Condense each expression to a single logarithm

The probability that the random variable has a value greater than 7 is undetermined.

The formula to calculate the probability of occurrence of an event 'A' can be written as -  

P(A) = n(A)/n(S)

where -

n(A) = Number of outcomes favorable to event A.

n(S) = Total number of outcomes

We have a random variable having a value greater than 7

Now -

Number of outcomes favorable to event A = (-∞, + ∞) - (- ∞, 7)

Total number of outcomes for event A = (-∞, + ∞)

P(A) = (-∞, + ∞) - (- ∞, 7) /  (-∞, + ∞)

P(A) = ∞/∞

P(A) = undetermined

Therefore, the probability that the random variable has a value greater than 7 is undetermined.

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Answer:

x=-1/13

Step-by-step explanation:

Answer:

Step-by-step explanation:

it is 2

The correct options are:

Given,

In the question:

Which statements are true about exponential decay functions?

Now, According to the question;

We know that the exponential function is given by:

[tex]f(x) = ab^x[/tex]

where a>0 and b are constants.

Also, it represents a growth function if b>1

and a decay function if 0<b<1

where b is the base.

Hence, the domain of the function is all the real numbers )

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Answer:

x=3

Step-by-step explanation:

I’m pretty sure these 2 angles are equivalent

64-4x=58-2x

6-4x=-2x

6=2x

3=x

Hopes this helps please mark brainliest

The number line that satisfies the inequality is option (B).

What are number lines?
Number lines are horizontal straight lines in mathematics where numbers are arranged in equal intervals. A numeric line can be used to represent every number in a sequence. The endpoints of this line go on infinitely. In other terms, it is an image of numbers on a straight line. It functions as a guide for distinguishing and organizing numbers. It can be used to represent any real number, including all whole numbers and natural numbers.

Solution Explained:
- (a+5) < 4/-2 <= -3-a

[tex]\left \{ {{- (a+5) < 4/-2} \atop { 4/-2 < -3-a}} \right.[/tex]

[tex]\left \{ {{-a - 5 < -2} \atop {-2 < = -a -3}} \right.[/tex]

[tex]\left \{ {{-a-5) +5 < -2+5} \atop {-2+3 < = (-a-3)+3}} \right.[/tex]

[tex]\left \{ {{-a- 5 +5 < 3} \atop {1 < = -a-3+3}} \right.[/tex]

[tex]\left \{ {{-a < 3} \atop {1 < = -a}} \right.[/tex]

[tex]\left \{ {a > -3} \atop {-a > = 1}} \right.[/tex]

[tex]\left \{ {{a > -3} \atop {a < = -1}} \right.[/tex]

[tex]-3 < a < = -1[/tex]

a ∈ (-3, -1]

Hence, the number line that satisfies the inequality -(a+5) < b/-2 <= -3-a is in option (B).

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An equation of the line that began with a y-intercept of (0, 4), shifted up 3 units, and is perpendicular to y = 3/4(x) - 2 is: A. y = -4/3(x) + 7.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

In Mathematics, the condition for perpendicularity of two lines is given by m₁ × m₂ = -1. Next, we would determine the slope of this equation that began with a y-intercept of (0, 4):

3/4 × m₂ = -1

3m₂/4 = -1

3m₂ = -4

m₂ = -4/3

In order to determine the new y-intercept, we would translate the equation by shifting it 3 units up:

Translation = y + 3 = 4 + 3 = 7.

Now, we can write this equation in slope-intercept form as follows:

y = mx + c

y = -4x/3 + 7 or y = -4/3(x) + 7.

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Complete Question:

What is the equation of the line that began with a y-intercept of (0,4), was shifted up 3 units, and is perpendicular to y = 3/4x-2?

answer choices:

A. y = -4/3(x) + 7

B. y=-3/4(x)+7

C. y=-3/4(x)+4

D. y =-4/3(x)+4

Bank A grants a shorter payment period and is the least costly, so the Ruffins should take the loan from Bank A.

In finance literature and practice, the loan interest (cost) increases with a more extended payment period.

In other words, a shorter payment period reduces the interest cost of a loan.  The loan cost is also influenced by the amount of the principal and the interest rate.

Down payment = 25%

Interest rate = 11%

Mortgage period = 25 years

2 points at closing

N (# of periods) = 300 months (25 years x 12)

I/Y (Interest per year) = 11%

PV (Present Value) = $142,500 ($190,000 - $47,500)

FV (Future Value) = $0

Results:

Period Payments (PMT) = $1,396.66

Sum of all periodic payments = $418,998

Total Interest = $276,498

Down payment = $47,500 ($190,000 x 25%)

2 points = $2,850 ($142,500 x 2%)

Sum of periodic payments = $418,998

Total costs = $469,348 ($47,500 + $2,850 + $418,998)

Down payment = 15%

Interest rate = 10%

Mortgage period = 30 years

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 10%

PV (Present Value) = $161,500

FV (Future Value) = $0

Results:

Period Payments (PMT) = $1,417.28

Sum of all periodic payments = $510,220.08

Total Interest = $348,720.08

Down payment = $28,500 ($190,000 x 15%)

Sum of periodic payments = $510,220.80

Total costs = $538,720.80 ($28,500 + $510,220.80)

Thus, we can recommend the Ruffins should go for a Bank A loan that costs less than Bank B's.

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Answer: 63

Step-by-step explanation:

When there are two lines intercepting the two angles opposite each other are the same

and GHK and IHF are opposite of each other so there for are equal

Answer:

120

Egg.    Egg tarts

2.75 = 1

330  = 1 x 330 divided by 2.75 = 120

The value of x is .[tex]\sqrt{170}[/tex]

What is Pythagorean Theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.

Here, the two sides of the triangle are, 7 and 11.

By Pythagorean theorem,

[tex]7^2 + 11^2 = x^2\\49 + 121 =x^2 \\170 = x^2\\x = \sqrt{170} \\[/tex]

Hence, the value of x is [tex]\sqrt{170}[/tex].

Here, the sum of two sides of triangle is not a perfect square.

Therefore, the side lengths is not a Pythagorean triple.

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Answer: 3(6+2), 3(5+3)

Step-by-step explanation:

Since 18+6 equals 24, you need to find the answers that are equivalent to 24.

3(6+2)

If you do order of operations, it would look like this

3(6+2)

3(8) or 3x8

24

3(5+3)

5+3 equals 8, so this is the same as the first answer.

The system of equations representing the amount invested are;

(a) x + y + z = 460,000

(b) 0.065·x + 0.07·y + 0.09·z = 36,350

(c) z = x + y

(d) There is one solution. The man invested $90,000 at 6.5%, $140,000 at 7% and $230,000 at 9%

A system of equations are two or more equations that have variables that are common to the equations in the system.

The questions in the parts (a) to (d) obtained from a similar question are;

(a) An equation stating the sum of the three investments

(b) The equation that states that of the sum of the return is 36,350

(c) The equation that states that the amount invested at 9% equals the sum of the other two investments

(d) Solve the derived system of equations

(a) The amount the man invests in the three rental properties = $460,000

Amount invested in the property that earns 6.5% = x

Amount invested in the property that earns 7% = y

The amount invested in the property that earns 9% = z

The equation that represents the sum of the three investments is therefore;

x + y + z = 460,000...(1)

(b) The equation that represents the sum of the returns from the three investment is found as follows;

6.5% = 0.065, 7% = 0.07, 9% = 0.09

(c) The equation stating the amount invested at 9% equals the sum of the other two investment is; z = x + y...(3)

(d) The system of equations is solved as follows;

From equation (1) and (2), we get;

x + y + z = 460,000

z + z = 460,000

2·z = 460000

· = 460,000 ÷ 2 = 230,000

The amount invested in the property that earns 9% per year is $230,000

Equation (3) indicates;

0.65·x + 0.07·y + 0.09 × 230,000 = 36,350

0.65·x + 0.07·y = 36,350 - 0.09 × 230,000 = 15650

The interest earned in the properties that earn 6.5% and 7% = $15650

0.65·x + 0.07·y = 15650...(4)

x + y = 230000...(5)

Equation (4) and (5) indicates;

y = 230,000 - x

0.065·x + 0.07×(230,000 - x) = 15650

16100 - 0.005·x = 15650

0.005·x = 16,100 - 15,650 = 450

x = 450 ÷ 0.005 = 90,000

The amount invested in the property that yields 6.5% per year = $90,000

Therefore;

The amount invested in the property that earns 7% per year = $230,000 - $90,000 = $140,000

There is one solution, the man invested $90,000 at 6.5%, $230,000 at 7%, and $230,000 at 9%

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The first derivative of the function f'(x) = 2 · [√(x + x²) + 3 · sin 3x]² · [(1 + 2 · x) / [2 · √(x + x²)] + 9 · cos 3x], whose value at x = 1 is - 35.909.

Herein we find a function whose first derivative has to be found. This can be done by using the following derivative rules:

Derivative of a power

f(x) = c · xⁿ → f'(x) = n · c · xⁿ ⁻ ¹

Chain rule

f[g(x)] = (df / dg) · (dg / dx)

Derivative of a sum of functions

d / dx [f(x) + g(x)] = df / dx + dg /dx

Derivative of the sine

d / dx [sin x] = cos x

Now we proceed to find the derivative of the function:

f'(x) = 2 · [√(x + x²) + 3 · sin 3x]² · [(1 + 2 · x) / [2 · √(x + x²)] + 9 · cos 3x]

And we evaluate the derivative at x = 1:

f'(1) = 2 · [√(1 + 1²) + 3 · sin 3]² · [(1 + 2) / [2 · √(1 + 1²)] + 9 · cos 3]

f'(1) = 2 · (√2 + 0.423)² · (3 / 2 - 8.910)

f'(1) = - 35.909

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The factoring of the polynomial f(x) = x^4 + 3x³ - 2x² + 48x - 288 is given as follows:

f(x) = (x - 4i)(x + 4i)(x + 6)(x - 3).

The polynomial is factored by it's linear factors, given as follows:

f(x) = (x - x')(x - x'')(x - x''')(x - x'''').

In which x', x'', x''' and x'''' are the roots of the polynomial f(x).

In this problem, we have that -4i is a root, hence, by the Conjugate Roots Theorem, 4i is also a root and hence:

f(x) = (x - 4i)(x + 4i)(x - x''')(x - x'''').

f(x) = (x² + 16)(x - x''')(x - x'''').

As a fourth order polynomial can be the product of two second order polynomials, hence:

x^4 + 3x³ - 2x² + 48x - 288 = (x² + 16)(ax² + bx + c)

x^4 + 3x³ - 2x² + 48x - 288 = ax^4 + bx³ + (c + 16)x² + 16bx + 16c.

Hence the coefficients are given as follows:

Then the equation for the final two factors is:

x² + 3x - 18 = 0.

Which is simplified as follows:

x² + 3x - 18 = (x + 6)(x - 3).

Hence the simplified polynomial is:

f(x) = (x - 4i)(x + 4i)(x + 6)(x - 3).

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Answer:

this is Ture

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

By changing both equations to slope-intercept, it is easier to determine whether two lines are perpendicular.

Since [tex]y = \frac{5}{2} x+ 5[/tex] is already in slope-intercept form, we just need to change the first given equation.

2x + 5y + 3 = 0

2x + 5y = -3

5y = -2x -3

[tex]y=\frac{-2}{5}x-\frac{3}{5}[/tex]

Two lines are perpendicular when the slope of the lines (coefficient of x) are negative reciprocals (opposite sign of the inverse of a number).

Comparing the two slopes [tex]\frac{5}{2}[/tex]  and [tex]\frac{-2}{5}[/tex], we can see they they both fit the criteria of being opposite signs and inverses of each other.

So  2x + 5y + 3 = 0 is perpendicular to y = (5/2)x+ 5.

Option (A) is the correct option and on simplifying the expression by combining like terms we get,

24 - 3p.

Given, the expression 6(4 - 2p) + 9p

On simplifying, we get

24 - 12p + 9p

24 - 3p

So, on simplifying the given expression, we get

24 - 3p

Hence, Option (A) is the correct option and on simplifying the expression by combining like terms we get,

24 - 3p

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The value of 200 US dollars into canadian dollars is 259.74

What is an example of a unitary method?

A single or unique unit is referenced to using the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.

Given That:

1 Canadian dollar is = 0.77 US dollar

So 1 US dollar is = 1/0.77 canadian dollar

So 200 US dollar is = 1/0.77 * 200 = 259.74 canadian dollar

Hence the answer is 259.74 dollar

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Answer:

um well fierst da answer is proberly yes and no

Step-by-step explanation:

i tried to do da work

Answer:

b and d are relative minimums (minima)

Step-by-step explanation:

An "absolute" minimum is the very lowest point on a graph. This graph doesn't have an "absolute" minimum because the end points both go to negative infinity (they go down forever)

But, this graph DOES have points that are "relative" minimums, which means the points are the minimum (lowest) in their neighborhood. In the immediate vicinity of the point, it is the lowest point.

In case there are further questions with this graph:

relative max: a and c

absolute max: f

x-intercepts: a,c,e,g

probably a 6th degree function,

multiplicity 2 at a and c

multiplicity 1 at e, g

leading coeffient is negative.

The standard deviation of death in an army corps each year is 0.78

From the question, we have the following parameters that can be used in our computation:

Distribution type = Poisson distribution

Average of the distribution = 0.61

The standard deviation of the distribution is calculated as:

Standard deviation = √Average of the distribution

Substitute the known values in the above equation, so, we have the following representation

Standard deviation = √0.61

Evaluate the square root expression

So, we have

Standard deviation = 0.78

Hence, the standard deviation is 0.78

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Answer:

The lines through the given points are parallel

Step-by-step explanation:

The given lines can be evaluated as follows

The first step is to calculate the slope [tex]m_{1}[/tex] of the first line using the slope formula as follows

[tex]m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Take two coordinates on the first line

[tex](10,5)~\text{and}~(-8,9)[/tex]

Substitute [tex]9[/tex] for [tex]y_{2}[/tex], [tex]-8[/tex] for [tex]x_{2}[/tex] , [tex]5[/tex] for [tex]y_{1}[/tex] , [tex]10[/tex] for [tex]x_{1}[/tex]  in the slope formula

[tex]m_{1}=\frac{9-5}{-8-10}[/tex]

Simplify the numerator and the denominator at the right side of the equation

[tex]m_{1}=\frac{4}{-18}[/tex]

Simplify the fraction at the right side of the equation

[tex]m_{1}=-\frac{2}{9}[/tex]

The slope of the first line is [tex]-\frac{2}{9}[/tex]

Take two coordinates on the second line

[tex](2,-4)~\text{and}~(11,-6)[/tex]

Substitute [tex]-6[/tex] for [tex]y_{2}[/tex], [tex]11[/tex] for [tex]x_{2}[/tex] , [tex]-4[/tex] for [tex]y_{1}[/tex] , [tex]2[/tex] for [tex]x_{1}[/tex]  in the slope formula

[tex]m_{2}=\frac{-6-(-4)}{11-2}[/tex]

Take out the brackets in the numerator at the right side of the equation

[tex]m_{2}=\frac{-6+4}{11-2}[/tex]

Simplify the numerator and the denominator at the right side of the equation

[tex]m_{2}=\frac{-2}{9}[/tex]

The slope of the second line is [tex]-\frac{2}{9}[/tex]

Since the slope of both lines are equal, then the lines through the given points are parallel

Hence the lines through the given points are parallel

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3 is an adjacent interior angle which is both adjacent and interior angle, this angle lie inside a triangle.

The two angles are said to be adjacent angles when they share the common vertex and side.

An interior angle is an angle inside a triangle.

The angle between the extended side and the side next to it is called an exterior angle.

Since we know that any two interior angles that share a common side are called the "adjacent interior angles" of the polygon, or just "adjacent angles".

Therefore,

In the diagram the adjacent angles are 3 and 4.

The interior angles from the diagram are 1, 2, and 3.

and the exterior angle is 4.

Hence , 3 is the only angle which is both adjacent and interior angle .

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Answer:

120 minutes

Step-by-step explanation:

d=rt

D-distance

r-unit rate

T- time

14=7t

/7. /7

2=t

2 hours

2 x60=120

120 minutes

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According to the given percentage, the shipping and handling fee that Elizabeth will pay is $16.6

Percentage:

Percentage refers one-hundredth (1/100) of something. And it refers to the rate or proportion of that one hundred.

Given,

Elizabeth buys a microscope priced at $83. Shipping and handling are an additional 20% of the price.

Here we need to find the shipping and handling will Elizabeth paid.

We know that, the price of the product is $83.

And the charges for the shipping and handling is 20%.

So, it can be written as the following form,

=> Additional charges = 20% of 83

=> Additional charges =  20/100 x 83

=> Additional charges = 20 x 0.83

=> Additional charges = 16.6

Therefore, the shipping and handling charges is $16.6

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The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9

The equation of the function is given as

f(x) = 3x²

Also, we have

Vertex = (5, 9)

The form of the equation is given as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

This means that

Vertex = (h, k) = (5, 9)

Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 5)² + 9

This also means that

f(x) = -3(x - 5)² + 9

The -3 is gotten from f(x) = -3x²

Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9

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The image of F after a counterclockwise rotation of 180° about G is F(2,7).

What is a line segment?

A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.

Here, we

Rotate FG through 180° about the origin O in an anticlockwise direction, the new position of points F and G are:

F (-2, -7) = F' (2, 7)

G (-4, -2) = G' (4, 2)

Thus, the new position of line segment FG is F'G'.

Hence, the image of F after a counterclockwise rotation of 180° about G is F(2,7).

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The variable 'c' in the given expression has No Solution.

Given, that

2/3c - 1 = 1 + 2/3c

Now, as we have same coefficient of the variable c i.e. 2/3

So, On subtracting 2/3c from both the sides, we get

2/3c - 2/3c - 1 = 1 +2/3c - 2/3c

-1 ≠ 1

Hence, we got no solutions that can satisfy the given expression.

So, the variable 'c' in the given expression has No Solution.

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