Serena is an account executive. She receives a base pay of $18 an hour plus a 15 percent bonus for all the sales she generates. Last week she generated $1,200 worth of sales. What is the minimum number of hours she could have worked to make $500?
PLEASE SHOW WORK.

ANSWER

(-2,-1)

(3,14)

EXPLANATION

The given system is

[tex]y = {x}^{2} + 2x - 1[/tex]

[tex] y - 3x = 5[/tex]

or

[tex]y = 3x + 5[/tex]

Equate both of them:

[tex]{x}^{2} + 2x - 1 = 3x + 5[/tex]

This implies that,

[tex]{x}^{2} - x - 6 = 0[/tex]

[tex](x - 3)(x + 2) = 0[/tex]

x=-2 or x=3

When x=-2, y=y=3(-2)+5=-1

(-2,-1) is a solution.

When x=3 , y=3(3)+5=14

(3,14) is also a solution.

ANSWER

C. 7

EXPLANATION

We want to evaluate

[tex]2 - ( - 8) + ( - 3) [/tex]

We use the order of operations PEDMAS.

Dealing with the parenthesis first,we have

[tex]2 - - 8+- 3[/tex]

Note that:

[tex] - - = + [/tex]

and

[tex] - + = - [/tex]

Our expression now becomes:

[tex]2 + 8 - 3[/tex]

Next, we add to get:

[tex]10 - 3[/tex]

We finally subtract to get,

[tex]7[/tex]

The correct answer is C

The answer is: C. 7

To solve the problem, first, we need to consider the signs out and inside of the parenthesis.

We must remember the following rule:

[tex]--=+\\+-=-[/tex]

We are given the following expression:

[tex]2-(-8)+(-3)[/tex]

Then, we can rewrite it using the rule of the signs, we have:

[tex]2--8+-3=2+8-3=2+8-3[/tex]

[tex]2+8-3=10-3=7[/tex]

Hence, the correct option is C. 7.

Have a nice day!

Answer:

3.8 meters

Step-by-step explanation:

In order to find the circumference for a circle, we use the formula π(radius)²

The circumference give is 45.84 and the π given is 3.14

All we have to do is to just substitute them.

45.84 = 3.14(radius)²

45.84 / 3.14 = radius²

14.6 = radius²

radius = √14.6

radius = 3.82 ≅ 3.8

Answer:

approx. 7.3 m

Step-by-step explanation:

The formula for the circumference of a circle is  s = r·Ф, where r is the radius and Ф is the central angle in radians.

Here C = 45.84 m = 2π·r.  Solving for the radius, r, we get:

       45.84 m

r = --------------- = 7.299 m, or approx. 7.3 m.

          2(3.14)

Answer:

g(x) = x^2 + 4x + 4

Step-by-step explanation:

In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.

Given the function;

f(x) = x2 - 6x + 9

a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;

g(x) = f(x+5)

g(x) = (x+5)^2 - 6(x+5) + 9

g(x) = x^2 + 10x + 25 - 6x -30 + 9

g(x) = x^2 + 4x + 4

Answer:

[tex](2-5i)(p+q)(i)=29i[/tex]

Step-by-step explanation:

We have the product of 2 complex numbers

[tex](2-5i)(p+q)(i)[/tex]

We know that:

[tex]p=2\\\\q=5i[/tex]

Then we substitute these values in the expression

[tex](2-5i)((2)+(5i))(i)[/tex]

[tex](2-5i)(2+5i)(i)[/tex]

The product of a complex number [tex]a + bi[/tex] by its conjugate [tex]a-bi[/tex] is always equal to:

[tex]a ^ 2 - (bi) ^ 2[/tex]

Then

[tex](2-5i)(2+5i)(i)=(2^2-5^2i^2)(i)[/tex]

Remember that:

[tex]i=\sqrt{-1}\\\\i^2 = -1[/tex]

So

[tex](2^2-5^2i^2)(i)= (4 - 25(-1))(i)\\\\(4 - 25(-1))(i) = (4+25)i=29i[/tex]

Finally

[tex](2-5i)(p+q)(i)=29i[/tex]

Answer:

29i

Step-by-step explanation:

Edge Verified

is noteworthy that the leading term has a negative coefficient, meaning this parabola is opening downwards like a "camel hump", so it reaches a maximum point and then goes back down, and of course the maximum point is at its vertex.

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ H(x)=\stackrel{\stackrel{a}{\downarrow }}{-\frac{1}{2}}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{-5} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{4}{2\left( -\frac{1}{2} \right)}~~,~~-5-\cfrac{4^2}{4\left( -\frac{1}{2} \right)} \right)\implies \left( 4~,~-5+\cfrac{16}{2} \right)\implies (4~~,~~3)[/tex]

Answer:

(4, -3)

Step-by-step explanation:

I'm assuming that you meant  H(x) = -(1/2)x^2 + 4x - 5.  Here, the coefficients of this quadratic are a = -1/2, b = 4 and c = -5.

The axis of symmetry is x = -b/(2a).  This axis goes through the vertex.  Here the axis of symmetry is  x = -(4) / [ 2(-1/2) ], or x = 4.

Evaluating H(x) at x = 4 gives us the y value of the vertex.  It is:

H(4) = (-1/2)(4)^2 + 4(4) - 5, or H(4) = -8 + 16 - 5, or 3.

We know that this function must have a max because a is - and therefore the graph opens down.

The vertex and the maximum is (4, 3).

The car, which depreciates at an annual rate of 1.4%, will be worth approximately £2590.34 in 5 years.

This is a problem related to depreciation, which is a concept in finance and economics. In this case, the car depreciates at a rate of 1.4% per year. This means that each year, the value of the car decreases by 1.4% of its value at the start of that year. This is an example of exponential decay.

To calculate the car's value after 5 years, we raise the depreciation rate (99.6%, or 0.996 in decimal form because the value decreases) to the power of 5, and then multiply it by the initial price of the car, £2700.

That is, Car Value = £2700 * (0.996)^5 = £2590.34

So, the car will be worth approximately £2590.34 in 5 years to the nearest penny.

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Answer:

Problem 12 is 112° and problem 13 is 68°

Step-by-step explanation:

Angles EPF and DPG are vertical angles; therefore, they are congruent.  That means, algebraically, that

4x + 48 = 7x

Solving for x:

48 = 3x  and  x = 16

Now that we know the value of x we can sub it back into the expression for the angle:

4(16) + 48 = 112.

For problem 13, angles DPE and EPF are supplementary, so that means that they add up to equal 180 degrees.  Therefore, 180 - 112 = 68 degrees.

Answer:

  about 0.53

Step-by-step explanation:

54% of the insured, or .54×900 = 486 individuals are males. That leaves 900-486 = 414 that are females. 43% of those, or .43×414 = 178 are over 25, so the remainder of the 395 who are over 25 are male.

Since 395 -178 = 217 of the males are over 25, there are 486 -217 = 269 who are under 25. Then the fraction of insureds who are under 25 that are male is ...

  269/(900 -395) = 269/505 ≈ 0.53

_____

It can be useful to make a 2-way table from the given information.

Final answer:

Using the provided data, the probability that a person under 25 years old selected randomly is male is calculated by dividing the number of males under 25 (found by subtraction from total males and males over 25) by the total number of individuals under 25.

Explanation:

The question asks us to calculate the probability that a person under 25 years old, selected randomly from a group of insured individuals, is male. To find this, we need to use the given data:

Total insured individuals: 900

Percentage of males: 54%

Individuals over 25 years old: 395

Probability that a randomly selected female is over 25: 0.43

To calculate the number of males and females, we take 54% of 900 to get the total males, which is 486. Since there are 900 insured individuals in total, the number of females would be 900 - 486 = 414. The number of females over 25 years old is 414 * 0.43 = 178.02, which we can round to 178.

Since there are 395 individuals over 25 years old in total and 178 of them are female, 395 - 178 gives us 217 males over 25 years old. Now, we need to find the number of individuals under 25 years old. There are 900 - 395 = 505 individuals under 25.

The probability that a randomly selected person under 25 is male can be found by dividing the number of males under 25 by the total number of people under 25. The number of males under 25 is the total number of males minus males over 25, which is 486 - 217 = 269. Therefore, the probability is 269 / 505.

Answer:

  y = x+6

Step-by-step explanation:

You can find an equation by using the 2-point form of the equation for a line:

  y = (y2 -y1)/(x2 -x1)·(x -x1) +y1

Filling in the given values, we have ...

  y = (9 -5)/(3 -(-1))·(x -(-1)) +5

  y = (4/4)(x +1) +5 . . . . simplifying a bit

  y = x +6

Answer:

The CORRECT answer is 97.4 in ^2

Step-by-step explanation:

Usatestprep , the other answer is wrong trust me.

What are the choices

Answer: 8 I think!

Hope it helps

Answer:

  (c) 16/9·π²·r⁶

Step-by-step explanation:

The water displaced is equivalent to the volume of the sphere, given as

  V = (4/3)π·r³

The product of two identical displaced volumes will be ...

  V² = ((4/3)π·r³)² = (4/3)²·π²·r⁶

  = 16/9·π²·r⁶ . . . . . . matches choice (c)

For this case we must simplify the following expression:

[tex]3-2y-1 + 5x ^ 2-7y + 7 + 4x ^ 2[/tex]

We combine similar terms, taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed.

[tex]3-1 + 7-2y-7y + 5x ^ 2 + 4x ^ 2 =\\9-9y + 9x ^ 2[/tex]

Answer:

[tex]9-9y + 9x ^ 2[/tex]

Answer:

16

Step-by-step explanation:

96 marbles = Box

Let's call blue marbles " 5 x " and red marbles " x "

So now an equation is setup ⇒

→ 5 x + x = 96

( Simplify )

→ 6 x = 96

( Divide by 6 from both sides to isolate x )

→ x = 16

red marbles " x " so x = 16

You would use the following equation:

96 = 5x + x

There is a total of 96 marbles. The right side of the equation represents how many blue marbles are in the box. X is red marbles in the box, since we know that red marbles is 5 times x

Add the common variables:

96 = 5x + x

96 = 6x

To solve for red marbles isolate x. To do this divide 6 to both sides. Division is the opposite of multiplication and will cancel 6 from the right side and bring it to the left

96 ÷ 6 = 6x ÷ 6

16 = x

You have 16 marbles in the box

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: 2048

Step-by-step explanation:

Tn = arⁿ⁻¹

T6 = ar⁶⁻¹

T6 = ar⁵

T6 = 2*4⁵

T6= 2048

ANSWER

[tex]a_{6} = 2048[/tex]

EXPLANATION

The general term of a geometric sequence is given by,

[tex] a_{n} = a_{1} ( {r})^{n - 1} [/tex]

The first term of the geometric sequence is 2

[tex]a_{1} =2[/tex]

The common ratio is 4. This means r=5.

The nth term of the sequence is

[tex]a_{n} = 2 ( {4})^{n - 1} [/tex]

The 6th term is

[tex]a_{6} = 2 ( {4})^{6 - 1} [/tex]

[tex]a_{6} = 2 ( {4})^{5} [/tex]

[tex]a_{6} = 2048[/tex]

Answer:

Actually, what you said you have so far is not correct.  The 2 correct answers are the 1st one (x + y = 15) and the 5th one (15x + 10y > 180)

Step-by-step explanation:

If tutoring French is x hours and scooping ice cream is y hours and he is going to work 15 hours for sure doing both, then we can add them together to get that x hours + y hours = 15 hours, or put simply:  x + y = 15.

Now we are going to throw in the added fun of the money he makes doing each.  The thing to realize here is that we can only add like terms.  So looking at the equation above, we have x hours of tutoring and y hours of scooping, so if we want to add them, we will add those number of hours together to get the total number of hours he worked, which we know to be 15.  The same goes for money.  If we add money earned from tutoring to money earned from scooping, we need that to be greater than the money he wants to earn which is 180 at least.  Because he wants to earn MORE than $180. we use the ">" sign.  Since he earns $15 an hour tutoring, that expression is $15x; since he earns $10 an hour scooping, that expression is $10y.  Now add them together (and you CAN because they are both expressions relating dollars to dollars) and set the sum > $180:

$15x + $10y > $180.  That's why your answer is not correct.  Use mine (with the understanding that you care about why yours is wrong and mine is correct) and you'll be fine.

ANSWER

15 gallons

EXPLANATION

The equation that models the situation is

[tex]g(m) = 15 - \frac{m}{32} [/tex]

When the tank was full the man did not cover any mile.

To find the the number of gallons of gases Vera's tank holds, we substitute m=0 into the equation to get,

[tex]g(0) = 15 - \frac{0}{32} = 15[/tex]

Therefore the correct answer is is option A 15 gallons

Final answer:

When Vera's tank is full, it holds 15 gallons of gas. This is found by setting the miles driven to zero in the equation g = 15 - (m/32).

Explanation:

To determine how many gallons of gas Vera's tank holds when full, we need to set m, the number of miles driven, to zero in the given equation g = 15 - (m/32). This is because we are interested in the initial amount of gas before any driving occurs.

Plugging m = 0 into the equation gives us:

g = 15 - (0/32)

g = 15

Therefore, when full, Vera's tank holds 15 gallons of gas. Among the provided options, the correct answer is 15 gallons.

Standard form for linear equations is in the form ax + by = c. Thus, 2x + 4y = -3 is already in standard form.

Answer:

It is already in standard form

Step-by-step explanation:

Standard form is ax+by=c

2x=ax

4y=by

-3=c

Nothing needs to be changed

Answer:

  see below

Step-by-step explanation:

Put the (x, y) values of point F into the equation for line AG and see if they work:

  y = (b/(a+c))x

For (x, y) = (a+c, b), this is ...

  b = (b/(a+c))(a+c) = b·(a+c)/(a+c) = b·1 = b . . . . . a true statement

Yes, F lies on line AG.

Answer:

D

Step-by-step explanation:

Answer:

Option B.

Step-by-step explanation:

Two events are said to be independent of each other, if the probability of one event ocurrin in not way affects the probability of the other event occurring.

The interception of two independent events P(A ∩ B) = P(A) × P(B), where:

P(A) = 0.70

P(B) = 0.20

P(A ∩ B) = P(A) × P(B) = 0.70x0.20 = 0.14

The two events are independent if the probability of buying Bread AND cheese equals: 0.14, which is Option B.

Answer:

B

Step-by-step explanation:

The surface area of the sphere is given by the equation

[tex]A=4\pi * r^{2}[/tex],

where A is the surface area and r is the radius.

We want to find the volume of the sphere, which is given by the equation

[tex]V = \frac{4}{3} * \pi * r^{3}[/tex],

where V is the volume and r is the radius.

Looking at these equations, we see that they both involve the sphere's radius. If we know what r is, we can calculate the volume.

We know that the sphere's surface area is [tex]36 \pi[/tex]. Plugging that in for A in the surface area equation, we get

[tex]36 \pi=4\pi * r^{2}[/tex], then divide by [tex]\pi[/tex]

[tex]36 = 4 * r^{2}[/tex], then divide by 4

[tex]r^{2} = 9[/tex], then take the square root of both sides

[tex]r = 3[/tex]

So the radius of the sphere is 3. Plugging this into the volume equation,

[tex]V = \frac{4}{3} * \pi * 3^{3}[/tex], simplify terms

[tex]V = \frac{4}{3} * \pi * 27[/tex], multiply [tex]\frac{4}{3}[/tex] by 27

[tex]V = 36 * \pi[/tex]

So the volume of the sphere is [tex]36\pi[/tex].

Answer:

36π ft^3

Step-by-step explanation:

The surface area (S) of a sphere can be defined as:

S = 4×π×r^2 = 36×π

Solve for r to get the radius of the sphere:

r = ([tex]\sqrt{36/4}[/tex] = 3

The voluem (V) of a sphere can be defined as:

V= (4/3)×π×r^3

The volume of the sphere is:

V = (4/3)×π×(3^3) = 36π ft^3

The volume of the sphere can be calculated from the surface area given.

Answer:

Step-by-step explanation:

Proof:

_____

Proof is always in the eye of the beholder, and the details depend on the supporting theorems and postulates you're allowed to invoke. The basic idea is that you have cut a vertex angle in half twice, and you're trying to show that the smallest part to the rest of it has the ratio 1 : 3.

Answer:

C. 531 would be your answer.

Answer: 531

Step-by-step explanation: 21 • 18 = 378 and 17 • 9 = 153. And those together and you get 531 as yours answer!

For this case we have that by definition, the Greatest Common Factor or GFC, of two or more integers is the largest integer that divides them without leaving a residue.

So:

We look for the factors of both numbers:

8: 1, 2, 4, 8

40: 1, 2, 4, 5, 8, 10, 20

It is observed that 8 is common.

So, the GFC of 8x and 40 is 8

Answer:

8

Answer:

(f+g)(x) = x^2 +10x +7

Step-by-step explanation:

(f+g)(x) = f(x) +g(x) = (15x +7) +(x^2 -5x)

= x^2 +x(15 -5) +7

= x^2 +10x +7

[tex]\bf 2m^2+3=m\implies 2m^2-m+3=0 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{2}m^2\stackrel{\stackrel{b}{\downarrow }}{-1}m\stackrel{\stackrel{c}{\downarrow }}{+3} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution}\qquad \checkmark\\ &\textit{two \underline{non-real roots}} \end{cases} \\\\\\ (-1)^2-4(2)(3)\implies 1-24\implies -23[/tex]

Answer:

a) the output of mine #1 in 5 days

b) x1·v1 +x2·v2 = (240, 2824)

c) x1 = 544/315 ≈ 1.727; x2 = 1482/315 ≈ 4.705

Step-by-step explanation:

a) If v1 represents the production of mine #1 for 1 day, then 5v1 represents that mine's production for 5 days.

__

b) The production of each mine, multiplied by the number of days of production, adds together to give the total desired production:

x1·v1 + x2·v2 = (240, 2824)

__

c) Treating the vector components separately, the vector equation gives rise to two linear equations:

30x1 +40x2 = 240

600x1 + 380x2 = 2824

These can be solved by any of the usual methods. My favorite for numbers that are large or relatively prime is Cramer's rule and/or a graphing calculator. The above equations can be reduced to standard form to make the numbers slightly more manageable:

3x1 +4x2 = 24

150x1 +95x2 = 706

By Cramer's rule, ...

x1 = (4·706 -95·24)/(4·150 -95·3) = 544/315

x2 = (24·150 -706·3)/315 = 1482/315

The vector 5v1 represents the output of 5 days of operation at mine #1. The vector equation x1v1 + x2v2 = (240, 2824) gives the number of days each mine should operate to hit certain production targets. The specific solution is not given.

a) 5v1 would represent the output of 5 days of operation at mine #1. Specifically, it would mean that in 5 days, mine #1 produces 150 metric tons of copper and 3000 kilograms of silver.

b) The vector equation we need to represent the situation could look something like this: x1v1 + x2v2 = (240, 2824). Here, x1 and x2 represent the number of days each mine should operate and v1 and v2 are the vectors that represent the daily output of each mine. The solution to this vector equation would give the number of days each mine needs to operate in order to fit these production targets.

c) Since we are not supposed to solve the equation, we will simply write it again here for reference: x1v1 + x2v2 = (240, 2824).

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Answer:

  200 ft²

Step-by-step explanation:

Each face is an isosceles right triangle with a hypotenuse of length 10 ft. The area of each of those triangles is

  A = 1/4·h² . . . . where the h in this formula is the hypotenuse length

So, the area of the four faces (the lateral area of the pyramid is 4 times this, or ...

  A = 4·1/4·(10 ft)² = 100 ft²

Of course, the base area is simply the area of the square base, the square of its side length:

  A = (10 ft)² = 100 ft²

So, the total area is the sum of the lateral area and the base area:

  total area = 100 ft² +100 ft² = 200 ft²

_____

If you think about this for a little bit, you will realize the pyramid must have zero height. That is, the slant height of a face is exactly the same as the distance from the center of an edge to the center of the base. "Not drawn to scale" is a good description.

Answer:

200 [tex]ft^{2}[/tex]

Step-by-step explanation:

Answer:

B) B(2,-3) and C(-2,3)

Step-by-step explanation:

The given point A, has coordinates (-2,-3).

When point A(-2,-3) is reflected over the y-axis to obtain point B, then the coordinates of B is obtained by negating the x-coordinate of A.

Therefore B will have coordinates (2,-3).

 When point A(-2,-3) is reflected over the x-axis to obtain point C, then the coordinates of C is obtained by negating the y-coordinate of A.

Hence the coordinates of C are (-2,3)