This graph describes which of the expressions given?

Answer:

See below.

Step-by-step explanation:

First, recall the meanings of the domain and range.

The domain is the span of x-values covered by the graph.

And the range is the span of y-values covered by the graph.

1)

So, we have here an absolute value function.

As we can see, the domain of the function is all real numbers because the graph stretches left and right infinitely. Therefore, the domain of the function is:

[tex]\{x|x\in\textbb{R}\}[/tex]

(You are correct!)

For the range, notice how the function stops at y=7. The highest point of the function is (-2,7). There graph doesn't and won't ever reach above y=7. Therefore, the range of the graph is all values less than or equal to 7. In set notation, this is:

[tex]\{y|y\leq 7\}[/tex]

2)

We have here an ellipse.

First, for the domain. We can see the the span of x-values covered by the ellipse is from x=-4 to x=6. In other words, the domain is all values in between these two numbers and including them. Therefore, we can write it as such:

[tex]-4\leq x\leq 6[/tex]

So x is all numbers greater than or equal to -4 but less than or equal to 6. This describes the span of x-values. In set notation, this is:

[tex]\{x|-4\leq x\leq 6\}[/tex]

For the range, we can see that the span of x values covered by the ellipse is from y=-5 to y=1. Just like the domain, we can write it like this:

[tex]-5\leq y\leq 1[/tex]

This represents all the y-values between -5 and 1, including -5 and 1.

In set notation, thi is:

[tex]\{y|-5\leq y\leq 1\}[/tex]

Correct question is;

The claim is that the proportion of adults who smoked a cigarette in the past week is less than 0.35, and the sample statistics include n = 1168 subjects with 385 saying that they smoked a cigarette in the past week. Find the value of the test statistic

Answer:

Test statistic is z = -1.46

Step-by-step explanation:

Let's first of all define the hypotheses:

Null hypothesis:

H0: p = 0.35, i.e 35% in the sample of 1,168 adults have smoked cigarettes in the previous week.

Alternative hypothesis:

Ha: p < 0.35, i.e less than 35% in the sample of 1,168 adults have smoked cigarette in the previous week.

The sample size is, n = 1,168 while the number of adults who smoked in the previous week would be; x = 385

Therefore, the sample proportion of adults who smoked in the previous week would be calculated as;

p^ = x/n = 385/1168 ≈ 0.3296

Now, from Central Limit Theorem for large samples, The sampling distribution of the sample proportion p^, will have a mean of μ = p = 0.35

Formula for standard deviation is;

σ = √[p (1 – p)/n]

σ = √(0.35 × (1 – 0.35)/1168)

σ = √0.0001947774

σ = 0.014

Formula for test statistic is;

z = (p^ - p)/σ

z = (0.3296 - 0.35)/0.014

z = - 1.46

Answer:

D. -4

Step-by-step explanation:

the slope formula is

m=(y2-y1)/(x2-x1)

(x2,y2) = (4,7)

(x1, y1) = (5,3)

So (7-3)/(4-5) = 4/-1 = -4

Answer:

-4

Step-by-step explanation:

I say so

Answer:

2.5

Step-by-step explanation:

8x + 2 = 7 + 5x + 15

Combine like terms:

8x + 2 = 7 + 5x + 15

8x + 2 = 22

      -2     -2

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

8x = 20

----    ----

8       8

x = 2.5

Hope this helped.

Answer: $ 39.60

Step-by-step explanation:

36 + (36*0.10) = 39.60

Answer:

45

62x

______

  90

2700+

_________

2790

Step-by-step explanation:

Answer:

4 ther are 4 line symmetery

Answer:

two lines of symmetry

(a vertical and a horizontal)

Answer:

x/4 +1

Step-by-step explanation:

Answer:

D. infinitely many

Step-by-step explanation:

Perpendicular lines can be drawn everywhere on the lone in infinitely different places, making the answer infinite.

The number of lines that can be drawn perpendicular to a given line at a given point on that line in space is infinite many.

The correct answer is an option (D)

For given question,

We can draw infinite perpendicular lines to a

Therefore, the number of lines that can be drawn perpendicular to a given line at a given point on that line in space is infinite many.

The correct answer is an option (D)

Learn more about the perpendicular lines here:

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Answer

20%

Step-by-step explanation:

9514 1404 393

Answer:

  -13/11

Step-by-step explanation:

Straightforward evaluation of the expression at x=1 gives (1 -1)/(1 -1) = 0/0, an indeterminate form. So, L'Hopital's rule applies. The ratio of derivatives is ...

  [tex]\displaystyle\lim_{x\to 1}\dfrac{n}{d}=\dfrac{n'}{d'}=\left.\dfrac{\dfrac{4}{3\sqrt[3]{4x-3}}-\dfrac{7}{2\sqrt{7x-6}}}{\dfrac{5}{2\sqrt{5x-4}}-\dfrac{2}{3\sqrt[3]{2x-1}}}\right|_{x=1}=\dfrac{4/3-7/2}{5/2-2/3}=\dfrac{8-21}{15-4}\\\\=\boxed{-\dfrac{13}{11}}[/tex]

Answer: No, the graph suggests that the increase in adoptions from 2000 to 2005 was more significant than it actually is

Step-by-step explanation:

Ok, in the graph we can see that the minimal value for the y-axis is y = 4000.

This means that the graph is like a "zoom" tath points to the tips of the boxes.

This makes the relative difference between the columns seems to be bigger than it actually is, so the correct answer would be:

"No, the graph suggests that the increase in adoptions from 2000 to 2005 was more significant than it actually is"

And remember that this happens for the people that only see the graph for a second and draw the conclusions (most of the people). While in the graph you can read all the information that you need to calculate exactly the relative change.

Answer:

2

Step-by-step explanation:

The slope is given by

m = ( y2-y1)/(x2-x1)

   = (7-3)/(10-8)

    = 4/2

    = 2

Answer:

17

Step-by-step explanation:

[tex]h(x) =x^2 +1\\k(x)=x-2\\\\3h(2)+2k(3)\\\\h(2)= ?\\k(3)=?\\\\h(2) = (2)^2 +1\\= 4+1\\h(2)=5\\\\\\k(3)= 3-2\\k(3) = 1\\\\3h(2) +2k(3)\\\\= 3(5)+2(1)\\=15+2\\3h(2)+2k(3) = 17[/tex]

5, 9, and 17

Step-by-step explanation:

Split up C into two component paths C₁ and C₂, where each line segment is respectively parameterized by

r₁(t) = (1 - t ) (3i + k) + t (4i + 3j + k) = (t + 3) i + 3t j + k

r₂(t) = (1 - t ) (4i + 3j + k) + t (4i + 5j + 4k) = 4i + (2t + 3) j + (3t + 1) k

both with 0 ≤ t ≤ 1.

It's a bit unclear what function you're supposed to integrate (looks like xyz ?) so I'll give a more general result. The line integral of a scalar function f(x, y, z) along the given path C is

[tex]\displaystyle \int_C f(x,y,z)\,\mathrm ds = \int_{C_1}f(\mathbf r_1(t))\left\|\frac{\mathrm d\mathbf r_1}{\mathrm dt}\right\|\,\mathrm dt + \int_{C_1}f(\mathbf r_2(t))\left\|\frac{\mathrm d\mathbf r_2}{\mathrm dt}\right\|\,\mathrm dt[/tex]

We have

dr₁/dt = i + 3j   ==>   || dr₁/dt || = √(1² + 3²) = √10

dr₂/dt = 2j + 3k   ==>   || dr₂/dt || = √(2² + 3²) = √13

Then the integrals reduce to

[tex]\displaystyle \int_0^1 \left(\sqrt{10}\,f(t+3,3t,1) + \sqrt{13}\,f(4,2t+3,3t+1)\right)\,\mathrm dt[/tex]

If indeed f(x, y, z) = xyz, then we have

[tex]\displaystyle \int_0^1 \left(3\sqrt{10}\,t(t+3) + 4\sqrt{13}\,(2t+3)(3t+1)\right)\,\mathrm dt = 11\sqrt{\frac52}+42\sqrt{13}[/tex]

Answer:

3(9t^5-7p^4)(9t^5+7p^4)

Step-by-step explanation:

243 t^10 - 147 p^8

3 ( 81 t^10-49 p^8 )

Then we need to factor what is in the parentheses

3 ( ( 9t^5) ^2 - ( 7p^4) ^2)

This is the difference of squares  ( a^2 -b^2) = ( a-b) (a+b)

3(9t^5-7p^4)(9t^5+7p^4)

Answer:

d. 19

Step-by-step explanation:

Degrees of freedom is the number is the number of value which is used in the final calculation. It calculate as n-1, where n is the sample size. The degrees of freedom for the given scenario is 19. The sample size is 20 so the degrees of freedom is 1 less which will be 19.

Answer:

11. Yes

12. No

Step-by-step explanation:

11. The x values only have 1 y value, so it makes it a function.

12. The x value 0 has 2 y values -4 and 4, therefore it is not a function, because in functions that x value can only have one y value,

Answer:

The answer is 216

Step-by-step explanation:

if there is a 2 cm border, that means that the sides will both become 2 centimeters longer. so (16+2)*(10*2) = 18*12 = 216.

Answer:

7:50 am

Step-by-step explanation:

Clara took 2 hours to reach, and she took a 20 min break, so she left at 7:50 and arrived at 10:10.

Answer:

7:50

Step-by-step explanation:

50 miles per hour/50 miles per 60 min.

50 miles + 50 miles = 100 miles.

if 50 miles takes 1 hour, 100 miles would equal to 2 hours.

considering clara took a 20 min break, thats 2 hours and 20 minutes.. subtract that from the time she arrived and you would get 7:50

Answer:

204

Step-by-step explanation:

To simplify the shape, you can do multiple things. I've opted to shave down both prongs to take it from a 'T' shape to a rectangular prism.

For height of the prongs, take 4 from 6.

6 - 4 = 2

Divide by 2 as there are 2 prongs.

2 / 2 = 1

Remember L * W * H

6 * 3 * 1 = 18

Remember that there are two prongs!

3 + 4 = 7

6 * 7 * 4 = 168

168 + 2(18) = 204

Answer: 125.6 in^2

Step-by-step explanation:

First, we have that the radius of this circle is r = 10in

Now, we know that the area of a circle is:

A = pi*r^2

Now, if we got only a section of the circle, defined by an angle x, then the area of that region is:

A = (x/360°)*pi*r^2

Notice that if x = 360°, then the area is the same as the area of the full circle, as expected.

Then each shaded area has an angle of 72°.

A = (72°/360°)*3.14*(10in)^2 = 62.8 in^2

And we have two of those, both of them with the same angle, so the total shaded area is:

2*A = 2*62.8 in^2 = 125.6 in^2

Answer:

6

Step-by-step explanation:

the | | are for absolute value, which means

|-6|=|6|= 6

Answer:

Below

Step-by-step explanation:

Let T be triangle, C the circle and S the square.

● T + T + T = 30

● 3T = 30

Divide both sides by 3

● 3T/3 = 30/3

● T = 10

So the triangle has a value of 10.

●30 T + C + C = 20C + S + S = 13T +C ×S/2

Add like terms together

●30 T + 2C = 20C +2S= 13T + C×S/2

Replace T by its value (T=10)

● 300 + 2C = 20C + 2S = 130 + C×S/2

Take only this part 20C + 2S = 130 + C × S/2

● 20C + 2S = 130 + C×S/2 (1)

Take this part (300+2C = 20C+2S) and express S in function of C

● 20C + 2S = 300 + 2C

Divide everything by 2 to make easier

● 10 C + S = 150+ C

● S = 150+C-10C

● S = 150-9C

Replace S by (5-9C) in (1)

● 20C + 2S = 130 + C×S/2

● 20C + 2(150-9C) = 130 +C× (150-9C)/2

● 20C + 300-18C= 130 + C×(75-4.5C)

● 2C + 300 = 130 + 75 -4.5C^2

● 2C +300-130 = 75C - 4.5C^2

● 2C -75C + 170 = -4.5C^2

● -73C + 170 = -4.5C^2

Multiply all the expression by -1

● -4.5C^2 +73C+ 170= 0

This is a quadratic equation, so we will use the discriminant method.

Let Y be the discriminant

● Y = b^2-4ac

● b = 73

● a = -4.5

● c = 170

● Y = 73^2 - 4×(-4.5)×170= 8389

So the equation has two solutions:

● C = (-b +/- √Y) /2a

√Y is approximatively 92

● C = (-73 + / - 92 )/ -9

● C = 18.34 or C = -2.11

Approximatively

● C = 18 or C = -2

■■■■■■■■■■■■■■■■■■■■■■■■■

● if C = 18

30T + 2C = 300 + 36 = 336

● if C = -2

30T + 2C = 300-4 = 296

If L(t) = ⟨5 + t, 1 + 5t⟩, then the tangent vector to L(t) is

dL/dt = ⟨1, 5⟩

Any line parallel to L(t) will have the same tangent vector, up to some scalar factor (that is, if the tangent vector is a multiple of ⟨1, 5⟩).

Any line r(t) with tangent vector T(t) = dr/dt that is perpendicular to L(t) will satisfy

T(t) • ⟨1, 5⟩ = 0

• r(t) = ⟨-5, -2t, 1 - 10t⟩ is parallel to L(t) because its tangent vector is

T(t) = ⟨-2, -10⟩ = -2 ⟨1, 5⟩

• r(t) = ⟨1 + 1.5t, 3 + 7.5t⟩ is parallel to L(t) because

T(t) = ⟨1.5, 7.5⟩ = 1.5 ⟨1, 5⟩

• r(t) = ⟨-2 - t, 2 - 2t⟩ is neither parallel nor perpendicular to L(t) because

T(t) = ⟨-1, -2⟩ ≠ k ⟨1, 5⟩

for any real k (in other words, there is no k such that -1 = k and -2 = 5k), and

⟨-1, -2⟩ • ⟨1, 5⟩ = -1 - 10 = -11 ≠ 0

• r(t) = ⟨3 + 15t, -3t⟩ is perpendicular to L(t) because

T(t) = ⟨15, -3⟩

and

⟨15, -3⟩ • ⟨1, 5⟩ = 15 - 15 = 0

Answer:

Step-by-step explanation:

12x - 9 = 8x + 7

4x - 9 = 7

4x = 16

x = 4

solution is C

The solution is Option C.

The value of x is given from the equation x = 4

A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.

The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn

Given data ,

Let the first line be represented as CD

Let the second line be represented as XY

Now , CD is the perpendicular bisector of XY

So , the point F is the midpoint of the line segment XY

The measure of line segment XF = 12x - 9

The measure of line segment FY = 8x + 7

From the perpendicular bisector theorem ,

The measure of line segment XF = The measure of line segment FY

Substituting the values in the equation , we get

12x - 9 = 8x + 7

Subtracting 8x on both sides of the equation , we get

4x - 9 = 7

Adding 9 on both sides of the equation , we get

4x = 16

Divide by 4 on both sides of the equation , we get

x = 4

Therefore , the value of x = 4

Hence , the value of the equation is x = 4

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We want to maximize [tex]x^3y^4z[/tex] subject to the constraint [tex]x+y+z=30[/tex].

The Lagrangian is

[tex]L(x,y,z,\lambda)=x^3y^4z-\lambda(x+y+z-30)[/tex]

with critical points where the derivatives vanish:

[tex]L_x=3x^2y^4z-\lambda=0[/tex]

[tex]L_y=4x^3y^3z-\lambda=0[/tex]

[tex]L_z=x^3y^4-\lambda=0[/tex]

[tex]L_\lambda=x+y+z-30=0[/tex]

[tex]\implies\lambda=3x^2y^4z=4x^3y^3z=x^3y^4[/tex]

We have

[tex]3x^2y^4z-4x^3y^3z=x^2y^3z(3y-4x)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}\\z=0,\text{ or}\\3y=4x\end{cases}[/tex]

[tex]3x^2y^4z-x^3y^4=x^2y^4(3z-x)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}\\3z=x\end{cases}[/tex]

[tex]4x^3y^3z-x^3y^4=x^3y^3(4z-y)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}4z=y\end{cases}[/tex]

Let's work with [tex]x=3z[/tex] and [tex]y=4z[/tex], for which we have

[tex]x+y+z=8z=30\implies z=\dfrac{15}4\implies\begin{cases}x=\frac{45}4\\y=15\end{cases}[/tex]

The smallest of these is C. 15/4.

Answer:

Tran family's sprinkler was used for 20 hours

Green's  family's sprinkler was used for 30 hours

Step-by-step explanation:

Let the hours for which Tran family's sprinkler used is x hours

water output rate for the Tran family's sprinkler = 35L per hour

water output from  Tran family's sprinkler in x hours = 35*x L = 35x

Let the hours for which Green family's sprinkler used is y hours

water output rate for the Green family's sprinkler = 40L per hour

water output from  Green family's sprinkler in x hours = 40*y L = 40y

Given

The families used their sprinklers for a combined total of 50 hours

thus

x + y = 50 -------------------equation 1

y = 50-x

total water output of 1900L

35x+40y = 1900  -------------------equation 1

using  y = 50-x in equation 2, we have

35x + 40(50-x) = 1900

35x + 2000 - 40x = 1900

=> -5x = 1900 - 2000 = -100

=> x = -100/-5 = 20

y = 50-20 = 30

Thus,

Tran family's sprinkler was used for 20 hours

Green's  family's sprinkler was used for 30 hours

Answer:

this is an inconsistent because no solutions

Answer:

sorry for doesn't know the answer