What are the solutions to the system of equations graphed below?

Answer:

AC = (20+ 10q)

Step-by-step explanation:

Given that,

Total cost, TC = 20q + 10q²

We need to find AC i.e. average cost.

It can be solved as follows :

[tex]AC=\dfrac{TC}{q}\\\\AC=\dfrac{20q + 10q^2}{q}\\\\AC=\dfrac{q(20+ 10q)}{q}\\\\AC={(20+ 10q)}[/tex]

So, the value of AC is (20+ 10q).

Answer:

The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.

Step-by-step explanation:

Volume of a sphere:

The volume of a sphere of radius r is given by:

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

How fast is the volume increasing:

To find this, we have to differentiate the variables of the problem, which are V and r, implicitly in function of time. So

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

The radius of a sphere is increasing at a rate of 2 mm/s.

This means that [tex]\frac{dr}{dt} = 2[/tex]

How fast is the volume increasing (in mm3/s) when the diameter is 100 mm?

Radius is half the diameter, so [tex]r = \frac{100}{2} = 50[/tex]

Then

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt} = 4\pi (50)^2(2) = 62832[/tex]

The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.

Answer:

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Step-by-step explanation:

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Answer: 10

Step-by-step explanation:

4 x 2 x 5 = 40

9 + 2 + 7 + 8 + 4 = 30

40 - 30 = 10

= 10

Answer:

-∞ <y<5

Step-by-step explanation:

The range of the graph is the values that y can take.  The graph can go from negative infinity to 5

-∞ <y<5

Square both sides:

x^2+2sqrt3+3=0

x^2=-2sqrt(3)-3

x=sqrt(2sqrt(3)+3)i

or

x=-sqrt(2sqrt(3)+3)i

Answer:

Bottom left

Step-by-step explanation:

Mark brainliest please

Yes, Lara is correct.

The steps are as follow:

So Lara is correct

Learn more about Congruent triangle here:

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⭕ 17.3

#CARRYONLEARNING

[tex]{hope it helps}}[/tex]

Answer:

7.3 units

Step-by-step explanation:

Hi there!

We're given an angle and one leg of this right triangle and we must solve for the other leg. Given this circumstance, we can use the tangent ratio:

[tex]tan\theta=\frac{opposite}{adjacent}[/tex]

Plug in all values

[tex]tan39=\frac{x}{9}\\9*tan39=x\\7.3=x[/tex]

Therefore, the value of x when rounded to the nearest tenth is 7.3 units.

I hope this helps!

Answer:

The area of the rectangle is increasing at a rate of 169 cm²/s

Step-by-step explanation:

Given;

increase in the length of the rectangle, [tex]\frac{dL}{dt} = 7 \ cm/s[/tex]

increase in the width of the rectangle, [tex]\frac{dW}{dt} = 8 \ cm/s[/tex]

length, L = 15 cm

width, W = 7 cm

The increase in Area is calculated as;

[tex]Area = Length \times Width\\\\A = LW\\\\\frac{dA}{dt} = L(\frac{dW}{dt} )\ + \ W(\frac{dL}{dt} )\\\\\frac{dA}{dt} = 15 \ cm(8\ \frac{ cm}{s} ) \ + \ 7 \ cm(7\ \frac{ cm}{s} ) \\\\\frac{dA}{dt} = 120 \ cm^2/s \ + \ 49 \ cm^2/s\\\\\frac{dA}{dt} = 169 \ cm^2/s[/tex]

Therefore, the area of the rectangle is increasing at a rate of 169 cm²/s

Answer:

7/8, 87.5%, 0.875

Step-by-step explanation:

There is only 1 5 on the spinner. And there are 8 equal sections.

The probability of spinning a 5 is 1/8.

So, the probability of not spinning a 5 is 7/8

To find the Percent and Decimal form, divide 7 by 8.

You get 0.875-the decimal form

Move the decimal point 2 places to the right:

87.5

Add the percent symbol, and you're done!

I hope this helps!

Tell me if you need more explaining :)

Answer:

No it is not since there is 15 defectice parts in 2machines and there is 8 broken parts in the one machine

Hope This Helps!!!

The number of new professors needed to hire to keep the ratio of students and professors the same is 16.66  professors.

Given,

A small college has 1200 students and 80 professors.

The college is planning to increase enrollment to 1450 students next year.

We need to find how many new professors should be hired to keep the

ratio of students to professors the same.

If the two ratios are the same then we called it that they are in proportion.

Example:

4/6 = 10/15

2/3 = 2/3

Find the ratio between the students and professors before the increase in enrollment.

= Number of students / Number of professors

= 1200 / 80

Dividing by 8

= 150 / 10

= 15 / 1

This means one professor for 15 students.

Find the number of students after the increase in enrollment.

= 1450

Find the number of new students enrolled.

= 1450 - 1200

= 250

Since the ratio between the students and professor is 15 students for one professor.

For 250 new students, the number of new professors we need is:

= 250 ÷ 15

= 16.66

This means we need around 16.66 new professors.

Thus the number of new professors needed to hire to keep the ratio of students and professors the same is 16.66 professors.

Learn more about finding the number of students in a college with students and professors relation is given here:

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Answer:

LP ⊥ PN

Step-by-step explanation:

Given

[tex]L = (-4, 1)[/tex]

[tex]M = (2, 4)[/tex]

[tex]N = (3, 2)[/tex]

[tex]P = (-3, -1)[/tex]

See attachment

Required

What proves LMNP is a rectangle

The additional information needed is LP ⊥ PN

Because:

[tex](a)\ LM= \sqrt{45}; MN = \sqrt{5}[/tex]

This can be true for other shapes, such as trapezoid, etc.

[tex](b)\ m(LP) = m(MN) = -2[/tex]

The slopes of LP and MN will be the same because both sides are parallel; However, this is not peculiar to rectangles alone. Same as option (c)

(d) LP ⊥ PN

This must be true i.e. LP must be perpendicular to PN

Answer:

d

Step-by-step explanation:

Answer:

Reduce if needed, asked or necessary

Step-by-step explanation:

1. 4/10

2. 2/6

3. 4/10

4. more likely

Answer:

Since Probability Is Usually Written In Fraction Form OR Ratios

(Although It Really Doesn't Matter):

1.  4/10 (2/5)

2.  2/6  (1/3)

3.  6/10 (3/5)

(All Fraction Form)

Last Question:

I can't really see the bottom but probably its 'More likely' since you can already see a bunch of red marbles.

Step-by-step explanation:

This is the basic fraction form :  ____ / ____

Based on what they ask, like the probability of picking out a black marble, count the number of black marbles in the particular bag and put that number as the numerator. The denominator is the total amount of marbles in that particular bag. Hope this helps!

Answer:

Area of a trapezoid= (big base+small base)/2 x height

A=(67+54)/2 x 18

A=60.5 x 18

A=1089  

Answer:

A, C, D, F

Step-by-step explanation:

Given the expression : (3/5)³

Recall :

a^b where, a = base ; b = exponent

In ; (3/5)^3

Base = 3/5 ; exponent = 3

Similarly ;

a^b = a in b places

(3/5)^3 = (3/5) * (3/5) * (3/5)

(3/5) * (3/5) * (3/5) = (3*3*3) / (5*5*5) = 27/125

Hence, A, C, D and F are all correct

Answer:

[tex]\frac{257357187500}{19683}[/tex]

Step-by-step explanation:

We can convert these mixed fractions to ordinary fractions.

[tex]4(1/3)=\frac{(4*3)+1}{3}=\frac{13}{3}[/tex]

[tex]3(1/3)=\frac{10}{3}[/tex]

[tex]3(1/2)=\frac{7}{2}[/tex]

[tex]9(3/4)=\frac{39}{4}[/tex]

Then we have:

[tex]\frac{13}{3}*(\frac{10}{3}*\frac{7}{2})^{7}*\frac{4}{39}[/tex]

[tex]\frac{257357187500}{19683}[/tex]

I hope it helps you!

Answer:

Hello good evening friend

Answer:

here is your answer

hope this will help for you

Answer:

(-1, -6)

Step-by-step explanation:

This a term in this function is not negative, which would make it be flipped over the x-axis. Therefore this function takes the typical parabola shape, and it will have a minimum point.

To find the x-value of the minimum use the formula -b / 2a.

-12 / 2(6) = -1

Then plug in the x-value and find the y-value for this function

f(-1) = 6(-1)^2 + 12(-1) = -6

Answer:

-12.15

Step-by-step explanation:

2(a+b)=-8.1

a+b=-4.05

3(a+b)=3(-4.05)

3(a+b)=-12.15

Answer:

y = 2x - 5

Step-by-step explanation:

We can use trial and error to solve this.

4 = x and 3 = y

y = x + 3: 4 + 3 = 7 ≠ 3 (not what we want)

y = 3x + 4: (3 x 4) - 4 = 8 ≠ 3 (not what we want)

y = 2x - 5: (2 x 4) - 5 = 3 (what we want)

y = 2x - 1: (2 x 4) - 1 = 7 ≠ 3 (not what we want)

The answer is y = 2x - 5

Answer:

sorry dko alm hahahahahahahahajshaja

Answer:

d

Step-by-step explanation:

because u did the math for you

Step-by-step explanation:

28:20

Once simplified its 7:5

Answer:

8ft

Step-by-step explanation:

We need to find out the length of the other leg of the triangle . Since it is a right angled triangle, we can use Pythagoras Theorem here , as,

[tex]\sf\implies h^2 = p^2 + b^2 \\\\\sf\implies (17ft)^2= p^2 + (15ft)^2\\\\\sf\implies 289 ft^2 - 225ft^2 = b^2 \\\\\sf\implies b^2 = 64 ft^2\\\\\sf\implies \underline{\underline{ base = 8 \ ft }}[/tex]

Answer:

The value of the test statistic is [tex]z = 1.34[/tex]

Step-by-step explanation:

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

Test if the mean is equal to 5:

This means that the null hypothesis is [tex]\mu = 5[/tex]

A simple random sample of wrist breadths of 40 women has a mean of 5.07 cm. The population standard deviation is 0.33 cm.

This means that [tex]n = 40, X = 5.07, \sigma = 0.33[/tex]

Find the value of the test statistic?

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{5.07 - 5}{\frac{0.33}{\sqrt{40}}}[/tex]

[tex]z = 1.34[/tex]

The value of the test statistic is [tex]z = 1.34[/tex]