In the design of a package, things to take into consideration are:
The sizeIts safetyIts durabilityIts storage space, etc.What is cost effectiveness?The most cost effective and efficient to pack 12 golf balls is through the use of a small golf bag or a small box that is made specially for that purpose.
The design of the box will be in a rectangle shape where there will be two rows of which the ball is made to fit in till the 12 balls are completely inside the box. The lock is automatic and it is one that can be easily closed and opened easily when one wants to take a ball.
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An empty lorry weighs 3500kg. It weighs 7250 kg when loaded with 50 bags of coffee .What is the average mass of each bag ?
Answer:
The average mass of one coffee bag is 75kg.
Step-by-step explanation:
The lorry on its own weighs 3500kg.
If it weighs 7250kg alongside coffee bags, we can make the assumption that to find the total mass of the coffee bags, we must take the combined total and subtract the lorry's weight from it.
7250kg subtract 3500kg is 3750kg.
There are 50 coffee bags, so this is the mass of all 50.
If we want to find the mass of one coffee bag, we have to divide the mass of 50 coffee bags by 50.
3750kg divided by 50 is 75kg.
The average mass of one coffee bag is 75kg.
Write the inverse of the function: f (x) = 2x+3
Answer:
[tex]y = \frac{x - 3}{2}[/tex]
Step-by-step explanation:
To find the inverse of a function, simply 'switch' the x and y's and solve for y. [tex]y = 2x + 3[/tex] becomes [tex]x = 2y + 3[/tex]. Now, solving for y, we get [tex]y = \frac{x - 3}{2}[/tex].
hope this helped! :)
73-74 express the limit as a definite integral.
73. [tex]\lim _{n \rightarrow \infty} \sum_{i=1}^{n} \frac{i^{4}}{n^{5}}[/tex] [hint: consider [tex]$f\mleft(x\mright)=x^4$.\rbrack[/tex]
Pull out a factor of 1/n from the summand and the result follows.
[tex]\displaystyle \lim_{n\to\infty} \sum_{i=1}^n \frac{i^4}{n^5} = \lim_{n\to\infty} \frac1n \sum_{i=1}^n \left(\frac in\right)^4 = \boxed{\int_0^1 x^4 \, dx}[/tex]
1. what are the amounts of interest and maturity value of a loan for 250,000.00 at 5.5% simple interest for 4 months?
the amount of maturity is 254583
Simplify each expression, and classify the result as rational or irrational.
The number 2√5×3√6 is irrational, number √42/√168 is rational as we know π is an irrational number but 22/7 is rational.
What is an irrational number?It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words the irrational number cannot be expressed in the form of p/q form.
A rational number is a sort of real number that has the form p/q and does not equal zero.
= 2√5×3√6
= 6√30
= √1080 = 32.863353450309965
The number is irrational.
= √42/√168
= 1/2
The number is rational.
= 5(4√5 - 3√5)
= 5√5
= √125 = 11.180339887498949
The above number is irrational.
= √64/32
= 1/4
The above number is rational.
= (5√3—√3)/2√3
= 2
The above number is rational.
Similarly, we can find whether a number is irrational or rational
Thus, the number 2√5×3√6 is irrational, number √42/√168 is rational as we know π is an irrational number but 22/7 is rational.
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Owen owns a small business selling ice-cream. He knows that in the last week 102 customers paid cash, 3 customers used a debit card, and 8 customers used a credit card.
The probability that the next costumer will pay with a credit card is 0.07.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the next costumer will pay with a credit card = number of customers that paid with a credit card / total number of customers
8 / ( 8 + 3 + 102)
= 8 / 113 = 0.07
Here is the complete question:
Owen owns a small business selling ice-cream.He knows that in the last week 102 customers paid cash, 3 costumers used a debit card, and 8 costumers used a credit card. Based on these results,express the probability that the next costumer will pay with a credit card as a decimal to the nearest hundredth
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four points are always complanar if
which of the following is a true statement
Answer:
b
Step-by-step explanation:
[tex] = \frac{68}{5} - \frac{18}{5} \\ [/tex]
[tex] = \frac{50}{5} \\ [/tex]
Change into lowest term
[tex]10...[/tex]
6) three fourth of cars in a showroom are land rover , one half of land rover are black. what fraction of land rover are black?
Answer:
3/8
Step-by-step explanation:
(3/4)/2=3/8
somebody please help me?
The events A and B are independent events, and the values of P(A) and P(B) are 7/12 and 1/2, respectively
The value of P(A)The event A is given as:
A : Sum greater than 6
In the sample space of a roll of two dice, there are 21 outcomes that are greater than 6, out of a total of 36 outcomes
This means that:
P(A) = 21/36
Simplify
P(A) = 7/12
The value of P(B)The event B is given as:
B : Sum is divisible by 2
In the sample space of a roll of two dice, there are 18 outcomes that are divisible by 2, out of a total of 36 outcomes
This means that:
P(B) = 18/36
Simplify
P(B) = 1/2
Hence, the probability values of P(A) and P(B) are 7/12 and 1/2, respectively
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If x and y vary inversely and x = -9 when y = -30, what is the constant of variation
Answer:
270
Step-by-step explanation:
x = k/y This is an inverse relationship with k = constant of proportion (or variation)
-9 = k/(-30)
k = -9 * -30 = 270
Answer:
Constant of variation = 270.
Step-by-step explanation:
y = k/x
-30 = k / -9
k = -30 * -9
k = 270
A class contains 5 girls and 5 boys. Two are selected for a class committee. What is the probability that a girl and boy are selected?
Answer:
20/39.
Step-by-step explanation:
There are a total of 13 students.
Prob(Boy is selected) = 8/13
Prob(Girl is then selected) = 5/12
So probability ( Boy selected then a girl) = 8/13 * 5/12 = 10/39
- and the probability of Girl then a boy selected is also 10/39
So the required probability = 2 * 10/39
= 20/39.
Please Help Me !! ITS A MATH PROBLEM
Answer:
Step-by-step explanation:
Remark
You are trying to convert the base function f(x) = x^2 into the child function g(x) = -(x + 3)^2 + 5
UP
Start with the simplest part of the transformations. + 5
If you have g(x) = f(x)+5 what you have done is move the function up 5 units on your grid.
Up side Down
Next is the - sign.
f(x) = x^2
g(x) = - f(x) = - x^2
This has the affect of turning x^2 upside down. It looks like a cup opening towards the counter or down.
Left right
The last step is left / right. This is the hard one. It moves in the opposite direction that you think it should. x +3 moves the parabola left, not right. If you want it to move right, use (x - 3)
Graph
I have enclosed a graph to show you exactly what is going on. The red line is f(x)=x^2
The blue line is g(x) = -(x + 3)^2 + 5
bonjour je n'y arrive pas, quelqu'un pourrait m'aider s'il vous plaît ?
Answers:
BD = 6
AC = 7.5
=================================================
Work Shown:
BD/BA = BE/BC
x/9 = 4/6
6x = 9*4
6x = 36
x = 36/6
x = 6
BD = 6
---------
DE/AC = BE/BC
5/y = 4/6
5*6 = y*4
30 = 4y
4y = 30
y = 30/4
y = 7.25
AC = 7.5
label the quadrants IV
Answer:
Quadrant IV is always in the bottom right corner.
9. Find the midpoint of the segment having endpoints (2.9,−4.4) and (4.4,−2.9).
Answer:
midpoint: (3.65, -3.65)
Explanation:
[tex]\sf (x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]
where (x1, y1), (x2, y2) are points
[tex]\rightarrow \sf (\dfrac{2.9+4.4}{2}, \dfrac{-4.4-2.9}{2})[/tex]
[tex]\rightarrow \sf (\dfrac{7.3}{2}, \dfrac{-7.3}{2})[/tex]
[tex]\rightarrow \sf (3.65, \ - 3.65)[/tex]
Please someone answer quick ( will give brainlessly)!!!!
Answer:
Step-by-step explanation:
For the length of AC
cosθ = 14/17
θ = arcCos 14/17
θ = 34.56
Let x = opposite
cot34.56 = 14/x
1.45=14/x
x1.45 = 14
x = 9.66
therefore, the length of AC is 9.66
For angle B is 34.56
For angle C is 55.44
For Angle C :
90 + c + 34.56 = 180
c = 180 - 124.56
c = 55.44
Can someone help me
5b^2+4=10b
Answer:
b = 5 ± √5 / 5
Step-by-step explanation:
Given :
5b² + 4 = 10bSubtract 10b from both sides :
5b² - 10b + 4 = 10b - 10b5b² - 10b + 4 = 0Splitting the middle term :
b = 10 ± √100 - 4(5)(4) / 10b = 10 ± √20 / 10b = 10 ± 2√5 / 10b = 5 ± √5 / 5It is recommended that one fire extinguisher be available for every 6,000 square feet inside a building. a school superintendent is working to determine the number of fire extinguishers needed for a school building that has a floor plan with 132,000 square feet. let the variable x represent the number of fire extinguishers.
A party favor is made up of four equal solids and is constructed from paper. each of the four solids is open at the end. the net represents one of the solids. a net of a solid has a square base with side lengths of 2 inches, and 4 triangular sides with a height of 3 inches. b is the base, and c, d, and a are the triangular sides. how much paper is needed to make a party favor? to calculate the surface area, you would exclude the area of face . one of the four pyramids has a surface area of in.2. one party favor, which consists of four of the equal solids, has a surface area of in.2.
The surface area of the solid is 4 + 6b
How to determine the area of the solid?The solid consist of the following shapes:
1 square of length 2 inches4 triangles of height 3 inches and base bThe area of the solid is:
Area = Area of square + 4 * area of triangle
This gives
Area = 2 * 2 + 4 * 0.5 * 3 * b
Evaluate
Area = 4 + 6b
Hence, the surface area of the solid is 4 + 6b
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QUESTION 10 SOMEONE HELP ME
-9<2x+1<5
A. -5
B. -4
C. 4>x>-3
D. 5>x>-2
Answer:
B
Step-by-step explanation:
1.
- 9 < 2x + 1
- 10 < 2x
X > - 5
2.
2x + 1 < 5
2x < 4
X < 2
Solve the following system of equations algebraically.
x+y=27
y=x+3
*first person to get it right gets brainliest :)
Answer:
(x, y) = (12, 15)
Step-by-step explanation:
The given expression for y suggests that using substitution would be a good choice for the method of solution.
__
x +(x +3) = 27 . . . . substitute for y using the second equation
2x = 24 . . . . . . . subtract 3
x = 12 . . . . . . . divide by 2
y = 12 +3 = 15 . . . . use the second equation to find y
The solution is (x, y) = (12, 15).
Which expression could represent the phrase shown? (1 point)
"Add 4 and 5, divide the sum by 3, and then add the product of 6 and 5"
Group of answer choices
4 + 5 ÷ 3 + (6 x 5)
(4 + 5) ÷ 3 + 6 x 5
4 + (5 ÷ 3) + 6 x 5
4 + 5 ÷ (3 + 6 x 5)
Answer:
(4+5) ÷ 3 + 6 x 5
Step-by-step explanation:
pemdas
Araba bought an electric Cooker for 540.00 ghanacedis at a discount of 10%.Find the actual price of the eletric cooker.
Answer:
600.00
Step-by-step explanation:
Understanding :
Let P be the actual price of the containerSince there was a 10% discount, 540.00 is 90% of the actual price0.9P = 540P = 540.00/0.9P = 600.00600.00 is the actual price of the electric cooker.
what is the essence of calculus?
*friendship
Differential Calculus, or Differentiation
If we have a function of one variable, ie of the form [tex]y=f(x)[/tex], then in its most basic form differentiation is the study of how a small change in one variable [tex]x[/tex] affects the other variable [tex]y[/tex].
As an real life example, consider the average speed of a moving car:
average speed = distance travelled/ time taken
Obviously, this is an average by definition, but if there existed a formal mathematical link between distance and time, could we build a function that would tell us the instantaneous velocity at every given moment? The study of differential calculus gives strategies for calculating the ratio of a little change in distance to a small change in time, and then calculating the real instantaneous speed by making the small change infinitely small.
Similarly if we wanted to find the gradient of the tangent to a curve at some particular point [tex]A[/tex] we would estimate the gradient by using a chord to a nearby point [tex]B[/tex]. As we move this nearby point [tex]B[/tex] closer to the tangent point [tex]A[/tex] the slope of the chord approaches the slope of the tangent with more and more accuracy. Again differential calculus provides techniques for us to make the point [tex]B[/tex] infinitesimally close to the point [tex]A[/tex] o that we can calculate the actual gradient of the tangent.
Integral Calculus, or Integration
Suppose we wanted to calculate the area under a curve, [tex]y=f(x)[/tex], bounded the [tex]x[/tex] =axis, and two points [tex]a[/tex] and [tex]b.[/tex] We could start by splitting the interval [tex][a,b][/tex] into [tex]n[/tex] regular strips, and estimating the area under the curve using trapezia (this is the essence of the trapezium rule which provides an estimate of such an area). If we increase [tex]n[/tex] then generally we would hope for a better approximation. The study of integration provides techniques for us to take an infinitely large number of infinitesimally small strips to gain an exact solution.
The Fundamental Theorem of Calculus
Given the above two notions, it would appear that there is no connection between them at first., The Fundamental Theorem of Calculus, on the other hand, is a theorem that connects the rate of change of the area function (which determines the area under a curve) to the function itself. In other words, the area function's derivative equals the function itself.
Visual for Fundamental Theorem of Calculus for integrals:
[tex]\int\limits^b_af {(x)} \, dx =F(b)-F(a).[/tex]
where F is an antiderivative of [tex]f[/tex]
Physics, Chemistry, all engineering sciences, statistics, economics, finance, biology, computer science, linguistics, to name but a few, are all areas that would be a desert without the use of calculus.
Leibnitz and Newton worked to define the velocity of a planet moving on a curved trajectory. That was not possible without calculus, and both had to invent differential calculus. Differential calculus allows to compare quantities along a curve, and thus their time rate of change.
All of classical physics can be summarized in this operation. Given second derivative (which is Force/mass), find the position as a function of time. This process is called integration. Half of calculus is made with integration, the other half with derivation. All of classical physics rests on these two parts of the calculus.
Quantum mechanics, quantum field theory, electromagnetism, fluid mechanics all use integration and derivation and much more. I rest my case. I hope this helps you gauge the place that calculus occupies in science.
Answer:
so what i think is that *friendshipStep-by-step explanation:
Solve the equation: 12w=102.
Hey there!
12w = 102
DIVIDE 12 to BOTH SIDES
12w/12 = 102/12
SIMPLIFY IT!
w = 102/12
w = 102 ÷ 6 / 12 ÷ 6
w = 17 / 2
w = 8 1/2
Therefore, your answer should be:
w = 17/2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
7 mi.
7 mi.
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
4)
C =
miles
One-third of the Socer training participants are four-fifths of the Dance training
students. Twelve Dance training students do not participate in the Soccer training.
What is the total number of students who participate in the Soccer training?
Answer:
There are a total of 144 students in soccer training.
Step-by-step explanation:
12x5=60
60-12=48
48=4/5
4/5=1/3
1/3 = 48
48x3= 144
Round to the nearest two decimal places
