18
The table shows information about the numbers of points scored by 28 students in a quiz.
Number of points
0
1
2
3
4
5
(a) Find the modal number of points.
(b) Work out the total number of points scored.
Frequency
5
4
5
5
6
3
(1)

x(t) = [tex]c_1e^1^4^t+c_2e^-^t[/tex]  , y(t) = [tex]2c_1e^1^4^t-c_2e^-^t[/tex]   is the general solution of the sytem of differention eqution dx/dt = 4x+ 5y , dy/dt = 10x + 9y .

given  dx/dt = 4x+ 5y  and dy/dt = 10x + 9y

X'(t) = [tex]\left[\begin{array}{ccc}4&5\\10&9\end{array}\right][/tex]  X

where X = [tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right][/tex]

so A = [tex]\left[\begin{array}{ccc}4&5\\10&9\end{array}\right][/tex]

now we need to find eigen value of the matrix and the corresponding eigen vector.

| A- λI | = 0

so after equation the value to zero

λ = 14 and λ = -1

now for the  λ = 14 corresponding eigen vector = [tex]\left[\begin{array}{ccc}1\\2\\\end{array}\right][/tex]

for λ = -1 corresponding eigen vector =  [tex]\left[\begin{array}{ccc}1\\-1\\\end{array}\right][/tex]

So general equation is given by:

X(t) = [tex]c_1e^1^4^t[/tex]  [tex]\left[\begin{array}{ccc}1\\2\\\end{array}\right][/tex]  +  [tex]c_2e^-^t[/tex]   [tex]\left[\begin{array}{ccc}1\\-1\\\end{array}\right][/tex]

after solving this

x(t) = [tex]c_1e^1^4^t+c_2e^-^t[/tex]

y(t) = [tex]2c_1e^1^4^t-c_2e^-^t[/tex]

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15%

If you take fiction plus non fiction it equals 10k books. 1500/10000 is 15%

Answer:

second option is the answer

Step-by-step explanation:

Fot every action,there is an equal and opposite reaction

The number which has a finite number of digits after the decimal point is a terminating decimal.

The decimal is said to be terminating decimal if that has a finite number of digits after the decimal point. Decimal numbers are used to represent the partial amount of whole just like fractions. The number which has a finite number of digits after the decimal point is referred to as a terminating decimal. A number has a terminating decimal expansion if the digits after the decimal point terminate or are finite. The fraction 5/10 has the decimal expansion of 0.5 which is a terminating decimal expansion because digits after the decimal point end after one digit. Terminating decimal has finite digits and non-terminating decimals do not have finite digits. A number with a terminating decimal is always a rational number.

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Triangle ABC is translated to triangle EFG because a vertical translation of 10 units and a horizontal translation of 5 units maps triangle ABC onto triangle EFG.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

Triangle ABC.

A = (-9, -2)

B = (-9, -7)

C = (-7, -7)

Triangle EFG.

E = (-4, 8)

F = (-4, 3)

G = (-2, 3)

Now,

With a vertical translation of 10 units up on triangle ABC and 5 units right of the horizontal translation will give us triangle EFG.

i.e,

(-9, -2) = (-9 + 5, - 2 + 10) = (-4, 8)

(-9, -7) = (-9 + 5, -7 + 10) = (-4, 3)

(-7, -7) = (-7 + 5, -7 + 10) = (-2, 3)

Thus,

Vertical translation of 10 units up and horizontal translation of 5 units right.

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Answer:

1: Congruent

2: 10

3: 5

Step-by-step explanation:

Answer: 37 degrees.

You use tan x to find the angle measure. So tan x = 9/12. When you plug it into a calculator, you get 36.86989765 so it rounds to 37.

Hope it helps.

The value of A in A## = ( A - 2 )## if x## = x² - x is 2 Or 3.

Topics in the reasoning part include coding, decoding, and reasoning. One of the most frequently occurring portions in all of the important competitive exams specifically created for employment procedures and higher education is this one. Because Coding-Decoding and Reasoning problems can be difficult for some applicants to complete, they avoid them and lose some quick and simple marks.

Given, x## is defined as x## = x² - x.

Therefore,

A## = (A - 2)##

= (A - 2)² - (A - 2).

= A² - 4A + 4 - A + 2.

= A² - 5A + 6.

Let, A² - 5A + 6 = 0.

A² - 3A - 2A + 6 = 0.

A(A - 3) - 2 (A - 3) = 0.

(A - 3)(A - 2) = 0.

A = 3 Or A = 2.

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Answer:

Altitude

Step-by-step explanation:

Find another name for the height of a prism or a pyramid.

Since we know that the height of a prism or pyramid is the perpendicular distance between the two ends of a prism or pyramid.

We can find the height of the pyramid by dropping an altitude from the top of the pyramid to the base of the pyramid.

Note to moderators:

Please don't delete this answer because I'm just trying to help others.

The height of the pyramid is also called the altitude of the pyramid. Since both of these terms represent the same thing, we can use the two terms interchangeably. The correct option is C.

A pyramid geometry is defined as a three dimensional object with a polygon as its base and the triangles forms the lateral faces which meet at a point above the base called the apex. The pyramids have different parts and some of these parts have more than one name.

The height of the pyramid indicate the perpendicular distance from the base of the pyramid to the apex of the pyramid. This line segment which is perpendicular to the base and runs from the base to the apex is defined as the altitude of the pyramid.

Based on the shape of the base, the pyramids are of many types like triangular pyramid, square pyramid, etc.

Thus the correct option is C.

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So Dylan needs 1.375 liters of water more for his experiment.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

To find out how much more water Dylan needs, we can subtract the amount of water he currently has from the amount of water he needs for the experiment.

2.5 - 1.125 = 1.375 liters

So Dylan needs 1.375 liters of water more.

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Answer:

A.

Step-by-step explanation:

A = 1.18, but rounded, is 1.2

Answer:

A) -13.2

Step-by-step explanation:

it's the closest one

The height of vase b is 34.56 cm.

In mathematics, volume is the space taken by an object.

V=pi*r²*h

Here, given that,

vase A has height 20cm =H

and volume 1500^3. =V

And, A & B similar vases.

Again, vase B has volume 2592cm^3 =v

let, h, the height of vase b.

both radius are equal

so, we get,  V/pi*H = v/pi*h

i.e. 1500/20=2592/h

so, h= 34.56 cm

Hence, the height of vase b is 34.56 cm.

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Answer:

[tex]df \: is \: correct \: answer[/tex]

Answer:

sorry, I forget how to do the other ones and I'm just as confused but for 4. AD is 20 and 5. GJ is 17

Step-by-step explanation:

4. side AD is equal to side CD so therefore its 20.

5. side are equal again so make

4x+5 = 2x+11

    -5         -5

4x = 2x+6

-2x  -2x

2x = 6

/3    /3

x = 3

2(3)+11

6+11

17

gopal:44

ram:112

i think, i hope

The simplified form of the given fraction is, [tex]\frac{1}{x^2y}[/tex].

What is simplified form of the expression?

If a fraction's top and bottom have only the number one in common, then it is expressed in its simplest form. The top and bottom cannot be divided further and remain whole numbers, in other words. The phrase "lowest terms" is another term for the simplest form.

Consider, the given expression

[tex]\frac{(\frac{1}{x^2}-\frac{2}{y} )}{y-2x^2}[/tex]

We have to find the simplified form of the given expression.

Taking cross multiplication of numerator of the above fraction.

[tex]\frac{(\frac{y-2x^2}{x^2y} )}{y-2x^2}[/tex]

Using: [tex]\frac{(\frac{a}{b} )}{c} = \frac{a}{b}*\frac{1}{c}[/tex]

⇒  [tex]\frac{(\frac{y-2x^2}{x^2y} )}{y-2x^2} = \frac{y-2x^2}{x^2y} *\frac{1}{y-2x^2} = \frac{1}{x^2y}[/tex]

Hence, the simplified form of the given fraction is, [tex]\frac{1}{x^2y}[/tex].

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The ratios equivalent to 2:14 are 3:21 and 16:112. Option A &C

Equivalent ratios are the ratios that are the same when we compare them. Two or more ratios can be compared with each other to check whether they are equivalent or not. For example, 1:2 and 2:4 are equivalent ratios.

2:14 = 2/14

Reducing 2/14 to the lowest terms = 1/7

2:14 is equivalent to 1:7

3:21 = 3/21 = 1/7

Reducing 3/21 to the lowest terms = 1/7

3:21 is equivalent to 1:7

1:2 = 1/2

1:2 is not equivalent to 1:7

16:112 = 16/112 = 1/7

Reducing 16/112 to the lowest terms = 1/7

16:112 is equivalent to 1:7

Hence, 2:14, 3:21 and 16:112 are all equivalent ratios

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The value of the missing length LN of the similar triangles is; LN = 18

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. This means therefore that, if two triangles are similar, then we can say that their corresponding angles are congruent and also their corresponding sides are in equal proportion.

In the given triangle attached, we can say that if we apply the concept of similar triangles, we will get;

LN/LK = MN/JK

We are told that;

MN is 12 more than LN. Thus; MN = 12 + LN

LK = 33

JK = 55

Thus;

LN/33 = (12 + LN)/55

55LN = 33(12 + LN)

55LN = 396 + 33LN

22LN = 396

LN = 396/22

LN = 18

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Answer:

5,775 for the cost of parking tuition

Step-by-step explanation:

45% = 0.45

0.45(10,500)= 4,725

10,500 - 4,725 = 5,775 for the cost of parking tuition

Answer:

The midpoint is,

(4.5, 6.5)

Step-by-step explanation:

Here, we want to find the midpoint between the two points

mathematically, we use the midpoint formula here

We have this as;

m = (x2+ x1)/2, (y2+ty1)/2

where (x1,y1) = (2,9)

(x2,y2) = (7,4)

substituting these points, we have

m = (2+ 7)/2, (9 + 4)/2 = 9/2,13/2 = (4.5, 6.5)

X = 38°

Step-by-step explanation:

The sum of the inner angles of a triangle is 180 degrees

Then.. :

136+ x= 180

180- 136= x

X= 44

88 + 44 + x = 180

142+ x = 180

X= 180-142

X = 38°

Espero haberte ayudado.

Answer:

d

Step-by-step explanation:

Answer:

Step-by-step explanation:

The coordinates for the enlargement would be (-5,4) (-5,-2) (-2,-2)

Answer:

540°

Step-by-step explanation:

An equilateral triangle has 3 interior angles of 60°

A square has 4 interior angles of 90°.

When the images are joined, two vertices of each figures are joined together, such that these angles will have now a measure of:

60° + 90° = 150°

Then this figure has:

one angle of 60°

two angles of 150°

and two angles of 90°

(the image below illustrates this situation)

The sum of the interior angles is:

S = 60° + 2*150° + 2*90° = 540°

Answer:

reciprocal

Step-by-step explanation:

mark me brainliest pls

Answer:

A linear function is a special type of function whose graphs are straight lines (as their name suggests). Let’s look at a straight line and find out what this particular shape of graph tells us about the relationship between the input  and the output  of a linear function.

Step-by-step explanation:

pls mark as brainliest

Y=4x-1

The equation of a line is:

Y=mx+c

We are told that the slope is 4 which is also gradient, meaning that M=4

Now we are left with:

Y=4x+c

There are two ways to get C:

1. We know that C represents the y-intercept so immediately we can conclude that C=-1

2. You can work it out by substituting the coordinate for the X and Y value:

-1=4(0)+c

-1=C

So in conclusion, the equation of the line is:

Y=4x-1

Answer: 90 degrees

Step-by-step explanation:

BD=CD

2(BD)= BC

2