how many sides does a regular polygon have if each interior angle measures 172

Answer: Let the width of the rectangle be w and the length be l. We are given that the area of the rectangle is 45 cm^2, so we can write the equation:

w * l = 45

To find the lengths of the sides, we need to solve for w and l. We can divide both sides of the equation by any non-zero number to find an equivalent expression. For example, we can divide both sides by 9:

(w/9) * (l/9) = 45/9

Simplifying, we get:

w/9 * l/9 = 5

So, w/9 = 5/l and w = 5l/9.

Substituting the expression for w into the original equation, we get:

(5l/9) * l = 45

Expanding and simplifying, we get:

5l^2/9 = 45

Multiplying both sides by 9, we get:

5l^2 = 405

Dividing both sides by 5, we get:

l^2 = 81

Taking the square root of both sides, we get:

l = 9

So, the length of the rectangle is 9 cm. To find the width, we can substitute the value of l back into the expression we derived earlier:

w = 5l/9

w = 5 * 9 / 9

w = 5

So, the width of the rectangle is 5 cm.

The lengths of the sides of the rectangle, both exactly and approximately, are 9 cm and 5 cm.

Step-by-step explanation:

The total time that tammy sent in total playing games is; 4.5 hours

The parameters given for Tammy in playing the game are;

Number of games played = 12 games

Time spent per game = ³/₈ hours

Thus;

Total time she spent playing game will be gotten by multiplying the time per game by number of games played to get;

Total time spent = ³/₈ * 12

= 9/2

= 4.5 hours

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Complete question is;

A game lasts 3/8 hours. Tammy played 12 of these games. For how long did she play in total? Write your answer in simplest form.

(a). Name of internet service provider is categorical variable because it cannot be quantified or measured. It can be divided into different categories according to the service they provide.

A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

Measurement scale used for determination is nominal scale, also called the categorical variable scale.

(b). Time in hours, spent surfing the internet per week is continuous numerical variable because time can be measured over an infinite number of real values within a given interval.

A variable is said to be continuous if it can assume an infinite number of real values within a given interval.

Measurement scale used for determination is ratio scale.

(c). Whether the individual uses a mobile phone to connect to the internet is categorical variable because the answer can only be yes or no and it cannot be measured numerically.

A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

Measurement scale used for determination is nominal scale, also called the categorical variable scale.

(d). Number of online purchases made in a month is discrete numerical variable because it is a value that arises through a counting process.

A discrete quantitative variable is one that can only take specific numeric values (rather than any value in an interval), but those numeric values have a clear quantitative interpretation.

Measurement scale used for determination is interval scale.

(e). Where the individual uses social networks to find sought -after information is categorical variable because the answer can only be yes or no and it cannot be measured numerically. It can be either he/she uses or he/she do not.

A categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property.

Measurement scale used for determination is nominal scale, also called the categorical variable scale.

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Answer:

6g+3g=11+3-5

combine like terms

9g=11+3-5

calculate the sum of difference

9g=9

Step-by-step explanation:

reduce the greatest common factor on both sides

of the equation

g=1

Let's call the number of hours of labor required to replace the water pump as "x".

The total cost of the water pump and labor was $668, so we can write an equation:

$490 + $89x = $668

Now we can solve for x by subtracting $490 from both sides:

$89x = $668 - $490

$89x = $178

And finally, dividing both sides by $89:

x = $178 / $89

x = 2 hours

So, 2 hours of labor were required to replace the water pump.

Answer:

The figure is made up of a rectangle and two triangles. The dimensions of the rectangle are 10 cm by 5 cm, so the area of the rectangle is 10 * 5 = 50 cm^2.

Each of the two triangles has a base of 4 cm and a height of 3 cm, so the area of each triangle is (1/2) * 4 * 3 = 6 cm^2. The total area of the two triangles is 2 * 6 = 12 cm^2.

The total area of the figure is the sum of the areas of the rectangle and the triangles: 50 + 12 = 62 cm^2.

Step-by-step explanation:

Using the concept of proportions, the first rate does not form a proportion while the second rate form a proportion and the the cost of 9 pizza is $152.55

Proportion is a mathematical concept that refers to the relationship between two values or sets of values. It expresses the relative sizes of two or more quantities and can be represented as a fraction, decimal, or percentage.

6.

16 players for 24 teams

20 players for 32 teams

Let's find the ratio of player to team if they're consistent.

16 / 24 = 2/3 ≠ 20 / 32 = 5/8

The rates do not form a proportion.

7.

10 inches in 6 hours

80 inches in 2 days

10 / 6 = 5/3  = 80 / 48 = 5/3

The rates form a proportion.

8.

4 pizza = 67.80

9 pizza = x

Cross multiply both sides

4x = 67.80 * 9

4x = 610.2

x = 610.2 / 4

x = 152.55

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The shape of the distribution is normal

The probability is 0.7764

What is Standard Deviation?

The standard deviation is a measure of the spread or dispersion of a set of data around its mean. It is calculated by finding the square root of the variance, which is the average of the squared differences between each data point and the mean. It is used to quantify the degree of variability or diversity in the data.

(a)

The distribution of heights of young men follows a normal distribution with a mean of 69.3 inches and a standard deviation of 2.8 inches. The distribution of heights of young women also follows a normal distribution with a mean of 64.5 inches and a standard deviation of 2.5 inches.

The difference between the height of a randomly selected young man (m) and a randomly selected young woman (w) follows a normal distribution with a mean of 69.3 - 64.5 = 4.8 inches (the difference in the means) and a standard deviation of √(2.8² + 2.5²) = 3.67 inches (the square root of the sum of the variances).

The shape of the distribution of the difference between the heights of a randomly selected young man and a randomly selected young woman is also normal, since the original distributions are normal. The centre of the distribution is 4.8 inches, and the spread is 3.67 inches.

(b)

We need to find the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman, or in other words, we need to find P(m - w > 2).

Using the formula for the difference of two normal distributions, we have:

z = (2 - 4.8) / 3.67 = -0.76

We need to find the probability that a standard normal variable Z is greater than -0.76. Using a standard normal table or calculator, we find that P(Z > -0.76) = 0.7764.

Therefore, the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is approximately 0.7764.

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The equation that represents the image will be w + 1.3 = 2.7. And the value of 'w' will be 1.4.

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

The length of both tapes is the same. Then the equation is given as,

w + 1.3 = 2.7

Simplify the equation for w, then we have

w + 1.3 = 2.7

w = 1.4

The equation that represents the image will be w + 1.3 = 2.7. And the value of 'w' will be 1.4.

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Answer:

10.00 & 0.05

Step-by-step explanation:

[tex]10.00 - 0.05 = 9.95[/tex]

The amount of money as change is $ 0.05 and the amount of money given is $ 10.00

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

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

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the cost of the item = $ 9.95

The amount of money given = $ 10.00

So , the amount of money received as change = amount of money given - cost of the item

On simplifying the equation , we get

The amount of money received as change = 10.00 - 9.95

The amount of money received as change = $ 0.05

Hence , the amount of change is $ 0.05

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a) The values are given as follows:

i) x1: -0.5.

ii) x2: -0.280125.

b) The solution of the equation is of: -0.25410169644.

The equation in this problem is given as follows:

y = (x³ - 1)/4.

The solution is obtained using a iterative solution method, until the difference between previous iterations is less than 10^-6, as the solution is exact to 6 decimal places.

Then the values are given as follows:

x1  = -1 -> attributed.

x2 = ((-1)³ - 1)/4 = -0.5.

x3 = ((-0.5)³ - 1)/4 = -0.28125.

x4 = ((-0.281255)³ - 1)/4 = -0.25556212524.

x5 = ((-0.25556212524)³ - 1)/4 = -0.25417281837

x6 = ((-0.25417281837)³ - 1)/4 = -0.25410513385

x7 = ((-0.25410513385)³ - 1)/4 = -0.25410185521.

x8 = ((-0.25410185521)³ - 1)/4 = -0.25410169644. -> difference less than six decimal places.

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An approximate solution to an equation is found using this iterative process.

Xₙ₊₁= (Xₙ)³ - 1 / 4 and x₁= -1

a)

(i) Work out the value of x₂

(ii) Work out the value of x₃

b) Work out the solution to 6 decimal places

Answer:

240/2, 360/3

Step-by-step explanation:

240/2 and 360/3 both involve division and both of their answers are equal to 120, assuming these count as number sentences.

Answer:

16 students are taking Physics and 12 are taking calculus

Step-by-step explanation:

40×40%=16 students taking Physics

40×30%=12 students taking calculus

16+12=28

40-28=12 students are taking both

We can see that the triangle is equilateral, thus, the value of x is 13.

We can see that it is a right triangle, and we know the value of one of the catheti and one of the angles.

Remember that the sum of the interior angles must be equal to 180°.

So if we have a right angle and a 45° angle, then the measure of the remaining angle is:

a = 180° - 90° - 45° = 45°

So we have an equilateral triangle, thus, the measure of x must be 13 units.

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Answer: 13

Step-by-step explanation: Just took the test

The values of x, y and z are given as follows:

Similar polygons are polygons that share these two features presented as follows:

There are two similar trapezoids for this problem, hence the proportional relationship for the side lengths is given as follows:

x/15 = 10/24 = y/16 = z/12.

Applying cross multiplication, the value of x is given as follows:

24x = 15 x 10

x = 15 x 10/24

x = 6.25.

The value of y is given as follows:

y = 16 x 10/24

y = 6.67.

The value of z is given as follows:

z = 12 x 10/24

z = 5.

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The total number of ways to choose a president, vice-president, and treasurer from a group of 4 freshmen and 4 sophomores so that at least one freshman is 314 ways.

We can approach this problem using the principle of inclusion-exclusion.

First, let's find the total number of ways to choose a president, vice-president, and treasurer from a group of 8 people without any restrictions. We can do this by using the permutation formula:

8P₃ = 8 x 7 x 6 = 336

Next, let's find the number of ways to choose the three positions where only freshmen are chosen. There are 4 freshmen to choose from, so we can select the president, vice-president, and treasurer in 4P₃  = 4 x 3 x 2 = 24 ways.

Similarly, there are 4 sophomores to choose from, so we can select the three positions where only sophomores are chosen in 4P₃  = 4 x 3 x 2 = 24 ways.

However, we have overcounted the cases where only freshmen or only sophomores are chosen, since the problem statement requires that at least one freshman and at least one sophomore hold at least one of the three positions. Therefore, we need to subtract the number of cases where only freshmen or only sophomores are chosen.

There is only one way to select the president, vice-president, and treasurer from the 4 freshmen, and likewise, there is only one way to select them from the 4 sophomores. Therefore, there are a total of 2 ways to select the three positions where only one class is represented.

Finally, we need to add back the cases where no freshman or no sophomore is chosen. This occurs only if all three positions are filled by juniors or seniors. There are 4 juniors and seniors to choose from, so we can select the three positions in 4P₃  = 4 x 3 x 2 = 24 ways.

Therefore, the total number of ways to choose a president, vice-president, and treasurer from a group of 4 freshmen and 4 sophomores so that at least one freshman and at least one sophomore holds at least one of these three positions is:

336 - 24 - 24 + 2 + 24 = 314 ways.

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The fraction of the students live more than 4 miles from school is 3/10.

A fraction represents a part of a number or any number of equal parts.

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

Given;

The percentage of students live more than 5 miles away=30%

Now,

The fraction;

=30/100

To convert it into the simplest from;

=30/100

=3/10

Therefore, the fraction in simplest form will be 3/10.

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The complete question is;

At Charles Walters Middle School, 30% of the students live more than 4 miles from school.What fraction of the students live more than 4 miles from school? Write your answer as a fraction in simplest form. ?​

The ratio of EP to PF is given as follows:

EP : PF = 2 : 7.

The ratio of EP to PF is obtained applying the proportions in the context of the problem.

Looking at the x-coordinates, we have that:

The ratio must necessarily be the same for the y-coordinates, hence the ratio is given as follows:

EP : PF = 4 : 14.

EP : PF = 2 : 7.

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The length of the candle that has been burning for the total of 240 minutes would be = 9 inches.

The rate at which a candle burns = 2 in/ 2 hours

That is,

2 in = 2 hour; 2 inches = 120 minutes

X in = 240 minutes

Make X the subject of formula;

X = 2×240/120

X= 480/120

X = 4+5

X = 9 inches

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Kendra hits the target more often than Dalisay.

What is the hit rate?

Hit rate is a measure of performance that calculates the proportion of successful hits or positive outcomes in a given situation, usually expressed as a percentage.

To compare Kendra and Dalisay's performance in hitting the target, we need to determine the hit rate for each archer.

Kendra hits the target 3 times for every 5 misses. The hit rate for Kendra can be calculated as:

hit rate = 3 / (3 + 5) = 3/8

Dalisay hits the target 5 times for every 7 misses. The hit rate for Dalisay can be calculated as:

hit rate = 5 / (5 + 7) = 5/12

Comparing the hit rates, we see that Kendra has a higher hit rate than Dalisay.

Therefore, Kendra hits the target more often than Dalisay.

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The solutions are given in the ordered pairs.

An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.

We have to choose a value for x to find the corresponding y value to make the equation true.

1)6x=7y

To find x:

divide both sides by 6.

We get, [tex]\frac{6x}{6} =\frac{7y}{6}[/tex]⇒[tex]x=\frac{7y}{6}[/tex]

To find y:

divide both sides by 7.

We get, [tex]\frac{6x}{7} =\frac{7y}{7}[/tex] ⇒ [tex]y=\frac{6x}{7}[/tex]

Therefore solution for the given equation is [tex](\frac{7y}{6} ,\frac{6x}{7})[/tex]

2) 5x+3y=9

To find x:

subtract 3y from both sides,

⇒ 5x=9-3y then divide 5 on both sides,

⇒ [tex]\frac{5x}{5}=\frac{9-3y}{5}[/tex]⇒ [tex]x= \frac{9-3y}{5}[/tex]

To find y:

subtract 5x from both sides.

⇒3y=9-5x, then divide by 3 on both sides we get,

[tex]\frac{3y}{3}=\frac{9-5x}{3}[/tex]⇒[tex]y=\frac{-5x}{3}+3[/tex]

The solution for this equation is [tex](\frac{9-3y}{5},\frac{-5x}{3}+3)[/tex]

3) y+5-(1/3)x =7

To find x:

subtract y-5 from both sides we get,

[tex]-\frac{1}{3}x=2-y[/tex] then multiply both sides by -3,

[tex]\frac{\frac{-1}{3}x }{\frac{-1}{3}}=\frac{2-y}{\frac{-1}{3}}[/tex]⇒x=3y-6

To find y:

Subtract 5 from both sides.[tex]y-\frac{1}{3}x = 7-5[/tex] and add [tex]\frac{1}{3} x[/tex]

we get, [tex]y=2+\frac{1}{3}x[/tex]

The solution for this equation is ([tex](3y-6, 2+\frac{1}{3})[/tex]

Hence, the solutions are given in the ordered pairs.

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Answer: Yes. for each input there is exactly

ONE output

Step-by-step explanation:

I did the test and it was true.

Answer:

37.437

Step-by-step explanation:

Answer:

37.437

Hope it helps

After dilation, the coordinates of image will be (-1,3).

What exactly is dilation?

Dilation is the process of modifying the size of an item or form by reducing or expanding its dimensions according to specific scaling variables. A circle of radius 10 unit, for example, is reduced to a circle with radius 5 unit. This approach is utilised in photography, arts and crafts, and the creation of logos, among other things. There are four primary types of transformations in geometry. They are as follows:

Dilation Properties

Some characteristics of forms that stay constant during dilation changes are:

Now,

As given dilation factor= -3

that means the image will be small and x coordinate will displace from its current value - 3 that is -1.

and y coordinate will be same that is 3

Hence,

          After dilation, the coordinates of image will be (-1,3).

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Answer:

285.50

Step-by-step explanation:

The total for the ratio of 1:4 is 5.  The ratio to the woman to the total is

4:5 or

[tex]\frac{4}{5}[/tex] = [tex]\frac{x}{2855}[/tex]  Cross multiply and solve for x

4(2855) = 5x

11420 = 5x  Divide both sides by 5

2284 =x

The woman's portion of the total is 2284.

The woman takes the 2284 and divides it in a ratio of 5:1:2.  The total is 8.

The daughter will receive the ratio of 1:8 of the total.

[tex]\frac{1}{8}[/tex] = [tex]\frac{x}{2284}[/tex]  cross multiply and solve for x

8x = 2284    Divide both sides by 8

x = 285.50

The daughter's portion is 285.50

The length of the other sides of ΔABC are AB =12 cm and BC = 16 cm.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, ΔABC ∼ΔA'B'C' and AC=20 cm A'C'=15 cm B'C'=12 cm and A'B'=9 cm.

Here, AB/A'B' = BC/B'C' = AC/A'C'

AB/9 = BC/12 = 20/15

AB/9 = BC/12 = 4/3

Now, AB/9 = 4/3

AB =12 cm

BC/12 = 4/3

BC = 16 cm

Therefore, the length of AB =12 cm and BC = 16 cm.

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[tex] \frac{9}{3} = \frac{x}{2} \\ [/tex]

Cross multiply...

[tex]3x = 18[/tex]

[tex]x = \frac{18}{3} \\ [/tex]

x = 6

Answer:

it's 6. 9 is divided by 3 and the answer is 3 .so 3=x÷2. and multiplie 2 in both side.so the answer is 6.

Answer:

B.

The equation you can use to find the area of a sphere when given radius is:

V = 4/3πr 3

Fitting 5 into the equation:

V = 4/3π5 3

V = 523.598776

Therefore, B is the correct answer.