Answer:
45.55 m to the nearest hundredth.
Step-by-step explanation:
tan 26 = opposite / adjacent side = h / 90 where h = height of the dam - Scarlett's height.
The height of the dam =
y = 90 tan 26
= 43.895 m
Now we need to add Scarlett's height
= 45.55 m.
Answer:
grg
Step-by-step explanation:
rgg
A hiker in Africa discovers a skull that contains 32% of its original amount of C-14. Find the age of the skull to the nearest year.
To estimate the age of the skull, we can use the concept of radioactive decay of carbon-14. We can set up an equation to find the original amount of C-14, and then calculate the number of half-lives that have occurred to determine the age of the skull.
Explanation:The age of the skull can be estimated using the concept of radioactive decay of carbon-14 (C-14). The half-life of C-14 is approximately 5730 years, which means that after 5730 years, half of the original amount of C-14 will remain. Since the skull contains 32% of its original amount of C-14, we can estimate that 68% has decayed. To find the age of the skull, we can set up the following equation:
0.68 * original amount = current amount
Solving for the original amount gives us:
original amount = current amount / 0.68
Now, we just need to divide the age of the skull by the half-life of C-14 to find the number of half-lives that have occurred. We can then multiply this by 5730 years to get the approximate age of the skull to the nearest year.
Cassie is travelling 675 miles today to visit her brother and his family. so far, she has stopped for gas three times. at the first stop, 7.1 gallons of gas and paid $23.79. at her second stop, she put in 5.8 of gas and paid $19.08. and, at her third stop, she put in 6.6 gallons and paid $20.39, the second part
if the gas station that cassie stopped, at last, lowers their price 6%, what will be their new price per gallon?
The last gas station she stopped at she got 6.6 gallons and paid $20.39
If they lower the price by 6%, that means she would pay 94% of the original amount ( 100% - 6% = 94%)
Multiply the amount she paid by 94%:
20.39 x 0.94 = 19.17
She would pay $19.17 total.
Now divide that by the number of gallons bought:
19.17 / 6.6 = $2.90 per gallon ( Rounded to the nearest cent).
Which of the following sets of triangles are similar according to the Angle-Angle Similarity Postulate?
equilateral triangles
equiangular triangles
both equilateral and equiangular triangles
neither equilateral nor equiangular triangles
Answer: both equilateral and equiangular triangles
Answer:
Yes
Both equilateral and equiangular triangles
Step-by-step explanation:
The AA (Angle-Angle) similarity states that if two pairs of corresponding angles are congruent, then the triangles are similar
In equilateral triangles, all angles are equal.The corresponding sides of two equilateral triangles are congruent thus they will be similar. An Equiangular triangle is also an equilateral triangle because its interior angles are the same and add up to 180°.
Both equilateral and equiangular triangles are similar by the Angle-Angle Similarity Postulate because they each have two congruent angles with any other triangle of the same type.
Explanation:The Angle-Angle (AA) Similarity Postulate states that two triangles are similar if two angles of one triangle are congruent to two angles of the other triangle. Equilateral triangles are similar by AA postulate because all angles in any equilateral triangle measure 60 degrees, thus any two will be congruent with any two angles in another equilateral triangle. Equiangular triangles are also similar by the AA postulate, as all their corresponding angles are equal. Consequently, both equilateral and equiangular triangles are similar according to the AA Similarity Postulate.
What is the vertex of the quadratic function f(x)=(x-6)(x+2)?
Answer:
(2, -16).
Step-by-step explanation:
(x - 6)(x + 2)
Convert to vertex form:
Expanding the parentheses we have:
x^2 + 2x - 6x - 12
= x^2 - 4x - 12
Completing the square:
= (x - 2)^2 - 4 - 12
= (x - 2)^2 - 16
So the vertex is (2, -16),
Select the correct answer.
A company made a profit of $25,000 over a period of 5 years on an initial investment of $10,000. What is its annualized ROI?
(final value – initial value)
? x 100
initial value
ROI !
ROI
annualized ROI = number of years
A. 50%
B. 25%
c. 30%
D. 40%
Reset
Next
Final answer:
The annualized ROI is calculated by dividing the total ROI, which is 150%, by the number of years, which is 5, resulting in an annualized ROI of 30%. The correct answer is option (C).
Explanation:
To calculate the annualized ROI, we first determine the total ROI by using the formula:
Total ROI = (final value – initial value) / initial value × 100
Substituting the given values:
Total ROI = ($25,000 – $10,000) / $10,000 × 100 = $15,000 / $10,000 × 100 = 150%
As this ROI was achieved over a period of 5 years, to find the annualized ROI, we divide the total ROI by the number of years:
Annualized ROI = Total ROI / number of years
Annualized ROI = 150% / 5 = 30%
Therefore, the correct answer is C. 30%.
Answer:
A. 50%
Step-by-step explanation:
You want the annualized ROI represented by a profit of $25,000 over a period of 5 years on a $10,000 investment.
ReturnYour formula seems to be ...
[tex]\text{annualized ROI}=\dfrac{\text{final value}-\text{initial value}}{(\text{initial value})(\text{number of years})}\times100\%[/tex]
The profit is the difference between final value and initial value, so this becomes ...
[tex]\text{annualized ROI}=\dfrac{\text{profit}}{(\text{initial value})(\text{number of years})}\times100\%\\\\\\\text{annualized ROI}=\dfrac{25000}{(10000)(5)}\times100\%=50\%[/tex]
The annualized ROI in this scenario is 50%, choice A.
__
Additional comment
The annualized ROI is effectively the "internal rate of return" for a given set of cash flows. If we assume $10,000 is paid at the beginning of year 1, and $5000 is received at the end of each of 5 years followed by repayment of the initial $10,000 investment along with the last dividend, then the IRR is exactly 50%.
If the total profit of $25000 is distributed differently in time, then the rate of return is different. For example, if $35,000 is received at the end of 5 years, the IRR is about 28.47%.
What is the center of a circle whose equation is x^2+y^2-12x-2y+12=0
Answer:
The center of this circle is at (6, 1).
Step-by-step explanation:
Rewrite x^2+y^2-12x-2y+12=0 by grouping like terms. Then:
x^2+y^2-12x-2y+12=0 becomes x^2 - 12x +y^2 - 2y + 12=0.
Next, complete the squares:
x^2 - 12x + 36 - 36 + y^2 - 2y + 1 - 1 + 12 = 0.
Rewriting the two perfect squares as squares of binomials, we get:
(x - 6)^2 - 36 + (y - 1)^2 - 1 + 12 = 0
Moving the constants to the right side:
(x - 6)^2 + (y - 1)^2 = 36 + 1 - 12 = 25
Then the desired equation is:
(x - 6)^2 + (y - 1)^2 = 5^2. The center of this circle is at (6, 1).
Which is the completely factored form of 4x3 + 10x2 – 6x?
Answer:
2x(x + 3)(2x - 1)
Step-by-step explanation:
Given
4x³ + 10x² - 6x ( factor out 2x from each term )
= 2x(2x² + 5x - 3)
To factorise the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × - 3 = - 6 and sum = + 5
The factors are + 6 and - 1
Use these factors to split the x- term
2x² + 6x - x - 3 ( factor the first/second and third/fourth terms )
2x(x + 3) - 1(x + 3) ← factor out (x + 3) from each term
(x + 3)(2x - 1), hence
2x² + 5x - 3 = (x + 3)(2x - 1)
Hence
4x³ + 10x² - 6x = 2x(x + 3)(2x - 1)
Answer:
B
Step-by-step explanation:
if y=12x+7 were changed to y=12x+2, how would the graph of the new function compare with its original
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 12x + 7 ← is in this form
with m = 12 and c = 7
y = 12x + 2 ← is also in this form
with m = 12 and c = 2
Since the slopes are equal the lines are parallel
c = 7 → c = 2 is a vertical translation of 5 units down
In comparison the line y = 12x + 2 is parallel to y = 12x + 7
and translated < 0, - 5 >
a soild right pyramid has a square base with an edge length of x cm and a height of y cm. which expression represents the volume of the pyramid
Answer:
The volume of the pyramid is [tex]V=\frac{1}{3}(x^{2})(y)\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}BH[/tex]
where
B is the area of the base
H is the height of pyramid
we know that
The area of the base is
[tex]B=x^{2}\ cm^{2}[/tex]
The height is equal to
[tex]H=y\ cm[/tex]
substitute
[tex]V=\frac{1}{3}(x^{2})(y)\ cm^{3}[/tex]
Which of these triangle appears not to be congruent to any others shown here? Check all that apply.
Answer: the actual answer is triangle b and triangle f
Triangle B and triangle F are not congruent with any other given triangles
What is congruency?Congruent triangles are triangles having both the same shape and the same size.Types of congruencies are SSS, SAS, AAS, ASA, RHS.How to find which of these triangle appears not to be congruent to any others shown ?Clearly we can see that triangle A and triangle E are congruent since they have the same shape and sizeAlso triangle C and triangle C are congruentSo we are left with triangle B and triangle F.
The size and shapes of these triangles does not matches with any other triangles.
So triangle B and triangle F are not congruent with any other given triangles.
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Why is the answer to this C and not E. Don’t you usually keep the negative number negative? Why is this one not left negative?
Answer:
C
Step-by-step explanation:
Given
x² = 7x - 3 ( subtract 7x - 3 from both sides )
x² - 7x + 3 = 0 ← in standard form
with a = 1, b = - 7, c = 3
Using the quadratic formula to solve for x
x = ( - (- 7) ± [tex]\sqrt{(-7)^2-(4(1)(3)}[/tex] ) / 2
= ( 7 ± [tex]\sqrt{49-12}[/tex] ) / 2
= [tex]\frac{7+/-\sqrt{37} }{2}[/tex] → C
Complete the recursive formula of the arithmetic sequence -16, -33, -50, -67, ....
The recursive formula for the sequence -16, -33, -50, -67, .... is f(n) = f(n - 1) - 17, f(1) = -16
Finding the recursive formula for the sequence
From the question, we have the following parameters that can be used in our computation:
-16, -33, -50, -67, ....
In the above sequence, we can see that -17 is added to the previous term to get the new term
This means that
First term, a = -16
Common difference, d = -17
The recursive formula for the sequence is then represented as
f(n) = f(n - 1) - 17, f(1) = -16
The function relating the height of an object off the ground to the time spent falling is a quadratic relationship. Travis drops a tennis ball from the top of an office building 90 meters tall. Three seconds later, the ball lands on the ground. After 2 seconds, how far is the ball off the ground?
30 meters
40 meters
50 meters
60 meters
Answer:
A. 30 meters
Step-by-step explanation:
Let's find the answer.
The problem established a quadratic relationship between height (h) and time (t), then we can establish:
h(t)=K*t where 'K' is a coefficient.
Because an experiment was done, we can find 'K' as follows:
h(t)=K*t
90meters=K*(3seconds)
90meters/3seconds=K
30m/s=K
Now we can solve the problem, so for 2 seconds:
h(t)=K*t
h(t)=(30m/s)*(2s)
h(t)=60m
But notice that the obtained 60 meters are the distance traveled in 2 seconds from the top the building to the ground. So 'how far from the ground' can be calculated as:
(far from the ground) = (total building height) - (distance traveled in 2s)
(far from the ground) = 90m - 60m = 30m
In conclusion, after 2 seconds, the ball is 30 meters far from the ground. The answer in then A. 30 meters.
Answer:
40 meters
Step-by-step explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 9.81 m/s²
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow u=\frac{s-\frac{1}{2}at^2}{t}\\\Rightarrow u=\frac{90-\frac{1}{2}\times 9.81\times 3^2}{3}\\\Rightarrow u=15.285\ m/s[/tex]
u = 15.285 m/s
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow s=15.285\times 2+\frac{1}{2}\times 9.81\times 2^2\\\Rightarrow s=50.19\ m[/tex]
The ball has fallen 50.19 m from the top of the building.
So, the ball is 90-50.19 = 39.81 = 40 meters off the ground
A line passes through the point (-2,7) and has a slope of -5
Answer:
y-7 = -5(x+2)
or
y = -5x-3
Step-by-step explanation:
We can use the point slope form of the equation
y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point
y-7 = -5(x--2)
y-7 = -5(x+2)
If we want the equation in slope intercept form
Distribute
y-7 = -5x-10
Add 7 to each side
y-7+7 = -5x-10+7
y = -5x-3
Remember that the slope intercept formula is:
y = mx + b
m is the slope
b is the y-intercept
We know that the slope of the line (m) will be -5
y = -5x + b
Now we must find b
To do that you must plug in the point the line goes through in the x and y of the equation.
(-2, 7)
7 = -5(-2) + b
7 = 10 + b
-3 = b
y = -5x - 3
Hope this helped!
~Just a girl in love with Shawn Mendes
1. Hector knows there is a relationship between the number of cars he washes and the time it takes
him to wash those cars. Identify the independent quantity and the dependent quantity in the
problem situation.
Answer:
The independent variable is the time (variable x)
The dependent variable is the number of cars he washes (variable y)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In this problem
The relationship between the number of cars he washes and the time it takes him to wash those cars represent a a proportional variation
Let
y -----> the number of cars he washes
x -----> the time
The linear equation is [tex]y=kx[/tex]
The independent variable is the time x
The dependent variable is the number of cars he washes y
Solve for x: [.02(x-2)]=1
Answer:
x=1.04 i bet u thats right no joke hope i helped ;)
Step-by-step explanation:
Chicago to Memphis is 527.4 miles Memphis to New Orleans is 393.8. How far is Chicago to new movie orleans
The total distance from Chicago to New Orleans is calculated by adding the distances from Chicago to Memphis and then from Memphis to New Orleans, which totals to 921.2 miles.
Explanation:In order to calculate the total distance from Chicago to New Orleans, we simply need to add the given distances. The distance from Chicago to Memphis is 527.4 miles and from Memphis to New Orleans is 393.8 miles. Hence, the total distance from Chicago to New Orleans would be 527.4 miles + 393.8 miles = 921.2 miles. So, the total travel distance from Chicago to New Orleans is 921.2 miles.
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Name the types of angles shown.
Check all that apply.
A. complementary angles
B. right angle
C. supplementary angles
D. straight angle
Answer:
C. supplementary angles
D. straight angle
The given angles ABD and DBC lies on a straight line. So they are straight angle.
We know that the sum of the straight angles is = 180 degrees. If the sum of two angles is 180 degrees, then they are also called supplementary angles.
It means the shown angles are also supplementary angles.
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Answer:
D and C
Step-by-step explanation:
The function f(x) = 3,267(1 + 0.02)* represents the amount of money in a savings account where x represents time in years. What does the 3,267 represent?
A.The amount of money in the savings account after one year
B.The amount of money added to the savings account each year
C .The initial amount of money placed in the savings account
D.The growth rate
Answer:
C .The initial amount of money placed in the savings account
Step-by-step explanation:
f(x) = 3,267(1 + 0.02)^x
This is in the form
y = a b^x
where a is the initial amount
b is the growth rate
x is the time
3267 is the initial amount
1.02 is the growth rate, so it grows by .02 or 2 percent
and x is the time
The function f(x) = 3,267(1 + 0.02)* represents the amount of money in a savings account where x represents time in years. What does the 3,267 represent?
Answer:
C .The initial amount of money placed in the savings account
Use the information given to identify the a9 term of the geometric sequence: a2 = 3, r = −1
Answer:
-3
Step-by-step explanation:
a₁ = a₂/r = 3/(-1)=-3
a₉ = a₁ · r⁸ = -3 · (-1)⁸ = -3 · 1 = -3
A. y-2=2(x-3)
B. y-3=2(x-2)
C. y-10=2(x-1)
D. y-1=2(x-10)
Answer:
C. y-10=2(x-1)
Step-by-step explanation:
We have two points on the line, we can find the slope
m = (y2-y1)/(x2-x1)
= (10-2)/(1--3)
= 8/(1+3)
=8/4
=2
The slope is 2
We can use point slope form using the point (1,10)
y-y1 = m(x-x1)
y-10 = 2(x-1)
Answer:
C. y - 10 = 2(x - 1)Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-3, 2) and (1, 10). Substitute:
[tex]m=\dfrac{10-2}{1-(-3)}=\dfrac{8}{4}=2[/tex]
Using the point (-3, 2):
[tex]y-2=2(x-(-3))\\\\y-2=2(x+3)[/tex]
Using the point (1, 10):
[tex]y-10=2(x-1)[/tex]
What is the value of x of angle A if angle B is 67 degrees and angle C is 52 degrees?
Answer:
x=61
Step-by-step explanation:
In a triangle all measure add up to 180 degrees, therefore
52+67=119
180-119=61
This means we have 61 degrees remaining to complete the triangle
Answer:
[tex]x=61^{\circ}[/tex]
Step-by-step explanation:
We have been that B is 67 degrees and angle C is 52 degrees. We are asked to find the value of x of angle A.
We will use angle sum property to solve our given problem.
Angle sum property of triangle states that sum of all angles of a triangle is equal to 180 degrees.
Using angle sum property, we can set an equation as:
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
Upon substituting our given values in above equation, we will get:
[tex]x+67^{\circ}+52^{\circ}=180^{\circ}[/tex]
[tex]x+119^{\circ}=180^{\circ}[/tex]
[tex]x+119^{\circ}-119^{\circ}=180^{\circ}-119^{\circ}[/tex]
[tex]x=61^{\circ}[/tex]
Therefore, the value of x is 61 degrees.
Which of the following is the graph of y=1/2 x+1?
Answer:
The top one
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{2}[/tex] x + 1 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex] and y- intercept c = + 1
Since m > 0 then graph slopes upwards from left to right
That indicates the top or bottom graphs
The bottom one has a y- intercept of c = - 1
While the top one has a y- intercept of c = + 1
Hence the top graph is the graph of y = [tex]\frac{1}{2}[/tex] x + 1
Hence, the graph of f(x) = 2x is A.
What is a function?function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
How to solve?On plotting the graph of f(x) = [tex]\frac{1}{2}x + 1[/tex],
we observe that it is coincident to option A.
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Sarah received scores of 85, 92 and 78 on her first three exams of the grading
period. What is the lowest score Sarah can earn on the next exam for the exam
average to be at least a 87 for the grading period.
Answer:
92
Step-by-step explanation:
The total Score is 85 + 92 + 79 + x = 4 * 87
The total Score needed is 4 * 87 = 348
So to get that score we need to add the other scores up
256 + x
which equals the total of the 4 tests.
256 + x = 348
Subtract 256 from both sides.
256 - 256 + x = 348 - 256
x = 92 Pretty high, but doable.
Really need help!! With picture
Answer:
In order:
2nd step
1st step
3rd step
4th step
Step-by-step explanation:
The checking part comes last.
Before you can determine the solution, your lines need to be graphed.
To graph your lines, they have to be in a form for you to determine how to graph them.
So the first step here is
"Write each equation in a form that is easy to graph"
The second step is:
To graph them
Third step is:
To see where they cross
The last step:
(Some people don't do it but should is check it).
2x^2+y^2=8xy, find the dy/dx.
Answer:
[tex]\frac{dy}{dx}=\frac{4y-2x}{y-4x}[/tex]
Step-by-step explanation:
[tex]\frac{d}{dx}(2x^2)=4x[/tex]
[tex]\frac{d}{dx}(y^2)=2y\frac{dy}{dx}[/tex]
[tex]\frac{d}{dx}(8xy)[/tex]
[tex]=8\frac{d}{dx}(xy)[/tex]
[tex]=8(\frac{d}{dx}(x)y+x\frac{d}{dx}(y))[/tex]
[tex]=8[1y+x\frac{dy}{dx}][/tex]
[tex]=8y+8x\frac{dy}{dx}[/tex]
Let's put it altogether now:
[tex]2x^2+y^2=8xy[/tex]
Differentiating both sides gives:
[tex]4x+2y\frac{dy}{dx}=8y+8x\frac{dy}{dx}[/tex]
We are solving for dy/dx so we need to gather those terms on one side and the terms without on the opposing side:
I'm going to first subtract 4x on both sides:
[tex]2y\frac{dy}{dx}=8y-4x+8x\frac{dy}{dx}[/tex]
I'm not going to subtract 8xdy/dx on both sides:
[tex]2y\frac{dy}{dx}-8x\frac{dy}{dx}=8y-4x[/tex]
It is time to factor the dy/dx out of the two terms on the left:
[tex]\frac{dy}{dx}(2y-8x)=8y-4x[/tex]
Divide both sides by (2y-8x):
[tex]\frac{dy}{dx}=\frac{8y-4x}{2y-8x}[/tex]
Reduce right hand side fraction:
[tex]\frac{dy}{dx}=\frac{4y-2x}{y-4x}[/tex]
Answer:
[tex]\frac{8y-4x}{2y-8x}[/tex]
Step-by-step explanation:
Differentiate implicitly with respect to x
noting that
[tex]\frac{d}{dx}[/tex] (y² ) = 2y[tex]\frac{dy}{dx}[/tex]
Differentiate 8xy using the product rule
Given
2x² + y² = 8xy, then
4x + 2y[tex]\frac{dy}{dx}[/tex] = 8x[tex]\frac{dy}{dx}[/tex] + 8y
Collect terms in [tex]\frac{dy}{dx}[/tex]
2y[tex]\frac{dy}{dx}[/tex] - 8x[tex]\frac{dy}{dx}[/tex] = 8y - 4x
[tex]\frac{dy}{dx}[/tex] (2y - 8x) = 8y - 4x
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{8y-4x}{2y-8x}[/tex]
Solve the system of equations.
2x + 2y + 3z = 5
6x + 3y + ôz = 6
3x + 4y + 4z = 9
a. (x = 0, y = 1, z = 0)
b. (x = 1, y = 0, z = 3)
c. (x = -2, y = 3, 2 = 2)
d. (x=-1, y = 2,2 = 1)
Answer:
x=-1, y = 2, z = 1
Step-by-step explanation:
We are given with three equations and we are asked to find the solution to them.
2x + 2y + 3z = 5 ------------- (A)
6x + 3y + 6z = 6 --------------(B)
3x + 4y + 4z = 9 ---------------(C)
Step 1 .
multiplying equation (A) by 3 and subtracting B from the result
6x + 6y + 9z = 15
6x + 3y + 6z = 6
- - - = -
_______________
3y+3z=9
y+z=3
y=3-z ----------------- (C)
Step 2.
Substituting this value of y in equation B and C
6x + 3(3-z) + 6z = 6
6x+9-3z+6z=6
6x+3z=-3
2x+z=-1 ----------------(D)
3x + 4(3-z) + 4z = 9
3x+12-4z+4z=9
3x=-3
x=-1 ------------ (E)
Putting this value f x in (D)
2(-1)+z=-1
-2+z=-1
z=1
Now we put this value of z in equation (C)
y=3-z
y=3-1
y=2
Hence we have
x=-1, y=2 and z=1
The yard is rectangular and is 50 feet wide by 100 feet long. How many feet of fencing to enclose the entire yard?
[tex]2\cdot50+2\cdot100=100+200=300[/tex]
300ft of fencing is required to enclose the whole yard.
Hope this helps.
r3t40
Answer:
300
Step-by-step explanation:
l + l + w + w
50 + 50 + 100 + 100 = 300
a researcher wishes to estimate the proportion of adults who have high speed internet access. what size sample should be obtained if she wishes the estimate to be within 0.04 with 90% confidence if she uses a previous estimate of 0.54
Answer:
421
Step-by-step explanation:
Margin of error = E = 0.04
Confidence Level = 90%
z value associated with this confidence level = z = 1.645
Previous estimate of population proportion = p = 0.54
q = 1 - p = 1 - 0.54 = 0.46
The formula of Margin of Error for population proportion is:
[tex]E=z\sqrt{\frac{pq}{n}}[/tex]
Here, n is the sample size.
Re-arranging the equation for n and using the values we get:
[tex]n=(\frac{z}{E})^{2} \times pq\\\\ n = (\frac{1.645}{0.04})^{2} \times 0.54 \times 0.46\\\\ n = 421[/tex]
Thus the minimum sample size required to estimate the proportion of adults who have high speed internet access is 421
If the sum of five consecutive odd integers is 265, what is the smallest of the five integers?
Answer:
The smallest integer = 49
Step-by-step explanation:
It is given that, the sum of five consecutive odd integers is 265
To find the smallest integer
Let 'x' be the smallest odd integer, the other integers are,
(x + 2), (x + 4), (x + 6), and (x + 8)
x + x + 2 + x + 4 + x + 6 + x + 8 = 265
5x + 20 = 265
5x = 245
x = 245/5 = 49
Therefore the smallest integer = 49
Answer:
49,50,51,52,53
Step-by-step explanation: