Answer:
Δπ Min = -0.0709
Δπ Max = -0.0535
Step-by-step explanation:
Here we have
[tex]z=\frac{(\hat{p_{1}}-\hat{p_{2}})-(\mu_{1}-\mu _{2} )}{\sqrt{\frac{\hat{p_{1}}(1-\hat{p_{1}}) }{n_{1}}-\frac{\hat{p_{2}}(1-\hat{p_{2}})}{n_{2}}}}[/tex]
Where:
[tex]{\hat{p_{1}}[/tex] = 13% = 0.13
[tex]\hat p_{2}[/tex] = 14% = 0.14
n₁ = 163
n₂ = 160
Therefore, we have;
[tex]z=\frac{(\hat{p_{1}}-\hat{p_{2}})}{\sqrt{\frac{\hat{p_{1}}(1-\hat{p_{1}}) }{n_{1}}-\frac{\hat{p_{2}}(1-\hat{p_{2}})}{n_{2}}}}[/tex]
Plugging the values gives
z = -0.263
CI 90% = critical z = [tex]\pm[/tex]1.644
The minimum difference in true proportion = -0.0709
The maximum difference in true proportion = 0.0535.
On Friday, a local hamburger shop sold a combined total of 294 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Friday?
Answer:
98 hamburgers were sold on Friday.
Step-by-step explanation:
294/3=98
98+98=196 cheese burgers
196+98=294 hamburgers and cheeseburgers in total
98 hamburgers
Math math math math mathematics maths
Answer:
Answer is 3
Step-by-step explanation:
As a brickmason's apprentice, you need to move the correct number bricks. The mason needs enough bricks to lay the next 4 rows. Each course is 24 bricks long. How many bricks do you need to move to complete the four rows?
Answer:
96 bricks
Step-by-step explanation:
In this question, we are asked to calculate the number of bricks which are needed by a mason given the number of bricks needed to complete each of the course.
From the question, we can identify that we have 4 rows to be filled with each of the rows being 24 bricks long.
now , to calculate the number of bricks needed to be moved by the mason, our work is pretty straightforward. what we simply need to do is to multiply the number of rows by the number of bricks per course.
According to this question specifically, this is equal to a value of 4 * 24 = 96 bricks
Threa consecutive integers have a sum of 30. Which equation can be used to find x, the value of the smallest of the three numbers?
Answer:
9
Step-by-step explanation:
X+X+1+X+2=30
3x+3=30
-3. -3
3X=27
Divide by 3
X=9
Answer:
x + (x + 1) + (x + 2) = 30
Biologists have discovered that the shoulder height h (in centimeters) of a male Asian elephant can be modeled by h = 62.5 3 t + 75.8, where t is the age (in years) of the elephant. Determine the age of an elephant with a shoulder height of 300 centimeters.
Final answer:
To determine the age of an elephant with a shoulder height of 300 centimeters, the given formula h = 62.5t + 75.8 is used. Subtracting 75.8 from 300 and then dividing by 62.5 yields the elephant's age as approximately 3.59 years.
Explanation:
The student is asking to determine the age of an Asian elephant based on a mathematical model for its shoulder height. Given the model h = 62.5t + 75.8, and knowing the elephant's shoulder height is 300 centimeters, we can set up the equation as follows:
300 = 62.5t + 75.8
To solve for t, we first subtract 75.8 from both sides:
224.2 = 62.5t
Then, we divide both sides by 62.5:
t = 224.2 / 62.5
t = 3.5872
Therefore, the age of the elephant is approximately 3.59 years.
The elephant is about 46.16 years old.
To find the age of the elephant given its shoulder height, we need to solve the equation for t . The equation given is:
[tex]h = 62.5\sqrt[3]{t} + 75.8[/tex]
Given h = 300 centimeters, we substitute h into the equation and solve for t :
[tex]300 = 62.5\sqrt[3]{t} + 75.8[/tex]
First, isolate the cube root term:
[tex]300 - 75.8 = 62.5\sqrt[3]{t} \\\\ 224.2 = 62.5\sqrt[3]{t}[/tex]
Next, divide both sides by 62.5:
[tex]\sqrt[3]{t} = \frac{224.2}{62.5} \\\\ \sqrt[3]{t} \approx 3.5872[/tex]
Now, to solve for t , cube both sides:
[tex]t \approx (3.5872)^3 \\\\ t \approx 46.16[/tex]
So, the elephant is about 46.16 years old.
The complete question is:
Biologists have discovered that the shoulder height (in centimeters) of a male Asian elephant can be modeled by [tex]h = 62.5\sqrt[3]{t} + 75.8[/tex], where t is the age (in years) of the elephant. Determine the age of an elephant with a shoulder height of 300 centimeters. Round your answer to the nearest tenth.
The elephant is about ____ years old.
In the city of Manhattan, it takes about 13 Starbucks to serve every 100,000 people. As of 2019, Manhattan has
approximately 1,629,000 people. If Manhattan is approximately 23 square miles, what is the density of Starbucks per
square mile in the city?
___Starbucks per square mile
Answer:
9.207
Step-by-step explanation:
To get the amount of starbucks for the population we can do
[tex]\frac{13 * 1629000}{100000}[/tex]
which gives us 211.77 total Starbucks in 23 miles.
To get starbucks per mile, we divide this number by 23.
This gives us 9.207
If two equations in a linear system have the same slope and the same -intercepts, the system will have:'
a ; infinite solutions
b ; no solution
c ; one solution
d ; two solutions
Answer:
The answer to your question is a. Infinite solution
Step-by-step explanation:
When two lines have the same slope and the same intercepts, this means that these lines are the same so they system of equations will have infinite solutions.
If the lines do not cross, there will be no solution.
If the lines cross in one point there will be one solution
If there are a quadratic and a linear function they will cross in two points.
Claudio bought tickets to a music festival that 225,000 people were expected to attend.what is the scientific notation?
Answer:
The number of people that attended in scientific notation is 2.25 x 10^5.
Step-by-step explanation:
What the answer to this plz need help ASAP
Answer:
A) 9841
Step-by-step explanation:
Formula of geometric sequence:
[tex]S_n=\frac{a_1*(r^n-1)}{r-1} \\[/tex]
First, calculate the common ratio (r) of the sequence.
It can be calculated by dividing any term of the geometric sequence by the term preceding it.
[tex]r = \frac{27}{9}\\ \\r=3[/tex]
Then
[tex]Sum = \frac{1(3^9-1)}{3-1} \\\\Sum = \frac{3^9-1}{2}\\ \\Sum=\frac{19683-1}{2} \\\\Sum = \frac{19682}{2} \\\\Sum=9841[/tex]
Use the Law of Sines to complete an expression that represents the angle measure x.
Answer:
sine (x) / 14.9 = sine (71) / 25.5
sine (x) = 14.9 * sine (71) / 25.5
sine (x) = 14.088248 / 25.5
sine (x) = 0.5524803137
Angle (x) = arc sine(0.5524803137)
Angle (x) = 33.537 degrees
Step-by-step explanation:
The expression which represents the angle measure x with the use of Law of Sines is x=sin⁻¹[(a sin b)/c].
What is the law of sine?The law of sine is nothing but the relationship between the sides of the triangle to the angle of the triangle (oblique triangle).
It can be given as,
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
Here (A,B,C) are the angle of the triangle and (a,b,c) are the sides of that triangle.
For the given problem it can also be given as,
[tex]x^o=\sin^{-1}\left(\dfrac{a\sin B}{c}\right)[/tex]
Put the values,
[tex]x^o=\sin^{-1}\left(\dfrac{(14.9)\sin (71)}{25.5}\right)\\x^o=\sin^{-1}\left(0.5523\right)\\x^o=33.54^o[/tex]
Thus, the expression which represents the angle measure x with the use of Law of Sines is x=sin⁻¹[(a sin b)/c].
Learn more about the sine law here;
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A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second. y=-16x^2+128x+136
Answer: The rocket will reach its max after 4 seconds
Step-by-step explanation:
Hi, to find the maximum height, we have to set the first derivative of the equation equal to zero.
y=-16x^2+128x+136
0 = (2)-16x +128
0= -32x+128
Solving for x:
32x = 128
x = 128/32
x = 4 seconds
The rocket will reach its max after 4 seconds
Feel free to ask for more if needed or if you did not understand something.
What is the range of the function represented by the graph?
Answer:
y ≥ 1
Step-by-step explanation:
Hence, range of given parabola is y[tex]\geq 1[/tex]
What is parabola ?
A parabola is a curve in which all points are at the same distance from two fixed points: the focus and the origin. a constant straight line (the directrix )
How to solve?
Generic equation of parabola y=p. (x−h[tex])^{2}[/tex]+k where (h,k) denotes the vertex. where parabola has range y[tex]\geq 0[/tex]. but as this curve is shifted at 0,1 hence range becomes y[tex]\geq 1[/tex]
Learn more about parabola
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Is 3 5/2 an acceptable answer?
Please explain your answer.
thx
yes, if the question is asking for a mixed number.
Answer:
5 1/2 would be a better answer or 5.5 in decimal form
hope this helps :)
Shelia deposited $800 into an account that earned 3% simple interest. She did not make any other deposits or withdrawals. After 5 years how much interest did Sheila earn?
Answer:
Sheila earned $120 in interest.
Step-by-step explanation:
In order to calculate the interest earned by Sheila we can use the simple interest formula shown bellow:
i = P*r*t
Where i is the interested earned, P is the amount invested, r is the interest rate and t is the total time. For this case we have:
i = 800*0.03*5
i = 24*5
i = 120
Sheila earned $120 in interest.
Answer: After 5 years, Sheila earns $120
Step-by-step explanation: The calculation of simple interest is given as
Interest = P x R x T
Where P = the amount invested initially (800), R = the rate of interest earned (3% or 0.03) and T = the number of years (5) investment was held
The interest she earned can now be calculated by substituting for the known values as follows;
Interest = 800 x 0.03 x 5
Interest = 120
Therefore after 5 years, Sheila earns $120
What is the y-intercept of y=3x-2
Answer:
This formula is in slope-intercept form. 3 is the slope (positive slope) and -2 is the y-intercept.
Hi there!
Your answer is:
The slope is 3 and the y-intercept is 2 or (0, 2).
Have a good day
~ Mqddie
which equation represents a circle with a center at (2,-8) and a radius of 11
Answer:
(x - 2)² + (y + 8)² = 121
Step-by-step explanation:
circle: (x – h)² + (y – k)² = r² (h , k) center r: radius
h = 2 k = - 8 r = 11
equation: (x - 2)² + (y + 8)² = 121
The equation of circle can be determine by using general equation of circle.
The equation for circle would be [tex](x - 2)^2+ (y + 8)^2 = 121[/tex].
Given:
The center of circle is [tex](2,-8)[/tex].
The radius is [tex]11[/tex].
Write the general equation of circle.
[tex](x-h)^2 + (y-k)^2= r^2[/tex]
Where, [tex](h,k)[/tex] is center of circle and [tex]r[/tex] is the radius of the circle.
Substitute [tex]2[/tex] for [tex]h[/tex], [tex]-8[/tex] for [tex]k[/tex] and [tex]11[/tex] for [tex]r[/tex] in above equation.
[tex](x - 2)^2 + (y + 8)^2 = 121[/tex]
Thus, the equation for circle would be [tex](x - 2)^2+ (y + 8)^2 = 121[/tex].
Learn more about equation of circle here:
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Without solving them, say whether these equations have a positive solution, a negative solution,
a zero solution, or no solution.
Positive solution= the answer is a positive number.
Negative solution= the answer is a negative number.
Zero solution= the answer is zero.
Negative solution= the variable goes away, so you can't solve it.
a. 3x=5
b. 5z+7=3
c. 7-5w=3
d. 4a=9
e. y=y+1
Answer:
a. 3x=5 Positive Solution
Reasoning: You're working with only positives
b. 5z+7=3 Negative Solution
Reasoning: If you carry the 7 over the non-coefficient numbers will be negative thus making your answer negative
c. 7-5w=3 Positive Solution
Reasoning: both the coefficients and the non coefficients will be negative if solved and thus will result in the negatives becoming positive when dividing the 5w
d. 4a=9 Positive
Reasoning: The first step would be to divide the 9 by 4 and the resulting number would be positive
e. y=y+1 Negative Solution (No solution)
Reasoning: y can never equal itself with changing. Thats like saying 0 is 1. This has no solution but based on the rules this is negative solution
The solutions to the equations are: a. Positive solution, b. Negative solution, c. Negative solution, d. Positive solution, and e. No solution.
Explanation:Let us analyze these equations one by one:
a. 3x=5: This equation involves multiplying a number by 3 to get 5. The solution here would be a positive number because 5/3 is positive.b. 5z+7=3: To find the value of 'z', we'd subtract 7 from both sides and then divide by 5. Considering that 3-7 is negative, and dividing a negative number by a positive number results in a negative answer, the solution of this equation will be negative.c. 7-5w=3: In this equation, subtracting 7 from 3 gives a negative number. Therefore, 'w' would be negative as dividing a negative number with a negative number results in a positive solution, which we can't have. Therefore, the solution of this equation will be negative.d. 4a=9: This equation involves dividing 9 by 4. The solution would be a positive number because 9/4 is positive.e. y=y+1: In this equation, when we attempt to isolate 'y', we're left with 0=1, which is not possible. Therefore, this equation has no solution.Learn more about Finding Solutions to Equations here:https://brainly.com/question/35067340
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Find the angle measure in degrees
Answer:
82°
Step-by-step explanation:
By inscribed angle theorem:
[tex]m\angle QRP = \frac{1}{2} \times 164 \degree \\ \\ \huge \red{ \boxed{\therefore \: m\angle QRP =82 \degree}}[/tex]
On a beach trip lucy rents a bike from wheel by the waves where they rent bikes for $12 plus $3 per hour if lucy spent $30 how many hours(h) did she ride a bike
Answer:
6 hours
Step-by-step explanation:
Make an equation
Each hour costs $3, and there is a $12 cost regardless of the hours. We know that Lucy spent $30.
3h+12=30
Subtract 12 from both side s
3h=18
Divide both sides by 3
h=6
So, she rented it for 6 hours
A lighthouse is set 10 meters back from the edge of the shoreline, and it's beacon is 52 meters above sea level. Lucy can see the beacon from her ship, and the of elevation is 18 degrees. Her eyes are 12 meters above sea level. How far is the ship from the shoreline to the nearest meter?
Answer:
The distance of the ship from the shoreline is 113 metres.
Step-by-step explanation:
Please kindly check the attached files for explanation
Answer:
The distance of the ship to the shoreline is 113 meters
Step-by-step explanation:
Here we have the following information
Location of lighthouse = 10 m back from the edge of the shoreline
Height of beacon above sea level = 52 m
Level of the eyes of Lucy above sea level = 12 m
Angle of elevation of the beacon from Lucy = 18°
Therefore, the beacon, the elevation of the eyes of Lucy and the base of the lighthouse at the same elevation with Lucy form a right triangle with opposite side to angle = 52 m and angle = 18 °
Therefore, from
[tex]Tan\theta =\frac{sin\theta }{cos\theta } = \frac{Opposite \, side \, to\, angle}{Adjacent\, side \, to\, angle}[/tex]
We have
[tex]Tan18 =\frac{52-12}{Adjacent } = \frac{40}{Adjacent}[/tex]
0.325 = [tex]\frac{40}{Adjacent}[/tex]
Where the adjacent side is the distance of the ship from the lighthouse
Adjacent side = 40/0.325 = 123.107 meters
We recall that the lighthouse is 10 m back from the edge of the shoreline, therefore the ship is 123.107 - 10 or 113.107 meters from the shore line which is 113 meters to the nearest meter.
Flying against the wind, an airplane travels 4560 kilometers in 6 hours. Flying with the wind, the same plane travels 3720 kilometers in 3 hours. What is the rate of the plane in still air and what is the rate of the wind?
Answer:
The speed rate of the plane in still air is 1006.67 km/h
The speed rate of the wind is 246.67 km/h
Step-by-step explanation:
To answer the question, we let the speed of the plane in still air = x km/h
Let the speed of the wind = y km/h
Therefore,
4560/(x - y) = 6 hours and
3720/(x + y) = 3 hours
4560 = 6·x - 6·y.........(1)
3720 = 3·x + 3·y ........(2)
Multiplying equation (2) by 2 and add to (1) gives
12080 = 12·x
x = 12080/12 = [tex]1006\frac{2}{3}[/tex] km/h
Substituting the value of x in (1) gives
4560 = 6040 - 6·y
6·y = 1480
y = 1480/6 = [tex]246\frac{2}{3}[/tex]
The speed rate of the plane in still air = 1006.67 km/h
The speed rate of the wind = 246.67 km/h.
if angle y measures 33 degrees what does angle x measure?
Answer:
<x = 147
Step-by-step explanation:
Supplementary angles is when the sum of the two angles are equal to 180
So the sum of angle x and angle y is equal to 180
y = 33
x + y = 180
x + 33 = 180
x = 180 - 33
x = 147
Answer:
x = 147°
Step-by-step explanation:
x ; y = suplementary =>
x + y = 180° } => x = 180° - 33° = 147°
y = 33°
What does automation mean in this sentence The automation telephone answering surveyed frustrated many people
Answer:
Automation means something that does not require human input, automatic.
Answer:
answer is the use of machines that function on their own.
Step-by-step explanation:
Sarah bought 3 1/2 pints of blueberries to make jelly. She ate 3/4 of a pint of berries on her way home. How many pints of berries does she have left to make jelly?
Answer:
11/4 or 2.75 pints
Step-by-step explanation:
We want to find the difference between the original amount of blueberries and the amount she ate
original amount-amount ate
3 1/2 -3/4
To subtract, we need common denominators
The common denominator of 2 and 4 is 4
3 1/2=7/2
Multiply by 2/2 to get a common denominator of 4
7/2*2/2=14/4
Now, we have common denominators and can subtract
14/4-3/4
Subtract the numerators, and leave the denominators as 4
11/4 =2.75
She has 11/4 or 2.75 pints left
20 points if you help me on this proublem
Answer:
1) f(x) = x/8 - 7
2) f(x) = 1 - x/3
3) f(x) = 20 - 0.25x
4) f(x) = x + 7
Step-by-step explanation:
f^-1 = 8(x + 7)
x + 7 = y/8
x = y/8 - 7
f(x) = x/8 - 7
f^-1 = -3(x - 1)
y/-3 = x - 1
x = 1 - y/3
f(x) = 1 - x/3
f^-1 = 4(20 - x)
y/4 = 20 - x
x = 20 - y/4
f(x) = 20 - x/4
f(x) = 20 - 0.25x
f^-1 = x - 7
y = x - 7
x = y + 7
f(x) = x + 7
Cheryl wants to find the number of hours seventh-graders do homework each week. There are 297 girls and boys in
seventh grade. Which is the best way for Cheryl to get a representative sample without spending too much time?
She can survey 15 of her friends in the school.
She can survey every sixth-grade student in the school.
She can randomly survey 50 girls in the entire school.
She can randomly survey 50 seventh-graders in the school.
Answer: She can randomly survey 50 seventh-graders in the school.
Step-by-step explanation: To get the best result without wasting to much time means she cannot afford to survey every student. To receive the best results it should be unbiased so random is the way to go. Randomly surveying 50 girls in her school does not guarantee that those girls are all seventh graders so the best answer is She can randomly survey 50 seventh-graders in the school.
plz help ive been stuck on this question for so long
Multiply each exponent inside the parentheses by the exponent on the outside:
8^(-5 x -4) / 2^(-2 x -4)
8^20 / 2^8
The answer is C
What is a linear function f for f(-4)=2,f(6)=3
Answer:
y - 3 = (1/10)(x - 6)
Step-by-step explanation:
Note how x (the "run") increases by 10 and how y (the "rise") by 1. Thus, the slope of the line connecting point (-4, 2) with point (6, 3) is
m = rise / run = 1/10.
Using the point-slope equation of a straight line, we derive the equation of this particular line as follows:
y - 3 = (1/10)(x - 6)
Professor York randomly surveyed 240 students at Oxnard University and found that 150 of the students surveyed watch more than 10 hours of television weekly. How many additional students would Professor York have to sample to estimate the proportion of all Oxnard University students who watch more than 10 hours of television each week within ±3 percent with 99 percent confidence?
Answer:
1727 students
Step-by-step explanation:
Here we have the formula for sample size given as
[tex]n = \frac{p(1-p)z^2}{ME^2}[/tex]
Where:
p = Mean
ME = Margin of error = 3
z = z score
Therefore, we have
p = 150/240 = 0.625
z at 99 % = 2.575
ME = [tex]\pm[/tex]3%
Therefore [tex]n = \frac{0.625(1-0.625)2.575^2}{0.03^2} = 1726.73[/tex]
The number of students Professor York have to sample to estimate the proportion of all Oxnard University students who watch more than 10 hours of television each week within ±3 percent with 99 percent confidence = 1727 students.
find the volume of the cylinder someone help please
Answer:
The answer to your question is in terms of π, Volume = 54π units³
as an exact number Volume = 169.56 units³
Step-by-step explanation:
Data
radius = 3
height = 6
π = 3.14
Process
1.- Look for the formula to calculate the volume of a cylinder
Volume = πr²h
2.- Substitution
Volume = π(3)²(6)
3.- Simplification
Volume = π(9)(6)
4.- Volume in terms of π
Volume = 54π units³
5.- As an exact number
Volume = 54(3.14)
-Result
Volume = 169.56 units³