The slope of line
g
is −12
-
1
2
.

−12
-
1
2
·
·
=
=
−1

Answer:

\(Probability = 0.504\)

Step-by-step explanation:

Given

\(Gems= 35\)

\(Real = 10\)

\(Fake = 25\)

Required

Determine the probability of selecting two fakes

The probability can be represented as thus: \(P(Fake\ and\ Fake)\)

Using the following probability formula, we have:

\(P(Fake\ and\ Fake) = P(Fake) * P(Fake)\)

Each probability is calculated by dividing number of fakes by total number of gems:

\(P(Fake\ and\ Fake) = \frac{25}{35} * \frac{25-1}{35-1}\)

The minus 1 (-1) represent the numbers of fake and total gems left after the first selection

\(P(Fake\ and\ Fake) = \frac{25}{35} * \frac{24}{34}\)

\(P(Fake\ and\ Fake) = \frac{5}{7} * \frac{12}{17}\)

\(P(Fake\ and\ Fake) = \frac{60}{119}\)

\(P(Fake\ and\ Fake) = 0.504\)

Hence, the required probability is approximately 0.504

f⁻¹(x) = 4x + 7

This can be solved using the concept of function.

Function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). A function is described as a relationship between a group of inputs and one output each. In simple terms, a function is a connection between inputs, with each input corresponding to exactly one output. Every function has its own domain and codomain, as well as a range. f(x), where x is the input, is a common way to refer to a function.

Given that,

f(x) = x -7/4

f⁻¹(x) = 4x + 7

Now, f (f⁻¹(x)) = f (4x + 7)

=  [{(x - 7) / 4} ÷ 4] + 7

= x          [Proved]

Next, f⁻¹(f(x))

= f⁻¹ (x -7/4)

= 4 × [(x -7/4)] + 7

= x          [Proved]

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Answer:

Step-by-step explanation:

using the value of x = 20 from number 11

solve the angle H

∠H = 3x - 2

plugin the value of x=20 into the equation

∠H = 3(20) - 2

∠H = 58

Answer:

4 miles

Step-by-step explanation:

30-18=12

12÷3=4

hope this helped :)

After substituting the given values of x and y in the equation, all that can apply are (0, 2), (3, 0), and (6, -2).

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

here, we have,

As per the given information in the question,

The given equation is,

y=-2x+6

Now, substitute the corresponding points and check,

The points are,

(1 ,4) ⇒ 4= -2*1+6

⇒4=4

This is correct.

(2, 3)  ⇒ 3 = -4+6

This is not correct.

(-1, 8)  ⇒ 8= 2+6

This is correct.

(10, -15) ⇒ -15=-20+6

This is not correct.

(0, 3)  ⇒ 3=6

This not correct.

(3,0)  ⇒ 0 = -6+6

This is correct.

(7, -8)  ⇒ -8= -14+6

This  is correct.

(-6,17)  ⇒ 17 = 12+6

This is not correct.

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I believe it is 35!

I hope this helps you, and don't forget to give this answer brainliest if it really helped!

The correct answer is option C: \(\(k + 4 = 16\).\) This linear equation represents the relationship between Tina and Kai's volunteer times.

To represent the given situation, the equation that correctly represents the relationship between Tina's volunteer times (Tina = 16) and Kai's volunteer times (Kai = k) is:

\(\[Tina = Kai + 4\]\)

In this equation, Tina's volunteer times are represented by "Tina," and Kai's volunteer times are represented by "Kai." Since Tina has volunteered 4 more times than Kai, we add 4 to Kai's volunteer times to get the total number of times Tina has volunteered.

Substituting the given values, we have:

\(\[16 = k + 4\]\)

This equation represents the fact that Tina has volunteered \(16\) times, which is equal to Kai's volunteer times (k) plus the additional 4 times that Tina volunteered.

Simplifying the equation:

\(\[k + 4 = 16\]\)

This equation is equivalent to the original equation and represents the relationship between Tina and Kai's volunteer times. Hence, the correct answer is option C: \(\(k + 4 = 16\).\)

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The pairs of complementary angles are:

1) 36° and 54°

4) 23° and 67°

5) 5° and 85°

Two angles A and B are complementary if the sum of the measures is equal to 90°.

For the given options, the 3 correct ones are:

1) 36° and 54°

The sum gives:

36° + 54° = 90°

So these are complementary.

4) 23° + 67° = 90°

These are also complementary.

5) 5° + 85° = 90°

These are also complementary.

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The statements that will be true about parallelogram ABCD are: A, B, D, and E.

Properties of a Parallelogram -

Diagonals of a parallelogram bisect each other into congruent segments.

Opposite angles and sides of a parallelogram are always congruent.

Alternate interior angles are always congruent in measure.

Thus, the following would be true of parallelogram ABCD:

AP ≅ CP (congruent segment's of a bisected diagonal)

BC ≅ AD (congruent opposite sides)

∠CAD ≅ ∠ACB (congruent angles)

∠BPC ≅ ∠APD (congruent angles)

Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.

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Answer:

3/45-8=12

Step-by-step explanation:

Answer:

It's more accurate because

Step-by-step explanation:

Expressing in the simplest radical form just means simplifying a radical so that there are no more square roots, cube roots, 4th roots, etc left to find. It also means removing any radicals in the denominator of a fraction.

Hours spent on reading = 5

Hours spent on watching tv= 6

Hours spent on playing outside = 4

let R represent hours spent on reading

let W represent hours on watching tv

let P represent hours spent playing outside

Using associative property

R + (W + P) = (R + W ) + P

=>

5 + (6 + 4) = (5 + 6) + 4Ho

0.2 × 10 = 2

u can check a calculator

Answer:

5km

Step-by-step explanation:

A - her office

E - her home

AB = 1km; BC = CE = 4km

AE - the shortest disctance between her office and home.

ADE - right triangle, where AD = 4km, ED = 3 (EC - CD) =>

According to the Pythagorean theorem , we make up the equation:

AE = √ED^2 + AD^2 = √25 = 5km

Answer:

x = 4, -2

Step-by-step explanation:

x^2-2x=8

Move the constant term to the right side of the equation.

x^2 - 2x = 8

Take half of the coefficient of x and square it.

(-2/2)^2 = 1

Add the square to both sides of the equation.

x^2 - 2x + 1 = 8 + 1

Factor the perfect square trinomial.

(x - 1)^2 = 9

Take the square root of both sides of the equation.

x-1=\(\sqrt{9}\)
x-1=±3

Isolate x to find the solutions.

Taking positive

x=3+1=4

x=4

Taking negative

x=-3+1

x=-2

The solutions are:

x = 4, -2

Answer:

\(x = -2,\;\;x=4\)

Step-by-step explanation:

To solve the quadratic equation x² - 2x = 8 by factoring, subtract 8 from both sides of the equation so that it is in the form ax² + bx + c = 0:

\(x^2-2x-8=8-8\)

\(x^2-2x-8=0\)

Find two numbers whose product is equal to the product of the coefficient of the x²-term and the constant term, and whose sum is equal to the coefficient of the x-term.

The two numbers whose product is -8 and sum is -2 are -4 and 2.

Rewrite the coefficient of the middle term as the sum of these two numbers:

\(x^2-4x+2x-8=0\)

Factor the first two terms and the last two terms separately:

\(x(x-4)+2(x-4)=0\)

Factor out the common term (x - 4):

\((x+2)(x-4)=0\)

Apply the zero-product property:

\(x+2=0 \implies x=-2\)

\(x-4=0 \implies x=4\)

Therefore, the solutions to the given quadratic equation are:

\(\boxed{x = -2,\;\;x=4}\)

For binomial probability mass function formula and compound interest formula, These both involve the use of exponents, they are not otherwise related to each other in any significant way.

What is Compound interest?

Compound interest is the interest that is earned not only on the initial principal amount of an investment, but also on any interest that has accumulated over time. In other words, it is interest that is "compounded" or added to the principal amount at specific intervals, such as daily, monthly, quarterly, or annually.

Now,

The binomial probability mass function formula and the compound interest formula are not directly related to each other, as they are used to model different types of phenomena.

The binomial probability mass function is used to calculate the probability of obtaining a certain number of successes in a fixed number of independent trials, where each trial has two possible outcomes (success or failure) and the probability is same. The binomial probability mass function is

P(x) = pˣ (1-p)ⁿ⁻ˣ

where X is the number of successes, k is the specific number of successes we are interested in, n is the total number of trials, p is the probability of success on each trial, and represents the binomial coefficient.

The compound interest formula, on the other hand, is used to calculate the value of an investment over time, assuming a fixed interest rate and compounding periods. The future value is

FV = PV x (1 + r/n)ⁿˣ

where FV is the future value of the investment, PV is the present value of the investment, r is the interest rate (expressed as a decimal), n = number of times interest is compounded per year, and x = number of years.

While both formulas involve the use of exponents, they are not otherwise related to each other in any significant way.

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The binomial probability mass function formula and the compound interest formula are not directly related to each other.

The binomial probability mass function formula is used to calculate the probability of observing a certain number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant across all trials. The formula is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where X is the random variable representing the number of successes, k is the number of successes we want to observe, n is the total number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials.

On the other hand, the compound interest formula is used to calculate the value of an investment that earns a fixed interest rate over a certain period of time, assuming that the interest is compounded at regular intervals. The formula is:

A = P * (1 + r/n)^(nt)

where A is the final amount of the investment, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, t is the number of years, and (1 + r/n)^(nt) represents the growth factor of the investment.

While both formulas involve exponents and use the terms (1 - p) and (1 + r/n), they are fundamentally different in their purpose and application.

Answer:

the answer is $521.10 per hour

Step-by-step explanat

if you want the unrounded answer its  $521.103333

The values of x and y are 20 and 12.

The values of x and y are -3 and 2.

We have,

In a parallelogram,

- Opposite sides are congruent:

The opposite sides of a parallelogram have equal lengths.

- Opposite angles are congruent:

The opposite angles of a parallelogram have equal

Now,

a)

Opposite angles are congruent:

So,

5x + 29 = 7x - 11

29 + 11 = 7x - 5x

40 = 2x

2x = 40

x = 40/2

x = 20

And,

3y + 15 = 5y - 9

15 + 9 = 5y - 3y

24 = 2y

y = 24/2

y = 12

b)

Opposite sides are congruent:

So,

-6x = -4x + 6

-6x + 4x = 6

-2x = 6

x = -3

And,

7y + 3 = 12y - 7

12y - 7y = 3 + 7

5y = 10

y = 2

Thus,

The values of x and y are 20 and 12.

The values of x and y are -3 and 2.

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The required expressions are

{f(x + h) - f(x)}/h = 6h + 12x - 5 and

{f(3 + h) - f(3)}/h = -6h - 35 - 102/h

Simplifying algebraic expressions is when we use a variety of techniques to make algebraic expressions more efficient and compact - in their simplest form.

The techniques depends on the nature of the expression to be simplified. Common techniques used in simplifying algebraic expressions are substitution, distribution and collection of like terms.

Given,

f(x) = 6x² - 5x

f(x + h) = (x + h) ( (6(x + h) - 5)

Then,

f(x + h) - f(x) = (x + h) ( (6(x +h)-5) - (6x² - 5x)

= x + h (6x + 6h - 5) - 6x² + 5x

= 6x² + 6hx - 5x + 6hx + 6h² - 5h - 6x² + 5x

= 6h² + 12hx - 5h

{f(x + h) - f(x)}/h = 6h + 12x - 5

Given,

f(3) = -51

f(3 + h) = (3 + h) ( 1 - 6(3 +h))

= (3 + h) (1 - 18 - 6h)

= (3 + h) ( -17 - 6h)

= -51 - 18h - 17h - 6h²

= -6h² - 35h - 51

f(3 + h) - f(3) = -6h² - 35h - 51 - 51

= -6h² - 35h - 102

{f(3 + h) - f(3)}/h = (-6h² - 35h - 102)/h

= -6h - 35 - 102/h

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The frequency of the wave in the stretched wire, evaluated using the formula for a standing wave in a vibrating string are as follows;

(a) The frequency of the first harmonic is about 28.013 Hz

(b) The frequency of the second harmonic is about 56.026 Hz

(c) The third harmonic frequency is about 84.039 Hz

A stretched string vibrates such that the wavelength of the wave in the string is proportional to the length of the string.

The frequency of a stretched string can be found with the formula;

\(f_1 = \dfrac{\sqrt{\dfrac{T}{m/L} } }{2\cdot L}\)

Where;

T = The tension in the wire = 578 N

m = The mass of the string = 0.341 g

L = The length of the string = 54.0 cm = 0.54 m

Therefore;

f₁ = (√(578/(0.341/0.54))/(2×0.54) ≈ 28.013

(b) A general formula for the frequency of a standing wave is presented as follows;

\(f_n= \dfrac{n \cdot v}{2\cdot L}\)

Where;

\(f_n = \dfrac{n\times \sqrt{\dfrac{T}{m/L} } }{2\cdot L}\)

Therefore, the second harmonics, f₂ = 2·f₁

f₂ = 2 × (√(578/(0.341/0.54))/(2×0.54) ≈ 56.026

(c) The third harmonics, f₃ = 3 × f₁

Therefore;

f₃ = 3 × (√(578/(0.341/0.54))/(2×0.54) ≈ 84.039

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Answer:

Step-by-step explanation:

Correct choice is D

Answer:

D

Step-by-step explanation:

Given

- (x + 1)² - 4 = 0 ( add 4 to both sides )

- (x + 1)² = 4 ( multiply both sides by - 1 )

(x + 1)² = - 4 ( take the square root of both sides )

x + 1 = ± \(\sqrt{-4}\) = ± 2i ( subtract 1 from both sides )

x = - 1 ± 2i , then

x = - 1 + 2i, x = - 1 - 2i → D

Answer:

2

Step-by-step explanation:

As this is when it hits the ground, the projectile is in the air for 6 seconds.

Physically speaking, the missile would have been at ground level two seconds prior to launch if x were negative. Thus, we disregard the unfavorable option.

Objects that are thrown, shot, or launched with a certain initial velocity and then move against the forces of gravity and air resistance are known as projectiles. Projectiles can be anything from arrows and bullets to rocks and water balloons. Typically, a bow, slingshot, gun, or cannon is used to fire them. When projectiles are launched, gravity, air resistance, and other forces influence their trajectories.

from the question:

We must discover the moment the missile strikes the ground in order to calculate how long it was in the air. The height of the missile above the earth would be zero at that point.

Thus we must resolve the following equation:

y = -3x² - 12x + 96 = 0

We can use the quadratic formula to solve this equation in the quadratic form:

x = (-b ± √(b² - 4ac)) / 2a

where a = -3, b = -12, and c = 96.

Plugging in these values, we get:

x = (-(-12) ± √((-12)² - 4(-3)(96))) / 2(-3)

x = (12 ± √(144 + 1152)) / (-6)

x = (12 ± √1296) / (-6)

x = (12 ± 36) / (-6)

So, the solutions are:

x = -2 or x = 6

Physically speaking, the missile would have been at ground level two seconds prior to launch if x were negative. Thus, we disregard the unfavorable option.

As a result, the missile is in the air for 6 seconds before it strikes the earth.

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Answer:

x = 6.8

Step-by-step explanation:

7x + 36 = 12x + 2 (alternate interior angles are congruent)

Collect like terms

7x - 12x = -36 + 2

-5x = -34

Divide both sides

-5x/-5 = -34/-5

x = 6.8

We can use the given formula for the rate of change of the weight of the solid to estimate the amount of solid 1 second later.

If there is 6 grams of solid at time t, then f(t) = 6 g.

To estimate the amount of solid 1 second later, we can use the derivative formula:

f'(t) = −2f(t)(5+ f(t))

We want to estimate the value of f(t+1), which represents the weight of the solid 1 second later.

To do this, we can use Euler's method, which is an approximation method for solving differential equations.

Euler's method uses the formula:

f(t+1) ≈ f(t) + f'(t)Δt

where Δt is the time step (in minutes).

Since we want to estimate the amount of solid 1 second later, we can set Δt = 1 minute.

Plugging in the values for f(t) and f'(t), we get:

f(t+1) ≈ f(t) + f'(t)Δt

f(t+1) ≈ 6 - 2(6)(5+6)

f(t+1) ≈ -66

Therefore, the estimated weight of the solid 1 second later is -66 grams. However, this result does not make physical sense since weight cannot be negative.

It is possible that the given formula for f'(t) does not accurately describe the behavior of the solid, or that there was an error in the calculation.

or maybe im just bad at maths

Step-by-step explanation:

4(2x-1) ,x=5

4(2(5)-1)

4(10-1)

4(9)

36

hope it's helpful ❤❤❤❤❤❤

THANK YOU.

#

Answer:

36

Step-by-step explanation:

when you plug 5 into this equation you get 36!

Answer x=12

Step-by-step explanation:

5/2x-7=3/4x+14

      +7.         +7

5/2x=3/4x+21

-3/4x -3/4x

5/2-3/4=7/4x

7/4x=21.         since there's a fraction on one side, multiply 4 with 21

7x=84

divide and you'll get x=12

\( \frac{5}{2} x(4) - 7(4) = \frac{3}{4} x(4) + 14(4) \\ 10x - 28 = 3x + 56\)

\(10x - 3x = 56 + 28 \\ 7x = 84 \\ x = \frac{84}{7} \\ x = 12\)

\( \large \boxed {x = 12}\)

The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

x = 136°

Step-by-step explanation:

the third angle of the triangle is 180 - (90+46), which is 44. Because a straight line is 180°, x is 180 - 44. x = 136°

Answer:

look according to the exterior angle of triangle

Step-by-step explanation:

exterior angle = sum of other two angle (except adjacent angle of that exterior angle)

so x=90°+46°=136°