The parts of algebraic expressions related to polynomials are variables and coefficients.
What are the parts of algebraic expressions?The parts of algebraic expressions are;
Variables which are letters that represent numbersCoefficients are numbers that multiply the variables Constant is a number that is not multiplied by any variablePolynomials are algebraic expressions composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, and multiplication
Polynomials consists of variables and coefficients. The variables in polynomials are also called indeterminates. The coefficients also multiply this variables.
Thus, the parts of algebraic expressions related to polynomials are variables and coefficients.
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Aisha wants to paint the four walls of her living room.
Each wall is 2.4 m high and 5.2 m long.
One wall has a door of 2 m by 0.8 m.
Tins of paint cost £12 per 2 litre tin.
Each litre of paint can cover 12 m2 of wall.
There is an offer of: Buy 2 tins get the 3rd at half price.
How much will Aisha pay to paint her living room?
The total amount Aisha would pay to paint her room is $54.
What is the cost of painting the rooms?The first step is to determine the area of the walls. The walls have the shape of a rectangle. Thus, the formula for the area of a rectangle would be used to determine the area of the wall.
Area of the three walls without a door : 3 x (length x width)
3 x (2.4 x 5.2) = 37.44 m²
Area of the fourth wall with a door : area of the wall - area of the door
(2.4 x 5.2) - (2 x 0.8) = 10.88m²
Total area of the walls : area of the three walls + area of the wall with the door
10.88m² + 37.44 m² = 48.32 m²
The next step is to determine the number of tins that would be needed:
48.32 /12 = 4.03
5 tins would needed
Cost of the 5 tins: (4 x 12) + (0.5 x 12) = $54
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A bird (B) is spotted flying 6,000 feet from a tower (). An observer (0) spots the top of tower (T) at a distance of 9,000 feet. What is the angle of depression from the bird (B) to the
observer (0)?
Using relations in a right triangle, it is found that the angle of depression is of θ = 56.31º.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.For this problem, we have that:
The opposite side to the angle of depression is the top of tower, at a height of 9000 feet.The adjacent side to the angle is the distance to the bird, of 6000 feet.Hence, considering θ as the depression angle, we have that:
tan(θ) = 9000/6000
tan(θ) = 1.5
θ = arctan(1.5)
θ = 56.31º.
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Point R divides PQin the ratio 1:3. If the x-coordinate of Ris -1 and the x-coordinate of Pis -3, what is the x-coordinate of Q?
Since Point R divides PQ in the ratio 1:3. the x-coordinate of Q is 3
The question has to do with line division
What is line division?This is the division of a line into a given ratio.
How to find the coordinate of Q?
Since Point R divides PQ in the ratio 1:3. If the x-coordinate of R is -1 and the x-coordinate of P is -3.
Let
x₁ = coordinate of P = -3, x₂ = coordinate of R = -3 and x₃= coordinate of Q.Since R divides PQ in the ratio, 1:3, we have that
PR/RQ = 1/3
(x₂ - x₁)/(x₃ - x₂) = 1/3
Substituting the values of the variables into the equation, we have
(x₂ - x₁)/(x₃ - x₂) = 1/3
(-1 - (-3))/(x₃ - (-3)) = 1/3
(-1 + 3)/(x₃ + 3) = 1/3
2/(x₃ + 3) = 1/3
x₃ + 3 = 2 × 3
x₃ + 3 = 6
x₃ = 6 - 3
x₃ = 3
So, the x-coordinate of Q is 3
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Sandy used a virtual coin toss app to show the results of flipping a coin 80 times, 800 times, and 3,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 80 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 800 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 3,000 flips.
Question 2(Multiple Choice Worth 2 points)
(Experimental Probability MC)
A spinner with 4 equal sections is spun 20 times. The frequency of spinning each color is recorded in the table below.
Outcome Frequency
Pink 6
White 3
Blue 7
Orange 4
What statement best compares the theoretical and experimental probability of landing on orange?
The theoretical probability of landing on orange is one fifth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fifth, and the experimental probability is 30%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 50%.
Question 3(Multiple Choice Worth 2 points)
(Experimental Probability MC)
Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting an orange marble.
0.27
0.33
0.40
0.67
Question 4(Multiple Choice Worth 2 points)
(Experimental Probability LC)
A number cube is tossed 60 times.
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
Determine the experimental probability of landing on a number less than 2.
35 over 60
25 over 60
13 over 60
12 over 60
Question 5(Multiple Choice Worth 2 points)
(Experimental Probability MC)
A coin is flipped 200 times. The table shows the frequency of each event.
Outcome Frequency
Heads 98
Tails 102
Determine the experimental probability of landing on heads.
102%
98%
50%
49%
Question 6 (Essay Worth 4 points)
(Experimental Probability HC)
A coin is flipped at the start of every game to determine if Team A (heads) or Team B (tails) will get the ball first.
Part A: Find the theoretical probability of a fair coin landing on heads. (1 point)
Part B: Flip a coin 14 times and record the frequency of each outcome. Be sure to include the frequency of each outcome in your answer. Then, determine the experimental probability of landing on heads and compare it to the theoretical probability. (3 points)
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The experimental probability of selecting an orange marble is 0.33.
The experimental probability of landing on a number less than 2 is 12 over 60.
The experimental probability of landing on heads is 49%.
The theoretical probability of a fair coin landing on heads is 0.5.
How to calculate the probability?It should be noted that a coin has a head and tail. Therefore, the probability of getting either will be:
= 1/2 = 0.5
Therefore, Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The statement that compares the theoretical and experimental probability of landing on orange is that the theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The experimental probability will be:
= 4/(6+3+7+4)
= 4/20 = 1/5
Based on the given frequency, the experimental probability of selecting an orange marble will be:
= 5/(4+6+5)
= 5/15
= 0.33
The experimental probability of landing on a number less than 2 is 12 over 60.
The experimental probability of landing on heads will be:
= 98/(98 + 102)
= 98/200
= 49%
The theoretical probability of a fair coin landing on heads will be:
= 1/2 = 0.5
Flip a coin 14 times and record the frequency of each outcome gives:
Head, Tail, Head, Head, Head, Tail, Tail, Head, Tail, Tail, Tail, Tail, Head, Head. The theoretical and experimental probability are 0.5.
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add and subtract function PLS HELP!!!!
Answer:
The first option:
[tex]6x^{2} -4x+6[/tex]
Step-by-step explanation:
Trust me I am right.
If you need work please ask!
Have a nice day!
Today, Stephen is three times as old as Gautham. Ten years ago Stephen turned 2. How old will Gautham be
in 8 years?
What is the five-number summary for this data set?
17, 21, 22, 26, 28, 31, 33, 41, 46, 52
Assume the numbers in each answer choice are listed in this order: min, Q1,
median, Q3, max.
Step-by-step explanation:
17, 21, 22, 26, 28, 31, 33, 41, 46, 52
min: 17
Q1: 26
median: 28
Q3: 31
max: 52
rounding to 1 significant figure, estimate the
answers to these questions:
a)
78 × 92
b)
615 × 38
C)
423 × 764
Answer:
a) 7000
b) 20000
c) 300000
Rounding is the act of replacing a number with values that are an approximation.
can be used to create simpler, or more explicit answersBasic rounding rules:
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 68 rounded to 1 significant figure would be 70.
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 13 rounded to 1 significant fugue is 10.
3. Zero digits that come after a non zero digit are non significant. Example: 10000 only has 1 significant figure
Calculations:
A) 78 x 92 = 7176
to round to 1 sig fig we must make all digits after 7 insignificantwe must also take note of whether the 7 will remain the same or be rounded upthe digit that comes after is a 1, following the rules of rounding it will remain a 7The answer for A is 7000
B) 615 x 38 = 23370
all digits after 2 must be insignificant the digit that comes after is a 3, following the rules of rounding the 2 will remain a 2Answer for B is 20000
C) 423 x 764 = 323172
all digits after 3 must be insignificantthe digit that comes after is a 2, following the rules of rounding the 3 will remain a 3Answer for C is 300000
Given a polynomial function f(x)=2x²+ 7x+6 and an exponential function g(x)=2+ 5, what key features do f(x) and g(x) have in common?
Both f(x) and g(x) increase over the interval of [-4,∞)
Both f(x) and g(x) have the same x-intercepts of (-2, 0) and (-1.5, 0).
Both fox) and gox) have the same y-intercept of (0,6)
Both f(x) and g(x) have the same range of (-00.01]
Since the common features of the polynomial function is f(x) = 2x² + 7x + 6 and exponential function g(x) = 2^x + 5 then:
Both f(x) and g(x) have the same y-intercept of (0,6)What is the polynomial function about?Polynomial functions are known to be a kind of an expressions that is made up of a set of variables of different extent or degrees, non-zero coefficients, positive exponents (of variables), and also it is made up of constants.
Note that the equation of the functions are stated as:
f(x) = 2x² + 7x + 6
g(x) = 2^x + 5
The right and next thing to do is to plot a graph of both functions (see image attached)
From the graph, we have the fact that Both f(x) and g(x) have the same y-intercept of (0,6)
Therefore, Since the common features of the polynomial function is f(x) = 2x² + 7x + 6 and exponential function g(x) = 2^x + 5 then:
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with a linear, exponential, or quadratic function.
You have to decide which of two prizes you will accept!
Prize A: $5,000 for the first month with a $100 increase every month thereafter.
Prize B: $2,000 for the first month with a 10% increase every month thereafter.
9. Create an equation for each situation (Prize A and Prize B).
The equation s for each scenario in which case, the former, Prize A is represented as a linear equation while the latter, Prize B is represented as an exponential function are;
Prize A = $5,000 + $100m (where m = no. of months).Prize B = $2,000(1.1)^m.What equations represents the given situation?It follows from the task content that in scenario which pertains to Prize A, the initial price which represents the y-intercept is; $5,000 while the slope which represents the increase per month is; $100.
Consequently, we have; Prize A = $5,000 + $100m
While, for Prize B, in which case the function via exponential, we have;
Prize B = $2,000(1.1)^m.
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PLEASE PLEASE PLEASE HELP ME ITS A MATH PROBLEM!!! EXPLANATIONS WELCOMED
Answer:
8
Step-by-step explanation:
The given ratios can be combined to a composite ratio using least common multiples.
Given ratiosWe can identify each of the entities with a 2-letter designation:
TT - Tumtum tree; TW - tulgey wood; BS - frumious Bandersnatch;
ST - slithy tove; BG - borogoves; MR - mome raths; JW - Jabberwocky;
JB - Jubjub birds.
Then the given ratios are ...
20 TT : 1 TW1 TW : 1 BS5 ST : 2 BG2 MR : 1 JW2 JB : 200 TT . . . . (reduces to 1 : 100)200 MR : 1 BG5 JB : 1 STComposite ratiosThe path from BS to JW is unique, so we can work our way there one ratio at a time. Having done this once, we can go back and do it again with the least possible multiplier.
Here, that turns out to be 125 Bandersnatches. We can combine these to the composite ratio ...
125 BS : 125 TW : 2500 TT : 25 JB : 5 ST : 2 BG : 400 MR : 200 JW
Then the ratio of Bandersnatches to Jabberwocks is 125 : 200 = 5 : 8.
If there are 5 frumious Bandersnatches, there should be 8 Jabberwocks.
__
Additional comment
We know 1 JW : 2 MR and 200 MR : 1 BG. In order to get a common value of 200 MR in these ratios, we need to multiply the first by 100:
100 JW : 200 MR : 1 BG
Next, we notice the other ratio involving BG is 2 BG : 5 ST, which means we need to multiply by 2 again:
200 JW : 400 MR : 2 BG : 5 ST
The number of JB is 5 times the number of ST, so this extends to ...
... 5 ST : 25 JB
The number of TT is 100 times the number of JB, so we have ...
... 5 ST : 25 JB : 2500 TT
Continuing in like fashion, we get the composite ratio shown above. We originally worked this starting from BS. Reducing the JB/TT ratio from 2/200 to 1/100 helped eliminate an extra factor of 2.
Step-by-step explanation:
it's not really a math problem per se, it is more like a regular riddle with numbers.
true, everything involving numbers is essentially math, but then what will you do in life with things like earning a salary, going shopping, checking a calendar and schedules for bus, train and flights or business meetings, sharing a pizza with friends, playing computer games, ...
life is for a big part numbers and therefore math.
so, don't be afraid, just use your brain and common sense !
let's think this through (just be strict, concentrated, and follow each line literally) :
5 fr. Band. means 5 tulgey woods.
which means 20×5 = 100 tumtum trees.
as there are 2 jubjub birds in 200 tumtum trees, that means that there is 1 jubjub bird in the given 100 tumtum trees.
as there are 5 jubjub birds in 1 slithy toves, but we have only 1 bird, that means we have only 1/5 slithy toves.
there are 5 slithy toves in 2 borogoves. that means 1 slithy toves in 2/5 borogoves. and 1/5 slithy toves in 2/5 / 5 = 2/25 borogoves.
there are 200 mome raths in each borogove. and we have 2/25 borogoves. that means we have
200 × 2/25 = 400/25 = 16 mome raths.
and there are 2 mome raths per jabberwocky. we have 16 raths. how many pairs of raths does that make ?
16/2 = 8 pairs of raths = jabberwocks.
so, there should be 8 jabberwocks.
you see ? that's all that was needed. this was like a labyrinth riddle, where you need to find the way from an inside starting point to the exit without crossing a line (or wall).
f(x) = x² + 3x, g(x) = 5x + 2, (f - g)(3) = ?
Answer:
1
Step-by-step explanation:
f(x) = x² + 3x
g(x) = 5x + 2
f(3) = 3² + 3 x 3
f(3) = 9 + 9
f(3) = 18
g(3) = 5(3) + 2
g(3) = 15 + 2
g(3) = 17
(f - g)(3) = 18 - 17
(f - g)(3) = 1.
Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x
I'll assume the ODE is
[tex]y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}[/tex]
Solve the homogeneous ODE,
[tex]y'' - 3y' + 2y = 0[/tex]
The characteristic equation
[tex]r^2 - 3r + 2 = (r - 1) (r - 2) = 0[/tex]
has roots at [tex]r=1[/tex] and [tex]r=2[/tex]. Then the characteristic solution is
[tex]y = C_1 e^x + C_2 e^{2x}[/tex]
For nonhomogeneous ODE (1),
[tex]y'' - 3y' + 2y = e^x[/tex]
consider the ansatz particular solution
[tex]y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x[/tex]
Substituting this into (1) gives
[tex]a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1[/tex]
For the nonhomogeneous ODE (2),
[tex]y'' - 3y' + 2y = e^{2x}[/tex]
take the ansatz
[tex]y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}[/tex]
Substitute (2) into the ODE to get
[tex]b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1[/tex]
Lastly, for the nonhomogeneous ODE (3)
[tex]y'' - 3y' + 2y = e^{-x}[/tex]
take the ansatz
[tex]y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}[/tex]
and solve for [tex]c[/tex].
[tex]ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16[/tex]
Then the general solution to the ODE is
[tex]\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}[/tex]
for each reasons it gives you the options to choose: commutative property of addition, associative property of addition, distributive property, and combining like terms
Answer:
associative
combining
commutative
Step-by-step explanation:
1. associative property of addition since the grouping is changed
2. combining like terms since it's the addition of 4 and 6
3. commutative property of addition since it's a change of order
4|a|+8-a if a=-2
ASAP GIVING BRAINLIEST PLEASE HELP!!
Answer: 18
Step-by-step explanation:
4 I-2I + (8+2)=
4(2) + 8+2=
8+8+2=
18
20 points and I will mark brainlyist to the first right answer.
Answer:
Step-by-step explanation:
Movie A: 267 students
Movie B: 217 students
Movie C: 233 students
Movie D: 183 students
A solid right pyramid has a regular hexagonal base with an area of 5.2 cm2 and a height of h cm. a solid right pyramid has a regular hexagonal base with an area of 5.2 centimeters squared and a height of h centimeters. which expression represents the volume of the pyramid?
The calculations show that this pyramid's volume is equivalent to:
5.2h/3 cm3.
What is a pyramid?A polyhedron constructed by joining a polygonal base and a point, is called a pyramid. A lateral face is a triangle formed by the base edge and vertex of each base. Conic solid with a polygonal basis describes it. The number of vertices, faces, and edges on a pyramid with an n-sided base is n + 1.
Given information:Base area = 5.2 [tex]cm^2[/tex].
Height in centimeters is equal to h.
How can the volume of a pyramid be calculated?The following formula is used to determine a pyramid's volume mathematically:
Base area divided by height equals one-third of the volume.
When we enter the parameters into the formula, we get;
Volume = 1/3 *5.2* h
Volume = 5.2h/3 [tex]cm^3.[/tex]
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I understand that the question you are looking for is :
A solid right pyramid has a regular hexagonal base with an area of 5. 2 cm2 and a height of h cm. a solid right pyramid has a regular hexagonal base with an area of 5. 2 centimeters squared and a height of h centimeters. which expression represents the volume of the pyramid? one-fifth(5. 2)h cm3 start fraction 1 over 5 h infraction(5. 2)h cm3 one-third(5. 2)h cm3 start fraction 1 over 3 h infraction(5. 2)h cm3
-5 ____ =2
please help me lol.
[tex] - 5 + x = 2 \\ add \: 5 \: to \: both \: sides \\ x = 2 + 5 = 7[/tex]
7 is your answer[tex] - 5 x =2 \\ x = -2/5[/tex]
Assuming you're multiplying:
Answer:
Step-by-step explanation:
Comment
The simple answer is you should put something equivalent to -2/5 in the blank. This is what will happen,
-5 * - 2/5
The 5's will cancel out. The minus sign that was in front of the 5 will become positive because 2 minuses make a plus.
Another way to do the problem is to call the ___ = x
-5 x = 2 Divide both sides by - 5
-5x/ -5 = 2/-5
x = - 2/5
It comes to the same thing.
A third way is just to multiply by - 0.4
-5 * -0.4 = 2
Brass is an alloy made by melting and mixing copper and zinc. A metallurgist has two brass
alloys, one that is 65% copper and one that is 90% copper. He would like to combine a
portion of each alloy to produce 500 g of a new alloy that is 75% copper.
Write a system of equations for this problem
Answer:
x +y = 5000.65x +0.95y = 0.75(500)solution: (x, y) = (300, 200)Step-by-step explanation:
A system of equations for the problem can be written using the two given relationships between quantities of brass alloys.
SetupLet x and y represent the quantities in grams of the 65% and 90% alloys used, respectively. There are two relations given in the problem statement.
x + y = 500 . . . . . . quantity of new alloy needed
0.65x +0.90y = 0.75(500) . . . . . quantity of copper in the new alloy
These are the desired system of equations.
SolutionThis problem does not ask for the solution, but it is easily found using substitution for x.
x = 500 -y
0.65(500 -y) +0.90y = 0.75(500)
(0.90 -0.65)y = 500(0.75 -0.65) . . . . . . subtract 0.65(500)
y = 500(0.10/0.25) = 200
x = 500 -200 = 300
300 grams of 65% copper and 200 grams of 90% copper are needed.
Diego wants to paint his room purple. He bought one gallon of purple paint that is 30% red paint and 70% blue paint. Diego wants to add more blue to the mix so that the paint mixture is 20% red, 80% blue.
1. How much blue paint should Diego add? Test the following possibilities: 0.2 gallons, 0.3 gallons, 0.4 gallons, 0.5 gallons.
0.2 gallons
0.2 gallons,
0.3 gallons
0.3 gallons,
0.4 gallons
0.4 gallons,
0.5 gallons
0.5 gallons,
BoldItalicUnderlineImage (12 image limit)Increase indentDecrease indentFormula keypadUndoRedoBullet listNumbered list
Edit imageView imageDelete image
2. Write an equation in which x
represents the amount of paint Diego should add.
3. Check that the amount of paint Diego should add is a solution to your equation.
idrk but I hope you have a good day and good luck with ur answer
help fast pls!
it doesn't have to be a long explanation i just need the answer and a lil blurb to know ur not lying tysm!!!
Answer:
c 0.5⁻ˣ
Step-by-step explanation:
The slowest rate is:
0.5⁻ˣ
Solve for x.
°x = 196
Enter your answers in the boxes. Enter the smallest answer first.
x= ____ and x= ____
4 andfirst find x by finding its smallest factor
The solution to the given system of equation is -7 and 7
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
Given:
4x² = 196
4x²/4= 196/4
x² = 49
x=√49
x= ±7
Hence, the solution to the given system of equation is -7 and 7
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Jaxon is training for a climbing competition.
He breaks his training up into strength and
endurance training in the ratio 5:3.
If he spends 4 hours on endurance training,
how long should he spend on strength training?
======================================================
Work Shown:
(x hours strength)/(4 hours endurance) = 5/3
x/4 = 5/3
3x = 4*5
3x = 20
x = 20/3
x = (18+2)/3
x = 18/3 + 2/3
x = 6 + 2/3
x = 6 & 2/3
He needs to spend 6 full hours, plus an additional 2/3 of an hour, on strength training.
1 hr = 60 min
2/3 hr = (2/3)*60 min
2/3 hr = 40 min
6 hr + 2/3 hr = 6 hr + 40 min
Therefore, he needs to spend 6 hours, 40 minutes on strength training.
This is equivalent to 6*60+40 = 360+40 = 400 minutes.
Kaitlin, Joe, and Miguel have a total 96 of in their wallets. Kaitlin has 6 less than Joe. Miguel has 4 times what Joe has. How much does each have?
Answer:
15, 11, 60
Step-by-step explanation:
Let Joe's amount be x
x + x - 6 + 4x = 96
6x - 6 = 96
6x = 90
x = 15
Joe has 15
Kaitlin has 11
Miguel has 60
In 4 weeks, Mark earns an average of $400 per
week. If, after working another 2 weeks at a
constalat salary, his average carnings per week
are $500, how much did he earn in the last 3
weeks?
Hundred chart: I am thinking of a number that is greater than 70 but less than 100.
It is not divisible by 10. It is not divisible by 4. It is not an odd number. What can I be
The numbers which is greater than 70 but less than 100, not divisible by 10, not divisible by 4, not an odd number are 74, 78, 82, 86, 94, 98
Even and odd numbersA number greater than 70 but less than 100Not divisible by 10Not divisible by 4Not odd numberA number greater than 70 but less than 100
71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 98
Not odd number
72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98
Not divisible by 10
72, 74, 76, 78, 82, 84, 86, 88, 92, 94, 96, 98
Not divisible by 4
74, 78, 82, 86, 94, 98
Therefore, the numbers which is greater than 70 but less than 100, not divisible by 10, not divisible by 4, not an odd number are 74, 78, 82, 86, 94, 98.
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Lamar is taking a stunt man training course. he scored a 99 on his first test, but he only scored an 85 on his second test. what is the lowest score that lamar can make on his third and final test in order to have an overal average of 90?
Answer:
86.
Step-by-step explanation:
His total score is 99 + 85 + x where x is score on third test,
99 + 85 + x = 3 *90 (as his average must be 90, so:
184 + x = 270
x = 270 - 184
= 86.
Answer:
86
Step-by-step explanation:
Let x be the required score for Lamar's third test in order to get an average of 90 or higher.
Start with the initial equation:
[tex]\frac{99+85+x}{3}\geq 90[/tex]
Simplify the numerator in the fraction:
[tex]\frac{184+x}{3}\geq90[/tex]
Multiply both sides by 3 to cancel out division on left side of equation:
[tex]184+x\geq 270[/tex]
Subtract 184 from both sides to isolate the x variable:
[tex]x\geq86[/tex]
Leaving us with x must be greater than or equal to 86.
4|a| + 8 -a, if a = -2
PLEASE HELP!!!!!!!!!!!!!! I'm stuck on this!!
4|a| + 8 - a, if a = -2
What we're doing here is plugging in the given value of a for every instance of a in the expression.
4|-2| + 8 - (-2)
---The absolute value of a number is its distance from 0. -2 is 2 units away from 0, so the absolute value of -2 is 2. And, remember two negatives make a positive!
4(2) + 8 + 2
8 + 8 + 2
16 + 2
18
Hope this helps!
One day, thirteen babies are born at a hospital. assuming each baby has an equal chance of being a boy or girl, what is the probability that at most eleven of the thirteen babies are girls?
Using the binomial distribution, there is a 0.9983 = 99.83% probability that at most eleven of the thirteen babies are girls.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are:
p = 0.5, n = 13
The probability that at most eleven of the thirteen babies are girls is:
[tex]P(X \leq 11) = 1 - P(X > 11)[/tex]
In which
P(X > 11) = P(X = 12) + P(X = 13)
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 12) = C_{13,12}.(0.5)^{12}.(0.5)^{1} = 0.0016[/tex]
[tex]P(X = 13) = C_{13,13}.(0.5)^{13}.(0.5)^{0} = 0.0001[/tex]
So:
P(X > 11) = P(X = 12) + P(X = 13) = 0.0016 + 0.0001 = 0.0017
[tex]P(X \leq 11) = 1 - P(X > 11) = 1 - 0.0017 = 0.9983[/tex]
0.9983 = 99.83% probability that at most eleven of the thirteen babies are girls.
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It is October and that means it is State Fair time again! Your uncle took you and 2 of your friends to the
fair. Admission for everyone to get into the fair was $20.00. You then went to the Midway, where they
have all of the rides, and he bout all-day ride passes for you and your friends. If your uncle spent a total
of $65.00 at the fair, how much did each of the all-day ride passes cost?
Answer: All-day ride passes cost $15 each
Step-by-step explanation:
It was $20 in total for everyone to get in, so subtract that from $65 to just focus on the all day passes
65-20=45
So the all day passes all together cost $45
Since your uncle bought it for you and 2 friends that's 3 people in total so divide 45 by 3
45 divided by 3 = 15
So each of the all day passes cost $15
Hope this helped :)
