Answer:
32760 ways
Step-by-step explanation:
Suppose we all want to play different games, so 4 different games. At the first game there are 15 choices, at the 2nd game there are 14, the 3rd one there are 13 selections, and at the last there are only 12 options to select from. Then the total number of ways you can choose the 4 games is
15*14*13*12 = 32760 ways
There are 1,365 ways to choose four games out of the 15 available games.
Step 1
To find the number of ways you can choose four games out of the 15 available games, we use the combination formula:
[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]
Where n is the total number of games (15) and k is the number of games to choose (4).
Step 2
Plugging in the values:
[tex]\[ C(15, 4) = \frac{15!}{4!(15-4)!} \][/tex]
[tex]\[ = \frac{15!}{4! \times 11!} \][/tex]
[tex]\[ = \frac{15 \times 14 \times 13 \times 12}{4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ = \frac{32,760}{24} \][/tex]
[tex]\[ = 1,365 \][/tex]
You can choose the four games out of the 15 available games in 1,365 ways, calculated using the combination formula.
A pure acid measuring x liters is added to 300 liters of a 20% acidic solution. The concentration of acid, f(x), in the new substance is equal to the liters of pure acid divided by the liters of the new substance, or f(x)=x+60/x+300. Which statement describes the meaning of the horizontal asymptote?
A The greater the amount of acid added to the new substance, the more rapid the increase in acid concentration.
B The greater the amount of acid added to the new substance, the closer the acid concentration is to one-fifth.
C As more pure acid is added, the concentration of acid approaches 0.
D As more pure acid is added, the concentration of acid approaches 1.
Final answer:
The horizontal asymptote indicates that as more pure acid is added, the concentration approaches 1, meaning the acid concentration trends towards 100% purity but never fully reaches it. (Option D)
Explanation:
The horizontal asymptote of the function f(x) = x + 60 / (x + 300) describes the behavior of the acid concentration as the volume of pure acid x becomes very large. When an increasingly larger volume of pure acid is added, the concentration of the acid in the new substance approaches a certain value. This implies that, no matter how much more acid is added past a certain point, the concentration doesn't change significantly.
The correct statement regarding the horizontal asymptote is: D. As more pure acid is added, the concentration of acid approaches 1. This means that the concentration of the acid will get closer and closer to 100%, or pure acid, but it will never actually reach that concentration because you are always adding the acid to some amount of solution.
which place is the tenths and what is it rounded to? please answer quick thx
Answer:
Step-by-step explanation:
see attached to identify which is the tenth's place
How you round the tenth's place depends on the digit in the hundredths place.
If the hundredths digit is less than 5, then you keep the tenths place the same (i.e round down)
If the hundredths digit is greater or equal than 5, then you increase the tenths place by 1 (i.e round up)
A chemist has a 30% and a 45% acid solution. What amount of each solution should be used to make 500ml of solution with 35% acidity?
A) 133
1
3
ml of 30% solution and 366
2
3
ml of 45% solution
B) 250 ml of each solution
C) 333
1
3
ml 30% solution and 166
2
3
ml of 45% solution
D) 400 ml of 30% solution and 100 ml of 45% solution
Answer:
The correct answer is 333 1/ 3 ml 30% solution and 166 2/ 3 ml of 45% solution.
step-by-step explanation:
Set up 2 equations. Let x be the 30% solution and y be the 45% solution. Then you have x + y =500 and .3x +.45y = .35*500. Then solve the system.
Answer:
A is your correct answer.
Step-by-step explanation:
A science class starts an experiment with 3 plants that are each 2.5 cm tall. They provide all of the needs of the plant and
track their growth. Plant A was 23.5 cm tall after two weeks. What was the average rate
of change in inches per day of Plant A?
Answer 67
Step-by-step explanation:65:&:8/&/&&:
Average rate of change in height will be 0.59 inch per day.
Linear equations and their applications,Linear equation consist of one or two variables with highest degree as 1.Experiment with plants started with,
3 plants of 2.5 cm height.Plant A was 23.5 cm tall after 2 weeks.Let the variable defining change in the height per day of the plant = x
Change in the height of plant A after 2 weeks or 14 days = 14x cm
Height of the plant A initially = 2.5 cm
Height of the plant after 2 weeks = 14x + 2.5
If height of the plant A after 2 weeks = y
Linear equation defining the height of the plant after 2 weeks will be,
y = 14x + 2.5
Plant A is 23.5 cm tall after 2 weeks,
23.5 = 14x + 2.5 [Substitution of y = 23.5]
23.5 - 2.5 = 14x + 2.5 - 2.5
21 = 14x
x = 1.5 cm
Since, 1 cm = 0.393701 inches
Therefore, 1.5 cm = 1.5 × 0.393701
= 0.591
≈ 0.59 inches per day
Hence, average rate of change in the height of plant A will be 0.59 inches per day.
Learn more about the linear equations here,
https://brainly.com/question/6873725?referrer=searchResults
The acces code to a house's security system consists of six digits. How many different codes are available each digit can be repeated?
In Mathematics, if a six-digit code can have each digit repeat there are 10 options (0-9) for each position. Having six positions, we multiply the possibilities together, leading us to a conclusion of 1,000,000 possible codes.
Explanation:The calculation of different codes for a house's security system is a problem of permutation and combination under the field of Mathematics. The code consists of six digits and each digit can be repeated, meaning that there are 10 possibilities (0-9) for each of the 6 positions in the code.
Therefore, for each of the six positions in the code, there are 10 possibilities. To determine the total number of possible codes, we would multiply the number of possibilities for each digit together: 10*10*10*10*10*10 = 1,000,000. So, there are one million possible combinations for the 6-digit code.
Learn more about Combinations here:https://brainly.com/question/39347572
#SPJ12
A farm has 28 chickens, 12 cows and 6 horses. What is the ratio of horses to total animals? Write your answer as a simplified ratio.
Answer:
3/23
Step-by-step explanation:
Numbers of horses : 6
Number of total animals in farm : 28 + 12 + 6 = 46
The ratio of horses to toral animals : 6/46 ➡ simplified 3/23
Given Z11 ~= Z13
Which lines, if any, must be parallel based on the given information? Justify your conclusion.
A) c || d, converse of the alternate exterior angles theorem.
B) a || b, converse of the corresponding angles theorem
C) c || d, converse of the same-side interior angles theorem.
D) Not enough information to make a conclusion.
Answer:
Line c ║ line d, applying the converse of the alternate exterior angles theorem.
Step-by-step explanation:
See the given diagram attached.
It is given that ∠ 11 = ∠ 13.
Hence, from this we can conclude that line c ║ line d, applying the converse of the alternate exterior angles theorem.
The alternate exterior angle theorem says that if one line is the transverse line of any two other parallel lines then the alternate exterior angles so generated will be equal. (Answer)
Answer:
c∥d, Converse of the Alternate Exterior Angles Theorem
Step-by-step explanation:
I took the test other answer is right
zen the
20,1.
A water tank is being filled by pumps at a constant rate. The volume of water in the tank V, in gallons, is
given by the equation:
v(t) = 65t + 280, where t is the time, in minutes, the pump has been on
(a) At what rate, in gallons per minute, is the (b) How many gallons of water were in the tank
water being pumped into the tank?
when the pumps were turned on?
Ult=65 1280
v101=6510) +250=280
rate is 65
wakers of gallon
tank had 280 gallons.
(c) What is the volume in the tank after two hours (d) The pumps will turn off when the volume in
of the pumps running?
the tank hits 10,000 gallons. To the nearest
minute, after how long does this happen?
edict
Answer:
(a) 65 gallons per minute
(b) 280 gallons
(c) 8080 gallons
(d) 150 minutes.
Step-by-step explanation:
Water is filled up by pumps into a tank at a constant rate.
The volume of water in the tank V, in gallons, is given by the equation
V(t) = 65t + 280 ......... (1), where t is the time, in minutes.
(a) The rate at which water is pumped into the tank is 65 gallons per minute. (Answer)
(b) 280 gallons of water was there in the tank when the pumps were turned on because f(0) = 65 × 0 + 280 = 280. (Answer)
(c) After 2 hours i.e. (2 × 60) = 120 minutes the volume of water in the tank will be f(120) = 65 × 120 + 280 = 8080 gallons. (Answer)
(d) The tank has a capacity of 10000 gallons of water.
So, if the tank starts to overflow after t minutes, then
10000 = 65t + 280
⇒ 65t = 9720
⇒ t = 149.53 minutes ≈ 150 minutes (Answer)
Final answer:
The rate at which water is being pumped into the tank is 65 gallons per minute, the tank initially had 280 gallons of water, after two hours the volume will be 8,080 gallons, and the pumps will turn off after approximately 150 minutes when the volume reaches 10,000 gallons.
Explanation:
The water tank problem can be analyzed step by step based on the given linear equation v(t) = 65t + 280, which describes the volume V of water in gallons as a function of time t in minutes.
(a) Rate of Water Being Pumped
The coefficient of t in the equation represents the rate at which water is being pumped into the tank. Therefore, the water is being pumped at a constant rate of 65 gallons per minute.
(b) Initial Volume of Water
The constant term in the equation, 280, represents the volume of water that was in the tank when the pumps were turned on. This means the tank initially had 280 gallons of water.
(c) Volume After Two Hours
To convert two hours to minutes, we multiply by 60 minutes per hour, giving us 120 minutes. Plugging this value into the equation gives us v(120) = 65(120) + 280 = 7,800 + 280 = 8,080 gallons. So, after two hours, the volume of water in the tank would be 8,080 gallons.
(d) Time to Reach 10,000 Gallons
To find the time when the volume reaches 10,000 gallons, we set the equation equal to 10,000 and solve for t: 10,000 = 65t + 280. Subtracting 280 from both sides gives us 9,720 = 65t, and dividing both sides by 65 gives us t ≈ 149.54 minutes. To the nearest minute, the pumps will turn off after approximately 150 minutes.
2 coins and 1 6 sided number cube. What is the probability of getting two heads and a 4?
Answer:
1/24 ≈ 4.2%
Step-by-step explanation:
P(head) = 1/2
P(4) = 1/6
P(2 heads and 4) = (1/2)² (1/6) = 1/24 ≈ 4.2%.
(PLEASE HELP) Which rules represent a transformation that maps one shape onto another to establish their congruence? Select all of the possible answers.
A) A dilation by scale factor of 3 about the origin.
B) A translation to the right 2 and down 6.
C) A reflection across the line y=2.
D) A counter-closckwise rotation of 90 degrees about the origin.
E) A horizontal stretch by a factor of 2 about the origin.
The possible transformations that establish congruence between shapes are dilation, translation, and reflection.
Explanation:The possible rules that represent a transformation mapping one shape onto another to establish congruence are:
A) A dilation by a scale factor of 3 about the origin.B) A translation to the right 2 and down 6.C) A reflection across the line y=2.A dilation by a scale factor of 3 about the origin stretches or shrinks the shape uniformly in all directions. A translation moves the shape without changing its size or shape. A reflection across a line is a flip of the shape over that line. These transformations can establish congruence between shapes.
Transformations that establish congruence between shapes by preserving size, shape, and orientation ensure that the transformed shape aligns with the original shape. The correct answer is option
B) A translation to the right 2 and down 6.
C) A reflection across the line y=2.
D) A counter-closckwise rotation of 90 degrees about the origin.
The rules that represent transformations mapping one shape onto another to establish congruence are:
B) A translation to the right 2 and down 6, which preserves both size and shape, simply moving the shape to a different location without changing its orientation or proportions.
C) A reflection across the line y=2, which reflects the shape across a line, maintaining its size and shape but reversing its orientation.
D) A counter-clockwise rotation of 90 degrees about the origin, which rotates the shape by a right angle, preserving its size and shape while changing its orientation.
These transformations preserve congruence by maintaining the size, shape, and orientation of the original shape.
Options B, C, and D represent transformations that map one shape onto another to establish their congruence, preserving size, shape, and orientation.
if the store design allows for 43 feet for each row how many total carts fit in a row?
The question lacks enough information to provide a definitive answer. If we know the width of a cart, we can divide 43 by the cart width to find out how many carts fit in a row.
Explanation:Unfortunately, we can't definitively answer this question as it doesn't specify the width of each cart. The number of carts that fit in a row greatly depends on the width of each cart. To calculate this, you would need to divide the total row width (43 feet) by the width of each individual cart. For example, if each cart was assumed to be 1 foot wide, then a total of 43 carts would fit in a row. However, if each cart was assumed to be 2 feet wide, then only 21 carts (with 1 foot left over) would fit in a row.
Learn more about Mathematical Division here:https://brainly.com/question/32582499
#SPJ11
use the identity below to complete the tasks a^3-b^3=(a-b)(a^2+ab+b^2) when using the identity for the difference of two cubes to factor 64x^6-27
Answer:
see explanation
Step-by-step explanation:
Given that the the difference of cubes is
a³ - b³ = (a - b)(a² + ab + b²)
Given
64[tex]x^{6}[/tex] - 27 ← a difference of cubes
with a = 4x² and b = 3, thus
= (4x²)³ - 3³
= (4x² - 3)(16[tex]x^{4}[/tex] + 12x² + 9) ← in factored form
The required expression (4x^2-3)(16x^4+12x^2+9).
To evaluate 64x^6-27 as a^3-b^3=(a-b)(a^2+ab+b^2).
What is identity?Cubic identity is given as [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex].
Here,
=64x^6-27
=(4x^2)^3-3^3
Such that, a =4x^2 and b = 3.
Put a and b in [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex].
[tex](4x^2)^3-3^3=(4x^2-3)(16x^4+12x^2+9).[/tex]
Thus, the required expression (4x^2-3)(16x^4+12x^2+9).
Learn more about identity here:
https://brainly.com/question/9704094
#SPJ2
PLEASE SHOW YOUR WORK I NEED THIS ASAP. thanks
Mrs. Bailey had 12 pieces of candy. She gave away some candy and has 3 pieces left. What is the percent decrease of candy?
Answer:75%
Step-by-step explanation:im sorry I can't get it out in words but you have the answer
Determine if the ordered pair (6, 4) is a solution to the inequality y is greater than negative one half times x plus 7. Yes, because (6, 4) is above the line No, because (6, 4) is below the line Yes, because (6, 4) is on the line No, because (6, 4) is on the line
Answer:
(6,4) is not a solution of y > -x/2 + 7 because (6,4) is on the line
The answer is D.
Hope this helps!
Answer:
No,because (6,4) is on the line.
Step-by-step explanation:
We are given that an inequality equation
[tex]y>-\frac{1}{2}x+7[/tex]
We have to find that the ordered pair (6,4) is a solution of given inequality or not.
[tex]y>-\frac{x}{2}+7[/tex]
Substitute x=6
[tex]y>-\frac{6}{2}+7[/tex]
[tex]y>-3+7[/tex]
[tex]y>4[/tex]
The value of y is greater than 4 not equal to 4.
Therefore, (6,4) is not a solution of given inequality.
No,because (6,4) is on the line.
If Logx (1 / 8) = - 3 / 2, then x is equal to
Answer:
Let's solve!
Step-by-step explanation:
[tex]logx^{\frac{1}{8} } = -\frac{3}{2}[/tex]
[tex]then[/tex]
[tex]10^{-\frac{3}{2}} = x^{\frac{1}{8} }[/tex]
[tex](10^{-\frac{3}{2} })^{8} = (x^{\frac{1}{8} })^{8}[/tex]
[tex]x = 10^{3*4} = 10^{-12}[/tex]
[tex]x= 10^{-12}[/tex]
If the equation looks like this, then it has the solution
[tex]x= 10^{-12}[/tex]
Another answer is
√x = 2 or x = 4
I hope this helps!
For more help:
https://brainly.com/question/9719370
https://brainly.com/question/7126917
https://brainly.com/question/3505855
How do you evaluate 9√9
Answer:
27
Step-by-step explanation:
square root of 9 is 3, so you multiply 3 by 9.
Answer:
27
Step-by-step explanation:
the Expression 4x^2-p(x)+7 leaves a remainder of -2 when divided by (x-3) find the value of p
A) 11
B)-2
C)15
D)40
Answer:
(c) For p = 15, [tex]4x^2-p(x)+7[/tex] leaves a remainder of -2 when divided by (x-3).
Step-by-step explanation:
Here, The dividend expression is [tex]4x^2-p(x)+7[/tex] = E(x)
The Divisor = (x-3)
Remainder = -2
Now, by REMAINDER THEOREM:
Dividend = (Divisor x Quotient) + Remainder
If ( x -3 ) divides the given polynomial with a remainder -2.
⇒ x = 3 is a solution of given polynomial E(x) - (-2) =
[tex]E(x) - (-2) = 4x^2-p(x)+7 -(-2) = 4x^2-p(x)+9[/tex] = S(x)
Now, S(3) = 0
⇒[tex]4x^2-p(x)+9 = 4(3)^2 - p(3) + 9 = 0\\\implies 36 - 3p + 9 = 0\\\implies 45= 3p , \\or p =15[/tex]
or, p =1 5
Hence, for p = 15, [tex]4x^2-p(x)+7[/tex] leaves a remainder of -2 when divided by (x-3).
Choose all which define events A and B as independent events.
P(A) = 0.6, P(B) = 0.4, P(A&B) = 0.24
P(A) = 0.3, P(B) = 0.4, P(A&B) = 0.70
P(A) = 0.5, P(B) = 0.1, P(A&B) = 0.60
P(A) = 0.3, P(B) = 0.2, P(A&B) = 0.06
There are 2 answers: Choice 1, Choice 4
=======================================
Why is this? Because we use the rule
P(A & B) = P(A) * P(B)
which only works if events A and B are independent
----
For the first answer choice,
P(A) * P(B) = 0.6*0.4 = 0.24 = P(A & B)
so that matches.
The same applies to the fourth answer choice as well
P(A) * P(B) = 0.3*0.2= 0.06 = P(A & B)
----
The other answer choices don't match up.
The second answer choice has
P(A) * P(B) = 0.3*0.4 = 0.12 but that doesn't match with the 0.70 given
Similarly for the third answer choice,
P(A) * P(B) = 0.5*0.1 = 0.05 which doesn't match with the 0.60
Answer:
Yes
Step-by-step explanation:
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n= 15, p=0.8, x = 12
P(12) =
(Do not round until the final answer. Then round to four decimal places as needed.)
Answer:
The probability of getting 12 successes out of 15 trials is [tex]P(12) = 0.2501[/tex].
Step-by-step explanation:
Given:
The probability distribution is binomial distribution.
Number of trials are, [tex]n=15[/tex]
Number of successes are, [tex]x=12[/tex]
Probability of success is, [tex]p=0.8[/tex]
Therefore, probability of failure is, [tex]q=1-p=1-0.8=0.2[/tex]
Now, probability of getting 12 successes out of 15 trials is given as:
[tex]P(X=x)=_{x}^{n}\textrm{C}p^{x}q^{n-x}\\P(12)=_{12}^{15}\textrm{C}(0.8)^{12}(0.2)^{15-12}\\P(12)=455\times 0.8^{12}\times 0.2^{3}\\P(12)=0.2501[/tex]
Therefore, the probability of getting 12 successes out of 15 trials is 0.2501.
Applying the binomial distribution, we get that P(X = 12) = 0.2501.
-------------------------
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, given by:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, defined by the formula below.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Considering that p is the probability of a success on a single trial.
For this problem, the parameters are [tex]n = 15, p = 0.8[/tex], and we want to find P(X = 12). Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 12) = C_{15,12}.(0.8)^{12}.(0.2)^{3} = 0.2501[/tex]
Thus P(X = 12) = 0.2501.
A similar problem is given at https://brainly.com/question/15557838
What is the quotient StartFraction 15 p Superscript negative 4 Baseline q Superscript negative 6 Baseline Over negative 20 p Superscript negative 12 Baseline q Superscript negative 3 Baseline EndFraction in simplified form? Assume p not-equals 0, q not-equals 0.
answer
Negative StartFraction 3 p Superscript 8 Baseline Over 4 q cubed EndFraction
Negative StartFraction 3 Over 4 p Superscript 16 Baseline q Superscript 9 Baseline EndFraction
Negative StartFraction p Superscript 8 Baseline Over 5 q cubed EndFraction
Negative StartFraction 1 Over 5 p Superscript 16 Baseline q Superscript 9 Baseline EndFraction
Answer:
Answer is A (-3p^8/4q^3)
Step-by-step explanation:
We want to simplify a fraction. The simplification is:
[tex]\frac{15*p^{-4}q^{-6}}{-20*p^{-12}*q^{-3}} = \frac{-3*p^8}{4*q^3}[/tex]
So we start with the fraction:
[tex]\frac{15*p^{-4}q^{-6}}{-20*p^{-12}*q^{-3}}[/tex]
Where:
p ≠ 0.q ≠ 0.Now, remember the rule:
[tex]\frac{x^n}{x^m} = x^{n - m}[/tex]
Then we can rewrite:
[tex]\frac{15*p^{-4}*q^{-6}}{-20*p^{-12}*q^{-3}} = \frac{15}{-20}*\frac{p^{-4}}{p^{-12}}*\frac{q^{-6}}{q^{-3}} \\\\= -\frac{-3}{4}*p^{-4 - (-12)}*q^{-6 - (-3)}\\\\= -\frac{-3}{4}*p^{8}*q^{-3}\\\\= \frac{-3*p^8}{4*q^3}[/tex]
And we can't keep simplifying this, so this is the correct answer.
If you want to learn more, you can read:
https://brainly.com/question/2468151
A community theater sold a total of 400 for price tickets for adults and children the price was $8.00 per adult to get in $5.00 per children’s ticket and the total revenue was $2750 how many adult tickets and how many Childers tickets were sold
Answer:
Number of children's tickets sold = 150
Number of adult's tickets sold = 250
Step-by-step explanation:
The total number of tickets sold = 400
Let us assume the number of children's tickets = m
So, the number of adult's ticket's sold = 400 - m
Here, the cost of 1 movie ticket for adult = $8.00
So, the cost of (400 -m) adult tickets = (400 - m) ( Cost of 1 adult ticket)
= (400 - m) ($8) = 3200 - 8 m
The cost of each ticket for child = $5.00
The cost of m children tickets = m ( Cost of 1 children ticket)
= m($5) = 5 m
Now, total cost of tickets = Money spend on (Adult's + children's) Ticket
⇒ 2750 = (3200 - 8 m) + (5 m)
or, 2750 - 3200 = -8 m + 5 m
or, -450 = -3 m
or, m = 450/3 = 150
or, m = 150
Hence, the number of children's tickets = m = 150
The number of adult's tickets sold = 400 - m = 400 -150 = 250
GIVING BRAINLEST!!!Joe and Tim observed two points, P and Q, on a number line. A number line is shown from negative 1 to positive 1 with increments of 1 over 8. The numbers negative 1, negative 6 over 8, negative 4 over 8, negative 2 over 8, 0, 2 over 8, 4 over 8, 6 over 8 are labeled on the number line. A point P is shown to the third place on the left of 0, and a point Q is shown to the third place on the right of 0. Joe said that the absolute values of the numbers represented by the two points are different. Tim said that the absolute values of the numbers represented by the two points are the same. Which of the following explains who is correct?
Answer:
Step-by-step explanation:
P is 5 ticks to the left of 0, so it would be -5/8
Q is 5 ticks to the right of 0, so it would be at 5/8
an absolute value turns a negative number into a positive number
so absolute value of P located at -5/8 = 5/8
this is the location of point Q
Joe said that the absolute values of the numbers represented by the two points are the same.
Answer:
Tim, because each point is fraction 3 over 8 units away from 0.
Step-by-step explanation:
That is how absolute value works.
how do i simplify 5 √640
Tommy has a lawn service. He earns $25 for every lawn he mows. Which of the following represents the rate of change of his income with respect to the number of lawns he mows?
Answer:
250 239 439for lawns he mods $25
what is 1 + 2(4x + 1)
1 + 2(4x + 1)
mutiply the bracket by 2
(2)(4x)= 8x
(2)(1)= 2
1+8x+2
1+2+8x ( rearranging)
answer:
3+8x or 8x+3
Answer:
8x+3
Step-by-step explanation:
1+8x+2
1+2=3
8x+3 or 3+8x
Find the domain of the following expressions:
Answer:
Part 1) The domain is the interval (-∞,-7) ∪ (-7,0) ∪ (0,∞)
Part 2) The domain is the interval (-∞,0) ∪ (0,2) (2,∞)
Part 3) The domain is the interval (-∞,-6) ∪ (-6,6) ∪ (6,∞)
Step-by-step explanation:
Part 1) we have
[tex]\frac{32}{y}-\frac{y+1}{y+7}[/tex]
we know that
The denominator cannot be equal to zero
so
The value of y cannot be equal to 0 or cannot be equal to -7
The domain for y is all real numbers except the number -7 and the number 0
The domain in interval notation is
(-∞,-7) ∪ (-7,0) ∪ (0,∞)
Part 2) we have
[tex]\frac{y^2+1}{y^2-2y}[/tex]
we know that
The denominator cannot be equal to zero
[tex]y^2-2y=0\\y^2=2y\\y=2[/tex]
so
The value of y cannot be equal to 0 or 2
The domain for y is all real numbers except the number 0 and 2
The domain in interval notation is
(-∞,0) ∪ (0,2) (2,∞)
Part 3) we have
[tex]\frac{y}{y-6}+\frac{15}{y+6}[/tex]
we know that
The denominator cannot be equal to zero
so
The value of y cannot be equal to 6 or cannot be equal to -6
The domain for y is all real numbers except the number -6 and the number 6
The domain in interval notation is
(-∞,-6) ∪ (-6,6) ∪ (6,∞)
two kinds of tickets to an outdoor concert were sold: lawn tickets and seat tickets. fewer than 400 tickets in total were sold.
solve:
a. write an inequality to describe the constraints. specify what each variable represents.
b. use graphing technology to graph the inequality. sketch the region on the coordinate plane.
c. name one solution to the inequality and explain what it represents in that situation.
d. answer the question about the situation: if you know that exactly 100 lawn tickets were sold, what can you say about the number of seat tickets?
Answer:
Part a) [tex]x+y < 400[/tex]
Part b) The graph in the attached figure
Part c) see the explanation
Part d) The number of seat tickets sold must be less than 300 tickets
Step-by-step explanation:
Part a) write an inequality to describe the constraints. specify what each variable represents
Let
x ----> number of lawn tickets sold
y ----> number of seat tickets sold
we know that
The sum of the number of lawn tickets sold plus the number of seat tickets sold must be less than 400 tickets
so
The linear inequality that represent this situation is
[tex]x+y < 400[/tex]
Part b) use graphing technology to graph the inequality. sketch the region on the coordinate plane
we have
[tex]x+y < 400[/tex]
using a graphing tool
The solution is the triangular shaded area of positive integers (whole numbers) of x and y
see the attached figure
Remember that the values of x and y cannot be a negative number
Part c) name one solution to the inequality and explain what it represents in that situation
we know that
If a ordered pair lie on the solution of the inequality, then the ordered pair is a solution of the inequality (the ordered pair must satisfy the inequality)
I take the point (200,100)
The point (200,100) lie on the triangular shaded area of the solution
Verify
Substitute the value of x and the value of y in the inequality and compare the result
For x=200,y=100
[tex]x+y < 400[/tex]
[tex]200+100 < 400[/tex]
[tex]300 < 400[/tex] --> is true
so
The ordered pair satisfy the inequality
therefore
The ordered pair is a solution of the inequality
That means ----> The number of lawn tickets sold was 200 and the number of seat tickets sold was 100
Part d) if you know that exactly 100 lawn tickets were sold, what can you say about the number of seat tickets?
we have that
x=100
substitute in the inequality
[tex]100+y < 400[/tex]
solve for y
subtract 100 both sides
[tex]y < 400-100[/tex]
[tex]y < 300[/tex]
therefore
The number of seat tickets sold must be less than 300 tickets
Find the product. Input your answer,
3 x7/8
Answer:
21/8
Step-by-step explanation:
3(7/8)=21/8
To multiply a whole number by a fraction, you have to change the whole number (the 3) into a fraction. To do this, simply put the 3 over 1.
3/1 x 7/8. Multiplying fractions is so easy because all you have to do is multiply the numerators together and then the denominators together.
3x7=21
1x8=8
21/8
This fraction cannot be reduced, but it can be rewritten as a mixed number.
21 divided by 8 is 2 with a remainder of 5.
The answer is 21/8 or 2 5/8. (they mean the same thing)
I’m stuck on how to do these for Geometry.
Answer:
[tex]67\dfrac{1}{2}[/tex] sq, units.
Step-by-step explanation:
See the diagram of the parallelogram with given dimensions.
We know, the area of a parallelogram = Length of any side × Perpendicular distance of this side from the opposite parallel side.
Here, it is given that the length of a pair of parallel sides is 9 units and the perpendicular distance between those parallel lines is 7.5 units.
Therefore, the area of the parallelogram is (9 × 7.5) = 67.5 square units. (Answer)
Hence, in fraction the area can be expressed as [tex]67\dfrac{1}{2}[/tex] sq, units. (Answer)
Alex owes his father $100. His father pays him $12.50 an hour to work at their family store. The function d=100-12.5h represents the amount of debt d Alex has. How many hours will it take him to pay off his debt?
8 Hours.
If you want his debt to be 0, as in he has nothing left to owe, we will set d (his debt) to 0
0 = 100 - 12.5h
Subtract 100 to move it to the other side
-100 = -12.5h
Divide each side by -12.5
8 = h