One day the level of the klater in the river klas 35cm above a mark. A week later it was 12cm below the mark. How far did the water level drop during the week?

Answer:

2

Step-by-step explanation:

he must multiply the bracket by -

There are total 576 numbers.

What do you mean by factorial?

The product of all positive integers less than or equal to a given non-negative integer, n!, is known as the factorial of that number in mathematics. The product of the factorial of n! with the following smaller factorial also equals the factorial of n!:

n! = n × (n-1) × (n-2) × (n-3) ..........3 × 2 × 1

Total number of digits = 7

Digits = 1,2,3,4,5,6,7

Number of odd digit = 4

Number of even digit = 3

Consider the 4 odd digits as a single unit. Number of ways in which the odd digits can be arranged within the unit = 4!

Take the unit of four odd digits with 3 even digits. So, there are 4 units. Number of possible arrangements of these 4 units= 4!

So, total number of 7-digit numbers that can be made = Number of ways in which the off digits can be arranged within the unit x Number of possible arrangements of 4 units

= 4! × 4!

= 24 × 24

= 576

Therefore, there are total 576 numbers.

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If it takes 6 minutes to set up an experiment using barium-122, then  12.5g of  barium-122 will be left when the experiment begins

Half life of barium-122 = 2 min

Mass of sample = 100 g

Mass of barium remain after 6 min = ?

Number of half lives = Time elapsed / half life

Number of half lives = 6 min/ 2 min

Number of half lives = 3

At time zero = 100 g

At 1st half life = 100 g/2 = 50 g

At 2nd half life = 50 g/2 = 25 g

At 3rd half life = 25 g/2 = 12.5 g

Therefore, If it takes 6 minutes to set up an experiment using barium-122, then  12.5g of  barium-122 will be left when the experiment begins.

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The question is from social studies

The correct statement is;-

Option d; Disability benefits for the worker and the worker's dependents are provided by the Federal Insurance

Given,

Federal Insurance;-

Federal government insurance is a type of insurance that covers all state personnel working in offices and legally authorized divisions. Taxes for social security are typically used to pay for the coverage it offers.

Contrary to many private sector health benefit plans, the Federal Employees Health Benefits (FEHB) program offers coverage without a physical examination, does not impose age or physical condition restrictions, offers a variety of health insurance plans to choose from, and cannot be terminated by the plan you enroll in.

Here,

The correct statement is;-

Option d; Disability benefits for the worker and the worker's dependents are provided by the Federal Insurance

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The probability we use is empirical probability.

The given statement,

The relative frequency of an event is used to calculate what type of probability,

Here, we use empirical probability.

The relative frequency of an event is closely related to an empirical probability, also known as an experimental probability. Empirical probability bases its estimation of the likelihood that a specific result will recur on the number of instances of that outcome within a sample set. The chance of "event X" occurring will be determined by how many times it occurs out of 100 trials.

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Step-by-step explanation:

The factors of -3 are -1, -3.

Substitution is one method for solving linear equation systems.

First, arrange the equations so that the variables are vertically arranged.

Step 2: Pick the variable that is most straightforward to take out, and multiply it by a different value in each equation so that its coefficients are the same.

Subtract the two equations in step three.

Solve the one variable system in step four.

Step 5: To find the other equation, re-enter that number into either equation.

Step 6: Reread the question and re-enter your responses to double-check.

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By solving the given word problem, the number of multiple-choice questions is 29 and short answers is 7.

In mathematics, word problem refers to a question including mathematical information written in ordinary language and requires students to apply their math knowledge to a real-life scenario. For the given case,

Let M be the number of multiple choice questions and N be the number of short answers.

As multiple-choice questions are worth 2 points each and the short answers are worth 6 points each and there is a total of 100 points:

2M + 6N = 100

The total number of questions on the test are 36:

M + N = 36

M = 36 – N

Substituting this into the first equation:

2(36 – N) + 6N = 100

72 – 2N + 6N = 100

4N = 100 – 72

4N = 28

N = 7

Substituting N in M = 36 – N

M = 36 – 7 = 29

Note: The question is incomplete. The complete question probably is: has a math test tomorrow with both multiple choice and short answer questions the multiple choice questions are worth 2 points apiece and the short answers are worth 6 points apiece. There is a total of 100 points in a test and 36 questions. How many questions of each type are on the test?

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The marginal product of the 13th worker is 10 units of output.

Given, L represent the number of workers hired by a firm, and Q represent that firm's quantity of output.

Two points on the firm's production function are

(L = 12, Q = 122) and (L = 13, Q = 132).

we have to find the marginal product of the 13th worker,

As, to find the marginal product we find the slope,

so, Marginal Product of 13th Worker = (132 - 122)/(13 - 12)

Marginal Product = 10/1

Marginal Product = 10

So, the marginal product of the 13th worker is 10 units of output.

Hence, the marginal product of the 13th worker is 10 units of output.

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The hourly pay before the increase for marta and khalid is 21 and 17.5.

Given:

the ratio of martas hourly pay to khalids hourly pay is 6:5 both marta and Khalid get an increase of 1.50 in their hourly pay The ratio of Martas hourly pay to Khalid hourly pay after this increase is 13:11

Let x and y be the hourly pay before increase

x/y = 6/5

x = 6/5*y

x + 1.50 / y + 1.50 = 13/11

11(x+1.50) = 13(y+1.50)

11x + 16.5 = 13y + 19.5

11(6/5*y) = 13y + 19.5 - 16.5

66y/5 = 13y + 3.5

66y - 13*5y / 5 = 3.5

66y - 65y = 17.5

y = 17.5

x = 6/5*17.5

= 105/5

x = 21

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Answer:

a) 21.817

b) 29.93

Step-by-step explanation:

a)

solution:

By using Pythagoras theorem

AB = √(AC²-BC²)

= √(24²-10²)

= √476

= 21.817

b)

solution:

By using Pythagoras theorem

AB=√(AC²-BC²)

=√(36²-20²)

=√896

=29.93

Answer:

Additive identity

Step-by-step explanation:

When a number that when added to any number it results in itself as the sum

The meaning to translate a triangle type of transformation that takes each point in a figure and slides it the same distance in the same direction.

Lets take an example:

ΔXYZ with coordinates,

X(-9,6) , Y(2,3) AND Z(-2,-8).

Translation:

X - 3 units in x direction

Y - 3 units in x direction

Z - 3 units in x direction

After translation:

New coordinates are represented in yellow dots in the figure uploaded.

X(-9,6)→X(-9+3,6)→X(-6,6)

Y(2,3)→Y(2+3,3)→Y(5,3)

Z(-2,-8)→Z(-2+3,-8)→Z(1,-8)

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We can identify a polynomial identity by applying algebraic identities of polynomials and principles, it is possible to prove polynomial identities by simplifying identity.

In particular, an expression must not contain any square roots of variables, any fractional or negative powers on the variables, and any variables in any fractions' denominators in order to qualify as a polynomial term. A sizable subset of algebraic expressions are polynomials. Polynomials are any expressions where the powers of the variables are all whole numbers. They frequently have a wide range of applications since they encompass such a sizable portion of all algebraic expressions.

Given,

We can identify a polynomial identity by,

Whatever the values given to the variables, the equation for the polynomial identity is always true. By applying algebraic identities of polynomials and principles, it is possible to prove polynomial identities by simplifying identity. When factorizing or extending a polynomial, we can employ polynomial identities to our advantage.

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If confidence level is 99%, more error would be included in null hypothesis area.

There is no difference between groups or correlation between variables, according to the null hypothesis in statistics. In a hypothesis test, it is one of two competing hypotheses regarding a population. You can reject the null hypothesis and determine that the effect is statistically significant when your sample contains enough evidence to support it.

If confidence level is 99%, is the result more reliable than confidence level 95%?

If c level is 99%, more error would be included in null hypothesis area, than level 95%. if c level is 99%, it means '99% of deviation would be regarded as in the null area anyway.

So actually, c level 99% means it's less precise than 95%, right? Rather, if confidence level is very small like 5%, so the 'c' value goes closer to μ0, it would mean that we will regard more values to be error. So it must be more precise.

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The sequence is convergent and the sum of the geometric series is 3/2=1.5.

The geometric series was significant in the early development of calculus, is utilized throughout mathematics, and can serve as an introduction to commonly used mathematical tools such as the Taylor series, complex Fourier series, and matrix exponential.

The name geometric series implies that each phrase is the geometric mean of its two nearby terms, in the same way that the word arithmetic series implies that each term.

Given the geometric series 1+1/3+1/9+1/27+...we must verify the value of its common ratio to determine whether the geometric series is convergent or divergent. The value of a geometric series common ratio is used to determine whether it is convergent or divergent.

If |r| <1, the series is convergent.

If |r| >1, the series is divergent.

The common ratio is r.

The common ratio r = (1/3)/1 = (1/9)/(1/3) = (1/27)/(1/9)=1/3 is derived from the given series.

Because r = 1/3, which is smaller than one, the series is convergent.

Because the geometric series tends to infinity, we will apply the formula for calculating a geometric series sum to infinity to get its sum.

The first term = 1

S = a/1-r

a is the first term = 1

r is the common ratio = 1/3

S = 1/1-(1/3)

S= 1/(2/3)

S= 3/2

S=1.5

The sum of the geometric series is 3/2=1.5

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Answer: x=1

Step-by-step explanation:

Total investment in the sinking fund compounded monthly will be $277.97

What is sinking fund?

A sinking fund may be a fund that an organization could place the money into from currently on to form their debt repayments easier. the foremost common example may be a bond fund employed by corporations to manage their debt.

Main body:

total money to accumulate = $46000

time = 9 years

rate = 9%

formula for sinking fund:

Contribution = Money to accumulate * (interest / ((interest + 1)compound frequency * period - 1))

investment = 46000((9/10) ^(12*8) - )

investment to be made = $277.97

Hence contribution every month is $277.97

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Solve a system of equations we get 28 number of songs that were dedicated and 14  number of birthday wishes.

Let x be No.of Listeners dedicate a song

y be the No. of Birth day wishes.

$10 to dedicate a song or $25 to wish someone Happy Birthday.

Forty-two listeners made one pledge each .

X+Y =42.

y = 42 -x

the station collected $630.

10x + 25y = 630

y = 42 -x in above equation .

10x + 25(42 -x) = 630

10x -25x +1050 = 630

-15x = 630 -1050 = -420

x = 420/15

x = 28

y= 14

we get 28 number of songs that were dedicated and 14  number of birthday wishes.

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Solve a system of equations we get 28 number of songs that were dedicated and 14  number of birthday wishes.

system of equations, or simultaneous equations Two or more equations to be solved concurrently in algebra (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

Let x be No.of Listeners dedicate a song

y be the No. of Birth day wishes.

$10 to dedicate a song or $25 to wish someone Happy Birthday.

Forty-two listeners made one pledge each .

X+Y =42.

y = 42 -x

the station collected $630.

10x + 25y = 630

y = 42 -x in above equation .

10x + 25(42 -x) = 630

10x -25x +1050 = 630

-15x = 630 -1050 = -420

x = 420/15

x = 28

y= 14

we get 28 number of songs that were dedicated and 14  number of birthday wishes.

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The accident proportions differ between the two age groups is [tex]\frac{11}{100}[/tex].

We have given that,

number of clients under age of 18 = 500

number of accident = 180

Proportion of client under age of 18 =  [tex]\frac{180}{500}[/tex]  = [tex]\frac{18}{50}[/tex]

number of clients over age of 18 = 600

number of accidents = 150

number of clients over age of 18 = [tex]\frac{150}{600}[/tex] = [tex]\frac{15}{60}[/tex] = [tex]\frac{1}{4}[/tex]

Now we have to find proportion of difference between two age group,

[tex]\frac{18}{50}[/tex]  -  [tex]\frac{1}{4}[/tex] =  [tex]\frac{72 - 50}{200}[/tex]

          = [tex]\frac{22}{200}[/tex]

          =  [tex]\frac{11}{100}[/tex]

Therefore the difference between two age groups is  [tex]\frac{11}{100}[/tex] .

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The graph of a straight line can be drawn as described in the solution.

To represent a straight line on a graph consider two points namely x and y-intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

The graph for a straight line for given points and y-intercept can be drawn as follows,

The point-slope equation of the straight line is,

y = mx + c

Where m is the slope and c is the y-intercept of the straight line.

Suppose there are two points (x₁, y₁) and (x₂, y₂).

Then the slope of the straight line passing through them is given as,

Slope = (y₂ - y₁)/(x₂ - x₁)

Substituting the slope in the  point-slope equation of the straight line the equation is obtained as,

y = ((y₂ - y₁)/(x₂ - x₁))x + c

Hence, the equation of the straight line passing through points (x₁, y₁) and (x₂, y₂) and having y-intercept c can be given as y = ((y₂ - y₁)/(x₂ - x₁))x + c.

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Answer:

414.69

Step-by-step explanation:

2*pi*r

We shall round it down to 16 in the circumstance when we need to determine the degrees of freedom for the t-distribution.

Any member of the family of continuous probability distributions known as the Student's t-distribution (or simply the t-distribution) in probability and statistics is used to estimate the mean of a normally distributed population when the sample size is small and the population's standard deviation is unknown.

Under the alias "Student," English statistician William Sealy Gosset created it.

The Student's t-test for determining the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and linear regression analysis are just a few commonly used statistical analyses that make use of the t-distribution.

So, in the given situation where we need to get the degrees of freedom for the t-distribution, we will round it down to 16.

Therefore, we shall round it down to 16 in the circumstance when we need to determine the degrees of freedom for the t-distribution.

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The standard deviation of the sampling distribution is 177

From the question, the given parameters are

Population standard deviation = 5 cm

Toy cars = 1250

Mean = 10.5

These can be represented as

σ = 5

n = 1250

μ = 10.5

The sampling standard deviation is calculated as

σₓ = σ√n

So, we have

σₓ = 5 * √1250

Evaluate

σₓ = 177

Hence, the sampling standard deviation is 177

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The height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.

Given,

In the question:

Its angle of elevation (to the peak) is 3.5 degrees.

After you drove 13 miles closer, the angle of elevation is 9 degrees.

To find the approximate height of the mountain.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.

Now, According to the question:

It is given that:

In traveling across flat land you notice a mountain directly in front of you.

Applying tan ratio:

tan3.5 = h/(15+x)

Here h is the height of the mountain and x is the distance between the base of the mountain and to the second position of the car.

h = (15 + x) tan3.5

h = x tan9

(15 + x) tan3.5 = x tan9

x = 9.44

h = 9.44 tan9

h = 1.49 miles

Hence, the height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.

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The percent decrease in capacity for a 12-Volt battery which had a capacity of 30 ampere-hour aging and has dropped to a capacity of 24 ampere-hours is 20%.

It is a product of the current that is drawn from the battery while the battery is able to supply the load until its voltage is dropped to lower than a certain value for each cell.

How to calculate the percent decrease of the battery capacity?
Original capacity = 30 ampere-hour

dropped capacity = 24 ampere-hour

% decrease = (original capacity - dropped capacity) / original capacity

= (30-24) / 30

= 0.2 * 100

= 20% decrease capacity.

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If you receive 400 points when you register on the game website. For every hour you play, you gain 50 extra points. You must play for 30 hours to reach 1,000 points.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, if you sign up with the game site, you get 400 points. You earn 50 more points for each hour that you play.

We have to find the hours you have to pay to get to 1,000 points,

The point remains after signing up,

=1,000 - 400

=600

If the earning is 50 more points for each hour that you play. The number of hours required,

=600 / 50

=30

Thus, you receive 400 points when you register on the game website. For every hour you play, you gain 50 extra points. You must play for 30 hours to reach 1,000 points.

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Answer:

Shirley is 28.

Step-by-step explanation:

Well, to quickly find it:

We'd have to find two numbers that fit this description.

We already know it is going to be within the late 20's and early 30's at the start.

So we start with:

28 + 3 = 31

Then to verify we add these two numbers:

31 + 28 = 59

Now applying to the descriptions,

Shirley would be three years younger Susan.

So Susan would be 31. Shirley is 28.

Chi-square test for independence to determine if gender and major are independent.

Hence, Chi-square test for independence to determine if gender and major are independent.

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The parametric representation for torus is x = bcos ∅ + a cos acos ∅

y = b sin ∅ + a cos a sin ∅

z = a sin a where , 0 ≤ a ≤ 2π , 0 ≤ ∅ ≤ 2π

Parametric equation are the set of equations that express a set of quantities as explicit function of the numbers of independent variables known as parameter

Parametric representation are generally non unique so that the quantities may be expressed by the number of different parameterizations

According to the question,

The torus obtained by rotating about the z-axis the circle in the xz-plane with center (b, 0, 0) and radius a < b.

z = a sin a

y = |PQ| and x = |OP|

but , |OQ| = |OR| + |RQ| = b + a cos a

sin ∅ = |PQ| / |OQ|

So that , y = |OQ| sin ∅ = (b + a cos a ) sin ∅

Similarly ,

cos ∅ = |OP| / |OQ|

so that x =  (b + a cos a ) cos ∅

Hence , a parametric representation for a torus is

x = bcos ∅ + a cos acos ∅

y = b sin ∅ + a cos a sin ∅

z = a sin a

where , 0 ≤ a ≤ 2π , 0 ≤ ∅ ≤ 2π

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