Cleo buys a new car for $18,900. The simple interest rate is 6.6% and the amount of loan (plus simple interest) is repayable in 5 years. What is the total amount that must be repaid?

Answer:

3 lessons

Step-by-step explanation:

150-40=110

110/35=3

she can take 3 lessons and it not cost more than $150

Answer:

G

Step-by-step explanation:

Co linear means that a point is on the same line as some given point.

AY forms a line segment and is part of EG which is a diagonal of the base..

Therefore AY and G are all colinear. The answer you want is G.

Answer:

7 hours 40 minutes in 2 weeks

Step-by-step explanation:

1.3 - 1 hour 20 minutes

1.5 - 1 and a half hours

2hours

add them all toghether = 3 hours 50 minutes

3 hours 50 minutes times 2 (2 weeks) = 7 hours 40 minutes

Answer: There are 22 adults , 12 children and 11 senior citizens on the tour bus.

Step-by-step explanation:

Let adult = x

children = y

senior citizen = z

Given : Total busload (x+ y + z) = 45

Total charge on day 1 = 558 $ = \(15\times x+8\times y+12\times z\)

Total charge on day 2 = 771 $ =  \(20\times x+12\times y+17\times z\)

Now we have 3 equations : x+ y+z =45

\(15\times x+8\times y+12\times z=558\)

\(20\times x+12\times y+17\times z=771\)

Solving for them we get: x= 22 , y = 12 and z= 11

Thus there are 22 adults , 12 children and 11 senior citizens.

Answer:

three thousand five hundred seventy nine

Step-by-step explanation:

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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Answer:

oc,2

Step-by-step explanation:

(__(_+)£)£(£886++17+£7+

Answer:

  B.  Incorrectly applied the distributive property

Step-by-step explanation:

You want to find Maria's error in her solution of -2(3x -5) = 40.

The solution can proceed as follows:

  -2(3x -5) = 40 . . . . . . . . given

  -6x +10 = 40 . . . . . . . . . use the distributive property

  -6x = 30 . . . . . . . . . . subtract 10

  x = -5 . . . . . . . . . . divide by -6

Comparing this solution to Maria's, we find that Maria incorrectly applied the distributive property. (She multiplied (-2)(-5) and got -10 instead of +10.)

Answer:

The sale price of item is 63.05 dollars

Step-by-step explanation:

Given that the price of item is $97

Let P be the price

\(P = 97\)

It is also mentioned in the question that on sale the item costs 65% of the original price so we have to calculate 65% of the item's original price to find the sale price.

Mathematically,

\(Sale\ Price = 65\%\ of\ P\\= 0.65 * 97\\= 63.05\)

Hence,

The sale price of item is 63.05 dollars

Answer:

they all have 52 left altogether

Step-by-step explanation:

they all have 2 rolls with 12 so that means they all have 24 if josiah hands out half of his tickets he would have 12 tickets left

If shawnda hands out 1 fourth of her tickets she will have 18 tickets

24 + 12 + 18 =54

Answer:

(a)

i) \(V=12.6m/s\)

ii) \(V=12.06m/s\)

iii) \(V=12.006m/s\)

(b)

\(V = 10m/s\)

Step-by-step explanation:

Given

\(s = 6t^2 + 4\)

Solving (a): Average velocity between t = 1 and t = 1 + h

When t = 1

\(t_1 = 1\)

\(s_1 = 6t^2 + 4 = 6 * 1^2 + 4 = 6 + 4 =10\)

i) h = 0.1

When t = 1 + h

\(t_2 = 1 + 0.1 = 1.1\)

\(s_2= 6t^2 + 4 = 6 * (1.1)^2 + 4 = 11.26\)

Average velocity is then calculated as:

\(V = \frac{s_2 - s_1}{t_2 - t_1}\)

\(V = \frac{11.26 - 10}{1.1- 1} = \frac{1.26}{0.1} = 12.6\)

\(V=12.6m/s\)

ii) h = 0.01

When t = 1 + h

\(t_2 = 1 + 0.01 = 1.01\)

\(s_2= 6t^2 + 4 = 6 * (1.01)^2 + 4 = 10.1206\)

Average velocity is then calculated as:

\(V = \frac{s_2 - s_1}{t_2 - t_1}\)

\(V = \frac{10.1206 - 10}{1.01- 1} = \frac{0.1206}{0.01} = 12.06\)

\(V=12.06m/s\)

ii) h = 0.001

When t = 1 + h

\(t_2 = 1 + 0.001 = 1.001\)

\(s_2= 6t^2 + 4 = 6 * (1.001)^2 + 4 = 10.012006\)

Average velocity is then calculated as:

\(V = \frac{s_2 - s_1}{t_2 - t_1}\)

\(V = \frac{10.012006 - 10}{1.001- 1} = \frac{0.012006 }{0.001} = 12.006\)

\(V=12.006m/s\)

Solving (b): Instantaneous velocity at t = 1

When t = 1

\(t = 1\)

\(s = 6t^2 + 4 = 6 * 1^2 + 4 = 6 + 4 =10\)

Velocity is:

\(V = \frac{s}{t}\)

\(V = \frac{10}{1}\)

\(V = 10m/s\)

Answer:

Starting with the equation:

(x + 1)^2 = 13/4

We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.

Taking the square root of both sides, we get:

x + 1 = ±√(13/4)

Simplifying under the radical:

x + 1 = ±(√13)/2

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± (√13)/2

Therefore, the solutions to the equation are:

x = -1 + (√13)/2 or x = -1 - (√13)/2

Step-by-step explanation:

The correct value of 2f(a-1) is 2a^2 - 12a + 10.

To find the value of 2f(a-1), we need to substitute (a-1) into the function f(x) and then multiply the result by 2.

Given: f(x) = x^2 - 4x

Substituting (a-1) into the function:

f(a-1) = (a-1)^2 - 4(a-1)

Expanding and simplifying:

f(a-1) = (a^2 - 2a + 1) - (4a - 4)

f(a-1) = a^2 - 2a + 1 - 4a + 4

f(a-1) = a^2 - 6a + 5

Now, we multiply the result by 2:

2f(a-1) = 2(a^2 - 6a + 5)

Expanding:

2f(a-1) = 2a^2 - 12a + 10

Therefore, the value of 2f(a-1) is 2a^2 - 12a + 10.

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Answer:157.5

Step-by-step explanation:becuase mutilpy 4.5x35 that equals 157.5

The solution of 3x−10>5 inequality is x>5 and is graphed with the image attached.

what is inequality?

Given inequality,

3x−10>5

3x>5+10

3x>15

x> (15/3)

x>5

The solution of 3x−10>5 inequality is x>5 and is graphed with the image attached.

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The given function is

To graph a linear equation we just need two points. Let's find the intercepts of the line.

Evaluate the function when x = 0.

The first point is (0,-4).

Evaluate the function when y = 0.

The second point is 8/3 or 2.7.

Then, plot both points and draw a line through them.

Answer:

Step-by-step explanation:

dimension

base=x, height =y, as they both are length so x, y >0

Volume of the crate= \(x^2y\) = \(16ft^3\)

cost

base=b unit money /\(ft^2\)

side material = b/2 unit money /\(ft^2\)

Top view= b/4 unit money /\(ft^2\)

Total Cost=\(bx^2 + \frac{b}{2} *4xy + \frac{b}{4} *x^2\) = \(2b( \frac{5}{8} *x^2 + xy)\)

function to be minimized  = \(\frac{5}{8}*x^2 + xy\\\)  , \(x^2y =16\)

put \(y=16/x^2\)

f(x) = \(\frac{5}{8}*x^2 + x*\frac{16}{x^2}\)

upon differentiating this equation

f'(x)=0

\(\frac{5}{4}*x -16x^-2 = 0\)

upon solving this we get \(x=4/\sqrt[3]{5}\) \(y= \sqrt[3]{25}\)

and further testing we get f"(\(\frac{4}{\sqrt[3]{5} }\)) >0 which proves that the point is local minimum.

Hence these are the dimensions of crate that minimizes the cost of material.

The dimensions that minimize the total cost of making the surface materials are \(2.3ft \text{ by } 2.3ft \text{ by }2.9ft\)

\(T=\text{Total cost of materials}\\m_b=\text{unit cost of materials used to construct the base}\\m_t=\text{unit cost of materials used to construct the top}\\m_s=\text{unit cost of materials used to construct the sides}\)

from the question, the crate has a square base and the volume is \(16ft^3\). So,

\(V=l^2h=16\\\implies h=\frac{16}{l^2}\)

Also,

\(m_b=2m_s\\m_t=\frac{m_s}{2}\)

Construct the formula for \(T\),

\(T=l^2\times m_b + l^2 \times m_t+4lh\times m_s\)

\(\text{where } l=\text{length of side of base/top}\\h=\text{height}\)

Eliminating \(h, m_b, \text{ and }m_t\), we have

\(T=m_s(\frac{5l^2}{2} + \frac{64}{l})\)

differentiating wrt \(l\) (\(m_s\) is a constant), we have

\(\frac{dT}{dl}=m_s(5l-\frac{64}{l^2})\)

The minimum total cost occurs when

\(m_s(5l-\frac{64}{l^2})=0\)

or, when

\(l=\frac{4}{\sqrt[3]{5}} \approx 2.3\)

(On carrying out the second derivative test, \(\frac{d^2T}{dl^2}>0\) when \(l=\frac{4}{\sqrt[3]{5}}\))

\(h=\frac{16}{l^2}=\sqrt[3]{5}^2\approx 2.9\)

Therefore, the dimensions that minimize the total cost of making the surface materials are \(2.3ft \text{ by } 2.3ft \text{ by }2.9ft\)

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Answer:

x = -5.5 or -5 1/2

Step-by-step explanation:

Answer:

f(x) = 12x = 10

Step-by-step explanation:

We need a linear equation in the slope-intercept form.

y = mx + b

where y = total pay, m = hourly salary, x = number of hours worked, and b = y-intercept, or initial value

Let's look in the table.

1 hour: $22

2 hours: $34

The difference in pay between 1 hour and 2 hours is $34 - $22 = $12.

The difference in time between 1 hour and 2 hours is 1 hour.

In 1 hour he earns $12. That means the slope is 12.

We know he earns $22 for working a total of 1 hour.

Start at 1 hour and $22 on the table.

Subtract 1 hour from 1 hour to get 0 hours.

Subtract $12 form $22 to get $10.

That means for 0 hours he gets $10. b = 10

The equation is

y = 12x + 10

In function form, we have:

f(x) = 12x = 10

Here we want to find a linear relation with only using the data in a table, we will find that the line is:

\(y = 12\cdot x + 12\)

We know that Damian's earns a set amount plus an hourly wage, then this can be modeled with a linear equation:

\(y = a\cdot x + b\)

Where a is the slope, which in this case is the hourly wage, and b is the y-intercept, which in this case is the set amount.

Such that x is the number of hours and y is the pay.

We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) the slope can be given as:

\(a = \frac{x_2 - x_1}{y_2 - y_1}\)

By looking at the table we can find two points of our line, for example, if we use the first and third points:

(1, 22) and (2, 34) then the slope will be:

\(a = \frac{34 - 22}{2 - 1} = 12\)

Then the line is something like:

\(y = 12\cdot x + b\)

To find the value of b, we can use one of the points, for example, the point (1, 22) means that when x = 1, we must have y = 22.

Replacing that in the above equation we have:

\(22 = 12\cdot1 + b\\\\22 = 12 + b\\\\22 - 12 = b = 12\)

Then the equation of the line is:

\(y = 12\cdot x + 12\)

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Answer:

2.r=1.94

1. c=0.85x+51/x

Step-by-step explanation:

Answer:

Adult males are flame-orange and black, with a solid-black head and one white bar on their black wings. Females and immature males are yellow-orange on the breast, grayish on the head and back, with two bold white wing bars

Answer:

It is purple

Step-by-step explanation:

Answer:

purple

because they interset each other

Step-by-step explanation:

Answer:    \(\displaystyle \frac{10}{3}\left(\frac{1}{3}\right)^{n-1}\)

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

Explanation:

a = 10/3 is the first term

r = 1/3 is the common ratio

Multiply each term by r = 1/3 to get the next term.

Example:

(10/3)*(1/3) = 10/9

We then plug those two items into the formula

\(a_n = a(r)^{n-1}\)

to end up with the answer shown above.

The value of n is a positive integer.

Answer:

In the equation y = 2 cos(5x + 3) - 6, we can ignore the coefficients 2 and -6 for the purposes of calculating the period because they do not change the period. They only change the amplitude (2) and vertical shift (-6) of the function.

The coefficient 5 in front of x inside the cosine function affects the period of the function. It is a horizontal compression/stretch of the graph of the function.

The period of the basic cosine function, y = cos(x), is 2π. When there is a coefficient (let's call it b) in front of x, such as y = cos(bx), the period becomes 2π/b.

So, in your case, b = 5, so the period T of the function y = 2 cos(5x + 3) - 6 is:

T = 2π / 5

This is the simplest form for the period of the given function.

Answer:

y = x + 1

Step-by-step explanation:

Parallel lines have same slope.

y = x - 1

Compare with the equation of line in slope y-intercept form: y = mx +b

Here, m is the slope and b is the y-intercept.

m =1

Now, the equation is,

         y = x + b

The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,

        -2 = -3 + b

  -2 + 3 = b

         \(\boxed{b= 1}\)

    Equation of line in slope-intercept form:

                  \(\boxed{\bf y = x + 1}\)      

The equation is :

Solution:

If two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.

We shouldn't forget about a point on the line : (-3, -2).

I plug that into a point-slope which is :

\(\sf{y-y_1=m(x-x_1)}\)

Slope is 1 so

\(\sf{y-y_1=1(x-x_1)}\)

Simplify

\(\sf{y-y_1=x-x_1}\)

Now I plug in the other numbers.

-3 and -2 are x and y, respectively.

\(\sf{y-(-2)=x-(-3)}\)

Simplify

\(\sf{y+2=x+3}\)

We're almost there, the objective is to have an equation in y = mx + b form.

So now I subtract 2 from each side

\(\sf{y=x+1}\)

Answer:

12.7 is the answer

Answer: 12.7

Step-by-step explanation:

If you like to round 12.654 to the nearest tenth, leaving only one number after the decimal point, then you have come to the right post

Answer:

$89.70

Step-by-step explanation:

To solve this equation, let's formulate a linear equation.

Let \(b\) equal bags of mulch.

Let \(t\) equal the total amount.

We know the price of each bag of mulch ($4.98), so we can represent this as:

\(4.98b\)

We also know that there's a fee of $15, so we can just represent this as:

\(15\)

Let's put these values into an equation:

\(t=4.98b+15\)

Now with an equation, we know that she purchases a total of 15 bags, so let's substitute \(15\) for \(b\):

\(t=4.98(15)+15\)

Multiply:

\(t=74.70+15\)

Add:

\(t=89.70\)

_

Check your work by substituting the total amount into the initial equation:

\(89.70=4.98b+15\)

Subtract \(15\) from both sides of the equation:

\(74.70=4.98b\)

Divide both sides of the equation by the coefficient of \(b\), which is \(4.98\):

\(15=b\)

Amber did in fact purchase 15 bags, so we know our total amount is correct!

The end behavior of the polynomials are as follows;

(a) y = x³ - 9·x² + 8·x - 14

End behavior; y → ∞ as x → ∞

\({}\)                        y → -∞ as x → -∞

(b) y = -8·x⁴ + 13·x + 800

End behavior; y → -∞ as x → -∞

\({}\)                        y → -∞ as x → ∞

The end behavior of a polynomial is the characteristics of the graph of the polynomial as the input (x-values), tends to plus and minus infinity.

The factors that effect the end behavior of a polynomial are;

The degree of the polynomial, (even or odd)

The sign of the leading coefficient of the polynomial (positive or negative)

The leading coefficient is the coefficient of the term with the highest degree.

(a) The polynomial, function, y = x³ - 9·x² + 8·x  - 14

The specified polynomial is a third degree polynomial, with a positive leading coefficient of 1, the end behavior is therefore;

y tends to positive infinity as x tends to positive infinity

y tends to negative infinity as x tends to negative infinity

End behavior;

y → ∞ as x → ∞

y → -∞ as x → -∞

(b) The polynomial function can be expressed as follows;

y = -8·x⁴ + 13·x + 800

The above polynomial of degree 4 is an even degree polynomial

The leading coefficient of the polynomial is -8, therefore, the leading coefficient is negative

The shape of the graph of the polynomial is therefore ∩ shaped, such that the end behavior is as follows;

y-values approaches negative infinity as x approaches negative infinity

y-values approaches negative infinity as x approaches positive infinity

End behavior;

y → -∞ as x → -∞

y → -∞ as x → ∞

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