A company claims that the mean weight per apple they ship is 120 grams with a standard deviation of 12 grams. Data generated from a sample of 49 apples randomly selected from a shipment indicated a mean weight of 122. 5 grams per apple. Calculate and interpret a 95% confidence interval for the mean weight per apple.

Answer:

2.5 dhs

Step-by-step explanation:

5% of AED50

50x5/100=250/100

=AED2.5

Answer: A range of values, created using sample, within which population parameter has a certain probability of occurring.

Reason: E.g. P(a<x>b) = 0.95

confidence interval is A range of values, is created using a sample, within a population parameter that has a certain probability of occurring.

A sampling method's degree of certainty or uncertainty is measured by confidence intervals. In statistics, the probability that a population parameter will fall between a set of values for a certain percentage of the time is referred to as a confidence interval. Confidence intervals that contain either 95% or 99% of expected observations are frequently utilized by analysts. To comprehend the statistical significance of their estimates, inferences, or predictions, statisticians and other analysts employ confidence intervals.

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The 95% confidence interval for the average apple weight is (119.14, 125.86).

An apple typically weighs 120 grams with a 12-gram standard deviation, according to one manufacturer. The average weight of an apple was 122. 5 grams, according to statistics created from a sample of 49 apples that were randomly chosen from a shipment.

Let, n = 49

x = 122.5 

σ = 12

To calculate and interpret a 95% confidence interval for the average apple weight, use the formula;

⇒ (x ± 1.96*σ/√n)

⇒ (122.5 ± 1.96*12/√49)

⇒ (119.14, 125.86)

Consequently, the average apple weight has a 95% confidence interval of (119.14, 125.86).

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Answer:

x = 8

Step-by-step explanation:

the exterior angles of a triangle sum to 360° , that is

20x + 8x + 17x = 360

45x = 360 ( divide both sides by 45 )

x = 8

Answer:

Refer to photo for drawing

Step-by-step explanation:

1. Draw the x y plane

2. Identify -8, -1, 0 on x plane

3. Identify -4, -3, -2 on y plane

4. Mark the intersection point (-8,-4) with x

5. Mark the intersection point (-1,-3) with x

6. Mark the intersection point (0,-2) with x

7. Draw a straight line through the x mark

The simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) in scientific notation is - 7.83 x 10^-8. Option A is correct.

We will solve the given expression using laws of exponents.

Some laws of exponents are:

We are given:

(3.7 x 10^-9) - (8.2 x 10^-8)

= (3.7 x 10^(-1 -9)) - (8.2 x 10^-8)

= (3.7 x 10^-1 x 10^-8) - (8.2 x 10^-8)

= (0.37 x 10^-8) - (8.2 x 10^-8)

= (0.37 - 8.2) x 10^-8

= - 7.83 x 10^-8

So, the simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) is - 7.83 x 10^-8.

Thus, the simplified value of (3.7 x 10^-9) - (8.2 x 10^-8) in scientific notation is - 7.83 x 10^-8. Option A is correct.

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Answer:

Y= -7

X= 4.4

Step-by-step explanation:

Y= 2 - ( x-3)^2

When x= 0

Y= 2- ( 0-3)^2

Y will equals -7

When y = 0

(x-3)= √2

X = 4.4

Answer:

-x-12

Step-by-step explanation:

1/2x+6

first divide by -1/2 or multiply by -2(its the reciprocal)

-2(1/2x+6)

-2*1/2x+6*-2

-x-12

The domain of the composite function is  - x - 3 ≥ 0 , x ≤ -3 .

The correct answer is (B).

Given,

In the question:

Over the set of real numbers.

F(x) = -x-3, G(v) = √y

G(F(x)) = √√-3-x

To find the domain of the composite function.

Now, According to the question:

Based on the given conditions:

The domain of F(x) = -x -3 is all real numbers.

The domain of

G(v) = √y is y ≥ 0

{The relationship of the domain of a composite function and the original functions}

So, - x - 3 ≥ 0 , x ≤ -3

Hence,  The domain of the composite function is  - x - 3 ≥ 0 , x ≤ -3 .

The correct answer is (B).

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Answer: 58

Step-by-step explanation:

First you substitute the values, so

4-9*-6

Then you solve using order of operations

Answer:

58

Step-by-step explanation:

y-9a

Let a = -6 and y=4

Substitute the values in

4 -9(-6)

Multiply first

4 + 54

Add

58

The linear equation of the given points (2, -2)  and (0, -1) is y = (-1/2)x - 1

The first point = (2, -2)

The second point = (0, -1)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line m = (-1 - -2) / (0 - 2)

= -1+2 / -2

= 1 / -2

= - 1/2

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

The point slope form  is

[tex]y-y_1=m(x-x_1)[/tex]

Substitute the values in the equation

y - -2 = (-1/2) (x-2)

y + 2 = -1/2 x + 1

y = (-1/2)x + 1 -2

y = (-1/2)x - 1

Hence, the linear equation of the given points (2, -2)  and (0, -1) is y = (-1/2)x - 1

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[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{18}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{7}}} \implies \cfrac{ -4 }{ -4 } \implies 1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{18}=\stackrel{m}{ 1}(x-\stackrel{x_1}{7}) \\\\\\ y-18=x-7\implies {\Large \begin{array}{llll} y=x+11 \end{array}}[/tex]

Answer:

the one that looks like a paper clip

Step-by-step explanation:

Using Rank theorem , the dimensions of col A and Null A add up to the number of colmns in A. It is true statement.

The rank of matrix A denoted as rank(A) is the dimension of the column space Col(A).

The nullity of matrix A written as nullity(A) is the dimension of the null space Nul(A)

Rank Theorem:

If A is a matrix with n columns, then

Rank (A) + nullity (A) = n

In other words we can say that

dim (Col(A) ) in column space + dim (Nul(A)) in empty space = total number of columns in A

The rank theorem is really important theorem.

It is gives a strong relationship between the Null space ( all possible vector x such that Ax = 0) and the column space (the set of vectors b matching Ax=b) explain the two main objectives. The more freedom we have for choosing x, the less freedom we have for choosing b, and vice versa.

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In comparison to her classmates, Kay did better in quiz 2.

According to the question,

Kay scored 15 on Quiz 1 which had a mean of 12 and a standard deviation of 2.4

= Z-score = 15 - 12/ 2.4 = 1.25

She scored 14 on Quiz 2 which had a mean of 11 and a standard deviation of 2

= Z-score = 14 - 11/ 2 = 1.5

As we can see the Z-score of Quiz 2 is more than the Z-score of Quiz 1 hence Kay did better in Quiz 2.

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∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel.

A pair of angles formed on each side of the transversal when it interacts with two parallel lines are known as consecutive angles. The angles in the same region (either interior or exterior) on each of the parallel lines form consecutive angles pairs and are supplementary.

Given that, in a race, all members of a rowing team should keep the oars parallel to produce maximum speed, and m∠1 = 6x + 18 and

m∠2 = 9x+12, and x = 10.

Putting the value of x, we get,

m∠1 = 6x + 18 = 6*10 + 18 = 78°

m∠2 = 9x+12 = 9*10 + 12 = 102°

m∠1 + m∠2 = 180°

Therefore, ∠1 and ∠2 are consecutive angles pairs.

We can prove that oars are parallel by converse of consecutive angles theorem.

Hence, ∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel

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Answer:

ten thousands

Step-by-step explanation:

Ten thousandths are in one hundredth.

What is fraction?

Fractions represent parts of a whole. In mathematics, fractions are represented as numbers that define part of a whole. A fraction can be a part or subset of any quantity of a whole, and a whole can be any number, value, or thing.

All fractions consist of a numerator and a denominator, separated by horizontal bars called fraction bars.

The denominator indicates the number of parts into which the whole is divided. Placed at the bottom of the break below the break bar. The

counter indicates how many sections of the fraction are displayed or selected. Placed at the top of the break above the break bar.

As we know ,

one hundredth is  1/100

one thosandth is 1/1000

But now , 10 × 1/1000 = 1/100

This means that there are 10 thousandths in one hundredth.

Hence, ten thousandths are in one hundredth.

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Circumcenter is equidistant from the vertices, perpendicular bisectors will cross. Incentre is equidistant from the sides. Where the angle bisector cross incenter

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

We have to choose the properties of circumcenter.

Circumcenter is equidistant from the vertices.

It is equidistant from the three vertices of the triangle, and thus you can construct a circle centered at the circumcenter and circumscribing the triangle.

and perpendicular bisectors will cross.

We have to choose the properties of incenter.

Incentre is equidistant from the sides.

Where the angle bisector cross incenter

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Answer:

a] 5 dogs

b] 16 dogs

Step-by-step explanation:

        The minimum number of dogs that could have a mass of more than 26 kg is 5. This is because dogs with a mass of 30 ≤ x ≤ 40 have a frequency of 5. The dogs in the 20 ≤ x ≤ 30 range could be more than 26 kg, but they could also be less than 26 kg, so these are not included in the minimum.

        The maximum number of dogs that could have a mass of 26 kg is 16 because both dogs in the 30 ≤ x ≤ 40 range (5) and 20 ≤ x ≤ 30 range (11) could weigh more than 26 kg. 11 + 5 = 16, giving us our answer for the maximum.

Answer:

The measure of angle 1=52

The measure of angle 2=58

The measure of angle 3=31

Step-by-step explanation:

The measure of angle 1 is 52 because the angle out of the triangle is 128. The measure of angle 1 plus 128 equals 180. Using this info you could do 180-128, which equals 52. The measure of angle 1 equals 52.

The measure of angle 2 is 58 because I already know 2 of the values of the triangle, in which Angle 2 is also in. One triangle adds up to 180. The values of the other 2 angles are 52 and 70. Using this information I can use the equation 52+70+x=180, which you then simplify to 122+x=180. X equals 58. The measure of angle 2 equals 58

The measure of angle 3 is 31 because the angle out of the triangle is 70. The missing angle plus 70 equals 180. Using this info I could do 180-70. The missing angle is 110. There is already one given angle, and I have figured out the other, using this info I can now finally find the measure of angle 3. I can find this out by using the equation 110+39+x=180. You would then simplify the equation to 149+x=180. X equals 31. The measure of angle 3 equals 31.

The system of equations is:

x + y = 20

2x + 3y  = 48

And its graph can be seen in the image at the end.

Let's define the variables:

Each bicycle has 2 wheels, each tricycle has 3 weels, and we know that there are 20 boxes and 48 wheels, then the system of equations is:

x + y = 20

2x + 3y = 48

To solve the system graphically we just need to graph both lines on the same coordinate axis and see at which point do the lines intersect, the graph is below.

The solution is x = 12, y = 8.

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Answer:

I don't know if its right.

Ans:1.215

Answer: False, adding two negatives does not make a bigger number. I know this because when adding the two negatives, the absolute value will get bigger. However, the value of the number gets smaller.

The exact values are sin2u=36/25, cos2u=-3.142 and tan2u=sin2u/cos2u

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

sin u=3/5, 0 < u < pi/2

tan u= 1/2, pi < u < 3pi/2

We need to find sin 2u, cos 2u, and tan 2u

sin2u=2sinucosu

tanu=sinu/cosu

1/2=3/5/cosu

cosu=3/5×2

cosu=6/5

So sin2u=2(3/5)(6/5)

sin2u=36/25

cos2u=1-2sin²u

=1-2(36/25)²

=1-2(1296/625)

=1-4.14

=-3.142

cos2u=-3.142

tan2u=sin2u/cos2u

Substitute the values of sin2u and cos2u

sin2u=36/25/(-3.142)

=1.44/-3.142

=-0.458

Hence, the exact values are sin2u=36/25, cos2u=-3.142 and tan2u=sin2u/cos2u

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Answer:

Step-by-step explanation:To determine if an ordered pair is a solution to a system of two equations, we substitute the values of the variables into each equation. If the ordered pair makes both equations true, it is a solution to the system.

Fatima paid $129.95 for pallet of grass cost and $ 76.20 for delivery. The total amount Fatima paid is $725.95.

Pallet Grass Cost: The quality and type of grass you want will impact the overall cost of sod. Most homeowners pay between $150 and $450 per pallet of sod for their yards or an average of $300. When it comes to square footage, sod costs between $0.35 and $0.85, or an average of $0.60 per square foot.

Given in the question:

Number of Pallets = 5

Cost of each pallet = $129.95

Total amount spend on Pallets

= Number of Pallets × Cost of each pallet

= 5 × $129.95  = $ 649.75

Also given;

Amount spend on Delivery = $76.20

Total Amount Paid by Fatima

= Total amount spend on Pallets + Amount spend on Delivery

=  $649.75 + $76.20

= $ 725.95

Hence Fatima paid a total amount of $725.95.

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