There are 4 different 12-bit strings possible that begin with 0101, end with 1100 or have 0110 as the four middle bits.
We have to find the number of 12-bit strings that are starting with 0101, end with 1100 or have 0110 in the middle bits.
So, the first four position are reserved for 0101 and we have two options for the middle four bits and the end four positions.
So, we can write here,
Total possible different positions for 1100 and 0110 is,
= 2 x 2
= 4
Because, the two combination can appear simultaneously or they can appear one by one.
So, the total different 12-bit strings possible that have 0101 in the start, 1100 in the end or 0101 in the middle are 4.
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a group of 15 people are ordering pizza each person wants 2 slices and each pizza has 15 slices how many pizzas should they buy
By conducting mathematical operations, we know that the group of friends will order 6 pizzas.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.
The operation's arity is determined by the number of operands.
Mathematical operations include addition, subtraction, multiplication, division, and finding the root.
So, a number of pizzas the friends should buy:
We know that a group is of 15 people.
They are ordering a pizza which have also 15 slices in each.
And each person wants 2 slices: That is
Then, the number of pizzas they have to order will be:
1 pizza (15 slices) * 2 = 2 pizza (30 slices)
Therefore, by conducting mathematical operations, we know that the group of friends will order 6 pizzas.
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How many numbers in the range 1000 - 9999 have no
repeated digits?
Answer:4536 numbers.
Step-by-step explanation:
Since 1 st digit cannot be zero the first digit can be anything from 1–9 ( total 9)
The second digit ( any 10- 1 above)
The third digit ( any 10–2 above)
The last digit ( any 10–3 above)
Total 9x9x8x7 =
4536
:)
why in models such as logistic regression we need to estimate the marginal effects of each independent variable in order to understand how a change in one independent variable affects our dependent variable.
In a simple linear regression model , if we change the input variable by 1 unit , output variable will change by its slope.
What is linear regression?
According on the value of another variable, a variable's value can be predicted using a linear regression analysis. The dependent variable is the one you're trying to forecast. The term "independent variable" refers to the variable you are using to forecast the value of the other variable.
For linear regression
Y=a + bx + error
If we neglect error
then Y=a + bx.
If x increases by 1
then Y = a +b(x+1) which implies
Y=a + bx + b.
So Y increases by its slope.
Hence their is an increase in the slope in y.
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The distance from the floor of one level of a building to the floor of the level above it is 9 feet 3/8 inches. If the distance from the floor to the ceiling is 8 feet 2 5/8 inches, how thick is the space between the ceiling of the one floor and the floor of the level above it?
The space between the ceiling of the one floor and the floor of the level above it will be;
⇒ 9 6/8 inches
What is mean by Subtraction?
Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The distance from the floor of one level of a building to the floor of the level above it is 9 feet 3/8 inches.
And, The distance from the floor to the ceiling is 8 feet 2 5/8 inches.
Now,
Since, The distance from the floor of one level of a building to the floor of the level above it is 9 feet 3/8 inches.
And, The distance from the floor to the ceiling is 8 feet 2 5/8 inches.
Hence, The space between the ceiling of the one floor and the floor of the level above it will be;
⇒ 9 feet 3/8 inches - 8 feet 2 5/8 inches
⇒ (9 × 12 + 3/8) inches - ( 8 × 12 + 21/8) inches
⇒ (108 + 3/8) - (96 + 21/8) inches
⇒ 867/8 - 789/8
⇒ 78/8
⇒ 9 6/8 inches
Thus, The space between the ceiling of the one floor and the floor of the level above it will be;
⇒ 9 6/8 inches
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the product of two positive integers is 18. the positive difference of these two integers is 3. what is the sum of the two integers?
The sum of the given two positive integers is 9.
According to the question,
We have the following information:
The product of two positive integers is 18. the positive difference of these two integers is 3.
Now, let's take the first positive integer (larger one) to be x and the second positive integer to be y.
xy = 18 ...(1)
x-y = 3
x = 3+y
Putting this value in equation 1:
(3+y)y = 18
[tex]y^{2} +3y-18 = 0[/tex]
[tex]y^{2}[/tex]+6y-3y-18 = 0
y(y+6)-3(y+6) = 0
(y+6) (y-3) = 0
y-3 = 0 and y+6 = 0
y = 3 or y = -6
Now, the number is positive so it will be 3.
Putting this value in equation 1:
xy = 18
3x = 18
Dividing by 3 on both sides of the equation:
x= 18/3
x = 6
Sum of integers = 3+6
Sum of integers = 9
Hence, the sum of the given two positive integers is 9.
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10 students have volunteered for a committee. 7 of them are seniors and 3 of them are juniors. 1) how many ways are there to select a committee of 8 students? 10!/(8!2) 2) how many ways are there to select a committee with 3 seniors and 5 juniors? 7!/(3!/4!)*(3!/(5!/(2)!)) 3) suppose the committee must have 8 students (either juniors or seniors) and that one of the 8 must be selected as chair. how many ways are there to make the selection?
(a) The number of ways of selecting a committee of 8 students = 45.
(b) The number of ways to select a committee with 3 seniors and 2 juniors are 105.
(c) The number of ways to select a committee having 8 students (either juniors or seniors) and that one of the 8 must be selected as chair = 360 ways
What is combination?
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Given that 10 students have volunteered for a committee. 7 of them are seniors and 3 are juniors.
a) Need to find the number of ways of selecting a committee of 8 students
The number of ways of selecting a committee of 8 students = [tex]10_C_8[/tex]
[tex]10C_8= \frac{10!}{8!(10-8)!}= \frac{10!}{8!(2!)}=45[/tex]
The number of ways of selecting a committee of 8 students = 45.
(b) Need to find the number of ways to select a committee with 3 seniors and 2 juniors
The number of ways to select a committee with 3 seniors and 2 juniors
= [tex]7_C_3(3_C_2)[/tex]
[tex]7_C_3*3_C_2 = \frac{7!}{3!*4!} *\frac{3!}{2!*1!} = 35 * 3 = 105[/tex]
The number of ways to select a committee with 3 seniors and 2 juniors are 105.
(c) Need to find the ways to make the select the committee must have 8 students (either juniors or seniors) and that one of the 8 must be selected as chair.
Number of ways = [tex]10_C_8*8_C_1[/tex]
[tex]10_C_8*8_C_1 = \frac{10!}{8!*2!} *\frac{8!}{7!*1!} = 45*8 = 360[/tex]
The number of ways to select a committee having 8 students (either juniors or seniors) and that one of the five must be selected as chair = 360 ways.
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Tiyanna works at a car dealership. When she sells a car, she earns a $1,400 commission and the dealership earns $33,600. At this rate, how much commission would Tiyanna earn if she sells a car for $42,000?
Answer: $1,751.4
Step-by-step explanation:
33600 = 100%
(1400*100)/33600 =
140000:33600 = 4.17
42,000 * 4.17% = 1,751.4
PLEASE HELP ME IM GROUNDED AND MY TRIMESTER ENDS TONIGHT
Answer:
Step-by-step explanation:
Set angle equations equal to each other(since lines are parallel)
7x-4= 5x+10
Add 4 to both sides to isolate x on left side
7x= 5x+14
Subtract 5x from both sides to get x on one side only.
2x=14
x=7
Baldwin bought 4.2 pounds of melon and 4.44 pounds of cherries. How much fruit did he buy in all?
Answer: 8.64
Step-by-step explanation:
If you add 4.44 and 4.2 you would get 8.64 pounds worth of fruits in total.
Answer:
8.64 pounds of fruit.
Step-by-step explanation:
4.2 + 4.44 = 8.64 pound of fruit
An object weighing 5 pounds on Earth will weigh 2 pounds on Mercury. The Statue of Liberty weighs 225 tons. What would it weigh on Mercury? Show all work:
Answer:
90 tons
Step-by-step explanation:
given that the ration of weight from earth to mercury is 5:2, we can make an equation:
x (weight of an item on Mercury) = 0.4(weight of an item on Earth)
x=0.4(225 tons)
x=90 tons
A rumor about canceling spring break is being spread around a school. The following equation models the number of students in the school who have heard the rumor after t days:
Equation: N (t) = 1800/1+149e^-0.625t
A.). How many people started the rumor?
B. ). How many students are in the school?
C.). To the nearest 1/10, how many days will it be before the rumor spreads to ½ the student body?
D.). The following equation represents the instantaneous rate of change in students per day of the spread of the rumor.
Another Equation: N^1 (t)=0.625N (1- N/1800)
N represents the number of students who have heard the rumor and t is time in days.
How many students have heard the rumor when the rumor is spreading the fastest?
What is the rate of change in students per day at this time ?
A) The number of people who have started the rumor is N(0)=12
B) The number of students who are in the school are 1800
C) The number of days the rumor spreads to ½ the student body are 8 days.
D) The number of students who have heard the rumor when the rumor is spreading the fastest are 900.
The rate of change in students per day at this time is 281.
What is meant by rate of change?The rate of change is a mathematical term that describes the percentage change in value over a given time period and represents the momentum of a variable.
A) Number of people who have heard the rumor after t days is given by:
N (t) = 1800/1+149e^-0.625t
At start t=0, so from the above equation at t=0, we get
N(0)=(1800)/1+149e^0
N(0)=1800/(1+149(1))
N(0)=1800/150
N(0)=12
B) At t=∞, all of the students would have heard the rumor. So putting t↔∞ in the above equation we get,
[tex]\lim_{t \to \infty}[/tex]N(t)=[tex]\lim_{t \to \infty}[/tex] 1800/1+149e^-0.625t
=1800/(1+0)
=1800
Therefore, the number of students in the school are 1800.
C) Putting N=1800/2 in the above equation, we get
1800/2= 1800/1+149e^-0.625t
1+149e^-0.625t=2
e^-0.625t=(2-1)/149
=1/149
Taking log on both sides, we get
ln(e^-0.625t)=ln(1/149)
-0.625t=-ln(149)
t=ln(149)/0.625
t=8.006≈8
D) N'(t)=0.625N(1-(N/1800)
=0.625(N-(N²/1800)
=(0.625/1800)(1800N-N²)
=(0.625/1800)(900²-900²+1800N-N²)
=(0.625/1800)(900²-(N²-1800N+900²)
N'(t)=(0.625/1800)(900²-(N-900)²)
For N to be maximum,
N=900
Thus, rumor is spreading fastest when 900 students have heard the rumor.
And rate of change in students per day is obtained by putting N=900 in expression of N'(t) as follows:
N'(t)=(0.625×900)(1-(900/800))
N'(t)=281.25≈281
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karrie was late to work 14 times last year. if she workded 250 days last year, what percent of the days was she left
By using the concept of percentage, it can be calculated that Karrie was late to work in 5.6 % of the days.
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
For example 9% means [tex]\frac{9}{100}[/tex]. Here 9 is expressed as a fraction of 100
Here the concept of percentage will be used
Number of days in which Karrie was late = 14
Total number of days she worked = 250
Percentage of days Karrie was late = [tex]\frac{14}{250} \times 100[/tex] = 5.6 %
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a password to a computer consists of 6 characters: a digit, a letter, a digit, a letter, a digit, and a letter in that order, where the numbers from 1 through 9 are allowed for digits. how many different passwords are possible?
As per the concept of probability, there are 4,717,440 number of passwords are possible.
Probability:
In statistics, probability refers the favorable outcome of the particular event.
Given,
A password to a computer consists of 6 characters: a digit, a letter, a digit, a letter, a digit, and a letter in that order, where the numbers from 1 through 9 are allowed for digits.
Here we need to find how many different passwords are possible.
Total number of characters = 6
According to this, each password would have
5 digits of 10 digits: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], and
one of 26 letters: [A to Z].
Here there is no repeats are allowed, and assuming only upper case letters are valid and the letter is the last character, then we can form 10*9*8*7*6 * 26 = 786,240 such passwords.
If the repetition is allowed then number of possible passwords is
786,240 * 6 = 4,717,440.
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The square of a number added to 2 times a number is 8. Find the number.
Answer:
x = -4 or 2
Step-by-step explanation:
Let the number be x.
Given condition:x² + 2x = 8
Subtract 8 to both sides
x² + 2x - 8 = 0
Using mid-term break method
=> 4 × -2 = 8 (side-term), 4 - 2 = 2 (mid-term)
So, we can break the mid-term into 4 and -2.
x² + 4x - 2x - 8 = 0
Take common
x(x + 4) - 2(x + 4) = 0
Take (x+4) common
(x+4)(x-2) = 0
Either
x + 4 = 0 OR x - 2 = 0 (Zero's method)
x = -4 OR x = 2
[tex]\rule[225]{225}{2}[/tex]
phenolphthalein has a pka of 9.7 and is colorless in its acid form and pink in its basic form. for ph= 5.3 calculate [in−]/[hin] . for ph= 11.4 calculate [in−]/[hin] .
Part a: [In⁻]/[HIn] = 4.0 × 10⁻⁶
Part b: [In⁻]/[HIn] = 50.11, for the given phenolphthalein solution.
Explain the term acid form?Typical aqueous acids include acetic acid, hydrochloric acid, and gastric acid, which activates digestive enzymes. Hydrochloric acid is a solution containing hydrogen chloride.Using the Henderson-Hasselbalch equation to determine the indicator's pH is as follows:
pH = pKa + log[In⁻]/[HIn]
In which,
Ka = dissociation constant of acid.
As the stated value-
Part a:
pKa = 9.7
pH = 5.3
Thus,
5.3 = 9.7 + log[In⁻]/[HIn]
log[In⁻]/[HIn] = - 4.4
[In⁻]/[HIn] = Antilog (-4.4)
[In⁻]/[HIn] = 4.0 × 10⁻⁶
Part b:
pKa = 9.7
pH = 11.4
Thus,
11.4 = 9.7 + log[In⁻]/[HIn]
log[In⁻]/[HIn] = 1.7
[In⁻]/[HIn] = Antilog (-4.4)
[In⁻]/[HIn] = 50.11
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Sean tutors math students to earn extra money. Sean chargers $20 per hour. Write an equation to model Sean's earnings, y, after x hours.
Answer:
y=20x
if he charges $20 and hour multiply your hours by 20 to get the total amount of earnings
a trough is 12 feet long and 3 feet across the top (see figure). its ends are isosceles triangles with altitudes of 3 feet. if water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising (in feet per minute) when \displaystyle hh is 1 foot deep?
If water is being pumped into the trough at 2 cubic feet per minute, then the water level rising (in feet per minute) when h is 1.6 foot deep is 0.1 feet cubic per minute.
Suppose that we have a function y = f(x), and wish to find the rate of change of y with respect to a third variable t, where we do not have y expressed explicitly in terms of t. We use the chain rule in differentiation to find this rate of change in a process called implicit differentiation.
dy/dt = dy/dx × dx/dt
If base is equal to the height, by similar triangles:
Volume v = base x height x length/2
= bhl/2
= h²12/2
= 6h².
Therefore,
dv/dt = 12hdh/dt
= 2 ft³/min
Now,
dh/dt = 2/(12h)
when h = 1.6,
dh/dt = 2/(12 × 1.6) ≈ 0.1 ft³/min
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PLEASE PROVIDE EXPLANATION!
In a two-digit number the units digit is three less than the tens digit. If the digits are reversed, the sum of the reversed number and the original number is 121. Find the original number.
Step-by-step explanation:
Also, we know that , because the unit digit is three less than tens digit, or tens digit is three more units than the unit digit. Then, the sum of the reversed number and the original number is 121, this would be expressed: Therefore, the digits are 7 and 4. The number would be 74.
Answer:
The original number is 74
Step-by-step explanation:
The answer of 74 provided by brey90 is absolutely correct. I am just providing a mathematical way of determining the number
Let the number be ab
That means [tex]b[/tex] is in the units place and [tex]a[/tex] is in the tens place.
The actual value of this two digit number is [tex]10a + b[/tex]
The difference between a and b is 3:
[tex]a - b = 3[/tex] [1]
If we reverse the number we get the number [tex]ba[/tex]
The actual value of [tex]ba[/tex] is [tex]10b + a[/tex]
The sum of [tex]ab[/tex] and [tex]ba[/tex] is 121. This means the sum of their actual values must be 121
So we get
[tex]10a + b + 10b + a = 121\\\\11a + 11b = 121\\\\[/tex]
Dividing both sides by 11 yields:
[tex]a + b = 11[/tex] [2]
Add [1] and [2] to get:
[tex]2a = 14\\\\a = 7\\\\[/tex]
Sub for a in Equation [1] to get
[tex]7 - b = 3\\\\b = 4\\\\[/tex]
So the original number is 74
Check
Reversed is 47
74 + 47 = 121
the average adult horse needs 2/5 bale of hay each day to meet dietary requirements. A horse farm has 44 bales of hay. How many horse can be fed with 44 bales of hay
The horse that can be fed with 44 bales of hay is 110 horses.
How many horses can be fed?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.
Given that the average adult horse needs 2/5 bale of hay each day to meet dietary requirements and a horse farm has 44 bales of hay.
The number of horses that can be fed will be:
= Total number of hay / Fraction needed
= 44 ÷ 2/5
= 44 × 5/2
= 22 × 5
= 110
100 horses can be fed.
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Solve for all values of c in simplest form
19 = | 5c - 4 |
The values of c in the given equation, 19 = | 5c - 4 |, are c = -3 and c = 4 3/5
Solving an equationFrom the question, we are to solve the given equation for all values of c
The given equation is
19 = | 5c - 4 |
From this equation, we can write that
19 = (5c - 4) and 19 = -(5c - 4)
Solving the first equation
19 = (5c - 4)
19 = 5c - 4
Add 4 to both sides of the equation
19 + 4 = 5c - 4 + 4
23 = 5c
Divide both sides by 5
23/5 = 5c/5
4 3/5 = c
Therefore,
c = 4 3/5
Solving the second equation
19 = -(5c - 4)
19 = -5c + 4
Subtract 4 from both sides of the equation
19 - 4 = -5c + 4 - 4
15 = -5c
Divide both sides by -5
15/-5 = -5c/-5
-3 = c
Therefore,
c = -3
Hence, the values of c are -3 and 4 3/5
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Someone pleasee helppp!
Geometry A
Answer: I think it is 5
Step-by-step explanation:
find the slope of the line that contains the following points: (17, -12) and (7,8)
The slope of the line that contains the points (17, -12) and (7, 8), is -2.
Calculating the slope of a line with given pointsFrom the question, we are to determine the slope of the line that contains the given points.
The given points are (17, -12) and (7, 8)
Using the formula for calculating slope,
m = (y₂ - y₁) / (x₂ - x₁)
Where m is the slope
Then,
The slope of the line is
m = (8 - (-12)) / (7 - 17)
m = (8 + 12) / (-10)
m = 20 / - 10
m = -2
Hence, the slope is -2
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can y’all help me w these 2 probs ! Find the square root of the number
Answer:
Step-by-step explanation:
4.) - 20
5.) 66 i
Feel free to double check with a calculator
(Hope that helps!)
What is the measure of angle o in parallelogram lmno? 35° 75° 105° 155
The measure of angle O in the given parallelogram is equal to 105°.
As given in the question,
Given parallelogram LMNO,
As shown in the attached diagram we have,
Measure of angle L = ( x + 40 )°
Measure of angle O = (3x)°
In the parallelogram LMNO,
LM is parallel to NO .
LO is the transversal.
∠MLO and ∠NOL are interior angles and are supplementary.
m ∠MLO + m ∠NOL = 180°
⇒ ( x + 40 )° + ( 3x )° = 180°
⇒ 4x° = 180° - 40°
⇒x = 140° / 4
⇒ x = 35°
Measure of ∠O = 3x°
= 3(35°)
= 105°
Therefore, the measure of ∠O in the parallelogram LMNO with the given conditions is equal to 105°.
The complete question is :
What is the measure of angle O in parallelogram LMNO?
Diagram of parallelogram LMNO is attached.
m∠O = ?
a. 35° b. 75° c. 105° d. 155°
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Answer: 105 degrees
Step-by-step explanation:
edge 2023, (Proving a Quad. is a Parallelogram)
write your answer as a mixed number in simplest from
3 9/10 + 4 9/10
The simplified form of the given fraction, 3 9/10 + 4 9/10 , in its simplest form is 8 4/5
Simplifying fractionsFrom the question, we are to write the given fraction as a mixed number in simplest form
The given fraction is
3 9/10 + 4 9/10
First, we will convert the fractions to improper fractions
39/10 + 49/10
Now, add the fractions
(39 + 49)/10
= 88/10
Write as a mixed fraction
8 8/10
Simplify the fraction
8 4/5
Hence, the fraction becomes 8 4/5
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There are 1,200 bacteria in a lab dish. The population decreases 10% per day. Calculate the average rate of change in the decrease in population for days 1 to 3 with the decrease for days 4 to 6.
The population decreases more quickly from day 1 to day 3 than from day 4 to day 6.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
The total number of bacteria in lab dish is 1200
The population decreases 10% per day
In first day:
10/100×1200=120
120 bacteria decreased in lab
1200-120=1080
In second day:
0.1×1080=108
1080-108=972
In third day
0.1×972=97.2
972-97.2=874.8
In fourth day
0.1×874.8=87.48
874.8-87.48=787.32
In fifth day
0.1×787.32=78.732
787.32-78.732
708.588
The population decreases more quickly from day 1 to day 3 than from day 4 to day 6.
Hence, the population decreases more quickly from day 1 to day 3 than from day 4 to day 6.
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Using the diagram of a regular hexagon, fill in the blanks for the steps to solve for the area of a hexagon with sides equal to 12 cm.
(1) How many equilateral triangles are there? _____
(2) What is the measure of each of the three angles in the equilateral triangle? _____
(3) If we cut an equilateral triangle down the middle (segment a), what special right triangle do you create? _____
(4) What is the vocabulary word for the segment a? _____
(5) What is the length of the short side of one of the 30-60-90 triangles? _____
(6) What is the length of the hypotenuse of one of the 30-60-90 triangles? _____
(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg of one of the 30-60-90 triangles. _____
(8) What is the height of one of the the equilateral triangles? _____
(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. _____
(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _____
The blanks are shown below for the area of hexagon with sides equal to 12cm.
What is Hexagon?In geometry, a hexagon is defined as a six-sided polygon. The two-dimensional form contains six sides, six vertices, and six angles.
All of the fill in the blanks are answered below:
(1) The number of equilateral triangles are 6
(2) The measure of each of the three angles in the equilateral triangle 60°
(3) If we cut an equilateral triangle down the middle the special right triangle we create is 30-60-90
(4) The vocabulary word for the green line is perpendicular bisector.
(5) The length of the short side of one 30-60-90 triangle is 4cm
(6) What is the length of the hypotenuse of one 30-60-90 triangle is 8cm
(7) Using the properties of 30-60-90 triangles, the length of the long leg. is 4√3cm
(8) The height of the equilateral triangle is 4√3cm
(9) The area of one equilateral triangle is ½(8)(4√3) = 16√3 cm²
(10) The area of one equilateral triangle by the number of triangles. is 8(16√3) = 128√3 cm²
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How many solutions does this equation have? –2g + 2g = 0
The equation -2g+2g has infinitely many solutions.
Define solving an equation.The method of solving equations involves determining the value of the unknown variable while maintaining the equality of the equation on both sides. When a condition on variable guarantees that two expressions in the variable have the same value, it qualifies as an equation. The equation's solution is the value of the variable for which the equation is true. An equation remains the same even when the LHS and RHS are flipped. After separating the variable whose value has to be calculated, the solution is found. We can answer it depending on the type of equation we are dealing with. Equations come in a variety of forms, including linear, quadratic, rational, and radical equations.
Consider the given equation
-2g + 2g = 0
Solve the equation,
0 = 0
This means that the equation is valid for all values of g.
Therefore, the equation can have infinitely many solutions.
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The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (3,48) and (7,112) to find the number of soda bottles the machine can make each minute.
The number of soda bottles the machine can make in each minute is 960 bottles
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the number of soda bottles the machine can make in 1 minute be = y
Now , the equation is
Let the first point in the graph be A ( x₁ , y₁ )
The value of A ( x₁ , y₁ ) = A ( 3 , 48 )
Let the second point in the graph be B ( x₂ , y₂ )
The value of B ( x₂ , y₂ ) = A ( 7 , 112 )
Now , the slope of the line joining the points can be found out from the equation of slope
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
So , the slope of the point is m = steep of the line or inclination
Slope m = y / x
Substituting the values for x and y , we get
Slope m = 48 / 3
Slope m = 16
Therefore , the equation of line will be y = mx + c
y = 16x
Now , there are 60 seconds in a minute
So , 1 minute = 60 seconds
Substituting the value of x = 60 in the equation , we get
y = 16x
y = 16 x 60
y = 960 bottles
Therefore , the value of y = 960
Hence , The number of soda bottles the machine can make in each minute is 960 bottles
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8x - 4y = -4 solve for y.
The equation 8x - 4y = -4 have y as the subject to be equal to 2x + 1 expresses in terms of x.
How to evaluate for yTo solve for y in the equation 8x - 4y = -4, we must make y the subject and it should be positive as follows;
8x - 4y = -4
add 4y to both sides
8x - 4y + 4y= -4 + 4y
8x = - 4 + 4y
also to make y the subject;
- 4 + 4y = 8x
add 4 to both sides
- 4 + 4 + 4y = 8x + 4
4y = 8x + 4
factorize the right hand side
4y = 4(2x + 1)
divide through by the coefficient of y
4y/4 = [4(2x + 1)]/4
y = 2x + 1
Hence, the equation 8x - 4y = -4 has y = 2x + 1
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