Answer:
a) P(X>4)=e-4*4.5 =1.523*10-8 ~ 0.0000
b) 1/4.5 =0..2222 Hours
c) P(X>6|X>4) =P(X>2)=e-2*4.5 =0.000123
Step-by-step explanation:
g Suppose you wish to perform a hypothesis test for a population mean. Suppose that the population standard deviation is known, the population distribution is Normal, and the sample is small. Would you perform a z-test or t-test?
Answer:
z-test.
Step-by-step explanation:
We want to perform an hypothesis test for a population mean.
In the case that the standard deviation of the population is known and the population distribution is normal, even if the sample is small, we will use a z-test.
The usual case is to not know the standard deviation of the population, in which case a t-test is adequate instead of a z-test, taking into account the degrees of freedom of the sample.
The mean MCAT score 29.5. Suppose that the Kaplan tutoring company obtains a sample of 40 students with a mean MCAT score of 32.2 with a standard deviation of 4.2. Test the claim that the students that took the Kaplan tutoring have a mean score greater than 29.5 at a 0.05 level of significance.
Answer:
We conclude that the students that took the Kaplan tutoring have a mean score greater than 29.5.
Step-by-step explanation:
We are given that the Kaplan tutoring company obtains a sample of 40 students with a mean MCAT score of 32.2 with a standard deviation of 4.2.
Let [tex]\mu[/tex] = population mean score
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 29.5 {means that the students that took the Kaplan tutoring have a mean score less than or equal to 29.5}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 29.5 {means that the students that took the Kaplan tutoring have a mean score greater than 29.5}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean MCAT score = 32.2
s = sample standard deviation = 4.2
n = sample of students = 40
So, the test statistics = [tex]\frac{32.2-29.5}{\frac{4.2}{\sqrt{40} } }[/tex] ~ [tex]t_3_9[/tex]
= 4.066
The value of t-test statistics is 4.066.
Now, at 0.05 level of significance, the t table gives a critical value of 1.685 at 39 degrees of freedom for the right-tailed test.
Since the value of our test statistics is more than the critical value of t as 4.066 > 1.685, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the students that took the Kaplan tutoring have a mean score greater than 29.5.
I just wish to double check!!
What is the simplified value of the expression below? -8 x (- 3)
A –24
B –11
C 11
D 24
Answer:
24
Step-by-step explanation:
=> (-8)(-3)
So, Here is the rule for it => ( - )( - ) = ( + )
=> +24
13. (8 points) The graph of the derivative, f'(x), of a function f() is shown.
(a) (2 points) On what intervals is f(x) increasing or decreasing?
(b) (2 points) At what values of x does f(2) have local maximum or minimum?
(c) (2 points) In what interval is f(x) concave upward or downward?
(d) (2 points) What are the x-coordinates of the inflection points of f(x)?
what is 9 - 4 1/2 ? i need help with that
Answer:
9 - 4 1/2 = 4 1/2.
To calculate this you can do (9 - 4 - 1) + (1 - 1/2).
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▹ Answer
4 1/2 or 4.5
▹ Step-by-Step Explanation
[tex]9 - 4\frac{1}{2} \\= 9 - \frac{9}{2} \\Common denominator = 2\\\\\frac{18}{2} - \frac{9}{2} \\= \frac{9}{2} \\\\= 4 \frac{1}{2} or 4.5[/tex]
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
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The graphs below have the same shape. What is the equation of the red
graph?
Step-by-step explanation:
If they have the same shape, the red graph is a translation of the blue, which is given to be y=x^2.
Since the red graph stays on the y axis at two units above the blue (y=x^2) curve, therefore the red curve is given by y=x^2+2.
The equation of the red graph is f(x) = x² + 2.
Option B is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
The graphs of f(x) = x² and f(x) = x² + 2 are both quadratic functions, which means they have a parabolic shape.
The graph of f(x) = x^2 is an upward-opening parabola with its vertex at the origin (0,0).
The parabola is symmetric about the y-axis and the x-axis.
The graph of f(x) = x² + 2 is also an upward-opening parabola, but it has been shifted upward by 2 units compared to the graph of f(x) = x².
This means that the vertex of the parabola has been shifted from (0,0) to (0,2).
Thus,
The equation of the red graph is f(x) = x² + 2.
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16 square meters is equivalent to how many square yards?
Answer:
16 square meters is equivalent to 19.14 square yards
Hope this helps you
Can someone divide this using long division please :)
(4x^3– 2x^2 – 3) divide by (2x^2 - 1)
Answer:
The quotient is 2x+1. The remainder is 2x-2
Step-by-step explanation:
Calculate the surface area of the following shape. Round all calculations to the nearest whole number
Answer:
total surface area = 672 cm^2
Step-by-step explanation:
radius of hemisphere, r = 7 cm
radius of base of cone, r = 7 cm
height of cone, h = 22-7 = 15 cm
slant length of cone, L = sqrt(7^2+15^2) = sqrt(274)
Area of the cone
= pi r L
= pi * 7 * sqrt(274)
= 115.87 pi
= 364.02 cm^2
Area of hemisphere
= 2 pi r^2
= 2 pi * 7^2
= 307.88 cm^2
Total surface area = 364.02 + 307.88 = 671.89 cm^2
Find the substance's half-life, in days.
Round your answer to the nearest tenth.
Answer:
t = 5.6 day
t =5 days 14 hours 24 minutes
Step-by-step explanation:
Half life is the time it will take for the original value or quantity I'd a particular substance to decrease by half of it's original self.
N = N•e(-kt)
N• = 25
K = 0.1229
Then
N = 25/2 = 12.5
The reason because at the half life , it's original value will decrease to half.
Let's solve for the half life t
N = N•e(-kt)
12.5 = 25e(-0.1229t)
12.5/25 = e(-0.1229t)
0.5 = e(-0.1229t)
In 0.5 =-0.1229t
-0.69314 = -0.1229t
-0.69314/-0.1229 = t
5.6399 = t
To the nearest tenth
5.6 days = t
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 21 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answer:
(x, y, z) = (45°, 57°, 78°)
Step-by-step explanation:
The problem statement tells you ...
x + y + z = 180
-3x +y +z = 0
0x -y +z = 21
__
Subtracting the second equation from the first gives ...
4x = 180
x = 45 . . . . . . divide by 4
Substituting this into the first equation and adding the third equation gives ...
(45 +y +z) +(-y +z) = (180) +(21)
2z = 156 . . . . simplify, subtract 45
z = 78 . . . . . . divide by 2
y = z -21 = 57
The angle measures are ...
(x, y, z) = (45°, 57°, 78°)
Karl has $1,500. He spends $375 on a phone and of the rest on a gaming system. What percent of his money is spent on the gaming system?
Answer:
75 %
Step-by-step explanation:
1500 - 375 =1125
So 1125 is spent on the gaming system
Take this over the total amount to get the decimal form
1125/1500 =.75
Change to percent form
75 %
Answer:
75%
Step-by-step explanation:
First we have to find the amount he is using for the gaming system which is
$1500 - $375 = $1125
Now we will express $1125 as a percentage of the total amount and we do that like this;
[tex]\frac{1125}{1500}[/tex] * 100%
= [tex]\frac{1125}{15}[/tex]
=75%
Which expression is equivalent to StartRoot 128 x Superscript 8 Baseline y cubed z Superscript 9 Baseline EndRoot? Assume y greater-than-or-equal-to 0 and z greater-than-or-equal-to 1 2 x squared z squared StartRoot 8 y cubed z EndRoot 4 x squared y z cubed StartRoot 2 x squared EndRoot 8 x Superscript 4 Baseline y z Superscript 4 Baseline StartRoot 2 y z EndRoot 64 x Superscript 4 Baseline y z Superscript 4 Baseline StartRoot 2 y z EndRoot
Answer:
Option C.
Step-by-step explanation:
The given expression is
[tex]\sqrt{128x^8y^3z^9}[/tex]
It can be written as
[tex]\sqrt{(64\cdot 2)\cdot x^8\cdot y^{2+1}\cdot z^{8+1}}[/tex]
[tex]=\sqrt{8^2\cdot 2\cdot (x^4)^2\cdot y^{2}\cdot y\cdot (z^{4})^2\cdot z}[/tex]
[tex]=\sqrt{(8x^4yz^4)^2\cdot 2yz}[/tex]
[tex]=8x^4yz^4\sqrt{2yz}[/tex]
Therefore, the correct option is C.
Answer:
c
Step-by-step explanation:
VERTICAL STRETCHES AND SHRINKS OF THE SQUARE ROOT FUNCTION
What is the domain of the function f(x) = Vo?
O all real numbers
O all real numbers less than 0
all real number less than or equal to 0
O all real numbers greater than or equal to 0
Answer:
all real numbers greater than or equal to zero
Step-by-step explanation:
The domain of the real function f(x) = sqrt(x) is
all real numbers greater than or equal to zero
because when x < 0, then f(x) will become complex, which does not belong to a real function.
These figures are similar. The
area of one is given. Find the
area of the other.
area=32 in
9 in
12 in
[ ?
Answer: 18 in²
Step-by-step explanation:
S(fig1)=32 in² . We know that the figures are similar and the correspondonding sides are a1=12 and a2=9
So the coefficient of similarity is k=9/12=3/4
S(fig2)=S(fig1)*k²
S(fig2)=32*(3/4)²=32*9/16=18 in²
The solution is A = 18 inches²
The proportion relation is given by k = 3/4 and the value of A = 18 inches²
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion equation be represented as A
Now , the constant of proportionality be k
From the figures , the two figures are similar
Constant of proportionality k = ( side of first figure / side of second figure)
k = 9/12
k = 3/4
Now , the area of the first figure A = 32 ( k )²
On simplifying the equation , we get
A = 32 ( 3/4 )²
A = ( 32 x 9 ) / 16
A = 2 x 9
A = 18 inches²
Therefore , the value of A is 18 inches²
Hence , the proportion is A = 18
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1 pizza costs £3.20 more than a bottle of coke. The total cost of the items is £19.40 for 3 pizzas and 1 bottle of coke How much does a pizza cost? How do you work this out please?
Answer:
Step-by-step explanation
p - the price of pizza
c- the price of a bottle of coke
p = c+3.2
3p + c=19.4
3* (c+3.2)+c=19.4
3*c+3*3.2+c=19.4
3c+c+9.6=19.4
4c+9.6=19.4
-9.6 -9.6
4c=9.8
:4. :4
c=2.45
p=2.45+3.2=5.65
verify : 3*5.65+2.45=16.95+2.45=19.40
Find the z-score corresponding to the given area. Remember, z is distributed as the standard normal distribution with mean of and standard deviation .
Answer:
Step-by-step explanation:
The z-score corresponding to a given area of a distribution, is the number of standard deviations that the values in that area have/are from the mean.
In this case, we have a STANDARD normal distribution. In a standard normal distribution, the mean is 0 and the standard deviation is 1.
The Z-score corresponding to a given area, say the 30th percentile is
X = 0 + (-0.524)(1)
Hence, the X (number of values in the given percentile - in this case, 30th) is same as the z-table or z-calculator value for the 30th percentile in ANY normal distribution.
The number of liver transplants performed in a particular country in year x is approximated by f (x )equalsnegative 239.7 plus 2390 ln x where x greater than or equals 5 and xequals5 corresponds to the year 1995. a) Estimate the number of transplants in 2013. b) Find f prime (23 ).
Answer:
a) 7265b) 103.913Step-by-step explanation:
Given the number of liver transplants performed in a particular country in year x approximated by f (x) = -239.7+ 2390lnx where x≥5. If x = 5 corresponds to year 1995. x will be equivalent to 23 in the year 2013.
a) Number of transplant in 2013 can be gotten by substituting x = 18 into the equation above.
f (x) = -239.7+ 2390lnx
f (23) = -239.7+ 2390ln 23
f (23) = -239.7+ 2390(3.14)
f(23) = 7264.9
The number of liver transplant in 2013 is approximately 7265
b) If f (x) = -239.7+ 2390lnx
f'(x) = 2390 * 1/x
f'(23) = 2390/23
f'(23) = 103.913
Which point is on the graph of f(x)=3.4x
Answer: The answer is (1, 12).
12 = 3 x 4^{1}
Step-by-step explanation: Hope it helps!
Answer:
Hi! The answer to your question is (1,12)
Step-by-step explanation:
The steps are:
I attached a picture to make sure if that’s the same problem as yours.
So in the picture you can see that there is option A, B, C, D
When we do A and B we will know that it is wrong
When we try C let’s see what we get!
When I did C I got 3.4₁ which equals to 12
Work:
Y=F [1] which equals to 3.4
3.4=12
So the answer will be C. (1,12)
Hope this helps! :)
Pamela is 7years older than jiri. The sum of their age is 91. What is Jori’s age
Answer:
[tex]\boxed{\sf \ \ \text{Jori is 42} \ \ }[/tex]
Step-by-step explanation:
Hello,
Let's not J Jori's age
Pamela is 7 years older than Jori so here age is J + 7
The sum of their age is 91 so
J + ( J + 7 ) = 91
<=>
2J + 7 = 91 subtract 7
2J = 91 - 7 = 84 divide by 2
J = 84/2 = 42
So Jori is 42 and Pamela is 49
hope this helps
Select the correct answer. What is the justification for step 3 in the solution process?
Answer:
Answer B
Step-by-step explanation:
Since you're dividing -0.3 by -2.5, you are using the division property of equality.
Answer:
The division property of equality.
Step-by-step explanation:
I did the test and I got it correct. Hope this helps. :D
Name the object that exhibits rotational symmetry. Question 7 options: sunglasses tent Ferris wheel a pair of scissors
The answer is Ferris wheel, since it is a circular object and will display symmetry even when rotated.
(1 point) A random sample of 1600 home owners in a particular city found 736 home owners who had a swimming pool in their backyard. Find a 95% confidence interval for the true percent of home owners in this city who have a swimming pool in their backyard. Express your results to the nearest hundredth of a percent.
Answer:
Answer: (0.4356,0.4844)
Step-by-step explanation:
Use Ti 84
use function "1-PropZInt".
Enter x = 736
n = 1600
c= 0.95
Answer: (0.4356,0.4844)
Solve for x.
Simplify your answer as much as possible.
For a certain salesman, the probability of selling a car today is 0.30. Find the odds in favor of him selling a car today.
Answer:
The odds in favor of him selling a car today are 3 to 10
Step-by-step explanation:
Probability and odds:
Suppose we have a probability p.
The odds are of: 10p to 10
In this question:
Probability of selling a car is 0.3.
10*0.3 = 3
So the odds in favor of him selling a car today are 3 to 10
There are four different answers to the mathematical question: 3 + 2 * 3^2 = ?
This is because the answer is dependent on the order of precedence. Consider the order of precedence and how it affects mathematical calculations. The four answers are below.
• ((3 + 2) * 3)^2 = 225
• (3 + 2) * (3^2) = 45
• 3 + ((2 * 3)^2) = 39
• 3 +( 2 * (3^2)) = 21
Answer:
The order in which you solve the operations will provide different results and to be able to get the right answer you have to be familiar with the order of operations to know the appropiate steps to solve an operation. According to the order of operations in mathematics, exponents are given precedence over addition and multiplication. Because of that, the exponent is the first you have to solve.
3 + 2 * 3^2
3+2*9
Then, mutiplication is given precedence over addition:
3+18
Now, you can solve the addition and the result is: 21
Because of this, the answer is:
• 3 +( 2 * (3^2)) = 21
if a varies inversely as the cube root of b and a=1 when b=64, find b
Answer:
b = 64/a³
Step-by-step explanation:
Using the given information, we can only find a relation between a and b. We cannot find any specific value for b.
Since a varies inversely as the cube root of b, we have ...
a = k/∛b
Multiplying by ∛b lets us find the value of k:
k = a·∛b = 1·∛64 = 4
Taking the cube of this equation gives ...
64 = a³b
b = 64/a³ . . . . . divide by a³
The value of b is ...
b = 64/a³
Find the length of MK
The length of the MK is 5 units if the length of MK = length of HK - length of HM.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
We have a number line shown in the picture.
From the number line:
Length of MK = Length of HK - length of HM
MK = 26 - 21
MK = 5 units
Thus, the length of the MK is 5 units if the length of MK = length of HK - length of HM.
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Does this table represent a function? Why or why not?
X
у
2
1
2
3
4
4
4
2
5
5
O A. Yes, because every walue corresponds to exactly one y value.
B. No, because one wwalue corresponds to two different yvalues,
C. Yes, because there are two walues that are the same.
O D. No, because two of the y values are the same,
Answer:
Option B is the right optionNo, because one X value corresponds to two different y- values.
Step-by-step explanation:
Function has only one output for each input.
Hope this helps..
Good luck on your assignment..
Unfortunately, the bus broke down at the distance of 50 km continue the story
Answer:
the driver tried to fix it by lighting up the engine thinking it would start again. it didnt and the entire engine set on fire. the bus doors were closed and everyone was trapped inside. everybody inside burnt to a crisp as the fire spread and local residents heard their screams as their skin melted. the end...