The graph shows the distribution of the number of text messages young adults send per day. The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 30 messages.

What percentage of young adults send more than 158 text messages per day?


16%

34%

68%

84%

If y = x + 6√(x + 4), then

y' = 1 + 3/√(x + 4)

Substituting y and y' into the DE gives

(y - x) y' = (x + 6√(x + 4) - x) (1 + 3/√(x + 4))

… = 6√(x + 4) (1 + 3/√(x + 4))

… = 6√(x + 4) + 18

on the left side, while on the right you get

y - x + 18 = x + 6√(x + 4) - x + 18

… = 6√(x + 4) + 18

so both sides match and the given function is indeed a solution to the DE.

Answer:

The solution set is {-2, 3}.

Step-by-step explanation:

We can do this by elimination after manipulating the 2 equations so that the coefficients of  y  will disappear after addition:

5x - 2y = -16        Multiply this by -5:

-25x + 10y = 80 ...........(A)

4x - 5y = -23       Multiply this by 2:

8x - 10y = -46..............(B)

Now add A and B:

-17x = 34

x = 34/-17

x = -2.

Now substitute x = -2 into the first original equation:

5(-2) - 2y = -16

-2y = -16 +10 = -6

y = -6/-2

y = 3.

Confirm these results by substitution in the second original equation:

4(-2) - 5(3)

= - 8  - 15 = -23.

Checks OK.

Answer:

[tex] x = 8\sqrt{2} [/tex]

Step-by-step explanation:

Leg = x

Hypotenuse = 16

[tex] x\sqrt{2} = 16 [/tex]

[tex] x = \dfrac{16}{\sqrt{2}} [/tex]

[tex] x = \dfrac{16}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}} [/tex]

[tex] x = \dfrac{16\sqrt{2}}{2} [/tex]

[tex] x = 8\sqrt{2} [/tex]

Answer:

50

Step-by-step explanation:

Sum Even numbers

n = 50

d = 2

a1 = 2

The last number is

an = a1 + (n-1)d

an = 2 + (50 - 1)*2

an = 2 + 49 * 2

an = 2 + 98

an = 100

Sum of the even numbers

Sum = (a1 + a50)*n/ 2

Sum = (2 + 100)*50/2

sum = 102 * 25

sum = 2550

Sum of the first 50 odd numbers

a1 = 1

n = 50

d = 2

l = ?

Find l

l = a1 + (n - 1)*2

l = 1 + 49*2

l = 99

Sum

Sum = (1 + 99)*50/2

Sum = 2500

The difference and answer is 2550 - 2500  = 50

Answer:

0.0444 = 4.44% probability that a part chosen at random (from the sample) was defective.

Step-by-step explanation:

Probability of a defective part:

0.04 of [tex]\frac{100}{180}[/tex], that is, coming from A.

0.05 of [tex]\frac{80}{180}[/tex], that is, coming from B. So

[tex]p = 0.04\frac{100}{180} + 0.05\frac{80}{180} = \frac{0.04*100 + 0.05*80}{180} = 0.0444[/tex]

0.0444 = 4.44% probability that a part chosen at random (from the sample) was defective.

9514 1404 393

Answer:

  19 hours

Step-by-step explanation:

Add up the numbers:

  3×3.5 +2×2.0 +4.5 = 19

Jacob trains 19 hours per week.

Answer:

85 rounded to the nearest dollar would be $1. 73 rounded to the nearest dollar would also be $1

Step-by-step explanation:

The sine curve equation, y = 10·sin(x·π/24), that models the entrance of the

tunnel with a cross section that is the shape of half of a sine curve and the

height of the tunnel at the edge of the road, (approximately 7.07 ft.) are

found by applying the following steps

(a) The equation for the sine curve is y = 10·sin(x·π/24)

(b) The height of the tunnel at the edge of the road is approximately 7.07 feet

The reason for the above answers are presented as follows;

(a) From a similar question posted online, the missing part of the question

is, what is the height of the tunnel at the edge of the road

The known parameters;

The shape of the tunnel = One-half sine curve cycle

The height of the road at its highest point = 10 ft.

The opening of the tunnel at road level = 24 ft.

The unknown parameter;

The equation of the sine curve that fits the opening

Method;

Model the sine curve equation of the tunnel using the general equation of a sine curve;

The general equation of a sine curve is y = A·sin(B·(x - C) + D

Where;

y = The height at point x

A = The amplitude = The distance from the centerline of the sine wave to the top of a crest

Therefore;

The amplitude, A = The height of half the sine wave = The height of the tunnel = 10 ft.

D = 0, C = 0 (The origin, (0, 0) is on the left end, which is the central line)

The period is the distance between successive points where the curve passes through the center line while rising to a crest

Therefore

The period, T = 2·π/B = 2 × Opening at the road level = 2 × 24 ft. = 48 ft.

T = 48 ft.

We get;

48 = 2·π/B

B = 2·π/48 = π/24

By plugging in the values for A, B, C, and D, we get;

y = 10·sin((π/24)·(x - 0) + 0 = 10·sin(x·π/24)

The equation of the sine curve that fits the opening is y = 10·sin(x·π/24)

(b) The height of the tunnel at the edge of the road is given by substituting

the value of x at the edge of the road into the equation for the sine curve

as  follows;

The width of the shoulders = 6 feet

∴ At the edge of the road, x = 0 + 6ft = 6 ft., and 6 ft. + 12 ft. = 18 ft.

Therefore, we get;

y = 10 × sin(6·π/24) = 10 × sin(π/4) = 5×√2

y = 10 × sin(18·π/24) = 10 × sin(3·π/4) = 5×√2

The height of the, y, tunnel at the edge of the road where, x = 6, and 18 is y = 5·√2 feet ≈ 7.07 ft.

Learn more about the sine curve here;

https://brainly.com/question/3827606

Answer:

Regular Polygons are never concave by definition.

Step-by-step explanation:

Answer:

[tex]P(G_1) = \frac{5}{13}[/tex]

[tex]P(G_2) = \frac{1}{3}[/tex]

[tex]P(X \ge 1) = \frac{25}{39}[/tex]

Step-by-step explanation:

Given

[tex]G = 5[/tex]

[tex]R = 4[/tex]

[tex]B = 4[/tex]

[tex]n = 13[/tex]

Solving (a): [tex]P(G_1)[/tex]

This is calculated as:

[tex]P(G_1) = \frac{G}{n}[/tex]

[tex]P(G_1) = \frac{5}{13}[/tex]

Solving (b): [tex]P(G_2)[/tex]

This is calculated as:

[tex]P(G_2) = \frac{G - 1}{n - 1}[/tex] -- this is so because the selection is without replacement

[tex]P(G_2) = \frac{5 - 1}{13 - 1}[/tex]

[tex]P(G_2) = \frac{4}{12}[/tex]

[tex]P(G_2) = \frac{1}{3}[/tex]

Solving (c): [tex]P(X \ge 1)[/tex]

Using the complement rule, we have:

[tex]P(X \ge 1) = 1 - P(X = 0)[/tex]

To calculate [tex]P(X = 0)[/tex], we have:

[tex]G = 5[/tex] --- Green

[tex]G' = 8[/tex] ---- Not green

The probability that both selections are not green is:

[tex]P(X = 0) = P(G'_1) * P(G'_2)[/tex]

So, we have:

[tex]P(X = 0) = \frac{G'}{n} * \frac{G'-1}{n-1}[/tex]

[tex]P(X = 0) = \frac{8}{13} * \frac{8-1}{13-1}[/tex]

[tex]P(X = 0) = \frac{8}{13} * \frac{7}{12}[/tex]

Simplify

[tex]P(X = 0) = \frac{2}{13} * \frac{7}{3}[/tex]

[tex]P(X = 0) = \frac{14}{39}[/tex]

Recall that:

[tex]P(X \ge 1) = 1 - P(X = 0)[/tex]

[tex]P(X \ge 1) = 1 - \frac{14}{39}[/tex]

Take LCM

[tex]P(X \ge 1) = \frac{39 -14}{39}[/tex]

[tex]P(X \ge 1) = \frac{25}{39}[/tex]

Answer:

Answer: 4 13/30 cups

Step-by-step explanation:

Since Lila used 1 2/5 times as much lemonade as Naomi did (3 1/6 cups), we have to multiply 1 2/5 by 3 1/6:

1 2/5 ⋅ 3 1/6 = ?

19/6 ⋅ 7/5 = 133/30

133/30 = 4 13/30

4 13/30 cups

These are variables on your graph

Answer:

U={-2,-1,0,1,2,3,4,5,6,7,8}

Answer:

B.

Step-by-step explanation:

Since C and A are parallel

and B is perpendicular to C

then B is also perpendicular to A

meaning they have the same angle so 90 Degrees.

Answer:

11

Step-by-step explanation:

Unknown number = x

If twice the difference of x and 8 is 6:

2(x-8) = 6

2x-16 = 6

2x = 6 + 16

2x = 22

x = 22/2

x = 11

Answer from Gauthmath

Answer:

Range: {-1, 0, 5/7, 4/5, 1, 2}

Step-by-step explanation:

We know that:

f(x) = (x + 1)/(2x - 1)

And:

f: A ⇒ B

where:

A={-1,0,1,2,3,4}

B= {-1,0,4/5,5/7,1,2,3,}

We want to find the range of f(x).

The range of f(x) will be the set of the outputs of f(x) (and because f goes from A to B, we will only take the outputs that belong to B).

Then we only need to evaluate all the values of A in f(x), and see if the output belongs to B.

we have:

f(x) = (x + 1)/(2x - 1)

f(-1) = (-1 + 1)/(2*-1 - 1) = 0   (this does belong to B)

f(0) = (0 + 1)/(2*0 - 1) = -1  (this does belong to B)

f(1) = (1 + 1)/(2*1 - 1) = 2  (this does belong to B)

f(2) = (2 + 1)/(2*2 - 1) = 1 (this does belong to B)

f(3) = (3 + 1)/(2*3 - 1) = 4/5  (this does belong to B)

f(4) = (4 + 1)/(2*4 - 1) = 5/7  (this does belong to B)

So the range of f(x) is the set with all these outputs, which is:

Range: {-1, 0, 5/7, 4/5, 1, 2}

Im sorry I don't know the answer to the question

9514 1404 393

Explanation:

A cone is a 3-dimensional object created by revolving a line about an axis that intersects that line. This figure is a "double-napped" cone. The point where the revolved line and the axis meet is the a.pex, or vertex, of the cone. Typically, we're concerned with a finite portion of the cone, from the vertex to a base that is a circle in a plane perpendicular to the axis.

A "conic" is a 2-dimensional figure that results from the intersection of a plane and a cone. There are four general categories, named according to the angle the plane makes with the axis and/or the side of the cone. These are illustrated in the attachment.

Producing these at home can be an interesting project. A circle can be made using a compass.

An ellipse can be drawn using a pair of pins and a loop of string. The pins would be placed at the foci of the ellipse, and the string would constrain the drawing instrument (pen or pencil) to have a constant total distance to the two foci.

A parabola can be drawn on graph paper using coordinates derived from an equation for it. It can also be drawn using a compass and a set square by plotting points that are equidistant from the focus and a line that is called the directrix. If you have a physical cone-shaped object, you can cut it at an angle that will produce a parabola.

A hyperbola can be drawn on graph paper from an equation. It can also be drawn using a compass by plotting points that have a constant difference in their distance to the two foci, or by plotting points whose ratio of distance to focus and directrix is a constant. A physical cone-shaped object can be cut to produce a hyperbola.

__

The general form equation for a conic is ...

  Ax² +Bxy +Cy² +Dx +Ey +F = 0

Usually, we're concerned with conics that have axes parallel to the coordinate axes, so B=0. The equation of an ellipse has A and C with the same sign. The equation of a hyperbola has A and C with opposite signs,

In standard form, the equations for figures centered at the origin are ...

__

The vertex of a conic is an extreme point on the (major) axis of the conic. The focus is a point used in the definition of the conic. The focus is "inside" the curve, on the axis of symmetry. The directrix is a line used in the definition of the conic. The directrix is "outside" the curve, perpendicular to the axis. The second attachment shows these for a parabola.

Answer:

breathing, jk buddy

Step-by-step explanation:

Answer:

español :/

Step-by-step explanation:

Answer:

256/5 pi

Step-by-step explanation:

= angle/360 × pi×r^2

= 72/360 × pi × 16^2

= 51.2 pi

= 256/5 pi

All you do is first you ha

Answer:

[tex]a_{n} = -64(-\frac{1}{4})^{n-1}[/tex]

it seems like the first term is -64, so lets write the formula accordingly:

a_n = a1(r)^(n-1)

where 'n' is the number of terms

a1 is the first term of the sequence

'r' is the ratio

the ratio is [tex]-\frac{1}{4}[/tex] because -64 * [tex]-\frac{1}{4}[/tex] = 16 and so on...

the explicit formula is :

[tex]a_{n}[/tex] = [tex]-64(-\frac{1}{4} )^{n-1}[/tex]

Answer:

Step-by-step explanation:

Everything is correct. But you forgot to add

x = 6 - square root of 26. The answer is

x = 6 + square root of 26 or

x = 6 - square root of 26

Answer:

a) 3.19

b) 3.29

c) 96.81

Step-by-step explanation:

Question a:

Levere's: 10.63s

Ross: 10.98s

10.98 - 10.63 = 0.35s shorter than 10.98s, so:

0.35*100%/10.98 = 3.19% shorter.

Question b:

35s longer than 10.63s, so:

0.35*100%/10.63 = 3.29% longer.

Question c:

3.19% shorter, so 100 - 3.19 = 96.81% of Ross.

Answer:

3h33j333jj3

Step-by-step explanation:b3n3n3nn3n33

Answer:

✔ positive

✔ 1

✔ closely

✔ increases

ED2021