As per the congruence theorem, we have proved that ΔABC ≅ΔDEF.
In math congruence theorem states that if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other.
Here we need to prove ΔABC ≅ΔDEF by using the congruence theorem.
Here we have given that ΔABC and ΔDEF,
=> ∠B≅∠E [right angle]
So, we have obtained that
=> ∠A≅∠D
As we know that there is two angles and one non included side of ΔABC is congruent the two corresponding angles and one non- included side of ΔDEF, therefore, by AAS congruence rule.
So, based on the given fact we have identified that
=> ΔABC ≅ΔDEF
Therefore, the AAS congruence postulate defined that the triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.
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need help with homework it was due the 15th
Here the correct answer is (8,4) means option B.
Given equations are,
y=x-4 -----------------(1)
y= -0.5x+8-----------(2)
Option A.(4,2): If we put x=4 in equation one then y=0 which does not satisfy equation 2.
Option B.(8,4): If we put x=8 in equation one then y=4 and which satisfies equation 2.
Option C.(2,4): If we put x=2 in equation one then y=-2 which does not satisfy equation 2.
Option D.(4,8): If we put x=4 in equation one then y=0 which does not satisfy equation 2.
Therefore the solution of the equations y=x-4 and y=-0.5x+8 is (8,4) which is option B.
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One of the roots of the equation 10x^2-33x=c=0 is 5.3. Find the other root and the coefficient c.
Answer:
another root=-2,c=-106
Step-by-step explanation:
let q and r be two roots of eqn 10x²-33x-c=0,--(1)
then,q=5.3
comparing eqn--(1) with ax²+bx+c=0,we get
a=10,b=-33,C=-c
we know,
q+r=-b/c
or,5.3+r=33/10
or,53+10r=33
or,10r=-20
or,r=-2
hence, another root=-2
again,we know
q×r=-C/a
or,5.3×-2=c/10
or,-106=c
hence,c=-106.
Larry and Peggy are making decisions about their bank accounts. Larry wants to deposit $350 as a principal amount, with an interest of 4% compounded quarterly. Peggy wants to deposit $350 as the principal amount, with an interest of 6% compounded monthly. Explain which method results in more money after 2 years. Show all work.
The method which result into more money after 2 years is Peggy method of saving at 6% interest rate and compounded monthly.
How to calculate compound interest?Larry:
Principal, P = $350Interest rate, r = 4% = 0.04Number of periods, n = 4Number of years, t = 2A = P(1 + r/n)^nt
A = 350.00(1 + 0.04/4)^(4×2)
A = 350.00(1 + 0.01)(8)
A = $379.00
Peggy
Principal, P = $350Interest rate, r = 6% = 0.06Number of periods, n = 12Number of years, t = 2A = P(1 + r/n)^nt
A = 350.00(1 + 0.06/12)^(12×2)
A = 350.00(1 + 0.005)(24)
A = $394.51
Therefore, Peggy has more money than Larry after two years.
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Answer:peggy account brings in more money after two years.
Step-by-step explanation:
LarryA=P(1 + r/n)^nt
A=350(1+0.04/4)^(4)(2)
A=350(1.01)^8
A=378.999
Peggy
A=P(1 + r/n)^nt
A=350(1+0.06/12)^(12)(2)
A=350(1.005)^24
A=394.505
So Peggy’s account brings in more money after two years.
What value of x makes the equation 1/2(5x+16)-3/2(x-8)=-4 true
Answer:
x=-24
Step-by-step explanation:
you would solve for x
1) multiply the equation out
2) put x on one side by subtracting and adding on each side (make sure to balance it out)
3) divide or multiple by the number on the number on the x
5/2x + 8 - 3/2x + 12 = -4
5/2 x - 3/2 x + 8 + 12 = -4
x + 20 = -4
x = -24
[tex]10x+6y=0\\\-7x+2y=31[/tex]solve the system by using substitution or elimination
The value of x= 93/11 and y=-155/11 when the system of equation are 10x+ 6y=0 and 7x+ 2y=31.
Given that,
The system of equation are 10x+ 6y=0 and 7x+ 2y=31.
We must resolve the equation system.
We know that,
Take the system of equations.
10x+ 6y=0 ------>equation(1)
7x+ 2y=31 ------->equation(2)
Multiply 3 to the equation(2) and subtract with equation(1)
3×(7x+ 2y=31)
21x+ 6y=93
10x+ 6y=0
----------------- (subtract)
11x+0=93
11x=93 (divide)
x=93/11
Substitute x=93/11 in equation(1)
10(93/11)+6y=0
930/11+6y=0
6y=-930/11
y=-155/11
Therefore, The value of x= 93/11 and y=-155/11 when the system of equation are 10x+ 6y=0 and 7x+ 2y=31.
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A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:
Likes hamburgers Does not like hamburgers Total
Likes burritos 39 77
Does not like burritos 95 33
Total 134 205
Part A: What percentage of the survey respondents liked hamburgers but do not like burritos? Show all work. (3 points)
Part B: What is the marginal relative frequency of all customers who like hamburgers? Show all work. (3 points)
Part C: Which category has the lowest joint relative frequency? Show all work. (4 points)
A: The percentage of respondents who like hamburgers but dislikes burritos is 46.34%
B: Marginal relative frequency of all who like hamburgers is 0.65.
C:Lowest joint frequency is of the respondents who like both.
What are relative frequencies?The word "relative" is used to describe how something is being viewed in connection to or in comparison to another event. How frequently an event occurs can be determined by looking at its frequency. On the other hand, relative frequency is a means to compare the frequency of a specific event to all other occurrences.
The ratio of the total number of events occurring in a scenario to the number of times an event occurs is known as relative frequency.
Two facts must be known in order to determine the relative frequency:
>>Number of total events/trials
>>Frequency count for a category/subgroup
Calculation:
Like Ham↓ Does Not Like Ham Total↓
Likes burritos → 39 38 77
Does not like burritos → 95 33 128
Total → 134 71 205
So, according to the above table, a total of 77 customers like burritos, out of which 38 do not like hamburgers, hence, the remaining 39 like Hamburgers.
A total of 128 customers do not like burritos, out of which 95 do like hamburgers, hence, the remaining 33 do not like Hamburgers.
A total of 134 customers like hamburgers, but 71 do not like it, hence, the total respondents are 205.
A:
Total people who liked hamburgers are 134 and those who doesnot like burritos and liked hamburgers are 95 and the total people participated in the survey are 205.
So the percentage of people is [tex]\frac{95}{205}*100[/tex] = 46.34%
B:
The marginal relative frequency is nothing but total people who like hamburgers out of the total respondents.. which is
[tex]\frac{134}{205}[/tex] = 0.65
C:
The category that has lowest joint relative frequency is
Case 1:
Likes both burritos and hamburgers:
[tex]\frac{39}{134}=0.29[/tex]
Likes burritos and dislikes hamburgers:
[tex]\frac{38}{71} = 0.53[/tex]
Likes hamburgers and dislikes burritos:
[tex]\frac{95}{134} = 0.71[/tex]
Who dislike both are:
[tex]\frac{33}{71}=0.47[/tex]
So the category which lowest joint frequency is Likes both burritos and Hamburgers.
A: The percentage of respondents who like hamburgers but dislikes burritos is 46.34%
B: Marginal relative frequency of all who like hamburgers is 0.65.
C:Lowest joint frequency is of the respondents who like both.
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Answer:
look at the link so you can get the straight up answers
Step-by-step explanation:
I did the same test got it all right
PLS give BRAINLIST mean the world
A frog in a hemispherical pod (see fig. ) just floats without sinking into sea water with density 1. 35g / c * m ^ 3 if the pod has radius 6 cm and negligible mass, what is the mass of the frog?.
Thus, the mass of the frog is 48.6π grams when it is in a hemispherical pod which just floats without sinking into sea water.
What is meant by buoyancy?The force imposed on a body by a fluid, such as water or air, in which the body is submerged or immersed is known as buoyancy. This force is equivalent to the mass of the fluid that the body has displaced. In mathematics, buoyancy is defined as the sum of the fluid density, gravitational acceleration, and body volume. Archimedes' principle, which asserts that the buoyant force on an item is equal to the weight of the fluid it displaces, is a name for this connection. A key idea in the study of fluid mechanics, buoyancy has many uses, including the construction of boats, planes, and other floating structures.
How to solve?
V = 2/3 * π * r^3,
V = 2/3 * π * 6^3 = 2/3 * π * 216 = 36π.
F = V * d,
F = 36π * 1.35g/c * m^3 = 48.6π g.
F = m + W,
48.6π g = m + 0 g.
m = 48.6π g.
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PLEASE HELP ILL THANK YOU GIVE YOU FIVE STARS AND GIVE YOU BRANLSIYEST!!!!!!!!!!!!!!!!
Triangle ABC has the following angle measures:
m∠A = (x + 4)°, m∠B = (2x − 11)°, m∠C = (3x + 25)°
What is m∠B?
27°
33°
43°
55°
Triangles are shapes that have a total angle measurement of 180°.
To find this answer, add the measures of all the angles and set the equation equal to 180:
(x + 4) + (2x − 11) + (3x + 25) = 180
NOW SOLVE FOR X!
x + 4 + 2x − 11 + 3x + 25 = 180
18 + 6x = 180
6x = 162
x = 27
Now plug 27 into the equation for m∠B:
m∠B = (2x − 11)
m∠B = 2(27) − 11
= 54 - 11
m∠B = 43
(a) Find the three consecutive natural numbers whose sum is 66.
(b) Find the three consecutive odd natural numbers whose sum is 39.
Answer:
(a) 21, 22, 23
(b) 11, 13, 15
Step-by-step explanation:
Natural numbers are the set of numbers 1, 2, 3... Not numbers that we think of as fractions or decimals or negative numbers.
Let x = the first number
Let x+ 1 = the second number
Let x+ 2 = the third number
x + x+ 1 + x + 2 = 66 Combine like terms
3x + 3 = 66 Subtract 3 from both sides
3x = 63 Divide both sides by 3
x = 21
Check:
21 + 22 + 23 = 66
Let x + the first number
Let x + 2 = the second number
Let x + 4 = the thirds number
x + x + 2 + x + 4 = 39 Combine like terms
3x + 6 = 39 Subtract 6 from both sides
3x = 33 Divide both sides by 3
x = 11
Check: 11 =+ 13 + 15 = 39
Question 2
The average distance from Jupiter to the Sun is about 5 x 10^8 miles. The average
distance from Venus to the Sun is about 7 x 10^7 miles.
The average distance from Jupiter to the Sun is about how many times as great as
the average distance from Venus to the Sun?
1. 1.4 times
2.7.1 times
3. 10 times
4. 430,000,000 times
When the average distance from Jupiter to the Sun is about 5 x 10^8 miles and the average distance from Venus to the Sun is about 7 x 10^7 miles. The average distance from Jupiter to the Sun is about 7.1 as great as the average distance from Venus to the Sun.
How to compare the distancesThe distances is compare using the mathematical operation called division,
the procedure is done as follows
= (The average distance from Jupiter to the Sun) / (The average
distance from Venus to the Sun)
= 5 x 10^8 miles / 7 x 10^7 miles.
= 7.14285
= 7.1
the comparison showed that the distance from Jupiter to Sun is 7.1 times greater than the distance form Venus to Sun
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Andrew invests $2834 in a savings account with a fixed annual rate of 2.5% compounded daily. What will the account balance be after 28 years?
The account balance(i.e. compound amount) will be $5706.84 after 28 years.
What is daily compounded interest?
Daily compounded interest is defined as an interest that is accrued daily and is computed by charging interest on principal plus interest earned daily. Due to the frequent compounding, daily compounded interest is higher than interest compounded on a monthly or quarterly basis.
Given, Principal = $2834
the annual rate = 2.5% = 0.025
time = 28 years
For compounded daily, n = 365
Now, the compound amount is calculated by
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
or, A = [tex]2834(1 + \frac{0.025}{365} )^{365*28}[/tex]
A = $5706.84
Hence, the account balance will be $5706.84 after 28 years.
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Of the 72 people who have taken their seats at a seminar, 6 have brown hair. Considering this data, how many of the next 84 people to take their seats should you expect to be brown-haired?
Element x decays radioactively with a half life of 8 minutes. If there are 170 grams of element x, how long, to the nearest tenth of a minute, would it take the element to decay to 5 grams?.
A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.
What is radioactive decay?
The release of energy in the form of ionizing radiation occurs during radioactive decay.
Ionizing radiation can harm DNA in genes and tissues because it can affect the atoms in living things.
We know that decay behaves exponentially and follows this model
[tex]m(t) = m_{0} . e^{t/T} \\[/tex]
The time constant can be described in terms of half-life (t1/2), in minutes, through the following expression
T = t1/2 /In2
If we know that t1/2 = 8 min , m₀ = 170g and m(t) = 5g then the time needed for the decay is:
τ ≈ 11.541 min
t = -τ .In m(t)/m₀
t ≈ 40.698 min
A time of 40.7 minutes is taken for 170 grams of element X to decay to 5 grams.
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Tyee has 39 m of fencing to build a three-sided fence around a rectangular plot of
land that sits on a riverbank. (The fourth side of the enclosure would be the river.)
The area of the land is 169 square meters. List each set of possible dimensions (length
and width) of the field.
The dimensions of a building to be fenced off around a rectangular parcel of land are 10.5 meters and 21 meters.
How come it's called a rectangle?The Latin word rectus, which meaning "right" or "straight," is the source of the English word "rectangle." The straight sides of a rectangle are a result of its right angles. Rectitude, which refers to moral uprightness, is another term with the same root.
Explanation:
The size of a rectangle
lw = area of rectangle
where,
= length
= width
Thus, perimeter equals 2w plus l.
42 = 2w + l
l = 42 - 2w
Hence,
area = w (42- 2w)
180 = 42w - 2w²
-2w² +42w - 180 = 0
-w² + 21w - 180 = 0
The following is where to find the dimension w;
w = - b / 2a
where
a = -1
b = 21
w = - 21 / 2 × -1
W=10.5 meters.
Then,
l = 42 - 2w
l = 42 - 2(10.5) (10.5)
l=21 meters .Consequently, the measurements are 10.5 meters and 21 meters.
The dimensions of a building to be fenced off around a rectangular parcel of land are 10.5 meters and 21 meters
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The tape diagram shows that Ehecatl's hair, which is now 12\,\text{cm}12cm12, start text, c, m, end text long, is 60\%60%60, percent as long as it was before his haircut.
A tape diagram with one tape split into 5 equal parts. The first 3 parts are shaded. A curved brace above the first 3 parts is labeled 12. A curved brace below the first 3 parts is labeled 60 percent.
A tape diagram with one tape split into 5 equal parts. The first 3 parts are shaded. A curved brace above the first 3 parts is labeled 12. A curved brace below the first 3 parts is labeled 60 percent.
Complete the table to show different percentages of Ehecatl's hair length before the haircut.
Length (\text{cm}cmstart text, c, m, end text) Percentage
60\%60%60, percent of Ehecatl's old hair length
20\%20%20, percent of Ehecatl's old hair length
100\%100%100, percent of Ehecatl's old hair length
The completed table of Ehecatl's hair length before the haircut is
Length (cm) Percentage
12 60% of Ehecatl's old hair
4 20% of Ehecatl's old hair
20 100% of Ehecatl's old hair
How to complete the missing information in the table?The complete question is added at the end of this solution and as an attachment
From the question, we have the following incomplete table that can be used in our computation:
Length (cm) Percentage
60% of Ehecatl's old hair
20% of Ehecatl's old hair
100% of Ehecatl's old hair
The first step is to determine the length of her hair before she cut it
The equation to calculate the new length of the hair after the cut is represented as
New length = Length of the hair before it was cut * Percentage
Substitute the known values in the above equation
So, we have the following representations
At 60%: 60% x 20 = 12cm
At 20%: 20% x 20 = 4cm
At 10%: 100% x 20 = 20cm
So, the missing values are 12 cm, 4 cm and 20 cm
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Complete question
The tape diagram shows that Ehecatl's hair, which is now 12cm long is 60% as long as it was before his haircut.
Complete the table to show different percentages of Ehecatl's hair length before the haircut.
when participants are sorted from lowest to highest on a variable, grouped into sets of two, and then one person from each set is assigned at random to each of the experimental groups, this is called
Sorting is the process of grouping individuals into sets of two according to how well they do on a certain measure, then randomly assigning one participant from each set to each of the experimental groups. The right response in this case is option D.
Any systematic arrangement process is called sorting, and there are two similar but different definitions of sorting: Organizing things in a sequence according to some condition is called ordering. Sorting things into categories is called categorization.
Sorting is the process of placing data in ascending or descending order based on a linear connection between the data pieces. Organizing things in a sequence according to some condition is called ordering. Sorting things into categories is called categorization.
Complete question:
When participants are sorted from lowest to highest on a variable, grouped into sets of two, and then one person from each set is assigned at random to each of the experimental groups, this is called
A.)random assignment
B.)matching
C.)biased choice
D.)sorting
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PLS HELP SUPER EASYY
The measure of the given angle ∠BDC or x is 55°.
What are angles?An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint.
The Latin word "angulus," which means "corner," is the source of the English term "angle."
The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.
A geometrical shape called an angle is created by connecting two rays at their termini.
In most cases, an angle is expressed in degrees.
So, we know that:
∠ABC = 80°
∠ABD = 25°
∠BDC = x°
Calculate for ∠BDC:
∠ABC - ∠ABD = ∠BDC
80 - 25 = x
x = 55°
Therefore, the measure of the given angle ∠BDC or x is 55°.
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geomtrynnnnnnnnnnnnnnnnnn
Answer:
D
Step-by-step explanation:
SY FOR
f(x)= x³ - 8x² + kx-20
When f(x) is divided by (x - 1), the remainder is R.
When f(x) is divided by (x - 2), the remainder is 4R.
Find the value of k.
Applying polynomial division and solving the equation for the value of k using the substitution method, The answer is 32.
What do you mean by a polynomial?Sums of terms with the form kxⁿ, where K is any number and N is a positive integer, are known as polynomials.
What is a substitution method for solving equation?For each of the variables, solve one equation. Solve the other equation by substituting this expression. To identify the matching variable, rewrite the value's original equation.
Divide f(x) by x-1 , we get
k-27=R
Divide f(x) by x-2, we get
2k-44=4R
substitute value of R in second equation and solve, we get
k=32
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The general form of an parabola is 4y2 + 40y + 3x + 103 = 0
What is the standard form of the parabola?
The standard form of the parabola is x = -4/3y² -40/3y -103/3
What is parabola?
A parabola is an approximately U-shaped, mirror-symmetrical planar curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. One way to describe a parabola is with a point and a line.
x = -4/3(y +5)² -1
Solve for x.
x = (4y² +40y +103)/(-3)
x = -4/3y² -40/3y -103/3 . . . . 'standard form' in the US
__
Taking our clues from the graph*, we can write the vertex form equation as ...
x = -4/3(y +5)² -1 . . . . . . 'standard form' in other places
____
* The vertex is (-1, -5), so for some leading coefficient, the equation will be ...
x = a(y -(-5))² +(-1) = a(y +5)² -1
The value of 'a' is the scale factor. Here, that is the difference between the parabola value (x = -2 1/3) and the vertex value (x = -1) one unit away from the vertex.
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determine the measure of each missing angle in the triangle? HELPP MEEE PLEASEE!!!!
Answer:
The answer is 70
Step-by-step explanation:
180-40=140
140/2=70
70+70=140
140+40=180
180= the measure of the whole triangle
PS: Hope this helps:)
Which of the following relations between input numbers and output numbers is NOT a function?
send a picture so i know what its asking for
The production rate per hour of a purse factory that can manufacture 200 purses in 8 hours.
Answer:
>:)
Step-by-step explanation:
200 purses, 8 hours
200/8 = 25
25 purses per hour!
Pls mark me as brainliest and give me 20 points I need it :) Hope this answer helped!!
Answer: The Factory manufactures 25 purses per hour
Step-by-step explanation:
200 purses / 8 hours
25 purses per hour
Question 3
The graph of the line y = 2x + 3 is shown. Which point is the solution of the inequality y < 2x + 3?
A. (-3,4)
B. (0, 3)
C. (3, 0)
D. (-2,-1)
Answer:
A(-3,4)
Step-by-step explanation:
The solution of the inequality y < 2x + 3 will be;
⇒ (3, 0)
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ y < 2x + 3
Now,
Since, The inequality is,
⇒ y < 2x + 3
Hence, The solution of the inequality is,
For point (- 3,4);
⇒ y < 2x + 3
⇒ 4 < 2 × - 3 + 3
⇒ 4 < - 3
Which is not true.
For point (3,0);
⇒ 0 < 2x + 3
⇒ 0 < 2 × 3 + 3
⇒ 0 < 9
Which is true.
Thus, The solution of the inequality y < 2x + 3 will be;
⇒ (3, 0)
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A recipe requires 1 1 cup of sugar for every 6 6 cups of flour. How many cups of sugar will be required for 18 18 cups of flour? enter the answer in the box.
Both 3 and 6 cups of sugar are used.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
2 cups of flour and 1 cup of sugar
Add the sugar and flour together for three cakes.
2 cups of wheat and 1 cup of sugar equals 3.
6 cups of flour and 3 cups of sugar
Hence, Both 3 and 6 cups of sugar are used.
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what is the probability that an electron will tunnel through a 0.50 nm air gap from a metal to a stm probe if the work function is 4.0 ev?
The probability that an electron will tunnel through a 0.50 nm air gap from a metal to a STM probe if the work function is 4.0 eV is 3.4 × 10^-5
The air gap from a metal to a STM = 0.50 nm
The work function = 4.0 eV
The probability is the ratio of the number of favorable outcomes to the total number of outcomes
The probability = Number of favorable outcomes / Total number of outcomes
The value of η = h / [tex]\sqrt{2m(U_0-E)}[/tex]
Substitute the values in the equation
= [tex]\frac{1.05(10^{-34})}{\sqrt{2(9.11(10^{-31})(4(1.6)(10^{-19})} }[/tex]
Do the arithmetic operation
= 0.0972 nm
The probability = exp (-1 / 0.972)
= 3.4 × 10^-5
Therefore, the probability is 3.4 × 10^-5
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0.27 times 35 = 9.45 because i just said so bye
Answer:
Yes, you're right.
Step-by-step explanation:
Just by doing the math, 0.27 times 35 is 9.45.
Plugging it in a calculator also says it's 9.45.
Charlie has twice as many brothers as Caleb.
Caleb has twice as many brothers as Angela.
Angela has 2 brothers.
How many brothers does Charlie have?
The domain of y = log2 (x+5) in the real numbers is
Answer: The final answer is 6
Step-by-step explanation: 2 x (x+5) = 6
or
Bill writes 4 pages per hour. Is the total number of pages written proportional to the number of hours spent writing?
The required proportional relationship between y = 4x, where, x it time and y is the total number of pages.
Given that,
Bill writes 4 pages per hour. The total number of pages written proportionally to the number of hours spent to be justified.
What is proportionality?Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
let the number of pages written in x hours be y,
According to the question,
y = 4x
Thus, the required proportional relationship between y = 4x, where, x it time and y is the total number of pages.
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