Answer:
a. 0.0385
b. 3.44% probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.43, n = 165[/tex]
a. Calculate the appropriate standard error calculation for the data.
[tex]s = \sqrt{\frac{0.43*0.57}{165}} = 0.0385[/tex]
b. What is probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home?
This is 1 subtracted by the pvalue of Z when X = 0.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.5 - 0.43}{0.0385}[/tex]
[tex]Z = 1.82[/tex]
[tex]Z = 1.82[/tex] has a pvalue of 0.9656
1 - 0.9656 = 0.0344
3.44% probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home
If the graph of the function y = f(x) is compressed horizontally by 3, and then reflected across the y -axis , then the resulting graph is the graph of the function :
(a) y = -f(3x) (b) y = f(-3x) (c)y=-f(1/3x)
(d) y = -f(1/3x)
(e) none
Answer:
Please check if the answer is correct or not....
Which expression is a trinomial? x + y – 13 4xyz
How do we write this as a power? [tex]4(\sqrt{7})x^{3[/tex]
Answer:
It might be 4 * [tex]7^{1/2}[/tex] * [tex]x^{3}[/tex]
PLEASE HELP ME OUT
Move point b to different locations in the coordinate plane. What do you notice about the relationship between BG and GF? Explain in terms of <BGF
Answer:
BG is always perpendicular to GF. The measure of angle BGF is always 90 degree
Step-by-step explanation:
Answer:
is always perpendicular to . The measure of is always 90°.
Step-by-step explanation:
Plato Awnser
What is the area of the triangle?
9 4 12
Answer:
13.636
Step-by-step explanation:
The area can be found using Heron's formula:
A = √(s(s-a)(s-b)(s-c))
where s=(a+b+c)/2.
For the given triangle, ...
a=9, b=4, c=12, s=(9+4+12)/2 = 12.5
A = √(12.5(3.5)(8.5)(0.5)) = √185.9375 ≈ 13.636
The area of the triangle is about 13.636 square units.
Answer:
24 units\
Step-by-step explanation:
Brainliest to whoever gets this correct! Does this graph show a function? Explain how you know.A.No; there are y-values that have more than one x-value.B.No; the graph fails the vertical line test.C.Yes; the graph passes the vertical line test.D.Yes; there are no y-values that have more than one x-value.
Answer:
B. No; the graph fails the vertical line test.
Step-by-step explanation:
If you hold a pencil up to the graph, the parabola would technically touch the pencil at more than one point. That means it failed the test, and therefore it is not a function.
hope this helped :)
What value of x is in the solution set of 4x – 12 5 16 + 8x?
-10
-9
-8
-7
Answer:
[tex] 4x-12= 16 +8x[/tex]
And we can subtract 4x in both sides and we got:
[tex] -12 = 16 +4x[/tex]
Now we can subtract in both sides 16 and we got:
[tex] -28 = 4x[/tex]
And if we divide both sides by 4 we got:
[tex] x = -7[/tex]
And the best solution would be:
-7
Step-by-step explanation:
For this case we assume the following equation:
[tex] 4x-12= 16 +8x[/tex]
And we can subtract 4x in both sides and we got:
[tex] -12 = 16 +4x[/tex]
Now we can subtract in both sides 16 and we got:
[tex] -28 = 4x[/tex]
And if we divide both sides by 4 we got:
[tex] x = -7[/tex]
And the best solution would be:
-7
Select all the correct equations.
Which equations have no real solution but have two complex solutions? PLZ 20 POINTS
Answer:
You did not post the options, but i will try to answer this in a general way.
Because we have two solutions, i know that we are talking about quadratic equations, of the form of:
0 = a*x^2 + b*x + c.
There are two easy ways to see if the solutions of this equation are real or not.
1) look at the graph, if the graph touches the x-axis, then we have real solutions (if the graph does not touch the x-axis, we have complex solutions).
2) look at the determinant.
The determinant of a quadratic equation is:
D = b^2 - 4*a*c.
if D > 0, we have two real solutions.
if D = 0, we have one real solution (or two real solutions that are equal)
if D < 0, we have two complex solutions.
Answer:
This was for 5 points. not 20 my dude. Also the first answer is correct.
Step-by-step explanation:
45 points! Yay An investment may earn interest using a simple interest rate or a compound interest rate. This expression can be used to find the value of an investment that is earning simple interest: P(1+rt) This expression can be used to find the value of an investment that is earning compound interest: P(1+r)t Use the drop-down menus to complete the statements about simple and compound interest. For an investment earning(simple interest,compound interest) , the interest is applied each year to the principal and to any interest that already accrued. For an investment earning(simple interest, compojnd interest) , the interest is applied each year only to the principal. Please help I'm literally the dumbest person i know •,-,•
Answer:
1. Compound Interest
2. Simple Interest
Step-by-step explanation:
Simple Interest multiplies the interest rate on the principal rate by the number of days.
Compound Interest multiplies the interest rate on the principal rate and existing rate by periods.
Answer:
:)
Step-by-step explanation:
EXPONENTIAL FUNCTIONS HELP Write the function for each graph described below. the graph of f(x) = 2x reflected across the x-axis. The graph of f(x)= 1/3x translated up 5 units. The graph of f(x) = 3x left 2 units, and down 3. The graph of f(x) = 1/2x translated down 2 units. The graph of f(x) = 4x stretched horizontally by a factor of 3. The graph of f(x) = 2x up 4 units, right 3.
Answer:
-2^x(1/3)^x +53^(x +2) -3(1/2)^x -24^(x/3)2^(x -3) +4Step-by-step explanation:
In general, the transformation ...
g(x) = f(x -h) +k
translates f(x) right h units and up k units.
The transformation ...
g(x) = f(x/a)
stretches the graph horizontally by a factor of "a".
The transformation ...
g(x) = -f(x)
causes the graph to be reflected over the x-axis.
___
Applying the above, we have ...
f(x) = 2^x reflected over x is g(x) = -2^x
f(x) = (1/3)^x translated up 5 is g(x) = (1/3)^x +5
f(x) = 3^x translated by (-2, -3) is g(x) = 3^(x +2) -3
f(x) = (1/2)^x translated down 2 is g(x) = (1/2)^x -2
f(x) = 4^x stretched horizontally by a factor of 3 is g(x) = 4^(x/3)
f(x) = 2^x translated by (3, 4) is g(x) = 2^(x -3) +4
Answer:
-2^x
(1/3)^x +5
3^(x +2) -3
(1/2)^x -2
4^(x/3)
2^(x -3) +4
Step-by-step explanation:
In general, the transformation ...
g(x) = f(x -h) +k
translates f(x) right h units and up k units.
The transformation ...
g(x) = f(x/a)
stretches the graph horizontally by a factor of "a".
The transformation ...
g(x) = -f(x)
causes the graph to be reflected over the x-axis.
___
Applying the above, we have ...
f(x) = 2^x reflected over x is g(x) = -2^x
f(x) = (1/3)^x translated up 5 is g(x) = (1/3)^x +5
f(x) = 3^x translated by (-2, -3) is g(x) = 3^(x +2) -3
f(x) = (1/2)^x translated down 2 is g(x) = (1/2)^x -2
f(x) = 4^x stretched horizontally by a factor of 3 is g(x) = 4^(x/3)
f(x) = 2^x translated by (3, 4) is g(x) = 2^(x -3) +4
What is the area of rectangle ABCD given the information below?
Answer: Area is 1840units²
Step-by-step explanation:
From the given information,
Firstly, area of a rectangle is given as
A = l × b ie, length multiply by the breadth.
One of the side of the rectangle is known , AD = 16 , now to calculate the other side, we need some calculations.Since FE = 23 and
FD = DE ,,therefore,
DE = 23/2.
From the information, DE = 1/10 of DC. We now find DC the required side for finding the area of the rectangle by simple equation. Since DE = 23/2 , the equation now looks like this to get DC
23/2 = DC/10. Now , solving this
2DC = 23 × 10
2DC = 230
DC = 230/2
= 115.
Now the area of the rectangle will be
A = 16 × 115
= 1840units²
Find the measure of ∠2.
Answer:
∠[tex]2=131[/tex]°
Step-by-step explanation:
We know that ∠[tex]4[/tex] is ≅ ∠[tex]1[/tex].
This means that ∠ [tex]1=49[/tex]°
Therefore, [tex]49+49=98[/tex]°
We know that a trapezoid is [tex]360[/tex]°.
To find ∠[tex]2[/tex] ,which is congruent to ∠[tex]3\\[/tex], we will have to subtract [tex]360[/tex]° from [tex]98[/tex]°.
[tex]360-98=262[/tex]°.
Because ∠[tex]2[/tex]≅∠[tex]3[/tex], we will have to divide [tex]262[/tex] by [tex]2[/tex] to see their measurement.
So,
[tex]\frac{262}{2}=131[/tex].
Hence, ∠[tex]2=131[/tex]°.
I really hope this helps:D
-Jazz
[URGENT] (15 points) F(x) is defined by the equation f(x) = 3x^2 + 3x - 7. What effect will multiplying
f(x) by 0.5 have on the graph?
Answer:
Options (B) and (C).
Step-by-step explanation:
When a quadratic function 'f' is multiplied by k,
1). If k > 0, function 'f' will be vertically stretched Or horizontally compressed.
2). If 0 < k < 1, function will be vertically compressed Or horizontally stretched.
Given quadratic function is,
f(x) = 3x² + 3x - 7
This function is multiplied by 0.5.
Since 0 < 0.5 < 1, therefore, the function will be compressed vertically Or stretched horizontally.
Therefore, Options B and C are the correct options.
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The non-even numbers are 1, 3, and 5 on the dice.
3 numbers out of 6.
3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
Total sides of 6-sided die = 6
Numbers not even = 3
Probability of not getting an even = 3/6
=> 1/2
calculate the force acting on a man of mass 600g running to a tree through a distance of 20m
120N
f= mgh
=o. 6x10x20
= 120N
Step-by-step explanation:
given,
mass ( m)=0.6kg
gravity=9.8 m/s^2
by the formula of force,
f= ma
=0.6×9.8
therefore force is 5.88 n.
The bill for dinner was $71. The bill included a
10% tax. What was the bill before the tax was
added?
Round your answer to the nearest cent.
Answer:
$63.90
Step-by-step explanation:
First we want to find 10% of 71, this is 7.1.
Since we want to know the price before the tax was added, we will subtract 7.1 from 71 to get our final answer, $63.9
Have a great day ;)
Answer:
$63.9 or rounded up- $64
Step-by-step explanation:
Step one: first you need to find 10% of 71. To do that you multiply 71 by 0.10. The answer is 7.1
Step two: next you would do 71-7.1 to take off the 10%. you get your answer as $64.
Don't forget to rate and thanks!
Transformation of exponential functions
Answer:
first option
Step-by-step explanation:
It's up by 4 units because because the +4 is outside of the exponent and also, it is a +4 not -4 which indicates that the translation is up.
In the past, 26% of all homes with a stay-at-home parent, the father is the stay-at-home parent. An independent research firm has been charged with conducting a sample survey to obtain more current information.(a) What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.04? Use a 95% confidence level. (Round your answer up to the nearest whole number.)(b) Repeat part (a) using a 99% confidence level. (Round your answer up to the nearest whole number.)
Answer:
(Round your answer up to the nearest whole number.)(b) Repeat part (a) using a 99% confidence level. (Round your answer up to the nearest whole number.)
Step-by-step explanation:
In a random sample of cars driven at low altitudes, of them exceeded a standard of grams of particulate pollution per gallon of fuel consumed. In an independent random sample of cars driven at high altitudes, of them exceeded the standard. Can you conclude that the proportion of high-altitude vehicles exceeding the standard is less than the proportion of low-altitude vehicles exceeding the standard
Complete question is;
In a random sample of 370 cars driven at low altitudes, 43 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 80 cars driven at high altitudes, 23 of them exceeded the standard. Can you conclude that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard at an level of significance? Group of answer choices
Answer:
Yes we can conclude that there is enough evidence to support the claim that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard (P-value = 0.00005).
Step-by-step explanation:
This is a hypothesis test for the difference between the proportions.
The claim is that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.
Then, the null and alternative hypothesis are:
H0 ; π1 - π2 = 0
H1 ; π1 - π2 < 0
The significance level would be established in 0.01.
The random sample 1 (low altitudes), of size n1 = 370 has a proportion of;
p1 = x1/n1
p1 = 43/370
p1 = 0.116
The random sample 2 (high altitudes), of size n2 = 80 has a proportion of;
p2 = x2/n2
p2 = 23/80
p2 = 0.288
The difference between proportions is pd = (p1-p2);
pd = p1 - p2 = 0.116 - 0.288
pd = -0.171
The pooled proportion, we need to calculate the standard error, is:
p = (x1 + x2)/(n1 + n2)
p = (43 + 23)/(370 + 80)
p = 66/450
p = 0.147
The estimated standard error of the difference between means is computed using the formula:
S_(p1-p2) = √[((p(1 - p)/n1) + ((p(1 - p)/n2)]
1 - p = 1 - 0.147 = 0.853
Thus;
S_(p1-p2) = √[((0.147 × 0.853)/370) + ((0.147 × 0.853)/80)]
S_(p1-p2) = 0.044
Now, we can use the formula for z-statistics as;
z = (pd - (π1 - π2))/S_(p1-p2)
z = (-0.171 - 0)/0.044
z = -3.89
Using z-distribution table, we have the p-value = 0.00005
Since the P-value of (0.00005) is smaller than the significance level (0.01), then the effect is significant.
We conclude that The null hypothesis is rejected.
Thus, there is enough evidence to support the claim that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.
Frequency table help
Answer: 1) 21-25
2) III
3) II
4) 8
5) 4
Step-by-step explanation:
Question 1: Which numbers are missing?
The previous interval ends at 20 the following interval starts at 26.
The missing interval is 21 - 25
Question 2: How many tally marks to draw?
The frequency is given as 3, so draw three tally marks: III
Question 3: How many tally marks to draw?
The frequency is given as 2, so draw two tally marks: II
Question 4: What is the frequency?
There are eight tally marks so the frequency is 8.
Question 5: What is the frequency?
There are four tally marks so the frequency is 4.
8. The sides of AABC inscribed in a circle are equidistant from the center,
Tricia says that AABC must be equilateral. Which explains whether Tricia is
correct? *
A. Tricia is correct because the sides of the triangle are congruent since they are
equidistant from the center of the circle,
B. Tricia is incorrect because the sides of the triangle are different lengths since the
chord of the circle can be any length,
C. Tricia is correct because the sides of the triangle are congruent since they are
inscribed in a circle,
D. Tricia is incorrect because the triangle has two congruent sides since one chord
has to be a diameter
PLEASE HELP ME
Answer:
Step-by-step explanation:
If the sides of triangle ABC inscribed in a circle are equidistant from the center, it means that the distance of each side from the center of the circle is the same. This means that the distance from the center of the circle to any point on a side of the triangle is the same for all 3 sides of the triangle.
If Tricia says that triangle ABC must be equilateral, then
A. Tricia is correct because the sides of the triangle are congruent since they are equidistant from the center of the circle,
A swimming pool is being drained at a constant rate of 3 inches (depth of the water) per hour. The depth of the water after 5 hours is 32 inches. Write the equation for this function in point slope form
Answer:
The equation in point slope form is [tex]y - 47\,in = \left(-3\,\frac{in}{h}\right)\cdot (t-0\,h)[/tex]
Step-by-step explanation:
Since the swimming pool is being drained at a constant rate, the equation of the process must be a first-order polynomial (linear function), where depth of water decrease as time goes by. The form of the expression is:
[tex]y = m \cdot t + b[/tex]
Where:
[tex]t[/tex] - Time, measured in hours.
[tex]b[/tex] - Initial depth of the water in swimming pool (slope), measured in inches.
[tex]m[/tex] - Draining rate, measured in inches per hour.
[tex]y[/tex] - Current depth of the water in swimming pool (x-Intercept), measured in inches.
If [tex]m = -3\,\frac{in}{h}[/tex] and [tex]y (5\,h) = 32\,in[/tex], the initial depth of the water in swimming pool is:
[tex]b = y - m\cdot t[/tex]
[tex]b = 32\,in -\left(-3\,\frac{in}{h} \right)\cdot (5\,h)[/tex]
[tex]b = 47\,in[/tex]
The equation in point slope form is:
[tex]y-y_{o} = m \cdot (t-t_{o})[/tex]
Where [tex]y_{o}[/tex] and [tex]t_{o}[/tex] are initial depth of the water in swimming pool and initial time, respectively. Then, the equation in point slope form is:
[tex]y - 47\,in = \left(-3\,\frac{in}{h}\right)\cdot (t-0\,h)[/tex]
Pls cam someone help me
Extremely confused with both if poss xxxx
Answer:
1. Red red blue blue
2. Red blue red blue
Step-by-step explanation:
A 50 percent chance
Write two point-slope equations for the line passing through the points (6, 5) and (3, 1). Show your work.
Answer:
y=-4/3x-3
Step-by-step explanation:
You look for the slope using the the slope formula (m=y2-y1/x2-x1)
You will end up with (m=1-5/3-6)
Simplify to end up with (-4/3) as your slope.
Then, pick a coordinate point. Your choices are (6,5) and (3,1). You will us it to plug into the equation.
I am picking (3,1) The y-value here is 1 and the x-value is 3.
Your equation to find b, or the y-intercept is going to be (1=-4/3(3)+b)
You will have to simplify.
1=-4/3(3)+b
You will multiply -4/3 and -3 and end up with 4 so it looks like...
1=4+b
You subtract 4 on both sides and then end up with....
-3=b
So, the final answer is: y=-4/3x-3
a manufacturer of bicycle parts requires that a bicycle chain have a width of 0.3 inch with an absolute deviation of at most 0.0003 inch. write and solve an absolute value inequality that represents the acceptable widths.
Answer:
[tex] |w-0.3| \leq 0.0003[/tex]
And solving we got:
[tex] -0.0003 \leq w-0.3 \leq 0.0003[/tex]
[tex]0.3-0.0003 \leq w \leq 0.3+0.0003[/tex]
[tex] 0.2997 \leq w \leq 0.3003[/tex]
Step-by-step explanation:
For this case we can define the following notation:
[tex] W[/tex] represent the width
And we want a maximum error of 0.0003 so we can set up the following equation:
[tex] |w-0.3| \leq 0.0003[/tex]
And solving we got:
[tex] -0.0003 \leq w-0.3 \leq 0.0003[/tex]
[tex]0.3-0.0003 \leq w \leq 0.3+0.0003[/tex]
[tex] 0.2997 \leq w \leq 0.3003[/tex]
Which of the following is parallel to
2Y = 6X + 4?
A. Y = -3X + 3
B. Y = 3X + 4
C. Y = x + 3
D. Y = -2X - 3
E. Y= 1/2 X + 3
Answer:
B. y = 3x + 4
Step-by-step explanation:
Step 1: Find slope-intercept form of 1st equation
2y = 6x + 4
2y/2 = 6x/2 + 4/2
y = 3x + 2
A parallel line has the same slope but different y-intercept:
y = -3x + 3 (No, different slope)
y = 3x + 4 (Yes, same slope, different y-int)
y = x + 3 (No, different slope)
y = -2x - 3 (No, different slope)
y = 1/2x + 3 (No, different slope)
PLEASE HELP I’LL MARK BRAINLIEST If 1 equals 1 2/3 how much does 1 1/2 equal?
Answer:
0.9 (9/10)
Step-by-step explanation:
(see picture)
help me pls help me pls
Answer:
It should be D if not Than A
Answer:
it should be D
Step-by-step explanation:
Please answer this correctly
Answer:
4
Step-by-step explanation:
Consider the following. x = 6 sin y , 0 ≤ y ≤ π, x = 0; about y = 4
(a) Set up an integral for the volume V of the solid obtained by rotating the region bounded by the given curve about the specified axis.
(b) Use your calculator to evaluate the integral correct to four decimal places.
Answer:
12pi(8-pi), or
183.158 to third decimal place
Step-by-step explanation:
The geometry is indicated in the attached figure.
A. by integration
We will find the volume of the solid by the method of shells, i.e. we will integrate strips parallel to the axis of rotation to form many thin shells, then integrate to get the sum of all these shells.
For each shell, of thickness dy, we integrate strips of length located at y
L(x) = y(x)
and area
L(x)dy
Each strip is at a distance of (4-y) from
for which the volume of each shell equals
dV = 2*pi*(4-y)*L(x)dy = 2*pi*(4-y)*y(x) dy
The total volume of the solid can be obtained by integrating y from 0 to pi
integral( dV ) from 0 to pi
= integral (2*pi*(4-y)*y(x) dy) for y from 0 to pi
= 12*pi(-sin(y)+y*cos(y)-4*cos(y)) for y from 0 to pi
=12(8-pi)*pi
= 183.158
B. Using Pappus theorem
Pappus theorem simplifies the calculation of volume of revolution by multiplying the area of the rotating region by 2pi times the distance between the centroid and the rotation axis.
Here the area of the figure is A=2*6=12, (2 is the area under the sine curve from 0 to pi), or
A = integral (6sin(x))dx, x from 0 to pi
= 6 cos(x), x from 0 to pi
= 6(1- (-1))
= 12
Distance from centroid to axis of rotation = (4-pi/2)
Volume = 2*pi*A*(4-pi/2) = 2*pi*12*(4-pi/2)
= 12pi(8-pi)
=183.158 as before