By the use of arithmethic, the final temperature in Sudbury is - 1 °C.
What is the final temperature of Sudbury?
In this problem we know that initial temperature and two consecutive changes in time. A temperature rise represents a positive change, whereas a temperature fall represents a negative change, then the final temperature is equal to sum of the initial temperature and its two changes:
T = T' + ΔT₁ + ΔT₂
T = 4 °C + 5 °C - 10 °C
T = 9 °C - 10 °C
T = - 1 °C
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If In triangleABC, (AB)^2 + (BC)^2 = (AC)^2, then triangleABC is a right triangle.
Determine whether this conjecture is true or false and find a counter example if it is false.
The triangle of ABC is a right-angle triangle is true.
In Triangle of ABC
⇒(AC)^2=(BC)^2+(AB)^2 ----equation (1)
given by
Pythagoras theorem,
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.
These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
The hypotenuse is the longest side in this situation because it makes an angle of 90°
⇒(hypotenuse)^2=(one side)^2+(other side)^2 ---equation (2)
comparing one (1) and (2)
we get, AC is a hypotenuse of a triangle.
⇒ hypotenuse is the longest side of a right-angled, opposite the right angle.
⇒ opposite angle of AC is ⇒∠ B.
Hence, ∠ B is a right angle of triangle ABC. so, the triangle of ABC is a right angle triangle is true.
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682,548-300,752=
92,730-5,472=
47,569+21,478=
741,658+32,567=
Answer:
1.381796
2.87258
3.69047
4.774225
Step-by-step explanation:
Align the numbers as an ordinary subtraction problem. Write the larger number above the smaller number. If the smaller number has fewer digits, line them up on the right, as you would in a decimal (base ten) subtraction problem.
Answer:
682,548 - 300,752 = 381,796
92,730 - 5,472 = 87,258
47,569 + 21,478 = 69,047
741,658 + 32,567 = 774,225
Step-by-step explanation:
Determine whether y is a function of x . Explain.
x² = 3y + y
After determining whether y is a function of x we have come to conclusion that y is not a function of x.
x² = 3y + y
x² = 4y
y = x²/ 4
Here x has two values of -x and x as -x² = x². Therefore, y is not a function of x.
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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You swim 4 lengths of a pool and break a record by 0.72 second. The table shows your time for each length compared to the previous record holder. How much faster or slower is your third length than the previous record holder?
IfIf you swim 4 lengths of a pool and break a record by 0.72 second. The table shows your time for each length compared to the previous record holder. How much faster or slower is your third length than the previous record holder is: 0.54 seconds.
How much faster or slower is the third lengthFirst step is to calculate the different in speed between first and fourth length
Using this formula
Speed =-First length time in seconds +(- Fourth length time in seconds)
Let plug in the formula
Speed=-0.23+(-0.42)
Speed=-0.65
Second step is to calculate the third length
Speed=-0.65+0.11
Speed=-0.54 seconds
Therefore If you swim 4 lengths of a pool and break a record by 0.72 second. The table shows your time for each length compared to the previous record holder. How much faster or slower is your third length than the previous record holder is: 0.54 seconds.
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While taking a personal finance course, Lakshmi decided to create and follow a personal financial plan. To estimate her annual expenses, she kept track of everything that she spent for one month. She was surprised to discover that she spent $150 on clothing and accessories. If Lakshmi decided to cut her monthly clothing and accessories expenditure in half, how much could she save in a year?
Using proportions, it is found that she would save $900 in a year.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
She spends $150 a month on clothing and accessories, hence, if she saves half of that, the amount saved in a month is:
0.5 x 150 = $75.
In a year, this amount will add up to:
75 x 12 = $900.
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Is the sequence geometric? If it is, what are a₁ and r ?
a. 2,4,8,16, . . . . . . . . .
The given sequence 2, 4, 8, 16,... is geometric, with a₁ = 2 and r = 2.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Now,
Given: 2, 4, 8, 16, ...
The sequence can also be written as: 2¹, 2², 2³, 2⁴,...
Thus, it follows the definition of geometric progression, having a₁ = 2 and a constant increment of 2, i.e., r = 2.
Hence, The given sequence 2, 4, 8, 16,... is geometric, with a₁ = 2 and r = 2.
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in his garden Tim plants the seed 4 3/4 below the ground. after one month the tomato plant has grown a total of 8 1/2. How many inches is the plant above the ground
Answer: 3 3/4
Step-by-step explanation:
The plant is 4 3/4 below ground, but then it grows 8 1/2.
Use subtraction to find the difference.
8 1/2 - 4 3/4 = 3 3/4
Answer:the answer would be 3 3/4
Step-by-step explanation:
pls help! 50pts
Which statement best describes why the steady state theory cannot explain the radiation detected in space?
Answer:
D. The theory is based on the idea that an explosion did not occur; therefore, evidence of radiation would not be predicted in the theory.
Step-by-step explanation:
You want to identify the statement that best describes why the steady state theory cannot explain the radiation detected in space.
RadiationThe Big Bang theory explains the cosmic background radiation as remanent thermal energy from the explosion creating the known universe. The Steady State theory presumes there was no explosion. It offers no alternative explanation for the observed cosmic background radiation.
The cosmic background radiation was first observed in 1965 by two radio astronomers who set out to map radio signals from the Milky Way. They found microwave signals that could not be attributed to a specific source, and were of the same intensity in every direction at every time of day or season of the year. The spectrum of this radiation is consistent with a source temperature of about 2.725 K, explained as the cooled remains of the hot plasma that once filled the universe.
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Help! 25 points! 5h=60. what does h equal to
Answer:
the answer is 12.
Step-by-step explanation:
to find the answer divide 60 by 5 and you'll get the answer (aka 12)
Answer:
12
Step-by-step explanation:
5h=60
h= 60÷5
=12
ans: h=12
Suppose you have a box with a 4 × 4 -in. square base and variable height h . The surface area of this box is a function of its height. Write a function to represent the surface area. Evaluate the function for h=6.5 in.
The total surface area of the box is 138in².
What is surface area of cuboid?
The six rectangular faces of a cuboid. Add the areas of each of the cuboid's six faces to determine its surface area. Additionally, we can label the prism's length (l), width (w), and height (h), and then calculate its surface area using the formula SA=2lw+2lh+2hw.Formula for calculating the surface area of the box S = 2(LW+LH+WH) where
L is the length of the box
W is the width of the box
H is the height of the box
If the box is square based with dimension 4 * 4in, then L = W = 4in. substituting this values given into the formula we will have;
S = 2(4(4)+4H + 4H)
S = 2(16+8H)
S = 32+16H
Hence, The function that represents the surface area of this box as a
function of its height is S = 32+16H where H is the height of the box
Given H = 6.5in, to evaluate the function, we will substitute h = 6.5in into the modeled equation;
S = 32+16H
S = 32+16(6.5)
S = 32+106
S = 138in²
Hence the total surface area of the box is 138in².
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Write each arithmetic series in summation notation. 7+9+11+ . . . . . . +21
The given arithmetic series can be expressed in summation notation as [tex]\sum\limits^8_{n=1} {(2n+5)}[/tex] or in simplified notation [tex]40+2 \sum\limits^8_{n=1} {n}[/tex]
The summation notation is used to express long summation in one expression.
The given arithmetic series is:
7+9+11+ . . . . . . +21
Find the explicit formula for the nth term in the given series.
Recall:
a(n) = a(1) + (n-1) . d
where:
a(1) = the first term
d = common difference = a(2) - a(1) = a(n) - a(n-1)
From the series, we get:
a(1) = 7
d = 9 - 7 = 2
Hence,
a(n) = a(1) + (n-1) . d
a(n) = 7 + (n-1) . 2
a(n) = 2n + 5
Find number of terms in the given series.
From the given series, we know that the last term is 21.
Let the last term be a(n), then,
a(n) = 2n + 5
21 = 2n + 5
2n = 16
n = 8
Write the summation notation with lower limit n = 1 and upper limit n = 8.
[tex]\sum\limits^8_{n=1} {a(n)}= \sum\limits^8_{n=1} {(2n+5)}[/tex]
If necessary, simplify the summation.
[tex]\sum\limits^8_{n=1} {(2n+5)}= \sum\limits^8_{n=1} {2n}+ \sum\limits^8_{n=1} {5}[/tex]
[tex]= \sum\limits^8_{n=1} {2n}+ 8\times5[/tex]
[tex]=40+2 \sum\limits^8_{n=1} {n}[/tex]
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1. Solve 5h+34 = 17 for h.
A -17/5
B -51/5
C 51/5
D 17/5
Answer:
A. -17/5
Step-by-step explanation:
h= -17/5
Hope this helps! :)
How to factor this? Please help. Question attached
Answer:
(y+4)²
Step-by-step explanation:
[tex](a+b)^2=a^2 + 2ab+b^2[/tex]
Here, a=y and b=4.
3 5/8 times 21 2/3 what is the answer
Answer:
78 13/24
Step-by-step explanation:
3 5/8=29/8
21 2/3=65/3
29/8×65/3=1885/24=78 13/24
So, your answer is 78 13/24
Hey there!
3 5/8 * 21 2/3
= 3 * 8 + 5 / 8 * 21 * 3 + 2 / 3
= 24 + 5 / 8 * 63 + 2 / 3
= 29 / 8 * 65 / 2
= 29 * 65 / 8 * 2
= 1,885 / 16
= 78 13/24
Therefore, your answer should be:
78 13/24
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Solve the system of equations. 4x – y = 4 2x2 – y = 4 (0, 4) and (0, –4) (1, 0) and (1, –6) (2, 4) and (0, –4) (3, 8) and (0, –4)
Answer: Choice C
(2, 4) and (0, -4)
========================================================
Explanation:
Let's solve the first equation for y
4x - y = 4
-y = -4x+4
y = 4x-4
Now plug this into the other equation and solve for x.
2x^2 - y = 4
2x^2 - ( y ) = 4
2x^2 - ( 4x-4 ) = 4
2x^2 - 4x+4 = 4
2x^2 - 4x+4-4 = 0
2x^2 - 4x = 0
2x(x - 2) = 0
2x = 0 or x-2 = 0
x = 0 or x = 2
-----------------
If x = 0, then,
y = 4x-4
y = 4(0)-4
y = -4
This gives one solution as (0, -4)
-----------------
If x = 2, then,
y = 4x-4
y = 4(2)-4
y = 4
The other solution is (2, 4)
-----------------
To check the answers, plug the x and y coordinates into each equation. You should get the same thing on both sides.
Below is verification using a graph. The points of intersection are the solutions.
What is 2 5/11×2??????
Answer: 4 10/11
Step-by-step explanation:
does anybody know what 4021836 - 1987269 is?
Well, doing 4021836 - 1987269 on paper, you would get the answer of 2034567
solu. 2034272
Alternate form. 2.034272*10^2
In the class of 2019, more than 1.6 million students took the SAT. The distribution of scores on the math section (out of 800) is
approximately normal with a mean of 528 and standard deviation of 117.
According to the given statement;
The probability of student Who scored less than 350 is 0.0643.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. The concept of probability was developed to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.
According to the given value;
Population Mean,μ = 528
Population Standard Deviation,σ = 117
X follows normal distribution
I.e X ~ N ( μ = 528 ,σ = 117 )
formula for z score is
Z =
0
Subtract the mean and then divide by the standard deviation to turn x into a standard Normal z
X ≤ 350
(x-528)/117 ≤ (350-528)/117
z ≤ -1.52
Now, by using standard normal distribution table
area left of -1.52
= 0.0643
Hence,The required probability is 0.0643.
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Find the diameter and radius of a circle with the given circumference. Round to the nearest hundredth. (Lesson 10-1) C=23cm
Answer:
radius: 3.66 Diameter: 7.32
Step-by-step explanation:
Radius = C/2π 3.6605636911136
Diameter = C/2π7.3211273822272
help please and thank you
Step-by-step explanation:
False!
the correct equation should be ( x - 3)² + 2
3 units shifted to the right and 2 units upward.
also you can expand the equation to find the axis of symmetry to be sure. :)
Find the length of BC .
A 18°
B 2.20cm
C 168°
D 30.79cm
The length of BC is B. 2.20 cm
As per the known fact, the linear angle is 180°. As per this writing the equation -
∠ BC + 168 = 180
∠ BC = 180 - 168
∠ BC = 12°
Now, using formula for calculation of length of arc -
Length = angle/360×2πr, where r refers to radius
Calculating radius as -
Radius = diameter ÷ 2
Radius = 21 ÷ 2
Radius = 10.5 centimeters
Now keep the values in formula to find the length of arc, which is the value of BC
Length = 12/360×2×3.14×10.5
Length = 252×3.14/360
Length = 2.2 centimeters
Hence, the length of BC is B 2.20cm.
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The complete question is attached in image.
ASAP PLEASE!!!!!!!!!!!!!
Need answers ASAP!!!!
solve the pairs of simultaneous equation x+ 2y =7 and 4x +2y =10
Answer:
Step-by-step explanation:
Okay
x+2y=7
x+2y-2y=7-2y
x=7-2y
4x+2y=10
4x+2y-2y=10-2y
4x=10-2y
divide both sides by 4
4x/4=(10/4)-(2y/4)
x=(5-y)/2
Hope this helps! ^^
.........................................................................................................
Answer:
256
Step-by-step explanation:
20-8=12
12+4=16
16x16=256
Answer:
256
Step-by-step explanation:
Find the distance between the two points rounding to the nearest tenth (if necessary).
(3, 1) and (5,-2)
8.06 is the distance between the two points .
What is distance in math?
The length or width between two objects, points, lines, etc. the quality or condition of being remote from something else in space; remoteness. a straight line in space It would take too long to walk seven miles in one hour. a big area.A wide body of water encircled the ship.Using their coordinates, an algebraic expression provides the distances between two places (see coordinate system). The distance formulas for points in rectangular coordinates in two- and three-dimensional Euclidean space are based on the Pythagorean theorem.distance d = [tex]\sqrt{( 5 + 3)^{2} + ( -2 + 1)^{2} }[/tex]
d = [tex]\sqrt{8^{2} + (-1)^{2} }[/tex]
d = [tex]\sqrt{64 + 1}[/tex]
d = √ 65
d = 8.06225 ≈ 8.06
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Evaluate each logarithm.
log₂ 1/2
Answer:
well done ......hope it's helpful
Find the value of x for the given values of a and b .
a+8=-4(x-b) , for a=8 and b=3
The value of x so that the equation based on a and b has a solution is x = -4/3
What are equations?An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.
Equations can be graphed, just like a function.
As we can see, we have the following equation:
a + 8 = -4(xb)
and we have the values of the coefficients a and b, and these are:
a = 8b = 3We substitute these values in the equation:
(8) + 8 = -4 [x(3)] We solve the equation
16 = -4(3x)
16 = -12x
x = 16-/12
x = 8/-6
x = 4/-3
x = -4/3
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what asserts that a 3-dimensional manifold is the same as the 3-dimensional sphere precisely when a certain algebraic condition is satisfied.
I will sleep with whoever is correct
In topology, the Pointcare conjecture is the one that states a 3-dimensional mainfold is the same as the 3-dimensional sphere.
What does topology studies?Topology is a branch derived from geometry, this branch focuses on studying and analyzing geometrical properties and spatial relationships. One of the focuses of this area is the equivalences of some shapes or spaces.
What is the Pointcare conjecture?This conjecture created by Pointcare in the 19th century proposes a three dimensional mainfold is the same or it is equivalent to a three dimensional sphere.
This conjecture was first proven as valid by Pointcare and other mathematicians/experts in the topic. However, some years later the same Pointcare and other experts showes this conjuction is not always true and therefore it is not valid.
Despide this, to this day this conjecture remains very popular and people around the world are still trying to prove it or dispprove it.
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Please show your work!! Identify the volume of the composite figure. Round to the nearest tenth.
The volume of the composite figure = 860.7 m³
How to Find the Volume of a the Composite Figure?The volume of the composite figure = volume of rectangular prism - Volume of cylinder.
Volume of rectangular prism = (length)(width)(height)
Length = 10 mWidth = 10 mHeight = 12 mVolume of rectangular prism = (10)(10)(12)
Volume of rectangular prism = 1,200 m³
Volume of the cylinder = πr²h
r = 3 m
h = 12 m
Volume of the cylinder = π(3²)(12)
Volume of the cylinder = 339.3 m³
The volume of the composite figure = 1,200 - 339.3
The volume of the composite figure = 860.7 m³
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Translate the sentence into an inequality.
The product of b and 7 is less than or equal to -24.
b*7<= -24
<= iz a less than or equal symbol
