Graph the piecewise function below.

Answer:

4 1/2 inches

Step-by-step explanation:

if you have an area of 54 square inches. Then you divide 54 by 12 and get 4 and 1/2 square inches

Answer:

4.5

Step-by-step explanation:

12x=54 x=4.5

4.5×12=54

Answer:

h = 440.94 feet

Step-by-step explanation:

It is given that,

An architect is standing 370 feet from the base of a building, x = 370 feet

The angle of elevation is 50°.

We need to find the approximate height of the building. let it is h. It can be calculated using trigonometry as follows :

\(\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{h}{x}\\\\h=x\tan\theta\\\\h=370\times \tan50\\\\h=440.94\ \text{feet}\)

So, the approximate height of the building is 440.94 feet

Answer:

So basically if there's 6 numbers on each dice, that means that there's a 5/6 chance of not getting a 3. So multiply that and you get 5/6*5/6. That is equal to 25/36 change.

Answer:

correct answer is c of your given questions

Answer:

15 days

Step-by-step explanation:

5 x 21 = 105

105/7 = 15

Answer:

15 days

Step-by-step explanation:

As the number of people in that family increases the time taken reduces, so the time is in inverse proportion to the number of people in that family.

Let the number of days taken by a family of 7 to finish a quantity of food be x.

⇒ \(\frac{x}{21}\) = \(\frac{1}{\frac{7}{5} }\)

⇒ \(\frac{x}{21}\) = \(\frac{5}{7}\)

⇒ x = \(\frac{21 * 5}{7}\)

x = 15

∴ It would take a family of 7 15 days to finish a quantity of food.

Hope this helps!!!

Answer:

(-13,-5)

Step-by-step explanation:

If you start at the black points and go 4 left and 2 down, you will be at the Red point (-13,-5)

Answer:

Step-by-step explanation:

6--6 = 12

4-1 = 3

12/3 = 4

y=4x

-6-4 = -10

y=4x-10

The formula of slope:

Slope = (d - b) / (c - a)

where (a, b) and (c, d) are the two points.

The equation of the line that passes through (1, -6) and (4, 6) is

y = 4x - 10

The equation of a line is given by:

y = mx + c

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

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The line passes through (1, -6) and (4, 6).

The formula of slope:

Slope = (d - b) / (c - a)

where (a, b) and (c, d) are the two points.

Now,

(1, -6) = (a, b) and (4, 6) = (c, d)

Slope = (6 + 6) / (4 - 1) = 12 / 3 = 4

m = 4

The equation of a line is given as y = mx + c.

(1, -6) = (x, y)

-6 = 4 x 1 + c

-6 = 4 + c

-6 - 4 = c

c = -10

Now,

The equation of the line that passes through (1, -6) and (4, 6) is

y = 4x - 10

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Answer:

43, it raises by 4 each time. good luck!

Step-by-step explanation:

Answer:

\(x + 2x + x + 10 = 90\\\\4x + 10 = 90\\\\4x = 80\\\\x = 20\)

Answer:

-23

Step-by-step explanation:

Substitute the value of the variable into the expression and simplify.

To construct the field F8, we need to find a finite field with 8 elements. The field F8 can be represented as F8 = {0, 1, α, α², α³, α⁴, α⁵, α⁶}, where α is a primitive element of the field.

In F8, addition and multiplication are performed modulo 2. We can represent the elements of F8 using their binary representations as follows:

0 -> 000

1 -> 001

α -> 010

α² -> 100

α³ -> 011

α⁴ -> 110

α⁵ -> 101

α⁶ -> 111

Addition Table for F8:

+   |  0  1  α  α² α³ α⁴ α⁵ α⁶

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

0   |  0  1  α  α² α³ α⁴ α⁵ α⁶

1   |  1  0  α³ α⁴ α  α² α⁶ α⁵

α   |  α  α³ 0  α⁵ α² α⁶ 1  α⁴

α² | α² α⁴ α⁵ 0  α⁶ α³ α  1

α³ | α³ α  α² α⁶ 0  1  α⁴ α⁵

α⁴ | α⁴ α² α⁶ α³ 1  0  α⁵ α

α⁵ | α⁵ α⁶ 1  α  α⁴ α⁵ α⁶ 0

α⁶ | α⁶ α⁵ α⁴ 1  α⁵ α  α³ α²

Multiplication Table for F8:

*   |  0  1  α  α² α³ α⁴ α⁵ α⁶

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

0   | 0  0  0  0  0  0  0  0

1    | 0  1  α  α² α³ α⁴ α⁵ α⁶

α   | 0  α  α² α³ α⁴ α⁵ α⁶ 1

α² | 0  α² α³ α⁴ α⁵ α⁶ 1  α

α³ | 0  α³ α⁴ α⁵ α⁶ 1  α α²

α⁴ | 0  α⁴ α⁵ α⁶ 1  α α² α³

α⁵ | 0  α⁵ α⁶ 1  α α² α³ α⁴

α⁶ | 0  α⁶ 1  α α² α³ α⁴ α⁵

In the addition table, each element added to itself yields 0, and the addition is commutative. In the multiplication table, each element multiplied by itself yields 1, and the multiplication is also commutative. These properties demonstrate that F8 is indeed a field.

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The first two are functions the third one is not a function and the fourth one is a function

On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.

When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.

Here,

U/5 = 17/11

U = 17/11 X 5

U = 7.72

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Hello !

Answer:

\(\boxed{\sf V{cone} \approx 2408.55 m^3}\)

Step-by-step explanation:

To find the volume of a cone with the radius of its base and its height, we will apply the following formula:

\( \sf V{cone} = \dfrac{\pi \times r^2 \times h}{3} \)

Where r is the radius of its base and h is its height.

Given:

Let's substitute our values into the formula:

\(\sf V{cone} = \dfrac{\pi (10)^2(23)}{3} = \dfrac{2300\pi}{3} \ \ \\\boxed{\sf V{cone} \approx 2408.55 m^3}\)

Have a nice day ;)

The balance outstanding on the loan immediately after the seventh quarterly payment, using an interest rate of 16% p.a. compounded quarterly and equal quarterly payments, is R$310.39.

To calculate the balance outstanding after the seventh quarterly payment, we need to use the formula for the present value of an ordinary annuity:

P = PMT * (1 - (1 + r)^(-n)) / r

Where:

P = Principal amount of the loan (R$1,000)

PMT = Equal quarterly payment

r = Interest rate per period (16% p.a. compounded quarterly = 4% per quarter)

n = Number of periods (10 payments)

First, we calculate the equal quarterly payment (PMT) using the present value of an ordinary annuity formula rearranged to solve for PMT:

PMT = P * (r / (1 - (1 + r)^(-n)))

PMT = 1000 * (0.04 / (1 - (1 + 0.04)^(-10))) = R$129.09

Next, we calculate the balance outstanding after the seventh quarterly payment. We can consider it as the present value of the remaining three payments:

Balance = PMT * (1 - (1 + r)^(-n_remaining)) / r

Where: n_remaining = Number of remaining payments (10 - 7 = 3)

Balance = 129.09 * (1 - (1 + 0.04)^(-3)) / 0.04 = R$310.39

Therefore, the balance outstanding on the loan immediately after the seventh quarterly payment is R$310.39.

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Answer:

(3,8)

Step-by-step explanation:

Answer:

V=2197

Step-by-step explanation:

The t value will be the result that is  58.851995039

The t-statistic for the observed correlation coefficient of 0.951 can be calculated to determine if it is statistically significant. Using the T.INV() spreadsheet function and the appropriate degrees of freedom.

We can test the null hypothesis of no correlation at the 5% significance level. Additionally, the T.DIST() function can be used to calculate the p-value of the t-statistic.

To calculate the t-statistic, we need to know the sample size (n) and the observed correlation coefficient (r). In this case, we have 37 monthly observations and a correlation coefficient of 0.951. The t-statistic can be calculated using the formula t = r x sqrt((n - 2) / (1 - r^2)). Plugging in the values, we find t = 0.951 x sqrt((37 - 2) / (1 - 0.951^2)).

By comparing this t-statistic to the critical value at the desired significance level (5% in this case), we can determine if the null hypothesis of no correlation can be rejected. Additionally, the p-value can be calculated using the T.DIST() function to determine the probability of obtaining a t-statistic as extreme as the observed value. If the p-value is less than the chosen significance level, the null hypothesis can be rejected.

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High intercorrelations between two or more independent variables in a multiple regression model are referred to as multicollinearity.

A single dependent variable and several independent variables can be analyzed using the statistical technique known as multiple regression. With the use of independent variables whose values are known, multiple regression analysis aims to predict the value of a single dependent variable.

Multicollinearity, also known as collinearity, is a phenomena in statistics when one predictor variable in a multiple regression model can be linearly predicted from the others with a high level of accuracy. In this case, minor adjustments to the model or the data may cause the multiple regression's coefficient estimates to fluctuate unpredictably.

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The eigenvalues of A are λ = 7 and λ = -1. PTAP will be a diagonal matrix with the eigenvalues as diagonal entries.

To find the matrix A associated with the quadratic form, we need to consider the coefficients of the quadratic terms in the equation. Given the equation 3x² - 8xy - 3y² + 15 = 0, the matrix A is given by:

A = [[3, -4], [-4, -3]]

To find the eigenvalues of A, we can solve for the characteristic equation by finding the determinant of (A - λI) equal to zero, where I is the identity matrix:

det(A - λI) = det([[3 - λ, -4], [-4, -3 - λ]])

Expanding the determinant, we have:

(3 - λ)(-3 - λ) - (-4)(-4) = λ² - 6λ + 9 - 16 = λ² - 6λ - 7

Setting the determinant equal to zero and solving for λ, we have:

λ² - 6λ - 7 = 0

Using the quadratic formula, we find the roots:

λ = (6 ± √(6² + 4(7))) / 2

= (6 ± √(36 + 28)) / 2

= (6 ± √64) / 2

= (6 ± 8) / 2

= 7, -1

So, the eigenvalues of A are λ = 7 and λ = -1.

To find an orthogonal matrix P such that PTAP is diagonal, we can find the eigenvectors corresponding to the eigenvalues λ = 7 and λ = -1. The eigenvectors are the normalized solutions to the equation (A - λI)v = 0.

For λ = 7:

(A - 7I)v = 0

[[-4, -4], [-4, -10]]v = 0

Solving the system of equations, we find v₁ = [-1, 1].

For λ = -1:

(A - (-1)I)v = 0

[[4, -4], [-4, -2]]v = 0

Solving the system of equations, we find v₂ = [1, 2].

To construct the orthogonal matrix P, we normalize the eigenvectors v₁ and v₂ to have unit length.

P = [[-1/√2, 1/√5], [1/√2, 2/√5]]

Therefore, PTAP will be a diagonal matrix with the eigenvalues as diagonal entries.

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Answer:

G

Step-by-step explanation:

Dude really

Answer:

A. G is the correct answer

Step-by-step explanation:

the quadrants are shown in the picture

and G. is the only one that fits the description

hope this helps <3

Answer:

Required system of inequalities to represent this situation:

Given:

Opal makes $15 per hour working for a photographer.

She also coaches a competitive soccer team for $10 per hour.

Defining variables

Let x = Number of hours she works as a photographer, y= Number of hours she works as coach.

Explanation

As she needs to earn at least $90 per week i.e.  

but she does not want to work more than 20 hours per week.

i.e.  

Required system of inequalities to represent this situation:

Step-by-step explanation:

HOPE THIS HELPS

Required system of inequalities to represent this situation 15x + 10y ≥ 20 and x + y ≤ 20.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

Given that Opal makes $15 per hour working for a photographer. She also coaches a competitive soccer team for $10 per hour.

Defining variables Let x = Number of hours she works as a photographer, y= Number of hours she works as a coach.

As she needs to earn at least $90 per week i.e. but she does not want to work more than 20 hours per week. The required system of inequalities to represent this situation.

15x + 10y ≥ 20

x + y ≤ 20.

Therefore, the required system of inequalities to represent this situation is 15x + 10y ≥ 20 and x + y ≤ 20.

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Answer:

y= 39/5\(y=\frac{39}{5}\)

Step-by-step explanation:

\(y=\frac{7*5}{5} +\frac{4}{5}\)

\(y=\frac{7*5+4}{5}\)

7 * 5 + 4 = 49

7 * 5 + 4

=35+ 4

= 39

y = 39/5

Answer:

120

Step-by-step explanation:

480 total

1/2 = 240 are cows

1/8 = 60 are goats

remaining = 480-240-60 = 180 are chickens & ducks

33.3333% of 180 = chickens  =180/3 = 60 chickens

so ducks = 180-60 =120

Answer:

120

Step-by-step explanation:

given that out of 480 animals 0.5 of the animals are cows . So ,

no. of cows = 0.5*480 = 240

Again, we are given that 1/8 of the animals are goats , so the number of goats would be ,

no. of goats = 1/8*480 = 60

Total no. of goats and cows ,

= 240 + 60 = 300

No. of remaining animals= 480 -300 = 180

Now out of these 180 animals 33⅓ % animals are chickens and remaining are ducks.

Percentage of ducks = (100 - 33⅓ )% = 66.67%

So the number of ducks would be ,

180 * 66.67/100 = 120

And we are done!

Answer:

-1

Step-by-step explanation:

the slope is going down 1

Answer:

The slope of the graph is -1

Step-by-step explanation:

The equivalent equations are A. 56 + 8x = 80,  B. 14 = 20 – 8x, and

D. 2x = 6

The equations which have the same set of solutions are known as Equivalent equations. This means that any value that satisfies one of the equations will also satisfy the others.

To determine if two equations are equivalent, we can simplify or transform one equation into another using various algebraic operations.

Some common algebraic operations include adding, subtracting, multiplying, and dividing both sides of an equation by the same non-zero value.

Here we have

1/4 (8x + 56) = 20  

Which can be simplified as follows

=> (8x + 56) = 80

=>  8x + 56 = 80

=>  8x = 80 - 56

=>  8x = 24

=>  2x = 6  

To find the equivalent equations simplify each option as follows

A. 56 + 8x = 80

=> 8x = 24

=> 2x = 6      [ Which is an equivalent equation ]

B. 14 = 20 – 8x

=> 8x = 6      [ Which is an equivalent equation ]

C. 2x + 14 = 5

=> 2x = -9     [ Which is not equivalent equation ]

D. 2x = 6       [ Which is an equivalent equation ]  

Therefore,

The equivalent equations are A. 56 + 8x = 80,  B. 14 = 20 – 8x, and

D. 2x = 6

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Answer:

use formula

area of semicircle + area of trapezium

The required area is \(938.4 m^2\)

The combination of solids includes shapes formed by two or solid shapes, which together form a new shape.

We can draw the given diagram as given below

So this includes the given shapes as,

ACEF=Rectangle

CDE=Triangle

Arc ABC=Half circle.