Answer:
100
Step-by-step explanation:
The number, when decreased by 40%, is equal to 100.
What is the percentage?
The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %.
Let the number be x then the number is calculated as:-We can see that the number is decreased by 40% then the remaining part is 60%
x ( 60% ) = 60
x ( 60 / 100 ) = 60
x = 100
Hence, the number, when decreased by 40%, is equal to 100.
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(0, 3) and (-2, -1)
Write an equation in slope intercept from of the line that passes through the given points.
Answer:
y = 2x + 3
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope-Intercept Form: y = mx + b
Step 1: Find slope m
m = (-1 - 3)/(-2 - 0)
m = -4/-2
m = 2
y = 2x + b
Step 2: Rewrite equation
y = 2x + 3
*You are given y-intercept (0, 3), so simply add it to your equation.
A tank contains 4,000 L of brine with 18 kg of dissolved salt. Pure water enters the tank at a rate of 40 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate.
a. How much salt is in the tank after t minutes?
b. How much salt is in the tank after 30 minutes? (Round your answer to one decimal place.
Answer:
(a)[tex]A(t)=18e^{ -\frac{t}{100}}[/tex]
(b)13.3 kg
Step-by-step explanation:
The volume of brine in the tank = 4000L
Initial Amount of salt, A(0)=18 kg
The rate of change in the amount of salt in the tank at any time t is represented by the equation:
[tex]\dfrac{dA}{dt}=$Rate In$-$Rate Out[/tex]
Rate In = (concentration of salt in inflow)(input rate of brine)
Since pure water enters the tank, concentration of salt in inflow =0
Rate In = 0
Rate Out=(concentration of salt in outflow)(output rate of brine)
[tex]=\frac{A(t)}{4000}\times 40\\ =\frac{A(t)}{100}[/tex]
Therefore:
[tex]\dfrac{dA}{dt}=-\dfrac{A(t)}{100}\\\dfrac{dA}{dt}+\dfrac{A(t)}{100}=0[/tex]
This is a linear D.E. which we can then solve for A(t).
Integrating Factor: [tex]e^{\int \frac{1}{100}d}t =e^{ \frac{t}{100}[/tex]
Multiplying all through by the I.F.
[tex]\dfrac{dA}{dt}e^{ \frac{t}{100}}+\dfrac{A(t)}{100}e^{ \frac{t}{100}}=0e^{ \frac{t}{100}}\\(Ae^{ \frac{t}{100}})'=0[/tex]
Taking integral of both sides
[tex]Ae^{ \frac{t}{100}}=C\\A(t)=Ce^{ -\frac{t}{100}}[/tex]
Recall our initial condition
A(0)=18 kg
[tex]18=Ce^{ -\frac{0}{100}}\\C=18[/tex]
Therefore, the amount of salt in the tank after t minutes is:
[tex]A(t)=18e^{ -\frac{t}{100}}[/tex]
(b)When t=30 mins
[tex]A(30)=18e^{ -\frac{30}{100}}\\=18e^{ -0.3}\\=13.3 $kg(correct to 1 decimal place)[/tex]
The amount of salt in the tank after 30 minutes is 13.3kg
In this exercise we have to use the integral to calculate the salt concentration:
(a)[tex]A(t)=18e^{-\frac{t}{100} }[/tex]
(b)[tex]13.3 kg[/tex]
Knowing that the volume of brine in the tank = 4000L, the initial Amount of salt, A(0)=18 kg. The rate of change in the amount of salt in the tank at any time t is represented by the equation:
[tex]\frac{dA}{dt} = Rate \ in - Rate \ out[/tex]
Rate In = (concentration of salt in inflow)(input rate of brine). Since pure water enters the tank, concentration of salt in inflow =0.
Rate In = 0
Rate Out=(concentration of salt in outflow)(output rate of brine)
[tex]\frac{A(t)}{4000}*(40)[/tex]
[tex]= \frac{A(t)}{100}[/tex]
Therefore:
[tex]\frac{dA}{dt} = \frac{A(t)}{100}\\\frac{dA}{dt} + \frac{A(t)}{100} = 0[/tex]
This is a linear D.E. which we can then solve for A(t). Integrating Factor: [tex]e^{\int\limits {\frac{t}{100} } \, dt\\e^{t/100}[/tex] . Multiplying all through by the Integrating Factor:
[tex]\frac{dA}{dt} = e^{t/100}+\frac{A(t)}{100}e^{t/100}\\(Ae^{1/100})'=0[/tex]
Taking integral of both sides:
[tex]Ae^{t/100}=C\\A(t)=Ce^{-t/100}[/tex]
Recall our initial condition:
[tex]A(0)=18 kg\\18=Ce^{0}\\C=18[/tex]
Therefore, the amount of salt in the tank after t minutes is:
[tex]A(t)=18e^{-t/100}[/tex]
(b)When t=30 mins
[tex]A(30)=18e^{-30/100}\\=18e^{-0.3}\\=13.3[/tex]
The amount of salt in the tank after 30 minutes is 13.3kg.
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Want Brainliest? Get this correct Which of the following is the product of the rational expressions shown below?
We multiply the numerators together to get x*2x = 2x^2 as the numerator for the answer.
The denominators pair up and multiply to get (x-5)(x+4) = x^2+4x-5x-20 = x^2-x-20. You can use the distributive property, FOIL, or the box method to expand out (x-5)(x+4)
So that's how we end up with (2x^2) all over (x^2-x-20) as the answer.
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. 3 0 -4 2 0 6 -3 0 8
a. The matrix is invertible. The columns of the given matrix span R^3.
b. The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.
c. The matrix is invertible. The given matrix has 2 pivot positions.
d. The matrix is not invertible. If the given matrix is A, the equation Ax = 0 has only the trivial solution.
Answer:
b. The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.
Step-by-step explanation:
A square matrix is said to be invertible if the product of the matrix and its inverse result into an identity matrix.
3 0 -4
2 0 6
-3 0 8
Since the second column elements are all zero, the determinant of the matrix is zero ad this implies that the inverse of the matrix does not exist(i.e it is not invertible )
A square matrix is said to be invertible if it has an inverse.
The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.
The matrix is given as:
[tex]\left[\begin{array}{ccc}3&0&-4\\2&0&6\\-3&0&8\end{array}\right][/tex]
Calculate the determinant
The determinant of the matrix calculate as:
[tex]|A| = 3 \times(0 \times 8- 6 \times 0) - 0(2 \times 8 - 6 \times -3) -4(2 \times 0 - 0 \times -3)[/tex]
[tex]|A| = 3 \times(0) - 0(34) -4(0)[/tex]
[tex]|A| = 0 - 0 -0[/tex]
[tex]|A| = 0[/tex]
When a matrix has its determinant to be 0, then
It is not invertibleIt does not form a linear independent set.Hence, the correct option is (b)
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make d the subject of the formula; n=k/d^2
Answer:
[tex]n = \frac{k}{ {d}^{2} } [/tex]
[tex] {d}^{2} = \frac{k}{n} [/tex]
[tex]d = \sqrt{ \frac{k}{n} } [/tex]
Here is the required firmula....Answer:
d = √(k/n)
Step-by-step explanation:
n = k/d²
n/1 = k/d²
Cross multiply.
k = nd²
Divide both sides by n.
k/n = nd²/n
k/n = d²
Take the square root on both sides.
√(k/n) = √(d²)
√(k/n) = d
What number must you add to complete the square?
X^2 + 8x= 11
A. 12
B. 16
c. 8
D. 4
Answer:
16
Step-by-step explanation:
X^2 + 8x= 11
Take the coefficient of x
8
Divide by 2
8/2 =4
Square it
4^2 = 16
Add 16 to each side
PLS HELP ASAP!!!!........
Answer:
aaaaha pues
Step-by-step explanation:
Answer:
what happened
Step-by-step explanation:
Work out the surface area of this sphere.
Give your answer to 1 decimal place.
Answer:
452.4
Step-by-step equation:
surface area of a sphere formula= 4πr²
plug 6 in for r
4π(6)² =452.389 rounded to 452.4
1. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Berwick sample is________.
a. 60
b. 75
c. 80
d. 90
2. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Milton sample is________.
a. 60
b. 75
c. 80
d. 90
3. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The expected frequency of satisfied customers from the Leesburg sample is________.
a. 60
b. 75
c. 80
d. 90
4. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The chi-square test statistic for these samples is_______.
a. 1.49
b. 2.44
c. 4.15
d. 5.33
5. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The degrees of freedom for the chi-square critical value is_______.
a. 1
b. 2
c. 3
d. 4
6. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
The chi-square critical value using alpha = 0.05 is_______.
a. 2.706
b. 3.841
c. 5.991
d. 7.815
7. Lisa is a regional manager for a restaurant chain that has locations in the towns of Berwick, Milton, and Leesburg. She would like to investigate if a difference exists in the proportion of customers who rate their experience as satisfactory or better between the three locations. The following data represent the number of customers who indicated they were satisfied from random samples taken at each location.
Berwick Milton Leesburg
Number Satisfied 80 85 60
Sample Size 100 120 80
Using alpha = 0.05, the conclusion for this chi-square test would be that because the test statistic is
A. More than the critical value, we can reject the null hypothesis and conclude that there is a difference in proportion of satisfied customers between these three locations.
B. Less than the critical value, we can reject the null hypothesis and conclude that there is a difference in proportion of satisfied customers between these three locations.
C. More than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
D. Less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Answer:
1) Option B is correct.
Expected frequency of satisfied customers from the Berwick sample = 75
2) Option D is correct.
Expected frequency of satisfied customers from the Milton sample = 90
3) Option A is correct.
Expected frequency of satisfied customers from the Leesburg sample = 60
4) Option B is correct.
The chi-square test statistic for these samples = 2.44
5) Option B is correct.
The degrees of freedom for the chi-square critical value = 2
6) Option C is correct.
The chi-square critical value using alpha = 0.05 is 5.991
7) Option D is correct.
The conclusion for this chi-square test would be that because the test statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Step-by-step explanation:
Berwick Milton Leesburg
Number Satisfied 80 85 60
Unsatisfied 20 35 20
Sample Size 100 120 80
Since this is a chi test that aims to check if there are differences in the proportion of expected number of customers for each location, we state the null and alternative hypothesis first.
The null hypothesis usually counters the claim we hope to test and would be that there is no difference between the proportion of expected frequency of satisfied customers at the three locations.
The alternative hypothesis confirms the claim we want to test and is that there is a significant difference between the proportion of expected frequency of satisfied customers at the three locations.
So, the total proportion of satisfied customers is used to calculate the expected number of satisfied customers for each of the three locations.
80+85+60= 225
Total number of customers = 100 + 120 + 80 = 300
Proportion of satisfied customers = (225/300) = 0.75
1) Expected frequency of satisfied customers from the Berwick sample = np = 100 × 0.75 = 75
2) Expected frequency of satisfied customers from the Milton sample = np = 120 × 0.75 = 90
3) Expected frequency of satisfied customers from the Leesburg sample = np = 80 × 0.75 = 60
4) Berwick Milton Leesburg
Number Satisfied 80 85 60
Unsatisfied 20 35 20
Sample Size 100 120 80
Proportion for unsatisfied ccustomers = 0.25
So, expected number of unsatisfied customers for the three branches are 25, 30 and 20 respectively.
Chi square test statistic is a sum of the square of deviations from the each expected value divided by the expected value.
χ² = [(X₁ - ε₁)²/ε₁] + [(X₂ - ε₂)²/ε₂] + [(X₃ - ε₃)²/ε₃] + [(X₄ - ε₄)²/ε₄] + [(X₅ - ε₅)²/ε₅] + [(X₆ - ε₆)²/ε₆]
X₁ = 80, ε₁ = 75
X₂ = 85, ε₂ = 90
X₃ = 60, ε₃ = 60
X₄ = 20, ε₄ = 25
X₅ = 35, ε₅ = 30
X₆ = 20, ε₆ = 20
χ² = [(80 - 75)²/75] + [(85 - 90)²/90] + [(60 - 60)²/60] + [(20 - 25)²/25] + [(35 - 30)²/30] + [(20 - 20)²/20]
χ² = 0.3333 + 0.2778 + 0 + 1 + 0.8333 + 0 = 2.4444 = 2.44
5) The degree of freedom for a chi-square test is
(number of rows - 1) × (number of columns - 1)
= (2 - 1) × (3 - 1) = 1 × 2 = 2
6) Using the Chi-square critical value calculator for a degree of freedom of 2 and a significance level of 0.05, the chi-square critical value is 5.991.
7) Interpretation of results.
If the Chi-square test statistic is less than the critical value, we fail to reject the null hypothesis.
If the Chi-square test statistic is unusually large and is greater than the critical value, we reject the null hypothesis.
For this question,
Chi-square test statistic = 2.44
Critical value = 5.991
2.44 < 5.991
test statistic < critical value
The test statistic is Less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.
Hope this Helps!!!
Please answer this correctly
Answer:
The second question
Step-by-step explanation:
The orca starts at -25 meters. She goes up 25 meters.
up 25 = +25
-25+25=0
Answer:
Option 2
Step-by-step explanation:
The orca swims at the elevation of -25 meters. The orca swims up 25 meters higher than before.
-25 + 25 = 0
Find the product of all positive integer values of $c$ such that $3x^2+7x+c=0$ has two real roots. I will award a lot of points
Answer: 24
Step-by-step explanation:
Let's find one solution:
3x² + 7x + c = 0
a=3 b=7 c=c
First, let's find c so that it has REAL ROOTS.
⇒ Discriminant (b² - 4ac) ≥ 0
7² - 4(3)c ≥ 0
49 - 12c ≥ 0
-12c ≥ -49
[tex]c\leq\dfrac{-49}{-12}\quad \rightarrow c\leq \dfrac{49}{12}[/tex]
Since c must be a positive integer, 1 ≤ c ≤ 4
Example: c = 4
3x² + 7x + 4 = 0
(3x + 4)(x + 1) = 0
x = -4/3, x = -1 Real Roots!
You need to use Quadratic Formula to solve for c = {1, 2, 3}
Valid solutions for c are: {1, 2, 3, 4)
Their product is: 1 x 2 x 3 x 4 = 24
Answer:
$3x^2+7x+c=0$
comparing above equation with ax²+bx+c
a=3
b=7
c=1
using quadratic equation formula
[tex]x = \frac{ - b + - \sqrt{b {}^{2} - 4ac} }{ 2a} [/tex]
x=(-7+-√(7²-4×3×1))/(2×3)
x=(-7+-√13)/6
taking positive
x=(-7+√13)/6=
taking negative
x=(-7-√13)/6=
If the 2412 leaves are not a random sample, but the researchers treated the 2412 leaves as a random sample, this most likely made the data more:_____________.1. accurate, but not precise2. precise, but not accurate3. neither4. both accurate and precise
Answer:
2. Precise but not accurate
Step-by-step explanation:
In a high precision, low accuracy case study, the measurements are all close to each other (high agreement between the measurements) but not near/or close to the center of the distribution (how close a measurement is to the correct value for that measurement)
F (X) = x² - 2x and 6(x) = 3x+1
A) Find F(g(-4))
B) Find F(g(x)) simply
C) find g^-1 (x)
Part A
g(x) = 3x+1
g(-4) = 3(-4)+1 ... every x replaced with -4
g(-4) = -12+1
g(-4) = -11
Plug this into the f(x) function
f(x) = x^2 - 2x
f( g(-4) ) = (g(-4))^2 - 2( g(-4) )
f( g(-4) ) = (-11)^2 - 2(-11)
f( g(-4) ) = 121 + 22
f( g(-4) ) = 143 is the answer====================================================
Part B
Plug the g(x) function into the f(x) function
f(x) = x^2 - 2x
f( g(x) ) = ( g(x) )^2 - 2( g(x) ) ... replace every x with g(x)
f( g(x) ) = (3x+1)^2 - 2(3x+1)
f( g(x) ) = (9x^2+6x+1) + (-6x-2)
f( g(x) ) = 9x^2+6x+1-6x-2
f( g(x) ) = 9x^2-1 is the answerNote that we can plug x = -4 into this result and we would get
f( g(x) ) = 9x^2-1
f( g(-4) ) = 9(-4)^2-1
f( g(-4) ) = 9(16)-1
f( g(-4) ) = 144-1
f( g(-4) ) = 143 which was the result from part A
====================================================
Part C
Replace g(x) with y. Then swap x and y. Afterward, solve for y to get the inverse.
[tex]g(x) = 3x+1\\\\y = 3x+1\\\\x = 3y+1\\\\3y+1 = x\\\\3y = x-1\\\\y = \frac{1}{3}(x-1)\\\\y = \frac{1}{3}x-\frac{1}{3}\\\\g^{-1}(x) = \frac{1}{3}x-\frac{1}{3}\\\\[/tex]
Which point is located at (Negative 3.5, Negative 4.5)? On a coordinate plane, point A is 3.5 units to the left and 4.5 units down. Point K is 3.5 units to the right and 4.5 units up. Point R is 3.5 units to the left and 4.5 units up. Point Y is 4.5 units to the left and 3.5 units down. point A point K point R point Y
Answer:
Point A
Step-by-step explanation:
We know that on a coordinate plane, negative numbers can be found by moving down or moving to the left. This point must be found by moving down and left. To establish whether it is point A or point Y, we can remember that x coordinates move left and right and y coordinates move up and down. So, we would need to move 3.5 units left for x and then 4.5 units down for y. This leads us to point A.
hope this helps!
Answer:
it is point A
Step-by-step explanation:
If f(x)=2x−1, show that f(f(x))=4x−3. Find f(f(f(x))).
Answer: f(f(f(x)))=8x-7
Step-by-step explanation:
Since we were given f(x) and f(f(x)), We plug that into f(x) again to get f(f(f(x))).
2(4x-3)-1 [distribute]
8x-6-1 [combine like terms]
8x-7
I don't know what to do.
Answer:
13 Compute using the 2 right angles, we know that m<FIG=90* and
I don't know what to do.
Answer:
104.93 in
Step-by-step explanation:
When we draw out a picture of our triangle, we should see that we need to use sin∅ to solve:
sin23° = 41/x
xsin23° = 41
x = 41/sin23°
x = 104.931
Determine whether the given value is from a discrete or continuous data set. When a car is randomly selected, it is found to have 8 windows. Choose the correct answer below. A. A discrete data set because there are a finite number of possible values. B. A continuous data set because there are infinitely many possible values and those values cannot be counted. C. A continuous data set because there are infinitely many possible values and those values can be counted. D. The data set is neither continuous nor discrete.
Answer:
A discrete data set because there are a finite number of possible values.
Step-by-step explanation:
We are given the following data set below;
When a car is randomly selected, it is found to have 8 windows.
Firstly, as we know that the discrete data is that data that have countable or finite values, and also we can observe at a point value.
On the other hand, the continuous data is that data in which there is a range of values and we can't count or observe each and every value.
So, in our question; as we can observe that we can count all the windows and it is also a finite number which means that the given data set is a discrete data set because there are a finite number of possible values.
forex is the name of the U.S. stock exchange.
-true
-false
Answer:
false
Step-by-step explanation:
hello
this is false
FOREX means Foreign Exchange
it refers to the foreign exchange market
hope this helps
Answer:
true, forex trading is a profitable than staking cryptocurrency. forex trading is the best thing I will refer someone I love because learning never stops and no on is above blowing accounts when beginning Forex
Find the value of c such that the three points (5,5), (-3,1), and (6,c) lie on the same line. Note: Three points are on the same line if the slope of the line through any two points is always the same.
Answer:
c = 5.5
Step-by-step explanation:
We can find the slope of the line using the given points (5,5) and (-3,1) using rise over run:
-4/-8 = 1/2
Now, we can plug in the slope and a point into the equation y = mx + b to find b:
5 = 1/2(5) + b
5 = 2.5 + b
2.5 = b
Then, we can plug in 6 in the point (6,c) to find c:
y = (1/2)(6) + 2.5
y = 3 + 2.5
y = 5.5
c = 5.5
Answer:
c = 5.5
Step-by-step explanation:
Find the slope with two points
m = (y2-y1)/(x2-x1)
m = (1-5)/(-3-5)
= -4/-8
= 1/2
If all the points are on the same line, then they have the same slope
m = (y2-y1)/(x2-x1)
Using the first and third points
1/2 = (c-5)/(6-5)
1/2 = (c-5)/1
1/2 = c-5
Add 5 to each side
5+1/2 = c
5.5 =c
Nine balls, each marked with a number from 1 to 9, are placed in a bag and one
Ball is taken out at random. What is the probability that the number on the ball is:
(a) odd, (b) a multiple of 3, (c) 5, (d) not a 7
Answer:
a =5/9 b=1/3 c=1/9 d=8/9
Step-by-step explanation:
there are total 9 numbers
in a
there are 5 odd numbers
in b
there are 3 multiplier of 3
in c
there is only one 5
in d
there are 8 numbers except 7
a) 5/9 b) 1/3 c) 1/9 d) 8/9
Step-by-step explanation:
a) odd numbers between 1 to 9 are 1,3,5,7,9. so there are 5 odd numbers.
total balls are 9
=> probability is 5/9
b) multiples of 3 = 3, 6,9 there are 3 numbers.
=> probability is = 3/9 = 1/3
c) 5. only one 5 is there between 1 to 9 numbers.
=> probability is 1/9
d) not a 7.
removing 7. there will 8 numbers.
=> probability is 8/9
Need help with this as soon as possible.
Answer:
after 9 weeks it would become 9*1+10=19 inches
and after w weeks it will be w*1+10 inches tall
hope this helps
Step-by-step explanation:
Answer:
a) 19 inches
b) 10+w inches
Step-by-step explanation:
The equation for this problem is 10 + w. In the first part, w = 9, so the plant is 19 inches tall.
Number of non sqaure number are there between 36² and 37²
Answer:
A 1,296
B 1,369
36 answer
Suppose that the scores of bowlers in particular league follow a normal distribution such that the standard deviation of the population is 6. Find the 95% confidence interval of the mean score for all bowlers in this league, using the accompanying data set of 10 random scores. Round your answers to two decimal places and use ascending order. Score 86 86 93 88 98 107 93 75 89
Answer:
A 95% confidence interval for the population mean score for all bowlers in this league is [86.64, 94.48].
Step-by-step explanation:
Since in the question only 9 random scores are given, so I am performing the calculation using 9 random scores.
We are given that the scores of bowlers in particular league follow a normal distribution such that the standard deviation of the population is 6.
The accompanying data set of 9 random scores in ascending order is given as; 75, 86, 86, 88, 89, 93, 93, 98, 107
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean score = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{815}{9}[/tex] = 90.56
[tex]\sigma[/tex] = population standard deviation = 6
n = sample of random scores = 9
[tex]\mu[/tex] = population mean score for all bowlers
Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\bar X-\mu}[/tex] < [tex]1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]
= [ [tex]90.56-1.96 \times {\frac{6}{\sqrt{9} } }[/tex] , [tex]90.56+1.96 \times {\frac{6}{\sqrt{9} } }[/tex] ]
= [86.64 , 94.48]
Therefore, a 95% confidence interval for the population mean score for all bowlers in this league is [86.64, 94.48].
20. The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of units over the ten-year span, (number of units sold, profit) for specific recorded years: (46,250), (48, 305), (50,350), (52, 390), (54, 410) a) Use linear regression to determine a function y, where profit in thousands of dollars depends on the number of units sold in hundreds. b) Predict when the profit will exceed one million dollars.
Answer:
20
Step-by-step explanation:
The linear function represents the number of units sold y in terms of profit x is y = 27.5x - 1015.
What is a linear function?
A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given pair of (number of units sold y, profit x)
Linear equation slope and y-intercept
A linear equation or function is given as ;
y = mx + c
Here, c is the y-intercept and m is the slope.
The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope m = (y₂ - y₁)/(x₂ - x₁)
Therefore slope of (46,250), (48, 305)
m = (305 - 250)/(48 - 46) = 27.5
Put, m = 27.5 and (46,250)
250 = 27.5(46) + c
c = -1015
y = 27.5x - 1015
Hence "The linear function represents the number of units sold y in terms of profit x is y = 27.5x - 1015".
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Arrange the functions for which the result is a non-infinite value and the limit exists in ascending order of their limit values as x tends to infinity. Please see picture attached.
Answer:
see attached
Step-by-step explanation:
The limit as x gets large is the ratio of the highest-degree terms. In most cases, the limit can be found by evaluating that ratio. Where an absolute value is involved, the absolute value of the highest-degree term is used.
If the ratio gives x to a positive power, the limit does not exist. If the ratio gives x to a negative power, the limit is zero.
The arrangement of functions according to the given condition
[tex]m(x)=\frac{4x^{2}-6 }{1-4x^{2} }[/tex]
[tex]h(x)=\frac{x^{3} -x^{2} +4}{1-3x^{2} }[/tex]
[tex]k(x)=\frac{5x+1000}{x^{2} }[/tex]
[tex]i(x)=\frac{x-1}{|1-4x| }[/tex]
[tex]g(x)=\frac{|4x-1|}{x-4}[/tex]
[tex]l(x)=\frac{5x^{2} -4}{x^{2} +1}[/tex]
[tex]f(x)=\frac{x^{2} -1000}{x-5}[/tex]
[tex]j(x)=\frac{x^{2}-1 }{|7x-1|}[/tex]
What is limit?A limit is the value that a function approaches as the input approaches some value.
According to the given question
[tex]l(x)=\frac{5x^{2} -4}{x^{2} +1}[/tex]
⇒[tex]\lim_{nx\to \infty} \frac{5x^{2} -1}{x^{2} +1}[/tex]
⇒[tex]\lim_{x \to \infty} \frac{x^{2} }{x^{2} } \frac{5-\frac{1}{x^{2} } }{1+\frac{1}{x^{2} } }[/tex]
= 5 ([tex]\frac{1}{x^{2} } = 0[/tex] ,as x tends to infinity [tex]\frac{1}{x^{2} }[/tex] tends to 0)
[tex]i(x)=\frac{x-1}{|1-4x|}[/tex]
⇒[tex]\lim_{x \to \infty} \frac{x-1}{|1-4x|}[/tex] = [tex]\lim_{x \to \infty} \frac{x}{x} \frac{1-\frac{1}{x} }{|\frac{-1}{4}+\frac{1}{x} | }[/tex] =[tex]\frac{1}{\frac{1}{4} }[/tex] =[tex]\frac{1}{4}[/tex]
As x tends to infinity 1/x tends to 0, and |[tex]\frac{-1}{4}[/tex]| gives 1/4
[tex]f(x)= \frac{x^{2} -1000}{x--5}[/tex]
⇒[tex]\lim_{x \to \infty} \frac{x^{2} -1000}{x-5}[/tex]= [tex]\lim_{x \to \infty} \frac{x^{2} }{x} \frac{1-\frac{1000}{x^{2} } }{1-\frac{5}{x} }[/tex]= [tex]\lim_{x \to \infty} x\frac{1-\frac{1000}{x^{2} } }{1-\frac{5}{x} }[/tex] ⇒ limit doesn't exist.
[tex]m(x)=\frac{4x^{2}-6 }{1-4x^{2} }[/tex]
⇒[tex]\lim_{x\to \infty} \frac{4x^{2} -6}{1-4x^{2} }[/tex]=[tex]\lim_{x\to \infty} \frac{x^{2} }{x^{2} } \frac{4-\frac{6}{x^{2} } }{\frac{1}{x^{2} } -4}[/tex] [tex]= \lim_{n \to \infty} \frac{4}{-4}[/tex] = -1
As x tends to infinity [tex]\frac{1}{x^{2} }[/tex] tends to 0.
[tex]g(x)=\frac{|4x-1|}{x-4}[/tex]
⇒[tex]\lim_{x\to \infty} \frac{|4x-1|}{x-4}[/tex] = [tex]\lim_{x \to \infty} \frac{|x|}{x} \frac{4-\frac{1}{x} }{1 -\frac{4}{x} } }[/tex] = 4
as x tends to infinity 1/x tends to 0
and |x|=x ⇒[tex]\frac{|x|}{x}=1[/tex]
[tex]h(x)=\frac{x^{3}-x^{2} +4 }{1-3x^{3} }[/tex][tex]\lim_{x \to \infty} \frac{x^{3} -x^{2} +4}{1-3x^{3} }[/tex][tex]= \lim_{x \to \infty} \frac{x^{3} }{x^{3} } \frac{1-\frac{1}{x}+\frac{4}{x^{3} } }{\frac{1}{x^{3} -3} }[/tex] = [tex]\frac{1}{-3}[/tex] =[tex]-\frac{1}{3}[/tex]
[tex]k(x)=\frac{5x+1000}{x^{2} }[/tex]
[tex]\lim_{x \to \infty} \frac{5x+1000}{x^{2} }[/tex] = [tex]\lim_{x \to \infty} \frac{x}{x} \frac{5+\frac{1000}{x} }{x}[/tex] =0
As x tends to infinity 1/x tends to 0
[tex]j(x)= \frac{x^{2}-1 }{|7x-1|}[/tex]
[tex]\lim_{x \to \infty} \frac{x^{2}-1 }{|7x-1|}[/tex] = [tex]\lim_{x \to \infty} \frac{x}{|x|}\frac{x-\frac{1}{x} }{|7-\frac{1}{x}| }[/tex] = [tex]\lim_{x \to \infty} 7x[/tex] = limit doesn't exist.
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please i need this answer right now !!!! Dx
Answer: the answer is d sin30degrees equal 5/x because sin is opposite over hyponuese
are the two triangles below similar
Answer:
Hey!
Your answer is YES!
AKA the Last Option on your screen!
Step-by-step explanation:
It is this because...
They both have the angles 105 in it...
And looking at the other angle on the smaller one (25)
50 + 25 = 75 ... 180 - 75 = 105
WE HAVE 105 as an angle on the larger triangle...which makes them SIMILAR but congruent Angles!
It cant be the "corresponding sides" as we do not have the notations (lines intersecting the sides) that let us know that the lines are the same.
Hope this helps!
Solve the system of equations for the variables: x+2y-z=3 x+y-2z= -1
Answer:
z=0
x= -5
y=4
Step-by-step explanation:
Check the attachment please
Hope this helps :)
Step-by-step explanation:
x + 2y − z = 3
x + y − 2z = -1
There are three variables but only two equations, so this system of equations is undefined. We cannot solve for the variables, but we can eliminate one of them and reduce this to a single equation.
Double the first equation:
2x + 4y − 2z = 6
Subtract the second equation.
(2x + 4y − 2z) − (x + y − 2z) = (6) − (-1)
2x + 4y − 2z − x − y + 2z = 7
x + 3y = 7
A rectangle is placed around a semicircle as shown below. The length of the rectangle is 12 cm. Find the area of the shaded region.
Use the value 3.14 for at, and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
15.48 ft^2
Step-by-step explanation:
According to the image we have the following information:
the length of the rectangle = diameter of the semicircle, therefore it is 12 feet
, the radius of the semicircle (half the diameter) = width of the rectangle = 12/2 ft = 6 ft
We also know that the area of the shaded region would be equal to the area of the rectangle minus the area of the semicircle.
Therefore, we replace:
Area of the rectangle = width * length
Ar = 6 ft * 12 ft = 72 ft ^ 2
Area of the semicircle = [1/2] * π * (r ^ 2)
As = [1/2] * 3.14 * (6 feet) ^ 2 = 56.52 ft ^ 2
We replace in the area of the shaded region
shaded region area = 72 ft ^ 2 - 56.52 ft ^ 2 =
Shaded region area = 15.48 ft ^ 2