Step-by-step explanation:
a² - 25b² can be expressed as a² - (5²)b²
this gives us: a² - (5b)²
using difference of two squares, we have:
(a - 5b)(a + 5b)
Oscar is trying to incorporate more exercise into his busy schedule. He has several short
exercise routines he can complete at home. Last week, he worked out for a total of 35
minutes by doing 2 arm routines and 1 abdominal routine. This week, he has completed 4
arm routines and 1 abdominal routine and spent a total of 55 minutes exercising. How long
does each routine last?
minutes to complete, and an abdominal routine takes
An arm routine takes
minutes to complete.
Answer:
The arm routine lasts 10 minutes, and the abs routine lasts 15 minutes.
Step-by-step explanation:
Since Oscar is trying to incorporate more exercise into his busy schedule, and he has several short exercise routines he can complete at home, and last week, he worked out for a total of 35 minutes by doing 2 arm routines and 1 abdominal routine while That this week, he has completed 4 arm routines and 1 abdominal routine and spent a total of 55 minutes exercising, to determine how long does each routine last the following calculation must be performed:
2ARM + 1ABS = 35
4ARM + 1ABS = 55
4ARM + 1ABS - 2ARM - 1ABS = 55 - 35
2ARM = 20
ARM = 20/2
ARM = 10
2 x 10 + ABS = 35
ABS = 15
Therefore, the arm routine lasts 10 minutes, and the abs routine lasts 15 minutes.
What is the range of the function represented by the graph?
Answer:
C
Step-by-step explanation:
The answer is c because the point where they meet is -6 so it has to be all real number greater than.
How is an equilateral triangle different from an isosceles triangle?
A.
An equilateral triangle cannot have two sides that are the same length.
B.
An equilateral triangle has to have three sides that are the same length.
C.
An equilateral triangle has to have a 90° angle.
D.
An equilateral triangle cannot have three sides that are the same length.
Answer: B
Step-by-step explanation: An Isosceles triangle has two equal sides. A equallateral triangle has all the sides equal
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.9 minutes and a standard deviation of 2.9 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway.
(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)
(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)
(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)
Answer:
a) 0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.
b) 0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes
c) 0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
Mean of 8.9 minutes and a standard deviation of 2.9 minutes.
This means that [tex]\mu = 8.9, \sigma = 2.9[/tex]
Sample of 37:
This means that [tex]n = 37, s = \frac{2.9}{\sqrt{37}}[/tex]
(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?
320/37 = 8.64865
Sample mean below 8.64865, which is the p-value of Z when X = 8.64865. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.64865 - 8.9}{\frac{2.9}{\sqrt{37}}}[/tex]
[tex]Z = -0.53[/tex]
[tex]Z = -0.53[/tex] has a p-value of 0.2981
0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.
(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?
275/37 = 7.4324
Sample mean above 7.4324, which is 1 subtracted by the p-value of Z when X = 7.4324. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{7.4324 - 8.9}{\frac{2.9}{\sqrt{37}}}[/tex]
[tex]Z = -3.08[/tex]
[tex]Z = -3.08[/tex] has a p-value of 0.001
1 - 0.001 = 0.999
0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.
(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?
Sample mean between 7.4324 minutes and 8.64865 minutes, which is the p-value of Z when X = 8.64865 subtracted by the p-value of Z when X = 7.4324. So
0.2981 - 0.0010 = 0.2971
0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes
What is the value of x?
x^2 + 21^2 = 29^2
x^2 + 441 = 841
x^2 = 841 - 441
x^2 = 400
x = √400
x = 20
Melissa has two coupons for shoes. Coupon A: Coupon B: 15% off of S41 shoes $10 rebate on S41 shoes Choose the coupon that gives the lower price. Then fill in the blank with the correct value.
Answer:22
Step-by-step explanation:
The complete sentence is
The price with coupon B is $10 less than the price with coupon A.
It depends on the original price of the S41 shoes.
Coupon A offers a 15% discount on S41 shoes, while Coupon B provides a $10 rebate on S41 shoes.
Let's assume the original price of the S41 shoes is P dollars.
Using Coupon A, the discounted price would be 85% of the original price = (0.85 * P) dollars.
Using Coupon B, the price after the $10 rebate = (P - $10) dollars.
Now, compare (0.85 * P) with (P - $10).
simplify the expression (0.85 * P) < (P - $10) as
0.85P < P - $10
0.85P - P < - $10
-0.15P < - $10
P > (- $10) / (-0.15)
P > $66.67
Therefore, if the original price of the S41 shoes is greater than $66.67, Coupon A (15% off) will give a lower price. If the original price is lower than $66.67, Coupon B ($10 rebate) will give a lower price.
Learn more about Inequality here:
https://brainly.com/question/20383699
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The diameters of bolts produced by a certain machine are normally distributed with a mean of 1.20 inches and a standard deviation of 0.01 inches. What proportion of bolts will have a diameter greater than 1.211 inches
Answer:
0.1357 = 13.57% of bolts will have a diameter greater than 1.211 inches
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Mean of 1.20 inches and a standard deviation of 0.01 inches.
This means that [tex]\mu = 1.20, \sigma = 0.01[/tex]
What proportion of bolts will have a diameter greater than 1.211 inches?
This is 1 subtracted by the p-value of Z when X = 1.211. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.211 - 1.20}{0.01}[/tex]
[tex]Z = 1.1[/tex]
[tex]Z = 1.1[/tex] has a p-value of 0.8643.
1 - 0.8643 = 0.1357
0.1357 = 13.57% of bolts will have a diameter greater than 1.211 inches
PLS HELP!! need the answer asap
Answer:
Step-by-step explanation:
x+2x+27=90
3x=90-27
3x=63
x=63/3
x=21
Answer:
x = 21
Step-by-step explanation:
Since ∠ PQR = 90° , then the sum of the 3 angles = 90° , that is
x + 2x + 27 = 90
3x + 27 = 90 ( subtract 27 from both sides )
3x = 63 ( divide both sides by 3 )
x = 21
Integrate Sin(3x)Cos(3x) dx
Answer:
[tex]I = \frac{1}{6}\cdot \sin^{2} 3x + C[/tex]
Where [tex]C[/tex] is the integration constant.
Step-by-step explanation:
We use integration by substitution to obtain the integral, where:
[tex]u = \sin 3x[/tex], [tex]du = 3\cdot \cos 3x\,dx[/tex]
[tex]I = \int {\sin 3x\cdot \cos 3x} \, dx[/tex]
[tex]I = \frac{1}{3} \int {u} \, du[/tex]
[tex]I = \frac{1}{6}\cdot u^{2} + C[/tex]
[tex]I = \frac{1}{6}\cdot \sin^{2} 3x + C[/tex]
Where [tex]C[/tex] is the integration constant.
A point with a positive x-coordinate and a negative y-coordinate is reflected over the y-axis.
Which sentence describes the coordinates of the new point?
The r-coordinate is positive, and the y-coordinate is negative.
The r-coordinate is negative, and the y-coordinate is negative.
The x-coordinate is positive, and the y-coordinate is positive.
The r-coordinate is negative, and the y-coordinate is positive.
Answer:
the x coordinate is negative and y coordinate is positive
Step-by-step explanation:
Assume that females have pulse rates that are normally distributed with a mean of beats per minute and a standard deviation of beats per minute.
a. If 1 adult female is randomly selected, find the probability that her pulse rate is between beats per minute and beats per minute.
b. If 4 adult females are selected, find the probability that they have pulse rates with a mean between 68 beats per minute and 76 beats per minute.
c. Why can the normal distribution be used in heartbeat even the sample side does not exceed 30?
Answer:
a) This is the p-value of Z when X = A subtracted by the p-value of Z when X = B.
b) P-value of Z when X = 76 subtracted by the p-value of X = 68.
c) Because the underlying distribution(pulse rates of females) is normal.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
In this question:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex].
standard deviation of beats per minute.
a. If 1 adult female is randomly selected, find the probability that her pulse rate is between A beats per minute and B beats per minute.
This is the p-value of Z when X = A subtracted by the p-value of Z when X = B.
b. If 4 adult females are selected, find the probability that they have pulse rates with a mean between 68 beats per minute and 76 beats per minute.
Sample of 4 means that we have [tex]n = 4, s = \frac{\sigma}{\sqrt{4}} = 0.5\sigma[/tex]
The formula for the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{X - \mu}{0.5\sigma}[/tex]
[tex]Z = 2\frac{X - \mu}{\sigma}[/tex]
This probability is the p-value of Z when X = 76 subtracted by the p-value of X = 68.
c. Why can the normal distribution be used in heartbeat even the sample side does not exceed 30?
Because the underlying distribution(pulse rates of females) is normal.
A triangular plaque has side lengths of 8 inches, 13 inches, and 15 inches.
Use Heron's Formula to find the area of the plaque.
==========================================================
Explanation:
a = 8, b = 13, and c = 15 are the sides of the triangle
s = (a+b+c)/2 = (8+13+15)/2 = 18 is the semi-perimeter, aka half the perimeter.
Those values are then plugged into Heron's Formula below
[tex]A = \sqrt{s*(s-a)*(s-b)*(s-c)}\\\\A = \sqrt{18*(18-8)*(18-13)*(18-15)}\\\\A = \sqrt{18*(10)*(5)*(3)}\\\\A = \sqrt{2700}\\\\A = \sqrt{900*3}\\\\A = \sqrt{900}*\sqrt{3}\\\\A = 30\sqrt{3}\\\\A \approx 51.9615\\\\A \approx 52\\\\[/tex]
The triangular plaque has an area of approximately 52 square inches.
Lakshmi donates 20% of her income to charity.
What fraction of her income does Lakshmi donate to charity
Answer:
1/5
Step-by-step explanation:
Answer:
as given 20%,
so 20% into fraction
20
100
=>1
5 is the answer
Which is the equation of a line that is perpendicular to the line with equation
Answer:
(D)
Step-by-step explanation:
The slope of the given line is (2/3) which means that a line perpendicular to it must have a slope of (-3/2).
Relationships in Figures
If one measurement of a golden rectangle is 5.4 inches, what is the other measurement?
a. 8.737
b. 7.018
c. 1.618
d. 3.782
Please select the best answer from the choices provided
Answer:
A. 8.737
Step-by-step explanation:
I calculated it logically
Plz help me well mark brainliest if correct
Answer:
C) 86
Step-by-step explanation:
To find the mean you first add all of the numbers together. So you would add 75+90+84+95=344. Then you would divide the sum by the amount if numbers there are. So it would be 344÷4 =86
Hope this helped :)
Answer:
x = 75, 90 , 84, 95
[tex]Mean = \frac{ \sum x}{n}= \frac{75+90+84+95}{4} = 86[/tex]
Convert 15meter to 5kilometer
Answer:
Step-by-step explanation:
1 m =0.001 km
15m=15*0.001
=0.015 km
HELP ME PLEASEEE!!!!Jordan spent 5 hours over the weekend studying for 3 tests. He spent an equal amount of time studying for each test. How long did Jordan spend studying for each test? Answers:
1 3/4 hours. 3/5 hours. 1/5 hours. or 1 2/3
Answer:
oh god I wanna feel dead oh god i wanna feel dead
Help me pls do correct it correctly
Answer:
Complementary Angles - 3rd one (at the bottom)
Supplementary Angles - 2nd one (at the top-right)
Vertical Angles - 1st one (at the top-left)
Feel free to mark it as brainliest :D
Find the volume of the trapezoidal prism following.
Answer:
60 cm³
Step-by-step explanation:
Applying,
Volume (V) = Area of the base(A)×Height(h)
V = Ah................ Equation 1
From the diagram,
A = Area of Trapezium
A = 1/2(a+b)c............. Equation 2
Substitute equation 2 into equation 1
V = [1/2(a+b)c]h........... Equation 3
Given: a = 3 cm, b = 7 cm, c = 3 cm, h = 4 cm
Substitute these values into equation 3
V = [3(3+7)/2]4
V = (3×10/2)4
V = (3×5)4
V = 15×4
V = 60 cm³
the cone has a radius of 6m and a height of 9cm what's the volume ?
Answer:
339.4cm³
Step-by-step explanation:
V
=
π
r
2
h
3
22/7×6²×9/3= 339.42
Find what is x for that angle?
Answer:
X 30
Step-by-step explanation:
I did the math and all you had to do was times all the nymbers!
A line passes through (-3,-2) and is perpendicular to 3x - 2y = 7.
What is the equation of the line in slope-intercept form?
Answer:
y=-2/3x
Step-by-step explanation:
Perpendicular gradients(slopes) are negative reciprocals so first rearrange the given equation to find the gradient. y=3/2x-7/2
the gradient of the new line will be m=-2/3 then use the point (-3,-2) to find the equation of the line
y=mx+b
-2=(-2/3)(-3)+b
-2=2+b
b=0
y=-2/3x
Mr. Chen writes the expression 4 ×
(
7
−
2
)
2
÷ 10 on the
board. evaluate the expression
Answer:
4*(7-2)2÷10
=4*5*1/5
=20/5
=4
Step-by-step explanation:
can you please help me with this question ❣
9514 1404 393
Answer:
see attached
Step-by-step explanation:
A graphing calculator is useful for this.
The region of interest is below the parabola and above the line.
2 Find the circumference and area of the pizza. Use 3.14 for pi. Round your answer to the nearest hundredth 13 in. The circumference of the pizza is
Answer:
A = 254.34 in² and circumference = 56.52 inch
Step-by-step explanation:
The attached figure shows a pizza having diameter of 18 inches
Radius of the pizza = 9 inches
The area of the pizza is given by :
[tex]A=\pi r^2\\\\=3.14\times 9^2\\\\=254.34\ in^2[/tex]
The circumference of the pizza is given by :
[tex]A=2\pi r\\\\=2\times 3.14\times 9\\\\=56.52\ inch[/tex]
Hence, this is the required solution.
A law firm hires the same number of lawyers every year. At the end of 12 years, the firm has hired 48 lawyers. How many lawyers has the firm hired in the last 5 years?
Answer:
20 lawyers
Step-by-step explanation:
48 ÷ 12 = 4
which means every year 4 lawyers are hired
5 × 4 = 20
so this means the law firm has hired 20 lawyers in the last 5 years
Need help with this question pls due today!!!!
Answer:
Step-by-step explanation:
area of circle=π*r^2
=3.14*2.5^2
=3.14*6.25
=19.625
=19.63
A man bought a house for 3600 Naira he repairs the house with 150 Naira if he sold the house for 4950 Naira . Find his percentage profit
9514 1404 393
Answer:
32%
Step-by-step explanation:
The man invested a total of ...
3600 +150 = 3750
in the house. He sold it for a profit of ...
4950 -3750 = 1200
The percentage profit on his investment is ...
(1200/3750) × 100% = 32%
Question and choices Are below
Answer:
9ft
Step-by-step explanation:
Use the pythagorean theorem.
15^2 = 12^2 + x^2
solve for x
x^2 = 81
x = 9