The most common ages of children that use the library are

Answer: [tex]f(x)=2x^2+5[/tex]

Step-by-step explanation:

First integrate f'(x) so we can find the funtion f(x):

[tex]4\int\limits {x} \, dx =4[\frac{1}{2} x^2]=2x^2+C=f(x)[/tex]

The initial conditions say that when x = 0, the function equals 5. Let's write that down:

[tex]f(0)=5=2(0^2)+C=C[/tex]

Therefore, the integration constant 'C' must equal 5. This means that our function is:

[tex]f(x)=2x^2+5[/tex]

General form of a quadratic equation: [tex]ax^2+bx+c[/tex]

  ⇒ since the equation: [tex]-x^2-2x+8[/tex]

     ⇒ so:

To calculate the x-coordinate of the vertex

  ⇒use x = [tex]-\frac{b}{2a}[/tex]   <--- this is a property that helps you find the vertex of the

                                 quadratic

      x = [tex]-\frac{(-2)}{2*(-1)} =-1[/tex]

Since x = -1:

    ⇒ we can plug in this x-value into the original equation to find the y-

         value

          [tex]y =-(-1)^2-2(-1)+8=-1+2+8=9[/tex]

So the coordinate of the vertex: (-1,9)

Hope that helps!

Answer:

4*10 = 40

43/5 = 8.6

40 + 8.6 = 48.6 candy in total.

Answer:

-30

Step-by-step explanation:

Using 'y' is vary inversely to 'x', the value of x₂ = -27.

The word inverse in mathematics "a function or operation which reverses the order or operation of another function or operation".

According to the question,

x₁ = 36,  y₁ = -6, y₂ = 8 and x₁ is inversely proportional to y₁ which mean

(x₁) (y₁) = k

(36)(-6)  = -216.

Formula for inverse is x = k([tex]\frac{1}{y}[/tex]).

In order to find x₂, x₂ = -216(1/8)

x₂ = -27

Hence, the value of x₂ = -27.

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#SPJ2

Hi there!

We have the numbers:

79  85  98  125  140

From the data, we can see that '98' is the median value as it is exactly in the middle. We can then split the data into equal groups on both sides of the median.

79  85

125  140

Since there are only two numbers, we can find the median of EACH sub-group (Q1 and Q3 respectively) by taking the average.

Q1 = (79 + 85)/2 = 82

Q3 = (140 + 125)/2 = 132.5

The IQR is simply the difference between Q3 and Q1, so:

IQR = 132.5 - 82 = 50.5

Answer:

1/5

Step-by-step explanation:

4/8-3/10=1/5

Answer:

yellow blue green gray black white

Answer:

The answer would be true

Step-by-step explanation:

[tex]1=5-4+3-2-1[/tex]

[tex]1=1+1-1[/tex]

[tex]1=2-1[/tex]

[tex]1=1[/tex]

Answer:

1. Choclate Drink

2. Coffee

3. 19 % difference

4.  1 % difference

5. 42% difference

Step-by-step explanation:

Answer:

Area of a sphere

Radius

15 m

Diameter

30 m

Volume

14,137 m³

Surface to volume ratio

0.2 1/m

Surface area

2,827.4 m²

Step-by-step explanation:

Answer:

f(h + 2) = 2h² +8h - 19

Step-by-step explanation:

f(x) = 2x² - 27

f(h + 2) = 2(h + 2)² - 27

f(h + 2) = 2(h²+4h+4) - 27

f(h + 2) = 2h² + 8h + 8 - 27

f(h + 2) = 2h² +8h - 19

I hope this helps!

Answer:

10 sqrt 3

Step-by-step explanation:

sqrt (30) * sqrt (10) = sqrt (300) = sqrt ( 4 * 25 * 3) = 10 sqrt 3

Answer: 120 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\sf a^{m}*a^{n} =a^{m +n}\\\\a^{\frac{1}{n}}=\sqrt[n]{a}[/tex]

[tex]\sf a^{-n}=\dfrac{1}{a^{n}}\\\\\dfrac{a^{n}}{a^{m}}=a^{n-m}\\\\\\a^{0}=1[/tex]

[tex]\sf (a^{n})^{m} = a^{n*m}\\\\(a^{n}*b^{m})^{p}=a^{np}b^{mp}\\\\(ab)^{n}=a^{n}b^{n}[/tex]

#GH

[tex]\\ \rm\Rrightarrow \dfrac{GH}{FG}=\dfrac{TS}{TU}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{GH}{36}=\dfrac{42}{28}=\dfrac{3}{2}[/tex]

[tex]\\ \rm\Rrightarrow GH=108/2=54[/tex]

#UV

[tex]\\ \rm\Rrightarrow \dfrac{UV}{TU}=\dfrac{JF}{FG}[/tex]

[tex]\\ \rm\Rrightarrow\dfrac{ UV}{28}=\dfrac{63}{36}=\dfrac{21}{12}=\dfrac{7}{4}[/tex]

[tex]\\ \rm\Rrightarrow UV=7(28)/4=7(7)=49[/tex]

#VW

[tex]\\ \rm\Rrightarrow \dfrac{VW}{SW}=\dfrac{IJ}{IH}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{VW}{35}=\dfrac{27}{45}=\dfrac{3}{5}[/tex]

[tex]\\ \rm\Rrightarrow VW=3(35)/5=3(7)=21[/tex]

FGHIJ ≅ UTSWV

making proportional equations

Answer:

I guess it is $105.Not so sure about my answer...

Answer:

12x + 16y = 3700

x + y = 250

x = 75 students

y = 175 adults

Step-by-step explanation:

y = 250 - x

12x + 16(250-x) = 3700

12x + 4000 - 16x = 3700

-4x = -300

x = 75

y = 250 - 75

y = 175

Answer:

Step-by-step explanation:

If you multiply top and bottom of 7/2 by 2 as in (7 *2) / (2 * 2) = 14 /4

If you multiply 7/2 top and bottom by 4, you get 28/8

So 14/4 and 28/8 are both the same as 7/2

Step-by-step explanation:

The equation of a circle is

[tex](x - h) {}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]

Where (h,k) is the center and

r is the radius.

Here the center is (-9,10).

To find the radius, find the distance from the center to a point on the circle.

So find the distance between (-9,10) and (-9,7).

[tex]r = \sqrt{(( - 9 - ( - 9) {}^{2} + (10 - 7) {}^{2} } [/tex]

[tex]r = \sqrt{0 + 9} [/tex]

[tex]r = \sqrt{9} [/tex]

[tex]r = 3[/tex]

So the radius is 3 so we plug in

[tex](x - ( - 9) {}^{2} + (y - 10) {}^{2} = {3}^{2} [/tex]

[tex](x + 9) {}^{2} + (y - 10) {}^{2} = 9[/tex]

Answer:

○ [tex]\displaystyle (x + 9)^2 + (y - 10)^2 = 9[/tex]

Explanation:

Accourding to one of the circle equations, [tex]\displaystyle (x - h)^2 + (y - k)^2 = r^2,[/tex]the centre of the circle is represented by [tex]\displaystyle (h, k).[/tex]Moreover, all negative symbols give you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must pay cloce attention to which term gets which symbol. Another thing you need to know is that the radius will ALWAYS be squared, so no matter how your equation comes about, make sure that the radius is squared.

I am joyous to assist you at any time.

To calculate a point estimate, we need to know the sample size.

===========================================================

Explanation:

Let's go through the answer choices.

Answer: 23

Step-by-step explanation:

Answer:

2800 ft³

Step-by-step explanation:

The required volume of given figure is 2800 ft³

I hope it helped you

Answer:

x = 1.

Step-by-step explanation:

[tex]\frac{1}{3}(6x-3)-\frac{1}{4}(20x+8)=-6\\\\[Distribute the first fraction into the parenthesis.]\\((\frac{1}{3}*6x)-(\frac{1}{3}*3))-\frac{1}{4}(20x+8)=-6\\\\2x-1-\frac{1}{4}(20x+8)=-6\\\\[Distribute the second fraction into the parenthesis.]\\2x-1-((\frac{1}{4}*20x)+(\frac{1}{4}*8))=-6\\\\2x-1-5x-2=-6\\\\[Combine like terms.]\\-3x-3=-6\\\\[Add 3 to both sides.]\\-3x=-3\\\\[Divide both sides by -3.]\\x=1[/tex]

Answer:

350 points are possible

Step-by-step explanation:

You take 329 divided by 94% or .94 to get 350.

100% of 350 is 350

To double check, 94% of 350 is 329 & 6% of 350 is 21.  329 +21 = 350

Answer:

21 and 35

Step-by-step explanation:

21 for the first box, when it is in parenthesis you multiply each, so then 35 for the second box

7 times 3 then 7 times 5

ok so they raised 12%

12%=12/100=0.12

12% of 552.5=.12 times 552.5=66.3 was raised

552.5-66.3=486.2

divide by 7

486.2/7=69.457 about 69.46

each member must raise at least 69.46

The volume of the cylinder container is the amount of milk in it

The most accurate measurement for the radius is 3 inches

The given parameters are:

The volume of a cylinder is:

V = πr²h

So, we have:

πr² * 8 = 231

Divide both sides by 8π

r² = 9.19

Take the square root of both sides

r = 3.03

Approximate

r = 3

Hence, the most accurate measurement for the radius is 3 inches

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