The booster club recently bought new baseball equipment. They spent $18 per glove and $24 dollars per catching mask and spent a total of $612. If they bought 8 more masks than gloves, how many of each did they buy? Write the system of equation and solve. PLEASE GIVE FULL WORK 100 POINTS

Answer: \(3+0.5n\)

Step-by-step explanation:

Given

Vine is 3 inches long

It grows 0.5 inches a week

So, after n weeks it is given by the sum of initial length and the growth in n weeks

\(\Rightarrow 3+0.5n\)

The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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Therefore ,on solving the provided question we can say that - Simple Interest after 5 year the car value is £7,689.6

Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it.

here,

rate = 10%

Time = 1 year

Principle = 12000

=>SI = PRT/100

=> SI =  10*1*12000/100

=> SI = 1200

and

=>  After 1 year = 12000 -1200 = 10800

and

for five  years

=> SI = PRT/100

=> SI = 10800 * 7.2 * 4 / 100

=> SI = 3110.4

After 5 year = 10800 - 3110.4  = 7,689.6

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The density of deer for 400 square miles is around 1:4 based on stated number of deers.

The density of deer will be given by the formula -

Population density of deer = number of deer/ area

Population density is the amount or number of individuals of a population on land per unit area.

Keep the value in formula to find the population density

Population density = 100/400

Cancelling zero as common in both numerator and denominator

Population density = 1:4

Thus, there is 1 deer for every 4 square mile.

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The amount of rice harvested this year from 690 acres of farmland was 5211570 bushels

An equation is an expression used to show the relationship between two or more numbers and variables.

This year, a large farm harvested rice from 690 acres of farmland. The crop yield was 7,553 bushels per acre.

Hence:

Amount of rice harvested =  7,553 bushels per acre * 690 acres = 5211570 bushels

The amount of rice harvested this year from 690 acres of farmland was 5211570 bushels

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Answer: B

Step-by-step explanation:

if on edg just took the quiz

Answer:

50

Step-by-step explanation:

The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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Answer:

\(\boxed {\boxed {\sf y-7= -2 (x-4)}}\)

Step-by-step explanation:

We have a point and the slope, so we can use the point-slope formula.

\(y-y_1=m(x-x_1)\)

Where m is the slope and (x₁, y₁) is the point the line passes through.

We know the slope of the line is -2 and the point it passes through is (4, 7).

Substitute the values into the formula.

\(y-7= -2 (x-4)\)

We are asked to write the equation in point-slope form, so this is our final answer.

The equation of the line in point-slope form is: y-7= -2 (x-4)

The graph of s(x) = -6x + \(8x^2\) + 5x + 3 is concave up at the point with x-coordinate -1. Let us consider the second derivative.

To determine the concavity of a function at a specific point, we need to analyze the second derivative of the function. If the second derivative is positive, the graph is concave up, and if it is negative, the graph is concave down.

Given s(x) = -6x + \(8x^2\) + 5x + 3, let's find the second derivative:

s'(x) = -6 + 16x + 5

s''(x) = 16

The second derivative is a constant, 16, which is positive. Since it is always positive, the graph of s(x) is concave up for all values of x. Therefore, at the point with x-coordinate -1, the graph is also concave up.

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Answer:

1 1/15

Step-by-step explanation:

4 x 4/15 = 4/1 x 4/15 = 16/15 = 1 1/15

Answer:

Step-by-step explanation:

well then the anwser is 1.99 because the one time fee is only for downloading one movie the first, but 1.99 is the money you have to pay everytime you download a movie.

Answer:

0

Step-by-step explanation:

12-(-4)(-3)

-3 x -4 = 12

12 - 12= 0

0.6%  is the probability of getting a king .

What is probability ?

Probability of K from full 52 card pack = 4/52 = 1/13

Probability of A from the remaining 51 cards = 4/51

“And" in probability means you Multiply.

1/13 x 4/51 = 4/663 = 0.6%

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Answer:

Solve systems of equations by graphing

A system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

Example

\(\left \{ {{y=2x+2} \atop {y=x-1}} \right.\)

Graph the equations in a coordinate plane

The two lines intersect in (-3, -4) which is the solution to this system of equations.

Step-by-step explanation:

The area of the rectangle is 3\(\sqrt{56}\)

Given,

A rectangle has a length of √7 and a width of 3√8.

We need to find the area of the rectangle.

The area is given by:

Area = Length x width

Find the length and width of a rectangle.

Length = \(\sqrt{7}\)

Width = 3\(\sqrt{8}\)

Find the area of the rectangle.

Area =  Length x width

       = \(\sqrt{7}\) x 3\(\sqrt{8}\)

When there are two different square roots we multiply them together under one root.

\(\sqrt{a\times b} ~~=~~\sqrt{a}\times\sqrt{b}\)

Now,

       = 3\(\sqrt{7\times8}\)

       = 3\(\sqrt{56}\)

Thus the area of the rectangle is 3\(\sqrt{56}\)

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Answer:

Start to end

1) N

2)P

3)J

4)B

5)A

6)i

7)L

8)E

9)G - 14b

10)H

11)O

12)M

13)C

14)D

15)K

16)F

Hope this helps, I've matched it up with the letters starting at the top box first, then going down.

The partial derivative of w=3zexyz with respect to z is obtained by differentiating exyz with respect to z, treating x and y as constants. This gives ∂w/∂z = 3exyz.

To find the partial derivatives of the given function f(x,y,z), we need to differentiate the function with respect to each variable, treating the other variables as constants.

We have the function:

f(x, y, z) = 6x sin(y − z) w=3zexyz

Let's find the first partial derivative of f with respect to x, y, and z.

Partial derivative of f with respect to x:

f_x = ∂f/∂x

f_x = 6 sin(y - z)

Partial derivative of f with respect to y:

f_y = ∂f/∂y

f_y = 6x cos(y - z)

Partial derivative of f with respect to z:

f_z = ∂f/∂z

f_z = -6x cos(y - z) + 3exyz

The partial derivative of w=3zexyz with respect to z is obtained by differentiating exyz with respect to z, treating x and y as constants. This gives ∂w/∂z = 3exyz.

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The dimensions of the rectangle with the maximum area that can be inscribed in a circle of radius 10 are 20 units by 40 units.

To find the dimensions of the rectangle with the maximum area inscribed in a circle, we need to consider that the diagonal of the rectangle will be equal to the diameter of the circle. In this case, the diameter is 2 times the radius, which is 20 units.

Let's assume the length of the rectangle is L and the width is W. The diagonal of the rectangle is the hypotenuse of a right triangle formed by the length, width, and diagonal. Using the Pythagorean theorem, we have:

L^2 + W^2 = 20^2

To find the maximum area of the rectangle, we need to maximize the product of length and width, which is LW. We can rewrite this equation in terms of one variable:

L = 20 - W^2/20

Substituting this expression for L in the area formula, we get:

Area = LW = W(20 - W^2/20)

To find the maximum area, we can take the derivative of the area function with respect to W and set it to zero:

d(Area)/dW = 20 - 3W^2/20 = 0

Solving this equation, we find W = ±20/√3. Since we're dealing with dimensions, we discard the negative solution. Thus, W = 20/√3.

Substituting this value of W back into the equation for L, we get:

L = 20 - (20/√3)^2/20

Calculating L, we find L ≈ 20√3/3.

Therefore, the dimensions of the rectangle with the maximum area are approximately 20√3/3 units by 20 units.

The rectangle with dimensions approximately 20√3/3 units by 20 units has the maximum area that can be inscribed in a circle of radius 10.

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Answer:

Option (2)

Step-by-step explanation:

Let the equation of the line is,

y - y' = m(x - x')

where (x', y') is a point lying on the given line.

And m = slope of the line = \(\frac{y_2-y_1}{x_2-x_1}\)

Line given in the graph passes through two points (-5, -1) and (-2, -3).

Slope of the line 'm' = \(\frac{-3+1}{-2+5}\)

                                 = \(-\frac{2}{3}\)

Therefore, equation of the line passing through(-5, -1) and slope of the line = \(-\frac{2}{3}\) will be,

y - (-1) = \(-\frac{2}{3}[x-(-5)]\)

\(y+1=-\frac{2}{3}(x+5)\)

\(y=-\frac{2}{3}x-\frac{10}{3}-1\)

\(y=-\frac{2}{3}x-\frac{13}{3}\)

Option (2) will be the answer.

Answer:

V+9

Step-by-step explanation:

more than means to add.

Answer:

Each banana would weigh ¼ of a pound

Step-by-step explanation:

If there are three bananas that all equal ¾ of a pound, then ¾÷3=¼

Answer:

c

Step-by-step explanation:

43% of elementary students chose something other than blue, red, or yellow as their favorite color.

Blue: 24%

Red: 17%

Yellow: 16%

Total: 24% + 17% + 16% = 57%

Percentage chose something other:

100% - 57% = 43%.

Therefore, 43% of elementary students chose something other than blue, red, or yellow as their favorite color.

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Answer:

about 76% (75.51) of the exhibits feature monkeys

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

To find circumference, it's 2(pi)r

Twice the radius is the diameter, so it's 10/2 = 5

2*3.14*5

Since you don't multiply pi, it's 10(pi)

Answer:

D. 10π

Step-by-step explanation:

C= 2πr

r being the radius of the circle

r= d/2

= 10/2 = 5

. C= 2πr

C= 2×π×r

= 2×π×5

= 10π

Answer:

y=5

x= -2/5

m= -96

t= 5/3

b= 20/3

x=3.5

Answer:

Review Vertex and Intercepts of a Quadratic Functions

The graph of a quadratic function of the form

f(x) = a x 2 + b x + c

is a vertical parabola with axis of symmetry parallel to the y axis and has a vertex V with coordinates (h , k), x - intercepts when they exist and a y - intercept as shown below in the graph. When the coefficient a is positive the vertex is the lowest point in the parabola that opens upward and when it is negative, the vertex is the highest point in the parabola that opens downward.

graph of parabola

The vertex has coordinates ( h , k) where     h = - b / 2a and k = f(h) = c - b 2 / 4a

The quadratic function of the parabola whose axis is vertical and whose vertex is at the point ( h , k ) is given by

Step-by-step explanation:

It is not possible for Sofia's money to decrease beyond 100 dollars if she initially had 500 dollars and her money decreases by 150 dollars per day. NO

If Sofia's money decreases by 150 dollars per day, it would take her 500/150 = 3.33 days for her money to reach 100 dollars. Since we cannot have a fraction of a day, the money will stop decreasing once it reaches 100 dollars. Therefore, her money cannot decrease beyond 100 dollars.

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