Step-by-step explanation:
1 meter = 1000 mm
the area of 1.6 m² means the side length of the square is
sqrt(1.6) = 1.264911064... m = 1,264.911064... mm
to create a square out of the rectangular pattern he needs to put e.g. 42 patterns along the 45 mm side and stack 45 patterns on top of the 42 mm side.
the minimum number of needed patterns we get via the last common multiple (LCM) of 42 and 45.
for this we use the prime factorization :
45 ÷ 2 no
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 3 no
5 ÷ 5 = 1
45 = 3² × 5¹
42 ÷ 2 = 21
21 ÷ 2 no
21 ÷ 3 = 7
7 ÷ 3 no
7 ÷ 5 no
7 ÷ 7 = 1
42 = 2¹ × 3¹ × 7¹
the LCM is the product of the longest streaks of each used prime factor.
LCM(42, 45) = 2¹ × 3² × 5¹ × 7¹ = 2×9×5×7 = 630
(i) he needs 210 patterns to form the smallest square.
this will be
14×45 mm on one side = 630 mm
15×42 mm on the other side = 630 mm
14×15 = 210 patterns.
(ii)
the limit per side length is as established
1,264.911064... mm
starting with the minimum of 630 mm how often can we add 42 mm in one direction and 45 mm in the other, and keep a 15 : 14 ratio between these numbers ?
and we need integer numbers, as we cannot use parts of the patterns (only full patterns).
45 × x <= 1264
x <= 1264/45 = 28.08888888... = integer 28
42 × y <= 1264
y <= 1264/42 = 30.0952381... = integer 30
30/28 = 15/14
so, the ratio is maintained for these numbers.
that means as maximum we can put
30×28 = 840 patterns as square inside the max. allowed area.
the dimensions of this max. square are therefore
30×42 = 1260 mm
28×45 = 1260 mm
the area of this square is then
1260mm × 1260 mm = 1,587,600 mm² = 1.5876 m²
How to Convert 11010112 to base 10?
Answer:
So this is all you need to do!
Hope it helped you:)
I need help asap. everythings in the image
The function in terms of the time (t) is t=d/r and the value of the time (t) for the given values is 5.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:
a= the slope
b=constant term that represents the y-intercept.
For the given example: a=2 and b=7.
In the exercise is asked the equation for the time (t) in the function of the distance (d) and the rate (r).
Thus, if d=rt, we will have t= d/r
Replacing the variables for the given values for finding t. The question gives:
distance (d) =40
rate (r) = 8
Thus, you will have t= 40/8. Then, t=5
Therefore, the answer is the fourth option.
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Craig has a watch that is losing time. For every minute that passes, his watch loses 10 seconds. If Craig set his watch correctly at 9am, what time whould it show when it is 10am on the house clock?
Answer:
9:50 am
Step-by-step explanation:
because 10 x 60 is equal to 1 hour, so you get 600 seconds subtracted from 10am. 600 seconds is equal to 10 minutes. so 10 am - 10 minutes = 9:50am
HELP ME WITH THIS PLEASEEEE
Answer:
the perpendicular bisector
Explanation:
The perpendicular bisector will intersect the segment at its midpoint.
A bird flies 50km everyday to collect food for his offspring and 20km to drink water. To fly this distance takes him 1 hour and 40 minutes. What’s his average speed over the whole day?
Answer:
42km/h
Step-by-step explanation:
70km=100 minutes
7km= 10min
42km=60min
42km/h
You inherit one million dollars. You invest it all in three accounts for one year. The first account pays 3% compounded annually, the second account pays 4% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $34,000 in interest. If you invest four times the money into the account that pays 3% compared to 2%, how much did you invest in each account?
The amount that was invested are at 3% = 400000, at 4% = 500000 and at 2% = 100000
How to solve for the amount investedWe have x + y + z = 1000000
((1+0.03)x - x)+ ((1+0.04)y - y) + ((1 + 0.02)z-z) = 34000
4z + x + z = 1000000
((1+0.03)4z - 4z)+ ((1+0.04)y - y) + ((1 + 0.02)z-z) = 34000
((1+0.03)4z - 1)+ ((1+0.04)y - 1) + ((1 + 0.02)z-1) = 34000
12/100z + 4/100y +2/100z = 34000
2y + 7z = 1700000
-2y - 10z = -2000000
2y + 7z = 1700000
Solve through the use of the simultaneous linear equation
z = 100000
y = 500000
x = 400000
The amount that was invested are at 3% = 400000, at 4% = 500000 and at 2% = 100000
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find derivative of y= sin x sin 3x
The derivative of y= sin x sin 3x is [tex]$=3 \cos x-3 \cos 3 x$[/tex]
What is a derivative?Futures contracts, options contracts, and credit default swaps are typical types of derivatives. Beyond this, a sizable number of derivative contracts satisfy the requirements of a wide range of counterparties.To find the derivative of y= sin x sin 3x:
[tex]$y=3 \sin (x)-\sin (3 x)$[/tex]
[tex]$y^{\prime}=3 \cos x-[\cos (3 x) \cdot 3]$[/tex]
[tex]$y^{\prime}=3(\cos x-\cos 3 x)$[/tex]
[tex]\frac{dx}{dy} =3 cosx - 3 cos x[/tex]
Differentiate [tex]sin 3x[/tex] using the chain rule
Given [tex]y=f^{'} (g(x))*g^{'}[/tex]←chain rule
y=[tex]y=3 sin x-sin 3x[/tex]
[tex]\frac{dx}{dy} =3 cos x - cos 3x*\frac{d}{dx} (3x)[/tex]
[tex]=3cosx-3cos3x[/tex]
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A tank holds 3,000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes.
a) The slope of the secant lines are: q = 5, f(q) = 2,076: m = - 131.1, q = 10, f(q) = 1,299: m = - 106.8, q = 20, f(q) = 357: m = - 81.6, q = 25, f(q) = 84: m = - 68.1, q = 30, f(q) = 0: m = - 51.
b) The estimated slope of the line tangent to the curve at the point (x, y) = (15, 765) is - 94.2 gallons per minute.
How to estimate the slope of a tangent line by averaging two adjacent secant lines
In this problem we must determine the slope of several lines based on the information given by the table and using the secant line formula:
m = [f(q) - f(p)] / (q - p) (1)
If we know that a = 15 and p = 765, then the slope of the secant lines are:
q = 5, f(q) = 2,076
m = [2,076 - 765] / (5 - 15)
m = - 131.1
q = 10, f(q) = 1,299
m = [1,299 - 765] / (10 - 15)
m = - 106.8
q = 20, f(q) = 357
m = [357 - 765] / (20 - 15)
m = - 81.6
q = 25, f(q) = 84
m = [84 - 765] / (25 - 15)
m = - 68.1
q = 30, f(q) = 0
m = [0 - 765] / (30 - 15)
m = - 51
The slope of the line tangent to the curve at the point (x, y) = (15, 765) can be estimated by averaging the slopes of the closest secant lines:
m' = [(- 106.8) + (- 81.6)] / 2
m' = - 94.2
The estimated slope of the line tangent to the curve at the point (x, y) = (15, 765) is - 94.2 gallons per minute.
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PLEASE HELP
Determine which quadratic equation reveals its maximum or minimum value without changing the form of the equation.
y=x² + 4x-3
y = -3(x+4)² + 1
y=(x-9)(x + 7)
y=2x²-5x+4-10
y=x²+(3+1)x-3
y=x²+3x+1x-3
y=x(x+3)-1(x+3)
y=(x-1)(x+3)
PLEASE HELP!!! WILL MARK BRAINLIEST!!!!!
The piecewise defined function is
f(t) = 800 * 1.5^t for 0 - 2
f(t) = 2700 * 1.05^t-3 for 3 to 9
How to determine the piecewise functions?On the domain of t = 0 to 2, we have:
f(0) = 800
f(1) = 1200
f(2) = 1800
The above function is a piecewise function with the following definition
f(0) = 800 --- initial value
r = 1200/800 = 1.5 --- rate
The function is then represented as:
f(t) = f(0) * r^t
This gives
f(t) = 800 * 1.5^t
On the domain of t = 3 to 9, we have:
f(3) = 2700
f(4) = 2835
The above function is a piecewise function with the following definition
f(3) = 800 --- initial value
r = 2835/2700 = 1.05 --- rate
The function is then represented as:
f(t) = f(3) * r^t-3
This gives
f(t) = 2700 * 1.05^t-3
Hence, the piecewise defined function is
f(t) = 800 * 1.5^t for 0 - 2
f(t) = 2700 * 1.05^t-3 for 3 to 9
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Which figure does NOT belong?
Answer:
C (third figure from left)
Step-by-step explanation:
The spirals in the first, second, and fourth figures are all clockwise from the outer end, i.e., if you trace these three spirals with your finger from the outside to the inside, your finger will move clockwise.
However, if you did the same with the third figure, you would see that the spiral is anti-clockwise from the outside moving in.
Therefore, the third figure doesn't belong.
The price of a product is reduced by 30%. By what percentage should be increased to make it 100%?
it should be 70 percent
Step-by-step explanation:
100 subtract by 30 is 70 percent
ONE HUNDRED LOTTERY TICKETS ARE SOLD FOR $5.00 EACH. ONE PRIZE OF $300
WILL BE AWARDED. STEVE PURCHASES ONE TICKET. FIND HIS EXPECTATION.
use a graphing device to find all solution of the question rounded to two decimal places.
x^3-x=log(x+1)
0.00.1.14
Answer:
Step-by-step explanation:
....
An oil-drilling company knows that it costs $25,000 to sink a test well. If oil is hit, the income for the drilling company will be $325,000. If only natural gas is hit, the income will be $155,000. If nothing is hit, there will be no income. If the probability of hitting oil is 1/40 and if the probability of hitting gas is 1/20, what is the expectation for the drilling company?
The expected value for the drilling company, using a discrete distribution, is of -$9,125, that is, a loss of $9,125.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
Considering the cost that it takes to sink a test well, and the probabilities of each outcome, the discrete distribution is given by:
P(X = 300,000) = 1/40 = 0.025.P(X = 130,000) = 1/20 = 0.05.P(X = -25,000) = 1 - (0.025 + 0.05) = 0.925.Hence the expected value is given as follows:
E(X) = 300000 x 0.025 + 130000 x 0 .05 - 25000 x 0.925 = -$9,125.
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Add the following polynomials, then place the answer in the proper location on the grid. Write your answer in descending powers of x.
x 4 -3x + 1, 4x 2 - 2x + 8, and x 3 - 9
The addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.
Polynomialx⁴ - 3x + 14x² - 2x + 8x³ - 9Adding the polynomial
(x⁴ - 3x + 1) + (4x² - 2x + 8) + (x³ - 9)
Open parenthesis= x⁴ - 3x + 1 + 4x² - 2x + 8 + x³ - 9
Collect like terms in descending powers= x⁴ + x³ + 4x² - 3x - 2x + 1 + 8 - 9
= x⁴ + x³ + 4x² - 5x
Therefore, the addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.
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If f(x) = -1x + 1and g(x) = x4, what is (f º g)(x)?
Answer:
(f º g) = [tex]-x^4+1[/tex]
Step-by-step explanation:
So it's important to note that the notation: "(f º g)" isn't f(x) * g(x), it's a composite function, where you essentially have two functions, with one of the functions being the argument of one of the functions.
This means we can plug in the function g(x) as x into the function f. So let's do that
Original Function:
f(x) = -1x + 1
Plug in x^4 (this is the value of g(x)) as x into the function
f(g(x)) = [tex]-(x^4)+1[/tex]
Distribute the negative sign
f(g(x)) = [tex]-x^4+1[/tex]
G wants to get over 9000 comments on his videos. He gets the same number of comments for each cat video that he uploads, and he gets the same number of comments for each dog video that he uploads. Let C represent the number of cat videos and D represent the number of dog videos that G should upload to achieve his goal.
750C+450D>9000 According to the inequality, how many comments does each cat video get, and how many comments does each dog video get?
can G achieve his goal by uploading 8 cat videos and 7 dog videos?
Answer:
Each Cat video gets 750 comments
Each dog video gets 450 comments
Hope this helps you!
Answer:
He gets 750 comments on the cat videos and 450 on the dog videos the answer to the second question is yes
Step-by-step explanation:
khan :)
200 divided by 115.3597
Answer:
Step-by-step explanation:
1.733707699
could you brainlyest me?
I, so confused please help me asap!
Quadrilaterals are plane shapes that are bounded by four straight sides. Thus, the required answers to the questions are:
46. True. Other examples include kites, rhombus, etc.
47. False.
46. When a plane shape is bounded by four straight sides of equal or different lengths, it is called a quadrilateral. Examples include trapezium, kite, rhombus, rectangle, square, etc. Each of these examples has individual properties.
Thus the required answer to question 46 is; True. It can be observed that with respect to their individual properties, other quadrilaterals which have a pair of opposite angles to be equal include: kite, rectangle, rhombus, etc.
47. A ray segment is a given line that points or heads in a specific direction. So that the direction in which the ray moves is very important.
Thus in the given question, the required answer is; False. This is because the two given rays are moving in opposite directions. Though the two rays may have the same length of the segment.
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The function y = x2 + 3 is a transformation of the function y = x2. How is the y-intercept of the function affected by the transformation?
The y-intercept of the graph of y = x2 is shifted down 3 units.
The y-intercept of the graph of y = x2 is shifted to the left 3 units.
The y-intercept of the graph of y = x2 is shifted to the right 3 units.
The y-intercept of the graph of y = x2 is shifted up 3 units.
-----------------------------------------------------------------------------------------------
Answer on Edmentum is:
The y-intercept of the graph of y = x2 is shifted up 3 units.
Explanation:
The graph of a function in the form y = f(x) + k is the graph of f shifted up k units. The graph of y = x2 + 3 is the graph of y = x2 shifted 3 units up, so the y-intercept of the graph of y = x2 is shifted up 3 units.
The y-intercept of the graph of y = x2 is shifted up 3 units.
Exponential equationThe standard exponential equation is expressed as y = ab^x. Exponential equation is inverse of logarithmic equation.
Translation of coordinatesTranslations is a transformation technique that changes the position of an object from one point on the plane to another.
Given the parent function f(x) = x^2
If the function is shifted 3 units up, the function g(x) is derived by adding 3 to the function f(x). The resulting function is given as;
g(x) = f(x) + 3
g(x) = x^2 + 3
Hence the equation of the new graph g(x) is expressed as g(x) = x^2 + 3
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Why my foot keep makin cheese?!?!?!?
Answer:i am not sure
Step-by-step explanation:
This question is very hard to answer
Answer: I think your brain needs cheese but..............................................
Step-by-step explanation:
Don't know
What is the standard form equation of the ellipse that has vertices (-15, 4) and (5, 4) and co-vertices (-5, -3) and
(-5, 11)?
Step-by-step explanation:
Notice that the main vertices (-15,4) and (5,4) both have the same y coordinate. This means that the focal axis is horizontal so we have a horizontal ellispe.
Equation of a horizontal ellipse is
[tex] \frac{(x - h) {}^{2} }{ {a}^{2} } + \frac{(y - k) {}^{2} }{ {b}^{2} } = 1[/tex]
I'll explain the variables.
Step 1: Find the center.
The center (h,k) is the midpoint of either the main or co vertices. It doesn't matter because of the definition of an ellipse.
So using the midpoint formula, let find the midpoint of the main vertices.
[tex]( \frac{ - 15 + 5}{2} ) = - 5[/tex]
[tex] \frac{4 + 4}{2} = 4[/tex]
So our center is (-5,4) so as of right now we have
[tex] \frac{(x + 5) {}^{2} }{ {a}^{2} } + \frac{(y - 4) {}^{2} }{ {b}^{2} } = 1[/tex]
Step 2: The variable a represents the semi major axis. This
basically means what is the distance from the center to either main vertex.
Here, let use (5,4). Using (5,4), our main vertex and (-5,4), our center.
Use the distance formula
[tex]a= \sqrt{(5 - ( - 5) {}^{2} + (4 - 4) {}^{2} } [/tex]
[tex]a = \sqrt{100} [/tex]
[tex]a= 10[/tex]
So our distance is 10, this means a=10
Step 3: The variable b represent the semi minor axis. This basically the distance from the center to either co vertex.
Using the distance formula,
[tex]b = \sqrt{ (- 5 - ( - 5) {}^{2} + (4 - 11) {}^{2} } [/tex]
[tex]b = \sqrt{49} [/tex]
[tex]b = 7[/tex]
So b=7, so finally we plug a=10, b=7
[tex] \frac{(x + 5) {}^{2} }{100} + \frac{(y - 4) {}^{2} }{49} = 1[/tex]
11/3=
7/2=
14/5=
21/4=
Answer:
1 (3.66)
2(3.5)
3(5.25)
Checking account A charges a monthly service fee of $12 and a wire transfer
fee of $10.50, while checking account B charges a monthly service fee of $21
and a wire transfer fee of $8.50. Which checking account is the better deal if
4 wire transfers are made per month?
A. Checking account B IS the better deal, because its total monthly
fees amount to $55, while those for checking account A amount to
$54.
B. Checking account B is the better deal, because its total monthly
fees amount to $54, while those for checking account A amount to
$55.
C. Checking account A is the better deal, because its total monthly
fees amount to $55, while those for checking account B amount to
$54.
c
D. Checking account A is the better deal, because its total monthly
fees amount to $54, while those for checking account B amount to
$55.
For only 4 wire transfers, Checking account A has a monthly fee of $54, while checking account B has a monthly fee of $55, so the correct option is D.
Which checking account is better?Checking account A charges a monthly fee of $12, plus $10.50 for each wire transfer, then the total cost if you make 4 wire transfers is:
C = $12 + $10.50*4 = $54
For checking account B, we have a fixed cost of $21, plus $8.50 per each wire transfer, then the total cost for 4 wire transfers is:
C' = $21 + 4*$8.50 = $55
So, if you make only 4 wire transfers per month, checking account A is a better option.
Then we can see that the correct option is D.
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24 is what percent of 480?
Answer:
5%.
Step-by-step explanation:
That is
(24/480 * 100
Now 480 / 24 = 20 so we have
(1/20) * 100
= 100/20
= 5%.
Answer:
24 is 5% of 480
Step-by-step explanation:
24 / 480 = 0.05
Percent is "for each 100"
Then:
0.05 * 100 = 5%
How to make 3 dimensional object become 4 dimensional object
Using Hinton's method;
Draw two ordinary 3D cubes in 2D space, one encompassing the other, separated by an "unseen" distanceThen draw lines between their equivalent vertices.The eight lines connecting the vertices of the two cubes in this case represent a single direction in the "unseen" fourth dimension.What is a 4 dimensional shape?A four-dimensional shape (4D) is a mathematical extension of a three-dimensional or 3D space.
Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called dimensions, to describe the sizes or locations of objects.
Using Hinton's method;
Draw two ordinary 3D cubes in 2D space, one encompassing the other, separated by an "unseen" distanceThen draw lines between their equivalent vertices.The eight lines connecting the vertices of the two cubes in this case represent a single direction in the "unseen" fourth dimension.Learn more about dimensional shapes here:
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I neeeeed heeeelp please
Answer:
10b/y^2
Step-by-step explanation:
Hope this helps! :)
Can u guys please give me the correct answer
Answer:
27°Step-by-step explanation:
in the smallest triangle (BCD) you have an angle of 90° and one of 63°, the sum of the internal angles in a triangle is 180°, remove the known angles from 180 ° and you will have the measure of the CBD angle
180 - 63 - 90 =
27°
Answer:
27°
Step-by-step explanation:
180°-90°-63° = 27°
11
A, B, C, and D have the coordinates (-8, 1), (-2, 4), (-3,-1), and (-6, 5), respectively. Which sentence about the points is true?
OA
A, B, C, and D lle on the same line.
OB.
AB and CD are perpendicular lines.
OC. AB and CD are parallel lines.
OD. AB and CD are intersecting lines but are not perpendicular.
OE. AC and BD are parallel lines.
For the given coordinates of A, B, C, and D as (-8, 1), (-2, 4), (-3,-1), and (-6, 5), respectively, OD, AB and CD are intersecting lines but are not perpendicular (third option) is the correct assertion.
Reasons for the Choice
Because parallel lines never intersect, the fact that lines AB and CD come to a point proves that they are not parallel. It indicates that they are intersecting lines. (Refer to the attached figure)The location where lines AB and CD intersect is not at a straight angle. As a result, lines AB and CD are not parallel.Because the distances separating the two lines differ, AC and BD are not parallel. As a result, lines AB and CD do indeed intersect, but not at a straight angle. Consequently, despite not being perpendicular, both lines intersect.Therefore, the lines OD, AB, and CD are intersecting lines but are not perpendicular.
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