Answer:
She spent = 11560 pesos
Amount left = 840 pesos
Step-by-step explanation:
Mrs. Alcántara makes a purchase at the fortuna supermarket, she only has 12,400 pesos, she buys several items and her purchase is equivalent to 13,600 pesos. How much do you have to pay if they give you a 15% discount? How many was left of what he had in cash?
Amount she has = 12400pesos
Item purchased = 13600 pesos
discount = 15 %
So, the total discount on the item purchased is
= 15 % of 13600
= 0.15 x 13600
= 2040 pesos
So, the amount spent = 13600 - 2040 = 11560 pesos
Amount she left = 12400 - 11560 = 840 pesos
Find the inverse of the given function. (pictured below)
Answer:
4
3
0
Step-by-step explanation:
f(x) = y = -1/2 × sqrt(x+3)
2y = -sqrt(x+3)
4y² = x + 3
x = 4y² - 3
now renaming this, so that the normal symbols and names are used for this function definition, so that the input variable is called "x" :
f-1(x) = 4x² - 3
basically, just by itself, this function would be defined for all possible real values of x.
but because it is the inverse of the original function, which generates only values of y<=0, then for the inverse function that same range applies for its input variable x
x<=0
A student selecting 3 classes for Winter quarter there are 4 drawing and design courses 3 general education courses and 3 other majors that can fit in their schedule it said student is only taking one course from each category determine the number of possible class schedules
Answer:
36 possible class schedules
Step-by-step explanation:
1st - 4 ways
2nd - 3 ways
3rd - 3 ways
4 x 3 x 3 = 36 possible class schedules
The number of possible class schedules is 36.
What is a permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.
Given:
A student selecting 3 classes for Winter quarter.
There are 4 drawing and design courses, 3 general education courses and 3 other majors that can fit in their schedule,
it said student is only taking one course from each category.
The possible class schedules,
= 4 x 3 x 3
= 36 possible ways.
Therefore, there are 36 possible ways.
To learn more about the permutation;
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You want to make a playlist with all different songs. How many ways can you make a playlist of 16 songs if you must play Leavon, Dream on, Here Comes the Sun, and Clocks in that order?
Answer in permutations
Answer: [tex]_{13} P _{13}[/tex]
Another acceptable answer is 13! where the exclamation mark is needed.
The numeric form is 6,227,020,800 which is a little over 6 billion.
==============================================================
Explanation:
Let's lump those four songs together to form a so called "mega song". So we treat those four items as one single item. This is ensure that those songs are played in the order we want. The other songs aren't treated this way.
We start with 16 songs and drop to 16-4 = 12 songs when taking out those four named songs. Then we add 1 to get 12+1 = 13 since we're adding in that "mega song" block.
---------------------------
So to recap so far, we've gone from 16 songs to 13 songs. The goal is to find out how many arrangements of 13 songs are possible. Order matters.
We'll use the nPr permutation function
[tex]_{n} P _{r} = \frac{n!}{(n-r)!}\\\\[/tex]
where in this case n = 13 and r = 13. Your teacher doesn't want you to evaluate this function. You simply need to state the symbolic form. So that's why we go from [tex]_{n} P _{r}[/tex] to [tex]_{13} P _{13}[/tex]
If you wanted to answer this in terms of factorial notation, then you could say this
[tex]_{n} P _{r} = \frac{n!}{(n-r)!}\\\\_{13} P _{13} = \frac{13!}{(13-13)!}\\\\_{13} P _{13} = \frac{13!}{(0)!}\\\\_{13} P _{13} = \frac{13!}{1}\\\\_{13} P _{13} = 13!\\\\[/tex]
So we can see that the notations [tex]_{13} P _{13}[/tex] and [tex]13![/tex] mean the exact same thing.
If you wanted to know the actual number of permutations, then,
13! = 13*12*11*10*9*8*7*6*5*4*3*2*1 = 6,227,020,800
which is a little over 6 billion permutations.
How many boxes could you stack safely on a pallet if the pallet is 5 feet deep, five feet across, every box. is 1 x 1 and the maximum safe stacking height is 5 boxes? *
Answer:
25 boxes could be stacked safely on the pallet.
Step-by-step explanation:
To determine how many boxes could you stack safely on a pallet if the pallet is 5 feet deep, five feet across, every box is 1 x 1 and the maximum safe stacking height is 5 boxes, the following calculation should be performed:
Pallet = 5 x 5 = 25 square feet
Box = 1 x 1 = 1 square foot
25/1 = 25
Therefore, 25 boxes could be stacked safely on the pallet.
(a) What is the probability that a person who was polled prefers chocolate ice cream to vanilla? Round your answer to four decimal places.
Answer:
[tex]P(k)=0.2628[/tex]
Step-by-step explanation:
Given
[tex]n = 1693[/tex] --- sample size
[tex]k = 445[/tex] --- those that prefer chocolate ice cream to vanilla
Required
[tex]P(k)[/tex]
This is calculated as:
[tex]P(k)=\frac{k}{n}[/tex] --- probability formula
So, we have:
[tex]P(k)=\frac{445}{1693}[/tex]
[tex]P(k)=0.2628[/tex]
Х/10 is between 1/5
and 0.6. What could the value of x be?
Answer:
2 < x < 6
Step-by-step explanation:
x/10
1/5 = 2/10
.6 = 6/10
2 < x < 6
???????????????????????????
Answer:
y-(-20)=1(x-(-10))
Step-by-step explanation:
If you're really in college you should know this, but here's the explanation:
m= -9-(-20)
1-(-10)
= 11
11
m = 1
The equation is y-y^1=m(x-x^1)
Replace the y^1, m, and x^1 from the first point
You get y-(-20)=1(x-(-10))
Or simplify that into y+20=x+10
You can also simplify it more but I don't think you need that for that question
If three sandwiches and two bags of chips cost
$22.00, and two sandwiches and one bag of chips
cost $14.25, how much does a bag of chips cost?
Answer:
Chips: 1.25 and Sandwiches: 6.5
Step-by-step explanation:
3s+2c=22
2s+c=14.25
The cost of bag and chips should be 1.25 and 6.5.
The calculation is as follows:3s+2c=22
2s+c=14.25
Here we need to multiply by 2 in equation 2
3s + 2c = 22
2s + 2c = 28.25
s = 6.5
Now
c should be
2(6.5) + c = 14.25
13 + c = 14.25
c = 1.25
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A guide wire of length 108 meters runs from the top of an antenna to the ground. If the angle of elevation to the top of the antenna is 42.3 degrees, then what is the height of the antenna
Answer: Approximately 72.69 meters
Step-by-step explanation:
Antenna height = h[tex]sin(42.3)=\frac{opposite}{hypotenuse} =\frac{h}{108} \\\\108*sin(42.3)=h\\\\h=72.685[/tex]
The height of the antenna by using the Pythagoras theorem is 72.68 meters.
What is trigonometry?"Trigonometry is one of the branches of mathematics that deals with the relationship between the sides of a triangle (right triangle) with its angles".
For the given situation,
Length of guidewire = 108 meters
Angle of elevation = 42.3 degrees
Height of the antenna be 'h'.
By Pythagoras theorem,
[tex]Sine[/tex] θ = [tex]\frac{Perpendicular}{hypotenuse}[/tex]
On substituting the above values,
⇒ [tex]Sine 42.3 = \frac{h}{108}[/tex]
⇒ [tex]0.6730 =\frac{h}{108}[/tex]
⇒ [tex]h=0.6730[/tex] × [tex]108[/tex]
⇒ [tex]h= 72.68[/tex]
Hence we can conclude that the height of the antenna is 72.68 meters.
Learn more about trigonometry here
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Solve this equation log3X + log3(x-6) = log3 7
Hello!
log₃(x) + log₃(x - 6) = log₃(7) <=>
<=> log₃(x * (x - 6)) = log₃(7) <=>
<=> log₃(x² - 6x) = log₃(7) <=>
<=> x² - 6x = 7 <=>
<=> x² - 6x - 7 = 0 <=>
<=> x² + x - 7x - 7 = 0 <=>
<=> x * (x + 1) - 7 * (x + 1) = 0 <=>
<=> (x + 1) * (x - 7) = 0 <=>
<=> x + 1 = 0 and x - 7 = 0 <=>
<=> x = -1 and x = 7, x ∈ { 6; +∞ } <=>
<=> x = 7
Good luck! :)
A regression analysis between sales (in $1000s) and price (in dollars) resulted in the following equation: ŷ = 50,000 − 8x The above equation implies that an increase of _____. a. $8 in price is associated with an increase of $8,000 in sales b. $1 in price is associated with a decrease of $8,000 in sales c. $1 in price is associated with a decrease of $42,000 in sales d. $1 in price is associated with a decrease of $8 in sales
Answer:
b. $1 in price is associated with a decrease of $8,000 in sales
Step-by-step explanation:
Linear function:
A linear function has the following format:
[tex]y = mx + b[/tex]
In which m is the slope, which represents by how much y changes when x changes by 1.
ŷ = 50,000 − 8x
This means that [tex]m = -8[/tex], in thousands of dollars, so when the price x increases by 1, the sales will be decrease by $8,000, and thus, the correct answer is given by option b.
The equation implies that an increase (b) $1 in price is associated with a decrease of $8,000 in sales
The regression equation is given as:
[tex]\^y= 50000 - 8\^x[/tex]
A linear regression equation is represented as:
[tex]\^y= b_o+ b_1\^x[/tex]
Where:
b1 represents the slope or the unit rate of the equation
By comparison:
[tex]b_1 =-8[/tex]
Because the value of b1 is negative;
Then it means that, the unit rate represents a decrement
Hence, the equation implies that (b) $1 in price is associated with a decrease of $8,000 in sales
Read more about regression equations at:
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53:28
Nathan and Jordan design surveys to determine the average amount of time bicyclists in a race spend training each
week. Nathan surveys every fifth bicyclist crossing the finish line after a race. Jordan surveys the first five bicyclists to
finish the race. Which best explains which sample is likely to be the most valid?
Nathan's because his sample was more random
Jordan's because his sample was more random
Nathan's because his sample contained elements of the population
Jordan's because his sample contained elements of the population
Answer:
Nathan's because his sample was more random
Step-by-step explanation:
Nathan's survey could be described as a Systematic random sampling technique whereby every 5th observation taken as a sample from the population. With these technique we have a more random observation than with.
Answer:
C
Step-by-step explanation:
The measures of two angles of a triangle are 101° and 37°. Find the measure of the third angle in degrees.
Answer:
42 degrees
Step-by-step explanation:
We already have the two angles for the triangle, we just need the third. For triangles, the can only add up to 180 degrees. 101+37=138 degrees, now we subtract 138 from 180.
180-138=42.
T=3 and t=5 to determine if the expression 4(t+3) and 4 t+12 are equivalent
Use cross products to identify the equation needed to solve this proportion:
5
x
=
2
9
Answer:
x=22.5
Step-by-step explanation:
We are given the proportion:
5/x=2/9
Cross multiply. Multiply the numerator (top number) of the first fraction by the denominator (bottom number) of the second. Then multiply the denominator of the first by the numerator of the second.
5*9=2*x
45=2x
2 and x are being multiplied. The opposite of multiplication is division. Divide both sides by 2. This will cancel out the 2 being multiplied by x, and leave x by itself.
45/2=2x/2
45/2=x
22.5=x
If we substitute 22.5 in for x, the final proportion will be:
5/22.5=2/9
Helpppppp ,would this just be -1.2?
Explanation:
The result of any absolute value function is never negative. It represents distance on a number line.
The distance from -1.2 to 0 on the number line is exactly 1.2 units.
So that's why |-1.2| = 1.2
In short, we erase the negative sign.
If 89 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by less than 48 grams
Answer:
0.6836
Step-by-step explanation:
(weight - mean weight) = 48
Variance, s² = 204,304
Sample size, n = 89
We need to obtain the Zscore :
Zscore = (X - mean) / standard Error
Zscore = (weight - mean weight ) / (s/√n)
s = √204304 = 452
The difference from the meanncoukdnbe either to the right or left :
Zscore = - 48 / (452/√89) OR 48 / (452/√89)
Zscore = - 48 / 47.911904 OR - 48 / 47.911904
Zscore = - 1.002 or 1.002
P(Z < - 1.002) = 0.1582 (using Z table)
P(Z < 1.002) = 0.8418
P(Z < 1.002) - P(Z < - 1.002)
0.8418 - 0.1582
= 0.6836
How do I do this equation
This question requires the manipulation of the Ideal Gas formula. By moving the variables around, you'll get :
V = nRT/P
n = PV/RT
There are three uncertain (random) variables in this problem. Choose the variables that should represent uncertainty in this model.
a. Yield
b. Initial Research and Development Cost
c. Pre-Orders Picked up
d. What type of fruit to grow
e. Pre-Orders Placed
f. Salvage Price
Answer:
a. Yield
c. Pre-Order picked up
e. Pre-Orders placed.
Step-by-step explanation:
Uncertain random variables are those over which the farmer has no control. These variables are uncontrollable and there can be no prediction for it. The farmer has no control over the yield produced. He can choose what type of fruits to grow and input method but he has no control over output generated.
You return from a trip with 480 Canadian dollars. How much are your Canadian dollars worth in U.S. dollars? Use the exchange rate shown below. Currency U.S. dollars per Canadian dollar Canadian dollars per U.S. dollar Canadian dollar 0.5823 1.717 The 480 Canadian dollars are equivalent to about $ (Round to the nearest cent as needed.)
591 Dollars 42 Cents (591 Dollars when rounded)
Solve the formula for t
Answer:
Step-by-step explanation:
S - 4πc^2 = 6πct
t = (S - 4πc^2)/6πc
t = S/(6πc) - 2/3 c
assuming c ≠ 0
Can someone help me find the volume of this?
Answer:
227.5
Step-by-step explanation:
basically for a triangle prism you would do is
(1÷2) since it's a triangle and multiple all 3 angels
ex: 1/2 × 5 × 7 × 13
Answer:
227.5 cubic yards
Step-by-step explanation:
Formula for area of triangular prism is:
1/2 • length x height x width
Use formula with the given dimensions:
1/2 • 7 • 5 • 13 = 227.5
Solve: |4x+3|=|2x+1|
Step-by-step explanation:
|4x+3|=|2x+1|THERE ARE TWO UNIQUE EQUATIONs
4x+3=2x+1
2x=-2
x=-1
(or)
4x+3= -(2x+1)
4x+3=-2x-1
6x=-4
x=-2/3
Therefore x=-1 , -2/3find the first three common multiplies
6 and 8
Answer:
24,48,72
Step-by-step explanation:
multiples of 6- 6,12,18,24,30,36,42,48,54,60,66,72
multiples of 8- 8,16,24,32,40,48,56,64,74,80
can anyone help me with this an explain
Answer:
si a forse that can t negativo AND f so ITS 0;3
Which of the following numbers are less than -0.65? Select all that apply.
-0.99
-4/5
-1/6
NEXT QUESTION
Answer -0.99 and -4/5
Step-by-step explanation:
-4/5 is equal to -0.8
Both -0.8 and 0.99 are to the left of -0.65, which is why they're less than 0.65.
1/6 = -0.16
Since -0.16 is to the right of -0.65 it is more than, not less
My reason:
As you go rightward, you increase the numbers by 1, which is why the numbers closer to the right are bigger than the numbers closer to the left.
(sorry for answering when it's already been two weeks lol. I felt the urge to answer-)
Write the range of the function using interval notation.
Answer:
[-3, -1]
Step-by-step explanation:
The minimum y value is -3.
The maximum y value is -1.
-3 and -1 are included, so we use square brackets.
Answer: [-3, -1]
Find the third term of a geometric progression if the sum of the first three terms is equal to 12, and the sum of the first six terms is equal to (−84).
Given:
The sum of the first three terms = 12
The sum of the first six terms = (−84).
To find:
The third term of a geometric progression.
Solution:
The sum of first n term of a geometric progression is:
[tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]
Where, a is the first term and r is the common ratio.
The sum of the first three terms is equal to 12, and the sum of the first six terms is equal to (−84).
[tex]\dfrac{a(r^3-1)}{r-1}=12[/tex] ...(i)
[tex]\dfrac{a(r^6-1)}{r-1}=-84[/tex] ...(ii)
Divide (ii) by (i), we get
[tex]\dfrac{r^6-1}{r^3-1}=\dfrac{-84}{12}[/tex]
[tex]\dfrac{(r^3-1)(r^3+1)}{r^3-1}=-7[/tex]
[tex]r^3+1=-7[/tex]
[tex]r^3=-7-1[/tex]
[tex]r^3=-8[/tex]
Taking cube root on both sides, we get
[tex]r=-2[/tex]
Putting [tex]r=-2[/tex] in (i), we get
[tex]\dfrac{a((-2)^3-1)}{(-2)-1}=12[/tex]
[tex]\dfrac{a(-8-1)}{-3}=12[/tex]
[tex]\dfrac{-9a}{-3}=12[/tex]
[tex]3a=12[/tex]
Divide both sides by 3.
[tex]a=4[/tex]
The nth term of a geometric progression is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Putting [tex]n=3,a=4,r=-2[/tex] in the above formula, we get
[tex]a_3=4(-2)^{3-1}[/tex]
[tex]a_3=4(-2)^{2}[/tex]
[tex]a_3=4(4)[/tex]
[tex]a_3=16[/tex]
Therefore, the third term of the geometric progression is 16.
An elected government official is interested in the opinion of teachers in her voting area. She randomly selected five schools at random from the 20 schools in her area and then interviews each of the teachers in those five schools. The government official is using
Answer:
a simple random sample (SRS).
Step-by-step explanation:
In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.
There are various types of sampling used by researchers and these are;
1. Systematic sampling.
2. Convenience sampling.
3. Stratified sampling.
4. Cluster sampling.
5. Random sampling.
Random sampling also referred to as simple random sample (SRS) involves randomly selecting a subset of a larger population.
In this scenario, an elected government official randomly selected five schools at random from the 20 schools in her area and then interviews each of the teachers in those five schools, in order to get their opinions about voting. Thus, the government official is using a simple random sample (SRS).
In a town. the population of registered voters is 46% democrat, 42% republican and 12% independent polling data shows 57% of democrats support the increase , 38% of republicans support the increase, and 76% of independents support the increase.
Required:
a. Find the probability that a randomly selected voter in the town supports the tax increase.
b. What is the probability that a randomly selected voter does not support the tax increase?
c. Suppose you find a voter at random who supports the tax increase. What is the probability he or she is a registered Independent?
Answer:
a) 0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.
b) 0.487 = 48.7% probability that a randomly selected voter does not support the tax increase.
c) 0.1777 = 17.77% probability he or she is a registered Independent.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
57% of 46%(democrats)
38% of 42%(republicans)
76% of 12%(independents)
So
[tex]P = 0.57*0.46 + 0.38*0.42 + 0.76*0.12 = 0.513[/tex]
0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.
Question b:
1 - 0.513 = 0.487
0.487 = 48.7% probability that a randomly selected voter does not support the tax increase.
c. Suppose you find a voter at random who supports the tax increase. What is the probability he or she is a registered Independent?
Event A: Supports the tax increase.
Event B: Is a independent.
0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.
This means that [tex]P(A) = 0.513[/tex]
Probability it supports a tax increase and is a independent:
76% of 12%, so:
[tex]P(A \cap B) = 0.76*0.12[/tex]
Thus
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.76*0.12}{0.513} = 0.1777[/tex]
0.1777 = 17.77% probability he or she is a registered Independent.
