Here we see 0 does indeed equal 0.
∴ our systems has an infinite amount of solutions.
Answer:
0
Step-by-step explanation:
y = 5x
20 x - 4 y = 0substitute the value of y in equation
= 20x - 4 ( 5x ) = 0multiply to get 20x
= 20x - 20x = 0collect like terms
= 0we can see here that 0 indeed equal 0.
so, system has an infinite solutions.
Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows:
Category Product 1 Product 2 Product 3
Profit/unit $30 $50 $20
Machine 1 time/unit 0.5 2.0 0.75
Machine 2 time/unit 1.0 1.0 0.5
Two operators are required for machine 1; thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 100 labor-hours is available for assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 20% of the units produced.
How many units of each product should be produced to maximize the total profit contribution?
Product # of units
1
2
3
What is the projected weekly profit associated with your solution?
Profit = $
How many hours of production time will be scheduled on each machine? If required, round your answers to two decimal places.
Machine Hours Schedule:
Machine 1 Hours
Machine 2 Hours
What is the value of an additional hour of labor? If required, round your answers to two decimal places.
$
Assume that labor capacity can be increased to 120 hours. Develop the optimal product mix, assuming that the extra hours are made available.
Product # of units
1
2
3
Profit = $
Would you be interested in using the additional 20 hours available for this resource?
Answer:
z (max) = 1250 $
x₁ = 25 x₂ = 0 x₃ = 25
Step-by-step explanation:
Profit $ mach. 1 mach. 2
Product 1 ( x₁ ) 30 0.5 1
Product 2 ( x₂ ) 50 2 1
Product 3 ( x₃ ) 20 0.75 0.5
Machinne 1 require 2 operators
Machine 2 require 1 operator
Amaximum of 100 hours of labor available
Then Objective Function:
z = 30*x₁ + 50*x₂ + 20*x₃ to maximize
Constraints:
1.-Machine 1 hours available 40
In machine 1 L-H we will need
0.5*x₁ + 2*x₂ + 0.75*x₃ ≤ 40
2.-Machine 2 hours available 40
1*x₁ + 1*x₂ + 0.5*x₃ ≤ 40
3.-Labor-hours available 100
Machine 1 2*( 0.5*x₁ + 2*x₂ + 0.75*x₃ )
Machine 2 x₁ + x₂ + 0.5*x₃
Total labor-hours :
2*x₁ + 5*x₂ + 2*x₃ ≤ 100
4.- Production requirement:
x₁ ≤ 0.5 *( x₁ + x₂ + x₃ ) or 0.5*x₁ - 0.5*x₂ - 0.5*x₃ ≤ 0
5.-Production requirement:
x₃ ≥ 0,2 * ( x₁ + x₂ + x₃ ) or -0.2*x₁ - 0.2*x₂ + 0.8*x₃ ≥ 0
General constraints:
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
The model is:
z = 30*x₁ + 50*x₂ + 20*x₃ to maximize
Subject to:
0.5*x₁ + 2*x₂ + 0.75*x₃ ≤ 40
1*x₁ + 1*x₂ + 0.5*x₃ ≤ 40
2*x₁ + 5*x₂ + 2*x₃ ≤ 100
0.5*x₁ - 0.5*x₂ - 0.5*x₃ ≤ 0
-0.2*x₁ - 0.2*x₂ + 0.8*x₃ ≥ 0
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
After 6 iterations with the help of the on-line solver AtomZmaths we find
z (max) = 1250 $
x₁ = 25 x₂ = 0 x₃ = 25
Which expression is equivalent to ?
x ^-5/3
Answer:
[tex] {x}^{ - \frac{5}{3} } \\ \frac{1}{ {x}^{ \frac{5}{3} } } [/tex]
7)
8)
13x + 1/9x + 3
A) 6
C) -7
B) 8
D) 7
Α)
C)
I
Answer:
b) 8
Step-by-step explanation:
the angles are a linear pair meaning that they have a sum of 180. So 22x+4+180. Solve that and x=8
Answer:
B) 8
Step-by-step explanation:
(13x + 1) + (9x + 3) = 180
Combine like terms
22x + 4 = 180
Subtract 4 from both sides
22x = 176
Divide both sides by 22
x = 8
Which statement correctly compares the centers of the distributions?
A. The median penguin height is greater at Park Zoo than at Cityview Zoo.
B. The median penguin heights are the same.
C. The median penguin height is greater at Cityview Zoo than at Park
Zoo.
D. The range of penguin heights is greater at Cityview Zoo than at
Park Zoo.
The median penguin height is greater at Cityview Zoo than at Park
Zoo, Option C is correct.
Mode is the most occuring number.
The range is the difference of the highest value and the lowest value.
The median is the middle value in a set of data
After finding the range and medians of the given data.
The median penguin at Cityview Zoo is 42 cm tall,
The median penguin at Park Zoo is barely 41 cm tall.
Cityview Zoo's median penguin height is higher than that of Park Zoo.
Hence, the median penguin height is greater at Cityview Zoo than at Park Zoo.
To learn more on Statistics click:
https://brainly.com/question/30218856
#SPJ7
A baseball is hit and its height at different one-second intervals is recorded (See attachment)
Answer:
[tex]h(t)[/tex] is likely a quadratic function.
Based on values in the table, domain of [tex]h(t)[/tex] : [tex]\lbrace 0,\, 1,\, 2,\, 3,\, 4,\, 5,\, 6,\, 7,\, 8\rbrace[/tex]; range of [tex]h(t)\![/tex]: [tex]\lbrace 0,\, 35.1,\, 60.1\, 75.2,\, 80.3,\, 75.3,\, 60.2,\, 35.0 \rbrace[/tex].
Step-by-step explanation:
By the power rule, [tex]h(t)[/tex] is a quadratic function if and only if its first derivative, [tex]h^\prime(t)[/tex], is linear.
In other words, [tex]h(t)[/tex] is quadratic if and only if [tex]h^\prime(t)[/tex] is of the form [tex]a\, x + b[/tex] for some constants [tex]a[/tex] and [tex]b[/tex]. Tables of differences of [tex]h(t)\![/tex] could help approximate whether [tex]h^\prime(t)\![/tex] is indeed linear.
Make sure that values of [tex]t[/tex] in the first row of the table are equally spaced. Calculate the change in [tex]h(t)[/tex] over each interval:
[tex]h(1) - h(0) = 35.1[/tex].[tex]h(2) - h(1) = 25.0[/tex].[tex]h(3) - h(2) = 15.1[/tex].[tex]h(4) - h(3) = 5.1[/tex].[tex]h(5) - h(4) = -5.0[/tex].[tex]h(6) - h(5) = -15.1[/tex].[tex]h(7) - h(6) = -25.2[/tex].[tex]h(8) - h(7) = -35.0[/tex].Consecutive changes to the value of [tex]h(t)[/tex] appears to resemble a line with slope [tex](-10)[/tex] within a margin of [tex]0.2[/tex]. Hence, it is likely that [tex]h(t)\![/tex] is indeed a quadratic function of [tex]t[/tex].
The domain of a function is the set of input values that it accepts. For the [tex]h(t)[/tex] of this question, the domain of [tex]h(t)\![/tex] is the set of values that [tex]t[/tex] could take. These are listed in the first row of this table.
On the other hand, the range of a function is the set of values that it outputs. For the [tex]h(t)[/tex] of this question, these are the values in the second row of the table.
Since both the domain and range of a function are sets, their members are supposed to be unique. For example, the number "[tex]0[/tex]" appears twice in the second row of this table: one for [tex]t = 0[/tex] and the other for [tex]t = 8[/tex]. However, since the range of [tex]h(t)[/tex] is a set, it should include the number [tex]0\![/tex] only once.
A muffin recipe calls for 3 times as much flour as sugar.
Use this information for
Write an expression that can be used to
find the amount of flour needed for a given
amount of sugar. Tell what the variable in
your expression represents
use the variable ( s ) to represent the amount of sugar
f=3s
f = the amount of flour
Hope this helps! :)