In a study; the sample is chosen by separating all cars by size, and selecting 10 of each size grouping What is the sampling method? Simple Random Systematic Stratified Cluster Convenience

Answer:

37 and -18

Step-by-step explanation:

Answer:

let x and y be two numbers

Zach is trying to find out the hypotenuse value of the right-angle triangle.

What is the right triangle?

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The Pythagorean theorem states that "in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides".

Zach is most likely trying to find the length of the hypotenuse of a right triangle, which is the side opposite the right angle, given the lengths of the other two sides.

In this case, given 32 inches, 20 inches, and 20 inches values, he's trying to find out the hypotenuse value of the right-angle triangle.

Hence, Zach is trying to find out the hypotenuse value of the right-angle triangle.

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Answer:

Step-by-step explanation:

The idea is, for each triangle, sort all of its sides and then store it in a map, if all those three sides are already present in the map then increase the frequency by 1, else its frequency will be 1. The count of elements of the map which have frequency 1 in the end will be the answer.

Margin of error is 0.017 pound(approximately.)

Now, According to the question:

We know that:

Formula of margin of error :

E = [tex]z^*[/tex] × [tex]\frac{s}{\sqrt{n} }[/tex]

where:

z* = critical value for confidence interval

s= standard deviation

n= sample size.

We have:

s= 0.15 pound

n= 300

Critical value for 95% confidence = 1.96

Then, Margin of error for 95% confidence interval will be :

E = (1.96)[tex]\frac{0.15}{\sqrt{300} }[/tex]

E = 0.0169740971 ≈ 0.017

Hence, Margin of error is 0.017 pound (approximately.)

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The solution to given equation (3/4)x + 3 - 2x = -(1/4) + (1/2)x + 5

is x = -1

Consider given equation.

(3/4)x + 3 - 2x = -(1/4) + (1/2)x + 5

We need to solve this equation.

First we combine the like terms on each side of the equation.

(3/4 - 2)x + 3 = (-1/4 + 5) + (1/2)x

Simplify each side of the above equation.

(-5/4)x + 3 = 19/4 + (1/2)x

Now subtract (1/2)x from each side,

(-5/4)x + 3 - (1/2)x = 19/4 + (1/2)x - (1/2)x

Simplify each side

(-5/4 - 1/2)x + 3 = 19/4 + 0

(-7/4)x + 3 = 19/4

Add -3 to each side of the equation.

(-7/4)x + 3 - 3= 19/4 - 3

(-7/4)x = 7/4

Multiply each side of equation by (-4/7)

(-7/4)x × (-4/7) = 7/4 × (-4/7)

x = -1

Therefore, the solution is x = -1

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48600 rupees is needed to exchange 450 us dollars

Percentage Decrease is the percentage change in the value when it is decreased over a period of time.

How to determine this

When 1 us dollar is exchanged at 120 rupees

And devaluated by 10%

i.e 10% of 120 rupees

= 10/100 * 120

= 1200/100

= 12 rupees devaluated

So, 120 - 12 = 108 rupees can be exchanged

How much is 450 us dollars

Let x represent the number

If 1 us dollars = 108 rupees

450 us dollars = x

x = 450 * 108/1 rupees

x = 48600 rupees

Therefore, 48600 rupees can be exchanged for 450 us dollars

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the product of x and a factor not depending on x

What is quadratic equation

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The equation given 3x(m-6n)²

This expression contains two factors:

1 factor: 3x

2 factor: (m-6n)²

Hence the product of x and a factor not depending on x.

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Both equations are satisfied, so the solutions to the equations are correct.

Matrix is a system of data or numbers arranged in rows and columns that is used to solve mathematical problems. It is a mathematical representation of a real-world situation. The rows represent the elements or items in the situation, while the columns represent the attributes or characteristics of the elements. Matrix can be used to solve various types of problems, such as linear equations, calculus, and statistics. It can also be used to represent data in graphs, tables, and other visual formats.

The augmented matrix in Exercise 12 is:

\begin{bmatrix}
1 & 4 & 5 & -10 \\
2 & 8 & 6 & -20
\end{bmatrix}

The corresponding equations are:

1x + 4y = -10
2x + 8y = -20

To verify that the solutions obtained in Exercise 12 are correct, we can substitute x=5 and y=-2 back into the equations:

1(5) + 4(-2) = -10
2(5) + 8(-2) = -20

Both equations are satisfied, so the solutions to the equations are correct.

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Both equations are satisfied, so the solutions to the equations are correct. This can be solved using the concept of matrix.

Matrix is a system of data or numbers arranged in rows and columns that is used to solve mathematical problems. It is a mathematical representation of a real-world situation. The rows represent the elements or items in the situation, while the columns represent the attributes or characteristics of the elements. Matrix can be used to solve various types of problems, such as linear equations, calculus, and statistics. It can also be used to represent data in graphs, tables, and other visual formats.

The augmented matrix in Exercise 12 is:

[tex]\left[\begin{array}{cccc}1&4&5&-10\\2&8&6&-20\end{array}\right][/tex]

The corresponding equations are:

1x + 4y = -10

2x + 8y = -20

To verify that the solutions obtained in Exercise 12 are correct, we can substitute x=5 and y=-2 back into the equations:

1(5) + 4(-2) = -10

2(5) + 8(-2) = -20

Both equations are satisfied, so the solutions to the equations are correct.

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Answer:

a. The area of the square is 25 feet x 25 feet = 625 square feet.

b. To find the percent of points that landed in the pond, we divide the number of points that landed in the pond by the total number of points generated and multiply by 100.

3,200 points / 5,000 points = 0.64

0.64 x 100 = 64%

so 64% of the points landed in the pond.

c. To find the area of the pond, we multiply the proportion of points that landed in the pond by the area of the square.

64% of the points landed in the pond = 0.64

Area of the pond = 0.64 x 625 square feet = 400 square feet. So, the area of the pond, to the nearest square foot, is 400 square feet.

Step-by-step explanation:

The amount of wood, in meters, needed to rebuild the frame is 1.8288 m.

What is amount and example?

amount to (something) : to produce (a total) when added together. The bill amounted to 10 dollars. They have debts amounting to thousands of dollars.

To calculate the amount of wood, in meters, needed to rebuild the frame, we can use the following formula:

wood (m) = (wood (ft) x 0.3048) / 6

Since each piece of wood provided measures 6 ft (approximately 1.8 to 8.7), we can calculate the amount of wood, in meters, needed to rebuild the frame as follows:

wood (m) = (6 ft x 0.3048) / 6

wood (m) = 1.8288 m      

Therefore, the amount of wood, in meters, needed to rebuild the frame is 1.8288 m.

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Answer:

The outcome of rolling a set of 2 fair dice is a number between 2 and 12, and there is a probability of 1/9 for each outcome.

For the outcomes 4,5,6, you will lose $6, and for the other outcomes, you will win $3.

There are 3 outcomes 4,5,6, and 9-3 = 6 outcomes where you win $3.

So your expected gain/loss per roll is:

(3/9) * $3 + (3/9) * (-$6) = -$1

Therefore, on average, you will lose $1 per each throwing.

Using half angle formula,

Half angle formulas are equations that contain the half angles of the trigonometric ratios.

Given that tanα = -1/2 and π/2 < α < π

To find sin(α/2), we use the half angle formula

sin(α/2) = √[(1 - cosα)/2]

Also, tan²α + 1 = sec²α = 1/cos²α

⇒ cosα = ±1/√(1 + tan²α)

Since π/2 < α < π

cosα = -1/√(1 + tan²α)

Substituing this into the equation for sin(α/2), we have

sin(α/2) = √[(1 - cosα)/2]

sin(α/2) = √[(1 - (-1/√(1 + tan²α)))/2]

Substituting  tanα = -1/2 into the equation, we have

sin(α/2) = √[(1 + 1/√(1 + tan²α))/2]

sin(α/2) = √[(1 + 1/√(1 + (-1/2)²))/2]

sin(α/2) = √[(1 + 1/√(1 + 1/4))/2]

sin(α/2) = √[(1 + 1/√(5/4))/2]

sin(α/2) = √[(1 + 1/√5/2)/2]

sin(α/2) = √[(1 + 2/√5)/2]

sin(α/2) = √[(√5 + 2)/√5)/2]

sin(α/2) = √[(√5 + 2)/2√5

sin(α/2) = √[(√5 + 2)/2√5 × √5/√5

sin(α/2) = √[5(√5 + 2)]/2 × 5

sin(α/2) = √[5(√5 + 2)]/10

So, sin(α/2) = √[5(√5 + 2)]/10

Using the half angle formula,  

tan(α/2) = sinα/(1 + cosα)

Using the trigonometric identity cosα = ±1/√(1 + tan²α)

cosα = ±1/√(1 + (-1/2)²)

cosα = ±1/√(1 + 1/4)

cosα = ±1/√(5/4)

cosα = ±1/√5/2

cosα = ±2/√5

Since π/2 < α < π

cosα = -2/√5

Also, since the trigonometric identity sinα = ±√(1 - cos²α)

So, sinα = ±√(1 - (-2/√5)²)

sinα = ±√(1 - 4/5)

sinα = ±1/√5

Since π/2 < α < π

sinα = +1/√5

Substituting cosα = -2/√5 and sinα = +1/√5 into the equation for tan(α/2), we have

tan(α/2) = sinα/(1 + cosα)

tan(α/2) = +1/√5/(1 + (-2/√5))

tan(α/2) = +1/√5/(1 - 2/√5)

tan(α/2) = +1/√5/(√5 - 2)/√5)

tan(α/2) = 1/(√5 - 2)

So, tan(α/2) = 1/(√5 - 2)

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The sample size (n) needed can be calculated using

[tex]0.025 =2.33\sqrt{\frac{0.79*0.21}{n} }[/tex].

Given:

We have the following confidence interval of proportions in a sample of n people who were polled, with a success probability of [tex]\pi[/tex] and a confidence level of [tex]1- \alpha[/tex].

π ± [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]

Here z is the z score which has a pvalue of

[tex]1 -\alpha /2[/tex]

The margin of error is given as:

[tex]M = z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]

79 percent of adults age 18 years and older in the United States use the Internet as found by a survey.

So, [tex]\pi =0.79[/tex]

98% confidence level

Now [tex]\pi =0.02[/tex], z is the value of Z that has a pvalue of  [tex]1-\frac{0.02}{2} =0.99[/tex].

So, Z =2.33.

The sample size (n) needed can be estimated using:

We have to find n for which M = 0.025

The required equation is:

[tex]M =z\sqrt{ \frac{\pi (1-\pi )}{n} }[/tex]

[tex]0.025 = 2.33\sqrt{\frac{0.79*0.21}{n} }[/tex]

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Answer:

Step-by-step explanation:

To calculate the total amount Daniel LaRusso will have to pay back in 2 years, we first need to calculate the interest he will owe on the loan.Simple Interest (I) = P * r * t

where P is the principal (the amount borrowed), r is the annual interest rate (expressed as a decimal), and t is the time (in years) for which the loan is borrowed.In this case, the principal is $1,200, the annual interest rate is 8%, and the time is 2 years.I = $1,200 * 0.08 * 2 = $192So, he will have to pay back a total of $1,200 (principal) + $192 (interest) = $1,392So, Daniel LaRusso will have to pay back a total of $1,392 in 2 years.

Answer:

---------------------------------

The amount of interest at 8% simple for 2 years is 16% of the loan:

The total amount including both the principal and interest is:

Correct choice is D.

The distance between base of ladder and the building should be

4.4 meter.

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

AC² = AB² + BC²

Given,

Height of the window from the ground AB = 9 meter

Length of the ladder AC = 10 meter

Distance between base of ladder and building BC = ?

By Pythagorean theorem,

In the right ΔABC

AC² = AB² + BC²

10² = 9² + BC²

BC² = 10² - 9²

BC² = 100 - 81

BC² = 19

BC = √19

BC = 4.359 meter

BC = 4.4 meter

Hence, base of ladder should be 4.4 meter away from the building.

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The p-value is a probability and it should be between 0 and 1.

The p-value of a hypothesis test is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true.

In this case, the null hypothesis is that the population proportion of students who went to the movie theatre last weekend is equal to 0.2 and the alternative hypothesis is that the population proportion is greater than 0.2.

Given that the test statistic is 2.25, the p-value would be the probability of getting a test statistic as extreme or more extreme than 2.25 assuming the null hypothesis is true. Without more information, we can't give you an exact p-value, but you can use a one-sided test and find the p-value using a z-table or using software that can calculate the p-value.

It is also important to note that the p-value is a probability and it should be between 0 and 1.

Therefore,  The p-value is a probability and it should be between 0 and 1.

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I would recommend asking many consumers a few brief questions in a survey. This method would help Bolt quickly and easily obtain a broad view of its consumers’ purchase original cost motivations, which could then be analyzed to develop more targeted strategies.

Surveys are a great way to quickly obtain a broad view of a target audience’s motivations for purchase. By asking many consumers a few brief questions, Bolt can gain insight into what motivates them to purchase their products, or why they may choose not to purchase them. This data can then be analyzed to develop more targeted strategies to increase sales. Surveys also provide an efficient way to sample a large number of people, allowing Bolt to get a representative statistical sample of its consumers’ motivations. This data can also be used to inform future marketing campaigns, allowing Bolt to better target their customers and maximize sales.

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I think the question should be tan theta = 1/√3, but I have given the solutions of both.

Hope it helps.

If you have any query, feel free to ask.

The length of segment $\overline{ab}$ is 12 + 4$[tex]\sqrt{11}[/tex]$ units.

What is right triangle ?

A right triangle is a type of triangle that has one angle that measures exactly 90 degrees, also known as a right angle. The side opposite the right angle is called the hypotenuse and it is the longest side of the triangle. The other two sides are called legs, and one of them is the base and the other one is the height.

We know that the medians are 6 and $2\sqrt{11}$ units, respectively.

Therefore, the length of $\overline{ab}$ is twice the median length from $a$ to segment $\overline{bc}$ + twice the median length from $b$ to segment $\overline{ac}$

so the length of $\overline{ab}$ = 2(6) + 2($2[tex]\sqrt{11}[/tex]$) = 12 + 4$\sqrt{11}$

so the length of $\overline{ab}$ = 12 + 4$[tex]\sqrt{11}[/tex]$ units.

Hence , The length of segment $\overline{ab}$ is 12 + 4$[tex]\sqrt{11}[/tex]$ units.

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Answer:

[tex]f(g(x)) = \boxed{\dfrac{x}{2}}[/tex]

[tex]g(f(x)) = \boxed{2x - 5}[/tex]

Step-by-step explanation:

We have the following two functions
[tex]f(x) = \dfrac{1}{x-5}\\\\g(x) = \dfrac{2}{x}+\:5[/tex]

To find [tex]f(g(x))[/tex]  substitute the expression for [tex]g(x)[/tex]  wherever you see an [tex]x[/tex] in [tex]f(x)[/tex]

[tex]\mathrm{For}\:f=\dfrac{1}{x-5}\:\mathrm{substitute}\:x\:\mathrm{with}\:\dfrac{2}{x}+5[/tex]

[tex]=\dfrac{1}{\dfrac{2}{x}+5-5}\\\\[/tex]

[tex]=\dfrac{1}{\dfrac{2}{x}}\\\\\\= \dfrac{x}{2}[/tex]    ANSWER

To find [tex]g(f(x)[/tex], substitute the expression for [tex]f(x)[/tex]  wherever you see an [tex]x[/tex] in [tex]g(x)[/tex]

[tex]\mathrm{For}\:g=\dfrac{2}{x}+5\:\mathrm{substitute}\:x\:\mathrm{with}\:\dfrac{1}{x-5}\\\\=\dfrac{2}{\dfrac{1}{x-5}}+5\\\\[/tex]

[tex]=2\left(x-5\right)+5\\\\= 2x - 10 + 5\\\\= 2x - 5\\\\[/tex]ANSWER

Note:

[tex]\dfrac{2}{\dfrac{1}{x-5}}=2\left(x-5\right)\\\\[/tex]

Answer:

6-y^2 can be factored by using the difference of squares formula which states that:

a^2 - b^2 = (a+b)(a-b)

We can factorize 6-y^2 by using the following:

6 - y^2 = (sqrt(6) + sqrt(-y^2))(sqrt(6) - sqrt(-y^2))

= (sqrt(6) + yi)(sqrt(6) - yi)

where i is the imaginary unit.

So, 6-y^2 = (sqrt(6) + yi)(sqrt(6) - yi) is the factored form of 6-y^2

Please note that the factorization is only true for real values of y, when y is not real the expression can't be factorized.

The correct term for each term is -

Federal Fund Rate

Bank holding company

Check clearing

Net worth

Discount rate

What is an account?

A certain kind of financial asset or debt that is kept and owned in your name.

When a bank borrows money from another bank, the interest rate it pays is called the Federal Fund Rate.

Ownership of more than one bank constitutes a bank holding company.

When a bank customer writes a check, the check will go through the process of check clearing.

A bank's total assets minus its total liabilities make up its net worth.

Banks repay loans from the Federal Reserve at a rate of interest called the discount rate.

Therefore, these are the key terms used in banking.

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Therefore , the solution of the given problem of ratio comes out to be  the coordinate P = (7, 0.4).

A ratio as well as fraction in mathematics shows how frequently one value is present in another. For instance, if there are eight grapefruit and six lemons in a fruit plate, the ratio from oranges to citrus is eight to six, or 8:6, which is comparable to the ratios 4:3 or the decimal 1.333.

Here,

Ratios are a useful tool for segmenting lines into smaller units.

P's coordinate is P = (7, -0.4)

The criteria are as follows:

A = (8,0)\sB = (3,-2) (3,-2)

m: n=1:4

Using P = mx2+nx1 my2+ny

m+n

m+n, line ratio is computed.

The result is:

P 1x3+4x8 /1x-2+4x0 = 1+4 / 7

=> P = 35, 2

=>P = (7, -0.4) (7, -0.4)

1+4

P therefore has the coordinate P = (7, 0.4).

Therefore , the solution of the given problem of ratio comes out to be  the coordinate P = (7, 0.4).

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As you move the graph of the line from left to right, the output value of the function increases.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The slope determines if the function is increasing or decreasing over it's domain, as follows:

A positive slope means that the function increases when it moves from left to right, that is, when x increases.

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The correct option when Triangle ABC is transformed to triangle A′ B′ C is A.The measure of angle BCA = The measure of angle C prime A prime B prime.

Triangle ABC is changed into triangle A′B′C′ and on the x- and y-axes, a coordinate grid ranging from -4 to -4 to 4 is displayed. A is at ordered pair negative 1, 3, B is at ordered pair 0, 1, and C is at ordered pair negative 3, 0 in the triangle ABC.

A triangle Primes A, B, and C have A prime is at ordered pair minus 1, minus 3, B prime is at ordered pair minus 0, and C prime is at ordered pair minus 3, 0.

A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.

Therefore,

<BAC = <B'A'C'

<ABC = <A'B'C'

<ACB = <A'C'B'

In this case, the correct option is A.

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The value of x in the simplest radical form is 6.633

What is value ?

Value in mathematics can refer to a number of concepts that are closely related. Any specific mathematical object can be a mathematical value in general. In elementary mathematics, this is typically a number, such as a real number like or an integer like 42.

The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value. For illustration, let's look at the number 45.

The things that someone values are known as their values. In other terms, values are what a person or a group of people see as "important." Examples include valor, integrity, freedom, and creativity, among others.

cos Ф = adjacent / hypotenuse

cos 45° = √22 / x

x = √22 / cos 45°

  = (√22* √2 )

  = √44

  = 6.633

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This exponential function represents growth at a rate of 26.2% per unit increase in x.

This represents growth at a rate of 26.2% per unit increase in x.

This is an exponential function, so it will represent either growth or decay. To determine whether it is growth or decay and what rate it is, we need to look at the coefficient of the exponential term, which in this case is 1.262. Since this is larger than 1, the function is growing, and the rate of increase is equal to the coefficient minus 1, which is 26.2%.

This exponential function represents growth at a rate of 26.2% per unit increase in x.

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The lateral surface area is 1562.5  If the floor of a cuboidal hall has a perimeter of 225m and height 25m.

What is volume of Cuboid ?

volume of cuboid can be defined as the product of length , breadth and height.

Given,

If the floor of a cuboidal hall has a perimeter of 225m and height 25m

Lateral Surface area = 2h(l+b)

Given perimeter is 225m

so,

perimeter = 4 (l+b+h)

225 = 4 (l+b+25)

Given h = 25

225 = 4(l+b) + 100

4(l+b) = 225-100

4(l+b) = 125

l+b = 125/ 4

So,

Lateral surface area = 2h (l+b)

= 2 * 25 * ( l+b)

= 50*125/4

= 1562.5

Hence , The lateral surface area is 1562.5  If the floor of a cuboidal hall has a perimeter of 225m and height 25m.

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Answer:

2

Step-by-step explanation:

-4+6=2