There are 2 pigeons jumped down to the street.
Total no. of pigeons on a curb=9
No. of pigeons fly away=3
No. of pigeons stayed in the curb=4
Thus, the total number of pigeon that jumped down to the street is 9 - 3 - 4 = 2
This exemplifies the pigeonhole principle, which asserts that if there are more pigeons than there are pigeonholes, then there must be at least one pigeonhole with at least two pigeons in it. II) We can state that at least one box contains two or more objects if n + 1 things are placed within n boxes.
Hence, there are 2 pigeons jumped down to the street.
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There are 2 pigeons jumped down to the street.
Total no. of pigeons on a curb=9
No. of pigeons fly away=3
No. of pigeons stayed in the curb=4
Thus, the total number of pigeon that jumped down to the street is 9 - 3 - 4 = 2
This exemplifies the pigeonhole principle, which asserts that if there are more pigeons than there are pigeonholes, then there must be at least one pigeonhole with at least two pigeons in it. II) We can state that at least one box contains two or more objects if n + 1 things are placed within n boxes.
Hence, there are 2 pigeons jumped down to the street.
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Find the point on the graph of the given function at which the slope of the tangent line is the given slope.
f(x)=x^3+6x^2+17x+14; slope of the tangent line=5
The point at which the slope of the tangent line is 5 is
The value of the points in the graph is a (2,80).
According to the statement
We have to find that the points on the graph.
So, For this purpose, we know that the
A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
From the given information:
f(x)=x^3+6x^2+17x+14; slope of the tangent line=5
Then
f(x)=x^3+6x^2+17x+14
Now find the drivative then
f'(x)=3x^2+12x+17
Then slope of the tangent line=5
Now,
3x^2+12x+17 = 5
3x^2+12x+12 = 0
x^2+4x+4 = 0
Now solve the equation then
x^2+2x+2x+4 = 0
x(x+2) +2(x+2) = 0
(x+2) (x+2) = 0
Here the values of the x become -2,-2.
Then
When x = 2
f(x)=2^3+6(2)^2+17(2)+14
f(x)=8+24+34+14
f(x) = 80.
So, The value of the points in the graph is a (2,80).
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Solve the equation 8t+30 - 2t - 16 = -22 for t.
Ot=-6
Ot= -4/
Ot=-7.5
Ot=15
Ot=6.6
Answer: -6
Step-by-step explanation:
8t+30-2t-16=-22
8t-2t+30-16=-22
6t+30-16=-22
6t+14=-22
6t=-22-14
6t=-36
t=-6
Use the maximum and minimum data entries and the number of classes to find the class width, the lower class limits, and the upper class limits.
min = 1, max = 30, 6 classes
Change. 0.99 into a present
Change 0.62
Answer: 99% 62%
Step-by-step explanation: Multiply the decimal by 100 to get a percentage.
Given Points D(-1,2) and T (-4,-4) Determine the length of segment DT. Round your answer to the nearest hundredth Hint: ( 2 decimal places )
Step-by-step explanation:
The formula for finding the length between two points is as follows:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
All we have to do is plug in our values and solve:
[tex]D=\sqrt{(-4-(-1))^2+(-4-2)^2}\\D=\sqrt{(-3)^2+(-6)^2}\\D=\sqrt{9+36}\\D=\sqrt{45}\\ D=6.71[/tex]
Explain. You stand at the edge of a 5m high diving platform. A beach ball is exactly 9 m from the base of the platfo
To the nearest tenth of a meter, what is the distance d from the top of the platform to the beach ball?
the distance, d from the top of the platform to the beach ball is equal to 10.29 m.
We are given that:
Height of the platform = 5 m
distance between bas of the platform and the beach = 9 m
We need to find the distance from the top of the platform to the beach ball.
We know that this distance d will be the hypotenuse of the triangle formed.
So, we have:
Perpendicular = 5 m
Base = 9 m
Hypotenuse = d
So, by using the Pythagoras theorem, we get that:
d² = 5² + 9²
d² = 25 + 81
d² = 106
d = √ 106
d = 10.29 m.
Therefore, we get that, the distance, d from the top of the platform to the beach ball is equal to 10.29 m.
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In ΔTUV, = 24 inches, = 29 inches and ∠T=130°. Find the area of ΔTUV, Round to the nearest square inch
The area of ΔTUV, to the nearest square inch is given as 267 square inch
Given data
ΔTUV, = 24 inches, = 29 inches and ∠T=130°
How to solve for are of triangle with two sides and one angle givenlet the Area of the triangle = A
let the two sides be a and b
let the given angle be β
A = a * b * sin β / 2
A = 24 * 29 * sin 130 / 2
A = 696 * 0.7660 / 2
A = 696 * 0.3830 = 266.583
A = 266.583 square inch
A = 267 square inch ( to the nearest square inch )
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How many gallons of a 80% antifreeze solution must be mixed with 70 gallons of 25% antifreeze to get a mixture that is 70% antifreeze?
The gallons of a 80% antifreeze solution must be mixed with 70 gallons of 25% antifreeze to get a mixture that is 70% antifreeze is x=315
Use a weighted average........ let x = an unknown number of gallons of the 80% solution.
then {x(80%) + 70 (25%)}/{x +70} =70%
{x*[tex]\frac{80}{100}[/tex] + 70*[tex]\frac{25}{100}[/tex]}/{x +70} =70%
{[tex]\frac{4x}{5}[/tex] +17.50}/{x +70} =70%
[tex]\frac{4x+87.5}{5x+350}[/tex] = [tex]\frac{70}{100}[/tex]
40x+875 = 35x + 2450
40x-35x = 2450-875
5x = 1575
x=315
Keep in mind that the substance with the highest concentration is the solvent.
There are numerous varieties of solutions. A solute, for instance, could be a gas, a liquid, or a solid. Additionally, solvents can be solids, liquids, or gases.
The behavior of several types of solutions at the microscopic level is depicted in the following illustrations. You'll see that the solute particles are evenly spaced out among the solvent particles in each instance.
A solution is a homogeneous mixture of one or more solutes dissolved in a solvent. solvent: the substance during which a solute dissolves to produce a homogeneous mixture. solute: the substance that dissolves during a solvent to produce a homogeneous mixture. The solute is the substance that is being dissolved, while the solvent is the dissolving medium. Solutions are often formed with many different types and forms of solutes and solvents.
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Solve for X using the image below
Answer:
x = 3.
Step-by-step explanation:
ADE and ABC are similar right isoceles triangles.
Step-by-step explanation:
AD / AB = ED /CB12 / 3 = 12 / X
X = 3 .........Squares of side A are cut from each corner of a 8 in x 6 in rectangle so that its sides can be folded to make a box with no top.Represent a function in of a that can define the volume of the box.
A rectangle measuring 8 inches by 6 inches needs squares of side. A function in an in which the box's volume is 4a³-28a²+48a.
Given that,
A square measuring 8 inches by 6 inches needs squares of side. A cut out of each corner so that the sides can be folded into a box without a top.
How much area a box can occupy is determined by its volume. You need to know a box's length, width, and height in order to compute its volume. By multiplying the base area by the box's height, one can get the volume of a box.
The measurement of how much space an object may occupy is called volume, which is also known as capacity. Both regular and irregular objects may be present. Cubes, blocks, cylinders, pyramids, cones, and spheres are examples of common objects.
A: area of the base
L: Length of the base
W: Width of the base
V(a)= (8-2a) (6-2a) (a)
V(a)= (48-16a-12a+4a²) (a)
V(a)= (48-28a+4a²) (a)
V(a)= 48a-28a²+4a³
V(a)=4a³-28a²+48a
Therefore, a function in an in which the box's volume is 4a³-28a²+48a.
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Abby has just started training for a marathon. She ran 15 miles in total during her first week of training. She wants to add an additional 2 miles to her weekly total during each subsequent week. Write an explicit rule for the arithmetic sequence that represents this situation and use it to find how many miles Abby will run during her twelfth week of training.
explanation please
The explicit rule for the arithmetic sequence that represents the number of miles that Abby will run in week n is:
[tex]a_n = 15 + 2n[/tex]
Using this rule, it is found that she will run 39 miles during her 12th week of training.
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
On the first week, she runs 15 miles, and for each subsequent week this amount increases by 2 miles, hence the first term and the common difference are given as follows:
[tex]a_1 = 15, d = 2[/tex]
The explicit rule for the arithmetic sequence that represents the number of miles that Abby will run in week n is:
[tex]a_n = 15 + 2n[/tex]
During the 12th week, the number of miles that she will run is found as follows:
[tex]a_{12} = 15 + 2(12) = 39[/tex]
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Help me with geometry
Answer:
X = 36.5
Z = 19
Angle RIG is 69
angle ZIM is 126.5
Step-by-step explanation:
angle AIZ and ZIP
x + 3x - 56 = 90
4x - 56 = 90
4x = 90 + 56
4x/4 = 146/4
x = 36.5
Plugin the value of x in (3x -56)
3x - 56
(3(36.5) - 56)
(109.5 - 56) = 53.5
Angle AIZ = 53.5
Angle RIG is 4z + 7. Convert the letter x in (x + 2) to Z and solve for z
4z + 7 + z + 2 = 90
5z + 9 = 90
5z = 90 - 9
5z/5 = 81/5
z = 16.2
Z + 2
16.2 + 2 = 18.2
Angle GIM is 18.2 degrees
Plugin the the value of z into 4z + 7 for angle RIG
4z + 7
(4(16.2) + 7) = 71.8
Angle RIG = 71.8 degrees
Simplify the expression 1-cotx/tanx-1
The expression 1-cotx/tanx-1 is cot x.
Given,
1-cotx/tanx-1
cot x = 1/tan x
1-cotx/tanx-1 = 1- (1/tan x) / tan x-1
= [(tan x -1 )/tan x ]/ [tan x -1]
= (tan x -1 )/ [tan x (tan x -1)]
= 1/tan x
= cot x
Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are examples of mathematical operators. For example, x + y is an expression in which x and y are terms separated by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which contain simply numbers, and algebraic expressions, which contain both numbers and variables.
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anne and nanny use a metal alloy that is 16% copper to make jewelry how many ounces of an alloy that is 10% copper must be mixed with an alloy that is 20% copper to form 55 ounces of the desired alloy
By solving a system of equations we conclude that they need to use 22 ounces of the 10% alloy and 33 ounces of the 20% alloy.
How many ounces of each alloy should they use?
First, let's define the variables we will use to solve this problem:
x = ounces of the 10% alloy copper they need to use.y = ounces of the 20% alloy copper they need to use.We know that they want to get 55 ounces, then:
x + y = 55
And the concentration of these 55 ounces must be 16%, then we can write other equation:
0.1*x + 0.2*y = 0.16*55
Then we have a system of equations:
x + y = 55
0.1*x + 0.2*y = 0.16*55
Isolating x on the first equation we get:
x = 55 - y
Now we can replace that in the other equation so we get:
0.1*(55 - y) + 0.2*y = 0.16*55 = 8.8
Now we can solve this for y.
5.5 - 0.1*y + 0.2*y = 8.8
5.5 + 0.1*y = 8.8
y = (8.8 - 5.5)/0.1 = 33
Then the value of x is:
x = 55 - y = 55 - 33 = 22
We conclude that they need to use 22 ounces of the 10% alloy and 33 ounces of the 20% alloy.
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order the following expressions from least to greatest.
2 √3 √pie
The order of expressions from the least to greatest is [tex]\sqrt{3}[/tex], [tex]\sqrt{pie}[/tex] and 2
In order to find the value of these given expressions, we will have to convert them into a standard form, therefore we will find the value of these expressions by removing the root and finding its actual value
Value of 2 will remain the same as it is already in standard form
Value of [tex]\sqrt{3}[/tex] in standard form = 1.732
Value of [tex]\sqrt{pie}[/tex] in standard form = [tex]\sqrt{3.1459}[/tex] = 1.77
No ordering these expressions we find that 2 is the greatest, followed by 1.77 and 1.732
Hence, the expressions from least to greatest is [tex]\sqrt{3}[/tex], [tex]\sqrt{pie}[/tex] and 2
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Write this English phrase as an algebraic expression. Let the variable x represent the number.
a number subtracted from twelve
translated into an algebraic expression:
The information translated to algebraic expression is 12 - x
What are algebraic expressions?Algebraic expressions are simply known as expressions composed of variables, terms, factors, constants and coefficients.
They are also made up of arithmetic operations such as multiplication, division, addition, subtraction, bracket, etc
From the information given, we have;
Let 'x' be the number
Let 'x' be subtracted from 132
This can be expressed as;
12 - x
Thus, the information translated to algebraic expression is 12 - x
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Which statement best describes a graph of paired points that form a proportional relationship?
OA straight line cannot be drawn through all the points, but the line passes through the point (0, 0).
OA straight line can be drawn through all the points, and the line passes through the point (0, 3).
OA straight line can be drawn through all the points, and the line passes through the point (0, 0).
OA straight line can be drawn through all the points, and the line passes through the point (3, 0).
1 2
If an air conditioner is rated at 16000 BTU per hour, how many watts does it require? Round to the nearest 100 watts
The number of watts will be 4700 watts to the nearest 100 watt.
How to calculate the value?It should be noted that 1 watt equals to 3.41 Btu per hour.
In this case, the air conditioner is rated at 16000 BTU per hour.
Therefore, the number of watt will be:
= 16000/3.41.
= 4692
= 4700 watts to the nearest 100 watt.
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convert 3.338 m cubed to cubic yards
4.3659392
hope this helps
HELP!!!!!!!!
Find the measurement indicated in each parallelogram.
The measurement of angle ∠D in parallelogram CDEF would be 89° and
the measurement of angle ∠D in parallelogram ABCD would be 57°.
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
In parallelogram CDEF,
∠C = ∠D
87 = 93 + 2x
2x = 87 - 93
2x = -6
x = -3
So the measurement of ∠D = 93 + 2(-2) = 89
In parallelogram ABCD,
∠A =∠C
57 = 3x + 21
3x = 57 - 21
3x = 36
x = 12
So the measurement of ∠C = 3(12) + 21 = 57
Hence, the measurement of angle ∠D in parallelogram CDEF would be 89° and the measurement of angle ∠D in parallelogram ABCD would be 57°.
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The heaviest load that an elevator can safely carry is 1,500 pounds. Gregg who weighs 155 pounds, is going to take boxes of supplies weighing 17 pounds each with him in the elevator. How many boxes of supplies can Gregg safely take with him on the elevator at one time?
Answer:
79 boxes
Step-by-step explanation:
1500-155= 1345
1345/17=79.11
Solve for x.
-20=-X
Answer:
x = 20
Step-by-step explanation:
-20 = -x
[tex]\frac{-20}{-1}[/tex] = [tex]\frac{-x}{-1}[/tex]
Simplify
x = 20
As Sara rode her bike at 9 mph, how many feet did she travel in 28 seconds? (1 mi =
5280 ft)
the answer was 369.6 I’m trying to know how that’s the answer
Answer:
Step-by-step explanation: This vould be the answer because it could have been turned into an epression
4 (-1/3) =
And
(-2/3) (-1/2) (-3/5) =
Answer:
EX1: 4×(-1/3)=-4/3
EX2: (-2/3)(-1/2)(-3/5)= -1/5
If n×n×n=60 , then which of the following best approximates n ?
[tex] \eta \times \eta \times \eta = 60 \\ \eta {}^{3} = 60 \\ \eta = \sqrt[3]{60} \approx3.91487[/tex]
I need help plsss
What is the equivalent decimal?
Drag the answer into the box to match the fraction.
10/66
A. 0.15
__
B. 0.15
__
C. 0.54
__
D. 0.46
The decimal form of the fraction 10 / 66 is 0.15.
How to convert from fraction to decimals?Fractions represent the parts of a whole or collection of objects.
In other words fractions are represented as a numerical value, which defines a part of a whole.
Fractions has a numerator and a denominator.
The numerator is at the top while the denominator is below.
A decimal is a number that consists of a whole and a fractional part.
Therefore, let's convert the fractions 10 / 66 to decimal.
Hence,
10 / 66 ÷ 2 / 2 = 5 / 33
Therefore,
5 / 33 = 0.15151515151 = 0.15
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Solve 17.04x6.2= how many gallons?
Answer:
17.04 x 6.2= 105.648
Hope this helps :)
Two circles each of radius 5 units, lie i perpendicular planes. they intersect in two points x and y thus determining a common chord XY. If XY = 8, compute the distance between the centers of the circle
The distance between the centers of the circle is [tex]3\sqrt{2}[/tex] units.
It is required to find the distance between the centers of the circle.
What is circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.
Given:
Radius =5 units
XY = 8
According to given question we have
XY=
[tex]\sqrt{3^{2}+3^{2} } \\\\=\sqrt{18} \\\\=\sqrt{9.2} \\\\=3\sqrt{2}[/tex]
Therefore, the distance between the centers of the circle is [tex]3\sqrt{2}[/tex] units.
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Geometry: What is the value of X
I know the answer is x=7
I just need to know, how do you get 7 as x.
So someone pls help with the strategies+details of every step!!
Answer:
x = 7
Step-by-step explanation:
The dashes on each side of the rectangle indicate congruency.
This means that PS = QR, or 2x - 3 = 11.
Now we would solve for this like normal.
2x - 3 = 11 add 3 to each side
+ 3 + 3
--------------
2x = 14 now divide by 2 to find x
÷ 2 ÷2
--------------
x = 7
what is 9/32 minus 1/16?
Answer: [tex]\frac{7}{32}[/tex]
Step-by-step explanation:
You want your numbers to have a common denominator which you can get by doubling both sides of the second number ([tex]\frac{1}{16} = \frac{2}{32}[/tex]).
[tex]\frac{9}{32} - \frac{2}{32} \\= \frac{7}{32}[/tex]
