A principal of a school with 484 students collected information about how many of the students wear glasses complete the two way frequency table. Plss help I didn’t understand how to do it!!

The sample size for the Domestic cars should be around 129 and the sample size for the Foreign cars should be around 135.

To determine the sample size, one can use the formula n = (z^2 * p * (1-p)) / (E^2) where n is the sample size, z is the z-score for the desired level of confidence (in this case, 98% or 2.33), p is the estimated proportion of successes (assumed to be 0.5), and E is the margin of error.

Using the above formula, n = (2.33^2 * 0.5 * (1-0.5)) / (7^2) = 129. For the foreign cars, n = (2.33^2 * 0.5 * (1-0.5)) / (8^2) = 135. These sample sizes will allow the car expert to estimate the mean number of days to sell for each group of cars with a margin of error of seven days for domestic cars and eight days for foreign cars, at a 98% confidence level.

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To graph the transformation of a logarithmic function, you will need to start by plotting the parent function. To graph the transformation of a logarithmic function, you should start by plotting the parent function and then apply the transformation by shifting, stretching, shrinking, and reflecting the graph.

This can be done by plotting points on the graph for a few different values of x. Once the parent function is graphed, you can then apply the transformation to the parent function. This can be done by shifting the graph up or down, stretching or shrinking it, and reflecting it across the x-axis or y-axis.

To graph the transformation of a logarithmic function, you should start by plotting the parent function and then apply the transformation by shifting, stretching, shrinking, and reflecting the graph.

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Standard form of polynomial  [g(x)-f(x)]  is   2[tex]x^{4}[/tex] -3/5[tex]x^{2}[/tex]+2x+7.

Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of the equation in this format is rather simple (x and y).

A polynomial example is 4 x 3 + 2 x 2 3 x + 1. There are four terms: 1, 4 x 3, 2 x 2, and 3 x. The coefficients are the numbers that are written in front of each variable in a phrase. Because those numbers appear in front of a variable, 4, 2, and -3 are coefficients.

polynomial [g(x)-f(x)] = 8+ 1/5[tex]x^{2}[/tex]+3x+2 -( -2[tex]x^{4}[/tex] -1 + 4/5[tex]x^{2}[/tex] -x )

                                   2[tex]x^{4}[/tex] -3/5[tex]x^{2}[/tex]+2x+7

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The line crosses the Oy axis in A(0,  y), so x=0 and we have:

y + 4=11 ⇒ y = 7

Y is equal to 7 at the line's intersection with the y-axis.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

The point where the line crosses the y-axis is when x = 0. To find the value of y at this point,

we can substitute x = 0 into the equation and solve for y:

y + 4 = 6(0) + 11

y + 4 = 11

y = 11 - 4

y = 7

Therefore, the value of y at the point where the line crosses the y-axis is 7.

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∠u,∠x→ Alternative interior angle.

∠w,∠s→Corresponding angle

∠t,∠y→Alternative exterior angle.

∠s,∠t→Supplementory angle

∠w,∠y→Supplementory angle

∠t,∠x→Corresponding angle

∠w,∠z→vertical angle

∠v,∠w→ Alternative interior angle.

∠v,∠z→Corresponding angle

∠s,∠z→Alternative exterior angle.

∠t,∠u→Vertical angle

∠w,∠x→Supplementory angle

∠w,∠s→Corresponding angle

∠s,∠v→Vertical angle

∠x,∠z→Supplementory angle

What is the supplementary angle?

When two angles add up to 180 degrees, they are called supplementary. To avoid confusion, remember that s comes after c in the alphabet and that 180 is greater than 90.

supplementary angles:

∠x,∠z; ∠w,∠x; ∠w,∠y;∠s,∠t

Corresponding angles:When two parallel lines intersect any other line, corresponding angles are formed in matching corners or corresponding corners with the transversal (i.e. the transversal). Angles p and w, for example, are the corresponding angles in the figure below.

Corresponding angles are ∠w,∠s; ∠v,∠z; ∠t,∠x.

Vertical angles: Vertical angles are the angles formed when two lines intersect. The term "vertical" in this context refers to the fact that they share the same Vertex (corner point), rather than the usual meaning of up-down.

∠s,∠v; ∠t,∠u; ∠w,∠z

Alternate interior angles :When two lines are cut by a third line, a transversal, the term alternate interior angles is frequently used. If k and l are parallel, then the pairs of alternate interior angles are congruent, according to the Alternate Interior Angles Theorem.

Alternate Interior Angles: ∠u,∠x; ∠v,∠w.

Similarly alternative exterior angles are: ∠s,∠z; ∠t,∠y.

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So, the volume of the can in cubic centimeters is 61.99 cm^3. If we round to the nearest tenth, the volume of the can is 62 cm^3.

A can of soda can be modeled as a right cylinder, which is a three-dimensional geometric shape with two circular bases that are connected by a curved surface. The volume of a cylinder can be calculated using the formula:

V = πr^2h

Where V is the volume, π is a constant (approximately equal to 3.14), r is the radius of the base and h is the height of the cylinder.

Given that the radius of the can is 2.6 cm and the height is 9.2 cm, we can substitute these values into the formula:

V = π (2.6 cm)^2 (9.2 cm)

To get the area of the base we need to square the radius and multiply by π, and then multiply it by the height to get the volume.

V = π * 6.76 * 9.2 = 61.99 cm^3

So the volume of the can in cubic centimeters is 61.99 cm^3. If we round to the nearest tenth, the volume of the can is 62 cm^3. This means that the can can hold 62 cubic centimeters of liquid.

It's worth noting that this is an approximation and the real value of π is not 3.14. Also, this answer is based on the assumption that the can is a perfect cylinder with no other gaps or spaces.

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By understanding the definition of the statistics method, it can be concluded that 57% is an example of the result of inference statistics.

In statistics, the population is defined as the entire research subject, while the sample is a representative or part of the population, which has the same characteristics that can describe and represent the entire population.

There are two methods used to perform data analysis:

a. Descriptive statistics: an analytical method used to describe the characteristics of data. The end result of this method is in the form of tables, charts, graphs, etc.

b. Inference statistics: an analytical method used to draw conclusions about a population based on a sample. The end result of this method is in the form of a possibility or probability and is expressed in percent units.

If we look at the given problem, it is stated that "in a sample of 1,600 registered voters, 912 or 57% approve of the way the president is doing his job"

By understanding the definition of descriptive and inference statistics, it can be concluded that 57% is an example of the result of Inference statistics.

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The composite figure has an area of 26 square units.

In this question we find a composite figure formed by the sum of the areas of two right triangles and rectangles, whose area formulas are shown below:

Right triangle

A = 0.5 · w · l

Rectangle

A = w · l

Where:

Now we proceed to determine the area of the composite figure:

A = 0.5 · 3 · 1 + 3 · 1 + 0.5 · 3 · 1 + √10 · √40

A = 1.5 + 3 + 1.5 + 20

A = 26

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To make a 360mL mixture that contains 9% vinegar, use 240mL of the first brand and 120mL of the second brand.

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

You want to set up an equation that will match the word problem. Let's call the amount of the first brand, F, and the amount of the second brand, S.

We want the total mixture to be 360mL so: F + S = 360

Also, you want the total mixture to contain 9% vinegar so:

.08F + .11S = .09(360)

Now, we can solve the system of equations using substitution.

F + S = 360

.08F + .11S = .09(360)

F = 360 - S      [solve 1st equation for F]

.08(360 - S) + .11S = .09(360)     [substitute into 2nd equation]

28.8 -.08S +.11S = 32.4

.03S = 3.6

S = 120

F + 120 = 360     [substitute answer for S back into original equation]

F = 240

Answer: To make a 360mL mixture that contains 9% vinegar, use 240mL of the first brand and 120mL of the second brand.

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A right angle is an angle that measures exactly 90 degrees.

A right angle is an angle that is exactly equal to 90 degrees (or π/2) in measure.

We can see many real-life examples of the right angles in our daily life. For example, the corner of a book, edges of the cardboard, etc.

Any shape that is a square or a rectangle, will have its corners equal to 90 degrees or right angle.

A right angle is hence called a 90-degree angle.

In geometry, the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle is known as an angle.

Angles created by two rays lie in the plane that contains the rays.

The intersection of two planes also forms angles.

The angle is also used to designate the measure of an angle or a rotation.

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The necessary information which is missing from this formula page is none of the above and is denoted as option D.

This is referred to as a sheet or page which helps a student recall formulas so that they can solve test items independently.

In the example given,  t-time V = d/t d-distance V = distance/time v-velocity and the meaning of their respective abbreviations were given for better explanation. We should note that a formula page lacks numerical values as only the formula for the parameter is given is contained which is why none of the above was chosen as the correct choice.

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The distance between two places can be calculated using various methods:

a. Distance = √ ( x₂ - x₁)² + ( y₂ - y₁)²

b. Distance = Speed × time taken

As given in the question,

Distance between two places can be calculated using various techniques:

a. If the coordinates of the two points representing the places are given as (x₁ , y₁) and (x₂ , y₂ ) then

distance between two places  = √ ( x₂ - x₁)² + ( y₂ - y₁)²

b. If the distance travelled between two place with known speed and time taken to cover that distance then

Distance =  Speed × time taken

If the distance between two places is small then it can be calculated using any measuring scale.

Therefore, the distance between the two given places is given by :

a. Distance = √ ( x₂ - x₁)² + ( y₂ - y₁)²

b. Distance = Speed × time taken

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Answer: Markup is the amount added to the cost price (wholesale price) to arrive at the selling price.

A markup of 35% means that the selling price will be 35/100 = 0.35 times the cost price more than the cost price.

If the boutique pays $30 for a sweater, the markup amount on this sweater is $30*0.35 = $10.5

Therefore, the selling price of the sweater will be the cost price plus markup amount, or $30 + $10.5 = $40.5

So the sale price of the sweater will be $40.5

Step-by-step explanation:

Answer:

The last one(D)

Step-by-step explanation:

-1×-1=1

1*3=3

____

9*1=9

12-9=3

11. a. GH ≅ AX and b. ∠W ≅ ∠F  

12. a. ∠T ≅ ∠K  and b. THPA ≅ KEBI

13. a. The relation between ∠S and ∠H is ∠S ≅ ∠H and the measure of ∠S = 90  

Figures and shapes that may be reversed or rearranged such that they match up with other figures and shapes are said to be congruent. These forms can be mirrored to create these shapes.

Two triangles are considered to be congruent when all three corresponding sides and angles have the same size.

11. Given ΔFGH ≅ ΔWAX  

Here is the corresponding side to GH is AX and the corresponding angle to the angle ∠W is ∠F  

a. GH ≅ AX

b. ∠W ≅ ∠F  

12. Given that BIKE ≅ PATH      

Here the corresponding angle to the angle ∠T is ∠K

a. ∠T ≅ ∠K

b. THPA ≅ KEBI

13. In ΔHOT and ΔSUN

∠O ≅ ∠U and ∠T ≅ ∠N

Since two pairs of angles are congruent  

a. The relation between ∠S and ∠H is ∠S ≅ ∠H

b. Given that ∠O = 27 and  ∠T = 63  

As we know the sum of angles in a triangle = 180°

=> ∠H + ∠O + ∠T = 180

=> ∠S + 27 + 63 = 180   [ ∵ ∠S ≅ ∠H ]

=> ∠S = 180 - 90 = 90

=>  ∠S = 90  

Therefore,

11. a. GH ≅ AX and b. ∠W ≅ ∠F  

12. a. ∠T ≅ ∠K  and b. THPA ≅ KEBI

13. a. The relation between ∠S and ∠H is ∠S ≅ ∠H and the measure of ∠S = 90  

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There are 40320 ways the 8 horses can finish the race in terms of color combination.

The number of color combinations in which the horses can finish is determined by the number of ways the 8 horses can be arranged.

This is known as a permutation.

The formula for permutation is:

n! / (n-r)!

where:

n = total number of items

r = number of items being selected at a time

In this case, we want to know the number of ways the 8 horses can be arranged in a race, so we will use 8 for n and 8 for r.

8! / (8-8)! = 8! / 0! = 8! = 8x7x6x5x4x3x2x1 = 40,320

So, there are 40320 ways the 8 horses can finish the race in terms of color combination.

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The amount of money that she invested in each account will be $2,272.73 and $7,727.27.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A business invests a total of $10,000 at 4.12 % and 5% simple interest. During one year, the two accounts earn $480.

Let 'x' be the amount invested with 4.12%. Then the amount of investment with 5% will be ($10,000 - x). Then the equation is given as,

(x · 4.12 · 1) / 100 + [($10,000) · 5 · 1] / 100 = $480

Simplify the equation, then we have

(x · 4.12 · 1) / 100 + [($10,000 - x) · 5 · 1] / 100 = $480

0.0412x + $500 - 0.05x = $480

0.0088x = $20

x = $2,272.73

Then the investment in other account is calculated as,

⇒ $10,000 - $2,272.73

⇒ $7,727.27

The amount of money that she invested in each account will be $2,272.73 and $7,727.27.

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Answer:

Choice A and C

Step-by-step explanation:

If 1 magnet costs $5, then 3 magnets cost $15 because adding 3 magnets to your bag, would equal to 5+5+5, or 5x3. If 1 bookmark cost $2, then 9 bookmarks would cost $18 to your bag, which would equal 9+9, or 9x2.

So, C is correct because 5x3 is 15, and 2x9 is 18. A is also correct because it's just the other way around, 2x9=18 and 5x3=15.

Answer:

Step-by-step explanation:

First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6.

The sizes of the the angles x and y in the trapezium are 48° and 115° respectively.

A trapezium is a quadrilateral and the sum of interior angles is 369° and also two angles on the same side are supplementary, that is the sum of the angles of two adjacent sides is 180°.

x + 132° = 180° {adjacent angles}

x = 180° - 132° {subtract 132° from both sides}

x = 48°

y + 65° = 180° {adjacent angles}

y = 180° - 65° {subtract 65° from both sides}

y = 115°

Therefore, the sizes of the adjacent angles x and y of the trapezium are 48° and 115° respectively.

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The right triangle shown in the figure is solved to get the dimensions as

c.

Angle B = 60 degrees, Side B C = 4 Start Root 3 End Root meters, Side A B = 8 Start Root 3 End Root meters

The dimension of the right triangle is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

Information from the question

opposite = a

adjacent = 12

hypotenuse = c

The opposite is calculated using tan, TOA

tan 30 = Opposite / Adjacent

tan 30 = a / 12

a = 12 * tan 30

a = BC = 4√3

The hypotenuse is calculated using cos, CAH

cos 30 = Adjacent / hypotenuse

cos 30 = 12 / c

c = 12 / cos 30

c = AB = 8√3

< A + < B + < C = 180 (sum of angles in a triangle)

30 + < B + 90 = 180

< B = 60

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All of the equations that are equivalent to n − 9 = 12 include the following:

A. n - n - 9 = 12 - n

D. n - 9 - n = 12 - n

In this exercise, you are to determine the equations that are equivalent to the given equation (mathematical expression). This ultimately implies that, the left-hand side (LHS) of the given equation (mathematical expression) must be equal to the left-hand side (LHS) of the given equation (mathematical expression).

By substracting the variable n from both sides of the given equation (mathematical expression), we have the following:

n - 9 - n = 12 - n (equivalent)

By collecting terms and rearranging the equation (mathematical expression), we have the following:

n - n - 9 = 12 - n (equivalent).

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Answer: A conclusion drawn from a study is considered to be an observation or an inference based on the data collected. In this case, the dentist conducted a survey to determine whether a certain brand of mouthwash improves gum health more than others. The conclusion drawn from the survey results is that the brand of mouthwash in question does improve gum health more than other brands.

It is important to note that this conclusion is based on the sample of patients that were surveyed. A sample is a subset of a population that is used to represent the characteristics of the entire population. In this instance, the sample of patients surveyed may not be representative of the entire population of people who use mouthwash. Therefore, the conclusion drawn from the study is based on the sample and may not be generalizable to the entire population.

The study conducted by the dentist is a survey study. A survey study is a research method in which data is collected through questionnaires or interviews from a sample of individuals.

Step-by-step explanation:

Triangle AFC is the triangle that appears to be consistent with triangle AFD.

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. There is an obtuse angle, or angle AFD, same like in the give triangle AFD.

Therefore, the opposite triangle must have an obtuse angle in order to be a congruent triangle. Only triangle AFC, out of the three that are given, has an acute angle. Additionally, they both support the same side, increasing the likelihood of congruence. There is no obtuse angle in the triangles BFC and DFE.

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The value of a polynomial at a particular point is defined as the value that the provided function yielded at that moment.

As an illustration, consider the polynomial function (x) = x + 1.

When x = 1 for example, the polynomial at that point is given by P(1) = 1+1 = 2.

Consequently, the polynomial P(x) has a value of 2 when x equals 1.

'What are polynomials?'

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

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Answer:

Step-by-step explanation:

You have to rationalize the denominator by multiplying by a unit multiplier of the conjugate of it which is 1+5i:

[tex]\frac{-3+5i}{1-5i}*\frac{1+5i}{1+5i}[/tex] You will FOIL the top and the bottom to get

[tex]\frac{-3-15i+5i+25i^2}{1+5i-5i-25i^2}[/tex].  Combine like terms to get

[tex]\frac{-3-10i+25i^2}{1-25i^2}[/tex].  Remember that i-squared = -1, so this simplification then becomes:

[tex]\frac{-3-10i+25(-1)}{1-25(-1)}[/tex] which simplifies a bit more to

[tex]\frac{-3-10i-25}{1+25}=\frac{-28-10i}{26}[/tex]  but we need to make sure we can match our answer to one of the ones given, so we'll split up that numerator over the denominator to get:

[tex]-\frac{28}{26}-\frac{10i}{26}[/tex] which then goes down to

[tex]-1\frac{1}{13}-\frac{5i}{13}[/tex] which is choice a.

If the computed upper deviation rate (sample deviation rate projected to the population and adjusted for sampling risk) exceeds the tolerable deviation rate during a compliance test that utilizes statistical sampling,

it means that the test results indicate, the population of items being tested is not in compliance with the standards or regulations.

There are several actions that the auditor could take in this situation, depending on the specific circumstances of the test and the nature of the non-compliance. These are:

Note that: the specific course of action will depend on the nature of the non-com pliance and the regulations or standards that apply. It is recommended that the debtor consults with legal or regulatory experts to ensure that they are taking the appropriate actions to address the non-compliance.

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150 pounds of candy priced at 45 dollar should be coupled with 200 pounds of candy priced at 80 dollar .

As different sweets are not distributed evenly, a mixture of various candies in a container is an example of a heterogeneous mixture. In addition, since the particles of various sweets do not interact, different candies are visible with the eye.

Let "x" stand for the number of pounds of candy costing 45 Dollar per pound, and "(350-x)" for the number of pounds of candy costing 80 Dollar per pound. The decimal equivalents of 45, 80, and 65 Dollar are 0.45, 0.80, and 0.65.

350*0.65=0.45x+(350-x)0.80

Solve it for x

x=150

350-150=200

Thus, 150 pounds of candy priced at 45 cents should be coupled with 200 pounds of candy priced at 80 cents.

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Answer:

5

Step-by-step explanation:

2,4,6,8,10