on a regular day during the NBA season are what roughly nine NBA games being played on regular days the NBA uses a total of 27 brand new basketballs on using each game uses that exact same number of basketballs fill out the table below using equivalent ratios?

Answer:

The solutions to the system of the equations are:

\(y=1,\:x=3\)

Step-by-step explanation:

Given the equations

\(y=\frac{2}{3}x-1;\:y=-x+4\)

solving the system of equation

\(\begin{bmatrix}y=\frac{2}{3}x-1\\ y=-x+4\end{bmatrix}\)

Arrange equation variables for elimination

\(\begin{bmatrix}y-\frac{2}{3}x=-1\\ y+x=4\end{bmatrix}\)

\(y+x=4\)

\(-\)

\(\underline{y-\frac{2}{3}x=-1}\)

\(\frac{5}{3}x=5\)

\(\begin{bmatrix}y-\frac{2}{3}x=-1\\ \frac{5}{3}x=5\end{bmatrix}\)

solving for x

\(\frac{5}{3}x=5\)

\(5x=15\)

Divide both sides by 15

\(\frac{5x}{5}=\frac{15}{5}\)

\(x=3\)

\(\mathrm{For\:}y-\frac{2}{3}x=-1\mathrm{\:plug\:in\:}x=3\)

\(y-\frac{2}{3}\cdot \:3=-1\)

\(y-2=-1\)

Add 2 to both sides

\(y-2+2=-1+2\)

\(y=1\)

Therefore, the solutions to the system of the equations are:

\(y=1,\:x=3\)

Answer:

r² = (9 - 4)² + (6 - 4)² = 5² + 2² = 25 + 4 = 29

So the equation of this circle is

(x - 4)² + (y - 4)² = 29

The function that represents the amount paid after t months is \(f(t) = 150 + 50t\)

From the complete question, we have the following highlights

Let the number of months be t.

So, the function that represents the amount paid after t months is:

f(t) = Sign up fee + Monthly Rate * t

This gives

\(f(t) = 150 + 50 \times t\)

Evaluate the product

\(f(t) = 150 + 50t\)

Hence, the function that represents the amount paid after t months is \(f(t) = 150 + 50t\)

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Answer:

The answer is B!!HOPE THIS HELPS :)

Step-by-step explanation:

I just guessed it and its right :)

Answer:

b

Step-by-step explanation:

After considering the given data we conclude that the answer for the sub questions are
a) Jeff consumes 33.33 units of good x.
b) the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c) The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.

a. To find Jeff's demand function for good x, we can use the following equation:
\(\frac{\partial U}{\partial x}=\frac{1}{x}=\frac{p_x}{p_y}=\frac{1}{2}\)
Solving for x, we get:
\(x=\frac{1}{2}y\)
Substituting the given values, we get:
\(x=\frac{1}{2}(200/3)=33.33\)
Therefore, Jeff consumes 33.33 units of good x.
b. If Px increases to 2, the new demand function for good x is:
\(x'=\frac{1}{2}y'\)where y'  is the amount of good y consumed at the new prices and income. To find the compensating variation, we need to find the amount of income Jeff would need at the original prices to achieve the same level of utility as he does at the new prices. We can use the following equation:
\(W'=W+CV\) where W is the original income, W' is the new income, and CV is the compensating variation.
Substituting the given values, we get:
\(8.51=\ln(33.33)+\ln(66.67)8.51=ln(33.33)+ln(66.67)\)
\(y'=\frac{W'}{2}\)
\(x'=\frac{1}{2}y'\) Solving for y', we get:
y'=100
Solving for x', we get:
x'=50
Therefore, the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c. To calculate the total effect, substitution effect, and income effect of the price change, we can use the following equations:
\(TE=\frac{\Delta U}{U_0}\)
\(SE=\frac{\Delta x_s}{x_0}\)
\(IE=\frac{\Delta x_i}{x_0}\)where \(\Delta U\)is the change in utility, \(U_0\) is the initial utility,\(\Delta x_s\) is the change in consumption due to the substitution effect, \(x_0\) is the initial consumption, and \(\Delta x_i\) is the change in consumption due to the income effect.
The change in consumption due to the price change can be calculated as:
as:
\(\Delta x=x'-x_0=\frac{1}{2}y'-\frac{1}{2}y_0\)
where \(y_0=2x_0\) and \(y'=2x'\)
Substituting the given values, we get:
\(\Delta x=x'-x_0=50-33.33=16.67\)
The substitution effect can be calculated as:
\(SE=\frac{\Delta x_s}{x_0}=\frac{x_s'-x_0}{x_0}=\frac{1}{2}\frac{y_0-y_s'}{x_0}=\frac{1}{2}\frac{p_x}{p_y}\frac{y_0}{x_0}\)
Substituting the given values, we get:
\(SE=\frac{1}{2}\frac{1}{2}\frac{2x_0}{4x_0}=\frac{1}{4}\)
The income effect can be calculated as:
\(IE=\frac{\Delta x_i}{x_0}=\frac{\Delta W}{W_0}=\frac{CV}{W_0}\)
Substituting the given values, we get:
\(IE=\frac{-100}{200}=-0.5\)
The total effect can be calculated as:
\(TE=SE+IE=\frac{1}{4}-0.5=-0.25\)
Therefore, the total effect of the price change is negative, indicating that Jeff will consume less of good x as a result of the price increase. The substitution effect is positive, indicating that Jeff will consume more of good x due to the relative price change. The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.
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a) The area οf the trapezium is apprοximately 792.37 cm²

b) There is nο real value οf DE that satisfies the equatiοn, and we cannοt find the perimeter οf the trapezium.

Trapezium area equals 12 x (a + b) x h. Trapezium perimeter = a + b + c + d. where the lengths οf a trapezium's sides are a, b, c, and d. Mοreοver, h is the separatiοn between a and b, the twο parallel sides.

(a) To find the area of a trapezium, we use the formula:

A = (a + b)h/2

The perpendicular distance between them is the height of the trapezium, which we can find by using the Pythagorean theorem on the right triangle ADE:

\(AD^2 + DE^2 = AE^2\\\\16^2 + 15^2 = AE^2\\\\AE =\sqrt{(256 + 225)}\\\\ = \sqrt{(481)}\\\\ = 21.93 cm\)

Sο, the height οf the trapezium is h = AE = sqrt(481) ≈ 21.93 cm.

Nοw we can plug in the values fοr a, b, and h in the fοrmula fοr the area:

A = (35.5 + 20) * 21.93 / 2

= 792.365

≈ 792.37 cm²

Therefοre, the area οf the trapezium is apprοximately 792.37 cm².

(b) Tο find the perimeter οf the trapezium, we simply add up the lengths οf all the sides:

Perimeter = AB + BC + CD + AD + CE + DE

Substituting the given values, we get:

Perimeter = 35.5 + 18 + 20 + 16 + 15 + DE

\(CD^2 + DE^2 = CE^2\\\\20^2 + DE^2 = 15^2\\\\DE^2 = 225 - 400 = -175\)

Therefore, there is no real value of DE that satisfies the equation, and we cannot find the perimeter of the trapezium.

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Hi there! :)

Answer:

\(\huge\boxed{n = -2}\)

5n + 6 = -3n - 10

Solve for n:

Add 3n to both sides:

5n + 3n + 6 = -3n + 3n - 10

8n + 6 = -10

Subtract 6 from both sides:

8n + 6 - 6 = -10 - 6

8n = -16

Divide both sides by 8:

8n/8 = -16/8

n = -2.

Answer:

n= -2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Change into improper fraction

\(-2\frac{5}{8}*4\frac{1}{3}=\frac{-21}{8}*\frac{13}{3}\\\\ = \frac{-7}{8}*\frac{13}{1}\\\\=\frac{-91}{8}\\\\=-11\frac{3}{8}\)

Answer:

Step-by-step explanation:

The sin(30) = 1/2

The sin(30) = 1/2 = opposite / hypotenuse

Opposite = 7

hypotenuse = opposite / sin(30)

hypotenuse = 7 / (1/2) = 7 *2 / 1 = 14

The long side can be found using the Pythagorian Theorem.

a^2 + b^2 = c^2

a = 7

b = ?

c = 14

14^2 = 7^2 + b^2

196 - 49 = b^2

147 = c^2

147 = 3*7 *7

sqrt(b^2) = sqrt(3*7*7)

b = 7 sqrt(3)

_________________________________

Median=3

Mean=3.12

Step by step explanation:

1. Arranging the data in ascending order:

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

N(total number of items)=9

Now,

Median= (N+1/2) th item

=(9+1/2)th item

=(10/2) th item

=5 th item.

Median= 3

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

2. Given data: 3,2,4,2,1,5,1,3,7

Summation FX= 28

N(total number of items)=9

Now,

Mean= summation FX/N

= 28/9

=3.12

Mean =3.12

Good luck on your assignment

_______________________________

Step-by-step explanation:

median (need to be arranged first):

1,1,2,2,3,3,4,5,7 (9 numbers)

median=9+1/2

=5 (5th)

=3

mean=x/n

=(1+1+2+2+3+3+4+5+7)/9

=28/9

=3.111

The function f(x, y) = xy e^(-xy) has first-order partial derivatives, a second-order Taylor polynomial around (0,0), and critical points at (0,0) and (1, y)

(a) The first-order partial derivatives of f(x, y) are obtained by differentiating the function with respect to x and y separately. The derivative with respect to x is given by y e^(-xy) - xy^2 e^(-xy), and the derivative with respect to y is x e^(-xy) - x^2 e^(-xy).

To find the second-order partial derivatives, we differentiate the first-order partial derivatives with respect to x and y again. The second derivative with respect to x is -y^2 e^(-xy) + 2xy^3 e^(-xy) - y e^(-xy) + xy^2 e^(-xy)², and the second derivative with respect to y is -x^2 e^(-xy) + 2x^3 e^(-xy) - x e^(-xy) + x^2 e^(-xy)². The mixed partial derivative ∂²f/∂x∂y is found to be 1 - 2xy e^(-xy) + xy^2 e^(-xy).

(b) The Taylor polynomial of degree 2 about (0,0) is determined by evaluating the function and its partial derivatives at (0,0) and constructing the polynomial using the Taylor series formula. The Taylor polynomial to the second degree is P2(x, y) = -1/2(x - 0)² - 1/2(y - 0)² + (x - 0)(y - 0).

(c) To find the critical points, we set both first-order partial derivatives equal to zero and solve the resulting equations. The nature of the critical points can be determined by analyzing the second-order partial derivatives or applying the second derivative test.

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Domain and range of a square root of a quadratic function is as [ 0, ∞ ) , and  [ 0 ,∞ ) respectively which is find by simplification.

Let us consider a square root quadratic function y = √x.

Domain of a square root quadratic function is :

All input values of x are domain of a function.

y = √x

⇒ x = y²

⇒ x ≥ 0

All the input values representing the domain are x > 0.

This implies domain is [0 , ∞ ).

And range of a square root quadratic function is:

All output values of y are range of a function.

y = √x

As we know x = y²

√y² = y > 0 .

Range is [ 0, ∞ ).

Therefore, domain and range of square root of a quadratic function is calculated by simplifying the function.

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Answer:

\(\huge\boxed{1.\ C\approx38cm;\ 2.\ C\approx57ft;\ 3.\ C\approx50in.}\)

Step-by-step explanation:

The formula of a circumference of a circle:

\(C=2\pi r\\\\r-\text{radius}\)

\(1.\\r=6cm\\\\C=2\pi\cdot6=12\pi\\\\\pi\approx3.14\\\\C\approx12\cdot3.14=37.68\approx38(cm)\\\\2.\\r=9ft\\\\C=2\pi\cdot9=18\pi\\\\\pi\approx3.14\\\\C\approx18\cdot3.14=56.52\approx57(ft)\\\\3.\\2r=16in.\to r=8in.\\\\C=2\pi\cdot8=16\pi\\\\\pi\approx3.14\\\\C\approx16\cdot3.14=50.24\approx50(in.)\)

The inflection points of the given function are at x = 0 only. The answer is D.

To find the inflection points of the given function, we need to find the second derivative of the function and set it equal to zero.

y = 5x^4 - x^5

y' = 20x^3 - 5x^4

y'' = 60x^2 - 20x^3

Setting y'' = 0, we get:

60x^2 - 20x^3 = 0

20x^2(3 - x) = 0

x = 0 or x = 3

Now, we need to determine whether these values of x correspond to inflection points. To do this, we can examine the sign of the second derivative in the intervals around each value of x.

For x < 0, y'' is positive (since both terms are positive), so there is a local minimum at x = -3.

For 0 < x < 3, y'' is negative (since 60x^2 < 20x^3), so there is a point of inflection at x = 0.

For x > 3, y'' is positive (since both terms are positive), so there is a local minimum at x = 3.

Therefore, the inflection points of the given function are at x = 0 only. The answer is D.

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Twο pοints (8,8) and (-2,6) are the set οf the equatiοn  \(y < \frac{3}{4} x+6\\\) οf the graph \(y = \frac{3}{4} x+6\).

Graph, a diagram that shοws hοw a variable varies in relatiοn tο οne οr mοre οther variables (such as a cοllectiοn οf pοints, lines, line segments, curves, οr regiοns).

Nοw we have tο find the value οf the equatiοn i.e. \(y < \frac{3}{4} x+6\\\),

(x, y) = (8,8) , we get 8 < 12 , First pοint

(x, y) = (-4,3) , we get 3 = 3 , Nο match

(x, y) = (6,-2) , we get -2 < 10.5 , Secοnd Pοint

(x, y) = (0, 8) , we get 8 > 6 , Nο Match

(x, y) = (-9,2) , we get 2>-0.75 , Nο Match

Sο, we get οur pοints, which are pοints (8,8) and (-2,6) fοr the equatiοn \(y < \frac{3}{4} x+6\\\).

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Each time X increases, there is a perfectly predictable increase in Y  is indicated by a Pearson correlation of r= +1.00 between X and Y

A Pearson correlation coefficient of +1.00 indicates a perfect positive linear relationship between the variables X and Y. It means that as X increases, Y increases in a perfectly predictable manner. The correlation coefficient of +1.00 indicates a strong and direct relationship between the two variables, where the values of Y can be precisely determined based on the values of X.

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Based on the ratio and the measurement on the scale drawing, Elena's bed's actual measurements are 200 cm by 150cm.

The scale is given as 1 is to 50.

This means that every centimeter on the drawing is 50 actual centimeters for the bed.

The dimensions are:

= 4 x 50 = 200 cm

= 3 x 50 = 150 cm

Remaining part of the question:

The ratio is 1 to 50

In conclusion, the actual measurements are 200 cm by 150 cm.

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The length of the path is determined by Pythagoras theorem and the length is equal to 14.14 feet.

The flower garden is in the shape of a square with a side length of 10 feet.

We have to find the length of the path at which Chi is paving the stones.

Since the length of the path is in the shape of the diagonal of the square.

Let, the length of the path be "L" feet.

By Pythagoras theorem,

\(10^{2} + 10^{2} =L^{2} \\100+100=L^{2} \\L^{2} = 200\\L=\sqrt{200} \\L=\sqrt[10]{2} = 14.142= 14.14 feet.\)

Hence, the length (L) of the path is equal to 14.14 feet.

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Complete question:- ChiChi is planning to put a path of paving stones throughthrough her flower garden and the path is situated as a diagonal of her garden as the garden is a square with a side length of 10 feet. What will be the length of the path? Round your answer to 2 decimal places.

Answer:

 10y + 3x

Step-by-step explanation:

 (4y + 6x) -  3 • (x - 2y)

Answer:

I think it's 10y+3x

Step-by-step explanation:

I search it up :(

Answer:

The t distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.

Hence, the correct option is A.

To estimate the population mean we use a t-distribution to calculate the confidence interval. When we use a t-distribution the sample standard deviation is used to estimate the population standard deviation

Answer:

\((x+2)(x+3)\)

Step-by-step explanation:

⭐What does factorisation mean?

⭐What are factors?

Thus, we have to write \(x^2+5x+6\) in terms of its factors.

I have a picture attached to this response to show you how factorisation works, but I will also explain it here.

How to factorise:

The picture of factorisation is attached to this response.

⭐ if this response helped you, please mark it the "brainliest"!⭐

The proportion of people who were caught after being on the 10 10 most wanted list. The Lower Endpoint is 0.297 and the Upper Endpoint is 0.377.

Point estimate of proportion of people who get caught is,  p = 98/291 =  0.337

Standard error of sample proportion, SE = \sqrt{p(1-p)/n} = \sqrt{0.337 * (1 - 0.337)/291} = 0.02770928

Z value for 85% confidence interval is  1.44

Lower Endpoint = 0.337 - 1.44 * 0.02770928  = 0.297

Upper Endpoint = 0.337 + 1.44 * 0.02770928  = 0.377

Proportion refers to the relationship between two or more quantities, expressed in terms of a ratio or a fraction. It is a fundamental concept in mathematics that is used to compare the relative size of one quantity to another. In other words, it is a way of describing how much of one thing there is in relation to another.

Proportions can be expressed in different ways, depending on the context and the purpose of the comparison. For example, a proportion can be expressed as a percentage, a decimal, or a fraction. In everyday life, we encounter proportions in a variety of situations, such as when we measure ingredients for a recipe, calculate the percentage of people who voted in an election, or compare the sizes of objects.

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Complete Question: -

The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught

Step 1 of 2: Suppose a sample of 291 suspected criminals is drawn. Of these people, 98 were captured. Using the data, estimate the proportion of people who were caught after being on the 10 Most Wanted list. Enter your answer as a fraction or a decimal number rounded to three decimal places.

Answer:

yes I think...........

Answer:

175

Step-by-step explanation:

use the calculator

The solution to the linear system is unique solution which is  x₁ = 1/6, x₂ = 3/2, and x₃ = 17/6.

The correct answer is option  A.

To solve the given system of linear equations using elementary row operations and back substitution, let's start by representing the augmented coefficient matrix:

[1  -4  5  |  23]

[2   1   1  |  10]

[-3  2  -3 |  -23]

We'll apply row operations to transform this matrix into echelon form:

1. Multiply Row 2 by -2 and add it to Row 1:

[1  -4   5   |  23]

[0   9   -9  |  -6]

[-3  2  -3  |  -23]

2. Multiply Row 3 by 3 and add it to Row 1:

[1  -4  5   |  23]

[0   9  -9  |  -6]

[0   -10 6  |  -68]

3. Multiply Row 2 by 10/9:

[1  -4  5    |  23]

[0   1   -1   |  -2/3]

[0   -10 6  |  -68]

4. Multiply Row 2 by 4 and add it to Row 1:

[1  0   1   |  5/3]

[0  1   -1  |  -2/3]

[0  -10 6  |  -68]

5. Multiply Row 2 by 10 and add it to Row 3:

[1  0   1   |  5/3]

[0  1   -1  |  -2/3]

[0  0   -4  |  -34/3]

Now, we have the augmented coefficient matrix in echelon form. Let's solve the system using back substitution:

From Row 3, we can deduce that -4x₃ = -34/3, which simplifies to x₃ = 34/12 = 17/6.

From Row 2, we can substitute the value of x₃ and find that x₂ - x₃ = -2/3, which becomes x₂ - (17/6) = -2/3. Simplifying, we get x₂ = 17/6 - 2/3 = 9/6 = 3/2.

From Row 1, we can substitute the values of x₂ and x₃ and find that x₁ + x₂ = 5/3, which becomes x₁ + 3/2 = 5/3. Simplifying, we get x₁ = 5/3 - 3/2 = 10/6 - 9/6 = 1/6.

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Answer: 52 seconds.

Step-by-step explanation:

|-3| + 23 = 26. 26 x 2 = 52.