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2 years ago

josh earns a weekly salary of $300 plus a 6% commission on sales. last week, his sales totaled $3500. what was his total pay?

1 answer:

5 0

Your answer is 510 if you find 6 percent of 3500, and then add that percentage with 300, you get your answer, which is 510

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The length of an equilateral triangle is increased by 7 inches, so the perimeter is now 36 inches. Find the original length of e

STALIN [3.7K]

The original length is 5 inches per side.

4 0

3 years ago

Write an equation of the line shown. Then use the equation to find the value of x when y=112

PtichkaEL [24]

Answer:

$y = 8x + 16$

$x = 12$

Step-by-step explanation:

Given two points on the line (0, 16) and (3, 40), an equation for the line can be written using the slope-intercept line equation which takes the format $y = mx + b$ .

Where,

$m = slope = \frac{y_2 - y_1}{x_2 - x_1}$

b = y-intercept or the point at which the line cuts the y-axis.

Let's find slope (m) using the slope formula:

Let,

$(0, 16) = (x_1, y_1)$

$(3, 40) = (x_2, y_2)$

$slope (m) = \frac{40 - 16}{3 - 0}$

$slope (m) = \frac{24}{3}$

$slope (m) = 8$

Find b. Substitute the values of x = 0, y = 16, and m = 8 in the slope-intercept formula to find b.

$y = mx + b$

$16 = 8(0) + b$

$16 = 0 + b$

$16 = b$

$b = 16$

Plug in the values of m and b into the slope-intercept formula to get the equation of the line.

$y = mx + b$

$y = 8x + 16$

Let's use the equation to find x when y = 112.

$y = 8x + 16$

Substitute y = 112 in the equation

$112 = 8x + 16$

$112 - 16 = 8x$

$96 = 8x$

Divide both sides by 8

$12 = x$

$x = 12$

8 0

2 years ago

If a person takes a prescribed dose of 10 milligrams of Valium, the amount of Valium in that person's bloodstream at any time ca

aleksandr82 [10.1K]

Answer:

(a)8.0mg

(b)36.87 hours

(c)-0.168

Step-by-step explanation:

The amount of Valium in that person's bloodstream at any time can be modeled with the exponential decay function $A ( t ) = 10 e^{ -0.0188 t$ (t in hours)

(a)After 12 Hours

$A ( 12) = 10 e^{ -0.0188*12}\\=7.98\\\approx 8.0 mg $(to the nearest tenth of a milligram)$

(b)If A(t)=5mg

Then:

$5= 10 e^{ -0.0188 t}\\$Divide both sides by 10\\0.5=e^{ -0.0188 t}\\$Take the natural logarithm of both sides\\ln (0.5)=-0.0188 t\\t=ln (0.5) \div (-0.0188)\\$t=36.87 hours (to two decimal places.)$

(c)

$A ( t ) = 10 e^{ -0.0188 t}\\A'(t)=10(-0.0188)e^{ -0.0188 t}\\A'(t)=-0.188e^{ -0.0188 t}\\$At 6 hours, the rate at which the amount of Valium is decaying therefore is:\\A'(6)=-0.188e^{ -0.0188*6}\\$=-0.168 ( to three decimal places)$

3 0

2 years ago

Which of the following expression expressions is equivalent to cos3x/sinxcosx?

77julia77 [94]

Correct Option:
Option B

Solution:
The given expression is:

$\frac{cos(3x)}{sin(x)cos(x)}$

cos(3x) can be written as cos(2x +x). Expanding it, we get:

$cos(3x) = cos(2x+x) \\ \\ 
cos(3x) =cos(2x)sin(x)-sin(2x)cos(x)$

Using this value of cos(3x) in given equation, we get:

$\frac{cos(3x)}{sin(x)cos(x)} \\ \\ 
= \frac{cos(2x)sin(x)-sin(2x)cos(x)}{sin(x)cos(x)} \\ \\ 
= \frac{cos(2x)sin(x)}{sin(x)cos(x)}- \frac{sin(2x)cos(x)}{sin(x)cos(x)} \\ \\ 
= \frac{cos(2x)}{cos(x)} - \frac{sin(2x)}{sin(x)} \\ \\ 
=sec(x)cos(2x)-csc(x)sin(2x)$

8 0

2 years ago

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A soccer ball has a 35 cm diameter. what is the volume of the contents of the ?

Anettt [7]

Answer:

To calculate the volume of a sphere, use the formula v = ⁴⁄₃πr³, where r is the radius of the sphere. If you don't have the radius, you can find it by dividing the diameter by 2. Once you have the radius, plug it into the formula and solve to find the volume.

Step-by-step explanation:

To find the volume of a soccer ball,the formula is V=4/3 πr^3,where r is the radius and π=3.14. A regulation soccer ball has a radius of 35cm. find the volume of a soccer ball to the nearest cubic centimeter. This is just some to keep in mind.

4 0

3 years ago

Read 2 more answers