When determining the quotient of two numbers written in scientific notation, the base numbers and the exponents of the powers of ten.

Answer:

256

Step-by-step explanation:

3 What is the sum of the geometric series 4 2,341 256 525 64 2,343 256 ... A: Geometric series are such finite or infinite series where every next term

Answer: 87.5%

Step-by-step explanation:

I hope this helps!

The probability that exactly two of them are delivered to the correct houses as calculated from the data is 4/24 = 1/ 6.

The total number of ways to deliver four packages can be found out by taking the factorial of 4 , i.e., the permutation of 4.

4 × 3 × 2 × 1 = 4!

= 4P4

= 24

A permutation is a referred to as a specific arrangement of items. The set members and elements are arranged in a sequence in a permutation. For example, the permutation of set A=1,6 is 2, as in 1,6,1. There are no alternative ways to arrange the items in set A.

In permutation, the elements must be arranged in a particular sequence, whereas in combination, the order of the elements is irrelevant.

To calculate the permutation we calculate it's factorial.

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Expression  8[cos(pi/2) + i sin (pi/2)]  is equal to ([tex]\sqrt{3\\}[/tex] + i )³.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression  ([tex]\sqrt{3\\}[/tex] + i )³ lets simplify it

Apply the binomial formula [tex](a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}[/tex]

You can find the coefficient multipliers in row 3 of Pascal's triangle.

=> 3[tex]\sqrt{3}[/tex] + 3*     ([tex]\sqrt{3}[/tex])²* i + 3* √3* (i)² + (i)³

=> 3√3 + 9i  - 3√3 -i

=> 8i

Now simplify the given equations in the options

For 6[cos(pi/2) + i sin (pi/2)]

=> 6[ 0  + 1*i ]

=> 6i

For 8[cos(pi/2) + i sin (pi/2)]

=> 8[ 0  + 1*i ]

=> 8i

For 6 [cos(pi/6) + i sin (pi/6)]

=> 6[ √3 / 2 + i/2]

For 8 [cos(pi/6) + i sin (pi/6)]

=> 8 [ √3 / 2 + i/2]

Therefore, ([tex]\sqrt{3\\}[/tex] + i )³ is equals to the value of equation  8 [cos(pi/2) +  i*sin(pi/2)].

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In interval (1, ∞), function h is decreasing, option (C) is correct.

Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.

The given function is,

h(x) = [tex]2^x[/tex] when x < 1,

And h(x) = √(x + 3) when x ≥ 1.

To find the interval when function h is decreasing,

Plot the graph of the function h(x) for the given intervals.

Since, in interval (-∞, 1) the graph is increasing.

And in the interval (1, ∞) the graph is decreasing.

Hence, correct option is option (C).

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Answer:14

Step-by-step explanation:

The equivalent exponential functions for this problem are defined as follows:

A. A(n) = 1,000(1.10)^t

B. A(n) = 1,000(1 + 0.008)^12t.

An increasing exponential function is defined as follows:

A(t) = A(0)(1 + r)^t.

In which the parameters are given as follows:

For this problem, the function is defined as follows:

A(n) = 1000(1 + 0.10)^t.

Hence:

A(n) = 1100(1.10)^t.

Meaning that option A is correct.

Using monthly compounding, then the function would be defined as follows:

A(n) = 1000(1 + 0.10/12)^12t.

A(n) = 1000(1 + 0.008)^12t.

Meaning that option B is also correct.

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Answer:

О  B. Standard deviation.

Step-by-step explanation:

Standard deviation measures the dispersion of a data distribution (variability in scores).

...

The complete sentence is  - The rate of change of the bus is less than the rate of change of the motorcycle. The bus is moving slower than the motorcycle.

As a set of inputs with one output for each, a function is defined as a relationship between them. A function, expressed simply, is an association between inputs where each input is connected to one and only one output. In mathematics, a function is an expression, rule, or law that establishes the relationship between two variables (the dependent variable). One input results in one output when using a function, which is a type of rule. by Alex Federspiel, the photo's author. Here, y=x2 serves as an illustration. A single output for y results from any input for x. Since x is the input value, we would state that y is a function of x.

given

as the graph shows that the bus and motorcycle travels a distance

The bus's rate of change is lower than the motorcycle's rate of change, to give the whole sentence. The motorcycle is traveling more slowly than the bus.

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Yes, the point (2,-1) lies on the curve y=1/(1-x) as when x=2, y=1/(1-2)=1/(-1)=-1, which is equal to -1.

y=1/(1-x)

y=1/(1-2)

y=1/(-1)

y=-1

Yes, the point (2,-1) lies on the curve y=1/(1-x). To prove this, we can substitute the x-coordinate of the point (2) into the equation. When x=2, the equation becomes y=1/(1-2). Simplifying this equation, we get y=1/(-1) which is equal to -1. Thus, y=-1, which is the same as the y-coordinate of the point (-1). This means that the point (2,-1) does indeed lie on the curve y=1/(1-x). This can be further verified by plotting the point (2,-1) on a graph and seeing that it is indeed located on the curve y=1/(1-x).

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The percentage for regular soda will be 20%.

The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

Since William's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 45 sodas in all, 9 of which were regular.

The percentage for regular will be:

= 9 /45 × 100

= 20%

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Answer is : Cos L = 55/73.

The fraction is 1/6 is less than 2/6.

Less than is the answer

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.

From the image, the fraction to the left is 1/6 and the fraction to the right is 2/6.

You can think of 1/6 as having a pizza divided into 6 equal portions and you are to pick 1 out of the 6 whereas in the case of 2/6 you are to pick 2 out of the 6. You will notice that you have less pizza in 1/6 than 2/6.

Thus, 1/6 is  less than 2/6

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The coach should choose Darius because he has highest probability of 65.21% of scoring a penalty kick

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

The top four players have the following statistics partaining to penalty kick

Brian Who made 7 out of 12

Darius who made 15 out of 23

Fong who made 12 out of 20 and Mike who made 19 out of 32

To get the best we have to put them on percentage.

% to score of Brian = 7/12 ×100 = 58.33%

% to score for Darius = 15/23 ×100 =

65.21%

% to score for Fong = 12/20× 100 = 60%

% to score for Mike = 19/32× 100 = 59.4%

Therefore out of the four top players Darius has higher probability to score. He is the best among them. Therefore the coach should choose Darius.

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There are 152  fish would you expect to be living in the pond if At the beginning of a study, 24 fish are caught.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

At the beginning of a study, 24 fish are caught, tagged and released back into a large pond containing fish.

The answer would be 152.

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given base of square =13cm

all sides of squares is equal so

area of square is a^2 =13cm*13cm =169cm^2

Answer:

[tex] 196 \: {cm}^{2} [/tex]

Explanation:

As the area of a square is

[tex]l {}^{2} [/tex]

Where l is the length. As we know that all rhe sides of a square are equal in length therefore, each side of the square has a length of 13 cm.

Now,

[tex] {l}^{2} [/tex]

[tex] {13}^{2} [/tex]

Which is equal to

[tex]169 \: cm {}^{2} [/tex]

Two rays that extend in opposing directions from the same endpoint but have different lengths are said to be a pair of opposite rays. Rays having same endpoint E but not in the opposite directions are ED and EC.

A pair of opposite rays is defined as two rays that have the same terminus and extend in opposite directions, but have different lengths.

Consequently, a straight line is always created when two rays that are facing one another unite.

Two rays that make up an angle are referred to as its two sides.

Each of these rays originates and finishes at the vertex.

A ray is always named by beginning with the letter of the endpoint (where the ray starts), followed by the name of another point along the ray in the direction the ray advances.

Rays ED and EC share the same terminal E but do not go in the opposite directions.

These two rays have different trajectories and collide at point E. The other pair of rays, EA and EB, also have the same end point (at E), but they do not travel in the other way.

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The equation (7x2-2xy +2)dx + (29-x2+7)dy = 0 is not exact, NS.

An equation is exact when the mixed partial derivatives of both sides of the equation are equal to each other. In this equation, we have derivatives of x and y, but the mixed partial derivatives are not equal, which means that the equation is not exact. Therefore, the solution is NS. An equation is exact if the sum of the differential terms on each side of the equation is equal to zero. This equation does not satisfy this condition, which is why it is not exact.

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Therefore , the solution to given problem of fraction comes out to be 5.2 metric tons per hour.

To represent a whole, divide it into any number of equally parts, or fractions. How many units of a particular size there are is expressed using fractions in standard English. 8, 3/4. Parts of a whole are included. Numbers in mathematics are stated as a ratio of such numerator to the denominator. These are each simple fractions that represent an integer. A fraction is contained in the fraction or population of a sophisticated fraction. When a fraction is true, its numerators are less than its denominators. An amount that makes up a fraction of a whole is called a fraction. You can assess the whole by dissecting it into smaller pieces. For instance, 12 is used to denote half of the a total number or item.

Here,

Given : Six and a half metric tons of soil are removed from a construction site by a construction company in one and a half hours.

Thus,

5/3 hours and 13/2 metric ton

So,

=> 13/2 / 5/4

=> 13/2 * 4/5

=> 52/10

=>5.2

Therefore , the solution to given problem of fraction comes out to be 5.2 metric tons per hour.

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The probability of all five people are still living is 0.1317.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability (Event) = Favorable Outcomes/Total Outcomes = x/n

Let us check simple application of probability to understand it better. Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.

As per the given data,

Probability of a person living in these conditions for 30 years or more[tex]$=p=2 / 3$[/tex]

Total number of samples[tex]$=n=5$[/tex]

Let [tex]$X$[/tex] be the number of people living.

[tex]$X \sim \[/tex] Binomial [tex](n=5, p=2 / 3)$[/tex]

Probability mass function of [tex]$X$[/tex]  :

[tex]$$P(X=x)=\left(\begin{array}{l}n \\x\end{array}\right) p^x(1-p)^{n-x}$$[/tex]

a) Probability that all five people are still living:

[tex]$$P(X=5)=\left(\begin{array}{l}5 \\5\end{array}\right)\left(\frac{2}{3}\right)^5\left(1-\frac{2}{3}\right)^{5-5}=0.1317$$[/tex]

b) Probability that at least three people are still living:

[tex]$$P(X=5)=\left(\begin{array}{l}5 \\5\end{array}\right)\left(\frac{2}{3}\right)^5\left(1-\frac{2}{3}\right)^{5-5}=0.1317$$[/tex][tex]$$\begin{aligned}& P(X \geq 3)=P(X=3)+P(X=4)+P(X=5)=\left(\begin{array}{l}5 \\3\end{array}\right)\left(\frac{2}{3}\right)^3\left(1-\frac{2}{3}\right)^{5-3}+ \\& \left(\begin{array}{l}5 \\4\end{array}\right)\left(\frac{2}{3}\right)^4\left(1-\frac{2}{3}\right)^{5-4}+\left(\begin{array}{l}5 \\5\end{array}\right)\left(\frac{2}{3}\right)^5\left(1-\frac{2}{3}\right)^{5-5} \\& =0.7902 \\&\end{aligned}$$[/tex] c) Probability that exactly two people are still living:

[tex]$$P(X=2)=\left(\begin{array}{l}5 \\2\end{array}\right)\left(\frac{2}{3}\right)^2\left(1-\frac{2}{3}\right)^{5-2}=0.1646$$[/tex]

Therefore, the probability of all five people are still living is 0.1317.

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The approximate solution to the given equation after three iterations of successive approximations is when x is about -37/16.

In the given question, we have to find in which value of x, the approximate solution to the given equation after three iterations of successive approximations.

The given function is

2/(x+4) = 3^x + 1

As we know that,

The technique known as the iteration method uses the beginning value to generate a number of subsequent approximations of the equation's solution.

Now subtract 3^x + 1 on both side, the function is

f(x) = -3^x - 1 + 2/(x+4)

Now differentiating the function f(x) with respect to x

f'(x) = -3^xIn3 - 2/(x+4)^2

Here, for this function

x             0,           -1,                -2,          -3    

x          -1.5,       -0.667,        -0.111,       0.963    

As we can see on the table that,

f(-3) = 0.963>0

f(-2) = -0.111<0

So the root of the function lies between -3 and -2.

So x(0) = -3+(-2)/2

x(0) = -3-2/2

x(0) = -5/2

x(0) = -2.5

This value is more near to the value -37/16 from the given option.

So, the approximate solution to the given equation after three iterations of successive approximations is when x is about -37/16.

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The complete question is given below:

After three iterations of successive approximations, the approximate solution to the given equation is when x is about 1.702

The given equation is x^3-x-1=0. To solve it using successive approximations, we need to start with an initial guess for the solution. Let us assume x0=1 as the initial guess. We can now calculate the successive approximations using the formula xn+1=xn-f(xn)/f'(xn).

In this case, f(x)=x3-x-1 and f'(x)=3x2-1.

For x0 = 1, x1 = x0 - f(x0)/f'(x0) = 1 - (1-1-1)/(3*12-1) = 2.

For x1 = 2, x2 = x1 - f(x1)/f'(x1) = 2 - (8-2-1)/(3*22-1) = 1.732

For x2 = 1.732, x3 = x2 - f(x2)/f'(x2) = 1.732 - (5.829-1.732-1)/(3*1.7322-1) = 1.702.

Therefore, after three iterations of successive approximations, the approximate solution to the given equation is when x is about 1.702.

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Answer: 1000

Step-by-step explanation:

268 / n = 0.268

(268 / n) x n = 0.268 x n

268 = 0.268n

268 / 0.268 = 0.268n / 0.268

1000 = n

Answer:

35 Feet

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The required scale factor with respect to the pre-image and image is equal to 2.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures, which can be used to either vertically or horizontally enlarge or reduce a function representing their size.

In Mathematics, the scale factor of any geometric figure can be calculated by using this mathematical expression:

Scale factor = Dimension of image/Dimension of pre-image

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor = -10/-5 = -4/-2

Scale factor = 2.

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