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The half-life of this sample is 535.1 days.

Half-life is defined as the time it will took a substance to reduce to half of its initial amount. The half-life of a substance is determined with respect to the rate of the reaction. It can be calculated using the formula below.

N(t) = N₀(1/2)^(t/T)

where N(t) = amount of substance remaining after time t

N₀ = initial amount of substance

t = time

T = half-life

If a sample of a certain substance decayed to 67.8% of its original amount after 300 days, then N(300) = 0.678N₀.

Plug in the given values to the equation.

N(t) = N₀(1/2)^(t/T)

0.678N₀ = N₀(1/2)^(300/T)

0.678 = (1/2)^(300/T)

T = 535.1 days

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Since the physics books must be together and the mathematics books must be together, There are 1728 ways to arrange the books.

The basic counting principle is a method for keeping track of all the potential outcomes in a situation. According to this statement, there are n m n times m n ways to carry out both of these actions if there are n ways to perform one action and m ways to perform another action after that. How selection is made based on options is determined by the Fundamental Principle of Counting. The approach of selection, taking into account all of the potential options and their combinations for calculating the probability, is made simpler by the Fundamental Principle of Counting.

Here,

There are 3 book,

3!=6

3 different mathematics books,

3!=6

4 different physics books,

4!=24

2 psychology books

2!=2

by fundamental counting principle,

6*6*24*2=1728

There are 1728 different ways to arrange the books because the mathematics and physics books must be together.

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The equation of the parabola from the vertex is f(x) = 7(x - 3)² + 5

The equation of the function is given as

f(x) = 7x²

Also, we have

Vertex = (3, 5)

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) = (3, 5)

Substitute (h, k) = (3, 5) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 3)² + 5

This also means that

f(x) = 7(x - 3)² + 5

The 7 is gotten from f(x) = 7x²

Hence, the equation of the parabola is f(x) = 7(x - 3)² + 5

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The coefficient of the third term in the given expression is -4

From the question, we are to determine the coefficient of the third term in the given expression.

A coefficient is the numerical value that is written along with a variable or it is multiplied by the variable.

The given expression is

5 – 2t3 – 4t3u3 + 8v

This can be properly written as

5 - 2t³ - 4t³u³ + 8v

The third term in this expression is - 4t³u³

In this term, the numerical value that is written along with the variable is -4

Hence, the coefficient is -4

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The proportional relationship between the amount of peaches in pounds x and the cost of peaches in dollars y is given as follows:

y = 2.5x.

A direct proportional relationship is a special case of a linear function, with an intercept of zero, hence the output variable symbolized by y is given by the multiplication of the input variable symbolized by x and the constant of proportionality symbolized by k, as follows:

y = kx.

In this problem, we have to find the constant k taking a point of the graph.

The point taken is:

(2,5).

Meaning that when x = 2, y = 5.

Hence the constant is calculated as follows:

5 = 2k

k = 5/2

k = 2.5.

Then the equation is:

y = 2.5x.

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A graph of the given mathematical expression (x = -6) is shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.

In this scenario, a number line would be used to graph the given mathematical expression because it only contains one (1) variable.

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The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality.Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.

Therefore, let's examine the provided graph first in order to locate the solution.We can see that 1 batch of cookies need 2 cups of flour

This provides us with a ratio of 2:1.

Constant proportionality is the ratio of two proportional quantities having a constant value.

Since the batch of cookies grows by 1 for every 2 cups added, we have a constant proportionality of 2 cups.

3y=2x

Divide each term in 3y=2x

by 3

and simplify.

Tap for more steps...

y=2x3

Since the equation can be written in the form y=kx

, y varies directly with x and k. The constant of variation, k, is 23

23

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Answer: 37%

Step-by-step explanation:

36.9 rounds up into 37%

Answer:

first angle =35

second angle=63

third angle=82

The value of g in the 20 sided regular polygon is 54.

If all the polygon sides and interior angles are equal, then they are known as regular polygons.

The polygon given is a 20 sided regular polygon and the measure of each angle is 3g degrees.

Therefore, let's find g.

The sum of interior angles of a 20 sided polygon is as follows:

180(n - 2) = 180(20 - 2) = 180(18) = 3240

Therefore,

each angle = 3240 / 20 = 162

Hence,

162 = 3g

g = 162 / 3

Therefore,

g = 54

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The null hypothesis is rejected if the p-value is lower than or equal to the chosen significance threshold; otherwise, it is not. To put it another way, if p, reject  [tex]H_{0}[/tex]; if p>, do not reject [tex]H_{0}[/tex].

This criterion, known as (alpha) in null hypothesis testing, is often set to 05. The rejection of the null hypothesis is if there is less than a 5% probability that a result as dramatic as the sample result would occur if the null hypothesis is accepted. The outcome is referred to as statistically significant when this occurs.

If a statistical test is run with a threshold of significance = 0.1, 0.05, and 0.01 the null hypothesis was rejected.

The alternative hypothesis is taken into consideration instead of the null hypothesis if the P value is less than alpha, the predetermined level of statistical significance.

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Answer:

120

Step-by-step explanation:

The original number from the given decimal number is  0.02.

For the given question;

Moving a decimal point 4 places towards the right corresponds to multiplying the given integer by 10,000 if it is x.

This results in:

10000x = 4.(1/x)

Simplifying.

x² = 4/10000

x > 0.

Taking square root of the number.

x = 2/100

x = 0.02

Thus, the original number from the given decimal number is  0.02.

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The error was made in the Step 1 as Distributive property of multiplication was not used correctly  .

In the question ,

it is given that

the equation is 2x -(1/4)(12x+4)= 3

Step 1 : by using the distributive property of multiplication ,

we get

2x - (1/4)*12x -(1/4)*4 = 3

2x - 3x - 1 = 3

So , after the first step the equation should be 2x - 3x - 1 = 3

we see that the  Distributive property of multiplication , was not used properly as the negative sign was not distributed to both the terms .

So ,  Step 1 is wrong.

Step 2 : Adding like terms

we get ,

-x - 1 = 3

Step 3 : Adding 1 to both the sides ,

we get

-x - 1 [tex]+[/tex] 1 = 3 + 1

Step 4:

-x = 4

x = -4

Therefore ,The error was made in the Step 1 as Distributive property of multiplication was not used correctly  .

The given question is incomplete , the complete question is

An equation and the steps to solve it are shown below:

2x -(1/4)(12x+4)= 3

Step 1: 2x + 3x + 1 = 3

Step 2: 5x+1=3

Step 3: 5x+1-1=3-1

Step 4: 5x = 2

In which step was the error made and why?

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Answer:

Answer:table B represents the linear equation which is:[tex]y=-3x+11[/tex]The graph of the linear function is also attached below.Step-by-step explanation:Given the table B values x

The greater principal is there for Account A as $400.

Simple interest can be defined as a type of interest where the rate is applied on the same principal.

Given that,

The interest for Account A is $15.75 and Account B is  $28.

The total time for interest is 21 months.

Rate of interest for Account A is  3% and Account B is 4%.

Now, the time period can be written in years as,

21 months = 21 / 12 years

                  = 7 / 4

Suppose the principal for Account A and Account B is P₁ and P₂ respectively.

The formula for simple interest is given as,

(P × r × t) / 100

Substitute the respective values for both the accounts to get,

For Account A,

15.75 = (P × 3 × 7 / 4) / 100

⇒ P = (1575 × 4) / (3 × 7)

⇒ P = 300

For Account B,

28 = (P × 4 × 7 / 4) / 100

⇒ P = 2800 / 7

⇒ P = 400

Hence, Account B had greater principal.

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The coupon that gives the lower price, based on the percentage discounts is Coupon B.

To find the coupon that gives the lower price, apply the coupons to the price of the bicycle to see which value would be less after the coupon is applied.

Coupon A value after discount is:

= 81 x ( 1 - discount)

= 81 x ( 1 - 20%)

= $64.80

Coupon B value after discount is:

= 81 - 19

= $62

The coupon that gives the lower price is Coupon B.

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Answer:

y + 1 = 1/2 (x - 3)

Step-by-step explanation:

Point-slope form of an equation is a shortcut, fill-in-the-blank way to write the equation of a line. All you need is slope (usually symbolized with an m) and a point (any point on the line)

Here's Point-slope:

y - Y = m (x - X)

The slope they gave you is 1/2, put that in for the m.

And also fill in 3 for the X and -1 for the Y. Because a point is (X,Y)

Just leave the first y as a y, right there. And leave the first x in the parentheses as an x. They are variables in the equation. They stay letters.

y - -1 = 1/2 (x - 3)

Simplify.

y + 1 = 1/2 (x - 3)

Minus a negative is the same as plus a positive, that's what happened there on the left. Also, when you write it, make sure the 1/2 is beside the parentheses on the right. The parentheses should not be on the bottom with the 2, but just beside the fraction.

A total of 30 golf balls are there in the bag that weighs 1110 grams.

A total of 69 golf balls weights 2553 grams in a bag.

It is asked that how much golf balls does make 1110 grams of weight.

Let us say that the weight of one ball is X.

So, Using unitary method,

We can write,

69 times mass of one golf ball = 2553 grams.

69X = 2553

X = 2553/69

X = 37 grams.

Hence, the weight of one ball is 37 grams.

Now, let us say that Y balls weights 1110 grams,

So, we can write,

Y time weight of one ball = 1110

37Y = 1110

Y = 1110/37

Y = 30.

Hence, 30 golf balls will weight 1110 grams.

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Answer:

30

Step-by-step explanation:

The density of this sand is 1600 kg/m³.

What is the meaning of density?

The amount of something per unit of length, area, or volume: as. : the substance's mass per unit volume. In grams per cubic centimeter, density.

Given that the dimension of a cuboid is length 45 cm, width 30 cm and height 42 cm.

The volume of the cuboid is (45 × 30 × 42) cm³

                                              = 56,700 cm³

                                              = (56,700/100³) m³

                                              = 0.0567 m³

The mass of the sand is 90.72 kg.

The density of the sand is

= mass /volume

=90.72 kg / 0.0567 m³

= 1600 kg/m³

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The value of c is 20.35 (approx).

The Pythagorean Theorem states that the hypotenuse, or side opposite the right angle, of a right triangle, which is represented by the square, is equal to the sum of the squares on the legs of the triangle (or, in popular algebraic notation, a2 + b2 = c2).

The following are some significant applications of the Pythagorean theorem in daily life: used in architecture and building, used to determine the shortest distance in two-dimensional navigation. used to measure how steep a mountain's or hill's slope is.

Let the other 2 sides of the triangle be named a and b

Given:- a = 15.5ft

            b = 13.2ft

According to the Pythagorean Theorem, We know that

[tex]a^{2}+b^{2}=c^{2}[/tex]

By substituting the values of a and b we get

[tex]15.5^{2}+13.2^{2}=c^{2}[/tex]

[tex]c^{2}= 414.5\\c=\sqrt{414.5}\\ c=20.35[/tex]

c is the hypotenuse of the triangle.

Hence the value of c is 20.35

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The license plate combinations with either three letters then three numbers or three numbers then three letters are 35152000.

The license plate combinations to be made are either three number followed by three letter or three letter followed by three number. we are here assuming that the repetition of the number and letter are allowed.

The number can be any three from 0-9. So, the total choices of number are 10.

The letter can be from A-Z. So, the total choices for letter are 26.

The total choices of the numbers possible are,

ΟΟΟ ΟΟΟ

1 2 3  4 5 6

The first three are the choices of letter and the last three are the choice of number. Two combinations are also possible by interchanging the position of the set of numbers and letters.

So, the possible combinations are,

2 x [26x26x26x10x10x10]

Hence,

The possible combinations for the license plate number are 35152000.

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The function g(x) is a horizontal dilation of scale factor k = 5/2 of function f(x).

We know that f(x) is a linear function:

f(x) = 2x + 4

Here we know that:

g(x) = 2*(0.4x) + 4

Notice that function g(x) can be written as:

g(x) = f(0.4*x)

So we have a horizontal dilation, remember a horizontal dilation of scale factor k can be written as:

g(x) =f(x/k)

Notice that 0.4 = 2/5

Then we have a horizontal dilation of scale factor 5/2.

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If k and n are non-negative integers and n is the greater of the two, then the ordered list of k of the n things without repetition is the k-permutation of the n separate objects.

The total number of ways to select k objects from a set of n elements is n(n1), with (nk+1) alternatives being available for the kth place.when ordering matters and repetition is not permitted. A k-permutation of the elements in set A is any of the chosen lists in the previous configuration (choose k elements, in any order, with no repetition). Pnk=0 if k is greater than n. This makes sense because it is impossible to select k unique elements from an n-element collection if k>n.

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x=12in

Slope of ramp= SecФ =5/3

Let the height of first point be H1

Let the height of second point be H2

Then, H1=27in (Provided in the question)

         H2=12in (Provided in the question)

The base of the right angled triangle then = H1-H2

Let the perpendicular be denoted as p

Let the base be denoted as b

Let the hypotenuse be denoted as h

then, b=H1-H2

b=27-12

b=15

The Formula of SecФ=1/CosФ

Since, CosФ= Base/Hypotenuse

SecФ=/Hypotenuse/Base

SecФ= h/b

SecФ= 5/3 (Provided in the question)

then,

5/3=15/b

cross multiplying

5b=15x3

b=15x3/5

cancelling out 15 by 5

b=3x3

b=9

From Pythagoras theorem

[tex]h^{2}[/tex]=[tex]p^{2}[/tex]+ [tex]b^{2}[/tex]

putting values in the equation above:

[tex]15^{2}[/tex]=[tex]p^{2}[/tex] +[tex]9^{2}[/tex]

15x15=[tex]p^{2}[/tex]+81

225-81=[tex]p^{2}[/tex]

[tex]\sqrt{225-81}[/tex]=p

[tex]\sqrt{144}[/tex]=p

12=p

Since slope of ramp is equivalent to angle of depression

thus, p=x

x=12in

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Answer:

ii think that the figure will be determined by 13#

Step-by-step explanation:

you have to round up to the nearest meter

Answer:

The rocket reaches its maximum height at 2.25 seconds.

It’s maximum height is 88 feet.

This can be found by finding the derivative of the function and setting it to zero.

-16x² +72x + 7

Taking first derivative and setting to zero:

-32x + 72 = 0

x = -72/-32=2.25

Find the height when x is 2 seconds by substituting this value into the original function:

-16 * (2.25)² + 72 * 2.25 + 7 = 88

Therefore the maximum turning point of the parabola will be (2.25, 88)

The correct way to write 0.0000250 m in scientific notation is 2.5 · 10⁻⁵ m.

Scientific notation is a convenient way to write numbers that are very large or very small. A number written in scientific notation consists of a number greater than or equal to 1 but less than 10 multiplied by a power of 10. Here are some examples of numbers written in scientific notation:

Since you're given a number less than 1, move the decimal point to the right until you have a number between 1 and 10. Then, count the number of times you moved the decimal and write that as negative exponent over a base of 10. Finally, write out number multiplied by the power. You'll get 2.5 · 10⁻⁵ if you do those things correctly.

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Answer:

A. 2.50 Times. 10–5 m

Step-by-step explanation:

other one is wrong

Expression x is equivalent to [tex]x^{1}[/tex] by using the exponent rule.

What do you mean by algebraic expression?

A mathematical expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

There are three primary categories of algebraic expressions, including:

Monomial expression

Binomial expression

Polynomial expression

An algebraic expression can be divided into two additional types in addition to the monomial, binomial, and polynomial types. These are:

Numeric Expression

Variable Expression

Numeric expression - A numeric expression consists of numbers and operations, but never include any variable.

Variable expression - A variable expression is an expression that contains variables along with numbers and operation to define an expression.

As we know, exponent form [tex]x^{n}[/tex] can be simplified as [tex]x \times x\times x\times ........n~ times[/tex]

In this way ,  [tex]x^{1}[/tex]can be written as x multiplied by 1 time which is equal to x

Therefore, expression x is equivalent to [tex]x^{1}[/tex].

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That is one way to find out the answer