The following data set represents the ACT scores for students in Mrs. Smith's collegescience class.18 32 16 2319 21 28 2922 30 19 21What ACT score is the mode for the class?

Given:

The angles of an isosceles triangle are,

∠M=40°

∠N=70°

The objective is to find the measure of ∠O.

An isosceles triangle is a triangle with two equal sides or two equal angles.

From the above figure, the two equal angles x are always larger than the third angle y.

Thus, the third angle will also be equal to the larger angle from the given agle.

Hence, the third angle is, ∠O = 70°.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

P(6,-6)

Q(9,-7)

R(7,-4)

A = ?

Step 02:

To solve the exercise we must know the length of the sides.To solve the exercise we must know the length of the sides.

A = (b * h) / 2

side PR = b

side PQ = h

Step 03:

A = (2.236*3.162) / 2 = 3.5355

The answer is:

3.54 ft²

Each digit has 10 possible values (the numbers from 0 to 9), so in order how many different numbers can be formed, we need to multiply the number of possible values of each digit.

If we have 9 digits, and each digit has 10 possible values, we need to multiply the number 10 by itself 9 times, that is:

So the number of different social security numbers is 10^9 (1,000,000,000, one billion)

The ages of the students of groups A and B are displayed in the histograms.

For group A

We can determine the number of students per age by looking at the bars of the histogram

2 are 15 years old

5 are 16 years old

6 are 17 years old

5 are 18 years old

2 are 19 years old

The total students for group A is

To calculate the average age on group a you have to use the following formula

Σxifi indicates the sum of each value of age multiplied by its observed frequency

n is the total number of students of the group

For group A the average value is

The average year of group A is 17 years old.

To determine the Median of the group, you have to calculate its position first.

The Median is in the tenth position. To determine the age it corresponds you have to look at the accumulated observed frequencies:

F(15)=2

F(16)=2+5=7

F(17)=7+6=13→ The 10nth observation corresponds to a 17 year old student

F(18)=13+5=18

F(19)=18+2=20

The median of group A is 17 years old.

For group B

As before we can determine the number of students per age by looking at the bars of the histogram

2 are 15 years old

3 are 16 years old

4 are 17 years old

5 are 18 years old

6 are 19 years old

The total number of students for group B is

The average age of group B can be calculated as

The average age for group B is 17.5 years old

Same as before, to determine the median you have to calculate its position in the sample and then locate it:

The median is in the 10nth position, to determine where the 10nth student is located you have to take a look at the accumulated frequencies:

F(15)=2

F(16)=2+3=5

F(17)=5+4=9

F(18)=9+5=14 →The 10nth observation corresponds to a 18 year old student

F(19)=14+6=20

The median of group B is 18 years old

So

The mean and median of group B are greater than the mean and median from group B. The correct choice is the first one.

Step 1

The degree of the leading term determines how many roots a polynomial has. Examine the highest-degree term of the polynomial – that is, the term with the highest exponent. That exponent is how many roots the polynomial will have. So if the highest exponent in your polynomial is 2, it'll have two roots; if the highest exponent is 3, it'll have three roots; and so on. A polynomial with a leading degree of 5 has 5 roots.

Step 2

Equilateral Triangle : All sides of triangle are equal

Issoceles Triangle : Only two sides of triangle are equal

Scalene Triangles : No sides of triangle are equal

In triangle A;

Sides of triangle are 8, 8, 4

Since two sides are equal i.e. both are of 8 unit

Thus, two sides are equal

Therefore triangle A is issoceled triangle.

Triangle 2

In the triangle,

All angles are equal which provides that all sides are equa

Therefore, Triangle B is an equilateral triangle

Triangle C;

In the given triangle one is of 90 degree

Since, all the angles areq different so, no two sides are equal

Therefore, triangle C is Scalene

Triangle D

In the given triangle as;

All four sides are equal, thus the triangle is an equilateral triangle

Equilateral triangle

Answer :

.

Let first put the equation of the first line in the form of slope intercept

So it's slope is -2, so the new slope is

Having the slope, we have that

so the equation is

The question asked to for the value of the expression below

Concept: Substitute the values in the formula given

Hence,

The final answer = -19

Energy = work per unit time

Energy = workdone / time

energy = mgh

m = 8kg

E = 2352J

since the bird is on the earth, definitely the gravitational force will be acting on it

g = 10m/s^2

2352 = 8 x 10 x h

2352 = 80 x h

2352 = 80h

divide both sides by 80

2352/80 = 80h/80

29.4 metres = h

h = 29.4 metres

The answer is 29.4 metres

29.6 °

Explanation

we have a right triangle( a triangle with an angle of 90°), so we can use a trigonometric function

so

Step 1

a) Let

so, we need to use a function that relates those values, it is

b) replace the values in the function and solve for the angle

therefore, the answer is

29.6

I hope this helps you

Based on the given situation, we can define the following expression

"at least" indicates that we have to use "greater than or equal to".

Let's solve for x

STEP 1

The formular for the length of an arc is denoted below:

STEP 2

Substitute the above value into the formular.

In conclusion, the Length of

we are given a polygon with 6 sides, therefore, is a hexagon. The interior angles of a hexagon always add up to 720 degrees.

Using the expression and the given angles, we can construct the following relationship:

Solving the operations we get:

Now we solve for "x" first by subtracting 595 to both sides:

Now we divide by 3:

Therefore, x = 45.

Now we use the expression for angle T:

Replacing the value of x, we get:

Therefore, angle T is 95 degrees.

1. Increases by 5 units

2. Any odd number multiplied by an even one yields an even number.

1) We can write out a sequence, an arithmetic one, to follow a pattern.

Note that the pattern here is the common difference between each term the first one is 5 and all the other ones increase by 5 units.

2) In this second case, we can pick "5" as well, but in this one, we'll make a Geometric Sequence for the following numbers will be written as the product of the prior term times 2:

Note that all the terms will be even numbers because any odd number multiplied by an even one yields another even number.

There are 105 handshakes that take place at the meeting.

To find the number of handshakes, we can use a formula that counts the number of combinations of two items from a set of n items.

The formula is:

[tex]n * (n - 1) / 2[/tex]

In this case, n is the number of people, which is 15.

So, we plug in 15 into the formula and get:

[tex]15 * (15 - 1) / 2[/tex]

Simplifying, we get:

[tex]15 * 14 / 2[/tex]

Multiplying, we get:

[tex]210 / 2[/tex]

Dividing, we get:

[tex]105[/tex]

Given the number of points Raina scored in her four basketball games:

Let be "x" the number of points Raina needs to score in her next game so that her average is 24 points per game.

By definition, the Mean (average) can be calculated by dividing the sum of the values by the total number of values. Therefore, you can set up the following equation:

Then, when you solve for "x", you get:

Hence, the answer is:

a) 400 ft in 15 seconds

d) 1200 ft in 45 seconds

Given:

Danny claimed the speed of his airplane was 27 feet per second

To find:

The statements in the options that support the above claim

rate of Danny's airplane = 27 ft/sec

a) rate = 400 feet in 15 seconds

We need tio get the rate in ft/sec

in 1 second = 400/15 = 26.67

Approximately, the rate = 27 ft/sec

b) rate = 3ft in 81 seconds

in 1 second = 3/81 = 0.037 ft/sec

c) rate = 1320 ft in 60 seconds

In 1 second = 1320/60 = 22

rate = 22 ft/sec

d) 1200 ft in 45 seconds

In 1 second = 1200/45 = 26.67

Approximately, rate = 27 ft/sec

The examples below that support his claim are the 1st and last option

The thousands digits are the fourth digit, in this case, 8. but you need to round to the nearest thousand, and like the number after 8 on 8958 is 9, the nearest thousand is 9.

So the answer is 9000

Here, we want to get the area of the triangular case

Mathematically, this is half the product of the base and the height of the case

We have this as;

Given data:

The given figure is shown below.

The area of the shaded region is,

Thus, the area of the shaded region is 42.92 sq-inches.

You have to multiply the fractions

First note that both values are negative. As a rule, when two negative values are mutiplied, the result will be positive, always.

Next, you have to multiply the numerators together and the denominators together as follows:

Given

we are given solid or space figures

Required

we need to find what gives surface area of a solid figure.

Explanation

The surface area of any solid shape is the sum of areas of all faces in that solid figure.

Example: when finding surface area of cube we add the area of each square constituting the cube.

The correct option A: y = -4 cos Ф/4, is the cosine function for the graph.

The ratio between the angle's adjacent leg and the hypotenuse when it is regarded as a leg of a right triangle is a trigonometric function for an acute angle.

For the given graph,

cosine function:  y = -4 cos Ф/4.

In which, -4 is the amplitude (maximum displacement from the x axis).

Negative sign shows, the displacement is taken along negative y-axis.

And,  Ф/4 is the phase angle.

Thus, the cosine function for the graph is  y = -4 cos Ф/4.

To know more about the cosine function, here

https://brainly.com/question/27587720

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Answer:

b. [tex]\displaystyle y = -4cos\:4\theta[/tex]

Step-by-step explanation:

[tex]\displaystyle y = 4cos\:(4\theta \pm \pi) \\ \\ \\ y = Acos(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\pm\frac{\pi}{4}} \hookrightarrow \frac{\pm\pi}{4} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 4[/tex]

OR

[tex]\displaystyle y = -Acos(B\theta - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{2}} \hookrightarrow \frac{2}{4}\pi \\ Amplitude \hookrightarrow 4[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that this cosine graph will have TWO equations because the curvature begins upward from [tex]\displaystyle [0, -4][/tex] instead of downward from [tex]\displaystyle [0, 4],[/tex] telling you that one equation will have a “negative” symbol inserted in the beginning of the equation. Before we go any further though, we must figure the period of the graph out. So, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [0, -4],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{2}, -4],[/tex] they are obviously [tex]\displaystyle \frac{\pi}{2}\:unit[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \frac{\pi}{2}.[/tex] Now, as you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4cos\:4\theta.[/tex] Now, if you look hard enough, you will see that both graphs are “mirror reflections” of one another, meaning you can figure the rest of the terms out one of two ways. The first way is to figure the appropriate C-term out that will make the graph horisontally shift and map onto the original cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also, keep in mind that −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the rightward graph is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex] on both sides of the y-axis, which means that in order to match the original graph, we need to shift the graph back, which means the C-term will be both negative and positive; and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\pm\frac{\pi}{4}} = \frac{\pm\pi}{4}.[/tex]So, one equation of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4cos\:(4\theta \pm \pi).[/tex] Now that we got this out the way, we can focuss on finding the second equation. Another way is to write an equation with a “negative” symbol inserted in the beginning [like I mentioned earlier]. Now, sinse we are writing an equation with the negative, the graph will not have a horisontal shift; so, C will be zero. With this said, the second equation is [tex]\displaystyle y = -4cos\:4\theta.[/tex] Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex] in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

that Solving for the retail price of a parrot with 20% markup and 3% taxes

We want to know the retail price of a parrot if it costs us $159.95 , knowing that we want to obtain 20% of profit and we're getting taxed 3%

Firts, we have to calculate the 20% of the original value ($159.95), and add that up. Then, we calculate the 3% of that value ($159.95 + 20% markup) and add it up, asl following:

Thus, the retail price of the parrot, with 20% markup and 3% taxes, should be $197.70

The answer is reflection

We write the following equations from the data of the statement of the problem:

• the area of the triangle is A = 28,

• the height h and the base b are related by the following equation:

The formula for the area of the triangle:

Replacing the data of the problem in the equation above:

We rewrite the equation in the following way:

We have a quadratic equation for the length of base b, the solutions to this equation are:

Because b is the length of one side of the triangle, and lengths are positive quantities, we must select the positive value of b, so we have:

Replacing this result in the equation for the height, we get:

Answer

• Base is ,4, inches,

• Height is, 14, inches.

the domain for f(x) is all real numbers greater than or equal to -2.

Remember in the real number domain we can't have negative values inside the square root because they are not defined.

The v means a root, so the only whole number is

The angle on a line is 180°

The sum of the three given angles is 180°:

Use this equation to find the value of x:

The question gives us the following parameters:

Recall that the sum of angles on a straight line is 180 degrees. This means that:

Recall that the sum of angles in a triangle is 180 degrees. Thus, we have:

The SECOND OPTION is correct.