31. You work 35 hours/week for 52 weeks and are given the option to be paid hourly or to go on salary. In which situation will you earn the most?
• $32,000/year
© $18.50/hour
• $30,000/year with a 5% bonus
) $17.50/hour and a $1,500 bonus at the end of the year

Answer:

5 yards

Step-by-step explanation:

15/3=5

Answer:

6.2 seconds

Explanation:

             Given function: h(t) = – 0.145t² + 0.019t + 5.5

solve the quadratic equation:  

using the formula:  [tex]\left[\begin{array}{ccc} t = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}\end{array}\right][/tex]

Solving steps:

→  –0.145t² + 0.019t + 5.5 = 0

→  [–0.145t² + 0.019t + 5.5 = 0 ]* 100

→  -145t² + 19t + 5500 = 0

→  [tex]t = \frac{ -19 \pm \sqrt{19^2 - 4 ( -145)(5500)}}{2(-145)}[/tex]

→  [tex]t_1=\frac{-19+\sqrt{3190361}}{2\left(-145\right)},\:t_2=\frac{-19-\sqrt{3190361}}{2\left(-145\right)}[/tex]

→  [tex]t = -6.09[/tex] , [tex]t = 6.2[/tex]

→  [tex]t = 6.2[/tex]

Time cannot be negative here.

Answer:

Step-by-step explanation:

When the frisbee hits the ground, the value of h is zero.

Find the time required:

ratio remains same.

[tex]\\ \tt\longrightarrow \dfrac{2}{14}=\dfrac{7}{2z}[/tex]

[tex]\\ \tt\longrightarrow 4z=14(7)[/tex]

[tex]\\ \tt\longrightarrow 4z=98[/tex]

[tex]\\ \tt\longrightarrow z=98/4[/tex]

[tex]\\ \tt\longrightarrow z=24.5[/tex]

Answer:

Explanation:

easy way to solve:

[tex]x^2-6x-7=0[/tex]

[tex]x^2+x-7x-7=0[/tex]

[tex]x(x+1)-7(x+1) =0[/tex]

[tex](x-7)(x+1)= 0[/tex]

[tex]x = 7, -1[/tex]

Mistake:

In step 5,

Josh should have given:

[tex](x-3)^2=16[/tex]

[tex]x-3 = \pm \sqrt{16}[/tex]     [ changing sides changes square sign to [tex]\pm[/tex] square root ]

[tex]x-3 = \pm 4[/tex]

[tex]x -3 = 4[/tex], [tex]x-3 = -4[/tex]

[tex]x = 7[/tex], [tex]x = -1[/tex]

Answer:

x³ + 1

Step-by-step explanation:

to evaluate (f ￮ g)(x) , substitute x = g(x) into f(x)

f(g(x) )

= f(x³)

= x³ + 1

Answer:

We cannot calculate this probability because the sampling distribution is not normal.

Step-by-step explanation:

Since the parent population is not normally distributed, the small sample size will result in a sampling distribution that isn't normal.

Answer:

x = 269

explanation:

solve:

5 * x = 1345

x = 1345/5

x = 269

Therefore x is 269.

note: changing sides changes multiplication(*) to division(/) and division(/) to multiplication(*).

Answer:

x = 269

Step-by-step explanation:

For this question, they are asking you to create a problem out of the information given. For this problem, we will require the use of division. Before we can solve, we need to create the problem first.

Because the problem says 5 multiplied by x, we have to multiply these two. (Important:) Anytime you are multiplying a coefficient (5 in this case) by a variable (x in this case) we have to put the coefficient in front of the variable, like this:

5x _ ___.

Now that we know that, the question states that this basically equals 1345. With that said, that just gave us the rest of the problem. Now let's put it together:

5x = 1345.

Now we can solve. To single out the variable (x) to find our answer, divide 5 into 1345:

5x = 1345

5        5

So, 1345 ÷ 5 = 269. After that, we are left with x and 269 (because the 5 was canceled out with the division). So, the answer is:

x = 269.

I hope that this helps.

Answer:

35 miles

Step-by-step explanation:

At the start, you lose $8.5 for tolls and the taxi cost.
You're left with $31.5 after that, every mile costs you $0.9, so you can go 31.5 : 0.9 = 35 miles.

Answer:

1. x = 56

2. y = 2

3. x = 6

4. y = 3

5. k = 10.2

6. w = 21

7. x = 72

Step-by-step explanation:

1. x + 4 = 60

x = 56

2. 3y - 2 = 4

3y = 6

y = 2

3. 3x - 7 = 11

3x = 18

x = 6

4. 5y + 3 = 18

5y = 15

y = 3

5. 3 + 6k = 64

6k = 61

k = 10.2

6. w ÷ 3 - 5 = 2

w ÷ 3 = 7

w = 21

7. x ÷ 8 + 3 = 12

x ÷ 8 = 9

x = 72

[tex]\bold{\huge{\green{\underline{ Solution }}}}[/tex]

[tex]\bold{\red{ x + 4 = 60 }}[/tex]

[tex]\sf{ x = 60 - 4 }[/tex]

[tex]\bold{ x = 56 }[/tex]

Hence , The value of x is 56 .

[tex]\bold{\red{ 3y - 2 = 4 }}[/tex]

[tex]\sf{ 3y = 4 + 2 }[/tex]

[tex]\sf{ 3y = 6}[/tex]

[tex]\sf{ y = }{\sf{\dfrac{6}{3}}}[/tex]

[tex]\bold{ y = 2 }[/tex]

Hence , The value of y is 2 .

[tex]\bold{\red{ 3x - 7 = 11 }}[/tex]

[tex]\sf{ 3x = 11 + 7 }[/tex]

[tex]\sf{ 3x = 18}[/tex]

[tex]\sf{ x = }{\sf{\dfrac{18}{3}}}[/tex]

[tex]\bold{ x = 6 }[/tex]

Hence , The value of x is 6 .

[tex]\bold{\red{ 5y + 3 = 18 }}[/tex]

[tex]\sf{ 5y = 18 - 3 }[/tex]

[tex]\sf{ 5y = 15}[/tex]

[tex]\sf{ y = }{\sf{\dfrac{15}{5}}}[/tex]

[tex]\bold{ y = 3 }[/tex]

Hence , The value of y is 3 .

[tex]\bold{\red{ 3 + 6k = 64 }}[/tex]

[tex]\sf{ 6k = 64 - 3 }[/tex]

[tex]\sf{ 6k = 61}[/tex]

[tex]\bold{ k = }{\sf{\dfrac{61}{6}}}[/tex]

Hence , The value of k is 61/6 .

[tex]\bold{\red{\dfrac{W}{3}}}{\bold{\red{ - 5 = 2 }}}[/tex]

[tex]\sf{\dfrac{W - 15}{3}}{\sf{ = 2 }}[/tex]

[tex]\sf{ W - 15 = 2}{\sf{\times{ 3 }}}[/tex]

[tex]\sf{ W - 15 = 6 }[/tex]

[tex]\sf{ W = 6 + 15 }[/tex]

[tex]\bold{ W = 21}[/tex]

Hence , The value of W is 21 .

[tex]\bold{\red{\dfrac{x}{8}}}{\red{\bold{ + 3 = 12 }}}[/tex]

[tex]\sf{\dfrac{x + 24 }{8 }}{\sf{ = 12 }}[/tex]

[tex]\sf{ x + 24 = 12}{\sf{\times{ 8 }}}[/tex]

[tex]\sf{ x + 24 = 96 }[/tex]

[tex]\sf{ x = 96 - 24 }[/tex]

[tex]\bold{ x = 72 }[/tex]

Hence, The value of x is 72 .

Answer: y=x

Step-by-step explanation:

The slope is (y2-y1)/(x2-x1) = 8/8 = 1

Plugging it into the equation y = mx+b:

y = x + b

Plugging in one of the coordinates:

4 = 4+b

b = 0

Therefore, the equation of the line is y=x

Answer:

24.05

Step-by-step explanation:

24.005 has more numbers but worth less

24.05 is more

Answer:

72

Step-by-step explanation:

=> 4(n+13)

putting the value of n which is 5

=> 4(5+13 )

=> 4(18)

=> 72

Answer:

7800

I already take a homework with this question

Answer:

ok so the shaded area will be the larger rectange minus the smaller one so lets find the area of both by multiplying the sides

(5x)(8x+1)=40x^2+5x

(4x)(2x)=8x^2

so

40x^2+5x-8x^2

32x^2+5x or

x(32x+5)

so a

Hope This Helps!!!

Answer:

4

Step-by-step explanation:

Let's say the amount of bushes sold (yield) is b, and the price per bushel is p.

When calculating total revenue, we want to multiply price by quantity. Quantity here is b, and price is p. Therefore, p*q = revenue = return.

Let's say that the amount of weeks is w.

Price after w weeks = 24 - 1.50 for each week = 24 - 1.50w

Yield after w weeks = 4 + 0.5 for each week = 4 + 0.5w

Revenue after w weeks = p * b = (24-1.50w) * (4+0.5w) = 96 - 6w + 12w - 0.75w² = -0.75w²+6w + 96.

We want to maximize revenue. First, we can find when the derivative of the function is 0.

d/dw(-0.75w²+6w + 96) = -1.5w + 6 = 0

subtract 6 from both sides

-1.5w = -6

divide both sides by -1.5 to isolate w

w = 4

plug that into our equation

-0.75(4)²+6(4) + 96 = -12 + 24 + 96 = 108

Because this function has a negative coefficient for the w², we can say that it is a parabola opening up downward, so when the derivative = 0, we have found the maximum of the function. Therefore, 4 is our answer

Answer:

Volume = 904.78 yards

Step-by-step explanation:

The formula for a sphere is:

V=4/3πr³

Since we already know that the radius is 3 yards and that π is 3.14 all we have to do is plug in the numbers.

V=4/3(3.14)(6)³

V=4/3(3.14)(216)

V=4.1897(216)

V≈904.78 yards

Answer:  [tex]\frac56[/tex]

Work Shown:

[tex]\frac{1}{2}+\frac{1}{3}\\\\\frac{3}{6}+\frac{2}{6}\\\\\frac{3+2}{6}\\\\\frac{5}{6}\\\\[/tex]

To visualize this, cut up a circle into 6 equal pieces.

3 of those pieces represent half the circle (3/6 = 1/2)

2 more pieces represent one third (2/6 = 1/3)

We have 3+2 = 5 pieces out of 6 total. This is visual confirmation that 1/2 + 1/3 = 5/6

Answer:

  (c)  (6, -3)

Step-by-step explanation:

Reflection over both axes is the same as reflection across the origin, or rotation 180° about the origin. It has the effect of negating both coordinates:

  (x, y) ⇒ (-x, -y) . . . . . reflection over both axes

The coordinates of A are (-6, 3), so the coordinates of A' will be ...

  A(-6, 3) ⇒ A'(6, -3)

Answer:

y = 28°

Step-by-step explanation:

The triangle is a right triangle which has 90 degrees.

The 3x falls under 90 degrees.

So:

→ 2y + 90° + 34° = 180°

→ 2y = 180° - 124°

→ 2y = 56°

→ y = 28°

Triangle

XYZ = right triangle

3x = 90°

X + Y + Z = 180°

34° + 3x + 2y = 180°

34° + 90° + 2y = 180°

2y = 180° - (34° + 90°)

2y = 56°

y = 28°

Answer:

105 minutes

Step-by-step explanation:

The pond is a prism. Its volume is the area of the trapezoidal base (the front and back faces) multiplied by the height (the 1 m edge).

Area of base of pond (front face) = (1/2)(B + b)h

Base = (1/2)(1.5 m + 0.6 m)(2 m)    [Here, height is the height oif the trapezoid, so it is 2 m]

Base = 2.1 m²

Volume = Base × Height

Volume = 2.1 m² × 1 m    [Here, height is the height of the prism, so it is 1 m]

Volume = 2.1 m³

The volume of the upper 30 cm (= 0.3 m) of the pond is:

V = LWH

V = 2 m × 1 m × 0.3 m

V = 0.6 m³

The volume of water decreased 0.6 m³ in 30 minutes.

In 60 minutes, it would decrease by 1.2 m³.

60 minutes = 1 hour

The flow rate is 1.2 m³ / hour.

The total volume of the pond is 2.1 m³.

Emptying out the pond completely means removing 2.1 m³ of water at the flow rate of 1.2 m³/hour.

flow rate = volume/time

time × flow rate = volume

time = volume / flow rate

time = 2.1 m³ / 1.2 m³/hour = 1.75 hour

time = 1.75 hour × 60 minutes/hour = 105 minutes

Answer: 105 minutes

Answer:

60 meters.

Step-by-step explanation:

Here the villa has length of 6 cm and breadth of 4 cm

Find perimeter using:

2(length + breadth)

2(6 + 4)

20 cm

Here in scale the drawing perimeter is 20 cm

3 meter = 300 cm ......this is for real.

1 cm here --> 20 cm

300 cm in real --> (20*300) cm

Real perimeter = 6000 cm

If 6000 cm converted to m:

(6000/100) = 60 meters.

Find perimeter using:

[tex]2(length + breadth)[/tex]

[tex]2(6+4)[/tex]

[tex]20 cm[/tex]

Here in scale the drawing perimeter is [tex]20 cm[/tex]

[tex]3 meter = 300 cm [/tex]

[tex]1 cm → 20 cm[/tex]

[tex]300 \: cm → (20×300) cm[/tex]

[tex]Real \: perimeter = 6000 cm[/tex]

If [tex]6000 \: cm[/tex]converted to m:

[tex](\frac{6000}{100}) = 60 \: meters[/tex]

Answer:

D

Step-by-step explanation:

V=(1/3)(pi)(r^2)(h)

=(pi/3)((x/2)^2)(x)

=(pi/3)(x^2/4)(x)

=x^3 * pi/12

Answer:

D

Step-by-step explanation:

One-twelfthπx3

Answer:

x = 10i - 10i

Step-by-step explanation:

3x^2 + 300 = 0

3(x^2 + 300) = 0

x^2 + 100 = 0

x^2 = -100

x = -100 (sqr root)

x = 10i - 10i

Hope this is more of the answer you where looking for.

Answer:

10

Step-by-step explanation:

it just is

[tex]\huge\blue{\mid{\fbox{\tt{\:ANSWER\:}}\mid}}[/tex]

____________________

The graph,

Answer: 1. x=2,-5/3

Step-by-step explanation: