Answer:
Step-by-step explanation:
The summary of the given data includes;
sample size for the first school [tex]n_1[/tex] = 42
sample size for the second school [tex]n_2[/tex] = 34
so 16 out of 42 i.e [tex]x_1[/tex] = 16 and 18 out of 34 i.e [tex]x_2[/tex] = 18 have ear infection.
the proportion of students with ear infection Is as follows:
[tex]\hat p_1 = \dfrac{16}{42}[/tex] = 0.38095
[tex]\hat p_2 = \dfrac{18}{34}[/tex] = 0.5294
Since this is a two tailed test , the null and the alternative hypothesis can be computed as :
[tex]H_0 :p_1 -p_2 = 0 \\ \\ H_1 : p_1 - p_2 \neq 0[/tex]
level of significance ∝ = 0.05,
Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.
The test statistics for the difference in proportion can be achieved by using a pooled sample proportion.
[tex]\bar p = \dfrac{x_1 +x_2}{n_1 +n_2}[/tex]
[tex]\bar p = \dfrac{16 +18}{42 +34}[/tex]
[tex]\bar p = \dfrac{34}{76}[/tex]
[tex]\bar p = 0.447368[/tex]
[tex]\bar p + \bar q = 1 \\ \\ \bar q = 1 -\bar p \\ \\\bar q = 1 - 0.447368 \\ \\\bar q = 0.552632[/tex]
The pooled standard error can be computed by using the formula:
[tex]S.E = \sqrt{ \dfrac{ \bar p \bar q}{ n_1} + \dfrac{\bar p \bar p}{n_2} }[/tex]
[tex]S.E = \sqrt{ \dfrac{ 0.447368 * 0.552632}{ 42} + \dfrac{ 0.447368 * 0.447368}{34} }[/tex]
[tex]S.E = \sqrt{ \dfrac{ 0.2472298726}{ 42} + \dfrac{ 0.2001381274}{34} }[/tex]
[tex]S.E = \sqrt{ 0.01177284105}[/tex]
[tex]S.E = 0.1085[/tex]
The test statistics is ;
[tex]z = \dfrac{\hat p_1 - \hat p_2}{S.E}[/tex]
[tex]z = \dfrac{0.38095- 0.5294}{0.1085}[/tex]
[tex]z = \dfrac{-0.14845}{0.1085}[/tex]
z = - 1.368
Decision Rule: Since the test statistics is greater than the rejection region - 1.96 , we fail to reject the null hypothesis.
Conclusion: There is insufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools
The function f(x) = (x - 4)(x - 2) is shown.
What is the range of the function?
o all real numbers less than or equal to 3
o all real numbers less than or equal to -1
O all real numbers greater than or equal to 3
O all real numbers greater than or equal to -1
2
61
-1028
-2
Answer:
all real numbers greater than or equal to -1
Step-by-step explanation:
In order to solve this problem we need to know the vertex and the direction its pointing.
First we expand,
x^2-6x+8
To find the x value of the vertex we use this formula (-b/2a).
-(-6)/2(1) = 3
Now we plug 3 in the equation to get the y value,
(3)^2 - 6(3) + 8 = 9 - 18 + 8 = -1
The vertex is (3,-1)
We know the graph points up because x^2 is positive
The vertex is the lowest point, so we now know that -1 is the starting range and if the graph is pointing up, that means all values greater than -1.
This leads to our answer all real numbers greater than or equal to -1.
HELP ME PLEASE!!!!!!!!! WORTH 100 POINTS WILL FOLLOW AND RATE BRAINLIEST ANSWER!!!!!!!!!!!! If the function f(x) has a domain of (a,b] and a range of [c,d), then what is the domain and range of g(x)=m×f(x)+n?(1 point) A.The domain of g(x) is (ma+n,mb+n], and the range is [c,d). B.The domain of g(x) is (a,b], and the range is [mc+n,md+n). C.The domain of g(x) is (a,b], and the range is [c,d). D.The domain of g(x) is (ma+n,mb+n], and the range is [mc+n,md+n).
Greetings from Brasil...
If domain is (a,b] and the range is [c,d), so:
f(a) = c
f(b) = d
so
g(x) = m × f(x) + n
g(a) = m × f(a) + n how f(a) = c, then
g(a) = mc + n
g(b) = m × f(b) + n
g(b) = md + n
So
Domain = (a; b]Range = [mc + n; md + n)Write a differential equation that fits the physical description. The at time t is proportional to the power of its .
Complete Question
The complete question is shown on the first uploaded image
Answer:
The differential equation that fits the physical description is [tex]\frac{d (v(t))}{dt} = z [v(t)]^2[/tex]
Step-by-step explanation:
From the question we are told that
The acceleration due to air resistance of a particle moving along a straight line at time t is proportional to the second power of its velocity v, this can be mathematically represented as
[tex]a(t) \ \ \alpha \ \ \ [v(t)]^2[/tex]
Where [tex]a(t)[/tex] is the acceleration at time t
and [tex]v(t)[/tex] is the velocity at time t
So
=> [tex]a(t)= z [v(t)]^2[/tex]
Where z is a constant
Generally acceleration is mathematically represented as
[tex]a(t) = \frac{d (v(t))}{dt}[/tex]
So
[tex]\frac{d (v(t))}{dt} = z [v(t)]^2[/tex]
A homeowner wants to build a fence to enclose a 320 square yard rectangular area in his backyard. Along one side the fence is to be made of heavy-duty material costing $9 per yard, while the material along the remaining three sides costs $1 per yard. Determine the least cost to the homeowner.
Answer:
Determination of the least cost of fence enclosure:
= cost of heavy-duty one side of the length plus cost of remaining three sides of the fence
= $416 ($360 + $56)
= $416
Step-by-step explanation:
Rectangular Fence Area = 320 square yard
Since fence is rectangular, the two sides are length and width
Length of rectangular is always greater than the width
Length cannot be 20 yard with width as 16 yard
Therefore, length = 40 yard and width = 8 yard.
Proof: Area of a rectangular = 40 x 8 = 320 square yard
Since, parameter = 2 (Length + Width)
= 2 x (40 + 8)
= 96 yards
Therefore, along one side with heavy-duty material is one length side of the fence = 40 yard
Cost of the one length with heavy-duty material = 40 x $9 = $360
Remaining three sides = 96 - 40 = 56 yard
Cost of remaining three sides = 56 x $1 = $56
Total cost of fencing = $416 ($360 + $56)
[tex] {4}^{3} [/tex]
evaluate this expression
Answer:
64
Step-by-step explanation:
Answer:
64
Step-by-step explanation:
4^3
= 4 * 4 * 4
= 16 * 4
= 64
Mr Osei has a rectangular field measured 85m long and 25m wide. How long is the distance around the field?
Answer:
220m
Step-by-step explanation:
l=85m
b=25m
perimeter=2(l+b)
2(85+25)
2(110)
=220m
perimeter is 220m
Answer:
Distance around the field is 220mStep-by-step explanation:
The distance around the field means the perimeter of the field
Since the field is rectangular
Perimeter of a rectangle = 2l + 2w
where l is the length
w is the width
From the question
l = 85m
w = 25m
Perimeter = 2(85) + 2(25)
Perimeter = 170 + 50
The final answer is
Perimeter = 220m
Hope this helps you
1 Dorji
ran 2km in 20 minutes. A that rake how far would he
run in an hour?
-->
Answer:
8km
Step-by-step explanation:
if he took 20km in 20min how about 1h
do cross multiplication( use 60min instead of 1h)1h = 60min
Zamba has found a little black dress on sale for 50% off the original price of $239.99. She also has a coupon offering free shipping and an additional 10% off of her entire online purchase. If she buys the dress and a pair of shoes costing $34.70, how much will she pay for her ensemble?
$108.00
$104.70
$94.23
$139.23
Answer:
$139.23
Step-by-step explanation:
50% off the original price of $239.99
= $239.99-(0.5*239.99)
= 239.99-119.995
= $119.995
She purchase a pair of shoes also worth $34.70
Total cost now= $119.995 + $34.70
Total cost now= $154.695
But she has a coupon that gives her 10% off her total sales
Now she wants pay
= $154.695 - 0.1(154.695)
= $154.695-15.4695
= $139.2255
Approximately $139.23
Mr Gomez wants to put a ceramic Tile border along for all four sides of his kitchen wall mr. Gomez has measured and knows he needs enough tiles to make three rows with 63 tiles in each row on each of his for how many tiles is mr. Goma's need to make the border tiles are sold in boxes with 14 tiles in each box how many boxes of tile does mr. Gomez need to buy show all your mathematical thinking please explain step by step
Answer:
14 boxes
Step-by-step explanation:
We are given that he needs 3 rows with 63 tiles per row.
Hence total number of tiles needed:
= 3 rows x 63 tiles per row
= 189 tiles
we are also given that tiles come in boxes of 14 tiles.
Hence the number of boxes of tiles needed,
= 189 tiles ÷ 14 tiles per box
= 13.5 boxes
but because he cannot just buy 0.5 of a box (i.e he needs to buy whole boxes), we must round this number up to the next whole box
hence
13.5 boxes rounded up to next whole box = 14 boxes.
If the bathtub holds a total of 46.2 gallons, how many minutes would it take to fill the entire tub? Write an equation in one variable to help you solve the problem. The variable represents the unknown time in minutes.
Answer:
46.2÷m=x
Step-by-step explanation:
u divide the amount of water by the time it takes to fill up(m). Witch will equal the amount per minute (x).
16.5/min
time = m
gallons / minutes = rate
46.2 = 16.5 (m)
46.2 / 16.5 = 16.5 (m) / 16.5
2.8 = minutes
In a small town 68% of the people owned television 72% on radio and 12% owned neither television nor radio (1)represent the information on a Veen diagram.
(2)what percentage of the population owned television.
Answer:
See attachment for Venn diagram
Percentage of only TV owners is 16%
Step-by-step explanation:
Given
[tex]TV\ Owners = 68\%[/tex]
[tex]Radio\ Owners = 72\%[/tex]
[tex]None = 12\%[/tex]
Required
Represent with a Venn Diagram
What percentage owned television
From the Venn Diagram and In sets theory; we have that
Total = (TV Owners - Radio and TV Owners) + (Radio Owner - Radio and TV Owners) + Radio and TV Owners + None
Represent Radio and TV Owners with y
[tex]Total = (TV\ Owners - y) + (Radio\ Owner - y) + y + None[/tex]
Substitute 68% for TV Owners, 72% for Radio Owners, 12& for None:
[tex]Total = 68\% - y + 72\%- y + y + 12\%[/tex]
Collect Like Terms
[tex]Total = 68\% + 72\%+ 12\%- y + y - y[/tex]
[tex]Total = 152\% - y[/tex]
In Sets, Total represents 100%; So, we have
[tex]100\% = 152\% - y[/tex]
Make y the subject of formula
[tex]y = 152\% - 100\%[/tex]
[tex]y = 52\%[/tex]
The percentage of only TV owners is calculated by subtracting y from TV owners
[tex]\%P = 68\% - 52\%[/tex]
[tex]\%P = 16\%[/tex]
Answer:
The answer is 90%
Step-by-step explanation:
m+1/4d=7 solve for d
Answer:
d = -4M + 28
Step-by-step explanation:
The regular hexagon ABCDEF rotates 240º counterclockwise about its center to form hexagon A′B′C′D′E′F′. Point C′ of the image coincides with point
of the preimage. Point D′ of the image coincides with point
of the preimage.
Answer:
Point C: G
Point D: F
Step-by-step explanation:
A hexagon has 6 sides.
360/6=60
Every 60°, it moves one section.
240/60=4.
So it moves 4 sections.
C would move 4 sections BACK (B, A, F, G)
D would also move 4 sections back (C, B, A, F)
Answer:
Point C is: E
point D is : F
Step-by-step explanation:
Will mark Brainliest! Which point is a vertex of the hyperbola?
A. (1,−15)
B. (1,−2)
C. (1,3)
D. (1,11)
Answer:
So (1,3) is a vertex (out of two) of the hyperbola.
Step-by-step explanation:
The vertices are marked by the dot on the hyperbola.
They are (1,3) and (1,-7).
However, (1,-7) is not on the list of answer choices, but (1,3) is.
So (1,3) is a vertex (out of two) of the hyperbola.
So (1,3) is a vertex (out of two) of the hyperbola.
What is hyperbola?a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant : a curve formed by the intersection of a double right circular cone with a plane that cuts both halves of the cone.
According to the question
The vertices are marked by the dot on the hyperbola.
They are (1,3) and (1,-7).
However, (1,-7) is not on the list of answer choices, but (1,3) is.
Hence , (1,3) is a vertex (out of two) of the hyperbola.
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For the following graph, state the polar coordinate with a positive r and positive q (in radians). Explain your steps as to how you determined the coordinate (in your own words). I'm looking for answers that involve π, not degrees for your angles. State the polar coordinate with (r, -q). Explain how you found the new angle. State the polar coordinate with (-r, q). Explain how you found the new angle. State the polar coordinate with (-r, -q). Explain how you found the new angle.
Answer:
Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )
Step-by-step explanation:
For the first two cases, ( r, θ ) r would be > 0, where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.
So when r is positive, we can tell that this point is 8 units from the pole, so r is going to be 8 in either case,
( 8, 240° ) - because r is positive, theta would have to be an angle with which it's terminal side passes through this point. As you can see that would be 2 / 3rd of 90 degrees more than a 180 degree angle,or 60 + 180 = 240 degrees.
( 8, - 120° ) - now theta will be the negative side of 360 - 240, or in other words - 120
Now let's consider the second two cases, where r is < 0. Of course the point will still be 8 units from the pole. Again for r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.
( - 8, 60° ) - theta will now be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Thus our second point for - r will be ( - 8, - 300° )
_________________________________
So we have the points ( 8, 240° ), ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). However we only want 3 cases, so we have points ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). Let's convert the degrees into radians,
Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )
I drive 13 miles each way to work every day. It sometimes takes me 20 minutes to get to work, and sometimes it takes me 30 minutes. If Distance = Rate x Time, at what rate am I going if it takes me 20 minutes to get to work? At 30 minutes?
Answer:
39 mph
26 mph
Step-by-step explanation:
distance = rate * time
20 minutes:
13 miles = rate * 20 minutes
rate = (13 miles)/(20 minutes) * (60 minutes)/(hour)
rate = 39 mph
30 minutes:
13 miles = rate * 30 minutes
rate = (13 miles)/(30 minutes) * (60 minutes)/(hour)
rate = 26 mph
When csc(Theta)sin(Theta) is simplified, what is the result? StartFraction 1 Over cosecant squared EndFraction StartFraction 1 Over sine squared EndFraction 0 1
Step-by-step explanation:
csc θ sin θ
(1 / sin θ) sin θ
1
The simplified value of the given expression comes to be 1.
The given expression is:
[tex]cosec\theta.sin\theta[/tex]
What is the trigonometric ratio [tex]cosec\theta[/tex]?The trigonometric ratio [tex]cosec\theta[/tex] is the ratio of the hypotenuse to the opposite side. It is the inverse of [tex]sin\theta[/tex].
[tex]cosec\theta=\frac{1}{sin\theta}[/tex]
We know that [tex]cosec\theta=\frac{1}{sin\theta}[/tex]
So [tex]cosec\theta.sin\theta[/tex]
[tex]=\frac{1}{sin\theta} .sin\theta[/tex]
=1
So, the simplified value is 1.
Hence, the simplified value of the given expression comes to be 1.
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I will rate you brainliest!
Answer:
B
Step-by-step explanation:
X must not be equal to -6, -1, 1 or 3
Please help! Find the equation of the line (graph provided in attached picture) Use exact numbers. y =_ x+_ ( _ represent blanks in the equation)
Answer:
[tex] y = \frac{3}{4}x - 2 [/tex]
Step-by-step explanation:
Equation of a line is given as [tex] y = mx + b [/tex]
Where,
m = slope of the line = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
b = y-intercept, which is the value at the point where the line intercepts the y-axis. At this point, x = 0.
Let's find m and b to derive the equation for the line.
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Use the coordinate pair of any two points on the line. Let's use the following,
[tex] (0, -2) = (x_1, y_1) [/tex] => on the line, when x = 0, y = -2
[tex] (4, 1) = (x_2, y_2) [/tex] => on the line, when x = 4, y = 1
Plug in the values and solve for m
[tex] m = \frac{1 - (-2)}{4 - 0} [/tex]
[tex] m = \frac{1 + 2}{4} [/tex]
[tex] m = \frac{3}{4} [/tex]
b = -2 (the line intercepts the y-axis at this point)
Our equation would be =>
[tex] y = mx + b [/tex]
[tex] y = \frac{3}{4}x + (-2) [/tex]
[tex] y = \frac{3}{4}x - 2 [/tex]
What is the approximate value of x in –2 ln (x + 1) − 3 = 7?
Answer:
x = 1/e^-5 - 1
Step-by-step explanation:
–2 ln (x + 1) − 3 = 7
–2 ln (x + 1) = 10
ln (x + 1) = –5
x + 1 = e^-5
x = e^-5 - 1
x = 1/e^-5 - 1
the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.
To solve the equation -2 ln(x + 1) - 3 = 7 for the approximate value of x, we will follow these steps:
1. Begin with the given equation: -2 ln(x + 1) - 3 = 7.
2. Move the constant term to the other side of the equation: -2 ln(x + 1) = 7 + 3.
3. Simplify: -2 ln(x + 1) = 10.
4. Divide both sides of the equation by -2 to isolate the natural logarithm term: ln(x + 1) = -5.
5. Rewrite the equation using the exponential form of natural logarithm: e⁻⁵ = x + 1.
6. Calculate the value of e⁻⁵: e⁻⁵ ≈ 0.0067.
7. Subtract 1 from both sides of the equation: x = 0.0067 - 1.
8. Simplify: x ≈ -0.9933.
Therefore, the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.
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A slope triangle for line l is shown on the graph below. If the
slope of the line is 4/3 what is the value of w?
Answer:
9
Step-by-step explanation:
What we have to note is that the slope of a line is rise/run. This means that the amount of y change in that line is 4, and the amount of x change is 3.
We can now use a proportion to find the value of w.
[tex]\frac{4}{3} = \frac{12}{x}[/tex]
Cross multiply:
[tex]12\cdot36 = 36\\\\36\div4=9[/tex]
Hope this helped!
Answer: 9
Step-by-step explanation:
A middle school has 470 students. Regina surveys a random sample of 40 students and finds that 28 have cell phones. How many students at the school are likely to have cell phones? A. 132 students B. 188 students C. 329 students D. 338 students Please include ALL work! <3
Answer:
C. 329
Step-by-step explanation:
So 28 is 70% of 40
so we know that 70% percent of students have phones
70% of 470
329
Thats how I solved it have a great day :)
Urgent, please answer and show your work. In how many ways can two bishops be placed on a chessboard so that they do not attack each other? Note: a bishop can move any number of squares diagonally. A bishop on a white square, therefore, moves along white squares only. A bishop on a black square moves diagonally along black squares only.
Answer:
use the formula of permutation and combination
Step-by-step explanation:
bag contains two red marbles, three green ones, one lavender one, two yellows, and two orange marbles. HINT [See Example 7.] How many possible sets of four marbles are there
Answer:
a lot,
Step-by-step explanation:
2*3*1*2*2/5
The number of possible sets of four marbles is 210.
What are permutation and combination?When the order of the arrangements counts, a permutation is a numerical approach that establishes the total number of alternative arrangements in a collection.
The number of alternative configurations in a collection of things when the order of the selection is irrelevant is determined by combination.
Total number of marbles;
2 red marbles + 3 green ones + 1 lavender one + 2 yellows + 2 orange marbles.
⇒ 10
Selection is 4 out of 10
By combination,
10C₄ = (10×9×8×7)/(4×3×2)
10C₄ = 210
Hence "The number of possible sets of four marbles is 210".
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What is the answer, what are the steps to solve this, and what do the parts of the equation represent?
Step-by-step explanation:
Just sub 4 into where n is
Need help please will mark brainliest
Step-by-step explanation:
Maximum = 62
Median = (34+37+39+32+48+45+53+62+58+61+60+41)/12= 47.5≈48
quartile
In increasing order
32, 34, 37, 39, 41, 45, 48, 53, 58, 60, 61, 62
Upper quartile= (58+60)/2 = 59
Lower quartile= (37+39)/2 = 38
Minimum= 32
the function y= -16t^2 + 248, models the hight y in feet of a stone t seconds after it dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground?
Answer:
[tex]t \: = 3.92 \: sec[/tex]
Step-by-step explanation:
When (t =0)
Height of cliff = 248 feet = 75.5m
Using Newton's equations of motion:
[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]
75.5 = 0 * t + 4.9 * t^2
Solving further :
[tex]t \: = 3.92 \: sec[/tex]
The solution system to 3y-2x=-9 and y=-2x+5
Answer:
[tex]\boxed{(3,-1)}[/tex]
Step-by-step explanation:
Hey there!
Well to find the solution the the given system,
3y - 2x = -9
y = -2x + 5
So to find x lets plug in -2x + 5 for y in 3y - 2x = -9.
3(-2x + 5) - 2x = -9
Distribute
-6x + 15 - 2x = -9
-8x + 15 = -9
-15 to both sides
-8x = -24
Divide -8 to both sides
x = 3
Now that we have x which is 3, we can plug in 3 for x in y = -2x + 5.
y = -2(3) + 5
y = -6 + 5
y = -1
So the solution is (3,-1).
Hope this helps :)
Sin tita= 0.6892.find the value Of tita correct to two decimal places
Answer:
[tex]\theta \approx 6.28n + 2.38, \quad n \in \mathbb{Z}[/tex]
or
[tex]\theta \approx 6.28n + 0.76, \quad n \in \mathbb{Z}[/tex]
Considering [tex]\theta \in (0, 2\pi][/tex]
[tex]\theta \approx 2.38[/tex]
or
[tex]\theta \approx 0.76[/tex]
Step-by-step explanation:
[tex]\sin(\theta)=0.6892[/tex]
We have:
[tex]\sin (x)=a \Longrightarrow x=\arcsin (a)+2\pi n \text{ or } x=\pi -\arcsin (a)+2\pi n \text{ as } n\in \mathbb{Z}[/tex]
Therefore,
[tex]\theta= \arcsin (0.6892)+2\pi n, \quad n \in \mathbb{Z}[/tex]
or
[tex]\theta = \pi -\arcsin (0.6892)+2\pi n, \quad n\in \mathbb{Z}[/tex]
---------------------------------
[tex]\theta \approx 6.28n + 2.38, \quad n \in \mathbb{Z}[/tex]
or
[tex]\theta \approx 6.28n + 0.76, \quad n \in \mathbb{Z}[/tex]
2. 2(x+4) -5 = 3 + 3
Step-by-step explanation:
2x + 8 - 5 = 6
2x + 3 = 6
2x = 6 - 3
2x = 3
x = 3/2
Answer:
2 ( x+4) -5 = 3+3
=) 2x +8-5=6
=) 2x+3=6
=) 2x= 6-3
=)2x = 3
=) x =3/2= 1.5
