Using the normal distribution, it is found that there is a 0.9938 = 99.38% probability that the average of these members is less than 35.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, we have that the parameters are given as follows:
[tex]\mu = 34, \sigma = 4, n = 100, s = \frac{4}{\sqrt{100}} = 0.4[/tex].
The probability that the average of these members is less than 35 is the p-value of Z when X = 35, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{35 - 34}{0.4}[/tex]
Z = 2.5
Z = 2.5 has a p-value of 0.9938.
0.9938 = 99.38% probability that the average of these members is less than 35.
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martina must choose a number between 49 and 95 that is multiple of 2,8 and 10. write all the numbers that she could choose.
Answer:
80
Step-by-step explanation:
10 limits it to 50, 60, 70, 80, and 90
2 eliminates none since 50=25, 60=30, 70=35, 80=40 and 90=45
8 divided by each number only leaves one option of 80. (80/8= 10) (80/10=8) (80/2=40)
O
O
O
-54-3 -2 -1 0 1 2 3 4 5 6 7
8
-5-4
-3 -2 -1 0 1 2 3 4 5 6 7 8
++
-5 -4
-3 -2 -1
0 1
2
3 4 5 6 7
8
+
-5 -4
-3 -2 -1 0 1
2
3
5
6
7
C
C
4
8
9 10 11 12 13
9 10 11 12 13
9 10 11 12 13
9 10 11 12 13
Step-by-step explanation:
separate the question into two inequalities then solve individually to derive at an answer then merge the two answers as one.
remember that < or > are open sets while <= or >= are closed set.
Rewrite the expression using the distributive property and a common factor.
27x+24x
0.5n+2.5
Answer:
x(27 +24) or 3x(9 +8)0.5(n +5) or 2.5(n/5 +1)Step-by-step explanation:
The distributive property of multiplication over addition tells us that the product of a value and a sum will be the same as the sum of products of the value and the sum's addends. This property can be used to add or remove parentheses from an arithmetic expression.
a(b +c) = ab +ac . . . . expression of the distributive property
__
When applying the distributive property to a sum, the first step is to look for a factor common to the terms of the sum. That factor need not be the greatest common factor, though it is often useful if it is.
Below, we have written each expression using two different common factors.
a)27x +24x = x(27 +24) = 3x(9 +8)
__
b)0.5n +2.5 = 0.5(n +5) = 2.5(n/5 +1)
_____
Additional comment
Finding a common factor can make use of knowledge of multiplication tables, rules of exponents, and identities involving various functions used in algebraic expressions. It is sometimes useful to list the prime factors of each of the terms as an aid to finding a common one. Where fractions are involved, it is sometimes helpful to express them all using a common denominator.
The Euclidean Algorithm can also be useful for finding common factors.
6 A cube has a surface area of 54 mm². The length of its sides is: A 3 mm B 4 mm C 5
mm D 6 mm E 7 mm
Answer:
A
Step-by-step explanation:
A cube has 6 square faces
given surface area = 54 mm² , then
area of one face = 54 mm² ÷ 6 = 9 mm²
the area (A) of a square is calculated as
A = s² ( s is the side length ) , so
s² = 9 ( take square root of both sides )
s = [tex]\sqrt{9}[/tex] = 3 mm
The triangles below are similar. Triangle Y X Z. Side Y X is 6 centimeters, X Z is 7 centimeters, and Z Y is 3 centimeters. Triangle A B C. Side A C is 14 centimeters, A B is 12 centimeters, and B C is 6 centimeters. Which similarity statement expresses the relationship between the two triangles? Triangle Z Y X is similar to triangle C A B Triangle Z Y X is similar to triangle A C B Triangle Z Y X is similar to triangle C B A Triangle Z Y X is similar to triangle A B C Mark this and return
Answer:
(c) Triangle Z Y X is similar to triangle C B A
Step-by-step explanation:
Triangles are similar when corresponding sides have the same ratio. Corresponding sides will have corresponding end point vertices. The similarity statement lists corresponding vertices in the same order.
__
corresponding sidesThe side lengths, smallest to largest, for the two triangles are ...
3 cm -- ZY6 cm -- YX7 cm -- XZAnd for the other triangle, ...
6 cm -- BC12 cm -- AB14 cm -- ACcorresponding verticesThe points joining the each side to the next one longer, in order for the two triangles, are ...
Y, X, Z and B, A, C
The vertices corresponding to ZYX in the same order are CBA.
triangle ZYX is similar to triangle CBA
Answer:
The answer is C
Step-by-step explanation:
HELP PLEASE !!!!!!!!!!!
Answer:
I think A sorry if wrong
Step-by-step explanation:
have a good day
Determine x to two decimal places.
*PICTURE ATTACHED*
*TRIGONOMETRY*
This rule is applied to triangles to determine the unknown sides and angles. The value of x from the diagram is 11.78m
Trigonometry ruleThis rule is applied to triangles to determine the unknown sides and angles.
Given the following parameter
Opposite = 5m
Adjacent = x
angle = 23 degrees
According to the theorem of tangents
tan23 = opposite/adjacent
tan23 = 5/x
x = 5/tan23
x = 11.78m
Hence the value of x from the diagram is 11.78m
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Jada fills the bathtub before taking a bath and then allows the water to drain when she is done. The graph below models the number of gallons of water, y, in the bathtub over time, t, in minutes.
On a graph, the graph increases, remains constant, and then decreases.
Is the number of gallons of water in the bathtub a function of time?
The number of gallons of water in the bathtub is a function of time. Therefore, it is true.
How to illustrate the graph?
The graph shows a curve that lets you find the number of gallons of water given any value of t betweeh 0 and 30 plus.
Hence, the number of gallons of time indeed is a function of time, in the interval shown by the graph.
The answer is true, because each t value is paired with exactly one number of gallons".
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Answer:
A
Step-by-step explanation:
Find the value of x. Show each step.
0.15x+(0.15-5-x)*0.2=0.1
Answer:
-21.4
Step-by-step explanation:
0.15x + 0.2(0.15-5-x) = 0.1
0.15x + 0.03 - 1 - 0.2x = 0.1
0.15x - 0.2x = 0.1 -0.03 + 1
-0.05x = 1.07
0.05x = -1.07
x = -21.4
Cheryl has a horse and cow ranch that contains 100 animals. The value of each horse is $500 and the value of each cow is $200. If the total value of the 100 animals is $31,000, how many horses and cows does Cheryl have on her ranch?
The number of the cows is 63 and the number of the horses is 37.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
Cheryl has a horse and cow ranch that contains 100 animals. The value of each horse is $500 The value of each cow is $200. If the total value of the 100 animals is $31,000.The number of horses and cows will be calculated by forming the expression from the given data in the question. So the two expressions are as follows.
h + c = 100
500h + 200c = 31000
Solving the above two equations by substitution method:-
h = 100 - c
Put the value of h in the second equation:-
500 ( 100 - c ) + 200c = 31000
50000 - 500c + 200c = 31000
50000 - 300c = 31000
50000 - 31000 = 300c
c = 19000 / 300
c = 63
Put the value of c in the first equation we will get the number of the horses.
h + c = 100
h + 63 = 100
h = 100-67 = 37
Therefore the number of the cows is 63 and the number of the horses is 37.
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Dan invests £8200 into his bank account.
He receives 2% per year compound interest.
How much will Dan have after 7 years?
Give your answer to the nearest penny where appropriate.
Answer: £ 3675.79
Step-by-step explanation:
A = P(1 + r)^t
A = final amount = x
P = initial principal balance = 3200
r = interest rate = 0.02
t = number of years elapsed = 7
x = 3200(1.02)^7
x = 3200 * 1.14868567
x = 3675.79414
x = 3675.79
Solve for x
3x-5=-x+3
Answer:
(3x - 5 = -x + 3) x = 2
Step-by-step explanation:
3x - 5 = -x + 3
3x = -x + (3 +5)
3x=-x + 8
(3x + x ) = 8
4x = 8
4/8 =2
x = 2
What is the relationship between the number of sides a regular polygon has and the number of lines of symmetry that can be found on it?
There are always more lines of symmetry than sides.
They are same value.
There are always more sides than lines of symmetry.
There is no relationship.
The number of sides equals the number of the line of symmetry. Then the correct option is B.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
The relationship between the number of sides a regular polygon has and the number of lines of symmetry will be
In a regular polygon, the amount of symmetry lines is equal to the total of sides.
Then the correct option is B.
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Answer:
B They are the same value!
Step-by-step explanation:
Why? Well go look in your lesson although because i got this correct i forgot ago and yeah (TRUST++)
Glen Cove has a population of 7,200, which is decreasing at a
rate of 80 people per year. Locust Valley has a population of
5,000 and is gaining 120 people per year. In how many years
will the populations of Glen Cove and Locust Valley be the same?
Please help!!
Answer:
11 years
Step-by-step explanation:
7200 - 80x = 5000 + 120x
-5000 + 80x -5000 + 80x
2200 = 200x
11 = x
(-14,-13), (-7,-7)
Can anyone help me solve this - algebra
Answer: y=6/7x-1
Step-by-step explanation:
I am assuming you want a line formula in y=mx+b
slope (y2-y1)/(x2-x1) = -7+13/-7+14 = 6/7
y+7=6/7(x+7)
y+7 = 6/7x+6
y=6/7x-1
If the quadratic equation has two rational roots,then the discriminant is_____and a perfect square
Answer:
Real and unequal
Answer:
The quadratic has two equal roots like d if it is perfect square and we may write: (x − d) 2 = x 2 − 2 d x + d 2 Then: Δ = 4 d 2 − 4 d 2 = 0 That is the discriminant is zero when the quadratic is perfect square.
Step-by-step explanation:
(06.03 HC)
Solve the following system of equations. Show all work and solutions.
y = 3x2 + 6x + 4
y = −3x2 + 4
By solving the two quadratic equations we found the values (0,-1).
What is a quadratic equation?It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given equations are;-
y = 3x² + 6x + 4y = -3x² + 4The two equations are solved by equating them and finding the value of x.
3x² + 6x + 4 = -3x² + 4
6x² + 6x = 0
6x ( x+1 ) = 0
6x = 0 so x = 0
( x+1 ) = 0 so x = -1
Therefore solving the two quadratic equations we found the values (0,-1).
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Solve the system using substitution.
y=-x-2,3x+3y=6
Step-by-step explanation:
x = -2-y
3(-2-y) +3y =6
-6-3y +3y=6
у=0
O=-x-2
х=-2
What expression is equivalent to the given expression?
The expression which is equivalent to the given expression is [tex]\frac{27 m^{5}}{n}[/tex]
Evaluating indicesFrom the question, we are to determine the expression which is equivalent to the given expression
The given expression is
[tex]\frac{(3m^{2}n)^{3} }{mn^{4} }[/tex]
Clearing the brackets, we get
[tex]\frac{3^{3} m^{2(3)}n^{3} }{mn^{4} }[/tex]
Simplifying, we get
[tex]\frac{27 m^{6}n^{3} }{mn^{4} }[/tex]
Then,
[tex]27 m^{6-1}n^{3-4}[/tex]
[tex]27 m^{5}n^{-1}[/tex]
= [tex]\frac{27 m^{5}}{n}[/tex]
Hence, the expression which is equivalent to the given expression is [tex]\frac{27 m^{5}}{n}[/tex]
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please help!! What is the most precise classification for the quadrilateral shown in the graph below?
Parallelogram is the most precise classification for the quadrilateral shown in the graph below.
What is a Parallelogram?This is a quadrilateral which has two pairs of parallel sides and the area is usually measured using base × height.
The opposite sides and angles are equal which is why parallelogram was chosen as the most appropriate choice.
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Daniel runs 40/5 miles in 124/₁ minutes. What is the unit rate in terms of miles per minute? What the answer:
Using the given information, the unit rate is 0.0645 miles/minute
Calculating rateFrom the question, we are to determine the unit rate
From the given information,
Daniel runs 40/5 miles in 124 minutes
That is,
Distance = 40/5 miles = 8 miles
Time = 124 minutes
Using the formula,
Rate = Distance / Time
Rate = 8 miles / 124 minutes
Rate = 0.0645 miles/minute
Hence, the unit rate is 0.0645 miles/minute
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The unit rate is 0.0645 miles/minute
We have calculated the rate
From the question, we are to determine the unit rate
From the given information,
Daniel runs 40/5 miles in 124 minutes
Distance = 40/5 miles
Distance = 8 miles
Time = 124 minutes
What is the formula of rate?Rate = Distance / Time
Rate = 8 miles / 124 minutes
Rate = 0.0645 miles/minute
Hence, the unit rate is 0.0645 miles/minute
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Evaluate each function.
14) g(x)= 3x² - 1; Find g(-3)
[tex]g(x) =3x^2 -1\\\\g(-3)=3(-3)^2 -1 \\ \\~~~~~~~~~=3(9) -1 \\\\~~~~~~~~~=27-1\\\\~~~~~~~~~=26[/tex]
Answer:
g(26)
Step-by-step explanation:
substitute -3 for x.
g(x)=3[tex]x^{2}[/tex]-1
[tex]g(-3)=3(-3)^{2} -1\\g(-3)= 3(9)-1\\g(-3)= 27-1\\g(-3)=26[/tex]
In a graph, x represents the number of months since a business opened, and y represents the total amount of money the business has earned. The following three points are from the graph:
The slope of the graph is 745 and the y-intercept of the graph is 500
Missing part of the questionThe following three points are from the graph: (2, 1990) (5, 4225) (9, 7205)
Find the slope and y-intercept
How to determine the slope?The points are given as:
(2, 1990) (5, 4225) (9, 7205)
The slope is calculated using:
m = (y2 - y1)/(x2 - x1)
So, we have:
m = (4225 - 1990)/(5 - 2)
Evaluate
m = 745
Hence, the slope of the graph is 745
How to determine the y-intercept?In (a), we have
m = 745
To calculate the y-intercept, we use the following points
(x1 , y1) = (0,y)
Recall that:
m = (y2 - y1)/(x2 - x1)
So, we have:
745 = (4225 - y)/(5 - 0)
Evaluate the difference
745 = (4225 - y)/(5)
Multiply both sides by 5
3725 = 4225 - y
Solve for y
y = 500
Hence, the y-intercept of the graph is 500
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Please help on this only if u know
Answer:
Option D ---> y=5x
Step-by-step explanation:
When a line is directly proportional it means it crosses the origin so has a y- and x-intercept of 0.
So if we use the format y=mx+c, it will work but our c value will be 0 as I explained above .
To work out the gradient we simply take 2 points (0,0) and (1,5)) on the graph and use the gradient formula :
m = change in y ÷ change in x
m = 5÷1
m = 5
Therefore our direct proportion equation will be y=5x
Hope this helped and have a good day
What is the value of x in the equation shown Below?2(x+4)-4x=10x-4
Answer: 1
Step-by-step explanation:
What is the amplitude of the graph below
The amplitude is 3
for a sine graph, the amplitude is the distance up or down from the midway point. The equation to find the amplitude is (max-min) / 2.
(3 - (-3)) / 2 = 3
Help please and thank you !! ill give brainle and 20 points !
Answer:
G 33%
Step-by-step explanation:
17/52 = 0.32692307692
0.32692307692 is about 33 %
Have a nice day! :)
What is the length of segment BC?
Answer:
[tex]BC=x=(13;+\infty)[/tex]
Step-by-step explanation:
Existence of Triangle
[tex]x-(2x-24) < x-2 < x+(2x-24)\\[/tex]
[tex]13 < x > 11[/tex]
[tex]x=(13;+\infty)[/tex]
According to the histogram shown, how many hostel rooms are there?
Answer:
10
Step-by-step explanation:
look at the y axis for the answer to a question like this
Answer:
There are 25 hostel rooms.
Step-by-step explanation:
We simply need to add up the height of each bar.
3+5+8+6+2+1=25 hostel rooms
Which fraction names the shaded part of the set?
Answer:
Hello! Your answer is 1/2
Step-by-step explanation:
there are six cubes and three of them are shaded. That is half of the parallelograms.
So 1/4 wouldn't make sense because there are three shaded out of six.
1/6 doesn't make sense because since there is six in total for it to be 1/6 there needs to be 1 shaded out of six.
And finally 1/3 doesn't make sense because 1/3 would have to be two out of six shaded.
Have a wonderful day/night/afternoon and good luck my friend!