A girl scored 18 out of 25 in English language and p% in mathematics. if her average score is 78% , what is the value of p ​

Answer:

216.

Step-by-step explanation:

These numbers are perfect cubes starting with 2^3.

2^3, 3^3,  4^3,  5^3 so the next one is 6^3, which is 216.

Step-by-step explanation:

Hi there!

Please see the answer in the picture.

Hope it helps!

1. Approach

One is given a trigonometric equation with and one is asked to prove that it is true. Using the attached image, combined with the knowledge of trigonometry, one can evaluate each trigonometric function. Then one can simplify each ratio to solve. To yield the most accurate result, one has to each of the ratios in a fractional form, rather than simplifying it into a decimal form. Remember the right angle trigonometric ratios, these ratios describe the relationship between the sides and angles in a right triangle. Such ratios are as follows,

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}\\\\csc(\theta)=\frac{hypotenuse}{opposite}\\\\sec(\theta)=\frac{hypotenuse}{adjacent}\\\\cot(\theta)=\frac{adjacent}{opposite}[/tex]

Please note that the terms (opposite) and (adjacent) are relative to the angle uses in the ratio, however the term (hypotenuse) refers to the side opposite the right angle, this side never changes its name. Use these ratios to evaluate the trigonometric functions. Then simplify to prove the identity.

2. Problem (9)

[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]

As per the attached image, the following statements regarding the value of each ratio can be made:

[tex]sin(60)=\frac{\sqrt{3}}{2}\\\\cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cos(60)=\frac{1}{2}[/tex]

Substitute,

[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]

[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]

Simplify,

[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{\frac{2\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{\frac{2\sqrt{3}}{2}}{1+1}=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{\sqrt{3}}{1+1}=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}[/tex]

Thus, this equation is true.

2. Problem (10)

Use a similar strategy to evaluate this equation,

[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]

Use the attached image to evaluate the ratios.

[tex]cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cot(60)=\frac{1}{\sqrt{3}}[/tex]

Substitute,

[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]

[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]

Simplify,

[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]

[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]

[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]

[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]

[tex]2-\sqrt{3}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]

[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}+1}}[/tex]

[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]

Rationalize the denominator,

[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]

[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}-1}[/tex]

[tex]2-\sqrt{3}=\frac{(\sqrt{3}-1)^2}{3-1}[/tex]

[tex]2-\sqrt{3}=\frac{3-2\sqrt{3}+1}{2}[/tex]

[tex]2-\sqrt{3}=\frac{4-2\sqrt{3}}{2}[/tex]

[tex]2-\sqrt{3}=2-\sqrt{3}[/tex]

Therefore, this equation is also true.

Answer:

The lower quartile is 23.4

Step-by-step explanation:

The given data are;

47.2, 33.8, 43, 62, 5.8, 9, 61.4, 30.8, 68.2, 51.6, 13.2, 17.4, 64.2, 50.6, 29.4, 40.4

Rearranging the data, we have;

5.8, 9, 13.2, 17.4, 29.4, 30.8, 33.8, 40.4, 43, 47.2, 50.6, 51.6, 61.4, 62, 64.2, 68.2

The lower quartile, Q₁, is the (n + 1)/4 th term which is (16 +1)/4 = 4.25th term

However since we have an even set of numbers, we place a separator at the middle and we look for the median of the left half as follows

5.8, 9, 13.2, 17.4, 29.4, 30.8, 33.8, 40.4║ 43, 47.2, 50.6, 51.6, 61.4, 62, 64.2, 68.2

We have two numbers (17.4 + 29.4) at the median of the left set of numbers, we find the average of the two numbers to get the lower quartile

The lower quartile is therefore = (17.4 + 29.4)/2 = 23.4.

Step-by-step explanation:

denominator

add numerator

Answer:

2x-2

Step-by-step explanation:

Being specifically asked to rationalise the denominator we focus on it as required.

To rationalise a term it has to be multiplied by its inverse.

The inverse of

[tex] \sqrt{x} - \sqrt{2 - x} [/tex]

is

[tex] \sqrt{x} + \sqrt{2 - x} [/tex]

Multiplying this two vives us a difference of two squares

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

which gives us

x-(2-x)

=2x-2

Answer: 1 U.S.dollar  = 0.85 euro.

1 euro = 1.18 dollars.

Step-by-step explanation:

The given equation: [tex]E=\dfrac{17}{20}D[/tex]

, where 'E' is the amount of euros that has the same value as 'D' U.S. Dollars.

At D= 1,

[tex]E=\dfrac{17}{20}=0.85\text{ euro}[/tex]

i.e. 1 U.S.dollar  = 0.85 euro.

At E= 1 , we have

[tex]1=\dfrac{17}{20}D\\\\\Rightarrow\ D= 20/17\approx1.18\text{ dollars}[/tex]

Hence, 1 euro = 1.18 dollars.

Step-by-step explanation:

It is read thus Y^3+X^2-7

The equation form from the given statement would be Y^3 + X^2 - 7.

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically.

For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4.

We have been given a statement as;

"A number y cubed plus x squared decreased by 7".

So, the equation form would be

Y^3 + X^2 - 7

Learn more about expression here;

https://brainly.com/question/14083225

#SPJ2

The complete question is

"A number y cubed plus x squared decreased by 7". write the expression.

Answer:

5/12

Step-by-step explanation:

We know its a right angled triangle because of phythogorean theorem,

h^2=p^2+b^2

Take angle A as reference,

13^2=12^2+5^2

or,169=144+25

169=169

Now,

We know,

Tanx=p/b

As we took angle A as reference,

p=5

b=12

h=13

Put that in tanx=p/b

We get,

tanx=p/b=5/12

Answer:

Step-by-step explanation:

[tex]tan \ A = \frac{opposite \ side}{adjacent \ side}\\\\tan \ A = \frac{5}{12}[/tex]

Answer:

13. [tex]\frac{\sqrt[5]{x^4} }{x}[/tex].

14. [tex]v = \pm3\sqrt{5}[/tex]

15. 2.

Step-by-step explanation:

13. [tex]x^{1/5} * x^{-2/5}[/tex]

= [tex]x^{1/5 + (-2/5)}[/tex]

= [tex]x^{1/5 - 2/5}[/tex]

= [tex]x^{-1/5}[/tex]

= [tex]\frac{1}{x^{1/5}}[/tex]

= [tex]\frac{x^{4/5}}{x^{1/5 + 4/5}}[/tex]

= [tex]\frac{x^{4/5}}{x}[/tex]

= [tex]\frac{\sqrt[5]{x^4} }{x}[/tex].

14. [tex]v^2 - 45 = 0[/tex]

[tex]v^2 = 45[/tex]

[tex]\sqrt{v^2} = \pm\sqrt{45}[/tex]

[tex]\sqrt{v^2} = \pm\sqrt{3^2 * 5}[/tex]

[tex]v = \pm3\sqrt{5}[/tex].

15. [tex]\sqrt[3]{2} * \sqrt[3]{4}[/tex]

= [tex]\sqrt[3]{2 * 4}[/tex]

= [tex]\sqrt[3]{2 * 2 * 2}[/tex]

= [tex]\sqrt[3]{2 ^3}[/tex]

= 2.

Hope this helps!

Answer: Hi!

Row A: 7, 11, 15, 19, 23

Row B: 51, 42, 33, 24, 15

Row C: 4, 8, 16, 32, 64

Row D: 64, 32, 16, 8, 4

(If you notice, Row C and Row D are just swapped in order!)

Hope this helps!

Hi there! Hopefully this helps!

--------------------------------------------------------------------------------------------------------------

A's rule, add 4: 7, 11, 15, 19, 23

B's rule, Subtract 9: 51, 42, 33, 24, 15

C's rule, Multiply by 2: 4, 8, 16, 32, 64

D's rule, Divide by 2: 64, 32, 16, 8, 4

Answer:

r=-11

Step-by-step explanation:

7r+2=5(r-4)

7r+2=5r-20

2r=-22

r=-11

Try this

(x^2 + x - 12) + (x^2 - 8x + 16)

2y - 1

√36

i wanted to help you! :)

Answer:

[tex]\frac{3}{3}[/tex] = 1   (everything basically cancels)

Step-by-step explanation:

Answer:

1). Algebraic expression - a letter or symbol used to represent an unknown.

2). Coefficient - a numerical value.

3). Constant - the constant preceding the variables in a product.

4). Expression - a mathematical expression containing one or more variables.

5). Variable - a mathematical phrase that cannot be determined true or false.

Answer:

[tex]\Large \boxed{\mathrm{When \ a \ number \ is \ not \ known}}[/tex]

Step-by-step explanation:

For example, a sum of a number and 6 is 12.

The number is unknown.

Let the number be x.

We can solve for x (unknown number). Subtract 6 from both sides of the equation.

Answer:

a = 2, b = 0 , x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given that x = 0 and x = 2 are zeros of p(x) , then

p(0) = 0 and p(2) = 0

p(0) = 2(0)³ - 5(0)² + a(0) + b = 0 , that is

0 - 0+ 0 + b = 0, then b = 0

p(2) = 2(2)³ - 5(2)² + 2a + b = 0 , that is

16 - 20 + 2a + 0 = 0

- 4 + 2a = 0 ( add 4 to both sides )

2a = 4 ( divide both sides by 2 )

a = 2

Then

p(x) = 2x³ - 5x² + 2x ← factor out x from each term

      = x(2x² - 5x + 2)

      = x(2x - 1)(x - 2)

To find zeros equate p(x) to zero

x(2x - 1)(x - 2) = 0

Equate each factor to zero and solve for x

x = 0

x - 2 = 0 ⇒ x = 2

These are the 2 zeros already known (given)

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex] ← third zero of p(x)

secA=√2

secA=sec45

A=45°

3cos²45+5tan²45/ 4tan²A-sin²45

= 3(1/√3)²+5(1)² / 4(1)²-(1/√2)²

=3/2+5/4-1/2

=13/7

Answer:

[tex]\frac{13}{7}[/tex]

Step-by-step explanation:

Using the identities

cos x =[tex]\frac{1}{secx}[/tex] , sin²x = 1 - cos²x

tan²x = sec²x - 1

Given

[tex]\frac{3cos^2A+5tan^2A}{4tan^2A-sin^2A}[/tex]

= [tex]\frac{3(\frac{1}{sec^2A}+5(sec^2A-1) }{4(sec^2A -(1-cos^2A)}[/tex]

= [tex]\frac{3.(\frac{1}{\sqrt{2})^2 } +5((\sqrt{2})^2-1) }{4((\sqrt{2})^2-1)-(1-(\frac{1}{\sqrt{2} })^2 }[/tex]

= [tex]\frac{\frac{3}{2}+5(2-1) }{4(2-1)-(1-\frac{1}{2} )}[/tex]

= [tex]\frac{\frac{3}{2} +5}{4-\frac{1}{2} }[/tex]

= [tex]\frac{\frac{13}{2} }{\frac{7}{2} }[/tex]

= [tex]\frac{13}{2}[/tex] × [tex]\frac{2}{7}[/tex]

= [tex]\frac{13}{7}[/tex]

Answer:

( 0,0) and (3,0)

Step-by-step explanation:

y=(2x(x-3))/(x-1)

Set y = 0

0 =(2x(x-3))/(x-1)

Multiply each side by x-1, which makes x not equal to 1

0 =(2x(x-3))

Using the zero product property

2x=0  x-3 =0

x=0   x= 3

The x intercepts are x=0   x= 3

( 0,0) and (3,0)

Answer:

[tex]3^7[/tex]

Step-by-step explanation:

[tex]3^2*3^5[/tex]

[tex]\text {Apply Product Rule: } a^b+a^c=a^{b+c}\\\\3^2*3^5=3^{2+5}=3^7[/tex]

The probability that neither of them draws the Leeks card is P = 4/6 = 0.667

Here we can assume that all the cards have the same probability of being randomly drawn.

The cards are:

So we have 6 cards. We want to find the probability that neither contestant draws the "Leeks" card.

Sammy draws first, the probability of drawing the Leeks card will be equal to the quotient between the number of Leeks cards (one) and the total number of cards (6).

Then the probability of drawing the leeks card is p = 1/6

This means that the probability of NOT drawing the leeks card is:

q = 1 - 1/6 = 5/6.

Now draws Hanna, now there are 5 cards in the deck (because one was already drawn). With the same approach as before, the probability of drawing the Leeks card is p = 1/5, then the probability of NOT drawing the card is:

q = 1 - 1/5 = 4/5.

The joint probability (this is, the probability of both of these events to happen together) is just the product of the individual probabilities.

Then the probability that neither of them draws the Leeks card is:

P = (4/5)*(5/6) = 4/6 = 0.667

If you want to learn more about probability, you can read:

https://brainly.com/question/24349426

Answer:

Step-by-step explanation:

y = - 5x + 30  and  x = 10  ⇒  y = -5•10 + 30 = -50 + 30 = -20

x = 10  and y = -20   ⇒  (10, -20)

Answer:

Its B. (10, –20)

Step-by-step explanation:

I just took the quiz on edge

Answer:

-3

Step-by-step explanation:

-5 = -8 - (- 3)

Answer:

1-10, -3, 2, 7

im sorry if i give a wrong answer

Answer:

2520

Step-by-step explanation:

The n th term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference.

To find the number of terms given [tex]a_{n}[/tex] = - 10 , d = - 2 and a₁ = 100, then

100 - 2(n - 1) = - 10 ( subtract 100 from both sides )

- 2(n - 1) = - 110 ( divide both sides by - 2 )

n - 1 = 55 ( add 1 to both sides )

n = 56 ← number of terms

Given n, a₁ and a₅₆ , then the sun of the terms is

[tex]S_{56}[/tex] = [tex]\frac{n}{2}[/tex] (a₁ + a₅₆ )

      = [tex]\frac{56}{2}[/tex] (100 - 10) = 28 × 90 = 2520

Answer:

12) 1/8 inch =  0.125 inch

    = 0.003175 m

    = 3.175 x 10-3 m

    = 0.3175 cm

13) 2 is rational and  π  is  irrattional.  π   is approximately   3.14 and is the bigger of two

14) C= 40,005,306.33 m

  = 4.0005 x 107 m

15)  12,615,800,000

= 1.26158 x 1010

=126158 x 105

16) Let's take speed of ant as 1Km/h=1000m/h. Then time 1666.875 days

Step-by-step explanation:

Answer:

1. x²-2x+15

This can't be factored, I've tried multiple ways now, but it just can't be factored.

2. y²-19y+90​

Let's factor y^2−19y+90

y^2−19y+90

The middle number is -19 and the last number is 90.

Factoring means we want something like

(y+_)(y+_)

Which numbers go in the blanks?

We need two numbers that...

   Add together to get -19

   Multiply together to get 90

Can you think of the two numbers?

Try -9 and -10:

   -9+-10 = -19

   -9*-10 = 90

Fill in the blanks in

(y+_)(y+_)

with -9 and -10 to get...

(y-9)(y-10)

Answer:

(y−9) (y−10)

The market price is Rs. 750 which was obtained by creating a mathematical relationship from the given parameters.

PERCENTAGE DISCOUNT = 20%

VAT LEVIED= 12%

PRICE SOLD = 672

Let the MARKET PRICE = m

Hence,

market price * (1 - discount) * (1 + VAT) = price sold

m * (1 - 20%) * (1 + 12%) = 672

m * (1 - 0.2) * (1 + 0.12) = 672

m * 0.8 * 1.12 = 672

0.896m = 672

m = 672 / 0.896

m = Rs. 750

Learn more :

https://brainly.com/question/20418815

The Market Price of the product is RS. 750.

The Market Price is calculated by dividing the components associated to Discount, which is less than 1, and the Value Added Tax, which more than 1, to the Resulting Price.

[tex]c_{M} = \frac{c_{R}}{\left(1-\frac{r_{D}}{100} \right)\cdot \left(1+\frac{r_{T}}{100} \right)}[/tex] (1)

Where:

[tex]c_{M}[/tex] - Market price, in monetary units.

[tex]c_{R}[/tex] - Resulting price, in monetary units.

[tex]r_{D}[/tex] - Discount rate, in percentage.

[tex]r_{T}[/tex] - Tax rate, in percentage.

If we know that [tex]c_{R} = 672[/tex], [tex]r_{D} = 20[/tex] and [tex]r_{T} = 12[/tex], then the market price is:

[tex]c_{M} = \frac{672}{\left(1-\frac{20}{100} \right)\cdot \left(1+\frac{12}{100} \right)}[/tex]

[tex]c_{M} = 750[/tex]

The market price of the product is RS. 750.

Answer:

62

Step-by-step explanation:

add 24 to the smaller number to get the greater one

Answer:

62

Step-by-step explanation:

let, the greater number be 'x' and smaller number be 'y'

x-y=24 i.e. x-38=24

or, X=24+38

X= 62

Answer:

Step-by-step explanation:

A "difference" indicates subtraction is being used. The difference between these 2 numbers is found the same way we find the distance between 2 points on a number line. Since both the difference and the distance have to be positive numbers, the formula to find it is

|a - b| which is the absolute value of a - b.

If a = -52 and b = -79:

| -52 - (-79) | = | -52 + 79 | = 27 OR

If a = -79 and b = -52:

| -79 - (-52) | = | -79 + 52 | = | -27 | = 27

Answer:5.173973328

Step-by-step explanation:

Answer:

that would be false

Step-by-step explanation:

all whole numbers are integers, but not all integers are whole numbers