Let x= the co-efficient of x^3-1. So the co-efficient of given function is x=1.
Define co-efficient.The term "coefficient" refers to a number or symbol that multiplies another number or symbol (used as a mathematical variable).
Write an example of co-efficient.An amount multiplied by a variable is known as a coefficient. As an illustration, 6z stands for 6 times z. Since z is a variable, 6 is a coefficient. For variables without a value, the coefficient is 1.
Let x= the co-efficient of x^3-1. So the co-efficient of given function is x=1.
The term multiplied with x^3 is the co-efficient of this expression. As there is not term with x^3 so it is 1.
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a 2 kg block is placed at the top of an incline and released from rest near earth’s surface and unknown distance h above the ground. the angle θ between the ground and the incline is also unknown. frictional forces between the block and the incline are considered to be negligible. the block eventually slides to the bottom of the incline after 0.75 s. the block’s velocity v as a function of time t is shown in the graph starting from the instant it is released. how could a student use the graph to determine the total energy of the block-earth system?
Therefore , the distance travelled by the 2kg block is 281.25m and the energy of the block earth is 14.0625 J
What is force?It can push or pull. Acceleration is caused by unbalanced forces.
The Newton is the symbol for a force (abbreviation is N).The force required to cause a mass of one kilogramme to alter its velocity by one metre per second (m/s) per second is one Newton. The formula is: 1 N = 1 kg m/s2 (kilogram metre per second squared)
Here,
Let s represent the block's total distance travelled.
As a result, the block's work will be equal to the potential energy contained in the spring.
It is given as,
(mgsinθ)×s= 1/2 k[tex]x^{2}[/tex]
( √2 ×10×sin45 ∘ )×s= 1/2 ×100 x (0.75*0.75)
s=281 . 25m
Thus, the distance travelled by the block is 281 . 25m.
For energy :
=> 1/2 m v^2
=> 1/2 * 2* (3.75)^2
=> 14.0625 J
Therefore , the distance travelled by the 2kg block is 281.25m and the energy of the block earth is 14.0625 J
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The distance travelled by the 2kg block is 281.25m and the energy of the block earth is 14.0625 J
What is meant by work in physics?When an object is moved over a distance by an external force, at least a portion of that force must be applied in the direction of the displacement. This is known as work in physics.
Define energy.The ability to exert a force that causes an item to move is what is meant by the definition of energy as the "power to accomplish work."
Let s= total distance travelled by block.
Therefore, the block's work will be equal to the spring's potential energy.
According to given information,
(mgsinθ)×s= 1/2 k
( √2 ×10×sin45 )×s= 1/2 ×100 x (0.75*0.75)
s=281 .25m
Therefore, the distance travelled by the block is 281 . 25m.
For energy we have:
=> E= 1/2 m v^2
=> E= 1/2 * 2* (3.75)^2
=>E= 14.0625 J
So , the distance travelled by the 2kg block is 281.25m and the energy of the block earth is 14.0625 J.
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A piece of conduit 39.0 ft long cuts across the corner of a room, as shown in the illustration. Find length x and Angle A. Round each answer to the appropriate number of significant digits
Answer:
x = 30.6 ft
A = 58.1°
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
As the triangle is a right triangle, use Pythagoras Theorem to find length x.
[tex]\implies x^2+19^2=36^2[/tex]
[tex]\implies x^2+361=1296[/tex]
[tex]\implies x^2=935[/tex]
[tex]\implies x=\sqrt{935}[/tex]
[tex]\implies x=30.6\; \sf ft \;\; (3\;s.f.)[/tex]
[tex]\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
From inspection of the given right triangle:
θ = AA = 19.0 ftH = 36.0 ftSubstitute the values into the formula and solve for A:
[tex]\implies \sf \cos A=\dfrac{19.0}{36.0}[/tex]
[tex]\implies \sf A= \cos^{-1}\left(\dfrac{19}{36}\right)[/tex]
[tex]\implies \sf A=58.1^{\circ}\;\;(3\;s.f.)[/tex]
In hopes of encouraging healthier snacks at school, Grace brought in a tray of carrot sticks and apple slices to share. She brought 20 snacks in all. 15 of the snacks were carrot sticks. What percentage of the snacks were carrot sticks?
Answer:
75%
Step-by-step explanation:
[tex]\frac{15}{20} \times 100=75\%[/tex]
Is triangle ABC = triangle DEF by HL? Explain.
Answer:
If in triangles ABC and DEF, angle A = angle D = right angle, AB = DE (leg), and BC = EF (hypotenuse), then triangle ABC is congruent to triangle DEF.
10.Rohan's maid has two children of same age. Both of them have equal number of dresses. Rohan on his birthday, plans to give both of them same number of dresses. What can you say about the number of dresses each one of them will have after Rohan's birthday? Which Euclid's axiom is used to answer this question?
Answer:
Step-by-step explanation:
Rohan is a generous person who cares deeply for his maid and her two children. On Rohan's birthday, he plans to give both of them the same number of dresses. This situation can be solved using Euclid’s axiom that states “things which are equal to the same thing are also equal to one another”. Therefore, after Rohan's birthday each child will have an equal number of dresses as they were given an identical amount from him.
This kind gesture by Rohan demonstrates his commitment towards taking care of those around him and providing fairness in all situations possible - it serves as a reminder that we should always strive for equality among people regardless of their backgrounds or social statuses in life! By following this axiom, everyone can benefit from having access to resources no matter what their circumstances may be; thus creating a more equitable society overall.
The act done by Rohana is praiseworthy and must serve as an example for others too so they understand how important it is treat everyone equally regardless if they belong to different castes or classes in our society! We should take measures like these on regular basis so that true justice prevails everywhere without any discrimination whatsoever- this would make sure everybody has access basic necessities such us clothes just like Rohana provided his maid's kids with new sets on his own birthday!
among all fractions $x$ that have a positive integer numerator and denominator and satisfy $$\frac{9}{11} \le x \le \frac{11}{13},$$ which fraction has the smallest denominator?
The fraction that has the smallest denominator is [tex]\frac{9}{11} < =\frac{5}{6} < =\frac{11}{13}[/tex]
Notice that the fractions seem to have the form n / [ n + 2] where n is an integer
Suppose that there exists a fraction such that
9/11 < n / [n + 2] < 11/13
We can split this into two inequalities
Looking at the inequality on the left....we have
9[n + 2] < 11n
9n + 18 < 11n
18 < 2n
9 < n or
n > 9
Looking at the inequality on the right.... we have
13(n) < 11[n + 2]
13n < 11n + 22
2n < 22
n < 11
This implies that
9 < n < 11
So...n = 10 is the only integer that satisfies this
And n + 2 = 12
So....the fraction is 10/12 = 5/6
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Which description of the graph of the linear inequality y ≥ 7x 4 is correct?
The answer to the above question will be as follows:
The correct option is option c.) The graph will be a solid line with a y-intercept of seven and a slope of negative four. The graph will be shaded above the line.
We solve the question in the following way,
Given inequality is y≥7x- 4
Let us first consider the linear equality of the equation as
y= 7x- 4
When we consider this with the general slope form of a straight line given by: y=mx+c, we get
m=7 and c= -4
Now, we know that for the ‘greater than or smaller than equal to’ sign, the graph is mapped using a solid line and is shaded away from the origin of the graph (0,0).
Thus for this graph, we will use a solid line to represent the line y=7x- 4 and shade the graph above the line. Therefore option (c.) is correct.
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Note that the full question is:
Which description of the graph of the linear inequality y ≥ 7x – 4 is correct?
a.) The graph will be a dashed line with a y-intercept of negative four and a slope of seven. The graph will be shaded below the line.
b.) The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.
c.) The graph will be a solid line with a y-intercept of seven and a slope of negative four. The graph will be shaded below the line.
d.) The graph will be a dashed line with a y-intercept of seven and a slope of negative four. The graph will be shaded above the line.
Dave wrote a whole number greater than 0 and less than 11 on a piece of paper.
Find the probability that Dave's number is each of the following.
6. P(7)
7. P(less than 5)
9. P(less than 1)
10. P(greater than 10)
8. P(odd)
11. P(divisible by 2 or 3)
You draw a card from a deck that has 12 star cards, 8 yellow moon cards,
6 blue moon cards, 9 planet cards, and 1 sun card. Find each of the following.
12. P(moon)
13. P(star)
14. P(blue moon or planet) HOW DO U DO THIS I DONT GET IT
0.03, 0.04, 0.38, and 1 are the figures that could represent an event's likelihood .Probability is calculated by dividing the total possible outcomes by the number of outcomes that are theoretically possible
How does probability work exactly?Probability is calculated by dividing the total possible outcomes by the number of outcomes that are theoretically possible. Probability differs from odds in this regard. Calculating odds involves dividing the likelihood of a particular event by the likelihood that it won't occur.
How do probability and an example work?The likelihood of success is a measure of probability. the number of potential outcomes. For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). We specify P(heads) = 12.
6. P(7) = 1/10
7. P(less than 5) = 4/10 = 2/5
8. P(greater than 10) = 5/10 = 1/2
11. P(divisible by 2 or 3) = 6/10 = 3/5
12. P(moon) = 8/36 = 2/9
13. P(star) = 12/36 = 1/3
14. P(blue moon or planet) = (6+9)/36= 15/36= 5/9
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Answer:
Step-by-step explanation:
6. P(7) = 1/10
7. P(less than 5) = 4/10 = 2/5
8. P(greater than 10) = 5/10 = 1/2
11. P(divisible by 2 or 3) = 6/10 = 3/5
12. P(moon) = 8/36 = 2/9
13. P(star) = 12/36 = 1/3
14. P(blue moon or planet) = (6+9)/36= 15/36= 5/9
Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. She worked 73 hours over the last two weeks and had a total of $2,830 in sales before taxes.
Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?
If Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. The amount that is closest to how much she will earn in hourly wages and commission for those two weeks is A $592.
What is earnings?Earnings can be defined as the money a person earn as wages or as salary.
First step is to find the amount that Sandy earns per hours
Earnings per hour = 9+ (0.15×9)
Earnings = $10.35 per hour
Second step is to find her earnings
Earnings =73 × $10.35
Earnings = $755.55
Closest amount is $592.
Therefore the correct option is A.
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The complete question is:
Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. She worked 73 hours over the last two weeks and had a total of $2,830 in sales before taxes.
Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?
A $592
B $890
C $386
D $298
A women put $600 into a savings account for one year. The rate of interest on the account was 6%. How much was the interest for the year in dollars and cents.
Answer:
The interest is $36 or $3600 cent
Step-by-step explanation:
6% = 0.06
Take 600 times 0.06 = $36
$1 = 100 cent
$36 = $3600 cent
So, the interest is $36 or $3600 cent
Answer:
Let A = total amount principal + interest
P = principal amount , $600
R = interest rate, 0.06
T = time , 1
A = P(1 + r)^t
A = 600(1 + 0.06) we dont have to put 1 as exponent
A = 600(1.06)
A = 636
Interest = A - P
Interest = 636 - 600
Interest = 36
Therefore, the interest will be $36 dollars. The women will have a total amount of $636 on the accountStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-What is the mean of the numbers 25 30 27 23 and 25?
The mean of the given data set is 26.
One of the most significant and often employed metrics of central tendency is the mean. In mathematics, there are various different kinds of means. In statistics, the mean is the product of all the values in a set of data divided by the total number of values in the data for a particular set of observations.
To put it another way, calculating the mean of a data set only requires adding up all the values and dividing the result by the total number of values.
The mean formula in statistics for a set is defined as the sum of the observations divided by the total number of observations.
Mean = 25+30+27+23+25/5
Mean = 130/5 = 26
Thus, the mean of the given data set is 26.
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The mean formula in statistics for a set is defined as the sum of the observations divided by the total number of observations.
Mean = 25+30+27+23+25/5
Mean = 130/5 = 26
Thus, the mean of the given data set is 26.
What does power of 1 2 mean?
The square root of some number 'X' is a number which, when you multiply it by itself, the answer is 'X'.
What is Square root ?The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is [tex]\sqrt{x}[/tex] . Finding the square root of a number is the opposite of squaring a number.
In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x.
For example, 4 and −4 are square roots of 16, because 4² = (−4)² = 16.
Thus , the square root of some number 'X' is a number which, when you multiply it by itself, the answer is 'X'.
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what is the inequality:the sign below the troll for driving on alligator alley. Passenger cars troll:2.50. write an inequality to represent the number of times someone can drive on alligator alley with $15.
Answer:
2.5n ≤ 15
Step-by-step explanation:
Let n = number of times
Each toll is $2.50, so the toll for n trips is n times $2.50, or 2.5n.
The total amount of money available is $15, so 2.5n must be less than or equal to 15.
Inequality:
2.5n ≤ 15
(In case you're asked next, here is the solution of the inequality:
Divide both sides by 2.5.
2.5n/2.5 ≤ 15/2.5
n ≤ 6
A person can drive up to 6 times with $6.)
Find the total surface area of the right solid shown.
Dimensions are in m. Round to the nearest
whole number.
The volumes of the cone and cylinder are 1256m³ and 5652m³
What is the formula volume of a cone and a cylinder?For a cylinder, the formula is πr²h. A cone is ⅓ the volume of a cylinder, or 1⁄3πr²h.
Given here dimensions as the height of the cone = 12m and radius of its circular base = 10m and the height of the cylinder = 18m
thus Volume of the cone = 1⁄3πr²h
= 1/3×3.14×100×12
= 1256m³
And the volume of the cylinder = πr²h
= 3.14×100×18
= 5652m³
Therefore the volumes of the cone and cylinder are 1256m³ and 5652m³
Hence, the volume of the solid is 1256+5652 =6908m³
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How do you find the length of an altitude of an isosceles triangle?
The altitude of an isosceles triangle is sqrt (a^2 - b^2 / 4).
In the triangle ABC, sides AB and AC are equal (say a) and side BC = b. Let us consider the triangle ADC which is the right triangle in the isosceles triangle ABC, and by Pythagoras' theorem,
we get that the altitude AD of the isosceles triangle can be obtained:
AD ^ 2 = AC ^ 2 - (BC / 2) ^2
AD ^ 2 = (a ^ 2 - b ^ 2 / 4)
AD = sqrt (a ^ 2 - b ^ 2 / 4).
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What is the parallel equation of Y 3X 1?
The parallel equation of y = 3x + 1 is y = 3x
How do one find the slope of a graph?The slope is computed mathematically as "rise over run" (change in y divided by change in x).
In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.
That is to say,
Determine the coordinates of two locations along the line that one choose.Evaluate the differences in these two positions' y-coordinates (rise).Evaluate the differences in these two locations' x-coordinates (run).In order to calculate the difference in y-coordinates (rise/run or slope), divide it by the difference in x-coordinates.Given equation: y = 3x + 1
A point from which the parallel line will pass through is (0,0)
To find the slope using the slope-intercept form:
The slope-intercept form is: y = mx + b
Where, m = slope
b = y - intercept
Now comparing this equation with given equation, we find, slope (m) = 3
To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.
Use the slope 3 and a given point (0,0) to substitute for x₁ and y₁ in the point slope form: y - y₁ = m (x - x₁), which is derived from the slope-equation,
m = (y₂ - y₁)/ (x₂ - x₁)
so, putting the value we get,
y - 0 = 3 ( x - 0 )
or, y + 0 = 3 ( x +0 )
or, y = 3x + 0
or, y = 3x
The graph is shown below:
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The complete question is as follows:
What is the parallel equation of y = 3x + 1
What can go into 98?
On the list of 98 factors, there are 1, 2, 7, 14, 49, and 98 factors. All of the factors of 98 are 1, 2, 7, 14, 49, and 98.
What are the factors?A factor is a number that completely divides another number.
To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
The two components that makeup 98 are: (1, 98), (2, 49), and (7, 14). 1, 2, and 7 make up the first three factors of 98.
So, in order to get what we can get into 98, we need to list down the factors of 98.
There are 1, 2, 7, 14, 49, and 98 on the list of 98 factors.
1, 2, 7, 14, 49, and 98 are all factors of 98.
Therefore, on the list of 98 factors, there are 1, 2, 7, 14, 49, and 98 factors. All of the factors of 98 are 1, 2, 7, 14, 49, and 98.
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What is the arithmetic mean of the data set 11 12 13 14 15 16 17 18 19 and 20?
The arithmetic mean of the set of numbers 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20 is 15.5. This is the average value of the set, and it is affected by all the values in the set.
The arithmetic mean, also known as the average, of a set of numbers is found by adding up all the numbers in the set and dividing by the total number of numbers in the set. In this case, the set of numbers is 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20. When we add up all the numbers in the set, we get a total of 155. There are 10 numbers in the set, so the average is 155 / 10 = 15.5.
To find the arithmetic mean, we first need to add up all the numbers in the set. Then, we divide that sum by the total number of numbers in the set. This gives us the average value of the set.
In summary, the arithmetic mean of the set of numbers 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20 is 15.5. This is the average value of the set, and it is affected by all the values in the set.
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The wholesale price for a pair of shoes is $4.50. A certain department store marks up the wholesale price by 90%. Find the price of the pair of shoes in the department store.
Round your answer to the nearest cent, as necessary.
help pls
Answer:$16.15
Step-by-step explanation:
The wholesale price:
$8.50
Selling Price:
$8.50 + 90% = $8.50 *1.9 = $16.15
Pair of shoes sold for $16.15 in the store
HOPE THIS HELPS!
Which of these numbers is closest to 1?
1.11
A
0.1
B
0.91
C
0.999
D
1.05
E
Answer:
C 0.91 D 0.999 E 1.05 and A 1.11 =1
For their class project, a group of statistics students decide to survey the student body to assess opinions about the proposed new student center. Their sample of 200 contained 50 first-year students, 50 sophomores, 50 juniors, and 50 seniors.
The sample size of 200 can be represented by the equation n1 + n2 + n3 + n4, where n1, n2, n3, and n4 represent the number of first-year, sophomore, junior, and senior students surveyed, respectively.
The sample of 200 students surveyed by the statistics students was composed of 50 first-year students, 50 sophomores, 50 juniors, and 50 seniors. This could be represented by the following formula:
Sample Size = 50 First-Years + 50 Sophomores + 50 Juniors + 50 Seniors
In order to break down this sample size into a mathematical formula, the students can use the following equation:
Sample Size (SS) = n1 + n2 + n3 + n4
Where n1, n2, n3, and n4 represent the number of first-year, sophomore, junior, and senior students surveyed, respectively.
Therefore, using the original sample size, the equation would be:
SS = 50 First-Years + 50 Sophomores + 50 Juniors + 50 Seniors
SS = n1 + n2 + n3 + n4
SS = 50 + 50 + 50 + 50
SS = 200
This shows that the sample size of 200 can be represented by the equation n1 + n2 + n3 + n4, where n1, n2, n3, and n4 represent the number of first-year, sophomore, junior, and senior students surveyed, respectively.
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A copy machine makes 28 coples per minute. How long does it take to make 126 copies?
Answer: 4.5 minutes
Step-by-step explanation:
Take 126 divided by 28 = 4.5 minutes
Mrs. Crosland asked students to factor the expression 28x−8. The students offered the answers shown in the box.
Which student(s) offered answer(s) equivalent to the original expression?
Responses
only Danny
only Danny
only Irene
only Irene
both Carlos and Danny
both Carlos and Danny
both Carlos and Irene
both Carlos and Irene
Both Carlos and Irene offered answers equivalent to the original expression.
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given expression is
28x − 8.
The prime factors of 28 is 2 and 7.
Rewrite 28 as the product prime factors:
28 = 7 × 2 × 2.
The prime factors of 8 is 2.
Rewrite 8 as the product prime factors:
8 = 2 × 2 × 2.
Replace 28 = 7 × 2 × 2 and 8 = 2 × 2 × 2 in the given expression:
28x − 8
= (7 × 2 × 2) x − (2 × 2 × 2)
Taking common 2
= 2[ (7 × 2)x − (2 × 2)] = 2(14x − 4)
Again taking common 2:
= 2× 2[ 7x − 2]
= 4(7x − 2)
Thus 2(14x − 4) and 4(7x − 2) is the equivalent expression of 28x − 8.
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Tara runs an amusement park ride and needs to count the people who get on the ride. At the beginning of her shift, 132 people had ridden the ride. This table shows the total number of riders for several times during tara's shift.
the equation in slope-intercept form that represents the total number of riders over time is: Y = 33x + 132
To find the equation in slope-intercept form that represents the total number of riders over time, we need to find the slope and the y-intercept of the line. The slope of a line is the change in y divided by the change in x, or the rise over the run. In this case, the change in y between the first and second times is 165 - 132 = 33, and the change in x is 1 - 0 = 1. So the slope of the line is 33/1 = 33. The y-intercept is the point at which the line crosses the y-axis, or the value of y when x is 0. In this case, the y-intercept is 132, since that is the total number of riders at the beginning of Tara's shift when x is 0.
Therefore, the equation in slope-intercept form that represents the total number of riders over time is:
Y = 33x + 132
Note that the slope (33) is the coefficient of the x term, and the y-intercept (132) is the constant term.
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How do you know if ASA is congruent?
As per the value of angle of the triangle, we have identified that the ASA is congruent.
In math the term triangle refers the three sided triangle that contains the three angles, sides and edge.
Here we need to find the process to know if ASA is congruent.
According to the definition of triangle, here we must know the definition of congruent.
The term congruent is defined as if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
In this theorem, we have to know that any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle then those two triangles are said to be congruent by ASA rule.
Based on this rule, we have identify that if the two triangle have the same angle, then it said to be congruent as per the ASA rule.
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A plumbing contractor obtains 60% of her boiler circulators from Company 1 whose defect rate is 0.005 and the rest from Company 2 whose defect rate is 0.01. If a circulator is defective, what is the probability that it came from the first company? Fill in the contingency table below in order to find the answer. Write your answer as a decimal using 4 significant digits, like for example 0.0247. Defective Non-Defective Total 600 Company 1 Company 2 Total 400 1000
The probability that it came from the first company is 1/2.88⁹.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
Given, A plumbing contractor obtains 60% of her boiler circulators from Company 1 whose defect rate is 0.005 so 40% of her boiler circulators from Company 2 whose defect rate is 0.01.
Now, The probability of the defect rate of company 1 is P(D1) = 0.005/60.
And, The probability of the defect rate of company 1 is P(D1) = 0.01/40.
Therefore, The probability of that it came from the first company is,
= (0.005/60)×( 0.01/40)/60.
= (1/12000)×(1/4000)/50.
= 1/2.88⁹
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Which triangles must be congruent? two isosceles triangles, each with both legs 40 inches long. two isosceles triangles, each with a base 40 inches long. two right triangles, each with both legs 40 inches long. two right triangles, each with a hypotenuse 40 inches long.
Answer:
(c) two right triangles, each with both legs 40 inches long
Step-by-step explanation:
You want to know which pair of triangles are congruent, given their descriptions.
Congruent trianglesThere are basically 4 theorems that allow you to claim congruence of triangles:
AAS, ASA, SAS, SSS
A fifth one applies to right triangles only: HL.
These tell you that you need to have three matching parts: 3 sides, 2 sides and the angle between (except right triangle), or 1 side and 2 angles.
ChoicesAn isosceles triangle with only one or two sides defined is not sufficient.
A right triangle with only the hypotenuse defined is not sufficient.
A right triangle with two legs and the (right) angle between them has a sufficient number of matching parts to be able to claim congruence to another triangle similarly defined.
In the blank alo write the reaon for your anwer a rational number P by Q i aid to be in a lowet form if P and Q have no Dah
P/Q is in the lowest form as the when the HCF is 1 and if we divide it by 1 P/Q remains same so it is the lowest form ,if P and Q have no common factor other than 1.
What is rational number?It is possible to express rational numbers in the form p/q, where p and q are integers and q≠0.
What is lowest form of Rational number?If there is just one other common factor between the denominator and numerator of a rational number, that number is said to be in its lowest form. In other words, if the HCF of a and b is 1 and a and b are relatively prime, then we can state that a rational number a/b is considered to be in its simplest form.
as described in the above contion in order to reduce any rational number to its lowest form we need to divide both numerator and denominator by the HCF of p,q . suppose if the HCF of p,q is 1 then divide p and q 1 won't change the value of the rational number.
so, now it is shown that the given rational number can't be further deduced and hence we conclude that a rational number is in lowest form when HCF of its numerator and denominatior is equal to 1.
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Complete question:
Write the reason why a rational number written in the form of p/q is said to be in lowest form if P and Q have no common factor other than 1.
What is expression example?
An example expression is the following:
$100 + $50n
What is an algebraic expression?An algebraic expression is a set of letters and numbers, in which the letters are called variables and take on an unknown value, the numbers are coefficients or independent terms while the variables are dependent terms.
We will write an algebraic expression to exemplify what has just been defined, with a verbal example.
A person has a business, and he adds $100 to the box (and his sales are on average $50 per hour, with this we build the expression of total income:
$100 + $50n
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Sheila travels 65 miles per hours for 8 hours. Find the distance traveled in miles.
Answer: 520 miles per hour
Step-by-step explanation:
65 times 8 = 520 miles per hour