Answer:
The p-value of the test is 0.1738, which means that for a level of significance above this, there is evidence of a change from the status quo.
Step-by-step explanation:
A high school has found over the years that out of all the students who are offered admission, the proportion who accept is 70%. Test if there is a change from status quo.
At the null hypothesis, we test if the proportion is 70%, that is:
[tex]H_0: p = 0.7[/tex]
At the alternate hypothesis, we test if there is a change from status quo, that is, the proportion is different from 70%. So
[tex]H_a: p \neq 0.7[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
70% is tested at the null hypothesis:
This means that [tex]\mu = 0.7, \sigma = \sqrt{0.7*0.3}[/tex]
Suppose they offer admission to 210 students and 156 accept.
This means that [tex]n = 210, X = \frac{156}{210} = 0.7429[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.7429 - 0.7}{\frac{\sqrt{0.7*0.3}}{\sqrt{210}}}[/tex]
[tex]z = 1.36[/tex]
P-value of the test and decision:
The p-value of the test is the probability that the sample proportion differs from 0.7 by at least 0.7429 - 0.7 = 0.0429, which is P(|z| > 1.36), which is 2 multiplied by the p-value of z = -1.36.
Looking at the z-table, z = -1.36 has a p-value of 0.0869
2*0.0869 = 0.1738
The p-value of the test is 0.1738, which means that for a level of significance above this, there is evidence of a change from the status quo.
The data in the table represents the value of a savings account at the end of each year for 6 years. The relationship between the increasing years and the increasing value of the account is exponential.
Answer:
1. Constant multiplicative.
2. 1.05.
Step-by-step explanation:
Their savings increase by 1.05x every year.
PLZ I NEED HELP, LAST QUESTION ! ! ! :,D
The function s(n) = 2n - 5 represents the value of the nth term in a sequence.
What is the sum of the 1st and 6th terms of the sequence?
Step-by-step explanation:
s(n) = 2n - 5
What is the sum 1st and 6th terms of the sequence? 12
s(1) = 2(1) - 5 = -3
s(2) = 2(2) - 5 = -1
s(3) = 2(3) - 5 = 1
s(4) = 2(4) - 5 = 3
s(5) = 2(5) - 5 = 5
s(6) = 2(6) - 5 = 7 add these numbers
Please help me with this question as soon as possible :)
The constant cost call c is $0.7 and the cost of per minute call m is $0.93.
What is system of equations?In algebra, a system of equations consists of two or more equations and looks for ways to solve them all together. A group of equations that have the same set of variables as solutions are referred to as a system of linear equations.
Let the constant cost be c and the per minute cost be denoted by m.
The equation for 5 minutes of the call is:
5.91 = 5m + c
c = 5.91 - 5m
The equation for 10 minutes of the call is:
10.06 = 10m + c
Substitute the value of c in the above equation:
10.06 = 10m + 5.91 - 5m
10.06 - 5.91 = 5m
4.69 = 5m
m = 0.93
Substitute the value of m:
10.06 = 10(0.93) + c
c= 0.7
Hence, the constant cost call c is $0.7 and the cost of per minute call m is $0.93.
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find in how many ways can two admirals, three generals and 4 lieutenants can be seated in a row of nine seats if the admirals must sit at each end?
Answer:
They can be seated in 10,080 ways.
Step-by-step explanation:
Arrangements of n elements:
The number of possible arrangements of n elements is given by:
[tex]A_n = n![/tex]
In this question:
In each end, the two admirals, so 2 possible outcomes.
In the middle seats, arrangements of 7 elements(3 generals, 4 lieutenants). So
[tex]2A_{7} = 2*7! = 10080[/tex]
They can be seated in 10,080 ways.
The number of ways they can be seated is 10,080 ways.
Permutations and combinationThe number of possible ways fof arranging n elements is given as:
P = n!
According to the question, there are 2 admirals! 3 generals and 4 lieutenant.
In each end, the two admirals, so 2 possible outcomes.
In the middle seats, arrangements of 7 elements(3 generals, 4 lieutenants). Hence the required number of combination will be given as:
Number of ways = 2*7!
Number of ways = = 100802
Hence the number of ways they can be seated is 10,080 ways.
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Prove that limx→2 2^x=4 using the formal definition of limit.
Answer:
Refer to step-by-step
Step-by-step explanation:
Prove that, [tex]\lim_{x \to \22} 2^{x}=4[/tex]
Plug in the value of 2 into the limit.
[tex](2)^{2}=4[/tex]
Thus we proved the limit.
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. The p-value for this test statistics is: a. 0.05 b. 0.0228 c. 0.0456 d. 0.025 brainly
Answer:
The appropriate answer is option b (0.0228).
Step-by-step explanation:
The given values are:
Random sample,
[tex]n=100[/tex]
Average length of time,
[tex]\bar{x}=3.1 \ minutes[/tex]
Waiting time,
[tex]\mu=3 \ minutes[/tex]
Standard deviation,
[tex]\sigma=0.5[/tex]
Now,
The test statistics will be:
⇒ [tex]z=\frac{(\bar{x}-\mu)}{\frac{\sigma}{\sqrt{n} } }[/tex]
On substituting the values, we get
⇒ [tex]=\frac{(3.1-3)}{\frac{0.5}{\sqrt{100} } }[/tex]
⇒ [tex]=\frac{0.1}{0.05}[/tex]
⇒ [tex]=2[/tex]
hence,
⇒ [tex]P(z >2 ) = 1 - P(z <2 )[/tex]
By using the table,
⇒ [tex]=1-0.9772[/tex]
⇒ [tex]=0.0228[/tex]
Which measure of center is the most appropriate for the data in Table 1 (Height) in Task 1? Give a reason for your answer.
Answer:
it is 62 or 58 because they are show the most times
Answer:
The answer is 61.
Step-by-step explanation:
Pleaseee helppppp it’s timedddddd!!!!!!!
Answer:
Option (4)
Step-by-step explanation:
Point to remember for the dilation,
Area scale factor = (Dimension scale factor)²
It's given in the question,
Dimension scale factor = [tex]\frac{2x}{5y}[/tex]
Therefore, area scale factor = [tex](\frac{2x}{5y})^2[/tex]
= [tex]\frac{4x^2}{25y^2}[/tex]
Option (4) will be the correct option.
What is the slope of a horizontal line? Write the equation of an example of a horizontal line.
The slope of the horizontal line will be zero.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope of the line is the ratio of the rise to the run.
The horizontal line always has zero slopes because the y coordinate will always be the same for two points.
The slope is calculated by the formula below,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
y₂ = y₁
Slope = ( y₁ - y₁ ) / ( x₂ - x₁ )
Slope = 0
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20 ounces at $7
17 ounces at x dollars
225 bushels for 3 acres
x bushels for 9.6 acres
9514 1404 393
Answer:
$5.95720 buStep-by-step explanation:
We assume the given ratios are proportional. I find it easiest to write the proportion with the unknown in the numerator.
a) dollars/ounces = x/17 = 7/20
Multiply by the inverse of the coefficient of x to solve.
x = 17(7/20) = 5.95 . . . dollars
__
b) bushels/acres = x/9.6 = 225/3
x = 9.6(225/3) = 720 . . . bushels
Once a week you babysit your neighbor's toddler after school, usually going to
a local playground. You notice that each swing on the swing set takes nearly
the same amount of time, about 2.7 seconds. Use the pendulum formula
below to find out how long the swing is. Round your answer to the tenths
place.
Answer:
l = 1.8 feet
Step-by-step explanation:
Given that,
The time period of the pendulum, T = 2.7 seconds
We need to find the length of the swing. The formula for the time period of a simple pendulum is given by :
[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]
Where
l is the length of the swing.
[tex]T^2=\dfrac{4\pi^2l}{g}\\\\l=\dfrac{T^2g}{4\pi^2}\\\\l=\dfrac{(2.7)^2\times 9.8}{4\times 3.14^2}\\\\l=1.8\ \text{feet}[/tex]
So, the length of the swing is 1.8 feet long.
Answer:5.4
Step-by-step explanation:
How many tens do u need to make 280
Answer:
28
Step-by-step explanation:
280 divided by 10 = 28
Simisola wants to compare the time take
to make yoghurt at different temperature
List the variables she should control.
Yogurt production is affected by the production technological conditions.
What is yoghurt different temperature?Yogurt production is affected by the production technological conditions. Increase in the incubation temperature (42-45ᵒC) resulted to increase in the coagulation of the milk protein present (induced by thermophilic bacteria) and viscosity. This also resulted in increased acidity of the yoghurt.The temperature must be 108°F to 112°F for yogurt bacteria to grow properly. Too high a temperature inactivates bacteria; too low a temperature prohibits growth. Inhibitor substances such as detergent from dishes. Wash and rinse dishes well before making yogurt.Making yogurt at home is a fairly straight-forward process. Heat milk to 180F (82C), cool that milk to at least 110F (43C), add live cultures, usually in the form of yogurt with said cultures, incubate, then chill.There are several variables in the process, some of which are: The fat content of the milk (I typically use whole), how long to hold the milk during the initial heat step, how long it takes to cool the milk, the temperature of the incubation step, and the length of time for incubation, to name a few.To learn more about yoghurt different temperature refers to;
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Write as an radical expression
U 2/5
Answer:
Step-by-step explanation:
An radical expression usually involves a radicand which is the number or expression inside the radical symbol √ and an index which is the number outside the radical symbol indicating the root, the radicand raised to the power of the reciprocal of the index.
But in the case of expression "U-2/5" it's not a radical expression as is. It's a fractional expression with variable U and a constant -2/5.
It can be written as √(U-2)/5 or U- √(2/5) if you want to express it as an radical expression.
What is the measure of Angle B A C?
Triangle A B C. Angle B is 50 degrees, angle C is 50 degrees, and angle A is blank.
50 degrees
80 degrees
100 degrees
130 degrees
The ratio of pens to pencils that Jose has on his desk is 5:3. If Jose has 15 pens on his desk then how many pencils does he have?
Answer:
9 pencils
Step-by-step explanation:
We know that the ratio is 5:3 and its pens to pencils. So, every 5 pens have 3 pencils. Now Jose has 15 pens, so his pen supply triples. therefore his pencil supply must also triple. So 3x3=9.
Let the no. of pencils be x,
= 5/3 = 15/x
Do cross multiplication
= 5x = 15 × 3
= x = 45/5
= x = 9
No of pencils = 9
Yasmeen is setting up a business.
She borrows $5000 from a loan company.
The loan company charges 6% per year simple interest.
How much interest will Yasmeen pay after 3 years?
PLEASE Help. The answers I got so far are A. 72. B. 301. C 90 and D 252. I am having the most trouble with B and D.
The correct solutions for this question are as:
(A) Bearing of B from A = 72°
(B) Bearing of B from C = 342°
(C) Bearing of A from B = 252°
(D) Bearing of A from C = 293°
Step by step solution:
(A) Bearing of B from A:
= 72° (Given in question)
(B) Bearing of B from C: = 342°
Solution:
As sum of co-interior angles is 180° , i.e. ∠NBC +∠NCB =180°
so, 162° + ∠NCB = 180°
∠NCB = 180°-162°
∠NCB = 18°
reflexive angle NCB =360° - ∠NCB
reflexive angle NCB = 360° - 18°
reflexive angle NCB = 342°
So, bearing of B from C: = 342°
(C) Bearing of A from B: = 252°
Solution:
First extend the line AB to any point (let's say "X")
So, ∠NBX = 72° [BY USING CORRESPONDING ANGLES]
Bearing of A from B = ∠NBX + 180°
Bearing of A from B =72° + 180°
Bearing of A from B =252°
(D) Bearing of A from C: = 293°
Solution:
Bearing of A from C= 360° - (∠BCA + ∠BCN)
Bearing of A from C= 360° - (49° + 18°)
Bearing of A from C= 360° - (67°)
Bearing of A from C= 293°
Important Points for "Bearing of Angles":
A bearing is an angle that is calculated clockwise from the north. A traverse should be regarded as anticlockwise unless differently stated or obvious from the bearings.
The angle between two lines cannot be directly read using a regular compass. By tracking the two lines bearings away from their point of confluence, the angles can be found.
Two angles—an inner angle and an exterior angle—are created when the two lines converge at a place. These two angles add up to a 360° angle.
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There are t counters in a box.
Write an expression for the total number of counters.
Answer: 4t
Step-by-step explanation:
You just do t times the amount of boxes you have, which is 4. So you have 4 times t, but in algebra, we don't write the multiplication sign. So the expression would be written as 4t. Yw!
Also please tell me if I was unhelpful/incorrect, thanks!
Solve the equation 5(4x-1.5x) + 12 = 4x- 124 for X
[tex] \sf \: 5(4x -1.5x) + 12 = 4x - 124 \\ \sf \: 5 \times 2.5x + 12 = 4x - 124 \\ \sf \: 12.5x + 12 = 4x - 124 \\ \sf \: 12.5x - 4x = - 124 - 12 \\ \sf \: 8.5x = - 136 \\ \sf \: x = - 16[/tex]
Check the correct operation each word represents.
Answer:
difference - subtraction
sum - addition
of - multiplication
per - division
decreased by - subtract
together - addition
quotient - division
product - multiplication
3 2/3 Divided by 1 2/7
Answer:
[tex]2 \frac{23}{27} [/tex]
I wish you luck in your assignments.
Julla drinks 20 cups of water per day. How many quart(s) of water does she drink per day? Julla drinks ? quart(s) of water per day.
Answer:
5 quarts
Step-by-step explanation:
there are 4 cups in a quart so 20/4=5 or
5x4=20 ykyk
i need help, this is pythagorean theorem !! i do not understand
In mathematics, the Pythagorean theorem is a fundamental relationship in Euclidean geometry between the three sides of a right triangle. State that the area of the square whose side is the hypotenuse
Fórmu
NEED HELP CLICK TO SEE LINKS WILL GET REPORTED
I'm not sure what the first and last question answers are sorry. But I know that the second question is 31 the third question is 10 and the fourth question is 12.
59.84 divided 32
What is the value of the expression?
Equations of Exponential Functions
Given the following table, determine the missing value.
a. 1.15 c. 15
b. 115 d. .15
Please select the best answer from the choices provided
Answer:
A. 1.15
Step-by-step explanation:
I calculated it logically
Write a number sentence using multiplication ti show what fraction represented on the mumber line is equivalent to 3/4
The fraction that is equivalent to 3/4 is seen as; 6/8
How to represent fractions?A number sentence is defined as a mathematical sentence that is made up of numbers and symbols.
We want to write a number sentence using multiplication to show a fraction that is equivalent to 3/4.
Now, for us to find the final equivalent fraction, what we have to do is that we will divide or multiply by denominator and numerator by the same number that is equal to one e.g 3/3; 5/5; 6/6, etc.
Since we want to find equivalent fraction of 3/4, let us multiply both numerator and denominator by 2 to get;
(3 * 2)/(4 * 2) = 6/8
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The graph shows Sam's earnings. What is the constant
of proportionality between Sam's earnings and the
number of hours he worked?
Answer:
8
Step-by-step explanation:
Constant of proportionality, k = y/x
y = earnings ($)
x = time (h)
Any point on the line can be used to determine the constant of proportionality. Let's use, (1, 8)
Constant of proportionality, k = y/x = 8/1
k = 8
Only answer if you know the real answer please appreciate it answer question number 2 please
Answer:
0.99
Step-by-step explanation:
Median is the middle term (or mean of the middle two terms) of a series arranged in order of magnitude.
Here the weights are already arranged in order and the middle term is 0.99
Therefor the median = 0.99