Which linear inequality is represented by the graph?

y ≤ One-thirdx − 1
y ≥ One-thirdx − 1
y < 3x − 1
y > 3x − 1

Answer: $51156

Step-by-step explanation:

a = b x p%

how much will the price increase

a = 49,000 x 4.4%

= 49,000 x 0.044

= $2156

price of next model

49,000 + 2156 = $51156

Considering it's discriminant, it is found that:

A. The classmate is wrong, as the discriminant is of zero, hence the equation has one solution.

B. The quadratic equation has 1 x-intercept.

A quadratic equation is modeled by:

y = ax^2 + bx + c

The discriminant is:

[tex]\Delta = b^2 - 4ac[/tex]

The solutions are as follows:

In this problem, the equation is:

y = 9x² - 6x + 1.

The coefficients are a = 9, b = -6 and c = 1, hence the discriminant is:

[tex]\Delta =(-6)^2 - 4(9)(1) = 36 - 36 = 0[/tex]

Since the discriminant is zero, the classmate is wrong, as it means that the equation has one solution = one x-intercept.

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The length of the apothem of the regular pentagon shown is 5.2 meters

Represent the central angle of the regular pentagon using x

The value of the central angle of the regular pentagon is then calculated as:

x = 360/n

Where n represents the number of sides

i.e n = 5

So, we have:

x = 360/5

Evaluate the quotient

x = 72

Represents the apothem with y.

The apothem is then calculated as:

tan(x/2) = (Side length/2)/Apothem

This gives

tan(72/2) = (7.6/2)/y

Evaluate the quotient

tan(36) =3.8/y

Multiply both sides by y

y tan(36) = 3.8

Divide both sides by tan(36)

y = 3.8/tan(36)

Evaluate the quotient

y = 5.2

Hence, the length of the apothem of the regular pentagon shown is 5.2 meters

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Answer:

[tex]-8x^2 - 4x + 29 \\[/tex]

Step-by-step explanation:

Second expression evaluates to:

[tex](5 + x -2x)^2 = (5 -x)^2 = (-x+5)^2 = x^2 + 2(-x)(5) +5^2 = x^2 -10x + 25[/tex]  (1)

For (1) We are using the rule [tex](a+b)^2 = a^2 +2ab + b^2\\\\[/tex]

Here [tex]a = -x, b = 5\\\\[/tex]

First expression evaluates to

[tex](3x)^2 -6x - 4 = 9x^2 -6x -4[/tex]    (2)

Subtract (2) from (1)

[tex]x^2 - 10x +25 - (9x^2 -6x -4) = x^2-9x^2 -10x - (-6x) +25 -(-4)\\\\= -8x^2 - 4x + 29 \\[/tex]

The missing angles are listed below:

sin 27.818° = 21 / 45

tan 26.565° = 8 / 16

cos 57.607° = 15 / 28

tan 38.956° = 38 / 47

sin 44.901° = 12 / 17

cos 52.398° = 36 / 59

tan 19.477° = 29 / 82

sin 16.601° = 8 / 28

tan 10.008° = 9 / 51

cos 36.870° = 16 / 20

sin 35.538° = 60 / 84

cos 53.576° = 19 / 32

tan 40.101° = 64 / 76

cos 39.571 = 37 / 48

cos 69.605° = 23 / 66

In this question we must find the measure of the angle associated to the rational numbers seen in the statement. There are two methods to estimate such measures: (i) Drawing an equivalent right triangle and estimate the measure of the angle by definition of trigonometric functions, (ii) Using inverse trigonometric functions and numerical methods since they are trascendent variables.

Herein we decided to use the second method by reasons of rapidness and effectivity:

sin 27.818° = 21 / 45

tan 26.565° = 8 / 16

cos 57.607° = 15 / 28

tan 38.956° = 38 / 47

sin 44.901° = 12 / 17

cos 52.398° = 36 / 59

tan 19.477° = 29 / 82

sin 16.601° = 8 / 28

tan 10.008° = 9 / 51

cos 36.870° = 16 / 20

sin 35.538° = 60 / 84

cos 53.576° = 19 / 32

tan 40.101° = 64 / 76

cos 39.571 = 37 / 48

cos 69.605° = 23 / 66

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Answer:

n=11

Step-by-step explanation:

(n+4)/10 = (n-8)/2

We can solve using cross products

(n+4) * 2 = 10 * ( n-8)

Distribute

2n+8 = 10n -80

Subtract 2n from each side

2n+8-2n = 10n-80-2n

8 = 8n-80

Add 80 to each side

8+80= 8n-80+80

88 = 8n

Divide each side by 8

88/8 = 8n/8

11 = n

Answer: n=11

Step-by-step explanation:

(n+4)/10 = (n-8)/2

multiply both sides by 10

n+4 = (n-8)/2*10

cancel

n+4=(n-8)*5

n+4=5(n-8)

multiply

n+4=5n-40

subtract both sides by 5n

n-5n+4=-40

subtract both sides by 4

n-5n=-40-4

subtract the like terms

-4n=-44

cancel the negatives

4n=44

divide each side by 4

n=11

The percentages for each outcome are given as follows:

a) 34.4%.

b) 29.4%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

P = a/b x 100%

For this problem, we already have the percentages, hence we just combine them.

For item a, he can be late in two ways, one that happens 24.4% of the time(waking up late), and the other 10%(stuck in traffic), hence the percentage is of 34.4%, as 24.4% + 10% = 34.4%.

For item b, the percentage stuck in traffic is of 5%, hence the percentage that he will be late is 24.4% + 5% = 29.4%.

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Answer:

f(–5)=–4

Step-by-step explanation:

as it is defined

Grandma should be able to make three slices of French toast by slicing one of the original slices into two.

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Answer:

the slope of the line passing through the points (-4,-4) and (2, 5) m=3/2.

Step-by-step explanation:

Hello!

To find the slope between two points use the formula

Answer: B

Step-by-step explanation:

The graph is shown in the attached image.

The equation of the function f(x) is f(x) = 2 sin(π/2(x + 6)) - 3

A sine function is represented as:

f(x) = A sin(B(x + C)) + D

Where

A = Amplitude

Period = 2π/B

C = Phase shift

D = Vertical shift

The requirements in the question are:

So, we can use the following assumptions

A = 2

Period = 4

C = 6

D = -3

So, we have:

f(x) = 2 sin(B(x + 6)) - 3

The value of B is

4 = 2π/B

This gives

B = π/2

So, we have:

f(x) = 2 sin(π/2(x + 6)) - 3

Using the representations in (a), we have:

See attachment for the graph of f(x)

Let θ = 3π

So, we have:

cos(3π)

This is calculated as:

cos(3π) = cos(2π + π)

Expand

cos(3π) = cos(2π) *cos(π) - sin(2π) *sin(π)

Evaluate

cos(3π) = -1

Let θ = 3π

So, we have:

sin(3π)

This is calculated as:

sin(3π) = sin(2π + π)

Expand

sin(3π) = sin(2π) *cos(π) + cos(2π) *sin(π)

Evaluate

sin(3π) = 0

Let θ = 3π

So, we have:

tan(2 * 3π)

tan(6π)

This is calculated as:

tan(6π) = tan(3π + 3π)

Evaluate

tan(3π) = 0

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Step-by-step explanation:

68% of all values are within 1 SD (110 ± 15).

95% of all values are within 2SD (110 ± 2×15 = 30)

99.7% of all values are within 3 SD (110 ± 3×15 = 45)

a)

95 is 110 - 15, so exactly 1 SD apart from the mean value.

68% or 0.68 is the probability of all values between 95 and 125.

so, 34% or 0.34 is the probability of all values between 95 and 110. and 50% or 0.5 is the probability of all values larger than 110.

so, the probability of all values larger than 95 is

0.34 + 0.5 = 0.84

b)

125 is 110 + 15, so exactly 1 SD apart from the mean value.

so, as per a) 34% or 0.34 is the probability of all values between 110 and 125. and 50% or 0.5 is the probability of all values larger than 110.

so, the probability of all values larger than 125 is

0.5 - 0.34 = 0.16

Answer:

B

Step-by-step explanation:

a dream like imageeeeee

Answer:

a) x + 10 = 45

b) 3 = 6 - x

c) d = s * t

Step-by-step explanation: This is actually pretty simple. Let's put down one theorem.

SYMMETRIC THEOREM OF PROPERTIES: If a equals b, then b must equal a. Thus, a = b and b = a.

This is all we're really doing.

Take a) for example, 45 = x + 10. Let's label (45) as A, and (x + 10) as B. Thus we have A = B. Now we know by the Symmetric Property, we have B = A. Thus, substituting B and A again, we get x + 10 = 45.

Just keep doing this with all the equations.

Hope this helped!

Since we know the sequence is quadratic, we expect the [tex]n[/tex]-th term to have the general form

[tex]x_n = an^2 + bn + c[/tex]

Plug in the first 3 known values of the sequence to form a system of equations.

[tex]x_1 = 3 = a + b + c[/tex]

[tex]x_2 = 12 = 4a + 2b + c[/tex]

[tex]x_3 = 25 = 9a + 3b + c[/tex]

Eliminating [tex]c[/tex] gives

[tex](4a + 2b + c) - (a + b + c) = 12 - 3 \implies 3a + b = 9[/tex]

[tex](9a + 3b + c) - (a + b + c) = 25 - 3 \implies 8a + 2b = 22 \implies 4a + b = 11[/tex]

Eliminating [tex]b[/tex] gives

[tex](4a + b) - (3a + b) = 11 - 9 \implies a = 2[/tex]

Solving for [tex]b,c[/tex], we get

[tex]4a + b = 11 \implies b = 11-4\cdot2 = 3[/tex]

[tex]a+b+c=3 \implies c=3-2-3 = -2[/tex]

So, the [tex]n[/tex]-th term of the sequence is

[tex]x_n = \boxed{2n^2 + 3n - 2}[/tex]

Answer:

  order: 2, 3, 1

Step-by-step explanation:

Reasonableness checks and your knowledge of integers and fractions will help you solve this. The offered questions are intended to help you think this through.

For an output of -31, the machine (x -2)² cannot possibly be last. Its output can only be positive.

  machine 2, (x-2)², cannot be last

Also, machine 3 cannot be last. For the output to be -31, the input to machine 3 must be -1/31. Neither of the other machines can produce a fraction with the inputs they might receive.

For an input of x=0, the machine 1/x cannot possibly be first. 1/0 is undefined.

The other two machines will give the following outputs for an input of 0:

  machine 1: 4(0) -32 = -32

  machine 2: (0 -2)² = 4

It is unlikely that machine 1 will be first, because the other two machines cannot do anything useful with -32 as an input.

  machine 3, 1/x, cannot be first

The reasoning of part (a) tells you the last machine must be machine 1. The reasoning of part (b) tells you the first machine cannot be 3, so must be 2. The order of the machines must be ...

If the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.

Given sample size be 300 and about 5% of the population has a particular genetic mutation.

We are required to find the standard deviation for the number of people with the genetic mutation in groups of 300.

Sample size=300

The standard deviation for the number of people with the genetic mutation is calculated as:

Standard deviation=[tex]\sqrt{np(1-p)}[/tex]

Use the known values in the above formula.

Standard deviation=[tex]\sqrt{300*0.05(1-0.05)}[/tex]

=[tex]\sqrt{14.25}[/tex]

=3.77

Hence if the sample size is 300 and about 5% of the population has a particular genetic mutation then the standard deviation for the number of people with the genetic mutation in such groups of 300 is 3.77.

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The probability that the battery life is  20 ± 2 hours (between 18 and 22 hours) for each of the phones is:

Using the normalcdf function on a calculator, the probability that Phone C's battery would last between 18 and 22 hours can be found by inputing the function:

normalcdf (20, IE99, 18, 2)

The result is 0.158655 or 15.9%.

For Phone T, the function is:

normalcdf (20, IE99, 20, 3)

The result is 0.5 or 50%.

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Answer: 27°

Step-by-step explanation:

The easiest way to find the measure of angle Z is to know that in a rhombus, the diagonals are perpendicular bisectors of each other. This means that all the four angles in the center are 90°.

Since we know that all angles in a triangle add up to 180°, we can set the sum of z, 63, and 90 to be 180 and solve for z.

[tex]z+63+90=180\\z+153=180\\z=27[/tex]

Hence, z is 27°.

a. The velocity t = [tex]v = Ce_{n} (\frac{mo}{mo - kt} ) - gt[/tex]

b. v60 = 7164

mdv/dt = ck - mg

dv/dt = ck/m - mg/m

= ck/m - g

dv = [tex](\frac{ck}{Mo-Kt} -g)dv[/tex]

Integrate the two sides of the equation to get

v [tex]-\frac{ck}{k} e_{n} (Mo- kt)-gt+c[/tex]

[tex]v = Ce_{n} (\frac{mo}{mo - kt} ) - gt[/tex]

b. fuel accounts for 55% of the mass

So final mass after fuel is burned out is = 0.45

c=2500

g=9.8

t=60

v = -2500ln0.45 - 9.8 x 60

= 7752 - 588

= 7164

A rocket, fired from rest at time t = 0, has an initial mass of m0 (including its fuel). Assuming that the fuel is consumed at a constant rate k, the mass m of the rocket, while fuel is being burned, will be given by m0 - kt. It can be shown that if air resistance is neglected and the fuel gases are expelled at a constant speed c relative to the rocket, then the velocity of the rocket will satisfy the equation where g is the acceleration due to gravity.

dv dt m =ck - mg

(a) Find v(t) keeping in mind that the mass m is a function of t.

v(t) =

m/sec

(b) Suppose that the fuel accounts for 55% of the initial mass of the rocket and that all of the fuel is consumed at 60 s. Find the velocity of the rocket in meters per second at the instant the fuel is exhausted. [Note: Take g = 9.8 m/s² and c = 2500 m/s.]

v(60) =

m/sec [Round to nearest whole number]

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Answer:

$279

Step-by-step explanation:

100% = $930

30% = ???

(30/100) × 930

=$279

Answer:

B

Step-by-step explanation:

• the opposite sides of a parallelogram are congruent , then

ZY = WX , that is

5x - 6 = 4x + 1 ( subtract 4x from both sides )

x - 6 = 1 ( add 6 to both sides )

x = 7

• the diagonals bisect each other , then

ZT = TX = 2x = 2 × 7 = 14

Answer:

13

Step-by-step explanation:

→ Substitute 3 into 2x

2 × 3

→ Evaluate

f ( x ) = 6

→ Substitute x = 3 into 3x - 2

3 × 3 - 2

→ Evaluate

7

→ Find the sum of the 2 results

13

When x = 3, the value of (f + g)(x) is 13.

To evaluate (f + g)(x) when f(x) = 2x and g(x) = 3x - 2, we substitute the given functions into the expression (f + g)(x).

(f + g)(x) = f(x) + g(x)

Substituting the given functions:

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

Simplifying the expression:

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

Combining like terms:

(f + g)(x) = 5x - 2

Now, to find the value of (f + g)(x) when x = 3, we substitute x = 3 into the expression:

(f + g)(3) = 5(3) - 2

Simplifying further:

(f + g)(3) = 15 - 2

(f + g)(3) = 13

Therefore, when x = 3, the value of (f + g)(x) is 13.

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Length: 2.6 meters

Width: 1.8 meters

Area: 4.68 meters

Since the scale is 1/40, we can multiply the centimeter measurements by 40 thus making it our scale factor.

Length

2.6 x 40 = 260

260 cm = 2.6 m

Width

4.5 x 40 = 180

180 cm= 1.8 m

Area

1.8 x 2.6 = 4.68 m

Length: 2.6 meters

Width: 1.8 meters

Area: 4.68 meters

Using the addition rule of the Sine function and the Cosine function, we obtain [tex]\cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex].

Given that

[tex]\sin x + \sin y = a\\\cos x + \cos y = b[/tex]

Then using the above formulas, we get:

[tex]2\sin\frac{x+y}{2}\cos\frac{x-y}{2}=a[/tex]       (1)

[tex]2\cos\frac{x+y}{2}\cos\frac{x-y}{2}=b[/tex]       (2)

Dividing the equation (1) by (2), we get:

[tex]\dfrac{\sin\dfrac{x+y}{2}}{\cos\frac{x-y}{2}}=\dfrac{a}{b}\\\Longrightarrow \tan\dfrac{x+y}{2}=\dfrac{a}{b}[/tex]             (3)

Now, we know that  [tex]\cos\theta=\dfrac{1}{\sqrt{1+\tan^2\theta}}[/tex].

Thus, using the above formula, we get from (3):

[tex]\cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\tan^2\dfrac{x+y}{2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\dfrac{a^2}{b^2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex]

Therefore, using the addition rule of the Sine function and the Cosine function, we obtain [tex]\cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex].

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Answer: 6.25

Step-by-step explanation: Here, you want to find how much of 6,298 pounds of food each person got. You can do this by dividing. 6,298/1,007 should get you the answer because it shows how the 6,298 pounds were distributed amongst the 1,007 people.