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What is the solution to the equation?

lnx−ln(4x−1)=ln5

Enter your answer in the box. Enter any fractions as simplified fractions.

One of the common terms for exponential decay is half-life, which refers to the period of time it takes for a quantity to fall by an exponential rate and halve its initial value.

In mathematics, the term "exponential decay" refers to the process of a constant percentage rate decline in a value over time. It can be written as [tex]y = a(1 - b)^x[/tex], where y represents the final amount, a represents the initial amount, b represents the decay factor, and x is the amount of time that has passed.

The exponential decay formula aids in determining the rapid decline over time, or exponential decline. The exponential decay formula is used to calculate various types of decay, including radioactivity decay, half-life, and population decay.

The time it takes for a quantity to drop by an exponential rate to halve its initial value is known as the half-life, which is one of the popular words used to describe exponential decay.

Each 20 minutes there is 1/2 as much    one hour is 3 half lives :

start 30      then    15     then    7.5     then   3.75  gm

30(1/2)3 = 3.75 gm

The complete question is;

Write an exponential decay function to model each situation. Then find the value of the function after the given amount of time. Bismuth-214 has a half-life of approximately 20 minutes. Find the amount of bismuth-214 left from a 30-gram sample after 1 hour.

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The solution to the equation 3(4x-10) = 2(3x-30) is x = -5.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

Let's solve for x:

3(4x - 10) = 2(3x - 30)

First, we can simplify both sides by distributing the coefficients:

12x - 30 = 6x - 60

Next, we'll move all the x terms to one side of the equation and the constants to the other side:

12x - 6x = -60 + 30

Simplifying further:

6x = -30

Finally, we can solve for x by dividing both sides by 6:

x = -5

Therefore, the solution to the equation 3(4x-10) = 2(3x-30) is x = -5.

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Answer:

2. KI = 20 ft 119 M K 4. YZ = 14.2 m 2 6. PO = 2.8 in R 311 8. WZ = 5.3 km w z 108

Step-by-step explanation:

The opportunity cost of Madeline based on the information would be 8 units of gizmos .

The benefit or gain that a person might have obtained or earned if he or she had not chosen the current alternative is known as opportunity cost.

Madeline has spent $24 ($2 x 12) on the widgets in this question since she purchased 12 of them at a cost of $2 each. In this case, her opportunity cost would be the gadgets she could have purchased, which works out to $24 / $3 = 8 units.

Therefore, the opportunity cost is 8 units.

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The tangent ratio of F by using the rule from trigonometry is 4/3

Trigonometric ratios are ratios that represent the length of a triangle's sides. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the fundamental trigonometric ratios.

The sine of the trigonometry ratio is sin θ = opposite/hypotenuse. The cosine of the trigonometry ratio is cos θ = adjacent/hypotenuse. The tangent of the trigonometry ratio is tan θ = opposite/adjacent. From the image given. The opposite side is the line facing the angle F;

Thus, the opposite side = 8, and the adjacent is the smallest side, which is 6.

Therefore, the tangent ratio for F is:

tan θ = 8/6

This can be reduced to 4/3

Therefore, we can conclude that the tangent ratio of F is 4/3.

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Answer: 225°

Step-by-step explanation:

The correct option is D)

Refer Figure

Given:

ABCD  is a square

ABP  is an equilateral triangle

AB=BP=BC  (△ABP is equilateral and AB and BC belong to a square, hence all are equal)

∠ABC=∠ABP+∠PBC=60°+∠PBC

90°−60°=∠PBC

∠PBC=30°

In △BPC

BP=BC

∠BPC=∠BCP= 2

180−∠PBC

​ ( angles opposite to equal sides of a triangle are equal)

∠APC=∠APB+∠BPC=(60+75)°=135°

Hence, Reflex ∠APC=(360−135)°=225°

Answer:

false

Step-by-step explanation:

I think it's false but I don't really remember, but I would go with someones else answer cause I'm not sure

Answer:

Below

Step-by-step explanation:

A)  Juan reads at   57 pages /hr

B)  Juan reads 9 pages more per hour (57-48) than Lexi

       in 7 hours this will be   7 hr * 9 p/hr = 63 pages

Answer:

b < -30

Step-by-step explanation:

27 > B + 57   Subtract 57 from both sides

27 - 57 > b +57 - 57

-30 > b

or

b < -30

The value of the given fraction is -1.33.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Any number can be expressed as fractions.

Given is an expression in fractions of the form,

(1 - 5) / (6 - 3) = (-4) / 3

Actually we got an improper fraction here.

Improper fractions have larger value on the numerator than the denominator.

If we need the answer in decimal form, just divide the number 4 by 3 and give negative sign for the answer.

So here the given answer is -1.33.

Hence the decimal form of the fraction (-4)/3 is -1.33.

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Answer:

y = 5

Step-by-step explanation:

2(y + 4) = 3(2y - 4)

2y + 8 = 6y - 12

-4y = -20

y = 5

Given inequality:

To graph it first, consider line:

Find two points on the line.

Let them be x- and y-intercepts:

Now, plot the two points.

Next, draw a dashed line trough the two points. Dashed line because the line is not included into solution set, due to '<' sign.

The last step, shade the area below the line. Below the line because 'y <' means 'y-values less than' which appears below the line.

Answer:

See attachment.

Step-by-step explanation:

Given linear inequality:

[tex]y < \dfrac{1}{2}x+2[/tex]

When graphing inequalities, temporarily replace the inequality sign for the equals sign:

[tex]\implies y=\dfrac{1}{2}x+2[/tex]

Find two points on the line by substituting two values of x into the equation:

[tex]x=0 \implies y=\dfrac{1}{2}(0)+2 =2\implies (0, 2)[/tex]

[tex]x=4 \implies \dfrac{1}{2}(4)+2=4 \implies (4,4)[/tex]

When graphing inequalities:

Therefore, to graph the given linear inequality:

Answer: y=2x-15

Step-by-step explanation:

Answer:

y=1/2x + 15

Since,her original flight plan time is X and hence the flight will reach 2 times faster the X becomes X/2 and the additional time 15 minutes which has already been delayed.So,she will arrive her destination in(1/2X+15)min from 4:00 p.m.

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Therefore ,As a result, the region's problem with the suggested solution is the playing field area measures 118 yards by 56 yards.

Add length and breadth together to calculate area. The calculation for area is L times B. Radius or area equals r2(=3.14) With the use of these techniques, it is also possible to determine the area of various quadrilaterals, a specific type of polygon with 4 sides and an angle smaller than 90 degrees. Application. Geometry has been based on the concept of area from its inception.

Here,

We find w = 56, which indicates that the parallelogram has a length of 56 yards.

Since the width is identical to 2w + 6, we can make the computation simpler by changing w to 56 to find the rectangle's length.

The rectangle's length is shown to be 118 yards.

The size of the playing area is accordingly 118 yard by 56 yards.

As a result, the proportions of the playing field—118 yards by 56 yards—are the answer to the dilemma at hand.

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The shadow of the tree at the same time of day was 113.29 foot long.

Foot, plural feet, any of numerous ancient, mediaeval, and modern linear measures based on the length of the human foot and used only in English-speaking countries, where it typically consists of 12 inches or one-third yard (typically 25 to 34 cm).

In most countries and all areas of science, the foot and its multiples and subdivisions have been largely replaced by the metre, the basic linear unit of the metric system. Since 1959, a foot in the US has been defined as exactly 30.48 centimetres.

We know that

1 feet = 12 inches

So, 5 feet 8 inches = 5[tex]\frac{2}{3}[/tex] feet

Now, lets find the shadow of tree

5[tex]\frac{2}{3}[/tex]/2 = 321/x

x = 113[tex]\frac{5}{11}[/tex]

x = 113.29

Thus, the tree's shadow at the same time of day was 113.29 foot long

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In 1663200 ways objects can be chosen if the order of the choices is relevant. The solution has been obtained using permutation.

What is permutation?

An arrangement of items in a specific manner or sequence is referred to as a permutation. It is important to think about both the selection and the arrangement when dealing with permutation. Briefly put, permutations depend much on ordering. In other words, a permutation is a combination that is ordered.

We want to choose 7 objects without replacement from 11 distinct objects

So, since the order of the choices is relevant, we will use permutation.

Therefore,

⇒nPr = n! ÷ (n - r)!

⇒11P7 = 11! ÷ (11 - 7)!

⇒11P7 = 11! / 4!

⇒11P7 = (11 * 10* 9 * 8 * 7* 6 * 5)

⇒11P7 = 1663200 ways

Hence, in 1663200 ways objects can be chosen if the order of the choices is relevant.

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Mode of data set -1, 0, 3 ,4, -3, -1 is - 1 with most often in data set.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The data set is,

⇒ -1, 0, 3 ,4, -3, -1

Now, We know that;

The mode is the value that appears the most often in the data set.

Here, In the data set - 1 is most often number.

So, The mode of data set = - 1

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Answer:

ST = 10

Step-by-step explanation:

Δ RSQ and Δ RTP are similar by the AA postulate , then

the ratios of corresponding sides are in proportion , that is

[tex]\frac{RS}{RT}[/tex] = [tex]\frac{RQ}{RP}[/tex] ( substitute values )

[tex]\frac{5}{RT}[/tex] = [tex]\frac{9}{9+18}[/tex] = [tex]\frac{9}{27}[/tex] = [tex]\frac{1}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

RT = 3 × 5 = 15

Then

ST = RT - RS = 15 - 5 = 10

The required equation of the line is given as y = 5x -6.

Given that,
To determine the equation of a line passing through the point P(9, -8) and perpendicular to the line AB y = 3x + 6.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

The slope of the given line
y = 3x + 6.
m = 3

The equation of the perpendicular line is given as,

y - y₁ = -1/m (x - x₁)

Substitute the value in the above equation,

y + 8 = -1 / 3 (x - 9)
y = -x/3 + 3 - 8
y = -x/3 - 5

Thus, the required equation of the line is given as y = -x/3 - 5.

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On solving the provided question, we can say that the linear function is  f(x) = -2x +3 and by the graph y = f(x) = -1

Two distinct but related concepts are referred to as linear functions in mathematics. A polynomial function of degree 0 or 1 is a linear function in calculus and related subjects if its graph is a straight line. Any function that depicts a straight line on a coordinate plane is said to be linear. For instance, y = 3x - 2 is a linear function since it depicts a straight line on the coordinate plane. f(x) = 3x - 2 can be used to represent the function since f(x) can be linked to y.

here,

the linear function is  f(x) = -2x +3

and by the graph y = f(x) = -2x +3 = -2(2) + 3 = -4+3 = -1

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If the sum of two digits t and u is t + u = 9, then the second equation is option 2: t = 1/2 u.

What is a digit?

In math, single integers called digits are used to represent values. To represent all mathematical values, the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are employed in various combinations and repetitions.

The first equation is as given t + u = 9

Second equation t = u/2 since the number in the tens position is one half of the one in the units. So if you divide u by two, you should have one t, as the equation states.

The second equation is t = (1/2)u => u = 2t

When we replace this in first equation we get -

t + 2t = 9  

3t = 9  

t = 9/3

t = 3

When we replace it again in the equation -

u = 2 t

= 2 · 3

= 6

The requested number is 36.

Therefore, the number is 36 and the second equation is t=u/2.

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Solving the example, hope it will help you with better understanding.

Given system:

We need to eliminate one of the variables c or d. Let us eliminate d.

We see the first equation has 3d and the second equation has - d. The coefficients of d are 3 and - 1. If we multiply the second one by 3 it will become - 3, then if we add them up they will cancel, 3d - 3d = 0. By doing this we'll eliminate the variable d and left with variable c in the resulting equation.

Demonstrating how it works:

2c + 3d = 12, we leave it as is

5c - d = 13, we multiply all terms of this by 3, it becomes, 15c - 3d = 39

Now add up the two equations:

Now we can find the value of d:

Our solution is:

Answer: |-1|

Step-by-step explanation:

So lets just solve all of this stuff so you can just look at it and get the answer. | - 28 | = 28, |-1| = 1, |6| = 6, |15| = 15. So we have 28, 1, 6, and 15. Put this in order we have: 28, 15, 6, 1 which means 1 is the least or your could say |-1| is the least. Have a good day ;)

The number of items must be made for the average cost to fall to $5 wil be; 900.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).

We are given that function = 40x +700 represents the average cost (in dollars) of making items.

Then the item made for function average cost to fall to $5.

= 40x + 700

= 40(5) + 700

= 200 + 700

= 900

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Answer:

-4

Step-by-step explanation:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-8)}{0-2}=\frac{8}{-2}=-4[/tex]

The slope of the line that passes through the points (2, -8) and the origin is calculated using the formula m = rise/run, which gives -4.

In this Mathematics problem, we are asked to find the slope of the line that passes through two points using the formula m = rise/run, where 'm' is the slope. The points provided are (2, -8) and the origin, which is (0, 0).

To find the slope (rise/run), we can subtract the y-values (rise) and the x-values (run) of the two points, respectively. So, the formula becomes: m = (-8 - 0) / (2 - 0) => m = -8/2 = -4.

Therefore, the slope of the line that passes through the points (2, -8) and the origin is -4.

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The values of ∠4 and  ∠3 are 116 degrees and 64 degrees respectively.

Given ,

What are supplementary angles ?

The angles are said to be in supplementary if and only if the sum of two angles is 180 degrees .

Angles 3 and 4 are supplementary.

The measure of angle 3 is

thirty-five more than one-fourth the measure of angle 4.

So,

∠3 + ∠4 = 180 degrees.

∠3 = 180-∠4 - equation 1

∠3 = 35 + (1/4 ) ∠4 - equation2

As equation 1 and 2 are equal

hence,

180-∠4 = 35 + (1/4) ∠4

180-35 = ∠4 +  (1/4) ∠4

145 =  ((1/4)+1) ∠4

145 = (5/4) ∠4

∠4 = 145 * 4 / 5

∠4 = 29*4

∠4 = 116

∠3  = 180-116

∠3 = 64

Hence the values of  ∠4 and  ∠3 are 116 degrees and 64 degrees respectively.

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Resolving F2 into components along the u and v axes, the magnitudes of the components are determined as 150 N and 77.6 N.

According to the sine law, the side length of a triangle should be divided by the sine of the opposite angle. That is, when we divide side a by the sine of angle A, we get the same result as side b divided by angle B and side c divided by angle C.

For the given diagram, first, draw the vector components. Then, by sine law, we get,

[tex]\begin{aligned}\frac{F_u}{\sin 75^{\circ}}=\frac{F_2}{\sin 75^{\circ}}=\frac{F_v}{\sin 30^{\circ}}\end{aligned}[/tex]

Now, substitute the value of F₂, and we get,

[tex]F_u=F_2=\mathrm{150\;N}[/tex]

Now, solve for [tex]F_v[/tex], we get,

[tex]\begin{aligned}F_v&=\frac{F_2\sin 30^{\circ}}{\sin75^{\circ}}\\&=\mathrm{\frac{150\;N\times 0.5}{0.966}}\\&=\mathrm{77.64\;N}\end{aligned}[/tex]

The required answers are 150 N and 77.64 N.

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Answer:

See below!

Step-by-step explanation:

254, 202, 284, 269, 151, 258, 202

Mean of the data:

[tex]\displaystyle Mean= \frac{Sum \ of \ data}{number \ of \ data} \\\\Mean = \frac{254+202+284+269+151+258+202}{7} \\\\Mean=\frac{1620}{7} \\\\\boxed{Mean = 231.4}[/tex]

Median of data:

Arrange the data in increasing order.

151, 202, 202, 254, 258, 269, 284

The middle value = 254

So,

Mode in data:

The mode, here, is 202. (occurring 2 times.)

So,

[tex]\rule[225]{225}{2}[/tex]