Sam makes $15 per hour mowing lawns. He makes an additional $16 each day because
his neighbor always gives him a tip. If Sam mows h lawns today, how much does he
make? Write an expression using h for lawns.

The interest rate which will save the most money if the balance on a loan from one month to the next is carried is the compound interest rate.

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

\(A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\\)

Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.

While carrying the balance on a loan from one month to the next month, the compound interest rate is better, as it allows the funds to grow faster than the other rate mentioned.

Thus, the interest rate which will save the most money if the balance on a loan from one month to the next is carried is the compound interest rate.

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There are 10 boys and 7 girls.

A boy and a girl have to be chosen for the school board.

How many possible pairs can be chosen from 10 boys and 7 girls?

For the 1st boy, any one of the 7 girls can be chosen, so 1×7 = 7 pairs

For the 2nd boy, any one of the 7 girls can be chosen, so 1×7 = 7 pairs

For the 3rd boy, any one of the 7 girls can be chosen, so 1×7 = 7 pairs

As you can see the pattern, for each boy there are 7 choices of girls so we can write

10×7 = 70 pairs

Therefore, 70 possible pairs can be chosen from 10 boys and 7 girls​.

The ratio that is equivalent to Stefanie's rate is 1 : 2

The given parameters are

Distance = 4 miles

Trips = 2

The ratio that is equivalent to Stefanie's rate is represented as

Rate = Trips/Distance

So, we have

Rate = 2 trips /4 miles

Evaluate

Rate = 1/2 trip per mile

Express as raton

Ratio = 1 : 2

Hence, the ratio that is equivalent to Stefanie's rate is 1 : 2

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The mean absolute deviation (MAD) for the given data is 1/20. This means that, on average, each data point in the set differs from the mean by 1/20.

To find the mean absolute deviation (MAD) of a set of data, we need to calculate the average difference between each data point and the mean of the data set. Here's how we can calculate it for the given data:

Step 1: Find the mean (average) of the data set.

Mean = (1/4 + 5/8 + 3/8 + 3/4 + 1/2) / 5 = 2/5

Step 2: Calculate the difference between each data point and the mean.

Differences: |1/4 - 2/5|, |5/8 - 2/5|, |3/8 - 2/5|, |3/4 - 2/5|, |1/2 - 2/5|

Step 3: Calculate the absolute value of each difference.

Absolute Differences: 1/20, 1/40, 1/40, 1/20, 1/10

Step 4: Find the average of the absolute differences.

MAD = (1/20 + 1/40 + 1/40 + 1/20 + 1/10) / 5 = 1/20

The MAD provides a measure of the average amount of variation or dispersion in the data set. In this case, a MAD of 1/20 indicates that the data points are relatively close to the mean, with most values falling within 1/20 of the mean value.

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To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.

The five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.

The five regular polyhedra are:

1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.

2. Cube: It has six square faces, and three squares meet at each vertex.

3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.

4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.

5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:

"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".

For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:

V - E + F = 2  

=>  kV/2 - kE/2 + F = 2  

=>  k(V/2 - E/2) + F = 2

Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:

k(V/2 - (nF)/2) + F = 2  

=>  (kV - knF + 2F)/2 = 2  

=>  kV - knF + 2F = 4

Now, we need to consider the conditions for a valid polyhedron:

1. The number of faces (F), edges (E), and vertices (V) must be positive integers.

2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.

Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:

(n, k) pairs:

(3, 3) - Tetrahedron

(4, 3) - Cube

(3, 4) - Octahedron

(5, 3) - Dodecahedron

(3, 5) - Icosahedron

Therefore, there exist only five regular polyhedra.

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Answer:

Step-by-step explanation:

100-74-26

26%->52

100%->52÷26×100

             = 200

The P-value is between 0.025 and 0.05. and t = -1.85

On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator.

Therefore tests the hypotheses:

\(H_0\) : μ = 25 versus Ha: μ < 25,

where μ = the true mean amount of time needed by students at this school to complete this portion of the exam.

The alternative hypothesis is:

\(H_1:\mu < 25\)

The test statistic is given by:

\(t=\frac{x-\mu}{\frac{s}{\sqrt{n} } }\)

The parameters are:

the values of the parameters are:

x = 23.5 , \(\mu=25\) , s = 4.8, n = 35

Plug all the values in above formula of t- statistic is:

\(t = \frac{23.5-25}{\frac{4.8}{\sqrt{35} } }\)

t = -1.85

Using a t-distribution , with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.

t = –1.85; the P-value is between 0.025 and 0.05.

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Answer:

n = 3

Step-by-step explanation:

28/4 = 21/n

7 = 21/n

7/7 = 21/7

n = 3

For similar triangles ABC and DEF, the value of N=3.

Similarity of a triangle is the ratio of their corresponding sides or angles which are equal.

The given triangles are ABC and DEF,

Side AB = 21, BC = 28, DE = N and EF = 4.

Also, triangle ABC is similar to triangle DEF.

By similar triangle property,

AB/CD = DE/EF

21/28 = N/4

N = 21/7

N = 3

In the triangle DEF, side DE = 3.

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The second difference of the given number table is: Option A: -2

The second difference method can be used to determine a quadratic model.  In order for us to calculate the second difference, we will select 3 consecutive y-values, and then subtract the first y-value from the second and the second y-value form the third. Then we will find the difference of these two resulting values. That difference is what we refer to as the second difference.

Thus, Applying the second difference concept to our problem, we have:

First difference:

-4 - (-9) = 5

-1 - (-4) = 3

Thus, second difference is:

3 - 5 = -2

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Answer:

\( - \frac{1}{3} \)

Step-by-step explanation:

① Identify 2 points on the line:

➙ (-3, 0) and (0, -1)

Find points that are easy to identify. The 2 points I have identified passes through each square of the graph nicely.

② Find slope using the gradient formula below:

\(\boxed{gradient = \frac{y1 - y2}{x1 - x2} }\)

Thus, slope of line

\( = \frac{0 - ( - 1)}{ - 3 - 0} \\ = \frac{0 + 1}{ - 3} \\ = \frac{1}{ - 3} \\ = - \frac{1}{3} \)

The width of the rectangular base of the pyramid is approximately 3.74 cm, and the length is approximately 11.22 cm (since it is given as 3x+1).

The base of a pyramid can be any polygon, such as a square or a triangle, but the height must always be measured perpendicular to the base.

Dimensions refer to the number of coordinates needed to specify the location of an object in space.

Based on the given information, we can set up an equation to solve for x, which is the width of the rectangular base of the pyramid:

Volume of pyramid = 1/3 × base area ×height

96 = 1/3 ×(3x+1) × x ×12

Simplifying the equation:

96 = 4x² + (4/3)x

Multiplying both sides by 3 to eliminate the fraction:

288 = 12x² + 4x

Rearranging the equation into a quadratic form:

12x² + 4x - 288 = 0

Dividing both sides by 4 to simplify the equation:

3x² + x - 72 = 0

We can then use the quadratic formula to solve for x:

x = (-b ± \(\sqrt{(b^2-4ac)}/2a\)

where a = 3, b = 1, and c = -72.

Plugging in the values:

x=(-1±\(\sqrt{1^2-4(3)(-72)} /2(3)\))

x=(-1±\(\sqrt{1+864} /6\))

x = (-1 ±\(\sqrt{865} /6\) )

Since the width of the base cannot be negative, we take the positive solution:

x = (-1 + √(865) / 6

Therefore, the width of the rectangular base of the pyramid is approximately 3.74 cm, and the length is approximately 11.22 cm (since it is given as 3x+1).

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The slope of the tangent line is:

a = (df(x1)/dx)

The slope of the normal one is:

a' = -1/(df(x1)/dx)

For any function y = f(x), we define the slope of the tangent line at the point x as the derivative evaluated in x.

So if we want to find the slope of the tangent line at the point (x1, y1), we just need to differentiate and evaluate in x1, then the slope will be given by:

df(x1)/dx

And the normal slope is the slope of the perpendicular line, two slopes are perpendicular if the product is -1, then:

a*(df(x1)/dx) = -1

a = -1/(df(x1)/dx)

Where df/dx reffers to the derivative of f(x).

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Answer:

\(\overrightarrow{AB}+\overrightarrow{CD}=(-3,-7)\)

Step-by-step explanation:

Vector Addition

We are given the points A=(1,3), B=(-4,5), C=(-2,10), D=(0,1). Find:

\(\overrightarrow{AB}+\overrightarrow{CD}\)

First, find both vectors from the initial and final points:

\(\overrightarrow{AB}=(-4-1,5-3)=(-5,2)\)

\(\overrightarrow{CD}=(0-(-2),1-10)=(2,-9)\)

Now find the sum of both vector by adding the components separately:

\(\overrightarrow{AB}+\overrightarrow{CD}=(-5,2)+(2,-9)=(-3,-7)\)

\(\boxed{\overrightarrow{AB}+\overrightarrow{CD}=(-3,-7)}\)

Answer:

Step-by-step explanation:

if it's

23 = 5 - (2/3)m

18 = (-2/3)m

m = 18(-3/2)

m = -27

if it's

23 = 5 - 2/(3m)

18 = -2/(3m)

18(3m) = -2

54m = - 2

m = -2/54

m = - 1/27

The transformation of f(x) to p(x) is that (a) the graph is reflected and shifted down

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

In the function equations, we can see that

f(x) = x²

p(x) = -f(x) - 3

So, we have

Vertical Difference = 0 - 3

Evaluate

Vertical Difference = - 3

This means that the transformation of f(x) to p(x) is that f(x) is reflected and shifted down 3 units to p(x).

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The exact average value of \(y = x^4\) on [1,2] is 31/5, and the decimal approximation is 6.200.

To find the average value of a function f(x) on an interval [a,b], we use the formula:

Average Value = (1/(b-a)) * ∫(a to b) f(x) dx

Using this formula, we can find the average values of the given functions on the interval [1,2]:

y = x

Average Value =\((1/(2-1)) * ∫(1 to 2) x dx= ∫(1 to 2) x dx= [x^2/2] from 1 to 2= (2^2/2) - (1^2/2)\)

= 3/2

Therefore, the exact average value of y = x on [1,2] is 3/2, and the decimal approximation is 1.500.

\(y = x^2\)

Average Value =\((1/(2-1)) * ∫(1 to 2) x^2 dx\)

\(= ∫(1 to 2) x^2 dx= [x^3/3] from 1 to 2= (2^3/3) - (1^3/3)\)

= 7/3

Therefore, the exact average value of\(y = x^2\) on [1,2] is 7/3, and the decimal approximation is 2.333.

y = x^3

Average Value = \((1/(2-1)) * ∫(1 to 2) x^3 dx\)

\(= ∫(1 to 2) x^3 dx= [x^4/4] from 1 to 2= (2^4/4) - (1^4/4)\)

= 15/4

Therefore, the exact average value of\(y = x^3\) on [1,2] is 15/4, and the decimal approximation is 3.750.

\(y = x^4\)

Average Value =\((1/(2-1)) * ∫(1 to 2) x^4 dx\)

\(= ∫(1 to 2) x^4 dx= [x^5/5] from 1 to 2= (2^5/5) - (1^5/5)\)

= 31/5

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Answer:

a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:

r^2 - 2r - 3 = 0

Factoring, we get:

(r - 3)(r + 1) = 0

So the roots are r = 3 and r = -1.

The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:

y_h = c1e^3x + c2e^(-x)

To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = Ae^4x

Taking the first and second derivatives of y_p, we get:

y_p' = 4Ae^4x

y_p'' = 16Ae^4x

Substituting these into the original differential equation, we get:

16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x

Simplifying, we get:

5Ae^4x = e^4x

So:

A = 1/5

Therefore, the particular solution is:

y_p = (1/5)*e^4x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^3x + c2e^(-x) + (1/5)*e^4x

b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:

r^2 + r - 2 = 0

Factoring, we get:

(r + 2)(r - 1) = 0

So the roots are r = -2 and r = 1.

The general solution to the homogeneous equation y'' + y' - 2y = 0 is:

y_h = c1e^(-2x) + c2e^x

To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax + B)e^x

Taking the first and second derivatives of y_p, we get:

y_p' = Ae^x + (Ax + B)e^x

y_p'' = 2Ae^x + (Ax + B)e^x

Substituting these into the original differential equation, we get:

2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x

Simplifying, we get:

3Ae^x = 3xe^x

So:

A = 1

Therefore, the particular solution is:

y_p = (x + B)e^x

Taking the derivative of y_p, we get:

y_p' = (x + 2 + B)e^x

Substituting back into the original differential equation, we get:

(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x

Simplifying, we get:

-xe^x - Be^x = 0

So:

B = -x

Therefore, the particular solution is:

y_p = xe^x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^(-2x) + c2e^x + xe^x

c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:

r^2 - 9r + 20 = 0

Factoring, we get:

(r - 5)(r - 4) = 0

So the roots are r = 5 and r = 4.

The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:

y_h = c1e^4x + c2e^5x

To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax^2 + Bx + C)e^4x

Taking the first and second derivatives of y_p, we get:

y_p' = (2Ax + B)e^4x + 4Axe^4x

y_p'' = 2Ae^4x +

Answer:

C.  The x-terms are the same, and the constant terms are the same.

Step-by-step explanation:

Solve for x:

7 (x - 4) = 8 (x + 8)

Hint: | Write the linear polynomial on the left-hand side in standard form.

Expand out terms of the left hand side:

7 x - 28 = 8 (x + 8)

Hint: | Write the linear polynomial on the left-hand side in standard form.

Expand out terms of the right hand side:

7 x - 28 = 8 x + 64

Hint: | Move terms with x to the left-hand side.

Subtract 8 x from both sides:

(7 x - 8 x) - 28 = (8 x - 8 x) + 64

Hint: | Combine like terms in 7 x - 8 x.

7 x - 8 x = -x:

-x - 28 = (8 x - 8 x) + 64

Hint: | Look for the difference of two identical terms.

8 x - 8 x = 0:

-x - 28 = 64

Hint: | Isolate terms with x to the left-hand side.

Add 28 to both sides:

(28 - 28) - x = 28 + 64

Hint: | Look for the difference of two identical terms.

28 - 28 = 0:

-x = 64 + 28

Hint: | Evaluate 64 + 28.

64 + 28 = 92:

-x = 92

Hint: | Multiply both sides by a constant to simplify the equation.

Multiply both sides of -x = 92 by -1:

(-x)/(-1) = -92

Hint: | Any nonzero number divided by itself is one.

(-1)/(-1) = 1:

Answer: x = -92

Answer:

only one.

We can construct onle one triangle with unique measurements.

Answer:

1 triangle can be constructed

Step-by-step explanation:

Answers:

======================================================

Explanation:

Point M is the segment bisector because it splits PQ into the equal halves of PM and MQ. The tickmarks indicate this visually.

Since PM and MQ are the same length, we can set them equal to one another and solve for x.

5x-3 = 11 - 2x

5x+2x = 11+3

7x = 14

x = 14/7

x = 2

The 2 you have in the box seems to indicate this might be what you found for x. It's not the final answer because we need to determine MQ based on this. Let's find the length of each smaller piece.

In short, MQ = 7

The fact that each piece is the same length (7 units) helps us verify we have the correct x value and correct final answer.

Answer:

y ÷ 4 - 3

Step-by-step explanation:

Since it asks for the quotient of y and 4, quotient indicates that it is division, so those two are going to be divided. It also says 3 less than. Less than means subtraction.

Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

Answer:

Matrix :

\(\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}\)

Solution Set : { x = 123, y = 246, z = 11 }

Step-by-step explanation:

Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,

x + y + z = 380,

And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.

5x + 3y + 10z = 1460

The silly string tickets were sold for twice as much as the car wash tickets.

y = 2x

Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.

System of Equations :

\(\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}\)

Matrix :

\(\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}\)

Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,

\(\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}\) - Swap Matrix Rows

\(\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}\) - Cancel leading Co - efficient in second row

\(\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}\) - Cancel leading Co - efficient in third row

\(\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}\) - Swap second and third rows

\(\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}\) - Cancel leading co - efficient in row three

And we can continue, canceling the leading co - efficient in each row until this matrix remains,

\(\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}\)

x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold

Answer:

False

Step-by-step explanation:

Exponents do involve multiplication, but the power that a number is raised to is not the number it is multiplied by. Instead, exponents are used to determine how many times that number is multiplied by itself (to a certain extent, to explain better, it will have five "2's" being multiplied in this case). So, in the case of \(2^{5}\), 2 is multiplied by itself 5 times, like so - 2×2×2×2×2 = 32. If we were to calculate 2×5, we would get 10, and \(32\neq10\) (32 is not equal to 10). Therefore, \(2^{5}\) is not the same as 2·5, and therefore the question is false.

Answer:

C

Step-by-step explanation:

Answer:

Angle T is congruent to Angle Z

Step-by-step explanation:

Since the 2 triangles are equal, that means that each pair of angles are also congruent. To know which angles are congruent, you check th order of how the triangles are named. Ex. Angle Q is congruent to Angle A, Angle P is congruent to Angle R, and Angle T is congruent to Angle Z.

Answer:

9 m²

Step-by-step explanation:

The perimeter of a square is 4x, where is the length of one side (because all the sides have the same length).

This means that 4x = 12, so x = 3, in other words the length of one side of the square is 3 m.

To work out the area of the square, multiply the length and the width together: 3 x 3 = 9 m²

Hope this helps!

Answer:

63

Step-by-step explanation: