Using the normal distribution, there is a 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.
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].For this problem, the parameters are given as follows:
[tex]\mu = 40, \sigma = 8, n = 16, s = \frac{8}{\sqrt{16}} = 2[/tex]
The probability that the sample mean will be within 2 points of the population mean is the p-value of Z when X = 40 + 2 = 42 subtracted by the p-value of Z when X = 40 - 2 = 38, hence:
X = 42:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (42 - 40)/2
Z = 1
Z = 1 has a p-value of 0.8413.
X = 38:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (38 - 40)/2
Z = -1
Z = -1 has a p-value of 0.1587.
0.8413 - 0.1587 = 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.
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On a necklace of 150 beads 75 beads are glass and 78 are ceramic what percent of beads are glass
Answer:
50%
Step-by-step explanation:
Divide the number of glass beads by the total number of beads:
75 glass beads / 150 total beads =
75 glass beads / 150 beads =
75/150 =
1/2 =
0.5 =
0.5 * 100% = ==> 100% = 1
50%
How many 1/12s must you add to get 1/12
Answer:
Step-by-step explanation:
One 1/12 is equal to 1/12, so you do not need to add any other fractions of 1/12 to get 1/12.
1/12 + 0 = 1/12
You can think of it in another way, if you want to add a certain number of fractions to obtain 1, you just need to add 12 of 1/12s to get 1, not one.
Find the value of X………….
The bases of a trapezium are parallel to each other.
The line x is parallel in this trapezium.
Hence,
Given two sides
If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root: a = √(c² - b²)If leg b is unknown, then: b = √(c² - a²)For hypotenuse c missing, the formula is: c = √(a² + b²)I think you should provide extra information for correct answer.
that the angles etc.
I have no idea about this.
Can anyone suggest any approach?
Answer:
Step-by-step explanation:
translate
HELP! Does the system shown always, sometimes, or never have a solution when a = b? a ≥ b? a ≤ b?
Answer: ok ok... If this is like pick one ima go for A. = b
Step-by-step explanation: i hope this helps<3
Find the equation of the line
The equation of the line is y = -3x + 16
What is the equation of a line?The general equation of a line is expressed as;
y = mx + c
Given that;
y is a point on the y-axism is the slope of the linex is a point on the x -axisc is the intercept of the line on the y-axisFrom the diagram shown, the coordinates of the line is expressed as;
(3, 7) and (2.5, 3)
The intercept. c = -3
Substitute the values
7 = -3(3) + c
expand the bracket
7 = -9 + c
collect like terms
c = 7 + 9
c = 16
The equation of the line is then given as;
y = -3x + 16
Hence, the equation is y = -3x + 16
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Is A ={ x x 2 )= 4 and 3x 9 an empty set justify your answer?
The value of 'x' is not same in both cases, so this is a empty set.
How to calculate A={x x 2}=4 and 3*9 an empty set?step1
Because here square of element of set should be 4 then element should be 2 or -2 but when 2 or -2 multiplied by 3 gives 6 or - 6 which is not equal to 9. So, no element exists which can satisfy both conditions.
A={x x 2}=4 and 3x=9 is not empty set because there is no element we can say that is an empty set but there is an element, so it is not an empty set.
step2
X^2=4
Therefore only 2's square is 4
In first equation X=2
But in second equation
3x=9
Therefore here X=3
One variable has only one value
Therefore it is an empty set
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Mason spent $50 on school supplies. after buying 12 erasers for $17.88, he had $32.12 left over. How much did each eraser cost? Please help I need my grades up!
Answer:
$1.49
Step-by-step explanation:
17.88/12 = 1.49
Answer:
each eraser cost $1.49
Step-by-step explanation:
take how much it cost 17.88
divide by how much you have 12
get how much one unit or 1 of what you have
17.88/12=1.49
a farmer planted 320 acres of one variety of wheat and one160 acres of a second variety. He also planted 40 acres of milo, and he has 440 acres that will lie fallow (not be planted) this year. What percent of his land di he plant in wheat? Round to the nearest percent
Percent of land planted with wheat is 50% of total land.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Given,
a farmer planted
320 acres of one variety of wheat
160 acres of a second variety of wheat.
He also planted 40 acres of milo,
and he has 440 acres that will lie fallow
Total land farmer has = 320 + 160 + 40 + 440 = 960 acres
Land planted with wheat = 320 + 160 = 480 acres
Percentage of land with wheat
= (land planted with wheat/ total land)× 100
= 480/960 × 100
= 0.5 × 100
= 50%
Hence, 50% of total land is planted with wheat.
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Does standard form have to be between 1 and 10?
No, standard form does not have to be between 1 and 10. Standard form refers to a way of writing a number in which the number is expressed as a decimal between 1 and 10, multiplied by a power of 10.
THE STANDARD FORMStandard form, also known as scientific notation, is a way of writing a number that is a product of a decimal between 1 and 10, and a power of 10. The decimal part is called the coefficient, and the power of 10 is called the exponent.
For example, 12,000 can be written in standard form as 1.2 x 10⁴. Here, the coefficient is 1.2 (a decimal between 1 and 10) and the exponent is 4, indicating that the number is being multiplied by 10 raised to the power of 4 (10,000).
It is important to note that standard form is not limited to positive numbers and decimals between 1 and 10. A negative number or decimal less than 1 can also be written in standard form, but it would be multiplied by a power of 10 that is less than 1.
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what is the exact length of third side
Answer:
Step-by-step explanation:
The sum of the squares of the shorter sides is equal to the square of hypotenuse!
What is the additive inverse of _2 9?
The additive inverse of 2 9 is -2 9. This means that if you add -2 9 to 2 9, the result will be zero. This is because any number plus its opposite will equal zero.
2 9 + (-2 9) = 0
20 + (-20) = 0
The additive inverse of a number is the opposite of that number. This means that the inverse of 2 9 would be -2 9. When you add a number and its inverse together, the result is always zero. This is because any number plus its opposite will equal zero. For example, if we take 2 9 and add it to its inverse -2 9, the result will be 0. This is because 20 + (-20) = 0. The same concept can be applied to other numbers as well. For instance, if we take 3 4 and add it to its inverse -3 4, the result will be 0 because 34 + (-34) = 0. This shows that the additive inverse of a number is the opposite of that number, and when a number and its inverse are added together, the result is always zero.
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Leo designs a banner for class elections. His banner has 3 congruent circles glued on a rectangular length of butcher paper. The circles touch the edges of the paper and do not overlap. VOTE FOR LEO! If the butcher paper is 24 inches long, what is the area of one circle? Use 3 for pi
Im having issues with this question does anyone know this question STEP BY STEP
The area of one circle is 48 in² if the butcher paper is 24 inches long.
What is area?
The area of a two-dimensional figure is the total area it takes up. It is the quantity, in other words, that counts the number of unit squares that cover the surface of a closed figure.
Square units—commonly expressed as square inches, square feet, etc.—are the accepted unit of area.
Given that:
3 congruent circles are perfectly fitted in the rectangular banner of length 24 inches,
⇒ diameter of each circle = length of rectangular banner/3
⇒ d = 24/3
⇒ d = 8
⇒ r = 8/2
⇒ r = 4
Area of circle, A = π r²
A = 3× 4 × 4 (used pi as 3 as instructed in the question)
A = 48 in²
Thus, the area of one circle is 48 in² if the butcher paper is 24 inches long.
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y -1/4 x = -1
y - 2 = 4x
A no solution
B infinite solutions
C one solution
Answer:
x=-4/5, y=-6/5. (-4/5, -6/5).
Step-by-step explanation:
y-1/4x=-1
y-2=4x
--------------
y=4x+2
4x+2-1/4x=-1
4x-1/4x=-1-2
16/4x-1/4x=-3
15/4x=-3
x=-3/(15/4)
x=(-3/1)(4/15)
x=-12/15=-4/5
y-2=4(-4/5)
y-2=-16/5
y=-16/5+2
y=-16/5+10/5
y=-6/5
Are triangles ABC and XYZ similar?
Therefore ,as a result, ABC is equivalent with XYZ, which is the answer to the triangle problem that was presented.
Tell us about the triangle.Given its three sides and three vertices, a triangular is a polygon. This geometric shape is fundamental. Triangle ABC is a triangle that has the points A, B, and C as its corners. In geometric shapes, when four pieces are not collinear, a single plane and triangle are obtained. Polygons include triangles since they have three sides and a top right corner.
Here.
Therefore,
∠ A = ∠X because ABC is identical with XYZ.
∠B and ∠Y have the same meaning.
∠Z equals ∠C, and
Line ab has the same value as xy.
Line bc and yz are interchangeable.
Line ac corresponds to xz.
Cpct was employed to find a solution.
Triangle segments that are congruent are matched.
As a result, ABC is symmetrical with XYZ is the answer to the presented triangle problem.
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Complete question is: Are triangles ABC and XYZ similar?
Please help me answer this question.
Verify the identity for trigonometric function attached. Thanks
Step-by-step explanation:
[tex] \frac{ \cot(x) - 1 }{ \cot(x) + 1} \\ \cot(x) = \frac{1}{ \tan(x) } \\ (\frac{1}{ \tan(x) } - 1) \div ( \frac{1}{ \tan(x) + 1} ) \\ multiply \: though \: by \: \tan(x) \\ \tan(x) \times ( \frac{1}{ \tan(x) } - 1 ) \div \tan(x) \times ( \frac{1}{ \tan(x) } + 1) \\ = 1 - \tan(x) \div 1 + \tan(x) \\ \frac{ \cot(x) - 1}{ \cot(x) + 1 } = \frac{1 - \tan(x) }{1 + \tan(x) } [/tex]
Convert this equation into standard form
The equation into standard form is x = 4
How to convert the equation into standard formFrom the question, we have the following parameters that can be used in our computation:
0 = x - 4
A linear equation in standard form is represented as
Ax + By = C
So, we have
0 = x - 4
Rewrite as
x - 4 = 0
Add 4 to all sides
x = 4
hence, the equation is x = 4
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Kaj signed up for a streaming music service where there's a fixed cost for monthly
membership and a cost per song downloaded. Her total cost per month is given by
the equation c = 1.5x + 6.99, where X represents the number of songs she
downloads and c represents the total cost, in dollars and cents. What could the
number 1.5 represent in the equation?
In the equation for total cost c = 1.5x + 6.99, 1.5 represents the cost of per song downloaded.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The equation for total cost per month is c = 1.5x + 6.99.
Where x represents the number of songs Kaj downloads and c represents the total cost, in dollars and cents.
So, c and x are variable components of the equation.
There are only two fixed components in the equation 1.5 and 6.99.
Since number of songs downloaded x is multiplied by 1.5, so 1.5 is the cost of per song downloaded.
Hence, 6.99 becomes the fixed monthly membership cost of the music service.
Therefore, 1.5 is cost of per song downloaded.
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Use the Distributive Property to expand 6(-4x + 3y)
Answer: -24x+18y
Step-by-step explanation:
6(-4x+3y)
=6*(-4x)+6*(3y)
=-24x+18y
Answer:
6(-4x + 3y)
Step-by-step explanation:
-24x + 18y
6(-4x + 3y)
y varies inversely with x. Write an equation relating x and y.
Then find the indicated value. Show your work.
y = 16 when x = 27. Find the value of y when
x = 18.
y = 3.2 when x = 30. Find the value of x when
y = 8.
The equation of variation is xy = 96. The value of y when x = 18 is 16/3 and the value of x when y = 8 is 12.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
y inversely varies as x.
That means, y ∝ 1/x.
So, y = kx, where k constant of variation.
Then, x × y = k
When y = 16, x = 6.
k = 6 × 16 = 96
So, the equation of variation is xy = 96.
When x = 18,
18y = 96
⇒ y = 96/18
⇒ y = 16/3
When y = 3.2,
3.2(30) = 96
When y = 8
8x = 96
⇒ x = 12
Therefore, the values are y = 16/3 and x = 12.
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Best Buy is selling a 62" TV for $1,250. The TV is on sale for 15% off and there is a 6% sales tax. What is the final cost of the TV? Please help me I don't know how to do it
Answer:
final cost of 42" TV after deducting 15% discount and adding 6.5% sales tax will be $1163.56
Step-by-step explanation:
final cost of 42" TV after deducting 15% discount and adding 6.5% sales tax will be $1163.56
The final cost of the TV would be $1,063.50.
To calculate this:
First, calculate the discount by multiplying the original price of the TV ($1,250) by 15% (0.15). This equals $187.50.
Subtract the discount from the original price of the TV ($1,250 - $187.50 = $1,062.50)
Next, calculate the sales tax by multiplying the price after the discount ($1,062.50) by 6% (0.06). This equals $63.75
Finally, add the sales tax to the price after the discount ($1,062.50 + $63.75 = $1,063.50)
I have a tape diagram it is, there is 1 bus for every 32 students on a field trip. there are 96 students on a field trip how many buses are needed?
Answer: 3
Step-by-step explanation:
32 x 3 = 96
Find the measures of an exterior angle and an interior angle given a regular polygon with 14 sides. Round to the nearest tenth, if necessary.
Answer:
The sum of the exterior angles is 360. 360/14 = 25.7 would be the measure of one exterior angle.
The sum of the interior angles is 1260. 1260/14 = 154.3 would be the measure of on interior angle.
Step-by-step explanation:
(n-2)180
n is the number of sides
(14-2)180
12(180) 1260
This is the sum of the interior angles of the polygon.
1260/14 = 154.3 Is the measure of one angle.
Can 7 cm 8 cm 11 cm form a triangle?
No, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side for a triangle to be formed.
In order to determine whether 7 cm, 8 cm, and 11 cm can form a triangle, we must first consider the Triangle Inequality Theorem. This theorem states that the sum of any two sides of a triangle must be greater than the length of the third side in order for a triangle to be formed. Therefore, in order for 7 cm, 8 cm, and 11 cm to form a triangle, the sum of any two sides must be greater than 11 cm. Since
7 cm + 8 cm = 15 cm,
which is less than 11 cm, 7 cm, 8 cm, and 11 cm cannot form a triangle.
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solve the compound inequality n+2≤−5 and n+6≥−6
Answer:
-12<=n<=-7
Step-by-step explanation:
Someone please help me !
Answer:
x² + 6² = 17²
6² + x² = 17²
Step-by-step explanation:
Pythagoras Theorem defines the equation of opposite² + adjacent² = hypotenuse². To make it simple, it's basically base² + height² = slope². Therefore:
[tex] \displaystyle{ {x}^{2} + {6}^{2} = {17}^{2} }[/tex]
Or you can also form as
[tex] \displaystyle{ {6}^{2} + {x}^{2} = {17}^{2} }[/tex]
Therefore, there are two correct answers here.
What value is equivalent to (8+2)2 + (6 − 4) × 3?
A.106
B.110
C.6
D.94
E.18
Answer:
A. 106
Step-by-step explanation:
Use the correct order of operations.
(8 + 2)² + (6 − 4) × 3 =
= 10² + 2 × 3
= 100 + 6
= 106
Tell whether the pairing is a function.
The relationship in this problem is a function, as each input is mapped to a single output.
When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
From the table, we have that:
The input 1 is mapped to the output 20.The input 2 is mapped to the output 21.The input 3 is mapped to the output 21.The input 4 is mapped to the output 22.Each input is mapped to a single output, hence the table represents a function.
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Help quick!
The figure is not drawn to scale.
Answer:
<f = 132°
Step-by-step explanation:
360 - 56 - 106 = f + g
f = 2g
198 = 3g
g = 66
f = 2g
f = 2(66)
f = 132
if theta is an angle in standard position and it’s terminal side passes through the point (21, -20), find the exact value of cot theta in simplest radical form
For the given data, ∅ is the given angle in standard position, terminal side passes through (21, -20) then the exact value of cot ∅= ( - √41/ 20 ) in simplest radical form.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
For the given angle ∅ (theta) in standard position:
Terminal side of ∅ is passes through the point ( 21, -20 )
( 21, -20) represents ∅ is in the second quadrant.
In second quadrant sine in positive and cosine is negative.
Base is negative and altitude is positive.
Base = 21
Altitude = -20
Using Pythagoras theorem,
Hypotenuse² = (21)² + (-20)²
⇒ Hypotenuse = √41
Cot ∅ = - √41/20 ( simplest radical form )
Then the exact value of
Cot ∅ = ( - √41/ 20 ) in simplest radical form.
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