A sales clerk makes $200 in commission on $1,700 worth of furniture. What’s her commission rate?

Answer:

3π/13

Step-by-step explanation:

In order to find the reference angle of a given angle, first of all, its quadrant is determined

In order to determine the quadrant,

10π/13=10(180)/13

=138.46

As the given angle belongs to 2nd quadrant, it will be subtracted from 180 degrees also denoted by pi.

So,

Reference angle for 10π/13= π-10π/13

=(13π-10π)/13

=3π/13

So the reference angle for 10π/13 is 3π/13 ..

Use trigonometry.

cos(18°) = x/25

Multiply both sides by 25.

cos(18°)25 = x

23.7764129074 = x

We round off to the nearest hundredth. This means to round off to two decimal places.

Doing so, we get 23,78 cm = x.

Answer:

The best answer would be B. systematic random sampling

Step-by-step explanation:

The best sampling method for choosing a committee is Cluster Sampling.

Simple random sampling - Simple random sampling is a sort of probability sampling in which a researcher selects a subset of a population at random.

Systematic random sampling  A probability sampling approach in which a random sample of a bigger population is selected with a defined periodic interval.

Stratified random sampling A form of sampling known as stratified random sampling includes dividing a population into smaller sub-groups known as strata.

Cluster Sampling  The population is divided into groups first. Every member of some of the groupings is included in the total sample. The teams are chosen at random.

If we are trying to choose a committee, cluster sampling method would be the best as there should be representatives of every group of the society in that committee and the representative from each group should be chosen completely randomly.

Hence the cluster sampling method is the best way to choose a committee.

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ANSWER

Option C

EXPLANATION

The given inequality is

[tex]y - 3 \: > \: 2x + 2[/tex]

We add 3 to both sides to get,

[tex]y \: > \: 2x + 2 + 3[/tex]

[tex]y \: > \: 2x +5[/tex]

The corresponding linear equation is

[tex]y = 2x + 5[/tex]

This becomes the dashed boundary line of the inequality.

We test the origin to determine which half plane to shade.

[tex]0\: > \: 2(0)+5[/tex]

[tex]0\: > \: 5[/tex]

This is false.

Hence we shade the upper half plane.

The correct answer is C

Answer:

106 m²

Step-by-step explanation:

Imagine this shape was a square, it's area would be 120 m².

Now imagine the little rectangle with 7 m as the side, you will have to work out the area of that so

Side = 7

4 + 4 + ? = 10

8 + ? = 10

? = 2

So the area of the little rectangle is 14 m²

Now we minus both of the areas : 120 - 14 = 106

The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is

[tex]V=\pi r^2h[/tex]

Differentiate both sides with respect to time:

[tex]\dfrac{\mathrm dV}{\mathrm dt}=2\pi rh\dfrac{\mathrm dr}{\mathrm dt}+\pi r^2\dfrac{\mathrm dh}{\mathrm dt}[/tex]

We're given that

[tex]\dfrac{\mathrm dr}{\mathrm dt}=6\dfrac{\rm in}{\rm s}[/tex]

[tex]\dfrac{\mathrm dh}{\mathrm dt}=-3\dfrac{\rm in}{\rm s}[/tex]

so that at the point when [tex]r=5\,\rm in[/tex] and [tex]h=11\,\rm in[/tex], the volume is undergoing a total change of

[tex]\dfrac{\mathrm dV}{\mathrm dt}=2\pi(5\,\mathrm{in})(11\,\mathrm{in})\left(6\dfrac{\rm in}{\rm s}\right)+\pi(5\,\mathrm{in})^2\left(-3\dfrac{\rm in}{\rm s}\right)[/tex]

[tex]\boxed{\dfrac{\mathrm dV}{\mathrm dt}=585\pi\dfrac{\mathrm{in}^3}{\rm s}}[/tex]

The volume of the right circular cylinder is changing at a rate of 255π cubic inches/sec with the radius increasing at 6 in./s and height decreasing at 3 in./s.

The question involves the application of calculus concepts particularly related to volume flow rate. The volume (V) of a right circular cylinder is given by V = πr²h, where r is the radius and h is the height. We can take the derivative in respect to time (t) of both sides, which will result in dV/dt = πrh(dr/dt) + πr²(dh/dt).

According to the problem, dr/dt = 6 in./s and dh/dt = -3 in./s. The volume is changing when the radius (r) is 5 in. and the height (h) is 11 in. Substituting all these values into the formula, we get: dV/dt = π(5)(11)(6) + π(5)²(-3). This equals 330π - 75π = 255π cubic inches/sec.

Thus, the volume of the cylinder is changing at a rate of 255π cubic inches/sec.

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If Eli has a total of 21 baseball cards, and wants each bag to have 3 cards, you would divide the number of total cards by the amount you want in each group. Dividing is like grouping.

So, the equation he'd use is: 21 / 3 = 7

I hope that helped.

Answer:

21÷3=7

Step-by-step explanation:

Dividing the number of available cards by the quantity in each bag will tell Eli how many bags he can fill.

___

Division can be thought of as "repeated subtraction" with the quotient telling you how many times the divisor can be subtracted from the dividend. One way Eli can do this repeated subtraction is to put the cards into piles of 3:

ccc . ccc . ccc . ccc . ccc . ccc . ccc

He will run out of cards when he has made 7 piles.

The answer is:

The area of the triangle is:

[tex]Area=13.2cm^{2}[/tex]

We can solve the problem using the Side-Angle-Side (SAS) method, to calculate the area of a triangle given two sides and a single angle.

The SAS method to calculate the area of a triangle is given by the following the equation:

[tex]Area=\frac{abSinC}{2}[/tex]

Where,

a and b are the known sides.

C is the known angle

Now, we are given a triangle with the following dimension:

[tex]Side_{a}=7cm\\Side_{b}=8cm\\\alpha=28\°[/tex]

Then, using the information and solving we have:

[tex]Area=\frac{7cm*8cm*Sin(28\°)}{2}[/tex]

[tex]Area=\frac{56cm^{2}*Sin(28\°)}{2}\\\\Area=\frac{56cm^{2}*0.47}{2}\\\\Area=\frac{26.32cm^{2}}{2}\\\\Area=13.16cm^{2}[/tex]

Hence, the area of the triangle, rounded to the nearest tenth is:

[tex]Area=13.2cm^{2}[/tex]

Have a nice day!

D is most likely right. Basically, I would turn them into decimals and divide using a graphing calculator.

Answer:

D

Step-by-step explanation:

Answer:

Both A and B

Step-by-step explanation:

A = {(3, −5), (4, 6), (−3, 9), (2, 7)}  

-Each x goes to a different y so this is a function

B = {(2, 4), (−1, −7), (5, 6), (4, 3)}

-Each x goes to a different y so this is a function

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

In calculating probability, remember that "AND" means "MULTIPLICATION" and "OR" means "ADDITION".

Since we want the probability of red necklace AND yellow bracelet, we calculate individual probabilities and "MULTIPLY" them.

Probability of red necklace:

There are 4 necklaces and 1 of them is red, hence probability of red necklace is 1/4

Probability of Yellow bracelet:

There are 2 bracelet and 1 of them is yellow, hence probability of yellow bracelet is 1/2

Now, we multiply both to get our answer.

1/4 * 1/2 = 1/8

Answer:

1/8

Step-by-step explanation:

Answer:

(5,0)

Step-by-step explanation:

Count how many units are there on the x-axis first and in this case it is 5 the count how many on the y axis (going up or down) and that is 0 so then use this for the coordinate: (x,y)=(5,0)

Answer:

(5,0)

Step-by-step explanation:

Count how many units are there on the x-axis first and in this case it is 5 the count how many on the y axis (going up or down) and that is 0 so then use this for the coordinate: (x,y)=(5,0)

Answer:

Donuts cost $2.00 and Cookies cost $1.50

Step-by-step explanation:

D = cost of a donut

C = cost of a cookie

4D + 10C = $23.00

8D + 6C = $25.00

Eliminate a variable when subtracting the two equations.  Change both values with C to 60 in order to eliminate the C variable and solve for D.

80D + 60C = $250.00 subtracted from 24D + 60C = $138

56D = $112.00  (Divide by 56 to single out the variable)

56D/56 = $112.00/56

D = $2.00

Use the D value to solve for C.

4(2) + 10C = $23.00

8 + 10C = $23.00

8 - 8 + 10C = $23.00 - 8

10C = $15.00

10C/10 = $15/10

C = $1.50

Check:

Bentley:  

4D + 10C = $23

4(2) + 10(1.50) = $23

8 + 15 = $23

23 = 23

Skylar:

8D + 6C = $25

8(2) + 6(1.50) = $25

16 + 9 = $25

25 = 25

Answer:

Each donut costs $2 and each cookie costs $1.5

Step-by-step explanation:

1. Let´s name the variables as the following:

x = price of one donut

y = price of one cookie

2. Write in an equation form which Bentley bought:

[tex]4x+10y=23[/tex] (Eq.1)

3. Write in an equation form which Skylar bought:

[tex]8x+6y=25[/tex] (Eq.2)

4. Solve for x in Eq.1:

[tex]4x+10y=23[/tex]

[tex]4x=23-10y[/tex]

[tex]x=\frac{23-10y}{4}[/tex] (Eq.3)

5. Replace Eq.3 in Eq.2 and solve for y:

[tex]8*(\frac{23-10y}{4})+6y=25[/tex]

[tex]\frac{184-80y}{4}+6y=25[/tex]

[tex]\frac{184-80y+24y}{4}=25[/tex]

[tex]184-80y+24y=100[/tex]

[tex]-80y+24y=100-184[/tex]

[tex]-56y=-84[/tex]

[tex]y=\frac{84}{56}[/tex]

[tex]y=1.5[/tex]

6. Replacing the value of y in Eq.3:

[tex]x=\frac{23-10*(1.5)}{4}[/tex]

[tex]x=\frac{23-10*(1.5)}{4}[/tex]

[tex]x=\frac{23-15}{4}[/tex]

[tex]x=\frac{8}{4}[/tex]

[tex]x=2[/tex]

Therefore each donut costs $2 and each cookie costs $1.5

Answer:

The graph of G is 3 units to the left of graph F

Step-by-step explanation:

I used Desmos graphing calculator to check my answer, but generally you can use this formula.

a(x + or - h) + or - k = y

h is vertical movement and k is horizontal movement.

Answer: Never mind that answer was incorrect it is not B!!

Step-by-step explanation:

5 1/4 in decimal form is 5.25 because 25 is 1/4 of 100.

The mixed fraction 5 1/4 is equivalent to 5.25 in decimal form. The fraction 1/4 is converted to decimal by dividing 1 by 4 to get 0.25 and then added to the whole number 5.

To convert the mixed fraction 5 1/4 to decimal form, you need to divide the numerator by the denominator for the fractional part and then add that result to the whole number part. In this case, 1 divided by 4 equals 0.25. Adding this result to the whole number 5 gives you 5.25, which is 5 1/4 in decimal form.

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Answer:

Step-by-step explanation:

I'm sure you want your functions to appear as perfectly formed as possible so that others can help you.  f(x) = 4(2)x should be written with the " ^ " sign to denote exponentation:  f(x) = 4(2)^x

                                                                                      f(b) - f(a)

The formula for "average rate of change" is a.r.c. = --------------

                                                                                           b - a

                                    change in function value

This is equivalent to  ---------------------------------------

                                            change in x value

For Section A:  x changes from 1 to 2 and the function changes from 4(2)^1 to  4(2)^2:  8 to 16.  Thus, "change in function value" is 8 for a 1-unit change in x from 1 to 2.  Thus, in this Section, the a.r.c. is:

                 8

               ------ = 8 units    (Section A)

                  1

Section B:  x changes from 3 to 4, a net change of 1 unit:  f(x) changes from

4(2)^3 to 4(2)^4, or 32 to 256, a net change of 224 units.  Thus, the a.r.c. is

        224 units

      ----------------- = 224 units (Section B)

            1 unit

The a.r.c for Section B is 28 times greater than the a.r.c. for Section A.

This change in outcome is so great because the function f(x) is an exponential function; as x increases in unit steps, the function increases much faster (we say "exponentially").

Answer:

Part A: Section A- 8, Section B- 32.

Part B: 4 times.

Step-by-step explanation:

The function is given by .

Section A is from x = 1 to x = 2.

Now, f(1) = 4 × 2 = 8 and f(2) = 4 × 2 × 2 = 16

Again, section B is from x = 3 to x = 4.

Now, f(3) = 4 × 2 × 2 × 2 = 32 and f(4) = 4 × 2 × 2 × 2 × 2 = 64

Part A:

In section A, the average rate of change is =  8

And in section B, the average rate of change is  =  32

Part B:

Therefore, the average rate of change of section B is greater than section A is (32 / 8 = 4)

Answer: 5.18 pounds

Step-by-step explanation:

Given: The pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to  the temperature of the gas.

Let 'p' denote the pressure exerted on the walls and 't' denotes  temperature of the gas.

Then the equation is given by :-

[tex]p=ct[/tex], where c is the proportionality constant.

Also, the pressure is 6 pounds per square inch when the temperature is 440° F.

[tex]\Rightarrow\ 6=440c\\\\\Rightarrow\ c=\dfrac{6}{440}=\dfrac{3}{220}[/tex]

Then, the final equation to calculate pressure becomes :-

[tex]p=\dfrac{3}{220}t[/tex]

Now, the pressure exerted when the temperature of the gas is 380°F is given by :-

[tex]p=\dfrac{3}{220}\times380=5.181818\approx5.18\text{ pounds}[/tex]

Answer:

31.41ft

Step-by-step explanation:

the area A of a circle is πr² = 78.5 square feet

3.1416* r² = 78.5

r² =78.5/3.1416 =  24.987

r = √24.987 = 4.999ft

the circumference C of a circle is 2πr

C = 2* 3.1416 * 4.999 = 31.41ft

Answer:

Step-by-step explanation:

[tex]-3(2x-5)<5(2-x)\qquad\text{use the distributive property}\\\\(-3)(2x)+(-3)(-5)<(5)(2)+(5)(-x)\\\\-6x+15<10-5x\qquad\text{subtract 15 from both sides}\\\\-6x<-5-5x\qquad\text{add 5x to both sides}\\\\-x<-5\qquad\text{change the signs}\\\\x>5[/tex]

Answer:

$10.50

Step-by-step explanation:

The first step is to determine the cost per student for the trip.

It cost $443.75 for 25 students, so

TS = 443.75 / 25 = $17.75 per student.

From that $17.75, we know we should remove $7.25 for the lunch in order to get the entrance fee:

EF = 17.75 - 7.25 = 10.50

The entrance fee for one student was $10.50

Answer:

Hence final answer is [tex](1,3)[/tex].

correct choice is D because both ends are open circles.

Step-by-step explanation:

Given inequality is [tex]\frac{x-1}{x-3}<0[/tex]

Setting both numerator and denominator =0 gives:

x-1=0,  x-3=0

or x=1, x=3

Using these critical points, we can divide number line into three sets:

[tex](-\infty,1)[/tex], [tex](1,3)[/tex] and [tex](3,\infty)[/tex]

We pick one number from each interval and plug into original inequality to see if that number satisfies the inequality or not.

Test for [tex](-\infty,1)[/tex].

Clearly x=0 belongs to [tex](-\infty,1)[/tex] interval then plug x=1 into [tex]\frac{x-1}{x-3}<0[/tex]

[tex]\frac{0-1}{0-3}<0[/tex]

[tex]\frac{-1}{-3}<0[/tex]

[tex]\frac{1}{3}<0[/tex]

Which is False.

Hence [tex](-\infty,1)[/tex] desn't belongs to the answer.

Similarly testing other intervals, we get that only [tex](1,3)[/tex] satisfies the original inequality.

Hence final answer is [tex](1,3)[/tex].

correct choice is D because both ends are open circles.

QA) Which solid figures can the staircase be broken into?

A) The staircase can be broken into 3 rectangular prisms.

QB) What are the dimensions of each solid figure?

A) We are given the height (2.5 ft) and the length (3 ft) of the entire staircase. To find the height and length of each step, just divide by 3:

2.5 / 3 = 5/6 ft high

3 / 3 = 1 ft long

Looking at the image given, we can see that the staircase is 6 ft wide.

Bottom prism: 3 ft long, 6 ft wide, and 5/6 ft high.

Middle prism: 2 ft long, 6 ft wide, and 5/6 ft high.

Top prism: 1 ft long, 6 ft wide, and 5/6 ft high.

QC) How much concrete will be needed to form the staircase?

A) To answer this question, we have to find the volume of each rectangular prism. The formula for the volume of a rectangular prism is

V = lwh; where l = length, w = width, and h = height.

We need to apply this formula to each prism. I'll go from the bottom up.

(1.) V = lwh; l = 3, w = 6, h = 5/6

V = (3)(6)(5/6)

V = 15 ft²

(2.) V = lwh; l = 2, w = 6, h = 5/6

V = (2)(6)(5/6)

V = 10 ft²

(3.) V = lwh; l = 1, w = 6, h = 5/6

V = (1)(6)(5/6)

V = 5 ft²

To find the amount of concrete needed to form the staircase, just add the volumes of the three rectangular prisms:

15 + 10 + 5 = 30 ft²

The contractor will need enough concrete to cover 30 ft² to form the staircase.

Hope this helps!

Final answer:

The staircase can be broken into rectangular prisms, each representing a step. The volume of each step is calculated using the given dimensions, which are then summed to find the total concrete needed.

Explanation:

To determine the amount of concrete needed to form a staircase, we need to calculate the volume of concrete required for each step and then sum them up. Since each step is of the same size, we can break down the staircase into a set of rectangular prisms, where each prism represents a step.

Dimensions of each solid figure (step): Given a stage height of 400 mm and 3 steps, the height of each step would be 400 mm / 3, which is around 133.33 mm or 13.33 cm. The length of the horizontal part of each step is 800 mm or 80 cm. Assuming a step width of 1,200 mm or 120 cm (since the steps must be wide enough for two people), we obtain the dimensions for each step.

To calculate the volume of each step, we use the formula for the volume of a rectangular prism: Volume = Length × Width × Height. Therefore, we have Volume = 80 cm × 120 cm × 13.33 cm for each step. To find the total volume for the staircase, we multiply the volume of one step by the number of steps (3 in this case).

Calculating the total concrete required: After finding the volume of one step, we multiply it by 3 (since there are 3 steps) to find the total concrete needed.

solution for #18 is C and for #19 is D

QUESTION 18

Use the Pythagorean Identity.

[tex] \cos^{2}( \theta) +\sin^{2}( \theta) = 1[/tex]

We substitute the given value into the formula,

[tex] \cos^{2}( \theta) +( { \frac{4}{7} })^{2} = 1[/tex]

[tex] \cos^{2}( \theta) + \frac{16}{49} = 1[/tex]

[tex] \cos^{2}( \theta) = 1 - \frac{16}{49} [/tex]

[tex]\cos^{2}( \theta) = \frac{33}{49} [/tex]

Since we are in the first quadrant, we take positive square root,

[tex]\cos( \theta) = \sqrt{\frac{33}{49} } [/tex]

[tex]\cos( \theta) = \frac{ \sqrt{33}}{7} [/tex]

The 3rd choice is correct.

QUESTION 19.

We want to simplify;

[tex]18 \sin( \theta) \sec( \theta) [/tex]

Recall the reciprocal identity

[tex] \sec( \theta) = \frac{1}{ \cos( \theta) } [/tex]

This implies that,

[tex]18 \sin( \theta) \sec( \theta) =18 \sin( \theta) \times \frac{1}{ \cos( \theta) } [/tex]

[tex]18 \sin( \theta) \sec( \theta) =18 \times \frac{\sin( \theta) }{ \cos( \theta) } [/tex]

This will give us:

[tex]18 \sin( \theta) \sec( \theta) =18 \tan( \theta) [/tex]

The correct choice is D.

Answer:

Step-by-step explanation:

The formula of a midpoint of a segment AB with endpoints at A(x₁, y₁) and B(x₂, y₂):

[tex]M_{AB}\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]

From the graph we have the points A(-2, 4) and C(3, -3).

Substitute:

[tex]M_{AC}(x,\ y)\\\\x=\dfrac{-2+3}{2}=\dfrac{1}{2}=0.5\\\\y=\dfrac{4+(-3)}{2}=\dfrac{1}{2}=0.5[/tex]

Answer:

0.5 0.5

Step-by-step explanation:

because it is logically correct now deal with it! hehehe have a grate day un like me!;)

the translation should make the equation

g(x)= (x+5)2

Answer:

b

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Based on the rate at which the population is decreasing, we can calculate that population in 2008 is A. 1,200 people

The population after a certain number of years is:

= Population now x (1 - rate) ^ number of years

The number of years is:

= 2008 - 2000

= 8 years

The population in 2008 is therefore:

= 1,300 x ( 1 - 1%)⁸

= 1,199.57

= 1,200 people

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Answer:

(x + 1) is a factor of f(x).

Step-by-step explanation:

Please share the answer choices.  Thank you.

If –1 is a root of f(x), which of the following must be true?  

(x + 1) is a factor of f(x).

Answer:

228.8 meters

Step-by-step explanation:

y = -0.04 x² + 9.1 x + 11.9

When the rocket lands, y = 0:

0 = -0.04 x² + 9.1 x + 11.9

Solving for x, start by multiplying by -1:

0 = 0.04 x² - 9.1 x - 11.9

Multiply by 100:

0 = 4x² - 910 x - 1190

Solve with quadratic formula:

x = [ -b ± √(b² - 4ac) ] / 2a

x = [ 910 ± √((-910)² - 4(4)(-1190)) ] / 2(4)

x = [ 910 ± √(847140) ] / 8

x ≈ -1.3, 228.8

Since x can't be negative, x = 228.8 meters.

Answer:

The rocket will land at 208.02 m. Hence, if you are on the same connexus assignment, your answer will be A.

Hope this helps! :D

Answer:

The area is

[tex]A=254.34\ in^2[/tex]

Step-by-step explanation:

The circumference of a circle is given by a following formula:

[tex]C = 2\pi r[/tex]

Where r is the radius of the circumference.

In this case we know that

[tex]C = 2\pi r=56.52\ in[/tex]

We solve the equation for r

[tex]C = 2\pi r=56.52\ in[/tex]

[tex]2\pi r=56.52\\\\r=\frac{56.52}{2\pi}\\\\r=9\ in[/tex]

The area of a circumference is given by the following formula

[tex]A=\pi r^2[/tex]

Now we substitute the value of r in the equation to find the area

[tex]A=\pi (9)^2[/tex]

[tex]A=3.14* (9)^2[/tex]

[tex]A=254.34\ in^2[/tex]

Answer:

x = 12z + 1  and y = 10z - 1

Step-by-step explanation:

To solve the system of equations, we can use the substitution method

If we call

3x - 4y + 4z = 7 I

x - y - 2z = 2 II

2x - 3y + 6z = 5 III

Clearing II  x = 2 + y + 2z

Now, replacing II in III

2(2 + y + 2z) - 3y +6z = 5

4 + 2y + 4z - 3y + 6z = 5

10z - y = 1 from here y = 10z - 1

Finally, replacing y in I

3x - 4(10z - 1) + 4z = 7

3x -40z + 4 + 4z = 7

3x - 36z = 3

3x = 36z + 3

x = 12z + 1

Done