The binomial distribution is a parametric probability distribution with two parameters, X and B. For a large number of trials, n, binomial probability tends to follow a continuous normal probability distribution.
What is meant by binomial distribution?The binomial distribution is a type of probability distribution that models the likelihood of one of two outcomes given a set of parameters. It sums up the number of trials when each trial has the same chance of achieving a single outcome.
Therefore,
The following is the definition of the Binomial distribution's probability mass function:
P (X = x) = (n x)p x(1p)n x, where x = 0, 1, 2, 3,..., n
Given,
Probability of defective, p = 0.03
Number of bulbs, n = 144
(i) The required probability is P(X = 5).
P(X = 5) = (1445) 0.035(1 − 0.03)144 − 5
= 144151 × (144 − 5) 1 × 0.035(1 − 0.03)144 − 5 ≈ 0.169
Within a carton of 144 bulbs, there is a 0.169 percent chance that 5 of them will be defective.
(ii) The required probability is P(X>2).
P(X>2) = 1 − P(X≤2)
= 1 − P(X = 0) − P(X = 1) − P(X = 2)
= 1 − 144101 × (144 − 0)10.030
Then simplifying,
(1 − 0.03)144 − 0 − 14411 × (144 − 1) 10.031 (1 − 0.03)144 − 1 − 14412 × (144 − 2)10.032 (1 − 0.03)144 − 2
= 1 − 0.01245 − 0.0554 − 0.1226
= 0.810
There is a 0.810 percent chance that there will be more than two faulty bulbs in a carton of 144 bulbs.
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Need help with this problem please help
The error is that the student used the formula for a reflection in the x-axis, and the correct endpoints are: C'(1, 1) and D'(3, -2)
What is the error in finding the coordinates of the image after a rotation of 270?Rotation simply means turning.
In a cartesian plane, if a point P, whose position vector is (x,y), is rotated through 270° about the origin, the position of the image P' is (y, -x)
But the reflection in the x-axis is defined as (x,y) => (x, -y) i.e. if a position vector of a point is (x,y), the position vector of its image in the x-axis is (x, -y)
Given: C(-1, 1) and D'(2, 3)
Therefore, the student used the formula for a reflection in the x-axis. The 2nd option is the answer.
The correct endpoints are: C'(1, 1) and D'(3, -2)
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A rectangular garden has an area of 72 square yards. The dimensions of the
garden are not prime numbers. What are the possible dimensions of the
garden
The possible dimensions of the rectangular garden with an area of 72 square yards are (4,18), (8,9), (6,12), (2,36)
What is meant by an area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.
Given,
The area of a rectangular garden is 72 square yards.
And also given that the dimensions of the garden are not prime numbers.
LCM of 72 is,
=2×2×2×3×3
Therefore, the possible dimensions of the garden are:
(4,18)
(8,9)
(6,12)
(2,36)
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75% of senior SH student wear eyeglasses of those who wear eyeglasses 20% are girls
Answer:
75% - 20% = 55%
Step-by-step explanation:
You have 72 square feet of material to build a rectangular box.
The length is twice the width and there is no top.
What values for W and L and H will create a box that encloses the maximum volume using the material you have?
W = ?
L = ?
H = ?
For the given conditions, the length of box=6.92 feet, width of box=3.46 feet and height of box=2.31 feet.
What is volume?Each object in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's boundaries in three dimensions is referred to as its volume. It is also referred to as the object's capacity.
Here,
area of material=72 feet²
V=lbh
l=2b
72=lb+2lh+2bh
substitute l as 2b,
72=2b²+4bh+2bh
36=b²+3bh
3bh=36-b²
h=(36-b²)/3b
v=lbh
v=2b*b*(36-b²)/3b
v=2b*(36-b²)/3
=(72b-2b³)/3
differentiate the v,
v'=1/3(72-6b²)
v'=0
72-6b²=0
6b²=72
b²=12
b=√12
b=3.46 feet
l=2b=6.92 feet
h=(36-b²)/3b
=(36-12)/3*3.46
h=2.31 feet
The box measures 6.92 feet long, 3.46 feet wide, and 2.31 feet tall under the specified circumstances.
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Answer:
[tex]W=2\sqrt{3}=3.46\; \sf ft\;(2\;d.p.)[/tex]
[tex]L=4\sqrt{3}=6.93\; \sf ft\;(2\;d.p.)[/tex]
[tex]H = \dfrac{4\sqrt{3}}{3}=2.31\; \sf ft\;(2\;d.p.)[/tex]
Step-by-step explanation:
If the length is twice the width:
W = widthL = 2W = lengthH = heightSurface area of the box
[tex]\implies SA = WL + 2WH + 2LH[/tex]
[tex]\implies SA = W(2W) + 2WH + 2(2W)H[/tex]
[tex]\implies SA = 2W^2 + 2WH + 4WH[/tex]
[tex]\implies SA = 2W^2 + 6WH[/tex]
If the surface area is 72 ft²:
[tex]\implies 2W^2 + 6WH = 72[/tex]
[tex]\implies 6WH = 72 - 2W^2[/tex]
[tex]\implies H = \dfrac{72 - 2W^2}{6W}[/tex]
[tex]\implies H = \dfrac{36 - W^2}{3W}[/tex]
Volume of the box
[tex]\implies V = LWH[/tex]
[tex]\implies V = (2W)WH[/tex]
[tex]\implies V = 2W^2H[/tex]
Substitute the found expression for H into the formula for volume:
[tex]\implies V = 2W^2\left(\dfrac{36 - W^2}{3W}\right)[/tex]
[tex]\implies V = \dfrac{2W^2(36 - W^2)}{3W}[/tex]
[tex]\implies V = \dfrac{2W(36 - W^2)}{3}[/tex]
[tex]\implies V = \dfrac{72W - 2W^3}{3}[/tex]
[tex]\implies V =24W-\dfrac{2}{3}W^3}[/tex]
To find the value of W when the volume is at its maximum, first differentiate the equation for volume with respect to W:
[tex]\implies \dfrac{\text{d}V}{\text{d}W}=24-2W^2[/tex]
Now set the derivative to zero and solve for W:
[tex]\implies 24-2W^2=0[/tex]
[tex]\implies 2W^2=24[/tex]
[tex]\implies W^2=12[/tex]
[tex]\implies W=\sqrt{12}[/tex]
[tex]\implies W=2\sqrt{3}[/tex]
As length is twice the width:
[tex]\implies L=2 \cdot 2\sqrt{3}[/tex]
[tex]\implies L=4\sqrt{3}[/tex]
To find H, substitute the found value of W into the expression for H:
[tex]\implies H = \dfrac{36 - W^2}{3W}[/tex]
[tex]\implies H = \dfrac{36 - (2\sqrt{3})^2}{3(2\sqrt{3})}[/tex]
[tex]\implies H = \dfrac{36 - 12}{6\sqrt{3}}[/tex]
[tex]\implies H = \dfrac{24}{6\sqrt{3}}[/tex]
[tex]\implies H = \dfrac{4}{\sqrt{3}}[/tex]
[tex]\implies H = \dfrac{4\sqrt{3}}{3}[/tex]
What’s M +3+ 2M plus one
Answer:
0
Step-by-step explanation:
A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 13 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly 4 insects will survive? Round your answer to four decimal places.
The probability that exactly 4 insects will survive is 0.8975
What is Probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, 0 indicates impossibility of the event and 1 indicates certainty.
probability= sample space/total possible outcome
the total possible outcome for the insecticide to kill insect is 60%
If 4 will survive out of 13, it means 7 will be killed by the insecticide, the percentage is now 7/13×100 = 53.85%
Therefore the probability for 4 insect to survive is 53.85/60= 0.8975
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IXL Please Help Fast!
In the given rectangular prism vector line IM and LM intersect each other. Option B is correct.
What is a rectangular prism?It is defined as a six-faced shape, a type of hexahedron in geometry. It is a three-dimensional shape. It is also called a cuboid.
Six faces, twelve sides, and eight vertices make up a rectangular prism (corners). Three of the 12 edges meet to create right angles at each vertex.
Since from all 12 edges vector line IM and LM meet to form right angles at each vertex.
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Thus, in the given rectangular prism vector line IM and LM intersect each other. Option B is correct.
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Find the measure of prq if p is 33, r is 17x + 1 and q is 10x + 1
The expression we get after measuring prq is 5610x²+ 891x+33.
Given that,
p is 33, r is 17x+1 and q is 10x+1
We have to find the measure of prq.
Take the,
p is 33, r is 17x+1 and q is 10x+1
Now,
prq
By multiply we get an expression
Multiplying each term to each other.
(33)(17x+1) (10x+1)
1st multiply 33 to 17x+1
(561x+33) (10x+1)
Now multiply each 561x with 10x+1 and 33 with 10x+1
5610x²+ 561x+ 330x+33
Adding 561x and 330x
5610x²+ 891x+33
Therefore, The expression we get after measuring prq is 5610x²+ 891x+33.
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Bob's Gift Shop sold 500 cards for Mother's Day. One salesman, Camila, sold 10% of the cards sold for Mother's Day. How many cards did Camila sell? answer: 50
The number of cards Camila sold is 50cards
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”. For example if 10% of 200 students in a school are boys, the the number of boys in the school is 10/100× 200= 20students
Similarly Camila sold 10% of the card sold on mother's day. The number of cards sold on mother's day is 500.
Therefore Camila sold 10/100×500= 50cards
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Answer:
Step-by-step explanation:
Find the y-intercept and x-intercept of the following linear equation.
−32x−3y=3
Plot 2 sets of coordinates
The y-intercept and x-intercept of the following linear equation is
x intercept = -0.094y intercept = -1How to find the interceptsx intercept
x intercept refers to the value of x when y is zero
−32x−3y=3
at y = 0
-32x - 3 * 0 = 3
-32x = 3
x = -3/32 = -0.09375
the coordinate is (-0.094, 0)
y intercept
y intercept refers to the value of y when x is zero
−32x −3y=3
at x = 0
0 - 3y = 3
y = -1
the coordinate is (0, -1)
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NO LINKS!! Describe the set of all points P(x, y) in a coordinate plane that satisfy the given condition. Part 2
Part (d)
If xy > 0, then the two items x and y must have the same sign.
Examples where x,y are both positive
x = 2 and y = 5 leads to xy = 2*5 = 10x = 7 and y = 4 leads to xy = 7*4 = 28Examples where x,y are both negative
x = -1 and y = -9 leads to xy = -1*(-9) = 9x = -12 and y = -3 leads to xy = -12*(-3) = 36This places us in either the first quadrant or third quadrant (Q1 and Q3)
Q1 is where x > 0 and y > 0 (northeast corner)Q3 is where x < 0 and y < 0 (southwest corner)Answer: The set of all points in quadrants I and III (x and y have the same sign)======================================================
Part (e)
If y < 0, then we have points like (2,-5) and (1,-7). The x coordinate doesn't matter as long as the y coordinate is negative.
Visually speaking we are below the x axis. This places the point in Q3, Q4, or on the negative y axis. The point cannot be on the x axis. You can think of this point as being underground or underwater.
Answer: The set of all points below the x axis======================================================
Part (f)
If x = 0, then the point is on the vertical y axis. Recall that y intercepts always occur when x = 0. Two examples would be (0,4) and (0,12).
Answer: The set of all points on the y axis.Answer:
(d) The set of all points in quadrants I and III (x and y have the same sign).
(e) The set of all points below the x-axis.
(f) The set of all points on the y-axis.
Step-by-step explanation:
The Cartesian plane is divided into four quadrants.
Quadrant I is the upper right quadrant and the rest follow in a counterclockwise direction.
Quadrant I: x > 0 and y > 0 → (x, y)Quadrant II: x < 0 and y > 0 → (-x, y)Quadrant III: x < 0 and y < 0 → (-x, -y)Quadrant IV: x > 0 and y < 0 → (x, -y)Part (d)
For xy > 0, x and y should either both be positive or both be negative, i.e. have the same sign.
x and y are both positive in quadrant I.x and y are both negative in quadrant III.Therefore, the description that satisfies the given condition is:
The set of all points in quadrants I and III (x and y have the same sign).Part (e)
For y < 0, y is always negative.
y is negative in quadrant III.y is negative in quadrant IV.Quadrants III and IV are below the x-axis.
Therefore, the description that satisfies the given condition is:
The set of all points below the x-axis.Part (f)
The only place where x = 0 is the y-axis.
Therefore, the description that satisfies the given condition is:
The set of all points on the y-axis.Which number line represents the solutions to |–2x| = 4?
(I want a clear explanation)
Answer:
third option
Step-by-step explanation:
| - 2x | = 4
the absolute value function always gives a positive value, however, the expression inside can be positive or negative , that is
- 2x = 4 ( divide both sides by - 2 )
x = - 2
or
- (- 2x) = 4
2x = 4 ( divide both sides by 2 )
x = 2
solutions are x = - 2 , x = 2
these are illustrated on the number line by solid circles at - 2 and 2
this is indicated on the third number line
Number line represents the solutions to |–2x| = 4 is third number line (x1 = -2, x2= 2).
Solving steps :
1. Calculate
Calculate the absolute value.
|-2x| = 4
Use |ab| = |a| * |b| to transform the expression.
|-2x|
|-2| * |x|
The absolute value of any number is always positive.
2 * |x|
We did it!
|-2x| = 4
2 * |x| = 4
2. Divide both sides
Divide both sides of the equation by 2.
2 * |x| = 4
2 * |x| ÷ 2 = 4 ÷ 2
Any expression divided by itself equals 1.
|x| = 4 ÷ 2
Calculate the quotient.
|x| = 2
3. Separate into possible cases
Use the absolute value definition to rewrite the absolute value equation as two separate equations.
|x| = 2
x = 2
x = -2
4. The equation has 2 solutions.
x1 = -2, x2= 2
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deposited $8500 into a savings account 3 years ago. The simple interest rate is 2%. How much money did marsha earn in interest?
Answer:Marsha earned interest = $850
Step-by-step explanation:
Amount deposited = $8500
Time = 2 years
Interest rate = 5% = 0.05
We need to find how much did Marsha earn in interest
The formula use is:
Where I is interest earned, P is amount deposited, r is interest rate and t is time.
Putting values and finding interest.
So, Marsha earned interest = $850
Find the accumulated value of an investment of $20,000 for 7 years at an interest rate of 4% if the money is a.
compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously.
Part a; compounded semiannually (n = 2); CI = $6,390.
Part b: compounded quarterly ( n = 4) ; CI = $6,425
Part c: compounded monthly (n = 12): CI = $6,450
Part d: compounded continuously; CI = $6,467.
What is known as the term compound interest?Compound interest is computed as interest on the base principal plus any interest income from prior periods. The frequency plan for compounding interest can be set to be continuous, daily, or yearly.The compound interest is calumniated by formula.
A = P(1 + r/100n)∧nt
In which,
A = amount after compounding
P = principal amount ($20,000 )
n = number of time principal amount compounded in a year.
t = total time in years (7 years)
r= rate of interest (4%)
Part a; compounded semiannually (n = 2)
A = P(1 + r/100n)∧nt
A = 20,000(1 + 4/200)∧(2x7)
A = 26390
CI = A - P
CI = 26,390 - 20,000
CI = $6,390.
Part b: compounded quarterly ( n = 4)
A = 20,000(1 + 4/400)∧(4x7)
A = 26425
CI = A - P
CI = 26,425 - 20,000
CI = $6,425
Part c: compounded monthly (n = 12)
A = 20,000(1 + 4/1200)∧(12x7)
A = 26450
CI = A - P
CI = 26,450- 20,000
CI = $6,450
Part d: compounded continuously.
P = P₀e∧rt
P = (20,000)(2.72)∧(0.04 x 7)
P = 20,000 x 1.32
P = 26,467
CI = 26,467 - 20, 000
CI = $6,467.
Thus, the for compounded continuously is $6,467.
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Using slope-intercept, standard form, or point slope -
An arrow released from a bow, traveling towards a target 200 yards away,
reaches a max height of 42.6 ft in only 1.5 seconds. What is the height of the
arrow at 2.5 seconds?
Thank you so much!
The height of the arrow at 2.5 seconds is 71 feet.
Given:
An arrow released from a bow, traveling towards a target 200 yards away,reaches a max height of 42.6 ft in only 1.5 seconds.
1.5 seconds = 42.6 feet
divide by 1.5 on both sides.
1 sec = 28.4 feet
0.5 sec = 28.4/2
0.5 sec = 14.2 feet
2.5 sec = 1.5 sec + 1 sec
= 42.6 + 28.4
= 71 feet
Therefore The height of the arrow at 2.5 seconds is 71 feet.
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You buy two tickets for a school raffle. If 358 tickets are sold, what is the probability that you will win the
raffle? Write your answer as a percent rounded to the nearest thousandth of a percent.
Answer:
0.559%
Step-by-step explanation:
The chance of winning equals the number of tickets bought divided by the total number of tickets
2 tickets are bought by the person, and 358 tickets are sold in total
2/358 would equal 0.00558659218..., and the percentage would be 0.558659...%
Rounding 0.558659 to the nearest thousandth's place would yield
0.559, so 0.559% would be the final answer
What is the area of this triangle? O 18 square units O 20 square units O 21 square units 024 square units
The area of this triangle is 21 square units.
From the graph:
The length of the base = 4 + 3 units
= 7 units
The length of the height = 3 + 3
= 6 units
Area of the triangle = 1/2 b *h
= 1/2*7*6
= 1*42/2
= 42/2
= 21 square units.
Therefore the area of this triangle is 21 square units.
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Triangle CDE is dilated by a scale factor of 1/4 to form triangle C'D'E'. Side D'E' measures 3.5. What is the measure of Side DE?
If triangle CDE is dilated by a scale factor of 1/4 to form triangle C'D'E' , then measure of the side DE is 14.
In the question ,
it is given that ,
The triangle CDE is dilated by scale factor of 1/4
and the new triangle formed after dilation is C'D'E' .
it is given that the measure of the side D'E' = 3.5 .
let the measure of the the side DE = x
So , according to the question ,
x *(1/4) = 3.5
On cross multiplication,
we get ,
x = 4* 3.5
x = 14
Therefore , If triangle CDE is dilated by a scale factor of 1/4 to form triangle C'D'E' , then measure of the side DE is 14.
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The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 65% pure fruit juice?
Please help this is due soon
Answer:
Okay, so let's make the variable x the 60% juice.
The equation:
0.60(x) + 1(120-x) = 0.7(120)
Multiply both sides by ten for easier calculation:
6x + 1200 - 10x = 840
Put x on one side and the numbers on the other:
-4x = -360
the negatives cancel out...
4x = 360
define x
x = 90
Step-by-step explanation:
In triangle EFG, m∠E = 84.3° and m∠F = 36.4°. Determine the measure of the exterior angle to ∠G.
47.9°
59.3°
121.1°
120.7°
By applying the exterior angle property, the measure of the exterior angle to ∠G in triangle EFG is equal to 120.7°
What is the exterior angle property?In Mathematics, the exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.
How to determine the value of ∠G?In order to determine the value of ∠G in triangle EFG (ΔEFG), we would have to apply exterior angle property. Mathematically, the exterior angle property can be used to model triangle EFG (ΔEFG) and this is given by:
m<G = m<E + m<F
Substituting the given parameters into the formula, we have;
m<G = 84.3° + 36.4°.
m<G = 120.7°.
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At Monroe College, 1/2 of the students are enrolled in an art class. Of the students enrolled in an art class, 3/10 are enrolled in a painting class. What fraction of the students at Monroe College are enrolled in a painting class?
Answer:7/10
Step-by-step explanation:
2 2/3 + 1 5/8
How do you solve this
How do you change the denominator so you can solve
Answer:25/.2
Step-by-step explanation:
i think this is right
Answer:
The answer would be 4 7/24
Step-by-step explanation:
We can obtain common denominators by multiplying both numerator (top) and denominator (bottom) by the same amount.
The LCM (least common multiple) for your question would be 24, so you would multiply in order to get the fractions to have a common denominator of 24, while keeping the same value.
HELP!! Simply the expression
Answer:
[tex]\frac{2x\sqrt{3y}}{{3y}}[/tex]
Step-by-step explanation:
Apply fractional law for squares:
[tex]\sqrt{\frac{4x^2}{3y}} = \frac{\sqrt{4x^2}}{\sqrt{{3y}}}[/tex]
Then simply:
[tex]\frac{2x}{\sqrt{{3y}}}[/tex]
Rationalize denominator:
[tex]\frac{2x}{\sqrt{{3y}}} \cdot \frac{\sqrt{{3y}}}{\sqrt{{3y}}} = \frac{2x\sqrt{3y}}{{3y}}[/tex]
NO LINKS!! Please help me with the Segment Proofs Part 1
Answers in bold
GivenGivenDefinition of midpointTransitive property of equalityAddition property of equalitySimplificationSubstitutionSegment addition postulateTransitive property of equalityDivision property of equality====================================================
Explanation:
Always start the proof with what you are given. It seems silly to repeat the given information, but it's just how all proofs are formed. This is to build from those given statements to lead to what we want to prove on the last line.
The term "midpoint" refers to splitting a segment into two equal smaller pieces. So for instance, if Q is the midpoint of PR, then the pieces PQ and QR are equal. Each smaller piece is half as long as PR.
The transitive property is the idea if A = B and B = C, then A = C. Think of it like substitution. Or you can think of a set of dominoes: A knocks down B, which knocks down C. Therefore A knocks down C.
The addition property of equality is where we go from A = B to A+C = B+C. I've added C to both sides. Adding the same thing to both sides will not change the equation. It keeps things balanced. When going from line 4 to line 5, we added PQ to both sides.
In line 6, we've gone from PQ+PQ to 2PQ.
In line 7, we replace PQ with QR on the right hand side. We use the substitution property here (refer to line 3 where we found PQ = QR)
Line 8 uses the segment addition postulate. If A,B,C are collinear, then AB+BC = AC. The point B doesn't necessarily need to be the midpoint.
Line 9 uses the transitive property again (we combine lines 7 and 8 to lead to line 9).
The final line has us divide both sides by 2 to get what is shown in the table. This is the division property of equality.
------------------------
Shortcut using informal logic:
PQ = QR
QR is half as long as QS
Therefore, PQ is also half as long as QS
Answer:
The last reason for [tex]PQ=\frac{1}{2}QS[/tex] is division property of equality
Step-by-step explanation:
The reason for [tex]PQ=\frac{1}{2}QS[/tex] can be evaluated as follows
For the statement [tex]Q[/tex] is the midpoint of [tex]\overline{PR}[/tex], the reason is given
For the statement [tex]R[/tex] is the midpoint of [tex]\overline{QS}[/tex], the reason is given
For the statement [tex]PQ=QR, QR=RS[/tex] , the reason is definition of midpoint
The midpoint of a line segment is the point that separates the line segment into two congruent parts.
For the statement [tex]PQ=RS[/tex] , the reason is transitive property
Transitive property says that if [tex]a=b[/tex], and [tex]b=c[/tex], then [tex]a=c[/tex]
In this statement [tex]PQ=QR, QR=RS[/tex], then [tex]PQ=RS[/tex]
For the statement [tex]PQ+PQ=PQ+RS[/tex] , the reason is addition property of equality
Addition property of equality says that if [tex]a=b[/tex], then [tex]a+c=b+c[/tex]
For the statement [tex]2PQ=PQ+RS[/tex] , the reason is combining of like terms of algebraic expression
Combining like terms is the process to add or to substract the coefficient of the terms
In this statement combining like terms is at the left side of the equation, [tex]PQ+PQ=2PQ[/tex]
For the statement [tex]2PQ=QR+RS[/tex] , the reason is substitution property
Substitution property of equality says that if [tex]a=b[/tex], then [tex]a[/tex] replaces [tex]b[/tex] in any equation, in this statement [tex]QR[/tex] replaces [tex]PQ[/tex]
For the statement [tex]QR+RS=QS[/tex] , the reason is substitution property and definition of midpoint
In this statement [tex]QR+RS[/tex] replaces [tex]2PQ[/tex], and [tex]QS[/tex] is the sum of two congruent parts [tex]QR+RS[/tex]
For the statement [tex]2PQ=QS[/tex] , the reason is substitution property
In this statement [tex]2PQ[/tex] replaces [tex]QR+RS[/tex]
For the statement [tex]PQ=\frac{1}{2}QS[/tex] , the reason is division property of equality
Division property of equality says that if [tex]a=b[/tex], and [tex]c\neq 0[/tex], then [tex]\frac{a}{c} =\frac{b}{c}[/tex]
In this statement [tex]\frac{2PQ}{2} =\frac{QS}{2}[/tex] or can be reduced into [tex]PQ=\frac{1}{2}QS[/tex]
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Express the trig ratio as fractions in simplest terms
The trigonometric ratio (trig ratio) for the angle in this right-angled triangle should be expressed as fractions in simplest terms as follows:
Sin(M) = 21/121
Cos(L) = 10/11
Tan(K) = 21/100
How to express the trig ratio as fractions?In Mathematics, a trigonometric ratio (trig ratio) can be calculated by using this mnemonic SOHCAHTOA:
Sinθ = Opposite/Hypotenuse
Sin(M) = KM/ML
Sin(M) = √21/11
Taking the square of both the numerator and denominator, we have:
Sin(M) = (√21)²/11²
Sin(M) = 21/121
For the cosine of an angle in a right-angled triangle, we have:
Cosθ = Adjacent/Hypotenuse
Cos(L) = KL/ML
Cos(L) = 10/11
For the tangent of an angle in a right-angled triangle, we have:
Tanθ = Opposite/Adjacent
Tan(K) = KM/KL
Tan(K) = √21/10
Taking the square of both the numerator and denominator, we have:
Tan(K) = (√21)²/10²
Tan(K) = 21/100
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Members of the drama club are selling tickets on the night of the their show. Some money is placed in the cashbox before any tickets are sold. As drama club members sell their tickets, they record the number of tickets sold and the total amount of money in the cash box
Number of Tickets sold
20
43
108
Money is the Cashbox (dollars) :
320
492.50
980
a. Assuming all of the tickets are the same price, write an equation. that describes the relationship between the number of tickets sold and the total amount of money in the cashbox
b. How much money is in the cashbox before any tickets are sold? Explain how you found your answer by using the equation from part a
c. What is the price of each ticket? Explain how you found your answer by using the equation from part a
From the question, we could give annotations for the number of tickets sold and the amount of money in the cashbox. We also find that there is 2 other elements related to the relationship between the tickets sold and the amount of money in the cashbox; the price of each ticket and the amount of money in the cashbox before any tickets are sold. Hence we could make some annotations:
m = money in the cashbox (after tickets are sold)
p = price of each tickets
x = number of tickets sold
c = money in the cashbox (before tickets are sold)
Based on the question, we know that the amount of money in the cashbox is dependeding on the number of tickets sold and the original amount of money in the cashbox before any tickets are sold. The relationship between the money in the cashbox and the number of tickets sold is depending on the price of each ticket. Based on this understanding, we could rewrite the relationship into such equation:
m = px + c ... (i)
Using data from the question, we could input the datas into equation (i):
m = px + c
320 = 20p + c ... (ii)
492.50 = 43 p + c ... (iii)
980 = 108 p + c ... (iv)
By using equation (ii) and (iv) we could find the value of p
320 = 20p + c
980 = 108p + c -
660 = 88p
p = 7.5 ... (v)
Using the finding value of p, we could find the value of c by using subtitution of equation (v) into equation (ii):
320 = 20p + c
320 = 20(7.5) + c
320 = 150 + c
c = 170 ... (vi)
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You have 4,592 grams of a radioactive kind of scandium. How much will be left after 168 days if its half-life is 84 days?
Answer:
1,148
Step-by-step explanation:
A rectangle's length is 5.1 more than 2 times its width. Its perimeter is 165.6. Write and solve a system of equations to find the dimensions of the rectangle.
Type the area of the rectangle, rounded to the nearest tenth.
The length of the rectangle is 56.9 unit and the breadth of the rectangle is 25.9 unit.
Area of the rectangle is 1473.7 sq. unit.
Given, a rectangle's length is 5.1 more than 2 times its width.
Its perimeter is 165.6.
Let the length of the rectangle be l,
breadth of the rectangle be b.
According to the question,
l = 5.1 + 2b
Using the formula of Perimeter,
Perimeter = 2(l + b)
165.6 = 2(5.1 + 2b + b)
165.6 = 2(5.1 + 3b)
82.8 = 5.1 + 3b
3b = 77.7
b = 25.9
Now, l = 5.1 + 2(25.9)
l = 5.1 + 51.8
l = 56.9
So, the length of the rectangle is 56.9 unit
and the breadth of the rectangle is 25.9 unit
Now, the area of the rectangle be,
Area = l×b
Area = 56.9×25.9
Area = 1,473.71
Area of the rectangle = 1473.7 sq. unit
Hence, the length of the rectangle is 56.9 unit and the breadth of the rectangle is 25.9 unit.
Area of the rectangle is 1473.7 sq. unit.
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Determine whether the figure is a parallelogram using the distance formula.
Q\left(-10,-2\right),R\left(1,-1\right),S\left(1,-7\right),T\left(-11,-8\right)Q(−10,−2),R(1,−1),S(1,−7),T(−11,−8)
The distance formula used to determine if the figure is a parallelogram indicates;
The length of QR ≈ 11.0 and the length of ST ≈ 12.0. The length of QS ≈ 12.1, and the length of RT ≈ 13.9. Therefore, QRST is not a parallelogramWhat is a parallelogram?A parallelogram is a quadrilateral that have two pairs of facing sides that are parallel and of the same length.
The length of the sides can be found by using the formula for finding the distance between two points on the coordinate plane as follows;
The distance between the points (x₁, y₁) and (x₂, y₂) is d = √(x₂ - x₁)² + (y₂ - y₁)²
The length of QR = √((1 - (-10))² + (-1 - (-2))²) = √(122) ≈ 11.0
Length of ST = √((1 - (-11))² + (-7 - (-8))²) = √(145) ≈ 12.0
Length of QS = √((1 - (-10))² + (-7 - (-2))²) = √(146) ≈ 12.1
Length of RT = √((1 - (-11))² + (-1 - (-8))²) = √(193) ≈ 13.9
The lengths of the opposite sides of a parallelogram are the same. The lengths of the sides of the quadrilateral QRST are different, therefore, quadrilateral QRST is not a parallelogram.
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what is 3 5/8 adding 1 2/8
Answer:
The solution is 4 7/8 or 39/8
Step-by-step explanation:
[tex] \sf 3 \frac{5}{8} + 1 \frac{2}{8} \\ \\ = \sf (3 + 1) + ( \frac{5}{8} + \frac{2}{8} ) \\ \\ = \sf 4 + \frac{7}{8} \\ \\ = \sf 4 \frac{7}{8} [/tex]
Or
[tex]\sf 3 \frac{5}{8} + 1 \frac{2}{8} \\ \\ = \frac{29}{8} + \frac{10}{8} \\ \\ = \sf \frac{39}{8} [/tex]