Solve the following equation exactly on the interval 0 ≤ θ ≤ 2π ? cos 2θ + sin θ = 0
hich numbers are to solve this problem? A bicycle shop sold 60 road bikes, 50 racing bikes, and 75 mountain bikes each month for 15 months. How many more mountain bikes than road bikes did the shop sell in the 15 months?
If the heights of 300 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many students have heights (a) greater than 72 inches, (b) less than or equal to 64 inches, (c) between 65 and 71 inches inclusive, (d) equal to 68 inches? assume the measurements to be recorded to the nearest inch.
The student can use the normal distribution and z-scores to estimate the number of students in different height ranges. The heights were estimated to be: about 28 students over 72 inches, 28 students less or equal to 64 inches, roughly 205 students between 65 and 71 inches, and it is statistically impossible to determine exactly 68 inches from the data given.
Explanation:This question is dealing with a concept in statistics known as the normal distribution. In this context, we are asked to find the proportion of students whose heights fall into various ranges, based on a known mean and standard deviation. With a mean of 68 inches and a standard deviation of 3 inches, we can calculate the z-score for each scenario:
Greater than 72 inches: Z = (72-68)/3 = 1.33. Looking at the z-table, the proportion associated with 1.33 is 0.9082, but we want greater than, so we subtract from 1, giving approximately 0.0918, or 9.18%. Multiply this percentage by the total number of students (300) to estimate the number of students taller than 72 inches. This yields an approximate total of 27.54, but since we cannot have fractional students, we would say approximately 28 students.Less than or equal to 64 inches: Z = (64-68)/3 = -1.33. The proportion for -1.33 on the z-table is 0.0918, which we interpret as 9.18%. This would amount to approximately 27 or 28 students.Between 65 and 71 inches: Calculate two z-scores: Z1 = (65-68)/3 = -1.00 and Z2 = (71-68)/3 = 1.00. Using the z-table, we find that the proportions for z-scores of -1.00 and 1.00 are approximately 0.1587 and 0.8413. So, the proportion between these two z-scores is 0.8413 - 0.1587 = 0.6826, or 68.26%. This correlates to roughly 205 students.Equal to 68 inches: It's impossible to exactly determine the number of students who are exactly 68 inches tall from the data given. The normal distribution is a continuous distribution, and the probability of any single, specific value (like exactly 68 inches) is technically zero. However, you can determine the number of students likely to be in a small range around 68 inches.Learn more about Normal Distribution here:https://brainly.com/question/34741155
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Create a factorable polynomial with a GCF of 2. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.
for halloween, lana received 7 4/8 pounds of candy. after a week her family had eaten 3 6/8 pounds, how many pounds does she have left?
Answer To Questions :
3 3/4
What percent of 450 is 60? Round to the nearest hundredth of a percent.
Find the area of the surface obtained by rotating the curve y x2 0 ≤ x ≤ 2 about the y axis
ds=√1+(dydx)2dx=√1+14(x4−2+1x4)dx
=√14(x4+2+1x4)dx=√122(x2+1x2)2dx
=12(x2+1x2)dx
Silver is a white metal and is an excellent conductor of heat and electricity. The density of silver is 10.49 g/cm3. Silver does not react with water but it does react with nitric acid. Silver tarnishes when exposed to air or light. What is a physical property of silver?
Answer:
The density of silver is 10.49 g/cm3.
Step-by-step explanation:
Physical properties are those that can be observed without any change in the identity of the element in question. In this case, the physical property that is mentioned is density. Other examples include color and hardness. On the other hand, chemical properties describe how a substance can change into a different substance. This would include characteristics such as flammability and corrosion resistance.
There are 44 colas and 22 lemon lime soda is in the cooler. Whatis the ratio of colas to lemon lime sodas?
Sonny substituted 5 for x in the proportion 16/x=48/15 and cross multiplied to get 240=240. Why is this?
A.because the cross sums of the proportion are equal
B.because the cross differences of the proportion are equal
C.because the cross products of the proportion are equal
D.because the cross quotients of the proportion are equal
the answer is c i just took the test
Answer:
i agree c
Step-by-step explanation:
because 16 times 15 = 240
and 48 times 5 =240
If I Row my canoe at 5 mph and I travel upstream at 3 mph, how fast will I be traveling downstream if I am rowing at the same rate ?
factor 2x^3+3x^3-18x-27
After combining like terms, the polynomial simplifies to 5x^3 - 18x - 27. It cannot be factored using basic techniques due to the lack of common factors and its incompatibility with simple factoring patterns.
Explanation:To factor the polynomial 2x^3 + 3x^3 - 18x - 27, we first combine like terms and then look for common factors or patterns that we can use to factor the polynomial.
Combining Like Terms
Combining the cubic terms, we get 5x^3. Therefore, the polynomial simplifies to 5x^3 - 18x - 27.
Factoring
We look for a greatest common factor (GCF) among the terms. In this case, there are no common factors other than 1.
Since there is no obvious way to factor by grouping, and the polynomial does not fit the patterns for difference of cubes or sum of cubes, we'd have to consider other methods such as Rational Root Theorem or synthetic division to find if the polynomial has rational roots and can be factored further. However, those methods are more complex and require trial and error or a systematic approach that typically isn't covered until more advanced algebra classes or college algebra.
Conclusion
Without additional methods, we conclude that the polynomial 5x^3 - 18x - 27 cannot be factored over the rationals using basic factoring techniques commonly taught in high school algebra.
To factor the expression 2x^3 + 3x^3 - 18x - 27, we can group the terms with common factors and factor out those common factors.
Explanation:To factor the expression 2x^3 + 3x^3 - 18x - 27, we can group the terms with common factors. The first two terms, 2x^3 and 3x^3, have a common factor of x^3. The last two terms, -18x and -27, have a common factor of -9. Factoring out these common factors, we get:
2x^3 + 3x^3 - 18x - 27 = x^3(2 + 3) - 9(2 + 3) = x^3(5) - 9(5) = 5x^3 - 45
So, the factored form of the expression is 5x^3 - 45.
Aurella wants to enlarge a 4-inch by 6 inch photo so that it has a width of 15 inches. Use a ratio table to determine the new length of the photo
[ 3+ ( 18 - 4 ) / 7 ] * 8
An object is traveling at a steady speed of 8 2/3 miles per hour. How long will it take the object to travel to 5 1/5 miles
Answer:
The answer is 36 minutes
Step-by-step explanation:
Distance is speed multiplied by time. ( when we have steady speed )
Distance=speed* time
We are looking for time.
Time=Distance /speed
Distance= 5 1/5 miles=5,20
Speed=8 2/3 miles=8,66
T=5.20/8.66666=0,60
1 hour is 60 minutes
T=0,60/60 minutes=36 minutes
The time that it'll take the object to travel in 5 1/5 miles is 36 minutes
Note that 1 hour = 60 minutes Since the object is traveling at a steady speed of 8 2/3 miles.
Let the time taken for the object be represented by x. The equation to solve the question will be:
5 1/5 / 8 2/3 = x / 60
Cross multiply
(8 2/3 × x) = (5 1/5 × 60)
8 2/3x = 312
x = 312/ 8.67
x = 36
Therefore, the time that it'll take the object to travel in 5 1/5 miles is 36 minutes.
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can someone please express 105/20 as a mixed number in simplist form
A cube has a volume of 125 cubic inches. What is the length of each edge? Enter your answer in the box.
Answer: 5 cm
Step-by-step explanation:
Given : The volume of a cube = 125 cubic inches.
The formula for the volume of a cube is :
[tex]V=s^3[/tex], where s is the side-length .
Substitute V= 125 in the above formula ,
[tex]125=s^3[/tex]
Taking cube root on both the sides , we get
[tex]\sqrt[3]{125}=s\\\\\Rightarrow\ s= \sqrt[3]{5^3}=5[/tex]
Hence, the side length of cube= [tex]5\ cm[/tex]
Each edge will be 5 inches.
Volume of the cube = 125 cubic inches
It should be noted that a cube's volume is gotten by multiplying the side thrice. In this case, let's say the value of each side is a. Therefore, based on the information given above:
a × a × a = 125
a³ = 125
a = 3✓125
a = 5
Therefore each edge is 5 inches.
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Which of the following numbers is a factor of 49 ?
Zach read a book for 10 minutes every weekend in the first month, 20 minutes in the second month, 40 minutes in the third month, and 80 minutes in the fourth month. Victoria read a book for 35 minutes every weekend in the first month, 50 minutes in the second month, 65 minutes in the third month, and 80 minutes in the fourth month. Which statement best describes the methods used by Zach and Victoria to increase the time they spent reading a book? Zach's method is linear because the number of minutes increased by an equal factor every month. Victoria's method is linear because the number of minutes increased by an equal number every month. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal factor every month. Both Victoria's and Zach's methods are exponential because the number of minutes increased by an equal number every month.
(NEVER MIND GUYS IM GOING WITH A)
What is the slope of the line tangent to the curve 3y^2-2x^2=6-2xy at the point (3 2)?
Only the Fahrenheit one plz
I NEED ANSWER RIGHT NOW!!!!!!!!! (30 POINTS + BRAINIEST ANSWER REWARD!!!!)
The graph below shows the velocity f(t) of a runner during a certain time interval:
graph of line segment going through ordered pairs 0, 4 and 4, 8. Graph of another line segment going through ordered pairs 4, 8 and 8, 0. Label on the x axis is time in seconds and label on the y axis is velocity in meters per second
Which of the following describes the intercepts on the graph?
A. The initial velocity of the runner was 4 m/s, and the runner stopped after 8 seconds.
B. The initial velocity of the runner was 8 m/s, and the runner stopped after 4 seconds.
C. The initial acceleration of the runner was 4 m/s2, and the runner stopped after 8 seconds.
D. The initial acceleration of the runner was 8 m/s2, and the runner stopped after 4 seconds.
What is the value of mc011-1.jpg?
–4
–2
2
4
the pic is the .jpg
The question is unclear as it references links rather than providing a specific mathematical problem to solve. A correct answer cannot be given.
Explanation:It appears there has been a misunderstanding. The actual mathematical question has not been provided in the text. Instead, there are references to image sources, licenses, and websites that do not contain a clear mathematical question to answer. Therefore, I'm unable to provide a value or solve the equation.
The value of the expression -2(7-15)/4 simplifies to 4 after following the order of operations: first subtracting inside the brackets, then multiplying by -2, and finally dividing by 4.
Explanation:The value of the given expression -2(7-15)/4 when simplified is computed in the following steps:
Calculate the value inside the brackets: 7 - 15 = -8.Multiply this result by -2: -2 * (-8) = 16.Divide the product by 4: 16 / 4 = 4.Therefore, the value of the entire expression is 4, which corresponds to answer option d)4.
A city's population is represented by the function P=25,000(1.0095)t , where t is time in years.
How could the function be rewritten to identify the daily growth rate of the population?
What is the approximate daily growth rate?
The daily population growth function is P=25,000((1.0095)1/365.25)t, and the daily growth rate is approximately 1.000026 or an increase of about 0.0026% per day.
Explanation:The city population growth function given, P=25,000(1.0095)t, is an exponential function. To identify the daily growth rate, we need to rewrite this function in terms of days. As there are approximately 365.25 days in a year, we substitute this into the formula for t. Hence, the daily population growth function becomes P=25,000(1.0095)t/365.25.
To find the approximate daily growth rate, we solve for the base of the exponent. Using the fact that (ab)c = abc, we can rewrite the function as P=25,000((1.0095)1/365.25)t.
Thus, the daily growth rate of the population is approximately the value of (1.0095)1/365.25, which calculates to about 1.000026, or an increase of about 0.0026% per day.
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how do the 8 differ in 38108
There are k types of coupons. independently of the types of previously collected coupons, each new coupon collected is of type i with probability pi, ki =1 pi = 1. if n coupons are collected, find the expected number of distinct types that appear in this set. (that is, find the expected number of types of coupons that appear at least once in the set of n coupons.)
Let X be the expected number of distinct types of coupons in the collection of k coupons X = X1 + X2 + ……. + Xx.
what 3050 divided by 100
Peter is a painter, and he wonders if he would have time to catch a paint bucket dropped from his ladder before it hits the ground. He drops a bucket from the top of his 9-foot ladder. The height, h, of the bucket can be represented by the equation, h= -16t^2 + 9, where the height is measured in feet from the ground, and the time since the bucket was dropped, t, is measured in seconds. After how many seconds does the bucket hit the ground? Do you think he could catch the bucket before it hits the ground.
The paint bucket dropped from the 9-foot ladder would hit the ground in approximately 0.75 seconds, according to the equation given for free fall. Given this quick time frame, it might be difficult for Peter to catch the bucket before it hits the ground.
Explanation:The situation described involves a physical phenomenon known as free fall, under the influence of gravity. In the case of the paint bucket, when it is dropped from the top of the ladder, the height h of the bucket from the ground at any time t is given by the equation h = -16t^2 + 9. The bucket hits the ground when h = 0.
To find when the bucket hits the ground, we solve the equation -16t^2 + 9 = 0 for t. Using the quadratic formula, we find the roots to be t = -0.75s and t = 0.75s. Since time cannot be negative in this situation, we discard the negative root. Thus, the bucket hits the ground after 0.75 seconds.
As to whether Peter could catch the bucket before it hits the ground, it does depend on his reflexes and agility, but generally it may be difficult to react and move quickly enough within such a brief time frame.
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write the following decimal as a fraction or mixed number in lowest terms 0.85
One integer is 5 more than another. Their product is 234. Find the integers?
Final answer:
The integers in question are 13 and 18, which fulfill both conditions of one integer being 5 more than the other and their product being 234.
Explanation:
We are looking for two integers where one is 5 more than the other and their product equals 234. Let's designate the smaller integer as x. Then the larger integer can be represented as x + 5. The equation describing their product is:
x * (x + 5) = 234
Expanding this, we get:
x2 + 5x - 234 = 0
Solving this quadratic equation, we can find the values of x that satisfy the equation. The factors of 234 that have a difference of 5 are 13 and 18. So, the two integers we are looking for are 13 and 18.