Explain how to convert a number of months to a fractional part of a year.Divide the number of months by 6

To solve this problem, use logarithmic properties to combine the two equations into one.

First, use the product rule to combine the two equations:
$\log_2(32) + \log_2(x-4) + \log_2(x) = 5$
Then use the power rule to combine the last two terms:
$\log_2(32) + \log_2(x^2 - 4x) = 5$
Finally, use the quotient rule to separate the terms:
$\log_2\frac{32}{x^2 - 4x} = 5$

To solve for $x$, take the inverse logarithm of both sides:
$\frac{32}{x^2 - 4x} = 2^5$
Expand and simplify the left side to get a quadratic equation:
$x^2 - 4x - 32 = 0$
Solve the quadratic equation using the quadratic formula:
$x = \frac{4 \pm \sqrt{4^2 + 4(32)}}{2}$
$x = \frac{4 \pm \sqrt{136}}{2}$
$x = 4 \pm \sqrt{17}$

Therefore, the solutions are:
$x = 4 + \sqrt{17}$
$x = 4 - \sqrt{17}$

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Answer:

13

Step-by-step explanation:

First drop the line.

How many units is it from Point [tex]r[/tex] to the x axis?

12.

How many units is it from Point [tex]r[/tex] to the y axis?

5.

Now we can use the Pythagorean Theorem.

[tex]12^5+5^2=c^2[/tex]

[tex]144+25=c^2[/tex]

[tex]c^2=169[/tex]

[tex]c=13[/tex]

Of these 12 individuals: Expected number of survivors ≈ 4.

Based on the given information, the chance of survival for the 12 people admitted to the hospital who tested positive for the disease is 30%.

If the chance of survival for a person who tests positive for the disease is 30%, and 12 people have been admitted and tested positive for the disease, then the expected number of survivors is 30% of 12, which is 3.6.

However, since it is not possible for 0.6 of a person to survive, we can round this number to the nearest whole number, which is 4.

Therefore, we can expect that 4 out of the 12 people who tested positive for the disease will survive. This can be written as:

Expected number of survivors = (Chance of survival) × (Number of people who tested positive) = (0.30) × (12) = 3.6 ≈ 4
So, the answer is 4.

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The original value of the oranges is 143.75.

A percentage is a number or a ratio that is expressed as a fraction of 100 i.e. out of 100.

In formula, x% of amount y = y*(x/100)

Given :

Tax paid by Rekha : 15%

Final Price paid by Rekha : 165.31

Let the original price of the oranges = x

The additional tax amount on oranges

           = 15% of original price of x

           = 15 * x / 100

           = 0.15 x

Total price paid by Rekha = Original price of orange + Tax amount

165.31 = x + 0.15x

165.31 = (1 + 0.15)x

165.31 = 1.15x

x = 165.31/1.15

x = 143.75

Thus, the original value of the oranges is 143.75.

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Answer:

5/33

Step-by-step explanation:

5/6 divided by 11/2

Invert the divider

5/6 x 2/ 11

10/66

Reduce to smallest fraction

5/33

Answer:

5/33

Step-by-step explanation:

Apply the fraction rule: a/b ÷ c/d = (a × d) ÷ (b × c) for 5/6 ÷ 11/2

a = 5

b = 6

c = 11

d = 2

(5 × 2) ÷ (6 × 11)

For "(6 × 11)", break 6 down into "2 × 3", so that you can cancel out the common factor, because there is also a 2 in "5 × 2".

= (5 × 2) ÷ (2 × 3 × 11)         -- cancel out the 2's

= 5 ÷ (3 × 11)     *****3 × 11 = 33*****

= 5/33

Therefore, the original price of the shirts was $18.75 each.

An equality on both sides of the equal to sign signifies a mathematical equation, which is a relationship between two expressions. Here is an example of an equation: 3y = 16.

If the selling price of the shirts was 80% of their regular price, then we can use the following equation to find the original price:

Original price * 0.8 = Selling price

Let's substitute the given values into the equation:

Original price * 0.8 = 15

To solve for the original price, we need to isolate it on one side of the equation. We can do this by dividing both sides by 0.8:

Original price = 15 ÷ 0.8

Original price = 18.75

Therefore, the original price of the shirts was $18.75 each.

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The solution is, the triangle ABC and DBC are congruent, by the Side-Angle-Side Triangle Congruence Theorem.  

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

As we can seen from the given figure that two triangles are given.

The triangles ABC and BDC are :

AB = CD

AC = BD

BC = BC

Hence using the SSS theorem of the triangle, the triangle ABC and DBC are congruent, Thus the angle A  is equal to angle D.

Hence the option D and E are correct. i.e. congruent by the Side-Angle-Side Triangle Congruence Theorem.  

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Answer:

Gina has 47 nickels

Step-by-step explanation:

Let's call the number of nickels that Gina has "n" and the number of dimes she has "d". We know that she has a total of 70 nickels and dimes, so:

n + d = 70 (equation 1)

We also know that the value of her nickels and dimes is $4.65, which is equal to 465 cents. Each nickel is worth 5 cents and each dime is worth 10 cents, so the value of n nickels is 5n cents and the value of d dimes is 10d cents. Therefore, we can write another equation based on the value of the coins:

5n + 10d = 465 (equation 2)

We can simplify equation 2 by dividing both sides by 5:

n + 2d = 93 (equation 3)

Now we have two equations with two variables. We can solve for one of the variables in terms of the other and substitute into the other equation to solve for the remaining variable. For example, we can solve equation 1 for d:

d = 70 - n

Substituting this expression for d into equation 3, we get:

n + 2(70 - n) = 93

Simplifying this equation, we get:

n + 140 - 2n = 93

-n + 140 = 93

-n = -47

n = 47

Therefore, Gina has 47 nickels and 23 dimes (since n + d = 70), and the total value of her coins is $4.65.

Answer:

47 nickels

Step-by-step explanation:

47 nickels

To solve for r, we can divide both sides of the equation by Pt: r = (A-P)/Pt

The formula A=P+Prt is used to calculate the total amount of money (A) after a certain period of time when a principal amount (P) is invested at a certain interest rate (r) for a certain amount of time (t). To solve for the specified variable r, we need to rearrange the formula and isolate r on one side of the equation. Here are the steps to do so:

Step 1: Subtract P from both sides of the equation to get:
A - P = P + Prt - P

Step 2: Simplify the right side of the equation to get:
A - P = Prt

Step 3: Divide both sides of the equation by Pt to get:
(A - P) / Pt = r

Step 4: Simplify the left side of the equation to get:
r = (A - P) / Pt

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Answer:

squareroot(256)

16

Step-by-step explanation:

im genius

25344 ft

We can use the conversion factors to convert 8 kilometers to another measure.

From the given conversion factors, we know that:

1 km ≈ 0.6 mi

1 mi = 5,280 ft

So, to convert 8 kilometers to feet, we can first convert it to miles and then convert miles to feet:

8 km x 0.6 mi/km = 4.8 miles

4.8 miles x 5,280 ft/mile = 25,344 ft

Therefore, 8 kilometers is equivalent to 25,344 feet.

The answer is option (C) 25,344 ft

The measure m∠UTS is approximately 90 degrees.

Rhombus is a parallelogram whose all sides are of equal lengths.

Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).

Its vertex angles are bisected by its diagonals.

The triangles on either side of the diagonals are isosceles and congruent.

We are given that;

Angle VUR=(10x-23)degree

Angle TUV=(3x+19)degree

Now,

Since RSTU is a rhombus, its diagonals are perpendicular bisectors of each other, which means that angle VUT is a right angle. Therefore, we have:

m∠VUR + m∠TUV + m∠VUT = 180°

Substituting the given values, we get:

(10x - 23) + (3x + 19) + 90 = 180

13x + 86 = 180

13x = 94

x = 7.23 (rounded to two decimal places)

Now, we can find m∠UTS as follows:

m∠UTS = m∠VUR + m∠TUV

Substituting the value of x, we get:

m∠UTS = (10x - 23) + (3x + 19)

m∠UTS = (10 × 7.23 - 23) + (3 × 7.23 + 19)

m∠UTS = 72.3 - 23 + 21.69 + 19

m∠UTS = 89.99

Therefore, the answer of the given rhombus will be 90 degrees.

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60Answer: it would be 60

Step-by-step explanation:

it’s going up and down by 10

(a) m∠BAC = 73°

(b) The value of y is 2.

A triangle that has two equal lengths of sides and two equal measures of angles is called an isosceles triangle.

(a) Given:

m∠BEA = 62°.

Assuming ABCD is a square.

The diagonal of the square divides the square into two isosceles right-angled triangles.

So, m∠BAD = 90° and m∠ABD = m∠ADB = m∠ABE = 45°.

So, the angle measure of ∠BAC,

m∠BAC = 180° - (45 + 62)

m∠BAC = 180° - 107°

m∠BAC = 73°

(b) Given:

BE = 6y + 2 and CE = 4y + 6.

Assuming ABCD is a square.

The diagonals of squares divide the diagonals into two equal parts.

So, BE = CE

6y + 2  = 4y + 6.

2y = 4

y = 2

Therefore, the value of y is 2.

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The Initial value problem is defined

as [tex] \frac{dy}{dt} =\alpha y(1 -y), y(0) = y_0[/tex]

a) Equilibrium points or critical values are y = 0 and y = 1. Also, y = 0, is unstable and y = 1, is asymptomatic stable.

b) The solution of above initial value problem is y = 1 , which means at the end the disease will spread through the entire population.

We have a population data which can be divided into two parts. Let consider x be the proportion of susceptible individuals and y the proportion of infectious individuals; then x + y = 1. Now, Initial value problem ( that a differential equation) is, [tex] \frac{dy}{dt} = \alpha y(1 -y), y(0) = y_0[/tex]

a) we have to determine equilibrium points and nature of asymptote for above equation. To determine the equilibrium solution of equation we must put, dy/dt = 0, for all t values. At equilibrium, dy/dt = 0

=> αy(1 - y ) = 0

=> y( 1 - y) = 0

=> either y = 0 or 1 - y = 0

=> y = 0 or y = 1

so, y = 0 is unstable and y = 1 , asymptomatic stable.

b) Now, we have to solve initial value problem, [tex]\frac{dy}{y(1 - y)} = \alpha dt [/tex]

Using partial fraction decomposition,

[tex] \frac{1}{y(1 - y) }= \frac{1}{y} - \frac{1}{1 - y}[/tex]

integrating both sides,

[tex]\int {( \frac{1}{y} - \frac{1}{(1 - y)})dy } = \int{ \alpha dt }[/tex]

[tex]ln (y) - ln (1 - y) = \alpha t + c[/tex]

[tex] ln( \frac{ y}{1- y}) \: = \alpha t + c [/tex]

[tex] \frac{y}{1 - y}= e^{\alpha t} c_1 [/tex]

using initial condition, [tex]y(0) = y_0 [/tex]

[tex] \frac{y_0}{1 - y_0}= 1 ×c_1 [/tex]

[tex]c_1 = \frac{ y_0}{1 - y_0}[/tex]

[tex]so, \frac{y}{1 - y} = \frac{ y_0}{1 - y_0}e^{\alpha t} [/tex]

cross multiplication

[tex]y(1 - y_0) = ((1 - y) y_0 )e^{\alpha t} [/tex]

[tex]y - yy_0 = y_0e^{\alpha t} - yy_0 e^{\alpha t} [/tex]

[tex]y = \frac{ y_0}{y_0 + ( 1 - y_0) e^{-\alpha t} }[/tex]

as [tex]t→ ∞ , e^{- \alpha t } → 0[/tex]

[tex]y = \frac{ y_0}{y_0 }= 1 [/tex]

So, y = 1, means that ultimately the disease spreads through the entire population.

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The probability of landing on a 6 is 1/6. The probability of rolling a 7 is zero.

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics refers to the study of events subject to probability.

If you roll a fair number cube, The probability of landing on a 6 is 1/6.

As, all the possible outcome is 6 and favourable outcome is 1 (6), Probability = 1/6 or 16.66%

The probability of rolling a 7 is zero as there is only 6 possible out come and 7 is the 7th outcome which is not possible, therefore 0.

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Answer: 24

Step-by-step explanation:

Answer:

60% of 44 is 26.4

Step-by-step explanation:

Answer:75

Step-by-step explanation:
7+5=12
15x5=75
75 is odd and I just went through the multiples of 15 haha

The sοlutiοn οf the given prοblem οf area cοmes οut tο be the side length rises by 1, the area grοws and then shrinks by an equal factοr.

Calculating hοw much space wοuld be needed tο fully cοver the οutside will reveal its οverall size. When determining the surface οf such a trapezοidal fοrm, the surrοundings are additiοnally taken intο accοunt. The surface area οf sοmething determines its οverall dimensiοns. The number οf edges here between cubοid's fοur trapezοidal extremities determines hοw much water it can hοld inside.

Here,

Optiοn B

The area grοws initially and then decreases by an amοunt equivalent tο the side length multiplied by 1. The area grοws befοre decreasing by an equivalent amοunt.

This is the case because a square's surface and side length are inversely prοpοrtiοnal. Where r is the οriginal side length, the area grοws by a factοr οf (1 + 2r + r2) as the side length rises by 1.

When r is big, hοwever, the term r2 dοminates and the area increase is less nοticeable.

Eventually, as r gets clοser tο infinite, the area increases οnly marginally and eventually reaches a limit.

As a result, as the side length rises by 1, the area grοws and then shrinks by an equal factοr.

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Complete question:

The graph of g(x) = 3x² + 6 is steeper and shifted upward compared to the graph of f(x) = x².

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The graphs of g(x) = 3x² + 6 and f(x) = x² are both quadratic functions, which means that their graphs are parabolas.

However, they have different coefficients and constant terms, which means that they will have different shapes and positions.

Here, the graph of g(x) = 3x² + 6 is steeper and shifted upward compared to the graph of f(x) = x².

Both graphs have a vertex at the origin, but g(x) has a larger coefficient of x², which makes it steeper, and an added constant term, which shifts it upward.

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The value of the matrix is [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]] when a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers.

According to the given equation, a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers, we can rearrange the equation to find the value of one of the variables in terms of the others. For example, we can rearrange the equation to find the value of x in terms of the other variables:

x = b+y-a = c+z+1-a

Similarly, we can rearrange the equation to find the value of y and z in terms of the other variables:

y = a+x-b = c+z+1-b

z = a+x-c-1 = b+y-c-1

Now, we can substitute these values into the given matrix to find the value of each element:

[[x,a+y,x+a],[y,b+y,y+b],[z,c+y,z+c]] = [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z+1-c-1]]

Simplifying the matrix, we get:

[[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]]

Therefore, the value of the matrix is [[b+y-a,a+x-b,c+z+1-a],[a+x-b,b+y-a,c+z+1-b],[a+x-c-1,b+y-c-1,c+z]] when a+x=b+y=c+z+1, where a,b,c,x,y, z are non-zero distinct real numbers.

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Answer:

18

Step-by-step explanation:

18

Answer: If you did 100 Joules of work to lift your backpack, then the work you did is equal to the force applied multiplied by the distance lifted. Let's say you lifted the backpack a distance of d meters with a force of F Newtons. Then:

100 J = F x d

Now, if half of everything falls out of your backpack, the force required to lift the backpack will be reduced by half, so the new force required will be F/2. The distance lifted remains the same. So the work done to lift the backpack using half the force is:

Work = (Force x Distance) / 2

= (F x d) / 2

But we know that F x d = 100 J, so we can substitute this in the equation above:

Work = (F x d) / 2

= 100 J / 2

= 50 J

Therefore, the work you will do to lift your backpack the same distance with half the force is 50 Joules.

Step-by-step explanation:

The solution to the equation is z = 15.

To solve the equation 2(2z-3)=3(z+3), we first need to simplify each side of the equation by distributing the numbers outside of the parentheses to the terms inside the parentheses.

On the left side of the equation, we have 2(2z-3). Distributing the 2 to the terms inside the parentheses gives us:

2(2z) - 2(3) = 4z - 6

On the right side of the equation, we have 3(z+3). Distributing the 3 to the terms inside the parentheses gives us:

3(z) + 3(3) = 3z + 9

Now we can rewrite the equation as:

4z - 6 = 3z + 9

Next, we want to get all of the z terms on one side of the equation and all of the constant terms on the other side. We can do this by subtracting 3z from both sides of the equation and adding 6 to both sides of the equation:

4z - 3z = 9 + 6

Simplifying gives us:

z = 15

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The probability that a student surveyed was either a boy or had a bicycle is 0.62.

What is probability?

The mathematical concept of probability is used to estimate an event's likelihood. It merely allows us to calculate the probability that an event will occur. On a scale of 0 to 1, where 0 corresponds to impossibility and 1 to a particular occurrence.

We are given that of 1000 students surveyed, 490 were boys and 320 had bicycles. Of those who had bicycles, 130 were girls.

So, Total number of boys = 490

Total number of girls with bicycle = 130

Total number of students that was either a boy or had a bicycle is

490 + 130 = 620

The probability is

620 / 1000 = 0.62

Hence, the probability that a student surveyed was either a boy or had a bicycle is 0.62.

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angle = tan⁻¹(2,500 / 31,680)

angle ≈ 4.51 degrees

Therefore, the angle of descent is approximately 4.51 degrees.

When two rays collide at a given point, an angle is created. Indicated by the symbol is the "angle," also known as the "opening" between these two beams. Many angles, such as 60°, 90°, etc., are usually stated as numbers in degrees.

To find the angle of descent, we can use the tangent function, which relates the opposite and adjacent sides of a right triangle:

tan(angle) = opposite / adjacent

In this case, the opposite side is the change in elevation, which is 2,500 feet, and the adjacent side is the distance traveled, which is 6 miles or 31,680 feet (since 1 mile = 5,280 feet).

So we have:

tan(angle) = 2,500 / 31,680

To solve for the angle, we can take the inverse tangent (or arctangent) of both sides:

angle = tan⁻¹(2,500 / 31,680)

Using a calculator, we get:

angle ≈ 4.51 degrees

Therefore, the angle of descent is approximately 4.51 degrees.

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By answering the above question, we may infer that Hence, when equation Mr. Haustra's tank is just 1/4 full, he can go around 70 miles.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

There are the following if Mr. Hamstra's automobile contains 14 2/5 gallons of fuel and his tank is only 1/4 full:

There are 3 1/2 gallons of gas in the tank (1/4) x 14 2/5.

If the automobile gets 20 miles per gallon on average, it may go as far as:

3 1/2 gallons x 20 miles per gallon is 70 miles.

Hence, when Mr. Hamstra's tank is just 1/4 full, he can go around 70 miles.

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[tex]10^{32} \times 10^{36}[/tex] can be written as [tex]10^{68}[/tex] using a single exponent.

What is an exponents?

In mathematics, exponents are a way to indicate the repeated multiplication of a number or phrase.

Exponents are numbers that are superscripted above other numbers. In other words, it denotes that a certain level of power has been conferred upon the base. Index and power are other names for the exponent. If m is a positive number and n is its exponent, the expression Mn means that m has been multiplied by itself n times.

Exponents are required for a more comprehensible representation of numerical quantities. Repeated multiplication is simple to write down when using exponents. If both n and x are positive integers, the expression xn means that x has been multiplied by itself n times.

When multiplying two numbers with the same base, we can add their exponents. Therefore:

[tex]10^{32} \times 10^{36 }= 10^{(32+36) }= 10^{68}[/tex]

Hence, [tex]10^{32} \times 10^{36}[/tex]can be written as [tex]10^{68}[/tex] using a single exponent.

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The expression can be written as a single logarithm using the laws of logarithms as: 2logx(y)+logx(z/y).

The exponent or power to which a base must be increased in accordance with the laws of logarithms to arrive at a certain number. If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n

Using the laws of logarithms, we can combine the given expression as follows:

2 log(x) - log(y) + log(z)

Now, using the law of logarithmic addition, we can combine the second and third terms as follows:

2 log(x) + log(z/y)

Therefore, the given expression as a single logarithm is:

2 log(x) + log(z/y)

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The unknown side 'x' is found using pythagorean theorem as: x = 12.69.

The Pythagorean Theorem has a name for Pythagoras of Samos, a religious figure and mathematician who held the view that everything in the cosmos is made up of numbers.

Pythagorean Theorem is also known as:

a²+ b² = c²

Given sides are:

13, 3 and x.

Then,

3²+ x² = 13²

x² = 13² - 3²

x² = 169 - 9

x² = 160

x = √160

x = 12.69

Thus, the unknown side 'x' is found using pythagorean theorem as: x = 12.69.

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