12.
If two groups of numbers have the same mean, then
a. their standard deviations must also be equal.
b. their medians must also be equal.
c. their modes must also be equal.
d. other measures of location need not be the same
13.
The Sample Mean
a. can never be negative.
b. can assume any value between the highest and the lowest value in the sample.
c. can never be zero.
d. is always smaller than the mean of the population from which the sample was taken

The angles of the parallelogram are 110° , 70° ,  110° and 70°

The sides are 39 and 27 units.

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure,

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data the parallelogram be represented as ABCD

where

The measure of ∠A = 4y°

The measure of ∠B = ( 6y + 4 )°

The measure of ∠C = 3z°

The measure of ∠D = ( 3y + 37 )°

From the parallelogram theorem , we get

The measure of ∠B = The measure of ∠D   be equation (1)

Substituting the values in the equation , we get

( 6y + 4 )°=  ( 3y + 37 )°

3y = 33

y = 11

Substituting the value of y in equation ( 1) , we get

( 6y + 4 )°= 70

The measure of ∠B  = 70°

So , the measure of ∠B = the measure of ∠D = 70°

The total internal angle = 360°

So , z° + z = 360° - 72° - 72°

2z° = 220°   be equation (3)

z = 110

And , The measure of ∠A = The measure of ∠C = 110°

The sides are ;

2n + 3 = 3n - 15

n = 18

Then ;

2n + 3 = 36 + 3 = 39 unit

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A problem is said to be infeasible if no solution exists which satisfies all the constraints.

Objective function: the expression that defines the quantity to be maximized or minimized in a linear programming model. Constraints: restrictions that limit the settings of the decision variables.

When it comes to linear programming, the solution which would be effective in satisfying all constraints in the given program in a simultaneous matter is called that of feasible programming. This is due to the fact that the program can satisfy all requirements at the same time.

Linear programming, also known as linear optimization, is a method for achieving the best result in a mathematical model with requirements represented by linear relationships. Linear programming is a special case of mathematical programming.

In linear programming, a solution that does not simultaneously satisfy all constraints is called an infeasible solution.

Therefore,

A problem is said to be infeasible if no solution exists which satisfies all the constraints.

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Answer:

Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. We may determine the scale factor by dividing these distances by 2.

Step-by-step explanation:

Answer:

vertex = (- 1, 0 )

Step-by-step explanation:

given a parabola in standard form

ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

y = x² + 2x + 1 ← is in standard form

with a = 1 and b = 2 , then

[tex]x_{vertex}[/tex] = - [tex]\frac{2}{2}[/tex] = - 1

substitute x = - 1 into y for corresponding y- coordinate

y = (- 1)² + 2(- 1) + 1 = 1 - 2 + 1 = 0

vertex = (- 1, 0 )

Multiplying each side of a false equation by the same number will result to a false equation

A false equation refers to equation where the left hand side of the equation is not equal to the right hand side of the equation.  

False equations are not useful and hence in math, converted effort are made towards getting a true equation.

A true equation refers to an equation where each side of the equation are same hence the equality sign is truly represented.

Example of true equation say 2x = 10 for x = 5

2 * 5 = 10 correct

multiplying the two sides by 3 results to

6x = 30

plugging in x = 5

6 * 5 = 30

for false equation, say 2x = 10 for x = 6

2 * 6 = 10 incorrect

multiplying the two sides by 3 results to

6x = 30

plugging in x = 6

6 * 6 = 30 incorrect hence false equation remains false

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The plane flew 95.08 miles.

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Given,

A plane veered off its course at an angle of 14°.

Plane ends up 23 miles due west of its planned destination.

By the figure,

Sin 14° = AB/AC

           = 23/AC

AC = 23/Sin 14°

AC = 23/0.2419

AC = 95.08 miles

Hence, 95.08 miles, the aero plane flew.

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a) A cross-section passing through the diagonals of opposite faces of a cube = 21 square inches.

b) A cross-section parallel to the base of a cube = 64 square inches.

c) A cross-section perpendicular to the base and passing through the diagonals of the base and opposite face of a right rectangular prism = 70 square inches.

d) A cross-section parallel to the base of a right rectangular prism = 300 square inches.

What is a cross-section?

A cross-section is a representation of a three-dimensional object as it would appear if it were sliced by a plane, revealing the internal structure of the object. The resulting shape that is formed is known as the cross-section.

a cross-section passing through the diagonals of opposite faces of a cube with edges that are 7 inches long and a diagonal that is approximately 10 inches = 21 square inches (since it will be a right triangle with legs of 7 inches and hypotenuse of 10 inches)

a cross-section parallel to the base of a cube whose edges are 8 inches long = 64 square inches (since the base will be a square with sides of 8 inches)

a cross-section perpendicular to the base and passing through the diagonals of the base and opposite face of a right rectangular prism that is 24 inches wide, 7 inches long, and 12 inches tall and measures 25 inches along the diagonal of the base = 70 square inches (since it will be a right triangle with legs of 12 inches and 24 inches and hypotenuse of 25 inches)

a cross-section parallel to the base of a right rectangular prism that is 3 inches long, 7 inches wide, and 11 inches tall = 300 square inches (since the base will be a rectangle with length of 3 inches and width of 7 inches)

Hence,

a) A cross-section passing through the diagonals of opposite faces of a cube = 21 square inches.

b) A cross-section parallel to the base of a cube = 64 square inches.

c) A cross-section perpendicular to the base and passing through the diagonals of the base and opposite face of a right rectangular prism = 70 square inches.

d) A cross-section parallel to the base of a right rectangular prism = 300 square inches.

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The diameter of the circle is 7.16 units.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

We are assuming that the area is given for a circle.

Now,

Area of a circle = πr².

Area of a circle = 40.3 units²

Now,

πr² = 40.3

r² = 40.3/3.14

r² = 12.83

r = √12.83

r = 3.58

The diameter of the circle.

= 2r

= 2 x 3.58

= 7.16 units.

Thus,

The diameter is 7.16 units.

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The five points on the graph are (0, 4), (2, 0), (4, 4) (- 2, 16) and (6, 16).

And, The graph of function y = (x - 2)² is shown in figure.

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The function is,

⇒ f (x) = (x - 2)²

Now, We have to find the value of points on the graph of function.

Here, The function is,

⇒ f (x) = (x - 2)²

Substitute f (x) = 0;

⇒ 0 = (x - 2)²

⇒ 0 = (x - 2)

⇒ x = 2

Hence, Point is, (2, 0)

Put x = 0;

⇒ f (x) = (x - 2)²

⇒ f (x) = (0 - 2)²

⇒ f (x) = 4

Hence, The point is, (0, 4)

Put x = 4;

⇒ f (x) = (x - 2)²

⇒ f (x) = (4 - 2)²

⇒ f (x) = 4

Hence, The points is, (4 4)

Put x = - 2;

⇒ f (x) = (x - 2)²

⇒ f (x) = (-2 - 2)²

⇒ f (x) = 16

Hence, The points is, (- 2, 16)

Put x = 6;

⇒ f (x) = (x - 2)²

⇒ f (x) = (6 - 2)²

⇒ f (x) = 16

Hence, The point is, (6, 16)

Thus, The five points on the graph are (0, 4), (2, 0), (4, 4) (- 2, 16) and

(6, 16).

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Answer:

0^5 = x^ 2 + 18

Step-by-step explanation:

I hope am not too late

Answer:

  197.2

Step-by-step explanation:

You want to use a table of logarithms to evaluate the product 13.81×14.28.

Logarithms turn a multiplication problem into an addition problem, along with some table look-ups. The basic idea is ...

  log(ab) = log(a) +log(b)

To find the logarithm of a number, it can help to write it in scientific notation. This puts one non-zero digit to the left of the decimal point and expresses the multiplier as a power of 10. The first attachment shows a number in scientific notation.

A log table is used to find the logarithm of the mantissa of the number in scientific notation. The result will be a decimal fraction between 0 and 1.

You start by locating the first digits of the mantissa in the left column of the table, and additional digits across the top. The second attachment shows a portion of a table of logarithms with the relevant table entries identified.

The log of 13.81 = 1.381×10¹ is found by locating 13 in the left column, and the next digit, 8, at the top of the table. The final digit, 1, is located at the top of the portion of the table labeled Mean Difference. The number in the Mean Difference column is added to the number found in row 13, column 8: 1399 +3 = 1402. This sum is the mantissa of the logarithm of 13.81. (See the third attachment for the naming we're using.)

Similarly, the log of 14.28 is found in row 14, column 2, and the value in Mean Difference column 8 is added to that: 1523 +24 = 1547.

The characteristic of each logarithm is the corresponding characteristic of the number in scientific notation. For each of these numbers, it is 1.

The logarithm of the product is the sum of these logarithms:

  log(1.381×10¹ · 1.428×10¹) = 1.1402 +1.1547 = 2.2949

The value corresponding to this logarithm is found by a procedure that is the reverse of the lookup procedure.

Our logarithm has a characteristic of 2, and a mantissa of 0.2949.

First, we locate the highest number in the table that is less than or equal to the mantissa. Here, that value is 2945, located in row 19, column 7 of the table. The value we want, 2949, is 4 more than this, so we look in the Mean Difference table on row 19 for a value of 4. That is found in column 2.

The mantissa of the antilog of 2949 is the row number (19) with the column numbers appended: 1972. The decimal point for this is located to the right of the leading digit: 1.972.

The characteristic of the antilog is the characteristic of the logarithm: 2.

Then the antilog in scientific notation is ...

  10^2.2949 = 1.972×10²

In standard form, this is ...

  1.972×10² = 197.2

The desired product is found to be 13.81×14.28 ≈ 197.2.

__

Additional comment

Different tables of logs may show the interpolation values (Mean Difference) differently. These values are intended to aid in interpolating between table values so that you can find logs and antilogs of numbers with 4 significant digits. (Larger tables let you work with more significant digits.)

In general, the number of significant digits in the values you work with will be less than or equal to the number of significant digits in the logs in the table. Here, the table has 4-digit logs, so our result, 197.2, can have at most 4 significant digits. (The actual product is 197.2068.)

When the characteristic of a number is negative, care must be taken to use correct values for the mantissa and characteristic of the logarithm. Table values are logs of numbers between 1 and 10, and are positive. The log of 0.003949 would be the sum of the negative characteristic -3 and the positive logarithm mantissa 0.5965. That sum would be -2.4035 = (-2) + (-0.4035). Since we want to keep the fractional part positive, we sometimes add and subtract a large positive number. The logarithm of 0.003949 might be expressed in this way as 7.5965-10, effectively the log of 3.949×10⁷×10⁻¹⁰.

The solution is Option D.

The proportion for the similar rectangles is given by the equation

12/4 = 24/8

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the equation will be

Let the length of the first rectangle be = L₁

Let the width of the first rectangle be = W₁

Let the length of the second rectangle be = L₂

Let the width of the second rectangle be = W₂

The two rectangles are similar ,

So , the proportion is given by

Length of the first rectangle : width of the first rectangle : : length of the second rectangle : width of the second rectangle

Substituting the values in the equation , we get

L₁ / W₁ = L₂ / W₂

12 / 4 = 24 / 8

On simplifying the equation , we get

3 = 3

Therefore , the value of A is 12 / 4 = 24 / 8

Hence , the proportion is 12 / 4 = 24 / 8

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The cost of admission for Garrett, his 2 parents, his grandmother, and his baby sister would vary depending on the county fair and their individual ages.

Cost is the monetary value of goods, services, or resources in exchange for money. It is the amount of money paid for goods or services, which includes all expenses incurred in the purchase or production of goods or services. Cost is determined by the sum of the total expenses involved in producing or acquiring a good or service. Cost is a major factor in decision-making, as it affects both the cost of production and the price of goods and services.

Generally, most county fairs charge a reasonable rate for children and seniors, and a slightly higher rate for adults.

For Garrett, he would likely qualify for the children's rate, which could range from free to around $10. For the 2 parents and the grandmother, the adult rate would likely apply, which is usually around $15. For the baby sister, some county fairs offer free admission for children under a certain age, while others offer a discounted rate.

Therefore, the total cost of admission for Garrett, his 2 parents, his grandmother, and his baby sister could range from free to around $50, depending on the county fair and the individual ages.

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Answer: answer is 20

Step-by-step explanation: 4+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=20

Answer:

∠ ABD = 20°

Step-by-step explanation:

since BD is the angle bisector of ∠ ABC , then

∠ ABD = ∠ CBD , so

∠ ABD = [tex]\frac{1}{2}[/tex] × ∠ ABC = [tex]\frac{1}{2}[/tex] × 40° = 20°

The number of hours they have worked would be = 3hours

The quantity of money each individual has would be = Eve = $48.8, While Nisha = 25.80.

A lifeguard is a trained individual who is specialised in swimming skills and whose job is to rescue drowning victims from a swimming pool or beach.

The number of hours both Eve and Nisha worked is the same = 3 hours.

The total amount earned by both at the end of the third hour = $25.80

But for Eve, the total amount of money ;

Eve has $16.00 as gift money and earns $7.00 per hour

16 + 7+ 25.80 = $48.8, While Nisha = 25.80.

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a. x-coordinate

b. y-coordinate

c. quadrant

d. intersection

e. ordered pair

f. origin

g. coordinate grid

h. y-axis

i. x-axis

j. number line

k. coordinates

l. axes (of a graph)

The axes of a graph are the two lines that define the coordinate system and divide the plane into four quadrants. These lines are called the x-axis and the y-axis. The x-axis is the horizontal line and the y-axis is the vertical line. The point where the two axes intersect is called the origin and is identified by the coordinates (0,0). The x-axis is typically used for the independent variable and the y-axis is used for the dependent variable. When plotting data on a graph, the x-axis is often labeled with the independent variable and the y-axis is labeled with the dependent variable. The axes of a graph provide a reference for determining the position of a point and are used for displaying data and drawing maps.

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Answer:

4.75

graph picture is attached.

press or click on the picture to see the whole graph

Step-by-step explanation:

put 1 where x is

y = 4 + (0.75*1)

y = 4 + .75

y = 4.75

number next to x is the SLOPE

The required rule is (x, y) → ( (1/2)x, (1/2)y) represents the dilation applied to the given triangle.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

The triangle is given in the question, as shown.

When it comes to transformations, dilation might imply growing or contracting the triangle by a scale factor.

As per the given transformation, the required rule would be

(x, y) → ( (1/2)x, (1/2)y)

Hence, the correct answer would be an option (A).

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Substituting the value of x and solving the function we get the value of y as y = 1

To evaluate the co-ordinate point (x, y) for the function

y = f(x) = -1.25x -0.25,

you need to substitute the value of x into the function and solve for y.

If x = -1,

then y = f(-1) = -1.25×(-1) - 0.25 = 1.25 - 0.25 = 1.

Therefore, the coordinate point (x, y) for the function:

y = f(x) = -1.25x - 0.25 when x = -1 is (-1, 1).

A function in mathematics is a collection of values connected by a predetermined rule or formula. The output value (also known as the dependent variable) is represented by a letter or a symbol that depends on the input value, whereas the input value (also known as the independent variable) is represented by a letter (such as x or y). Functions are frequently used to represent relationships between several numbers or to simulate real-world occurrences.

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The correct answer is C, 36.6. To solve this problem, use the distance formula to calculate the distance between the two points.

The distance formula is:

d = √((x² - x)² + (y² - y)²)

In this problem, the first point is 13 – 31i and the second point is 25 + bi. Plugging these values into the distance formula, we get:

d = √((25 - 13)² + (b - (-31))²

Simplifying and solving for b, we get:

37 = √(144 + b² + 62)

⟹ 37² = 144 + b² + 62

⟹ b² = 37² - 144 - 62

⟹ b² = 1189

⟹ b = 34.6

Therefore, the value of b is 36.6.

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Answer:

4

Step-by-step explanation:

4 on edge got it right

Answer:

not sure

Step-by-step explanation:

lolshjshebshuzhsbbsjxhgdpsizhgxe

Penelope should have added 4 to both sides instead of adding 1.

And the solution is x = (√3 - 4)/2.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

Penelope determined the solutions of the quadratic function by completing the square.

For that,

f(x) = 4x² + 8x + 1

–1 = 4x² + 8x

–1 = 4(x² + 2x)

Add 4 to both sides,

–1 + 4 = 4(x² + 2x + 1)

3 = 4(x + 2)²

3/4= (x + 2)²

x + 2 = √3/2

x = √3/2 - 2

x = (√3 - 4)/2

Therefore, Penelope should have added 4 to both sides.

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Answer:

ur mom

112213917342381

Step-by-step explanation:

The percent sales tax of the initial price of the sneakers would be = 5%

Sales tax is defined as the amount of money that a particular good is being sold after the addition of its consumption tax funds imposed by the government.

The initial amount of the sneakers = $48

The price after tax = $50.40

The increased difference from the former price = 50.40 - 48 = $2.4

The percentage increase would be;

= 2.4/48 × 100

= 240/48

= 5%.

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Step-by-step explanation:

We use soh,cah,toa

since we where giving the hypotenuse and we are looking for adjacent we use CAH.

cos35=x\12

0.852×12=x

10.23

so therefore to d nearest tenth is 10.2

The best description about the sampling distribution of means for the student's sample is mu x = 45, sigma x = 3.75, shape of distribution unknown.

Sampling distribution is defined as the probability distribution of a statistical measure which is got by the repeated sampling of a specific population.

Given that,

μ = 45 minutes and σ = 15 minutes

Sampling distribution of means for the student's sample is :

μₓ = μ = 45

σₓ = σ / √n, where n is the sample size.

σₓ = 15 / √(16) = 15 / 4 = 3.75

Now since the sample size 16 which is less than 30, shape of the distribution is unknown.

Hence the sampling distribution is, μₓ = 45, σₓ = 3.75, and the shape of distribution is unknown.

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