Answer:
The 99% confidence interval estimate for the difference between the percentage of women and men who prefer the beach over the mountains is -18.72% < (p₁ - p₂) < 4.72%
Step-by-step explanation:
The given parameters are;
Sample size of the women sample, n₁ = 200
Percentage of the women that prefer beach, p₁ = 45%, [tex]\hat p_1[/tex] = 0.45
Sample size of the men sample n₂ = 300
Percentage of the men that prefer beach, p₂ = 52%, [tex]\hat p_2[/tex] = 0.52
Confidence level of the confidence interval = 99%
α = 1 - 0.99 = 0.01, therefore, α/2 = 0.005
The equation for the confidence interval for the difference between two proportions is given as follows;
[tex]\left (\hat{p}_{1} - \hat{p}_{2} \right )\pm z_{\alpha /2}\sqrt{\dfrac{\hat{p}_{1}(1-\hat{p}_{1})}{n_{1}}+\dfrac{\hat{p}_{2}(1-\hat{p}_{2})}{n_{2}}}[/tex]
[tex]z_{\alpha /2}[/tex] = ±2.57 from the z score tables
Plugging in the vales, we have;
[tex]\left (0.45 - 0.52 \right )\pm 2.57\sqrt{\dfrac{0.45(1-0.45)}{200}+\dfrac{0.52(1-0.52)}{300}}[/tex]
Which gives;
-0.1872 < [tex](\hat p_1 - \hat p_2)[/tex] < 0.0472
The 99% confidence interval estimate for the difference between the percentage of women and men who prefer the beach over the mountains = -18.72% < (p₁ - p₂) < 4.72%.
g(x)=x^3+6x^2+12x+8 determine
Answer:
g(-1) = 1
Step-by-step explanation:
g(-1) = (-1)^3 + 6(-1)^2 + 12(-1) + 8
g(-1) = 1
what is the equation of the line? please help !!!! first and correct answer will get brainesttt
Answer:
y=1/2x-4
Step-by-step explanation
Jeremy’s bank account started at a balance of $124 this week. Since then, he wrote a check, which decreased his balance by $147. Jeremy was then charged an overdraft fee, decreasing his balance by $32. Finally, he deposited a paycheck, which increased his balance by $567. What is Jeremy’s ending balance after these transactions, in dollars?
Answer:
$512
Step-by-step explanation:
His bank account started at a balance of $124.
He wrote a check, which decreased his balance by $147. His new balance is:
124 - 147 = -$23
Jeremy was then charged an overdraft fee, decreasing his balance by $32. That is:
-23 - 32 = -$55
He deposited a paycheck, which increased his balance by $567. His account balance will become:
-55 + 567 = $512
His account balance after those transactions is $512.
what is the quotient of the rational expression below? 3x+1/x+8 ÷ x-7/5x
Answer:
8x^2 + 45/5x
Step-by-step explanation:
write the division as a fraction
3x+ 1/x + 8/x - 7/5x
using a=a/1, convert the expression into a fraction
3x/1 - 7/5x
calculate the product
3x/1 - 7x/5
expand the fraction to get the least common denominator
5 x 3x/ 5 x 1 - 7x/5
multiply the numbers
15x/5 - 7x/5
write all numerators above the common denominator
15x - 7x/5
collect like terms
8x/5
write the factor as a product
8/5 x + 1/x + 8/x
calculate the product
8x/5 + 5 x 1/5x + 5 x 8/5x
expand the fraction to get the least common denominator
X x 8x/X x 5 + 5/5x + 5 x 8/5x
multiply the numbers
X x 8x/X x 5 + 5/5x + 40/5x
calculate the product
8x^2/5x + 5/5x +40/5x
write all numerators above the common denominator
8x^2 + 5 + 40/5x
add the numbers and that's the answer
8x^2 + 45/5x
(that was l o n g)
On Monday, Avi walked from his home to the school track and walked
4 laps around the track for a total of 3.5 miles. On Saturday, Avi ran from
his home to the school track, ran 2 laps, and then ran home for a total of
4 miles. Let x represent the distance from Avi’s home to the school track,
and let y represent the distance of one lap around the track.
1. Write a system of equations to represent this situation.
2. What is the distance from Avi’s home to the school track and around
the track?
3. On Saturday, Avi walked from his home to the school track, walked 6
times around the track, and then walked home. How far did he walk in all?
Avi knows that the distance from his home to the library and back is
at least 2.5 miles. He also knows that the distance from his home to
the library and then to the school track is less than 3 miles. Let p
represent the distance from Avi’s home to the library, and let q
represent the distance from the library to the school track.
4. Write a system of inequalities to represent this situation.
5. Can the distance from Avi’s home to the library be 2 miles and the
distance from the library to the school track be 1 mile?
9514 1404 393
Answer:
x+4y=3.5; 2x+2y=4x=1.5; y=0.56 miles2p≥2.5; p+q<3NoStep-by-step explanation:
1. x +4y = 3.5 . . . . variables are defined in the problem statement
2x +2y = 4
__
2. Subtract half the second equation from the first.
(x +4y) -(1/2)(2x +2y) = (3.5) -(1/2)(4)
3y = 1.5
y = 0.5
x = 2 -y = 1.5
The distance from home is 1.5 miles; the distance around the track is 0.5 miles.
__
3. 2x +6y = 2(1.5) +6(0.5) = 3+3 = 6
Avi walked 6 miles on Saturday.
__
4. 2p ≥ 2.5 . . . . variables are defined in the problem statement
p +q < 3
__
5. No.
2 + 1 < 3 is NOT TRUE
they paid $13 for each pepperoni pizza and $11for each plain pizza the club bought total of 18 pizzas for the party and paint a total of $212 Drag and drop the numbers to the boxes to create an equation which models this situation if x=the number of pepperoni pizza and y=the numbers of plain pizza boght
Complete question;
A booster club paid for pizzas for an end of season party. They paid $13 for each pepperoni pizza and $11 for each plain pizza. The club bought a
total of 18 pizzas for the party and paid a total of $212.
Drag and drop the numbers to the boxes to create an equation which models this situation if x = the number of pepperoni pizzas and y = the number of plain pizzas bought.
Answer:
13x + 11y = 212
Step-by-step explanation:
They bought 2 different recipe of pizza. The first is the pepperoni pizza and the second kind is the plain pizza. The pepperoni pizza cost $13 each while the plain Pizza cost $11 each. The total number of pizza bought is 18 in number.
The total cost of the pizza is also $212.
number of pizza bought = 18
total cost of pizza = $212
x = the number of pepperoni pizzas
y = the number of plain pizzas
The number of pepperoni pizzas multiply by the cost for each will give the cost of the pepperoni pizzas. This same method is applied to get the cost of the plain pizzas.
Therefore, adding the individual cost of the kinds of pizza will give the total cost of the pizzas.
13x + 11y = 212
At my friend’s middle school the ratio of teachers to students is 1:9. If there are 45 teachers at the school, how many students are there? Show your work or explain how you determine your answer.
Write a literal/explicit equation to model the situation above. Where Y is the number of students and X the number of teachers at the school
Answer:
405 students
Step-by-step explanation:
1=teachers
9=students
1=45 teachers
9=y students
y=9 x 45
y=405 students
Which number is less than 0.37? A. 0.72 B. 0.5 C. 0.35 D. 0.41
Answer:
0.35 is less than 0.37 because 35 < 37.
Answer:
C is the correct answer
Step-by-step explanation:
If p=3(2q+r), express q in terms of p and r.
Answer:
[tex]q=\frac{1}{6}p- \frac{1}{2}r[/tex]
Step-by-step explanation:
[tex]p=3(2q+r)[/tex]
[tex]2q+r=\frac{p}{3}[/tex]
[tex]2q=\frac{p}{3} -r[/tex]
[tex]q=\frac{p}{6}- \frac{r}{2}[/tex]
The product of a number and its ___________ is
A).opposite
B)reciprocal
C)factor
D)quotient
Answer:
Most definitely reciprocal
May You Please Help Me With This Problem
Answer:
x² + x - 8
Step-by-step explanation:
(f . g)(x) is same with (f(g(x))
so insert the g(x) equation into f(x) and change the x on it
f(g(x)) = g(x) - 2
f(g(x)) = (x² + x - 6) - 2 = x² + x - 6 - 2 = x² + x -8
so
(f.g)(x) is x² + x - 8
A right circular solid cone of base radius 42cm and height 84cm has the same volume as a solid cylinder of height 112cm find the radius of the cylinder
Answer:
21 cm
Step-by-step explanation:
Volume of cone is given by [tex]1/3(\pi r^2h)[/tex]
volume of cylinder is given by [tex]\pi r^2h[/tex]
where r is the radius of base and h is the height
_________________________________
For cone
radius = 42cm
height = 84
volume = [tex]1/3(\pi *42^2*84)[/tex] (1)
________________________________
For cone
radius = to find let it be r
height =112
volume = [tex]\pi *r^2*112[/tex] (2)
_______________________________________
since , volume of both solid are same
thus, equation 1 = equation 2
[tex]1/3(\pi *42^2*84) = \pi *r^2*112\\=> r^2 = 1/3((\pi *42^2*84) / 112*\pi \\=> r^2 = 1/3(42*42*84/112) = 441\\=> r = \sqrt{441} \\=> r = 21[/tex]
Thus, radius of cylinder is 21 cm
The final velocity, V, of an object under constant acceleration can be found using the formula v2=v2+2as, where v is the initial velocity (in meters per second), a is acceleration (in meters per second), and s is the distance (in meters). What is the formula solved for a?
Answer: a = (V^2 - v^2)/2s
Step-by-step explanation:
The equation for the final velocity is:
V^2 = v^2 + 2*a*s
where V is the final velocity, v is the initial velocity, a is the acceleration and s is the distance.
Now, we want to solve this formula for a, this would mean isolate a in one side of the equation, this is pretty simple, first we pass subtract v^2 in both sides.
V^2 - v^2 = v^2 + 2*a*s - v^2
V^2 - v^2 = 2*a*s
now we can divide by 2*s in both sides:
(V^2 - v^2)/2s = 2*a*s/2s = a
a = (V^2 - v^2)/2s
Veronica wants to check her work after evaluating -108 divided by (-6). What steps can she follow to verify her answer? A. Divide her answer by –6 and see if the result is –108. B. Divide her answer by –108 and see if the result is –6. C. Multiply her answer by –6 and see if the result is –108. D. Multiply her answer by –108 and see if the result is –6.
Answer:
C. Multiply her answer by –6 and see if the result is –108.
Step-by-step explanation:
Answer:
The answer is c
Step-by-step explanation:
hope this helps c:
somebody come help me I'm stuck in this problem how do I simplify it using exponent rule
Answer:
-5x^4y^3
Step-by-step explanation:
so you divide -25 by 5 and the rule is if it is division for exponents then you subtract the exponent so 6-2=4, 7-4=3, 3-3=0. z^0 is 1 so we don't have to write it out.
screenshot below-mathematics ,help please!!
Answer:
(a) range = difference between highest
mark and lowest mark
range of marks = 10 - 6
= 4
(b) total students = marks × frequency
(6×5)+(7×4)+(8×7)+(9×10)+(10×4)
= 30+28+56+90+40
= 244 students
(c) total frequency = 5+4+7+10+4
= 30
mean mark = total students/total
frequency
= 244/30
= 8.133
Answer:range-4 , no. of students-30, mean mark is 26
Step-by-step explanation:
Divide $1200 in the ratio 5:3:2
Answer:
Step-by-step explanation:
16
Grace wanted to pick a card randomly from a regular deck of 52 cards. Fifty of the cards were regular playing
cards, and the rest of the cards were jokers. What is the probability that Grace picks a joker?
Answer:
2:52 or 1:26 (simplest form)probability.
What would the base be to the solution to
4^8*4^2?
Answer:
It can would be 4
Step-by-step explanation:
When you multiply exponents you add the exponents
so you get 4^10
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!!!
Answer:
Multiply 5 to both sides to get
(x+3)^2 = 100
Step-by-step explanation:
Please refer to the picture above.
Simplify the equation by aiming to eliminate the fraction in the right hand side of the equation by multiplying the denominator to both sides of the equation in step 2
Answer:
[tex](x + 3)^{2}[/tex] = 100
Step-by-step explanation:
Please answer correctly !!!! Will mark brainliest !!!!!!!!!
Answer:
[tex]b= \frac{-4}{7} a - \frac{52}{7}[/tex]
Step-by-step explanation:
1st, isolate b.
7b=-4a-52
Next, divide both sides by 7.
b=(-4a/7)-(52/7)
list the integers that satisfy both these inequalities 2x+9 0 x > -12 put the answer on the first line
Answer:
The Answer is 5
Step-by-step explanation:
Given that 3m=2c-5k,express c in terms of k and m.
Answer:
The answer is
[tex]c = \frac{3m + 5k}{2} [/tex]
Step-by-step explanation:
You have to move all the unrelated terms to the other side :
[tex]3m = 2c - 5k[/tex]
[tex]3m + 5k = 2c[/tex]
[tex]2c = 3m + 5k[/tex]
Next you have to divide it by 2 :
[tex]c = \frac{3m + 5k}{2} [/tex]
In a box-and-whisker plot, the interquartile
range is a measure of the spread of the
middle half of the data. Find the interquartile
range for the data set: 10, 3, 7, 6, 9, 12, 13.
Answer:
IQR=8
Step-by-step explanation:
write numbers in ascending order
3 6 9 10 12 13
find the middle, in this case, it's two numbers (10 and 12)
3 6 are on the left, find the middle between them; 3+6/2
4.5
12 and 13 are on the right, find the middle between them;
12+13/2
12.5
IQR=12.5-4.5
Solve each equation and check your solution:
A) -2w=26
B)3n-3=17
C)15 - w = 45
D) 5c- 7c= 32
E) 6+ 6h = 2h -5
F) 2.5x - 4 + 1.2x = 3.5
Answer:
A. w = 26/2 = -13
B. 3n = 20
n = 20/3
C. -w = 30
w = -30
D. -2c = 32
c = -16
E. 4h = -11
h = -11/4
F. 3.7x = 7.5
x = 75/37
Answer:
x = 75/37
Step-by-step explanation:
how to write 70 persent as fraction
Answer:
70/100 or 7/10
Step-by-step explanation:
As a percentage 70 percent is 70%.
As a fraction because 70 is out of 100 it would obviously be 70/100 but you can simplify to 7/10 and it is still equal to 70%
Please help! Correct answer only please! I need to finish this assignment by today.
The aspect ratio of a rectangular shape is it's length divided by it's width (L/W). If the aspect ratio of a chalkboard is 4:3 and the width is 7 in,
what is the length of the chalkboard?
A. 6.67 in
B. 9.33 in
C. 12 in
D. 14 in
Answer:
B
Step-by-step explanation:
If the ratio of the length of the chalkboard to the width is 4:3, this means that the length of this one is 7* 4/3=28/3. This can be rewritten as approximately 9.33 inches, or answer choice B. Hope this helps!
PLEASE HELP RIGHT NOW I WILL MARK AS BRAINIEST!!!!!!!!!!!!!!!!
Select three (3) TRUE statements ABOUT quadrilaterals.
a.) A quadrilateral is a polygon with 4 sides and 4 angles.
b.) The sum of the angle measurements in a quadrilateral are 180 degrees.
c.) A rectangle is a parallelogram with 4 right angles.
d.) A square is a rectangle with all 4 equal sides.
e.) A quadrilateral is not a polygon.
f.) All the angles measures in a quadrilateral have to be right angles.
Answer:
A, B and E
Step-by-step explanation:
Which equation models a line that is perpendicular to y = x - 1 and goes through the point (5,4)
Answer:
y = - x + 9
Step-by-step explanation:
Because the line is perpendicular, the slope with be the opposite reciprocal. So, if the slope is 1 as in the equation y = x - 1, the opposite reciprocal is -1.
So the equation that is perpendicular will look like this so far:
y = -x + b (b represents our y-intercept that we have not found yet)
Now we will find the y-intercept. We can find it by substituting the coordinates (5,4) as x and y into the equation right above ^^.
So, 4 = -(5) +b or 4 = -5 + b
Add 5 to both sides to isolate b on the right side. b = 9
Therefore, the y-intercept is 9.
Now we have found everything we need for the equation, which is
y = - x + 9
Find the distance from point B to point C. Please help 25 points!!
Answer:
9.6 = BC
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opposite/ adjacent
tan 58 = BC / 6
Multiply each side by 6
6 tan 58 = BC
9.602007174 =BC
Round to the nearest tenth
9.6 = BC
Answer:
BC= 9.6
Hope it helps :)