Answers
Answer:
-5, -3, -1 , 1 , 3
Step-by-step explanation:
Related Questions
slope of (-2, -5) and (1, -3)
Answers
Start by making a table for the ordered pairs with the x-values
in the left column and the y-values in the right column.
--x--|--y--
-2 | -5
1 | -3
|
|
Now remember that the slope is equal to the rate of change
or the change in y over the change in x.
We can see that the y-values go from -5 to -3 so the change in y is 2.
The x-values go from -2 to 1 so the change in x is 3.
So the change in y over the change in x is 2/3.
This means that the slope is also equal to 2/3.
Which comparison is correct?
0.298 < 0.289
0.420 > 0.42
1.32 < 1.319
d) 3.544 > 3.455
Answers
Step-by-step explanation:
Option D is the correct answer because 3.544 is greater than 3.455
Option D is true in given comparison.
Here,
We have to find the correct comparison.
What is Decimal expansion?
The decimal expansion terminates or ends after finite numbers of steps. Such types of decimal expansion are called terminating decimals.
Now,
In option D;
The one tenth of 3.544 is 5 and place value of one tenth number in 3.455 is 4.
Clearly, 5 > 4
So, 3.544 > 3.455
Hence, option D; 3.544 > 3.455 is true.
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Make sure you answer this 100% correctly
Answers
Answer:
A
Step-by-step explanation:
f(x) = x² + 3x + 5
Substitute x value with (a+ h)
f(a+h) = (a+h)² + 3(a+h) + 5
= a² +2ah +h² + 3a + 3h + 5
Can somebody help me with this question
Answers
Or x(x+8)
Both answer are correct just choose one
Explain
Area =1/2 base x height
Base : 2x
Height: x+8
Area : 1/2 base x height 1/2 x(2x) x (x+8)
1/2 x (2x) x (x+8)
Cancel 2
( x) x (x+8)
Open the bracket
X^2 +8x
Have a great day
Stay safe
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of 50 business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of 50 business travelers follow. Click on the datafile logo to reference the data. 6 4 6 8 7 7 6 3 3 8 10 4 8 7 8 7 5 9 5 8 4 3 8 5 5 4 4 4 8 4 5 6 2 5 9 9 8 4 8 9 9 5 9 7 8 3 10 8 9 6Develop a 95% confidence interval estimate of the population mean rating for Miami.
Answers
Answer:
The 95% confidence interval for the population mean rating is (5.73, 6.95).
Step-by-step explanation:
We start by calculating the mean and standard deviation of the sample:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\[/tex]
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=6.34.
The sample size is N=50.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=50-1=49[/tex]
The t-value for a 95% confidence interval and 49 degrees of freedom is t=2.01.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.01 \cdot 0.305=0.61[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 6.34-0.61=5.73\\\\UL=M+t \cdot s_M = 6.34+0.61=6.95[/tex]
The 95% confidence interval for the mean is (5.73, 6.95).
A triangle has sides of lengths 9, 7, and 12. Is it a right triangle? Explain.
Answers
Answer:
Yes based on the numbers .
Step-by-step explanation:
Answer:Yes
Step-by-step explanation:Based on the number given, it shows that there is a hypotenuse (The longest side of a right triangle, in this case being 12), And opposite (Another part of the right triangle, that could be either 9 or 7), and the adjacent (The line next to the opposite, which could be 9 or 7)
If someone weighs 130 kilos what is the conversion in lbs
Answers
Answer:
286.60
Please tell me if I'm wrong.
A positive integer is twice another. The sum of the reciprocals of the two positive integers is 3/14. Find the two integers.
Answers
Answer:
The integers are 7 and 14.
Step-by-step explanation:
y = 2x
1/y + 1/x = 3/14
1/(2x) + 1/x 3/14
1/(2x) + 2/(2x) = 3/14
3/(2x) = 3/14
1/2x = 1/14
2x = 14
x = 7
y = 2x = 2(7) = 14
Answer: The integers are 7 and 14.
The required two integers are 7 and 14
This is a question on word problems leading to the simultaneous equation:
Let the two unknown integers be x and y. If a positive integer is twice another, then x = 2y .......... 1
Also, if the sum of the reciprocals of the two positive integers is 3/14, then:
[tex]\frac{1}{x}+ \frac{1}{y} =\frac{3}{14}[/tex] ..........2
Substitute equation 1 into 2
[tex]\frac{1}{2y} +\frac{1}{y} =\frac{3}{14} \\[/tex]
Find the LCM of 2y and y
[tex]\frac{1+2}{2y} =\frac{3}{14} \\\frac{3}{2y} =\frac{3}{14} \\\\cross \ multiply\\2y \times 3=3 \times 14\\6y=42\\y=\frac{42}{6}\\y=7[/tex]
Substitute y = 7 into equation 1:
Recall that x = 2y
[tex]x = 2(7)\\x = 14[/tex]
Hence the required two integers are 7 and 14.
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Hippocrates magazine states that 32 percent of all Americans take multiple vitamins regularly. Suppose a researcher surveyed 750 people to test this claim and found that 261 did regularly take a multiple vitamin. Is this sufficient evidence to conclude that the actual percentage is different from 32% at the 5% significance level?
Select the [p-value, Decision to Reject (RHo) or Failure to Reject (FRHo)1.
a) [p-value = 0.069, FRHI
b) [p-value = 0.009, RH01
c) [p-value = 0.009, FRHol
d) [p-value = 0.019, FRH)]
e) [p-value = 0.019, RHo]
Answers
Answer:
Step-by-step explanation:
We would set up the hypothesis test.
For the null hypothesis,
p = 0.32
For the alternative hypothesis,
p ≠ 0.32
This is a two tailed test
Considering the population proportion, probability of success, p = 0.32
q = probability of failure = 1 - p
q = 1 - 0.32 = 0.68
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 261
n = number of samples = 750
P = 261/750 = 0.35
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.35 - 0.32)/√(0.32 × 0.68)/750 = 1.8
Recall, population proportion, p = 0.32
The difference between sample proportion and population proportion(P - p) is 0.35 - 0.32 = 0.03
Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.32 - 0.03 = 0.29
the p for the right tail is 0.32 + 0.03 = 0.35
These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area
From the normal distribution table, the area above the z score in the right tail 1 - 0.9641 = 0.0359
We would double this area to include the area in the right tail of z = 0.44 Thus
p = 0.0359 × 2 = 0.07
Since alpha, 0.05 < the p value, 0.07 then we would fail to reject the null hypothesis. Therefore, this is not sufficient evidence to conclude that the actual percentage is different from 32% at the 5% significance level.
A car travelling from Ibadan to Lagos at 90 km/hr
takes 1 hour 20 min. How fast must one travel to
cover the distance in one hour?
Answers
Answer:
A velocity of 120km/h is needed to cover the distance in one hour
Step-by-step explanation:
The velocity formula is:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance and t is the time.
A car travelling from Ibadan to Lagos at 90 km/hr takes 1 hour 20 min.
This means that [tex]v = 90, t = 1 + \frac{20}{60} = 1.3333[/tex]
We use this to find d.
[tex]v = \frac{d}{t}[/tex]
[tex]90 = \frac{d}{1.3333}[/tex]
[tex]d = 90*1.3333[/tex]
[tex]d = 120[/tex]
The distance is 120 km.
How fast must one travel to cover the distance in one hour?
Velocity for a distance of 120 km(d = 120) in 1 hour(t = 1). So
[tex]v = \frac{d}{t}[/tex]
[tex]v = \frac{120}{1}[/tex]
[tex]v = 120[/tex]
A velocity of 120km/h is needed to cover the distance in one hour
Plz. Can anyone explain and tell the answer of this question.I promise I will mark it as brainliest Question.
Answers
Answer:
x = 15
y = 90
Step-by-step explanation:
Step 1: Find x
We use Definition of Supplementary Angles
9x + 3x = 180
12x = 180
x = 15
Step 2: Find y
All angles in a triangle add up to 180°
3(15) + 3(15) + y = 180
45 + 45 + y = 180
90 + y = 180
y = 90°
Which best describes the circumference of a circle?
Answers
Answer: A
Step-by-step explanation: A diameter is 2 times a circumference, and so a diameter is a line crossing through the center of a circle, since we know that, a circumference is just half of that, just half the center in the middle of a circle to the edge of a point on a circle.
When exchanging US Dollars (USD) for Philippine Peso (PHP) the number of Philippine Pesos received is directly proportional to the number of US Dollars to be exchanged. If 550 USD can be converted into 24,334.75 PHP.
Find the constant of proportionality k.
k= ______ (If needed, round answer to 3 decimal places.)
Using the k from above find the amount of PHP given that you have 900 USD to convert. You will receive ________ PHP (If needed, round answer to 2 decimal places.)
Answers
Answer:
(a)k=44.245
(b)39820.50 PHP
Step-by-step explanation:
Part A
Let the number of PHP =y
Let the number of USD =x
The number of Philippine Pesos(y) received is directly proportional to the number of US Dollars(x) to be exchanged.
The equation of proportion is: y=kx
If 550 USD can be converted into 24,334.75 PHP.
x=550y=24,334.75Substitution into y=kx gives:
[tex]24,334.75=550k\\$Divide both sides by 550$\\k=24,334.75 \div 550\\k=44.245[/tex]
The constant of proportionality k=44.245
Part B
The equation connecting y and x then becomes:
y=44.245x
If x=900 USD
Then:
y=44.245 X 900
y= 39820.50
Therefore, given that you have 900 USD to convert. You will receive 39820.50 PHP
John had $800 Tasha has $500 Kyle had $300 Who had the most money.
Answers
Answer:
Step-by-step explanation:Josh
By comparing the given numbers, Jhon had most money.
How to compare integers?As you move to the right on the number line, integers get larger in value. As you move to the left on the number line, integers get smaller in value.
The rules of the ordering and the comparing of the integers are given below:
If we compare numbers with different signs, then the negative number is less than positive.If numbers are both positive, then this is the case when we compare whole numbers.If numbers are both negative, then we compare numbers without signs. The bigger is the positive number; the smaller is its corresponding negative number.Given that, John had $800 Tasha has $500 Kyle had $300.
Here, 300<500<800
Therefore, by comparing the given numbers, Jhon had most money.
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The nth term of a geometric sequence is given by an = 27(0.1)n - 1. Write the first five terms of this sequence.
Answers
Answer:
The first first five terms of this sequence are
27 ,2.7 ,0.27 ,0.027 , 0.0027Step-by-step explanation:
[tex]a(n) = 27(0.1)^{n - 1} [/tex]
where n is the number of term
For the first term
n = 1
[tex]a(1) = 27(0.1)^{1 - 1} = 27(0.1) ^{0} [/tex]
= 27(1)
= 27Second term
n = 2
[tex]a(2) = 27(0.1)^{2 - 1} = 27(0.1)^{1} [/tex]
= 27(0.1)
= 2.7Third term
n = 3
[tex]a(3) = 27(0.1)^{3 - 1} = 27(0.1)^{2} [/tex]
= 0.27Fourth term
n = 4
[tex]a(4) = 27(0.1)^{4 - 1} = 27(0.1)^{3} [/tex]
= 0.027Fifth term
n = 5
[tex]a(5) = 27(0.1)^{5 - 1} = 27(0.1)^{4} [/tex]
= 0.0027Hope this helps you
What is the value of x?
Enter your answer in the box.
Answers
Answer:
x=11
Step-by-step explanation:
Since the lines in the middle are parallel, we know that both sides are proportional to each other.
6:48 can be simplified to 1:8
Since we know the left side ratio is 1:8, we need to match the right side with the same ratio
We can multiply the ratio by 5 to match 5:3x+7
5:40
5:3x+7
Now we can set up the equation: 40=3x+7
Subtract 7 from both sides
3x=33
x=11
Find f o g and g o f to determine if f and g are inverse functions. If they are not inverses, pick the function that would be the inverse with f(x). f(x) = (-2/x) – 1; g(x) = -2/(x+1) Choices: a. g(x) has to be: (1+x)/2 b. g(x) has to be: x/2 c. g(x) has to be: 2 – (1/x) d. Inverses
Answers
Answer:
(f o g) = x, then, g(x) is the inverse of f(x).
Step-by-step explanation:
You have the following functions:
[tex]f(x)=-\frac{2}{x}-1\\\\g(x)=-\frac{2}{x+1}[/tex]
In order to know if f and g are inverse functions you calculate (f o g) and (g o f):
[tex]f\ o\ g=f(g(x))=-\frac{2}{-\frac{2}{x+1}}-1=x+1-1=x[/tex]
[tex]g\ o\ f=g(f(x))=-\frac{2}{-\frac{2}{x}+1}=-\frac{2}{\frac{-2+x}{x}}=\frac{2x}{2-x}[/tex]
(f o g) = x, then, g(x) is the inverse of f(x).
which statement is the contrapositive of p ? p: if two angles are complementary, then the sum of their measures is 90
Answers
Answer: If the sum of the measures of two angles is not 90°, then they are not complementary angles.
Step-by-step explanation:
Contrapositive of p → q is ~q → ~p where p is the hypothesis and q is the conclusion.
Hypothesis (p) = Two angles are complementary
~p = Two angles are not complementary
Conclusion (q) = The sum of their measures is 90°
~q = The sum of their measures is not 90°
~ p → ~q = If the sum of the measures of two angles is not 90°,
then they are not complementary angles.
If the contrapositive of p is if two angles are NOT complementary, then the sum of their measures is NOT 90deegrees
Contrapositive statementsThese are statements that negates the given statement:
Given the statement; If two angles are complementary, then the sum of their measures is 90
Form the hypothesisHypothesis (p) = Two angles are complementary
~p = Two angles are not complementary
Conclusion (q) = The sum of their measures is 90°
~q = The sum of their measures is not 90°
Hence the statement that is the contrapositive of p is if two angles are NOT complementary, then the sum of their measures is NOT 90deegrees
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The angles in a triangle are such that one angle is 30 degrees more than the smallest angle while the third angle is four times as large as the smallest angle find the measure are of all three angles
Answers
Answer:
25, 55, 100
Step-by-step explanation:
Let's call the smallest angle x, therefore the other two angles would be x + 30 and 4x. Since the sum of angles in a triangle is 180° we can write:
x + x + 30 + 4x = 180
6x + 30 = 180
6x = 150
x = 25°
x + 30 = 25 + 30 = 55°
4x = 25 * 4 = 100°
The sum of angles is 180.
[tex] \alpha + \beta + \gamma = 180 [/tex]
[tex] \alpha + ( \alpha + 30) + (4 \alpha ) = 180[/tex]
[tex]6 \alpha = 150[/tex]
[tex] \alpha = 25 \\ \beta= 25+30=55 \\ \gamma= 4.25 =100[/tex]
Still timed. More math needing help with, i'll double points and mark brainliest! 1. (y - 6) (y + 3) 2. (4x - 5) (x - 7) 3.(3x - 2) ( 4x - 1)
Answers
Answer:
1. y² - 3x - 18
2. 4x² - 33x + 35
3. 12x² - 11x + 2
Step-by-step explanation:
All we do with these questions are expanding the factored binomials. Use FOIL:
1. y² + 3y - 6y - 18
y² - 3y - 18
2. 4x² - 28x - 5x + 35
4x² - 33x + 35
3. 12x² - 3x - 8x + 2
12x² - 11x + 2
Answer:
1) (y-6) (y+3)
=> [tex]y^2+3y-6y-18[/tex]
=> [tex]y^2-3y-18[/tex]
2) (4x-5) (x-7)
=> [tex]4x^2-28x-5x+35[/tex]
=> [tex]4x^2-33x+35[/tex]
3) (3x - 2) ( 4x - 1)
=> [tex]12x^2-3x-8x+3[/tex]
=> [tex]12x^2-11x+3[/tex]
I NEED HELP PLEASE, THANKS!
Answers
Answer:
the 3rd option is the answer
Step-by-step explanation:
I hope the attached file is self-explanatory
Amanda is constructing equilateral triangle JKL inscribed in circle M. To construct the inscribed polygon, she is going to use a compass to partition the circle into congruent arcs. To what width should she set the compass when partitioning the circle? A. The width must be equal to the radius of circle M. B. The width must be equal the diameter of circle M. C. The width can be equal to either the radius or the diameter of circle M. D. The width can be any size greater than the radius but less than the diameter of circle M. E. The width must be less than the radius of circle M. help meee please!!!!!!!!!!!!!!!!!
Answers
Given:
An equilateral triangle JKL inscribed in circle M.
Solution:
To draw an equilateral triangle inscribed in circle follow the steps:
1: Draw a circle with any radius.
2. Take any point A, anywhere on the circumference of the circle.
3. Place the compass on point A, and swing a small arc crossing the circumference of the circle.
Remember the span of the compass should be the same as the radius of the circle.
4. Place the compass at the intersection of the previous arc and the circumference and draw another arc but don't change the span of the compass.
5. Repeat this process until you return to point A.
6. Join the intersecting points on the circle to form the equilateral triangle.
So the correct option is A. The width must be equal to the radius of circle M.
What is 2x-y=6 converted to slope intercept form
Answers
Answer:
y = 2x - 6
Explanation:
* note
the equation provided is written in standard form.
· standard form → Ax + By = C
· slope-intercept form → y = mx + b
To convert the given equation to slope-intercept form, start by subtracting '2x' from both sides of the equation. This will move 'y' to the left side of the equation.
2x - y = 6
2x - 2x - y = 6 - 2x
-y = -2x + 6
Next, multiply both sides of the equation by negative one.
-y = -2x + 6
(-y × -1) = (-2x × -1) + (6 × -1)
y = 2x - 6
Therefore, the given equation should be y = 2x - 6 when converted to slope-intercept form.
The equation is in slope-intercept form, y = 2x - 6, where the slope (m) is 2 and the y-intercept (b) is -6.
Given is an equation of a line we need to convert it into slope-intercept form,
To convert the equation 2x - y = 6 to slope-intercept form (y = mx + b), where "m" represents the slope and "b" represents the y-intercept, we need to isolate the "y" variable on one side of the equation.
Starting with the given equation:
2x - y = 6
Move the 2x term to the right side by adding "y" to both sides:
2x = y + 6
Rearrange the equation by swapping the sides:
y + 6 = 2x
Move the constant term (6) to the right side by subtracting 6 from both sides:
y = 2x - 6
Hence the equation is in slope-intercept form, y = 2x - 6, where the slope (m) is 2 and the y-intercept (b) is -6.
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The amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and standard deviation 13 mL. Suppose that 43 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.
What is the distribution of XX? XX ~ N(_______,_________)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(______,_________)
If a single randomly selected individual is observed, find the probability that this person consumes is between 61.4 mL and 62.8 mL. ________
For the group of 43 pancake eaters, find the probability that the average amount of syrup is between 61.4 mL and 62.8 mL. _________
For part d), is the assumption that the distribution is normal necessary? No Yes
please only answer if you are able to answer all parts correctly
Answers
Answer:
(a) X ~ N([tex]\mu=63, \sigma^{2} = 13^{2}[/tex]).
[tex]\bar X[/tex] ~ N([tex]\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}[/tex]).
(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is 0.0398.
(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is 0.2512.
(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.
Step-by-step explanation:
We are given that the amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and a standard deviation of 13 mL.
Suppose that 43 randomly selected people are observed pouring syrup on their pancakes.
(a) Let X = amount of syrup that people put on their pancakes
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean amount of syrup = 63 mL
[tex]\sigma[/tex] = standard deviation = 13 mL
So, the distribution of X ~ N([tex]\mu=63, \sigma^{2} = 13^{2}[/tex]).
Let [tex]\bar X[/tex] = sample mean amount of syrup that people put on their pancakes
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean amount of syrup = 63 mL
[tex]\sigma[/tex] = standard deviation = 13 mL
n = sample of people = 43
So, the distribution of [tex]\bar X[/tex] ~ N([tex]\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}[/tex]).
(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < X < 62.8 mL)
P(61.4 mL < X < 62.8 mL) = P(X < 62.8 mL) - P(X [tex]\leq[/tex] 61.4 mL)
P(X < 62.8 mL) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{62.8-63}{13}[/tex] ) = P(Z < -0.02) = 1 - P(Z [tex]\leq[/tex] 0.02)
= 1 - 0.50798 = 0.49202
P(X [tex]\leq[/tex] 61.4 mL) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{61.4-63}{13}[/tex] ) = P(Z [tex]\leq[/tex] -0.12) = 1 - P(Z < 0.12)
= 1 - 0.54776 = 0.45224
Therefore, P(61.4 mL < X < 62.8 mL) = 0.49202 - 0.45224 = 0.0398.
(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < [tex]\bar X[/tex] < 62.8 mL)
P(61.4 mL < [tex]\bar X[/tex] < 62.8 mL) = P([tex]\bar X[/tex] < 62.8 mL) - P([tex]\bar X[/tex] [tex]\leq[/tex] 61.4 mL)
P([tex]\bar X[/tex] < 62.8 mL) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{62.8-63}{\frac{13}{\sqrt{43} } }[/tex] ) = P(Z < -0.10) = 1 - P(Z [tex]\leq[/tex] 0.10)
= 1 - 0.53983 = 0.46017
P([tex]\bar X[/tex] [tex]\leq[/tex] 61.4 mL) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{61.4-63}{\frac{13}{\sqrt{43} } }[/tex] ) = P(Z [tex]\leq[/tex] -0.81) = 1 - P(Z < 0.81)
= 1 - 0.79103 = 0.20897
Therefore, P(61.4 mL < X < 62.8 mL) = 0.46017 - 0.20897 = 0.2512.
(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.
You want to be able to withdraw $4000 a month for 30 years how much would you need to have in your account with an APR of 3.4% to accomplish this goal
Answers
Answer:
$904,510.28
Step-by-step explanation:
If we assume the withdrawals are at the beginning of the month, we can use the annuity-due formula.
P = A(1 +r/n)(1 -(1 +r/n)^(-nt))/(r/n)
where r is the APR, n is the number of times interest is compounded per year (12), A is the amount withdrawn, and t is the number of years.
Filling in your values, we have ...
P = $4000(1 +.034/12)(1 -(1 +.034/12)^(-12·30))/(.034/12)
P = $904,510.28
You need to have $904,510.28 in your account when you begin withdrawals.
Answer:
You need to have $904,510.28 in your account when you begin
HELP!!!! 25 POINTS AND BRAINLIEST ANSWER!!!!
Look at photo above!
Answers
Answer:
8.96 seconds
Step-by-step explanation:
In a random sample of 2,305 college students, 339 reported getting 8 or more hours of sleep per night. Create a 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night. Use a TI-83, TI-83 plus, or TI-84 calculator, rounding your answers to three decimal places.
Answers
Answer:
The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 2305, \pi = \frac{339}{2305} = 0.147[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 - 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.133[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 + 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.161[/tex]
The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).
what is the volume of a cone with a radius of 3 and a height of 17
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
V ≈ 160.22
▹ Step-by-Step Explanation
V = πr²[tex]\frac{h}{3}[/tex]
V = π3²[tex]\frac{17}{3}[/tex]
V ≈ 160.22
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State the coordinates of the vertex for each of the following
Answers
Answer:
[a] y=x^2+3, vertex, V(0,3)
[b] y=2x^2, vertex, V(0,0)
[c] y=-x^2 + 4, vertex, V(0,4)
[d] y= (1/2)x^2 - 5, vertex, V(0,-5)
Step-by-step explanation:
The vertex, V, of a quadratic can be found as follows:
1. find the x-coordinate, x0, by completing the square
2. find the y-coordinate, y0, by substituting the x-value of the vertex.
[a] y=x^2+3, vertex, V(0,3)
y=(x-0)^2 + 3
x0=0, y0=0^2+3=3
vertex, V(0,3)
[b] y=2x^2, vertex, V(0,0)
y=2(x-0)^2+0
x0 = 0, y0=0^2 + 0 = 0
vertex, V(0,0)
[c] y=-x^2 + 4, vertex, V(0,4)
y=-(x^2-0)^2 + 4
x0 = 0, y0 = 0^2 + 4 = 4
vertex, V(0,4)
y = (1/2)(x-0)^2 -5
x0 = 0, y0=(1/2)0^2 -5 = -5
vertex, V(0,-5)
Conclusion:
When the linear term (term in x) is absent, the vertex is at (0,k)
where k is the constant term.
Consider a comparison of two models. The "complete" model has both curvature and interaction. The "reduced" model has curvature, but no interaction. You compare the two models using a nested (subset) F-test and determine that you should "reject H0 ". True or False: The reduced model fits the data better than the complete model. Group of answer choicesTrueFalse
Answers
Answer:
True
Step-by-step explanation:
The reduced model and complete are the two models that can be used to determine test the hypothesis. The best way to determine which model fits the data set is to determine the F-test. The Full model is unrestricted model whereas reduced model is restricted model. F-test determines which model to choose for hypothesis testing for better and accurate results.