Mariah has been hired as a receptionist. She is paid a flat rate of $225 each week and earns an additional $11.25 for every hour that she works. If her goal is to make $675 in one week, how many hours must Mariah work? 36 40 60 72

Answer:

A. $336.16

Step-by-step explanation:

The payment per $100 can be set up as a ratio:  

[tex]\frac{3.52}{100}[/tex]

Let the unknown payment be x. Now setting up the ratio over the full value:  

[tex]\frac{x}{9550}[/tex]

Set them equal and solve for x:  

[tex]\frac{3.52}{100}=\frac{x}{9550}[/tex]

1[tex]100x=33616[/tex]

This gives x = $336.16

Therefore, the answer is option A.

double every 6 months 

in 6 months there would be 250*2 = 500 crickets

 in 1 year there would be 500*2 = 1000 crickets

in 1.5 years there would be 1000 *2 = 2000 crickets

 in 2 years there would be 2000 *2 = 4000 crickets

Answer:

-5, 6i

Step-by-step explanation:

The polynomial equation of least degree with the roots -1, 3, and (+/-)3i is x⁴ - 2x³ + 10x² + 2x - 27 = 0.

We have to find the polynomial equation of least degree with the given roots -1, 3, and (+/-)3i. As complex roots occur in conjugate pairs, if 3i is a root, then -3i must also be a root. Therefore, our polynomial will be of degree 4 since it has four roots in total.

The polynomial of least degree with roots x1, x2, x3, x4 can be expressed as:

(x - x1)(x - x2)(x - x3)(x - x4) = 0

Plugging in the roots given, we get:

(x + 1)(x - 3)(x - 3i)(x + 3i) = 0

To simplify this expression, let's first multiply the complex factors:

(x - 3i)(x + 3i) = x² - (3i)² = x² + 9

Now, multiply the remaining real factors with the result we just got:

(x + 1)(x - 3)(x² + 9) = 0

Expanding this, we obtain the polynomial equation:

x⁴ - 2x³ + 10x² + 2x - 27 = 0

This is the simplified equation of the polynomial with roots -1, 3, and (+/-)3i.

Answer:

The solution to the given inequality is (-∞,5].

Step-by-step explanation:

An inequality is a relation which makes a non-equal comparison between two numbers.

Given : 7-3(x+5)+8x≤17

=7-3(x+5)+8x ≤ 17

= 7- 3x - 15 + 8x ≤ 17

= -8 + 5x ≤ 17

Adding 8 on both sides:

= -8 +8+ 5x ≤ 17+8

= 5x ≤ 25

x ≤ 5

The solution to the inequality : (-∞,5].

Answer:

His answer will have a very large value.

Step-by-step explanation:

Lets take an example:

Let the item price be = $50

John is calculating 6% tax on an item. This becomes:

[tex]0.06\times50=3[/tex] dollars

But he accidentally divides by 0.06. This becomes: [tex]\frac{50}{0.06}= 833.33[/tex] dollars

We can see that the answer is completely wrong and the value is very large.

A standard form or a scientific notation is known as the value of any number that can be expressed or written as a decimal, usually within the range of 1.0 - 10.0 multiplied by the power of 10.

It is an effective technique of expressing large numbers in a simpler form.

From the information given, we are not provided with any decimal number to be converted into a standard form but we have a number in its standard form already.

i.e.

5.708 × 10⁻⁸

The standard number from above can be converted back into its decimal form, which is:

= 0.00000005708

From the above explanation, we can conclude that we've understood how to approach and solve questions related to the Standard form.

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Final answer:

The least number of hours Ammon could have worked is 13 hours, and Nakia worked 16 hours since Nakia worked 3 hours more than Ammon, and together they worked more than 27 hours.

Explanation:

Let's denote the number of hours that Ammon worked as A and the number of hours that Nakia worked as N. According to the question, Nakia worked 3 more hours than Ammon, which can be written as N = A + 3. It's also given that together they worked more than 27 hours, so we can write this as A + N > 27. Substituting the first equation into the second, we get A + (A + 3) > 27, which simplifies to 2A + 3 > 27. By subtracting 3 from both sides, we get 2A > 24. Dividing by 2 gives us A > 12. Since A must be a whole number, the smallest whole number greater than 12 is 13.

Now that we know A is at least 13, we can find the minimum number of hours Nakia worked, which is A + 3. That gives us N = 13 + 3 = 16. Therefore, the least number of hours Ammon worked is 13 hours and Nakia worked 16 hours.

Answer:

amount evaporated =  0.635 liters

Step-by-step explanation:

The scientist initially had 5 liters of water in a container . After evaporation took place he had only 4.365 liters of water remaining in the container.

The amount of water that evaporated can be computed when you remove the amount of water remaining after evaporation from the  initial amount before evaporation.

Mathematically,  

amount evaporated = initial amount before evaporation - amount remaining after evaporation

initial amount before evaporation = 5 liters

amount remaining after evaporation = 4.365 liters

amount evaporated =  5 - 4.365

amount evaporated =  0.635 liters

A) (-6,0) =  -6-3, 0+4 so it moves to (-9,4)

B) (3,-4) = 3-3, -4+4 so it moves to (0,0)

Answer: It's B

B) m∠A=25° and m∠B=25°

Answer: (a,a)

Step-by-step explanation:

Given: A  right isosceles triangle which is placed on the coordinate plane such that one of the legs of the triangle lies along the x-axis and the other leg is parallel to the y-axis.

From the given figure one vertex is on origin(0,0) and second on x -axis as (a,0) .ii.e. one side of the triangle is on the x axis with length 'a' and the side parallel to the y axis should perpendicular to the x axis with length 'a'.(∵ two sides are equal in a right isosceles triangle)

So the coordinates should she assign to the third vertex of the right isosceles triangle is (a,a).[as the point lie above the point (a,0), so its x abscissa should be same]

The third vertex of a right isosceles triangle where one leg lies on the x-axis and the second leg is parallel to the y-axis would have equal x and y coordinates, assuming the second vertex is at (a,0). Therefore, the third vertex would be at (a,a), for any real numerical value of 'a'. This makes use of key concepts in coordinate geometry.

In the context of mathematics, specifically coordinate geometry, Mei can assign the third vertex of this right isosceles triangle to any point that is equally distant from both the x and y axes. Assuming the other two vertices of the triangle are at the origin (0,0) and on the x-axis (a,0), then the coordinates of the third vertex would be (a,a).

Right isosceles triangle is a special type of triangle where two sides are equal in length and the angle between them is 90 degrees. Since the legs of the triangle are along the x and y axes, this leads to the third vertex being on the line y=x.

A coordinate proof involves using the properties and definition of the geometric figures in the coordinate plane. It involves calculations with the coordinates of the vertices of the figures. In the case of coordinate geometry, it's essential to understand the placement of points on the x-y plane.

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The maximum age of a fossil that could be dated using 40K is approximately 5.36 billion years.

Potassium-40 (40K) has a half-life of 1.25 billion years.

The minimum detectable amount for dating using 40K is 0.1%. If a dinosaur is dated using 40K to be 67 million years old, we can calculate the maximum age of a fossil that could be dated using 40K.

To find the maximum age, we can set up a proportion using the half-life of 40K:

(67 million years) / (1.25 billion years) = (x years) / (100%)

Solving for x, we get:

x = (67 million years) * (100%) / (1.25 billion years)

Calculating this, we find that the maximum age of a fossil that could be dated using 40K is approximately 5.36 billion years.

Answer:

[tex]\displaystyle \frac{dy}{dx} = \frac{-2}{x^\Big{\frac{3}{2}}}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \frac{4}{\sqrt{x}}[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

Step-by-step explanation:

The equation of this circle is:

(x - 1)² + (y - 1)² = 5²

Just supposing we choose x = 2.  What's the corresponding y-value?

Actually, there are two unique y-values for each x value.

Let x = 2 in (x - 1)² + (y - 1)² = 5².  Then:

(2 - 1)² + (y - 1)² = 5², or

   1²      + (y - 1)² = 25

Solving for (y - 1)², we get  (y - 1)² = 25 - 4, or 24.

Taking the square root of both sides:

y - 1 = ±√24, so that y = 1 ±√24,

This simplifies to y = 1 ± 2√6.

Therefore, if x = 2, y has two values:

(2, 1+2√6) and

(2, 1-2√6

An obtuse triangle will have one and only one obtuse angle.

The other two angles are acute angles.

The sum of the two angles other than the obtuse angle is less than 90º.

The side opposite to the obtuse angle is the longest side of the triangle.

The points of concurrency, the Circumcenter and the Orthocenter lie outside of an obtuse triangle, while Centroid and Incenter lie inside the triangle.

The equation for the function f would be; f(x) = -1.75x + 18.75.

An equation is an expression that shows the relationship between two or more numbers and variables.

Function is a type of relation, or rule, that maps one input to specific output.

Given that f is a linear function such that f(5) = 10 and f(9) = 3, then

Consider that the function of x would be;

f(x) = -1.75x + 18.75

Now plug x = 5 in the given function, if it satisfy the function

f(5) = -1.75(5) + 18.75

f (5) =10

Again plug x = 9 in the given function, if it satisfy the function

f(9) = -1.75(9) + 18.75

f(9) =3

Therefore, the equation for the function f would be; f(x) = -1.75x + 18.75.

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