9.03 divided by 899.8 is closest to a.0.01
Answer: a) 0.01
Step-by-step explanation:
Write a quadratic equation in standard form that has two solutions, 9 and -2
(the leading coefficient must be 1.)
How much would $200 invested at 5% interest compounded monthly be
worth after 9 years?
9514 1404 393
Answer:
$313.37
Step-by-step explanation:
The compound interest formula is used to find that value.
A = P(1 +r/12)^(12t)
P compounded monthly at annual rate r for t years.
A = $200(1 +0.05/12)^(12·9) ≈ $313.37
A particular variety of watermelon weighs on average 22.4 pounds with a standard deviation of 1.36 pounds. Consider the sample mean weight of 64 watermelons of this variety. Assume the individual watermelon weights are independent.
Required:
a. What is the expected value of the sample mean weight?
b. What is the standard deviation of the sample mean weight?
c. What is the approximate probability the sample mean weight will be less than 22.02?
d. What is the value c such that the approximate probability the sample mean will be less than c is 0.9?
Answer:
a) 22.4 pounds.
b) 0.17 pounds.
c) 0.0127 = 1.27% approximate probability the sample mean weight will be less than 22.02.
d) c = 22.62
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.
Average 22.4 pounds with a standard deviation of 1.36 pounds.
This means that [tex]\mu = 22.4, \sigma = 1.36[/tex]
Consider the sample mean weight of 64 watermelons of this variety.
This means that [tex]n = 64, s = \frac{1.36}{\sqrt{64}} = 0.17[/tex]
a. What is the expected value of the sample mean weight?
By the Central Limit Theorem, 22.4 pounds.
b. What is the standard deviation of the sample mean weight?
By the Central Limit Theorem, 0.17 pounds.
c. What is the approximate probability the sample mean weight will be less than 22.02?
This is the p-value of Z when X = 22.02. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{22.02 - 22.4}{0.17}[/tex]
[tex]Z = -2.235[/tex]
[tex]Z = -2.235[/tex] has a p-value of 0.0127.
0.0127 = 1.27% approximate probability the sample mean weight will be less than 22.02.
d. What is the value c such that the approximate probability the sample mean will be less than c is 0.9?
This is the 90th percentile, that is, [tex]X = c[/tex] when z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.28 = \frac{c - 22.4}{0.17}[/tex]
[tex]c - 22.4 = 1.28*0.17[/tex]
[tex]c = 22.62[/tex]
A study examined the relationship between having a baccalaureate degree and passing a cultural competency exam among a group of 987 randomly selected registered nurses at your hospital. The researchers report that more registered nurses with a baccalaureate degree passed the cultural competency exam (OR 1.54, 95% CI 0.98-1.79). Interpret this information.
Answer:
More nurses with a baccalaureate degree is estimated to pass the exam but this was not a significant difference.
Step-by-step explanation:
One book is 4cm thick, find out how many such books can be placed in a space of 53cm.
Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
Whose plant grew at a faster rate, and what was the rate?
Suzanne’s at 2 inches per week
Suzanne’s at 1.5 inches per week
Megan’s at 3 inches per week
Megan’s at 2.5 inches per week
Answer: Megan's at 3 inches per week
Answer: D (Megan's at 2.5 inches per week)
Step-by-step explanation: Its right.
How to multiply
(c+7)(3x-2)
Answer:
3cx - 2c + 21x - 14
Step-by-step explanation:
( c + 7 ) ( 3x - 2 )
= c ( 3x - 2 ) + 7 ( 3x - 2 )
= c ( 3x ) - c ( 2 ) + 7 ( 3x ) - 7 ( 2 )
= 3cx - 2c + 21x - 14
Answer:
3cx-2c+21x-14
Step-by-step explanation:
try to expand it by multiplying everything in the first brackets by every thing in the second brackets.
c(3x-2)+7(3x-2)
3cx-2c+21x-14
I hope this helps
If x = 1, y = 7, and z = 15, determine a number that when added to x, y, and z yields
consecutive terms of a geometric sequence. What are the first three terms in the
geometric sequence?
You're looking for a number w such that the numbers
{1 + w, 7 + w, 15 + w}
form a geometric sequence, which in turn means there is a constant r for which
7 + w = r (1 + w)
15 + w = r (7 + w)
Solving for r, we get
r = (7 + w) / (1 + w) = (15 + w) / (7 + w)
Solve this for w :
(7 + w)² = (15 + w) (1 + w)
49 + 14w + w ² = 15 + 16w + w ²
2w = 34
w = 17
Then the three terms in the sequence are
{18, 24, 32}
and indeed we have 24/18 = 4/3 and 32/24 = 4/3.
Simplify the following expression by using these values:
m = −6; n = 2; p = 4
[tex]-3m^{2}[/tex]+4n-p
Hi there!
Given the expression below:-
[tex] \large{ - 3 {m}^{2} + 4n - p}[/tex]
We are also given these three values below:
m = -6n = 2p = 4Simply substitute these values in:-
[tex] \large{ - 3 {( - 6)}^{2} + 4(2) - 4}[/tex]
Any negative numbers squared would result in positive.
[tex] \large{ - 3(36) + 8 - 4} \\ \large{ - 108 + 4} \\ \large \boxed{ - 104}[/tex]
Hence, the answer is -104 when substituting values in the expression.
Let me know if you have any questions!
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{-3m}\mathsf{^2}\large\textsf{ + 4n - p}\\\large\textsf{= -3(-6)}\mathsf{^2}\large\textsf{ + 4(2) - 4}\\\\\large\textsf{(-6)}^2\\\large\textsf{= (-6)(-6)}\\\large\textsf{= \bf 36}\\\\\large\textsf{= -3(36) + 4(2) - 4}\\\\\large\text{-3(36)}\\\large\textsf{= \bf -108}\\\\\large\textsf{= -108 + 4(2) - 4}\\\\\large\textsf{4(2)}\\\large\textsf{= \bf 8}\\\\\large\textsf{= -108 + 8 - 4}\\\\\large\textsf{-108 + 8}\\\large\textsf{= \bf -100}\\\\\large\textsf{-100 - 4}\\\large\text{ = \bf -104}[/tex]
[tex]\boxed{\boxed{\huge\text{Therefore, your answer is: \boxed{\bf -104}}}}\huge\checkmark[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A circle has a radius of 10 units and is centered at (-9,9). What is the equation of this circle? \sqrt{9
square root of, 98, end square write the equation of this circle.
A circle has an equation of a form,
[tex](x-a)^2+(y-b)^2=r^2[/tex]
Where [tex](a, b)[/tex] is the center and [tex]r[/tex] is the radius.
The coordinates of your circle center are [tex](a,b)=(-9,9)[/tex] and the radius is [tex]r=\sqrt{98}[/tex], so plug that in,
[tex](x-(-9))^2+(y-9)^2=\sqrt{98}^2[/tex]
and simplify to get the equation,
[tex](x+9)^2+(y-9)^2=98[/tex]
Hope this helps :)
A powerful women's group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Construct a 90% confidence interval estimate of the difference between the proportion of men and women who believe that sexual discrimination is a problem. What is the lower limit?
Answer:
the lower limit is 35% women believed and 65% of men believed in serial discrimination
Mr. Montes is writing a short, three-question, true or false quiz for his Algebra 2 classes. He had planned on using a random answer generator to determine which of true or false would be the correct answer for each quiz question, but his internet is not working. Instead, he writes each possible answer combination on a small slip of paper, folds each paper in half, and then places them in a box. Without looking, he draws one of the slips of paper.
Use what you know about counting methods and set operations to answer the following questions.
After grading the quizzes, Mr. Montes decides that his students could use some additional practice with the concepts tested. He writes a take-home assignment for his students. The assignment starts with two true or false questions and then has 3 multiple choice questions. The multiple choice questions each have 4 answer options, only 1 of which is correct. Luckily, Mr. Montes’ internet is working when he writes the quiz and he is able to use a random answer generator.
After grading the take-home assignments, Mr. Montes randomly selects 5 take-home assignments to analyze. He considers the student’s responses to the three multiple choice questions, which are as shown.
Student 1: Student 2: Student 3: Student 4: Student 5:
{C, A, C} {C, B, B} {C, B, C} {C, B, A} {C, A, A}
Amisha was too tired to work on the take home assignment Mr. Montes gave her, so she randomly selected answers without reading any of the questions. Suppose that you wanted to find the odds that Amisha answered at least 3 of the 5 questions correctly. Do you think you would use a permutation or a combination?
1. The correct responses for the multiple choice questions are, in order, C, B, and A. If Set 1 represents the subset of these students who answered C for number 1, Set 2 represents the subset of these students who answered B for number 2, and Set 3 represents the subset of students who answered A for number 3, find each of the following. Explain what each notation means in context of this scenario.
a. Set 1 ∩ Set 2
b. Set 2 ∪ Set 3
c. The complement of Set 1
2. Amisha was too tired to work on the take home assignment Mr. Montes gave her, so she randomly selected answers without reading any of the questions. Suppose that you wanted to find the odds that Amisha answered at least 3 of the 5 questions correctly. Do you think you would use a permutation or a combination?
Answer:
There are 4 questions to answer here and the answers are given below:
1. COMBINATION
2. SET 2
3. {S2, S3, S4, S5}
4. { } OR ∅
Step-by-step explanation:
The key topics here are PERMUTATION & COMBINATION and SETS & VENN DIAGRAMS.
The assignment has 5 questions in all. The options for each question are listed below and separated by commas:
1. True, False
2. True, False
3. A, B, C, D
4. A, B, C, D
5. A, B, C, D
Mr. Montes derives his answers from a random answer generator; same way Amisha generated her answers by random selection.
QUESTION 1
If you want to find the odds that Amisha got at least 3/5 of the answers correctly, would you use a permutation or a combination?
ANSWER TO QUESTION 1
You would use a combination. Note that as much as 'permutation' is distinctly defined from 'combination', in many complex cases both are used to derive the solution. In this case though, a combination is used. For each of the 5 questions, there are a number of possible answers. Questions 1 and 2 have only two possible answers (also known as options) while questions 3, 4 and 5 have four possible answers/options to choose from. Amisha can only have one set of five answers; each to each question. So this is a combination! If you want to find the odds that Amisha got at least 3 of her 5 answers correct, you would use a combination of the various possible answers to check.
QUESTION 2
Find "Set 1 ∩ Set 2" and explain the notation in the sentence.
ANSWER TO QUESTION 2
First list out relevant information:
- The correct answers to questions 3, 4 and 5 are respectively C, B, A
- The universal set consists of five students: S1, S2, S3, S4, S5 hence
Ц = {S1, S2, S3, S4, S5}
Next, enlist the elements of each defined set
Set 1: {S1, S2, S3, S4, S5} Set 2: {S2, S3, S4} Set 3: {S4, S5}
Note: Set 1 is equal to the universal set.
Now this notation "∩" means "intersect". It requires an action - checking out which elements in one set also appear in a second set and then bringing those elements to form a new set.
In the case of this question, we're to find Set 1 intersect Set 2. The elements present in Set 1 and also present in Set 2 are {S2, S3, S4}.
If you look closely, you'll observe that these are the same elements in Set 2! This brings to remembrance, one of the laws of sets:
The intersect of any subset and the universal set (recall that Set 1 happens to be equal to or have the same elements as the universal set) is equal to that subset.
So the answer to question 2 is
Set 1 ∩ Set 2 = Set 2
QUESTION 3
Find "Set 2 ∪ Set 3" and explain the notation in the sentence.
ANSWER TO QUESTION 3
The notation ∪ represents "union". This is the act of putting together the elements in two sets, to form a new set. In this activity, if an element appears in both sets, it is only written once in the new set, not twice.
So, Set 2 union Set 3 = {S2, S3, S4, S5}
As earlier stated, Student 4 isn't appearing twice in the new set.
QUESTION 4
Find the ' of Set 1 and explain the notation in this sentence.
ANSWER TO QUESTION 4
The symbol ' means "complement of a set". Finding the complement of a set is like subtracting the elements of that set from the universal set.
Since Set 1 contains the same elements as the universal set, subtracting Set 1 from the universal set will give you nothing. In this case, the complement of Set 1 is a null set!
Set 1 ' Ц = { } or ∅
where the empty bracket symbol and the slashed zero symbol represent null set.
Kudos!
how many degrees are there in the angle made by the heart hand and the minute hand of a clock when it is 9 o'clock
both angles are 90 degrees
1. Plot the following points by hand or using an online graphing calculator. What is the function that best fits the points?
(0, 3), (1, 6), (2, 12), (3, 24)
•Linear
•Exponential
•Quadratic
at a local college, four sections of economics are taught during the day and two sections are taught at night. 85 percent of the day sections are taught by full-time faculty. 30 percent of the evening sections are taught by full-time faculty. if jane has a part-time teacher for her economics course, what is the probability that she is taking a night class
Answer:
Hence The probability that she is taking a night class given that Jane has a part-time teacher = P(jane has a part-time teacher and she is taking night class )/P(jane has a part-time teacher) = 0.6999.
Step-by-step explanation:
Probability(full-time teacher/ day ) = 0.85
Probability(part-time teacher/ day ) = 1- 0.85 = 0.15
Probability(full-time teacher/ night) = 0.30
Probability(part-time teacher/ night) = 1 - 0.30 = 0.70
total no of section = 4+2 = 6
P(jane has part time teacher) = P(jane is from day section)*Probability(part-time teacher/ day )+P(jane is from night section)*Probability(part-time teacher/ night)
= (4/6)(0.15)+(2/6)(0.70) = 0.33
P(jane has part time teacher and she is taking night class ) = P(jane is from night section)*Probability(part-time teacher/ night) = (2/6)(0.70) = 0.23
According to Bayes theorem :
The probability that she is taking a night class given that Jane has a part-time teacher = P(jane has a part-time teacher and she is taking night class )/P(jane has a part-time teacher)
= 0.23/0.33
= 0.6999
Use a half-angle identity to find the exact value of cos 15
Answer:
It's too short. Write at least 20 characters to explain it well.
You have collected data about the average response time of participants in your study. You are delighted to find that the variable is normally distributed. More than half your respondents take longer than 16 seconds to respond and one third take less than 12 seconds to respond. What is the median response time of your participants
Answer:
15
Step-by-step explanation:
It's 15 because it would be the median (middle) between 16 and 12 if there was more variability in 16 seconds.
Identify the decimals labeled with letters A B and C on the scale
Answer:
A. 37.39 B. 37.41 C. 37.27
Player Productions theatre finds that their ticket sales for Friday night performances (number of tickets sold) is given by the function h , where h ( t ) measures the number of tickets sold, and where t is the play length (measured in hours). Regal Theatre found that their ticket sales for Friday nights performances can be modeled by the function, g , where g (t)= 1.6h(t + 0.25).
Required:
How do the ticket sales for Friday night perfomances at Player Productions compare to the ticket sales for a Friday night perfomance at Regal Theatre?
Answer:
Regal Theatre makes 1.6 times more than Player Productions when they have 0.25 hours longer productions
Step-by-step explanation:
Given
[tex]h(t) \to[/tex] player production theatre
[tex]g(t) \to[/tex] regal theatre
Where:
[tex]g(t) = 1.6h(t + 0.25)[/tex]
Required
Compare both functions
We start from the bracket
[tex]t + 0.25[/tex]
The + in [tex]t + 0.25[/tex] means longer hours of production
So:
[tex]t + 0.25[/tex] means 0.25 hours longer that player productions
[tex]g(t) = 1.6h(t + 0.25)[/tex] can be rewritten as:
[tex]g(t) = 1.6 * h(t + 0.25)[/tex]
The above means 1.6 times player production when they have 0.25 longer hours.
Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. let x represent the length of each of the equal pieces of yarn that julie decides to cut. what is the equation that can be used to determine the total length of all the yarn that she ends up cutting, y? is the graph of the equation continuous or discrete?
Answer:
The answer is below
Step-by-step explanation:
Let x represent the length of each of the equal piece of yarn. Since they are 4 equal pieces of yarn, then the total length of the equal pieces of yarn = 4x.
Also, besides cutting the 4 equal pieces of yarn Julie further cuts a yarn 7.75 inches long, therefore if y represent the total length of all the yarn that she ends up cutting, hence:
y = 4x + 7.75
Since the graph produced by this equation have all points connected to each other, hence this is a continuous graph.
Find the length of the segment indicated. circles 4
I need more information, comment on my "answer".
the mean if 5 numbers is 19 what is the sum of the number?
Answer:
95
Step-by-step explanation:
Use the mean formula: mean = sum of elements / number of elements
Plug in the mean and number of elements, then solve for the sum of the numbers:
mean = sum of elements / number of elements
19 = sum of elements / 5
95 = sum of elements
So, the sum of the numbers is 95.
I need help so what’s 6 divide by 2(1+2)=
Answer:
9
Step-by-step explanation:
Divide 6 by 2:
3(1+2)
Add 1 and 2:
3 x 3
Multiply 3 by 3:
3 x 3 = 9
Answer:
1
Step-by-step explanation:
6
------
2(1+2)
6
-----
2(3)
6
-----
6
1
Please help me with this on the image
Answer:
a) Obtuse angle b) Reflex anglePLS HELP! What is the mistake made below in solving x2 – 12x + 10 = 0 using the completing the square method?
x2 – 12x + 10 = 0
x2 – 12x + (- 6)2 = - 10 + (- 6)2
x2 – 12x + 36 = 26
(x – 6)(x – 6) = 26
x – 6 = √26
x = 6 + √26
Answer:
Step-by-step explanation:
Everything is correct. But you forgot to add
x = 6 - square root of 26. The answer is
x = 6 + square root of 26 or
x = 6 - square root of 26
I need help asap with this question
In a trapezoid, the midline is the average of the two bases.
PW = (YZ + TM) / 2
29 = (23 + 11x + 2) / 2
58 = 23 + 11x + 2
58 = 25 + 11x
11x = 33
x = 3
Hope this helps!
Please help im new and i need help!
Please help me if you onlw the answers please!!
9514 1404 393
Answer:
a) 2.038 seconds
b) 5.918 meters
c) 1.076 seconds
Step-by-step explanation:
For the purpose of answering these questions, it is convenient to put the given equation into vertex form.
h = -4.9t² +9.2t +1.6
= -4.9(t² -(9.2/4.9)t) +1.6
= -4.9(t² -(9.2/4.9)t +(4.6/4.9)²) +1.6 +4.9(4.6/4.9)²
= -4.9(t -46/49)² +290/49
__
a) To find h = 0, we solve ...
0 = -4.9(t -46/49)² +290/49
290/240.1 = (t -46/49)² . . . . subtract 290/49 and divide by -4.9
√(2900/2401) +46/49 = t ≈ 2.0378 . . . . seconds
The ball takes about 2.038 seconds to fall to the ground.
__
b) The maximum height is the h value at the vertex of the function. It is the value of h when the squared term is zero:
290/49 m ≈ 5.918 m
The maximum height of the ball is about 5.918 m.
__
c) We want to find t for h ≥ 4.5.
h ≥ 4.5
-4.9(t -46/49)² +290/49 ≥ 4.5
Subtracting 290/49 and dividing by -4.9, we have ...
(t -46/49)² ≥ 695/2401
Taking the square root, and adding 46/49, we find the time interval to be ...
-√(695/2401) +46/49 ≤ t ≤ √(695/2401) +46/49
The difference between the interval end points is the time above 4.5 meters. That difference is ...
2√(695/2401) ≈ 1.076 . . . . seconds
The ball is at or above 4.5 meters for about 1.076 seconds.
__
I like a graphing calculator for its ability to answer these questions quickly and easily. The essentials for answering this question involve typing a couple of equations and highlighting a few points on the graph.
_____
Additional comment
I have a preference for "exact" answers where possible, so have used fractions, rather than their rounded decimal equivalents. The calculator I use deals with these fairly nicely. Unfortunately, the mess of numbers can tend to obscure the working.
"Vertex form" for a quadratic is ...
y = a(x -h)² +k . . . . where the vertex is (h, k) and 'a' is a vertical scale factor.
In the above, we have 'a' = -4.9, and (h, k) = (46/49, 290/49) ≈ (0.939, 5.918)
do the two trapezoids in the figure appear to be similar? why or why not?
Answer:
The answer is D cuz two if the corresponding angles are congruent.
Can somebody help me find the answer to this problem please ?
Answer:
Step-by-step explanation:
Answer:
D. x = -2y + 4
Step-by-step explanation:
4x + 8y = 16
Solve for x
Our objective here is to isolate x ( in other words we want to get x by itself ) using inverse operations.
So let's begin
4x + 8y = 16
First we want to get rid of 8y
Notice how 8y is being added to 4x
Well we can get rid of it by applying it's inverse operation. The opposite of addition is subtraction. So to get rid of 8y we would simply subtract 8y.
Important note! Whatever we do to one side we must do to the other
So we would subtract 8y from both sides
4x + 8y - 8y = 16 - 8y
The 8y on the left hand side cancels out and the 8y on the right side stays as it is as you can't subtract 8y from 16
We then have 4x = 16 - 8y
Next we want to get rid of 4 from 4x.
4x is the same as 4*x which is multiplication
The inverse of multiplication is division so to get rid of the 4 we divide both sides by 4
4x/4 = (16-8y)/4
4x/4 = x
16-8y/4 ( simply divide 16 by 4 and -8y by 4 )
16-8y/4 = 4 - 2y
We're left with x = 4 - 2y which can also be written as x = -2y + 4
If sin(x) = 1 and cos(x) = 0, what is cot(x)?
0
1
undefined
Answer:
It's 0
Edge said it's 0
The value of the ratio of the cos(x) and the sin(x) is 0.
Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the ratios of the lengths of its sides. These ratios are fundamental in trigonometry and have applications in various fields, such as physics, engineering, and navigation.
Trigonometry is a branch of mathematics that deals with the relationships and properties of angles and triangles. It explores the ratios between the sides of a triangle and the angles within that triangle. The word "trigonometry" is derived from two Greek words: "trigonal," meaning "triangle," and "metron," meaning "measure."
The value of the sin(x) is 1. The value of cos(x) is 0.
The formula for the cot(x) is written below:
cot(x) = cos(x) / sin(x)
cot(x) = 0 / 1
cot(x) = 0
To know more about trigonometry follow
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