Answer:
10Step-by-step explanation:
-2n - 6 = ?let n be -8-2 (-8) - 6 = ?= 10[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
A community swimming pool is a rectangular prism that is 30 feet long, 12 feet wide, and 5 feet deep. The wading pool is half as long, half as deep, and the same width as the larger pool.
How many times greater is the volume of the swimming pool than the volume of the wading pool?
A professor wondered if there was a difference in the proportion of students who dropped math classes between females and males. The professor randomly selected 20 math classes around campus and recorded the gender of the individual and whether or not a student enrolled in the class at the beginning of the term dropped the class at some point during the term. Assuming all conditions are satisfied, which of the following tests should the researcher use? Choose the correct answer below.
a) Chi-square goodness of fit test
b) two-sample z-test for proportions C
c) paired t-test
d) one-sample z-test for proportions
e) two-sample t-test
Answer:
b) two-sample z-test for proportions
Step-by-step explanation:
The most appropriate test to use for the research hypothesis stated above is the two sample z-test for proportions, this is because, the experiment has two independent groups (male and female) with the result of each group not affecting the result of the other. The experiment clearly stses that, it is to estimate the difference in proportion, hence, it is a test of proportions rather than mean. Also when performing, a two sample tests of proportion, the Z distribution is used.
Which of the following graphs represents the line that passes through (–2, –3) and has a slope of 2/3?
Answer:
Step-by-step explanation:
If ABCD is dilated by a factor of 3, the
coordinate of D' would be:
4
с
3
B
2
1
-5
-4
-3
-2
-1 0
1
N
3
4
5
DAN
- 1
-2
D
-3
D' = ([?], [ ]
Enter
Pls help me
Answer:
(6,-6)
Step-by-step explanation:
First let's identify the current coordinates of D
It appears that D is located at (2 , -2)
Now let's find the coordinate of D if it were dilated by a scale factor of 3.
To find the coordinates of a point after a dilation you simply multiply the x and y values of the pre image coordinates by the scale factor
In this case the scale factor is 3 and the coordinates are (2,-2)
That being said let's apply the dilation rule
Current coordinates: (2,-2)
Scale factor:3
Multiply x and y values by scale factor
(2 * 3 , -2 * 3) --------> (6 , -6)
The coordinates of D' would be (6,-6)
From a club of 24 people, in how many ways can a group of four members be selected to attend a conference?
Answer:
255,024
Step-by-step explanation:
24 x 23 x 22 x 21
24 options for the first member
23 options for the second member
22 options for the third member
21 options for the last member
find the value of x²-6x+13 when x=3+2i
Answer:
18
Step-by-step explanation:
x squared -6 +13
5 squared-6×3+2+13
25-20+13
5+13
=18
Your small business spent $40 on food and another $60 on materials. Then, you sold an item for $120, but you had to pay a $90 service fee. Finally, you were given a refund from the Internal Revenue Service (IRS) for $70. If the expression describing these transactions is the following, then how does it evaluate?
Answer:
40$+60$=100$ spent
120$sold
90$ payed
70$ refund
120 (sold) -90 (payed) =30+70 (refund) =100$ (profit)
Step-by-step explanation:
You spent 100$
And you sold and got 120 but you payed 90$ from 120$ money left is 30$
Then they refunded you (pay back the money (give you the money ))
So the money that your left with is 30$ and the refund money is 70$
So add the money that your left with is gives you 100$
In 2012 your car was worth $10,000. In 2014 your car was worth $8,850. Suppose the value of your car decreased at a constant rate of change. Define a function f to determine the value of your car (in dollars) in terms of the number of years t since 2012.
Answer:
The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:
[tex]f(t) = 10000(0.9407)^t[/tex]
Step-by-step explanation:
Value of the car:
Constant rate of change, so the value of the car in t years after 2012 is given by:
[tex]f(t) = f(0)(1-r)^t[/tex]
In which f(0) is the initial value and r is the decay rate, as a decimal.
In 2012 your car was worth $10,000.
This means that [tex]f(0) = 10000[/tex], thus:
[tex]f(t) = 10000(1-r)^t[/tex]
2014 your car was worth $8,850.
2014 - 2012 = 2, so:
[tex]f(2) = 8850[/tex]
We use this to find 1 - r.
[tex]f(t) = 10000(1-r)^t[/tex]
[tex]8850 = 10000(1-r)^2[/tex]
[tex](1-r)^2 = \frac{8850}{10000}[/tex]
[tex](1-r)^2 = 0.885[/tex]
[tex]\sqrt{(1-r)^2} = \sqrt{0.885}[/tex]
[tex]1 - r = 0.9407[/tex]
Thus
[tex]f(t) = 10000(1-r)^t[/tex]
[tex]f(t) = 10000(0.9407)^t[/tex]
A baseball team plays in a stadium that holds 58000 spectators. With the ticket price at $12 the average attendance has been 25000. When the price dropped to $9, the average attendance rose to 29000. Assume that attendance is linearly related to ticket price.
Required:
a. Find the demand function p(x), where x is the number of the spectators.
b. How should ticket prices be set to maximize revenue?
Answer:
We need to assume that the relationship is linear.
a) Remember that a linear relation is written as:
y = a*x + b
then we will have:
p(x) = a*x + b
where a is the slope and b is the y-intercept.
If we know that the line passes through the points (a, b) and (c, d), then the slope can be written as:
y = (d - b)/(c - a)
In this case, we know that:
if the ticket has a price of $12, the average attendance is 25,000
Then we can define this with the point:
(25,000 , $12)
We also know that when the price is $9, the attendance is 29,000
This can be represented with the point:
(29,000, $9)
Then we can find the slope as:
a = ($9 - $12)/(29,000 - 25,000) = -$3/4,000 = -$0.00075
Then the equation is something like:
y = (-$0.00075)*x + b
to find the value of b we can use one of the known points.
For example, the point (25,000 , $12) means that when x = 25,000, the price is $12
then:
$12 = (-$0.00075)*25,000 + b
$12 = -$18.75 + b
$12 + $18.75 = b
$30.75 = b
Then the equation is:
p(x) = (-$0.00075)*x + $30.75
b) We want to find the ticket price such that it maximizes the revenue.
The revenue will be equal to the price per ticket, p(x) times the total attendance, x.
Then the revenue can be written as:
r(x) = x*p(x) = x*( (-$0.00075)*x + $30.75 )
r(x) = (-$0.00075)*x^2 + $30.75*x
So we want to find the maximum revenue.
Notice that this is a quadratic equation with a negative leading coefficient, thus the maximum will be at the vertex.
Remember that for an equation like:
y = a*x^2 + bx + c
the x-value of the vertex is:
x = -b/2a
Then in our case, the x-value will be:
x = -$30.75/(2*(-$0.00075)) = 20,500
Then the revenue is maximized for x = 20,500
And the price for this x-vale is given by:
p( 20,500) = (-$0.00075)*20,500 + $30.75 = $15.375
which should be rounded to $15.38
Consider an urn initially containing n balls, numbered 1 through n, and suppose that balls will be randomly drawn from the urn, one by one, and without replacement (so that after n draws, it is empty). Letting X be the number of successes that will occur, where a success is considered to occur on the ith draw if the ball obtained is numbered i or smaller, give the expected value of X. (E.g., if n = 5, and the balls are drawn in the order 3, 1, 5, 4, 2, then x = 3, because the 2nd, 4th, and 5th draws result in successes, but the 1st and 3rd draws don’t.)
what is the least common multiple between 25 and 8
Answer:
200
Step-by-step explanation:
Break down 25 = 5*5
Break down 8 = 2*2*2
They have no common factors
The least common multiple is
5*5*2*2*2 = 25*8 = 200
Answer:
200
Step-by-step explanation:
list the factors of 25: 5,5
factors of 8:2,2,2,
PLEASE HELP ME !!!!
How many solutions does the system of equations below have?
y = x - 3
3y-3x = -9
A. Exactly 1 solution
B. At least 1 solution
C. More than 1 solution
D. No solution
9514 1404 393
Answer:
C. More than 1 solution
Step-by-step explanation:
Divide the second equation by 3.
y -x = -3
Add x.
y = x -3
This matches the first equation exactly, meaning that any solution to the first equation is also a solution to the second equation. There are an infinite number of possibilities. There is "More than 1 solution."
Factorise: 25x^2 - 1/49
Answer:
[tex] (5x + \frac{1}{7} )(5x - \frac{1}{7} )[/tex]Step-by-step explanation:
Given,
[tex] {25x}^{2} - \frac{1}{49} [/tex]
[tex] = {(5x)}^{2} - {( \frac{1}{7}) }^{2} [/tex]
Since,
[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]
Then,
[tex] = (5x + \frac{1}{7} )(5x - \frac{1}{7} )(ans)[/tex]
Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. AAS Postulate
Answer:
YWX = DFE
Step-by-step explanation:
AAS means angle angle side. so, we need 2 angles and 1 side.
we have 1 side and one angle confirmed.
so, we need one of the other two angles (W or Y vs. F or D) confirmed.
they probably want W and F as answer, as Y and D would make it a special case of AAS : ASA.
Find y' for the following.
Answer:
[tex]\displaystyle y' = \frac{\sqrt{y} + y}{4\sqrt{x}y \Big( y^\Big{\frac{3}{2}} + \sqrt{y} + 2y \Big) + \sqrt{x} + x}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{\sqrt{x} + 1}{\sqrt{y} + 1} = y^2[/tex]
Step 2: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx} \bigg[ \frac{\sqrt{x} + 1}{\sqrt{y} + 1} \bigg] = \frac{dy}{dx}[ y^2][/tex]Quotient Rule: [tex]\displaystyle \frac{(\sqrt{x} + 1)'(\sqrt{y} + 1) - (\sqrt{y} + 1)'(\sqrt{x} + 1)}{(\sqrt{y} + 1)^2} = \frac{dy}{dx}[ y^2][/tex]Rewrite: [tex]\displaystyle \frac{(x^\Big{\frac{1}{2}} + 1)'(y^\Big{\frac{1}{2}} + 1) - (y^\Big{\frac{1}{2}} + 1)'(x^\Big{\frac{1}{2}} + 1)}{(y^\Big{\frac{1}{2}} + 1)^2} = \frac{dy}{dx}[ y^2][/tex]Basic Power Rule [Addition/Subtraction, Chain Rule]: [tex]\displaystyle \frac{\frac{1}{2}x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - \frac{1}{2}y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}{(y^\Big{\frac{1}{2}} + 1)^2} = 2yy'[/tex]Factor: [tex]\displaystyle \frac{\frac{1}{2} \bigg[ x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1) \bigg] }{(y^\Big{\frac{1}{2}} + 1)^2} = 2yy'[/tex]Rewrite: [tex]\displaystyle \frac{x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}{2(y^\Big{\frac{1}{2}} + 1)^2} = 2yy'[/tex]Rewrite: [tex]\displaystyle x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) - y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}= 4yy'(y^\Big{\frac{1}{2}} + 1)^2[/tex]Isolate y' terms: [tex]\displaystyle x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) = 4yy'(y^\Big{\frac{1}{2}} + 1)^2 + y^\Big{\frac{-1}{2}}y'(x^\Big{\frac{1}{2}} + 1)}[/tex]Factor: [tex]\displaystyle x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1) = y' \bigg[ 4y(y^\Big{\frac{1}{2}} + 1)^2 + y^\Big{\frac{-1}{2}}(x^\Big{\frac{1}{2}} + 1)} \bigg][/tex]Isolate y': [tex]\displaystyle \frac{x^\Big{\frac{-1}{2}}(y^\Big{\frac{1}{2}} + 1)}{4y(y^\Big{\frac{1}{2}} + 1)^2 + y^\Big{\frac{-1}{2}}(x^\Big{\frac{1}{2}} + 1)} = y'[/tex]Rewrite/Simplify: [tex]\displaystyle y' = \frac{\sqrt{y} + y}{4\sqrt{x}y \Big( y^\Big{\frac{3}{2}} + \sqrt{y} + 2y \Big) + \sqrt{x} + x}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
How long will it take for money to double if it is invested at 7% compounded monthly?
Which values of x are solutions to this equation? -1/2x^2 + 5x = 8
A) -2
B) 2
C) -8
D) -1.5
E) 11.5
F) 8
Answer:
2, 8
Step-by-step explanation:
-1/2x^2 + 5x = 8
-x^2 + 10x = 16 (Multiplying both sides of the equation by 2)
-x^2 + 10x - 16 = 0
x^2 - 10x + 16 = 0 (changing the signs)
x^2 -2x -8x +16 = 0
x (x-2) -8 (x-2) = 0
(x-2) (x-8)
x-2 = 0
x = 2
or
x -8 = 0
x = 8
Answer from Gauthmath
The values of x are solutions to this equation that is 2, 8
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We are given that the equation as;
-1/2x² + 5x = 8
-x² + 10x = 16
Now Multiplying both sides of the equation by 2;
-x² + 10x - 16 = 0
Or
x² - 10x + 16 = 0
x² -2x -8x +16 = 0
x (x-2) -8 (x-2) = 0
(x-2) (x-8)
The solution are;
x-2 = 0
x = 2
or
x -8 = 0
x = 8
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ2
Find f′ in terms of g′
f(x)=x2g(x)
Select one:
f′(x)=2xf′(x)+2xg′(x)
f′(x)=2xg′(x)
f′(x)=2x+g′(x)
f′(x)=x2g(x)+2x2g′(x)
f′(x)=2xg(x)+x2g′(x)
9514 1404 393
Answer:
(e) f′(x)=2xg(x)+x²g′(x)
Step-by-step explanation:
The product rule applies.
(uv)' = u'v +uv'
__
Here, we have u=x² and v=g(x). Then u'=2x and v'=g'(x).
f(x) = x²·g(x)
f'(x) = 2x·g(x) +x²·g'(x)
Use the compound interest formula to find the annual interest rate, r, if in 2 years an investment of 4,000 grows to 4410 The rate is %.
Answer:
5%
Step-by-step explanation:
Bank amount=PA*(1+r/100)^t
4410=4000*(1+x/100)^2
1.05=(1+x/100), x=5%
PLEASE HELPPPPPPPPP!!!!!!!!!!!
(b) How much the selling price should be fixed for pulse bought for Rs.70 per kg. to earn a profit of Rs.6 after allowing a 5 % discount?
Answer:
Rs. 80
Step-by-step explanation:
Given that :
Purchase price = 70
Profit = 6
Discount = 5%
Let selling price = x
Selling price * (1 - discount) = (purchase price + profit)
x * (1 - 5%) = (70 + 6)
x * (1 - 0.05) = 76
x * 0.95 = 76
0.95x = 76
x = 76 / 0.95
x = 80
Hence, selling price = Rs. 80
72a^7/-9 as a monomial
Answer:
− 8 a ^7
Step-by-step explanation:
See picture for steps :)
Solve for Y equals -2 over 3x minus 1
Answer:
y=-\frac{2}{3}\approx -0.666666667
help with summer school
Answer:
19
Step-by-step explanation:
3a -2^3 ÷b
Let a = 7 and b = 4
3*7 -2^3 ÷4
PEMDAS says exponents first
3*7 -8 ÷4
Multiply and divide from left to right
21 - 2
Subtract
19
An investment of $8,120 is earning interest at the rate of 5.8% compounded quarterly over 11 years. How much
interest is earned on the investment? Show your work.
Answer:
5180.56 Dollars...........
ASAP PLSSSSSSSS TYYYYYY
Answer:
20% of students prefer to go to the aquarium
50% of teachers prefer to go to the aquarium
Step-by-step explanation:
1.
8 students prefer the aquarium out of 40 students.
Set up an equation:
Variable x = percentage of students
8/40 = x/100
Cross multiply:
8 × 100 = 40 × x
800 = 40x
20 = x
Divide:
20%
Check your work:
40 students × 20%
Convert percentage into decimal:
40 × 0.20
8
8 students prefered the aquarium so this is correct!
2.
5 teachers prefer the aquarium out of 10 teachers.
Set up an equation:
Variable x = percentage of teachers
5/10 = x/100
5 × 100 = 10 × x
500 = 10x
50 = x
50%
Check your work:
10 × 0.50
5
Correct!
The salt content in snack bags of pretzels is Normally distributed, with a mean of 180 mg and a standard deviation of 15 mg. Eighty four percent of bags have a salt content higher than which value?
Find the z-table here.
165.2 mg
179.2 mg
187.0 mg
194.9 mg
I think its (A), 165.2mg
Answer: Yes you are correct. The answer is choice A
============================================================
Explanation:
If you used the z-table, you should find that P(Z < 1) = 0.84 approximately.
So by symmetry, P(Z > -1) = 0.84 approximately as well.
We'll convert the z score z = -1 into its corresponding x score
z = (x-mu)/sigma
-1 = (x-180)/15
-15 = x-180
x-180 = -15
x = -15+180
x = 165
We don't land on any of the answer choices listed, but we get fairly close to 165.2, which is choice A. So you are correct.
I have a feeling that the table you have is probably more accurate than the one I'm using, so it's possible that you'd land exactly on 165.2 when following the steps above.
Answer:
194.9
Step-by-step explanation:
ON EDG
Given that 3x-7y=-27 and 5x+9y=17. Find the values of x and y that satisfy both equations, using elimination method.
here's the answer to your question
solve for x
3x-7y=-27
5x+9y=17
multiply 9, 7
27x -63y =-243
35x +63y = 119
add and cancel y out
62x = -124
x = -2
plug in x
-6-7y=-27
-7y=-21
y = 3
answer:
y = 3
x = -2
PLSSS HELP IM STRUGGLING SO HARD !!! ———————
Answer:
C)
Step-by-step explanation:
Just see the length of the R line, A and B are almost the same large when you add them.
The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 6.05 ounces and a standard deviation of .18 ounces. Suppose that you draw a random sample of 36 cans.
a. Find the probability that the mean weight of the sample is less than 5.97 ounces.
b. Suppose your random sample of 36 cans of salmon produced a mean weight that is less than 5.97 ounces. Comment on the statement made by the manufacturer.
Answer:
a) 0.0038 = 0.38% probability that the mean weight of the sample is less than 5.97 ounces.
b) Given a mean of 6.05 ounces, it is very unlikely that a sample mean of less than 5.97 ounces, which means that the true mean must be recalculated.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 6.05 ounces and a standard deviation of .18 ounces.
This means that [tex]\mu = 6.05, \sigma = 0.18[/tex]
Sample of 36:
This means that [tex]n = 36, s = \frac{0.18}{\sqrt{36}} = 0.03[/tex]
a. Find the probability that the mean weight of the sample is less than 5.97 ounces.
This is the p-value of z when X = 5.97. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5.97 - 6.05}{0.03}[/tex]
[tex]Z = -2.67[/tex]
[tex]Z = -2.67[/tex] has a p-value of 0.0038.
0.0038 = 0.38% probability that the mean weight of the sample is less than 5.97 ounces.
b. Suppose your random sample of 36 cans of salmon produced a mean weight that is less than 5.97 ounces. Comment on the statement made by the manufacturer.
Given a mean of 6.05 ounces, it is very unlikely that a sample mean of less than 5.97 ounces, which means that the true mean must be recalculated.
