1. In a class test of 30 questions, 5 marks are given for every correct answer and (-2) marks are given for every incorrect answer. Rehana answered all questions but only 18 of her answers were correct. Find her total score.​

Functions are written in terms of variables. The value of the function when x  is -8 is 124

Functions are written in terms of variables. Given the function below;

g(x) = 2x^2 - 4

If the value of x is -8, substiute

g(-8) = 2(-8)^2 -4

g(-8) = 2(64) - 4

g(-8) = 124

Hence the value of the function when x  is -8 is 124

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Step-by-step explanation:

[tex] \sin( \alpha - \beta ) = \sin( \alpha ) \cos( \beta ) - \cos( \alpha ) \sin( \beta ) [/tex]

Using the Pythagorean theorem,

[tex] \cos( \alpha ) = \frac{4}{5} [/tex]

[tex] \sin( \beta ) = \frac{8}{10} [/tex]

[tex] \sin( \alpha - \beta ) = ( \frac{3}{5} )( \frac{3}{5} ) - ( \frac{4}{5} )( \frac{4}{5} )[/tex]

[tex] \frac{9}{25} - \frac{16}{25} = \frac{ - 7}{25} [/tex]

The correct value in its simplified form 32 = 32

So that we can write this expression in its correct form - it's just multiplying the terms outside the parentheses - for the terms that are inside the symbol.

4( 5 + 3 ) = 2( 22 - 6 )

4 · 5 + 4 · 3 = 2 · 22 - 2 · 6

20 + 12 = 44 - 12

32 = 32

Therefore, the correct simplified form of this question is 32 = 32. So, the equality is true.

Area

B

The equation that best models the data is (a) y = 186 - 6.2x

The data is not provided; so I would give a general guide on how to model a linear equation.

Assume the points on the line are:

(0,186) and (1,179.8)

Start by calculating the slope of the line using:

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

This gives

[tex]m = \frac{179.8 - 186}{1 - 0}[/tex]

Evaluate

m = -6.2

The equation is then calculated using:

[tex]y = m(x - x_1) + y_1[/tex]

This gives

y = -6.2(x - 0) + 186

Evaluate

y = -6.2x + 186

Rewrite as:

y = 186 - 6.2x

Hence, the equation that best models the data is (a) y = 186 - 6.2x

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[tex]\displaystyle |\Omega|=\binom{40}{2}=\dfrac{40!}{2!38!}=\dfrac{39\cdot40}{2}=780\\|A|=\binom{10}{2}=\dfrac{10!}{2!8!}=\dfrac{9\cdot10}{2}=45\\\\P(A)=\dfrac{45}{780}=\dfrac{3}{52}\approx5,8\%[/tex]

The sinusoidal function described is f(x) = 4*cos(x/2) + 2.

First, the amplitude is equal to half of the difference between the maximum and the minimum, so the amplitude is:

A = (6 - (-2))/2 = 4

The midline is equal to the minimum plus the amplitude:

M = -2 + 4 = 2.

now, we know that the y-intercept (when the function is evaluated in x = 0) is 6, so from that we conclude that we have a cosine function:

f(x) = 4*cos(kx) + 2

Notice that when evaluated in zero, we get:

f(0) = 4*cos(0) + 2 = 6.

Finally, we need to find the value of k.

Notice that the period of this function is 4π, while the period of the general cosine function is 2π, then we must have:

k*4π = 2π

Solving for k, we get:

h = (2π)/(4π) = 1/2.

Then the sinusoidal function described is f(x) = 4*cos(x/2) + 2.

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[tex]\text{Nth term of an arithmetic series} = a +(n-1)d \\\\\text{Nth term of an geometric series}= ar^{n-1}\\\\\text{where,}\\\\\text{a = first term.}\\\\\text{d = common difference.}\\\\\text{r = common ratio.}[/tex]

The number is that was multiplied by 6 is 2.

The equation that can be derived from the question is :

7 + (6a) = 19

Where a is the unknown number that 6 was multiplied with

Given the above equation, in order to determine the value of a, take the following steps:

Combine similar terms: 6a = 19 - 7

Subtract similar terms: 6a = 12

Divide both sides by 6: a = 12 / 6

a = 2

Here is the complete question:

Seven increased by the product of six and the number is 19. What is the number?

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Answer:

603.44 [in²]

Step-by-step explanation:

A = πr²/2 = 192.08 * π [in²] ≈ 603.44 [in²]

Answer:

The area of the semicircle having a radius of 19.6 meters is

603.68 [tex]m^{2}[/tex].

Detailed Answer:

The formula for the area of a circle is π[tex]r^{2}[/tex]. Therefore, the formula for the area of a semi-circle is ([tex]\frac{1}{2}[/tex] π[tex]r^{2}[/tex]).When the calculation is done

[tex]\frac{1}{2}[/tex] ×[tex]\frac{22}{7}[/tex] × 19.6 × 19.6 = 603.68 meters squared.

Answer:

t = -25

Step-by-step explanation:

-4/5=20/t

you are asked to find the value of t.

so let's make t the subject of the equation by Cross multiplication.

-4t= 100

dividing through by -4

t = -100/4

t= -25

The answer would be A; Three choices for size, two choices for the crust, and two choices for topping.

The true statement are those statements that satisfy the given condition.

A tree diagram. The sizes are large, medium, and small.

The crusts are thin or thick. The toppings are tomato or meatball.

Sizes;

Small, Medium, and Large,

so they have 3 choices for size.

Crust;

Thin or thick for each size,

so they have 2 choices for the crust.

Topping;

Tomato or meatball for each one,

So, they have 2 choices for toppings.

The answer would be A; Three choices for size, two choices for the crust, and two choices for topping.

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Answer:

A

Step-by-step explanation:

did the test

Answer:

x+y = 15

2x - y = 6

using elimination method

3x = 21

x = 7

therefore

7+y = 15

y = 15 - 7

y = 8

Answer:

Step-by-step explanation:

Comment

He added 42 to both sides of the equation. What that did is eliminated 42 on the left and changed the value on the right. Now what he has is the unknown on the left and an integer on the right.

We conclude that the image after the dilation is:

y =  -6 + (21/8)*x

For a function y = f(x), a dilation of scale factor k is written as:

g(x) = k*f(x)

In this case, our function is given by:

-7x + 8y = -16

Solving for y we get:

y = (-16/8) + (7/8)*x

y = -2 + (7/8)*x

Now we apply a scale factor k = 3, so we get the dilated line:

y = 3*( -2 + (7/8)*x) = -6 + (21/8)*x

So we conclude that the image after the dilation is:

y =  -6 + (21/8)*x

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Answer:

d) $8,100

Step-by-step explanation:

Given information:

If the money triples (multiplies by 3) every 10 years,
then in 40 years time it will triple 4 times, as 40 ÷ 10 = 4

⇒ Account balance after 40 years = $100 × 3 × 3 × 3 × 3

                                                         = $100 × 3⁴

                                                         = $8,100

Proof

In 10 years time the balance of the account will be:

$100 x 3 = $300

In another 10 years time, the balance of the account will be:

$300 x 3 = $900

In another 10 years time, the balance of the account will be:

$900 x 3 = $2700

In another 10 years time, the balance of the account will be:

$2700 x 3 = $8100

The equation that represents the statement is 2^2 + 1 = 21 and it is false

The statement is given as:

Two to the second power + 1 equals 21

Equals mean =

So, we have:

Two to the second power + 1 = 21

Two to the second power means 2^2

So, we have

2^2 + 1 = 21

Evaluate the exponent

4 + 1 = 21

Evaluate the sum

5 = 21

The above equation is false, because 5 does not equal 21

Hence, the equation that represents the statement is 2^2 + 1 = 21 and it is false

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Answer:

Step-by-step explanation:

Two to the second power +1 equals 21 what is the Equation

2 to the 2nd power is conventionally written as 2², with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 2^2.

so

2² + 1 = 21

4 + 1 = 21

5 = 21

the equation is false

Answer:

y = - 10x + 40

Step-by-step explanation:

Two points

[tex](0,40), (4, 0)[/tex]

Slope

[tex]m=\frac{0-40}{4-0} =-\frac{40}{4} =-10[/tex]

Equation:

[tex]y-40=-10(x-0)[/tex]

[tex]y-40=-10x[/tex]

[tex]y=-10x+40[/tex]

Hope this helps

The graph of vector v with an initial point at R (–19, 6) and terminal point at S (–35, 13). Option C; v = -16i + 7j represents the linear form of RS.

If we have given a vector v of initial point A and terminal point B

v = ai + bj

then the components form as;

AB = xi + yj

Here, xi and yj are the components of the vector.

c

Given;

The graph of vector v with an initial point at R (–19, 6) and terminal point at S (–35, 13).

v = (-35 +19)i + (13 - 6)j

v = (-16)i + (7)j

v = -16i + 7j

Thus, Option C; v = -16i + 7j represents the linear form of RS.

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Answer:

v = -16i + 7j

Step-by-step explanation:

I took the test :)

The number line that represents the solution set for the inequality is the number line on option B.

Option B is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Let's simplify the inequality.

2x - 6 ≥ 6(x - 2) + 8

2x - 6 ≥ 6x - 12 + 8

2x - 6x ≥ 6x - 4

-4x ≥ 6x - 4

-4x - 6x ≥ - 4

-10x ≥ -4

x ≥ 4/10

x ≥ 2/5

x ≥ 0.4

Now,

This number line will start from 0.4 till infinity on the right side of the number line.

Thus,

The number line on option B is the correct answer.

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The 46th term of the arithmetic progression is 288.

An arithmetic progression is a series of numbers called a sequence and the difference from one interval to another is constant.

From the given information:

156, 153, 150, ...

The 46th term will be:

[tex]\mathbf{a_{46} = a+ (n - 1) d}[/tex]

[tex]\mathbf{a_{46} = 153+ (46 - 1) 3}[/tex]

[tex]\mathbf{a_{46} = 153 + (45) 3}[/tex]

[tex]\mathbf{a_{46} =288}[/tex]

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Answer:

Based on the model produced by the scatterplot, log of stock prices is calculated from the scatter plot and 10 is raised to the power of the result to obtain the estimated stock price. Hence, a reasonable estimate for the stock price would be ; $185.05

From the scatter plot model :

Week number, x = 95

log y = 0.0022(95) + 2.0583

log y = 2.2673

y = estimated stock price

Raise the power of both sides to the power of 10

Therefore, a reasonble estimate for the stock price would be $185.05

ANSWER = C

(i) In decimals: 0.65

(ii) In percentage: 65%

The graph shows that after the spinner is spun after 40 times. The Fraction of wins is 0.65 out of 1. Look at the very end of the graph to look at the conclusion for probability. Similar cases when, after the spinner is spun after 20 times, the probability is 0.65.

Answer:

0.65 or 65%

Step-by-step explanation:

Evaluando una ecuación exponencial, veremos que luego de 5 años el capital se convierte en $12,884.08

Esta situación se podra modelar con la ecuación exponencial:

f(n) = $8,000*(1 + 10%/100%)ⁿ

Donde n es el número de años.

Podemos simplificar la ecuación para obtener:

f(n) = $8,000*(1.1)ⁿ

Ahora queremos ver el valor que toma esto cuando n = 5, asi obtenemos:

f(n) = $8,000*(1.1)⁵ = $12,884.08

Así que luego de 5 años, el capital se convierte en $12,884.08.

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