What is the solution to the compound inequality in interval notation?
4(x +1) > -4 or 2x - 4 < -10

Answer:

option 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0-(-2)}{4-0}[/tex] = [tex]\frac{0+2}{4}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = [tex]\frac{1}{2}[/tex] x - 2

The statement that "close to 60 country songs" but probably not exactly 60 country songs is, best prediction to complete the given statement .

So, the correct option is option (B).

Mekala has MP3 player Jumble has 4 techno songs, 2 country songs, and 3 jazz songs on it.

firstly, we represent this songs in ratio format :

Now, the ratio of techno songs to country songs to jazz songs = 4 : 2 : 3

Let the total number of songs which is unknowns be" x". So,

Total number of techno songs = 4x

Total number of country songs = 2x

Total number of jazz songs = 3x

Total number of songs that Mekala plans to Listen = 270

Then, 4 x + 2 x + 3 x = 270

=> 9 x = 270

Dividing both sides by 9, we get

=> x = 30

So, Number of techno songs = 4 × 30

= 120

Number of country songs = 2×30 = 60

Number of jazz songs = 3 × 30 = 90

but all this is based on prediction only.

Hence, the total country songs are close to 60 but not exactly 60.

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Complete question:

Mekala has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Mekala's Jumble has 4 techno songs, 2 country songs, and3 jazz songs on it. Mekala plans to listen to 270 songs.

Complete the following statement with the best prediction.

Mekala will listen to...

Please choose from one of the following options.

a) Exactly 60 country songs

b) Close to 60 country songs but probably not exactly 60country songs

c)Exactly 210 country songs

d)Close to 210 country songs but probably not exactly 210 country songs

Answer:

a = −1 / 2 b^3 + 1 / 2 bh

Step-by-step explanation:

1 )

h = 2a / b^1 + b^2

2 ) Multiply both sides by b.

bh = b^3 + 2a

3 ) Flip the equation.

b^3 + 2a = bh

4 ) Add -b^3 to both sides.

b^3 + 2a + −b^3 = bh + −b^3

2a = −b^3 + bh

5 ) Divide both sides by 2.

2a / 2 = −b^3 + bh / 2

a = −1 / 2 b^3 + 1 / 2 bh

Hope this helps! :)

By using the concept of unitary method, ratio and percentage, it can be calculated that-

7) Option D is correct

6) Option C is correct

8) Option D is correct

What is Unitary method, ratio and percentage?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Ratio is used to determine how much one quantity is bigger  as compared to another. The first part of the ratio is called antecedant and the second part of the ratio is called consequent.

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

Here, unitary method, ratio and percentage will be used.
7) The scale on a map reads [tex]\frac{1}{2} \ inch = 30 \ miles\\[/tex]

1 inch = [tex]30 \div \frac{1}{2} \ miles[/tex] = 60  miles

[tex]\frac{23}{4} \ inches[/tex] = [tex]\frac{23}{4} \times 60 \ miles[/tex] = 345 miles

Option D is correct

6) Let the number of empty seats be 3x and the number of full seats be 7x

Total number of seats = 3x + 7x = 10x

By the problem,

7x  = 203

x = [tex]\frac{203}{7}[/tex]

x = 29

Total number of seats = [tex]29 \times 10[/tex] = 290

Option C is correct

8) Let the number of students be x

Percentage of students in the band = [tex]\frac{37.5}{100} \times x[/tex]

By the problem,

[tex]\frac{37.5}{100} \times x =42\\x = \frac{42 \times 100}{37.5}\\x = 112[/tex]

Option D is correct

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The dimensions of the rectangle are length is 108 inches and width is 60 inches.

The area of Rectangle is length times of width.

The perimeter of a rectangle is 96 inches.

The length of the rectangle is 12 less than twice the width.

Length L=2W-12

Width=W

Perimeter=2(Length+Width)

=2(2W-12+W)

96=2(W-12)

Divide both sides by 2

48=W-12

Add 12 on both sides

60=W

Now length=2(60)-12

=120-12=108

Hence, the dimensions of the rectangle are length is 108 inches and width is 60 inches.

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constructing cones a right triangle whose hypotenuse is 23 m long is revolved about one of its legs to generate a right circular cone. radius: 11.5 m height: 23 m volume: 1650.6 m³

The hypotenuse of the triangle is 23 m. This means that the two sides are 11.5 m and 11.5 m. This gives us the radius of the cone.

The height of the cone is the same as the hypotenuse, so the height is 23 m.

The volume of a right circular cone can be calculated using the following formula: V = (πr²h)/3. In this case, the radius is 11.5 m, the height is 23 m, and π = 3.14. Plugging these values into the formula, we get a volume of 1650.6 m³.

V = (πr²h)/3

V = (3.14 × 11.5² × 23)/3

V = 1650.6 m³

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The required type ii error probability of the test using is 0.085.

It is determined by duplicating the pretest chances by the probability of a positive or negative test (as we will show). Post-test  probability  is characterized, as the likelihood of the objective problem after a symptomatic experimental outcome is known.

We have,

standard deviation = 7, mean = 6, size of the sample = 23.

P(type II error) = P(Xbar >=8 given mean =6)

=P(Z>(8-6)×√(23)/7) =P(Z>1.37)=1-P(Z<1.37)

=1-0.9147=0.0853 =0.085

Thus, required probability is 0.085

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The best approximation for the area of this circle with a radius of 8in is 201.0 in².

A circle is a two-dimensional object made up of points that are spaced out from a given point (center) on the plane by a fixed or constant distance (radius). The area, a circle occupies in a two-dimensional plane is known as the area of the circle. Therefore, the area that a circle with radius r encloses is πr².

Given the radius r of the circle is 8 in. Then, the area is,

A = 3.14×(8 in)² =200.96 in²=201.0 in²

The answer is 201.0 in² and the correct option is option c.

The complete question is -

What is the best approximation for the area of this circle? Circle with radius labeled 8 in. Use 3.14 to approximate pi.  a) 25.1 in² b) 50.2 in² c) 201.0 in² d) 803.8 in²

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Therefore lifetime value is such that   the total lifetime of all batteries in a package exceeds that value for only 5% of all packages is 13.548 hours

In statistics, the standard deviation measures how widely distributed or how much a bunch of values can vary. While a big standard deviation shows that values are scattered throughout a wider range, a low standard deviation suggests that values are frequently close to the set's mean.

Here,

given that the  lifetime of a certain type of battery is normally distributed with mean value 13 hours and standard deviation 1 hour.

Sample size=n =9

Sample mean =X' N is(13,1/3)

If c is the lifetime value, then only 5% of all packages will have a total battery lifetime that is longer than that amount.

Then we have P(X>c) =0.05

Convert into Z score to get

P(x-13/(1/3) > z) = 0.05

z =1.645 from std normal distribution table

Hence x = 13 + 1.645/3

x=13.548

Therefore lifetime value is such that   the total lifetime of all batteries in a package exceeds that value for only 5% of all packages is 13.548 hours.

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Answer: Area=35km^2

Step-by-step explanation:

You need to find the areas of the rectangle and then the triangle.

First, you start with splitting up the figure to a rectangle and a triangle.

Secondly 6*5= 30 so the area of the rectangle is 30 km.

Thirdly, you add that to the area of the triangle, which you figure out because the opposite side of the figure is 6 km so the remaining length is going to be 2km. The area of a triangle is (1/2)(Base)(Height), so (1/2)(5)(2)= 5.

Add the 30 with the 5 and you get a total of 35 km for the area.

Answer:

i think the answer is 240km cuz you multiply 8x5x6. hope this helps, boo!

Step-by-step explanation:

The solution is 16 units

The length of the line segment is 16 units

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:  y=f(x+c) (same output, but c units earlier)

Right shift by c units:  y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the length of the line segment be = A

Now , the initial length of the line segment = 16 units

The line is reflected across the y-axis

So , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y)

And , the resulting line is translated 5 units down

But , the line segment does not change in dimension at all

So , the reflection and a translation does not affect the length of the line segment

Hence , the length of the line segment is 16 units

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Answer:

A strong positive association

Step-by-step explanation:

A perfect fit for a positive line would be 1.  A perfect fit for a negative line would be -1.

The scale goes from 1 tp -1.  

.86 is pretty close to 1.

Answer: 3:2

Step-by-step explanation:

We know that every 3 child tickets were sold for every 2 adults tickets sold

So the ratio is 3:2

Answer: A

Step-by-step explanation:

adding two circles to the left side would result in square triangle circle circle and if you add a square to the right it would be circle circle triangle square thus balancing it

The value of the larger of the two numbers is 5.73.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Two numbers = M and N

M + N = 8 _____(1)

M = 8 - N _____(2)

MN = 13 _____(3)

Putting (2) in (3) we get,

(8 - N)N = 13

8N - N² = 13

N² - 8N + 13 = 0

This is in the form of ax² + bx + c = 0

a = 1, b = -8 and c = 13

Using the determinant we have,

N = -b ± √(b² - 4ac) / 2a

N = 8 ± √(64 - 52) / 2

N = 8 ± √12 / 2

N = 8 ± 2√3 / 2

N = 4 ± √3

N = 4 + √3 and N = 4 - √3

[√3 = 1.73]

N = 5.73

N = 2.27

Now,

When N = 5.73, M = 8 - 5.73 = 2.27

When N = 2.27, M = 8 - 2.27 = 5.73

Now,

The two numbers are 5.73 and 2.27

Thus,

The larger of the two numbers is 5.73.

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The equation of the line passing through the points (0, -6) and (7, 4) in slope-intercept form is y = [tex]\frac{10}{7}[/tex]x - 6.

Slope of a line is defined as the tangent of the angle that the line makes with X axis.

Slope, usually denoted by 'm' of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by,

m = (y₂ - y₁) / (x₂ - x₁)

The equation of a line in slope-intercept form is y = mx + b, where b is y intercept and m is the slope.

Here, we have two points (0, -6) and (7, 4).

m = (4 - -6) / (7 - 0) = 10/7

y intercept is the y coordinate of the point where the line touches with the Y axis. x coordinate will be zero there.

We already have such point (0, -6).

So b = -6

Substituting these in slope-intercept form,

y =  [tex]\frac{10}{7}[/tex]x - 6

Hence, the equation of the given line in slope intercept form is y = [tex]\frac{10}{7}[/tex]x - 6.

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To dilate a rectangle by 2 , multiplied by the scale factor with every coordinates of rectangle

Assume that, the origin (0, 0) be the center of dilation in the coordinate plane.

Let ABCD be a Rectangle in the coordinate plane. The points in the coordinate planes are A(-2, 2), B(3, 2), C(3, -2), D(-2, -2)

We have to dilate by scale factor 2, then every coordinate point of the original triangle will multiplied by the scale factor

Coordinates of new rectangles : A'(-4,4) , B'( 6, 4) ,C(6, -4) and D'(-4,  -4)

Therefore, When we dilate a rectangle by scale factor 2 ,

The dilated triangle will be A’B’C’D’ and the coordinate points obtained are  A'(-4,4) , B'( 6, 4) ,C(6, -4) and D'(-4,  -4)

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The unknown wavelength of a light with m= 4 bright fring overlaps m = 3 bright orange fringe and used in a double slit is 450 nm.

Double Slit experiment:

In modern physics, the double-slit experiment shows that light and matter can exhibit properties of both classically defined waves and particles.

Furthermore, it demonstrates the fundamental stochastic nature of quantum mechanical phenomena.

Formula ,

λ = x.d/n.L

where , λ = wavelength of light used (nm)

x = distance from central fringe (m)

d = distance between the slits (m)

n = the order of the fringe

L = length from slits to the viewing screen (m)

thus, taking ratios for the two waves: let w = unknown wavelength

600/w = 4/3 (as other factors are same for both)

thus, w = 450 nm

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Complete questions :

A double slit is illuminated simultaneously with light of wavelength 700 nm and light of an unknown wavelength. The m = 4 bright fringe of the unknown wavelength overlaps the m = 3 bright orange fringe What is the unknown wavelength? Express your answer to three significant figures and include the appropriate units.

Ngoc should predict that the home is located in Smavile based on the real estate advertisement

From the question, we have the following parameters that can be used in our computation:

Function 1: p = 150 + 0.041a (Smavile)

Function 2: p = 250 + 0.198a (Fancyville )

Where

a = area

p = price

From the question, we have

a = area = 2800

p = price = 280000

Using the above as a guide, we have the following:

So, we have

Function 1: p = 150 + 0.041 * 2800 (Smavile)

Evaluate the expression

p = 264.8 -- false

Function 2: p = 250 + 0.198 * 2800 (Fancyville )

Evaluate the expression

p = 804.4 --- false

264.8  is closer to 280 than 804.4

Hence, the home is in Smavile

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Answer: C. 20

Step-by-step explanation:

Ley y be the duck mass, and x be the number of weeks

Our equation will be

y = 0.042x + 0.05

Then we plug 0.89 in the y

0.89 = 0.042x + 0.05

0.84 = 0.042x

x = 20 Weeks

So the answer is C. 20 weeks

The value x from given triangle FGH of x is 11.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

From the given figure, ∠G=2x+8, ∠H=65° and ∠JFG=9x-4.

Here, ∠JFG=∠G+∠H

⇒ 9x-4=2x+8+65

⇒ 9x-2x=73+4

⇒ 7x=77

⇒ x=11

Hence, the value of x is 11.

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Answer: 34

Step-by-step explanation:

Therefore, [tex]x^{2}[/tex] + 3 x -5 = 0 ,[tex]x^{2}[/tex] - x =0 and 7 [tex]x^{2}[/tex] + 14 x = 0  are quadratic equation.

Equation: a claim that two expressions with variable- and/or number-filled expressions are equivalent. Mathematical development has been sparked by the desire to find solutions to equations, which are really just questions.

Here,

Given:

[tex]x^{2}[/tex] + 3 x -5 = 0

[tex]x^{2}[/tex] - x =0

3 x + 7 .5 x - 7 = 0

7 [tex]x^{2}[/tex] + 14 x = 0

[tex]x^{3}[/tex]- 3 x2 + 1 = 0

x - 5 = 9 x + 7

The [tex]x^{2}[/tex] is present in equation which are quadratic

thus,

[tex]x^{2}[/tex] + 3 x -5 = 0

[tex]x^{2}[/tex] - x =0

7 [tex]x^{2}[/tex] + 14 x = 0

these following above equations are quadratic equation .

Therefore, [tex]x^{2}[/tex] + 3 x -5 = 0 ,[tex]x^{2}[/tex] - x =0 and 7 [tex]x^{2}[/tex] + 14 x = 0  are quadratic equation.

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It will take 5 weeks for every member to play each of the other members of the club.

What are the arrangements?

A strategy or preparation for something, especially for it to occur in a certain way: Two days a week, she had the plan to work from home. The motel was filled, so we had to find another place to stay.

Here, we have

A chess club meets every week and has 6 members.

Each member of the club plays one opponent each week.

We have to find out how many weeks will it take for every member to play each of the other members of the club.

Total number of matches played = (6×5)/2 = 15

Games per week = 3

Every member is to play each of the other members of the club = 15÷3= 5.

Hence, it will take 5 weeks for every member to play each of the other members of the club.

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Answer:6 3/10

Step-by-step explanation:

use Desmos calculator

If the sample mean is 12.8, sample standard deviation is 2 and sample size is 20, then the student's t-distribution should be use to perform the hypothesis test

The population mean = 13

The sample mean = 12.8

The standard deviation = 2

The sample size of the population = 20

The given condition is the underlying population is normal.

Here population standard deviation is missing in the given data. So to perform a hypothesis test when the population standard deviation is missing then we have to use the student t-distribution

Therefore, the student's t-distribution should be use to perform the hypothesis test

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Answer:

Step-by-step explanation:

a + b)^6 will have 7 terms so you want row 6 of the triangle 1 6 15 20 15 6 1

so (a + b)^6 = a^6 + 6a^(5)b + 15a^(4)b^2 + 20a^(3)b^3 + 15a^(2)b^4 + 6ab^5 + b^6

given a = d and b = -5y

∴ (d − 5y)^6 = d^6 + 6d^(5)(-5y) + 15d^(4)(-5y)^2 + 20d^(3)(-5y)^3 + 15d^(2)(-5y)^4 +