This graph shows the solution to which inequality?
(32)
(-3.-6);
A ys 1/x - 2
B. y> fx-2
C. yzfx-2
***-2

Answer:

Step-by-step explanation:

Um where is the diagrahm

Answer:

m>-7

Step-by-step explanation:

expand

-10m+15-4<81

-10m+11<81

collect like terms

-10m<81-11

-10m<70

m>-7

Step-by-step explanation:

x²-xy-xy+y²

x²+2xy+y²

hope it helps

Answer:

A. 2x + 1

Step-by-step explanation:

f(x) = 2x + 7

g(x) = x - 3

To find f(g(x)), substitute x = x - 3 into f(x) = 2x + 7

Thus:

f(g(x)) = 2(x - 3) + 7

f(g(x)) = 2x - 6 + 7

Add like terms

f(g(x)) = 2x + 1

9514 1404 393

Answer:

  D.  f^-1(x) = 3 -7x

Step-by-step explanation:

Solve x = f(y) for y to find the inverse function.

  x = f(y)

  x = (3 -y)/7 . . . . . . use the function definition

  7x = 3 -y . . . . . . . .multiply by 7

  y = 3 -7x . . . . . . . add y-7x to both sides

Then the inverse function is ...

  [tex]\boxed{f^{-1}(x)=3-7x}[/tex]

Step-by-step explanation:

√19200cm²

=138.56cm

then the highest possible volume

=(138.56)³

=2660195.926cm³

The largest possible volume of the box is; V = 25600 cm³

Let us denote the following of the square box;

Length = x

Width = y

height = h

Formula for volume of a box is;

V = length * width * height

Thus; V = xyh

but we are dealing with a square box and as such, the base sides are all equal and so; x = y. Thus;

V = x²h

The box has an open top and as such, the surface are of the box is;

S = x² + 4xh

We are given S = 19200 cm². Thus;

19200 = x² + 4xh

h = (19200 - x²)/4x

Put (19200 - x²)/4x for h in volume equation to get;

V = x²(19200 - x²)/4x

V = 4800x - 0.25x³

To get largest possible volume, it will be dimensions when dV/dx = 0. Thus;

dV/dx = 4800 - 0.75x²

At dV/dx = 0, we have;

4800 - 0.75x² = 0

0.75x² = 4800

x² = 4800/0.75

x² = 6400

x = √6400

x = 80 cm

From h = (19200 - x²)/4x;

h = (19200 - 80²)/(4 × 80)

h = (19200 - 6400)/3200

h = 4 cm

Largest possible volume = 80² × 4

Largest possible volume = 25600 cm³

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Answer:

7 : 8

Step-by-step explanation:

that is the procedure above

Answer:

[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]

Step-by-step explanation:

Given

[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]

[tex]P(1) = 2[/tex]

Required

The solution

We have:

[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]

[tex]\frac{dP}{dt} = (Pt)^\frac{1}{2}[/tex]

Split

[tex]\frac{dP}{dt} = P^\frac{1}{2} * t^\frac{1}{2}[/tex]

Divide both sides by [tex]P^\frac{1}{2}[/tex]

[tex]\frac{dP}{ P^\frac{1}{2}*dt} = t^\frac{1}{2}[/tex]

Multiply both sides by dt

[tex]\frac{dP}{ P^\frac{1}{2}} = t^\frac{1}{2} \cdot dt[/tex]

Integrate

[tex]\int \frac{dP}{ P^\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]

Rewrite as:

[tex]\int dP \cdot P^\frac{-1}{2} = \int t^\frac{1}{2} \cdot dt[/tex]

Integrate the left hand side

[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{-1}{2}+1} = \int t^\frac{1}{2} \cdot dt[/tex]

[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]

[tex]2P^{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]

Integrate the right hand side

[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{1}{2} +1 }}{\frac{1}{2} +1 } + c[/tex]

[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{3}{2}}}{\frac{3}{2} } + c[/tex]

[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex] ---- (1)

To solve for c, we first make c the subject

[tex]c = 2P^{\frac{1}{2}} - \frac{2}{3}t^\frac{3}{2}[/tex]

[tex]P(1) = 2[/tex] means

[tex]t = 1; P =2[/tex]

So:

[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1^\frac{3}{2}[/tex]

[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1[/tex]

[tex]c = 2\sqrt 2 - \frac{2}{3}[/tex]

So, we have:

[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex]

[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + 2\sqrt 2 - \frac{2}{3}[/tex]

Divide through by 2

[tex]P^{\frac{1}{2}} = \frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3}[/tex]

Square both sides

[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]

Answer:

There are 256 pairs in all.

Answer: [tex]n=13[/tex]

Step-by-step explanation:

Given

Sum of the first 10 terms is equal to sum of 20, 21, and 22 term

[tex]\Rightarrow \dfrac{10}{2}[2a+(10-1)d]=[a+19d]+[a+20d]+[a+21d]\\\\\Rightarrow 5[2a+9d]=3a+60d\\\Rightarrow 10a+45d=3a+60d\\\Rightarrow 7a=15d[/tex]

No of terms to give a sum of 960

[tex]\Rightarrow 960=\dfrac{n}{2}[2a+(n-1)d]\\\\\Rightarrow 1920=n[2a+(n-1)\cdot \dfrac{7}{15}a]\\\\\Rightarrow 28,800=n[30a+7a(n-1)]\\\\\Rightarrow a=\dfrac{28,800}{n[30+7n-7]}\\\\\Rightarrow a=\dfrac{28,800}{n[23+7n]}[/tex]

Value of first term is less than 20

[tex]\therefore \dfrac{28,800}{n[23+7n]}<20\\\\\Rightarrow 28,800<20n[23+7n]\\\Rightarrow 0<460n+140n^2-28,800\\\Rightarrow 140n^2+460n-28,800>0\\\\\Rightarrow n>12.79\\\\\text{For integer value }\\\Rightarrow n=13[/tex]

Answer:

15

Step-by-step explanation:

In the previous answer halfway through they used the equation: 960 = (n÷2)×(2a+(n-1)×(7a÷15))

Using this equation we can substitute an number to replace n, the higher the number is the smaller a would be.

When we substitute 15 into a, then it leaves us with the answer to be a = 15 which is a positive integer and also is smaller than 20, this then let’s us know that 15 is how many terms can be summed up to make 960.

To double check this answer you can find that d = 7 by changing the a into 15 in the formula 7a/15 (found in the previous answer.

Then in the expression: (n÷2)×(2a+(n-1)×d)

substitute:

n = 14 (must be an even number for the equation to work)

a = 15

d = 7

This will give you an answer of 847, but this is only 14 terms as we changed n into 14. To add the final term you need to complete the following equation: 847+(a+(n-1)×d)

substituting:

n = 15

a = 15

d = 7

This will give you the answer of 960, again proving that it takes 15 terms to sum together to make the number 960.

I hope this has helped you.

P.S. Everything in the previous solution was right apart from the start of the last section and the answer

The function has the characteristics is (b) y= (2x^2 - 8) / (x^2 - 9)

The features are given as:

The function that has the above features is (b).

This is proved as follows:

y= (2x^2 - 8) / (x^2 - 9)

Set the denominator not equal to 0, to determine the domain

x^2 - 9 ≠ 0

Add 9 to both sides

x^2 ≠ 9

Take the square roots

x ≠ ±3 --- domain

Replace ≠ with =

x = ±3 --- vertical asymptote

Set the numerator to 0

2x^2 - 8 = 0

Divide through by 2

x^2 - 4 = 0

This gives

x^2 = 4

Take the square roots

x = 2 ---- horizontal asymptote

Hence, the function has the characteristics is (b) y= (2x^2 - 8) / (x^2 - 9)

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Answer:

She had 8 doubles.

Step-by-step explanation:

This question is solved by a system of equations.

I am going to say that:

x is the number of singles.

y is the number of doubles

z is the number of triples.

46 hits

This means that [tex]x + y + z = 46[/tex]

46 hits totaled 66 bases

This means that:

[tex]x + 2y + 3z = 66[/tex]

4 times as many singles as doubles

This means that [tex]x = 4y[/tex]

So

[tex]x + 2y + 3z = 66[/tex]

[tex]4y + 2y + 3z = 66[/tex]

[tex]6y + 3z = 66[/tex]

And

[tex]x + y + z = 46[/tex]

[tex]4y + y + z = 46[/tex]

[tex]5y + z = 46 \rightarrow z = 46 - 5y[/tex]

Then

[tex]6y + 3z = 66[/tex]

[tex]6y + 3(46 - 5y) = 66[/tex]

[tex]6y + 138 - 15y = 66[/tex]

[tex]9y = 72[/tex]

[tex]y = \frac{72}{9}[/tex]

[tex]y = 8[/tex]

She had 8 doubles.

Answer:

[tex]\frac{28}{n}[/tex]

Step-by-step explanation:

Hello!

[tex]\large\boxed{(x + 2)(x + 3)}[/tex]

x² + 5x + 6

Find two numbers that add up to 5 and multiply to 6. We get:

2, 3

Therefore:

(x + 2)(x + 3)

The answer for the first line segment : (-3,-7) (-4,0)

The answer for 2nd line segment is :(-3,8) (-9,-5)

Step-by-step explanation:

Let do line segment QR and ST. first.

Step 1: Find a line that contains a points that is perpendicular to the line of reflection

"A reflection of a pre image and new image is perpendicular to the line of reflection.

This means for points Q,S,T and R, there is a line that. contains one point that is perpendicular to the line of reflection.

A line that is perpendicular to the line of reflection is the negative reciprocal of the slope so this means all 4 lines must be on a different slopes but the slopes must be 1/2.

To simplify, things, here are the lines that will all 4 points be on

Step 2: Find a point where both the line and line of reflection intersect at.

Now we need to find a line where both the line of reflections and the 4 lines will intersect at separately.

Step 3: Find the endpoints given the midpoint and the originally endpoint.

A reflection per and new image is equidistant from the point of reflection. So we. an say that the point where the line intersect is the midpoint of the pre and new image.

Using this info,

Connect R prime and Q prime. And that the new line segments

Connects S prime and T prime and that the new line segments.

Answer:

The probability that the mean of the sample would differ from the population mean by less than 36 points=0.9216

Step-by-step explanation:

We are given that

The variance of the scores on a skill evaluation test=143,641

Mean=1517 points

n=343

We have to find the probability that the mean of the sample would differ from the population mean by less than 36 points.

Standard deviation,[tex]\sigma=\sqrt{143641}[/tex]

[tex]P(|x-\mu|<36)=P(|\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}|<\frac{36}{\frac{\sqrt{143641}}{\sqrt{343}}})[/tex]

[tex]=P(|Z|<\frac{36}{\sqrt{\frac{143641}{343}}})[/tex]

[tex]=P(|Z|<1.76)[/tex]

[tex]=0.9216[/tex]

Hence,  the probability that the mean of the sample would differ from the population mean by less than 36 points=0.9216

Answer:

A sample of 17 must be selected.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.96}{2} = 0.02[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.02 = 0.98[/tex], so Z = 2.054.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The standard deviation from a previous study is 4 hours.

This means that [tex]\sigma = 4[/tex]

How large a sample must be selected if he wants to be 96% confident of finding whether the true mean differs from the sample mean by 2 hours?

A sample of n is required.

n is found for M = 2. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]2 = 2.054\frac{4}{\sqrt{n}}[/tex]

[tex]2\sqrt{n} = 2.054*4[/tex]

Simplifying both sides by 2:

[tex]\sqrt{n} = 2.054*2[/tex]

[tex](\sqrt{n})^2 = (2.054*2)^2[/tex]

[tex]n = 16.88[/tex]

Rounding up:

A sample of 17 must be selected.

Answer:

42%

Step-by-step explanation:

to find percentages, you move the decimal point twice to the right

Answer:

[tex]-5 \to -24[/tex]

[tex]-1 \to -4[/tex]

[tex]2 \to 11[/tex]

[tex]3 \to 16[/tex]

[tex]4 \to 21[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5x + 1[/tex]

Required

Complete the table (see attachment)

When x = -5

[tex]f(-5) = 5 * -5 + 1 = -24[/tex]

When x = -1

[tex]f(-1) = 5 * -1 + 1 = -4[/tex]

When x = 2

[tex]f(2) = 5 * 2 + 1 = 11[/tex]

When x = 3

[tex]f(3) = 5 * 3 + 1 = 16[/tex]

When x = 4

[tex]f(4) = 5 * 4 + 1 = 21[/tex]

So, the table is:

[tex]-5 \to -24[/tex]

[tex]-1 \to -4[/tex]

[tex]2 \to 11[/tex]

[tex]3 \to 16[/tex]

[tex]4 \to 21[/tex]

Answer:

36

Step-by-step explanation:

(h · f)(x) = h(f(x))

h(f(x)) = h(2x+8)

h(f(x))= 3(2x+8) - 6

h(f(x)) = 6x + 24 - 6

h(f(x))= 6x + 18

If x = 3

h(f(x))= 6(3) + 18

h(f(x))= 18 + 18

h(f(x))= 36

Hence (h · f)(3) = 36

Answer:

Step-by-step explanation:

a.

(1.36 L)/(10 hr) = (0.136 L)/(hr)

Flow rate = (0.136 L)/(hr) × (1000 mL)/L = (136 mL)/(hr)

136 mL × (27 mg)/(100 mL) = 36.72 mg

Delivery rate = (36.72 mg)/(hr)

b.

(136 mL)/(hr) × (13 gtt)/(mL) = (1868 gtt)/(hr)

c.

10 hr × (36.72 mg)/)hr) = 367.2 mg

Hello,

answer C (11,-23)

[tex]\left\{\begin{array}{ccc}3a+b&=&10\\-4a-2b&=&2\end{array}\right.\\\\\\\left\{\begin{array}{ccc}6a+2b&=&20\\-4a-2b&=&2\end{array}\right.\\\\\\\left\{\begin{array}{ccc}3a+b&=&10\\2a&=&22\end{array}\right.\\\\\\\left\{\begin{array}{ccc}a&=&11\\b&=&10-3*11\end{array}\right.\\\\\\\left\{\begin{array}{ccc}a&=&11\\b&=&-21\end{array}\right.\\[/tex]

Answer: C. (11,-23)

Step-by-step explanation:

9514 1404 393

Answer:

  12

Step-by-step explanation:

In base-5 arithmetic, ...

  41 -24 = 12

_____

If we use : to separate columns with different place value, this can be looked at a couple of ways.

Subtraction by addition

  2 : 4 + 0 : 2 = 3 : 1 . . . . . make the 1s place match

  3 : 1 + 1 : 0 = 4 : 1 . . . . . . make the 5s place match

The total amount added was 0:2 +1:0 = 1:2.

Subtraction using borrowing

  4 : 1 - 2 : 4 = (4-1) : (5+1) - 2 : 4

  = (4-1-2) : (5+1)-4 = 1:2

Answer:

-  [tex]\frac{4}{\sqrt{29} }[/tex]

Step-by-step explanation:

The equations for the 1st object :

x₁ = 10 cos(2t),  and  y₁ = 6 sin(2t)

2nd object :

x₂ = 4 cos(t), y₂ = 4 sin(t)

Determine rate at which distance between objects will continue to change

solution Attached below

Distance( D )  = [tex]\sqrt{(10cos2(t) - 4cos(t))^2 + (6sin2(t) -4sin(t))^2}[/tex]

hence; dD/dt = - [tex]\frac{4}{\sqrt{29} }[/tex]

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

Explanation:

We have an octagon because there are n = 8 sides. The diagram below shows one way to number the sides so you can count them efficiently (without missing any or double counting any).

----------------

Plug n = 8 into the formula below

S = 180(n-2)

S = 180(8-2)

S = 180(6)

S = 1080

The 8 interior angles add up to 1080 degrees.

Answer:

The right answer is "[tex]x\simeq 254[/tex]".

Step-by-step explanation:

Let the number of earlier case will be "x".

Now,

⇒ [tex]x+x\times \frac{26.3}{100}=321[/tex]

or,

⇒ [tex]x+x\times 0.263=321[/tex]

By taking "x" common, we get

⇒   [tex]x(1+0.263)=321[/tex]

⇒                    [tex]x=\frac{321}{1.263}[/tex]

⇒                       [tex]=254.15[/tex]

or,

⇒                    [tex]x\simeq 254[/tex]

Answer:

perimeter=9cm

Area=2cm^2

step by step explanation:

Firstly solve the sides that don't have figures using trigonometry

#1..sin15°=opposite/hypotenuse

sin15=opposite/4

opposite=sin15×4

=1.035, round off to 1cm

Then find the value of the base

tan15=opposite/adjacent

tan15=1/adjacent

1=tan15adjascent

1/tan15=adjacent

adjacent or base=3.7 round off to 4cm

After finding these values find the perimeter

p=side+side+side

p=4cm+4cm+1cm

p=9cm

Find the area

1/2bh

1/2×4×1

A=2cm2