Are these two expressions equivalent?
2 • (3 • 7) and (2 • 3) • 7

A. Yes, because of the associative property

B. Yes, because of the distributive property

C. Yes, because of the commutative property

D. No, these two expressions are not equivalent

1. Jada's data set has a mean of 5, Diego's data set has a mean of 6, and Lin's data set has a mean of 4.

2. The data set that has the greatest variability is Lin's data set because it has the highest standard deviation of 3.6.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Question 1.

In this scenario and exercise, we would determine the mean of the three data sets based on the number of text messages sent by Jada, and Diego, and Lin over 6 days as follows;

Mean number of text for Jada = (4 + 4 + 4 + 6 + 6 + 6)/6

Mean number of text for Jada = 30/6

Mean number of text for Jada = 5.

Mean number of text for Diego = (4 + 5 + 5 + 6 + 8 + 8)/6

Mean number of text for Diego = 36/6

Mean number of text for Diego = 6.

Mean number of text for Lin = (1 + 1 + 2 + 2 + 9 + 9)/6

Mean number of text for Lin = 24/6

Mean number of text for Lin = 4.

Question 2.

In Statistics, variability is a measure of the spread of a data set. Also, we would use standard deviation to determine the variability in each data set as follows;

Standard deviation = √(1/n × ∑(xi - u₁)²)

Standard deviation for Jada = √(1/6 × [(4 - 5)² + (4 - 5)² + (4 - 5)² + (6 - 5)² + (6 - 5)² + (6 - 5)²]

Standard deviation for Jada = √(6/6) = 1

Standard deviation for Diego = √(1/6 × [(4 - 6)² + (5 - 6)² + (5 - 6)² + (6 - 6)² + (8 - 6)² + (8 - 6)²]

Standard deviation for Diego = √(14/6) = 1.53

Standard deviation for Lin = √(1/6 × [(1 - 4)² + (1 - 4)² + (2 - 4)² + (2 - 4)² + (9 - 4)² + (9 - 4)²]

Standard deviation for Lin = √(76/6) = 3.6

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~

Answer:

D. \(L > J > K\)

Step-by-step explanation:

Thus, we have to utilize the angle relationships in a triangle.

⭐The largest side is always opposite of the largest angle

⭐The smallest side is always opposite of the smallest angle

1. Identify the side lengths of triangle JKL

2. Determine which vertecies are opposite of each side length (draw the figure)

3. Determine which angles are the greatest, smallest, and in-between

4. Write what you found in #3 in terms of inequalities

∠L > ∠J > ∠K

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The length of the line segment WK for the triangle ∆WGN is equal to 13.52 rounded to the nearest hundredth.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the sine of the angle S in the right triangle ∆KSW, the angle m∠KSW = m∠HSR = 51°

line segments;

SW = SR + RW

SW = 3.6 + 13.5

SW = 17.4

sin 51° = WK/17.4 {opposite/hypotenuse}

WK = 17.4 × sin 51° {cross multiply}

WK = 13.5223

Therefore, the length of the line segment WK for the triangle ∆WGN is derived as 13.52 rounded up to the nearest hundredth, using the trigonometric ratio is sine.

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Answer: hi

Step-by-step explanation: :)

Question A is the survey that you expect to have fair results regarding attitudes about carnivals

This survey question is the most neutral and fair among the options provided. It doesn't include any leading or biased language that may influence the respondent's answer.

Option B uses the adjective "exciting," which could lead people to think positively about carnivals.

Option C brings in the unrelated factor of "traveling across town," which could negatively influence the response based on travel preference rather than attitude towards carnivals. Option D uses negative descriptors "noisy" and "overpriced," which could lead people to think negatively about carnivals.

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Answer:

A is the corect answer

Step-by-step explanation:

when solved it will equal 0=4 which is a contridition.

Answer:

B,C And D have no solution

A has infinit solutions

Given statement solution is :- a) The area of one semi-circle at one end is  58.09 square feet.

b) The area of the garden is 274.42 square feet.

c) The area in square metres is approximately 58.09 square feet.

The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.

a) To find the area of one semi-circle at one end, we need to calculate the area of a complete circle and then divide it by 2. The formula for the area of a circle is A = πr², where A represents the area and r is the radius.

Since the diameter of the semi-circle is equal to the width of the rectangular portion, which is 8.6 feet, the radius will be half of that, which is 8.6 / 2 = 4.3 feet.

Now we can calculate the area of the semi-circle:

A = (π * 4.3²) / 2

A ≈ 58.09 square feet

b) To find the area of the garden, we need to sum the area of the rectangular portion with the areas of the two semi-circles.

Area of the rectangular portion = length * width

Area of the rectangular portion = 18.4 feet * 8.6 feet

Area of the rectangular portion ≈ 158.24 square feet

Area of the two semi-circles = 2 * (area of one semi-circle)

Area of the two semi-circles ≈ 2 * 58.09 square feet

Area of the two semi-circles ≈ 116.18 square feet

Total area of the garden = area of the rectangular portion + area of the two semi-circles

Total area of the garden ≈ 158.24 square feet + 116.18 square feet

Total area of the garden ≈ 274.42 square feet

c) To convert the area from square feet to square meters, we need to know the conversion factor. Since 1 foot is approximately 0.3048 meters, we can use this conversion factor to convert the area.

Area in square meters = Total area of the garden * (0.3048)²

Area in square meters ≈ 274.42 square feet * 0.3048²

Area in square meters ≈ 25.49 square meters

Therefore, the area of one semi-circle at one end is approximately 58.09 square feet. The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.

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The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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Answer:

0.56

Step-by-step explanation:

Since 1/10 is 0.1 as a decimal you will then change it to 5.6 x 0.1 which would equal 0.56

Hope this helps :)

Answer:

5.6×1/10=0.56

Hope that helps

Have a good day :)

Answer:

c=109.96

Step-by-step explanation:

Answer:

109.96

Step-by-step explanation:

Answer:

the perimeter of cube is

28×4=112 ft

Answer:112

Step-by-step explanation: 28•4=112ft

Answer:

45:55

75:85

Step-by-step explanation:

a:b

a = zoo

b = carnival

total amount:

15 x 3 = 45

15 x 3 = 45 + 10 = 55

45:55

5 people:

15 x 5 = 75

15 x 3 = 75 + 10 = 85

75:85

The correct answer is:

C) Because the P-value is greater than α = 0.10, there is not convincing evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.

The student set up a hypothesis test to investigate whether there is evidence that the true proportion of flips for which the penny stack will land on its edge differs from 0.5. The null hypothesis is that the proportion is 0.5, and the alternative hypothesis is that it differs from 0.5.

The student obtained a standardized test statistic of z = -0.80 and a P-value of 0.2119.

To make a conclusion, the student needs to compare the P-value to the significance level α.

The significance level is given as 0.10, which means that the student is willing to accept a 10% chance of making a Type I error (rejecting the null hypothesis when it is actually true).

Since the P-value of 0.2119 is greater than α = 0.10, there is not convincing evidence to reject the null hypothesis. Therefore, the student cannot conclude that the true proportion of flips for which the penny stack will land on its edge differs from 0.5.

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Answer:

1, 3, 5

You can tell by looking that her science mean is greater than her math mean.

The higher range number means that her scores in math are more varied and spread out than her science scores.

You can tell by looking that the median scores are the same.

Step-by-step explanation:

Answer:A , C , E

Step-by-step explanation:

i got it from the dude above me

Answer:

x=9

Step-by-step explanation:

-2x+6=x-3

-1x+6=-3

-1x=-9

divide both sides by -1

x=9

hope this helps

Answer:

Step-by-step explanation:

Given system:

Substitute y and solve for x:

Find y:

Solution is:

If m = -5 or m = 3, the system of linear equations has no solution.

To determine the values of m for which the system of linear equations has no solution, we need to check the determinant of the coefficient matrix, which is:

| 3 m |

| m+2 5 |

The determinant is

=  (3 x 5) - (m x (m+2))

= 15 - m^2 - 2m

= -(m^2 + 2m - 15)

= -(m+5)(m-3)

So, for the system to have no solution, the determinant must be zero, so we have:

-(m+5)(m-3) = 0

This gives us two values of m: m = -5 and m = 3.

Thus, if m = -5 or m = 3, the system of linear equations has no solution.

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By the principle of mathematical induction, it has been proved that

\(p^3 + 11p\) is divisible by 6

What is Principle of mathematical induction?

Let the statement be given by P(n). At first P(n) is proved to be true for 1. Then it is assumed that P(n) is true for all n. If P(n) is true for (n+1) then by Principle of Mathematical induction, P(n) is true for all natural numbers

The given expression is \(p^3 + 11p\)

For p = 1

\((1)^3 + 11 \times 1\\12\)

which is a multiple of 6

Let it be true for p = m

\(m^3 + 11m\) is a multiple of 6

\(m^3 + 11m = 6k\), where k is any integer

For p = m + 1

\((m+1)^3 + 11(m+1) \\m^3+3m^2+ 3m +1+11m+11\\m^3+11m +3m^2+3m+12\\m^3+11m + 3m(m+1) + 12\)

Now,

\(m^3 + 11m\) is divisible by 6

We know that the product of two consecutive integers are divisible by 6

\(3m(m+1)\) is divisible by 6

12 is divisible by 6

\((m+1)^3 + 11(m+1)\) is divisible by 6

So it is true for p = m + 1

By the principle of Mathematical induction, it is true for all natural numbers and eventually for all integers

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The additive inverse are;

For expression;

a) 3-5

Additive inverse = - 3 - (-5)

For expression;

b) 5 - 3

Additive inverse = - 5 - (-3)

What is additive inverse?

The Property of Additive Inverse states that the summation of a number and it's Additive inverse is zero.

The expressions are;

3 - 5 and 5 - 3

Now, The Property of Additive Inverse states that the summation of a number and it's Additive inverse = 0

And, An Additive inverse of a positive integer is a negative integer and vice versa.

For example: 7 - 7 = 0

Here, The additive inverse of 7 = -7

Since, For the question above, we are asked to use the additive inverses and their properties to find the equivalent expressions.

a) 3 - 5

Hence, Additive inverse = - 3 - (-5)

                                      = -3 + 5

                                      = 2

b) 5 - 3

Hence, Additive inverse = - 5 - (-3)

                                      = - 5 + 3

                                      = - 2

So, The additive inverse are;

For expression;

a) 3-5

Additive inverse = - 3 - (-5)

For expression;

b) 5 - 3

Additive inverse = - 5 - (-3)

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Answer:

3-5:

3+(-5)

-5+3

5-3:

-3+5

5+(-3)

Step-by-step explanation:

hope this helps ya (⁠☆⁠▽⁠☆⁠)

9514 1404 393

Answer:

  about 0.299 kg/m³

Step-by-step explanation:

Density is the ratio of mass to volume.

  ρ = M/V

  ρ = (10 kg)/(4/3π(2 m)³) = 15/(16π) kg/m³ ≈ 0.299 kg/m³

Hence , 10 liters of a 10% acid solution and 50 liters of a 40% acid solution must be used.

Let the amount of 10 % acid solution be " x " and the amount  40 % acid solution be " y " .

The total volume of the resulting solution is 60 L which can be given by

      x + y = 60       .....(1)

The total acid in the resulting solution is 35 % acid solution which is given by     0.10 x + 0.40 y = 0.35(60)            .....(2)

Multiplying by 100 in equation (2) , we get

        10 x + 40 y = 2100          .....(3)

Putting x = 60 - y in equation (3) , we get

   10 ( 60 - y ) + 40 y = 2100

        600 - 10y + 40y = 2100

                 30y = 1500

                    y = 50

Putting y = 50 equation (1) , we get

      x = 60 - 50 = 10

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Answer:

  A

Step-by-step explanation:

It looks like you can make the short table ...

(recipe, ounces, servings, ounces/serving)

(A, 28, 14, 28/14 = 2.00)

(B, 9, 12, 9/12 = 0.75)

(C, 1.3, 1, 1.3/1 = 1.30)

Recipe A uses the most flour per serving of pizza.

Answer:

A

Step-by-step explanation:

To make a rigid motion, e have to maintain the relative positions and distances of the points. To accomplish this, we can't multiply f(x) or x alone.

In the first option, only f(x) is mutiplied, which makes it a non rigid motion.

In the third option, both are multiplied, by this don't garantee a rigid motion depending on the function.

I the fourth option, only x is multiplied, not a ridig motion.

In the second option, there is a substraction in x, which moves all points equally in x axis, and a sum in the f, which moves all the points equally in the y axis. So this is the right option.

Concluding, the option that transforms f(x) in a ridig motion is the second:

The angles that are 118 degrees are ∠1 , ∠3, ∠5 and ∠7.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles etc.

Therefore, let's find the angle relationship in the line and find the angles that are 118 degrees.

Hence,

∠3 = 180 - 62 = 118 degrees(angles on a straight line)

∠1 ≅ ∠3 (vertically opposite angles)

∠7 ≅ ∠3 (alternate interior angles)

∠5 ≅ ∠7 (vertically opposite angles)

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The length of the sides of EFG are 144 cm, 128 cm and 112 cm. And length of the longest side of QRS is 360 cm.

A triangle is a polygon with three sides and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is represented as ΔABC.

In Euclidean geometry, any three points, if not collinear, define a unique triangle and, at the same time, a unique plane (that is, two-dimensional Euclidean space). That is, there is only one plane containing this triangle, and all triangles are contained in one plane. If all geometries were just Euclidean planes, there would be only one plane and all triangles would be in it. But this is not the case in high dimensional Euclidean space. This article is about triangles in Euclidean geometry, specifically the Euclidean plane, unless otherwise stated.

According to the question:

Triangles EFG and QRS are similar

So EF/QR = FG/RS = EG/QS

Therefore,

The length of the sides of EFG are 144 cm, 128 cm and 112 cm.

Here, 112 is smallest side of triangle EFG  

Let, the smallest side of EFG  be EF so QR is also the smallest side of triangle QRS i.e. QR = 280 cm & other sides be assumed "x" & "y"

Now,

   112/280 = 144/x = 128/y

⇒ 2/5 = 144/x = 128/y

Taking first two, we get

x = 360 cm

Now,

Taking first and third , we get ,

y = 320 cm

So others two sides of triangle QRS are 320 cm & 360 cm.

And length of the longest side of QRS is 360 cm.

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Answer: 2/5

Step-by-step explanation:

Answer:

0 < A < 90

0 < C < 90

Step-by-step explanation:

If B is the right angle of the triangle, then the sum of the other angles, A and C, must equate 90° since all angles in a triangle sum to 180°:

A + C = 90

A and C could both be anything between 0 and 90, but they must satisfy the equation above:

0 < A < 90

0 < C < 90