Jim Smith is a salesman who receives a $1,100 draw per week. He receives a 12% commission on all sales. Sales for Jim were $205,000 for the month. Assuming a four-week month. Jim's commission after the draw is

Answer:

The rate is 13 miles per hour

Step-by-step explanation:

* Lets explain how to solve the problem

- Jim lives three miles east of State College

- At noon, he leaves his house and begins to walk due east at a

 constant speed of 2 miles per hour

- Annie lives four miles north of State College

- At noon, she leaves her house and begins to bicycle due north at a

 constant speed of 8 miles per hour

- The east is perpendicular to the north

* Lets solve the problem

∵ At noon means 12 p.m

∵ They moved till 1 p.m

∵ Jim walked for 1 hour and Annie bicycled for 1 hour

∵ The rate of Jim is 2 miles per hour

∵ The rate of Annie is 8 miles per hour

- The distance = rate × time

∴ Jim walked = 2 × 1 = 2 miles

∴ Annie bicycled = 8 × 1 = 8 miles

- Lets calculate the distance of Jim from the State College till his

 position at 1 p.m

∵ Jim lives three miles east of State College

∴ His distance at 1 p.m = 3 + 2 = 5 miles east

- Lats calculate the distance of Annie from the State College till her

 position at 1 p.m

∵ Annie lives four miles north of State College

∴ Her distance at 1 p.m = 4 + 8 = 12 miles North

- Lets find the distance between them at 1 p.m

∵ The north ⊥ east

- Use Pythagoras Theorem to find the distance

∴ The distance = √(5² + 12)² = √(25 + 144) = √169 = 13 miles

- The rate = distance/time

∵ The distance between them is 13 miles in 1 hour

∴ The rate = 13/1 = 13 miles per hour

* The rate is 13 miles per hour

Answer:

is the equal sign supposed to be there? if it wasnt then answer would be 42x^6y^11

Step-by-step explanation:

Answer:

4 units

Step-by-step explanation:

just took a quiz and got it right

Answer: 4

Step-by-step explanation:

took the test

Answer:

4x+5y-34=0

Step-by-step explanation:

The slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.

My goal is to put in in this form first.  Then I will aim to put it in general form, ax+by+c=0.

So let's give it a go:

m is the change of y over the change of x.

To compute this I'm going to line my points up and subtract vertically, then put 2nd difference over 1st difference.  Like this:

( 1 , 6)

-(6 , 2)

----------

-5   4

So the slope is 4/-5 or -4/5.

So m=-4/5.

Now we are going to find b given y=mx+b and m=-4/5 and we have a point (x,y)=(1,6) [didn't matter what point you chose here].

6=-4/5 (1)+b

6=-4/5    +b

Add 4/5 on both sides:

6+4/5=b

30/5+4/5=b

34/5=b

So the y-intercept is 34/5.

The equation in slope-intercept form is:

y=-4/5 x + 34/5.

In general form, it is sometimes the goal to make all of your coefficients integers so let's do that.  To get rid of the fractions, I'm going to multiply both sides by 5.  This clears the 5's that were on bottom since 5/5=1.

5y=-4x+34

Now add 4x on both sides:

4x+5y=34   This is standard form.

Subtract 34 on both sides:

4x+5y-34=0

Answer:

The second one, with the 0-5 having 7 students.

Step-by-step explanation:

Add up the number of students who fell into each category (0-5, 6-11, etc), then plot them as shown.

The second one, with the 0-5 having 7 students.

Add up the number of students who fell into each category (0-5, 6-11, etc), then plot them as shown.

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

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Answer:

-x < 8

Step-by-step explanation:

-x/4 < 2

-x/4 (x4) < 2 (4)

-x < 8

Answer:

It's asking for you to calculate the volume of a cylinder and multiply it by 2/3. This is because the question is asking how much water is in a cylindrical vase with the height and radius.

The formula to calculate the volume of a cylinder is : 3.14 (r^2) (h)

R being the radius and H being the height.

Plug in the values then multiply it all by 2/3

Hoped this help you solve your problem.

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=5\\ h=14 \end{cases}\implies V=\pi (5)^2(14)\implies V=350\pi \\\\\\ \stackrel{\pi =3.14}{V=1099}~\hfill \stackrel{\textit{how much is }\frac{2}{3}\textit{ of that?}}{1099\cdot \cfrac{2}{3}\implies \cfrac{2198}{3}}\implies \stackrel{\textit{rounded up}}{732.7}[/tex]

Answer:

segment SV

Step-by-step explanation:

Observing the figure

we know that

The side that is common to triangle SUV and triangle VTS is only the segment SV

There are no common angles to triangle SUV and triangle VTS

therefore

The answer is the segment SV

Answer:

[tex]\huge \boxed{y=-2}[/tex]

Step-by-step explanation:

First thing you do is switch sides.

[tex]\displaystyle 2y-3=-7[/tex]

Then add 3 from both sides of equation.

[tex]\displaystyle 2y-3+3=-7+3[/tex]

Simplify.

[tex]\displaystyle 2y=-4[/tex]

Divide by 2 from both sides of equation.

[tex]\displaystyle \frac{2y}{2}=\frac{-4}{2}[/tex]

Simplify, to find the answer.

[tex]\displaystyle -4\div2=-2[/tex]

[tex]\large \boxed{y=-2}[/tex], which is our answer.

Hope this helps!

−7=2y−3

Step 1: Flip the equation.

2y−3=−7

Step 2: Add 3 to both sides.

2y−3+3=−7+3

2y=−4

Step 3: Divide both sides by 2.

2y/2=-4/2

y=−2

Answer:

1.584

Step-by-step explanation:

1.584 = 3.96 × 0.4

Answer:

3.96*0.4 is 1.584

Answer:

i think the answer is 7776

for two dice its 6x6 36 then 36×6 216 then 216×6 1296 then 1296×6 7776

Answer: 7776 possible outcomes

Step-by-step explanation:

You know that each dice has 6 possible results.

1, 2, 3, 4 , 5 , 6

Then, if you throw 2 dice, the possible results are 6(for the first one)*6(for the second one) = 6*6 = 36

then, as you add another die, you add another 6 to that equation, this means that for 5 dice we have

combinations = 6*6*6*6*6 = 6^5 = 7776

But in this situation most of the numbers can be repeated, for example, then number 6, can be made from (1 + 1 + 1 + 1 + 2), (1 + 2 + 1 + 1 + 1), (1 + 1 + 1 + 2 + 1 +1)

etc, this means that the die that rolls a 2 can change, but the end result of the addition is the same, in this case the total range of possible values is the amount of dice times the biggest value minus the amount of dice times the smallest value:

5*6 - 5*1 = 30 - 5 = 25 possible results

So you have 7776 combinations that give a only 25 possible results (a number between 5 and 30)

Answer:B 42

Step-by-step explanation:

V=pi/4 x D^2 x H

3.14/4 x 36 x 1.5 = 42 ft^3

Answer:

B) 42

Step-by-step explanation:

The area of a cylinder is pi*r^2*h where r is the radius and h is the height. Plugging in 3 for the radius(radius=diameter/2) and 1.5 for height you get area=pi*9*1.5. Assuming pi as 3.14 you get 3.14*9*1.5 which is 42.39 which is approx. 42.

Answer:

x + 5y = 7

Step-by-step explanation:

You can find which one is correct by plugging in -3 for each x value and then solving for y.

x + 5y = 7

(-3) + 5y = 7

5y = 10

y = 2

When x = -3, y=2

(2) + 5y = 7

5y = 5

y = 1

When x=2, y=1

The equation of straight line that represents a line that passes through points (−3, 2) and (2, 1) is Option (D) x + 5y = 7.

The equation of a straight line passing through the points (x1,y1) and (x2,y2) and having slope m is given by -

y - y1 = m(x - x1) .

The slope m, can be calculated as m =  (y2 - y1)/(x2 - x1) .

Thus the equation of straight line in slope intercept form is -

[tex]y - y1 = \frac{y2 - y1}{x2 - x1} (x - x1)[/tex]

Given points are (-3,2) and (2,1) .

We have x1 = -3 , x2 = 2 , y1 = 2 , y2 = 1

Slope (m) = (1 - 2)/(2 - (-3)) = -1/5

Putting the required values to find the equation of straight line in slope intercept form -

⇒ y - 2 = (-1/5)*(x - (-3))

⇒ (y - 2)*5 = -1*(x + 3)

⇒ 5y - 10  =  -x - 3

∴  x  +  5y = 7

The required equation is Option (D) x + 5y = 7.

Thus, the equation of straight line that represents a line that passes through points (−3, 2) and (2, 1) is Option(D) x + 5y = 7.

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Answer:

D. Negative slope

Step-by-step explanation:

Since it is a proportional relation, it must be linear. A line has a slope. Since it is decreasing, it is a negative slope.

Answer:

A

Step-by-step explanation:

Given the 2 equations

y = x² - 4x + 8 → (1)

y = 2x + 3 → (2)

Since both express y in terms of x we can equate the left sides, that is

x² - 4x + 8 = 2x + 3 ( subtract 2x + 3 from both sides )

x² - 6x + 5 = 0 ← in standard form

(x - 1)(x - 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 5 = 0 ⇒ x = 5

Substitute these values into (2) for corresponding values of y

x = 1 : y = (2 × 1) + 3 = 2 + 3 = 5 ⇒ (1, 5)

x = 5 : y = (2 × 5) + 3 = 10 + 3 = 13 ⇒ (5, 13)

Solutions are (1, 5) and (5, 13)

Answer:

A. [tex](1,5)[/tex] and [tex](5,13)[/tex]

Step-by-step explanation:

We have been given a system of equations. We are asked to find the solution of our given system.

[tex]\left \{ {{y=x^2-4x+8}\atop {y=2x+3}} \right.[/tex]

Equate both equations:

[tex]x^2-4x+8=2x+3[/tex]

[tex]x^2-4x-2x+8-3=2x-2x+3-3[/tex]

[tex]x^2-6x+5=0[/tex]

Split the middle term:

[tex]x^2-5x-x+5=0[/tex]

[tex]x(x-5)-1(x-5)=0[/tex]

[tex](x-5)(x-1)=0[/tex]

Use zero product property:

[tex](x-5)=0\text{ (or) }(x-1)=0[/tex]

[tex]x=5\text{ (or) }x=1[/tex]

Now, we will substitute both values of x, in our given equation to solve for y.

[tex]y=2x+3[/tex]

[tex]y=2(1)+3[/tex]

[tex]y=2+3[/tex]

[tex]y=5[/tex]

One solution: [tex](1,5)[/tex]

[tex]y=2x+3[/tex]

[tex]y=2(5)+3[/tex]

[tex]y=10+3[/tex]

[tex]y=13[/tex]

2nd solution: [tex](5,13)[/tex]

Therefore, option A is the correct choice.

Answer:

y = 4sin [(1/2)t - (4/3)π ]  - 2

Step-by-step explanation:

For this question, do not be intimidated by the terminology, just realize the following:

for y = a sin [ (2π/T) t ]

a = amplitude = given as 4

T = period = given as 4π

phase shift is simply horizontal shift, positive values means the graph moves by that amount to left and negative values means the graph moves to the right.

vertical shift ... is well a shift vertically. positive values move the graph up vertically and negative values move the graph down vertically.

so... if we start with the basic formula:

y = a sin [ (2π/T) t ]

given a = 4 and T = 4π (substitute these values into the formula)

y = (4) sin [ (2π/4π) t ] = (4) sin [ (1/2) t ]

y = 4sin [(1/2)t ]

Now for the shifts:

given phase shift, aka horizontal shift is -(4/3)π, equation becomes

y = 4sin [(1/2)t - (4/3)π ]

given vertical shift is -2, the equation simply becomes

y = 4sin [(1/2)t - (4/3)π ]  - 2

Answer: Hello there!

here we have two equations:

1) x + 3y = 7

2) 2x + 4y = 8

a) first we want to isolate x in the first equation:

x + 3y = 7

x = 7 -3y

done!

b) now we want to replace it in the second equation, and in this way get a equation that depends only on the variable y.

2x + 4y = 8

2(7 - 3y) + 4y = 8

c) now we sole this equation and obtain the value of y.

14 - 6y + 4y = 8

14 - 2y = 8

-2y = 8 - 14 = -6

y = 6/2 = 3

d) now we have the value of y, and we can substitute it on the equation that we got in the part a)

x = 7 - 3y

x = 7 - 3*3 = 7 - 9 = -2

e) now we knowt that x = -2 and y = 3, then the pair (x,y) can be written as:

(-2,3).

The solution to the system of equations, as an ordered pair, is (-2,3).

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives step by step of the solution for the system of linear equations. The exercise found the value of y, then you should find the value of x.

The step 4 of the question shows: x = 7 − 3(3). Therefore:

x = 7 − 3(3)

x = 7 − 9

x= -2

You can check the values found for x and y from equation 2x + 4y = 8. Therefore:

2*(-2)+4*(3)

-4+12=8

Thus, the values found for x and y are correct.

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Answer:

There are 97920 ways to formed the committee

Step-by-step explanation:

* Lets solve explain the combination

- combination is a collection of the objects where the order doesn't

 matter

- Combinations is nCr, where n is the total number and r is the number  

 of the choices

# Example: chose a group of three students from the group of 10

  students  n = 10 and r = 3,then 10C3 is 120

* Lets solve the problem

- The club has 30 members

- There are 3 lawyers, 4 teachers , 5 doctors in the group

- We want to formed a committee of 8 contains 1 teacher, 2 lawyers,

  2 doctors

∵ There are 4 teachers, we want to chose 1 of them

∴ 4C1 = 4

∵ There are 3 lawyers, we want to chose 2 of them

∴ 3C2 = 3

∵ There are 5 doctors, we want to chose 2 of them

∴ 5C2 = 10

- To find how many ways multiply 4C1 by 3C2 by 5C2

∵ 4C1 × 3C2 × 5C2 = 4 × 3 × 10 = 120

∵ The total numbers of the teachers, the lawyers and the doctors is

   4 + 3 + 5 = 12 members from the 30 members

∴ There are 120 ways to chose 5 members from 12 members

∵ The committee has 8 members

∴ We want to chose another 3 from the rest of the members

∵ The rest of the members = 30 - 12 = 18

∴ We must to find 18C3

∵ 18C3 = 816

- To find the total ways of the 8 members multiply the ways of the 5

  members and the 3 members

∴ The total number of ways = 120 × 816 = 97920

∴ There are 97920 ways to formed the committee

the answer is 63 because 63*2=126 and 126+54=180 and all triangles add up to 180

Answer:

B) 63 degrees

Step-by-step explanation:

All triangles equal up to 180 degrees so you would subtract the lengths you are given by 180.

So 180 - 54 = 126

Now you would divide 126 by 2 since this is an isosceles triangle. Isosceles triangles have two equal sides so 126 divided by 2 equals 63 degrees.

So y = 63 degrees

Answer:  The expressions for the length and width of the new patio are

[tex]\ell=x+4,~~w=x-4.[/tex]

And the area of the new patio is 384 sq. feet.

Step-by-step explanation:  Given that Stephen has a square brick patio. He wants to reduce the width by 4 feet and increase the length by 4 feet.

The length of one side of the square patio is represented by x.

We are to write the expressions for the length and width of the new patio and then to find the area of the new patio if the original patio measures 20 feet by 20 feet.

Since Stephen wants to reduce width of the patio by 4 feet, so the width of the new patio will be

[tex]w=(x-4)~\textup{feet}.[/tex]

The length of the patio is increased by 4 feet, so the length of the new patio will be

[tex]\ell=(x+4)~\textup{feet}.[/tex]

Now, if the original patio measures 20 feet by 20 feet, then we must have

[tex]w=x-4=20-4=16~\textup{feet}[/tex]

and

[tex]\ell=x+4=20+4=24~\textup{feet}.[/tex]

Therefore, the area of the new patio is given by

[tex]A_n=\ell \times w=24\times16=384~\textup{sq. feet}.[/tex]

Thus, the expressions for the length and width of the new patio are

[tex]\ell=x+4,~~w=x-4.[/tex]

And the area of the new patio is 384 sq. feet.

Final answer:

Stephon is altering his square patio's dimensions by reducing the width by 4 feet and increasing the length by 4 feet. For an original side length of 20 feet, the new dimensions are 24 feet by 16 feet, resulting in an area of 384 square feet.

Explanation:

Stephon has a square brick patio and is planning on changing its dimensions. Initially, the patio is a square with each side measuring x feet. To find the expressions for the new length and width of the patio after the alterations:

Given that the original side length of the patio is 20 feet, we can substitute this value into the expressions:

To find the area of the new patio, multiply the new length by the new width:

Area = Length × Width = 24 feet × 16 feet = 384 square feet.

Answer:

B. 43.3 cm

Step-by-step explanation:

The formula for the circumference of a circle is [tex]2 \pi r[/tex] if you want it in terms of the radius but you can also say the circumference is [tex]d \pi[/tex] if you want it in terms of the diameter since you know the radius is twice the diameter.

So we are actually given the diameter which is 13.8 cm.

So the Circumference is just pi times that.

So I'm going to put pi times 13.8 in my calculator and select the closest answer.

13.8*pi=43.35 cm.

Answer:

the answer is B

Step-by-step explanation:

Answer:

The correct  answer is the option "B":

B.(-x-6i)(x-6i)

The expression -x^2-36 can be factored as a difference of squares and is equivalent to -(x+6)(x-6).

The expression -x^2-36 can be equivalent to other algebraic forms depending on the manipulation or factoring techniques applied. To simplify or manipulate this expression, one can factor it as the difference of squares. The difference of squares is a pattern where you have an expression in the form of a^2 - b^2, which can be factored into (a+b)(a-b). In the case of -x^2-36, it can be written as -(x^2 - 36), which then can be factored as -(x+6)(x-6). This follows the pattern of a difference of squares since x^2 is the square of x, and 36 is the square of 6.

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Answer:

C.  2x - 3(-3x - 4) = -21.

Step-by-step explanation:

y + 3x = -4

2x - 3y = -21

From the first equation y = -3x - 4.

Substituting this for y in the second equation, we have:

2x - 3(-3x - 4) = -21.

The indicated z score is -1.08

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.8599.

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1 and it is given by the probability density function and distribution function

. Areas of the normal distribution are often represented by tables of the standard normal distribution.

Shaded area is 0.8599 according to the attachment. Then the lookup area is

Find the indicated z score.

[tex]Z = \frac{ (X - \mu)}{\sigma}[/tex]

where Z is the value on the standard normal distribution, X is the value on the original distribution, μ is the mean of the original distribution, and σ is the standard deviation of the original distribution.

According to the picture below z is

[tex]Z = \frac{ (0.8599 - 0.5)}{1} = 0.3599[/tex]

Then if we look at the table, the z score is -(1.0 + 0.08) = -1.08 (C)

The normal distribution is the most important probability distribution in statistics because it fits many natural phenomena. It learns about heights, blood pressure, measurement error, and IQ scores. The normal distribution is also known as the Gaussian distribution and the bell curve.

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To find the indicated z-score, we use the z-score formula and refer to the z-table. The z-score that corresponds to a shaded area of 0.8599 is approximately 1.28.

The z-score formula is used to find the indicated z-score. In this case, since the shaded area is 0.8599, we need to find the z-score that corresponds to this area. Referring to the z-table, we find that a z-score of approximately 1.28 corresponds to an area of 0.9. Therefore, the indicated z-score is 1.28.

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Answer:

The Answer is A, a line segment that has both endpoints on a circle.

Step-by-step explanation:

Answer:

Option A: A chord is a line segment that has both endpoints on a circle.

Step-by-step explanation:

A chord of a circle is a line segment whose endpoints both lie on the circle.

In general a chord is a line segment that connects two distinct points on a circle. Its also called a secant in a circle, that intersects the circle at exactly two points.

Here, option A is correct.

For this case we have that by definition, the point-slope equation of a line is given by:

[tex]y-y_ {0} = m (x-x_ {0})[/tex]

Where:

m: It is the slope of the line

[tex](x_ {0}, y_ {0}):[/tex] It is a point through which the line passes

We have as data that:

[tex](x_ {0}, y_ {0}) = (1, -4)[/tex]

Substituting:

[tex]y - (- 4) = m (x-1)\\y + 4 = m (x-1)[/tex]

All that remains is to replace the value of the slope.

Answer:

[tex]y + 4 = m (x-1)[/tex]

Answer:

Step-by-step explanation:

note :

the area of a circle  is : A= π×r²    ....r : radius and : D=2r   ... D : diameter

47) D = 10 cm      r= 10cm/2 = 5 cm

A=π×r²  = 3.1448×5²  =78.62cm²

48) A= 3.1448×2²= 12.58cm²