Answer:
7
Step-by-step explanation:
Let's call the missing card number "x".
The mean is the sum divided by the number of elements, so we know that:
[tex]\frac{12 + 6 + 15 + x}{4} = 10\\~\\12 + 6 + 15 + x = 40\\33 + x = 40\\x = 7[/tex]
The number on the 4th card is 7 according to the given question when The mean of the 4 numbers on Ed's cards is 10
To work out the number on the 4th card, we can use the information given about the mean of the four numbers.
Mean is calculated by summing all the values and then dividing by the number of values. In this case, the mean is 10 and there are four numbers.
Given:
Mean = 10
Number of cards = 4
To find the sum of the four numbers, we multiply the mean by the number of cards:
Sum of the four numbers = Mean * Number of cards
Sum of the four numbers = 10 * 4
Sum of the four numbers = 40
Now, let's find the number on the 4th card. We subtract the sum of the three known numbers from the sum of the four numbers:
Number on the 4th card = Sum of the four numbers - Sum of the three known numbers
Number on the 4th card = 40 - (12 + 6 + 15)
Number on the 4th card = 40 - 33
Number on the 4th card = 7
Therefore, the number on the 4th card is 7.
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Full question
Ed has 4 cards.
There is a number on each card.
12
6
15
?
The mean of the 4 numbers on Ed's cards is 10
Work out the number on the 4th card.
( No graph Needed)
Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 36 hours. hours and a standard deviation of 5.5 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 9 batteries.
a. What can you say about the shape of the distribution of the sample mean?
b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)
c. What proportion of the samples will have a mean useful life of more than 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
d. What proportion of the sample will have a mean useful life greater than 34.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
Answer:
a) By the Central Limit Theorem, it is approximately normal.
b) The standard error of the distribution of the sample mean is 1.8333.
c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.
d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours
e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours
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 estabilishes 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.
Mean of 36 hours and a standard deviation of 5.5 hours.
This means that [tex]\mu = 36, \sigma = 5.5[/tex]
a. What can you say about the shape of the distribution of the sample mean?
By the Central Limit Theorem, it is approximately normal.
b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)
Sample of 9 means that [tex]n = 9[/tex]. So
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333[/tex]
The standard error of the distribution of the sample mean is 1.8333.
c. What proportion of the samples will have a mean useful life of more than 38 hours?
This is 1 subtracted by the pvalue of Z when X = 38. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{38 - 36}{1.8333}[/tex]
[tex]Z = 1.09[/tex]
[tex]Z = 1.09[/tex] has a pvalue of 0.8621
1 - 0.8621 = 0.1379
0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.
d. What proportion of the sample will have a mean useful life greater than 34.5 hours?
This is 1 subtracted by the pvalue of Z when X = 34.5. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{34.5 - 36}{1.8333}[/tex]
[tex]Z = -0.82[/tex]
[tex]Z = -0.82[/tex] has a pvalue of 0.2061.
1 - 0.2061 = 0.7939
0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.
e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?
pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So
0.8621 - 0.2061 = 0.656
0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours
the number of bacteria present in a culture after t minutes is given as b=10e
Answer:
Step-by-step explanation:
I have no clue I just need 5 pionts
The distance around a triangle is 34 centimeters. If two sides are equal and the length of the third side is 6 centimeters, what is the length of each of the other two sides?
Subtract 6 from the total then divide by 2.
34-6 = 28
28/2 = 14
The length of the other two sides are 14 cm each
Simplify the expression
4p−5(p+6)
Please help, thank you :)
Answer:
-p - 30
Step-by-step explanation:
Hope this helps
Answer:
-p-30
Step-by-step explanation:
4p-5(p+6) Distribute -4 to p and 6
4p-5p-30 simplify by adding the p variables
-p-30
What is 0.36 written as a rational number?
Answer:
If you mean what is the square root of 36, then the answer is 6.
6 × 6 = 36.
Remeber sqaure root means what two numbers multplied together equal another number. It is irrational when the number doesn't repeat or terminate.
Hope this helps!!
[tex]if \: a = 3 + 2 \sqrt{2} .find \: a \times \frac{1}{a} [/tex]
Answer:
1
Step-by-step explanation:
Given that,
[tex]a=3+2\sqrt{2}[/tex]
We need to find the value of [tex]a\times \dfrac{1}{a}[/tex].
So,
[tex]=3+2\sqrt{2} \times \dfrac{1}{3+2\sqrt{2}}\\\\=\dfrac{3+2\sqrt{2}}{3+2\sqrt{2}}[/tex]
As numerator and dinominator is same. It means,
[tex]=\dfrac{3+2\sqrt{2}}{3+2\sqrt{2}}\\\\=1[/tex]
So, the value of the given expression is equal to 1.
True or False: When conducting a survey of a group of people, you must interview every person in that population.
Helpppppp me confused
Answer:
A = 4.5
B = 40.5
C = 4π or 12.566
D = 16
Step-by-step explanation:
A
6 x .5 = 3
3 x .5 = 1.5
1.5 x 3 = 4.5
B
12 x 3/4 = 9
1/2 (9)(9) = 40.5
C
8 x .25 = 2
π2² = 4π or 12.566
D
24 x 1/3 = 8
6 x 1/3 = 2
2 x 8 = 16
The coordinates of the vertices of ABC are A(-5, 2) B(-2, 4), and C(-4, 7). What are the coordinates of the image of A after the translation (x, y) = (x+6, y-5)?
Translation will reduce x coordinate by 2: (0,4), (5,6) and (3,2)
Rotation 90 CCW will change (x,y) to (-y,x): (-4,0),(-6,5),(-2,3)
A florist uses 7 red roses for every 4 white roses in her bouquets. Select the ratio of white roses to red roses. Please select 3 answers. 4 : 7
4 to 7
7 to 4
4/7
7/4
7 : 4
Answer:
Step-by-step explanation:
7 red roses
4 white roses
the answer would be 4 to 7, 4/7, and 4:7
I hope this helps!
Which equation shows y = (x − 4)2− 3 written in standard form?
Answer:
2 x − y = 11
Step-by-step explanation:
A pool can be filled by one pipe in 6 hours and by a second in 12 hours . How long will it take using both pipes to fill the pool?
Answer:
4 hours
Step-by-step explanation:
Part of the pool filled by first pipe in an hour = 1/6
Part of the pool filled by second pipe in an hour = 1/12
Part of the pool filled by first pipe and second pipe in an hour = 1/6 +1/12
[tex]=\frac{1*2}{6*2}+\frac{1}{12}\\= \frac{2}{12}+\frac{1}{12}\\\\=\frac{3}{12}\\\\=\frac{1}{4}[/tex]
Time taken by both the pipes to fill the pool = 4 hours
PLEASE HELP!!
Rita and her two children live in subsidized housing and pay monthly rent of $230. The cost of heating
is included in the rent. The electric bill averages $56 a month while the water and sewage bill averages
$35 for every 3 months of use. Telephone costs average $19.50 a month. Rita carries no renters
insurance on her personal property. What is Rita's total annual cost of renting?
Answer:
$3806
Step-by-step explanation:
230.0
56.0
+ 19.50
305.50
305.5x12=3666
35x4=140
3666+140=3806
The store ordered small and large poster. 12 times as many small posters were ordered as large posters. How many more small posters were ordered than large posters.
Answer:
so how many large and small posters were there before they order 12 times the amount.
Step-by-step explanation:
let f(x)=ln(x^2) and g(x)=√e^3x. find fog(x) and its domian
Answer:
[tex](f\ o\ g)(x) = 3x[/tex]
[tex]-\infty < x < \infty[/tex]
Step-by-step explanation:
Given
[tex]f(x) = ln(x^2)[/tex]
[tex]g(x)=\sqrt{e^{3x}}[/tex]
Solving (a): (f o g)(x)
This is calculated as:
[tex](f\ o\ g)(x) = f(g(x))[/tex]
We have:
[tex]f(x) = ln(x^2)[/tex]
[tex]f(g(x)) = \ln((g(x))^2)[/tex]
Substitute: [tex]g(x)=\sqrt{e^{3x}}[/tex]
[tex]f(g(x)) = \ln(\sqrt{e^{3x}})^2[/tex]
Evaluate the square
[tex]f(g(x)) = \ln(e^{3x})[/tex]
Using laws of natural logarithm:
[tex]\ln(e^{ax}) = ax[/tex]
So:
[tex]f(g(x)) = \ln(e^{3x})[/tex]
[tex]f(g(x)) = 3x[/tex]
Hence:
[tex](f\ o\ g)(x) = 3x[/tex]
Solving (b): The domain
We have:
[tex]f(g(x)) = 3x[/tex]
The above function has does not have any undefined points and domain constraints.
Hence, the domain is: [tex]-\infty < x < \infty[/tex]
Determine if the following shapes
are similar.
Answer:
No
Step-by-step explanation:
25-18 = 7 w
45-36=9 l
They don't match up ^
0 3. The pentagon ABCDE is graphed on a coordinate plane with vertices A(0, 0), B(3,5),
pentagon's area?
25 sq. units
15 sq. units
40 sq. units
Answer:
Option A
Step-by-step explanation:
The complete question is
The pentagon ABCDE is graphed on a coordinate plane with vertices A(0, 0), B(3, 5), C(3, 8), D(8, 5), and E(8, 0). What is the pentagon's perimeter?
Solution -
We will find the length of all the sides of pentagon and then add them
Length of AB = Sqrt ((3-0)^2+(5-0)^2) = Square root of 9+25 = 5.83
Length of BC = Sqrt ((3-3)^2+(8-5)^2) = Square root of 9 = 3
Length of CD = Sqrt ((8-3)^2+(5-8)^2) = Square root of 5^2+-3^2
= 5.83
Length of DE = Sqrt ((8-8)^2+(0-5)^2) = Square root of 25 = 5
Length of EA = Sqrt ((8-0)^2+(0-0)^2) = Square root of 64= 8
Perimeter=8+5+5.83+5.83+3= 27.66 units =27.66 units
Option A
Answer:
40 sq. units
Step-by-step explanation:
Plz help me ASAP no bots plz
Answer:
...
Step-by-step explanation:
the vertex is (-1 , 0)
false
true
the domain is R (all real numbers) ( -♾, +♾ )
the range is negative infinity -♾
Find the quotient using long division
4x^2-11x+5/x-4
Step-by-step explanation:
hope this help and pls rate to make me recommended for answering many mathematics questions! have a great day
In the first week of July, a record 1,100 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week, 130 more people went to the pool than in the second week. In the fourth week, 350 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
Once u type the answer please type how u got it thanks<3
Answer:
[tex]2\frac{3}{4}[/tex]
Step-by-step explanation:
Let's bring them to the same denominator: 4
[tex]2\frac{1}{4} = 2 + \frac{1}{4} = \frac{2\cdot 4}{4} + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4}\\~\\5 = \frac{5\cdot 4}{4} = \frac{20}{4}\\~\\5 - 2\frac{1}{4} = \frac{20}{4} - \frac{9}{4} = \frac{11}{4} = \frac{8}{4} + \frac{3}{4} = \frac{2\cdot 4}{4} + \frac{3}{4} = 2 + \frac{3}{4} = 2\frac{3}{4}[/tex]
There are 25 students in Ms. Hunter's class. Seventeen of the students in her class rode the bus home today. The rest walked home. Which model best represents the percentage of students that rode the bus home and the percentage of students that walked home?
A 32% walked home 68% rode the bus
B 68% walked home 32% rode the bus
C 8% walked home 17% rode the bus
D 17% walked home 25% rode the bus
Answer:
68% rode the bus; 32% walked home
Step-by-step explanation:
write an equation of a line passing thru the point (-4,-11) and perpendicular to the line 4x+5y= -45
Answer:
y = 5/4x - 6
Step-by-step explanation:
First, put 4x + 5y= -45 in y = mx + b form
4x + 5y= -45
5y = -4x - 45
y = -4/5x - 9
So, the slope is -4/5. Perpendicular lines have a opposite reciprocal slope, so the line's slope will be 5/4
To find the equation of the perpendicular line, plug in the slope and given point into y = mx + b, and solve for b
y = mx + b
-11 = 5/4(-4) + b
-11 = -5 + b
-6 = b
Plug in b and the slope into y = mx + b
y = 5/4x - 6
So, the equation is y = 5/4x - 6
Find the length of are ab
Answer:
20.97?
Step-by-step explanation:
Use the Sine rule!
Please help name brainliest
To honor veterans, Carl has planned a Walking for Vets Program. He has mapped out a 1000 mile path and plans to walk 12 hours per day. If Carl exercises regularly, which is the best approximation of how long the walk will take?
Answer:
20 days
Step-by-step explanation:
Will give brainliest for correct answer
Answer:
4 = function
5 = function
6 = not a function
Step-by-step explanation:
The first two pass the vertical line test
while the last ne doesn't
Ill gove brainlyist and 40 points pleaseee
Find the area of this triangle,
Round to the nearest tenth.
4 ft
37
10 ft
[? ] ft2
Answer:
12
Step-by-step explanation:
Hello There!
When we are given two side lengths and the included angle we use this formula to solve for the area
[tex]A=\frac{1}{2} absin(C)[/tex]
where a and b = the side lengths and c = the included angle
The triangle gives us the following information
side length - 10 ft
side length - 4 ft
included angle - 37
Given this information we plug it into the formula
[tex]A=\frac{1}{2} 4*10sin(37)\\10*4=40\\40sin(37)=24.07260093\\\frac{24.07260093}{2} =12.03630046[/tex]
Finally we round to the nearest tenth and get that the area of the triangle is 12ft²
A C (prima) = 14cm AC= 5cm
Cual es la razón de la homotecia?
ppppppppppppppppppppppppppppllllllllllllllllllllllllllllllllllllllllllllllllllllllllllzzzzzzzzzzzzzzzzzzz hheellpp
Answer:
12 because imagine 40 / 3 ok? now what makes 160 40 x 4 so you do that for the button 4 x 3 please put heart
simplify
[tex] {a}^{3} - {b}^{3} [/tex]
Answer:
[tex] {a}^{3} - {b}^{3} [/tex]
[tex] = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]
Hence, simplified.