Answer:
The 98% confidence interval for the difference of the mean amount of June precipitation in Michigan cities and Ohio cities is (-1.77, 0.29).
Step-by-step explanation:
The (1 - α)% confidence interval for the difference between two population mean is:
[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n-1)}\cdot\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}[/tex]
Compute the value of sample means and sample standard deviations from the provided data.
[tex]\bar x_{1}=3.142\\\\\bar x_{2}=3.882\\\\s_{1}=0.4396\\\\s_{2}=0.4283\\n_{1}=n_{2}=5[/tex]
The critical value of t for 98% confidence level and (n - 1) = 4 degrees of freedom is:
[tex]t_{\alpha/2, (n-1)}=t_{0.02/2, 4}=3.747[/tex]
Compute the 98% confidence interval for the difference of the mean amount of June precipitation in Michigan cities and Ohio cities as follows:
[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n-1)}\cdot\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}[/tex]
[tex]=(3.142-3.882)\pm3.747\cdot\sqrt{\frac{0.4396^{2}}{5}+\frac{0.4283^{2}}{5}}\\\\=-0.74\pm 1.0285\\\\=(-1.7685, 0.2885)\\\\\approx (-1.77, 0.29)[/tex]
Thus, the 98% confidence interval for the difference of the mean amount of June precipitation in Michigan cities and Ohio cities is (-1.77, 0.29).
(25 points) PLEASE HELP! Gotta get this done before my mom comes home
1. The owner of an organic fruit stand also sells nuts. She wants to mix cashews worth $5.50 per pound with peanuts worth $2.30 per pound to get a 1/2 pound mixture that is worth $2.80 per pound. How much of each kind of nut should she include in the mixed bag?
A. Cashews: 0.10 lb.; peanuts: 0.40 1b.
B. Cashews: 0.42 lb.; peanuts: 0.08 1b.
C. Cashews: 0.40 lb.; peanuts: 0.10 1b
D. Cashews: 0.27 lb.; peanuts: 0.23 1b.
E. Cashews: 0.23 lb.; peanuts: 0.27 1b.
F. Cashews: 0.08 lb.; peanuts: 0.42 1b
2. A nursery owner has 288 rose bushes. There are 36 fewer red roses than pink roses. How many of each type of roses are there?
A. Red roses: 162; pink roses: 252.
B. Red roses: 162; pink roses: 126.
C. Red roses: 99; pink roses: 126.
D. Red roses: 126; pink roses: 162
E. Red roses: 126; pink roses: 99
F. Red roses: 252; pink roses: 162
3. The sum of the ages of Stephanie and Heather is 46. Heather is two years younger than Stephanie. Write a system of equations to determine the ages of Stephanie and Heather.
A) S + H = 46
H = S + 2
B) S - H = 46
H - 2 = S
C) S + H = 46
H = S - 2
D) S - H = 2
H = S - 46
E) S + H = 2
H = S - 46
F) 2S – H = 46
4. You want to borrow three rock CDs from your friend. She loves math puzzles and she always makes you solve one before you can borrow her stuff. Here’s the puzzle: Before you borrow three CDs, she will have 39 CDs. She will have half as many country CDs as rock CDs, and one-fourth as many soundtracks as country CDs. How many of each type of CD does she have after you borrow three rock CDs?
A. After borrowing 3 rock CDs, your friend will have 21 rock CDs, 12 country CDs, and 3 soundtracks.
B. After borrowing 3 rock CDs, your friend will have 24 rock CDs, 12 country CDs, and 3 soundtracks.
C. After borrowing 3 rock CDs, your friend will have 25 rock CDs, 10 country CDs, and 4 soundtracks.
D. After borrowing 3 rock CDs, your friend will have 21 rock CDs, 9 country CDs, and 3 soundtracks.
E. After borrowing 3 rock CDs, your friend will have 24 rock CDs, 12 country CDs, and no soundtracks.
F. After borrowing 3 rock CDs, your friend will have 18 rock CDs, 15 country CDs, and 3 soundtracks.
5. Three times the width of a certain rectangle exceeds twice its length by two inches. Four times its length is twelve more than its perimeter. Write a system of equations that could be used to solve this problem. (hint: P = 2L + 2W)
A) 3W = 2L + 2
2L = 2W + 12
B) 3W + 2 = 2L
4L = P – 12
C) 3W = 2L + 2
4L + 12 = P
D) 2W + 2 = 2L
4L = 12 + P
E) 3W + 2 = 2L
4L = 12 + P
F) 2L – 2 = 3W
P = 4L - 12
Thank you!!!!
The radius of circle is 11 miles. What is the area of a sector bounded by a
300° arc?
The area of a circle is pi x r^2
Area of full circle: 3.14 x 11^2
Area = 379.94 square miles.
To find the area of the bounded arc, multiply the full area by the fraction of a full circle the arc is:
379.94 x 300/360 = 316.62 square miles
Answer:
316.62 miles²
Step-by-step explanation:
Area of circle = 3.14 × r²
3.14 × 11²
= 379.94 (area of whole circle)
We need to find the area of the blue shaded sector.
300/360 × 379.94
= 316.62
HELP PLEASE FOR 35 POINTS!!!! Solve the rational equation 3 divided by x equals quantity 4 times x plus 3 divided by x squared, and check for extraneous solutions.
Answer:
[tex]x=-3[/tex]
Step-by-step explanation:
So, we are given:
[tex]\frac{3}{x}=\frac{4x+3}{x^2}[/tex]
First, we should immediately rule out 0 as an answer. This is because the if [tex]x=0[/tex], the equation would be undefined.
[tex]x\neq 0[/tex]
Now, cross multiply.
[tex]3(x^2)=x(4x+3)[/tex]
[tex]3x^2=4x^2+3x[/tex]
Divide everything by x (and we can do this safely because we already know x cannot be equal to zero).
[tex]3x=4x+3[/tex]
[tex]-x=3[/tex]
[tex]x=-3[/tex]
We didn't run into any possibilities for extraneous solutions.
Losses covered by a flood insurance policy are uniformly distributed on the interval (0,2). The insurer pays the amount of the loss in excess of a deductible d. The probability that the insurer pays at least 1.20 on a random loss is 0.30. Calculate the probability that the insurer pays at least 1.44 on a random loss.
Answer:
The probability that the insurer pays at least 1.44 on a random loss is 0.18.
Step-by-step explanation:
Let the random variable X represent the losses covered by a flood insurance policy.
The random variable X follows a Uniform distribution with parameters a = 0 and b = 2.
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b\\\\\Rightarrow f_{X}(x)=\frac{1}{2}[/tex]
It is provided, the probability that the insurer pays at least 1.20 on a random loss is 0.30.
That is:
[tex]P(X\geq 1.2+d)=0.30\\[/tex]
⇒
[tex]P(X\geq 1.2+d)=\int\limits^{2}_{1.2+d}{\frac{1}{2}}\, dx[/tex]
[tex]0.30=\frac{2-1.2-d}{2}\\\\0.60=0.80-d\\\\d=0.80-0.60\\\\d=0.20[/tex]
The deductible d is 0.20.
Compute the probability that the insurer pays at least 1.44 on a random loss as follows:
[tex]P(X\geq 1.44+d)=P(X\geq 1.64)[/tex]
[tex]=\int\limits^{2}_{1.64}{\frac{1}{2}}\, dx\\\\=|\frac{x}{2}|\limits^{2}_{1.64}\\\\=\frac{2-1.64}{2}\\\\=0.18[/tex]
Thus, the probability that the insurer pays at least 1.44 on a random loss is 0.18.
an office supply company sells two types of printers. they charge $95 for one of the printers and $125 for the other. if the company sold 32 printers for a total of$3340 last month, how many of each type were sold
Answer:
22 of the 95$ ones and 10 of the 125
Step-by-step explanation:
22 times 95 = 2090
10 times 125 = 1250
2090+1250=3340
hope this helped
Solve the equation.
y + 3 = -y + 9
y= 1
y=3
y = 6
y = 9
Answer: y=3
Step-by-step explanation:
To solve the equation, we want to get the same terms onto the same side and solve.
y+3=-y+9 [add y on both sides]
2y+3=9 [subtract 3 on both sides]
2y=6 [divide 2 on both sides]
y=3
Answer:
y=3
Step-by-step explanation:
(a) The only even prime number is ....
Answer:
2 is the only even prime number
Answer:
2
Step-by-step explanation:
2 is the only even prime number. There is no even prime number other than 2. Prime numbers are the numbers which can only be divided by 1 and the number itself.
3/25 as a percentage
Answer:
12%
Step-by-step explanation:
3/25 = .12
.12 x 100 = 12%
Answer:
12%
Step-by-step explanation:
All you have to do is divide this on a calculator and multiply it by 100. 3/25 = 0.12; 0.12 x 100 = 12%.
Find the area under the standard normal curve to the right of z = 2.
Answer:
0.0228
Step-by-step explanation:
A suitable probability calculator (or spreadsheet) can tell you this.
It is about 0.0228.
The formula relating linear velocity v and angular velocity ω for a circle of radius r is______ , where the angular velocity must be measured in radians per unit time.
Answer:
[tex]v=wr[/tex]
Step-by-step explanation:
The formula relating linear velocity v and angular velocity ω for a circle of radius r is
[tex]v=wr------1[/tex]
where v = linear velocity in m/s
w= angular velocity in rad/s
r= radius of curve
Both linear and angular velocity relates to speeds of objects, while linear velocity is to objects that moves, angular velocity is to objects that turns
Which of the following expressions could be used to find 80% of X (the lines are there to show the different expressions)
Answer:
80/100 times x => [tex] \frac{80}{100}*x [/tex]
(0.8) times x => [tex] (0.8)*x [/tex]
4/5 times x => [tex] \frac{4}{5}*x [/tex]
8/10 times x => [tex] \frac{8}{10}*x [/tex]
Step-by-step explanation:
80% of x means 80 ÷ 100 × x
that is: [tex] \frac{80}{100}*x = \frac{8}{10}*x = \frac{4}{5}*x = (0.8)*x [/tex]
Therefore, the expressions that can be used to find 80% of x are:
80/100 times x => [tex] \frac{80}{100}*x [/tex]
(0.8) times x => [tex] (0.8)*x [/tex]
4/5 times x => [tex] \frac{4}{5}*x [/tex]
8/10 times x => [tex] \frac{8}{10}*x [/tex]
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime?
Answer:
[tex]B'(x,y) = (0,-2)[/tex]
Step-by-step explanation:
Given
The attached grid
Translation rule: [tex](x,y) = (x + 5, y - 2)[/tex]
Required
Determine the coordinates of B'
First, we have to write out the coordinates of B
[tex]B(x,y) = (-5,0)[/tex]
Next is to apply the translation rule [tex](x,y) = (x + 5, y - 2)[/tex]
[tex]B(x,y) = (-5,0)[/tex] becomes
[tex]B'(x,y) = B(x+5,y-2)[/tex]
Substitute -5 for x and 0 for y
[tex]B'(x,y) = (-5+5,0-2)[/tex]
[tex]B'(x,y) = (0,-2)[/tex]
A line has a slope of $-\frac{3}{7},$ and its $y$-intercept is $(0,18)$. What is its $x$-intercept?
Answer:
(42, 0)
Step-by-step explanation:
Since we know the slope and y-intercept we can write the equation of the line in slope-intercept form which is y = mx + b; therefore, the equation is y = -3/7x + 18. To find the x-intercept, we just plug in y = 0 which becomes:
0 = -3/7x + 18
-18 = -3/7x
x = 42
[tex]\text{In order to find your x intercept, plug in 0 to y and solve:}\\\\0=-\frac{3}{7}x+18\\\\\text{Subtract 18 from both sides}\\\\-18=-\frac{3}{7}x\\\\\text{Multiply both sides by 7}\\\\-126=-3x\\\\\text{Divide both sides by 3}\\\\42 = x\\\\\text{This means that the x-intercept is (42,0)}\\\\\boxed{\text{x-intercept: (42,0)}}[/tex]
The JUST-SAY-MOW lawn mowing company consists of two people: Marsha and Bob. If Marsha cuts the lawn by herself, she can do it in 3 hours. If Bob cuts the same lawn himself, it takes him an hour longer than Marsha. How long would it take them if they worked together? Round to the nearest hundredth of an hour.
Answer:
it will take them 1.71 hours to finish cutting the lawn if they work together.
Step-by-step explanation:
If Marsha cuts the lawn by herself it will take her 3 hours, this mean that in one hour she cuts 1/3 of the lawn.
On the other hand Bob needs one more hour to finish the lawn, this means it takes him 4 hours to cut it and therefore he cuts 1/4 of the lawn per hour.
Now, to know how much they cut by working together we need to sum up the amount of lawn they cut per hour:
Working together in one hour: Marsha's one hour + Bob's one hour
Working together in one hour: [tex]\frac{1}{3}+ \frac{1}{4}=\frac{4+3}{12}=\frac{7}{12}[/tex]
Therefore, working together they will cut 7/12 in one hour.
Now, to know how long will it take it to cut the entire lawn (which is equivalent to 12/12), we can write this in terms of proportions
Time Total amount of lawn
1 hour 7/12
x hours 12/12
Solving for x (to know the amount of hours it will take them) we have:
[tex]x=\frac{12}{12}[/tex]÷[tex]\frac{7}{12}[/tex]=[tex]1[/tex]×[tex]\frac{12}{7}=\frac{12}{7}=1.714[/tex]
Rounded to the nearest hundredth, we have that working together it will take them 1.71 hours to finish cutting the lawn.
Which of the binomials below is a factor of this trinomial?
5x2-18x+9
O A. 5x-3
O B. X-1
O c. X+1
O D. 5x+3
Answer:
The answer is option A.
Step-by-step explanation:
here, 5x^2-18x+9
=5x^2-(15+3)x+9
=5x^2-15x-3x+9
=5x(x-3)-3(x-3)
=(5x-3)(x-3)
so, the answer from the above options is (5x-3).
hope it helps..
Shawn has a bank account with $4,625. He decides to invest the money at 3.52% interest,
compounded annually. How much will the investment be worth after 9 years? Round to
the nearest dollar.
Answer: The investment will be 6314 after 9 years.
Step-by-step explanation:
Formula to calculate the accumulated amount in t years:
[tex]A=P(1+r)^t[/tex], whereP= principal amount, r= rate of interest ( in decimal)
Given: P = $4,625
r= 3.52% = 0.0352
t= 9 years
Then, the accumulated amount after 9 years would be:
[tex]A=4625(1+0.0352)^9\\\\=4625(1.0352)^9\\\\=4625(1.36527)\approx6314[/tex]
Hence, the investment will be 6314 after 9 years.
(3x + 4y)^3
i am confused
pls help
ANSWER
(a+b)(a^2+ab+b^2)=(3x+4y) 9x^2+12xy+16y^2)
Using this model, what would be the cost of a flight that travels 1375 miles?
Round your answer to the nearest dollar.
Answer:
C) $143.
Step-by-step explanation:
We are given an equation: y = 0.0714x + 44.8.
x is the number of miles, and y is the cost.
y = 0.0714 * 1,375 + 44.8
y = 98.175 + 44.8
y = 142.975
So, the cost is about C) $143.
Hope this helps!
Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Round all answers using one decimal place.
Answer:
The missing side is [tex]B = 6.0\ cm[/tex]
The missing angles are [tex]\alpha = 56.2[/tex] and [tex]\theta = 93.8[/tex]
Step-by-step explanation:
Given
[tex]A = 10\ cm[/tex]
[tex]C = 12\ cm[/tex]
[tex]\beta = 30[/tex]
The implication of this question is to solve for the missing side and the two missing angles
Represent
Angle A with [tex]\alpha[/tex]
Angle B with [tex]\beta[/tex]
Angle C with [tex]\theta[/tex]
Calculating B
This will be calculated using cosine formula as thus;
[tex]B^2 = A^2 + C^2 - 2ACCos\beta[/tex]
Substitute values for A, C and [tex]\beta[/tex]
[tex]B^2 = 10^2 + 12^2 - 2 * 10 * 12 * Cos30[/tex]
[tex]B^2 = 100 + 144 - 240 * 0.8660[/tex]
[tex]B^2 = 100 + 144 - 207.8[/tex]
[tex]B^2 = 36.2[/tex]
Take Square root of both sides
[tex]B = \sqrt{36.2}[/tex]
[tex]B = 6.0[/tex] (Approximated)
Calculating [tex]\alpha[/tex]
This will be calculated using cosine formula as thus;
[tex]A^2 = B^2 + C^2 - 2BCCos\alpha[/tex]
Substitute values for A, B and C
[tex]A^2 = B^2 + C^2 - 2BCCos\alpha[/tex]
[tex]10^2 = 6^2 + 12^2 - 2 * 6 * 12 * Cos\alpha[/tex]
[tex]100 = 36 + 144 - 144Cos\alpha[/tex]
Collect Like Terms
[tex]100 - 36 - 144 = -144Cos\alpha[/tex]
[tex]-80 = -144Cos\alpha[/tex]
Divide both sides by -144
[tex]\frac{-80}{-144} = Cos\alpha[/tex]
[tex]0.5556 = Cos\alpha[/tex]
[tex]\alpha = cos^{-1}(0.5556)[/tex]
[tex]\alpha = 56.2[/tex] (Approximated)
Calculating [tex]\theta[/tex]
This will be calculated using cosine formula as thus;
[tex]C^2 = B^2 + A^2 - 2BACos\theta[/tex]
Substitute values for A, B and C
[tex]12^2 = 6^2 + 10^2 - 2 * 6 * 10Cos\theta[/tex]
[tex]144 = 36 + 100 - 120Cos\theta[/tex]
Collect Like Terms
[tex]144 - 36 - 100 = -120Cos\theta[/tex]
[tex]8 = -120Cos\theta[/tex]
Divide both sides by -120
[tex]\frac{8}{-120} = Cos\theta[/tex]
[tex]-0.0667= Cos\theta[/tex]
[tex]\theta = cos^{-1}(-0.0667)[/tex]
[tex]\theta = 93.8[/tex] (Approximated)
Select all the correct coordinate pairs and the correct graph. Select the correct zeros and the correct graph of the function below.
Answer:
(0, 0), (-1, 0), (2, 0), (3, 0) are the zeros.
First graph in top row is the answer.
Step-by-step explanation:
The given function is, f(x) = x⁴ - 4x³ + x² + 6x
For zeros of the given function, f(x) = 0
x⁴ - 4x³ + x² + 6x = 0
x(x³ - 4x² + x + 6) = 0
Therefore, x = 0 is the root.
Possible rational roots = [tex]\frac{\pm 1, \pm 2, \pm 3, \pm 6}{\pm1}[/tex]
= {±1. ±2, ±3, ±6}
By substituting x = -1 in the polynomial,
x⁴ - 4x³ + x² + 6x = (-1)⁴ - 4(-1)³+ (-1)² + 6(-1)
= 1 + 4 + 1 - 6
= 0
Therefore, x = -1 is also a root of this function.
For x = 2,
x⁴ - 4x³ + x² + 6x = (2)⁴ - 4(2)³+ (2)² + 6(2)
= 16 - 32 + 4 + 12
= 0
Therefore, x = 2 is a root of the function.
For x = 3,
x⁴ - 4x³ + x² + 6x = (3)⁴ - 4(3)³+ (3)² + 6(3)
= 81 - 108 + 9 + 18
= 0
Therefore, x = 3 is a root of the function.
x = 0, -1, 2, 3 are the roots of the given function.
In other words, (0, 0), (-1, 0), (2, 0), (3, 0) are the zeros.
From these points, first graph in top row is the answer.
Trigonometry Dilemma
Answer:
17.1
Step-by-step explanation:
The missing side is x
tan 25° = [tex]\frac{opposite }{adjacent }[/tex] tan 25° = [tex]\frac{8}{x}[/tex]switch tan 25° and x
x = [tex]\frac{8}{tan 25}[/tex] x= 17.15≈17.1What is the solution to the system that is created by the equation y = 2 x + 10 and the graph shown below? On a coordinate plane, a line goes through (negative 2, 0) and (0, 2). (–8, –6) (–4, –2) (0, 2) (2, 4)
Answer:
(–8, –6)
Step-by-step explanation:
The given points represent the x- and y- intercepts of the line, so we can write the equation in intercept form as ...
x/(x-intercept) +y/(y-intercept) = 1
x/(-2) +y/2 = 1 . . . use the given intercepts
x - y = -2 . . . . . multiply by -2
Then the system is ...
y = 2x +10x - y = -2Using the first to substitute into the second, we get ...
x - (2x +10) = -2
-8 = x . . . . . . . . . . . add x+2, simplify
y = 2(-8) +10 = -6
The solution is (x, y) = (-8, -6).
Answer:
(-8,-6)
Step-by-step explanation:
Got it right on edge soooo <3
Find the area under the standard normal probability distribution between the following pairs of z-scores. a. z=0 and z=3.00 e. z=−3.00 and z=0 b. z=0 and z=1.00 f. z=−1.00 and z=0 c. z=0 and z=2.00 g. z=−1.58 and z=0 d. z=0 and z=0.79 h. z=−0.79 and z=0
Answer:
a. P(0 < z < 3.00) = 0.4987
b. P(0 < z < 1.00) = 0.3414
c. P(0 < z < 2.00) = 0.4773
d. P(0 < z < 0.79) = 0.2852
e. P(-3.00 < z < 0) = 0.4987
f. P(-1.00 < z < 0) = 0.3414
g. P(-1.58 < z < 0) = 0.4429
h. P(-0.79 < z < 0) = 0.2852
Step-by-step explanation:
Find the area under the standard normal probability distribution between the following pairs of z-scores.
a. z=0 and z=3.00
From the standard normal distribution tables,
P(Z< 0) = 0.5 and P (Z< 3.00) = 0.9987
Thus;
P(0 < z < 3.00) = 0.9987 - 0.5
P(0 < z < 3.00) = 0.4987
b. b. z=0 and z=1.00
From the standard normal distribution tables,
P(Z< 0) = 0.5 and P (Z< 1.00) = 0.8414
Thus;
P(0 < z < 1.00) = 0.8414 - 0.5
P(0 < z < 1.00) = 0.3414
c. z=0 and z=2.00
From the standard normal distribution tables,
P(Z< 0) = 0.5 and P (Z< 2.00) = 0.9773
Thus;
P(0 < z < 2.00) = 0.9773 - 0.5
P(0 < z < 2.00) = 0.4773
d. z=0 and z=0.79
From the standard normal distribution tables,
P(Z< 0) = 0.5 and P (Z< 0.79) = 0.7852
Thus;
P(0 < z < 0.79) = 0.7852- 0.5
P(0 < z < 0.79) = 0.2852
e. z=−3.00 and z=0
From the standard normal distribution tables,
P(Z< -3.00) = 0.0014 and P(Z< 0) = 0.5
Thus;
P(-3.00 < z < 0 ) = 0.5 - 0.0013
P(-3.00 < z < 0) = 0.4987
f. z=−1.00 and z=0
From the standard normal distribution tables,
P(Z< -1.00) = 0.1587 and P(Z< 0) = 0.5
Thus;
P(-1.00 < z < 0 ) = 0.5 - 0.1586
P(-1.00 < z < 0) = 0.3414
g. z=−1.58 and z=0
From the standard normal distribution tables,
P(Z< -1.58) = 0.0571 and P(Z< 0) = 0.5
Thus;
P(-1.58 < z < 0 ) = 0.5 - 0.0571
P(-1.58 < z < 0) = 0.4429
h. z=−0.79 and z=0
From the standard normal distribution tables,
P(Z< -0.79) = 0.2148 and P(Z< 0) = 0.5
Thus;
P(-0.79 < z < 0 ) = 0.5 - 0.2148
P(-0.79 < z < 0) = 0.2852
A ball always bounces to 3/5 of the height from which it is dropped. The ball is dropped from 1.8m and bounces 3 times. How high will it rise from the third bounce?
Answer: 0.388 m
Step-by-step explanation:
Ok, if the ball is dropped from 1.8 meters, then the height after the first bounce will be 3/5 times 1.8 meters:
h1 = (3/5)*1.8m = 1.08m
now we can think that the ball is dropped from a height of 1.08 meters, then the height after the second rebound will be:
h2 = (3/5)*1.08m = 0.648m
Now, using the same method as before, the height after the third bounce will be:
h3 = (3/5)*0.648m = 0.388 m
Notice that we can write this relation as:
h(n) = 1.8m*(3/5)^n
where n is the number of bounces.
if n = 0 we have the initial height, and if n = 3 we are on the third bounce, then:
h(3) = 1.8m*(3/5)^3 = 0.388 m
Price of an item is reduced by 40% of its original price. A week later it’s reduced 20% of the reduced price. What’s the actual % of the reduction from the original price
Answer: 52%
Step-by-step explanation:
Let the original price be 100.
After 40% reduction, price will be 100 - 40% = 60
After further 20% reduction, price will be 60 - 20% = 48
%age = (cur val - orig. val ) / orig val x 100
= (48 - 100) / 100 x 100%
= -52
The actual percentage of reduction is 52%
The first reduction is given as:
[tex]r_1 = 40\%[/tex]
The second reduction is given as:
[tex]r_2 = 20\%[/tex]
Assume that the original price of the item is x.
After the first reduction of 40%, the new price would be:
[tex]New = x\times (1 -r_1)[/tex]
So, we have:
[tex]New = x\times (1 -40\%)[/tex]
[tex]New = x\times 0.6[/tex]
[tex]New = 0.6x[/tex]
After the second reduction of 20% on the reduced price, the new price would be:
[tex]New = 0.6x\times (1 -r_2)[/tex]
So, we have:
[tex]New = 0.6x\times (1 -20\%)[/tex]
[tex]New = 0.6x\times 0.8[/tex]
[tex]New = 0.48x[/tex]
Recall that the original price is x.
So, the actual reduction is:
[tex]Actual = \frac{x - 0.48x}{x}[/tex]
[tex]Actual = \frac{0.52x}{x}[/tex]
Divide
[tex]Actual = 0.52[/tex]
Express as percentage
[tex]Actual = 52\%[/tex]
Hence, the actual percentage of reduction is 52%
Read more about percentage change at:
https://brainly.com/question/809966
consider the distribution of monthly social security (OASDI) payments. Assume a normal distribution with a standard deviation of $116. if one-fourth of payments are above $1214,87 what is the mean monthly payment?
Answer:
$1137
Step-by-step explanation:
Solution:-
We will define the random variable as follows:
X: Monthly social security (OASDI) payments
The random variable ( X ) is assumed to be normally distributed. This implies that most monthly payments are clustered around the mean value ( μ ) and the spread of payments value is defined by standard deviation ( σ ).
The normal distribution is defined by two parameters mean ( μ ) and standard deviation ( σ ) as follows:
X ~ Norm ( μ , σ^2 )
We will define the normal distribution for (OASDI) payments as follows:
X ~ Norm ( μ , 116^2 )
We are to determine the mean value of the distribution by considering the area under neat the normal distribution curve as the probability of occurrence. We are given that 1/4 th of payments lie above the value of $1214.87. We can express this as:
P ( X > 1214.87 ) = 0.25
We need to standardize the limiting value of x = $1214.87 by determining the Z-score corresponding to ( greater than ) probability of 0.25.
Using standard normal tables, determine the Z-score value corresponding to:
P ( Z > z-score ) = 0.25 OR P ( Z < z-score ) = 0.75
z-score = 0.675
- Now use the standardizing formula as follows:
[tex]z-score = \frac{x - u}{sigma} \\\\1214.87 - u = 0.675*116\\\\u = 1214.87 - 78.3\\\\u = 1136.57[/tex]
Answer: The mean value is $1137
A 60-watt light bulb advertises that it will last 1500 hours. The lifetimes of these light bulbs is approximately normally distributed with a mean of 1550 hours and a standard deviation of 57 hours. What proportion of these light bulbs will last less than the advertised time
Answer:
The proportion of these light bulbs that will last less than the advertised time is 18.94% or 0.1894
Step-by-step explanation:
The first thing to do here is to calculate the z-score
Mathematically;
z-score = (x - mean)/SD
= (1500-1550)/57 = -50/57 = -0.88
So the proportion we will need to find is;
P( z < -0.88)
We shall use the standard score table for this and our answer from the table is 0.1894 which is same as 18.94%
Need Assistance
Show Work
Answer:
-52, and the opposite of this is 52.
Step-by-step explanation:
If we are losing 52 pounds, then our number is -52 since we are losing 52 pounds (adding a negative number to a positive number is the same as subtracting that number).
The opposite of a number is when we negate the number, or multiply it by -1.
A negative number times a negative number is a positive number.
[tex]-52\cdot-1 = 52\cdot1 = 52[/tex]
Hope this helped!
Answer:
Hey there!
Loss of 52 pounds, -52
Opposite, 52
Hope this helps :)
For problems 14 and 15, a drain pipe is to be laid between 2 points. One point is 15
feet higher in elevation than the other. The pipe is to slope at an angle of 12° with
the horizontal.
Find the length of the drain pipe. Round to 2 decimal
places.
Answer:
Length of the drain pipe is 72.15 feet.
Step-by-step explanation:
From the figure attached,
A drain pipe is to be laid between two pints P and Q.
Point P is 15 ft higher than the other point Q.
Angle of elevation of point P from point Q is 12°.
Let the length of pipe is l feet.
By applying Sine rule in the given right triangle PRQ,
Sin(∠Q) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
Sin(12) = [tex]\frac{\text{PR}}{\text{PQ}}[/tex]
0.20791 = [tex]\frac{15}{l}[/tex]
[tex]l=\frac{15}{0.20791}[/tex]
[tex]l=72.146[/tex]
l = 72.15 ft
Therefore, length of the drain pipe is 72.15 feet.
find the standard deviation for the binomial distribution which has the stated values of n and p n=47 p= 0.4 round you answer to the nearest hundredth
Answer:
Option (3)
Step-by-step explanation:
Standard deviation for the binomial distribution is given by,
σ = [tex]\sqrt{n\times P(1-P)}[/tex]
where n = Number of trials
P = probability of success of an individual trail
If n = 47 and P = 0.4
σ = [tex]\sqrt{47\times 0.4(1-0.4)}[/tex]
= [tex]\sqrt{47\times 0.24}[/tex]
= [tex]\sqrt{11.28}[/tex]
= 3.3586
≈ 3.36
Therefore, standard deviation for the binomial distribution will be 3.36.
Option (3) will be the answer.