The nonempty set with no accumulation points and no isolated points cannot exist. An example of a nonempty set with no interior points and no isolated points is the set of all rational numbers within the interval (0, 1). A nonempty set with no boundary points and no isolated points also cannot exist.
Explanation:(a) A nonempty set with no accumulation points and no isolated points cannot exist. An accumulation point in a set is a value that every open interval contains a point from the set different than itself. An isolated point is a point that has an open interval containing only itself. Every point in a nonempty set must be either an accumulated point or an isolated point.
(b) An example of a nonempty set with no interior points and no isolated points is the set of all rational numbers within the interval (0, 1). An interior point is a point where an open interval around the point lies completely within the set, which doesn't exist for this set. Also, this set does not contain any isolated points because between any two rational numbers, there always exists another rational number.
(c) A nonempty set with no boundary points and no isolated points cannot exist. A boundary point is a point that every neighborhood contains at least one point from the set and its complement. If a set does not have any boundary points, it means it cannot be separated from its complement, so it must be an empty set.
Learn more about Set Theory here:https://brainly.com/question/27333813
#SPJ12
I need help with this math question. Can you fill all the blanks please
Answer:
Δ ABC was dilated by a scale factor of 1/3, reflected across the y-axis
and moved through the translation (1 , -2)
Step-by-step explanation:
* Lets explain how to solve the problem
- The similar triangles have equal ratios between their
corresponding side
- So lets find from the graph the corresponding sides and calculate the
ratio, which is the scale factor of the dilation
- In Δ ABC :
∵ The length of the vertical line is y2 - y1
- Let A is (x1 , y1) and B is (x2 , y2)
∵ A = (-6 , 0) and B = (-6 , 3)
∴ AB = 3 - 0 = 3
- The corresponding side to AB is FE
∵ The length of the vertical line is y2 - y1
- Let F is (x1 , y1) , E is (x2 , y2)
∵ F = (3 , -2) and E = (3 , -1)
∵ FE = -1 - -2 = -1 + 2 = 1
∵ Δ ABC similar to Δ FED
∵ FE/AB = 1/3
∴ The scale factor of dilation is 1/3
* Δ ABC was dilated by a scale factor of 1/3
- From the graph Δ ABC in the second quadrant in which x-coordinates
of any point are negative and Δ FED in the fourth quadrant in which
x-coordinates of any point are positive
∵ The reflection of point (x , y) across the y-axis give image (-x , y)
* Δ ABC is reflected after dilation across the y-axis
- Lets find the images of the vertices of Δ ABC after dilation and
reflection and compare it with the vertices of Δ FED to find the
translation
∵ A = (-6 , 0) , B = (-6 , 3) , C (-3 , 0)
∵ Their images after dilation are A' = (-2 , 0) , B' = (-2 , 1) , C' = (-1 , 0)
∴ Their image after reflection are A" = (2 , 0) , B" = (2 , 1) , C" = (1 , 0)
∵ The vertices of ΔFED are F = (3 , -2) , E = (3 , -1) , D = (2 , -2)
- Lets find the difference between the x-coordinates and the
y- coordinates of the corresponding vertices
∵ 3 - 2 = 1 and -2 - 0 = -2
∴ The x-coordinates add by 1 and the y-coordinates add by -2
∴ Their moved 1 unit to the right and 2 units down
* The Δ ABC after dilation and reflection moved through the
translation (1 , -2)
MAJOR HELPPPP!!!!
An earthquake registered 7.4 on the Richter scale. If the reference intensity of this quake was 2.0 × 10^11, what was its intensity?
The correct answer would be: C. 5.02 x 10^18
Here's how you solve it!
Since the earthquake registered is 7.4 on the scale let it represent RS=7.4
The reference intensity is 2.0 x 10^11 so let it represent RI= 2.0 x 10^11
Now you need to use the formula.
[tex]RS=log(\frac{I}{I_{r} } )[/tex]
Then we need to plug in the values for the formula
[tex]7.4=log(\frac{I}{2.0 x 10^{11} } )[/tex]
[tex]I=10^{7.4}[/tex] x [tex]2.0[/tex] x [tex]10^{11}[/tex]
[tex]I= 5.02[/tex] x [tex]10^{18}[/tex]
Hope this helps! :3
Answer:
5.02×10^18
I got it right.
A garden hose can fill a swimming pool in 4 days and a larger hose can fill the pool in 2 days. How long will it take to fill the pool if both the hoses are used?
The garden house takes 4 days, so that means it fills 1/4 of the pool per day ( 1/4 x 4 days = 1)
The larger hose takes 2 days, so this means it fills 1/2 the pool per day ( 1/2 x 2 days = 1)
Using both the garden hose and larger hose means 1/4 + 1/2 = 3/4 of the pool is filled in one day.
Now we need to find X ( the number of days to completely fill the pool.
Multiply the amount per day by the number of days to equal 1 ( 1 pool):
3/4 * x = 1
To solve for x, multiply both sides of the equation by the reciprocal of 3/4, which is 4/3:
x = 4/3 *1
x = 4/3 = 1 and 1/3 days.
It will take 4/3 days or approximately 1.33 days to fill the pool when both hoses are used together.
To solve this problem, we need to understand the rate at which each hose fills the pool and then combine these rates to find the total rate when both hoses are used together.
Let's denote the fill rate of the first garden hose as 1/4 pool per day and the larger hose as 1/2 pool per day.
Using both hoses together, you add their rates to get the combined rate.
So, the combined rate of both hoses is:
1/4 + 1/2 = 3/4 pool per day.
This means three-quarters of the pool is filled in one day with both hoses working together.
To find the time (t) it takes to fill one entire pool, you can set up the equation:
3/4 * t = 1 (quantity is equal to 1 full pool)
t = 4/3 days
Therefore, it will take 4/3 days, or approximately 1.33 days, to fill the pool when both hoses are used together.
Suppose the nightly rate for a three-star hotel in paris is thought to be bell-shaped and symmetrical with a mean of 160 euros and a standard deviation of 8 euros. What is the percentage of hotels with rates between 144 and 176 euros?
Answer:
95.44% of hotels are with rate between 144 and 176 euros
Step-by-step explanation:
Given
Mean = μ = 160 euros
SD = σ = 8 euros
We have to find the z-scores for both values
So,
z-score for 144 = z_1 = (x-μ)/σ = (144-160)/8 = -16/8 = -2
z-score for 176 = z_2 = (x-μ)/σ = (176-160)/8 = 16/8 = 2
Now the area to the left of z_1 = 0.0228
Area to the left of z_2 = 0.9772
Area between z_1 and z_2 = z_2-z_1
= 0.9772-0.0228
=0.9544
Converting into percentage
95.44%
Therefore, 95.44% of hotels are with rate between 144 and 176 euros..
Using the Empirical Rule for a bell-shaped distribution, we find that approximately 95% of the hotel rates are between 144 and 176 euros.
Explanation:The question asks for the percentage of hotels with rates between 144 and 176 euros given a bell-shaped and symmetrical distribution of nightly rates for a three-star hotel in Paris, with a mean of 160 euros and a standard deviation of 8 euros. To solve this, we can apply the Empirical Rule which states that approximately 95% of data within a bell-shaped distribution lies within two standard deviations of the mean.
Calculating two standard deviations from the mean (160 ± (2 × 8)), we get the range from 144 to 176 euros. Therefore, using the Empirical Rule, we can conclude that approximately 95% of the hotel rates fall within the given range.
A dataset has 1000 records and one variable with 5% of the values missing, spread randomly throughout the records in the variable column. An analysis decides to remove records that have missing values. About how many records would you expect would be removed?
Answer:
50
Step-by-step explanation:
it is given that there is one variable with 1000 records
we have to find the records which is expected would be removed
it is given that one variable is missing with 5% that 0.05
we can find missing records by multiplying total number of records and the missing value with one variable
so the expected record removed will be =0.05×1000=50
Arc CD is 1/4 of the circumference of a circle. What is the radian measure of the central angle?
Answer:
[tex]\frac{\pi}{2}[/tex] radians
Step-by-step explanation:
We can use the concept of proportion to answer this question.
The arc CD is given to be 1/4 in measure of the circumference of the circle. A complete circle is 360 degrees in measure which in radian measure is 2π
So, the arc which 1/4 in measure of the circumference will make an angle which is 1/4 of the angle of the entire circle.
i.e.
Angle formed by the arc =[tex]\frac{1}{4} \times 2 \pi =\frac{\pi}{2}[/tex] radians
Therefore, the radian measure of the central angle of arc CD is [tex]\frac{\pi}{2}[/tex] radians
A firefighter determines that 350 feet of hose is needed to reach a particular building. If the hoses are 60 feet in length, what is the minimum number of lengths of hose needed?
Answer:
6 lengths
Step-by-step explanation:
You essentially want the smallest integer solution to ...
60x ≥ 350
x ≥ 350/60
x ≥ 5 5/6
The smallest integer solution to this is x = 6.
The minimum number of lengths of hose needed is 6.
_____
Informally, you know that dividing the required total length by the length of one hose will tell you the number of required hoses. You also know the ratio 350/60 is equivalent to 35/6 and that this will be between 5 and 6. (5·6 = 30; 6·6 = 36) The next higher integer value will be 6.
Find the missing length on the triangle. Round your answer to the nearest tenth if
necessary
a: 15
B: 113
c: 12
d: 10.6
Answer:
D. 10.6
Step-by-step explanation:
Using Pythagoras' theorem
hyp² = side ² + side²
hyp² = 7² + 8²
hyp² = 49 + 64
hyp² = 113
hyp = sqrt of 113
hyp = 10.6
PLEASE DO MARK ME AS BRAINLIEST IF MY ANSWER IS HELPFUL ;)
The correct answer is option d. 10.6.
Given:
AB = 7BC = 8∠B = 90°The hypotenuse is AC. Therefore, we use the formula:
AC² = AB² + BC²
Substituting the given values:
AC² = 7² + 8²
AC² = 49 + 64
AC² = 113
Now, take the square root of both sides to find AC:
AC = √113 ≈ 10.6
Thus, the missing length AC is approximately 10.6.
The correct answer is d. 10.6.
Complete question: Find the missing length on the triangle. AB = 7, BC = 8 ∠B = 90°. Round your answer to the nearest tenth if necessary
a. 15
b. 113
c. 12
d. 10.6
Find the the measure of angle C
Answer:
65.4
Step-by-step explanation:
Use the Law of Sines here. The Law is as follows:
[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]
We only have need for 2 of those 3 proportions. Since we can have only 1 unknown in a single equation, we have to use angle C as that unknown. That means that other angle and side have to be given in the problem. Angle B is given as 45 and side b is given as 7, so we will use those.
[tex]\frac{sinC}{9}=\frac{sin45}{7}[/tex]
We solve for sinC:
[tex]sinC=\frac{9sin45}{7}[/tex]
Doing that on our calculator gives us
sinC = .9091372901
Taking the inverse sin in degree mode gives you that angle C = 65.4
A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce: f(n) = 9(0.7)n What does the number 9 in the function represent?
Answer:
9 represents the initial height from which the ball was dropped
Step-by-step explanation:
Bouncing of a ball can be expressed by a Geometric Progression. The function for the given scenario is:
[tex]f(n)=9(0.7)^{n}[/tex]
The general formula for the geometric progression modelling this scenario is:
[tex]f(n)=f_{0}(r)^{n}[/tex]
Here,
[tex]f_{0}[/tex] represents the initial height i.e. the height from which the object was dropped.
r represents the percentage the object covers with respect to the previous bounce.
Comparing the given scenario with general equation, we can write:
[tex]f_{0}[/tex] = 9
r = 0.7 = 70%
i.e. the ball was dropped from the height of 9 feet initially and it bounces back to 70% of its previous height every time.
Find the equation of a line given the point and slope below. Arrange your answer in the form y = mx + b, where b is the constant.
(1, 3)
m = 3
i need help with this question and others like it, an explanation would be great, im on a deadline and need to finish these as soon as possible ty
Answer:
y = 3x
Step-by-step explanation:
y = mx + b
(x,y) = (1,3)
m = 3
3 = 3(1) + b
3 = 3 + b
3 - 3 = b
0 = b
y = 3x
For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
According to the data we have to:
[tex]m = 3\\(x, y) :( 1,3)[/tex]
So, the equation is of the form:
[tex]y = 3x + b[/tex]
We substitute the point and find b:
[tex]3 = 3 (1) + b\\3 = 3 + b\\b = 3-3\\b = 0[/tex]
Finally, the equation is of the form:
[tex]y = 3x[/tex]
Answer:
[tex]y = 3x[/tex]
If angle A is 45 degrees and angle B is 60 degrees.
Find sin(A)cos(B)
½ (sin(105) + sin(345))
½ (sin(105) - sin(345))
½ (sin(345) + cos(105))
½ (sin(345) - cos(105))
Answer:
(1/2)(sin(105°) +sin(345°))
Step-by-step explanation:
The relevant identity is ...
sin(α)cos(β) = (1/2)(sin(α+β) +sin(α-β))
This falls out directly from the sum and difference formulas for sine.
Here, you have α = 45° and β = 60°, so the relevant expression is ...
sin(45°)cos(60°) = (1/2)(sin(45°+60°) +sin(45°-60°)) = (1/2(sin(105°) +sin(-15°))
Recognizing that -15° has the same trig function values that 345° has, this can be written ...
sin(45°)cos(60°) = (1/2)(sin(105°) +sin(345°))
Given that angle A is 45 degrees and angle B is 60 degrees, we use the product-to-sum identity in Trigonometry to find sin(A)cos(B). The correct answer after simplifying the formula sin(A)cos(B) = ½ [sin(A + B) + sin(A - B)] is ½ [sin(105) + sin(345)].
Explanation:In Mathematics, especially Trigonometry, there is a formula known as product-to-sum identities. One of the identities is Sin(A)Cos(B) = ½ [sin(A + B) + sin(A - B)].
Given that angle A is 45 degrees and angle B is 60 degrees, we will find sin(A)cos(B) by substituting A and B in the formula.
On substitution you get ½ [sin(45 + 60) + sin(45 - 60)], which simplifies to ½ [sin(105) + sin(-15)]. Note that sin(-15) is equivalent to sin(345) in the unit circle, therefore the expression further simplifies to ½ [sin(105) + sin(345)].
Learn more about Product-to-Sum Identity here:https://brainly.com/question/34814515
#SPJ11
If point P is 4/7 of the distance from M to N, then point P partitions the directed line segment from M to N into a ..
A. 4:1
b. 4:3
c. 4:7
d: 4:11
Answer:
b) 4:3
Step-by-step explanation:
The point P is 4/7 of the distance from point M to point N. This means that moving from M to N, the total distance is divided into 7 equal parts and the point P lies after the 4 parts starting from M.
So, out of 7, 4 parts are present between M and P. and the remaining 3 parts are present between P and N. In other words we can say,when we move from M towards N, the line segment MP covers 4 out of 7 parts and the line segment PN covers the 3 parts.
So, we can conclude here that the point P partitions the directed line segment from M to N into a 4:3
Answer:
B. 4:3 is your answer
Use the properties of logarithms and the values below to find the logarithm indicated.
Answer:
-2B
Step-by-step explanation:
log₉ (1/16)
log₉ (16^-1)
log₉ (4^-2)
Using exponent property of logs:
-2 log₉ (4)
Substituting:
-2B
Answer:
-2B
(I guess this is what you are looking for; didn't need A or C).
Step-by-step explanation:
It seems like to wants us to to find [tex]\log_9(\frac{1}{16})[/tex] in terms of [tex]A,B,C[/tex].
First thing I'm going to do is rewrite [tex]\log_9(\frac{1}{16})[/tex] using the quotient rule.
The quotient rule says:
[tex]\log_m(\frac{a}{b})=\log_m(a)-\log_m(b)[/tex]
So that means for our expression we have:
[tex]\log_9(\frac{1}{16})=\log_9(1)-\log_9(16)[/tex]
Second thing I'm going to do is say that [tex]\log_9(1)=0 \text{ since } 9^0=1[/tex].
[tex]\log_9(\frac{1}{16})=\log_9(1)-\log_9(16)[/tex]
[tex]\log_9(\frac{1}{16})=-\log_9(16)[/tex]
Now I know 16 is 4 squared so the third thing I'm going to do is replace 16 with 4^2 with aim to use power rule.
[tex]\log_9(\frac{1}{16})=\log_9(1)-\log_9(16)[/tex]
[tex]\log_9(\frac{1}{16})=-\log_9(16)[/tex]
[tex]\log_9(\frac{1}{16})=-\log_9(4^2)[/tex]
The fourth thing I'm going to is apply the power rule. The power rule say [tex]\log_a(b^x)=x\log_a(b)[/tex]. So I'm applying that now:
[tex]\log_9(\frac{1}{16})=\log_9(1)-\log_9(16)[/tex]
[tex]\log_9(\frac{1}{16})=-\log_9(16)[/tex]
[tex]\log_9(\frac{1}{16})=-2\log_9(4)[/tex]
So we are given that [tex]\log_9(4)[/tex] is [tex]B[/tex]. So this is the last thing I'm going to do is apply that substitution:
[tex]\log_9(\frac{1}{16})=\log_9(1)-\log_9(16)[/tex]
[tex]\log_9(\frac{1}{16})=-\log_9(16)[/tex]
[tex]\log_9(\frac{1}{16})=-2\log_9(4)[/tex]
[tex]\log_9(\frac{1}{16})=-2B[/tex]
Given |u| = 2.5, |v| = 3.2, and the angle between the vectors is 60°, find the value of u · v?
Step-by-step explanation:
u.v=|u||v|cos60°
u.v=(2.5)(3.2)(1/2)
u.v=(8)(1/2)
u.v=4
Bernard solved the equation 5x+(-4)=6x+4 using algebra tiles.Which explains why Bernard added 5 negative x-tiles to both sides in the first step of the solution ?
Answer:
To remove 5x and create and linear equation
Step-by-step explanation:
5x+(-4)=6x+4
The equation can be solved by arranging terms so that numbers can be on one side and other constants will be on the other side.
This is given by the associative rule that states:
(-5x) + 5x + (-4) = 6x +4 - 5x
giving:
-4 = x + 4
this gives, x= -8
Hence a linear equation with a solution.
The function A(d) =0.65d+195 models the amount A, in dollars, the thomas's company pays him based on round trip distance d, in miles, that thomas travels to the job site. How much does thomas's pay increase for every mile of travel?
Answer:
$0.65
Step-by-step explanation:
When d increases by 1, A(d) increases by 0.65 dollars.
Thomas gets paid $0.65 for every mile of travel.
please help!!!
Which ordered triple represents all of the solutions to the system of equations shown below?
2x - 2y - z = 6
-x + y + 3z = -3
3x - 3y + 2z = 9
a(-x, x + 2, 0)
b(x, x - 3, 0)
c(x + 2, x, 0)
d(0, y, y + 4)
What is the solution to the system of equations shown below?
2x - y + z = 4
4x - 2y + 2z = 8
-x + 3y - z = 5
a (5, 4, -2)
b (0, -5, -1)
c No Solution
d Infinite Solutions
Answer:
b (x, x - 3, 0)d Infinite SolutionsStep-by-step explanation:
1. A graphing calculator or any of several solvers available on the internet can tell you the reduced row-echelon form of the augmented matrix ...
[tex]\left[\begin{array}{ccc|c}2&-2&-1&6\\-1&1&3&-3\\3&-3&2&9\end{array}\right][/tex]
is the matrix ...
[tex]\left[\begin{array}{ccc|c}1&-1&0&3\\0&0&1&0\\0&0&0&0\end{array}\right][/tex]
The first row can be interpreted as the equation ...
x -y = 3
x -3 = y . . . . . add y-3
The second row can be interpreted as the equation ...
z = 0
Then the solution set is ...
(x, y, z) = (x, x -3, 0) . . . . matches selection B
__
2. The second equation is 2 times the first equation, so the system of equations is dependent. There are infinite solutions.
NEEED HPP!!!
Kelly bought a new car for $20,000. The car depreciates at a rate of 10% per year.
What is the decay factor for the value of the car?
Write an equation to model the car’s value.
Use your equation to determine the value of the car six years after Kelly purchased it.
Answer:
a) decay factor is b = 0.9
b) y = 20,000(0.9)^x
c) y = $10,629
Step-by-step explanation:
a) What is the decay factor for the value of the car?
The formula used to find the decay factor is
y = a(b)^x
where y = future value
a = current value
b = decay factor
x = time
The decay factor is: b = 1-r
We are given rate r = 10% or 0.1
b = 1 - 0.1
b = 0.9
So, decay factor is b = 0.9
b) Write an equation to model the car’s value.
Using the formula:
y = a(1-r)^x
y = 20,000(1-0.1)^x
y = 20,000(0.9)^x
c) Use your equation to determine the value of the car six years after Kelly purchased it.
y = 20,000(0.9)^x
We need to find value after 6 years, so x=6
y = 20,000(0.9)^6
y = 10,628.82
y = $10,629
Someone Please Help Me With This
n
_ = 1 6
3
Answer:
n=48
Step-by-step explanation:
n
_ = 1 6
3
Multiply each side by 3
n/3 * 3 = 16*3
n = 48
Identify y. HELP ASAP!
Answer:
y = 2
Step-by-step explanation:
I am assuming there was some info that got left out of this that states somewhere along the line that this is right triangle inscribed in a circle or something like that. That means that angle R is a right angle. Therefore,
53y - 16 = 90 so
53y = 106 and
y = 2
The value of y is 2.
What is the value of inscribed angle in a semi circle?Using the Inscribed angle theorem, in a semi-circle, the inscribed arc measures 180° for which inscribed angle in semi-circle will be half of 180° i.e. the inscribed angle in semi-circle will be right-angle i.e. 90°.
Here As PQ crosses the center of the circle M. so PQ ia the diameter.
the measure of the arc PRQ is 180°.
then using inscribed angle theorem, ∠PRQ will be half of 180°.
So, ∠PRQ =90°
Given, ∠PRQ= 53y-16°
⇒90°=53y-16°
⇒53y=90°+16°=116°
⇒y=116°/53°
⇒y=2
Therefore the value of y is 2.
Learn more about inscribed angle in semicircle
here: https://brainly.com/question/8156314
#SPJ2
Help please if you can?
If f(x) = -2x - 5 and g(x) = x^4 what is (gºf)(-4)
Answer:
81
Step-by-step explanation:
g(x) = x^4 put f(x) in for x in g(x)
g(f(x)) = (f(x))^4 Substitute the value for f(x) which is (-2x - 5) put - 4 in for the x in f(x)
g(f(x) = (-2x - 5)^4
g(f(x)) = (- 2*(- 4) - 5)^4 Combine
g(f(x)) = (8 - 5)^4 Subtract
g(-4) = (3)^4 Raise 3 to the 4th power
g(-4) = 81 Answer.
What is the measure x?
Answer:
x° = 78°
Step-by-step explanation:
x° is the measure of external angle BHC of triangle BHD. As such, its measure is the sum of the opposite interior angles at B and D:
47° + 31° = x° = 78°
A person's website specializes in the sale of rare or unusual vegetable seeds. He sells packets of sweet-pepper seeds for $2.32 each and packets of hot-pepper seeds for $4.56 each. He also offers a 16-packet mixed pepper assortment combining packets of both types of seeds at $3.16 per packet. How many packets of each type of seed are in the assortment?
There are _____packets of sweet-pepper seeds and _____- packets of hot-pepper seeds.
Answer:
There are 10 packets of sweet-pepper seeds and 6 packets of hot-pepper seeds.
Step-by-step explanation:
Let h represent the number of packets of hot pepper seeds. Then 16-h is the number of packets of sweet pepper seeds. The total cost of a 16-packet mix is ...
4.56h + 2.32(16 -h) = 3.16·16
2.24h + 37.12 = 50.56 . . . . . . . simplify
2.24h = 13.44 . . . . . . . . . . . . . . subtract 37.12
13.44/2.24 = h = 6 . . . . . . . . . . divide by 2.24
16 -h = 16 -6 = 10 . . . . . . . . . . . number of sweet pepper seed packets
There are 10 packets of sweet-pepper seeds and 6 packets of hot-pepper seeds.
A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled?
Answer:1866
Step-by-step explanation:
Given
n=200
x=118
Population proportion P=[tex]\frac{118}{200}[/tex]=0.59
[tex]\alpha [/tex]=0.005
Realiability =99%
[tex]Z_{\frac{\alpha }{2}}=2.576[/tex]
Margin of erroe is given by [tex]\sqrt{\frac{p\left ( 1-p \right )}{N}}[/tex]
0.03= [tex]\sqrt{\frac{0.59\left ( 1-0.59 \right )}{N}}[/tex]
85.667=[tex]\sqrt{\frac{N}{0.6519}}[tex]
N=1865.88[tex]\approx 1866 Students[/tex]
To estimate the proportion of students receiving financial aid within 3% with 99% reliability, the dean needs to sample about 1846 students. This is calculated using the formula for the sample size in a proportion estimation with a 99% confidence level and a 3% margin of error.
Explanation:The subject matter of your question involves using statistics to estimate a population proportion with a specified confidence level and margin of error. This can be calculated using the formula for the sample size in a proportion estimation: n = (Z² * p * (1-p)) / E², where Z is the Z-score, p is the preliminary estimate of the proportion, and E is the desired margin of error.
In this case, the Z-score for a 99% confidence level is approximately 2.58 (you can find this value in a standard normal distribution table). The preliminary estimate of the proportion (p) can be obtained from the initial sample: 118 in 200. So, p = 118/200 = 0.59. The desired margin of error (E) is 3%, or 0.03.
Putting these values into the formula, we get n = (2.58²* 0.59 * (1 - 0.59)) / 0.03² = approximately 1846. This means the dean would need to randomly sample about 1846 students to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability.
Learn more about Proportion Estimation here:https://brainly.com/question/32913852
#SPJ3
Find the roots of the parabola given by the following equation.
2x2+ 5x - 9 = 2x
Answer:
x=-3 or x=3/2
Step-by-step explanation:
We are given the following equation:
2x^2+5x-9=2x
We are asked to find the roots. That means just solve it for x.
2x^2+5x-9=2x
Subtract 2x on both sides:
2x^2+3x-9=0
Let's see if we can put this in factored form.
Compare
2x^2+3x-9=0
and
ax^2+bx+c=0.
a=2, b=3 , c=-9
We have to find two numbers that multiply to be ac and add up to be b.
ac=-18
b=3
What are two numbers that multiply to be -18 and add to be 3?
Say -3 and 6.
So we are going to factor 2x^2-3x+6x-9=0
The first two terms have a common factor of x.
The last two terms have a common factor of 3.
2x^2-3x+6x-9=0
x(2x-3)+3(2x-3)=0
Now we can factor the (x-3) out of those 2 terms there since they share that common factor:
(x+3)(2x-3)=0
(x+3)(2x-3)=0 implies x+3=0 or 2x-3=0.
So we must solve x+3=0 and 2x-3=0
x+3=0
Subtract 3 on both sides:
x=-3
2x-3=0
Add 3 on both sides:
2x=3
Divide both sides by 2:
x=3/2
The solutions are x=3 or x=-3/2
If the distance from Bermuda to San Juan is 954 miles, what is the distance from San Juan to Miami. Round your answer to nearest mile
954 mi.
1058 mi
1061 mi
1088 mi
Answer: 1088 :)
Step-by-step explanation:
The distance from San Juan to Miami is 1088 miles.
What is a triangle?
A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. Types of triangles include: scalene, right triangle, isosceles and equilateral triangle.
What is the distance from San Juan to Miami?The law of sine would be used to determine the distance.
(a / sin a) = (b / sin b) = (c / sin c)
(a / sin 63) = [960 / (180 - 62 - 63)]
a / sin 63 = 960 / sin 54
a = (sin 63 x 960) / sin 54
a = 1088 miles
Please find attached the complete question. To learn more about a triangle, please check: https://brainly.com/question/9329354
WHEN gEORGE AND aNTHEA WERE MARRIED 120 OF THE GUEST aNTHEA'S FAMILY OR FRIENDS. THIS WAS 60 PERCENT OF THE TOTAL number of guest. How many guest were altogether ?
Answer:
Step-by-step explanation:
In this problem, we will use ratios
60%------->120 guests
30%-------->60guests
10%---------->20guests
Multiply by 10 to both sides to get 200
100%--------> 200 guests
hope this helps!
Find the complete factored form of the polynomial: 25mn^2 +5mn
[tex]25mn^2 +5mn =5mn(5n+1)[/tex]
The complete factored form of the polynomial 25mn^2 + 5mn is mn(25n + 5).
Explanation:The given polynomial is 25mn^2 + 5mn. To find the complete factored form, we can factor out the GCF (Greatest Common Factor) from each term, which in this case is mn:
Factor out mn from each term: mn(25n + 5)So, the complete factored form of the polynomial 25mn^2 + 5mn is mn(25n + 5).
Learn more about Factoring Polynomials here:https://brainly.com/question/35418869
#SPJ2
Mary, who has type O blood, is expecting a child with her husband, who has type B blood. Mary's husband's father has type A blood. What is the probability that the child will have type O blood
Answer:
50% is the answer.
Step-by-step explanation:
All three persons have different blood groups.
Mary has O blood type.
Her husband has B blood type.
Her father in law has A blood type.
As everyone has different blood groups and the child's group depends on parents blood groups so we have 2 options left.
Hence, the probability that the child will have type O blood is = [tex]\frac{1}{2}[/tex] =50%
Answer:
50/ 50
Step-by-step explanation:
The father's father blood doesn't really matter since the husband has type B. It's just a 50/50 chance between B and O.