Answer:
207.35yd²
Step-by-step explanation:
A simple random sample of 49 8th graders at a large suburban middle school indicated that 88% of them are involved with some type of after school activity. Find the margin of error associated with a 90% confidence interval that estimates the proportion of them that are involved in an after school activity.
Answer:
The margin of error associated with a 90% confidence interval that estimates the proportion of them that are involved in an after school activity is 0.0764.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
A simple random sample of 49 8th graders at a large suburban middle school indicated that 88% of them are involved with some type of after school activity.
This means that [tex]n = 49, \pi = 0.88[/tex]
Margin of error:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.645\sqrt{\frac{0.88*0.12}{49}}[/tex]
[tex]M = 0.0764[/tex]
The margin of error associated with a 90% confidence interval that estimates the proportion of them that are involved in an after school activity is 0.0764.
Find sin 0
A. 16/20
B. 12/16
C. 12/20
D. 16/12
Answer:
16/20
Step-by-step explanation:
Since this is a right triangle
sin theta = opp side / hypotenuse
sin theta = 16/20
Answer:
A.
[tex]{ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }} \\ \\ { \tt{ \sin( \theta) = \frac{16}{20} }}[/tex]
please explain this to me.
Answer:
Equation of line:- y=2x-7
slope(m)=2
slope of parallel line (m)=2
∴ Equation of parallel line:- y=2x+b
it passes through the point (-3,6)
6=2(-3)+b 6+6=b
b=12
∴ y=2x+12
OAmalOHopeO
Can someone help me with this math homework please!
Answer:
(6,1)
Step-by-step explanation:
a rectangle has a perimeter equal to 24 if we consider its width x how could we talk about its length y in terms of x what are the possible values of x what aree the possible values of y
PLZ HELP
wait ik you from rsm
need help with this!!
Answer:
{ 1,3,4,6,7}
Step-by-step explanation:
Do B∩C first
This is B intersect C which means what they have in common
B∩C = {3,6,7}
Then A∪(B∩C)
A union {3,6,7} which means join together ( combine with no duplicates) the two sets
{ 1,3,4,6,7}
Does (x, y) satisfy an equation?
Answer:
Yeah
Step-by-step explanation:
Find the height of a rectangular prism with a 3 in by 4 in base and a volume of 20 cubic inches
Answer:
1 2/3 inches.
Step-by-step explanation:
Volume = area of the base * height so:
20 = 3*4 * h
h = 20/12
h = 1 2/3 inches.
Student Council members are designing a large poster that will tell people who each member is and what position each person holds. Each member gets a triangle piece of paper to decorate, then all the pieces will be fitted together to form the final display. The triangles are identical and fit together to form a regular polygon. It will look similar to the shape below:
A) If there are 8 council members, what type of polygon will be formed?
B) To achieve this shape, what type of triangles will the individual pieces be? What will be the measures of each of the three angles in each of the triangles?
C) What will be the sum of the measures of the internal angles of the final shape?
D) Redo parts (b) and (c) if the Council decides to include triangles for the two staff advisors, assuming the poster will still form a regular polygon, but now with 10 triangles.
A) With 8 council members, the polygon formed with the triangles will be an octagon.
A polygon formed with a set of isosceles triangles will have as many sides as triangles you are using. An octagon is a geometric figure that has 8 equal sides to it.The final shape should look just like the one you posted with your question.
B) The individual pieces should be isosceles triangles. The three angles of each triangle should measure 45°, 67.5° and 67.5°.
An isosceles triangle is the one that has two sides of the same length and one side with a different length.We need two sides of the triangles to be the same. The base of the triangle's length will depend on the number of triangles we are using to form the final polygon.
The number of triangles will define the angle between the two sides of equal length. You can find this by dividing 360° into the number of triangles:
[tex]\frac{360^{o}}{8}=45^{o}[/tex]
The other two angles should measure the same, so we can find them by subtracting the 45° from 180° (which is what we get when adding the three angles of any triangle) and then dividing the answer into 2.
180°-45°=135°
[tex]\frac{135^{o}}{2}=67.5^{o}[/tex]
C) The sum of the measures of the internal angles of the final shape should add up to 360°, that way we can guarantee that the figure is closed:
45°+45°+45°+45°+45°+45°+45°+45°=360°
D)
D.B) The individual pieces should be isosceles triangles. The three angles of each triangle should measure 36°, 72° and 72°.
The number of triangles will define the angle between the two sides of equal length. You can find this by dividing 360° into the number of triangles:
[tex]\frac{360^{o}}{10}=36^{o}[/tex]
The other two angles should measure the same, so we can find them by subtracting the 36° from 180° (which is what we get when adding the three angles of any triangle) and then dividing the answer into 2.
180°-36°=144°
[tex]\frac{144^{o}}{2}=72^{o}[/tex]
C) The sum of the measures of the internal angles of the final shape should add up to 360°, that way we can guarantee that the figure is closed:
36°+36°+36°+36°+36°+36°+36°+36°+36°+36°=360°
You can find further information on the following links:
https://brainly.ph/question/6658482
If X is a continuous random variable than P (X= a)= ______ for any number a.
Answer:
P (X= a) = 0, for any number a.
Step-by-step explanation:
In a continuous random variable, the probability of an exact value, that is, P(X = x), is always 0, thus, the correct answer is:
P (X= a) = 0, for any number a.
convert into power notation -1/81
Answer:
-1/9^2 is the power notation for your questions
Step-by-step explanations
You are riding your bike. At 8:00am you have ridden your bike 23 miles. By 9:00pm you have ridden 179 miles. Find the rate of change in miles per hour. If needed, round your answer to the nearest whole number.
Answer:
12 miles/hour
Step-by-step explanation:
8am to 9pm = 13 hours
in that time we were driving 179-23 = 156 miles.
so, our speed was 156 miles / 13 hours.
now simplify it to our standard miles/hour format :
156/13 = 12
therefore, or standardized speed was
12 miles/hour
If log 3=x and log 5=y find the value of log 75
Answer:
Step-by-step explanation:
75 = 5 * 5 * 3
Log3 + log(5) + log(5) = 1.8751
log(75) = 1.87506 which is the same answer we got from adding the logs.
A circle has a radius of 3. An arc in this circle has a central angle of 20°. What is the length of the arc? Either enter an exact answer in terms of or use 3.14 for 1 and enter your answer as a decimal.
Answer:
[tex]\frac{\pi }{3}[/tex]
[tex]2 * \pi * 3 * \frac{20}{360}[/tex]
120[tex]\pi[/tex]/360 = [tex]\frac{\pi }{3}[/tex]
Step-by-step explanation:
A building in the shape of a pentagon is regular and has 50 feet long walls. What interior angles are formed when two of the walls meet?
A. 72
B. 90
C. 900
D. 108
Answer:
[tex]\text{D. }108^{\circ}[/tex]
Step-by-step explanation:
The sum of the interior angles of a polygon with [tex]n[/tex] sides is given by [tex]180(n-2)[/tex].
A pentagon is a shape with 5 sides and 5 angles. Therefore, the sum of its interior angles is equal to:
[tex]180(5-2),\\180\cdot 3=540^{\circ}[/tex]
Regular polygons can be defined as polygons with equal side lengths and angles. Therefore, to find the measure of each interior angle of a regular polygon, divide the sum of the interior angles (540 degrees) by the number of angles the polygon has (5 sides).
Therefore, each interior angle in a regular polygon has a measure of:
[tex]\frac{540}{5}=\boxed{108^{\circ}}[/tex]
Each interior angle in a regular polygon has a measure of is 108°. Therefore, option D is the correct answer.
What is the formula to find the number of sides with interior angle?We can find the number of sides in a polygon using the value of interior angle. Interior angle = 180°(n-2)/n, where n is the number of sides of the polygon.
The sum of the interior angles of a polygon with n sides is given by 180(n-2).
A pentagon is a shape with 5 sides and 5 angles. Therefore, the sum of its interior angles is equal to:
180(5-2) =540°
Therefore, option D is the correct answer.
Learn more about the interior angles of regular polygon here:
brainly.com/question/29774899.
#SPJ2
What could be the coefficient of x once the variable term is isolated on one side of the equation? Check all that apply.
3x - 6(5x + 3) = 9x + 6
1. Distribute: 3x - 30x - 18 = 9x + 6
2. Combine like terms: -27x - 18 = 9x + 6
–36
–27
–24
24
27
36
Answer:
-36,36
Step-by-step explanation:
3x - 6(5x + 3) = 9x + 6
Distribute:
3x - 30x - 18 = 9x + 6
Combine like terms:
-27x - 18 = 9x + 6
There are two possible ways to isolate x
On the left
Subtract 9x from each side
-27x - 18 -9x = 9x-9x + 6
-36x -18 = 6
On the right
Add 27x from each side
-27x - 18 +27x = 9x+27x + 6
-18 =36x+ 6
This table shows the relationship of the total number of pieces of fruit to the number of bananas.
Why is StartFraction 6 Over 5 EndFraction not equivalent to Three-halves?
Given:
The table that shows the relationship of the total number of pieces of fruit to the number of bananas.
To find:
Why is [tex]\dfrac{6}{5}[/tex] not equivalent to [tex]\dfrac{3}{2}[/tex].
Solution:
If a, b, c are real numbers, then
[tex]\dfrac{a}{b}=\dfrac{a\times c}{b\times c}[/tex]
The given fraction is [tex]\dfrac{3}{2}[/tex]. It can be written as:
[tex]\dfrac{3\times 2}{2\times 2}=\dfrac{6}{4}[/tex]
The number 3 is multiplied by 2 to get 6. So, the 2 should also be multiplied by 2. The ratio should be [tex]\dfrac{6}{4}[/tex], not [tex]\dfrac{6}{5}[/tex].
Therefore, the correct option is A.
Which expression is equivalent to ((2x²) (3x) (4x)??
A.24x7
B.48x?
C.9677
D.576x12
Answer:
24x^4
Step-by-step explanation:
((2x²) (3x) (4x)
Add the exponents when multiplying
2*3*4 x^(2+1+1)
24x^4
For what value of k are the roots of the quadratic
equation kx²+ 4x+ 1=0 equals and reals."
Answer:
k ≥ 4
Step-by-step explanation:
A Quadratic equation is given to us and we need to find out the value of k for which the equation has real roots. The given equation is ,
[tex]\rm\implies kx^2 +4x +1=0[/tex]
With respect to Standard form of Quadratic equation :-
[tex]\rm\implies ax^+bx+c=0[/tex]
For real roots ,
[tex]\rm\implies Discriminant = b^2-4ac\geq 0[/tex]
Substitute the respective values ,
[tex]\rm\implies b^2-4ac \geq 0\\[/tex]
[tex]\rm\implies 4^2 - 4(k)(1) \geq 0 \\[/tex]
Simplify the LHS ,
[tex]\rm\implies 16 - 4k \geq 0 \\[/tex]
Add 4k both sides ,
[tex]\rm\implies 4k\geq 16 [/tex]
Divide both sides by 4 ,
[tex]\rm\implies \boxed{\blue{\rm k \geq 4}}[/tex]
“The length of a rectangle is two feet greater than twice its width. If the perimeter is 25 feet, find the width.” Which of the following translations is correct?
Answer:
b is the answer
Step-by-step explanation:
What do I do for this question
Answer:
Step-by-step explanation:
a + 9 = 15
a = 15 - 9
a = 6
c + 9 = 16
c = 16 - 9
c = 7
d = c + 9
= 7 + 9
= 16
e = d + 15
= 16 + 15
e = 31
P(selecting a boy) = total boy /total pupils = 16/31
What is the area of polygon
Identify the equation of the circle that has its center at (9, 12) and passes through the origin.
Answer:
(x-9)^2 +(y-12)^2 = 225
Step-by-step explanation:
First find the length of the radius
If is the distance from the center to the point
d = sqrt( (x2-x1)^2 + (y2-y1)^2 )
= sqrt( (0-9)^2 + (0-12)^2)
= sqrt ( 81+144)
= sqrt(225)
= 15
The equation for a circle is
( x-h) ^2+ (y-k)^2 = r^2
(x-9)^2 +(y-12)^2 = 15^2
(x-9)^2 +(y-12)^2 = 225
Can someone please help?
Will mark brainliest!
Answer:
108 degrees
Step-by-step explanation:
an arithmetic progression means that there is a constant inbetween all of the angles. Since the smallest angle is 12 degrees, ( i just guessed and checked) and came up with the angles :
12, 60, 108
these have a constant of 48
Answer:
108°
Step-by-step explanation:
Since the angles are in arithmetic progression , then the angles are
a + a + d + a + 2d
a is the first term and d the common difference
Sum the angles and equate to 180 with a = 12
a + a + d + a + 2d = 180
12 + 12 + d + 12 + 2d = 180 , that is
36 + 3d = 180 ( subtract 36 from both sides )
3d = 144 ( divide both sides by 3 )
d = 48
Then the largest angle is
a + 2d = 12 + 2(48) = 12 + 96 = 108°
The circles are concentric. True False
Answer:
true, to my knowledge concentric circles are just circles that all have one main center.
Step-by-step explanation:
Find the equation of the line perpendicular to y = 3x - 6 that runs through the point (-1, -3).
y
=
1
3
x
+
8
3
y=
3
1
x+
3
8
y
=
−
1
3
x
−
10
3
y=
3
−1
x−
3
10
y = -3x + 8
y
=
3
x
+
10
y=3x+10
Answer:
Step-by-step explanation:
I'll get you the answer. You pick it from what you are given.
The slope of the perpendicular is m1 * m2 = - 1
m1 = 3
m2 = -1 / m1
m2 = -1 / 3
So far what you have is
y = (-1/3) x + b
Use the point go get b
x = -1
y = - 3
y = (-1/3) *x + b
-3 = (-1/3)*-1 + b
-3 = 1/3 + b
-3 - 1/3 = b
b = -3.33333 or
b = -3 1/3
b = -10/3
So the answer is
y = (- 1/3) x - 10/3 or
y = (-1 / 3)x - 3.3333 or
y = (-1/3 )x - (3 1/3)
please answer all the questions above.
Answer:
hope it was helpful!! You are welcome to ask any question
Answer:
Step-by-step explanation:
1) 7 - ( 3+4) = 7 + [- (3+ 4)] = 7 + (-3) + (-4)
(-) is distributed to 3 and 4
A
2) C
I (-3) - 4 I
3) 5 + 3 = 8 miles
B
The median house price in Waterloo Region increased by 3.6% from Jan 1, 2018 to Jan 1, 2019. A home
was purchased in Waterloo Region on April 1, 2019 for $600,000.
(a) Assume this trend continues, write an exponential equation that models the Resale Value of this
home over time.
(b) At this rate, determine the date of the resale price of the home would reach $1 million (Show your
work to accurate to the nearest month)
(c) Use your exponential equation to determine the expected resale value of the home on April 1, 2020.
Answer:
The right answer is:
(a) [tex]P(t) = P_o \ e^{0.03536t}[/tex]
(b) [tex]t = 14 \ years \ 6 \ months[/tex]
(c) [tex]P(t) = =621,595.6[/tex] ($)
Step-by-step explanation:
Given:
House price increment rate,
= 3.6% annually
(a)
Let the exponential equation will be:
⇒ [tex]P(t) = P_o e^{Kt}[/tex]
here,
t = 0
P = P₀
t = 1 yr
then,
[tex]P(1) = P_o +3.6 \ persent \ P_o[/tex]
[tex]=1.036 \ P_o[/tex]
now,
⇒ [tex]1.036 P_o = P_o \ e^{K.1}[/tex]
[tex]ln(1.036) = K[/tex]
[tex]K = 0.03536[/tex]
Thus, the exponential equation will be "[tex]P(t) = P_o \ e^{0.03536t}[/tex]".
(b)
We know,
[tex]P_o = 600,000[/tex] ($)
[tex]P(t) = 10,00,000[/tex] ($)
∵ [tex]P(t) = P_o \ e^{0.03536t}[/tex]
[tex]1000000=600000 \ e^{0.03536 t}[/tex]
[tex]\frac{5}{3}= e^{0.03536 t}[/tex]
[tex]ln(\frac{5}{3} )=0.03536 t[/tex]
[tex]\frac{\frac{0.5}{0825} }{0.03536} =t[/tex]
[tex]t = 14.45 \ years[/tex]
or,
[tex]t = 14 \ years \ 6 \ months[/tex]
(c)
[tex]P_o=600,000[/tex] ($)
[tex]t = 1 year[/tex]
Now,
⇒ [tex]P(t) = P_o \ e^{0.03536 t}[/tex]
[tex]=600000 \ e^{ 0.03536\times 1}[/tex]
[tex]=621,595.6[/tex] ($)
Which expressions are equivalent to the given expression?
Answer:
The answers are option B and E.
Instructions: Find the missing side lengths. Leave your answers as radicals in simplest
form.
Answer:
x = 40
y= 20
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 60 = 20 sqrt(3)/ x
x sin 60 = 20 sqrt(3)
x = 20 sqrt(3)/ sin 60
x = 20 sqrt(3)/ sqrt(3)/2
x = 20 *2
x = 40
tan theta = opp /adj
tan 60 = 20 sqrt(3)/y
y = 20 sqrt(3)/ tan 60
y = 20 sqrt(3) / sqrt(3)
y = 20
